Properties

Label 6026.2.a.i.1.1
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.98476 q^{3}\) \(+1.00000 q^{4}\) \(+1.57995 q^{5}\) \(+2.98476 q^{6}\) \(+2.90984 q^{7}\) \(-1.00000 q^{8}\) \(+5.90879 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.98476 q^{3}\) \(+1.00000 q^{4}\) \(+1.57995 q^{5}\) \(+2.98476 q^{6}\) \(+2.90984 q^{7}\) \(-1.00000 q^{8}\) \(+5.90879 q^{9}\) \(-1.57995 q^{10}\) \(-4.95802 q^{11}\) \(-2.98476 q^{12}\) \(-4.16275 q^{13}\) \(-2.90984 q^{14}\) \(-4.71578 q^{15}\) \(+1.00000 q^{16}\) \(+2.92081 q^{17}\) \(-5.90879 q^{18}\) \(+2.68824 q^{19}\) \(+1.57995 q^{20}\) \(-8.68519 q^{21}\) \(+4.95802 q^{22}\) \(+1.00000 q^{23}\) \(+2.98476 q^{24}\) \(-2.50375 q^{25}\) \(+4.16275 q^{26}\) \(-8.68205 q^{27}\) \(+2.90984 q^{28}\) \(+5.30982 q^{29}\) \(+4.71578 q^{30}\) \(-3.13133 q^{31}\) \(-1.00000 q^{32}\) \(+14.7985 q^{33}\) \(-2.92081 q^{34}\) \(+4.59742 q^{35}\) \(+5.90879 q^{36}\) \(+4.98422 q^{37}\) \(-2.68824 q^{38}\) \(+12.4248 q^{39}\) \(-1.57995 q^{40}\) \(+6.04686 q^{41}\) \(+8.68519 q^{42}\) \(-0.659532 q^{43}\) \(-4.95802 q^{44}\) \(+9.33562 q^{45}\) \(-1.00000 q^{46}\) \(-6.46454 q^{47}\) \(-2.98476 q^{48}\) \(+1.46720 q^{49}\) \(+2.50375 q^{50}\) \(-8.71791 q^{51}\) \(-4.16275 q^{52}\) \(+1.53961 q^{53}\) \(+8.68205 q^{54}\) \(-7.83345 q^{55}\) \(-2.90984 q^{56}\) \(-8.02376 q^{57}\) \(-5.30982 q^{58}\) \(-3.36081 q^{59}\) \(-4.71578 q^{60}\) \(-8.26073 q^{61}\) \(+3.13133 q^{62}\) \(+17.1937 q^{63}\) \(+1.00000 q^{64}\) \(-6.57696 q^{65}\) \(-14.7985 q^{66}\) \(-4.81120 q^{67}\) \(+2.92081 q^{68}\) \(-2.98476 q^{69}\) \(-4.59742 q^{70}\) \(-13.2195 q^{71}\) \(-5.90879 q^{72}\) \(+1.36743 q^{73}\) \(-4.98422 q^{74}\) \(+7.47308 q^{75}\) \(+2.68824 q^{76}\) \(-14.4271 q^{77}\) \(-12.4248 q^{78}\) \(-1.09845 q^{79}\) \(+1.57995 q^{80}\) \(+8.18746 q^{81}\) \(-6.04686 q^{82}\) \(-5.31930 q^{83}\) \(-8.68519 q^{84}\) \(+4.61474 q^{85}\) \(+0.659532 q^{86}\) \(-15.8485 q^{87}\) \(+4.95802 q^{88}\) \(+9.76882 q^{89}\) \(-9.33562 q^{90}\) \(-12.1130 q^{91}\) \(+1.00000 q^{92}\) \(+9.34627 q^{93}\) \(+6.46454 q^{94}\) \(+4.24730 q^{95}\) \(+2.98476 q^{96}\) \(+0.168734 q^{97}\) \(-1.46720 q^{98}\) \(-29.2959 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.98476 −1.72325 −0.861626 0.507544i \(-0.830554\pi\)
−0.861626 + 0.507544i \(0.830554\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.57995 0.706577 0.353288 0.935514i \(-0.385063\pi\)
0.353288 + 0.935514i \(0.385063\pi\)
\(6\) 2.98476 1.21852
\(7\) 2.90984 1.09982 0.549909 0.835225i \(-0.314662\pi\)
0.549909 + 0.835225i \(0.314662\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.90879 1.96960
\(10\) −1.57995 −0.499625
\(11\) −4.95802 −1.49490 −0.747450 0.664318i \(-0.768722\pi\)
−0.747450 + 0.664318i \(0.768722\pi\)
\(12\) −2.98476 −0.861626
\(13\) −4.16275 −1.15454 −0.577270 0.816553i \(-0.695882\pi\)
−0.577270 + 0.816553i \(0.695882\pi\)
\(14\) −2.90984 −0.777689
\(15\) −4.71578 −1.21761
\(16\) 1.00000 0.250000
\(17\) 2.92081 0.708400 0.354200 0.935170i \(-0.384753\pi\)
0.354200 + 0.935170i \(0.384753\pi\)
\(18\) −5.90879 −1.39272
\(19\) 2.68824 0.616725 0.308362 0.951269i \(-0.400219\pi\)
0.308362 + 0.951269i \(0.400219\pi\)
\(20\) 1.57995 0.353288
\(21\) −8.68519 −1.89526
\(22\) 4.95802 1.05705
\(23\) 1.00000 0.208514
\(24\) 2.98476 0.609262
\(25\) −2.50375 −0.500749
\(26\) 4.16275 0.816383
\(27\) −8.68205 −1.67086
\(28\) 2.90984 0.549909
\(29\) 5.30982 0.986009 0.493005 0.870027i \(-0.335899\pi\)
0.493005 + 0.870027i \(0.335899\pi\)
\(30\) 4.71578 0.860980
\(31\) −3.13133 −0.562404 −0.281202 0.959649i \(-0.590733\pi\)
−0.281202 + 0.959649i \(0.590733\pi\)
\(32\) −1.00000 −0.176777
\(33\) 14.7985 2.57609
\(34\) −2.92081 −0.500914
\(35\) 4.59742 0.777106
\(36\) 5.90879 0.984799
\(37\) 4.98422 0.819401 0.409700 0.912220i \(-0.365633\pi\)
0.409700 + 0.912220i \(0.365633\pi\)
\(38\) −2.68824 −0.436090
\(39\) 12.4248 1.98956
\(40\) −1.57995 −0.249813
\(41\) 6.04686 0.944361 0.472180 0.881502i \(-0.343467\pi\)
0.472180 + 0.881502i \(0.343467\pi\)
\(42\) 8.68519 1.34015
\(43\) −0.659532 −0.100578 −0.0502889 0.998735i \(-0.516014\pi\)
−0.0502889 + 0.998735i \(0.516014\pi\)
\(44\) −4.95802 −0.747450
\(45\) 9.33562 1.39167
\(46\) −1.00000 −0.147442
\(47\) −6.46454 −0.942950 −0.471475 0.881879i \(-0.656278\pi\)
−0.471475 + 0.881879i \(0.656278\pi\)
\(48\) −2.98476 −0.430813
\(49\) 1.46720 0.209599
\(50\) 2.50375 0.354083
\(51\) −8.71791 −1.22075
\(52\) −4.16275 −0.577270
\(53\) 1.53961 0.211481 0.105741 0.994394i \(-0.466279\pi\)
0.105741 + 0.994394i \(0.466279\pi\)
\(54\) 8.68205 1.18148
\(55\) −7.83345 −1.05626
\(56\) −2.90984 −0.388844
\(57\) −8.02376 −1.06277
\(58\) −5.30982 −0.697214
\(59\) −3.36081 −0.437540 −0.218770 0.975776i \(-0.570204\pi\)
−0.218770 + 0.975776i \(0.570204\pi\)
\(60\) −4.71578 −0.608805
\(61\) −8.26073 −1.05768 −0.528839 0.848722i \(-0.677373\pi\)
−0.528839 + 0.848722i \(0.677373\pi\)
\(62\) 3.13133 0.397680
\(63\) 17.1937 2.16620
\(64\) 1.00000 0.125000
\(65\) −6.57696 −0.815771
\(66\) −14.7985 −1.82157
\(67\) −4.81120 −0.587782 −0.293891 0.955839i \(-0.594950\pi\)
−0.293891 + 0.955839i \(0.594950\pi\)
\(68\) 2.92081 0.354200
\(69\) −2.98476 −0.359323
\(70\) −4.59742 −0.549497
\(71\) −13.2195 −1.56887 −0.784434 0.620212i \(-0.787047\pi\)
−0.784434 + 0.620212i \(0.787047\pi\)
\(72\) −5.90879 −0.696358
\(73\) 1.36743 0.160046 0.0800229 0.996793i \(-0.474501\pi\)
0.0800229 + 0.996793i \(0.474501\pi\)
\(74\) −4.98422 −0.579404
\(75\) 7.47308 0.862917
\(76\) 2.68824 0.308362
\(77\) −14.4271 −1.64412
\(78\) −12.4248 −1.40683
\(79\) −1.09845 −0.123586 −0.0617929 0.998089i \(-0.519682\pi\)
−0.0617929 + 0.998089i \(0.519682\pi\)
\(80\) 1.57995 0.176644
\(81\) 8.18746 0.909718
\(82\) −6.04686 −0.667764
\(83\) −5.31930 −0.583869 −0.291934 0.956438i \(-0.594299\pi\)
−0.291934 + 0.956438i \(0.594299\pi\)
\(84\) −8.68519 −0.947632
\(85\) 4.61474 0.500539
\(86\) 0.659532 0.0711192
\(87\) −15.8485 −1.69914
\(88\) 4.95802 0.528527
\(89\) 9.76882 1.03549 0.517746 0.855534i \(-0.326771\pi\)
0.517746 + 0.855534i \(0.326771\pi\)
\(90\) −9.33562 −0.984061
\(91\) −12.1130 −1.26978
\(92\) 1.00000 0.104257
\(93\) 9.34627 0.969163
\(94\) 6.46454 0.666766
\(95\) 4.24730 0.435764
\(96\) 2.98476 0.304631
\(97\) 0.168734 0.0171324 0.00856620 0.999963i \(-0.497273\pi\)
0.00856620 + 0.999963i \(0.497273\pi\)
\(98\) −1.46720 −0.148209
\(99\) −29.2959 −2.94435
\(100\) −2.50375 −0.250375
\(101\) −7.93894 −0.789954 −0.394977 0.918691i \(-0.629247\pi\)
−0.394977 + 0.918691i \(0.629247\pi\)
\(102\) 8.71791 0.863202
\(103\) 11.7967 1.16236 0.581180 0.813775i \(-0.302591\pi\)
0.581180 + 0.813775i \(0.302591\pi\)
\(104\) 4.16275 0.408191
\(105\) −13.7222 −1.33915
\(106\) −1.53961 −0.149540
\(107\) 5.22241 0.504869 0.252435 0.967614i \(-0.418769\pi\)
0.252435 + 0.967614i \(0.418769\pi\)
\(108\) −8.68205 −0.835431
\(109\) −7.46020 −0.714557 −0.357279 0.933998i \(-0.616295\pi\)
−0.357279 + 0.933998i \(0.616295\pi\)
\(110\) 7.83345 0.746890
\(111\) −14.8767 −1.41203
\(112\) 2.90984 0.274954
\(113\) 12.0064 1.12946 0.564732 0.825274i \(-0.308979\pi\)
0.564732 + 0.825274i \(0.308979\pi\)
\(114\) 8.02376 0.751494
\(115\) 1.57995 0.147331
\(116\) 5.30982 0.493005
\(117\) −24.5968 −2.27398
\(118\) 3.36081 0.309388
\(119\) 8.49910 0.779111
\(120\) 4.71578 0.430490
\(121\) 13.5820 1.23473
\(122\) 8.26073 0.747891
\(123\) −18.0484 −1.62737
\(124\) −3.13133 −0.281202
\(125\) −11.8556 −1.06039
\(126\) −17.1937 −1.53173
\(127\) 10.4798 0.929930 0.464965 0.885329i \(-0.346067\pi\)
0.464965 + 0.885329i \(0.346067\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.96855 0.173321
\(130\) 6.57696 0.576837
\(131\) 1.00000 0.0873704
\(132\) 14.7985 1.28804
\(133\) 7.82237 0.678285
\(134\) 4.81120 0.415624
\(135\) −13.7172 −1.18059
\(136\) −2.92081 −0.250457
\(137\) −9.48217 −0.810116 −0.405058 0.914291i \(-0.632749\pi\)
−0.405058 + 0.914291i \(0.632749\pi\)
\(138\) 2.98476 0.254080
\(139\) 17.1336 1.45325 0.726625 0.687034i \(-0.241088\pi\)
0.726625 + 0.687034i \(0.241088\pi\)
\(140\) 4.59742 0.388553
\(141\) 19.2951 1.62494
\(142\) 13.2195 1.10936
\(143\) 20.6390 1.72592
\(144\) 5.90879 0.492399
\(145\) 8.38927 0.696691
\(146\) −1.36743 −0.113169
\(147\) −4.37923 −0.361193
\(148\) 4.98422 0.409700
\(149\) 16.0611 1.31578 0.657890 0.753114i \(-0.271449\pi\)
0.657890 + 0.753114i \(0.271449\pi\)
\(150\) −7.47308 −0.610174
\(151\) −5.62376 −0.457655 −0.228828 0.973467i \(-0.573489\pi\)
−0.228828 + 0.973467i \(0.573489\pi\)
\(152\) −2.68824 −0.218045
\(153\) 17.2585 1.39526
\(154\) 14.4271 1.16257
\(155\) −4.94736 −0.397382
\(156\) 12.4248 0.994782
\(157\) 2.63971 0.210672 0.105336 0.994437i \(-0.466408\pi\)
0.105336 + 0.994437i \(0.466408\pi\)
\(158\) 1.09845 0.0873883
\(159\) −4.59536 −0.364435
\(160\) −1.57995 −0.124906
\(161\) 2.90984 0.229328
\(162\) −8.18746 −0.643268
\(163\) −12.1135 −0.948803 −0.474402 0.880309i \(-0.657336\pi\)
−0.474402 + 0.880309i \(0.657336\pi\)
\(164\) 6.04686 0.472180
\(165\) 23.3810 1.82021
\(166\) 5.31930 0.412857
\(167\) 7.22648 0.559202 0.279601 0.960116i \(-0.409798\pi\)
0.279601 + 0.960116i \(0.409798\pi\)
\(168\) 8.68519 0.670077
\(169\) 4.32851 0.332962
\(170\) −4.61474 −0.353935
\(171\) 15.8843 1.21470
\(172\) −0.659532 −0.0502889
\(173\) 10.6149 0.807035 0.403517 0.914972i \(-0.367787\pi\)
0.403517 + 0.914972i \(0.367787\pi\)
\(174\) 15.8485 1.20148
\(175\) −7.28551 −0.550733
\(176\) −4.95802 −0.373725
\(177\) 10.0312 0.753992
\(178\) −9.76882 −0.732204
\(179\) −9.66447 −0.722357 −0.361178 0.932497i \(-0.617625\pi\)
−0.361178 + 0.932497i \(0.617625\pi\)
\(180\) 9.33562 0.695836
\(181\) −15.4462 −1.14811 −0.574053 0.818818i \(-0.694630\pi\)
−0.574053 + 0.818818i \(0.694630\pi\)
\(182\) 12.1130 0.897873
\(183\) 24.6563 1.82265
\(184\) −1.00000 −0.0737210
\(185\) 7.87484 0.578970
\(186\) −9.34627 −0.685302
\(187\) −14.4814 −1.05899
\(188\) −6.46454 −0.471475
\(189\) −25.2634 −1.83764
\(190\) −4.24730 −0.308131
\(191\) 0.917679 0.0664009 0.0332005 0.999449i \(-0.489430\pi\)
0.0332005 + 0.999449i \(0.489430\pi\)
\(192\) −2.98476 −0.215407
\(193\) −22.1129 −1.59172 −0.795859 0.605482i \(-0.792980\pi\)
−0.795859 + 0.605482i \(0.792980\pi\)
\(194\) −0.168734 −0.0121144
\(195\) 19.6306 1.40578
\(196\) 1.46720 0.104800
\(197\) 4.11730 0.293345 0.146673 0.989185i \(-0.453144\pi\)
0.146673 + 0.989185i \(0.453144\pi\)
\(198\) 29.2959 2.08197
\(199\) −8.82532 −0.625610 −0.312805 0.949817i \(-0.601269\pi\)
−0.312805 + 0.949817i \(0.601269\pi\)
\(200\) 2.50375 0.177042
\(201\) 14.3603 1.01290
\(202\) 7.93894 0.558582
\(203\) 15.4508 1.08443
\(204\) −8.71791 −0.610376
\(205\) 9.55376 0.667264
\(206\) −11.7967 −0.821913
\(207\) 5.90879 0.410690
\(208\) −4.16275 −0.288635
\(209\) −13.3284 −0.921942
\(210\) 13.7222 0.946922
\(211\) −2.67508 −0.184160 −0.0920802 0.995752i \(-0.529352\pi\)
−0.0920802 + 0.995752i \(0.529352\pi\)
\(212\) 1.53961 0.105741
\(213\) 39.4571 2.70356
\(214\) −5.22241 −0.356996
\(215\) −1.04203 −0.0710659
\(216\) 8.68205 0.590739
\(217\) −9.11169 −0.618542
\(218\) 7.46020 0.505268
\(219\) −4.08146 −0.275799
\(220\) −7.83345 −0.528131
\(221\) −12.1586 −0.817876
\(222\) 14.8767 0.998459
\(223\) −18.3835 −1.23105 −0.615527 0.788116i \(-0.711057\pi\)
−0.615527 + 0.788116i \(0.711057\pi\)
\(224\) −2.90984 −0.194422
\(225\) −14.7941 −0.986274
\(226\) −12.0064 −0.798652
\(227\) −23.7503 −1.57636 −0.788182 0.615442i \(-0.788978\pi\)
−0.788182 + 0.615442i \(0.788978\pi\)
\(228\) −8.02376 −0.531386
\(229\) −1.46778 −0.0969936 −0.0484968 0.998823i \(-0.515443\pi\)
−0.0484968 + 0.998823i \(0.515443\pi\)
\(230\) −1.57995 −0.104179
\(231\) 43.0614 2.83323
\(232\) −5.30982 −0.348607
\(233\) 0.0638321 0.00418178 0.00209089 0.999998i \(-0.499334\pi\)
0.00209089 + 0.999998i \(0.499334\pi\)
\(234\) 24.5968 1.60795
\(235\) −10.2137 −0.666267
\(236\) −3.36081 −0.218770
\(237\) 3.27862 0.212969
\(238\) −8.49910 −0.550915
\(239\) 6.88773 0.445530 0.222765 0.974872i \(-0.428492\pi\)
0.222765 + 0.974872i \(0.428492\pi\)
\(240\) −4.71578 −0.304403
\(241\) −6.04018 −0.389082 −0.194541 0.980894i \(-0.562322\pi\)
−0.194541 + 0.980894i \(0.562322\pi\)
\(242\) −13.5820 −0.873083
\(243\) 1.60854 0.103188
\(244\) −8.26073 −0.528839
\(245\) 2.31810 0.148098
\(246\) 18.0484 1.15073
\(247\) −11.1905 −0.712034
\(248\) 3.13133 0.198840
\(249\) 15.8768 1.00615
\(250\) 11.8556 0.749812
\(251\) −13.1367 −0.829180 −0.414590 0.910008i \(-0.636075\pi\)
−0.414590 + 0.910008i \(0.636075\pi\)
\(252\) 17.1937 1.08310
\(253\) −4.95802 −0.311708
\(254\) −10.4798 −0.657560
\(255\) −13.7739 −0.862555
\(256\) 1.00000 0.0625000
\(257\) 13.6320 0.850338 0.425169 0.905114i \(-0.360215\pi\)
0.425169 + 0.905114i \(0.360215\pi\)
\(258\) −1.96855 −0.122556
\(259\) 14.5033 0.901192
\(260\) −6.57696 −0.407886
\(261\) 31.3746 1.94204
\(262\) −1.00000 −0.0617802
\(263\) 25.0039 1.54181 0.770903 0.636953i \(-0.219805\pi\)
0.770903 + 0.636953i \(0.219805\pi\)
\(264\) −14.7985 −0.910785
\(265\) 2.43251 0.149428
\(266\) −7.82237 −0.479620
\(267\) −29.1576 −1.78441
\(268\) −4.81120 −0.293891
\(269\) 23.5338 1.43488 0.717440 0.696621i \(-0.245314\pi\)
0.717440 + 0.696621i \(0.245314\pi\)
\(270\) 13.7172 0.834805
\(271\) −3.11828 −0.189422 −0.0947110 0.995505i \(-0.530193\pi\)
−0.0947110 + 0.995505i \(0.530193\pi\)
\(272\) 2.92081 0.177100
\(273\) 36.1543 2.18816
\(274\) 9.48217 0.572839
\(275\) 12.4136 0.748570
\(276\) −2.98476 −0.179661
\(277\) −25.9233 −1.55758 −0.778792 0.627283i \(-0.784167\pi\)
−0.778792 + 0.627283i \(0.784167\pi\)
\(278\) −17.1336 −1.02760
\(279\) −18.5024 −1.10771
\(280\) −4.59742 −0.274748
\(281\) 23.3456 1.39268 0.696342 0.717710i \(-0.254810\pi\)
0.696342 + 0.717710i \(0.254810\pi\)
\(282\) −19.2951 −1.14901
\(283\) −8.89929 −0.529008 −0.264504 0.964385i \(-0.585208\pi\)
−0.264504 + 0.964385i \(0.585208\pi\)
\(284\) −13.2195 −0.784434
\(285\) −12.6772 −0.750931
\(286\) −20.6390 −1.22041
\(287\) 17.5954 1.03862
\(288\) −5.90879 −0.348179
\(289\) −8.46888 −0.498170
\(290\) −8.38927 −0.492635
\(291\) −0.503632 −0.0295234
\(292\) 1.36743 0.0800229
\(293\) −16.9497 −0.990210 −0.495105 0.868833i \(-0.664870\pi\)
−0.495105 + 0.868833i \(0.664870\pi\)
\(294\) 4.37923 0.255402
\(295\) −5.30992 −0.309156
\(296\) −4.98422 −0.289702
\(297\) 43.0458 2.49777
\(298\) −16.0611 −0.930397
\(299\) −4.16275 −0.240738
\(300\) 7.47308 0.431458
\(301\) −1.91914 −0.110617
\(302\) 5.62376 0.323611
\(303\) 23.6958 1.36129
\(304\) 2.68824 0.154181
\(305\) −13.0516 −0.747331
\(306\) −17.2585 −0.986600
\(307\) −1.38029 −0.0787775 −0.0393888 0.999224i \(-0.512541\pi\)
−0.0393888 + 0.999224i \(0.512541\pi\)
\(308\) −14.4271 −0.822059
\(309\) −35.2102 −2.00304
\(310\) 4.94736 0.280991
\(311\) 0.482578 0.0273645 0.0136822 0.999906i \(-0.495645\pi\)
0.0136822 + 0.999906i \(0.495645\pi\)
\(312\) −12.4248 −0.703417
\(313\) 8.07664 0.456519 0.228259 0.973600i \(-0.426697\pi\)
0.228259 + 0.973600i \(0.426697\pi\)
\(314\) −2.63971 −0.148967
\(315\) 27.1652 1.53059
\(316\) −1.09845 −0.0617929
\(317\) 4.82347 0.270913 0.135457 0.990783i \(-0.456750\pi\)
0.135457 + 0.990783i \(0.456750\pi\)
\(318\) 4.59536 0.257695
\(319\) −26.3262 −1.47399
\(320\) 1.57995 0.0883221
\(321\) −15.5876 −0.870017
\(322\) −2.90984 −0.162159
\(323\) 7.85184 0.436888
\(324\) 8.18746 0.454859
\(325\) 10.4225 0.578135
\(326\) 12.1135 0.670905
\(327\) 22.2669 1.23136
\(328\) −6.04686 −0.333882
\(329\) −18.8108 −1.03707
\(330\) −23.3810 −1.28708
\(331\) 3.07731 0.169144 0.0845721 0.996417i \(-0.473048\pi\)
0.0845721 + 0.996417i \(0.473048\pi\)
\(332\) −5.31930 −0.291934
\(333\) 29.4507 1.61389
\(334\) −7.22648 −0.395415
\(335\) −7.60147 −0.415313
\(336\) −8.68519 −0.473816
\(337\) 34.3457 1.87093 0.935466 0.353416i \(-0.114980\pi\)
0.935466 + 0.353416i \(0.114980\pi\)
\(338\) −4.32851 −0.235440
\(339\) −35.8361 −1.94635
\(340\) 4.61474 0.250270
\(341\) 15.5252 0.840737
\(342\) −15.8843 −0.858923
\(343\) −16.0996 −0.869297
\(344\) 0.659532 0.0355596
\(345\) −4.71578 −0.253889
\(346\) −10.6149 −0.570660
\(347\) −0.367674 −0.0197378 −0.00986888 0.999951i \(-0.503141\pi\)
−0.00986888 + 0.999951i \(0.503141\pi\)
\(348\) −15.8485 −0.849571
\(349\) −0.894177 −0.0478642 −0.0239321 0.999714i \(-0.507619\pi\)
−0.0239321 + 0.999714i \(0.507619\pi\)
\(350\) 7.28551 0.389427
\(351\) 36.1412 1.92908
\(352\) 4.95802 0.264263
\(353\) 8.63781 0.459744 0.229872 0.973221i \(-0.426169\pi\)
0.229872 + 0.973221i \(0.426169\pi\)
\(354\) −10.0312 −0.533153
\(355\) −20.8862 −1.10853
\(356\) 9.76882 0.517746
\(357\) −25.3678 −1.34260
\(358\) 9.66447 0.510783
\(359\) −19.1586 −1.01115 −0.505577 0.862781i \(-0.668720\pi\)
−0.505577 + 0.862781i \(0.668720\pi\)
\(360\) −9.33562 −0.492031
\(361\) −11.7734 −0.619650
\(362\) 15.4462 0.811833
\(363\) −40.5390 −2.12774
\(364\) −12.1130 −0.634892
\(365\) 2.16048 0.113085
\(366\) −24.6563 −1.28881
\(367\) 17.2141 0.898569 0.449284 0.893389i \(-0.351679\pi\)
0.449284 + 0.893389i \(0.351679\pi\)
\(368\) 1.00000 0.0521286
\(369\) 35.7296 1.86001
\(370\) −7.87484 −0.409393
\(371\) 4.48002 0.232591
\(372\) 9.34627 0.484582
\(373\) 0.494841 0.0256219 0.0128110 0.999918i \(-0.495922\pi\)
0.0128110 + 0.999918i \(0.495922\pi\)
\(374\) 14.4814 0.748817
\(375\) 35.3860 1.82733
\(376\) 6.46454 0.333383
\(377\) −22.1035 −1.13839
\(378\) 25.2634 1.29941
\(379\) −11.2343 −0.577067 −0.288533 0.957470i \(-0.593168\pi\)
−0.288533 + 0.957470i \(0.593168\pi\)
\(380\) 4.24730 0.217882
\(381\) −31.2796 −1.60250
\(382\) −0.917679 −0.0469525
\(383\) 12.7838 0.653219 0.326610 0.945159i \(-0.394094\pi\)
0.326610 + 0.945159i \(0.394094\pi\)
\(384\) 2.98476 0.152315
\(385\) −22.7941 −1.16170
\(386\) 22.1129 1.12551
\(387\) −3.89704 −0.198098
\(388\) 0.168734 0.00856620
\(389\) −25.2337 −1.27940 −0.639699 0.768626i \(-0.720941\pi\)
−0.639699 + 0.768626i \(0.720941\pi\)
\(390\) −19.6306 −0.994036
\(391\) 2.92081 0.147712
\(392\) −1.46720 −0.0741046
\(393\) −2.98476 −0.150561
\(394\) −4.11730 −0.207427
\(395\) −1.73551 −0.0873228
\(396\) −29.2959 −1.47218
\(397\) −2.61143 −0.131064 −0.0655318 0.997850i \(-0.520874\pi\)
−0.0655318 + 0.997850i \(0.520874\pi\)
\(398\) 8.82532 0.442373
\(399\) −23.3479 −1.16886
\(400\) −2.50375 −0.125187
\(401\) 6.70995 0.335079 0.167539 0.985865i \(-0.446418\pi\)
0.167539 + 0.985865i \(0.446418\pi\)
\(402\) −14.3603 −0.716226
\(403\) 13.0350 0.649318
\(404\) −7.93894 −0.394977
\(405\) 12.9358 0.642786
\(406\) −15.4508 −0.766808
\(407\) −24.7119 −1.22492
\(408\) 8.71791 0.431601
\(409\) −14.4763 −0.715805 −0.357903 0.933759i \(-0.616508\pi\)
−0.357903 + 0.933759i \(0.616508\pi\)
\(410\) −9.55376 −0.471827
\(411\) 28.3020 1.39603
\(412\) 11.7967 0.581180
\(413\) −9.77943 −0.481214
\(414\) −5.90879 −0.290401
\(415\) −8.40424 −0.412548
\(416\) 4.16275 0.204096
\(417\) −51.1396 −2.50432
\(418\) 13.3284 0.651912
\(419\) −25.0401 −1.22329 −0.611646 0.791132i \(-0.709492\pi\)
−0.611646 + 0.791132i \(0.709492\pi\)
\(420\) −13.7222 −0.669575
\(421\) −33.5078 −1.63307 −0.816536 0.577294i \(-0.804109\pi\)
−0.816536 + 0.577294i \(0.804109\pi\)
\(422\) 2.67508 0.130221
\(423\) −38.1976 −1.85723
\(424\) −1.53961 −0.0747699
\(425\) −7.31296 −0.354731
\(426\) −39.4571 −1.91170
\(427\) −24.0374 −1.16325
\(428\) 5.22241 0.252435
\(429\) −61.6025 −2.97420
\(430\) 1.04203 0.0502512
\(431\) −12.3898 −0.596796 −0.298398 0.954442i \(-0.596452\pi\)
−0.298398 + 0.954442i \(0.596452\pi\)
\(432\) −8.68205 −0.417715
\(433\) 20.4285 0.981733 0.490867 0.871235i \(-0.336680\pi\)
0.490867 + 0.871235i \(0.336680\pi\)
\(434\) 9.11169 0.437375
\(435\) −25.0400 −1.20057
\(436\) −7.46020 −0.357279
\(437\) 2.68824 0.128596
\(438\) 4.08146 0.195020
\(439\) 9.67055 0.461550 0.230775 0.973007i \(-0.425874\pi\)
0.230775 + 0.973007i \(0.425874\pi\)
\(440\) 7.83345 0.373445
\(441\) 8.66936 0.412826
\(442\) 12.1586 0.578326
\(443\) 26.6064 1.26411 0.632053 0.774925i \(-0.282212\pi\)
0.632053 + 0.774925i \(0.282212\pi\)
\(444\) −14.8767 −0.706017
\(445\) 15.4343 0.731655
\(446\) 18.3835 0.870486
\(447\) −47.9387 −2.26742
\(448\) 2.90984 0.137477
\(449\) −10.3336 −0.487674 −0.243837 0.969816i \(-0.578406\pi\)
−0.243837 + 0.969816i \(0.578406\pi\)
\(450\) 14.7941 0.697401
\(451\) −29.9805 −1.41173
\(452\) 12.0064 0.564732
\(453\) 16.7856 0.788655
\(454\) 23.7503 1.11466
\(455\) −19.1379 −0.897200
\(456\) 8.02376 0.375747
\(457\) 1.45972 0.0682827 0.0341414 0.999417i \(-0.489130\pi\)
0.0341414 + 0.999417i \(0.489130\pi\)
\(458\) 1.46778 0.0685848
\(459\) −25.3586 −1.18364
\(460\) 1.57995 0.0736657
\(461\) −5.60953 −0.261262 −0.130631 0.991431i \(-0.541700\pi\)
−0.130631 + 0.991431i \(0.541700\pi\)
\(462\) −43.0614 −2.00340
\(463\) 0.661601 0.0307472 0.0153736 0.999882i \(-0.495106\pi\)
0.0153736 + 0.999882i \(0.495106\pi\)
\(464\) 5.30982 0.246502
\(465\) 14.7667 0.684789
\(466\) −0.0638321 −0.00295697
\(467\) −20.9449 −0.969214 −0.484607 0.874732i \(-0.661037\pi\)
−0.484607 + 0.874732i \(0.661037\pi\)
\(468\) −24.5968 −1.13699
\(469\) −13.9998 −0.646453
\(470\) 10.2137 0.471122
\(471\) −7.87890 −0.363040
\(472\) 3.36081 0.154694
\(473\) 3.26998 0.150354
\(474\) −3.27862 −0.150592
\(475\) −6.73067 −0.308824
\(476\) 8.49910 0.389555
\(477\) 9.09722 0.416533
\(478\) −6.88773 −0.315037
\(479\) −25.4412 −1.16244 −0.581219 0.813747i \(-0.697424\pi\)
−0.581219 + 0.813747i \(0.697424\pi\)
\(480\) 4.71578 0.215245
\(481\) −20.7481 −0.946031
\(482\) 6.04018 0.275123
\(483\) −8.68519 −0.395190
\(484\) 13.5820 0.617363
\(485\) 0.266593 0.0121054
\(486\) −1.60854 −0.0729649
\(487\) −33.4736 −1.51683 −0.758417 0.651770i \(-0.774027\pi\)
−0.758417 + 0.651770i \(0.774027\pi\)
\(488\) 8.26073 0.373946
\(489\) 36.1559 1.63503
\(490\) −2.31810 −0.104721
\(491\) −9.23297 −0.416678 −0.208339 0.978057i \(-0.566806\pi\)
−0.208339 + 0.978057i \(0.566806\pi\)
\(492\) −18.0484 −0.813686
\(493\) 15.5090 0.698489
\(494\) 11.1905 0.503484
\(495\) −46.2862 −2.08041
\(496\) −3.13133 −0.140601
\(497\) −38.4668 −1.72547
\(498\) −15.8768 −0.711457
\(499\) −31.5925 −1.41427 −0.707136 0.707077i \(-0.750013\pi\)
−0.707136 + 0.707077i \(0.750013\pi\)
\(500\) −11.8556 −0.530197
\(501\) −21.5693 −0.963645
\(502\) 13.1367 0.586319
\(503\) 16.3391 0.728523 0.364261 0.931297i \(-0.381321\pi\)
0.364261 + 0.931297i \(0.381321\pi\)
\(504\) −17.1937 −0.765867
\(505\) −12.5432 −0.558163
\(506\) 4.95802 0.220411
\(507\) −12.9196 −0.573778
\(508\) 10.4798 0.464965
\(509\) 19.6485 0.870903 0.435452 0.900212i \(-0.356589\pi\)
0.435452 + 0.900212i \(0.356589\pi\)
\(510\) 13.7739 0.609918
\(511\) 3.97901 0.176021
\(512\) −1.00000 −0.0441942
\(513\) −23.3395 −1.03046
\(514\) −13.6320 −0.601280
\(515\) 18.6382 0.821297
\(516\) 1.96855 0.0866604
\(517\) 32.0513 1.40962
\(518\) −14.5033 −0.637239
\(519\) −31.6829 −1.39072
\(520\) 6.57696 0.288419
\(521\) −7.98997 −0.350047 −0.175024 0.984564i \(-0.556000\pi\)
−0.175024 + 0.984564i \(0.556000\pi\)
\(522\) −31.3746 −1.37323
\(523\) −42.3639 −1.85245 −0.926223 0.376976i \(-0.876964\pi\)
−0.926223 + 0.376976i \(0.876964\pi\)
\(524\) 1.00000 0.0436852
\(525\) 21.7455 0.949051
\(526\) −25.0039 −1.09022
\(527\) −9.14602 −0.398407
\(528\) 14.7985 0.644022
\(529\) 1.00000 0.0434783
\(530\) −2.43251 −0.105661
\(531\) −19.8583 −0.861778
\(532\) 7.82237 0.339143
\(533\) −25.1716 −1.09030
\(534\) 29.1576 1.26177
\(535\) 8.25116 0.356729
\(536\) 4.81120 0.207812
\(537\) 28.8461 1.24480
\(538\) −23.5338 −1.01461
\(539\) −7.27439 −0.313330
\(540\) −13.7172 −0.590296
\(541\) −31.3746 −1.34890 −0.674449 0.738321i \(-0.735619\pi\)
−0.674449 + 0.738321i \(0.735619\pi\)
\(542\) 3.11828 0.133942
\(543\) 46.1032 1.97848
\(544\) −2.92081 −0.125229
\(545\) −11.7868 −0.504890
\(546\) −36.1543 −1.54726
\(547\) −33.5092 −1.43275 −0.716375 0.697716i \(-0.754200\pi\)
−0.716375 + 0.697716i \(0.754200\pi\)
\(548\) −9.48217 −0.405058
\(549\) −48.8110 −2.08320
\(550\) −12.4136 −0.529319
\(551\) 14.2741 0.608096
\(552\) 2.98476 0.127040
\(553\) −3.19633 −0.135922
\(554\) 25.9233 1.10138
\(555\) −23.5045 −0.997711
\(556\) 17.1336 0.726625
\(557\) 37.1042 1.57216 0.786078 0.618127i \(-0.212108\pi\)
0.786078 + 0.618127i \(0.212108\pi\)
\(558\) 18.5024 0.783269
\(559\) 2.74547 0.116121
\(560\) 4.59742 0.194276
\(561\) 43.2236 1.82490
\(562\) −23.3456 −0.984776
\(563\) −18.6130 −0.784443 −0.392222 0.919871i \(-0.628293\pi\)
−0.392222 + 0.919871i \(0.628293\pi\)
\(564\) 19.2951 0.812470
\(565\) 18.9695 0.798053
\(566\) 8.89929 0.374065
\(567\) 23.8242 1.00052
\(568\) 13.2195 0.554679
\(569\) 6.11142 0.256204 0.128102 0.991761i \(-0.459112\pi\)
0.128102 + 0.991761i \(0.459112\pi\)
\(570\) 12.6772 0.530988
\(571\) 33.1298 1.38644 0.693219 0.720727i \(-0.256192\pi\)
0.693219 + 0.720727i \(0.256192\pi\)
\(572\) 20.6390 0.862961
\(573\) −2.73905 −0.114426
\(574\) −17.5954 −0.734419
\(575\) −2.50375 −0.104413
\(576\) 5.90879 0.246200
\(577\) 12.5125 0.520902 0.260451 0.965487i \(-0.416129\pi\)
0.260451 + 0.965487i \(0.416129\pi\)
\(578\) 8.46888 0.352259
\(579\) 66.0016 2.74293
\(580\) 8.38927 0.348346
\(581\) −15.4783 −0.642149
\(582\) 0.503632 0.0208762
\(583\) −7.63340 −0.316143
\(584\) −1.36743 −0.0565847
\(585\) −38.8619 −1.60674
\(586\) 16.9497 0.700184
\(587\) −8.60823 −0.355299 −0.177650 0.984094i \(-0.556849\pi\)
−0.177650 + 0.984094i \(0.556849\pi\)
\(588\) −4.37923 −0.180596
\(589\) −8.41778 −0.346848
\(590\) 5.30992 0.218606
\(591\) −12.2891 −0.505508
\(592\) 4.98422 0.204850
\(593\) −32.8502 −1.34900 −0.674498 0.738277i \(-0.735640\pi\)
−0.674498 + 0.738277i \(0.735640\pi\)
\(594\) −43.0458 −1.76619
\(595\) 13.4282 0.550502
\(596\) 16.0611 0.657890
\(597\) 26.3415 1.07808
\(598\) 4.16275 0.170228
\(599\) −32.4045 −1.32401 −0.662006 0.749498i \(-0.730295\pi\)
−0.662006 + 0.749498i \(0.730295\pi\)
\(600\) −7.47308 −0.305087
\(601\) 26.5066 1.08123 0.540614 0.841271i \(-0.318192\pi\)
0.540614 + 0.841271i \(0.318192\pi\)
\(602\) 1.91914 0.0782181
\(603\) −28.4284 −1.15769
\(604\) −5.62376 −0.228828
\(605\) 21.4589 0.872429
\(606\) −23.6958 −0.962578
\(607\) 1.31780 0.0534877 0.0267439 0.999642i \(-0.491486\pi\)
0.0267439 + 0.999642i \(0.491486\pi\)
\(608\) −2.68824 −0.109023
\(609\) −46.1168 −1.86875
\(610\) 13.0516 0.528443
\(611\) 26.9103 1.08867
\(612\) 17.2585 0.697631
\(613\) 27.4062 1.10693 0.553463 0.832874i \(-0.313306\pi\)
0.553463 + 0.832874i \(0.313306\pi\)
\(614\) 1.38029 0.0557041
\(615\) −28.5157 −1.14986
\(616\) 14.4271 0.581283
\(617\) −0.0454317 −0.00182901 −0.000914505 1.00000i \(-0.500291\pi\)
−0.000914505 1.00000i \(0.500291\pi\)
\(618\) 35.2102 1.41636
\(619\) −39.0324 −1.56884 −0.784422 0.620228i \(-0.787040\pi\)
−0.784422 + 0.620228i \(0.787040\pi\)
\(620\) −4.94736 −0.198691
\(621\) −8.68205 −0.348399
\(622\) −0.482578 −0.0193496
\(623\) 28.4257 1.13885
\(624\) 12.4248 0.497391
\(625\) −6.21254 −0.248501
\(626\) −8.07664 −0.322807
\(627\) 39.7820 1.58874
\(628\) 2.63971 0.105336
\(629\) 14.5580 0.580464
\(630\) −27.1652 −1.08229
\(631\) −16.7170 −0.665493 −0.332746 0.943016i \(-0.607975\pi\)
−0.332746 + 0.943016i \(0.607975\pi\)
\(632\) 1.09845 0.0436941
\(633\) 7.98449 0.317355
\(634\) −4.82347 −0.191565
\(635\) 16.5576 0.657067
\(636\) −4.59536 −0.182218
\(637\) −6.10757 −0.241991
\(638\) 26.3262 1.04226
\(639\) −78.1114 −3.09004
\(640\) −1.57995 −0.0624532
\(641\) 16.8115 0.664012 0.332006 0.943277i \(-0.392275\pi\)
0.332006 + 0.943277i \(0.392275\pi\)
\(642\) 15.5876 0.615195
\(643\) −32.8091 −1.29386 −0.646932 0.762548i \(-0.723948\pi\)
−0.646932 + 0.762548i \(0.723948\pi\)
\(644\) 2.90984 0.114664
\(645\) 3.11021 0.122464
\(646\) −7.85184 −0.308926
\(647\) −5.86103 −0.230421 −0.115210 0.993341i \(-0.536754\pi\)
−0.115210 + 0.993341i \(0.536754\pi\)
\(648\) −8.18746 −0.321634
\(649\) 16.6630 0.654079
\(650\) −10.4225 −0.408803
\(651\) 27.1962 1.06590
\(652\) −12.1135 −0.474402
\(653\) 27.0456 1.05838 0.529188 0.848505i \(-0.322497\pi\)
0.529188 + 0.848505i \(0.322497\pi\)
\(654\) −22.2669 −0.870705
\(655\) 1.57995 0.0617339
\(656\) 6.04686 0.236090
\(657\) 8.07987 0.315226
\(658\) 18.8108 0.733322
\(659\) −1.48147 −0.0577099 −0.0288550 0.999584i \(-0.509186\pi\)
−0.0288550 + 0.999584i \(0.509186\pi\)
\(660\) 23.3810 0.910103
\(661\) −32.4112 −1.26065 −0.630324 0.776332i \(-0.717078\pi\)
−0.630324 + 0.776332i \(0.717078\pi\)
\(662\) −3.07731 −0.119603
\(663\) 36.2905 1.40941
\(664\) 5.31930 0.206429
\(665\) 12.3590 0.479261
\(666\) −29.4507 −1.14119
\(667\) 5.30982 0.205597
\(668\) 7.22648 0.279601
\(669\) 54.8705 2.12142
\(670\) 7.60147 0.293671
\(671\) 40.9569 1.58112
\(672\) 8.68519 0.335038
\(673\) 44.5513 1.71733 0.858664 0.512540i \(-0.171295\pi\)
0.858664 + 0.512540i \(0.171295\pi\)
\(674\) −34.3457 −1.32295
\(675\) 21.7376 0.836682
\(676\) 4.32851 0.166481
\(677\) −32.8608 −1.26294 −0.631471 0.775400i \(-0.717549\pi\)
−0.631471 + 0.775400i \(0.717549\pi\)
\(678\) 35.8361 1.37628
\(679\) 0.490991 0.0188425
\(680\) −4.61474 −0.176967
\(681\) 70.8891 2.71647
\(682\) −15.5252 −0.594491
\(683\) −34.5906 −1.32357 −0.661787 0.749692i \(-0.730202\pi\)
−0.661787 + 0.749692i \(0.730202\pi\)
\(684\) 15.8843 0.607350
\(685\) −14.9814 −0.572410
\(686\) 16.0996 0.614686
\(687\) 4.38097 0.167144
\(688\) −0.659532 −0.0251444
\(689\) −6.40900 −0.244163
\(690\) 4.71578 0.179527
\(691\) −46.8383 −1.78181 −0.890906 0.454187i \(-0.849930\pi\)
−0.890906 + 0.454187i \(0.849930\pi\)
\(692\) 10.6149 0.403517
\(693\) −85.2466 −3.23825
\(694\) 0.367674 0.0139567
\(695\) 27.0703 1.02683
\(696\) 15.8485 0.600738
\(697\) 17.6617 0.668985
\(698\) 0.894177 0.0338451
\(699\) −0.190524 −0.00720626
\(700\) −7.28551 −0.275366
\(701\) −33.9576 −1.28256 −0.641281 0.767306i \(-0.721597\pi\)
−0.641281 + 0.767306i \(0.721597\pi\)
\(702\) −36.1412 −1.36406
\(703\) 13.3988 0.505345
\(704\) −4.95802 −0.186863
\(705\) 30.4854 1.14815
\(706\) −8.63781 −0.325088
\(707\) −23.1011 −0.868806
\(708\) 10.0312 0.376996
\(709\) −13.9892 −0.525374 −0.262687 0.964881i \(-0.584609\pi\)
−0.262687 + 0.964881i \(0.584609\pi\)
\(710\) 20.8862 0.783847
\(711\) −6.49054 −0.243414
\(712\) −9.76882 −0.366102
\(713\) −3.13133 −0.117269
\(714\) 25.3678 0.949365
\(715\) 32.6087 1.21950
\(716\) −9.66447 −0.361178
\(717\) −20.5582 −0.767761
\(718\) 19.1586 0.714994
\(719\) 7.46332 0.278335 0.139167 0.990269i \(-0.455557\pi\)
0.139167 + 0.990269i \(0.455557\pi\)
\(720\) 9.33562 0.347918
\(721\) 34.3265 1.27838
\(722\) 11.7734 0.438159
\(723\) 18.0285 0.670487
\(724\) −15.4462 −0.574053
\(725\) −13.2944 −0.493743
\(726\) 40.5390 1.50454
\(727\) 17.2487 0.639720 0.319860 0.947465i \(-0.396364\pi\)
0.319860 + 0.947465i \(0.396364\pi\)
\(728\) 12.1130 0.448936
\(729\) −29.3635 −1.08754
\(730\) −2.16048 −0.0799629
\(731\) −1.92637 −0.0712492
\(732\) 24.6563 0.911323
\(733\) 36.3583 1.34293 0.671463 0.741038i \(-0.265666\pi\)
0.671463 + 0.741038i \(0.265666\pi\)
\(734\) −17.2141 −0.635384
\(735\) −6.91898 −0.255210
\(736\) −1.00000 −0.0368605
\(737\) 23.8540 0.878675
\(738\) −35.7296 −1.31523
\(739\) −29.9814 −1.10288 −0.551442 0.834213i \(-0.685922\pi\)
−0.551442 + 0.834213i \(0.685922\pi\)
\(740\) 7.87484 0.289485
\(741\) 33.4009 1.22701
\(742\) −4.48002 −0.164467
\(743\) −33.9101 −1.24404 −0.622020 0.783001i \(-0.713688\pi\)
−0.622020 + 0.783001i \(0.713688\pi\)
\(744\) −9.34627 −0.342651
\(745\) 25.3759 0.929700
\(746\) −0.494841 −0.0181174
\(747\) −31.4306 −1.14999
\(748\) −14.4814 −0.529494
\(749\) 15.1964 0.555264
\(750\) −35.3860 −1.29212
\(751\) 35.0857 1.28029 0.640147 0.768252i \(-0.278873\pi\)
0.640147 + 0.768252i \(0.278873\pi\)
\(752\) −6.46454 −0.235738
\(753\) 39.2098 1.42889
\(754\) 22.1035 0.804961
\(755\) −8.88528 −0.323369
\(756\) −25.2634 −0.918822
\(757\) −23.0994 −0.839561 −0.419781 0.907626i \(-0.637893\pi\)
−0.419781 + 0.907626i \(0.637893\pi\)
\(758\) 11.2343 0.408048
\(759\) 14.7985 0.537152
\(760\) −4.24730 −0.154066
\(761\) −29.9840 −1.08692 −0.543459 0.839436i \(-0.682886\pi\)
−0.543459 + 0.839436i \(0.682886\pi\)
\(762\) 31.2796 1.13314
\(763\) −21.7080 −0.785883
\(764\) 0.917679 0.0332005
\(765\) 27.2676 0.985861
\(766\) −12.7838 −0.461896
\(767\) 13.9902 0.505157
\(768\) −2.98476 −0.107703
\(769\) −30.0495 −1.08361 −0.541806 0.840503i \(-0.682259\pi\)
−0.541806 + 0.840503i \(0.682259\pi\)
\(770\) 22.7941 0.821443
\(771\) −40.6881 −1.46535
\(772\) −22.1129 −0.795859
\(773\) 37.4894 1.34840 0.674200 0.738549i \(-0.264489\pi\)
0.674200 + 0.738549i \(0.264489\pi\)
\(774\) 3.89704 0.140076
\(775\) 7.84006 0.281623
\(776\) −0.168734 −0.00605722
\(777\) −43.2889 −1.55298
\(778\) 25.2337 0.904671
\(779\) 16.2554 0.582411
\(780\) 19.6306 0.702890
\(781\) 65.5427 2.34530
\(782\) −2.92081 −0.104448
\(783\) −46.1002 −1.64749
\(784\) 1.46720 0.0523998
\(785\) 4.17062 0.148856
\(786\) 2.98476 0.106463
\(787\) 11.2174 0.399857 0.199929 0.979810i \(-0.435929\pi\)
0.199929 + 0.979810i \(0.435929\pi\)
\(788\) 4.11730 0.146673
\(789\) −74.6306 −2.65692
\(790\) 1.73551 0.0617466
\(791\) 34.9367 1.24220
\(792\) 29.2959 1.04099
\(793\) 34.3874 1.22113
\(794\) 2.61143 0.0926760
\(795\) −7.26045 −0.257502
\(796\) −8.82532 −0.312805
\(797\) −15.1338 −0.536068 −0.268034 0.963409i \(-0.586374\pi\)
−0.268034 + 0.963409i \(0.586374\pi\)
\(798\) 23.3479 0.826506
\(799\) −18.8817 −0.667986
\(800\) 2.50375 0.0885208
\(801\) 57.7219 2.03950
\(802\) −6.70995 −0.236936
\(803\) −6.77976 −0.239252
\(804\) 14.3603 0.506448
\(805\) 4.59742 0.162038
\(806\) −13.0350 −0.459137
\(807\) −70.2427 −2.47266
\(808\) 7.93894 0.279291
\(809\) −10.9435 −0.384752 −0.192376 0.981321i \(-0.561619\pi\)
−0.192376 + 0.981321i \(0.561619\pi\)
\(810\) −12.9358 −0.454518
\(811\) 0.376068 0.0132055 0.00660276 0.999978i \(-0.497898\pi\)
0.00660276 + 0.999978i \(0.497898\pi\)
\(812\) 15.4508 0.542215
\(813\) 9.30732 0.326422
\(814\) 24.7119 0.866151
\(815\) −19.1388 −0.670402
\(816\) −8.71791 −0.305188
\(817\) −1.77298 −0.0620288
\(818\) 14.4763 0.506151
\(819\) −71.5730 −2.50096
\(820\) 9.55376 0.333632
\(821\) 28.4953 0.994493 0.497246 0.867609i \(-0.334345\pi\)
0.497246 + 0.867609i \(0.334345\pi\)
\(822\) −28.3020 −0.987146
\(823\) −2.03754 −0.0710241 −0.0355121 0.999369i \(-0.511306\pi\)
−0.0355121 + 0.999369i \(0.511306\pi\)
\(824\) −11.7967 −0.410956
\(825\) −37.0517 −1.28997
\(826\) 9.77943 0.340270
\(827\) −25.1963 −0.876161 −0.438080 0.898936i \(-0.644342\pi\)
−0.438080 + 0.898936i \(0.644342\pi\)
\(828\) 5.90879 0.205345
\(829\) −12.0311 −0.417858 −0.208929 0.977931i \(-0.566998\pi\)
−0.208929 + 0.977931i \(0.566998\pi\)
\(830\) 8.40424 0.291716
\(831\) 77.3750 2.68411
\(832\) −4.16275 −0.144317
\(833\) 4.28540 0.148480
\(834\) 51.1396 1.77082
\(835\) 11.4175 0.395119
\(836\) −13.3284 −0.460971
\(837\) 27.1864 0.939699
\(838\) 25.0401 0.864998
\(839\) 6.72287 0.232099 0.116050 0.993243i \(-0.462977\pi\)
0.116050 + 0.993243i \(0.462977\pi\)
\(840\) 13.7222 0.473461
\(841\) −0.805792 −0.0277859
\(842\) 33.5078 1.15476
\(843\) −69.6811 −2.39995
\(844\) −2.67508 −0.0920802
\(845\) 6.83884 0.235263
\(846\) 38.1976 1.31326
\(847\) 39.5215 1.35797
\(848\) 1.53961 0.0528703
\(849\) 26.5622 0.911613
\(850\) 7.31296 0.250832
\(851\) 4.98422 0.170857
\(852\) 39.4571 1.35178
\(853\) 23.7875 0.814467 0.407234 0.913324i \(-0.366493\pi\)
0.407234 + 0.913324i \(0.366493\pi\)
\(854\) 24.0374 0.822544
\(855\) 25.0964 0.858279
\(856\) −5.22241 −0.178498
\(857\) 39.1973 1.33895 0.669477 0.742833i \(-0.266518\pi\)
0.669477 + 0.742833i \(0.266518\pi\)
\(858\) 61.6025 2.10308
\(859\) −42.1297 −1.43745 −0.718723 0.695296i \(-0.755273\pi\)
−0.718723 + 0.695296i \(0.755273\pi\)
\(860\) −1.04203 −0.0355329
\(861\) −52.5181 −1.78981
\(862\) 12.3898 0.421999
\(863\) 41.9476 1.42791 0.713957 0.700189i \(-0.246901\pi\)
0.713957 + 0.700189i \(0.246901\pi\)
\(864\) 8.68205 0.295369
\(865\) 16.7710 0.570232
\(866\) −20.4285 −0.694190
\(867\) 25.2776 0.858472
\(868\) −9.11169 −0.309271
\(869\) 5.44616 0.184748
\(870\) 25.0400 0.848935
\(871\) 20.0278 0.678617
\(872\) 7.46020 0.252634
\(873\) 0.997017 0.0337439
\(874\) −2.68824 −0.0909311
\(875\) −34.4979 −1.16624
\(876\) −4.08146 −0.137900
\(877\) −3.78112 −0.127679 −0.0638397 0.997960i \(-0.520335\pi\)
−0.0638397 + 0.997960i \(0.520335\pi\)
\(878\) −9.67055 −0.326365
\(879\) 50.5907 1.70638
\(880\) −7.83345 −0.264065
\(881\) −9.42863 −0.317659 −0.158829 0.987306i \(-0.550772\pi\)
−0.158829 + 0.987306i \(0.550772\pi\)
\(882\) −8.66936 −0.291912
\(883\) −40.0826 −1.34889 −0.674443 0.738327i \(-0.735616\pi\)
−0.674443 + 0.738327i \(0.735616\pi\)
\(884\) −12.1586 −0.408938
\(885\) 15.8488 0.532753
\(886\) −26.6064 −0.893859
\(887\) 15.3085 0.514008 0.257004 0.966410i \(-0.417265\pi\)
0.257004 + 0.966410i \(0.417265\pi\)
\(888\) 14.8767 0.499230
\(889\) 30.4945 1.02275
\(890\) −15.4343 −0.517358
\(891\) −40.5936 −1.35994
\(892\) −18.3835 −0.615527
\(893\) −17.3782 −0.581541
\(894\) 47.9387 1.60331
\(895\) −15.2694 −0.510401
\(896\) −2.90984 −0.0972111
\(897\) 12.4248 0.414853
\(898\) 10.3336 0.344838
\(899\) −16.6268 −0.554535
\(900\) −14.7941 −0.493137
\(901\) 4.49689 0.149813
\(902\) 29.9805 0.998240
\(903\) 5.72816 0.190621
\(904\) −12.0064 −0.399326
\(905\) −24.4043 −0.811225
\(906\) −16.7856 −0.557663
\(907\) −27.7325 −0.920844 −0.460422 0.887700i \(-0.652302\pi\)
−0.460422 + 0.887700i \(0.652302\pi\)
\(908\) −23.7503 −0.788182
\(909\) −46.9096 −1.55589
\(910\) 19.1379 0.634416
\(911\) −28.5947 −0.947383 −0.473692 0.880691i \(-0.657079\pi\)
−0.473692 + 0.880691i \(0.657079\pi\)
\(912\) −8.02376 −0.265693
\(913\) 26.3732 0.872825
\(914\) −1.45972 −0.0482832
\(915\) 38.9558 1.28784
\(916\) −1.46778 −0.0484968
\(917\) 2.90984 0.0960915
\(918\) 25.3586 0.836959
\(919\) −4.07715 −0.134493 −0.0672464 0.997736i \(-0.521421\pi\)
−0.0672464 + 0.997736i \(0.521421\pi\)
\(920\) −1.57995 −0.0520895
\(921\) 4.11984 0.135754
\(922\) 5.60953 0.184740
\(923\) 55.0296 1.81132
\(924\) 43.0614 1.41661
\(925\) −12.4792 −0.410314
\(926\) −0.661601 −0.0217415
\(927\) 69.7041 2.28938
\(928\) −5.30982 −0.174303
\(929\) −36.9161 −1.21118 −0.605589 0.795778i \(-0.707062\pi\)
−0.605589 + 0.795778i \(0.707062\pi\)
\(930\) −14.7667 −0.484219
\(931\) 3.94418 0.129265
\(932\) 0.0638321 0.00209089
\(933\) −1.44038 −0.0471559
\(934\) 20.9449 0.685338
\(935\) −22.8800 −0.748256
\(936\) 24.5968 0.803973
\(937\) −19.7459 −0.645072 −0.322536 0.946557i \(-0.604535\pi\)
−0.322536 + 0.946557i \(0.604535\pi\)
\(938\) 13.9998 0.457111
\(939\) −24.1068 −0.786697
\(940\) −10.2137 −0.333133
\(941\) −18.8650 −0.614981 −0.307491 0.951551i \(-0.599489\pi\)
−0.307491 + 0.951551i \(0.599489\pi\)
\(942\) 7.87890 0.256708
\(943\) 6.04686 0.196913
\(944\) −3.36081 −0.109385
\(945\) −39.9151 −1.29844
\(946\) −3.26998 −0.106316
\(947\) −20.2305 −0.657404 −0.328702 0.944434i \(-0.606611\pi\)
−0.328702 + 0.944434i \(0.606611\pi\)
\(948\) 3.27862 0.106485
\(949\) −5.69228 −0.184779
\(950\) 6.73067 0.218372
\(951\) −14.3969 −0.466852
\(952\) −8.49910 −0.275457
\(953\) −48.5232 −1.57182 −0.785910 0.618341i \(-0.787805\pi\)
−0.785910 + 0.618341i \(0.787805\pi\)
\(954\) −9.09722 −0.294533
\(955\) 1.44989 0.0469174
\(956\) 6.88773 0.222765
\(957\) 78.5774 2.54005
\(958\) 25.4412 0.821968
\(959\) −27.5916 −0.890981
\(960\) −4.71578 −0.152201
\(961\) −21.1948 −0.683702
\(962\) 20.7481 0.668945
\(963\) 30.8581 0.994389
\(964\) −6.04018 −0.194541
\(965\) −34.9373 −1.12467
\(966\) 8.68519 0.279441
\(967\) −35.1041 −1.12887 −0.564436 0.825477i \(-0.690906\pi\)
−0.564436 + 0.825477i \(0.690906\pi\)
\(968\) −13.5820 −0.436542
\(969\) −23.4359 −0.752868
\(970\) −0.266593 −0.00855978
\(971\) −39.0796 −1.25412 −0.627062 0.778969i \(-0.715743\pi\)
−0.627062 + 0.778969i \(0.715743\pi\)
\(972\) 1.60854 0.0515940
\(973\) 49.8560 1.59831
\(974\) 33.4736 1.07256
\(975\) −31.1086 −0.996272
\(976\) −8.26073 −0.264420
\(977\) 18.3768 0.587925 0.293962 0.955817i \(-0.405026\pi\)
0.293962 + 0.955817i \(0.405026\pi\)
\(978\) −36.1559 −1.15614
\(979\) −48.4340 −1.54796
\(980\) 2.31810 0.0740490
\(981\) −44.0808 −1.40739
\(982\) 9.23297 0.294636
\(983\) 36.2338 1.15568 0.577840 0.816150i \(-0.303896\pi\)
0.577840 + 0.816150i \(0.303896\pi\)
\(984\) 18.0484 0.575363
\(985\) 6.50514 0.207271
\(986\) −15.5090 −0.493906
\(987\) 56.1458 1.78714
\(988\) −11.1905 −0.356017
\(989\) −0.659532 −0.0209719
\(990\) 46.2862 1.47107
\(991\) −11.2022 −0.355848 −0.177924 0.984044i \(-0.556938\pi\)
−0.177924 + 0.984044i \(0.556938\pi\)
\(992\) 3.13133 0.0994199
\(993\) −9.18503 −0.291478
\(994\) 38.4668 1.22009
\(995\) −13.9436 −0.442042
\(996\) 15.8768 0.503076
\(997\) −15.2277 −0.482265 −0.241133 0.970492i \(-0.577519\pi\)
−0.241133 + 0.970492i \(0.577519\pi\)
\(998\) 31.5925 1.00004
\(999\) −43.2733 −1.36911
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 \(a_p\))