Properties

Label 6034.2.a.n.1.3
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.58057 q^{3}\) \(+1.00000 q^{4}\) \(-2.90281 q^{5}\) \(+2.58057 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+3.65935 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.58057 q^{3}\) \(+1.00000 q^{4}\) \(-2.90281 q^{5}\) \(+2.58057 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+3.65935 q^{9}\) \(+2.90281 q^{10}\) \(+1.98237 q^{11}\) \(-2.58057 q^{12}\) \(-1.13704 q^{13}\) \(+1.00000 q^{14}\) \(+7.49092 q^{15}\) \(+1.00000 q^{16}\) \(+6.51845 q^{17}\) \(-3.65935 q^{18}\) \(+6.40456 q^{19}\) \(-2.90281 q^{20}\) \(+2.58057 q^{21}\) \(-1.98237 q^{22}\) \(+2.52978 q^{23}\) \(+2.58057 q^{24}\) \(+3.42633 q^{25}\) \(+1.13704 q^{26}\) \(-1.70150 q^{27}\) \(-1.00000 q^{28}\) \(+2.57764 q^{29}\) \(-7.49092 q^{30}\) \(+4.87090 q^{31}\) \(-1.00000 q^{32}\) \(-5.11564 q^{33}\) \(-6.51845 q^{34}\) \(+2.90281 q^{35}\) \(+3.65935 q^{36}\) \(+2.00820 q^{37}\) \(-6.40456 q^{38}\) \(+2.93422 q^{39}\) \(+2.90281 q^{40}\) \(+2.58506 q^{41}\) \(-2.58057 q^{42}\) \(-0.614210 q^{43}\) \(+1.98237 q^{44}\) \(-10.6224 q^{45}\) \(-2.52978 q^{46}\) \(+6.59057 q^{47}\) \(-2.58057 q^{48}\) \(+1.00000 q^{49}\) \(-3.42633 q^{50}\) \(-16.8213 q^{51}\) \(-1.13704 q^{52}\) \(+4.77337 q^{53}\) \(+1.70150 q^{54}\) \(-5.75444 q^{55}\) \(+1.00000 q^{56}\) \(-16.5274 q^{57}\) \(-2.57764 q^{58}\) \(-4.80681 q^{59}\) \(+7.49092 q^{60}\) \(+5.92659 q^{61}\) \(-4.87090 q^{62}\) \(-3.65935 q^{63}\) \(+1.00000 q^{64}\) \(+3.30062 q^{65}\) \(+5.11564 q^{66}\) \(-12.9538 q^{67}\) \(+6.51845 q^{68}\) \(-6.52829 q^{69}\) \(-2.90281 q^{70}\) \(+7.79301 q^{71}\) \(-3.65935 q^{72}\) \(+11.5052 q^{73}\) \(-2.00820 q^{74}\) \(-8.84190 q^{75}\) \(+6.40456 q^{76}\) \(-1.98237 q^{77}\) \(-2.93422 q^{78}\) \(-4.85103 q^{79}\) \(-2.90281 q^{80}\) \(-6.58720 q^{81}\) \(-2.58506 q^{82}\) \(-11.5978 q^{83}\) \(+2.58057 q^{84}\) \(-18.9219 q^{85}\) \(+0.614210 q^{86}\) \(-6.65179 q^{87}\) \(-1.98237 q^{88}\) \(+0.899500 q^{89}\) \(+10.6224 q^{90}\) \(+1.13704 q^{91}\) \(+2.52978 q^{92}\) \(-12.5697 q^{93}\) \(-6.59057 q^{94}\) \(-18.5912 q^{95}\) \(+2.58057 q^{96}\) \(+7.62399 q^{97}\) \(-1.00000 q^{98}\) \(+7.25417 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.58057 −1.48989 −0.744947 0.667124i \(-0.767525\pi\)
−0.744947 + 0.667124i \(0.767525\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.90281 −1.29818 −0.649089 0.760712i \(-0.724850\pi\)
−0.649089 + 0.760712i \(0.724850\pi\)
\(6\) 2.58057 1.05351
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 3.65935 1.21978
\(10\) 2.90281 0.917951
\(11\) 1.98237 0.597706 0.298853 0.954299i \(-0.403396\pi\)
0.298853 + 0.954299i \(0.403396\pi\)
\(12\) −2.58057 −0.744947
\(13\) −1.13704 −0.315358 −0.157679 0.987490i \(-0.550401\pi\)
−0.157679 + 0.987490i \(0.550401\pi\)
\(14\) 1.00000 0.267261
\(15\) 7.49092 1.93415
\(16\) 1.00000 0.250000
\(17\) 6.51845 1.58096 0.790479 0.612490i \(-0.209832\pi\)
0.790479 + 0.612490i \(0.209832\pi\)
\(18\) −3.65935 −0.862517
\(19\) 6.40456 1.46931 0.734653 0.678443i \(-0.237345\pi\)
0.734653 + 0.678443i \(0.237345\pi\)
\(20\) −2.90281 −0.649089
\(21\) 2.58057 0.563127
\(22\) −1.98237 −0.422642
\(23\) 2.52978 0.527496 0.263748 0.964592i \(-0.415041\pi\)
0.263748 + 0.964592i \(0.415041\pi\)
\(24\) 2.58057 0.526757
\(25\) 3.42633 0.685267
\(26\) 1.13704 0.222992
\(27\) −1.70150 −0.327455
\(28\) −1.00000 −0.188982
\(29\) 2.57764 0.478656 0.239328 0.970939i \(-0.423073\pi\)
0.239328 + 0.970939i \(0.423073\pi\)
\(30\) −7.49092 −1.36765
\(31\) 4.87090 0.874839 0.437420 0.899257i \(-0.355892\pi\)
0.437420 + 0.899257i \(0.355892\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.11564 −0.890518
\(34\) −6.51845 −1.11791
\(35\) 2.90281 0.490665
\(36\) 3.65935 0.609892
\(37\) 2.00820 0.330145 0.165073 0.986281i \(-0.447214\pi\)
0.165073 + 0.986281i \(0.447214\pi\)
\(38\) −6.40456 −1.03896
\(39\) 2.93422 0.469851
\(40\) 2.90281 0.458975
\(41\) 2.58506 0.403718 0.201859 0.979415i \(-0.435302\pi\)
0.201859 + 0.979415i \(0.435302\pi\)
\(42\) −2.58057 −0.398191
\(43\) −0.614210 −0.0936661 −0.0468330 0.998903i \(-0.514913\pi\)
−0.0468330 + 0.998903i \(0.514913\pi\)
\(44\) 1.98237 0.298853
\(45\) −10.6224 −1.58350
\(46\) −2.52978 −0.372996
\(47\) 6.59057 0.961334 0.480667 0.876903i \(-0.340395\pi\)
0.480667 + 0.876903i \(0.340395\pi\)
\(48\) −2.58057 −0.372473
\(49\) 1.00000 0.142857
\(50\) −3.42633 −0.484557
\(51\) −16.8213 −2.35546
\(52\) −1.13704 −0.157679
\(53\) 4.77337 0.655673 0.327837 0.944734i \(-0.393680\pi\)
0.327837 + 0.944734i \(0.393680\pi\)
\(54\) 1.70150 0.231545
\(55\) −5.75444 −0.775928
\(56\) 1.00000 0.133631
\(57\) −16.5274 −2.18911
\(58\) −2.57764 −0.338461
\(59\) −4.80681 −0.625794 −0.312897 0.949787i \(-0.601299\pi\)
−0.312897 + 0.949787i \(0.601299\pi\)
\(60\) 7.49092 0.967074
\(61\) 5.92659 0.758822 0.379411 0.925228i \(-0.376127\pi\)
0.379411 + 0.925228i \(0.376127\pi\)
\(62\) −4.87090 −0.618605
\(63\) −3.65935 −0.461035
\(64\) 1.00000 0.125000
\(65\) 3.30062 0.409391
\(66\) 5.11564 0.629691
\(67\) −12.9538 −1.58255 −0.791277 0.611458i \(-0.790583\pi\)
−0.791277 + 0.611458i \(0.790583\pi\)
\(68\) 6.51845 0.790479
\(69\) −6.52829 −0.785913
\(70\) −2.90281 −0.346953
\(71\) 7.79301 0.924860 0.462430 0.886656i \(-0.346978\pi\)
0.462430 + 0.886656i \(0.346978\pi\)
\(72\) −3.65935 −0.431259
\(73\) 11.5052 1.34658 0.673292 0.739377i \(-0.264880\pi\)
0.673292 + 0.739377i \(0.264880\pi\)
\(74\) −2.00820 −0.233448
\(75\) −8.84190 −1.02098
\(76\) 6.40456 0.734653
\(77\) −1.98237 −0.225911
\(78\) −2.93422 −0.332235
\(79\) −4.85103 −0.545784 −0.272892 0.962045i \(-0.587980\pi\)
−0.272892 + 0.962045i \(0.587980\pi\)
\(80\) −2.90281 −0.324545
\(81\) −6.58720 −0.731911
\(82\) −2.58506 −0.285472
\(83\) −11.5978 −1.27303 −0.636514 0.771265i \(-0.719624\pi\)
−0.636514 + 0.771265i \(0.719624\pi\)
\(84\) 2.58057 0.281563
\(85\) −18.9219 −2.05236
\(86\) 0.614210 0.0662319
\(87\) −6.65179 −0.713147
\(88\) −1.98237 −0.211321
\(89\) 0.899500 0.0953468 0.0476734 0.998863i \(-0.484819\pi\)
0.0476734 + 0.998863i \(0.484819\pi\)
\(90\) 10.6224 1.11970
\(91\) 1.13704 0.119194
\(92\) 2.52978 0.263748
\(93\) −12.5697 −1.30342
\(94\) −6.59057 −0.679766
\(95\) −18.5912 −1.90742
\(96\) 2.58057 0.263379
\(97\) 7.62399 0.774099 0.387050 0.922059i \(-0.373494\pi\)
0.387050 + 0.922059i \(0.373494\pi\)
\(98\) −1.00000 −0.101015
\(99\) 7.25417 0.729072
\(100\) 3.42633 0.342633
\(101\) 2.33560 0.232401 0.116200 0.993226i \(-0.462928\pi\)
0.116200 + 0.993226i \(0.462928\pi\)
\(102\) 16.8213 1.66556
\(103\) 18.3712 1.81016 0.905082 0.425237i \(-0.139809\pi\)
0.905082 + 0.425237i \(0.139809\pi\)
\(104\) 1.13704 0.111496
\(105\) −7.49092 −0.731039
\(106\) −4.77337 −0.463631
\(107\) −2.88941 −0.279330 −0.139665 0.990199i \(-0.544603\pi\)
−0.139665 + 0.990199i \(0.544603\pi\)
\(108\) −1.70150 −0.163727
\(109\) −2.71556 −0.260103 −0.130052 0.991507i \(-0.541514\pi\)
−0.130052 + 0.991507i \(0.541514\pi\)
\(110\) 5.75444 0.548664
\(111\) −5.18229 −0.491881
\(112\) −1.00000 −0.0944911
\(113\) −4.37988 −0.412024 −0.206012 0.978549i \(-0.566049\pi\)
−0.206012 + 0.978549i \(0.566049\pi\)
\(114\) 16.5274 1.54793
\(115\) −7.34349 −0.684784
\(116\) 2.57764 0.239328
\(117\) −4.16083 −0.384669
\(118\) 4.80681 0.442503
\(119\) −6.51845 −0.597546
\(120\) −7.49092 −0.683825
\(121\) −7.07023 −0.642748
\(122\) −5.92659 −0.536568
\(123\) −6.67093 −0.601497
\(124\) 4.87090 0.437420
\(125\) 4.56806 0.408580
\(126\) 3.65935 0.326001
\(127\) −3.46348 −0.307334 −0.153667 0.988123i \(-0.549108\pi\)
−0.153667 + 0.988123i \(0.549108\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.58501 0.139553
\(130\) −3.30062 −0.289483
\(131\) 6.91733 0.604370 0.302185 0.953249i \(-0.402284\pi\)
0.302185 + 0.953249i \(0.402284\pi\)
\(132\) −5.11564 −0.445259
\(133\) −6.40456 −0.555345
\(134\) 12.9538 1.11903
\(135\) 4.93915 0.425094
\(136\) −6.51845 −0.558953
\(137\) −9.42199 −0.804975 −0.402487 0.915426i \(-0.631854\pi\)
−0.402487 + 0.915426i \(0.631854\pi\)
\(138\) 6.52829 0.555725
\(139\) 13.8129 1.17159 0.585796 0.810458i \(-0.300782\pi\)
0.585796 + 0.810458i \(0.300782\pi\)
\(140\) 2.90281 0.245333
\(141\) −17.0075 −1.43229
\(142\) −7.79301 −0.653975
\(143\) −2.25403 −0.188491
\(144\) 3.65935 0.304946
\(145\) −7.48242 −0.621381
\(146\) −11.5052 −0.952178
\(147\) −2.58057 −0.212842
\(148\) 2.00820 0.165073
\(149\) 17.7245 1.45205 0.726024 0.687670i \(-0.241366\pi\)
0.726024 + 0.687670i \(0.241366\pi\)
\(150\) 8.84190 0.721938
\(151\) −12.8493 −1.04566 −0.522831 0.852436i \(-0.675124\pi\)
−0.522831 + 0.852436i \(0.675124\pi\)
\(152\) −6.40456 −0.519478
\(153\) 23.8533 1.92843
\(154\) 1.98237 0.159744
\(155\) −14.1393 −1.13570
\(156\) 2.93422 0.234925
\(157\) −3.64473 −0.290881 −0.145440 0.989367i \(-0.546460\pi\)
−0.145440 + 0.989367i \(0.546460\pi\)
\(158\) 4.85103 0.385928
\(159\) −12.3180 −0.976883
\(160\) 2.90281 0.229488
\(161\) −2.52978 −0.199375
\(162\) 6.58720 0.517539
\(163\) −10.5676 −0.827719 −0.413859 0.910341i \(-0.635819\pi\)
−0.413859 + 0.910341i \(0.635819\pi\)
\(164\) 2.58506 0.201859
\(165\) 14.8497 1.15605
\(166\) 11.5978 0.900166
\(167\) 15.6309 1.20956 0.604779 0.796393i \(-0.293261\pi\)
0.604779 + 0.796393i \(0.293261\pi\)
\(168\) −2.58057 −0.199095
\(169\) −11.7071 −0.900549
\(170\) 18.9219 1.45124
\(171\) 23.4365 1.79224
\(172\) −0.614210 −0.0468330
\(173\) −11.8062 −0.897605 −0.448803 0.893631i \(-0.648149\pi\)
−0.448803 + 0.893631i \(0.648149\pi\)
\(174\) 6.65179 0.504271
\(175\) −3.42633 −0.259007
\(176\) 1.98237 0.149426
\(177\) 12.4043 0.932366
\(178\) −0.899500 −0.0674204
\(179\) 24.2091 1.80947 0.904736 0.425973i \(-0.140068\pi\)
0.904736 + 0.425973i \(0.140068\pi\)
\(180\) −10.6224 −0.791748
\(181\) 7.57652 0.563158 0.281579 0.959538i \(-0.409142\pi\)
0.281579 + 0.959538i \(0.409142\pi\)
\(182\) −1.13704 −0.0842831
\(183\) −15.2940 −1.13056
\(184\) −2.52978 −0.186498
\(185\) −5.82942 −0.428587
\(186\) 12.5697 0.921656
\(187\) 12.9220 0.944947
\(188\) 6.59057 0.480667
\(189\) 1.70150 0.123766
\(190\) 18.5912 1.34875
\(191\) 6.92951 0.501401 0.250701 0.968065i \(-0.419339\pi\)
0.250701 + 0.968065i \(0.419339\pi\)
\(192\) −2.58057 −0.186237
\(193\) −9.54025 −0.686722 −0.343361 0.939203i \(-0.611565\pi\)
−0.343361 + 0.939203i \(0.611565\pi\)
\(194\) −7.62399 −0.547371
\(195\) −8.51749 −0.609950
\(196\) 1.00000 0.0714286
\(197\) −7.74105 −0.551527 −0.275764 0.961225i \(-0.588931\pi\)
−0.275764 + 0.961225i \(0.588931\pi\)
\(198\) −7.25417 −0.515531
\(199\) −19.2459 −1.36431 −0.682155 0.731208i \(-0.738957\pi\)
−0.682155 + 0.731208i \(0.738957\pi\)
\(200\) −3.42633 −0.242278
\(201\) 33.4281 2.35784
\(202\) −2.33560 −0.164332
\(203\) −2.57764 −0.180915
\(204\) −16.8213 −1.17773
\(205\) −7.50394 −0.524098
\(206\) −18.3712 −1.27998
\(207\) 9.25736 0.643431
\(208\) −1.13704 −0.0788396
\(209\) 12.6962 0.878212
\(210\) 7.49092 0.516923
\(211\) 8.33381 0.573723 0.286862 0.957972i \(-0.407388\pi\)
0.286862 + 0.957972i \(0.407388\pi\)
\(212\) 4.77337 0.327837
\(213\) −20.1104 −1.37794
\(214\) 2.88941 0.197516
\(215\) 1.78294 0.121595
\(216\) 1.70150 0.115773
\(217\) −4.87090 −0.330658
\(218\) 2.71556 0.183921
\(219\) −29.6900 −2.00627
\(220\) −5.75444 −0.387964
\(221\) −7.41175 −0.498568
\(222\) 5.18229 0.347813
\(223\) −6.71223 −0.449484 −0.224742 0.974418i \(-0.572154\pi\)
−0.224742 + 0.974418i \(0.572154\pi\)
\(224\) 1.00000 0.0668153
\(225\) 12.5382 0.835878
\(226\) 4.37988 0.291345
\(227\) −11.3594 −0.753948 −0.376974 0.926224i \(-0.623035\pi\)
−0.376974 + 0.926224i \(0.623035\pi\)
\(228\) −16.5274 −1.09455
\(229\) −5.31810 −0.351430 −0.175715 0.984441i \(-0.556224\pi\)
−0.175715 + 0.984441i \(0.556224\pi\)
\(230\) 7.34349 0.484215
\(231\) 5.11564 0.336584
\(232\) −2.57764 −0.169231
\(233\) 15.7607 1.03252 0.516258 0.856433i \(-0.327324\pi\)
0.516258 + 0.856433i \(0.327324\pi\)
\(234\) 4.16083 0.272002
\(235\) −19.1312 −1.24798
\(236\) −4.80681 −0.312897
\(237\) 12.5184 0.813160
\(238\) 6.51845 0.422529
\(239\) 17.3945 1.12516 0.562578 0.826744i \(-0.309810\pi\)
0.562578 + 0.826744i \(0.309810\pi\)
\(240\) 7.49092 0.483537
\(241\) 19.1506 1.23360 0.616800 0.787120i \(-0.288429\pi\)
0.616800 + 0.787120i \(0.288429\pi\)
\(242\) 7.07023 0.454492
\(243\) 22.1033 1.41792
\(244\) 5.92659 0.379411
\(245\) −2.90281 −0.185454
\(246\) 6.67093 0.425323
\(247\) −7.28224 −0.463358
\(248\) −4.87090 −0.309302
\(249\) 29.9290 1.89668
\(250\) −4.56806 −0.288909
\(251\) 13.4578 0.849450 0.424725 0.905322i \(-0.360371\pi\)
0.424725 + 0.905322i \(0.360371\pi\)
\(252\) −3.65935 −0.230517
\(253\) 5.01495 0.315287
\(254\) 3.46348 0.217318
\(255\) 48.8292 3.05780
\(256\) 1.00000 0.0625000
\(257\) −12.9478 −0.807659 −0.403830 0.914834i \(-0.632321\pi\)
−0.403830 + 0.914834i \(0.632321\pi\)
\(258\) −1.58501 −0.0986786
\(259\) −2.00820 −0.124783
\(260\) 3.30062 0.204696
\(261\) 9.43250 0.583857
\(262\) −6.91733 −0.427354
\(263\) −1.97613 −0.121854 −0.0609268 0.998142i \(-0.519406\pi\)
−0.0609268 + 0.998142i \(0.519406\pi\)
\(264\) 5.11564 0.314846
\(265\) −13.8562 −0.851181
\(266\) 6.40456 0.392689
\(267\) −2.32122 −0.142057
\(268\) −12.9538 −0.791277
\(269\) −4.54980 −0.277406 −0.138703 0.990334i \(-0.544293\pi\)
−0.138703 + 0.990334i \(0.544293\pi\)
\(270\) −4.93915 −0.300587
\(271\) 17.2187 1.04596 0.522979 0.852345i \(-0.324820\pi\)
0.522979 + 0.852345i \(0.324820\pi\)
\(272\) 6.51845 0.395239
\(273\) −2.93422 −0.177587
\(274\) 9.42199 0.569203
\(275\) 6.79225 0.409588
\(276\) −6.52829 −0.392957
\(277\) −21.9013 −1.31592 −0.657960 0.753053i \(-0.728581\pi\)
−0.657960 + 0.753053i \(0.728581\pi\)
\(278\) −13.8129 −0.828441
\(279\) 17.8243 1.06712
\(280\) −2.90281 −0.173476
\(281\) 13.3125 0.794156 0.397078 0.917785i \(-0.370024\pi\)
0.397078 + 0.917785i \(0.370024\pi\)
\(282\) 17.0075 1.01278
\(283\) −29.5155 −1.75451 −0.877257 0.480021i \(-0.840629\pi\)
−0.877257 + 0.480021i \(0.840629\pi\)
\(284\) 7.79301 0.462430
\(285\) 47.9760 2.84185
\(286\) 2.25403 0.133284
\(287\) −2.58506 −0.152591
\(288\) −3.65935 −0.215629
\(289\) 25.4902 1.49943
\(290\) 7.48242 0.439383
\(291\) −19.6743 −1.15333
\(292\) 11.5052 0.673292
\(293\) −9.52720 −0.556585 −0.278293 0.960496i \(-0.589768\pi\)
−0.278293 + 0.960496i \(0.589768\pi\)
\(294\) 2.58057 0.150502
\(295\) 13.9533 0.812392
\(296\) −2.00820 −0.116724
\(297\) −3.37300 −0.195721
\(298\) −17.7245 −1.02675
\(299\) −2.87647 −0.166350
\(300\) −8.84190 −0.510488
\(301\) 0.614210 0.0354025
\(302\) 12.8493 0.739395
\(303\) −6.02719 −0.346253
\(304\) 6.40456 0.367326
\(305\) −17.2038 −0.985086
\(306\) −23.8533 −1.36360
\(307\) 3.69455 0.210859 0.105430 0.994427i \(-0.466378\pi\)
0.105430 + 0.994427i \(0.466378\pi\)
\(308\) −1.98237 −0.112956
\(309\) −47.4081 −2.69695
\(310\) 14.1393 0.803060
\(311\) 23.9231 1.35656 0.678278 0.734806i \(-0.262727\pi\)
0.678278 + 0.734806i \(0.262727\pi\)
\(312\) −2.93422 −0.166117
\(313\) −33.2825 −1.88124 −0.940619 0.339464i \(-0.889754\pi\)
−0.940619 + 0.339464i \(0.889754\pi\)
\(314\) 3.64473 0.205684
\(315\) 10.6224 0.598506
\(316\) −4.85103 −0.272892
\(317\) −19.3951 −1.08934 −0.544669 0.838651i \(-0.683345\pi\)
−0.544669 + 0.838651i \(0.683345\pi\)
\(318\) 12.3180 0.690761
\(319\) 5.10983 0.286096
\(320\) −2.90281 −0.162272
\(321\) 7.45633 0.416172
\(322\) 2.52978 0.140979
\(323\) 41.7478 2.32291
\(324\) −6.58720 −0.365956
\(325\) −3.89588 −0.216105
\(326\) 10.5676 0.585285
\(327\) 7.00769 0.387526
\(328\) −2.58506 −0.142736
\(329\) −6.59057 −0.363350
\(330\) −14.8497 −0.817451
\(331\) 27.1421 1.49186 0.745932 0.666022i \(-0.232004\pi\)
0.745932 + 0.666022i \(0.232004\pi\)
\(332\) −11.5978 −0.636514
\(333\) 7.34869 0.402706
\(334\) −15.6309 −0.855287
\(335\) 37.6024 2.05444
\(336\) 2.58057 0.140782
\(337\) −17.3713 −0.946277 −0.473139 0.880988i \(-0.656879\pi\)
−0.473139 + 0.880988i \(0.656879\pi\)
\(338\) 11.7071 0.636784
\(339\) 11.3026 0.613873
\(340\) −18.9219 −1.02618
\(341\) 9.65590 0.522896
\(342\) −23.4365 −1.26730
\(343\) −1.00000 −0.0539949
\(344\) 0.614210 0.0331160
\(345\) 18.9504 1.02026
\(346\) 11.8062 0.634703
\(347\) −0.864319 −0.0463991 −0.0231995 0.999731i \(-0.507385\pi\)
−0.0231995 + 0.999731i \(0.507385\pi\)
\(348\) −6.65179 −0.356574
\(349\) −25.4451 −1.36205 −0.681023 0.732262i \(-0.738465\pi\)
−0.681023 + 0.732262i \(0.738465\pi\)
\(350\) 3.42633 0.183145
\(351\) 1.93468 0.103266
\(352\) −1.98237 −0.105660
\(353\) 15.7488 0.838225 0.419113 0.907934i \(-0.362341\pi\)
0.419113 + 0.907934i \(0.362341\pi\)
\(354\) −12.4043 −0.659283
\(355\) −22.6217 −1.20063
\(356\) 0.899500 0.0476734
\(357\) 16.8213 0.890280
\(358\) −24.2091 −1.27949
\(359\) −0.999205 −0.0527360 −0.0263680 0.999652i \(-0.508394\pi\)
−0.0263680 + 0.999652i \(0.508394\pi\)
\(360\) 10.6224 0.559851
\(361\) 22.0183 1.15886
\(362\) −7.57652 −0.398213
\(363\) 18.2452 0.957626
\(364\) 1.13704 0.0595971
\(365\) −33.3975 −1.74811
\(366\) 15.2940 0.799429
\(367\) 4.80614 0.250879 0.125439 0.992101i \(-0.459966\pi\)
0.125439 + 0.992101i \(0.459966\pi\)
\(368\) 2.52978 0.131874
\(369\) 9.45963 0.492449
\(370\) 5.82942 0.303057
\(371\) −4.77337 −0.247821
\(372\) −12.5697 −0.651709
\(373\) 8.96656 0.464271 0.232135 0.972683i \(-0.425429\pi\)
0.232135 + 0.972683i \(0.425429\pi\)
\(374\) −12.9220 −0.668178
\(375\) −11.7882 −0.608740
\(376\) −6.59057 −0.339883
\(377\) −2.93089 −0.150948
\(378\) −1.70150 −0.0875159
\(379\) −1.64987 −0.0847481 −0.0423740 0.999102i \(-0.513492\pi\)
−0.0423740 + 0.999102i \(0.513492\pi\)
\(380\) −18.5912 −0.953711
\(381\) 8.93776 0.457896
\(382\) −6.92951 −0.354544
\(383\) 20.0532 1.02467 0.512336 0.858785i \(-0.328780\pi\)
0.512336 + 0.858785i \(0.328780\pi\)
\(384\) 2.58057 0.131689
\(385\) 5.75444 0.293273
\(386\) 9.54025 0.485586
\(387\) −2.24761 −0.114252
\(388\) 7.62399 0.387050
\(389\) −15.7411 −0.798103 −0.399052 0.916928i \(-0.630661\pi\)
−0.399052 + 0.916928i \(0.630661\pi\)
\(390\) 8.51749 0.431300
\(391\) 16.4903 0.833949
\(392\) −1.00000 −0.0505076
\(393\) −17.8507 −0.900447
\(394\) 7.74105 0.389989
\(395\) 14.0817 0.708525
\(396\) 7.25417 0.364536
\(397\) −10.6432 −0.534167 −0.267084 0.963673i \(-0.586060\pi\)
−0.267084 + 0.963673i \(0.586060\pi\)
\(398\) 19.2459 0.964712
\(399\) 16.5274 0.827406
\(400\) 3.42633 0.171317
\(401\) 29.4967 1.47300 0.736498 0.676439i \(-0.236478\pi\)
0.736498 + 0.676439i \(0.236478\pi\)
\(402\) −33.4281 −1.66724
\(403\) −5.53841 −0.275888
\(404\) 2.33560 0.116200
\(405\) 19.1214 0.950151
\(406\) 2.57764 0.127926
\(407\) 3.98098 0.197330
\(408\) 16.8213 0.832780
\(409\) −19.1462 −0.946721 −0.473360 0.880869i \(-0.656959\pi\)
−0.473360 + 0.880869i \(0.656959\pi\)
\(410\) 7.50394 0.370593
\(411\) 24.3141 1.19933
\(412\) 18.3712 0.905082
\(413\) 4.80681 0.236528
\(414\) −9.25736 −0.454975
\(415\) 33.6664 1.65262
\(416\) 1.13704 0.0557480
\(417\) −35.6451 −1.74555
\(418\) −12.6962 −0.620990
\(419\) −17.8133 −0.870235 −0.435117 0.900374i \(-0.643293\pi\)
−0.435117 + 0.900374i \(0.643293\pi\)
\(420\) −7.49092 −0.365520
\(421\) 5.94280 0.289634 0.144817 0.989458i \(-0.453741\pi\)
0.144817 + 0.989458i \(0.453741\pi\)
\(422\) −8.33381 −0.405684
\(423\) 24.1172 1.17262
\(424\) −4.77337 −0.231815
\(425\) 22.3344 1.08338
\(426\) 20.1104 0.974353
\(427\) −5.92659 −0.286808
\(428\) −2.88941 −0.139665
\(429\) 5.81669 0.280832
\(430\) −1.78294 −0.0859809
\(431\) 1.00000 0.0481683
\(432\) −1.70150 −0.0818637
\(433\) 18.1765 0.873508 0.436754 0.899581i \(-0.356128\pi\)
0.436754 + 0.899581i \(0.356128\pi\)
\(434\) 4.87090 0.233811
\(435\) 19.3089 0.925792
\(436\) −2.71556 −0.130052
\(437\) 16.2021 0.775053
\(438\) 29.6900 1.41864
\(439\) 17.9837 0.858314 0.429157 0.903230i \(-0.358811\pi\)
0.429157 + 0.903230i \(0.358811\pi\)
\(440\) 5.75444 0.274332
\(441\) 3.65935 0.174255
\(442\) 7.41175 0.352541
\(443\) −2.28928 −0.108767 −0.0543834 0.998520i \(-0.517319\pi\)
−0.0543834 + 0.998520i \(0.517319\pi\)
\(444\) −5.18229 −0.245941
\(445\) −2.61108 −0.123777
\(446\) 6.71223 0.317833
\(447\) −45.7393 −2.16340
\(448\) −1.00000 −0.0472456
\(449\) 39.6537 1.87138 0.935688 0.352828i \(-0.114780\pi\)
0.935688 + 0.352828i \(0.114780\pi\)
\(450\) −12.5382 −0.591055
\(451\) 5.12453 0.241305
\(452\) −4.37988 −0.206012
\(453\) 33.1586 1.55793
\(454\) 11.3594 0.533122
\(455\) −3.30062 −0.154735
\(456\) 16.5274 0.773967
\(457\) 14.7836 0.691547 0.345774 0.938318i \(-0.387617\pi\)
0.345774 + 0.938318i \(0.387617\pi\)
\(458\) 5.31810 0.248499
\(459\) −11.0912 −0.517692
\(460\) −7.34349 −0.342392
\(461\) 7.90304 0.368081 0.184041 0.982919i \(-0.441082\pi\)
0.184041 + 0.982919i \(0.441082\pi\)
\(462\) −5.11564 −0.238001
\(463\) 3.28792 0.152802 0.0764012 0.997077i \(-0.475657\pi\)
0.0764012 + 0.997077i \(0.475657\pi\)
\(464\) 2.57764 0.119664
\(465\) 36.4875 1.69207
\(466\) −15.7607 −0.730099
\(467\) 5.23293 0.242151 0.121076 0.992643i \(-0.461366\pi\)
0.121076 + 0.992643i \(0.461366\pi\)
\(468\) −4.16083 −0.192335
\(469\) 12.9538 0.598149
\(470\) 19.1312 0.882457
\(471\) 9.40548 0.433382
\(472\) 4.80681 0.221252
\(473\) −1.21759 −0.0559847
\(474\) −12.5184 −0.574991
\(475\) 21.9442 1.00687
\(476\) −6.51845 −0.298773
\(477\) 17.4674 0.799780
\(478\) −17.3945 −0.795606
\(479\) 10.8596 0.496189 0.248094 0.968736i \(-0.420196\pi\)
0.248094 + 0.968736i \(0.420196\pi\)
\(480\) −7.49092 −0.341912
\(481\) −2.28340 −0.104114
\(482\) −19.1506 −0.872287
\(483\) 6.52829 0.297047
\(484\) −7.07023 −0.321374
\(485\) −22.1310 −1.00492
\(486\) −22.1033 −1.00262
\(487\) 2.07254 0.0939158 0.0469579 0.998897i \(-0.485047\pi\)
0.0469579 + 0.998897i \(0.485047\pi\)
\(488\) −5.92659 −0.268284
\(489\) 27.2705 1.23321
\(490\) 2.90281 0.131136
\(491\) 21.7367 0.980962 0.490481 0.871452i \(-0.336821\pi\)
0.490481 + 0.871452i \(0.336821\pi\)
\(492\) −6.67093 −0.300749
\(493\) 16.8022 0.756735
\(494\) 7.28224 0.327644
\(495\) −21.0575 −0.946465
\(496\) 4.87090 0.218710
\(497\) −7.79301 −0.349564
\(498\) −29.9290 −1.34115
\(499\) 37.8548 1.69461 0.847307 0.531104i \(-0.178223\pi\)
0.847307 + 0.531104i \(0.178223\pi\)
\(500\) 4.56806 0.204290
\(501\) −40.3367 −1.80211
\(502\) −13.4578 −0.600652
\(503\) 34.4778 1.53729 0.768644 0.639676i \(-0.220932\pi\)
0.768644 + 0.639676i \(0.220932\pi\)
\(504\) 3.65935 0.163000
\(505\) −6.77982 −0.301698
\(506\) −5.01495 −0.222942
\(507\) 30.2111 1.34172
\(508\) −3.46348 −0.153667
\(509\) −6.28091 −0.278396 −0.139198 0.990265i \(-0.544453\pi\)
−0.139198 + 0.990265i \(0.544453\pi\)
\(510\) −48.8292 −2.16219
\(511\) −11.5052 −0.508961
\(512\) −1.00000 −0.0441942
\(513\) −10.8974 −0.481131
\(514\) 12.9478 0.571101
\(515\) −53.3281 −2.34992
\(516\) 1.58501 0.0697763
\(517\) 13.0649 0.574595
\(518\) 2.00820 0.0882350
\(519\) 30.4666 1.33734
\(520\) −3.30062 −0.144742
\(521\) −6.23753 −0.273271 −0.136636 0.990621i \(-0.543629\pi\)
−0.136636 + 0.990621i \(0.543629\pi\)
\(522\) −9.43250 −0.412849
\(523\) −9.15761 −0.400434 −0.200217 0.979752i \(-0.564165\pi\)
−0.200217 + 0.979752i \(0.564165\pi\)
\(524\) 6.91733 0.302185
\(525\) 8.84190 0.385892
\(526\) 1.97613 0.0861635
\(527\) 31.7507 1.38308
\(528\) −5.11564 −0.222629
\(529\) −16.6002 −0.721748
\(530\) 13.8562 0.601876
\(531\) −17.5898 −0.763333
\(532\) −6.40456 −0.277673
\(533\) −2.93932 −0.127316
\(534\) 2.32122 0.100449
\(535\) 8.38742 0.362620
\(536\) 12.9538 0.559517
\(537\) −62.4733 −2.69592
\(538\) 4.54980 0.196156
\(539\) 1.98237 0.0853865
\(540\) 4.93915 0.212547
\(541\) −28.2732 −1.21556 −0.607781 0.794105i \(-0.707940\pi\)
−0.607781 + 0.794105i \(0.707940\pi\)
\(542\) −17.2187 −0.739604
\(543\) −19.5518 −0.839046
\(544\) −6.51845 −0.279476
\(545\) 7.88276 0.337660
\(546\) 2.93422 0.125573
\(547\) 10.2786 0.439480 0.219740 0.975558i \(-0.429479\pi\)
0.219740 + 0.975558i \(0.429479\pi\)
\(548\) −9.42199 −0.402487
\(549\) 21.6875 0.925598
\(550\) −6.79225 −0.289622
\(551\) 16.5087 0.703292
\(552\) 6.52829 0.277862
\(553\) 4.85103 0.206287
\(554\) 21.9013 0.930496
\(555\) 15.0432 0.638550
\(556\) 13.8129 0.585796
\(557\) −24.0966 −1.02100 −0.510502 0.859876i \(-0.670541\pi\)
−0.510502 + 0.859876i \(0.670541\pi\)
\(558\) −17.8243 −0.754564
\(559\) 0.698382 0.0295384
\(560\) 2.90281 0.122666
\(561\) −33.3460 −1.40787
\(562\) −13.3125 −0.561553
\(563\) 0.526606 0.0221938 0.0110969 0.999938i \(-0.496468\pi\)
0.0110969 + 0.999938i \(0.496468\pi\)
\(564\) −17.0075 −0.716143
\(565\) 12.7140 0.534881
\(566\) 29.5155 1.24063
\(567\) 6.58720 0.276636
\(568\) −7.79301 −0.326987
\(569\) −12.4883 −0.523536 −0.261768 0.965131i \(-0.584306\pi\)
−0.261768 + 0.965131i \(0.584306\pi\)
\(570\) −47.9760 −2.00949
\(571\) −24.3382 −1.01852 −0.509261 0.860612i \(-0.670081\pi\)
−0.509261 + 0.860612i \(0.670081\pi\)
\(572\) −2.25403 −0.0942457
\(573\) −17.8821 −0.747035
\(574\) 2.58506 0.107898
\(575\) 8.66788 0.361476
\(576\) 3.65935 0.152473
\(577\) 5.25267 0.218672 0.109336 0.994005i \(-0.465128\pi\)
0.109336 + 0.994005i \(0.465128\pi\)
\(578\) −25.4902 −1.06025
\(579\) 24.6193 1.02314
\(580\) −7.48242 −0.310691
\(581\) 11.5978 0.481159
\(582\) 19.6743 0.815524
\(583\) 9.46257 0.391899
\(584\) −11.5052 −0.476089
\(585\) 12.0781 0.499369
\(586\) 9.52720 0.393565
\(587\) 20.9982 0.866689 0.433344 0.901228i \(-0.357333\pi\)
0.433344 + 0.901228i \(0.357333\pi\)
\(588\) −2.58057 −0.106421
\(589\) 31.1960 1.28541
\(590\) −13.9533 −0.574448
\(591\) 19.9763 0.821717
\(592\) 2.00820 0.0825363
\(593\) −19.7126 −0.809499 −0.404749 0.914428i \(-0.632641\pi\)
−0.404749 + 0.914428i \(0.632641\pi\)
\(594\) 3.37300 0.138396
\(595\) 18.9219 0.775721
\(596\) 17.7245 0.726024
\(597\) 49.6656 2.03268
\(598\) 2.87647 0.117627
\(599\) −22.9220 −0.936566 −0.468283 0.883578i \(-0.655127\pi\)
−0.468283 + 0.883578i \(0.655127\pi\)
\(600\) 8.84190 0.360969
\(601\) −25.3592 −1.03442 −0.517212 0.855857i \(-0.673030\pi\)
−0.517212 + 0.855857i \(0.673030\pi\)
\(602\) −0.614210 −0.0250333
\(603\) −47.4024 −1.93037
\(604\) −12.8493 −0.522831
\(605\) 20.5236 0.834402
\(606\) 6.02719 0.244838
\(607\) 29.1523 1.18326 0.591628 0.806211i \(-0.298486\pi\)
0.591628 + 0.806211i \(0.298486\pi\)
\(608\) −6.40456 −0.259739
\(609\) 6.65179 0.269544
\(610\) 17.2038 0.696561
\(611\) −7.49375 −0.303165
\(612\) 23.8533 0.964213
\(613\) −2.94461 −0.118932 −0.0594658 0.998230i \(-0.518940\pi\)
−0.0594658 + 0.998230i \(0.518940\pi\)
\(614\) −3.69455 −0.149100
\(615\) 19.3645 0.780851
\(616\) 1.98237 0.0798718
\(617\) 13.7412 0.553202 0.276601 0.960985i \(-0.410792\pi\)
0.276601 + 0.960985i \(0.410792\pi\)
\(618\) 47.4081 1.90703
\(619\) −20.5462 −0.825821 −0.412910 0.910772i \(-0.635488\pi\)
−0.412910 + 0.910772i \(0.635488\pi\)
\(620\) −14.1393 −0.567849
\(621\) −4.30444 −0.172731
\(622\) −23.9231 −0.959229
\(623\) −0.899500 −0.0360377
\(624\) 2.93422 0.117463
\(625\) −30.3919 −1.21568
\(626\) 33.2825 1.33024
\(627\) −32.7634 −1.30844
\(628\) −3.64473 −0.145440
\(629\) 13.0903 0.521946
\(630\) −10.6224 −0.423207
\(631\) 0.981310 0.0390653 0.0195327 0.999809i \(-0.493782\pi\)
0.0195327 + 0.999809i \(0.493782\pi\)
\(632\) 4.85103 0.192964
\(633\) −21.5060 −0.854787
\(634\) 19.3951 0.770278
\(635\) 10.0538 0.398975
\(636\) −12.3180 −0.488442
\(637\) −1.13704 −0.0450512
\(638\) −5.10983 −0.202300
\(639\) 28.5174 1.12813
\(640\) 2.90281 0.114744
\(641\) −32.9942 −1.30319 −0.651597 0.758565i \(-0.725901\pi\)
−0.651597 + 0.758565i \(0.725901\pi\)
\(642\) −7.45633 −0.294278
\(643\) −16.8176 −0.663221 −0.331610 0.943416i \(-0.607592\pi\)
−0.331610 + 0.943416i \(0.607592\pi\)
\(644\) −2.52978 −0.0996874
\(645\) −4.60100 −0.181164
\(646\) −41.7478 −1.64255
\(647\) −18.2813 −0.718710 −0.359355 0.933201i \(-0.617003\pi\)
−0.359355 + 0.933201i \(0.617003\pi\)
\(648\) 6.58720 0.258770
\(649\) −9.52886 −0.374040
\(650\) 3.89588 0.152809
\(651\) 12.5697 0.492646
\(652\) −10.5676 −0.413859
\(653\) 20.3973 0.798208 0.399104 0.916906i \(-0.369321\pi\)
0.399104 + 0.916906i \(0.369321\pi\)
\(654\) −7.00769 −0.274022
\(655\) −20.0797 −0.784580
\(656\) 2.58506 0.100930
\(657\) 42.1016 1.64254
\(658\) 6.59057 0.256927
\(659\) 13.0636 0.508885 0.254443 0.967088i \(-0.418108\pi\)
0.254443 + 0.967088i \(0.418108\pi\)
\(660\) 14.8497 0.578025
\(661\) 33.9887 1.32201 0.661004 0.750383i \(-0.270131\pi\)
0.661004 + 0.750383i \(0.270131\pi\)
\(662\) −27.1421 −1.05491
\(663\) 19.1265 0.742814
\(664\) 11.5978 0.450083
\(665\) 18.5912 0.720937
\(666\) −7.34869 −0.284756
\(667\) 6.52088 0.252489
\(668\) 15.6309 0.604779
\(669\) 17.3214 0.669683
\(670\) −37.6024 −1.45271
\(671\) 11.7487 0.453552
\(672\) −2.58057 −0.0995477
\(673\) −26.2276 −1.01100 −0.505500 0.862827i \(-0.668692\pi\)
−0.505500 + 0.862827i \(0.668692\pi\)
\(674\) 17.3713 0.669119
\(675\) −5.82992 −0.224394
\(676\) −11.7071 −0.450275
\(677\) 20.3660 0.782731 0.391365 0.920235i \(-0.372003\pi\)
0.391365 + 0.920235i \(0.372003\pi\)
\(678\) −11.3026 −0.434074
\(679\) −7.62399 −0.292582
\(680\) 18.9219 0.725620
\(681\) 29.3137 1.12330
\(682\) −9.65590 −0.369744
\(683\) 16.8941 0.646434 0.323217 0.946325i \(-0.395236\pi\)
0.323217 + 0.946325i \(0.395236\pi\)
\(684\) 23.4365 0.896118
\(685\) 27.3503 1.04500
\(686\) 1.00000 0.0381802
\(687\) 13.7237 0.523593
\(688\) −0.614210 −0.0234165
\(689\) −5.42752 −0.206772
\(690\) −18.9504 −0.721430
\(691\) −9.44415 −0.359272 −0.179636 0.983733i \(-0.557492\pi\)
−0.179636 + 0.983733i \(0.557492\pi\)
\(692\) −11.8062 −0.448803
\(693\) −7.25417 −0.275563
\(694\) 0.864319 0.0328091
\(695\) −40.0962 −1.52094
\(696\) 6.65179 0.252136
\(697\) 16.8506 0.638261
\(698\) 25.4451 0.963112
\(699\) −40.6716 −1.53834
\(700\) −3.42633 −0.129503
\(701\) 5.24585 0.198133 0.0990665 0.995081i \(-0.468414\pi\)
0.0990665 + 0.995081i \(0.468414\pi\)
\(702\) −1.93468 −0.0730198
\(703\) 12.8616 0.485084
\(704\) 1.98237 0.0747132
\(705\) 49.3695 1.85936
\(706\) −15.7488 −0.592715
\(707\) −2.33560 −0.0878393
\(708\) 12.4043 0.466183
\(709\) −50.6151 −1.90089 −0.950445 0.310893i \(-0.899372\pi\)
−0.950445 + 0.310893i \(0.899372\pi\)
\(710\) 22.6217 0.848976
\(711\) −17.7516 −0.665739
\(712\) −0.899500 −0.0337102
\(713\) 12.3223 0.461474
\(714\) −16.8213 −0.629523
\(715\) 6.54303 0.244696
\(716\) 24.2091 0.904736
\(717\) −44.8877 −1.67636
\(718\) 0.999205 0.0372900
\(719\) −42.6211 −1.58950 −0.794750 0.606938i \(-0.792398\pi\)
−0.794750 + 0.606938i \(0.792398\pi\)
\(720\) −10.6224 −0.395874
\(721\) −18.3712 −0.684178
\(722\) −22.0183 −0.819438
\(723\) −49.4196 −1.83793
\(724\) 7.57652 0.281579
\(725\) 8.83187 0.328007
\(726\) −18.2452 −0.677144
\(727\) −8.75765 −0.324803 −0.162402 0.986725i \(-0.551924\pi\)
−0.162402 + 0.986725i \(0.551924\pi\)
\(728\) −1.13704 −0.0421415
\(729\) −37.2774 −1.38065
\(730\) 33.3975 1.23610
\(731\) −4.00370 −0.148082
\(732\) −15.2940 −0.565282
\(733\) 41.3253 1.52639 0.763193 0.646171i \(-0.223631\pi\)
0.763193 + 0.646171i \(0.223631\pi\)
\(734\) −4.80614 −0.177398
\(735\) 7.49092 0.276307
\(736\) −2.52978 −0.0932490
\(737\) −25.6791 −0.945901
\(738\) −9.45963 −0.348214
\(739\) −3.24551 −0.119388 −0.0596939 0.998217i \(-0.519012\pi\)
−0.0596939 + 0.998217i \(0.519012\pi\)
\(740\) −5.82942 −0.214294
\(741\) 18.7924 0.690354
\(742\) 4.77337 0.175236
\(743\) 10.7203 0.393290 0.196645 0.980475i \(-0.436995\pi\)
0.196645 + 0.980475i \(0.436995\pi\)
\(744\) 12.5697 0.460828
\(745\) −51.4509 −1.88502
\(746\) −8.96656 −0.328289
\(747\) −42.4405 −1.55282
\(748\) 12.9220 0.472473
\(749\) 2.88941 0.105577
\(750\) 11.7882 0.430444
\(751\) 38.3101 1.39795 0.698977 0.715144i \(-0.253639\pi\)
0.698977 + 0.715144i \(0.253639\pi\)
\(752\) 6.59057 0.240334
\(753\) −34.7289 −1.26559
\(754\) 2.93089 0.106737
\(755\) 37.2992 1.35746
\(756\) 1.70150 0.0618831
\(757\) −19.3269 −0.702448 −0.351224 0.936291i \(-0.614234\pi\)
−0.351224 + 0.936291i \(0.614234\pi\)
\(758\) 1.64987 0.0599260
\(759\) −12.9414 −0.469745
\(760\) 18.5912 0.674375
\(761\) 40.4724 1.46712 0.733562 0.679623i \(-0.237857\pi\)
0.733562 + 0.679623i \(0.237857\pi\)
\(762\) −8.93776 −0.323781
\(763\) 2.71556 0.0983098
\(764\) 6.92951 0.250701
\(765\) −69.2418 −2.50344
\(766\) −20.0532 −0.724552
\(767\) 5.46554 0.197349
\(768\) −2.58057 −0.0931184
\(769\) −39.0371 −1.40771 −0.703857 0.710342i \(-0.748540\pi\)
−0.703857 + 0.710342i \(0.748540\pi\)
\(770\) −5.75444 −0.207376
\(771\) 33.4126 1.20333
\(772\) −9.54025 −0.343361
\(773\) −1.13850 −0.0409490 −0.0204745 0.999790i \(-0.506518\pi\)
−0.0204745 + 0.999790i \(0.506518\pi\)
\(774\) 2.24761 0.0807886
\(775\) 16.6893 0.599499
\(776\) −7.62399 −0.273685
\(777\) 5.18229 0.185914
\(778\) 15.7411 0.564344
\(779\) 16.5561 0.593185
\(780\) −8.51749 −0.304975
\(781\) 15.4486 0.552794
\(782\) −16.4903 −0.589691
\(783\) −4.38587 −0.156738
\(784\) 1.00000 0.0357143
\(785\) 10.5800 0.377615
\(786\) 17.8507 0.636712
\(787\) −33.4257 −1.19150 −0.595749 0.803171i \(-0.703145\pi\)
−0.595749 + 0.803171i \(0.703145\pi\)
\(788\) −7.74105 −0.275764
\(789\) 5.09956 0.181549
\(790\) −14.0817 −0.501003
\(791\) 4.37988 0.155731
\(792\) −7.25417 −0.257766
\(793\) −6.73877 −0.239301
\(794\) 10.6432 0.377713
\(795\) 35.7570 1.26817
\(796\) −19.2459 −0.682155
\(797\) 36.2674 1.28466 0.642329 0.766429i \(-0.277968\pi\)
0.642329 + 0.766429i \(0.277968\pi\)
\(798\) −16.5274 −0.585064
\(799\) 42.9604 1.51983
\(800\) −3.42633 −0.121139
\(801\) 3.29159 0.116302
\(802\) −29.4967 −1.04157
\(803\) 22.8075 0.804860
\(804\) 33.4281 1.17892
\(805\) 7.34349 0.258824
\(806\) 5.53841 0.195082
\(807\) 11.7411 0.413306
\(808\) −2.33560 −0.0821662
\(809\) −26.1990 −0.921109 −0.460555 0.887631i \(-0.652349\pi\)
−0.460555 + 0.887631i \(0.652349\pi\)
\(810\) −19.1214 −0.671858
\(811\) 12.7871 0.449017 0.224509 0.974472i \(-0.427922\pi\)
0.224509 + 0.974472i \(0.427922\pi\)
\(812\) −2.57764 −0.0904575
\(813\) −44.4340 −1.55837
\(814\) −3.98098 −0.139533
\(815\) 30.6758 1.07453
\(816\) −16.8213 −0.588865
\(817\) −3.93374 −0.137624
\(818\) 19.1462 0.669433
\(819\) 4.16083 0.145391
\(820\) −7.50394 −0.262049
\(821\) 53.2922 1.85991 0.929955 0.367673i \(-0.119845\pi\)
0.929955 + 0.367673i \(0.119845\pi\)
\(822\) −24.3141 −0.848052
\(823\) 39.0942 1.36274 0.681369 0.731940i \(-0.261385\pi\)
0.681369 + 0.731940i \(0.261385\pi\)
\(824\) −18.3712 −0.639990
\(825\) −17.5279 −0.610242
\(826\) −4.80681 −0.167250
\(827\) −0.946616 −0.0329171 −0.0164585 0.999865i \(-0.505239\pi\)
−0.0164585 + 0.999865i \(0.505239\pi\)
\(828\) 9.25736 0.321716
\(829\) −21.0822 −0.732214 −0.366107 0.930573i \(-0.619310\pi\)
−0.366107 + 0.930573i \(0.619310\pi\)
\(830\) −33.6664 −1.16858
\(831\) 56.5178 1.96058
\(832\) −1.13704 −0.0394198
\(833\) 6.51845 0.225851
\(834\) 35.6451 1.23429
\(835\) −45.3737 −1.57022
\(836\) 12.6962 0.439106
\(837\) −8.28786 −0.286470
\(838\) 17.8133 0.615349
\(839\) −9.55939 −0.330027 −0.165013 0.986291i \(-0.552767\pi\)
−0.165013 + 0.986291i \(0.552767\pi\)
\(840\) 7.49092 0.258461
\(841\) −22.3558 −0.770888
\(842\) −5.94280 −0.204802
\(843\) −34.3538 −1.18321
\(844\) 8.33381 0.286862
\(845\) 33.9837 1.16907
\(846\) −24.1172 −0.829167
\(847\) 7.07023 0.242936
\(848\) 4.77337 0.163918
\(849\) 76.1668 2.61404
\(850\) −22.3344 −0.766064
\(851\) 5.08030 0.174150
\(852\) −20.1104 −0.688972
\(853\) −7.00511 −0.239850 −0.119925 0.992783i \(-0.538265\pi\)
−0.119925 + 0.992783i \(0.538265\pi\)
\(854\) 5.92659 0.202804
\(855\) −68.0319 −2.32664
\(856\) 2.88941 0.0987580
\(857\) 2.70650 0.0924524 0.0462262 0.998931i \(-0.485281\pi\)
0.0462262 + 0.998931i \(0.485281\pi\)
\(858\) −5.81669 −0.198578
\(859\) 0.297337 0.0101450 0.00507250 0.999987i \(-0.498385\pi\)
0.00507250 + 0.999987i \(0.498385\pi\)
\(860\) 1.78294 0.0607976
\(861\) 6.67093 0.227345
\(862\) −1.00000 −0.0340601
\(863\) 46.0947 1.56908 0.784541 0.620077i \(-0.212899\pi\)
0.784541 + 0.620077i \(0.212899\pi\)
\(864\) 1.70150 0.0578863
\(865\) 34.2711 1.16525
\(866\) −18.1765 −0.617663
\(867\) −65.7794 −2.23398
\(868\) −4.87090 −0.165329
\(869\) −9.61652 −0.326218
\(870\) −19.3089 −0.654634
\(871\) 14.7290 0.499072
\(872\) 2.71556 0.0919604
\(873\) 27.8989 0.944234
\(874\) −16.2021 −0.548045
\(875\) −4.56806 −0.154429
\(876\) −29.6900 −1.00313
\(877\) −44.4785 −1.50193 −0.750966 0.660341i \(-0.770412\pi\)
−0.750966 + 0.660341i \(0.770412\pi\)
\(878\) −17.9837 −0.606920
\(879\) 24.5856 0.829253
\(880\) −5.75444 −0.193982
\(881\) −29.6437 −0.998722 −0.499361 0.866394i \(-0.666432\pi\)
−0.499361 + 0.866394i \(0.666432\pi\)
\(882\) −3.65935 −0.123217
\(883\) −25.0955 −0.844531 −0.422266 0.906472i \(-0.638765\pi\)
−0.422266 + 0.906472i \(0.638765\pi\)
\(884\) −7.41175 −0.249284
\(885\) −36.0075 −1.21038
\(886\) 2.28928 0.0769097
\(887\) −54.5257 −1.83079 −0.915397 0.402553i \(-0.868123\pi\)
−0.915397 + 0.402553i \(0.868123\pi\)
\(888\) 5.18229 0.173906
\(889\) 3.46348 0.116161
\(890\) 2.61108 0.0875237
\(891\) −13.0582 −0.437467
\(892\) −6.71223 −0.224742
\(893\) 42.2097 1.41249
\(894\) 45.7393 1.52975
\(895\) −70.2745 −2.34902
\(896\) 1.00000 0.0334077
\(897\) 7.42293 0.247844
\(898\) −39.6537 −1.32326
\(899\) 12.5554 0.418747
\(900\) 12.5382 0.417939
\(901\) 31.1150 1.03659
\(902\) −5.12453 −0.170628
\(903\) −1.58501 −0.0527459
\(904\) 4.37988 0.145673
\(905\) −21.9932 −0.731080
\(906\) −33.1586 −1.10162
\(907\) 18.2279 0.605246 0.302623 0.953110i \(-0.402138\pi\)
0.302623 + 0.953110i \(0.402138\pi\)
\(908\) −11.3594 −0.376974
\(909\) 8.54679 0.283479
\(910\) 3.30062 0.109414
\(911\) −22.4477 −0.743725 −0.371862 0.928288i \(-0.621281\pi\)
−0.371862 + 0.928288i \(0.621281\pi\)
\(912\) −16.5274 −0.547277
\(913\) −22.9911 −0.760895
\(914\) −14.7836 −0.488998
\(915\) 44.3956 1.46767
\(916\) −5.31810 −0.175715
\(917\) −6.91733 −0.228430
\(918\) 11.0912 0.366063
\(919\) −4.93541 −0.162804 −0.0814021 0.996681i \(-0.525940\pi\)
−0.0814021 + 0.996681i \(0.525940\pi\)
\(920\) 7.34349 0.242108
\(921\) −9.53405 −0.314158
\(922\) −7.90304 −0.260273
\(923\) −8.86097 −0.291662
\(924\) 5.11564 0.168292
\(925\) 6.88075 0.226238
\(926\) −3.28792 −0.108048
\(927\) 67.2265 2.20801
\(928\) −2.57764 −0.0846153
\(929\) 8.54064 0.280209 0.140105 0.990137i \(-0.455256\pi\)
0.140105 + 0.990137i \(0.455256\pi\)
\(930\) −36.4875 −1.19647
\(931\) 6.40456 0.209901
\(932\) 15.7607 0.516258
\(933\) −61.7353 −2.02112
\(934\) −5.23293 −0.171227
\(935\) −37.5100 −1.22671
\(936\) 4.16083 0.136001
\(937\) 53.8206 1.75824 0.879121 0.476598i \(-0.158130\pi\)
0.879121 + 0.476598i \(0.158130\pi\)
\(938\) −12.9538 −0.422955
\(939\) 85.8879 2.80284
\(940\) −19.1312 −0.623992
\(941\) −0.412475 −0.0134463 −0.00672315 0.999977i \(-0.502140\pi\)
−0.00672315 + 0.999977i \(0.502140\pi\)
\(942\) −9.40548 −0.306447
\(943\) 6.53963 0.212960
\(944\) −4.80681 −0.156448
\(945\) −4.93915 −0.160671
\(946\) 1.21759 0.0395872
\(947\) 8.24183 0.267823 0.133912 0.990993i \(-0.457246\pi\)
0.133912 + 0.990993i \(0.457246\pi\)
\(948\) 12.5184 0.406580
\(949\) −13.0819 −0.424656
\(950\) −21.9442 −0.711962
\(951\) 50.0505 1.62300
\(952\) 6.51845 0.211264
\(953\) 18.6670 0.604685 0.302342 0.953199i \(-0.402231\pi\)
0.302342 + 0.953199i \(0.402231\pi\)
\(954\) −17.4674 −0.565530
\(955\) −20.1151 −0.650908
\(956\) 17.3945 0.562578
\(957\) −13.1863 −0.426252
\(958\) −10.8596 −0.350859
\(959\) 9.42199 0.304252
\(960\) 7.49092 0.241768
\(961\) −7.27433 −0.234656
\(962\) 2.28340 0.0736198
\(963\) −10.5734 −0.340722
\(964\) 19.1506 0.616800
\(965\) 27.6936 0.891488
\(966\) −6.52829 −0.210044
\(967\) −8.28689 −0.266488 −0.133244 0.991083i \(-0.542539\pi\)
−0.133244 + 0.991083i \(0.542539\pi\)
\(968\) 7.07023 0.227246
\(969\) −107.733 −3.46089
\(970\) 22.1310 0.710585
\(971\) 34.8723 1.11910 0.559552 0.828795i \(-0.310973\pi\)
0.559552 + 0.828795i \(0.310973\pi\)
\(972\) 22.1033 0.708962
\(973\) −13.8129 −0.442820
\(974\) −2.07254 −0.0664085
\(975\) 10.0536 0.321973
\(976\) 5.92659 0.189705
\(977\) 25.1110 0.803374 0.401687 0.915777i \(-0.368424\pi\)
0.401687 + 0.915777i \(0.368424\pi\)
\(978\) −27.2705 −0.872013
\(979\) 1.78314 0.0569893
\(980\) −2.90281 −0.0927270
\(981\) −9.93718 −0.317270
\(982\) −21.7367 −0.693645
\(983\) 2.05677 0.0656008 0.0328004 0.999462i \(-0.489557\pi\)
0.0328004 + 0.999462i \(0.489557\pi\)
\(984\) 6.67093 0.212661
\(985\) 22.4708 0.715981
\(986\) −16.8022 −0.535092
\(987\) 17.0075 0.541353
\(988\) −7.28224 −0.231679
\(989\) −1.55382 −0.0494085
\(990\) 21.0575 0.669252
\(991\) −20.7825 −0.660176 −0.330088 0.943950i \(-0.607078\pi\)
−0.330088 + 0.943950i \(0.607078\pi\)
\(992\) −4.87090 −0.154651
\(993\) −70.0421 −2.22272
\(994\) 7.79301 0.247179
\(995\) 55.8674 1.77112
\(996\) 29.9290 0.948338
\(997\) −17.8038 −0.563852 −0.281926 0.959436i \(-0.590973\pi\)
−0.281926 + 0.959436i \(0.590973\pi\)
\(998\) −37.8548 −1.19827
\(999\) −3.41695 −0.108108
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 \(a_p\))