Properties

Label 6010.2.a.c.1.1
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.06059\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.06059 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-3.06059 q^{6}\) \(+0.302669 q^{7}\) \(+1.00000 q^{8}\) \(+6.36721 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.06059 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-3.06059 q^{6}\) \(+0.302669 q^{7}\) \(+1.00000 q^{8}\) \(+6.36721 q^{9}\) \(+1.00000 q^{10}\) \(+0.393686 q^{11}\) \(-3.06059 q^{12}\) \(-2.37935 q^{13}\) \(+0.302669 q^{14}\) \(-3.06059 q^{15}\) \(+1.00000 q^{16}\) \(-0.379772 q^{17}\) \(+6.36721 q^{18}\) \(+0.653758 q^{19}\) \(+1.00000 q^{20}\) \(-0.926345 q^{21}\) \(+0.393686 q^{22}\) \(+0.240229 q^{23}\) \(-3.06059 q^{24}\) \(+1.00000 q^{25}\) \(-2.37935 q^{26}\) \(-10.3056 q^{27}\) \(+0.302669 q^{28}\) \(-10.4861 q^{29}\) \(-3.06059 q^{30}\) \(+1.32728 q^{31}\) \(+1.00000 q^{32}\) \(-1.20491 q^{33}\) \(-0.379772 q^{34}\) \(+0.302669 q^{35}\) \(+6.36721 q^{36}\) \(+8.99410 q^{37}\) \(+0.653758 q^{38}\) \(+7.28221 q^{39}\) \(+1.00000 q^{40}\) \(-8.36579 q^{41}\) \(-0.926345 q^{42}\) \(-0.545077 q^{43}\) \(+0.393686 q^{44}\) \(+6.36721 q^{45}\) \(+0.240229 q^{46}\) \(-4.02658 q^{47}\) \(-3.06059 q^{48}\) \(-6.90839 q^{49}\) \(+1.00000 q^{50}\) \(+1.16233 q^{51}\) \(-2.37935 q^{52}\) \(-5.16043 q^{53}\) \(-10.3056 q^{54}\) \(+0.393686 q^{55}\) \(+0.302669 q^{56}\) \(-2.00089 q^{57}\) \(-10.4861 q^{58}\) \(-5.74265 q^{59}\) \(-3.06059 q^{60}\) \(+2.10133 q^{61}\) \(+1.32728 q^{62}\) \(+1.92715 q^{63}\) \(+1.00000 q^{64}\) \(-2.37935 q^{65}\) \(-1.20491 q^{66}\) \(+16.1213 q^{67}\) \(-0.379772 q^{68}\) \(-0.735243 q^{69}\) \(+0.302669 q^{70}\) \(-9.79169 q^{71}\) \(+6.36721 q^{72}\) \(+13.1760 q^{73}\) \(+8.99410 q^{74}\) \(-3.06059 q^{75}\) \(+0.653758 q^{76}\) \(+0.119157 q^{77}\) \(+7.28221 q^{78}\) \(+6.29968 q^{79}\) \(+1.00000 q^{80}\) \(+12.4397 q^{81}\) \(-8.36579 q^{82}\) \(+0.717328 q^{83}\) \(-0.926345 q^{84}\) \(-0.379772 q^{85}\) \(-0.545077 q^{86}\) \(+32.0937 q^{87}\) \(+0.393686 q^{88}\) \(-9.68315 q^{89}\) \(+6.36721 q^{90}\) \(-0.720154 q^{91}\) \(+0.240229 q^{92}\) \(-4.06226 q^{93}\) \(-4.02658 q^{94}\) \(+0.653758 q^{95}\) \(-3.06059 q^{96}\) \(-14.8895 q^{97}\) \(-6.90839 q^{98}\) \(+2.50668 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.06059 −1.76703 −0.883516 0.468401i \(-0.844830\pi\)
−0.883516 + 0.468401i \(0.844830\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.06059 −1.24948
\(7\) 0.302669 0.114398 0.0571990 0.998363i \(-0.481783\pi\)
0.0571990 + 0.998363i \(0.481783\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.36721 2.12240
\(10\) 1.00000 0.316228
\(11\) 0.393686 0.118701 0.0593505 0.998237i \(-0.481097\pi\)
0.0593505 + 0.998237i \(0.481097\pi\)
\(12\) −3.06059 −0.883516
\(13\) −2.37935 −0.659913 −0.329956 0.943996i \(-0.607034\pi\)
−0.329956 + 0.943996i \(0.607034\pi\)
\(14\) 0.302669 0.0808916
\(15\) −3.06059 −0.790241
\(16\) 1.00000 0.250000
\(17\) −0.379772 −0.0921082 −0.0460541 0.998939i \(-0.514665\pi\)
−0.0460541 + 0.998939i \(0.514665\pi\)
\(18\) 6.36721 1.50077
\(19\) 0.653758 0.149982 0.0749912 0.997184i \(-0.476107\pi\)
0.0749912 + 0.997184i \(0.476107\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.926345 −0.202145
\(22\) 0.393686 0.0839342
\(23\) 0.240229 0.0500912 0.0250456 0.999686i \(-0.492027\pi\)
0.0250456 + 0.999686i \(0.492027\pi\)
\(24\) −3.06059 −0.624740
\(25\) 1.00000 0.200000
\(26\) −2.37935 −0.466629
\(27\) −10.3056 −1.98332
\(28\) 0.302669 0.0571990
\(29\) −10.4861 −1.94723 −0.973613 0.228207i \(-0.926714\pi\)
−0.973613 + 0.228207i \(0.926714\pi\)
\(30\) −3.06059 −0.558785
\(31\) 1.32728 0.238387 0.119193 0.992871i \(-0.461969\pi\)
0.119193 + 0.992871i \(0.461969\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.20491 −0.209748
\(34\) −0.379772 −0.0651303
\(35\) 0.302669 0.0511604
\(36\) 6.36721 1.06120
\(37\) 8.99410 1.47862 0.739311 0.673365i \(-0.235152\pi\)
0.739311 + 0.673365i \(0.235152\pi\)
\(38\) 0.653758 0.106054
\(39\) 7.28221 1.16609
\(40\) 1.00000 0.158114
\(41\) −8.36579 −1.30652 −0.653259 0.757135i \(-0.726599\pi\)
−0.653259 + 0.757135i \(0.726599\pi\)
\(42\) −0.926345 −0.142938
\(43\) −0.545077 −0.0831234 −0.0415617 0.999136i \(-0.513233\pi\)
−0.0415617 + 0.999136i \(0.513233\pi\)
\(44\) 0.393686 0.0593505
\(45\) 6.36721 0.949167
\(46\) 0.240229 0.0354199
\(47\) −4.02658 −0.587337 −0.293668 0.955907i \(-0.594876\pi\)
−0.293668 + 0.955907i \(0.594876\pi\)
\(48\) −3.06059 −0.441758
\(49\) −6.90839 −0.986913
\(50\) 1.00000 0.141421
\(51\) 1.16233 0.162758
\(52\) −2.37935 −0.329956
\(53\) −5.16043 −0.708839 −0.354420 0.935087i \(-0.615322\pi\)
−0.354420 + 0.935087i \(0.615322\pi\)
\(54\) −10.3056 −1.40242
\(55\) 0.393686 0.0530847
\(56\) 0.302669 0.0404458
\(57\) −2.00089 −0.265024
\(58\) −10.4861 −1.37690
\(59\) −5.74265 −0.747629 −0.373815 0.927503i \(-0.621950\pi\)
−0.373815 + 0.927503i \(0.621950\pi\)
\(60\) −3.06059 −0.395120
\(61\) 2.10133 0.269048 0.134524 0.990910i \(-0.457050\pi\)
0.134524 + 0.990910i \(0.457050\pi\)
\(62\) 1.32728 0.168565
\(63\) 1.92715 0.242799
\(64\) 1.00000 0.125000
\(65\) −2.37935 −0.295122
\(66\) −1.20491 −0.148314
\(67\) 16.1213 1.96953 0.984766 0.173882i \(-0.0556313\pi\)
0.984766 + 0.173882i \(0.0556313\pi\)
\(68\) −0.379772 −0.0460541
\(69\) −0.735243 −0.0885128
\(70\) 0.302669 0.0361758
\(71\) −9.79169 −1.16206 −0.581030 0.813882i \(-0.697350\pi\)
−0.581030 + 0.813882i \(0.697350\pi\)
\(72\) 6.36721 0.750383
\(73\) 13.1760 1.54213 0.771067 0.636754i \(-0.219723\pi\)
0.771067 + 0.636754i \(0.219723\pi\)
\(74\) 8.99410 1.04554
\(75\) −3.06059 −0.353406
\(76\) 0.653758 0.0749912
\(77\) 0.119157 0.0135791
\(78\) 7.28221 0.824548
\(79\) 6.29968 0.708770 0.354385 0.935100i \(-0.384690\pi\)
0.354385 + 0.935100i \(0.384690\pi\)
\(80\) 1.00000 0.111803
\(81\) 12.4397 1.38219
\(82\) −8.36579 −0.923847
\(83\) 0.717328 0.0787370 0.0393685 0.999225i \(-0.487465\pi\)
0.0393685 + 0.999225i \(0.487465\pi\)
\(84\) −0.926345 −0.101072
\(85\) −0.379772 −0.0411920
\(86\) −0.545077 −0.0587771
\(87\) 32.0937 3.44081
\(88\) 0.393686 0.0419671
\(89\) −9.68315 −1.02641 −0.513206 0.858266i \(-0.671542\pi\)
−0.513206 + 0.858266i \(0.671542\pi\)
\(90\) 6.36721 0.671163
\(91\) −0.720154 −0.0754927
\(92\) 0.240229 0.0250456
\(93\) −4.06226 −0.421237
\(94\) −4.02658 −0.415310
\(95\) 0.653758 0.0670742
\(96\) −3.06059 −0.312370
\(97\) −14.8895 −1.51180 −0.755898 0.654690i \(-0.772799\pi\)
−0.755898 + 0.654690i \(0.772799\pi\)
\(98\) −6.90839 −0.697853
\(99\) 2.50668 0.251931
\(100\) 1.00000 0.100000
\(101\) −18.4852 −1.83935 −0.919675 0.392680i \(-0.871548\pi\)
−0.919675 + 0.392680i \(0.871548\pi\)
\(102\) 1.16233 0.115087
\(103\) 5.65667 0.557368 0.278684 0.960383i \(-0.410102\pi\)
0.278684 + 0.960383i \(0.410102\pi\)
\(104\) −2.37935 −0.233314
\(105\) −0.926345 −0.0904020
\(106\) −5.16043 −0.501225
\(107\) 9.97666 0.964480 0.482240 0.876039i \(-0.339823\pi\)
0.482240 + 0.876039i \(0.339823\pi\)
\(108\) −10.3056 −0.991661
\(109\) 16.0324 1.53563 0.767814 0.640673i \(-0.221344\pi\)
0.767814 + 0.640673i \(0.221344\pi\)
\(110\) 0.393686 0.0375365
\(111\) −27.5272 −2.61277
\(112\) 0.302669 0.0285995
\(113\) −10.2264 −0.962015 −0.481008 0.876716i \(-0.659729\pi\)
−0.481008 + 0.876716i \(0.659729\pi\)
\(114\) −2.00089 −0.187400
\(115\) 0.240229 0.0224015
\(116\) −10.4861 −0.973613
\(117\) −15.1498 −1.40060
\(118\) −5.74265 −0.528654
\(119\) −0.114945 −0.0105370
\(120\) −3.06059 −0.279392
\(121\) −10.8450 −0.985910
\(122\) 2.10133 0.190245
\(123\) 25.6043 2.30866
\(124\) 1.32728 0.119193
\(125\) 1.00000 0.0894427
\(126\) 1.92715 0.171685
\(127\) 19.9875 1.77361 0.886803 0.462148i \(-0.152921\pi\)
0.886803 + 0.462148i \(0.152921\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.66826 0.146882
\(130\) −2.37935 −0.208683
\(131\) 9.27593 0.810441 0.405221 0.914219i \(-0.367195\pi\)
0.405221 + 0.914219i \(0.367195\pi\)
\(132\) −1.20491 −0.104874
\(133\) 0.197872 0.0171577
\(134\) 16.1213 1.39267
\(135\) −10.3056 −0.886968
\(136\) −0.379772 −0.0325652
\(137\) 0.364833 0.0311698 0.0155849 0.999879i \(-0.495039\pi\)
0.0155849 + 0.999879i \(0.495039\pi\)
\(138\) −0.735243 −0.0625880
\(139\) −8.30581 −0.704489 −0.352245 0.935908i \(-0.614581\pi\)
−0.352245 + 0.935908i \(0.614581\pi\)
\(140\) 0.302669 0.0255802
\(141\) 12.3237 1.03784
\(142\) −9.79169 −0.821701
\(143\) −0.936717 −0.0783322
\(144\) 6.36721 0.530601
\(145\) −10.4861 −0.870826
\(146\) 13.1760 1.09045
\(147\) 21.1438 1.74391
\(148\) 8.99410 0.739311
\(149\) 12.1058 0.991743 0.495872 0.868396i \(-0.334849\pi\)
0.495872 + 0.868396i \(0.334849\pi\)
\(150\) −3.06059 −0.249896
\(151\) −20.5589 −1.67306 −0.836531 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(152\) 0.653758 0.0530268
\(153\) −2.41809 −0.195491
\(154\) 0.119157 0.00960191
\(155\) 1.32728 0.106610
\(156\) 7.28221 0.583043
\(157\) −7.47357 −0.596456 −0.298228 0.954495i \(-0.596395\pi\)
−0.298228 + 0.954495i \(0.596395\pi\)
\(158\) 6.29968 0.501176
\(159\) 15.7939 1.25254
\(160\) 1.00000 0.0790569
\(161\) 0.0727099 0.00573034
\(162\) 12.4397 0.977356
\(163\) −2.21871 −0.173782 −0.0868912 0.996218i \(-0.527693\pi\)
−0.0868912 + 0.996218i \(0.527693\pi\)
\(164\) −8.36579 −0.653259
\(165\) −1.20491 −0.0938023
\(166\) 0.717328 0.0556755
\(167\) −12.5368 −0.970129 −0.485064 0.874479i \(-0.661204\pi\)
−0.485064 + 0.874479i \(0.661204\pi\)
\(168\) −0.926345 −0.0714690
\(169\) −7.33870 −0.564515
\(170\) −0.379772 −0.0291272
\(171\) 4.16261 0.318323
\(172\) −0.545077 −0.0415617
\(173\) 7.28234 0.553666 0.276833 0.960918i \(-0.410715\pi\)
0.276833 + 0.960918i \(0.410715\pi\)
\(174\) 32.0937 2.43302
\(175\) 0.302669 0.0228796
\(176\) 0.393686 0.0296752
\(177\) 17.5759 1.32108
\(178\) −9.68315 −0.725783
\(179\) 11.8959 0.889144 0.444572 0.895743i \(-0.353356\pi\)
0.444572 + 0.895743i \(0.353356\pi\)
\(180\) 6.36721 0.474584
\(181\) −20.4579 −1.52062 −0.760310 0.649560i \(-0.774953\pi\)
−0.760310 + 0.649560i \(0.774953\pi\)
\(182\) −0.720154 −0.0533814
\(183\) −6.43131 −0.475416
\(184\) 0.240229 0.0177099
\(185\) 8.99410 0.661259
\(186\) −4.06226 −0.297859
\(187\) −0.149511 −0.0109333
\(188\) −4.02658 −0.293668
\(189\) −3.11919 −0.226888
\(190\) 0.653758 0.0474286
\(191\) 9.68976 0.701127 0.350563 0.936539i \(-0.385990\pi\)
0.350563 + 0.936539i \(0.385990\pi\)
\(192\) −3.06059 −0.220879
\(193\) −3.47297 −0.249990 −0.124995 0.992157i \(-0.539891\pi\)
−0.124995 + 0.992157i \(0.539891\pi\)
\(194\) −14.8895 −1.06900
\(195\) 7.28221 0.521490
\(196\) −6.90839 −0.493457
\(197\) −7.43346 −0.529612 −0.264806 0.964302i \(-0.585308\pi\)
−0.264806 + 0.964302i \(0.585308\pi\)
\(198\) 2.50668 0.178142
\(199\) 3.67524 0.260531 0.130265 0.991479i \(-0.458417\pi\)
0.130265 + 0.991479i \(0.458417\pi\)
\(200\) 1.00000 0.0707107
\(201\) −49.3407 −3.48023
\(202\) −18.4852 −1.30062
\(203\) −3.17382 −0.222759
\(204\) 1.16233 0.0813791
\(205\) −8.36579 −0.584292
\(206\) 5.65667 0.394119
\(207\) 1.52959 0.106314
\(208\) −2.37935 −0.164978
\(209\) 0.257376 0.0178030
\(210\) −0.926345 −0.0639239
\(211\) −20.2472 −1.39387 −0.696936 0.717134i \(-0.745454\pi\)
−0.696936 + 0.717134i \(0.745454\pi\)
\(212\) −5.16043 −0.354420
\(213\) 29.9684 2.05340
\(214\) 9.97666 0.681990
\(215\) −0.545077 −0.0371739
\(216\) −10.3056 −0.701210
\(217\) 0.401726 0.0272710
\(218\) 16.0324 1.08585
\(219\) −40.3263 −2.72500
\(220\) 0.393686 0.0265423
\(221\) 0.903609 0.0607833
\(222\) −27.5272 −1.84751
\(223\) 10.8134 0.724117 0.362058 0.932155i \(-0.382074\pi\)
0.362058 + 0.932155i \(0.382074\pi\)
\(224\) 0.302669 0.0202229
\(225\) 6.36721 0.424480
\(226\) −10.2264 −0.680247
\(227\) −27.9968 −1.85822 −0.929108 0.369808i \(-0.879423\pi\)
−0.929108 + 0.369808i \(0.879423\pi\)
\(228\) −2.00089 −0.132512
\(229\) −21.2086 −1.40151 −0.700753 0.713404i \(-0.747152\pi\)
−0.700753 + 0.713404i \(0.747152\pi\)
\(230\) 0.240229 0.0158402
\(231\) −0.364689 −0.0239948
\(232\) −10.4861 −0.688448
\(233\) −29.8509 −1.95559 −0.977797 0.209553i \(-0.932799\pi\)
−0.977797 + 0.209553i \(0.932799\pi\)
\(234\) −15.1498 −0.990374
\(235\) −4.02658 −0.262665
\(236\) −5.74265 −0.373815
\(237\) −19.2807 −1.25242
\(238\) −0.114945 −0.00745078
\(239\) −9.17427 −0.593434 −0.296717 0.954965i \(-0.595892\pi\)
−0.296717 + 0.954965i \(0.595892\pi\)
\(240\) −3.06059 −0.197560
\(241\) 14.5645 0.938183 0.469092 0.883149i \(-0.344581\pi\)
0.469092 + 0.883149i \(0.344581\pi\)
\(242\) −10.8450 −0.697144
\(243\) −7.15592 −0.459052
\(244\) 2.10133 0.134524
\(245\) −6.90839 −0.441361
\(246\) 25.6043 1.63247
\(247\) −1.55552 −0.0989753
\(248\) 1.32728 0.0842824
\(249\) −2.19545 −0.139131
\(250\) 1.00000 0.0632456
\(251\) −15.5634 −0.982352 −0.491176 0.871060i \(-0.663433\pi\)
−0.491176 + 0.871060i \(0.663433\pi\)
\(252\) 1.92715 0.121399
\(253\) 0.0945750 0.00594588
\(254\) 19.9875 1.25413
\(255\) 1.16233 0.0727876
\(256\) 1.00000 0.0625000
\(257\) 16.5130 1.03005 0.515026 0.857174i \(-0.327782\pi\)
0.515026 + 0.857174i \(0.327782\pi\)
\(258\) 1.66826 0.103861
\(259\) 2.72223 0.169151
\(260\) −2.37935 −0.147561
\(261\) −66.7674 −4.13280
\(262\) 9.27593 0.573069
\(263\) −4.57687 −0.282222 −0.141111 0.989994i \(-0.545067\pi\)
−0.141111 + 0.989994i \(0.545067\pi\)
\(264\) −1.20491 −0.0741572
\(265\) −5.16043 −0.317002
\(266\) 0.197872 0.0121323
\(267\) 29.6361 1.81370
\(268\) 16.1213 0.984766
\(269\) 28.5382 1.74001 0.870003 0.493046i \(-0.164117\pi\)
0.870003 + 0.493046i \(0.164117\pi\)
\(270\) −10.3056 −0.627181
\(271\) −5.55300 −0.337320 −0.168660 0.985674i \(-0.553944\pi\)
−0.168660 + 0.985674i \(0.553944\pi\)
\(272\) −0.379772 −0.0230270
\(273\) 2.20410 0.133398
\(274\) 0.364833 0.0220404
\(275\) 0.393686 0.0237402
\(276\) −0.735243 −0.0442564
\(277\) 15.4924 0.930846 0.465423 0.885088i \(-0.345902\pi\)
0.465423 + 0.885088i \(0.345902\pi\)
\(278\) −8.30581 −0.498149
\(279\) 8.45107 0.505952
\(280\) 0.302669 0.0180879
\(281\) −7.89919 −0.471226 −0.235613 0.971847i \(-0.575710\pi\)
−0.235613 + 0.971847i \(0.575710\pi\)
\(282\) 12.3237 0.733866
\(283\) −21.8084 −1.29637 −0.648187 0.761481i \(-0.724472\pi\)
−0.648187 + 0.761481i \(0.724472\pi\)
\(284\) −9.79169 −0.581030
\(285\) −2.00089 −0.118522
\(286\) −0.936717 −0.0553892
\(287\) −2.53206 −0.149463
\(288\) 6.36721 0.375191
\(289\) −16.8558 −0.991516
\(290\) −10.4861 −0.615767
\(291\) 45.5705 2.67139
\(292\) 13.1760 0.771067
\(293\) 22.3147 1.30364 0.651821 0.758373i \(-0.274005\pi\)
0.651821 + 0.758373i \(0.274005\pi\)
\(294\) 21.1438 1.23313
\(295\) −5.74265 −0.334350
\(296\) 8.99410 0.522771
\(297\) −4.05719 −0.235422
\(298\) 12.1058 0.701268
\(299\) −0.571589 −0.0330558
\(300\) −3.06059 −0.176703
\(301\) −0.164978 −0.00950915
\(302\) −20.5589 −1.18303
\(303\) 56.5757 3.25019
\(304\) 0.653758 0.0374956
\(305\) 2.10133 0.120322
\(306\) −2.41809 −0.138233
\(307\) 11.9437 0.681661 0.340830 0.940125i \(-0.389292\pi\)
0.340830 + 0.940125i \(0.389292\pi\)
\(308\) 0.119157 0.00678957
\(309\) −17.3127 −0.984887
\(310\) 1.32728 0.0753845
\(311\) −16.4766 −0.934303 −0.467151 0.884177i \(-0.654720\pi\)
−0.467151 + 0.884177i \(0.654720\pi\)
\(312\) 7.28221 0.412274
\(313\) 2.42399 0.137012 0.0685060 0.997651i \(-0.478177\pi\)
0.0685060 + 0.997651i \(0.478177\pi\)
\(314\) −7.47357 −0.421758
\(315\) 1.92715 0.108583
\(316\) 6.29968 0.354385
\(317\) −29.9367 −1.68141 −0.840707 0.541490i \(-0.817860\pi\)
−0.840707 + 0.541490i \(0.817860\pi\)
\(318\) 15.7939 0.885680
\(319\) −4.12825 −0.231137
\(320\) 1.00000 0.0559017
\(321\) −30.5344 −1.70427
\(322\) 0.0727099 0.00405196
\(323\) −0.248279 −0.0138146
\(324\) 12.4397 0.691095
\(325\) −2.37935 −0.131983
\(326\) −2.21871 −0.122883
\(327\) −49.0687 −2.71350
\(328\) −8.36579 −0.461924
\(329\) −1.21872 −0.0671902
\(330\) −1.20491 −0.0663282
\(331\) −10.5453 −0.579622 −0.289811 0.957084i \(-0.593592\pi\)
−0.289811 + 0.957084i \(0.593592\pi\)
\(332\) 0.717328 0.0393685
\(333\) 57.2673 3.13823
\(334\) −12.5368 −0.685984
\(335\) 16.1213 0.880802
\(336\) −0.926345 −0.0505362
\(337\) −21.1632 −1.15283 −0.576415 0.817157i \(-0.695549\pi\)
−0.576415 + 0.817157i \(0.695549\pi\)
\(338\) −7.33870 −0.399173
\(339\) 31.2987 1.69991
\(340\) −0.379772 −0.0205960
\(341\) 0.522532 0.0282967
\(342\) 4.16261 0.225088
\(343\) −4.20964 −0.227299
\(344\) −0.545077 −0.0293886
\(345\) −0.735243 −0.0395841
\(346\) 7.28234 0.391501
\(347\) −7.28255 −0.390948 −0.195474 0.980709i \(-0.562625\pi\)
−0.195474 + 0.980709i \(0.562625\pi\)
\(348\) 32.0937 1.72040
\(349\) 1.21409 0.0649887 0.0324944 0.999472i \(-0.489655\pi\)
0.0324944 + 0.999472i \(0.489655\pi\)
\(350\) 0.302669 0.0161783
\(351\) 24.5207 1.30882
\(352\) 0.393686 0.0209836
\(353\) −19.5750 −1.04187 −0.520936 0.853596i \(-0.674417\pi\)
−0.520936 + 0.853596i \(0.674417\pi\)
\(354\) 17.5759 0.934148
\(355\) −9.79169 −0.519689
\(356\) −9.68315 −0.513206
\(357\) 0.351800 0.0186192
\(358\) 11.8959 0.628720
\(359\) −0.360464 −0.0190245 −0.00951227 0.999955i \(-0.503028\pi\)
−0.00951227 + 0.999955i \(0.503028\pi\)
\(360\) 6.36721 0.335581
\(361\) −18.5726 −0.977505
\(362\) −20.4579 −1.07524
\(363\) 33.1921 1.74213
\(364\) −0.720154 −0.0377463
\(365\) 13.1760 0.689664
\(366\) −6.43131 −0.336170
\(367\) −25.9109 −1.35254 −0.676268 0.736656i \(-0.736404\pi\)
−0.676268 + 0.736656i \(0.736404\pi\)
\(368\) 0.240229 0.0125228
\(369\) −53.2667 −2.77296
\(370\) 8.99410 0.467581
\(371\) −1.56190 −0.0810898
\(372\) −4.06226 −0.210618
\(373\) −28.1904 −1.45964 −0.729821 0.683638i \(-0.760397\pi\)
−0.729821 + 0.683638i \(0.760397\pi\)
\(374\) −0.149511 −0.00773103
\(375\) −3.06059 −0.158048
\(376\) −4.02658 −0.207655
\(377\) 24.9502 1.28500
\(378\) −3.11919 −0.160434
\(379\) 8.83096 0.453616 0.226808 0.973940i \(-0.427171\pi\)
0.226808 + 0.973940i \(0.427171\pi\)
\(380\) 0.653758 0.0335371
\(381\) −61.1736 −3.13402
\(382\) 9.68976 0.495771
\(383\) −23.8392 −1.21813 −0.609064 0.793121i \(-0.708455\pi\)
−0.609064 + 0.793121i \(0.708455\pi\)
\(384\) −3.06059 −0.156185
\(385\) 0.119157 0.00607278
\(386\) −3.47297 −0.176769
\(387\) −3.47062 −0.176421
\(388\) −14.8895 −0.755898
\(389\) 7.53468 0.382023 0.191012 0.981588i \(-0.438823\pi\)
0.191012 + 0.981588i \(0.438823\pi\)
\(390\) 7.28221 0.368749
\(391\) −0.0912323 −0.00461381
\(392\) −6.90839 −0.348926
\(393\) −28.3898 −1.43208
\(394\) −7.43346 −0.374492
\(395\) 6.29968 0.316971
\(396\) 2.50668 0.125966
\(397\) 32.0835 1.61022 0.805112 0.593123i \(-0.202105\pi\)
0.805112 + 0.593123i \(0.202105\pi\)
\(398\) 3.67524 0.184223
\(399\) −0.605605 −0.0303182
\(400\) 1.00000 0.0500000
\(401\) −10.4304 −0.520871 −0.260436 0.965491i \(-0.583866\pi\)
−0.260436 + 0.965491i \(0.583866\pi\)
\(402\) −49.3407 −2.46089
\(403\) −3.15806 −0.157314
\(404\) −18.4852 −0.919675
\(405\) 12.4397 0.618134
\(406\) −3.17382 −0.157514
\(407\) 3.54085 0.175514
\(408\) 1.16233 0.0575437
\(409\) 1.01459 0.0501684 0.0250842 0.999685i \(-0.492015\pi\)
0.0250842 + 0.999685i \(0.492015\pi\)
\(410\) −8.36579 −0.413157
\(411\) −1.11660 −0.0550781
\(412\) 5.65667 0.278684
\(413\) −1.73812 −0.0855273
\(414\) 1.52959 0.0751752
\(415\) 0.717328 0.0352123
\(416\) −2.37935 −0.116657
\(417\) 25.4207 1.24486
\(418\) 0.257376 0.0125887
\(419\) 22.6659 1.10730 0.553651 0.832749i \(-0.313234\pi\)
0.553651 + 0.832749i \(0.313234\pi\)
\(420\) −0.926345 −0.0452010
\(421\) −20.7214 −1.00990 −0.504950 0.863149i \(-0.668489\pi\)
−0.504950 + 0.863149i \(0.668489\pi\)
\(422\) −20.2472 −0.985616
\(423\) −25.6381 −1.24656
\(424\) −5.16043 −0.250612
\(425\) −0.379772 −0.0184216
\(426\) 29.9684 1.45197
\(427\) 0.636007 0.0307785
\(428\) 9.97666 0.482240
\(429\) 2.86691 0.138416
\(430\) −0.545077 −0.0262859
\(431\) 9.10219 0.438437 0.219219 0.975676i \(-0.429649\pi\)
0.219219 + 0.975676i \(0.429649\pi\)
\(432\) −10.3056 −0.495830
\(433\) −31.4151 −1.50971 −0.754856 0.655890i \(-0.772293\pi\)
−0.754856 + 0.655890i \(0.772293\pi\)
\(434\) 0.401726 0.0192835
\(435\) 32.0937 1.53878
\(436\) 16.0324 0.767814
\(437\) 0.157052 0.00751281
\(438\) −40.3263 −1.92687
\(439\) −0.429760 −0.0205113 −0.0102557 0.999947i \(-0.503265\pi\)
−0.0102557 + 0.999947i \(0.503265\pi\)
\(440\) 0.393686 0.0187683
\(441\) −43.9872 −2.09463
\(442\) 0.903609 0.0429803
\(443\) 33.5818 1.59552 0.797760 0.602975i \(-0.206018\pi\)
0.797760 + 0.602975i \(0.206018\pi\)
\(444\) −27.5272 −1.30639
\(445\) −9.68315 −0.459025
\(446\) 10.8134 0.512028
\(447\) −37.0508 −1.75244
\(448\) 0.302669 0.0142998
\(449\) −20.7822 −0.980772 −0.490386 0.871505i \(-0.663144\pi\)
−0.490386 + 0.871505i \(0.663144\pi\)
\(450\) 6.36721 0.300153
\(451\) −3.29350 −0.155085
\(452\) −10.2264 −0.481008
\(453\) 62.9224 2.95635
\(454\) −27.9968 −1.31396
\(455\) −0.720154 −0.0337614
\(456\) −2.00089 −0.0937000
\(457\) −1.56659 −0.0732822 −0.0366411 0.999328i \(-0.511666\pi\)
−0.0366411 + 0.999328i \(0.511666\pi\)
\(458\) −21.2086 −0.991014
\(459\) 3.91379 0.182680
\(460\) 0.240229 0.0112007
\(461\) −7.95973 −0.370722 −0.185361 0.982671i \(-0.559345\pi\)
−0.185361 + 0.982671i \(0.559345\pi\)
\(462\) −0.364689 −0.0169669
\(463\) −40.2680 −1.87141 −0.935705 0.352782i \(-0.885236\pi\)
−0.935705 + 0.352782i \(0.885236\pi\)
\(464\) −10.4861 −0.486806
\(465\) −4.06226 −0.188383
\(466\) −29.8509 −1.38281
\(467\) −34.5397 −1.59831 −0.799154 0.601126i \(-0.794719\pi\)
−0.799154 + 0.601126i \(0.794719\pi\)
\(468\) −15.1498 −0.700300
\(469\) 4.87942 0.225311
\(470\) −4.02658 −0.185732
\(471\) 22.8735 1.05396
\(472\) −5.74265 −0.264327
\(473\) −0.214589 −0.00986682
\(474\) −19.2807 −0.885594
\(475\) 0.653758 0.0299965
\(476\) −0.114945 −0.00526850
\(477\) −32.8575 −1.50444
\(478\) −9.17427 −0.419621
\(479\) 2.87871 0.131532 0.0657659 0.997835i \(-0.479051\pi\)
0.0657659 + 0.997835i \(0.479051\pi\)
\(480\) −3.06059 −0.139696
\(481\) −21.4001 −0.975761
\(482\) 14.5645 0.663396
\(483\) −0.222535 −0.0101257
\(484\) −10.8450 −0.492955
\(485\) −14.8895 −0.676096
\(486\) −7.15592 −0.324599
\(487\) −4.69576 −0.212785 −0.106393 0.994324i \(-0.533930\pi\)
−0.106393 + 0.994324i \(0.533930\pi\)
\(488\) 2.10133 0.0951227
\(489\) 6.79055 0.307079
\(490\) −6.90839 −0.312089
\(491\) 4.22768 0.190793 0.0953964 0.995439i \(-0.469588\pi\)
0.0953964 + 0.995439i \(0.469588\pi\)
\(492\) 25.6043 1.15433
\(493\) 3.98234 0.179355
\(494\) −1.55552 −0.0699861
\(495\) 2.50668 0.112667
\(496\) 1.32728 0.0595967
\(497\) −2.96364 −0.132937
\(498\) −2.19545 −0.0983803
\(499\) 33.4020 1.49528 0.747639 0.664105i \(-0.231187\pi\)
0.747639 + 0.664105i \(0.231187\pi\)
\(500\) 1.00000 0.0447214
\(501\) 38.3701 1.71425
\(502\) −15.5634 −0.694628
\(503\) 20.2165 0.901408 0.450704 0.892673i \(-0.351173\pi\)
0.450704 + 0.892673i \(0.351173\pi\)
\(504\) 1.92715 0.0858423
\(505\) −18.4852 −0.822582
\(506\) 0.0945750 0.00420437
\(507\) 22.4608 0.997517
\(508\) 19.9875 0.886803
\(509\) −30.5279 −1.35313 −0.676563 0.736384i \(-0.736532\pi\)
−0.676563 + 0.736384i \(0.736532\pi\)
\(510\) 1.16233 0.0514686
\(511\) 3.98796 0.176417
\(512\) 1.00000 0.0441942
\(513\) −6.73739 −0.297463
\(514\) 16.5130 0.728357
\(515\) 5.65667 0.249263
\(516\) 1.66826 0.0734409
\(517\) −1.58521 −0.0697174
\(518\) 2.72223 0.119608
\(519\) −22.2882 −0.978345
\(520\) −2.37935 −0.104341
\(521\) 24.1994 1.06019 0.530096 0.847937i \(-0.322156\pi\)
0.530096 + 0.847937i \(0.322156\pi\)
\(522\) −66.7674 −2.92233
\(523\) 12.2653 0.536325 0.268162 0.963374i \(-0.413584\pi\)
0.268162 + 0.963374i \(0.413584\pi\)
\(524\) 9.27593 0.405221
\(525\) −0.926345 −0.0404290
\(526\) −4.57687 −0.199561
\(527\) −0.504064 −0.0219574
\(528\) −1.20491 −0.0524371
\(529\) −22.9423 −0.997491
\(530\) −5.16043 −0.224155
\(531\) −36.5646 −1.58677
\(532\) 0.197872 0.00857885
\(533\) 19.9051 0.862187
\(534\) 29.6361 1.28248
\(535\) 9.97666 0.431328
\(536\) 16.1213 0.696335
\(537\) −36.4086 −1.57115
\(538\) 28.5382 1.23037
\(539\) −2.71974 −0.117147
\(540\) −10.3056 −0.443484
\(541\) −2.98187 −0.128200 −0.0641002 0.997943i \(-0.520418\pi\)
−0.0641002 + 0.997943i \(0.520418\pi\)
\(542\) −5.55300 −0.238522
\(543\) 62.6131 2.68698
\(544\) −0.379772 −0.0162826
\(545\) 16.0324 0.686754
\(546\) 2.20410 0.0943266
\(547\) 0.380513 0.0162696 0.00813478 0.999967i \(-0.497411\pi\)
0.00813478 + 0.999967i \(0.497411\pi\)
\(548\) 0.364833 0.0155849
\(549\) 13.3796 0.571028
\(550\) 0.393686 0.0167868
\(551\) −6.85539 −0.292050
\(552\) −0.735243 −0.0312940
\(553\) 1.90672 0.0810819
\(554\) 15.4924 0.658208
\(555\) −27.5272 −1.16847
\(556\) −8.30581 −0.352245
\(557\) 37.7655 1.60018 0.800088 0.599882i \(-0.204786\pi\)
0.800088 + 0.599882i \(0.204786\pi\)
\(558\) 8.45107 0.357762
\(559\) 1.29693 0.0548542
\(560\) 0.302669 0.0127901
\(561\) 0.457592 0.0193195
\(562\) −7.89919 −0.333207
\(563\) 24.6905 1.04058 0.520291 0.853989i \(-0.325824\pi\)
0.520291 + 0.853989i \(0.325824\pi\)
\(564\) 12.3237 0.518921
\(565\) −10.2264 −0.430226
\(566\) −21.8084 −0.916675
\(567\) 3.76511 0.158120
\(568\) −9.79169 −0.410850
\(569\) 39.8520 1.67068 0.835341 0.549732i \(-0.185270\pi\)
0.835341 + 0.549732i \(0.185270\pi\)
\(570\) −2.00089 −0.0838079
\(571\) 37.8580 1.58431 0.792154 0.610322i \(-0.208960\pi\)
0.792154 + 0.610322i \(0.208960\pi\)
\(572\) −0.936717 −0.0391661
\(573\) −29.6564 −1.23891
\(574\) −2.53206 −0.105686
\(575\) 0.240229 0.0100182
\(576\) 6.36721 0.265300
\(577\) 26.4122 1.09955 0.549777 0.835312i \(-0.314713\pi\)
0.549777 + 0.835312i \(0.314713\pi\)
\(578\) −16.8558 −0.701108
\(579\) 10.6293 0.441740
\(580\) −10.4861 −0.435413
\(581\) 0.217113 0.00900736
\(582\) 45.5705 1.88896
\(583\) −2.03159 −0.0841398
\(584\) 13.1760 0.545227
\(585\) −15.1498 −0.626367
\(586\) 22.3147 0.921814
\(587\) −42.1756 −1.74077 −0.870387 0.492368i \(-0.836132\pi\)
−0.870387 + 0.492368i \(0.836132\pi\)
\(588\) 21.1438 0.871954
\(589\) 0.867721 0.0357538
\(590\) −5.74265 −0.236421
\(591\) 22.7508 0.935841
\(592\) 8.99410 0.369655
\(593\) 20.6911 0.849683 0.424841 0.905268i \(-0.360330\pi\)
0.424841 + 0.905268i \(0.360330\pi\)
\(594\) −4.05719 −0.166468
\(595\) −0.114945 −0.00471229
\(596\) 12.1058 0.495872
\(597\) −11.2484 −0.460366
\(598\) −0.571589 −0.0233740
\(599\) −32.8420 −1.34189 −0.670943 0.741509i \(-0.734111\pi\)
−0.670943 + 0.741509i \(0.734111\pi\)
\(600\) −3.06059 −0.124948
\(601\) −1.00000 −0.0407909
\(602\) −0.164978 −0.00672399
\(603\) 102.648 4.18014
\(604\) −20.5589 −0.836531
\(605\) −10.8450 −0.440912
\(606\) 56.5757 2.29823
\(607\) −4.05152 −0.164446 −0.0822231 0.996614i \(-0.526202\pi\)
−0.0822231 + 0.996614i \(0.526202\pi\)
\(608\) 0.653758 0.0265134
\(609\) 9.71377 0.393622
\(610\) 2.10133 0.0850804
\(611\) 9.58063 0.387591
\(612\) −2.41809 −0.0977453
\(613\) 30.3621 1.22631 0.613157 0.789961i \(-0.289899\pi\)
0.613157 + 0.789961i \(0.289899\pi\)
\(614\) 11.9437 0.482007
\(615\) 25.6043 1.03246
\(616\) 0.119157 0.00480095
\(617\) −18.9474 −0.762792 −0.381396 0.924412i \(-0.624556\pi\)
−0.381396 + 0.924412i \(0.624556\pi\)
\(618\) −17.3127 −0.696420
\(619\) 26.6354 1.07057 0.535283 0.844673i \(-0.320205\pi\)
0.535283 + 0.844673i \(0.320205\pi\)
\(620\) 1.32728 0.0533049
\(621\) −2.47572 −0.0993470
\(622\) −16.4766 −0.660652
\(623\) −2.93079 −0.117419
\(624\) 7.28221 0.291522
\(625\) 1.00000 0.0400000
\(626\) 2.42399 0.0968820
\(627\) −0.787721 −0.0314586
\(628\) −7.47357 −0.298228
\(629\) −3.41571 −0.136193
\(630\) 1.92715 0.0767797
\(631\) 50.1155 1.99507 0.997533 0.0701957i \(-0.0223624\pi\)
0.997533 + 0.0701957i \(0.0223624\pi\)
\(632\) 6.29968 0.250588
\(633\) 61.9682 2.46302
\(634\) −29.9367 −1.18894
\(635\) 19.9875 0.793181
\(636\) 15.7939 0.626271
\(637\) 16.4375 0.651276
\(638\) −4.12825 −0.163439
\(639\) −62.3457 −2.46636
\(640\) 1.00000 0.0395285
\(641\) 3.86427 0.152630 0.0763148 0.997084i \(-0.475685\pi\)
0.0763148 + 0.997084i \(0.475685\pi\)
\(642\) −30.5344 −1.20510
\(643\) −21.3635 −0.842496 −0.421248 0.906946i \(-0.638408\pi\)
−0.421248 + 0.906946i \(0.638408\pi\)
\(644\) 0.0727099 0.00286517
\(645\) 1.66826 0.0656875
\(646\) −0.248279 −0.00976840
\(647\) 19.5335 0.767941 0.383971 0.923345i \(-0.374556\pi\)
0.383971 + 0.923345i \(0.374556\pi\)
\(648\) 12.4397 0.488678
\(649\) −2.26080 −0.0887442
\(650\) −2.37935 −0.0933257
\(651\) −1.22952 −0.0481887
\(652\) −2.21871 −0.0868912
\(653\) −42.5938 −1.66682 −0.833411 0.552653i \(-0.813615\pi\)
−0.833411 + 0.552653i \(0.813615\pi\)
\(654\) −49.0687 −1.91874
\(655\) 9.27593 0.362440
\(656\) −8.36579 −0.326629
\(657\) 83.8943 3.27303
\(658\) −1.21872 −0.0475106
\(659\) 3.46889 0.135129 0.0675644 0.997715i \(-0.478477\pi\)
0.0675644 + 0.997715i \(0.478477\pi\)
\(660\) −1.20491 −0.0469011
\(661\) 10.5580 0.410659 0.205329 0.978693i \(-0.434173\pi\)
0.205329 + 0.978693i \(0.434173\pi\)
\(662\) −10.5453 −0.409855
\(663\) −2.76558 −0.107406
\(664\) 0.717328 0.0278377
\(665\) 0.197872 0.00767315
\(666\) 57.2673 2.21906
\(667\) −2.51907 −0.0975390
\(668\) −12.5368 −0.485064
\(669\) −33.0953 −1.27954
\(670\) 16.1213 0.622821
\(671\) 0.827265 0.0319362
\(672\) −0.926345 −0.0357345
\(673\) −28.4403 −1.09629 −0.548147 0.836382i \(-0.684667\pi\)
−0.548147 + 0.836382i \(0.684667\pi\)
\(674\) −21.1632 −0.815174
\(675\) −10.3056 −0.396664
\(676\) −7.33870 −0.282258
\(677\) −0.161383 −0.00620246 −0.00310123 0.999995i \(-0.500987\pi\)
−0.00310123 + 0.999995i \(0.500987\pi\)
\(678\) 31.2987 1.20202
\(679\) −4.50657 −0.172946
\(680\) −0.379772 −0.0145636
\(681\) 85.6869 3.28353
\(682\) 0.522532 0.0200088
\(683\) −20.8736 −0.798707 −0.399353 0.916797i \(-0.630765\pi\)
−0.399353 + 0.916797i \(0.630765\pi\)
\(684\) 4.16261 0.159162
\(685\) 0.364833 0.0139396
\(686\) −4.20964 −0.160725
\(687\) 64.9109 2.47651
\(688\) −0.545077 −0.0207808
\(689\) 12.2785 0.467772
\(690\) −0.735243 −0.0279902
\(691\) 12.3797 0.470946 0.235473 0.971881i \(-0.424336\pi\)
0.235473 + 0.971881i \(0.424336\pi\)
\(692\) 7.28234 0.276833
\(693\) 0.758694 0.0288204
\(694\) −7.28255 −0.276442
\(695\) −8.30581 −0.315057
\(696\) 32.0937 1.21651
\(697\) 3.17709 0.120341
\(698\) 1.21409 0.0459540
\(699\) 91.3612 3.45560
\(700\) 0.302669 0.0114398
\(701\) −9.45537 −0.357124 −0.178562 0.983929i \(-0.557145\pi\)
−0.178562 + 0.983929i \(0.557145\pi\)
\(702\) 24.5207 0.925474
\(703\) 5.87997 0.221767
\(704\) 0.393686 0.0148376
\(705\) 12.3237 0.464137
\(706\) −19.5750 −0.736714
\(707\) −5.59490 −0.210418
\(708\) 17.5759 0.660542
\(709\) 25.5181 0.958354 0.479177 0.877718i \(-0.340935\pi\)
0.479177 + 0.877718i \(0.340935\pi\)
\(710\) −9.79169 −0.367476
\(711\) 40.1114 1.50429
\(712\) −9.68315 −0.362891
\(713\) 0.318852 0.0119411
\(714\) 0.351800 0.0131658
\(715\) −0.936717 −0.0350312
\(716\) 11.8959 0.444572
\(717\) 28.0787 1.04862
\(718\) −0.360464 −0.0134524
\(719\) −6.07987 −0.226741 −0.113370 0.993553i \(-0.536165\pi\)
−0.113370 + 0.993553i \(0.536165\pi\)
\(720\) 6.36721 0.237292
\(721\) 1.71210 0.0637618
\(722\) −18.5726 −0.691201
\(723\) −44.5760 −1.65780
\(724\) −20.4579 −0.760310
\(725\) −10.4861 −0.389445
\(726\) 33.1921 1.23188
\(727\) −42.1326 −1.56261 −0.781305 0.624149i \(-0.785446\pi\)
−0.781305 + 0.624149i \(0.785446\pi\)
\(728\) −0.720154 −0.0266907
\(729\) −15.4178 −0.571029
\(730\) 13.1760 0.487666
\(731\) 0.207005 0.00765635
\(732\) −6.43131 −0.237708
\(733\) 39.4881 1.45852 0.729262 0.684234i \(-0.239863\pi\)
0.729262 + 0.684234i \(0.239863\pi\)
\(734\) −25.9109 −0.956387
\(735\) 21.1438 0.779899
\(736\) 0.240229 0.00885497
\(737\) 6.34674 0.233785
\(738\) −53.2667 −1.96078
\(739\) 9.43579 0.347101 0.173551 0.984825i \(-0.444476\pi\)
0.173551 + 0.984825i \(0.444476\pi\)
\(740\) 8.99410 0.330630
\(741\) 4.76080 0.174892
\(742\) −1.56190 −0.0573391
\(743\) 9.27233 0.340169 0.170084 0.985429i \(-0.445596\pi\)
0.170084 + 0.985429i \(0.445596\pi\)
\(744\) −4.06226 −0.148930
\(745\) 12.1058 0.443521
\(746\) −28.1904 −1.03212
\(747\) 4.56738 0.167112
\(748\) −0.149511 −0.00546666
\(749\) 3.01962 0.110335
\(750\) −3.06059 −0.111757
\(751\) 30.1938 1.10179 0.550894 0.834575i \(-0.314287\pi\)
0.550894 + 0.834575i \(0.314287\pi\)
\(752\) −4.02658 −0.146834
\(753\) 47.6331 1.73585
\(754\) 24.9502 0.908631
\(755\) −20.5589 −0.748216
\(756\) −3.11919 −0.113444
\(757\) −8.16053 −0.296600 −0.148300 0.988942i \(-0.547380\pi\)
−0.148300 + 0.988942i \(0.547380\pi\)
\(758\) 8.83096 0.320755
\(759\) −0.289455 −0.0105066
\(760\) 0.653758 0.0237143
\(761\) −6.29743 −0.228282 −0.114141 0.993465i \(-0.536411\pi\)
−0.114141 + 0.993465i \(0.536411\pi\)
\(762\) −61.1736 −2.21609
\(763\) 4.85252 0.175673
\(764\) 9.68976 0.350563
\(765\) −2.41809 −0.0874261
\(766\) −23.8392 −0.861346
\(767\) 13.6638 0.493370
\(768\) −3.06059 −0.110440
\(769\) −14.2318 −0.513213 −0.256606 0.966516i \(-0.582604\pi\)
−0.256606 + 0.966516i \(0.582604\pi\)
\(770\) 0.119157 0.00429410
\(771\) −50.5395 −1.82014
\(772\) −3.47297 −0.124995
\(773\) −31.3779 −1.12858 −0.564291 0.825576i \(-0.690851\pi\)
−0.564291 + 0.825576i \(0.690851\pi\)
\(774\) −3.47062 −0.124749
\(775\) 1.32728 0.0476773
\(776\) −14.8895 −0.534500
\(777\) −8.33164 −0.298896
\(778\) 7.53468 0.270131
\(779\) −5.46921 −0.195955
\(780\) 7.28221 0.260745
\(781\) −3.85486 −0.137938
\(782\) −0.0912323 −0.00326246
\(783\) 108.066 3.86197
\(784\) −6.90839 −0.246728
\(785\) −7.47357 −0.266743
\(786\) −28.3898 −1.01263
\(787\) 16.1594 0.576019 0.288009 0.957628i \(-0.407007\pi\)
0.288009 + 0.957628i \(0.407007\pi\)
\(788\) −7.43346 −0.264806
\(789\) 14.0079 0.498695
\(790\) 6.29968 0.224133
\(791\) −3.09520 −0.110053
\(792\) 2.50668 0.0890711
\(793\) −4.99980 −0.177548
\(794\) 32.0835 1.13860
\(795\) 15.7939 0.560154
\(796\) 3.67524 0.130265
\(797\) −25.9997 −0.920957 −0.460478 0.887671i \(-0.652322\pi\)
−0.460478 + 0.887671i \(0.652322\pi\)
\(798\) −0.605605 −0.0214382
\(799\) 1.52918 0.0540985
\(800\) 1.00000 0.0353553
\(801\) −61.6546 −2.17846
\(802\) −10.4304 −0.368311
\(803\) 5.18721 0.183053
\(804\) −49.3407 −1.74011
\(805\) 0.0727099 0.00256269
\(806\) −3.15806 −0.111238
\(807\) −87.3438 −3.07465
\(808\) −18.4852 −0.650309
\(809\) 34.8638 1.22575 0.612873 0.790181i \(-0.290014\pi\)
0.612873 + 0.790181i \(0.290014\pi\)
\(810\) 12.4397 0.437087
\(811\) 17.2743 0.606582 0.303291 0.952898i \(-0.401915\pi\)
0.303291 + 0.952898i \(0.401915\pi\)
\(812\) −3.17382 −0.111379
\(813\) 16.9954 0.596056
\(814\) 3.54085 0.124107
\(815\) −2.21871 −0.0777179
\(816\) 1.16233 0.0406895
\(817\) −0.356348 −0.0124670
\(818\) 1.01459 0.0354744
\(819\) −4.58537 −0.160226
\(820\) −8.36579 −0.292146
\(821\) 34.9707 1.22049 0.610243 0.792214i \(-0.291072\pi\)
0.610243 + 0.792214i \(0.291072\pi\)
\(822\) −1.11660 −0.0389461
\(823\) −24.5645 −0.856265 −0.428133 0.903716i \(-0.640828\pi\)
−0.428133 + 0.903716i \(0.640828\pi\)
\(824\) 5.65667 0.197059
\(825\) −1.20491 −0.0419497
\(826\) −1.73812 −0.0604769
\(827\) 21.7667 0.756901 0.378451 0.925621i \(-0.376457\pi\)
0.378451 + 0.925621i \(0.376457\pi\)
\(828\) 1.52959 0.0531569
\(829\) −41.9351 −1.45647 −0.728233 0.685330i \(-0.759658\pi\)
−0.728233 + 0.685330i \(0.759658\pi\)
\(830\) 0.717328 0.0248988
\(831\) −47.4158 −1.64484
\(832\) −2.37935 −0.0824891
\(833\) 2.62361 0.0909028
\(834\) 25.4207 0.880245
\(835\) −12.5368 −0.433855
\(836\) 0.257376 0.00890152
\(837\) −13.6785 −0.472797
\(838\) 22.6659 0.782981
\(839\) 1.34936 0.0465851 0.0232926 0.999729i \(-0.492585\pi\)
0.0232926 + 0.999729i \(0.492585\pi\)
\(840\) −0.926345 −0.0319619
\(841\) 80.9589 2.79169
\(842\) −20.7214 −0.714107
\(843\) 24.1762 0.832672
\(844\) −20.2472 −0.696936
\(845\) −7.33870 −0.252459
\(846\) −25.6381 −0.881454
\(847\) −3.28245 −0.112786
\(848\) −5.16043 −0.177210
\(849\) 66.7465 2.29073
\(850\) −0.379772 −0.0130261
\(851\) 2.16065 0.0740660
\(852\) 29.9684 1.02670
\(853\) 38.6294 1.32265 0.661323 0.750101i \(-0.269995\pi\)
0.661323 + 0.750101i \(0.269995\pi\)
\(854\) 0.636007 0.0217637
\(855\) 4.16261 0.142358
\(856\) 9.97666 0.340995
\(857\) −50.7150 −1.73239 −0.866196 0.499704i \(-0.833442\pi\)
−0.866196 + 0.499704i \(0.833442\pi\)
\(858\) 2.86691 0.0978746
\(859\) 42.3999 1.44667 0.723333 0.690499i \(-0.242609\pi\)
0.723333 + 0.690499i \(0.242609\pi\)
\(860\) −0.545077 −0.0185870
\(861\) 7.74961 0.264106
\(862\) 9.10219 0.310022
\(863\) 40.2068 1.36866 0.684328 0.729174i \(-0.260096\pi\)
0.684328 + 0.729174i \(0.260096\pi\)
\(864\) −10.3056 −0.350605
\(865\) 7.28234 0.247607
\(866\) −31.4151 −1.06753
\(867\) 51.5886 1.75204
\(868\) 0.401726 0.0136355
\(869\) 2.48010 0.0841316
\(870\) 32.0937 1.08808
\(871\) −38.3582 −1.29972
\(872\) 16.0324 0.542927
\(873\) −94.8043 −3.20864
\(874\) 0.157052 0.00531236
\(875\) 0.302669 0.0102321
\(876\) −40.3263 −1.36250
\(877\) 2.34974 0.0793450 0.0396725 0.999213i \(-0.487369\pi\)
0.0396725 + 0.999213i \(0.487369\pi\)
\(878\) −0.429760 −0.0145037
\(879\) −68.2963 −2.30358
\(880\) 0.393686 0.0132712
\(881\) 7.06575 0.238051 0.119026 0.992891i \(-0.462023\pi\)
0.119026 + 0.992891i \(0.462023\pi\)
\(882\) −43.9872 −1.48112
\(883\) 53.2309 1.79136 0.895681 0.444696i \(-0.146688\pi\)
0.895681 + 0.444696i \(0.146688\pi\)
\(884\) 0.903609 0.0303917
\(885\) 17.5759 0.590807
\(886\) 33.5818 1.12820
\(887\) −29.9113 −1.00432 −0.502162 0.864774i \(-0.667462\pi\)
−0.502162 + 0.864774i \(0.667462\pi\)
\(888\) −27.5272 −0.923754
\(889\) 6.04960 0.202897
\(890\) −9.68315 −0.324580
\(891\) 4.89734 0.164067
\(892\) 10.8134 0.362058
\(893\) −2.63241 −0.0880902
\(894\) −37.0508 −1.23916
\(895\) 11.8959 0.397637
\(896\) 0.302669 0.0101115
\(897\) 1.74940 0.0584107
\(898\) −20.7822 −0.693510
\(899\) −13.9180 −0.464193
\(900\) 6.36721 0.212240
\(901\) 1.95978 0.0652899
\(902\) −3.29350 −0.109662
\(903\) 0.504929 0.0168030
\(904\) −10.2264 −0.340124
\(905\) −20.4579 −0.680042
\(906\) 62.9224 2.09046
\(907\) −5.96352 −0.198015 −0.0990077 0.995087i \(-0.531567\pi\)
−0.0990077 + 0.995087i \(0.531567\pi\)
\(908\) −27.9968 −0.929108
\(909\) −117.699 −3.90384
\(910\) −0.720154 −0.0238729
\(911\) −29.5363 −0.978581 −0.489290 0.872121i \(-0.662744\pi\)
−0.489290 + 0.872121i \(0.662744\pi\)
\(912\) −2.00089 −0.0662559
\(913\) 0.282402 0.00934615
\(914\) −1.56659 −0.0518183
\(915\) −6.43131 −0.212612
\(916\) −21.2086 −0.700753
\(917\) 2.80753 0.0927129
\(918\) 3.91379 0.129174
\(919\) 2.98568 0.0984886 0.0492443 0.998787i \(-0.484319\pi\)
0.0492443 + 0.998787i \(0.484319\pi\)
\(920\) 0.240229 0.00792012
\(921\) −36.5547 −1.20452
\(922\) −7.95973 −0.262140
\(923\) 23.2978 0.766858
\(924\) −0.364689 −0.0119974
\(925\) 8.99410 0.295724
\(926\) −40.2680 −1.32329
\(927\) 36.0172 1.18296
\(928\) −10.4861 −0.344224
\(929\) 18.5062 0.607170 0.303585 0.952804i \(-0.401816\pi\)
0.303585 + 0.952804i \(0.401816\pi\)
\(930\) −4.06226 −0.133207
\(931\) −4.51642 −0.148020
\(932\) −29.8509 −0.977797
\(933\) 50.4281 1.65094
\(934\) −34.5397 −1.13017
\(935\) −0.149511 −0.00488953
\(936\) −15.1498 −0.495187
\(937\) −24.6054 −0.803822 −0.401911 0.915679i \(-0.631654\pi\)
−0.401911 + 0.915679i \(0.631654\pi\)
\(938\) 4.87942 0.159319
\(939\) −7.41883 −0.242104
\(940\) −4.02658 −0.131332
\(941\) −21.6435 −0.705558 −0.352779 0.935707i \(-0.614763\pi\)
−0.352779 + 0.935707i \(0.614763\pi\)
\(942\) 22.8735 0.745259
\(943\) −2.00971 −0.0654451
\(944\) −5.74265 −0.186907
\(945\) −3.11919 −0.101467
\(946\) −0.214589 −0.00697690
\(947\) 43.9424 1.42794 0.713968 0.700178i \(-0.246896\pi\)
0.713968 + 0.700178i \(0.246896\pi\)
\(948\) −19.2807 −0.626209
\(949\) −31.3503 −1.01767
\(950\) 0.653758 0.0212107
\(951\) 91.6240 2.97111
\(952\) −0.114945 −0.00372539
\(953\) 52.7051 1.70728 0.853642 0.520860i \(-0.174389\pi\)
0.853642 + 0.520860i \(0.174389\pi\)
\(954\) −32.8575 −1.06380
\(955\) 9.68976 0.313553
\(956\) −9.17427 −0.296717
\(957\) 12.6349 0.408427
\(958\) 2.87871 0.0930071
\(959\) 0.110424 0.00356576
\(960\) −3.06059 −0.0987801
\(961\) −29.2383 −0.943172
\(962\) −21.4001 −0.689967
\(963\) 63.5234 2.04701
\(964\) 14.5645 0.469092
\(965\) −3.47297 −0.111799
\(966\) −0.222535 −0.00715995
\(967\) 30.6050 0.984190 0.492095 0.870542i \(-0.336231\pi\)
0.492095 + 0.870542i \(0.336231\pi\)
\(968\) −10.8450 −0.348572
\(969\) 0.759880 0.0244109
\(970\) −14.8895 −0.478072
\(971\) 0.654697 0.0210102 0.0105051 0.999945i \(-0.496656\pi\)
0.0105051 + 0.999945i \(0.496656\pi\)
\(972\) −7.15592 −0.229526
\(973\) −2.51391 −0.0805922
\(974\) −4.69576 −0.150462
\(975\) 7.28221 0.233217
\(976\) 2.10133 0.0672619
\(977\) 50.6299 1.61979 0.809896 0.586573i \(-0.199523\pi\)
0.809896 + 0.586573i \(0.199523\pi\)
\(978\) 6.79055 0.217138
\(979\) −3.81212 −0.121836
\(980\) −6.90839 −0.220680
\(981\) 102.082 3.25922
\(982\) 4.22768 0.134911
\(983\) −30.6793 −0.978516 −0.489258 0.872139i \(-0.662732\pi\)
−0.489258 + 0.872139i \(0.662732\pi\)
\(984\) 25.6043 0.816234
\(985\) −7.43346 −0.236850
\(986\) 3.98234 0.126823
\(987\) 3.73000 0.118727
\(988\) −1.55552 −0.0494876
\(989\) −0.130943 −0.00416375
\(990\) 2.50668 0.0796676
\(991\) 28.0894 0.892288 0.446144 0.894961i \(-0.352797\pi\)
0.446144 + 0.894961i \(0.352797\pi\)
\(992\) 1.32728 0.0421412
\(993\) 32.2748 1.02421
\(994\) −2.96364 −0.0940009
\(995\) 3.67524 0.116513
\(996\) −2.19545 −0.0695654
\(997\) 14.8062 0.468916 0.234458 0.972126i \(-0.424669\pi\)
0.234458 + 0.972126i \(0.424669\pi\)
\(998\) 33.4020 1.05732
\(999\) −92.6900 −2.93258
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 \(a_p\))