Properties

Label 6034.2.a.n.1.14
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.685916 q^{3}\) \(+1.00000 q^{4}\) \(+1.44966 q^{5}\) \(-0.685916 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.52952 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.685916 q^{3}\) \(+1.00000 q^{4}\) \(+1.44966 q^{5}\) \(-0.685916 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.52952 q^{9}\) \(-1.44966 q^{10}\) \(-0.0308170 q^{11}\) \(+0.685916 q^{12}\) \(+6.22014 q^{13}\) \(+1.00000 q^{14}\) \(+0.994342 q^{15}\) \(+1.00000 q^{16}\) \(-5.48560 q^{17}\) \(+2.52952 q^{18}\) \(+1.99267 q^{19}\) \(+1.44966 q^{20}\) \(-0.685916 q^{21}\) \(+0.0308170 q^{22}\) \(+8.11388 q^{23}\) \(-0.685916 q^{24}\) \(-2.89850 q^{25}\) \(-6.22014 q^{26}\) \(-3.79278 q^{27}\) \(-1.00000 q^{28}\) \(+2.29482 q^{29}\) \(-0.994342 q^{30}\) \(+3.66210 q^{31}\) \(-1.00000 q^{32}\) \(-0.0211379 q^{33}\) \(+5.48560 q^{34}\) \(-1.44966 q^{35}\) \(-2.52952 q^{36}\) \(+6.75121 q^{37}\) \(-1.99267 q^{38}\) \(+4.26649 q^{39}\) \(-1.44966 q^{40}\) \(+5.26102 q^{41}\) \(+0.685916 q^{42}\) \(-5.40770 q^{43}\) \(-0.0308170 q^{44}\) \(-3.66693 q^{45}\) \(-8.11388 q^{46}\) \(-3.31714 q^{47}\) \(+0.685916 q^{48}\) \(+1.00000 q^{49}\) \(+2.89850 q^{50}\) \(-3.76266 q^{51}\) \(+6.22014 q^{52}\) \(-2.40729 q^{53}\) \(+3.79278 q^{54}\) \(-0.0446741 q^{55}\) \(+1.00000 q^{56}\) \(+1.36680 q^{57}\) \(-2.29482 q^{58}\) \(+4.54061 q^{59}\) \(+0.994342 q^{60}\) \(-6.20443 q^{61}\) \(-3.66210 q^{62}\) \(+2.52952 q^{63}\) \(+1.00000 q^{64}\) \(+9.01707 q^{65}\) \(+0.0211379 q^{66}\) \(-0.636232 q^{67}\) \(-5.48560 q^{68}\) \(+5.56544 q^{69}\) \(+1.44966 q^{70}\) \(+1.56907 q^{71}\) \(+2.52952 q^{72}\) \(-8.94194 q^{73}\) \(-6.75121 q^{74}\) \(-1.98812 q^{75}\) \(+1.99267 q^{76}\) \(+0.0308170 q^{77}\) \(-4.26649 q^{78}\) \(-7.94777 q^{79}\) \(+1.44966 q^{80}\) \(+4.98703 q^{81}\) \(-5.26102 q^{82}\) \(-3.11054 q^{83}\) \(-0.685916 q^{84}\) \(-7.95223 q^{85}\) \(+5.40770 q^{86}\) \(+1.57405 q^{87}\) \(+0.0308170 q^{88}\) \(+9.22104 q^{89}\) \(+3.66693 q^{90}\) \(-6.22014 q^{91}\) \(+8.11388 q^{92}\) \(+2.51190 q^{93}\) \(+3.31714 q^{94}\) \(+2.88868 q^{95}\) \(-0.685916 q^{96}\) \(+18.0193 q^{97}\) \(-1.00000 q^{98}\) \(+0.0779523 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.685916 0.396014 0.198007 0.980201i \(-0.436553\pi\)
0.198007 + 0.980201i \(0.436553\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.44966 0.648306 0.324153 0.946005i \(-0.394921\pi\)
0.324153 + 0.946005i \(0.394921\pi\)
\(6\) −0.685916 −0.280024
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.52952 −0.843173
\(10\) −1.44966 −0.458421
\(11\) −0.0308170 −0.00929169 −0.00464584 0.999989i \(-0.501479\pi\)
−0.00464584 + 0.999989i \(0.501479\pi\)
\(12\) 0.685916 0.198007
\(13\) 6.22014 1.72516 0.862579 0.505923i \(-0.168848\pi\)
0.862579 + 0.505923i \(0.168848\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.994342 0.256738
\(16\) 1.00000 0.250000
\(17\) −5.48560 −1.33045 −0.665226 0.746642i \(-0.731665\pi\)
−0.665226 + 0.746642i \(0.731665\pi\)
\(18\) 2.52952 0.596213
\(19\) 1.99267 0.457150 0.228575 0.973526i \(-0.426593\pi\)
0.228575 + 0.973526i \(0.426593\pi\)
\(20\) 1.44966 0.324153
\(21\) −0.685916 −0.149679
\(22\) 0.0308170 0.00657021
\(23\) 8.11388 1.69186 0.845931 0.533292i \(-0.179045\pi\)
0.845931 + 0.533292i \(0.179045\pi\)
\(24\) −0.685916 −0.140012
\(25\) −2.89850 −0.579699
\(26\) −6.22014 −1.21987
\(27\) −3.79278 −0.729922
\(28\) −1.00000 −0.188982
\(29\) 2.29482 0.426138 0.213069 0.977037i \(-0.431654\pi\)
0.213069 + 0.977037i \(0.431654\pi\)
\(30\) −0.994342 −0.181541
\(31\) 3.66210 0.657733 0.328867 0.944376i \(-0.393333\pi\)
0.328867 + 0.944376i \(0.393333\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.0211379 −0.00367963
\(34\) 5.48560 0.940772
\(35\) −1.44966 −0.245037
\(36\) −2.52952 −0.421587
\(37\) 6.75121 1.10989 0.554946 0.831886i \(-0.312739\pi\)
0.554946 + 0.831886i \(0.312739\pi\)
\(38\) −1.99267 −0.323254
\(39\) 4.26649 0.683186
\(40\) −1.44966 −0.229211
\(41\) 5.26102 0.821633 0.410817 0.911718i \(-0.365244\pi\)
0.410817 + 0.911718i \(0.365244\pi\)
\(42\) 0.685916 0.105839
\(43\) −5.40770 −0.824667 −0.412333 0.911033i \(-0.635286\pi\)
−0.412333 + 0.911033i \(0.635286\pi\)
\(44\) −0.0308170 −0.00464584
\(45\) −3.66693 −0.546634
\(46\) −8.11388 −1.19633
\(47\) −3.31714 −0.483855 −0.241927 0.970294i \(-0.577780\pi\)
−0.241927 + 0.970294i \(0.577780\pi\)
\(48\) 0.685916 0.0990034
\(49\) 1.00000 0.142857
\(50\) 2.89850 0.409909
\(51\) −3.76266 −0.526877
\(52\) 6.22014 0.862579
\(53\) −2.40729 −0.330666 −0.165333 0.986238i \(-0.552870\pi\)
−0.165333 + 0.986238i \(0.552870\pi\)
\(54\) 3.79278 0.516133
\(55\) −0.0446741 −0.00602386
\(56\) 1.00000 0.133631
\(57\) 1.36680 0.181037
\(58\) −2.29482 −0.301325
\(59\) 4.54061 0.591137 0.295568 0.955322i \(-0.404491\pi\)
0.295568 + 0.955322i \(0.404491\pi\)
\(60\) 0.994342 0.128369
\(61\) −6.20443 −0.794396 −0.397198 0.917733i \(-0.630017\pi\)
−0.397198 + 0.917733i \(0.630017\pi\)
\(62\) −3.66210 −0.465088
\(63\) 2.52952 0.318690
\(64\) 1.00000 0.125000
\(65\) 9.01707 1.11843
\(66\) 0.0211379 0.00260189
\(67\) −0.636232 −0.0777281 −0.0388640 0.999245i \(-0.512374\pi\)
−0.0388640 + 0.999245i \(0.512374\pi\)
\(68\) −5.48560 −0.665226
\(69\) 5.56544 0.670000
\(70\) 1.44966 0.173267
\(71\) 1.56907 0.186214 0.0931072 0.995656i \(-0.470320\pi\)
0.0931072 + 0.995656i \(0.470320\pi\)
\(72\) 2.52952 0.298107
\(73\) −8.94194 −1.04658 −0.523288 0.852156i \(-0.675295\pi\)
−0.523288 + 0.852156i \(0.675295\pi\)
\(74\) −6.75121 −0.784812
\(75\) −1.98812 −0.229569
\(76\) 1.99267 0.228575
\(77\) 0.0308170 0.00351193
\(78\) −4.26649 −0.483085
\(79\) −7.94777 −0.894194 −0.447097 0.894486i \(-0.647542\pi\)
−0.447097 + 0.894486i \(0.647542\pi\)
\(80\) 1.44966 0.162076
\(81\) 4.98703 0.554114
\(82\) −5.26102 −0.580982
\(83\) −3.11054 −0.341426 −0.170713 0.985321i \(-0.554607\pi\)
−0.170713 + 0.985321i \(0.554607\pi\)
\(84\) −0.685916 −0.0748395
\(85\) −7.95223 −0.862540
\(86\) 5.40770 0.583127
\(87\) 1.57405 0.168756
\(88\) 0.0308170 0.00328511
\(89\) 9.22104 0.977428 0.488714 0.872444i \(-0.337466\pi\)
0.488714 + 0.872444i \(0.337466\pi\)
\(90\) 3.66693 0.386529
\(91\) −6.22014 −0.652048
\(92\) 8.11388 0.845931
\(93\) 2.51190 0.260471
\(94\) 3.31714 0.342137
\(95\) 2.88868 0.296373
\(96\) −0.685916 −0.0700060
\(97\) 18.0193 1.82958 0.914792 0.403926i \(-0.132355\pi\)
0.914792 + 0.403926i \(0.132355\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.0779523 0.00783450
\(100\) −2.89850 −0.289850
\(101\) 6.47759 0.644545 0.322272 0.946647i \(-0.395553\pi\)
0.322272 + 0.946647i \(0.395553\pi\)
\(102\) 3.76266 0.372559
\(103\) 13.5189 1.33206 0.666028 0.745927i \(-0.267993\pi\)
0.666028 + 0.745927i \(0.267993\pi\)
\(104\) −6.22014 −0.609935
\(105\) −0.994342 −0.0970378
\(106\) 2.40729 0.233816
\(107\) 0.845463 0.0817340 0.0408670 0.999165i \(-0.486988\pi\)
0.0408670 + 0.999165i \(0.486988\pi\)
\(108\) −3.79278 −0.364961
\(109\) −17.5845 −1.68429 −0.842145 0.539251i \(-0.818707\pi\)
−0.842145 + 0.539251i \(0.818707\pi\)
\(110\) 0.0446741 0.00425951
\(111\) 4.63076 0.439532
\(112\) −1.00000 −0.0944911
\(113\) 13.1439 1.23647 0.618235 0.785993i \(-0.287848\pi\)
0.618235 + 0.785993i \(0.287848\pi\)
\(114\) −1.36680 −0.128013
\(115\) 11.7623 1.09684
\(116\) 2.29482 0.213069
\(117\) −15.7340 −1.45461
\(118\) −4.54061 −0.417997
\(119\) 5.48560 0.502864
\(120\) −0.994342 −0.0907706
\(121\) −10.9991 −0.999914
\(122\) 6.20443 0.561723
\(123\) 3.60862 0.325378
\(124\) 3.66210 0.328867
\(125\) −11.4501 −1.02413
\(126\) −2.52952 −0.225348
\(127\) 1.40559 0.124726 0.0623629 0.998054i \(-0.480136\pi\)
0.0623629 + 0.998054i \(0.480136\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.70923 −0.326579
\(130\) −9.01707 −0.790849
\(131\) 13.9716 1.22071 0.610353 0.792129i \(-0.291027\pi\)
0.610353 + 0.792129i \(0.291027\pi\)
\(132\) −0.0211379 −0.00183982
\(133\) −1.99267 −0.172786
\(134\) 0.636232 0.0549621
\(135\) −5.49823 −0.473213
\(136\) 5.48560 0.470386
\(137\) 2.12475 0.181529 0.0907646 0.995872i \(-0.471069\pi\)
0.0907646 + 0.995872i \(0.471069\pi\)
\(138\) −5.56544 −0.473762
\(139\) −12.8453 −1.08952 −0.544760 0.838592i \(-0.683379\pi\)
−0.544760 + 0.838592i \(0.683379\pi\)
\(140\) −1.44966 −0.122518
\(141\) −2.27528 −0.191613
\(142\) −1.56907 −0.131673
\(143\) −0.191686 −0.0160296
\(144\) −2.52952 −0.210793
\(145\) 3.32670 0.276268
\(146\) 8.94194 0.740041
\(147\) 0.685916 0.0565734
\(148\) 6.75121 0.554946
\(149\) 19.0524 1.56084 0.780418 0.625259i \(-0.215007\pi\)
0.780418 + 0.625259i \(0.215007\pi\)
\(150\) 1.98812 0.162330
\(151\) −14.7131 −1.19733 −0.598667 0.800998i \(-0.704303\pi\)
−0.598667 + 0.800998i \(0.704303\pi\)
\(152\) −1.99267 −0.161627
\(153\) 13.8759 1.12180
\(154\) −0.0308170 −0.00248331
\(155\) 5.30879 0.426412
\(156\) 4.26649 0.341593
\(157\) −5.26211 −0.419962 −0.209981 0.977705i \(-0.567340\pi\)
−0.209981 + 0.977705i \(0.567340\pi\)
\(158\) 7.94777 0.632290
\(159\) −1.65120 −0.130948
\(160\) −1.44966 −0.114605
\(161\) −8.11388 −0.639464
\(162\) −4.98703 −0.391818
\(163\) 11.7413 0.919649 0.459824 0.888010i \(-0.347912\pi\)
0.459824 + 0.888010i \(0.347912\pi\)
\(164\) 5.26102 0.410817
\(165\) −0.0306427 −0.00238553
\(166\) 3.11054 0.241425
\(167\) −9.95291 −0.770180 −0.385090 0.922879i \(-0.625830\pi\)
−0.385090 + 0.922879i \(0.625830\pi\)
\(168\) 0.685916 0.0529195
\(169\) 25.6902 1.97617
\(170\) 7.95223 0.609908
\(171\) −5.04049 −0.385456
\(172\) −5.40770 −0.412333
\(173\) 15.1987 1.15553 0.577767 0.816202i \(-0.303924\pi\)
0.577767 + 0.816202i \(0.303924\pi\)
\(174\) −1.57405 −0.119329
\(175\) 2.89850 0.219106
\(176\) −0.0308170 −0.00232292
\(177\) 3.11447 0.234098
\(178\) −9.22104 −0.691146
\(179\) 23.3175 1.74284 0.871418 0.490542i \(-0.163201\pi\)
0.871418 + 0.490542i \(0.163201\pi\)
\(180\) −3.66693 −0.273317
\(181\) 10.4772 0.778768 0.389384 0.921076i \(-0.372688\pi\)
0.389384 + 0.921076i \(0.372688\pi\)
\(182\) 6.22014 0.461068
\(183\) −4.25572 −0.314592
\(184\) −8.11388 −0.598164
\(185\) 9.78693 0.719549
\(186\) −2.51190 −0.184181
\(187\) 0.169050 0.0123622
\(188\) −3.31714 −0.241927
\(189\) 3.79278 0.275884
\(190\) −2.88868 −0.209567
\(191\) 10.2549 0.742020 0.371010 0.928629i \(-0.379012\pi\)
0.371010 + 0.928629i \(0.379012\pi\)
\(192\) 0.685916 0.0495017
\(193\) 9.26826 0.667144 0.333572 0.942725i \(-0.391746\pi\)
0.333572 + 0.942725i \(0.391746\pi\)
\(194\) −18.0193 −1.29371
\(195\) 6.18495 0.442913
\(196\) 1.00000 0.0714286
\(197\) 10.5984 0.755108 0.377554 0.925988i \(-0.376765\pi\)
0.377554 + 0.925988i \(0.376765\pi\)
\(198\) −0.0779523 −0.00553983
\(199\) 19.5234 1.38397 0.691987 0.721910i \(-0.256735\pi\)
0.691987 + 0.721910i \(0.256735\pi\)
\(200\) 2.89850 0.204955
\(201\) −0.436401 −0.0307814
\(202\) −6.47759 −0.455762
\(203\) −2.29482 −0.161065
\(204\) −3.76266 −0.263439
\(205\) 7.62667 0.532670
\(206\) −13.5189 −0.941906
\(207\) −20.5242 −1.42653
\(208\) 6.22014 0.431289
\(209\) −0.0614081 −0.00424769
\(210\) 0.994342 0.0686161
\(211\) 21.5412 1.48296 0.741478 0.670977i \(-0.234125\pi\)
0.741478 + 0.670977i \(0.234125\pi\)
\(212\) −2.40729 −0.165333
\(213\) 1.07625 0.0737434
\(214\) −0.845463 −0.0577947
\(215\) −7.83931 −0.534636
\(216\) 3.79278 0.258066
\(217\) −3.66210 −0.248600
\(218\) 17.5845 1.19097
\(219\) −6.13342 −0.414458
\(220\) −0.0446741 −0.00301193
\(221\) −34.1212 −2.29524
\(222\) −4.63076 −0.310796
\(223\) −16.5991 −1.11156 −0.555779 0.831330i \(-0.687580\pi\)
−0.555779 + 0.831330i \(0.687580\pi\)
\(224\) 1.00000 0.0668153
\(225\) 7.33181 0.488787
\(226\) −13.1439 −0.874317
\(227\) 2.51733 0.167081 0.0835404 0.996504i \(-0.473377\pi\)
0.0835404 + 0.996504i \(0.473377\pi\)
\(228\) 1.36680 0.0905187
\(229\) 9.48297 0.626652 0.313326 0.949646i \(-0.398557\pi\)
0.313326 + 0.949646i \(0.398557\pi\)
\(230\) −11.7623 −0.775586
\(231\) 0.0211379 0.00139077
\(232\) −2.29482 −0.150662
\(233\) 6.67919 0.437568 0.218784 0.975773i \(-0.429791\pi\)
0.218784 + 0.975773i \(0.429791\pi\)
\(234\) 15.7340 1.02856
\(235\) −4.80871 −0.313686
\(236\) 4.54061 0.295568
\(237\) −5.45150 −0.354113
\(238\) −5.48560 −0.355578
\(239\) −8.65865 −0.560082 −0.280041 0.959988i \(-0.590348\pi\)
−0.280041 + 0.959988i \(0.590348\pi\)
\(240\) 0.994342 0.0641845
\(241\) 30.2892 1.95110 0.975549 0.219781i \(-0.0705342\pi\)
0.975549 + 0.219781i \(0.0705342\pi\)
\(242\) 10.9991 0.707046
\(243\) 14.7990 0.949359
\(244\) −6.20443 −0.397198
\(245\) 1.44966 0.0926151
\(246\) −3.60862 −0.230077
\(247\) 12.3947 0.788655
\(248\) −3.66210 −0.232544
\(249\) −2.13357 −0.135209
\(250\) 11.4501 0.724168
\(251\) −27.4516 −1.73273 −0.866363 0.499414i \(-0.833549\pi\)
−0.866363 + 0.499414i \(0.833549\pi\)
\(252\) 2.52952 0.159345
\(253\) −0.250046 −0.0157203
\(254\) −1.40559 −0.0881944
\(255\) −5.45456 −0.341578
\(256\) 1.00000 0.0625000
\(257\) −17.6464 −1.10075 −0.550377 0.834916i \(-0.685516\pi\)
−0.550377 + 0.834916i \(0.685516\pi\)
\(258\) 3.70923 0.230926
\(259\) −6.75121 −0.419500
\(260\) 9.01707 0.559215
\(261\) −5.80480 −0.359308
\(262\) −13.9716 −0.863170
\(263\) 31.6063 1.94893 0.974465 0.224540i \(-0.0720878\pi\)
0.974465 + 0.224540i \(0.0720878\pi\)
\(264\) 0.0211379 0.00130095
\(265\) −3.48974 −0.214373
\(266\) 1.99267 0.122178
\(267\) 6.32486 0.387075
\(268\) −0.636232 −0.0388640
\(269\) 8.76947 0.534684 0.267342 0.963602i \(-0.413855\pi\)
0.267342 + 0.963602i \(0.413855\pi\)
\(270\) 5.49823 0.334612
\(271\) 3.46805 0.210669 0.105334 0.994437i \(-0.466409\pi\)
0.105334 + 0.994437i \(0.466409\pi\)
\(272\) −5.48560 −0.332613
\(273\) −4.26649 −0.258220
\(274\) −2.12475 −0.128361
\(275\) 0.0893231 0.00538639
\(276\) 5.56544 0.335000
\(277\) −7.15105 −0.429665 −0.214832 0.976651i \(-0.568921\pi\)
−0.214832 + 0.976651i \(0.568921\pi\)
\(278\) 12.8453 0.770407
\(279\) −9.26337 −0.554583
\(280\) 1.44966 0.0866335
\(281\) −1.72925 −0.103158 −0.0515792 0.998669i \(-0.516425\pi\)
−0.0515792 + 0.998669i \(0.516425\pi\)
\(282\) 2.27528 0.135491
\(283\) −6.18264 −0.367520 −0.183760 0.982971i \(-0.558827\pi\)
−0.183760 + 0.982971i \(0.558827\pi\)
\(284\) 1.56907 0.0931072
\(285\) 1.98139 0.117368
\(286\) 0.191686 0.0113347
\(287\) −5.26102 −0.310548
\(288\) 2.52952 0.149053
\(289\) 13.0918 0.770105
\(290\) −3.32670 −0.195351
\(291\) 12.3597 0.724540
\(292\) −8.94194 −0.523288
\(293\) −12.7021 −0.742063 −0.371032 0.928620i \(-0.620996\pi\)
−0.371032 + 0.928620i \(0.620996\pi\)
\(294\) −0.685916 −0.0400034
\(295\) 6.58232 0.383237
\(296\) −6.75121 −0.392406
\(297\) 0.116882 0.00678220
\(298\) −19.0524 −1.10368
\(299\) 50.4695 2.91873
\(300\) −1.98812 −0.114784
\(301\) 5.40770 0.311695
\(302\) 14.7131 0.846643
\(303\) 4.44308 0.255249
\(304\) 1.99267 0.114287
\(305\) −8.99429 −0.515011
\(306\) −13.8759 −0.793234
\(307\) 11.3220 0.646181 0.323090 0.946368i \(-0.395278\pi\)
0.323090 + 0.946368i \(0.395278\pi\)
\(308\) 0.0308170 0.00175596
\(309\) 9.27282 0.527512
\(310\) −5.30879 −0.301519
\(311\) −27.8624 −1.57993 −0.789966 0.613150i \(-0.789902\pi\)
−0.789966 + 0.613150i \(0.789902\pi\)
\(312\) −4.26649 −0.241543
\(313\) −2.64490 −0.149499 −0.0747494 0.997202i \(-0.523816\pi\)
−0.0747494 + 0.997202i \(0.523816\pi\)
\(314\) 5.26211 0.296958
\(315\) 3.66693 0.206608
\(316\) −7.94777 −0.447097
\(317\) 21.6517 1.21608 0.608042 0.793905i \(-0.291955\pi\)
0.608042 + 0.793905i \(0.291955\pi\)
\(318\) 1.65120 0.0925945
\(319\) −0.0707196 −0.00395954
\(320\) 1.44966 0.0810382
\(321\) 0.579917 0.0323678
\(322\) 8.11388 0.452169
\(323\) −10.9310 −0.608216
\(324\) 4.98703 0.277057
\(325\) −18.0291 −1.00007
\(326\) −11.7413 −0.650290
\(327\) −12.0615 −0.667002
\(328\) −5.26102 −0.290491
\(329\) 3.31714 0.182880
\(330\) 0.0306427 0.00168682
\(331\) 8.21795 0.451699 0.225850 0.974162i \(-0.427484\pi\)
0.225850 + 0.974162i \(0.427484\pi\)
\(332\) −3.11054 −0.170713
\(333\) −17.0773 −0.935831
\(334\) 9.95291 0.544599
\(335\) −0.922317 −0.0503916
\(336\) −0.685916 −0.0374198
\(337\) 0.122451 0.00667033 0.00333517 0.999994i \(-0.498938\pi\)
0.00333517 + 0.999994i \(0.498938\pi\)
\(338\) −25.6902 −1.39736
\(339\) 9.01558 0.489659
\(340\) −7.95223 −0.431270
\(341\) −0.112855 −0.00611145
\(342\) 5.04049 0.272559
\(343\) −1.00000 −0.0539949
\(344\) 5.40770 0.291564
\(345\) 8.06798 0.434365
\(346\) −15.1987 −0.817086
\(347\) 15.9204 0.854650 0.427325 0.904098i \(-0.359456\pi\)
0.427325 + 0.904098i \(0.359456\pi\)
\(348\) 1.57405 0.0843782
\(349\) −15.4343 −0.826180 −0.413090 0.910690i \(-0.635551\pi\)
−0.413090 + 0.910690i \(0.635551\pi\)
\(350\) −2.89850 −0.154931
\(351\) −23.5917 −1.25923
\(352\) 0.0308170 0.00164255
\(353\) −12.2792 −0.653555 −0.326777 0.945101i \(-0.605963\pi\)
−0.326777 + 0.945101i \(0.605963\pi\)
\(354\) −3.11447 −0.165532
\(355\) 2.27461 0.120724
\(356\) 9.22104 0.488714
\(357\) 3.76266 0.199141
\(358\) −23.3175 −1.23237
\(359\) 8.69460 0.458883 0.229442 0.973322i \(-0.426310\pi\)
0.229442 + 0.973322i \(0.426310\pi\)
\(360\) 3.66693 0.193264
\(361\) −15.0293 −0.791014
\(362\) −10.4772 −0.550672
\(363\) −7.54442 −0.395979
\(364\) −6.22014 −0.326024
\(365\) −12.9627 −0.678501
\(366\) 4.25572 0.222450
\(367\) 19.3936 1.01234 0.506169 0.862434i \(-0.331061\pi\)
0.506169 + 0.862434i \(0.331061\pi\)
\(368\) 8.11388 0.422965
\(369\) −13.3079 −0.692779
\(370\) −9.78693 −0.508798
\(371\) 2.40729 0.124980
\(372\) 2.51190 0.130236
\(373\) −10.3958 −0.538276 −0.269138 0.963102i \(-0.586739\pi\)
−0.269138 + 0.963102i \(0.586739\pi\)
\(374\) −0.169050 −0.00874136
\(375\) −7.85381 −0.405569
\(376\) 3.31714 0.171068
\(377\) 14.2741 0.735155
\(378\) −3.79278 −0.195080
\(379\) 12.1040 0.621740 0.310870 0.950452i \(-0.399380\pi\)
0.310870 + 0.950452i \(0.399380\pi\)
\(380\) 2.88868 0.148186
\(381\) 0.964115 0.0493931
\(382\) −10.2549 −0.524687
\(383\) −24.9672 −1.27577 −0.637883 0.770134i \(-0.720190\pi\)
−0.637883 + 0.770134i \(0.720190\pi\)
\(384\) −0.685916 −0.0350030
\(385\) 0.0446741 0.00227680
\(386\) −9.26826 −0.471742
\(387\) 13.6789 0.695337
\(388\) 18.0193 0.914792
\(389\) −7.59387 −0.385025 −0.192512 0.981295i \(-0.561664\pi\)
−0.192512 + 0.981295i \(0.561664\pi\)
\(390\) −6.18495 −0.313187
\(391\) −44.5095 −2.25094
\(392\) −1.00000 −0.0505076
\(393\) 9.58336 0.483416
\(394\) −10.5984 −0.533942
\(395\) −11.5215 −0.579711
\(396\) 0.0779523 0.00391725
\(397\) −27.8996 −1.40024 −0.700120 0.714025i \(-0.746870\pi\)
−0.700120 + 0.714025i \(0.746870\pi\)
\(398\) −19.5234 −0.978618
\(399\) −1.36680 −0.0684257
\(400\) −2.89850 −0.144925
\(401\) −29.8254 −1.48941 −0.744704 0.667395i \(-0.767409\pi\)
−0.744704 + 0.667395i \(0.767409\pi\)
\(402\) 0.436401 0.0217657
\(403\) 22.7788 1.13469
\(404\) 6.47759 0.322272
\(405\) 7.22948 0.359236
\(406\) 2.29482 0.113890
\(407\) −0.208052 −0.0103128
\(408\) 3.76266 0.186279
\(409\) −20.0637 −0.992085 −0.496043 0.868298i \(-0.665214\pi\)
−0.496043 + 0.868298i \(0.665214\pi\)
\(410\) −7.62667 −0.376654
\(411\) 1.45740 0.0718880
\(412\) 13.5189 0.666028
\(413\) −4.54061 −0.223429
\(414\) 20.5242 1.00871
\(415\) −4.50921 −0.221348
\(416\) −6.22014 −0.304968
\(417\) −8.81076 −0.431465
\(418\) 0.0614081 0.00300357
\(419\) 35.1960 1.71944 0.859718 0.510769i \(-0.170639\pi\)
0.859718 + 0.510769i \(0.170639\pi\)
\(420\) −0.994342 −0.0485189
\(421\) −22.9700 −1.11949 −0.559746 0.828664i \(-0.689101\pi\)
−0.559746 + 0.828664i \(0.689101\pi\)
\(422\) −21.5412 −1.04861
\(423\) 8.39077 0.407973
\(424\) 2.40729 0.116908
\(425\) 15.9000 0.771263
\(426\) −1.07625 −0.0521445
\(427\) 6.20443 0.300253
\(428\) 0.845463 0.0408670
\(429\) −0.131481 −0.00634795
\(430\) 7.83931 0.378045
\(431\) 1.00000 0.0481683
\(432\) −3.79278 −0.182480
\(433\) −30.5862 −1.46988 −0.734941 0.678131i \(-0.762790\pi\)
−0.734941 + 0.678131i \(0.762790\pi\)
\(434\) 3.66210 0.175787
\(435\) 2.28184 0.109406
\(436\) −17.5845 −0.842145
\(437\) 16.1683 0.773434
\(438\) 6.13342 0.293066
\(439\) 21.7019 1.03578 0.517888 0.855448i \(-0.326718\pi\)
0.517888 + 0.855448i \(0.326718\pi\)
\(440\) 0.0446741 0.00212975
\(441\) −2.52952 −0.120453
\(442\) 34.1212 1.62298
\(443\) 18.8299 0.894634 0.447317 0.894375i \(-0.352380\pi\)
0.447317 + 0.894375i \(0.352380\pi\)
\(444\) 4.63076 0.219766
\(445\) 13.3673 0.633672
\(446\) 16.5991 0.785990
\(447\) 13.0684 0.618112
\(448\) −1.00000 −0.0472456
\(449\) 14.2002 0.670150 0.335075 0.942192i \(-0.391238\pi\)
0.335075 + 0.942192i \(0.391238\pi\)
\(450\) −7.33181 −0.345625
\(451\) −0.162129 −0.00763436
\(452\) 13.1439 0.618235
\(453\) −10.0919 −0.474161
\(454\) −2.51733 −0.118144
\(455\) −9.01707 −0.422727
\(456\) −1.36680 −0.0640064
\(457\) −6.48130 −0.303182 −0.151591 0.988443i \(-0.548440\pi\)
−0.151591 + 0.988443i \(0.548440\pi\)
\(458\) −9.48297 −0.443110
\(459\) 20.8057 0.971126
\(460\) 11.7623 0.548422
\(461\) −36.2829 −1.68986 −0.844931 0.534875i \(-0.820359\pi\)
−0.844931 + 0.534875i \(0.820359\pi\)
\(462\) −0.0211379 −0.000983424 0
\(463\) 21.2718 0.988584 0.494292 0.869296i \(-0.335427\pi\)
0.494292 + 0.869296i \(0.335427\pi\)
\(464\) 2.29482 0.106534
\(465\) 3.64138 0.168865
\(466\) −6.67919 −0.309407
\(467\) 31.3240 1.44950 0.724750 0.689012i \(-0.241955\pi\)
0.724750 + 0.689012i \(0.241955\pi\)
\(468\) −15.7340 −0.727303
\(469\) 0.636232 0.0293785
\(470\) 4.80871 0.221809
\(471\) −3.60937 −0.166311
\(472\) −4.54061 −0.208998
\(473\) 0.166649 0.00766254
\(474\) 5.45150 0.250396
\(475\) −5.77574 −0.265009
\(476\) 5.48560 0.251432
\(477\) 6.08928 0.278809
\(478\) 8.65865 0.396038
\(479\) 13.2576 0.605756 0.302878 0.953029i \(-0.402053\pi\)
0.302878 + 0.953029i \(0.402053\pi\)
\(480\) −0.994342 −0.0453853
\(481\) 41.9935 1.91474
\(482\) −30.2892 −1.37964
\(483\) −5.56544 −0.253236
\(484\) −10.9991 −0.499957
\(485\) 26.1218 1.18613
\(486\) −14.7990 −0.671298
\(487\) −7.13345 −0.323247 −0.161624 0.986852i \(-0.551673\pi\)
−0.161624 + 0.986852i \(0.551673\pi\)
\(488\) 6.20443 0.280861
\(489\) 8.05354 0.364193
\(490\) −1.44966 −0.0654888
\(491\) 2.55846 0.115462 0.0577309 0.998332i \(-0.481613\pi\)
0.0577309 + 0.998332i \(0.481613\pi\)
\(492\) 3.60862 0.162689
\(493\) −12.5885 −0.566956
\(494\) −12.3947 −0.557663
\(495\) 0.113004 0.00507915
\(496\) 3.66210 0.164433
\(497\) −1.56907 −0.0703824
\(498\) 2.13357 0.0956074
\(499\) 25.5539 1.14395 0.571974 0.820272i \(-0.306178\pi\)
0.571974 + 0.820272i \(0.306178\pi\)
\(500\) −11.4501 −0.512064
\(501\) −6.82686 −0.305002
\(502\) 27.4516 1.22522
\(503\) −19.9164 −0.888029 −0.444014 0.896020i \(-0.646446\pi\)
−0.444014 + 0.896020i \(0.646446\pi\)
\(504\) −2.52952 −0.112674
\(505\) 9.39028 0.417862
\(506\) 0.250046 0.0111159
\(507\) 17.6213 0.782590
\(508\) 1.40559 0.0623629
\(509\) −25.4468 −1.12791 −0.563955 0.825806i \(-0.690721\pi\)
−0.563955 + 0.825806i \(0.690721\pi\)
\(510\) 5.45456 0.241532
\(511\) 8.94194 0.395568
\(512\) −1.00000 −0.0441942
\(513\) −7.55776 −0.333683
\(514\) 17.6464 0.778351
\(515\) 19.5977 0.863580
\(516\) −3.70923 −0.163290
\(517\) 0.102224 0.00449583
\(518\) 6.75121 0.296631
\(519\) 10.4250 0.457607
\(520\) −9.01707 −0.395425
\(521\) −12.9030 −0.565292 −0.282646 0.959224i \(-0.591212\pi\)
−0.282646 + 0.959224i \(0.591212\pi\)
\(522\) 5.80480 0.254069
\(523\) 2.69005 0.117628 0.0588138 0.998269i \(-0.481268\pi\)
0.0588138 + 0.998269i \(0.481268\pi\)
\(524\) 13.9716 0.610353
\(525\) 1.98812 0.0867689
\(526\) −31.6063 −1.37810
\(527\) −20.0888 −0.875083
\(528\) −0.0211379 −0.000919909 0
\(529\) 42.8351 1.86240
\(530\) 3.48974 0.151585
\(531\) −11.4856 −0.498431
\(532\) −1.99267 −0.0863931
\(533\) 32.7243 1.41745
\(534\) −6.32486 −0.273703
\(535\) 1.22563 0.0529887
\(536\) 0.636232 0.0274810
\(537\) 15.9939 0.690187
\(538\) −8.76947 −0.378079
\(539\) −0.0308170 −0.00132738
\(540\) −5.49823 −0.236606
\(541\) 39.4037 1.69410 0.847049 0.531514i \(-0.178377\pi\)
0.847049 + 0.531514i \(0.178377\pi\)
\(542\) −3.46805 −0.148965
\(543\) 7.18651 0.308403
\(544\) 5.48560 0.235193
\(545\) −25.4915 −1.09194
\(546\) 4.26649 0.182589
\(547\) −22.0756 −0.943886 −0.471943 0.881629i \(-0.656447\pi\)
−0.471943 + 0.881629i \(0.656447\pi\)
\(548\) 2.12475 0.0907646
\(549\) 15.6942 0.669813
\(550\) −0.0893231 −0.00380875
\(551\) 4.57282 0.194809
\(552\) −5.56544 −0.236881
\(553\) 7.94777 0.337973
\(554\) 7.15105 0.303819
\(555\) 6.71301 0.284951
\(556\) −12.8453 −0.544760
\(557\) 41.5496 1.76051 0.880257 0.474498i \(-0.157370\pi\)
0.880257 + 0.474498i \(0.157370\pi\)
\(558\) 9.26337 0.392150
\(559\) −33.6367 −1.42268
\(560\) −1.44966 −0.0612591
\(561\) 0.115954 0.00489558
\(562\) 1.72925 0.0729439
\(563\) −0.0444233 −0.00187222 −0.000936109 1.00000i \(-0.500298\pi\)
−0.000936109 1.00000i \(0.500298\pi\)
\(564\) −2.27528 −0.0958065
\(565\) 19.0541 0.801611
\(566\) 6.18264 0.259876
\(567\) −4.98703 −0.209436
\(568\) −1.56907 −0.0658367
\(569\) 5.30329 0.222325 0.111163 0.993802i \(-0.464543\pi\)
0.111163 + 0.993802i \(0.464543\pi\)
\(570\) −1.98139 −0.0829915
\(571\) 4.51455 0.188928 0.0944641 0.995528i \(-0.469886\pi\)
0.0944641 + 0.995528i \(0.469886\pi\)
\(572\) −0.191686 −0.00801481
\(573\) 7.03401 0.293850
\(574\) 5.26102 0.219591
\(575\) −23.5181 −0.980771
\(576\) −2.52952 −0.105397
\(577\) −44.9834 −1.87268 −0.936341 0.351092i \(-0.885810\pi\)
−0.936341 + 0.351092i \(0.885810\pi\)
\(578\) −13.0918 −0.544546
\(579\) 6.35725 0.264198
\(580\) 3.32670 0.138134
\(581\) 3.11054 0.129047
\(582\) −12.3597 −0.512327
\(583\) 0.0741855 0.00307245
\(584\) 8.94194 0.370020
\(585\) −22.8089 −0.943030
\(586\) 12.7021 0.524718
\(587\) 25.7132 1.06130 0.530649 0.847592i \(-0.321948\pi\)
0.530649 + 0.847592i \(0.321948\pi\)
\(588\) 0.685916 0.0282867
\(589\) 7.29736 0.300683
\(590\) −6.58232 −0.270990
\(591\) 7.26964 0.299033
\(592\) 6.75121 0.277473
\(593\) 16.9784 0.697220 0.348610 0.937268i \(-0.386654\pi\)
0.348610 + 0.937268i \(0.386654\pi\)
\(594\) −0.116882 −0.00479574
\(595\) 7.95223 0.326010
\(596\) 19.0524 0.780418
\(597\) 13.3914 0.548073
\(598\) −50.4695 −2.06385
\(599\) 4.67359 0.190958 0.0954789 0.995431i \(-0.469562\pi\)
0.0954789 + 0.995431i \(0.469562\pi\)
\(600\) 1.98812 0.0811649
\(601\) −28.1126 −1.14674 −0.573368 0.819298i \(-0.694363\pi\)
−0.573368 + 0.819298i \(0.694363\pi\)
\(602\) −5.40770 −0.220401
\(603\) 1.60936 0.0655383
\(604\) −14.7131 −0.598667
\(605\) −15.9448 −0.648250
\(606\) −4.44308 −0.180488
\(607\) 16.3675 0.664335 0.332168 0.943220i \(-0.392220\pi\)
0.332168 + 0.943220i \(0.392220\pi\)
\(608\) −1.99267 −0.0808134
\(609\) −1.57405 −0.0637839
\(610\) 8.99429 0.364168
\(611\) −20.6331 −0.834725
\(612\) 13.8759 0.560901
\(613\) 24.0957 0.973218 0.486609 0.873620i \(-0.338234\pi\)
0.486609 + 0.873620i \(0.338234\pi\)
\(614\) −11.3220 −0.456919
\(615\) 5.23125 0.210944
\(616\) −0.0308170 −0.00124165
\(617\) 20.1151 0.809802 0.404901 0.914361i \(-0.367306\pi\)
0.404901 + 0.914361i \(0.367306\pi\)
\(618\) −9.27282 −0.373008
\(619\) 15.6598 0.629419 0.314709 0.949188i \(-0.398093\pi\)
0.314709 + 0.949188i \(0.398093\pi\)
\(620\) 5.30879 0.213206
\(621\) −30.7742 −1.23493
\(622\) 27.8624 1.11718
\(623\) −9.22104 −0.369433
\(624\) 4.26649 0.170796
\(625\) −2.10623 −0.0842490
\(626\) 2.64490 0.105712
\(627\) −0.0421208 −0.00168214
\(628\) −5.26211 −0.209981
\(629\) −37.0344 −1.47666
\(630\) −3.66693 −0.146094
\(631\) −6.11162 −0.243300 −0.121650 0.992573i \(-0.538818\pi\)
−0.121650 + 0.992573i \(0.538818\pi\)
\(632\) 7.94777 0.316145
\(633\) 14.7754 0.587271
\(634\) −21.6517 −0.859901
\(635\) 2.03762 0.0808604
\(636\) −1.65120 −0.0654742
\(637\) 6.22014 0.246451
\(638\) 0.0707196 0.00279982
\(639\) −3.96899 −0.157011
\(640\) −1.44966 −0.0573027
\(641\) 12.6500 0.499645 0.249823 0.968292i \(-0.419628\pi\)
0.249823 + 0.968292i \(0.419628\pi\)
\(642\) −0.579917 −0.0228875
\(643\) 31.2782 1.23349 0.616747 0.787162i \(-0.288450\pi\)
0.616747 + 0.787162i \(0.288450\pi\)
\(644\) −8.11388 −0.319732
\(645\) −5.37710 −0.211723
\(646\) 10.9310 0.430074
\(647\) 29.2020 1.14805 0.574024 0.818839i \(-0.305382\pi\)
0.574024 + 0.818839i \(0.305382\pi\)
\(648\) −4.98703 −0.195909
\(649\) −0.139928 −0.00549266
\(650\) 18.0291 0.707158
\(651\) −2.51190 −0.0984489
\(652\) 11.7413 0.459824
\(653\) −8.40767 −0.329018 −0.164509 0.986376i \(-0.552604\pi\)
−0.164509 + 0.986376i \(0.552604\pi\)
\(654\) 12.0615 0.471641
\(655\) 20.2541 0.791391
\(656\) 5.26102 0.205408
\(657\) 22.6188 0.882444
\(658\) −3.31714 −0.129316
\(659\) 6.67436 0.259996 0.129998 0.991514i \(-0.458503\pi\)
0.129998 + 0.991514i \(0.458503\pi\)
\(660\) −0.0306427 −0.00119276
\(661\) −10.8115 −0.420520 −0.210260 0.977646i \(-0.567431\pi\)
−0.210260 + 0.977646i \(0.567431\pi\)
\(662\) −8.21795 −0.319400
\(663\) −23.4043 −0.908947
\(664\) 3.11054 0.120712
\(665\) −2.88868 −0.112018
\(666\) 17.0773 0.661732
\(667\) 18.6199 0.720966
\(668\) −9.95291 −0.385090
\(669\) −11.3856 −0.440192
\(670\) 0.922317 0.0356322
\(671\) 0.191202 0.00738128
\(672\) 0.685916 0.0264598
\(673\) −21.6068 −0.832880 −0.416440 0.909163i \(-0.636722\pi\)
−0.416440 + 0.909163i \(0.636722\pi\)
\(674\) −0.122451 −0.00471664
\(675\) 10.9934 0.423135
\(676\) 25.6902 0.988084
\(677\) 29.8146 1.14587 0.572934 0.819602i \(-0.305805\pi\)
0.572934 + 0.819602i \(0.305805\pi\)
\(678\) −9.01558 −0.346241
\(679\) −18.0193 −0.691518
\(680\) 7.95223 0.304954
\(681\) 1.72667 0.0661663
\(682\) 0.112855 0.00432145
\(683\) −3.13287 −0.119876 −0.0599380 0.998202i \(-0.519090\pi\)
−0.0599380 + 0.998202i \(0.519090\pi\)
\(684\) −5.04049 −0.192728
\(685\) 3.08015 0.117686
\(686\) 1.00000 0.0381802
\(687\) 6.50452 0.248163
\(688\) −5.40770 −0.206167
\(689\) −14.9737 −0.570451
\(690\) −8.06798 −0.307143
\(691\) 17.5682 0.668324 0.334162 0.942516i \(-0.391547\pi\)
0.334162 + 0.942516i \(0.391547\pi\)
\(692\) 15.1987 0.577767
\(693\) −0.0779523 −0.00296116
\(694\) −15.9204 −0.604329
\(695\) −18.6212 −0.706342
\(696\) −1.57405 −0.0596644
\(697\) −28.8598 −1.09314
\(698\) 15.4343 0.584198
\(699\) 4.58136 0.173283
\(700\) 2.89850 0.109553
\(701\) 16.6710 0.629654 0.314827 0.949149i \(-0.398053\pi\)
0.314827 + 0.949149i \(0.398053\pi\)
\(702\) 23.5917 0.890410
\(703\) 13.4529 0.507386
\(704\) −0.0308170 −0.00116146
\(705\) −3.29837 −0.124224
\(706\) 12.2792 0.462133
\(707\) −6.47759 −0.243615
\(708\) 3.11447 0.117049
\(709\) −3.03723 −0.114065 −0.0570327 0.998372i \(-0.518164\pi\)
−0.0570327 + 0.998372i \(0.518164\pi\)
\(710\) −2.27461 −0.0853647
\(711\) 20.1040 0.753960
\(712\) −9.22104 −0.345573
\(713\) 29.7139 1.11279
\(714\) −3.76266 −0.140814
\(715\) −0.277879 −0.0103921
\(716\) 23.3175 0.871418
\(717\) −5.93911 −0.221800
\(718\) −8.69460 −0.324480
\(719\) 38.2013 1.42467 0.712333 0.701841i \(-0.247638\pi\)
0.712333 + 0.701841i \(0.247638\pi\)
\(720\) −3.66693 −0.136659
\(721\) −13.5189 −0.503470
\(722\) 15.0293 0.559332
\(723\) 20.7758 0.772662
\(724\) 10.4772 0.389384
\(725\) −6.65153 −0.247032
\(726\) 7.54442 0.280000
\(727\) −11.0846 −0.411104 −0.205552 0.978646i \(-0.565899\pi\)
−0.205552 + 0.978646i \(0.565899\pi\)
\(728\) 6.22014 0.230534
\(729\) −4.81019 −0.178155
\(730\) 12.9627 0.479773
\(731\) 29.6645 1.09718
\(732\) −4.25572 −0.157296
\(733\) −4.23493 −0.156421 −0.0782103 0.996937i \(-0.524921\pi\)
−0.0782103 + 0.996937i \(0.524921\pi\)
\(734\) −19.3936 −0.715831
\(735\) 0.994342 0.0366769
\(736\) −8.11388 −0.299082
\(737\) 0.0196068 0.000722225 0
\(738\) 13.3079 0.489869
\(739\) −31.7481 −1.16787 −0.583937 0.811799i \(-0.698489\pi\)
−0.583937 + 0.811799i \(0.698489\pi\)
\(740\) 9.78693 0.359775
\(741\) 8.50171 0.312318
\(742\) −2.40729 −0.0883743
\(743\) −28.5024 −1.04565 −0.522826 0.852439i \(-0.675122\pi\)
−0.522826 + 0.852439i \(0.675122\pi\)
\(744\) −2.51190 −0.0920905
\(745\) 27.6195 1.01190
\(746\) 10.3958 0.380618
\(747\) 7.86817 0.287881
\(748\) 0.169050 0.00618108
\(749\) −0.845463 −0.0308926
\(750\) 7.85381 0.286780
\(751\) −48.3090 −1.76282 −0.881411 0.472351i \(-0.843406\pi\)
−0.881411 + 0.472351i \(0.843406\pi\)
\(752\) −3.31714 −0.120964
\(753\) −18.8295 −0.686183
\(754\) −14.2741 −0.519833
\(755\) −21.3289 −0.776239
\(756\) 3.79278 0.137942
\(757\) −12.3826 −0.450053 −0.225027 0.974353i \(-0.572247\pi\)
−0.225027 + 0.974353i \(0.572247\pi\)
\(758\) −12.1040 −0.439637
\(759\) −0.171510 −0.00622543
\(760\) −2.88868 −0.104784
\(761\) −5.64665 −0.204691 −0.102345 0.994749i \(-0.532635\pi\)
−0.102345 + 0.994749i \(0.532635\pi\)
\(762\) −0.964115 −0.0349262
\(763\) 17.5845 0.636602
\(764\) 10.2549 0.371010
\(765\) 20.1153 0.727271
\(766\) 24.9672 0.902102
\(767\) 28.2432 1.01980
\(768\) 0.685916 0.0247509
\(769\) 14.5728 0.525510 0.262755 0.964863i \(-0.415369\pi\)
0.262755 + 0.964863i \(0.415369\pi\)
\(770\) −0.0446741 −0.00160994
\(771\) −12.1040 −0.435914
\(772\) 9.26826 0.333572
\(773\) 4.71945 0.169747 0.0848734 0.996392i \(-0.472951\pi\)
0.0848734 + 0.996392i \(0.472951\pi\)
\(774\) −13.6789 −0.491677
\(775\) −10.6146 −0.381288
\(776\) −18.0193 −0.646855
\(777\) −4.63076 −0.166128
\(778\) 7.59387 0.272253
\(779\) 10.4835 0.375609
\(780\) 6.18495 0.221457
\(781\) −0.0483541 −0.00173025
\(782\) 44.5095 1.59166
\(783\) −8.70376 −0.311047
\(784\) 1.00000 0.0357143
\(785\) −7.62825 −0.272264
\(786\) −9.58336 −0.341827
\(787\) −27.2083 −0.969871 −0.484935 0.874550i \(-0.661157\pi\)
−0.484935 + 0.874550i \(0.661157\pi\)
\(788\) 10.5984 0.377554
\(789\) 21.6793 0.771803
\(790\) 11.5215 0.409918
\(791\) −13.1439 −0.467342
\(792\) −0.0779523 −0.00276991
\(793\) −38.5924 −1.37046
\(794\) 27.8996 0.990119
\(795\) −2.39367 −0.0848946
\(796\) 19.5234 0.691987
\(797\) 32.0017 1.13356 0.566779 0.823870i \(-0.308189\pi\)
0.566779 + 0.823870i \(0.308189\pi\)
\(798\) 1.36680 0.0483843
\(799\) 18.1965 0.643746
\(800\) 2.89850 0.102477
\(801\) −23.3248 −0.824141
\(802\) 29.8254 1.05317
\(803\) 0.275564 0.00972445
\(804\) −0.436401 −0.0153907
\(805\) −11.7623 −0.414568
\(806\) −22.7788 −0.802350
\(807\) 6.01512 0.211742
\(808\) −6.47759 −0.227881
\(809\) −19.2720 −0.677568 −0.338784 0.940864i \(-0.610016\pi\)
−0.338784 + 0.940864i \(0.610016\pi\)
\(810\) −7.22948 −0.254018
\(811\) 32.7314 1.14935 0.574677 0.818380i \(-0.305128\pi\)
0.574677 + 0.818380i \(0.305128\pi\)
\(812\) −2.29482 −0.0805325
\(813\) 2.37879 0.0834278
\(814\) 0.208052 0.00729223
\(815\) 17.0208 0.596214
\(816\) −3.76266 −0.131719
\(817\) −10.7758 −0.376996
\(818\) 20.0637 0.701510
\(819\) 15.7340 0.549790
\(820\) 7.62667 0.266335
\(821\) 18.9537 0.661488 0.330744 0.943721i \(-0.392700\pi\)
0.330744 + 0.943721i \(0.392700\pi\)
\(822\) −1.45740 −0.0508325
\(823\) 14.1095 0.491827 0.245914 0.969292i \(-0.420912\pi\)
0.245914 + 0.969292i \(0.420912\pi\)
\(824\) −13.5189 −0.470953
\(825\) 0.0612681 0.00213308
\(826\) 4.54061 0.157988
\(827\) −50.3314 −1.75020 −0.875098 0.483946i \(-0.839203\pi\)
−0.875098 + 0.483946i \(0.839203\pi\)
\(828\) −20.5242 −0.713266
\(829\) 31.8882 1.10752 0.553762 0.832675i \(-0.313192\pi\)
0.553762 + 0.832675i \(0.313192\pi\)
\(830\) 4.50921 0.156517
\(831\) −4.90502 −0.170153
\(832\) 6.22014 0.215645
\(833\) −5.48560 −0.190065
\(834\) 8.81076 0.305092
\(835\) −14.4283 −0.499312
\(836\) −0.0614081 −0.00212385
\(837\) −13.8896 −0.480094
\(838\) −35.1960 −1.21582
\(839\) 27.8915 0.962921 0.481460 0.876468i \(-0.340107\pi\)
0.481460 + 0.876468i \(0.340107\pi\)
\(840\) 0.994342 0.0343081
\(841\) −23.7338 −0.818407
\(842\) 22.9700 0.791600
\(843\) −1.18612 −0.0408521
\(844\) 21.5412 0.741478
\(845\) 37.2419 1.28116
\(846\) −8.39077 −0.288481
\(847\) 10.9991 0.377932
\(848\) −2.40729 −0.0826666
\(849\) −4.24077 −0.145543
\(850\) −15.9000 −0.545365
\(851\) 54.7785 1.87778
\(852\) 1.07625 0.0368717
\(853\) −1.47676 −0.0505634 −0.0252817 0.999680i \(-0.508048\pi\)
−0.0252817 + 0.999680i \(0.508048\pi\)
\(854\) −6.20443 −0.212311
\(855\) −7.30698 −0.249894
\(856\) −0.845463 −0.0288973
\(857\) 51.1010 1.74558 0.872788 0.488100i \(-0.162310\pi\)
0.872788 + 0.488100i \(0.162310\pi\)
\(858\) 0.131481 0.00448868
\(859\) 36.8114 1.25599 0.627994 0.778218i \(-0.283876\pi\)
0.627994 + 0.778218i \(0.283876\pi\)
\(860\) −7.83931 −0.267318
\(861\) −3.60862 −0.122981
\(862\) −1.00000 −0.0340601
\(863\) −10.8980 −0.370971 −0.185486 0.982647i \(-0.559386\pi\)
−0.185486 + 0.982647i \(0.559386\pi\)
\(864\) 3.79278 0.129033
\(865\) 22.0328 0.749139
\(866\) 30.5862 1.03936
\(867\) 8.97986 0.304972
\(868\) −3.66210 −0.124300
\(869\) 0.244927 0.00830857
\(870\) −2.28184 −0.0773615
\(871\) −3.95745 −0.134093
\(872\) 17.5845 0.595486
\(873\) −45.5802 −1.54266
\(874\) −16.1683 −0.546900
\(875\) 11.4501 0.387084
\(876\) −6.13342 −0.207229
\(877\) −21.8750 −0.738666 −0.369333 0.929297i \(-0.620414\pi\)
−0.369333 + 0.929297i \(0.620414\pi\)
\(878\) −21.7019 −0.732405
\(879\) −8.71255 −0.293867
\(880\) −0.0446741 −0.00150596
\(881\) −39.1598 −1.31933 −0.659663 0.751561i \(-0.729301\pi\)
−0.659663 + 0.751561i \(0.729301\pi\)
\(882\) 2.52952 0.0851734
\(883\) 24.2995 0.817742 0.408871 0.912592i \(-0.365923\pi\)
0.408871 + 0.912592i \(0.365923\pi\)
\(884\) −34.1212 −1.14762
\(885\) 4.51491 0.151767
\(886\) −18.8299 −0.632602
\(887\) 36.8751 1.23814 0.619072 0.785334i \(-0.287509\pi\)
0.619072 + 0.785334i \(0.287509\pi\)
\(888\) −4.63076 −0.155398
\(889\) −1.40559 −0.0471419
\(890\) −13.3673 −0.448074
\(891\) −0.153685 −0.00514866
\(892\) −16.5991 −0.555779
\(893\) −6.60996 −0.221194
\(894\) −13.0684 −0.437071
\(895\) 33.8024 1.12989
\(896\) 1.00000 0.0334077
\(897\) 34.6178 1.15586
\(898\) −14.2002 −0.473867
\(899\) 8.40388 0.280285
\(900\) 7.33181 0.244394
\(901\) 13.2054 0.439936
\(902\) 0.162129 0.00539831
\(903\) 3.70923 0.123435
\(904\) −13.1439 −0.437158
\(905\) 15.1884 0.504880
\(906\) 10.0919 0.335282
\(907\) 10.8381 0.359874 0.179937 0.983678i \(-0.442411\pi\)
0.179937 + 0.983678i \(0.442411\pi\)
\(908\) 2.51733 0.0835404
\(909\) −16.3852 −0.543463
\(910\) 9.01707 0.298913
\(911\) −27.6501 −0.916087 −0.458044 0.888930i \(-0.651450\pi\)
−0.458044 + 0.888930i \(0.651450\pi\)
\(912\) 1.36680 0.0452594
\(913\) 0.0958576 0.00317242
\(914\) 6.48130 0.214382
\(915\) −6.16932 −0.203952
\(916\) 9.48297 0.313326
\(917\) −13.9716 −0.461384
\(918\) −20.8057 −0.686690
\(919\) 20.4983 0.676177 0.338088 0.941114i \(-0.390220\pi\)
0.338088 + 0.941114i \(0.390220\pi\)
\(920\) −11.7623 −0.387793
\(921\) 7.76594 0.255896
\(922\) 36.2829 1.19491
\(923\) 9.75984 0.321249
\(924\) 0.0211379 0.000695386 0
\(925\) −19.5684 −0.643404
\(926\) −21.2718 −0.699035
\(927\) −34.1963 −1.12315
\(928\) −2.29482 −0.0753312
\(929\) 12.9612 0.425243 0.212621 0.977135i \(-0.431800\pi\)
0.212621 + 0.977135i \(0.431800\pi\)
\(930\) −3.64138 −0.119406
\(931\) 1.99267 0.0653071
\(932\) 6.67919 0.218784
\(933\) −19.1113 −0.625675
\(934\) −31.3240 −1.02495
\(935\) 0.245064 0.00801445
\(936\) 15.7340 0.514281
\(937\) −33.4423 −1.09251 −0.546256 0.837618i \(-0.683947\pi\)
−0.546256 + 0.837618i \(0.683947\pi\)
\(938\) −0.636232 −0.0207737
\(939\) −1.81418 −0.0592035
\(940\) −4.80871 −0.156843
\(941\) −11.1379 −0.363084 −0.181542 0.983383i \(-0.558109\pi\)
−0.181542 + 0.983383i \(0.558109\pi\)
\(942\) 3.60937 0.117600
\(943\) 42.6873 1.39009
\(944\) 4.54061 0.147784
\(945\) 5.49823 0.178858
\(946\) −0.166649 −0.00541824
\(947\) −34.2659 −1.11349 −0.556745 0.830683i \(-0.687950\pi\)
−0.556745 + 0.830683i \(0.687950\pi\)
\(948\) −5.45150 −0.177056
\(949\) −55.6202 −1.80551
\(950\) 5.77574 0.187390
\(951\) 14.8513 0.481585
\(952\) −5.48560 −0.177789
\(953\) 37.6925 1.22098 0.610490 0.792024i \(-0.290973\pi\)
0.610490 + 0.792024i \(0.290973\pi\)
\(954\) −6.08928 −0.197148
\(955\) 14.8661 0.481056
\(956\) −8.65865 −0.280041
\(957\) −0.0485077 −0.00156803
\(958\) −13.2576 −0.428334
\(959\) −2.12475 −0.0686116
\(960\) 0.994342 0.0320922
\(961\) −17.5890 −0.567387
\(962\) −41.9935 −1.35392
\(963\) −2.13862 −0.0689159
\(964\) 30.2892 0.975549
\(965\) 13.4358 0.432513
\(966\) 5.56544 0.179065
\(967\) −24.3424 −0.782798 −0.391399 0.920221i \(-0.628009\pi\)
−0.391399 + 0.920221i \(0.628009\pi\)
\(968\) 10.9991 0.353523
\(969\) −7.49773 −0.240862
\(970\) −26.1218 −0.838720
\(971\) −44.0029 −1.41212 −0.706061 0.708151i \(-0.749529\pi\)
−0.706061 + 0.708151i \(0.749529\pi\)
\(972\) 14.7990 0.474679
\(973\) 12.8453 0.411800
\(974\) 7.13345 0.228570
\(975\) −12.3664 −0.396042
\(976\) −6.20443 −0.198599
\(977\) −7.29605 −0.233421 −0.116711 0.993166i \(-0.537235\pi\)
−0.116711 + 0.993166i \(0.537235\pi\)
\(978\) −8.05354 −0.257524
\(979\) −0.284165 −0.00908196
\(980\) 1.44966 0.0463076
\(981\) 44.4803 1.42015
\(982\) −2.55846 −0.0816438
\(983\) −33.3403 −1.06339 −0.531695 0.846936i \(-0.678445\pi\)
−0.531695 + 0.846936i \(0.678445\pi\)
\(984\) −3.60862 −0.115038
\(985\) 15.3641 0.489541
\(986\) 12.5885 0.400898
\(987\) 2.27528 0.0724229
\(988\) 12.3947 0.394327
\(989\) −43.8775 −1.39522
\(990\) −0.113004 −0.00359150
\(991\) 18.3156 0.581815 0.290907 0.956751i \(-0.406043\pi\)
0.290907 + 0.956751i \(0.406043\pi\)
\(992\) −3.66210 −0.116272
\(993\) 5.63682 0.178879
\(994\) 1.56907 0.0497679
\(995\) 28.3022 0.897239
\(996\) −2.13357 −0.0676046
\(997\) −42.8296 −1.35643 −0.678214 0.734864i \(-0.737246\pi\)
−0.678214 + 0.734864i \(0.737246\pi\)
\(998\) −25.5539 −0.808894
\(999\) −25.6059 −0.810134
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 \(a_p\))