Properties

Label 6026.2.a.i.1.20
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 1.20
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.76687 q^{3}\) \(+1.00000 q^{4}\) \(-0.379310 q^{5}\) \(-1.76687 q^{6}\) \(-0.00141487 q^{7}\) \(-1.00000 q^{8}\) \(+0.121841 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.76687 q^{3}\) \(+1.00000 q^{4}\) \(-0.379310 q^{5}\) \(-1.76687 q^{6}\) \(-0.00141487 q^{7}\) \(-1.00000 q^{8}\) \(+0.121841 q^{9}\) \(+0.379310 q^{10}\) \(-1.92533 q^{11}\) \(+1.76687 q^{12}\) \(-0.508617 q^{13}\) \(+0.00141487 q^{14}\) \(-0.670192 q^{15}\) \(+1.00000 q^{16}\) \(-3.60561 q^{17}\) \(-0.121841 q^{18}\) \(+5.47957 q^{19}\) \(-0.379310 q^{20}\) \(-0.00249990 q^{21}\) \(+1.92533 q^{22}\) \(+1.00000 q^{23}\) \(-1.76687 q^{24}\) \(-4.85612 q^{25}\) \(+0.508617 q^{26}\) \(-5.08534 q^{27}\) \(-0.00141487 q^{28}\) \(+1.18532 q^{29}\) \(+0.670192 q^{30}\) \(+7.55554 q^{31}\) \(-1.00000 q^{32}\) \(-3.40181 q^{33}\) \(+3.60561 q^{34}\) \(+0.000536675 q^{35}\) \(+0.121841 q^{36}\) \(-0.946095 q^{37}\) \(-5.47957 q^{38}\) \(-0.898661 q^{39}\) \(+0.379310 q^{40}\) \(+7.34729 q^{41}\) \(+0.00249990 q^{42}\) \(-2.24582 q^{43}\) \(-1.92533 q^{44}\) \(-0.0462156 q^{45}\) \(-1.00000 q^{46}\) \(+0.668739 q^{47}\) \(+1.76687 q^{48}\) \(-7.00000 q^{49}\) \(+4.85612 q^{50}\) \(-6.37065 q^{51}\) \(-0.508617 q^{52}\) \(+0.305012 q^{53}\) \(+5.08534 q^{54}\) \(+0.730296 q^{55}\) \(+0.00141487 q^{56}\) \(+9.68170 q^{57}\) \(-1.18532 q^{58}\) \(+8.06109 q^{59}\) \(-0.670192 q^{60}\) \(-12.9193 q^{61}\) \(-7.55554 q^{62}\) \(-0.000172390 q^{63}\) \(+1.00000 q^{64}\) \(+0.192923 q^{65}\) \(+3.40181 q^{66}\) \(+4.52748 q^{67}\) \(-3.60561 q^{68}\) \(+1.76687 q^{69}\) \(-0.000536675 q^{70}\) \(-2.54728 q^{71}\) \(-0.121841 q^{72}\) \(-10.5179 q^{73}\) \(+0.946095 q^{74}\) \(-8.58016 q^{75}\) \(+5.47957 q^{76}\) \(+0.00272410 q^{77}\) \(+0.898661 q^{78}\) \(-14.5022 q^{79}\) \(-0.379310 q^{80}\) \(-9.35068 q^{81}\) \(-7.34729 q^{82}\) \(+9.23516 q^{83}\) \(-0.00249990 q^{84}\) \(+1.36764 q^{85}\) \(+2.24582 q^{86}\) \(+2.09432 q^{87}\) \(+1.92533 q^{88}\) \(-5.09908 q^{89}\) \(+0.0462156 q^{90}\) \(+0.000719627 q^{91}\) \(+1.00000 q^{92}\) \(+13.3497 q^{93}\) \(-0.668739 q^{94}\) \(-2.07845 q^{95}\) \(-1.76687 q^{96}\) \(-18.6859 q^{97}\) \(+7.00000 q^{98}\) \(-0.234585 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.76687 1.02010 0.510052 0.860143i \(-0.329626\pi\)
0.510052 + 0.860143i \(0.329626\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.379310 −0.169632 −0.0848162 0.996397i \(-0.527030\pi\)
−0.0848162 + 0.996397i \(0.527030\pi\)
\(6\) −1.76687 −0.721323
\(7\) −0.00141487 −0.000534771 0 −0.000267386 1.00000i \(-0.500085\pi\)
−0.000267386 1.00000i \(0.500085\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.121841 0.0406138
\(10\) 0.379310 0.119948
\(11\) −1.92533 −0.580509 −0.290254 0.956950i \(-0.593740\pi\)
−0.290254 + 0.956950i \(0.593740\pi\)
\(12\) 1.76687 0.510052
\(13\) −0.508617 −0.141065 −0.0705324 0.997509i \(-0.522470\pi\)
−0.0705324 + 0.997509i \(0.522470\pi\)
\(14\) 0.00141487 0.000378141 0
\(15\) −0.670192 −0.173043
\(16\) 1.00000 0.250000
\(17\) −3.60561 −0.874488 −0.437244 0.899343i \(-0.644045\pi\)
−0.437244 + 0.899343i \(0.644045\pi\)
\(18\) −0.121841 −0.0287183
\(19\) 5.47957 1.25710 0.628549 0.777770i \(-0.283649\pi\)
0.628549 + 0.777770i \(0.283649\pi\)
\(20\) −0.379310 −0.0848162
\(21\) −0.00249990 −0.000545523 0
\(22\) 1.92533 0.410482
\(23\) 1.00000 0.208514
\(24\) −1.76687 −0.360662
\(25\) −4.85612 −0.971225
\(26\) 0.508617 0.0997479
\(27\) −5.08534 −0.978674
\(28\) −0.00141487 −0.000267386 0
\(29\) 1.18532 0.220109 0.110055 0.993926i \(-0.464897\pi\)
0.110055 + 0.993926i \(0.464897\pi\)
\(30\) 0.670192 0.122360
\(31\) 7.55554 1.35702 0.678508 0.734593i \(-0.262627\pi\)
0.678508 + 0.734593i \(0.262627\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.40181 −0.592180
\(34\) 3.60561 0.618356
\(35\) 0.000536675 0 9.07146e−5 0
\(36\) 0.121841 0.0203069
\(37\) −0.946095 −0.155537 −0.0777685 0.996971i \(-0.524780\pi\)
−0.0777685 + 0.996971i \(0.524780\pi\)
\(38\) −5.47957 −0.888903
\(39\) −0.898661 −0.143901
\(40\) 0.379310 0.0599741
\(41\) 7.34729 1.14745 0.573727 0.819047i \(-0.305497\pi\)
0.573727 + 0.819047i \(0.305497\pi\)
\(42\) 0.00249990 0.000385743 0
\(43\) −2.24582 −0.342485 −0.171242 0.985229i \(-0.554778\pi\)
−0.171242 + 0.985229i \(0.554778\pi\)
\(44\) −1.92533 −0.290254
\(45\) −0.0462156 −0.00688942
\(46\) −1.00000 −0.147442
\(47\) 0.668739 0.0975457 0.0487728 0.998810i \(-0.484469\pi\)
0.0487728 + 0.998810i \(0.484469\pi\)
\(48\) 1.76687 0.255026
\(49\) −7.00000 −1.00000
\(50\) 4.85612 0.686760
\(51\) −6.37065 −0.892069
\(52\) −0.508617 −0.0705324
\(53\) 0.305012 0.0418967 0.0209483 0.999781i \(-0.493331\pi\)
0.0209483 + 0.999781i \(0.493331\pi\)
\(54\) 5.08534 0.692027
\(55\) 0.730296 0.0984731
\(56\) 0.00141487 0.000189070 0
\(57\) 9.68170 1.28237
\(58\) −1.18532 −0.155641
\(59\) 8.06109 1.04946 0.524732 0.851267i \(-0.324165\pi\)
0.524732 + 0.851267i \(0.324165\pi\)
\(60\) −0.670192 −0.0865214
\(61\) −12.9193 −1.65415 −0.827076 0.562091i \(-0.809997\pi\)
−0.827076 + 0.562091i \(0.809997\pi\)
\(62\) −7.55554 −0.959555
\(63\) −0.000172390 0 −2.17191e−5 0
\(64\) 1.00000 0.125000
\(65\) 0.192923 0.0239292
\(66\) 3.40181 0.418734
\(67\) 4.52748 0.553120 0.276560 0.960997i \(-0.410806\pi\)
0.276560 + 0.960997i \(0.410806\pi\)
\(68\) −3.60561 −0.437244
\(69\) 1.76687 0.212707
\(70\) −0.000536675 0 −6.41449e−5 0
\(71\) −2.54728 −0.302306 −0.151153 0.988510i \(-0.548299\pi\)
−0.151153 + 0.988510i \(0.548299\pi\)
\(72\) −0.121841 −0.0143591
\(73\) −10.5179 −1.23103 −0.615513 0.788127i \(-0.711051\pi\)
−0.615513 + 0.788127i \(0.711051\pi\)
\(74\) 0.946095 0.109981
\(75\) −8.58016 −0.990751
\(76\) 5.47957 0.628549
\(77\) 0.00272410 0.000310439 0
\(78\) 0.898661 0.101753
\(79\) −14.5022 −1.63163 −0.815813 0.578316i \(-0.803710\pi\)
−0.815813 + 0.578316i \(0.803710\pi\)
\(80\) −0.379310 −0.0424081
\(81\) −9.35068 −1.03896
\(82\) −7.34729 −0.811372
\(83\) 9.23516 1.01369 0.506845 0.862037i \(-0.330811\pi\)
0.506845 + 0.862037i \(0.330811\pi\)
\(84\) −0.00249990 −0.000272761 0
\(85\) 1.36764 0.148342
\(86\) 2.24582 0.242173
\(87\) 2.09432 0.224535
\(88\) 1.92533 0.205241
\(89\) −5.09908 −0.540501 −0.270251 0.962790i \(-0.587107\pi\)
−0.270251 + 0.962790i \(0.587107\pi\)
\(90\) 0.0462156 0.00487155
\(91\) 0.000719627 0 7.54374e−5 0
\(92\) 1.00000 0.104257
\(93\) 13.3497 1.38430
\(94\) −0.668739 −0.0689752
\(95\) −2.07845 −0.213245
\(96\) −1.76687 −0.180331
\(97\) −18.6859 −1.89726 −0.948632 0.316381i \(-0.897532\pi\)
−0.948632 + 0.316381i \(0.897532\pi\)
\(98\) 7.00000 0.707107
\(99\) −0.234585 −0.0235767
\(100\) −4.85612 −0.485612
\(101\) −13.3930 −1.33265 −0.666325 0.745661i \(-0.732134\pi\)
−0.666325 + 0.745661i \(0.732134\pi\)
\(102\) 6.37065 0.630788
\(103\) −3.83841 −0.378210 −0.189105 0.981957i \(-0.560559\pi\)
−0.189105 + 0.981957i \(0.560559\pi\)
\(104\) 0.508617 0.0498740
\(105\) 0.000948236 0 9.25384e−5 0
\(106\) −0.305012 −0.0296254
\(107\) 18.1475 1.75438 0.877192 0.480139i \(-0.159414\pi\)
0.877192 + 0.480139i \(0.159414\pi\)
\(108\) −5.08534 −0.489337
\(109\) 11.3384 1.08602 0.543009 0.839727i \(-0.317285\pi\)
0.543009 + 0.839727i \(0.317285\pi\)
\(110\) −0.730296 −0.0696310
\(111\) −1.67163 −0.158664
\(112\) −0.00141487 −0.000133693 0
\(113\) 10.4493 0.982985 0.491492 0.870882i \(-0.336452\pi\)
0.491492 + 0.870882i \(0.336452\pi\)
\(114\) −9.68170 −0.906774
\(115\) −0.379310 −0.0353708
\(116\) 1.18532 0.110055
\(117\) −0.0619706 −0.00572918
\(118\) −8.06109 −0.742083
\(119\) 0.00510147 0.000467651 0
\(120\) 0.670192 0.0611799
\(121\) −7.29311 −0.663010
\(122\) 12.9193 1.16966
\(123\) 12.9817 1.17052
\(124\) 7.55554 0.678508
\(125\) 3.73852 0.334384
\(126\) 0.000172390 0 1.53577e−5 0
\(127\) −21.7549 −1.93043 −0.965216 0.261453i \(-0.915798\pi\)
−0.965216 + 0.261453i \(0.915798\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.96809 −0.349371
\(130\) −0.192923 −0.0169205
\(131\) 1.00000 0.0873704
\(132\) −3.40181 −0.296090
\(133\) −0.00775289 −0.000672260 0
\(134\) −4.52748 −0.391115
\(135\) 1.92892 0.166015
\(136\) 3.60561 0.309178
\(137\) −8.79911 −0.751758 −0.375879 0.926669i \(-0.622659\pi\)
−0.375879 + 0.926669i \(0.622659\pi\)
\(138\) −1.76687 −0.150406
\(139\) −11.3192 −0.960084 −0.480042 0.877246i \(-0.659379\pi\)
−0.480042 + 0.877246i \(0.659379\pi\)
\(140\) 0.000536675 0 4.53573e−5 0
\(141\) 1.18158 0.0995068
\(142\) 2.54728 0.213763
\(143\) 0.979254 0.0818894
\(144\) 0.121841 0.0101534
\(145\) −0.449605 −0.0373377
\(146\) 10.5179 0.870467
\(147\) −12.3681 −1.02010
\(148\) −0.946095 −0.0777685
\(149\) −14.8851 −1.21943 −0.609716 0.792620i \(-0.708716\pi\)
−0.609716 + 0.792620i \(0.708716\pi\)
\(150\) 8.58016 0.700567
\(151\) −12.3707 −1.00671 −0.503357 0.864079i \(-0.667902\pi\)
−0.503357 + 0.864079i \(0.667902\pi\)
\(152\) −5.47957 −0.444451
\(153\) −0.439312 −0.0355163
\(154\) −0.00272410 −0.000219514 0
\(155\) −2.86589 −0.230194
\(156\) −0.898661 −0.0719505
\(157\) −13.5907 −1.08466 −0.542330 0.840166i \(-0.682458\pi\)
−0.542330 + 0.840166i \(0.682458\pi\)
\(158\) 14.5022 1.15373
\(159\) 0.538918 0.0427390
\(160\) 0.379310 0.0299871
\(161\) −0.00141487 −0.000111508 0
\(162\) 9.35068 0.734659
\(163\) −11.3765 −0.891080 −0.445540 0.895262i \(-0.646988\pi\)
−0.445540 + 0.895262i \(0.646988\pi\)
\(164\) 7.34729 0.573727
\(165\) 1.29034 0.100453
\(166\) −9.23516 −0.716788
\(167\) 1.61910 0.125290 0.0626450 0.998036i \(-0.480046\pi\)
0.0626450 + 0.998036i \(0.480046\pi\)
\(168\) 0.00249990 0.000192871 0
\(169\) −12.7413 −0.980101
\(170\) −1.36764 −0.104893
\(171\) 0.667638 0.0510556
\(172\) −2.24582 −0.171242
\(173\) −9.21369 −0.700504 −0.350252 0.936656i \(-0.613904\pi\)
−0.350252 + 0.936656i \(0.613904\pi\)
\(174\) −2.09432 −0.158770
\(175\) 0.00687080 0.000519383 0
\(176\) −1.92533 −0.145127
\(177\) 14.2429 1.07056
\(178\) 5.09908 0.382192
\(179\) −7.06964 −0.528410 −0.264205 0.964467i \(-0.585110\pi\)
−0.264205 + 0.964467i \(0.585110\pi\)
\(180\) −0.0462156 −0.00344471
\(181\) −7.90374 −0.587481 −0.293740 0.955885i \(-0.594900\pi\)
−0.293740 + 0.955885i \(0.594900\pi\)
\(182\) −0.000719627 0 −5.33423e−5 0
\(183\) −22.8268 −1.68741
\(184\) −1.00000 −0.0737210
\(185\) 0.358863 0.0263841
\(186\) −13.3497 −0.978847
\(187\) 6.94198 0.507648
\(188\) 0.668739 0.0487728
\(189\) 0.00719511 0.000523367 0
\(190\) 2.07845 0.150787
\(191\) −14.0450 −1.01626 −0.508130 0.861280i \(-0.669663\pi\)
−0.508130 + 0.861280i \(0.669663\pi\)
\(192\) 1.76687 0.127513
\(193\) 9.71943 0.699620 0.349810 0.936821i \(-0.386246\pi\)
0.349810 + 0.936821i \(0.386246\pi\)
\(194\) 18.6859 1.34157
\(195\) 0.340871 0.0244103
\(196\) −7.00000 −0.500000
\(197\) 16.7363 1.19241 0.596206 0.802832i \(-0.296674\pi\)
0.596206 + 0.802832i \(0.296674\pi\)
\(198\) 0.234585 0.0166712
\(199\) −4.41855 −0.313223 −0.156611 0.987660i \(-0.550057\pi\)
−0.156611 + 0.987660i \(0.550057\pi\)
\(200\) 4.85612 0.343380
\(201\) 7.99948 0.564240
\(202\) 13.3930 0.942326
\(203\) −0.00167708 −0.000117708 0
\(204\) −6.37065 −0.446035
\(205\) −2.78690 −0.194645
\(206\) 3.83841 0.267435
\(207\) 0.121841 0.00846856
\(208\) −0.508617 −0.0352662
\(209\) −10.5500 −0.729757
\(210\) −0.000948236 0 −6.54345e−5 0
\(211\) 10.2292 0.704209 0.352105 0.935961i \(-0.385466\pi\)
0.352105 + 0.935961i \(0.385466\pi\)
\(212\) 0.305012 0.0209483
\(213\) −4.50072 −0.308384
\(214\) −18.1475 −1.24054
\(215\) 0.851863 0.0580966
\(216\) 5.08534 0.346014
\(217\) −0.0106901 −0.000725693 0
\(218\) −11.3384 −0.767931
\(219\) −18.5838 −1.25578
\(220\) 0.730296 0.0492366
\(221\) 1.83387 0.123360
\(222\) 1.67163 0.112192
\(223\) 27.9242 1.86995 0.934973 0.354720i \(-0.115424\pi\)
0.934973 + 0.354720i \(0.115424\pi\)
\(224\) 0.00141487 9.45351e−5 0
\(225\) −0.591677 −0.0394451
\(226\) −10.4493 −0.695075
\(227\) 11.2019 0.743497 0.371749 0.928333i \(-0.378758\pi\)
0.371749 + 0.928333i \(0.378758\pi\)
\(228\) 9.68170 0.641186
\(229\) 12.6638 0.836850 0.418425 0.908251i \(-0.362582\pi\)
0.418425 + 0.908251i \(0.362582\pi\)
\(230\) 0.379310 0.0250109
\(231\) 0.00481313 0.000316681 0
\(232\) −1.18532 −0.0778204
\(233\) −22.5854 −1.47962 −0.739810 0.672816i \(-0.765085\pi\)
−0.739810 + 0.672816i \(0.765085\pi\)
\(234\) 0.0619706 0.00405114
\(235\) −0.253659 −0.0165469
\(236\) 8.06109 0.524732
\(237\) −25.6236 −1.66443
\(238\) −0.00510147 −0.000330679 0
\(239\) 1.23332 0.0797771 0.0398885 0.999204i \(-0.487300\pi\)
0.0398885 + 0.999204i \(0.487300\pi\)
\(240\) −0.670192 −0.0432607
\(241\) −9.02566 −0.581394 −0.290697 0.956815i \(-0.593887\pi\)
−0.290697 + 0.956815i \(0.593887\pi\)
\(242\) 7.29311 0.468819
\(243\) −1.26544 −0.0811780
\(244\) −12.9193 −0.827076
\(245\) 2.65517 0.169632
\(246\) −12.9817 −0.827685
\(247\) −2.78700 −0.177332
\(248\) −7.55554 −0.479778
\(249\) 16.3174 1.03407
\(250\) −3.73852 −0.236445
\(251\) 6.91948 0.436754 0.218377 0.975865i \(-0.429924\pi\)
0.218377 + 0.975865i \(0.429924\pi\)
\(252\) −0.000172390 0 −1.08595e−5 0
\(253\) −1.92533 −0.121044
\(254\) 21.7549 1.36502
\(255\) 2.41645 0.151324
\(256\) 1.00000 0.0625000
\(257\) −15.9208 −0.993110 −0.496555 0.868005i \(-0.665402\pi\)
−0.496555 + 0.868005i \(0.665402\pi\)
\(258\) 3.96809 0.247042
\(259\) 0.00133860 8.31768e−5 0
\(260\) 0.192923 0.0119646
\(261\) 0.144422 0.00893947
\(262\) −1.00000 −0.0617802
\(263\) 18.2098 1.12286 0.561432 0.827523i \(-0.310251\pi\)
0.561432 + 0.827523i \(0.310251\pi\)
\(264\) 3.40181 0.209367
\(265\) −0.115694 −0.00710704
\(266\) 0.00775289 0.000475360 0
\(267\) −9.00942 −0.551368
\(268\) 4.52748 0.276560
\(269\) −10.1764 −0.620466 −0.310233 0.950661i \(-0.600407\pi\)
−0.310233 + 0.950661i \(0.600407\pi\)
\(270\) −1.92892 −0.117390
\(271\) 11.2418 0.682888 0.341444 0.939902i \(-0.389084\pi\)
0.341444 + 0.939902i \(0.389084\pi\)
\(272\) −3.60561 −0.218622
\(273\) 0.00127149 7.69541e−5 0
\(274\) 8.79911 0.531573
\(275\) 9.34964 0.563804
\(276\) 1.76687 0.106353
\(277\) −14.6965 −0.883026 −0.441513 0.897255i \(-0.645558\pi\)
−0.441513 + 0.897255i \(0.645558\pi\)
\(278\) 11.3192 0.678882
\(279\) 0.920578 0.0551136
\(280\) −0.000536675 0 −3.20725e−5 0
\(281\) −13.5224 −0.806678 −0.403339 0.915051i \(-0.632150\pi\)
−0.403339 + 0.915051i \(0.632150\pi\)
\(282\) −1.18158 −0.0703619
\(283\) 8.72783 0.518816 0.259408 0.965768i \(-0.416473\pi\)
0.259408 + 0.965768i \(0.416473\pi\)
\(284\) −2.54728 −0.151153
\(285\) −3.67236 −0.217532
\(286\) −0.979254 −0.0579045
\(287\) −0.0103955 −0.000613625 0
\(288\) −0.121841 −0.00717957
\(289\) −3.99960 −0.235271
\(290\) 0.449605 0.0264017
\(291\) −33.0156 −1.93541
\(292\) −10.5179 −0.615513
\(293\) 4.12146 0.240778 0.120389 0.992727i \(-0.461586\pi\)
0.120389 + 0.992727i \(0.461586\pi\)
\(294\) 12.3681 0.721323
\(295\) −3.05765 −0.178023
\(296\) 0.946095 0.0549906
\(297\) 9.79096 0.568129
\(298\) 14.8851 0.862268
\(299\) −0.508617 −0.0294141
\(300\) −8.58016 −0.495376
\(301\) 0.00317755 0.000183151 0
\(302\) 12.3707 0.711854
\(303\) −23.6637 −1.35944
\(304\) 5.47957 0.314275
\(305\) 4.90043 0.280598
\(306\) 0.439312 0.0251138
\(307\) −17.2682 −0.985549 −0.492774 0.870157i \(-0.664017\pi\)
−0.492774 + 0.870157i \(0.664017\pi\)
\(308\) 0.00272410 0.000155220 0
\(309\) −6.78199 −0.385814
\(310\) 2.86589 0.162772
\(311\) −1.05410 −0.0597726 −0.0298863 0.999553i \(-0.509515\pi\)
−0.0298863 + 0.999553i \(0.509515\pi\)
\(312\) 0.898661 0.0508767
\(313\) 0.128938 0.00728802 0.00364401 0.999993i \(-0.498840\pi\)
0.00364401 + 0.999993i \(0.498840\pi\)
\(314\) 13.5907 0.766970
\(315\) 6.53892e−5 0 3.68426e−6 0
\(316\) −14.5022 −0.815813
\(317\) −14.2027 −0.797701 −0.398850 0.917016i \(-0.630591\pi\)
−0.398850 + 0.917016i \(0.630591\pi\)
\(318\) −0.538918 −0.0302210
\(319\) −2.28214 −0.127775
\(320\) −0.379310 −0.0212041
\(321\) 32.0643 1.78966
\(322\) 0.00141487 7.88477e−5 0
\(323\) −19.7572 −1.09932
\(324\) −9.35068 −0.519482
\(325\) 2.46991 0.137006
\(326\) 11.3765 0.630089
\(327\) 20.0335 1.10785
\(328\) −7.34729 −0.405686
\(329\) −0.000946181 0 −5.21646e−5 0
\(330\) −1.29034 −0.0710309
\(331\) −8.05620 −0.442809 −0.221404 0.975182i \(-0.571064\pi\)
−0.221404 + 0.975182i \(0.571064\pi\)
\(332\) 9.23516 0.506845
\(333\) −0.115274 −0.00631695
\(334\) −1.61910 −0.0885934
\(335\) −1.71732 −0.0938271
\(336\) −0.00249990 −0.000136381 0
\(337\) 9.93115 0.540984 0.270492 0.962722i \(-0.412814\pi\)
0.270492 + 0.962722i \(0.412814\pi\)
\(338\) 12.7413 0.693036
\(339\) 18.4625 1.00275
\(340\) 1.36764 0.0741708
\(341\) −14.5469 −0.787759
\(342\) −0.667638 −0.0361017
\(343\) 0.0198082 0.00106954
\(344\) 2.24582 0.121087
\(345\) −0.670192 −0.0360819
\(346\) 9.21369 0.495331
\(347\) 2.13350 0.114532 0.0572662 0.998359i \(-0.481762\pi\)
0.0572662 + 0.998359i \(0.481762\pi\)
\(348\) 2.09432 0.112267
\(349\) −34.2009 −1.83073 −0.915367 0.402621i \(-0.868099\pi\)
−0.915367 + 0.402621i \(0.868099\pi\)
\(350\) −0.00687080 −0.000367259 0
\(351\) 2.58649 0.138057
\(352\) 1.92533 0.102620
\(353\) 21.9828 1.17002 0.585012 0.811025i \(-0.301090\pi\)
0.585012 + 0.811025i \(0.301090\pi\)
\(354\) −14.2429 −0.757003
\(355\) 0.966208 0.0512810
\(356\) −5.09908 −0.270251
\(357\) 0.00901365 0.000477053 0
\(358\) 7.06964 0.373642
\(359\) −16.8272 −0.888104 −0.444052 0.896001i \(-0.646460\pi\)
−0.444052 + 0.896001i \(0.646460\pi\)
\(360\) 0.0462156 0.00243578
\(361\) 11.0256 0.580297
\(362\) 7.90374 0.415412
\(363\) −12.8860 −0.676339
\(364\) 0.000719627 0 3.77187e−5 0
\(365\) 3.98954 0.208822
\(366\) 22.8268 1.19318
\(367\) 29.5616 1.54310 0.771552 0.636166i \(-0.219481\pi\)
0.771552 + 0.636166i \(0.219481\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0.895204 0.0466024
\(370\) −0.358863 −0.0186564
\(371\) −0.000431554 0 −2.24051e−5 0
\(372\) 13.3497 0.692149
\(373\) 21.1401 1.09459 0.547296 0.836939i \(-0.315657\pi\)
0.547296 + 0.836939i \(0.315657\pi\)
\(374\) −6.94198 −0.358961
\(375\) 6.60550 0.341106
\(376\) −0.668739 −0.0344876
\(377\) −0.602876 −0.0310497
\(378\) −0.00719511 −0.000370076 0
\(379\) −15.6054 −0.801594 −0.400797 0.916167i \(-0.631267\pi\)
−0.400797 + 0.916167i \(0.631267\pi\)
\(380\) −2.07845 −0.106622
\(381\) −38.4381 −1.96924
\(382\) 14.0450 0.718605
\(383\) 20.3815 1.04145 0.520724 0.853725i \(-0.325662\pi\)
0.520724 + 0.853725i \(0.325662\pi\)
\(384\) −1.76687 −0.0901654
\(385\) −0.00103328 −5.26606e−5 0
\(386\) −9.71943 −0.494706
\(387\) −0.273634 −0.0139096
\(388\) −18.6859 −0.948632
\(389\) −8.97921 −0.455264 −0.227632 0.973747i \(-0.573098\pi\)
−0.227632 + 0.973747i \(0.573098\pi\)
\(390\) −0.340871 −0.0172607
\(391\) −3.60561 −0.182343
\(392\) 7.00000 0.353553
\(393\) 1.76687 0.0891270
\(394\) −16.7363 −0.843162
\(395\) 5.50083 0.276777
\(396\) −0.234585 −0.0117883
\(397\) 35.5793 1.78567 0.892836 0.450381i \(-0.148712\pi\)
0.892836 + 0.450381i \(0.148712\pi\)
\(398\) 4.41855 0.221482
\(399\) −0.0136984 −0.000685776 0
\(400\) −4.85612 −0.242806
\(401\) 18.2529 0.911508 0.455754 0.890106i \(-0.349370\pi\)
0.455754 + 0.890106i \(0.349370\pi\)
\(402\) −7.99948 −0.398978
\(403\) −3.84287 −0.191427
\(404\) −13.3930 −0.666325
\(405\) 3.54680 0.176242
\(406\) 0.00167708 8.32322e−5 0
\(407\) 1.82154 0.0902906
\(408\) 6.37065 0.315394
\(409\) −10.8381 −0.535907 −0.267954 0.963432i \(-0.586347\pi\)
−0.267954 + 0.963432i \(0.586347\pi\)
\(410\) 2.78690 0.137635
\(411\) −15.5469 −0.766872
\(412\) −3.83841 −0.189105
\(413\) −0.0114054 −0.000561223 0
\(414\) −0.121841 −0.00598818
\(415\) −3.50299 −0.171955
\(416\) 0.508617 0.0249370
\(417\) −19.9996 −0.979386
\(418\) 10.5500 0.516016
\(419\) 2.87582 0.140493 0.0702465 0.997530i \(-0.477621\pi\)
0.0702465 + 0.997530i \(0.477621\pi\)
\(420\) 0.000948236 0 4.62692e−5 0
\(421\) −7.16331 −0.349118 −0.174559 0.984647i \(-0.555850\pi\)
−0.174559 + 0.984647i \(0.555850\pi\)
\(422\) −10.2292 −0.497951
\(423\) 0.0814801 0.00396170
\(424\) −0.305012 −0.0148127
\(425\) 17.5093 0.849324
\(426\) 4.50072 0.218061
\(427\) 0.0182792 0.000884593 0
\(428\) 18.1475 0.877192
\(429\) 1.73022 0.0835357
\(430\) −0.851863 −0.0410805
\(431\) −2.42077 −0.116604 −0.0583021 0.998299i \(-0.518569\pi\)
−0.0583021 + 0.998299i \(0.518569\pi\)
\(432\) −5.08534 −0.244669
\(433\) 36.5252 1.75529 0.877644 0.479312i \(-0.159114\pi\)
0.877644 + 0.479312i \(0.159114\pi\)
\(434\) 0.0106901 0.000513143 0
\(435\) −0.794395 −0.0380883
\(436\) 11.3384 0.543009
\(437\) 5.47957 0.262123
\(438\) 18.5838 0.887968
\(439\) 6.17395 0.294667 0.147333 0.989087i \(-0.452931\pi\)
0.147333 + 0.989087i \(0.452931\pi\)
\(440\) −0.730296 −0.0348155
\(441\) −0.852890 −0.0406138
\(442\) −1.83387 −0.0872283
\(443\) 11.6133 0.551764 0.275882 0.961192i \(-0.411030\pi\)
0.275882 + 0.961192i \(0.411030\pi\)
\(444\) −1.67163 −0.0793320
\(445\) 1.93413 0.0916865
\(446\) −27.9242 −1.32225
\(447\) −26.3000 −1.24395
\(448\) −0.00141487 −6.68464e−5 0
\(449\) 38.3018 1.80757 0.903786 0.427985i \(-0.140776\pi\)
0.903786 + 0.427985i \(0.140776\pi\)
\(450\) 0.591677 0.0278919
\(451\) −14.1459 −0.666107
\(452\) 10.4493 0.491492
\(453\) −21.8575 −1.02695
\(454\) −11.2019 −0.525732
\(455\) −0.000272962 0 −1.27966e−5 0
\(456\) −9.68170 −0.453387
\(457\) 17.3618 0.812152 0.406076 0.913839i \(-0.366897\pi\)
0.406076 + 0.913839i \(0.366897\pi\)
\(458\) −12.6638 −0.591742
\(459\) 18.3357 0.855839
\(460\) −0.379310 −0.0176854
\(461\) 10.5671 0.492158 0.246079 0.969250i \(-0.420858\pi\)
0.246079 + 0.969250i \(0.420858\pi\)
\(462\) −0.00481313 −0.000223927 0
\(463\) −17.5900 −0.817477 −0.408739 0.912651i \(-0.634031\pi\)
−0.408739 + 0.912651i \(0.634031\pi\)
\(464\) 1.18532 0.0550273
\(465\) −5.06367 −0.234822
\(466\) 22.5854 1.04625
\(467\) −9.62455 −0.445371 −0.222686 0.974890i \(-0.571482\pi\)
−0.222686 + 0.974890i \(0.571482\pi\)
\(468\) −0.0619706 −0.00286459
\(469\) −0.00640581 −0.000295793 0
\(470\) 0.253659 0.0117004
\(471\) −24.0131 −1.10647
\(472\) −8.06109 −0.371042
\(473\) 4.32395 0.198816
\(474\) 25.6236 1.17693
\(475\) −26.6095 −1.22093
\(476\) 0.00510147 0.000233826 0
\(477\) 0.0371631 0.00170158
\(478\) −1.23332 −0.0564109
\(479\) −5.59212 −0.255511 −0.127755 0.991806i \(-0.540777\pi\)
−0.127755 + 0.991806i \(0.540777\pi\)
\(480\) 0.670192 0.0305899
\(481\) 0.481199 0.0219408
\(482\) 9.02566 0.411107
\(483\) −0.00249990 −0.000113749 0
\(484\) −7.29311 −0.331505
\(485\) 7.08774 0.321838
\(486\) 1.26544 0.0574015
\(487\) −24.1604 −1.09481 −0.547405 0.836868i \(-0.684384\pi\)
−0.547405 + 0.836868i \(0.684384\pi\)
\(488\) 12.9193 0.584831
\(489\) −20.1009 −0.908995
\(490\) −2.65517 −0.119948
\(491\) 35.3399 1.59487 0.797434 0.603406i \(-0.206190\pi\)
0.797434 + 0.603406i \(0.206190\pi\)
\(492\) 12.9817 0.585261
\(493\) −4.27381 −0.192483
\(494\) 2.78700 0.125393
\(495\) 0.0889803 0.00399937
\(496\) 7.55554 0.339254
\(497\) 0.00360407 0.000161665 0
\(498\) −16.3174 −0.731199
\(499\) 33.8086 1.51348 0.756740 0.653716i \(-0.226791\pi\)
0.756740 + 0.653716i \(0.226791\pi\)
\(500\) 3.73852 0.167192
\(501\) 2.86075 0.127809
\(502\) −6.91948 −0.308832
\(503\) −7.02915 −0.313414 −0.156707 0.987645i \(-0.550088\pi\)
−0.156707 + 0.987645i \(0.550088\pi\)
\(504\) 0.000172390 0 7.67886e−6 0
\(505\) 5.08008 0.226061
\(506\) 1.92533 0.0855913
\(507\) −22.5123 −0.999805
\(508\) −21.7549 −0.965216
\(509\) −1.58356 −0.0701900 −0.0350950 0.999384i \(-0.511173\pi\)
−0.0350950 + 0.999384i \(0.511173\pi\)
\(510\) −2.41645 −0.107002
\(511\) 0.0148815 0.000658318 0
\(512\) −1.00000 −0.0441942
\(513\) −27.8655 −1.23029
\(514\) 15.9208 0.702235
\(515\) 1.45595 0.0641567
\(516\) −3.96809 −0.174685
\(517\) −1.28754 −0.0566261
\(518\) −0.00133860 −5.88148e−5 0
\(519\) −16.2794 −0.714587
\(520\) −0.192923 −0.00846024
\(521\) −34.3233 −1.50373 −0.751866 0.659316i \(-0.770846\pi\)
−0.751866 + 0.659316i \(0.770846\pi\)
\(522\) −0.144422 −0.00632116
\(523\) −1.56653 −0.0684998 −0.0342499 0.999413i \(-0.510904\pi\)
−0.0342499 + 0.999413i \(0.510904\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0.0121398 0.000529825 0
\(526\) −18.2098 −0.793984
\(527\) −27.2423 −1.18669
\(528\) −3.40181 −0.148045
\(529\) 1.00000 0.0434783
\(530\) 0.115694 0.00502543
\(531\) 0.982174 0.0426227
\(532\) −0.00775289 −0.000336130 0
\(533\) −3.73695 −0.161865
\(534\) 9.00942 0.389876
\(535\) −6.88352 −0.297601
\(536\) −4.52748 −0.195557
\(537\) −12.4912 −0.539033
\(538\) 10.1764 0.438736
\(539\) 13.4773 0.580509
\(540\) 1.92892 0.0830075
\(541\) 31.3319 1.34706 0.673532 0.739158i \(-0.264776\pi\)
0.673532 + 0.739158i \(0.264776\pi\)
\(542\) −11.2418 −0.482875
\(543\) −13.9649 −0.599292
\(544\) 3.60561 0.154589
\(545\) −4.30075 −0.184224
\(546\) −0.00127149 −5.44148e−5 0
\(547\) 16.2649 0.695437 0.347719 0.937599i \(-0.386956\pi\)
0.347719 + 0.937599i \(0.386956\pi\)
\(548\) −8.79911 −0.375879
\(549\) −1.57411 −0.0671814
\(550\) −9.34964 −0.398670
\(551\) 6.49507 0.276699
\(552\) −1.76687 −0.0752031
\(553\) 0.0205188 0.000872547 0
\(554\) 14.6965 0.624394
\(555\) 0.634065 0.0269146
\(556\) −11.3192 −0.480042
\(557\) 5.38541 0.228187 0.114094 0.993470i \(-0.463604\pi\)
0.114094 + 0.993470i \(0.463604\pi\)
\(558\) −0.920578 −0.0389712
\(559\) 1.14226 0.0483126
\(560\) 0.000536675 0 2.26786e−5 0
\(561\) 12.2656 0.517854
\(562\) 13.5224 0.570407
\(563\) −15.3128 −0.645356 −0.322678 0.946509i \(-0.604583\pi\)
−0.322678 + 0.946509i \(0.604583\pi\)
\(564\) 1.18158 0.0497534
\(565\) −3.96351 −0.166746
\(566\) −8.72783 −0.366858
\(567\) 0.0132300 0.000555608 0
\(568\) 2.54728 0.106881
\(569\) −21.7737 −0.912799 −0.456400 0.889775i \(-0.650861\pi\)
−0.456400 + 0.889775i \(0.650861\pi\)
\(570\) 3.67236 0.153818
\(571\) −3.36689 −0.140900 −0.0704499 0.997515i \(-0.522443\pi\)
−0.0704499 + 0.997515i \(0.522443\pi\)
\(572\) 0.979254 0.0409447
\(573\) −24.8157 −1.03669
\(574\) 0.0103955 0.000433899 0
\(575\) −4.85612 −0.202514
\(576\) 0.121841 0.00507672
\(577\) 22.8252 0.950225 0.475112 0.879925i \(-0.342407\pi\)
0.475112 + 0.879925i \(0.342407\pi\)
\(578\) 3.99960 0.166362
\(579\) 17.1730 0.713686
\(580\) −0.449605 −0.0186688
\(581\) −0.0130666 −0.000542093 0
\(582\) 33.0156 1.36854
\(583\) −0.587249 −0.0243214
\(584\) 10.5179 0.435233
\(585\) 0.0235060 0.000971855 0
\(586\) −4.12146 −0.170256
\(587\) −8.35029 −0.344654 −0.172327 0.985040i \(-0.555128\pi\)
−0.172327 + 0.985040i \(0.555128\pi\)
\(588\) −12.3681 −0.510052
\(589\) 41.4011 1.70590
\(590\) 3.05765 0.125881
\(591\) 29.5709 1.21638
\(592\) −0.946095 −0.0388843
\(593\) −18.5999 −0.763807 −0.381903 0.924202i \(-0.624731\pi\)
−0.381903 + 0.924202i \(0.624731\pi\)
\(594\) −9.79096 −0.401728
\(595\) −0.00193504 −7.93288e−5 0
\(596\) −14.8851 −0.609716
\(597\) −7.80702 −0.319520
\(598\) 0.508617 0.0207989
\(599\) 39.1876 1.60116 0.800581 0.599225i \(-0.204524\pi\)
0.800581 + 0.599225i \(0.204524\pi\)
\(600\) 8.58016 0.350283
\(601\) −33.6229 −1.37151 −0.685754 0.727834i \(-0.740527\pi\)
−0.685754 + 0.727834i \(0.740527\pi\)
\(602\) −0.00317755 −0.000129507 0
\(603\) 0.551635 0.0224643
\(604\) −12.3707 −0.503357
\(605\) 2.76635 0.112468
\(606\) 23.6637 0.961271
\(607\) 20.5460 0.833936 0.416968 0.908921i \(-0.363093\pi\)
0.416968 + 0.908921i \(0.363093\pi\)
\(608\) −5.47957 −0.222226
\(609\) −0.00296319 −0.000120075 0
\(610\) −4.90043 −0.198413
\(611\) −0.340132 −0.0137603
\(612\) −0.439312 −0.0177581
\(613\) 34.4490 1.39138 0.695692 0.718341i \(-0.255098\pi\)
0.695692 + 0.718341i \(0.255098\pi\)
\(614\) 17.2682 0.696888
\(615\) −4.92409 −0.198559
\(616\) −0.00272410 −0.000109757 0
\(617\) −6.13888 −0.247142 −0.123571 0.992336i \(-0.539435\pi\)
−0.123571 + 0.992336i \(0.539435\pi\)
\(618\) 6.78199 0.272811
\(619\) −47.8651 −1.92386 −0.961931 0.273293i \(-0.911887\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(620\) −2.86589 −0.115097
\(621\) −5.08534 −0.204068
\(622\) 1.05410 0.0422656
\(623\) 0.00721454 0.000289045 0
\(624\) −0.898661 −0.0359752
\(625\) 22.8626 0.914503
\(626\) −0.128938 −0.00515341
\(627\) −18.6405 −0.744428
\(628\) −13.5907 −0.542330
\(629\) 3.41125 0.136015
\(630\) −6.53892e−5 0 −2.60517e−6 0
\(631\) 9.96437 0.396675 0.198338 0.980134i \(-0.436446\pi\)
0.198338 + 0.980134i \(0.436446\pi\)
\(632\) 14.5022 0.576867
\(633\) 18.0738 0.718367
\(634\) 14.2027 0.564059
\(635\) 8.25183 0.327464
\(636\) 0.538918 0.0213695
\(637\) 3.56031 0.141065
\(638\) 2.28214 0.0903508
\(639\) −0.310364 −0.0122778
\(640\) 0.379310 0.0149935
\(641\) −32.2108 −1.27225 −0.636125 0.771586i \(-0.719464\pi\)
−0.636125 + 0.771586i \(0.719464\pi\)
\(642\) −32.0643 −1.26548
\(643\) 12.3029 0.485179 0.242589 0.970129i \(-0.422003\pi\)
0.242589 + 0.970129i \(0.422003\pi\)
\(644\) −0.00141487 −5.57538e−5 0
\(645\) 1.50513 0.0592646
\(646\) 19.7572 0.777335
\(647\) −16.7819 −0.659764 −0.329882 0.944022i \(-0.607009\pi\)
−0.329882 + 0.944022i \(0.607009\pi\)
\(648\) 9.35068 0.367329
\(649\) −15.5203 −0.609223
\(650\) −2.46991 −0.0968776
\(651\) −0.0188881 −0.000740283 0
\(652\) −11.3765 −0.445540
\(653\) −26.3896 −1.03271 −0.516353 0.856376i \(-0.672711\pi\)
−0.516353 + 0.856376i \(0.672711\pi\)
\(654\) −20.0335 −0.783370
\(655\) −0.379310 −0.0148209
\(656\) 7.34729 0.286863
\(657\) −1.28151 −0.0499967
\(658\) 0.000946181 0 3.68860e−5 0
\(659\) 44.4639 1.73207 0.866035 0.499984i \(-0.166661\pi\)
0.866035 + 0.499984i \(0.166661\pi\)
\(660\) 1.29034 0.0502264
\(661\) −10.1306 −0.394035 −0.197018 0.980400i \(-0.563126\pi\)
−0.197018 + 0.980400i \(0.563126\pi\)
\(662\) 8.05620 0.313113
\(663\) 3.24022 0.125840
\(664\) −9.23516 −0.358394
\(665\) 0.00294074 0.000114037 0
\(666\) 0.115274 0.00446676
\(667\) 1.18532 0.0458960
\(668\) 1.61910 0.0626450
\(669\) 49.3386 1.90754
\(670\) 1.71732 0.0663457
\(671\) 24.8740 0.960249
\(672\) 0.00249990 9.64357e−5 0
\(673\) −33.3597 −1.28592 −0.642961 0.765899i \(-0.722294\pi\)
−0.642961 + 0.765899i \(0.722294\pi\)
\(674\) −9.93115 −0.382534
\(675\) 24.6951 0.950513
\(676\) −12.7413 −0.490050
\(677\) 27.2696 1.04806 0.524028 0.851701i \(-0.324429\pi\)
0.524028 + 0.851701i \(0.324429\pi\)
\(678\) −18.4625 −0.709050
\(679\) 0.0264381 0.00101460
\(680\) −1.36764 −0.0524467
\(681\) 19.7924 0.758445
\(682\) 14.5469 0.557030
\(683\) −46.6768 −1.78604 −0.893020 0.450018i \(-0.851418\pi\)
−0.893020 + 0.450018i \(0.851418\pi\)
\(684\) 0.667638 0.0255278
\(685\) 3.33759 0.127523
\(686\) −0.0198082 −0.000756281 0
\(687\) 22.3754 0.853675
\(688\) −2.24582 −0.0856212
\(689\) −0.155134 −0.00591015
\(690\) 0.670192 0.0255138
\(691\) −32.8833 −1.25094 −0.625470 0.780248i \(-0.715093\pi\)
−0.625470 + 0.780248i \(0.715093\pi\)
\(692\) −9.21369 −0.350252
\(693\) 0.000331908 0 1.26081e−5 0
\(694\) −2.13350 −0.0809867
\(695\) 4.29349 0.162861
\(696\) −2.09432 −0.0793849
\(697\) −26.4914 −1.00343
\(698\) 34.2009 1.29452
\(699\) −39.9056 −1.50937
\(700\) 0.00687080 0.000259692 0
\(701\) 26.6298 1.00579 0.502897 0.864347i \(-0.332268\pi\)
0.502897 + 0.864347i \(0.332268\pi\)
\(702\) −2.58649 −0.0976207
\(703\) −5.18419 −0.195525
\(704\) −1.92533 −0.0725636
\(705\) −0.448184 −0.0168796
\(706\) −21.9828 −0.827332
\(707\) 0.0189493 0.000712663 0
\(708\) 14.2429 0.535282
\(709\) −14.3389 −0.538507 −0.269254 0.963069i \(-0.586777\pi\)
−0.269254 + 0.963069i \(0.586777\pi\)
\(710\) −0.966208 −0.0362611
\(711\) −1.76697 −0.0662665
\(712\) 5.09908 0.191096
\(713\) 7.55554 0.282957
\(714\) −0.00901365 −0.000337328 0
\(715\) −0.371441 −0.0138911
\(716\) −7.06964 −0.264205
\(717\) 2.17913 0.0813810
\(718\) 16.8272 0.627985
\(719\) 51.3498 1.91503 0.957513 0.288391i \(-0.0931204\pi\)
0.957513 + 0.288391i \(0.0931204\pi\)
\(720\) −0.0462156 −0.00172235
\(721\) 0.00543086 0.000202256 0
\(722\) −11.0256 −0.410332
\(723\) −15.9472 −0.593083
\(724\) −7.90374 −0.293740
\(725\) −5.75608 −0.213776
\(726\) 12.8860 0.478244
\(727\) −21.6817 −0.804129 −0.402065 0.915611i \(-0.631707\pi\)
−0.402065 + 0.915611i \(0.631707\pi\)
\(728\) −0.000719627 0 −2.66712e−5 0
\(729\) 25.8162 0.956154
\(730\) −3.98954 −0.147659
\(731\) 8.09756 0.299499
\(732\) −22.8268 −0.843704
\(733\) −47.5951 −1.75797 −0.878983 0.476853i \(-0.841778\pi\)
−0.878983 + 0.476853i \(0.841778\pi\)
\(734\) −29.5616 −1.09114
\(735\) 4.69134 0.173043
\(736\) −1.00000 −0.0368605
\(737\) −8.71689 −0.321091
\(738\) −0.895204 −0.0329529
\(739\) −8.57556 −0.315457 −0.157729 0.987482i \(-0.550417\pi\)
−0.157729 + 0.987482i \(0.550417\pi\)
\(740\) 0.358863 0.0131921
\(741\) −4.92427 −0.180898
\(742\) 0.000431554 0 1.58428e−5 0
\(743\) −24.1915 −0.887501 −0.443751 0.896150i \(-0.646352\pi\)
−0.443751 + 0.896150i \(0.646352\pi\)
\(744\) −13.3497 −0.489423
\(745\) 5.64605 0.206855
\(746\) −21.1401 −0.773993
\(747\) 1.12523 0.0411698
\(748\) 6.94198 0.253824
\(749\) −0.0256764 −0.000938195 0
\(750\) −6.60550 −0.241199
\(751\) −1.13442 −0.0413954 −0.0206977 0.999786i \(-0.506589\pi\)
−0.0206977 + 0.999786i \(0.506589\pi\)
\(752\) 0.668739 0.0243864
\(753\) 12.2258 0.445535
\(754\) 0.602876 0.0219554
\(755\) 4.69233 0.170771
\(756\) 0.00719511 0.000261684 0
\(757\) 38.9407 1.41533 0.707663 0.706550i \(-0.249750\pi\)
0.707663 + 0.706550i \(0.249750\pi\)
\(758\) 15.6054 0.566813
\(759\) −3.40181 −0.123478
\(760\) 2.07845 0.0753934
\(761\) −13.4093 −0.486088 −0.243044 0.970015i \(-0.578146\pi\)
−0.243044 + 0.970015i \(0.578146\pi\)
\(762\) 38.4381 1.39247
\(763\) −0.0160423 −0.000580772 0
\(764\) −14.0450 −0.508130
\(765\) 0.166635 0.00602471
\(766\) −20.3815 −0.736414
\(767\) −4.10000 −0.148043
\(768\) 1.76687 0.0637565
\(769\) 36.6950 1.32326 0.661628 0.749832i \(-0.269866\pi\)
0.661628 + 0.749832i \(0.269866\pi\)
\(770\) 0.00103328 3.72367e−5 0
\(771\) −28.1300 −1.01308
\(772\) 9.71943 0.349810
\(773\) −6.72378 −0.241838 −0.120919 0.992662i \(-0.538584\pi\)
−0.120919 + 0.992662i \(0.538584\pi\)
\(774\) 0.273634 0.00983558
\(775\) −36.6907 −1.31797
\(776\) 18.6859 0.670784
\(777\) 0.00236514 8.48490e−5 0
\(778\) 8.97921 0.321920
\(779\) 40.2599 1.44246
\(780\) 0.340871 0.0122051
\(781\) 4.90435 0.175492
\(782\) 3.60561 0.128936
\(783\) −6.02778 −0.215415
\(784\) −7.00000 −0.250000
\(785\) 5.15510 0.183993
\(786\) −1.76687 −0.0630223
\(787\) 26.8116 0.955731 0.477866 0.878433i \(-0.341411\pi\)
0.477866 + 0.878433i \(0.341411\pi\)
\(788\) 16.7363 0.596206
\(789\) 32.1744 1.14544
\(790\) −5.50083 −0.195711
\(791\) −0.0147844 −0.000525672 0
\(792\) 0.234585 0.00833561
\(793\) 6.57099 0.233343
\(794\) −35.5793 −1.26266
\(795\) −0.204417 −0.00724992
\(796\) −4.41855 −0.156611
\(797\) −52.8691 −1.87272 −0.936360 0.351040i \(-0.885828\pi\)
−0.936360 + 0.351040i \(0.885828\pi\)
\(798\) 0.0136984 0.000484917 0
\(799\) −2.41121 −0.0853025
\(800\) 4.85612 0.171690
\(801\) −0.621279 −0.0219518
\(802\) −18.2529 −0.644533
\(803\) 20.2504 0.714621
\(804\) 7.99948 0.282120
\(805\) 0.000536675 0 1.89153e−5 0
\(806\) 3.84287 0.135359
\(807\) −17.9804 −0.632940
\(808\) 13.3930 0.471163
\(809\) −11.4132 −0.401265 −0.200633 0.979667i \(-0.564300\pi\)
−0.200633 + 0.979667i \(0.564300\pi\)
\(810\) −3.54680 −0.124622
\(811\) −39.8012 −1.39761 −0.698805 0.715312i \(-0.746284\pi\)
−0.698805 + 0.715312i \(0.746284\pi\)
\(812\) −0.00167708 −5.88541e−5 0
\(813\) 19.8628 0.696617
\(814\) −1.82154 −0.0638451
\(815\) 4.31523 0.151156
\(816\) −6.37065 −0.223017
\(817\) −12.3061 −0.430537
\(818\) 10.8381 0.378944
\(819\) 8.76804e−5 0 3.06380e−6 0
\(820\) −2.78690 −0.0973227
\(821\) −2.07902 −0.0725584 −0.0362792 0.999342i \(-0.511551\pi\)
−0.0362792 + 0.999342i \(0.511551\pi\)
\(822\) 15.5469 0.542261
\(823\) 12.6739 0.441783 0.220891 0.975298i \(-0.429103\pi\)
0.220891 + 0.975298i \(0.429103\pi\)
\(824\) 3.83841 0.133717
\(825\) 16.5196 0.575140
\(826\) 0.0114054 0.000396845 0
\(827\) −16.3840 −0.569728 −0.284864 0.958568i \(-0.591948\pi\)
−0.284864 + 0.958568i \(0.591948\pi\)
\(828\) 0.121841 0.00423428
\(829\) −9.78416 −0.339818 −0.169909 0.985460i \(-0.554347\pi\)
−0.169909 + 0.985460i \(0.554347\pi\)
\(830\) 3.50299 0.121590
\(831\) −25.9668 −0.900779
\(832\) −0.508617 −0.0176331
\(833\) 25.2392 0.874488
\(834\) 19.9996 0.692530
\(835\) −0.614141 −0.0212532
\(836\) −10.5500 −0.364878
\(837\) −38.4225 −1.32808
\(838\) −2.87582 −0.0993435
\(839\) −44.3840 −1.53231 −0.766153 0.642658i \(-0.777832\pi\)
−0.766153 + 0.642658i \(0.777832\pi\)
\(840\) −0.000948236 0 −3.27173e−5 0
\(841\) −27.5950 −0.951552
\(842\) 7.16331 0.246864
\(843\) −23.8923 −0.822896
\(844\) 10.2292 0.352105
\(845\) 4.83290 0.166257
\(846\) −0.0814801 −0.00280135
\(847\) 0.0103188 0.000354559 0
\(848\) 0.305012 0.0104742
\(849\) 15.4210 0.529247
\(850\) −17.5093 −0.600563
\(851\) −0.946095 −0.0324317
\(852\) −4.50072 −0.154192
\(853\) 9.78672 0.335091 0.167545 0.985864i \(-0.446416\pi\)
0.167545 + 0.985864i \(0.446416\pi\)
\(854\) −0.0182792 −0.000625502 0
\(855\) −0.253242 −0.00866068
\(856\) −18.1475 −0.620269
\(857\) −29.7961 −1.01782 −0.508908 0.860821i \(-0.669950\pi\)
−0.508908 + 0.860821i \(0.669950\pi\)
\(858\) −1.73022 −0.0590687
\(859\) 23.9499 0.817162 0.408581 0.912722i \(-0.366024\pi\)
0.408581 + 0.912722i \(0.366024\pi\)
\(860\) 0.851863 0.0290483
\(861\) −0.0183675 −0.000625962 0
\(862\) 2.42077 0.0824517
\(863\) 25.4201 0.865311 0.432655 0.901559i \(-0.357577\pi\)
0.432655 + 0.901559i \(0.357577\pi\)
\(864\) 5.08534 0.173007
\(865\) 3.49484 0.118828
\(866\) −36.5252 −1.24118
\(867\) −7.06679 −0.240001
\(868\) −0.0106901 −0.000362847 0
\(869\) 27.9215 0.947173
\(870\) 0.794395 0.0269325
\(871\) −2.30275 −0.0780257
\(872\) −11.3384 −0.383966
\(873\) −2.27671 −0.0770551
\(874\) −5.47957 −0.185349
\(875\) −0.00528953 −0.000178819 0
\(876\) −18.5838 −0.627888
\(877\) −38.1391 −1.28787 −0.643933 0.765082i \(-0.722698\pi\)
−0.643933 + 0.765082i \(0.722698\pi\)
\(878\) −6.17395 −0.208361
\(879\) 7.28209 0.245619
\(880\) 0.730296 0.0246183
\(881\) −13.3811 −0.450819 −0.225410 0.974264i \(-0.572372\pi\)
−0.225410 + 0.974264i \(0.572372\pi\)
\(882\) 0.852890 0.0287183
\(883\) 11.2906 0.379958 0.189979 0.981788i \(-0.439158\pi\)
0.189979 + 0.981788i \(0.439158\pi\)
\(884\) 1.83387 0.0616798
\(885\) −5.40248 −0.181602
\(886\) −11.6133 −0.390156
\(887\) 23.8266 0.800018 0.400009 0.916511i \(-0.369007\pi\)
0.400009 + 0.916511i \(0.369007\pi\)
\(888\) 1.67163 0.0560962
\(889\) 0.0307804 0.00103234
\(890\) −1.93413 −0.0648322
\(891\) 18.0031 0.603128
\(892\) 27.9242 0.934973
\(893\) 3.66440 0.122625
\(894\) 26.3000 0.879604
\(895\) 2.68158 0.0896354
\(896\) 0.00141487 4.72676e−5 0
\(897\) −0.898661 −0.0300054
\(898\) −38.3018 −1.27815
\(899\) 8.95577 0.298692
\(900\) −0.591677 −0.0197226
\(901\) −1.09975 −0.0366381
\(902\) 14.1459 0.471009
\(903\) 0.00561434 0.000186833 0
\(904\) −10.4493 −0.347538
\(905\) 2.99797 0.0996558
\(906\) 21.8575 0.726166
\(907\) −12.3276 −0.409330 −0.204665 0.978832i \(-0.565611\pi\)
−0.204665 + 0.978832i \(0.565611\pi\)
\(908\) 11.2019 0.371749
\(909\) −1.63182 −0.0541240
\(910\) 0.000272962 0 9.04859e−6 0
\(911\) −30.5427 −1.01192 −0.505962 0.862556i \(-0.668862\pi\)
−0.505962 + 0.862556i \(0.668862\pi\)
\(912\) 9.68170 0.320593
\(913\) −17.7807 −0.588456
\(914\) −17.3618 −0.574278
\(915\) 8.65844 0.286239
\(916\) 12.6638 0.418425
\(917\) −0.00141487 −4.67232e−5 0
\(918\) −18.3357 −0.605170
\(919\) 37.0261 1.22138 0.610688 0.791871i \(-0.290893\pi\)
0.610688 + 0.791871i \(0.290893\pi\)
\(920\) 0.379310 0.0125055
\(921\) −30.5107 −1.00536
\(922\) −10.5671 −0.348008
\(923\) 1.29559 0.0426448
\(924\) 0.00481313 0.000158340 0
\(925\) 4.59435 0.151061
\(926\) 17.5900 0.578044
\(927\) −0.467677 −0.0153605
\(928\) −1.18532 −0.0389102
\(929\) −34.1550 −1.12059 −0.560294 0.828294i \(-0.689312\pi\)
−0.560294 + 0.828294i \(0.689312\pi\)
\(930\) 5.06367 0.166044
\(931\) −38.3569 −1.25710
\(932\) −22.5854 −0.739810
\(933\) −1.86246 −0.0609743
\(934\) 9.62455 0.314925
\(935\) −2.63316 −0.0861136
\(936\) 0.0619706 0.00202557
\(937\) −44.4718 −1.45283 −0.726416 0.687255i \(-0.758815\pi\)
−0.726416 + 0.687255i \(0.758815\pi\)
\(938\) 0.00640581 0.000209157 0
\(939\) 0.227817 0.00743454
\(940\) −0.253659 −0.00827346
\(941\) −44.8441 −1.46187 −0.730937 0.682444i \(-0.760917\pi\)
−0.730937 + 0.682444i \(0.760917\pi\)
\(942\) 24.0131 0.782390
\(943\) 7.34729 0.239261
\(944\) 8.06109 0.262366
\(945\) −0.00272917 −8.87801e−5 0
\(946\) −4.32395 −0.140584
\(947\) 13.0581 0.424331 0.212165 0.977234i \(-0.431948\pi\)
0.212165 + 0.977234i \(0.431948\pi\)
\(948\) −25.6236 −0.832215
\(949\) 5.34957 0.173655
\(950\) 26.6095 0.863325
\(951\) −25.0943 −0.813738
\(952\) −0.00510147 −0.000165340 0
\(953\) −25.4899 −0.825699 −0.412850 0.910799i \(-0.635466\pi\)
−0.412850 + 0.910799i \(0.635466\pi\)
\(954\) −0.0371631 −0.00120320
\(955\) 5.32741 0.172391
\(956\) 1.23332 0.0398885
\(957\) −4.03225 −0.130344
\(958\) 5.59212 0.180673
\(959\) 0.0124496 0.000402019 0
\(960\) −0.670192 −0.0216304
\(961\) 26.0862 0.841492
\(962\) −0.481199 −0.0155145
\(963\) 2.21112 0.0712522
\(964\) −9.02566 −0.290697
\(965\) −3.68667 −0.118678
\(966\) 0.00249990 8.04330e−5 0
\(967\) −7.41726 −0.238523 −0.119261 0.992863i \(-0.538053\pi\)
−0.119261 + 0.992863i \(0.538053\pi\)
\(968\) 7.29311 0.234409
\(969\) −34.9084 −1.12142
\(970\) −7.08774 −0.227574
\(971\) 55.5575 1.78292 0.891462 0.453096i \(-0.149680\pi\)
0.891462 + 0.453096i \(0.149680\pi\)
\(972\) −1.26544 −0.0405890
\(973\) 0.0160152 0.000513425 0
\(974\) 24.1604 0.774148
\(975\) 4.36401 0.139760
\(976\) −12.9193 −0.413538
\(977\) 0.424018 0.0135655 0.00678277 0.999977i \(-0.497841\pi\)
0.00678277 + 0.999977i \(0.497841\pi\)
\(978\) 20.1009 0.642756
\(979\) 9.81740 0.313766
\(980\) 2.65517 0.0848162
\(981\) 1.38148 0.0441074
\(982\) −35.3399 −1.12774
\(983\) 25.9567 0.827891 0.413945 0.910302i \(-0.364150\pi\)
0.413945 + 0.910302i \(0.364150\pi\)
\(984\) −12.9817 −0.413842
\(985\) −6.34824 −0.202272
\(986\) 4.27381 0.136106
\(987\) −0.00167178 −5.32134e−5 0
\(988\) −2.78700 −0.0886662
\(989\) −2.24582 −0.0714131
\(990\) −0.0889803 −0.00282798
\(991\) −11.5205 −0.365962 −0.182981 0.983116i \(-0.558575\pi\)
−0.182981 + 0.983116i \(0.558575\pi\)
\(992\) −7.55554 −0.239889
\(993\) −14.2343 −0.451711
\(994\) −0.00360407 −0.000114314 0
\(995\) 1.67600 0.0531328
\(996\) 16.3174 0.517035
\(997\) −33.5593 −1.06283 −0.531417 0.847110i \(-0.678340\pi\)
−0.531417 + 0.847110i \(0.678340\pi\)
\(998\) −33.8086 −1.07019
\(999\) 4.81122 0.152220
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 \(a_p\))