Properties

Label 6010.2.a.c.1.5
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 1.5
Root \(-0.981279\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.98128 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.98128 q^{6}\) \(-4.22080 q^{7}\) \(+1.00000 q^{8}\) \(+0.925466 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.98128 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.98128 q^{6}\) \(-4.22080 q^{7}\) \(+1.00000 q^{8}\) \(+0.925466 q^{9}\) \(+1.00000 q^{10}\) \(+0.530338 q^{11}\) \(-1.98128 q^{12}\) \(-0.100776 q^{13}\) \(-4.22080 q^{14}\) \(-1.98128 q^{15}\) \(+1.00000 q^{16}\) \(-3.01879 q^{17}\) \(+0.925466 q^{18}\) \(-1.24304 q^{19}\) \(+1.00000 q^{20}\) \(+8.36259 q^{21}\) \(+0.530338 q^{22}\) \(+8.77835 q^{23}\) \(-1.98128 q^{24}\) \(+1.00000 q^{25}\) \(-0.100776 q^{26}\) \(+4.11023 q^{27}\) \(-4.22080 q^{28}\) \(+1.18004 q^{29}\) \(-1.98128 q^{30}\) \(+3.73228 q^{31}\) \(+1.00000 q^{32}\) \(-1.05075 q^{33}\) \(-3.01879 q^{34}\) \(-4.22080 q^{35}\) \(+0.925466 q^{36}\) \(+5.95866 q^{37}\) \(-1.24304 q^{38}\) \(+0.199665 q^{39}\) \(+1.00000 q^{40}\) \(-10.4027 q^{41}\) \(+8.36259 q^{42}\) \(+9.82863 q^{43}\) \(+0.530338 q^{44}\) \(+0.925466 q^{45}\) \(+8.77835 q^{46}\) \(-2.60238 q^{47}\) \(-1.98128 q^{48}\) \(+10.8152 q^{49}\) \(+1.00000 q^{50}\) \(+5.98106 q^{51}\) \(-0.100776 q^{52}\) \(+6.07027 q^{53}\) \(+4.11023 q^{54}\) \(+0.530338 q^{55}\) \(-4.22080 q^{56}\) \(+2.46280 q^{57}\) \(+1.18004 q^{58}\) \(-11.8884 q^{59}\) \(-1.98128 q^{60}\) \(-9.97802 q^{61}\) \(+3.73228 q^{62}\) \(-3.90621 q^{63}\) \(+1.00000 q^{64}\) \(-0.100776 q^{65}\) \(-1.05075 q^{66}\) \(-7.26948 q^{67}\) \(-3.01879 q^{68}\) \(-17.3924 q^{69}\) \(-4.22080 q^{70}\) \(+15.6832 q^{71}\) \(+0.925466 q^{72}\) \(-15.2789 q^{73}\) \(+5.95866 q^{74}\) \(-1.98128 q^{75}\) \(-1.24304 q^{76}\) \(-2.23845 q^{77}\) \(+0.199665 q^{78}\) \(-8.86443 q^{79}\) \(+1.00000 q^{80}\) \(-10.9199 q^{81}\) \(-10.4027 q^{82}\) \(-10.8435 q^{83}\) \(+8.36259 q^{84}\) \(-3.01879 q^{85}\) \(+9.82863 q^{86}\) \(-2.33799 q^{87}\) \(+0.530338 q^{88}\) \(-12.3021 q^{89}\) \(+0.925466 q^{90}\) \(+0.425356 q^{91}\) \(+8.77835 q^{92}\) \(-7.39468 q^{93}\) \(-2.60238 q^{94}\) \(-1.24304 q^{95}\) \(-1.98128 q^{96}\) \(+9.19718 q^{97}\) \(+10.8152 q^{98}\) \(+0.490810 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.98128 −1.14389 −0.571946 0.820291i \(-0.693811\pi\)
−0.571946 + 0.820291i \(0.693811\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.98128 −0.808854
\(7\) −4.22080 −1.59531 −0.797657 0.603111i \(-0.793927\pi\)
−0.797657 + 0.603111i \(0.793927\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.925466 0.308489
\(10\) 1.00000 0.316228
\(11\) 0.530338 0.159903 0.0799515 0.996799i \(-0.474523\pi\)
0.0799515 + 0.996799i \(0.474523\pi\)
\(12\) −1.98128 −0.571946
\(13\) −0.100776 −0.0279502 −0.0139751 0.999902i \(-0.504449\pi\)
−0.0139751 + 0.999902i \(0.504449\pi\)
\(14\) −4.22080 −1.12806
\(15\) −1.98128 −0.511564
\(16\) 1.00000 0.250000
\(17\) −3.01879 −0.732163 −0.366082 0.930583i \(-0.619301\pi\)
−0.366082 + 0.930583i \(0.619301\pi\)
\(18\) 0.925466 0.218134
\(19\) −1.24304 −0.285172 −0.142586 0.989782i \(-0.545542\pi\)
−0.142586 + 0.989782i \(0.545542\pi\)
\(20\) 1.00000 0.223607
\(21\) 8.36259 1.82487
\(22\) 0.530338 0.113069
\(23\) 8.77835 1.83041 0.915206 0.402986i \(-0.132028\pi\)
0.915206 + 0.402986i \(0.132028\pi\)
\(24\) −1.98128 −0.404427
\(25\) 1.00000 0.200000
\(26\) −0.100776 −0.0197638
\(27\) 4.11023 0.791014
\(28\) −4.22080 −0.797657
\(29\) 1.18004 0.219128 0.109564 0.993980i \(-0.465054\pi\)
0.109564 + 0.993980i \(0.465054\pi\)
\(30\) −1.98128 −0.361730
\(31\) 3.73228 0.670337 0.335168 0.942158i \(-0.391207\pi\)
0.335168 + 0.942158i \(0.391207\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.05075 −0.182912
\(34\) −3.01879 −0.517717
\(35\) −4.22080 −0.713446
\(36\) 0.925466 0.154244
\(37\) 5.95866 0.979597 0.489798 0.871836i \(-0.337070\pi\)
0.489798 + 0.871836i \(0.337070\pi\)
\(38\) −1.24304 −0.201647
\(39\) 0.199665 0.0319720
\(40\) 1.00000 0.158114
\(41\) −10.4027 −1.62463 −0.812317 0.583216i \(-0.801794\pi\)
−0.812317 + 0.583216i \(0.801794\pi\)
\(42\) 8.36259 1.29038
\(43\) 9.82863 1.49885 0.749426 0.662088i \(-0.230329\pi\)
0.749426 + 0.662088i \(0.230329\pi\)
\(44\) 0.530338 0.0799515
\(45\) 0.925466 0.137960
\(46\) 8.77835 1.29430
\(47\) −2.60238 −0.379596 −0.189798 0.981823i \(-0.560783\pi\)
−0.189798 + 0.981823i \(0.560783\pi\)
\(48\) −1.98128 −0.285973
\(49\) 10.8152 1.54503
\(50\) 1.00000 0.141421
\(51\) 5.98106 0.837515
\(52\) −0.100776 −0.0139751
\(53\) 6.07027 0.833815 0.416908 0.908949i \(-0.363114\pi\)
0.416908 + 0.908949i \(0.363114\pi\)
\(54\) 4.11023 0.559332
\(55\) 0.530338 0.0715108
\(56\) −4.22080 −0.564029
\(57\) 2.46280 0.326206
\(58\) 1.18004 0.154947
\(59\) −11.8884 −1.54773 −0.773866 0.633349i \(-0.781680\pi\)
−0.773866 + 0.633349i \(0.781680\pi\)
\(60\) −1.98128 −0.255782
\(61\) −9.97802 −1.27755 −0.638777 0.769392i \(-0.720559\pi\)
−0.638777 + 0.769392i \(0.720559\pi\)
\(62\) 3.73228 0.474000
\(63\) −3.90621 −0.492136
\(64\) 1.00000 0.125000
\(65\) −0.100776 −0.0124997
\(66\) −1.05075 −0.129338
\(67\) −7.26948 −0.888109 −0.444054 0.896000i \(-0.646460\pi\)
−0.444054 + 0.896000i \(0.646460\pi\)
\(68\) −3.01879 −0.366082
\(69\) −17.3924 −2.09379
\(70\) −4.22080 −0.504483
\(71\) 15.6832 1.86125 0.930624 0.365976i \(-0.119265\pi\)
0.930624 + 0.365976i \(0.119265\pi\)
\(72\) 0.925466 0.109067
\(73\) −15.2789 −1.78826 −0.894128 0.447812i \(-0.852203\pi\)
−0.894128 + 0.447812i \(0.852203\pi\)
\(74\) 5.95866 0.692680
\(75\) −1.98128 −0.228778
\(76\) −1.24304 −0.142586
\(77\) −2.23845 −0.255096
\(78\) 0.199665 0.0226076
\(79\) −8.86443 −0.997326 −0.498663 0.866796i \(-0.666175\pi\)
−0.498663 + 0.866796i \(0.666175\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.9199 −1.21332
\(82\) −10.4027 −1.14879
\(83\) −10.8435 −1.19022 −0.595112 0.803643i \(-0.702892\pi\)
−0.595112 + 0.803643i \(0.702892\pi\)
\(84\) 8.36259 0.912433
\(85\) −3.01879 −0.327433
\(86\) 9.82863 1.05985
\(87\) −2.33799 −0.250659
\(88\) 0.530338 0.0565343
\(89\) −12.3021 −1.30402 −0.652012 0.758209i \(-0.726075\pi\)
−0.652012 + 0.758209i \(0.726075\pi\)
\(90\) 0.925466 0.0975527
\(91\) 0.425356 0.0445894
\(92\) 8.77835 0.915206
\(93\) −7.39468 −0.766793
\(94\) −2.60238 −0.268415
\(95\) −1.24304 −0.127533
\(96\) −1.98128 −0.202213
\(97\) 9.19718 0.933832 0.466916 0.884302i \(-0.345365\pi\)
0.466916 + 0.884302i \(0.345365\pi\)
\(98\) 10.8152 1.09250
\(99\) 0.490810 0.0493283
\(100\) 1.00000 0.100000
\(101\) −0.696428 −0.0692972 −0.0346486 0.999400i \(-0.511031\pi\)
−0.0346486 + 0.999400i \(0.511031\pi\)
\(102\) 5.98106 0.592213
\(103\) −0.109262 −0.0107659 −0.00538294 0.999986i \(-0.501713\pi\)
−0.00538294 + 0.999986i \(0.501713\pi\)
\(104\) −0.100776 −0.00988190
\(105\) 8.36259 0.816105
\(106\) 6.07027 0.589596
\(107\) −11.7250 −1.13350 −0.566749 0.823890i \(-0.691799\pi\)
−0.566749 + 0.823890i \(0.691799\pi\)
\(108\) 4.11023 0.395507
\(109\) −7.56174 −0.724283 −0.362141 0.932123i \(-0.617954\pi\)
−0.362141 + 0.932123i \(0.617954\pi\)
\(110\) 0.530338 0.0505658
\(111\) −11.8058 −1.12055
\(112\) −4.22080 −0.398828
\(113\) −9.90909 −0.932169 −0.466084 0.884740i \(-0.654336\pi\)
−0.466084 + 0.884740i \(0.654336\pi\)
\(114\) 2.46280 0.230662
\(115\) 8.77835 0.818585
\(116\) 1.18004 0.109564
\(117\) −0.0932647 −0.00862233
\(118\) −11.8884 −1.09441
\(119\) 12.7417 1.16803
\(120\) −1.98128 −0.180865
\(121\) −10.7187 −0.974431
\(122\) −9.97802 −0.903367
\(123\) 20.6107 1.85841
\(124\) 3.73228 0.335168
\(125\) 1.00000 0.0894427
\(126\) −3.90621 −0.347993
\(127\) 10.1010 0.896323 0.448162 0.893953i \(-0.352079\pi\)
0.448162 + 0.893953i \(0.352079\pi\)
\(128\) 1.00000 0.0883883
\(129\) −19.4733 −1.71453
\(130\) −0.100776 −0.00883864
\(131\) 15.1653 1.32499 0.662497 0.749064i \(-0.269497\pi\)
0.662497 + 0.749064i \(0.269497\pi\)
\(132\) −1.05075 −0.0914559
\(133\) 5.24661 0.454939
\(134\) −7.26948 −0.627988
\(135\) 4.11023 0.353752
\(136\) −3.01879 −0.258859
\(137\) 6.86463 0.586485 0.293242 0.956038i \(-0.405266\pi\)
0.293242 + 0.956038i \(0.405266\pi\)
\(138\) −17.3924 −1.48054
\(139\) −5.33765 −0.452734 −0.226367 0.974042i \(-0.572685\pi\)
−0.226367 + 0.974042i \(0.572685\pi\)
\(140\) −4.22080 −0.356723
\(141\) 5.15604 0.434217
\(142\) 15.6832 1.31610
\(143\) −0.0534454 −0.00446933
\(144\) 0.925466 0.0771222
\(145\) 1.18004 0.0979972
\(146\) −15.2789 −1.26449
\(147\) −21.4279 −1.76734
\(148\) 5.95866 0.489798
\(149\) 2.94235 0.241046 0.120523 0.992711i \(-0.461543\pi\)
0.120523 + 0.992711i \(0.461543\pi\)
\(150\) −1.98128 −0.161771
\(151\) 10.3478 0.842094 0.421047 0.907039i \(-0.361663\pi\)
0.421047 + 0.907039i \(0.361663\pi\)
\(152\) −1.24304 −0.100823
\(153\) −2.79378 −0.225864
\(154\) −2.23845 −0.180380
\(155\) 3.73228 0.299784
\(156\) 0.199665 0.0159860
\(157\) 10.7164 0.855264 0.427632 0.903953i \(-0.359348\pi\)
0.427632 + 0.903953i \(0.359348\pi\)
\(158\) −8.86443 −0.705216
\(159\) −12.0269 −0.953795
\(160\) 1.00000 0.0790569
\(161\) −37.0517 −2.92008
\(162\) −10.9199 −0.857949
\(163\) −0.373966 −0.0292913 −0.0146457 0.999893i \(-0.504662\pi\)
−0.0146457 + 0.999893i \(0.504662\pi\)
\(164\) −10.4027 −0.812317
\(165\) −1.05075 −0.0818006
\(166\) −10.8435 −0.841615
\(167\) −5.64002 −0.436438 −0.218219 0.975900i \(-0.570025\pi\)
−0.218219 + 0.975900i \(0.570025\pi\)
\(168\) 8.36259 0.645188
\(169\) −12.9898 −0.999219
\(170\) −3.01879 −0.231530
\(171\) −1.15039 −0.0879723
\(172\) 9.82863 0.749426
\(173\) −7.93500 −0.603287 −0.301643 0.953421i \(-0.597535\pi\)
−0.301643 + 0.953421i \(0.597535\pi\)
\(174\) −2.33799 −0.177243
\(175\) −4.22080 −0.319063
\(176\) 0.530338 0.0399758
\(177\) 23.5542 1.77044
\(178\) −12.3021 −0.922084
\(179\) −20.4271 −1.52679 −0.763395 0.645932i \(-0.776469\pi\)
−0.763395 + 0.645932i \(0.776469\pi\)
\(180\) 0.925466 0.0689802
\(181\) −16.1239 −1.19848 −0.599238 0.800571i \(-0.704530\pi\)
−0.599238 + 0.800571i \(0.704530\pi\)
\(182\) 0.425356 0.0315295
\(183\) 19.7692 1.46138
\(184\) 8.77835 0.647148
\(185\) 5.95866 0.438089
\(186\) −7.39468 −0.542204
\(187\) −1.60098 −0.117075
\(188\) −2.60238 −0.189798
\(189\) −17.3485 −1.26192
\(190\) −1.24304 −0.0901792
\(191\) −9.40217 −0.680317 −0.340158 0.940368i \(-0.610481\pi\)
−0.340158 + 0.940368i \(0.610481\pi\)
\(192\) −1.98128 −0.142986
\(193\) 10.0203 0.721276 0.360638 0.932706i \(-0.382559\pi\)
0.360638 + 0.932706i \(0.382559\pi\)
\(194\) 9.19718 0.660319
\(195\) 0.199665 0.0142983
\(196\) 10.8152 0.772513
\(197\) −3.88607 −0.276871 −0.138436 0.990371i \(-0.544207\pi\)
−0.138436 + 0.990371i \(0.544207\pi\)
\(198\) 0.490810 0.0348804
\(199\) −12.8979 −0.914310 −0.457155 0.889387i \(-0.651132\pi\)
−0.457155 + 0.889387i \(0.651132\pi\)
\(200\) 1.00000 0.0707107
\(201\) 14.4029 1.01590
\(202\) −0.696428 −0.0490005
\(203\) −4.98073 −0.349579
\(204\) 5.98106 0.418758
\(205\) −10.4027 −0.726559
\(206\) −0.109262 −0.00761262
\(207\) 8.12406 0.564661
\(208\) −0.100776 −0.00698756
\(209\) −0.659229 −0.0455998
\(210\) 8.36259 0.577073
\(211\) −18.4433 −1.26969 −0.634843 0.772641i \(-0.718935\pi\)
−0.634843 + 0.772641i \(0.718935\pi\)
\(212\) 6.07027 0.416908
\(213\) −31.0727 −2.12907
\(214\) −11.7250 −0.801504
\(215\) 9.82863 0.670307
\(216\) 4.11023 0.279666
\(217\) −15.7532 −1.06940
\(218\) −7.56174 −0.512145
\(219\) 30.2717 2.04557
\(220\) 0.530338 0.0357554
\(221\) 0.304221 0.0204641
\(222\) −11.8058 −0.792351
\(223\) 22.0052 1.47358 0.736789 0.676122i \(-0.236341\pi\)
0.736789 + 0.676122i \(0.236341\pi\)
\(224\) −4.22080 −0.282014
\(225\) 0.925466 0.0616977
\(226\) −9.90909 −0.659143
\(227\) −14.6503 −0.972376 −0.486188 0.873854i \(-0.661613\pi\)
−0.486188 + 0.873854i \(0.661613\pi\)
\(228\) 2.46280 0.163103
\(229\) −17.3362 −1.14561 −0.572805 0.819692i \(-0.694145\pi\)
−0.572805 + 0.819692i \(0.694145\pi\)
\(230\) 8.77835 0.578827
\(231\) 4.43500 0.291802
\(232\) 1.18004 0.0774736
\(233\) 12.0048 0.786459 0.393230 0.919440i \(-0.371358\pi\)
0.393230 + 0.919440i \(0.371358\pi\)
\(234\) −0.0932647 −0.00609691
\(235\) −2.60238 −0.169761
\(236\) −11.8884 −0.773866
\(237\) 17.5629 1.14083
\(238\) 12.7417 0.825922
\(239\) 27.5016 1.77893 0.889467 0.457000i \(-0.151076\pi\)
0.889467 + 0.457000i \(0.151076\pi\)
\(240\) −1.98128 −0.127891
\(241\) −13.2419 −0.852983 −0.426491 0.904492i \(-0.640251\pi\)
−0.426491 + 0.904492i \(0.640251\pi\)
\(242\) −10.7187 −0.689027
\(243\) 9.30470 0.596897
\(244\) −9.97802 −0.638777
\(245\) 10.8152 0.690957
\(246\) 20.6107 1.31409
\(247\) 0.125268 0.00797062
\(248\) 3.73228 0.237000
\(249\) 21.4839 1.36149
\(250\) 1.00000 0.0632456
\(251\) −3.04529 −0.192217 −0.0961084 0.995371i \(-0.530640\pi\)
−0.0961084 + 0.995371i \(0.530640\pi\)
\(252\) −3.90621 −0.246068
\(253\) 4.65549 0.292688
\(254\) 10.1010 0.633796
\(255\) 5.98106 0.374548
\(256\) 1.00000 0.0625000
\(257\) −17.9678 −1.12080 −0.560401 0.828222i \(-0.689353\pi\)
−0.560401 + 0.828222i \(0.689353\pi\)
\(258\) −19.4733 −1.21235
\(259\) −25.1503 −1.56276
\(260\) −0.100776 −0.00624986
\(261\) 1.09209 0.0675986
\(262\) 15.1653 0.936913
\(263\) 0.207779 0.0128122 0.00640610 0.999979i \(-0.497961\pi\)
0.00640610 + 0.999979i \(0.497961\pi\)
\(264\) −1.05075 −0.0646691
\(265\) 6.07027 0.372894
\(266\) 5.24661 0.321690
\(267\) 24.3740 1.49166
\(268\) −7.26948 −0.444054
\(269\) 32.4104 1.97610 0.988048 0.154148i \(-0.0492633\pi\)
0.988048 + 0.154148i \(0.0492633\pi\)
\(270\) 4.11023 0.250141
\(271\) 2.36018 0.143371 0.0716853 0.997427i \(-0.477162\pi\)
0.0716853 + 0.997427i \(0.477162\pi\)
\(272\) −3.01879 −0.183041
\(273\) −0.842748 −0.0510054
\(274\) 6.86463 0.414707
\(275\) 0.530338 0.0319806
\(276\) −17.3924 −1.04690
\(277\) −7.91946 −0.475834 −0.237917 0.971285i \(-0.576465\pi\)
−0.237917 + 0.971285i \(0.576465\pi\)
\(278\) −5.33765 −0.320131
\(279\) 3.45409 0.206791
\(280\) −4.22080 −0.252241
\(281\) 15.4693 0.922820 0.461410 0.887187i \(-0.347344\pi\)
0.461410 + 0.887187i \(0.347344\pi\)
\(282\) 5.15604 0.307038
\(283\) 30.3044 1.80141 0.900706 0.434429i \(-0.143050\pi\)
0.900706 + 0.434429i \(0.143050\pi\)
\(284\) 15.6832 0.930624
\(285\) 2.46280 0.145884
\(286\) −0.0534454 −0.00316029
\(287\) 43.9079 2.59180
\(288\) 0.925466 0.0545336
\(289\) −7.88693 −0.463937
\(290\) 1.18004 0.0692945
\(291\) −18.2222 −1.06820
\(292\) −15.2789 −0.894128
\(293\) 11.2466 0.657034 0.328517 0.944498i \(-0.393451\pi\)
0.328517 + 0.944498i \(0.393451\pi\)
\(294\) −21.4279 −1.24970
\(295\) −11.8884 −0.692167
\(296\) 5.95866 0.346340
\(297\) 2.17981 0.126486
\(298\) 2.94235 0.170446
\(299\) −0.884647 −0.0511604
\(300\) −1.98128 −0.114389
\(301\) −41.4847 −2.39114
\(302\) 10.3478 0.595451
\(303\) 1.37982 0.0792685
\(304\) −1.24304 −0.0712929
\(305\) −9.97802 −0.571340
\(306\) −2.79378 −0.159710
\(307\) −13.5263 −0.771986 −0.385993 0.922502i \(-0.626141\pi\)
−0.385993 + 0.922502i \(0.626141\pi\)
\(308\) −2.23845 −0.127548
\(309\) 0.216478 0.0123150
\(310\) 3.73228 0.211979
\(311\) −19.4234 −1.10140 −0.550699 0.834704i \(-0.685639\pi\)
−0.550699 + 0.834704i \(0.685639\pi\)
\(312\) 0.199665 0.0113038
\(313\) −24.8018 −1.40188 −0.700942 0.713219i \(-0.747237\pi\)
−0.700942 + 0.713219i \(0.747237\pi\)
\(314\) 10.7164 0.604763
\(315\) −3.90621 −0.220090
\(316\) −8.86443 −0.498663
\(317\) −18.3022 −1.02795 −0.513977 0.857804i \(-0.671828\pi\)
−0.513977 + 0.857804i \(0.671828\pi\)
\(318\) −12.0269 −0.674435
\(319\) 0.625822 0.0350393
\(320\) 1.00000 0.0559017
\(321\) 23.2305 1.29660
\(322\) −37.0517 −2.06481
\(323\) 3.75246 0.208792
\(324\) −10.9199 −0.606662
\(325\) −0.100776 −0.00559005
\(326\) −0.373966 −0.0207121
\(327\) 14.9819 0.828501
\(328\) −10.4027 −0.574395
\(329\) 10.9841 0.605575
\(330\) −1.05075 −0.0578418
\(331\) −8.11182 −0.445866 −0.222933 0.974834i \(-0.571563\pi\)
−0.222933 + 0.974834i \(0.571563\pi\)
\(332\) −10.8435 −0.595112
\(333\) 5.51453 0.302195
\(334\) −5.64002 −0.308608
\(335\) −7.26948 −0.397174
\(336\) 8.36259 0.456217
\(337\) −5.34930 −0.291395 −0.145697 0.989329i \(-0.546543\pi\)
−0.145697 + 0.989329i \(0.546543\pi\)
\(338\) −12.9898 −0.706554
\(339\) 19.6327 1.06630
\(340\) −3.01879 −0.163717
\(341\) 1.97937 0.107189
\(342\) −1.15039 −0.0622058
\(343\) −16.1031 −0.869488
\(344\) 9.82863 0.529924
\(345\) −17.3924 −0.936373
\(346\) −7.93500 −0.426588
\(347\) −5.05294 −0.271256 −0.135628 0.990760i \(-0.543305\pi\)
−0.135628 + 0.990760i \(0.543305\pi\)
\(348\) −2.33799 −0.125330
\(349\) −21.1201 −1.13053 −0.565267 0.824908i \(-0.691227\pi\)
−0.565267 + 0.824908i \(0.691227\pi\)
\(350\) −4.22080 −0.225611
\(351\) −0.414213 −0.0221090
\(352\) 0.530338 0.0282671
\(353\) 18.4134 0.980044 0.490022 0.871710i \(-0.336989\pi\)
0.490022 + 0.871710i \(0.336989\pi\)
\(354\) 23.5542 1.25189
\(355\) 15.6832 0.832376
\(356\) −12.3021 −0.652012
\(357\) −25.2449 −1.33610
\(358\) −20.4271 −1.07960
\(359\) −2.92099 −0.154164 −0.0770819 0.997025i \(-0.524560\pi\)
−0.0770819 + 0.997025i \(0.524560\pi\)
\(360\) 0.925466 0.0487763
\(361\) −17.4549 −0.918677
\(362\) −16.1239 −0.847451
\(363\) 21.2368 1.11464
\(364\) 0.425356 0.0222947
\(365\) −15.2789 −0.799732
\(366\) 19.7692 1.03335
\(367\) 13.5315 0.706339 0.353169 0.935559i \(-0.385104\pi\)
0.353169 + 0.935559i \(0.385104\pi\)
\(368\) 8.77835 0.457603
\(369\) −9.62738 −0.501181
\(370\) 5.95866 0.309776
\(371\) −25.6214 −1.33020
\(372\) −7.39468 −0.383396
\(373\) 11.7727 0.609569 0.304785 0.952421i \(-0.401416\pi\)
0.304785 + 0.952421i \(0.401416\pi\)
\(374\) −1.60098 −0.0827846
\(375\) −1.98128 −0.102313
\(376\) −2.60238 −0.134207
\(377\) −0.118920 −0.00612469
\(378\) −17.3485 −0.892309
\(379\) 16.1520 0.829674 0.414837 0.909896i \(-0.363839\pi\)
0.414837 + 0.909896i \(0.363839\pi\)
\(380\) −1.24304 −0.0637664
\(381\) −20.0130 −1.02530
\(382\) −9.40217 −0.481057
\(383\) 5.99445 0.306302 0.153151 0.988203i \(-0.451058\pi\)
0.153151 + 0.988203i \(0.451058\pi\)
\(384\) −1.98128 −0.101107
\(385\) −2.23845 −0.114082
\(386\) 10.0203 0.510019
\(387\) 9.09606 0.462379
\(388\) 9.19718 0.466916
\(389\) 7.07504 0.358719 0.179360 0.983784i \(-0.442597\pi\)
0.179360 + 0.983784i \(0.442597\pi\)
\(390\) 0.199665 0.0101104
\(391\) −26.4999 −1.34016
\(392\) 10.8152 0.546249
\(393\) −30.0466 −1.51565
\(394\) −3.88607 −0.195778
\(395\) −8.86443 −0.446018
\(396\) 0.490810 0.0246641
\(397\) 1.12705 0.0565649 0.0282824 0.999600i \(-0.490996\pi\)
0.0282824 + 0.999600i \(0.490996\pi\)
\(398\) −12.8979 −0.646515
\(399\) −10.3950 −0.520400
\(400\) 1.00000 0.0500000
\(401\) −18.1263 −0.905184 −0.452592 0.891718i \(-0.649501\pi\)
−0.452592 + 0.891718i \(0.649501\pi\)
\(402\) 14.4029 0.718350
\(403\) −0.376124 −0.0187361
\(404\) −0.696428 −0.0346486
\(405\) −10.9199 −0.542615
\(406\) −4.98073 −0.247189
\(407\) 3.16010 0.156641
\(408\) 5.98106 0.296106
\(409\) −8.94909 −0.442504 −0.221252 0.975217i \(-0.571014\pi\)
−0.221252 + 0.975217i \(0.571014\pi\)
\(410\) −10.4027 −0.513755
\(411\) −13.6007 −0.670875
\(412\) −0.109262 −0.00538294
\(413\) 50.1784 2.46912
\(414\) 8.12406 0.399276
\(415\) −10.8435 −0.532284
\(416\) −0.100776 −0.00494095
\(417\) 10.5754 0.517878
\(418\) −0.659229 −0.0322440
\(419\) 18.7687 0.916911 0.458456 0.888717i \(-0.348403\pi\)
0.458456 + 0.888717i \(0.348403\pi\)
\(420\) 8.36259 0.408053
\(421\) −15.5120 −0.756010 −0.378005 0.925803i \(-0.623390\pi\)
−0.378005 + 0.925803i \(0.623390\pi\)
\(422\) −18.4433 −0.897804
\(423\) −2.40841 −0.117101
\(424\) 6.07027 0.294798
\(425\) −3.01879 −0.146433
\(426\) −31.0727 −1.50548
\(427\) 42.1153 2.03810
\(428\) −11.7250 −0.566749
\(429\) 0.105890 0.00511243
\(430\) 9.82863 0.473979
\(431\) 6.46497 0.311407 0.155703 0.987804i \(-0.450236\pi\)
0.155703 + 0.987804i \(0.450236\pi\)
\(432\) 4.11023 0.197754
\(433\) −20.4238 −0.981507 −0.490754 0.871298i \(-0.663278\pi\)
−0.490754 + 0.871298i \(0.663278\pi\)
\(434\) −15.7532 −0.756178
\(435\) −2.33799 −0.112098
\(436\) −7.56174 −0.362141
\(437\) −10.9118 −0.521982
\(438\) 30.2717 1.44644
\(439\) 18.6018 0.887816 0.443908 0.896072i \(-0.353592\pi\)
0.443908 + 0.896072i \(0.353592\pi\)
\(440\) 0.530338 0.0252829
\(441\) 10.0091 0.476623
\(442\) 0.304221 0.0144703
\(443\) 12.2738 0.583147 0.291573 0.956548i \(-0.405821\pi\)
0.291573 + 0.956548i \(0.405821\pi\)
\(444\) −11.8058 −0.560276
\(445\) −12.3021 −0.583177
\(446\) 22.0052 1.04198
\(447\) −5.82961 −0.275731
\(448\) −4.22080 −0.199414
\(449\) −27.2626 −1.28660 −0.643301 0.765613i \(-0.722436\pi\)
−0.643301 + 0.765613i \(0.722436\pi\)
\(450\) 0.925466 0.0436269
\(451\) −5.51697 −0.259784
\(452\) −9.90909 −0.466084
\(453\) −20.5019 −0.963265
\(454\) −14.6503 −0.687573
\(455\) 0.425356 0.0199410
\(456\) 2.46280 0.115331
\(457\) −19.2314 −0.899606 −0.449803 0.893128i \(-0.648506\pi\)
−0.449803 + 0.893128i \(0.648506\pi\)
\(458\) −17.3362 −0.810069
\(459\) −12.4079 −0.579151
\(460\) 8.77835 0.409293
\(461\) 11.5699 0.538862 0.269431 0.963020i \(-0.413164\pi\)
0.269431 + 0.963020i \(0.413164\pi\)
\(462\) 4.43500 0.206335
\(463\) −0.00174954 −8.13082e−5 0 −4.06541e−5 1.00000i \(-0.500013\pi\)
−4.06541e−5 1.00000i \(0.500013\pi\)
\(464\) 1.18004 0.0547821
\(465\) −7.39468 −0.342920
\(466\) 12.0048 0.556111
\(467\) −32.4183 −1.50014 −0.750070 0.661358i \(-0.769980\pi\)
−0.750070 + 0.661358i \(0.769980\pi\)
\(468\) −0.0932647 −0.00431116
\(469\) 30.6831 1.41681
\(470\) −2.60238 −0.120039
\(471\) −21.2322 −0.978329
\(472\) −11.8884 −0.547206
\(473\) 5.21250 0.239671
\(474\) 17.5629 0.806691
\(475\) −1.24304 −0.0570344
\(476\) 12.7417 0.584015
\(477\) 5.61783 0.257223
\(478\) 27.5016 1.25790
\(479\) 6.16045 0.281478 0.140739 0.990047i \(-0.455052\pi\)
0.140739 + 0.990047i \(0.455052\pi\)
\(480\) −1.98128 −0.0904326
\(481\) −0.600489 −0.0273800
\(482\) −13.2419 −0.603150
\(483\) 73.4097 3.34026
\(484\) −10.7187 −0.487216
\(485\) 9.19718 0.417622
\(486\) 9.30470 0.422070
\(487\) −24.9602 −1.13105 −0.565527 0.824730i \(-0.691327\pi\)
−0.565527 + 0.824730i \(0.691327\pi\)
\(488\) −9.97802 −0.451684
\(489\) 0.740932 0.0335061
\(490\) 10.8152 0.488580
\(491\) 15.8961 0.717382 0.358691 0.933456i \(-0.383223\pi\)
0.358691 + 0.933456i \(0.383223\pi\)
\(492\) 20.6107 0.929203
\(493\) −3.56230 −0.160438
\(494\) 0.125268 0.00563608
\(495\) 0.490810 0.0220603
\(496\) 3.73228 0.167584
\(497\) −66.1955 −2.96928
\(498\) 21.4839 0.962717
\(499\) −3.29567 −0.147535 −0.0737673 0.997275i \(-0.523502\pi\)
−0.0737673 + 0.997275i \(0.523502\pi\)
\(500\) 1.00000 0.0447214
\(501\) 11.1745 0.499238
\(502\) −3.04529 −0.135918
\(503\) 25.1867 1.12302 0.561509 0.827471i \(-0.310221\pi\)
0.561509 + 0.827471i \(0.310221\pi\)
\(504\) −3.90621 −0.173996
\(505\) −0.696428 −0.0309907
\(506\) 4.65549 0.206962
\(507\) 25.7365 1.14300
\(508\) 10.1010 0.448162
\(509\) 20.5352 0.910207 0.455104 0.890438i \(-0.349602\pi\)
0.455104 + 0.890438i \(0.349602\pi\)
\(510\) 5.98106 0.264846
\(511\) 64.4891 2.85283
\(512\) 1.00000 0.0441942
\(513\) −5.10916 −0.225575
\(514\) −17.9678 −0.792526
\(515\) −0.109262 −0.00481464
\(516\) −19.4733 −0.857263
\(517\) −1.38014 −0.0606986
\(518\) −25.1503 −1.10504
\(519\) 15.7215 0.690095
\(520\) −0.100776 −0.00441932
\(521\) −0.894877 −0.0392053 −0.0196026 0.999808i \(-0.506240\pi\)
−0.0196026 + 0.999808i \(0.506240\pi\)
\(522\) 1.09209 0.0477995
\(523\) 22.9521 1.00362 0.501812 0.864977i \(-0.332667\pi\)
0.501812 + 0.864977i \(0.332667\pi\)
\(524\) 15.1653 0.662497
\(525\) 8.36259 0.364973
\(526\) 0.207779 0.00905959
\(527\) −11.2669 −0.490796
\(528\) −1.05075 −0.0457279
\(529\) 54.0594 2.35041
\(530\) 6.07027 0.263676
\(531\) −11.0023 −0.477458
\(532\) 5.24661 0.227469
\(533\) 1.04835 0.0454089
\(534\) 24.3740 1.05476
\(535\) −11.7250 −0.506916
\(536\) −7.26948 −0.313994
\(537\) 40.4717 1.74648
\(538\) 32.4104 1.39731
\(539\) 5.73571 0.247054
\(540\) 4.11023 0.176876
\(541\) −34.2710 −1.47343 −0.736714 0.676205i \(-0.763623\pi\)
−0.736714 + 0.676205i \(0.763623\pi\)
\(542\) 2.36018 0.101378
\(543\) 31.9459 1.37093
\(544\) −3.01879 −0.129429
\(545\) −7.56174 −0.323909
\(546\) −0.842748 −0.0360663
\(547\) −28.2684 −1.20867 −0.604334 0.796731i \(-0.706561\pi\)
−0.604334 + 0.796731i \(0.706561\pi\)
\(548\) 6.86463 0.293242
\(549\) −9.23431 −0.394111
\(550\) 0.530338 0.0226137
\(551\) −1.46683 −0.0624893
\(552\) −17.3924 −0.740268
\(553\) 37.4150 1.59105
\(554\) −7.91946 −0.336466
\(555\) −11.8058 −0.501126
\(556\) −5.33765 −0.226367
\(557\) −32.4389 −1.37448 −0.687241 0.726430i \(-0.741178\pi\)
−0.687241 + 0.726430i \(0.741178\pi\)
\(558\) 3.45409 0.146223
\(559\) −0.990490 −0.0418933
\(560\) −4.22080 −0.178362
\(561\) 3.17198 0.133921
\(562\) 15.4693 0.652532
\(563\) −19.8704 −0.837437 −0.418718 0.908116i \(-0.637521\pi\)
−0.418718 + 0.908116i \(0.637521\pi\)
\(564\) 5.15604 0.217108
\(565\) −9.90909 −0.416878
\(566\) 30.3044 1.27379
\(567\) 46.0908 1.93563
\(568\) 15.6832 0.658051
\(569\) −19.7541 −0.828136 −0.414068 0.910246i \(-0.635893\pi\)
−0.414068 + 0.910246i \(0.635893\pi\)
\(570\) 2.46280 0.103155
\(571\) −44.2621 −1.85231 −0.926156 0.377140i \(-0.876908\pi\)
−0.926156 + 0.377140i \(0.876908\pi\)
\(572\) −0.0534454 −0.00223466
\(573\) 18.6283 0.778209
\(574\) 43.9079 1.83268
\(575\) 8.77835 0.366082
\(576\) 0.925466 0.0385611
\(577\) −46.1403 −1.92085 −0.960423 0.278544i \(-0.910148\pi\)
−0.960423 + 0.278544i \(0.910148\pi\)
\(578\) −7.88693 −0.328053
\(579\) −19.8530 −0.825062
\(580\) 1.18004 0.0489986
\(581\) 45.7681 1.89878
\(582\) −18.2222 −0.755333
\(583\) 3.21930 0.133330
\(584\) −15.2789 −0.632244
\(585\) −0.0932647 −0.00385602
\(586\) 11.2466 0.464593
\(587\) −10.3313 −0.426419 −0.213210 0.977006i \(-0.568392\pi\)
−0.213210 + 0.977006i \(0.568392\pi\)
\(588\) −21.4279 −0.883672
\(589\) −4.63935 −0.191161
\(590\) −11.8884 −0.489436
\(591\) 7.69939 0.316711
\(592\) 5.95866 0.244899
\(593\) −14.6996 −0.603640 −0.301820 0.953365i \(-0.597594\pi\)
−0.301820 + 0.953365i \(0.597594\pi\)
\(594\) 2.17981 0.0894388
\(595\) 12.7417 0.522359
\(596\) 2.94235 0.120523
\(597\) 25.5544 1.04587
\(598\) −0.884647 −0.0361759
\(599\) −16.2736 −0.664922 −0.332461 0.943117i \(-0.607879\pi\)
−0.332461 + 0.943117i \(0.607879\pi\)
\(600\) −1.98128 −0.0808854
\(601\) −1.00000 −0.0407909
\(602\) −41.4847 −1.69079
\(603\) −6.72766 −0.273971
\(604\) 10.3478 0.421047
\(605\) −10.7187 −0.435779
\(606\) 1.37982 0.0560513
\(607\) 8.74412 0.354913 0.177456 0.984129i \(-0.443213\pi\)
0.177456 + 0.984129i \(0.443213\pi\)
\(608\) −1.24304 −0.0504117
\(609\) 9.86822 0.399880
\(610\) −9.97802 −0.403998
\(611\) 0.262257 0.0106098
\(612\) −2.79378 −0.112932
\(613\) 30.3287 1.22497 0.612483 0.790484i \(-0.290171\pi\)
0.612483 + 0.790484i \(0.290171\pi\)
\(614\) −13.5263 −0.545877
\(615\) 20.6107 0.831105
\(616\) −2.23845 −0.0901899
\(617\) 21.6643 0.872172 0.436086 0.899905i \(-0.356364\pi\)
0.436086 + 0.899905i \(0.356364\pi\)
\(618\) 0.216478 0.00870801
\(619\) −8.68872 −0.349229 −0.174615 0.984637i \(-0.555868\pi\)
−0.174615 + 0.984637i \(0.555868\pi\)
\(620\) 3.73228 0.149892
\(621\) 36.0810 1.44788
\(622\) −19.4234 −0.778806
\(623\) 51.9249 2.08033
\(624\) 0.199665 0.00799301
\(625\) 1.00000 0.0400000
\(626\) −24.8018 −0.991281
\(627\) 1.30612 0.0521613
\(628\) 10.7164 0.427632
\(629\) −17.9879 −0.717225
\(630\) −3.90621 −0.155627
\(631\) 20.6798 0.823248 0.411624 0.911354i \(-0.364962\pi\)
0.411624 + 0.911354i \(0.364962\pi\)
\(632\) −8.86443 −0.352608
\(633\) 36.5412 1.45238
\(634\) −18.3022 −0.726874
\(635\) 10.1010 0.400848
\(636\) −12.0269 −0.476897
\(637\) −1.08991 −0.0431838
\(638\) 0.625822 0.0247765
\(639\) 14.5142 0.574174
\(640\) 1.00000 0.0395285
\(641\) −0.615269 −0.0243016 −0.0121508 0.999926i \(-0.503868\pi\)
−0.0121508 + 0.999926i \(0.503868\pi\)
\(642\) 23.2305 0.916834
\(643\) −8.45656 −0.333494 −0.166747 0.986000i \(-0.553326\pi\)
−0.166747 + 0.986000i \(0.553326\pi\)
\(644\) −37.0517 −1.46004
\(645\) −19.4733 −0.766759
\(646\) 3.75246 0.147638
\(647\) 33.2576 1.30749 0.653745 0.756715i \(-0.273197\pi\)
0.653745 + 0.756715i \(0.273197\pi\)
\(648\) −10.9199 −0.428975
\(649\) −6.30485 −0.247487
\(650\) −0.100776 −0.00395276
\(651\) 31.2115 1.22328
\(652\) −0.373966 −0.0146457
\(653\) −28.3789 −1.11055 −0.555277 0.831666i \(-0.687388\pi\)
−0.555277 + 0.831666i \(0.687388\pi\)
\(654\) 14.9819 0.585839
\(655\) 15.1653 0.592556
\(656\) −10.4027 −0.406159
\(657\) −14.1401 −0.551656
\(658\) 10.9841 0.428206
\(659\) −33.8124 −1.31714 −0.658572 0.752518i \(-0.728839\pi\)
−0.658572 + 0.752518i \(0.728839\pi\)
\(660\) −1.05075 −0.0409003
\(661\) −34.6501 −1.34773 −0.673866 0.738853i \(-0.735368\pi\)
−0.673866 + 0.738853i \(0.735368\pi\)
\(662\) −8.11182 −0.315275
\(663\) −0.602747 −0.0234087
\(664\) −10.8435 −0.420808
\(665\) 5.24661 0.203455
\(666\) 5.51453 0.213684
\(667\) 10.3588 0.401095
\(668\) −5.64002 −0.218219
\(669\) −43.5985 −1.68562
\(670\) −7.26948 −0.280845
\(671\) −5.29173 −0.204285
\(672\) 8.36259 0.322594
\(673\) 33.9018 1.30682 0.653409 0.757005i \(-0.273338\pi\)
0.653409 + 0.757005i \(0.273338\pi\)
\(674\) −5.34930 −0.206047
\(675\) 4.11023 0.158203
\(676\) −12.9898 −0.499609
\(677\) −8.49652 −0.326548 −0.163274 0.986581i \(-0.552205\pi\)
−0.163274 + 0.986581i \(0.552205\pi\)
\(678\) 19.6327 0.753988
\(679\) −38.8195 −1.48975
\(680\) −3.01879 −0.115765
\(681\) 29.0264 1.11229
\(682\) 1.97937 0.0757940
\(683\) 42.8371 1.63912 0.819558 0.572996i \(-0.194219\pi\)
0.819558 + 0.572996i \(0.194219\pi\)
\(684\) −1.15039 −0.0439861
\(685\) 6.86463 0.262284
\(686\) −16.1031 −0.614821
\(687\) 34.3479 1.31045
\(688\) 9.82863 0.374713
\(689\) −0.611737 −0.0233053
\(690\) −17.3924 −0.662116
\(691\) 24.9210 0.948040 0.474020 0.880514i \(-0.342802\pi\)
0.474020 + 0.880514i \(0.342802\pi\)
\(692\) −7.93500 −0.301643
\(693\) −2.07161 −0.0786941
\(694\) −5.05294 −0.191807
\(695\) −5.33765 −0.202469
\(696\) −2.33799 −0.0886214
\(697\) 31.4036 1.18950
\(698\) −21.1201 −0.799409
\(699\) −23.7848 −0.899624
\(700\) −4.22080 −0.159531
\(701\) 12.9906 0.490647 0.245323 0.969441i \(-0.421106\pi\)
0.245323 + 0.969441i \(0.421106\pi\)
\(702\) −0.414213 −0.0156334
\(703\) −7.40682 −0.279353
\(704\) 0.530338 0.0199879
\(705\) 5.15604 0.194188
\(706\) 18.4134 0.692996
\(707\) 2.93949 0.110551
\(708\) 23.5542 0.885220
\(709\) 35.0433 1.31608 0.658039 0.752984i \(-0.271386\pi\)
0.658039 + 0.752984i \(0.271386\pi\)
\(710\) 15.6832 0.588578
\(711\) −8.20372 −0.307664
\(712\) −12.3021 −0.461042
\(713\) 32.7632 1.22699
\(714\) −25.2449 −0.944765
\(715\) −0.0534454 −0.00199874
\(716\) −20.4271 −0.763395
\(717\) −54.4884 −2.03491
\(718\) −2.92099 −0.109010
\(719\) −16.5186 −0.616039 −0.308019 0.951380i \(-0.599666\pi\)
−0.308019 + 0.951380i \(0.599666\pi\)
\(720\) 0.925466 0.0344901
\(721\) 0.461172 0.0171749
\(722\) −17.4549 −0.649603
\(723\) 26.2358 0.975720
\(724\) −16.1239 −0.599238
\(725\) 1.18004 0.0438257
\(726\) 21.2368 0.788172
\(727\) 32.1976 1.19414 0.597072 0.802187i \(-0.296331\pi\)
0.597072 + 0.802187i \(0.296331\pi\)
\(728\) 0.425356 0.0157647
\(729\) 14.3245 0.530538
\(730\) −15.2789 −0.565496
\(731\) −29.6705 −1.09740
\(732\) 19.7692 0.730692
\(733\) −48.4593 −1.78989 −0.894943 0.446181i \(-0.852784\pi\)
−0.894943 + 0.446181i \(0.852784\pi\)
\(734\) 13.5315 0.499457
\(735\) −21.4279 −0.790380
\(736\) 8.77835 0.323574
\(737\) −3.85529 −0.142011
\(738\) −9.62738 −0.354389
\(739\) 29.2098 1.07450 0.537250 0.843423i \(-0.319463\pi\)
0.537250 + 0.843423i \(0.319463\pi\)
\(740\) 5.95866 0.219045
\(741\) −0.248191 −0.00911752
\(742\) −25.6214 −0.940591
\(743\) −32.6377 −1.19736 −0.598681 0.800988i \(-0.704308\pi\)
−0.598681 + 0.800988i \(0.704308\pi\)
\(744\) −7.39468 −0.271102
\(745\) 2.94235 0.107799
\(746\) 11.7727 0.431031
\(747\) −10.0352 −0.367170
\(748\) −1.60098 −0.0585375
\(749\) 49.4889 1.80829
\(750\) −1.98128 −0.0723461
\(751\) 38.0341 1.38789 0.693943 0.720030i \(-0.255872\pi\)
0.693943 + 0.720030i \(0.255872\pi\)
\(752\) −2.60238 −0.0948990
\(753\) 6.03356 0.219875
\(754\) −0.118920 −0.00433081
\(755\) 10.3478 0.376596
\(756\) −17.3485 −0.630958
\(757\) −13.0065 −0.472730 −0.236365 0.971664i \(-0.575956\pi\)
−0.236365 + 0.971664i \(0.575956\pi\)
\(758\) 16.1520 0.586668
\(759\) −9.22383 −0.334804
\(760\) −1.24304 −0.0450896
\(761\) −11.1052 −0.402564 −0.201282 0.979533i \(-0.564511\pi\)
−0.201282 + 0.979533i \(0.564511\pi\)
\(762\) −20.0130 −0.724994
\(763\) 31.9166 1.15546
\(764\) −9.40217 −0.340158
\(765\) −2.79378 −0.101009
\(766\) 5.99445 0.216588
\(767\) 1.19806 0.0432595
\(768\) −1.98128 −0.0714932
\(769\) 38.0655 1.37268 0.686338 0.727283i \(-0.259217\pi\)
0.686338 + 0.727283i \(0.259217\pi\)
\(770\) −2.23845 −0.0806683
\(771\) 35.5992 1.28208
\(772\) 10.0203 0.360638
\(773\) 13.3518 0.480231 0.240115 0.970744i \(-0.422815\pi\)
0.240115 + 0.970744i \(0.422815\pi\)
\(774\) 9.09606 0.326951
\(775\) 3.73228 0.134067
\(776\) 9.19718 0.330159
\(777\) 49.8298 1.78763
\(778\) 7.07504 0.253653
\(779\) 12.9310 0.463300
\(780\) 0.199665 0.00714917
\(781\) 8.31738 0.297619
\(782\) −26.4999 −0.947636
\(783\) 4.85025 0.173334
\(784\) 10.8152 0.386257
\(785\) 10.7164 0.382486
\(786\) −30.0466 −1.07173
\(787\) −42.7857 −1.52515 −0.762573 0.646903i \(-0.776064\pi\)
−0.762573 + 0.646903i \(0.776064\pi\)
\(788\) −3.88607 −0.138436
\(789\) −0.411668 −0.0146558
\(790\) −8.86443 −0.315382
\(791\) 41.8243 1.48710
\(792\) 0.490810 0.0174402
\(793\) 1.00554 0.0357079
\(794\) 1.12705 0.0399974
\(795\) −12.0269 −0.426550
\(796\) −12.8979 −0.457155
\(797\) 25.1817 0.891981 0.445991 0.895038i \(-0.352851\pi\)
0.445991 + 0.895038i \(0.352851\pi\)
\(798\) −10.3950 −0.367979
\(799\) 7.85602 0.277926
\(800\) 1.00000 0.0353553
\(801\) −11.3852 −0.402277
\(802\) −18.1263 −0.640062
\(803\) −8.10296 −0.285947
\(804\) 14.4029 0.507950
\(805\) −37.0517 −1.30590
\(806\) −0.376124 −0.0132484
\(807\) −64.2140 −2.26044
\(808\) −0.696428 −0.0245003
\(809\) −40.4736 −1.42298 −0.711488 0.702699i \(-0.751978\pi\)
−0.711488 + 0.702699i \(0.751978\pi\)
\(810\) −10.9199 −0.383687
\(811\) 31.3771 1.10180 0.550899 0.834572i \(-0.314285\pi\)
0.550899 + 0.834572i \(0.314285\pi\)
\(812\) −4.98073 −0.174789
\(813\) −4.67617 −0.164000
\(814\) 3.16010 0.110762
\(815\) −0.373966 −0.0130995
\(816\) 5.98106 0.209379
\(817\) −12.2173 −0.427430
\(818\) −8.94909 −0.312897
\(819\) 0.393652 0.0137553
\(820\) −10.4027 −0.363279
\(821\) −42.4491 −1.48148 −0.740742 0.671789i \(-0.765526\pi\)
−0.740742 + 0.671789i \(0.765526\pi\)
\(822\) −13.6007 −0.474380
\(823\) −51.7268 −1.80308 −0.901541 0.432693i \(-0.857563\pi\)
−0.901541 + 0.432693i \(0.857563\pi\)
\(824\) −0.109262 −0.00380631
\(825\) −1.05075 −0.0365824
\(826\) 50.1784 1.74593
\(827\) −31.4371 −1.09318 −0.546588 0.837401i \(-0.684074\pi\)
−0.546588 + 0.837401i \(0.684074\pi\)
\(828\) 8.12406 0.282331
\(829\) −18.9051 −0.656601 −0.328300 0.944573i \(-0.606476\pi\)
−0.328300 + 0.944573i \(0.606476\pi\)
\(830\) −10.8435 −0.376382
\(831\) 15.6907 0.544303
\(832\) −0.100776 −0.00349378
\(833\) −32.6487 −1.13121
\(834\) 10.5754 0.366195
\(835\) −5.64002 −0.195181
\(836\) −0.659229 −0.0227999
\(837\) 15.3405 0.530246
\(838\) 18.7687 0.648354
\(839\) −3.25070 −0.112227 −0.0561133 0.998424i \(-0.517871\pi\)
−0.0561133 + 0.998424i \(0.517871\pi\)
\(840\) 8.36259 0.288537
\(841\) −27.6075 −0.951983
\(842\) −15.5120 −0.534580
\(843\) −30.6490 −1.05561
\(844\) −18.4433 −0.634843
\(845\) −12.9898 −0.446864
\(846\) −2.40841 −0.0828030
\(847\) 45.2417 1.55452
\(848\) 6.07027 0.208454
\(849\) −60.0416 −2.06062
\(850\) −3.01879 −0.103543
\(851\) 52.3071 1.79307
\(852\) −31.0727 −1.06453
\(853\) 24.1730 0.827668 0.413834 0.910352i \(-0.364189\pi\)
0.413834 + 0.910352i \(0.364189\pi\)
\(854\) 42.1153 1.44115
\(855\) −1.15039 −0.0393424
\(856\) −11.7250 −0.400752
\(857\) 39.8298 1.36056 0.680279 0.732953i \(-0.261858\pi\)
0.680279 + 0.732953i \(0.261858\pi\)
\(858\) 0.105890 0.00361503
\(859\) −43.0036 −1.46726 −0.733632 0.679547i \(-0.762176\pi\)
−0.733632 + 0.679547i \(0.762176\pi\)
\(860\) 9.82863 0.335154
\(861\) −86.9938 −2.96474
\(862\) 6.46497 0.220198
\(863\) −7.04963 −0.239972 −0.119986 0.992776i \(-0.538285\pi\)
−0.119986 + 0.992776i \(0.538285\pi\)
\(864\) 4.11023 0.139833
\(865\) −7.93500 −0.269798
\(866\) −20.4238 −0.694030
\(867\) 15.6262 0.530694
\(868\) −15.7532 −0.534699
\(869\) −4.70115 −0.159475
\(870\) −2.33799 −0.0792654
\(871\) 0.732589 0.0248228
\(872\) −7.56174 −0.256073
\(873\) 8.51167 0.288076
\(874\) −10.9118 −0.369097
\(875\) −4.22080 −0.142689
\(876\) 30.2717 1.02279
\(877\) −12.8520 −0.433980 −0.216990 0.976174i \(-0.569624\pi\)
−0.216990 + 0.976174i \(0.569624\pi\)
\(878\) 18.6018 0.627781
\(879\) −22.2827 −0.751575
\(880\) 0.530338 0.0178777
\(881\) 43.2443 1.45694 0.728469 0.685079i \(-0.240232\pi\)
0.728469 + 0.685079i \(0.240232\pi\)
\(882\) 10.0091 0.337023
\(883\) −12.6452 −0.425544 −0.212772 0.977102i \(-0.568249\pi\)
−0.212772 + 0.977102i \(0.568249\pi\)
\(884\) 0.304221 0.0102321
\(885\) 23.5542 0.791764
\(886\) 12.2738 0.412347
\(887\) 38.0927 1.27903 0.639514 0.768780i \(-0.279136\pi\)
0.639514 + 0.768780i \(0.279136\pi\)
\(888\) −11.8058 −0.396175
\(889\) −42.6345 −1.42992
\(890\) −12.3021 −0.412369
\(891\) −5.79125 −0.194014
\(892\) 22.0052 0.736789
\(893\) 3.23485 0.108250
\(894\) −5.82961 −0.194971
\(895\) −20.4271 −0.682801
\(896\) −4.22080 −0.141007
\(897\) 1.75273 0.0585220
\(898\) −27.2626 −0.909765
\(899\) 4.40425 0.146890
\(900\) 0.925466 0.0308489
\(901\) −18.3248 −0.610489
\(902\) −5.51697 −0.183695
\(903\) 82.1928 2.73521
\(904\) −9.90909 −0.329571
\(905\) −16.1239 −0.535975
\(906\) −20.5019 −0.681131
\(907\) 32.2222 1.06992 0.534960 0.844877i \(-0.320327\pi\)
0.534960 + 0.844877i \(0.320327\pi\)
\(908\) −14.6503 −0.486188
\(909\) −0.644521 −0.0213774
\(910\) 0.425356 0.0141004
\(911\) −13.2276 −0.438250 −0.219125 0.975697i \(-0.570320\pi\)
−0.219125 + 0.975697i \(0.570320\pi\)
\(912\) 2.46280 0.0815514
\(913\) −5.75070 −0.190320
\(914\) −19.2314 −0.636118
\(915\) 19.7692 0.653551
\(916\) −17.3362 −0.572805
\(917\) −64.0096 −2.11378
\(918\) −12.4079 −0.409522
\(919\) 59.8759 1.97512 0.987561 0.157235i \(-0.0502579\pi\)
0.987561 + 0.157235i \(0.0502579\pi\)
\(920\) 8.77835 0.289414
\(921\) 26.7994 0.883069
\(922\) 11.5699 0.381033
\(923\) −1.58049 −0.0520223
\(924\) 4.43500 0.145901
\(925\) 5.95866 0.195919
\(926\) −0.00174954 −5.74936e−5 0
\(927\) −0.101118 −0.00332115
\(928\) 1.18004 0.0387368
\(929\) 1.14314 0.0375051 0.0187526 0.999824i \(-0.494031\pi\)
0.0187526 + 0.999824i \(0.494031\pi\)
\(930\) −7.39468 −0.242481
\(931\) −13.4437 −0.440598
\(932\) 12.0048 0.393230
\(933\) 38.4831 1.25988
\(934\) −32.4183 −1.06076
\(935\) −1.60098 −0.0523576
\(936\) −0.0932647 −0.00304845
\(937\) −7.60417 −0.248418 −0.124209 0.992256i \(-0.539639\pi\)
−0.124209 + 0.992256i \(0.539639\pi\)
\(938\) 30.6831 1.00184
\(939\) 49.1394 1.60360
\(940\) −2.60238 −0.0848803
\(941\) 35.7215 1.16449 0.582244 0.813014i \(-0.302175\pi\)
0.582244 + 0.813014i \(0.302175\pi\)
\(942\) −21.2322 −0.691783
\(943\) −91.3189 −2.97375
\(944\) −11.8884 −0.386933
\(945\) −17.3485 −0.564346
\(946\) 5.21250 0.169473
\(947\) −20.1569 −0.655013 −0.327506 0.944849i \(-0.606208\pi\)
−0.327506 + 0.944849i \(0.606208\pi\)
\(948\) 17.5629 0.570416
\(949\) 1.53974 0.0499821
\(950\) −1.24304 −0.0403294
\(951\) 36.2618 1.17587
\(952\) 12.7417 0.412961
\(953\) 46.2528 1.49827 0.749137 0.662415i \(-0.230468\pi\)
0.749137 + 0.662415i \(0.230468\pi\)
\(954\) 5.61783 0.181884
\(955\) −9.40217 −0.304247
\(956\) 27.5016 0.889467
\(957\) −1.23993 −0.0400812
\(958\) 6.16045 0.199035
\(959\) −28.9742 −0.935627
\(960\) −1.98128 −0.0639455
\(961\) −17.0701 −0.550649
\(962\) −0.600489 −0.0193606
\(963\) −10.8511 −0.349671
\(964\) −13.2419 −0.426491
\(965\) 10.0203 0.322565
\(966\) 73.4097 2.36192
\(967\) −20.8826 −0.671538 −0.335769 0.941944i \(-0.608996\pi\)
−0.335769 + 0.941944i \(0.608996\pi\)
\(968\) −10.7187 −0.344513
\(969\) −7.43466 −0.238836
\(970\) 9.19718 0.295304
\(971\) −43.3521 −1.39123 −0.695617 0.718413i \(-0.744869\pi\)
−0.695617 + 0.718413i \(0.744869\pi\)
\(972\) 9.30470 0.298448
\(973\) 22.5292 0.722252
\(974\) −24.9602 −0.799776
\(975\) 0.199665 0.00639441
\(976\) −9.97802 −0.319389
\(977\) −40.2151 −1.28659 −0.643297 0.765617i \(-0.722434\pi\)
−0.643297 + 0.765617i \(0.722434\pi\)
\(978\) 0.740932 0.0236924
\(979\) −6.52430 −0.208517
\(980\) 10.8152 0.345478
\(981\) −6.99813 −0.223433
\(982\) 15.8961 0.507266
\(983\) −13.3486 −0.425754 −0.212877 0.977079i \(-0.568283\pi\)
−0.212877 + 0.977079i \(0.568283\pi\)
\(984\) 20.6107 0.657046
\(985\) −3.88607 −0.123821
\(986\) −3.56230 −0.113447
\(987\) −21.7626 −0.692712
\(988\) 0.125268 0.00398531
\(989\) 86.2792 2.74352
\(990\) 0.490810 0.0155990
\(991\) −35.3546 −1.12308 −0.561538 0.827451i \(-0.689790\pi\)
−0.561538 + 0.827451i \(0.689790\pi\)
\(992\) 3.73228 0.118500
\(993\) 16.0718 0.510023
\(994\) −66.1955 −2.09959
\(995\) −12.8979 −0.408892
\(996\) 21.4839 0.680744
\(997\) 46.6368 1.47700 0.738501 0.674253i \(-0.235534\pi\)
0.738501 + 0.674253i \(0.235534\pi\)
\(998\) −3.29567 −0.104323
\(999\) 24.4914 0.774875
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 \(a_p\))