Properties

Label 8002.2.a.d.1.10
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 1.10
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.73719 q^{3}\) \(+1.00000 q^{4}\) \(-4.28393 q^{5}\) \(-2.73719 q^{6}\) \(+2.06732 q^{7}\) \(+1.00000 q^{8}\) \(+4.49223 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.73719 q^{3}\) \(+1.00000 q^{4}\) \(-4.28393 q^{5}\) \(-2.73719 q^{6}\) \(+2.06732 q^{7}\) \(+1.00000 q^{8}\) \(+4.49223 q^{9}\) \(-4.28393 q^{10}\) \(-4.65115 q^{11}\) \(-2.73719 q^{12}\) \(-7.04120 q^{13}\) \(+2.06732 q^{14}\) \(+11.7259 q^{15}\) \(+1.00000 q^{16}\) \(+3.79446 q^{17}\) \(+4.49223 q^{18}\) \(-1.74040 q^{19}\) \(-4.28393 q^{20}\) \(-5.65865 q^{21}\) \(-4.65115 q^{22}\) \(-0.612761 q^{23}\) \(-2.73719 q^{24}\) \(+13.3520 q^{25}\) \(-7.04120 q^{26}\) \(-4.08451 q^{27}\) \(+2.06732 q^{28}\) \(+7.92947 q^{29}\) \(+11.7259 q^{30}\) \(+1.07513 q^{31}\) \(+1.00000 q^{32}\) \(+12.7311 q^{33}\) \(+3.79446 q^{34}\) \(-8.85624 q^{35}\) \(+4.49223 q^{36}\) \(+2.44096 q^{37}\) \(-1.74040 q^{38}\) \(+19.2731 q^{39}\) \(-4.28393 q^{40}\) \(-8.48552 q^{41}\) \(-5.65865 q^{42}\) \(+8.97146 q^{43}\) \(-4.65115 q^{44}\) \(-19.2444 q^{45}\) \(-0.612761 q^{46}\) \(+1.99611 q^{47}\) \(-2.73719 q^{48}\) \(-2.72620 q^{49}\) \(+13.3520 q^{50}\) \(-10.3862 q^{51}\) \(-7.04120 q^{52}\) \(+7.08196 q^{53}\) \(-4.08451 q^{54}\) \(+19.9252 q^{55}\) \(+2.06732 q^{56}\) \(+4.76381 q^{57}\) \(+7.92947 q^{58}\) \(+7.17783 q^{59}\) \(+11.7259 q^{60}\) \(-10.7917 q^{61}\) \(+1.07513 q^{62}\) \(+9.28686 q^{63}\) \(+1.00000 q^{64}\) \(+30.1640 q^{65}\) \(+12.7311 q^{66}\) \(-10.0032 q^{67}\) \(+3.79446 q^{68}\) \(+1.67725 q^{69}\) \(-8.85624 q^{70}\) \(-9.46462 q^{71}\) \(+4.49223 q^{72}\) \(+16.3706 q^{73}\) \(+2.44096 q^{74}\) \(-36.5471 q^{75}\) \(-1.74040 q^{76}\) \(-9.61542 q^{77}\) \(+19.2731 q^{78}\) \(+8.98411 q^{79}\) \(-4.28393 q^{80}\) \(-2.29658 q^{81}\) \(-8.48552 q^{82}\) \(+8.10098 q^{83}\) \(-5.65865 q^{84}\) \(-16.2552 q^{85}\) \(+8.97146 q^{86}\) \(-21.7045 q^{87}\) \(-4.65115 q^{88}\) \(-12.0925 q^{89}\) \(-19.2444 q^{90}\) \(-14.5564 q^{91}\) \(-0.612761 q^{92}\) \(-2.94283 q^{93}\) \(+1.99611 q^{94}\) \(+7.45576 q^{95}\) \(-2.73719 q^{96}\) \(-8.55655 q^{97}\) \(-2.72620 q^{98}\) \(-20.8940 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.73719 −1.58032 −0.790160 0.612901i \(-0.790002\pi\)
−0.790160 + 0.612901i \(0.790002\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.28393 −1.91583 −0.957916 0.287050i \(-0.907325\pi\)
−0.957916 + 0.287050i \(0.907325\pi\)
\(6\) −2.73719 −1.11745
\(7\) 2.06732 0.781373 0.390686 0.920524i \(-0.372238\pi\)
0.390686 + 0.920524i \(0.372238\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.49223 1.49741
\(10\) −4.28393 −1.35470
\(11\) −4.65115 −1.40238 −0.701188 0.712977i \(-0.747347\pi\)
−0.701188 + 0.712977i \(0.747347\pi\)
\(12\) −2.73719 −0.790160
\(13\) −7.04120 −1.95288 −0.976439 0.215793i \(-0.930766\pi\)
−0.976439 + 0.215793i \(0.930766\pi\)
\(14\) 2.06732 0.552514
\(15\) 11.7259 3.02762
\(16\) 1.00000 0.250000
\(17\) 3.79446 0.920291 0.460146 0.887843i \(-0.347797\pi\)
0.460146 + 0.887843i \(0.347797\pi\)
\(18\) 4.49223 1.05883
\(19\) −1.74040 −0.399275 −0.199638 0.979870i \(-0.563977\pi\)
−0.199638 + 0.979870i \(0.563977\pi\)
\(20\) −4.28393 −0.957916
\(21\) −5.65865 −1.23482
\(22\) −4.65115 −0.991629
\(23\) −0.612761 −0.127770 −0.0638848 0.997957i \(-0.520349\pi\)
−0.0638848 + 0.997957i \(0.520349\pi\)
\(24\) −2.73719 −0.558727
\(25\) 13.3520 2.67041
\(26\) −7.04120 −1.38089
\(27\) −4.08451 −0.786064
\(28\) 2.06732 0.390686
\(29\) 7.92947 1.47247 0.736233 0.676728i \(-0.236603\pi\)
0.736233 + 0.676728i \(0.236603\pi\)
\(30\) 11.7259 2.14085
\(31\) 1.07513 0.193098 0.0965492 0.995328i \(-0.469219\pi\)
0.0965492 + 0.995328i \(0.469219\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.7311 2.21620
\(34\) 3.79446 0.650744
\(35\) −8.85624 −1.49698
\(36\) 4.49223 0.748704
\(37\) 2.44096 0.401292 0.200646 0.979664i \(-0.435696\pi\)
0.200646 + 0.979664i \(0.435696\pi\)
\(38\) −1.74040 −0.282330
\(39\) 19.2731 3.08617
\(40\) −4.28393 −0.677349
\(41\) −8.48552 −1.32522 −0.662608 0.748967i \(-0.730550\pi\)
−0.662608 + 0.748967i \(0.730550\pi\)
\(42\) −5.65865 −0.873149
\(43\) 8.97146 1.36814 0.684068 0.729419i \(-0.260209\pi\)
0.684068 + 0.729419i \(0.260209\pi\)
\(44\) −4.65115 −0.701188
\(45\) −19.2444 −2.86878
\(46\) −0.612761 −0.0903467
\(47\) 1.99611 0.291163 0.145581 0.989346i \(-0.453495\pi\)
0.145581 + 0.989346i \(0.453495\pi\)
\(48\) −2.73719 −0.395080
\(49\) −2.72620 −0.389456
\(50\) 13.3520 1.88826
\(51\) −10.3862 −1.45435
\(52\) −7.04120 −0.976439
\(53\) 7.08196 0.972783 0.486391 0.873741i \(-0.338313\pi\)
0.486391 + 0.873741i \(0.338313\pi\)
\(54\) −4.08451 −0.555832
\(55\) 19.9252 2.68672
\(56\) 2.06732 0.276257
\(57\) 4.76381 0.630983
\(58\) 7.92947 1.04119
\(59\) 7.17783 0.934474 0.467237 0.884132i \(-0.345249\pi\)
0.467237 + 0.884132i \(0.345249\pi\)
\(60\) 11.7259 1.51381
\(61\) −10.7917 −1.38174 −0.690868 0.722981i \(-0.742771\pi\)
−0.690868 + 0.722981i \(0.742771\pi\)
\(62\) 1.07513 0.136541
\(63\) 9.28686 1.17003
\(64\) 1.00000 0.125000
\(65\) 30.1640 3.74139
\(66\) 12.7311 1.56709
\(67\) −10.0032 −1.22209 −0.611045 0.791596i \(-0.709251\pi\)
−0.611045 + 0.791596i \(0.709251\pi\)
\(68\) 3.79446 0.460146
\(69\) 1.67725 0.201917
\(70\) −8.85624 −1.05852
\(71\) −9.46462 −1.12324 −0.561622 0.827394i \(-0.689822\pi\)
−0.561622 + 0.827394i \(0.689822\pi\)
\(72\) 4.49223 0.529414
\(73\) 16.3706 1.91603 0.958017 0.286711i \(-0.0925619\pi\)
0.958017 + 0.286711i \(0.0925619\pi\)
\(74\) 2.44096 0.283756
\(75\) −36.5471 −4.22010
\(76\) −1.74040 −0.199638
\(77\) −9.61542 −1.09578
\(78\) 19.2731 2.18225
\(79\) 8.98411 1.01079 0.505396 0.862888i \(-0.331347\pi\)
0.505396 + 0.862888i \(0.331347\pi\)
\(80\) −4.28393 −0.478958
\(81\) −2.29658 −0.255176
\(82\) −8.48552 −0.937069
\(83\) 8.10098 0.889199 0.444599 0.895730i \(-0.353346\pi\)
0.444599 + 0.895730i \(0.353346\pi\)
\(84\) −5.65865 −0.617409
\(85\) −16.2552 −1.76312
\(86\) 8.97146 0.967418
\(87\) −21.7045 −2.32697
\(88\) −4.65115 −0.495815
\(89\) −12.0925 −1.28180 −0.640901 0.767624i \(-0.721439\pi\)
−0.640901 + 0.767624i \(0.721439\pi\)
\(90\) −19.2444 −2.02854
\(91\) −14.5564 −1.52593
\(92\) −0.612761 −0.0638848
\(93\) −2.94283 −0.305157
\(94\) 1.99611 0.205883
\(95\) 7.45576 0.764944
\(96\) −2.73719 −0.279364
\(97\) −8.55655 −0.868786 −0.434393 0.900723i \(-0.643037\pi\)
−0.434393 + 0.900723i \(0.643037\pi\)
\(98\) −2.72620 −0.275387
\(99\) −20.8940 −2.09993
\(100\) 13.3520 1.33520
\(101\) −0.356227 −0.0354459 −0.0177229 0.999843i \(-0.505642\pi\)
−0.0177229 + 0.999843i \(0.505642\pi\)
\(102\) −10.3862 −1.02838
\(103\) 7.99950 0.788214 0.394107 0.919065i \(-0.371054\pi\)
0.394107 + 0.919065i \(0.371054\pi\)
\(104\) −7.04120 −0.690447
\(105\) 24.2412 2.36570
\(106\) 7.08196 0.687861
\(107\) −5.24711 −0.507257 −0.253629 0.967302i \(-0.581624\pi\)
−0.253629 + 0.967302i \(0.581624\pi\)
\(108\) −4.08451 −0.393032
\(109\) 13.6531 1.30773 0.653863 0.756613i \(-0.273147\pi\)
0.653863 + 0.756613i \(0.273147\pi\)
\(110\) 19.9252 1.89979
\(111\) −6.68139 −0.634169
\(112\) 2.06732 0.195343
\(113\) 7.99975 0.752553 0.376277 0.926507i \(-0.377204\pi\)
0.376277 + 0.926507i \(0.377204\pi\)
\(114\) 4.76381 0.446172
\(115\) 2.62502 0.244785
\(116\) 7.92947 0.736233
\(117\) −31.6307 −2.92426
\(118\) 7.17783 0.660773
\(119\) 7.84435 0.719091
\(120\) 11.7259 1.07043
\(121\) 10.6332 0.966658
\(122\) −10.7917 −0.977035
\(123\) 23.2265 2.09426
\(124\) 1.07513 0.0965492
\(125\) −35.7796 −3.20022
\(126\) 9.28686 0.827339
\(127\) 20.9325 1.85746 0.928729 0.370760i \(-0.120903\pi\)
0.928729 + 0.370760i \(0.120903\pi\)
\(128\) 1.00000 0.0883883
\(129\) −24.5566 −2.16209
\(130\) 30.1640 2.64556
\(131\) 7.61448 0.665280 0.332640 0.943054i \(-0.392061\pi\)
0.332640 + 0.943054i \(0.392061\pi\)
\(132\) 12.7311 1.10810
\(133\) −3.59796 −0.311983
\(134\) −10.0032 −0.864148
\(135\) 17.4978 1.50597
\(136\) 3.79446 0.325372
\(137\) 17.2028 1.46973 0.734866 0.678212i \(-0.237245\pi\)
0.734866 + 0.678212i \(0.237245\pi\)
\(138\) 1.67725 0.142777
\(139\) −0.705096 −0.0598055 −0.0299027 0.999553i \(-0.509520\pi\)
−0.0299027 + 0.999553i \(0.509520\pi\)
\(140\) −8.85624 −0.748489
\(141\) −5.46375 −0.460130
\(142\) −9.46462 −0.794253
\(143\) 32.7497 2.73867
\(144\) 4.49223 0.374352
\(145\) −33.9693 −2.82100
\(146\) 16.3706 1.35484
\(147\) 7.46212 0.615465
\(148\) 2.44096 0.200646
\(149\) −10.5970 −0.868138 −0.434069 0.900880i \(-0.642923\pi\)
−0.434069 + 0.900880i \(0.642923\pi\)
\(150\) −36.5471 −2.98406
\(151\) −12.8896 −1.04894 −0.524470 0.851429i \(-0.675737\pi\)
−0.524470 + 0.851429i \(0.675737\pi\)
\(152\) −1.74040 −0.141165
\(153\) 17.0456 1.37805
\(154\) −9.61542 −0.774832
\(155\) −4.60576 −0.369944
\(156\) 19.2731 1.54309
\(157\) 1.86205 0.148608 0.0743040 0.997236i \(-0.476326\pi\)
0.0743040 + 0.997236i \(0.476326\pi\)
\(158\) 8.98411 0.714737
\(159\) −19.3847 −1.53731
\(160\) −4.28393 −0.338674
\(161\) −1.26677 −0.0998356
\(162\) −2.29658 −0.180437
\(163\) 4.99759 0.391441 0.195721 0.980660i \(-0.437295\pi\)
0.195721 + 0.980660i \(0.437295\pi\)
\(164\) −8.48552 −0.662608
\(165\) −54.5392 −4.24587
\(166\) 8.10098 0.628758
\(167\) −4.50548 −0.348645 −0.174322 0.984689i \(-0.555774\pi\)
−0.174322 + 0.984689i \(0.555774\pi\)
\(168\) −5.65865 −0.436574
\(169\) 36.5785 2.81373
\(170\) −16.2552 −1.24672
\(171\) −7.81828 −0.597879
\(172\) 8.97146 0.684068
\(173\) 2.21520 0.168419 0.0842094 0.996448i \(-0.473164\pi\)
0.0842094 + 0.996448i \(0.473164\pi\)
\(174\) −21.7045 −1.64541
\(175\) 27.6029 2.08659
\(176\) −4.65115 −0.350594
\(177\) −19.6471 −1.47677
\(178\) −12.0925 −0.906370
\(179\) −5.07565 −0.379372 −0.189686 0.981845i \(-0.560747\pi\)
−0.189686 + 0.981845i \(0.560747\pi\)
\(180\) −19.2444 −1.43439
\(181\) 5.48808 0.407926 0.203963 0.978979i \(-0.434618\pi\)
0.203963 + 0.978979i \(0.434618\pi\)
\(182\) −14.5564 −1.07899
\(183\) 29.5390 2.18358
\(184\) −0.612761 −0.0451733
\(185\) −10.4569 −0.768808
\(186\) −2.94283 −0.215779
\(187\) −17.6486 −1.29059
\(188\) 1.99611 0.145581
\(189\) −8.44398 −0.614209
\(190\) 7.45576 0.540897
\(191\) −13.8102 −0.999269 −0.499634 0.866236i \(-0.666532\pi\)
−0.499634 + 0.866236i \(0.666532\pi\)
\(192\) −2.73719 −0.197540
\(193\) −5.47424 −0.394045 −0.197022 0.980399i \(-0.563127\pi\)
−0.197022 + 0.980399i \(0.563127\pi\)
\(194\) −8.55655 −0.614324
\(195\) −82.5647 −5.91258
\(196\) −2.72620 −0.194728
\(197\) −15.8978 −1.13267 −0.566335 0.824175i \(-0.691639\pi\)
−0.566335 + 0.824175i \(0.691639\pi\)
\(198\) −20.8940 −1.48487
\(199\) −3.90842 −0.277060 −0.138530 0.990358i \(-0.544238\pi\)
−0.138530 + 0.990358i \(0.544238\pi\)
\(200\) 13.3520 0.944132
\(201\) 27.3808 1.93129
\(202\) −0.356227 −0.0250640
\(203\) 16.3927 1.15055
\(204\) −10.3862 −0.727177
\(205\) 36.3513 2.53889
\(206\) 7.99950 0.557351
\(207\) −2.75266 −0.191323
\(208\) −7.04120 −0.488220
\(209\) 8.09488 0.559934
\(210\) 24.2412 1.67281
\(211\) −27.9217 −1.92221 −0.961104 0.276188i \(-0.910929\pi\)
−0.961104 + 0.276188i \(0.910929\pi\)
\(212\) 7.08196 0.486391
\(213\) 25.9065 1.77508
\(214\) −5.24711 −0.358685
\(215\) −38.4331 −2.62112
\(216\) −4.08451 −0.277916
\(217\) 2.22263 0.150882
\(218\) 13.6531 0.924702
\(219\) −44.8095 −3.02795
\(220\) 19.9252 1.34336
\(221\) −26.7176 −1.79722
\(222\) −6.68139 −0.448425
\(223\) −20.1877 −1.35187 −0.675935 0.736961i \(-0.736260\pi\)
−0.675935 + 0.736961i \(0.736260\pi\)
\(224\) 2.06732 0.138129
\(225\) 59.9804 3.99869
\(226\) 7.99975 0.532135
\(227\) −24.2855 −1.61189 −0.805944 0.591991i \(-0.798342\pi\)
−0.805944 + 0.591991i \(0.798342\pi\)
\(228\) 4.76381 0.315491
\(229\) 27.1669 1.79524 0.897619 0.440772i \(-0.145295\pi\)
0.897619 + 0.440772i \(0.145295\pi\)
\(230\) 2.62502 0.173089
\(231\) 26.3193 1.73168
\(232\) 7.92947 0.520595
\(233\) −25.7002 −1.68367 −0.841837 0.539731i \(-0.818526\pi\)
−0.841837 + 0.539731i \(0.818526\pi\)
\(234\) −31.6307 −2.06776
\(235\) −8.55120 −0.557819
\(236\) 7.17783 0.467237
\(237\) −24.5912 −1.59737
\(238\) 7.84435 0.508474
\(239\) −6.99025 −0.452161 −0.226081 0.974109i \(-0.572591\pi\)
−0.226081 + 0.974109i \(0.572591\pi\)
\(240\) 11.7259 0.756906
\(241\) −1.08519 −0.0699031 −0.0349516 0.999389i \(-0.511128\pi\)
−0.0349516 + 0.999389i \(0.511128\pi\)
\(242\) 10.6332 0.683530
\(243\) 18.5397 1.18932
\(244\) −10.7917 −0.690868
\(245\) 11.6788 0.746133
\(246\) 23.2265 1.48087
\(247\) 12.2545 0.779736
\(248\) 1.07513 0.0682706
\(249\) −22.1740 −1.40522
\(250\) −35.7796 −2.26290
\(251\) 0.470311 0.0296857 0.0148429 0.999890i \(-0.495275\pi\)
0.0148429 + 0.999890i \(0.495275\pi\)
\(252\) 9.28686 0.585017
\(253\) 2.85005 0.179181
\(254\) 20.9325 1.31342
\(255\) 44.4936 2.78630
\(256\) 1.00000 0.0625000
\(257\) −13.7274 −0.856289 −0.428144 0.903710i \(-0.640833\pi\)
−0.428144 + 0.903710i \(0.640833\pi\)
\(258\) −24.5566 −1.52883
\(259\) 5.04625 0.313559
\(260\) 30.1640 1.87069
\(261\) 35.6210 2.20488
\(262\) 7.61448 0.470424
\(263\) −5.75753 −0.355024 −0.177512 0.984119i \(-0.556805\pi\)
−0.177512 + 0.984119i \(0.556805\pi\)
\(264\) 12.7311 0.783546
\(265\) −30.3386 −1.86369
\(266\) −3.59796 −0.220605
\(267\) 33.0995 2.02565
\(268\) −10.0032 −0.611045
\(269\) 10.0363 0.611923 0.305962 0.952044i \(-0.401022\pi\)
0.305962 + 0.952044i \(0.401022\pi\)
\(270\) 17.4978 1.06488
\(271\) 12.2574 0.744583 0.372292 0.928116i \(-0.378572\pi\)
0.372292 + 0.928116i \(0.378572\pi\)
\(272\) 3.79446 0.230073
\(273\) 39.8437 2.41145
\(274\) 17.2028 1.03926
\(275\) −62.1024 −3.74492
\(276\) 1.67725 0.100958
\(277\) 29.6381 1.78078 0.890389 0.455200i \(-0.150432\pi\)
0.890389 + 0.455200i \(0.150432\pi\)
\(278\) −0.705096 −0.0422888
\(279\) 4.82971 0.289147
\(280\) −8.85624 −0.529262
\(281\) 13.4393 0.801719 0.400860 0.916139i \(-0.368712\pi\)
0.400860 + 0.916139i \(0.368712\pi\)
\(282\) −5.46375 −0.325361
\(283\) −14.2486 −0.846994 −0.423497 0.905897i \(-0.639198\pi\)
−0.423497 + 0.905897i \(0.639198\pi\)
\(284\) −9.46462 −0.561622
\(285\) −20.4078 −1.20886
\(286\) 32.7497 1.93653
\(287\) −17.5423 −1.03549
\(288\) 4.49223 0.264707
\(289\) −2.60209 −0.153064
\(290\) −33.9693 −1.99475
\(291\) 23.4209 1.37296
\(292\) 16.3706 0.958017
\(293\) −22.8332 −1.33393 −0.666966 0.745088i \(-0.732407\pi\)
−0.666966 + 0.745088i \(0.732407\pi\)
\(294\) 7.46212 0.435200
\(295\) −30.7493 −1.79030
\(296\) 2.44096 0.141878
\(297\) 18.9977 1.10236
\(298\) −10.5970 −0.613866
\(299\) 4.31457 0.249518
\(300\) −36.5471 −2.11005
\(301\) 18.5469 1.06902
\(302\) −12.8896 −0.741713
\(303\) 0.975061 0.0560158
\(304\) −1.74040 −0.0998189
\(305\) 46.2309 2.64717
\(306\) 17.0456 0.974430
\(307\) 19.7499 1.12718 0.563592 0.826053i \(-0.309419\pi\)
0.563592 + 0.826053i \(0.309419\pi\)
\(308\) −9.61542 −0.547889
\(309\) −21.8962 −1.24563
\(310\) −4.60576 −0.261590
\(311\) 9.57097 0.542720 0.271360 0.962478i \(-0.412527\pi\)
0.271360 + 0.962478i \(0.412527\pi\)
\(312\) 19.2731 1.09113
\(313\) −11.9806 −0.677182 −0.338591 0.940934i \(-0.609950\pi\)
−0.338591 + 0.940934i \(0.609950\pi\)
\(314\) 1.86205 0.105082
\(315\) −39.7842 −2.24159
\(316\) 8.98411 0.505396
\(317\) −20.3207 −1.14132 −0.570662 0.821185i \(-0.693314\pi\)
−0.570662 + 0.821185i \(0.693314\pi\)
\(318\) −19.3847 −1.08704
\(319\) −36.8812 −2.06495
\(320\) −4.28393 −0.239479
\(321\) 14.3624 0.801629
\(322\) −1.26677 −0.0705944
\(323\) −6.60388 −0.367450
\(324\) −2.29658 −0.127588
\(325\) −94.0145 −5.21498
\(326\) 4.99759 0.276791
\(327\) −37.3711 −2.06662
\(328\) −8.48552 −0.468534
\(329\) 4.12660 0.227507
\(330\) −54.5392 −3.00228
\(331\) 2.75256 0.151294 0.0756471 0.997135i \(-0.475898\pi\)
0.0756471 + 0.997135i \(0.475898\pi\)
\(332\) 8.10098 0.444599
\(333\) 10.9654 0.600898
\(334\) −4.50548 −0.246529
\(335\) 42.8532 2.34132
\(336\) −5.65865 −0.308705
\(337\) 13.5761 0.739537 0.369768 0.929124i \(-0.379437\pi\)
0.369768 + 0.929124i \(0.379437\pi\)
\(338\) 36.5785 1.98961
\(339\) −21.8969 −1.18927
\(340\) −16.2552 −0.881561
\(341\) −5.00058 −0.270797
\(342\) −7.81828 −0.422764
\(343\) −20.1071 −1.08568
\(344\) 8.97146 0.483709
\(345\) −7.18520 −0.386838
\(346\) 2.21520 0.119090
\(347\) −24.8795 −1.33560 −0.667800 0.744341i \(-0.732764\pi\)
−0.667800 + 0.744341i \(0.732764\pi\)
\(348\) −21.7045 −1.16348
\(349\) −8.01230 −0.428889 −0.214444 0.976736i \(-0.568794\pi\)
−0.214444 + 0.976736i \(0.568794\pi\)
\(350\) 27.6029 1.47544
\(351\) 28.7599 1.53509
\(352\) −4.65115 −0.247907
\(353\) 6.37884 0.339511 0.169756 0.985486i \(-0.445702\pi\)
0.169756 + 0.985486i \(0.445702\pi\)
\(354\) −19.6471 −1.04423
\(355\) 40.5457 2.15194
\(356\) −12.0925 −0.640901
\(357\) −21.4715 −1.13639
\(358\) −5.07565 −0.268257
\(359\) 26.0215 1.37336 0.686680 0.726960i \(-0.259067\pi\)
0.686680 + 0.726960i \(0.259067\pi\)
\(360\) −19.2444 −1.01427
\(361\) −15.9710 −0.840579
\(362\) 5.48808 0.288447
\(363\) −29.1052 −1.52763
\(364\) −14.5564 −0.762963
\(365\) −70.1305 −3.67080
\(366\) 29.5390 1.54403
\(367\) −31.1860 −1.62790 −0.813949 0.580937i \(-0.802686\pi\)
−0.813949 + 0.580937i \(0.802686\pi\)
\(368\) −0.612761 −0.0319424
\(369\) −38.1189 −1.98439
\(370\) −10.4569 −0.543629
\(371\) 14.6407 0.760106
\(372\) −2.94283 −0.152579
\(373\) −15.1527 −0.784576 −0.392288 0.919842i \(-0.628316\pi\)
−0.392288 + 0.919842i \(0.628316\pi\)
\(374\) −17.6486 −0.912588
\(375\) 97.9356 5.05737
\(376\) 1.99611 0.102942
\(377\) −55.8330 −2.87555
\(378\) −8.44398 −0.434312
\(379\) 28.0140 1.43898 0.719492 0.694501i \(-0.244375\pi\)
0.719492 + 0.694501i \(0.244375\pi\)
\(380\) 7.45576 0.382472
\(381\) −57.2962 −2.93538
\(382\) −13.8102 −0.706590
\(383\) −30.4461 −1.55572 −0.777860 0.628437i \(-0.783695\pi\)
−0.777860 + 0.628437i \(0.783695\pi\)
\(384\) −2.73719 −0.139682
\(385\) 41.1918 2.09933
\(386\) −5.47424 −0.278632
\(387\) 40.3018 2.04866
\(388\) −8.55655 −0.434393
\(389\) −12.7784 −0.647892 −0.323946 0.946076i \(-0.605010\pi\)
−0.323946 + 0.946076i \(0.605010\pi\)
\(390\) −82.5647 −4.18083
\(391\) −2.32510 −0.117585
\(392\) −2.72620 −0.137694
\(393\) −20.8423 −1.05135
\(394\) −15.8978 −0.800918
\(395\) −38.4873 −1.93650
\(396\) −20.8940 −1.04996
\(397\) 19.7669 0.992072 0.496036 0.868302i \(-0.334788\pi\)
0.496036 + 0.868302i \(0.334788\pi\)
\(398\) −3.90842 −0.195911
\(399\) 9.84832 0.493033
\(400\) 13.3520 0.667602
\(401\) −1.35492 −0.0676617 −0.0338308 0.999428i \(-0.510771\pi\)
−0.0338308 + 0.999428i \(0.510771\pi\)
\(402\) 27.3808 1.36563
\(403\) −7.57018 −0.377098
\(404\) −0.356227 −0.0177229
\(405\) 9.83840 0.488874
\(406\) 16.3927 0.813558
\(407\) −11.3533 −0.562762
\(408\) −10.3862 −0.514192
\(409\) 15.1138 0.747330 0.373665 0.927564i \(-0.378101\pi\)
0.373665 + 0.927564i \(0.378101\pi\)
\(410\) 36.3513 1.79527
\(411\) −47.0873 −2.32265
\(412\) 7.99950 0.394107
\(413\) 14.8389 0.730173
\(414\) −2.75266 −0.135286
\(415\) −34.7040 −1.70355
\(416\) −7.04120 −0.345223
\(417\) 1.92998 0.0945117
\(418\) 8.09488 0.395933
\(419\) −0.572505 −0.0279687 −0.0139843 0.999902i \(-0.504452\pi\)
−0.0139843 + 0.999902i \(0.504452\pi\)
\(420\) 24.2412 1.18285
\(421\) −17.7182 −0.863532 −0.431766 0.901986i \(-0.642109\pi\)
−0.431766 + 0.901986i \(0.642109\pi\)
\(422\) −27.9217 −1.35921
\(423\) 8.96699 0.435990
\(424\) 7.08196 0.343931
\(425\) 50.6638 2.45755
\(426\) 25.9065 1.25517
\(427\) −22.3099 −1.07965
\(428\) −5.24711 −0.253629
\(429\) −89.6423 −4.32797
\(430\) −38.4331 −1.85341
\(431\) 10.7600 0.518291 0.259146 0.965838i \(-0.416559\pi\)
0.259146 + 0.965838i \(0.416559\pi\)
\(432\) −4.08451 −0.196516
\(433\) −28.4859 −1.36895 −0.684474 0.729038i \(-0.739968\pi\)
−0.684474 + 0.729038i \(0.739968\pi\)
\(434\) 2.22263 0.106690
\(435\) 92.9805 4.45807
\(436\) 13.6531 0.653863
\(437\) 1.06645 0.0510152
\(438\) −44.8095 −2.14108
\(439\) 7.51679 0.358757 0.179378 0.983780i \(-0.442591\pi\)
0.179378 + 0.983780i \(0.442591\pi\)
\(440\) 19.9252 0.949897
\(441\) −12.2467 −0.583175
\(442\) −26.7176 −1.27082
\(443\) −12.5262 −0.595138 −0.297569 0.954700i \(-0.596176\pi\)
−0.297569 + 0.954700i \(0.596176\pi\)
\(444\) −6.68139 −0.317085
\(445\) 51.8034 2.45571
\(446\) −20.1877 −0.955916
\(447\) 29.0060 1.37194
\(448\) 2.06732 0.0976716
\(449\) −0.194462 −0.00917723 −0.00458862 0.999989i \(-0.501461\pi\)
−0.00458862 + 0.999989i \(0.501461\pi\)
\(450\) 59.9804 2.82750
\(451\) 39.4675 1.85845
\(452\) 7.99975 0.376277
\(453\) 35.2813 1.65766
\(454\) −24.2855 −1.13978
\(455\) 62.3586 2.92342
\(456\) 4.76381 0.223086
\(457\) 28.1871 1.31854 0.659268 0.751908i \(-0.270866\pi\)
0.659268 + 0.751908i \(0.270866\pi\)
\(458\) 27.1669 1.26942
\(459\) −15.4985 −0.723408
\(460\) 2.62502 0.122392
\(461\) −4.75490 −0.221458 −0.110729 0.993851i \(-0.535319\pi\)
−0.110729 + 0.993851i \(0.535319\pi\)
\(462\) 26.3193 1.22448
\(463\) −26.9723 −1.25351 −0.626755 0.779216i \(-0.715617\pi\)
−0.626755 + 0.779216i \(0.715617\pi\)
\(464\) 7.92947 0.368117
\(465\) 12.6069 0.584629
\(466\) −25.7002 −1.19054
\(467\) −0.677155 −0.0313350 −0.0156675 0.999877i \(-0.504987\pi\)
−0.0156675 + 0.999877i \(0.504987\pi\)
\(468\) −31.6307 −1.46213
\(469\) −20.6799 −0.954908
\(470\) −8.55120 −0.394438
\(471\) −5.09680 −0.234848
\(472\) 7.17783 0.330387
\(473\) −41.7277 −1.91864
\(474\) −24.5912 −1.12951
\(475\) −23.2379 −1.06623
\(476\) 7.84435 0.359545
\(477\) 31.8138 1.45665
\(478\) −6.99025 −0.319726
\(479\) 34.6760 1.58439 0.792194 0.610270i \(-0.208939\pi\)
0.792194 + 0.610270i \(0.208939\pi\)
\(480\) 11.7259 0.535213
\(481\) −17.1873 −0.783674
\(482\) −1.08519 −0.0494290
\(483\) 3.46740 0.157772
\(484\) 10.6332 0.483329
\(485\) 36.6556 1.66445
\(486\) 18.5397 0.840979
\(487\) 17.8032 0.806740 0.403370 0.915037i \(-0.367839\pi\)
0.403370 + 0.915037i \(0.367839\pi\)
\(488\) −10.7917 −0.488517
\(489\) −13.6794 −0.618602
\(490\) 11.6788 0.527596
\(491\) 4.05148 0.182841 0.0914205 0.995812i \(-0.470859\pi\)
0.0914205 + 0.995812i \(0.470859\pi\)
\(492\) 23.2265 1.04713
\(493\) 30.0881 1.35510
\(494\) 12.2545 0.551357
\(495\) 89.5086 4.02311
\(496\) 1.07513 0.0482746
\(497\) −19.5664 −0.877672
\(498\) −22.1740 −0.993639
\(499\) −11.5589 −0.517446 −0.258723 0.965952i \(-0.583302\pi\)
−0.258723 + 0.965952i \(0.583302\pi\)
\(500\) −35.7796 −1.60011
\(501\) 12.3324 0.550970
\(502\) 0.470311 0.0209910
\(503\) −12.7786 −0.569768 −0.284884 0.958562i \(-0.591955\pi\)
−0.284884 + 0.958562i \(0.591955\pi\)
\(504\) 9.28686 0.413670
\(505\) 1.52605 0.0679083
\(506\) 2.85005 0.126700
\(507\) −100.123 −4.44660
\(508\) 20.9325 0.928729
\(509\) 9.43871 0.418363 0.209182 0.977877i \(-0.432920\pi\)
0.209182 + 0.977877i \(0.432920\pi\)
\(510\) 44.4936 1.97021
\(511\) 33.8432 1.49714
\(512\) 1.00000 0.0441942
\(513\) 7.10869 0.313856
\(514\) −13.7274 −0.605488
\(515\) −34.2693 −1.51008
\(516\) −24.5566 −1.08105
\(517\) −9.28423 −0.408320
\(518\) 5.04625 0.221719
\(519\) −6.06344 −0.266155
\(520\) 30.1640 1.32278
\(521\) −6.72953 −0.294826 −0.147413 0.989075i \(-0.547095\pi\)
−0.147413 + 0.989075i \(0.547095\pi\)
\(522\) 35.6210 1.55909
\(523\) 41.7310 1.82477 0.912384 0.409336i \(-0.134240\pi\)
0.912384 + 0.409336i \(0.134240\pi\)
\(524\) 7.61448 0.332640
\(525\) −75.5545 −3.29747
\(526\) −5.75753 −0.251040
\(527\) 4.07952 0.177707
\(528\) 12.7311 0.554050
\(529\) −22.6245 −0.983675
\(530\) −30.3386 −1.31783
\(531\) 32.2445 1.39929
\(532\) −3.59796 −0.155992
\(533\) 59.7483 2.58798
\(534\) 33.0995 1.43235
\(535\) 22.4783 0.971820
\(536\) −10.0032 −0.432074
\(537\) 13.8930 0.599529
\(538\) 10.0363 0.432695
\(539\) 12.6800 0.546164
\(540\) 17.4978 0.752983
\(541\) −19.2831 −0.829047 −0.414523 0.910039i \(-0.636052\pi\)
−0.414523 + 0.910039i \(0.636052\pi\)
\(542\) 12.2574 0.526500
\(543\) −15.0219 −0.644653
\(544\) 3.79446 0.162686
\(545\) −58.4887 −2.50538
\(546\) 39.8437 1.70515
\(547\) −12.8816 −0.550778 −0.275389 0.961333i \(-0.588807\pi\)
−0.275389 + 0.961333i \(0.588807\pi\)
\(548\) 17.2028 0.734866
\(549\) −48.4788 −2.06902
\(550\) −62.1024 −2.64806
\(551\) −13.8005 −0.587920
\(552\) 1.67725 0.0713883
\(553\) 18.5730 0.789805
\(554\) 29.6381 1.25920
\(555\) 28.6226 1.21496
\(556\) −0.705096 −0.0299027
\(557\) −15.9809 −0.677131 −0.338566 0.940943i \(-0.609942\pi\)
−0.338566 + 0.940943i \(0.609942\pi\)
\(558\) 4.82971 0.204458
\(559\) −63.1699 −2.67180
\(560\) −8.85624 −0.374245
\(561\) 48.3077 2.03955
\(562\) 13.4393 0.566901
\(563\) 24.3742 1.02725 0.513625 0.858015i \(-0.328302\pi\)
0.513625 + 0.858015i \(0.328302\pi\)
\(564\) −5.46375 −0.230065
\(565\) −34.2704 −1.44176
\(566\) −14.2486 −0.598915
\(567\) −4.74777 −0.199388
\(568\) −9.46462 −0.397127
\(569\) 29.4925 1.23639 0.618195 0.786025i \(-0.287864\pi\)
0.618195 + 0.786025i \(0.287864\pi\)
\(570\) −20.4078 −0.854790
\(571\) −15.4754 −0.647626 −0.323813 0.946121i \(-0.604965\pi\)
−0.323813 + 0.946121i \(0.604965\pi\)
\(572\) 32.7497 1.36933
\(573\) 37.8011 1.57916
\(574\) −17.5423 −0.732200
\(575\) −8.18161 −0.341197
\(576\) 4.49223 0.187176
\(577\) −20.4856 −0.852827 −0.426413 0.904528i \(-0.640223\pi\)
−0.426413 + 0.904528i \(0.640223\pi\)
\(578\) −2.60209 −0.108233
\(579\) 14.9841 0.622716
\(580\) −33.9693 −1.41050
\(581\) 16.7473 0.694796
\(582\) 23.4209 0.970829
\(583\) −32.9393 −1.36421
\(584\) 16.3706 0.677420
\(585\) 135.504 5.60238
\(586\) −22.8332 −0.943232
\(587\) 19.7002 0.813113 0.406556 0.913626i \(-0.366729\pi\)
0.406556 + 0.913626i \(0.366729\pi\)
\(588\) 7.46212 0.307733
\(589\) −1.87115 −0.0770994
\(590\) −30.7493 −1.26593
\(591\) 43.5153 1.78998
\(592\) 2.44096 0.100323
\(593\) −40.3808 −1.65824 −0.829121 0.559069i \(-0.811159\pi\)
−0.829121 + 0.559069i \(0.811159\pi\)
\(594\) 18.9977 0.779485
\(595\) −33.6046 −1.37766
\(596\) −10.5970 −0.434069
\(597\) 10.6981 0.437844
\(598\) 4.31457 0.176436
\(599\) 32.1171 1.31227 0.656135 0.754644i \(-0.272190\pi\)
0.656135 + 0.754644i \(0.272190\pi\)
\(600\) −36.5471 −1.49203
\(601\) 31.2226 1.27360 0.636799 0.771030i \(-0.280258\pi\)
0.636799 + 0.771030i \(0.280258\pi\)
\(602\) 18.5469 0.755914
\(603\) −44.9368 −1.82997
\(604\) −12.8896 −0.524470
\(605\) −45.5520 −1.85195
\(606\) 0.975061 0.0396092
\(607\) −9.88634 −0.401274 −0.200637 0.979666i \(-0.564301\pi\)
−0.200637 + 0.979666i \(0.564301\pi\)
\(608\) −1.74040 −0.0705826
\(609\) −44.8701 −1.81823
\(610\) 46.2309 1.87183
\(611\) −14.0550 −0.568606
\(612\) 17.0456 0.689026
\(613\) −2.67726 −0.108134 −0.0540668 0.998537i \(-0.517218\pi\)
−0.0540668 + 0.998537i \(0.517218\pi\)
\(614\) 19.7499 0.797040
\(615\) −99.5007 −4.01225
\(616\) −9.61542 −0.387416
\(617\) −34.1745 −1.37581 −0.687907 0.725799i \(-0.741470\pi\)
−0.687907 + 0.725799i \(0.741470\pi\)
\(618\) −21.8962 −0.880793
\(619\) 14.2245 0.571729 0.285865 0.958270i \(-0.407719\pi\)
0.285865 + 0.958270i \(0.407719\pi\)
\(620\) −4.60576 −0.184972
\(621\) 2.50283 0.100435
\(622\) 9.57097 0.383761
\(623\) −24.9990 −1.00156
\(624\) 19.2731 0.771543
\(625\) 86.5169 3.46067
\(626\) −11.9806 −0.478840
\(627\) −22.1572 −0.884875
\(628\) 1.86205 0.0743040
\(629\) 9.26213 0.369305
\(630\) −39.7842 −1.58504
\(631\) −21.0628 −0.838499 −0.419249 0.907871i \(-0.637707\pi\)
−0.419249 + 0.907871i \(0.637707\pi\)
\(632\) 8.98411 0.357369
\(633\) 76.4270 3.03770
\(634\) −20.3207 −0.807039
\(635\) −89.6733 −3.55858
\(636\) −19.3847 −0.768653
\(637\) 19.1957 0.760561
\(638\) −36.8812 −1.46014
\(639\) −42.5172 −1.68195
\(640\) −4.28393 −0.169337
\(641\) −1.38934 −0.0548756 −0.0274378 0.999624i \(-0.508735\pi\)
−0.0274378 + 0.999624i \(0.508735\pi\)
\(642\) 14.3624 0.566837
\(643\) −19.7197 −0.777668 −0.388834 0.921308i \(-0.627122\pi\)
−0.388834 + 0.921308i \(0.627122\pi\)
\(644\) −1.26677 −0.0499178
\(645\) 105.199 4.14220
\(646\) −6.60388 −0.259826
\(647\) 1.27750 0.0502236 0.0251118 0.999685i \(-0.492006\pi\)
0.0251118 + 0.999685i \(0.492006\pi\)
\(648\) −2.29658 −0.0902183
\(649\) −33.3852 −1.31048
\(650\) −94.0145 −3.68755
\(651\) −6.08376 −0.238441
\(652\) 4.99759 0.195721
\(653\) −44.5950 −1.74514 −0.872569 0.488491i \(-0.837548\pi\)
−0.872569 + 0.488491i \(0.837548\pi\)
\(654\) −37.3711 −1.46132
\(655\) −32.6199 −1.27456
\(656\) −8.48552 −0.331304
\(657\) 73.5405 2.86909
\(658\) 4.12660 0.160872
\(659\) 28.5111 1.11063 0.555317 0.831638i \(-0.312597\pi\)
0.555317 + 0.831638i \(0.312597\pi\)
\(660\) −54.5392 −2.12293
\(661\) −24.8512 −0.966599 −0.483299 0.875455i \(-0.660562\pi\)
−0.483299 + 0.875455i \(0.660562\pi\)
\(662\) 2.75256 0.106981
\(663\) 73.1311 2.84018
\(664\) 8.10098 0.314379
\(665\) 15.4134 0.597707
\(666\) 10.9654 0.424899
\(667\) −4.85887 −0.188136
\(668\) −4.50548 −0.174322
\(669\) 55.2577 2.13639
\(670\) 42.8532 1.65556
\(671\) 50.1939 1.93771
\(672\) −5.65865 −0.218287
\(673\) −24.0020 −0.925210 −0.462605 0.886565i \(-0.653085\pi\)
−0.462605 + 0.886565i \(0.653085\pi\)
\(674\) 13.5761 0.522932
\(675\) −54.5366 −2.09911
\(676\) 36.5785 1.40687
\(677\) −9.69296 −0.372531 −0.186265 0.982499i \(-0.559638\pi\)
−0.186265 + 0.982499i \(0.559638\pi\)
\(678\) −21.8969 −0.840944
\(679\) −17.6891 −0.678846
\(680\) −16.2552 −0.623358
\(681\) 66.4742 2.54730
\(682\) −5.00058 −0.191482
\(683\) −16.7310 −0.640193 −0.320097 0.947385i \(-0.603715\pi\)
−0.320097 + 0.947385i \(0.603715\pi\)
\(684\) −7.81828 −0.298939
\(685\) −73.6955 −2.81576
\(686\) −20.1071 −0.767694
\(687\) −74.3610 −2.83705
\(688\) 8.97146 0.342034
\(689\) −49.8655 −1.89973
\(690\) −7.18520 −0.273536
\(691\) 0.679125 0.0258351 0.0129176 0.999917i \(-0.495888\pi\)
0.0129176 + 0.999917i \(0.495888\pi\)
\(692\) 2.21520 0.0842094
\(693\) −43.1946 −1.64083
\(694\) −24.8795 −0.944411
\(695\) 3.02058 0.114577
\(696\) −21.7045 −0.822707
\(697\) −32.1979 −1.21958
\(698\) −8.01230 −0.303270
\(699\) 70.3464 2.66074
\(700\) 27.6029 1.04329
\(701\) −17.4003 −0.657202 −0.328601 0.944469i \(-0.606577\pi\)
−0.328601 + 0.944469i \(0.606577\pi\)
\(702\) 28.7599 1.08547
\(703\) −4.24826 −0.160226
\(704\) −4.65115 −0.175297
\(705\) 23.4063 0.881532
\(706\) 6.37884 0.240071
\(707\) −0.736434 −0.0276964
\(708\) −19.6471 −0.738384
\(709\) −51.7250 −1.94257 −0.971287 0.237911i \(-0.923537\pi\)
−0.971287 + 0.237911i \(0.923537\pi\)
\(710\) 40.5457 1.52165
\(711\) 40.3586 1.51357
\(712\) −12.0925 −0.453185
\(713\) −0.658796 −0.0246721
\(714\) −21.4715 −0.803551
\(715\) −140.297 −5.24683
\(716\) −5.07565 −0.189686
\(717\) 19.1337 0.714559
\(718\) 26.0215 0.971112
\(719\) −24.0634 −0.897412 −0.448706 0.893679i \(-0.648115\pi\)
−0.448706 + 0.893679i \(0.648115\pi\)
\(720\) −19.2444 −0.717196
\(721\) 16.5375 0.615889
\(722\) −15.9710 −0.594379
\(723\) 2.97037 0.110469
\(724\) 5.48808 0.203963
\(725\) 105.875 3.93209
\(726\) −29.1052 −1.08020
\(727\) 23.8542 0.884704 0.442352 0.896841i \(-0.354144\pi\)
0.442352 + 0.896841i \(0.354144\pi\)
\(728\) −14.5564 −0.539496
\(729\) −43.8571 −1.62434
\(730\) −70.1305 −2.59565
\(731\) 34.0418 1.25908
\(732\) 29.5390 1.09179
\(733\) 32.5574 1.20254 0.601268 0.799048i \(-0.294663\pi\)
0.601268 + 0.799048i \(0.294663\pi\)
\(734\) −31.1860 −1.15110
\(735\) −31.9672 −1.17913
\(736\) −0.612761 −0.0225867
\(737\) 46.5266 1.71383
\(738\) −38.1189 −1.40317
\(739\) −3.57997 −0.131691 −0.0658456 0.997830i \(-0.520974\pi\)
−0.0658456 + 0.997830i \(0.520974\pi\)
\(740\) −10.4569 −0.384404
\(741\) −33.5430 −1.23223
\(742\) 14.6407 0.537476
\(743\) 22.4272 0.822775 0.411388 0.911460i \(-0.365044\pi\)
0.411388 + 0.911460i \(0.365044\pi\)
\(744\) −2.94283 −0.107889
\(745\) 45.3967 1.66321
\(746\) −15.1527 −0.554779
\(747\) 36.3915 1.33149
\(748\) −17.6486 −0.645297
\(749\) −10.8474 −0.396357
\(750\) 97.9356 3.57610
\(751\) 25.1674 0.918371 0.459186 0.888340i \(-0.348141\pi\)
0.459186 + 0.888340i \(0.348141\pi\)
\(752\) 1.99611 0.0727907
\(753\) −1.28733 −0.0469129
\(754\) −55.8330 −2.03332
\(755\) 55.2181 2.00959
\(756\) −8.44398 −0.307105
\(757\) −34.9213 −1.26924 −0.634618 0.772826i \(-0.718843\pi\)
−0.634618 + 0.772826i \(0.718843\pi\)
\(758\) 28.0140 1.01752
\(759\) −7.80113 −0.283163
\(760\) 7.45576 0.270449
\(761\) −27.0027 −0.978847 −0.489423 0.872046i \(-0.662793\pi\)
−0.489423 + 0.872046i \(0.662793\pi\)
\(762\) −57.2962 −2.07562
\(763\) 28.2252 1.02182
\(764\) −13.8102 −0.499634
\(765\) −73.0220 −2.64012
\(766\) −30.4461 −1.10006
\(767\) −50.5406 −1.82491
\(768\) −2.73719 −0.0987699
\(769\) 37.4667 1.35108 0.675542 0.737321i \(-0.263910\pi\)
0.675542 + 0.737321i \(0.263910\pi\)
\(770\) 41.1918 1.48445
\(771\) 37.5744 1.35321
\(772\) −5.47424 −0.197022
\(773\) −18.1944 −0.654407 −0.327204 0.944954i \(-0.606106\pi\)
−0.327204 + 0.944954i \(0.606106\pi\)
\(774\) 40.3018 1.44862
\(775\) 14.3551 0.515652
\(776\) −8.55655 −0.307162
\(777\) −13.8126 −0.495523
\(778\) −12.7784 −0.458129
\(779\) 14.7682 0.529126
\(780\) −82.5647 −2.95629
\(781\) 44.0214 1.57521
\(782\) −2.32510 −0.0831453
\(783\) −32.3880 −1.15745
\(784\) −2.72620 −0.0973641
\(785\) −7.97690 −0.284708
\(786\) −20.8423 −0.743420
\(787\) −6.29325 −0.224330 −0.112165 0.993690i \(-0.535779\pi\)
−0.112165 + 0.993690i \(0.535779\pi\)
\(788\) −15.8978 −0.566335
\(789\) 15.7595 0.561052
\(790\) −38.4873 −1.36932
\(791\) 16.5380 0.588025
\(792\) −20.8940 −0.742437
\(793\) 75.9866 2.69836
\(794\) 19.7669 0.701501
\(795\) 83.0427 2.94522
\(796\) −3.90842 −0.138530
\(797\) 41.3364 1.46421 0.732105 0.681191i \(-0.238538\pi\)
0.732105 + 0.681191i \(0.238538\pi\)
\(798\) 9.84832 0.348627
\(799\) 7.57417 0.267955
\(800\) 13.3520 0.472066
\(801\) −54.3222 −1.91938
\(802\) −1.35492 −0.0478440
\(803\) −76.1422 −2.68700
\(804\) 27.3808 0.965646
\(805\) 5.42676 0.191268
\(806\) −7.57018 −0.266648
\(807\) −27.4712 −0.967034
\(808\) −0.356227 −0.0125320
\(809\) −4.05082 −0.142419 −0.0712096 0.997461i \(-0.522686\pi\)
−0.0712096 + 0.997461i \(0.522686\pi\)
\(810\) 9.83840 0.345686
\(811\) 4.21213 0.147908 0.0739540 0.997262i \(-0.476438\pi\)
0.0739540 + 0.997262i \(0.476438\pi\)
\(812\) 16.3927 0.575273
\(813\) −33.5508 −1.17668
\(814\) −11.3533 −0.397933
\(815\) −21.4093 −0.749936
\(816\) −10.3862 −0.363588
\(817\) −15.6139 −0.546263
\(818\) 15.1138 0.528442
\(819\) −65.3907 −2.28494
\(820\) 36.3513 1.26944
\(821\) 21.1500 0.738142 0.369071 0.929401i \(-0.379676\pi\)
0.369071 + 0.929401i \(0.379676\pi\)
\(822\) −47.0873 −1.64236
\(823\) 32.6668 1.13869 0.569347 0.822097i \(-0.307196\pi\)
0.569347 + 0.822097i \(0.307196\pi\)
\(824\) 7.99950 0.278676
\(825\) 169.986 5.91816
\(826\) 14.8389 0.516310
\(827\) −4.48374 −0.155915 −0.0779574 0.996957i \(-0.524840\pi\)
−0.0779574 + 0.996957i \(0.524840\pi\)
\(828\) −2.75266 −0.0956616
\(829\) 25.9655 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(830\) −34.7040 −1.20459
\(831\) −81.1251 −2.81420
\(832\) −7.04120 −0.244110
\(833\) −10.3444 −0.358413
\(834\) 1.92998 0.0668299
\(835\) 19.3012 0.667945
\(836\) 8.09488 0.279967
\(837\) −4.39137 −0.151788
\(838\) −0.572505 −0.0197769
\(839\) 24.9040 0.859782 0.429891 0.902881i \(-0.358552\pi\)
0.429891 + 0.902881i \(0.358552\pi\)
\(840\) 24.2412 0.836403
\(841\) 33.8765 1.16816
\(842\) −17.7182 −0.610609
\(843\) −36.7859 −1.26697
\(844\) −27.9217 −0.961104
\(845\) −156.700 −5.39064
\(846\) 8.96699 0.308291
\(847\) 21.9823 0.755320
\(848\) 7.08196 0.243196
\(849\) 39.0013 1.33852
\(850\) 50.6638 1.73775
\(851\) −1.49573 −0.0512729
\(852\) 25.9065 0.887542
\(853\) 46.6597 1.59760 0.798799 0.601598i \(-0.205469\pi\)
0.798799 + 0.601598i \(0.205469\pi\)
\(854\) −22.3099 −0.763429
\(855\) 33.4929 1.14543
\(856\) −5.24711 −0.179343
\(857\) 24.3353 0.831278 0.415639 0.909530i \(-0.363558\pi\)
0.415639 + 0.909530i \(0.363558\pi\)
\(858\) −89.6423 −3.06034
\(859\) 42.6621 1.45561 0.727806 0.685783i \(-0.240540\pi\)
0.727806 + 0.685783i \(0.240540\pi\)
\(860\) −38.4331 −1.31056
\(861\) 48.0166 1.63640
\(862\) 10.7600 0.366487
\(863\) −7.06902 −0.240632 −0.120316 0.992736i \(-0.538391\pi\)
−0.120316 + 0.992736i \(0.538391\pi\)
\(864\) −4.08451 −0.138958
\(865\) −9.48977 −0.322662
\(866\) −28.4859 −0.967992
\(867\) 7.12242 0.241890
\(868\) 2.22263 0.0754409
\(869\) −41.7865 −1.41751
\(870\) 92.9805 3.15233
\(871\) 70.4348 2.38659
\(872\) 13.6531 0.462351
\(873\) −38.4380 −1.30093
\(874\) 1.06645 0.0360732
\(875\) −73.9677 −2.50057
\(876\) −44.8095 −1.51397
\(877\) 51.1578 1.72748 0.863739 0.503940i \(-0.168117\pi\)
0.863739 + 0.503940i \(0.168117\pi\)
\(878\) 7.51679 0.253679
\(879\) 62.4990 2.10804
\(880\) 19.9252 0.671679
\(881\) −45.8500 −1.54473 −0.772363 0.635182i \(-0.780925\pi\)
−0.772363 + 0.635182i \(0.780925\pi\)
\(882\) −12.2467 −0.412367
\(883\) 51.9155 1.74710 0.873548 0.486738i \(-0.161813\pi\)
0.873548 + 0.486738i \(0.161813\pi\)
\(884\) −26.7176 −0.898608
\(885\) 84.1668 2.82924
\(886\) −12.5262 −0.420826
\(887\) 26.8011 0.899895 0.449947 0.893055i \(-0.351443\pi\)
0.449947 + 0.893055i \(0.351443\pi\)
\(888\) −6.68139 −0.224213
\(889\) 43.2741 1.45137
\(890\) 51.8034 1.73645
\(891\) 10.6818 0.357853
\(892\) −20.1877 −0.675935
\(893\) −3.47404 −0.116254
\(894\) 29.0060 0.970105
\(895\) 21.7437 0.726813
\(896\) 2.06732 0.0690643
\(897\) −11.8098 −0.394319
\(898\) −0.194462 −0.00648928
\(899\) 8.52518 0.284331
\(900\) 59.9804 1.99935
\(901\) 26.8722 0.895243
\(902\) 39.4675 1.31412
\(903\) −50.7664 −1.68940
\(904\) 7.99975 0.266068
\(905\) −23.5105 −0.781517
\(906\) 35.2813 1.17214
\(907\) 30.3717 1.00847 0.504237 0.863565i \(-0.331774\pi\)
0.504237 + 0.863565i \(0.331774\pi\)
\(908\) −24.2855 −0.805944
\(909\) −1.60025 −0.0530770
\(910\) 62.3586 2.06717
\(911\) 56.9981 1.88843 0.944216 0.329328i \(-0.106822\pi\)
0.944216 + 0.329328i \(0.106822\pi\)
\(912\) 4.76381 0.157746
\(913\) −37.6789 −1.24699
\(914\) 28.1871 0.932345
\(915\) −126.543 −4.18338
\(916\) 27.1669 0.897619
\(917\) 15.7415 0.519832
\(918\) −15.4985 −0.511527
\(919\) 57.5064 1.89696 0.948480 0.316836i \(-0.102621\pi\)
0.948480 + 0.316836i \(0.102621\pi\)
\(920\) 2.62502 0.0865445
\(921\) −54.0592 −1.78131
\(922\) −4.75490 −0.156594
\(923\) 66.6423 2.19356
\(924\) 26.3193 0.865840
\(925\) 32.5919 1.07161
\(926\) −26.9723 −0.886365
\(927\) 35.9355 1.18028
\(928\) 7.92947 0.260298
\(929\) −10.9728 −0.360006 −0.180003 0.983666i \(-0.557611\pi\)
−0.180003 + 0.983666i \(0.557611\pi\)
\(930\) 12.6069 0.413395
\(931\) 4.74467 0.155500
\(932\) −25.7002 −0.841837
\(933\) −26.1976 −0.857670
\(934\) −0.677155 −0.0221572
\(935\) 75.6054 2.47256
\(936\) −31.6307 −1.03388
\(937\) 10.2475 0.334770 0.167385 0.985892i \(-0.446468\pi\)
0.167385 + 0.985892i \(0.446468\pi\)
\(938\) −20.6799 −0.675222
\(939\) 32.7932 1.07016
\(940\) −8.55120 −0.278910
\(941\) 22.6313 0.737759 0.368879 0.929477i \(-0.379742\pi\)
0.368879 + 0.929477i \(0.379742\pi\)
\(942\) −5.09680 −0.166063
\(943\) 5.19959 0.169322
\(944\) 7.17783 0.233619
\(945\) 36.1734 1.17672
\(946\) −41.7277 −1.35668
\(947\) 32.7523 1.06431 0.532154 0.846648i \(-0.321383\pi\)
0.532154 + 0.846648i \(0.321383\pi\)
\(948\) −24.5912 −0.798686
\(949\) −115.269 −3.74178
\(950\) −23.2379 −0.753938
\(951\) 55.6217 1.80366
\(952\) 7.84435 0.254237
\(953\) −55.2141 −1.78856 −0.894281 0.447507i \(-0.852312\pi\)
−0.894281 + 0.447507i \(0.852312\pi\)
\(954\) 31.8138 1.03001
\(955\) 59.1618 1.91443
\(956\) −6.99025 −0.226081
\(957\) 100.951 3.26328
\(958\) 34.6760 1.12033
\(959\) 35.5636 1.14841
\(960\) 11.7259 0.378453
\(961\) −29.8441 −0.962713
\(962\) −17.1873 −0.554141
\(963\) −23.5712 −0.759572
\(964\) −1.08519 −0.0349516
\(965\) 23.4513 0.754923
\(966\) 3.46740 0.111562
\(967\) 0.0328189 0.00105538 0.000527692 1.00000i \(-0.499832\pi\)
0.000527692 1.00000i \(0.499832\pi\)
\(968\) 10.6332 0.341765
\(969\) 18.0761 0.580688
\(970\) 36.6556 1.17694
\(971\) −12.3380 −0.395945 −0.197972 0.980208i \(-0.563436\pi\)
−0.197972 + 0.980208i \(0.563436\pi\)
\(972\) 18.5397 0.594662
\(973\) −1.45766 −0.0467304
\(974\) 17.8032 0.570451
\(975\) 257.336 8.24134
\(976\) −10.7917 −0.345434
\(977\) −47.8317 −1.53027 −0.765136 0.643869i \(-0.777328\pi\)
−0.765136 + 0.643869i \(0.777328\pi\)
\(978\) −13.6794 −0.437418
\(979\) 56.2440 1.79757
\(980\) 11.6788 0.373066
\(981\) 61.3326 1.95820
\(982\) 4.05148 0.129288
\(983\) −48.0491 −1.53253 −0.766265 0.642525i \(-0.777887\pi\)
−0.766265 + 0.642525i \(0.777887\pi\)
\(984\) 23.2265 0.740434
\(985\) 68.1049 2.17000
\(986\) 30.0881 0.958199
\(987\) −11.2953 −0.359533
\(988\) 12.2545 0.389868
\(989\) −5.49736 −0.174806
\(990\) 89.5086 2.84477
\(991\) −23.7365 −0.754014 −0.377007 0.926210i \(-0.623047\pi\)
−0.377007 + 0.926210i \(0.623047\pi\)
\(992\) 1.07513 0.0341353
\(993\) −7.53428 −0.239093
\(994\) −19.5664 −0.620608
\(995\) 16.7434 0.530801
\(996\) −22.1740 −0.702609
\(997\) −38.6008 −1.22250 −0.611250 0.791437i \(-0.709333\pi\)
−0.611250 + 0.791437i \(0.709333\pi\)
\(998\) −11.5589 −0.365889
\(999\) −9.97014 −0.315441
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 \(a_p\))