Properties

Label 8018.2.a.j.1.12
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.51480 q^{3}\) \(+1.00000 q^{4}\) \(-1.33044 q^{5}\) \(-1.51480 q^{6}\) \(-3.41282 q^{7}\) \(+1.00000 q^{8}\) \(-0.705394 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.51480 q^{3}\) \(+1.00000 q^{4}\) \(-1.33044 q^{5}\) \(-1.51480 q^{6}\) \(-3.41282 q^{7}\) \(+1.00000 q^{8}\) \(-0.705394 q^{9}\) \(-1.33044 q^{10}\) \(-1.69974 q^{11}\) \(-1.51480 q^{12}\) \(-1.37538 q^{13}\) \(-3.41282 q^{14}\) \(+2.01534 q^{15}\) \(+1.00000 q^{16}\) \(+3.29766 q^{17}\) \(-0.705394 q^{18}\) \(-1.00000 q^{19}\) \(-1.33044 q^{20}\) \(+5.16972 q^{21}\) \(-1.69974 q^{22}\) \(-9.07443 q^{23}\) \(-1.51480 q^{24}\) \(-3.22993 q^{25}\) \(-1.37538 q^{26}\) \(+5.61291 q^{27}\) \(-3.41282 q^{28}\) \(-4.00309 q^{29}\) \(+2.01534 q^{30}\) \(-3.30245 q^{31}\) \(+1.00000 q^{32}\) \(+2.57476 q^{33}\) \(+3.29766 q^{34}\) \(+4.54054 q^{35}\) \(-0.705394 q^{36}\) \(-7.04888 q^{37}\) \(-1.00000 q^{38}\) \(+2.08342 q^{39}\) \(-1.33044 q^{40}\) \(+3.82702 q^{41}\) \(+5.16972 q^{42}\) \(-2.87399 q^{43}\) \(-1.69974 q^{44}\) \(+0.938483 q^{45}\) \(-9.07443 q^{46}\) \(+0.403746 q^{47}\) \(-1.51480 q^{48}\) \(+4.64731 q^{49}\) \(-3.22993 q^{50}\) \(-4.99528 q^{51}\) \(-1.37538 q^{52}\) \(-3.47236 q^{53}\) \(+5.61291 q^{54}\) \(+2.26140 q^{55}\) \(-3.41282 q^{56}\) \(+1.51480 q^{57}\) \(-4.00309 q^{58}\) \(-4.97524 q^{59}\) \(+2.01534 q^{60}\) \(+5.81073 q^{61}\) \(-3.30245 q^{62}\) \(+2.40738 q^{63}\) \(+1.00000 q^{64}\) \(+1.82986 q^{65}\) \(+2.57476 q^{66}\) \(+2.62930 q^{67}\) \(+3.29766 q^{68}\) \(+13.7459 q^{69}\) \(+4.54054 q^{70}\) \(-1.72879 q^{71}\) \(-0.705394 q^{72}\) \(-2.94738 q^{73}\) \(-7.04888 q^{74}\) \(+4.89269 q^{75}\) \(-1.00000 q^{76}\) \(+5.80091 q^{77}\) \(+2.08342 q^{78}\) \(-13.6615 q^{79}\) \(-1.33044 q^{80}\) \(-6.38624 q^{81}\) \(+3.82702 q^{82}\) \(-13.8574 q^{83}\) \(+5.16972 q^{84}\) \(-4.38733 q^{85}\) \(-2.87399 q^{86}\) \(+6.06387 q^{87}\) \(-1.69974 q^{88}\) \(+0.930086 q^{89}\) \(+0.938483 q^{90}\) \(+4.69393 q^{91}\) \(-9.07443 q^{92}\) \(+5.00253 q^{93}\) \(+0.403746 q^{94}\) \(+1.33044 q^{95}\) \(-1.51480 q^{96}\) \(+19.0674 q^{97}\) \(+4.64731 q^{98}\) \(+1.19899 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.51480 −0.874568 −0.437284 0.899324i \(-0.644060\pi\)
−0.437284 + 0.899324i \(0.644060\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.33044 −0.594990 −0.297495 0.954723i \(-0.596151\pi\)
−0.297495 + 0.954723i \(0.596151\pi\)
\(6\) −1.51480 −0.618413
\(7\) −3.41282 −1.28992 −0.644962 0.764215i \(-0.723127\pi\)
−0.644962 + 0.764215i \(0.723127\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.705394 −0.235131
\(10\) −1.33044 −0.420722
\(11\) −1.69974 −0.512491 −0.256246 0.966612i \(-0.582486\pi\)
−0.256246 + 0.966612i \(0.582486\pi\)
\(12\) −1.51480 −0.437284
\(13\) −1.37538 −0.381463 −0.190731 0.981642i \(-0.561086\pi\)
−0.190731 + 0.981642i \(0.561086\pi\)
\(14\) −3.41282 −0.912113
\(15\) 2.01534 0.520359
\(16\) 1.00000 0.250000
\(17\) 3.29766 0.799799 0.399900 0.916559i \(-0.369045\pi\)
0.399900 + 0.916559i \(0.369045\pi\)
\(18\) −0.705394 −0.166263
\(19\) −1.00000 −0.229416
\(20\) −1.33044 −0.297495
\(21\) 5.16972 1.12813
\(22\) −1.69974 −0.362386
\(23\) −9.07443 −1.89215 −0.946075 0.323948i \(-0.894990\pi\)
−0.946075 + 0.323948i \(0.894990\pi\)
\(24\) −1.51480 −0.309206
\(25\) −3.22993 −0.645987
\(26\) −1.37538 −0.269735
\(27\) 5.61291 1.08021
\(28\) −3.41282 −0.644962
\(29\) −4.00309 −0.743355 −0.371678 0.928362i \(-0.621217\pi\)
−0.371678 + 0.928362i \(0.621217\pi\)
\(30\) 2.01534 0.367950
\(31\) −3.30245 −0.593137 −0.296569 0.955012i \(-0.595842\pi\)
−0.296569 + 0.955012i \(0.595842\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.57476 0.448209
\(34\) 3.29766 0.565543
\(35\) 4.54054 0.767492
\(36\) −0.705394 −0.117566
\(37\) −7.04888 −1.15883 −0.579415 0.815033i \(-0.696719\pi\)
−0.579415 + 0.815033i \(0.696719\pi\)
\(38\) −1.00000 −0.162221
\(39\) 2.08342 0.333615
\(40\) −1.33044 −0.210361
\(41\) 3.82702 0.597680 0.298840 0.954303i \(-0.403400\pi\)
0.298840 + 0.954303i \(0.403400\pi\)
\(42\) 5.16972 0.797705
\(43\) −2.87399 −0.438279 −0.219140 0.975693i \(-0.570325\pi\)
−0.219140 + 0.975693i \(0.570325\pi\)
\(44\) −1.69974 −0.256246
\(45\) 0.938483 0.139901
\(46\) −9.07443 −1.33795
\(47\) 0.403746 0.0588924 0.0294462 0.999566i \(-0.490626\pi\)
0.0294462 + 0.999566i \(0.490626\pi\)
\(48\) −1.51480 −0.218642
\(49\) 4.64731 0.663902
\(50\) −3.22993 −0.456782
\(51\) −4.99528 −0.699479
\(52\) −1.37538 −0.190731
\(53\) −3.47236 −0.476965 −0.238482 0.971147i \(-0.576650\pi\)
−0.238482 + 0.971147i \(0.576650\pi\)
\(54\) 5.61291 0.763821
\(55\) 2.26140 0.304927
\(56\) −3.41282 −0.456057
\(57\) 1.51480 0.200640
\(58\) −4.00309 −0.525632
\(59\) −4.97524 −0.647721 −0.323860 0.946105i \(-0.604981\pi\)
−0.323860 + 0.946105i \(0.604981\pi\)
\(60\) 2.01534 0.260180
\(61\) 5.81073 0.743988 0.371994 0.928235i \(-0.378674\pi\)
0.371994 + 0.928235i \(0.378674\pi\)
\(62\) −3.30245 −0.419411
\(63\) 2.40738 0.303301
\(64\) 1.00000 0.125000
\(65\) 1.82986 0.226967
\(66\) 2.57476 0.316931
\(67\) 2.62930 0.321220 0.160610 0.987018i \(-0.448654\pi\)
0.160610 + 0.987018i \(0.448654\pi\)
\(68\) 3.29766 0.399900
\(69\) 13.7459 1.65481
\(70\) 4.54054 0.542699
\(71\) −1.72879 −0.205170 −0.102585 0.994724i \(-0.532711\pi\)
−0.102585 + 0.994724i \(0.532711\pi\)
\(72\) −0.705394 −0.0831314
\(73\) −2.94738 −0.344964 −0.172482 0.985013i \(-0.555179\pi\)
−0.172482 + 0.985013i \(0.555179\pi\)
\(74\) −7.04888 −0.819416
\(75\) 4.89269 0.564959
\(76\) −1.00000 −0.114708
\(77\) 5.80091 0.661075
\(78\) 2.08342 0.235901
\(79\) −13.6615 −1.53704 −0.768522 0.639823i \(-0.779008\pi\)
−0.768522 + 0.639823i \(0.779008\pi\)
\(80\) −1.33044 −0.148748
\(81\) −6.38624 −0.709582
\(82\) 3.82702 0.422624
\(83\) −13.8574 −1.52105 −0.760526 0.649308i \(-0.775059\pi\)
−0.760526 + 0.649308i \(0.775059\pi\)
\(84\) 5.16972 0.564063
\(85\) −4.38733 −0.475873
\(86\) −2.87399 −0.309910
\(87\) 6.06387 0.650115
\(88\) −1.69974 −0.181193
\(89\) 0.930086 0.0985889 0.0492944 0.998784i \(-0.484303\pi\)
0.0492944 + 0.998784i \(0.484303\pi\)
\(90\) 0.938483 0.0989248
\(91\) 4.69393 0.492057
\(92\) −9.07443 −0.946075
\(93\) 5.00253 0.518739
\(94\) 0.403746 0.0416432
\(95\) 1.33044 0.136500
\(96\) −1.51480 −0.154603
\(97\) 19.0674 1.93600 0.967999 0.250956i \(-0.0807448\pi\)
0.967999 + 0.250956i \(0.0807448\pi\)
\(98\) 4.64731 0.469449
\(99\) 1.19899 0.120503
\(100\) −3.22993 −0.322993
\(101\) −2.12217 −0.211164 −0.105582 0.994411i \(-0.533671\pi\)
−0.105582 + 0.994411i \(0.533671\pi\)
\(102\) −4.99528 −0.494606
\(103\) 8.09522 0.797645 0.398823 0.917028i \(-0.369419\pi\)
0.398823 + 0.917028i \(0.369419\pi\)
\(104\) −1.37538 −0.134867
\(105\) −6.87799 −0.671223
\(106\) −3.47236 −0.337265
\(107\) 0.314171 0.0303720 0.0151860 0.999885i \(-0.495166\pi\)
0.0151860 + 0.999885i \(0.495166\pi\)
\(108\) 5.61291 0.540103
\(109\) 4.65436 0.445806 0.222903 0.974841i \(-0.428447\pi\)
0.222903 + 0.974841i \(0.428447\pi\)
\(110\) 2.26140 0.215616
\(111\) 10.6776 1.01347
\(112\) −3.41282 −0.322481
\(113\) 6.05343 0.569459 0.284730 0.958608i \(-0.408096\pi\)
0.284730 + 0.958608i \(0.408096\pi\)
\(114\) 1.51480 0.141874
\(115\) 12.0730 1.12581
\(116\) −4.00309 −0.371678
\(117\) 0.970186 0.0896938
\(118\) −4.97524 −0.458008
\(119\) −11.2543 −1.03168
\(120\) 2.01534 0.183975
\(121\) −8.11088 −0.737352
\(122\) 5.81073 0.526079
\(123\) −5.79716 −0.522712
\(124\) −3.30245 −0.296569
\(125\) 10.9494 0.979346
\(126\) 2.40738 0.214466
\(127\) −17.2322 −1.52911 −0.764554 0.644559i \(-0.777041\pi\)
−0.764554 + 0.644559i \(0.777041\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.35351 0.383305
\(130\) 1.82986 0.160490
\(131\) 13.8383 1.20905 0.604527 0.796585i \(-0.293362\pi\)
0.604527 + 0.796585i \(0.293362\pi\)
\(132\) 2.57476 0.224104
\(133\) 3.41282 0.295929
\(134\) 2.62930 0.227137
\(135\) −7.46764 −0.642712
\(136\) 3.29766 0.282772
\(137\) −8.81438 −0.753063 −0.376532 0.926404i \(-0.622883\pi\)
−0.376532 + 0.926404i \(0.622883\pi\)
\(138\) 13.7459 1.17013
\(139\) −13.5085 −1.14578 −0.572888 0.819634i \(-0.694177\pi\)
−0.572888 + 0.819634i \(0.694177\pi\)
\(140\) 4.54054 0.383746
\(141\) −0.611592 −0.0515054
\(142\) −1.72879 −0.145077
\(143\) 2.33780 0.195496
\(144\) −0.705394 −0.0587828
\(145\) 5.32587 0.442289
\(146\) −2.94738 −0.243927
\(147\) −7.03973 −0.580627
\(148\) −7.04888 −0.579415
\(149\) −8.44192 −0.691589 −0.345795 0.938310i \(-0.612391\pi\)
−0.345795 + 0.938310i \(0.612391\pi\)
\(150\) 4.89269 0.399486
\(151\) 20.4415 1.66351 0.831754 0.555145i \(-0.187337\pi\)
0.831754 + 0.555145i \(0.187337\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −2.32615 −0.188058
\(154\) 5.80091 0.467450
\(155\) 4.39370 0.352911
\(156\) 2.08342 0.166807
\(157\) 20.3889 1.62721 0.813606 0.581416i \(-0.197501\pi\)
0.813606 + 0.581416i \(0.197501\pi\)
\(158\) −13.6615 −1.08685
\(159\) 5.25991 0.417138
\(160\) −1.33044 −0.105180
\(161\) 30.9694 2.44073
\(162\) −6.38624 −0.501750
\(163\) 17.7092 1.38709 0.693544 0.720414i \(-0.256048\pi\)
0.693544 + 0.720414i \(0.256048\pi\)
\(164\) 3.82702 0.298840
\(165\) −3.42556 −0.266680
\(166\) −13.8574 −1.07555
\(167\) 12.2727 0.949691 0.474845 0.880069i \(-0.342504\pi\)
0.474845 + 0.880069i \(0.342504\pi\)
\(168\) 5.16972 0.398853
\(169\) −11.1083 −0.854486
\(170\) −4.38733 −0.336493
\(171\) 0.705394 0.0539428
\(172\) −2.87399 −0.219140
\(173\) −6.43453 −0.489208 −0.244604 0.969623i \(-0.578658\pi\)
−0.244604 + 0.969623i \(0.578658\pi\)
\(174\) 6.06387 0.459700
\(175\) 11.0232 0.833273
\(176\) −1.69974 −0.128123
\(177\) 7.53647 0.566476
\(178\) 0.930086 0.0697129
\(179\) 3.93151 0.293855 0.146928 0.989147i \(-0.453062\pi\)
0.146928 + 0.989147i \(0.453062\pi\)
\(180\) 0.938483 0.0699504
\(181\) −12.8893 −0.958054 −0.479027 0.877800i \(-0.659010\pi\)
−0.479027 + 0.877800i \(0.659010\pi\)
\(182\) 4.69393 0.347937
\(183\) −8.80208 −0.650668
\(184\) −9.07443 −0.668976
\(185\) 9.37811 0.689492
\(186\) 5.00253 0.366804
\(187\) −5.60517 −0.409890
\(188\) 0.403746 0.0294462
\(189\) −19.1558 −1.39338
\(190\) 1.33044 0.0965202
\(191\) 14.6660 1.06119 0.530597 0.847624i \(-0.321968\pi\)
0.530597 + 0.847624i \(0.321968\pi\)
\(192\) −1.51480 −0.109321
\(193\) −8.39534 −0.604309 −0.302155 0.953259i \(-0.597706\pi\)
−0.302155 + 0.953259i \(0.597706\pi\)
\(194\) 19.0674 1.36896
\(195\) −2.77187 −0.198498
\(196\) 4.64731 0.331951
\(197\) 21.4394 1.52749 0.763745 0.645518i \(-0.223358\pi\)
0.763745 + 0.645518i \(0.223358\pi\)
\(198\) 1.19899 0.0852083
\(199\) 3.84538 0.272592 0.136296 0.990668i \(-0.456480\pi\)
0.136296 + 0.990668i \(0.456480\pi\)
\(200\) −3.22993 −0.228391
\(201\) −3.98285 −0.280928
\(202\) −2.12217 −0.149316
\(203\) 13.6618 0.958871
\(204\) −4.99528 −0.349739
\(205\) −5.09162 −0.355614
\(206\) 8.09522 0.564020
\(207\) 6.40104 0.444903
\(208\) −1.37538 −0.0953657
\(209\) 1.69974 0.117574
\(210\) −6.87799 −0.474627
\(211\) −1.00000 −0.0688428
\(212\) −3.47236 −0.238482
\(213\) 2.61877 0.179435
\(214\) 0.314171 0.0214763
\(215\) 3.82367 0.260772
\(216\) 5.61291 0.381910
\(217\) 11.2706 0.765101
\(218\) 4.65436 0.315233
\(219\) 4.46467 0.301695
\(220\) 2.26140 0.152464
\(221\) −4.53554 −0.305094
\(222\) 10.6776 0.716635
\(223\) −25.7019 −1.72113 −0.860564 0.509343i \(-0.829888\pi\)
−0.860564 + 0.509343i \(0.829888\pi\)
\(224\) −3.41282 −0.228028
\(225\) 2.27837 0.151892
\(226\) 6.05343 0.402668
\(227\) 4.95645 0.328971 0.164486 0.986379i \(-0.447404\pi\)
0.164486 + 0.986379i \(0.447404\pi\)
\(228\) 1.51480 0.100320
\(229\) −8.83498 −0.583832 −0.291916 0.956444i \(-0.594293\pi\)
−0.291916 + 0.956444i \(0.594293\pi\)
\(230\) 12.0730 0.796068
\(231\) −8.78719 −0.578155
\(232\) −4.00309 −0.262816
\(233\) 16.3043 1.06813 0.534064 0.845444i \(-0.320664\pi\)
0.534064 + 0.845444i \(0.320664\pi\)
\(234\) 0.970186 0.0634231
\(235\) −0.537159 −0.0350404
\(236\) −4.97524 −0.323860
\(237\) 20.6945 1.34425
\(238\) −11.2543 −0.729508
\(239\) −5.20338 −0.336579 −0.168289 0.985738i \(-0.553824\pi\)
−0.168289 + 0.985738i \(0.553824\pi\)
\(240\) 2.01534 0.130090
\(241\) 25.2116 1.62402 0.812011 0.583642i \(-0.198373\pi\)
0.812011 + 0.583642i \(0.198373\pi\)
\(242\) −8.11088 −0.521387
\(243\) −7.16490 −0.459628
\(244\) 5.81073 0.371994
\(245\) −6.18296 −0.395015
\(246\) −5.79716 −0.369613
\(247\) 1.37538 0.0875135
\(248\) −3.30245 −0.209706
\(249\) 20.9912 1.33026
\(250\) 10.9494 0.692502
\(251\) 23.6548 1.49308 0.746538 0.665343i \(-0.231715\pi\)
0.746538 + 0.665343i \(0.231715\pi\)
\(252\) 2.40738 0.151651
\(253\) 15.4242 0.969710
\(254\) −17.2322 −1.08124
\(255\) 6.64591 0.416183
\(256\) 1.00000 0.0625000
\(257\) −18.4024 −1.14791 −0.573954 0.818888i \(-0.694591\pi\)
−0.573954 + 0.818888i \(0.694591\pi\)
\(258\) 4.35351 0.271038
\(259\) 24.0565 1.49480
\(260\) 1.82986 0.113483
\(261\) 2.82375 0.174786
\(262\) 13.8383 0.854930
\(263\) 16.7685 1.03399 0.516997 0.855987i \(-0.327050\pi\)
0.516997 + 0.855987i \(0.327050\pi\)
\(264\) 2.57476 0.158466
\(265\) 4.61976 0.283789
\(266\) 3.41282 0.209253
\(267\) −1.40889 −0.0862227
\(268\) 2.62930 0.160610
\(269\) −25.6422 −1.56343 −0.781715 0.623635i \(-0.785655\pi\)
−0.781715 + 0.623635i \(0.785655\pi\)
\(270\) −7.46764 −0.454466
\(271\) −21.3945 −1.29963 −0.649813 0.760094i \(-0.725153\pi\)
−0.649813 + 0.760094i \(0.725153\pi\)
\(272\) 3.29766 0.199950
\(273\) −7.11034 −0.430338
\(274\) −8.81438 −0.532496
\(275\) 5.49005 0.331063
\(276\) 13.7459 0.827406
\(277\) 13.9758 0.839725 0.419862 0.907588i \(-0.362078\pi\)
0.419862 + 0.907588i \(0.362078\pi\)
\(278\) −13.5085 −0.810186
\(279\) 2.32953 0.139465
\(280\) 4.54054 0.271349
\(281\) 14.4950 0.864698 0.432349 0.901706i \(-0.357685\pi\)
0.432349 + 0.901706i \(0.357685\pi\)
\(282\) −0.611592 −0.0364198
\(283\) −8.77714 −0.521747 −0.260873 0.965373i \(-0.584010\pi\)
−0.260873 + 0.965373i \(0.584010\pi\)
\(284\) −1.72879 −0.102585
\(285\) −2.01534 −0.119379
\(286\) 2.33780 0.138237
\(287\) −13.0609 −0.770962
\(288\) −0.705394 −0.0415657
\(289\) −6.12546 −0.360321
\(290\) 5.32587 0.312746
\(291\) −28.8832 −1.69316
\(292\) −2.94738 −0.172482
\(293\) 9.95726 0.581709 0.290855 0.956767i \(-0.406060\pi\)
0.290855 + 0.956767i \(0.406060\pi\)
\(294\) −7.03973 −0.410565
\(295\) 6.61925 0.385388
\(296\) −7.04888 −0.409708
\(297\) −9.54051 −0.553596
\(298\) −8.44192 −0.489028
\(299\) 12.4808 0.721784
\(300\) 4.89269 0.282480
\(301\) 9.80840 0.565347
\(302\) 20.4415 1.17628
\(303\) 3.21466 0.184677
\(304\) −1.00000 −0.0573539
\(305\) −7.73082 −0.442666
\(306\) −2.32615 −0.132977
\(307\) −25.9108 −1.47881 −0.739404 0.673262i \(-0.764893\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(308\) 5.80091 0.330537
\(309\) −12.2626 −0.697595
\(310\) 4.39370 0.249546
\(311\) −2.62501 −0.148851 −0.0744254 0.997227i \(-0.523712\pi\)
−0.0744254 + 0.997227i \(0.523712\pi\)
\(312\) 2.08342 0.117951
\(313\) 24.4886 1.38418 0.692088 0.721813i \(-0.256691\pi\)
0.692088 + 0.721813i \(0.256691\pi\)
\(314\) 20.3889 1.15061
\(315\) −3.20287 −0.180461
\(316\) −13.6615 −0.768522
\(317\) 23.0562 1.29496 0.647482 0.762081i \(-0.275822\pi\)
0.647482 + 0.762081i \(0.275822\pi\)
\(318\) 5.25991 0.294961
\(319\) 6.80422 0.380963
\(320\) −1.33044 −0.0743738
\(321\) −0.475904 −0.0265624
\(322\) 30.9694 1.72585
\(323\) −3.29766 −0.183487
\(324\) −6.38624 −0.354791
\(325\) 4.44240 0.246420
\(326\) 17.7092 0.980820
\(327\) −7.05040 −0.389888
\(328\) 3.82702 0.211312
\(329\) −1.37791 −0.0759666
\(330\) −3.42556 −0.188571
\(331\) 31.1190 1.71045 0.855227 0.518253i \(-0.173418\pi\)
0.855227 + 0.518253i \(0.173418\pi\)
\(332\) −13.8574 −0.760526
\(333\) 4.97224 0.272477
\(334\) 12.2727 0.671533
\(335\) −3.49812 −0.191123
\(336\) 5.16972 0.282031
\(337\) 23.9576 1.30505 0.652527 0.757765i \(-0.273709\pi\)
0.652527 + 0.757765i \(0.273709\pi\)
\(338\) −11.1083 −0.604213
\(339\) −9.16972 −0.498031
\(340\) −4.38733 −0.237936
\(341\) 5.61331 0.303978
\(342\) 0.705394 0.0381433
\(343\) 8.02929 0.433541
\(344\) −2.87399 −0.154955
\(345\) −18.2881 −0.984597
\(346\) −6.43453 −0.345922
\(347\) −35.7022 −1.91660 −0.958298 0.285771i \(-0.907750\pi\)
−0.958298 + 0.285771i \(0.907750\pi\)
\(348\) 6.06387 0.325057
\(349\) 4.64600 0.248695 0.124347 0.992239i \(-0.460316\pi\)
0.124347 + 0.992239i \(0.460316\pi\)
\(350\) 11.0232 0.589213
\(351\) −7.71991 −0.412058
\(352\) −1.69974 −0.0905966
\(353\) 36.2241 1.92801 0.964006 0.265880i \(-0.0856624\pi\)
0.964006 + 0.265880i \(0.0856624\pi\)
\(354\) 7.53647 0.400559
\(355\) 2.30005 0.122074
\(356\) 0.930086 0.0492944
\(357\) 17.0480 0.902274
\(358\) 3.93151 0.207787
\(359\) 25.3870 1.33987 0.669936 0.742419i \(-0.266321\pi\)
0.669936 + 0.742419i \(0.266321\pi\)
\(360\) 0.938483 0.0494624
\(361\) 1.00000 0.0526316
\(362\) −12.8893 −0.677446
\(363\) 12.2863 0.644865
\(364\) 4.69393 0.246029
\(365\) 3.92130 0.205250
\(366\) −8.80208 −0.460092
\(367\) 36.8464 1.92337 0.961684 0.274160i \(-0.0883998\pi\)
0.961684 + 0.274160i \(0.0883998\pi\)
\(368\) −9.07443 −0.473037
\(369\) −2.69956 −0.140533
\(370\) 9.37811 0.487545
\(371\) 11.8505 0.615248
\(372\) 5.00253 0.259369
\(373\) 17.8694 0.925241 0.462620 0.886556i \(-0.346909\pi\)
0.462620 + 0.886556i \(0.346909\pi\)
\(374\) −5.60517 −0.289836
\(375\) −16.5861 −0.856504
\(376\) 0.403746 0.0208216
\(377\) 5.50578 0.283562
\(378\) −19.1558 −0.985270
\(379\) −8.25938 −0.424256 −0.212128 0.977242i \(-0.568039\pi\)
−0.212128 + 0.977242i \(0.568039\pi\)
\(380\) 1.33044 0.0682501
\(381\) 26.1032 1.33731
\(382\) 14.6660 0.750377
\(383\) −26.7949 −1.36915 −0.684577 0.728941i \(-0.740013\pi\)
−0.684577 + 0.728941i \(0.740013\pi\)
\(384\) −1.51480 −0.0773016
\(385\) −7.71775 −0.393333
\(386\) −8.39534 −0.427311
\(387\) 2.02729 0.103053
\(388\) 19.0674 0.967999
\(389\) −37.8046 −1.91677 −0.958384 0.285482i \(-0.907846\pi\)
−0.958384 + 0.285482i \(0.907846\pi\)
\(390\) −2.77187 −0.140359
\(391\) −29.9244 −1.51334
\(392\) 4.64731 0.234725
\(393\) −20.9621 −1.05740
\(394\) 21.4394 1.08010
\(395\) 18.1759 0.914526
\(396\) 1.19899 0.0602514
\(397\) −24.5588 −1.23257 −0.616285 0.787523i \(-0.711363\pi\)
−0.616285 + 0.787523i \(0.711363\pi\)
\(398\) 3.84538 0.192751
\(399\) −5.16972 −0.258810
\(400\) −3.22993 −0.161497
\(401\) 1.90144 0.0949536 0.0474768 0.998872i \(-0.484882\pi\)
0.0474768 + 0.998872i \(0.484882\pi\)
\(402\) −3.98285 −0.198646
\(403\) 4.54213 0.226260
\(404\) −2.12217 −0.105582
\(405\) 8.49650 0.422194
\(406\) 13.6618 0.678024
\(407\) 11.9813 0.593890
\(408\) −4.99528 −0.247303
\(409\) 3.94505 0.195070 0.0975351 0.995232i \(-0.468904\pi\)
0.0975351 + 0.995232i \(0.468904\pi\)
\(410\) −5.09162 −0.251457
\(411\) 13.3520 0.658605
\(412\) 8.09522 0.398823
\(413\) 16.9796 0.835510
\(414\) 6.40104 0.314594
\(415\) 18.4365 0.905011
\(416\) −1.37538 −0.0674337
\(417\) 20.4626 1.00206
\(418\) 1.69974 0.0831371
\(419\) −7.58752 −0.370674 −0.185337 0.982675i \(-0.559338\pi\)
−0.185337 + 0.982675i \(0.559338\pi\)
\(420\) −6.87799 −0.335612
\(421\) 2.32906 0.113512 0.0567558 0.998388i \(-0.481924\pi\)
0.0567558 + 0.998388i \(0.481924\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −0.284800 −0.0138474
\(424\) −3.47236 −0.168632
\(425\) −10.6512 −0.516660
\(426\) 2.61877 0.126880
\(427\) −19.8310 −0.959688
\(428\) 0.314171 0.0151860
\(429\) −3.54128 −0.170975
\(430\) 3.82367 0.184394
\(431\) −32.3917 −1.56025 −0.780127 0.625621i \(-0.784846\pi\)
−0.780127 + 0.625621i \(0.784846\pi\)
\(432\) 5.61291 0.270051
\(433\) −6.39386 −0.307269 −0.153635 0.988128i \(-0.549098\pi\)
−0.153635 + 0.988128i \(0.549098\pi\)
\(434\) 11.2706 0.541008
\(435\) −8.06760 −0.386812
\(436\) 4.65436 0.222903
\(437\) 9.07443 0.434089
\(438\) 4.46467 0.213330
\(439\) −27.0707 −1.29202 −0.646008 0.763331i \(-0.723563\pi\)
−0.646008 + 0.763331i \(0.723563\pi\)
\(440\) 2.26140 0.107808
\(441\) −3.27818 −0.156104
\(442\) −4.53554 −0.215734
\(443\) −26.1683 −1.24329 −0.621647 0.783297i \(-0.713536\pi\)
−0.621647 + 0.783297i \(0.713536\pi\)
\(444\) 10.6776 0.506737
\(445\) −1.23742 −0.0586594
\(446\) −25.7019 −1.21702
\(447\) 12.7878 0.604842
\(448\) −3.41282 −0.161240
\(449\) 11.6674 0.550619 0.275309 0.961356i \(-0.411220\pi\)
0.275309 + 0.961356i \(0.411220\pi\)
\(450\) 2.27837 0.107404
\(451\) −6.50495 −0.306306
\(452\) 6.05343 0.284730
\(453\) −30.9647 −1.45485
\(454\) 4.95645 0.232618
\(455\) −6.24498 −0.292769
\(456\) 1.51480 0.0709368
\(457\) −33.8111 −1.58162 −0.790808 0.612064i \(-0.790340\pi\)
−0.790808 + 0.612064i \(0.790340\pi\)
\(458\) −8.83498 −0.412832
\(459\) 18.5095 0.863948
\(460\) 12.0730 0.562905
\(461\) 2.22299 0.103535 0.0517675 0.998659i \(-0.483515\pi\)
0.0517675 + 0.998659i \(0.483515\pi\)
\(462\) −8.78719 −0.408817
\(463\) −14.0372 −0.652364 −0.326182 0.945307i \(-0.605762\pi\)
−0.326182 + 0.945307i \(0.605762\pi\)
\(464\) −4.00309 −0.185839
\(465\) −6.65556 −0.308644
\(466\) 16.3043 0.755280
\(467\) 7.36968 0.341028 0.170514 0.985355i \(-0.445457\pi\)
0.170514 + 0.985355i \(0.445457\pi\)
\(468\) 0.970186 0.0448469
\(469\) −8.97331 −0.414349
\(470\) −0.537159 −0.0247773
\(471\) −30.8850 −1.42311
\(472\) −4.97524 −0.229004
\(473\) 4.88504 0.224614
\(474\) 20.6945 0.950528
\(475\) 3.22993 0.148200
\(476\) −11.2543 −0.515840
\(477\) 2.44938 0.112149
\(478\) −5.20338 −0.237997
\(479\) −10.6119 −0.484872 −0.242436 0.970167i \(-0.577946\pi\)
−0.242436 + 0.970167i \(0.577946\pi\)
\(480\) 2.01534 0.0919874
\(481\) 9.69491 0.442050
\(482\) 25.2116 1.14836
\(483\) −46.9123 −2.13458
\(484\) −8.11088 −0.368676
\(485\) −25.3680 −1.15190
\(486\) −7.16490 −0.325006
\(487\) −30.9772 −1.40371 −0.701856 0.712319i \(-0.747645\pi\)
−0.701856 + 0.712319i \(0.747645\pi\)
\(488\) 5.81073 0.263040
\(489\) −26.8258 −1.21310
\(490\) −6.18296 −0.279318
\(491\) −11.8094 −0.532951 −0.266476 0.963842i \(-0.585859\pi\)
−0.266476 + 0.963842i \(0.585859\pi\)
\(492\) −5.79716 −0.261356
\(493\) −13.2008 −0.594535
\(494\) 1.37538 0.0618814
\(495\) −1.59518 −0.0716979
\(496\) −3.30245 −0.148284
\(497\) 5.90005 0.264653
\(498\) 20.9912 0.940638
\(499\) −4.86110 −0.217613 −0.108806 0.994063i \(-0.534703\pi\)
−0.108806 + 0.994063i \(0.534703\pi\)
\(500\) 10.9494 0.489673
\(501\) −18.5907 −0.830569
\(502\) 23.6548 1.05576
\(503\) −10.8269 −0.482749 −0.241375 0.970432i \(-0.577598\pi\)
−0.241375 + 0.970432i \(0.577598\pi\)
\(504\) 2.40738 0.107233
\(505\) 2.82342 0.125641
\(506\) 15.4242 0.685689
\(507\) 16.8268 0.747306
\(508\) −17.2322 −0.764554
\(509\) 4.47330 0.198275 0.0991377 0.995074i \(-0.468392\pi\)
0.0991377 + 0.995074i \(0.468392\pi\)
\(510\) 6.64591 0.294286
\(511\) 10.0589 0.444977
\(512\) 1.00000 0.0441942
\(513\) −5.61291 −0.247816
\(514\) −18.4024 −0.811693
\(515\) −10.7702 −0.474591
\(516\) 4.35351 0.191653
\(517\) −0.686264 −0.0301818
\(518\) 24.0565 1.05698
\(519\) 9.74699 0.427845
\(520\) 1.82986 0.0802448
\(521\) −10.9369 −0.479154 −0.239577 0.970877i \(-0.577009\pi\)
−0.239577 + 0.970877i \(0.577009\pi\)
\(522\) 2.82375 0.123592
\(523\) −33.9413 −1.48415 −0.742076 0.670316i \(-0.766158\pi\)
−0.742076 + 0.670316i \(0.766158\pi\)
\(524\) 13.8383 0.604527
\(525\) −16.6978 −0.728754
\(526\) 16.7685 0.731144
\(527\) −10.8903 −0.474391
\(528\) 2.57476 0.112052
\(529\) 59.3453 2.58023
\(530\) 4.61976 0.200669
\(531\) 3.50950 0.152299
\(532\) 3.41282 0.147964
\(533\) −5.26362 −0.227993
\(534\) −1.40889 −0.0609686
\(535\) −0.417985 −0.0180710
\(536\) 2.62930 0.113568
\(537\) −5.95544 −0.256996
\(538\) −25.6422 −1.10551
\(539\) −7.89923 −0.340244
\(540\) −7.46764 −0.321356
\(541\) −21.9795 −0.944972 −0.472486 0.881338i \(-0.656643\pi\)
−0.472486 + 0.881338i \(0.656643\pi\)
\(542\) −21.3945 −0.918974
\(543\) 19.5247 0.837883
\(544\) 3.29766 0.141386
\(545\) −6.19233 −0.265250
\(546\) −7.11034 −0.304295
\(547\) 7.50662 0.320960 0.160480 0.987039i \(-0.448696\pi\)
0.160480 + 0.987039i \(0.448696\pi\)
\(548\) −8.81438 −0.376532
\(549\) −4.09885 −0.174935
\(550\) 5.49005 0.234097
\(551\) 4.00309 0.170537
\(552\) 13.7459 0.585065
\(553\) 46.6244 1.98267
\(554\) 13.9758 0.593775
\(555\) −14.2059 −0.603008
\(556\) −13.5085 −0.572888
\(557\) 18.3852 0.779005 0.389503 0.921025i \(-0.372647\pi\)
0.389503 + 0.921025i \(0.372647\pi\)
\(558\) 2.32953 0.0986167
\(559\) 3.95284 0.167187
\(560\) 4.54054 0.191873
\(561\) 8.49068 0.358477
\(562\) 14.4950 0.611434
\(563\) 38.1339 1.60715 0.803576 0.595203i \(-0.202928\pi\)
0.803576 + 0.595203i \(0.202928\pi\)
\(564\) −0.611592 −0.0257527
\(565\) −8.05372 −0.338823
\(566\) −8.77714 −0.368931
\(567\) 21.7951 0.915306
\(568\) −1.72879 −0.0725385
\(569\) −19.8800 −0.833412 −0.416706 0.909041i \(-0.636815\pi\)
−0.416706 + 0.909041i \(0.636815\pi\)
\(570\) −2.01534 −0.0844134
\(571\) 36.9444 1.54607 0.773037 0.634362i \(-0.218737\pi\)
0.773037 + 0.634362i \(0.218737\pi\)
\(572\) 2.33780 0.0977482
\(573\) −22.2160 −0.928086
\(574\) −13.0609 −0.545152
\(575\) 29.3098 1.22230
\(576\) −0.705394 −0.0293914
\(577\) 30.2144 1.25784 0.628921 0.777469i \(-0.283497\pi\)
0.628921 + 0.777469i \(0.283497\pi\)
\(578\) −6.12546 −0.254786
\(579\) 12.7172 0.528510
\(580\) 5.32587 0.221145
\(581\) 47.2929 1.96204
\(582\) −28.8832 −1.19725
\(583\) 5.90211 0.244440
\(584\) −2.94738 −0.121963
\(585\) −1.29077 −0.0533669
\(586\) 9.95726 0.411331
\(587\) 8.57185 0.353798 0.176899 0.984229i \(-0.443393\pi\)
0.176899 + 0.984229i \(0.443393\pi\)
\(588\) −7.03973 −0.290314
\(589\) 3.30245 0.136075
\(590\) 6.61925 0.272510
\(591\) −32.4762 −1.33589
\(592\) −7.04888 −0.289707
\(593\) −10.9435 −0.449397 −0.224699 0.974428i \(-0.572140\pi\)
−0.224699 + 0.974428i \(0.572140\pi\)
\(594\) −9.54051 −0.391452
\(595\) 14.9731 0.613839
\(596\) −8.44192 −0.345795
\(597\) −5.82496 −0.238400
\(598\) 12.4808 0.510379
\(599\) −24.7178 −1.00994 −0.504972 0.863136i \(-0.668497\pi\)
−0.504972 + 0.863136i \(0.668497\pi\)
\(600\) 4.89269 0.199743
\(601\) −10.4790 −0.427449 −0.213725 0.976894i \(-0.568559\pi\)
−0.213725 + 0.976894i \(0.568559\pi\)
\(602\) 9.80840 0.399761
\(603\) −1.85469 −0.0755288
\(604\) 20.4415 0.831754
\(605\) 10.7910 0.438717
\(606\) 3.21466 0.130587
\(607\) −18.2506 −0.740768 −0.370384 0.928879i \(-0.620774\pi\)
−0.370384 + 0.928879i \(0.620774\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −20.6949 −0.838598
\(610\) −7.73082 −0.313012
\(611\) −0.555305 −0.0224652
\(612\) −2.32615 −0.0940289
\(613\) 30.7226 1.24087 0.620437 0.784256i \(-0.286955\pi\)
0.620437 + 0.784256i \(0.286955\pi\)
\(614\) −25.9108 −1.04568
\(615\) 7.71276 0.311009
\(616\) 5.80091 0.233725
\(617\) 18.7514 0.754901 0.377451 0.926030i \(-0.376801\pi\)
0.377451 + 0.926030i \(0.376801\pi\)
\(618\) −12.2626 −0.493274
\(619\) 30.2250 1.21485 0.607424 0.794378i \(-0.292203\pi\)
0.607424 + 0.794378i \(0.292203\pi\)
\(620\) 4.39370 0.176455
\(621\) −50.9340 −2.04391
\(622\) −2.62501 −0.105253
\(623\) −3.17421 −0.127172
\(624\) 2.08342 0.0834037
\(625\) 1.58214 0.0632855
\(626\) 24.4886 0.978760
\(627\) −2.57476 −0.102826
\(628\) 20.3889 0.813606
\(629\) −23.2448 −0.926831
\(630\) −3.20287 −0.127605
\(631\) −36.3344 −1.44645 −0.723225 0.690612i \(-0.757341\pi\)
−0.723225 + 0.690612i \(0.757341\pi\)
\(632\) −13.6615 −0.543427
\(633\) 1.51480 0.0602077
\(634\) 23.0562 0.915678
\(635\) 22.9264 0.909805
\(636\) 5.25991 0.208569
\(637\) −6.39184 −0.253254
\(638\) 6.80422 0.269382
\(639\) 1.21948 0.0482418
\(640\) −1.33044 −0.0525902
\(641\) 17.2843 0.682688 0.341344 0.939938i \(-0.389118\pi\)
0.341344 + 0.939938i \(0.389118\pi\)
\(642\) −0.475904 −0.0187824
\(643\) 22.9355 0.904486 0.452243 0.891895i \(-0.350624\pi\)
0.452243 + 0.891895i \(0.350624\pi\)
\(644\) 30.9694 1.22036
\(645\) −5.79208 −0.228063
\(646\) −3.29766 −0.129745
\(647\) −20.3085 −0.798408 −0.399204 0.916862i \(-0.630713\pi\)
−0.399204 + 0.916862i \(0.630713\pi\)
\(648\) −6.38624 −0.250875
\(649\) 8.45662 0.331951
\(650\) 4.44240 0.174245
\(651\) −17.0727 −0.669133
\(652\) 17.7092 0.693544
\(653\) 18.7836 0.735060 0.367530 0.930012i \(-0.380203\pi\)
0.367530 + 0.930012i \(0.380203\pi\)
\(654\) −7.05040 −0.275692
\(655\) −18.4109 −0.719375
\(656\) 3.82702 0.149420
\(657\) 2.07906 0.0811119
\(658\) −1.37791 −0.0537165
\(659\) 4.56516 0.177833 0.0889167 0.996039i \(-0.471659\pi\)
0.0889167 + 0.996039i \(0.471659\pi\)
\(660\) −3.42556 −0.133340
\(661\) −9.42639 −0.366644 −0.183322 0.983053i \(-0.558685\pi\)
−0.183322 + 0.983053i \(0.558685\pi\)
\(662\) 31.1190 1.20947
\(663\) 6.87042 0.266825
\(664\) −13.8574 −0.537773
\(665\) −4.54054 −0.176075
\(666\) 4.97224 0.192670
\(667\) 36.3258 1.40654
\(668\) 12.2727 0.474845
\(669\) 38.9331 1.50524
\(670\) −3.49812 −0.135144
\(671\) −9.87675 −0.381288
\(672\) 5.16972 0.199426
\(673\) 26.5563 1.02367 0.511835 0.859084i \(-0.328966\pi\)
0.511835 + 0.859084i \(0.328966\pi\)
\(674\) 23.9576 0.922813
\(675\) −18.1293 −0.697799
\(676\) −11.1083 −0.427243
\(677\) −1.64399 −0.0631835 −0.0315918 0.999501i \(-0.510058\pi\)
−0.0315918 + 0.999501i \(0.510058\pi\)
\(678\) −9.16972 −0.352161
\(679\) −65.0734 −2.49729
\(680\) −4.38733 −0.168246
\(681\) −7.50802 −0.287708
\(682\) 5.61331 0.214945
\(683\) −3.20287 −0.122555 −0.0612773 0.998121i \(-0.519517\pi\)
−0.0612773 + 0.998121i \(0.519517\pi\)
\(684\) 0.705394 0.0269714
\(685\) 11.7270 0.448065
\(686\) 8.02929 0.306560
\(687\) 13.3832 0.510601
\(688\) −2.87399 −0.109570
\(689\) 4.77582 0.181944
\(690\) −18.2881 −0.696216
\(691\) −35.1314 −1.33646 −0.668231 0.743954i \(-0.732948\pi\)
−0.668231 + 0.743954i \(0.732948\pi\)
\(692\) −6.43453 −0.244604
\(693\) −4.09192 −0.155439
\(694\) −35.7022 −1.35524
\(695\) 17.9722 0.681725
\(696\) 6.06387 0.229850
\(697\) 12.6202 0.478024
\(698\) 4.64600 0.175854
\(699\) −24.6976 −0.934150
\(700\) 11.0232 0.416637
\(701\) −40.6089 −1.53378 −0.766889 0.641780i \(-0.778196\pi\)
−0.766889 + 0.641780i \(0.778196\pi\)
\(702\) −7.71991 −0.291369
\(703\) 7.04888 0.265854
\(704\) −1.69974 −0.0640614
\(705\) 0.813686 0.0306452
\(706\) 36.2241 1.36331
\(707\) 7.24258 0.272385
\(708\) 7.53647 0.283238
\(709\) 6.61864 0.248568 0.124284 0.992247i \(-0.460337\pi\)
0.124284 + 0.992247i \(0.460337\pi\)
\(710\) 2.30005 0.0863194
\(711\) 9.63677 0.361407
\(712\) 0.930086 0.0348564
\(713\) 29.9678 1.12230
\(714\) 17.0480 0.638004
\(715\) −3.11029 −0.116318
\(716\) 3.93151 0.146928
\(717\) 7.88206 0.294361
\(718\) 25.3870 0.947433
\(719\) −6.02280 −0.224613 −0.112306 0.993674i \(-0.535824\pi\)
−0.112306 + 0.993674i \(0.535824\pi\)
\(720\) 0.938483 0.0349752
\(721\) −27.6275 −1.02890
\(722\) 1.00000 0.0372161
\(723\) −38.1904 −1.42032
\(724\) −12.8893 −0.479027
\(725\) 12.9297 0.480198
\(726\) 12.2863 0.455988
\(727\) −30.5647 −1.13358 −0.566791 0.823862i \(-0.691815\pi\)
−0.566791 + 0.823862i \(0.691815\pi\)
\(728\) 4.69393 0.173969
\(729\) 30.0121 1.11156
\(730\) 3.92130 0.145134
\(731\) −9.47743 −0.350536
\(732\) −8.80208 −0.325334
\(733\) −2.54785 −0.0941068 −0.0470534 0.998892i \(-0.514983\pi\)
−0.0470534 + 0.998892i \(0.514983\pi\)
\(734\) 36.8464 1.36003
\(735\) 9.36593 0.345467
\(736\) −9.07443 −0.334488
\(737\) −4.46913 −0.164622
\(738\) −2.69956 −0.0993721
\(739\) 47.3283 1.74100 0.870499 0.492170i \(-0.163796\pi\)
0.870499 + 0.492170i \(0.163796\pi\)
\(740\) 9.37811 0.344746
\(741\) −2.08342 −0.0765365
\(742\) 11.8505 0.435046
\(743\) 6.21476 0.227997 0.113999 0.993481i \(-0.463634\pi\)
0.113999 + 0.993481i \(0.463634\pi\)
\(744\) 5.00253 0.183402
\(745\) 11.2315 0.411489
\(746\) 17.8694 0.654244
\(747\) 9.77495 0.357647
\(748\) −5.60517 −0.204945
\(749\) −1.07221 −0.0391776
\(750\) −16.5861 −0.605640
\(751\) −14.1073 −0.514783 −0.257391 0.966307i \(-0.582863\pi\)
−0.257391 + 0.966307i \(0.582863\pi\)
\(752\) 0.403746 0.0147231
\(753\) −35.8321 −1.30580
\(754\) 5.50578 0.200509
\(755\) −27.1962 −0.989770
\(756\) −19.1558 −0.696691
\(757\) 47.9900 1.74423 0.872113 0.489304i \(-0.162749\pi\)
0.872113 + 0.489304i \(0.162749\pi\)
\(758\) −8.25938 −0.299994
\(759\) −23.3645 −0.848078
\(760\) 1.33044 0.0482601
\(761\) −43.1871 −1.56553 −0.782766 0.622316i \(-0.786192\pi\)
−0.782766 + 0.622316i \(0.786192\pi\)
\(762\) 26.1032 0.945620
\(763\) −15.8845 −0.575056
\(764\) 14.6660 0.530597
\(765\) 3.09479 0.111893
\(766\) −26.7949 −0.968138
\(767\) 6.84286 0.247081
\(768\) −1.51480 −0.0546605
\(769\) −26.4903 −0.955263 −0.477632 0.878560i \(-0.658505\pi\)
−0.477632 + 0.878560i \(0.658505\pi\)
\(770\) −7.71775 −0.278128
\(771\) 27.8758 1.00392
\(772\) −8.39534 −0.302155
\(773\) −32.5049 −1.16912 −0.584560 0.811351i \(-0.698733\pi\)
−0.584560 + 0.811351i \(0.698733\pi\)
\(774\) 2.02729 0.0728696
\(775\) 10.6667 0.383159
\(776\) 19.0674 0.684478
\(777\) −36.4407 −1.30730
\(778\) −37.8046 −1.35536
\(779\) −3.82702 −0.137117
\(780\) −2.77187 −0.0992488
\(781\) 2.93850 0.105148
\(782\) −29.9244 −1.07009
\(783\) −22.4690 −0.802977
\(784\) 4.64731 0.165975
\(785\) −27.1262 −0.968176
\(786\) −20.9621 −0.747694
\(787\) −8.97760 −0.320017 −0.160008 0.987116i \(-0.551152\pi\)
−0.160008 + 0.987116i \(0.551152\pi\)
\(788\) 21.4394 0.763745
\(789\) −25.4009 −0.904297
\(790\) 18.1759 0.646668
\(791\) −20.6593 −0.734559
\(792\) 1.19899 0.0426042
\(793\) −7.99199 −0.283804
\(794\) −24.5588 −0.871559
\(795\) −6.99799 −0.248193
\(796\) 3.84538 0.136296
\(797\) −36.7219 −1.30076 −0.650379 0.759610i \(-0.725390\pi\)
−0.650379 + 0.759610i \(0.725390\pi\)
\(798\) −5.16972 −0.183006
\(799\) 1.33142 0.0471021
\(800\) −3.22993 −0.114195
\(801\) −0.656077 −0.0231813
\(802\) 1.90144 0.0671423
\(803\) 5.00978 0.176791
\(804\) −3.98285 −0.140464
\(805\) −41.2028 −1.45221
\(806\) 4.54213 0.159990
\(807\) 38.8427 1.36733
\(808\) −2.12217 −0.0746578
\(809\) 13.5360 0.475901 0.237950 0.971277i \(-0.423524\pi\)
0.237950 + 0.971277i \(0.423524\pi\)
\(810\) 8.49650 0.298537
\(811\) 45.7810 1.60759 0.803794 0.594907i \(-0.202811\pi\)
0.803794 + 0.594907i \(0.202811\pi\)
\(812\) 13.6618 0.479436
\(813\) 32.4084 1.13661
\(814\) 11.9813 0.419944
\(815\) −23.5609 −0.825304
\(816\) −4.99528 −0.174870
\(817\) 2.87399 0.100548
\(818\) 3.94505 0.137935
\(819\) −3.31107 −0.115698
\(820\) −5.09162 −0.177807
\(821\) 6.08793 0.212470 0.106235 0.994341i \(-0.466120\pi\)
0.106235 + 0.994341i \(0.466120\pi\)
\(822\) 13.3520 0.465704
\(823\) −24.5573 −0.856014 −0.428007 0.903775i \(-0.640784\pi\)
−0.428007 + 0.903775i \(0.640784\pi\)
\(824\) 8.09522 0.282010
\(825\) −8.31631 −0.289537
\(826\) 16.9796 0.590795
\(827\) 44.1891 1.53661 0.768303 0.640086i \(-0.221101\pi\)
0.768303 + 0.640086i \(0.221101\pi\)
\(828\) 6.40104 0.222452
\(829\) 43.4526 1.50917 0.754586 0.656201i \(-0.227838\pi\)
0.754586 + 0.656201i \(0.227838\pi\)
\(830\) 18.4365 0.639939
\(831\) −21.1705 −0.734396
\(832\) −1.37538 −0.0476828
\(833\) 15.3252 0.530988
\(834\) 20.4626 0.708562
\(835\) −16.3281 −0.565057
\(836\) 1.69974 0.0587868
\(837\) −18.5364 −0.640710
\(838\) −7.58752 −0.262106
\(839\) −3.59994 −0.124284 −0.0621419 0.998067i \(-0.519793\pi\)
−0.0621419 + 0.998067i \(0.519793\pi\)
\(840\) −6.87799 −0.237313
\(841\) −12.9753 −0.447423
\(842\) 2.32906 0.0802648
\(843\) −21.9569 −0.756237
\(844\) −1.00000 −0.0344214
\(845\) 14.7789 0.508411
\(846\) −0.284800 −0.00979162
\(847\) 27.6809 0.951128
\(848\) −3.47236 −0.119241
\(849\) 13.2956 0.456303
\(850\) −10.6512 −0.365334
\(851\) 63.9646 2.19268
\(852\) 2.61877 0.0897175
\(853\) 10.9039 0.373343 0.186672 0.982422i \(-0.440230\pi\)
0.186672 + 0.982422i \(0.440230\pi\)
\(854\) −19.8310 −0.678602
\(855\) −0.938483 −0.0320954
\(856\) 0.314171 0.0107381
\(857\) −32.4946 −1.10999 −0.554997 0.831852i \(-0.687281\pi\)
−0.554997 + 0.831852i \(0.687281\pi\)
\(858\) −3.54128 −0.120897
\(859\) −22.5303 −0.768725 −0.384363 0.923182i \(-0.625579\pi\)
−0.384363 + 0.923182i \(0.625579\pi\)
\(860\) 3.82367 0.130386
\(861\) 19.7846 0.674258
\(862\) −32.3917 −1.10327
\(863\) 48.2969 1.64404 0.822022 0.569455i \(-0.192846\pi\)
0.822022 + 0.569455i \(0.192846\pi\)
\(864\) 5.61291 0.190955
\(865\) 8.56074 0.291074
\(866\) −6.39386 −0.217272
\(867\) 9.27882 0.315125
\(868\) 11.2706 0.382551
\(869\) 23.2211 0.787722
\(870\) −8.06760 −0.273517
\(871\) −3.61629 −0.122533
\(872\) 4.65436 0.157616
\(873\) −13.4500 −0.455213
\(874\) 9.07443 0.306947
\(875\) −37.3684 −1.26328
\(876\) 4.46467 0.150847
\(877\) −50.3611 −1.70058 −0.850288 0.526318i \(-0.823572\pi\)
−0.850288 + 0.526318i \(0.823572\pi\)
\(878\) −27.0707 −0.913593
\(879\) −15.0832 −0.508744
\(880\) 2.26140 0.0762318
\(881\) 53.6654 1.80803 0.904016 0.427498i \(-0.140605\pi\)
0.904016 + 0.427498i \(0.140605\pi\)
\(882\) −3.27818 −0.110382
\(883\) 16.8234 0.566153 0.283077 0.959097i \(-0.408645\pi\)
0.283077 + 0.959097i \(0.408645\pi\)
\(884\) −4.53554 −0.152547
\(885\) −10.0268 −0.337048
\(886\) −26.1683 −0.879142
\(887\) −34.5624 −1.16049 −0.580246 0.814441i \(-0.697044\pi\)
−0.580246 + 0.814441i \(0.697044\pi\)
\(888\) 10.6776 0.358317
\(889\) 58.8103 1.97243
\(890\) −1.23742 −0.0414785
\(891\) 10.8550 0.363655
\(892\) −25.7019 −0.860564
\(893\) −0.403746 −0.0135108
\(894\) 12.7878 0.427688
\(895\) −5.23064 −0.174841
\(896\) −3.41282 −0.114014
\(897\) −18.9059 −0.631249
\(898\) 11.6674 0.389346
\(899\) 13.2200 0.440912
\(900\) 2.27837 0.0759458
\(901\) −11.4506 −0.381476
\(902\) −6.50495 −0.216591
\(903\) −14.8577 −0.494434
\(904\) 6.05343 0.201334
\(905\) 17.1484 0.570033
\(906\) −30.9647 −1.02873
\(907\) −3.97159 −0.131875 −0.0659373 0.997824i \(-0.521004\pi\)
−0.0659373 + 0.997824i \(0.521004\pi\)
\(908\) 4.95645 0.164486
\(909\) 1.49697 0.0496513
\(910\) −6.24498 −0.207019
\(911\) −16.7147 −0.553784 −0.276892 0.960901i \(-0.589304\pi\)
−0.276892 + 0.960901i \(0.589304\pi\)
\(912\) 1.51480 0.0501599
\(913\) 23.5541 0.779526
\(914\) −33.8111 −1.11837
\(915\) 11.7106 0.387141
\(916\) −8.83498 −0.291916
\(917\) −47.2274 −1.55959
\(918\) 18.5095 0.610903
\(919\) 45.0691 1.48669 0.743346 0.668907i \(-0.233237\pi\)
0.743346 + 0.668907i \(0.233237\pi\)
\(920\) 12.0730 0.398034
\(921\) 39.2496 1.29332
\(922\) 2.22299 0.0732102
\(923\) 2.37775 0.0782647
\(924\) −8.78719 −0.289077
\(925\) 22.7674 0.748588
\(926\) −14.0372 −0.461291
\(927\) −5.71031 −0.187551
\(928\) −4.00309 −0.131408
\(929\) 16.2331 0.532590 0.266295 0.963892i \(-0.414200\pi\)
0.266295 + 0.963892i \(0.414200\pi\)
\(930\) −6.65556 −0.218245
\(931\) −4.64731 −0.152310
\(932\) 16.3043 0.534064
\(933\) 3.97636 0.130180
\(934\) 7.36968 0.241143
\(935\) 7.45733 0.243881
\(936\) 0.970186 0.0317115
\(937\) −47.8440 −1.56299 −0.781497 0.623909i \(-0.785544\pi\)
−0.781497 + 0.623909i \(0.785544\pi\)
\(938\) −8.97331 −0.292989
\(939\) −37.0952 −1.21056
\(940\) −0.537159 −0.0175202
\(941\) −37.5434 −1.22388 −0.611941 0.790904i \(-0.709611\pi\)
−0.611941 + 0.790904i \(0.709611\pi\)
\(942\) −30.8850 −1.00629
\(943\) −34.7280 −1.13090
\(944\) −4.97524 −0.161930
\(945\) 25.4857 0.829049
\(946\) 4.88504 0.158826
\(947\) 5.96089 0.193703 0.0968515 0.995299i \(-0.469123\pi\)
0.0968515 + 0.995299i \(0.469123\pi\)
\(948\) 20.6945 0.672125
\(949\) 4.05377 0.131591
\(950\) 3.22993 0.104793
\(951\) −34.9254 −1.13253
\(952\) −11.2543 −0.364754
\(953\) −21.8039 −0.706298 −0.353149 0.935567i \(-0.614889\pi\)
−0.353149 + 0.935567i \(0.614889\pi\)
\(954\) 2.44938 0.0793015
\(955\) −19.5122 −0.631400
\(956\) −5.20338 −0.168289
\(957\) −10.3070 −0.333178
\(958\) −10.6119 −0.342856
\(959\) 30.0819 0.971394
\(960\) 2.01534 0.0650449
\(961\) −20.0938 −0.648188
\(962\) 9.69491 0.312577
\(963\) −0.221614 −0.00714141
\(964\) 25.2116 0.812011
\(965\) 11.1695 0.359558
\(966\) −46.9123 −1.50938
\(967\) 52.0431 1.67359 0.836796 0.547514i \(-0.184426\pi\)
0.836796 + 0.547514i \(0.184426\pi\)
\(968\) −8.11088 −0.260693
\(969\) 4.99528 0.160471
\(970\) −25.3680 −0.814516
\(971\) −41.5607 −1.33375 −0.666873 0.745172i \(-0.732367\pi\)
−0.666873 + 0.745172i \(0.732367\pi\)
\(972\) −7.16490 −0.229814
\(973\) 46.1020 1.47796
\(974\) −30.9772 −0.992575
\(975\) −6.72932 −0.215511
\(976\) 5.81073 0.185997
\(977\) −44.8146 −1.43375 −0.716873 0.697204i \(-0.754427\pi\)
−0.716873 + 0.697204i \(0.754427\pi\)
\(978\) −26.8258 −0.857793
\(979\) −1.58091 −0.0505260
\(980\) −6.18296 −0.197508
\(981\) −3.28315 −0.104823
\(982\) −11.8094 −0.376853
\(983\) 59.9488 1.91207 0.956034 0.293254i \(-0.0947382\pi\)
0.956034 + 0.293254i \(0.0947382\pi\)
\(984\) −5.79716 −0.184807
\(985\) −28.5237 −0.908842
\(986\) −13.2008 −0.420400
\(987\) 2.08725 0.0664380
\(988\) 1.37538 0.0437568
\(989\) 26.0798 0.829290
\(990\) −1.59518 −0.0506981
\(991\) 45.1889 1.43547 0.717737 0.696315i \(-0.245178\pi\)
0.717737 + 0.696315i \(0.245178\pi\)
\(992\) −3.30245 −0.104853
\(993\) −47.1389 −1.49591
\(994\) 5.90005 0.187138
\(995\) −5.11604 −0.162189
\(996\) 20.9912 0.665131
\(997\) −37.9300 −1.20126 −0.600628 0.799529i \(-0.705083\pi\)
−0.600628 + 0.799529i \(0.705083\pi\)
\(998\) −4.86110 −0.153876
\(999\) −39.5648 −1.25177
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 \(a_p\))