Properties

Label 6023.2.a.b.1.14
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.20648 q^{2}\) \(-1.66546 q^{3}\) \(+2.86855 q^{4}\) \(+2.85921 q^{5}\) \(+3.67480 q^{6}\) \(-0.996345 q^{7}\) \(-1.91643 q^{8}\) \(-0.226251 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.20648 q^{2}\) \(-1.66546 q^{3}\) \(+2.86855 q^{4}\) \(+2.85921 q^{5}\) \(+3.67480 q^{6}\) \(-0.996345 q^{7}\) \(-1.91643 q^{8}\) \(-0.226251 q^{9}\) \(-6.30878 q^{10}\) \(+4.63930 q^{11}\) \(-4.77745 q^{12}\) \(+1.51057 q^{13}\) \(+2.19841 q^{14}\) \(-4.76189 q^{15}\) \(-1.50853 q^{16}\) \(+2.86077 q^{17}\) \(+0.499218 q^{18}\) \(-1.00000 q^{19}\) \(+8.20177 q^{20}\) \(+1.65937 q^{21}\) \(-10.2365 q^{22}\) \(-4.55077 q^{23}\) \(+3.19174 q^{24}\) \(+3.17506 q^{25}\) \(-3.33304 q^{26}\) \(+5.37318 q^{27}\) \(-2.85806 q^{28}\) \(-8.47482 q^{29}\) \(+10.5070 q^{30}\) \(+9.31539 q^{31}\) \(+7.16140 q^{32}\) \(-7.72657 q^{33}\) \(-6.31222 q^{34}\) \(-2.84875 q^{35}\) \(-0.649012 q^{36}\) \(+3.67526 q^{37}\) \(+2.20648 q^{38}\) \(-2.51579 q^{39}\) \(-5.47948 q^{40}\) \(+4.17881 q^{41}\) \(-3.66136 q^{42}\) \(-10.4376 q^{43}\) \(+13.3081 q^{44}\) \(-0.646899 q^{45}\) \(+10.0412 q^{46}\) \(-10.5636 q^{47}\) \(+2.51239 q^{48}\) \(-6.00730 q^{49}\) \(-7.00570 q^{50}\) \(-4.76449 q^{51}\) \(+4.33314 q^{52}\) \(-7.87956 q^{53}\) \(-11.8558 q^{54}\) \(+13.2647 q^{55}\) \(+1.90943 q^{56}\) \(+1.66546 q^{57}\) \(+18.6995 q^{58}\) \(+4.45425 q^{59}\) \(-13.6597 q^{60}\) \(+0.678642 q^{61}\) \(-20.5542 q^{62}\) \(+0.225424 q^{63}\) \(-12.7844 q^{64}\) \(+4.31902 q^{65}\) \(+17.0485 q^{66}\) \(+10.1411 q^{67}\) \(+8.20625 q^{68}\) \(+7.57912 q^{69}\) \(+6.28572 q^{70}\) \(-1.30386 q^{71}\) \(+0.433595 q^{72}\) \(-5.52882 q^{73}\) \(-8.10939 q^{74}\) \(-5.28793 q^{75}\) \(-2.86855 q^{76}\) \(-4.62235 q^{77}\) \(+5.55103 q^{78}\) \(-9.51275 q^{79}\) \(-4.31319 q^{80}\) \(-8.27006 q^{81}\) \(-9.22046 q^{82}\) \(-4.61347 q^{83}\) \(+4.75998 q^{84}\) \(+8.17952 q^{85}\) \(+23.0303 q^{86}\) \(+14.1145 q^{87}\) \(-8.89092 q^{88}\) \(-6.53101 q^{89}\) \(+1.42737 q^{90}\) \(-1.50505 q^{91}\) \(-13.0541 q^{92}\) \(-15.5144 q^{93}\) \(+23.3085 q^{94}\) \(-2.85921 q^{95}\) \(-11.9270 q^{96}\) \(-3.54978 q^{97}\) \(+13.2550 q^{98}\) \(-1.04965 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20648 −1.56022 −0.780108 0.625645i \(-0.784836\pi\)
−0.780108 + 0.625645i \(0.784836\pi\)
\(3\) −1.66546 −0.961552 −0.480776 0.876843i \(-0.659645\pi\)
−0.480776 + 0.876843i \(0.659645\pi\)
\(4\) 2.86855 1.43427
\(5\) 2.85921 1.27868 0.639338 0.768926i \(-0.279209\pi\)
0.639338 + 0.768926i \(0.279209\pi\)
\(6\) 3.67480 1.50023
\(7\) −0.996345 −0.376583 −0.188291 0.982113i \(-0.560295\pi\)
−0.188291 + 0.982113i \(0.560295\pi\)
\(8\) −1.91643 −0.677562
\(9\) −0.226251 −0.0754171
\(10\) −6.30878 −1.99501
\(11\) 4.63930 1.39880 0.699402 0.714729i \(-0.253450\pi\)
0.699402 + 0.714729i \(0.253450\pi\)
\(12\) −4.77745 −1.37913
\(13\) 1.51057 0.418956 0.209478 0.977813i \(-0.432824\pi\)
0.209478 + 0.977813i \(0.432824\pi\)
\(14\) 2.19841 0.587551
\(15\) −4.76189 −1.22951
\(16\) −1.50853 −0.377131
\(17\) 2.86077 0.693838 0.346919 0.937895i \(-0.387228\pi\)
0.346919 + 0.937895i \(0.387228\pi\)
\(18\) 0.499218 0.117667
\(19\) −1.00000 −0.229416
\(20\) 8.20177 1.83397
\(21\) 1.65937 0.362104
\(22\) −10.2365 −2.18244
\(23\) −4.55077 −0.948902 −0.474451 0.880282i \(-0.657353\pi\)
−0.474451 + 0.880282i \(0.657353\pi\)
\(24\) 3.19174 0.651511
\(25\) 3.17506 0.635012
\(26\) −3.33304 −0.653662
\(27\) 5.37318 1.03407
\(28\) −2.85806 −0.540123
\(29\) −8.47482 −1.57373 −0.786867 0.617122i \(-0.788298\pi\)
−0.786867 + 0.617122i \(0.788298\pi\)
\(30\) 10.5070 1.91831
\(31\) 9.31539 1.67309 0.836547 0.547895i \(-0.184571\pi\)
0.836547 + 0.547895i \(0.184571\pi\)
\(32\) 7.16140 1.26597
\(33\) −7.72657 −1.34502
\(34\) −6.31222 −1.08254
\(35\) −2.84875 −0.481527
\(36\) −0.649012 −0.108169
\(37\) 3.67526 0.604210 0.302105 0.953275i \(-0.402311\pi\)
0.302105 + 0.953275i \(0.402311\pi\)
\(38\) 2.20648 0.357938
\(39\) −2.51579 −0.402848
\(40\) −5.47948 −0.866382
\(41\) 4.17881 0.652621 0.326310 0.945263i \(-0.394195\pi\)
0.326310 + 0.945263i \(0.394195\pi\)
\(42\) −3.66136 −0.564961
\(43\) −10.4376 −1.59171 −0.795857 0.605484i \(-0.792980\pi\)
−0.795857 + 0.605484i \(0.792980\pi\)
\(44\) 13.3081 2.00627
\(45\) −0.646899 −0.0964340
\(46\) 10.0412 1.48049
\(47\) −10.5636 −1.54087 −0.770433 0.637521i \(-0.779960\pi\)
−0.770433 + 0.637521i \(0.779960\pi\)
\(48\) 2.51239 0.362632
\(49\) −6.00730 −0.858185
\(50\) −7.00570 −0.990756
\(51\) −4.76449 −0.667161
\(52\) 4.33314 0.600898
\(53\) −7.87956 −1.08234 −0.541170 0.840913i \(-0.682019\pi\)
−0.541170 + 0.840913i \(0.682019\pi\)
\(54\) −11.8558 −1.61337
\(55\) 13.2647 1.78862
\(56\) 1.90943 0.255158
\(57\) 1.66546 0.220595
\(58\) 18.6995 2.45537
\(59\) 4.45425 0.579894 0.289947 0.957043i \(-0.406362\pi\)
0.289947 + 0.957043i \(0.406362\pi\)
\(60\) −13.6597 −1.76346
\(61\) 0.678642 0.0868911 0.0434456 0.999056i \(-0.486166\pi\)
0.0434456 + 0.999056i \(0.486166\pi\)
\(62\) −20.5542 −2.61039
\(63\) 0.225424 0.0284008
\(64\) −12.7844 −1.59805
\(65\) 4.31902 0.535709
\(66\) 17.0485 2.09853
\(67\) 10.1411 1.23894 0.619469 0.785021i \(-0.287348\pi\)
0.619469 + 0.785021i \(0.287348\pi\)
\(68\) 8.20625 0.995154
\(69\) 7.57912 0.912418
\(70\) 6.28572 0.751287
\(71\) −1.30386 −0.154739 −0.0773696 0.997002i \(-0.524652\pi\)
−0.0773696 + 0.997002i \(0.524652\pi\)
\(72\) 0.433595 0.0510997
\(73\) −5.52882 −0.647100 −0.323550 0.946211i \(-0.604876\pi\)
−0.323550 + 0.946211i \(0.604876\pi\)
\(74\) −8.10939 −0.942698
\(75\) −5.28793 −0.610597
\(76\) −2.86855 −0.329045
\(77\) −4.62235 −0.526765
\(78\) 5.55103 0.628530
\(79\) −9.51275 −1.07027 −0.535134 0.844767i \(-0.679739\pi\)
−0.535134 + 0.844767i \(0.679739\pi\)
\(80\) −4.31319 −0.482229
\(81\) −8.27006 −0.918895
\(82\) −9.22046 −1.01823
\(83\) −4.61347 −0.506394 −0.253197 0.967415i \(-0.581482\pi\)
−0.253197 + 0.967415i \(0.581482\pi\)
\(84\) 4.75998 0.519357
\(85\) 8.17952 0.887194
\(86\) 23.0303 2.48342
\(87\) 14.1145 1.51323
\(88\) −8.89092 −0.947776
\(89\) −6.53101 −0.692286 −0.346143 0.938182i \(-0.612509\pi\)
−0.346143 + 0.938182i \(0.612509\pi\)
\(90\) 1.42737 0.150458
\(91\) −1.50505 −0.157772
\(92\) −13.0541 −1.36099
\(93\) −15.5144 −1.60877
\(94\) 23.3085 2.40408
\(95\) −2.85921 −0.293348
\(96\) −11.9270 −1.21729
\(97\) −3.54978 −0.360425 −0.180213 0.983628i \(-0.557679\pi\)
−0.180213 + 0.983628i \(0.557679\pi\)
\(98\) 13.2550 1.33895
\(99\) −1.04965 −0.105494
\(100\) 9.10781 0.910781
\(101\) 3.19030 0.317447 0.158724 0.987323i \(-0.449262\pi\)
0.158724 + 0.987323i \(0.449262\pi\)
\(102\) 10.5127 1.04092
\(103\) −6.81128 −0.671136 −0.335568 0.942016i \(-0.608928\pi\)
−0.335568 + 0.942016i \(0.608928\pi\)
\(104\) −2.89490 −0.283869
\(105\) 4.74448 0.463014
\(106\) 17.3861 1.68869
\(107\) −9.82688 −0.950000 −0.475000 0.879986i \(-0.657552\pi\)
−0.475000 + 0.879986i \(0.657552\pi\)
\(108\) 15.4132 1.48314
\(109\) −14.5679 −1.39536 −0.697678 0.716411i \(-0.745783\pi\)
−0.697678 + 0.716411i \(0.745783\pi\)
\(110\) −29.2683 −2.79063
\(111\) −6.12100 −0.580979
\(112\) 1.50301 0.142021
\(113\) −5.41146 −0.509067 −0.254533 0.967064i \(-0.581922\pi\)
−0.254533 + 0.967064i \(0.581922\pi\)
\(114\) −3.67480 −0.344176
\(115\) −13.0116 −1.21334
\(116\) −24.3104 −2.25717
\(117\) −0.341768 −0.0315964
\(118\) −9.82821 −0.904760
\(119\) −2.85031 −0.261287
\(120\) 9.12584 0.833072
\(121\) 10.5231 0.956650
\(122\) −1.49741 −0.135569
\(123\) −6.95963 −0.627529
\(124\) 26.7217 2.39968
\(125\) −5.21788 −0.466702
\(126\) −0.497394 −0.0443113
\(127\) 2.67749 0.237589 0.118795 0.992919i \(-0.462097\pi\)
0.118795 + 0.992919i \(0.462097\pi\)
\(128\) 13.8858 1.22734
\(129\) 17.3833 1.53052
\(130\) −9.52984 −0.835822
\(131\) −3.51171 −0.306820 −0.153410 0.988163i \(-0.549025\pi\)
−0.153410 + 0.988163i \(0.549025\pi\)
\(132\) −22.1640 −1.92913
\(133\) 0.996345 0.0863940
\(134\) −22.3762 −1.93301
\(135\) 15.3630 1.32224
\(136\) −5.48247 −0.470118
\(137\) −7.90848 −0.675667 −0.337833 0.941206i \(-0.609694\pi\)
−0.337833 + 0.941206i \(0.609694\pi\)
\(138\) −16.7232 −1.42357
\(139\) −13.9366 −1.18208 −0.591042 0.806641i \(-0.701283\pi\)
−0.591042 + 0.806641i \(0.701283\pi\)
\(140\) −8.17179 −0.690642
\(141\) 17.5933 1.48162
\(142\) 2.87693 0.241427
\(143\) 7.00798 0.586037
\(144\) 0.341306 0.0284421
\(145\) −24.2313 −2.01230
\(146\) 12.1992 1.00962
\(147\) 10.0049 0.825190
\(148\) 10.5427 0.866602
\(149\) 1.10069 0.0901718 0.0450859 0.998983i \(-0.485644\pi\)
0.0450859 + 0.998983i \(0.485644\pi\)
\(150\) 11.6677 0.952663
\(151\) 22.0629 1.79545 0.897726 0.440554i \(-0.145218\pi\)
0.897726 + 0.440554i \(0.145218\pi\)
\(152\) 1.91643 0.155443
\(153\) −0.647252 −0.0523272
\(154\) 10.1991 0.821868
\(155\) 26.6346 2.13934
\(156\) −7.21666 −0.577795
\(157\) −22.8750 −1.82563 −0.912814 0.408376i \(-0.866095\pi\)
−0.912814 + 0.408376i \(0.866095\pi\)
\(158\) 20.9897 1.66985
\(159\) 13.1231 1.04073
\(160\) 20.4759 1.61876
\(161\) 4.53414 0.357340
\(162\) 18.2477 1.43368
\(163\) 11.6444 0.912060 0.456030 0.889965i \(-0.349271\pi\)
0.456030 + 0.889965i \(0.349271\pi\)
\(164\) 11.9871 0.936037
\(165\) −22.0918 −1.71985
\(166\) 10.1795 0.790083
\(167\) −1.69408 −0.131092 −0.0655460 0.997850i \(-0.520879\pi\)
−0.0655460 + 0.997850i \(0.520879\pi\)
\(168\) −3.18007 −0.245348
\(169\) −10.7182 −0.824476
\(170\) −18.0479 −1.38421
\(171\) 0.226251 0.0173019
\(172\) −29.9407 −2.28296
\(173\) −5.03574 −0.382860 −0.191430 0.981506i \(-0.561312\pi\)
−0.191430 + 0.981506i \(0.561312\pi\)
\(174\) −31.1432 −2.36096
\(175\) −3.16345 −0.239135
\(176\) −6.99851 −0.527533
\(177\) −7.41836 −0.557598
\(178\) 14.4105 1.08012
\(179\) 11.1998 0.837111 0.418555 0.908191i \(-0.362537\pi\)
0.418555 + 0.908191i \(0.362537\pi\)
\(180\) −1.85566 −0.138313
\(181\) 21.3420 1.58634 0.793168 0.609003i \(-0.208430\pi\)
0.793168 + 0.609003i \(0.208430\pi\)
\(182\) 3.32085 0.246158
\(183\) −1.13025 −0.0835504
\(184\) 8.72126 0.642939
\(185\) 10.5083 0.772588
\(186\) 34.2322 2.51003
\(187\) 13.2720 0.970543
\(188\) −30.3023 −2.21002
\(189\) −5.35354 −0.389413
\(190\) 6.30878 0.457687
\(191\) −19.8342 −1.43515 −0.717577 0.696480i \(-0.754749\pi\)
−0.717577 + 0.696480i \(0.754749\pi\)
\(192\) 21.2919 1.53661
\(193\) −8.97106 −0.645751 −0.322876 0.946441i \(-0.604650\pi\)
−0.322876 + 0.946441i \(0.604650\pi\)
\(194\) 7.83251 0.562342
\(195\) −7.19315 −0.515112
\(196\) −17.2322 −1.23087
\(197\) −6.82131 −0.485998 −0.242999 0.970027i \(-0.578131\pi\)
−0.242999 + 0.970027i \(0.578131\pi\)
\(198\) 2.31603 0.164593
\(199\) 4.42136 0.313422 0.156711 0.987645i \(-0.449911\pi\)
0.156711 + 0.987645i \(0.449911\pi\)
\(200\) −6.08479 −0.430260
\(201\) −16.8896 −1.19130
\(202\) −7.03934 −0.495286
\(203\) 8.44384 0.592641
\(204\) −13.6672 −0.956893
\(205\) 11.9481 0.834490
\(206\) 15.0289 1.04712
\(207\) 1.02962 0.0715634
\(208\) −2.27873 −0.158002
\(209\) −4.63930 −0.320907
\(210\) −10.4686 −0.722402
\(211\) 9.62297 0.662473 0.331236 0.943548i \(-0.392534\pi\)
0.331236 + 0.943548i \(0.392534\pi\)
\(212\) −22.6029 −1.55237
\(213\) 2.17152 0.148790
\(214\) 21.6828 1.48221
\(215\) −29.8432 −2.03529
\(216\) −10.2974 −0.700646
\(217\) −9.28134 −0.630059
\(218\) 32.1439 2.17706
\(219\) 9.20802 0.622220
\(220\) 38.0505 2.56537
\(221\) 4.32138 0.290688
\(222\) 13.5058 0.906453
\(223\) −5.62330 −0.376564 −0.188282 0.982115i \(-0.560292\pi\)
−0.188282 + 0.982115i \(0.560292\pi\)
\(224\) −7.13522 −0.476742
\(225\) −0.718361 −0.0478907
\(226\) 11.9403 0.794255
\(227\) 14.0935 0.935416 0.467708 0.883883i \(-0.345080\pi\)
0.467708 + 0.883883i \(0.345080\pi\)
\(228\) 4.77745 0.316394
\(229\) 14.4900 0.957525 0.478763 0.877944i \(-0.341085\pi\)
0.478763 + 0.877944i \(0.341085\pi\)
\(230\) 28.7098 1.89307
\(231\) 7.69832 0.506512
\(232\) 16.2414 1.06630
\(233\) 17.1006 1.12030 0.560149 0.828392i \(-0.310744\pi\)
0.560149 + 0.828392i \(0.310744\pi\)
\(234\) 0.754103 0.0492973
\(235\) −30.2036 −1.97027
\(236\) 12.7772 0.831727
\(237\) 15.8431 1.02912
\(238\) 6.28915 0.407665
\(239\) 23.7055 1.53338 0.766692 0.642015i \(-0.221901\pi\)
0.766692 + 0.642015i \(0.221901\pi\)
\(240\) 7.18343 0.463688
\(241\) 26.0845 1.68025 0.840126 0.542391i \(-0.182481\pi\)
0.840126 + 0.542391i \(0.182481\pi\)
\(242\) −23.2191 −1.49258
\(243\) −2.34612 −0.150504
\(244\) 1.94672 0.124626
\(245\) −17.1761 −1.09734
\(246\) 15.3563 0.979081
\(247\) −1.51057 −0.0961151
\(248\) −17.8523 −1.13362
\(249\) 7.68353 0.486924
\(250\) 11.5131 0.728155
\(251\) 4.41109 0.278426 0.139213 0.990262i \(-0.455543\pi\)
0.139213 + 0.990262i \(0.455543\pi\)
\(252\) 0.646640 0.0407345
\(253\) −21.1124 −1.32733
\(254\) −5.90783 −0.370690
\(255\) −13.6226 −0.853083
\(256\) −5.06979 −0.316862
\(257\) −22.3700 −1.39540 −0.697701 0.716389i \(-0.745794\pi\)
−0.697701 + 0.716389i \(0.745794\pi\)
\(258\) −38.3560 −2.38794
\(259\) −3.66183 −0.227535
\(260\) 12.3893 0.768354
\(261\) 1.91744 0.118686
\(262\) 7.74852 0.478705
\(263\) −6.67943 −0.411872 −0.205936 0.978566i \(-0.566024\pi\)
−0.205936 + 0.978566i \(0.566024\pi\)
\(264\) 14.8075 0.911336
\(265\) −22.5293 −1.38396
\(266\) −2.19841 −0.134793
\(267\) 10.8771 0.665669
\(268\) 29.0904 1.77698
\(269\) −5.93768 −0.362027 −0.181014 0.983481i \(-0.557938\pi\)
−0.181014 + 0.983481i \(0.557938\pi\)
\(270\) −33.8982 −2.06298
\(271\) −28.2007 −1.71307 −0.856536 0.516087i \(-0.827388\pi\)
−0.856536 + 0.516087i \(0.827388\pi\)
\(272\) −4.31554 −0.261668
\(273\) 2.50659 0.151706
\(274\) 17.4499 1.05419
\(275\) 14.7301 0.888256
\(276\) 21.7411 1.30866
\(277\) 11.5208 0.692218 0.346109 0.938194i \(-0.387503\pi\)
0.346109 + 0.938194i \(0.387503\pi\)
\(278\) 30.7507 1.84431
\(279\) −2.10762 −0.126180
\(280\) 5.45945 0.326265
\(281\) 6.25471 0.373125 0.186562 0.982443i \(-0.440265\pi\)
0.186562 + 0.982443i \(0.440265\pi\)
\(282\) −38.8193 −2.31165
\(283\) 26.6041 1.58145 0.790724 0.612172i \(-0.209704\pi\)
0.790724 + 0.612172i \(0.209704\pi\)
\(284\) −3.74017 −0.221939
\(285\) 4.76189 0.282070
\(286\) −15.4630 −0.914344
\(287\) −4.16354 −0.245766
\(288\) −1.62027 −0.0954756
\(289\) −8.81601 −0.518589
\(290\) 53.4658 3.13962
\(291\) 5.91201 0.346568
\(292\) −15.8597 −0.928118
\(293\) −9.19726 −0.537310 −0.268655 0.963236i \(-0.586579\pi\)
−0.268655 + 0.963236i \(0.586579\pi\)
\(294\) −22.0756 −1.28747
\(295\) 12.7356 0.741496
\(296\) −7.04340 −0.409389
\(297\) 24.9278 1.44646
\(298\) −2.42864 −0.140687
\(299\) −6.87425 −0.397548
\(300\) −15.1687 −0.875764
\(301\) 10.3994 0.599413
\(302\) −48.6813 −2.80129
\(303\) −5.31332 −0.305242
\(304\) 1.50853 0.0865199
\(305\) 1.94038 0.111106
\(306\) 1.42815 0.0816418
\(307\) 25.2512 1.44116 0.720582 0.693370i \(-0.243875\pi\)
0.720582 + 0.693370i \(0.243875\pi\)
\(308\) −13.2594 −0.755526
\(309\) 11.3439 0.645332
\(310\) −58.7687 −3.33784
\(311\) 19.0851 1.08222 0.541109 0.840953i \(-0.318005\pi\)
0.541109 + 0.840953i \(0.318005\pi\)
\(312\) 4.82134 0.272955
\(313\) −1.50541 −0.0850907 −0.0425453 0.999095i \(-0.513547\pi\)
−0.0425453 + 0.999095i \(0.513547\pi\)
\(314\) 50.4733 2.84837
\(315\) 0.644534 0.0363154
\(316\) −27.2878 −1.53506
\(317\) −1.00000 −0.0561656
\(318\) −28.9558 −1.62376
\(319\) −39.3173 −2.20134
\(320\) −36.5533 −2.04339
\(321\) 16.3663 0.913475
\(322\) −10.0045 −0.557528
\(323\) −2.86077 −0.159177
\(324\) −23.7231 −1.31795
\(325\) 4.79614 0.266042
\(326\) −25.6931 −1.42301
\(327\) 24.2623 1.34171
\(328\) −8.00842 −0.442191
\(329\) 10.5250 0.580264
\(330\) 48.7452 2.68333
\(331\) −26.1955 −1.43984 −0.719918 0.694059i \(-0.755821\pi\)
−0.719918 + 0.694059i \(0.755821\pi\)
\(332\) −13.2339 −0.726307
\(333\) −0.831533 −0.0455677
\(334\) 3.73795 0.204532
\(335\) 28.9956 1.58420
\(336\) −2.50320 −0.136561
\(337\) 33.3015 1.81405 0.907024 0.421080i \(-0.138349\pi\)
0.907024 + 0.421080i \(0.138349\pi\)
\(338\) 23.6494 1.28636
\(339\) 9.01255 0.489495
\(340\) 23.4634 1.27248
\(341\) 43.2170 2.34033
\(342\) −0.499218 −0.0269946
\(343\) 12.9598 0.699761
\(344\) 20.0029 1.07849
\(345\) 21.6703 1.16669
\(346\) 11.1112 0.597344
\(347\) −1.93502 −0.103877 −0.0519387 0.998650i \(-0.516540\pi\)
−0.0519387 + 0.998650i \(0.516540\pi\)
\(348\) 40.4880 2.17038
\(349\) −8.13301 −0.435350 −0.217675 0.976021i \(-0.569847\pi\)
−0.217675 + 0.976021i \(0.569847\pi\)
\(350\) 6.98009 0.373102
\(351\) 8.11656 0.433230
\(352\) 33.2239 1.77084
\(353\) 12.7288 0.677488 0.338744 0.940879i \(-0.389998\pi\)
0.338744 + 0.940879i \(0.389998\pi\)
\(354\) 16.3685 0.869974
\(355\) −3.72799 −0.197861
\(356\) −18.7345 −0.992927
\(357\) 4.74707 0.251242
\(358\) −24.7121 −1.30607
\(359\) 25.0364 1.32137 0.660686 0.750663i \(-0.270266\pi\)
0.660686 + 0.750663i \(0.270266\pi\)
\(360\) 1.23974 0.0653400
\(361\) 1.00000 0.0526316
\(362\) −47.0906 −2.47503
\(363\) −17.5259 −0.919869
\(364\) −4.31730 −0.226288
\(365\) −15.8080 −0.827431
\(366\) 2.49387 0.130357
\(367\) −32.2111 −1.68141 −0.840704 0.541495i \(-0.817859\pi\)
−0.840704 + 0.541495i \(0.817859\pi\)
\(368\) 6.86496 0.357861
\(369\) −0.945461 −0.0492187
\(370\) −23.1864 −1.20540
\(371\) 7.85076 0.407591
\(372\) −44.5038 −2.30741
\(373\) −33.9916 −1.76002 −0.880010 0.474955i \(-0.842464\pi\)
−0.880010 + 0.474955i \(0.842464\pi\)
\(374\) −29.2843 −1.51426
\(375\) 8.69016 0.448758
\(376\) 20.2445 1.04403
\(377\) −12.8018 −0.659326
\(378\) 11.8125 0.607568
\(379\) −20.7053 −1.06356 −0.531779 0.846883i \(-0.678476\pi\)
−0.531779 + 0.846883i \(0.678476\pi\)
\(380\) −8.20177 −0.420742
\(381\) −4.45925 −0.228454
\(382\) 43.7638 2.23915
\(383\) −3.48169 −0.177906 −0.0889531 0.996036i \(-0.528352\pi\)
−0.0889531 + 0.996036i \(0.528352\pi\)
\(384\) −23.1261 −1.18015
\(385\) −13.2162 −0.673562
\(386\) 19.7945 1.00751
\(387\) 2.36151 0.120042
\(388\) −10.1827 −0.516949
\(389\) 34.3179 1.73999 0.869993 0.493064i \(-0.164123\pi\)
0.869993 + 0.493064i \(0.164123\pi\)
\(390\) 15.8715 0.803686
\(391\) −13.0187 −0.658384
\(392\) 11.5126 0.581474
\(393\) 5.84861 0.295023
\(394\) 15.0511 0.758262
\(395\) −27.1989 −1.36853
\(396\) −3.01097 −0.151307
\(397\) −18.9587 −0.951509 −0.475755 0.879578i \(-0.657825\pi\)
−0.475755 + 0.879578i \(0.657825\pi\)
\(398\) −9.75563 −0.489006
\(399\) −1.65937 −0.0830724
\(400\) −4.78966 −0.239483
\(401\) −11.1614 −0.557374 −0.278687 0.960382i \(-0.589899\pi\)
−0.278687 + 0.960382i \(0.589899\pi\)
\(402\) 37.2667 1.85869
\(403\) 14.0715 0.700953
\(404\) 9.15154 0.455306
\(405\) −23.6458 −1.17497
\(406\) −18.6312 −0.924649
\(407\) 17.0507 0.845170
\(408\) 9.13082 0.452043
\(409\) −32.2735 −1.59582 −0.797910 0.602776i \(-0.794061\pi\)
−0.797910 + 0.602776i \(0.794061\pi\)
\(410\) −26.3632 −1.30199
\(411\) 13.1712 0.649689
\(412\) −19.5385 −0.962593
\(413\) −4.43797 −0.218378
\(414\) −2.27183 −0.111654
\(415\) −13.1908 −0.647513
\(416\) 10.8178 0.530385
\(417\) 23.2107 1.13663
\(418\) 10.2365 0.500685
\(419\) 18.5806 0.907721 0.453861 0.891073i \(-0.350046\pi\)
0.453861 + 0.891073i \(0.350046\pi\)
\(420\) 13.6098 0.664089
\(421\) 20.2117 0.985057 0.492528 0.870296i \(-0.336073\pi\)
0.492528 + 0.870296i \(0.336073\pi\)
\(422\) −21.2329 −1.03360
\(423\) 2.39004 0.116208
\(424\) 15.1007 0.733353
\(425\) 9.08310 0.440595
\(426\) −4.79141 −0.232144
\(427\) −0.676161 −0.0327217
\(428\) −28.1889 −1.36256
\(429\) −11.6715 −0.563505
\(430\) 65.8483 3.17549
\(431\) 20.6809 0.996162 0.498081 0.867130i \(-0.334038\pi\)
0.498081 + 0.867130i \(0.334038\pi\)
\(432\) −8.10559 −0.389980
\(433\) −34.2036 −1.64372 −0.821861 0.569688i \(-0.807064\pi\)
−0.821861 + 0.569688i \(0.807064\pi\)
\(434\) 20.4791 0.983028
\(435\) 40.3561 1.93493
\(436\) −41.7889 −2.00132
\(437\) 4.55077 0.217693
\(438\) −20.3173 −0.970798
\(439\) 4.94993 0.236247 0.118124 0.992999i \(-0.462312\pi\)
0.118124 + 0.992999i \(0.462312\pi\)
\(440\) −25.4210 −1.21190
\(441\) 1.35916 0.0647218
\(442\) −9.53504 −0.453536
\(443\) 15.1771 0.721086 0.360543 0.932743i \(-0.382591\pi\)
0.360543 + 0.932743i \(0.382591\pi\)
\(444\) −17.5584 −0.833284
\(445\) −18.6735 −0.885209
\(446\) 12.4077 0.587521
\(447\) −1.83315 −0.0867049
\(448\) 12.7377 0.601799
\(449\) 15.6330 0.737767 0.368884 0.929476i \(-0.379740\pi\)
0.368884 + 0.929476i \(0.379740\pi\)
\(450\) 1.58505 0.0747199
\(451\) 19.3868 0.912888
\(452\) −15.5230 −0.730142
\(453\) −36.7448 −1.72642
\(454\) −31.0969 −1.45945
\(455\) −4.30324 −0.201739
\(456\) −3.19174 −0.149467
\(457\) −19.6187 −0.917726 −0.458863 0.888507i \(-0.651743\pi\)
−0.458863 + 0.888507i \(0.651743\pi\)
\(458\) −31.9719 −1.49395
\(459\) 15.3714 0.717477
\(460\) −37.3244 −1.74026
\(461\) −19.2375 −0.895980 −0.447990 0.894038i \(-0.647860\pi\)
−0.447990 + 0.894038i \(0.647860\pi\)
\(462\) −16.9862 −0.790269
\(463\) 32.2853 1.50043 0.750213 0.661196i \(-0.229951\pi\)
0.750213 + 0.661196i \(0.229951\pi\)
\(464\) 12.7845 0.593505
\(465\) −44.3588 −2.05709
\(466\) −37.7321 −1.74791
\(467\) −21.9740 −1.01683 −0.508417 0.861111i \(-0.669769\pi\)
−0.508417 + 0.861111i \(0.669769\pi\)
\(468\) −0.980377 −0.0453180
\(469\) −10.1041 −0.466563
\(470\) 66.6437 3.07404
\(471\) 38.0974 1.75544
\(472\) −8.53628 −0.392914
\(473\) −48.4231 −2.22650
\(474\) −34.9574 −1.60565
\(475\) −3.17506 −0.145682
\(476\) −8.17625 −0.374758
\(477\) 1.78276 0.0816270
\(478\) −52.3058 −2.39241
\(479\) −0.636927 −0.0291020 −0.0145510 0.999894i \(-0.504632\pi\)
−0.0145510 + 0.999894i \(0.504632\pi\)
\(480\) −34.1018 −1.55653
\(481\) 5.55174 0.253137
\(482\) −57.5550 −2.62156
\(483\) −7.55141 −0.343601
\(484\) 30.1862 1.37210
\(485\) −10.1495 −0.460867
\(486\) 5.17667 0.234819
\(487\) −21.5537 −0.976693 −0.488346 0.872650i \(-0.662400\pi\)
−0.488346 + 0.872650i \(0.662400\pi\)
\(488\) −1.30057 −0.0588741
\(489\) −19.3932 −0.876993
\(490\) 37.8987 1.71209
\(491\) 14.1894 0.640359 0.320180 0.947357i \(-0.396257\pi\)
0.320180 + 0.947357i \(0.396257\pi\)
\(492\) −19.9640 −0.900049
\(493\) −24.2445 −1.09192
\(494\) 3.33304 0.149960
\(495\) −3.00116 −0.134892
\(496\) −14.0525 −0.630976
\(497\) 1.29909 0.0582722
\(498\) −16.9535 −0.759707
\(499\) −9.38643 −0.420194 −0.210097 0.977681i \(-0.567378\pi\)
−0.210097 + 0.977681i \(0.567378\pi\)
\(500\) −14.9678 −0.669378
\(501\) 2.82142 0.126052
\(502\) −9.73298 −0.434404
\(503\) −24.5717 −1.09560 −0.547800 0.836609i \(-0.684535\pi\)
−0.547800 + 0.836609i \(0.684535\pi\)
\(504\) −0.432011 −0.0192433
\(505\) 9.12174 0.405912
\(506\) 46.5841 2.07092
\(507\) 17.8507 0.792777
\(508\) 7.68052 0.340768
\(509\) 12.6386 0.560197 0.280099 0.959971i \(-0.409633\pi\)
0.280099 + 0.959971i \(0.409633\pi\)
\(510\) 30.0581 1.33099
\(511\) 5.50861 0.243687
\(512\) −16.5851 −0.732966
\(513\) −5.37318 −0.237232
\(514\) 49.3589 2.17713
\(515\) −19.4749 −0.858165
\(516\) 49.8649 2.19518
\(517\) −49.0080 −2.15537
\(518\) 8.07975 0.355004
\(519\) 8.38681 0.368140
\(520\) −8.27713 −0.362976
\(521\) 0.204005 0.00893761 0.00446880 0.999990i \(-0.498578\pi\)
0.00446880 + 0.999990i \(0.498578\pi\)
\(522\) −4.23079 −0.185176
\(523\) −10.9746 −0.479885 −0.239943 0.970787i \(-0.577129\pi\)
−0.239943 + 0.970787i \(0.577129\pi\)
\(524\) −10.0735 −0.440064
\(525\) 5.26860 0.229940
\(526\) 14.7380 0.642609
\(527\) 26.6492 1.16086
\(528\) 11.6557 0.507250
\(529\) −2.29048 −0.0995859
\(530\) 49.7104 2.15928
\(531\) −1.00778 −0.0437339
\(532\) 2.85806 0.123913
\(533\) 6.31238 0.273419
\(534\) −24.0001 −1.03859
\(535\) −28.0971 −1.21474
\(536\) −19.4348 −0.839457
\(537\) −18.6528 −0.804926
\(538\) 13.1014 0.564840
\(539\) −27.8697 −1.20043
\(540\) 44.0696 1.89645
\(541\) −32.5754 −1.40053 −0.700263 0.713885i \(-0.746934\pi\)
−0.700263 + 0.713885i \(0.746934\pi\)
\(542\) 62.2243 2.67276
\(543\) −35.5441 −1.52535
\(544\) 20.4871 0.878377
\(545\) −41.6528 −1.78421
\(546\) −5.53074 −0.236694
\(547\) −16.9940 −0.726612 −0.363306 0.931670i \(-0.618352\pi\)
−0.363306 + 0.931670i \(0.618352\pi\)
\(548\) −22.6858 −0.969091
\(549\) −0.153543 −0.00655307
\(550\) −32.5016 −1.38587
\(551\) 8.47482 0.361039
\(552\) −14.5249 −0.618220
\(553\) 9.47797 0.403044
\(554\) −25.4204 −1.08001
\(555\) −17.5012 −0.742884
\(556\) −39.9777 −1.69543
\(557\) −6.23451 −0.264165 −0.132082 0.991239i \(-0.542166\pi\)
−0.132082 + 0.991239i \(0.542166\pi\)
\(558\) 4.65042 0.196868
\(559\) −15.7667 −0.666859
\(560\) 4.29742 0.181599
\(561\) −22.1039 −0.933227
\(562\) −13.8009 −0.582155
\(563\) −21.3677 −0.900540 −0.450270 0.892892i \(-0.648672\pi\)
−0.450270 + 0.892892i \(0.648672\pi\)
\(564\) 50.4673 2.12505
\(565\) −15.4725 −0.650932
\(566\) −58.7013 −2.46740
\(567\) 8.23983 0.346040
\(568\) 2.49875 0.104845
\(569\) −25.5911 −1.07283 −0.536417 0.843953i \(-0.680223\pi\)
−0.536417 + 0.843953i \(0.680223\pi\)
\(570\) −10.5070 −0.440090
\(571\) −25.0555 −1.04854 −0.524271 0.851552i \(-0.675662\pi\)
−0.524271 + 0.851552i \(0.675662\pi\)
\(572\) 20.1027 0.840538
\(573\) 33.0330 1.37997
\(574\) 9.18675 0.383448
\(575\) −14.4490 −0.602564
\(576\) 2.89249 0.120520
\(577\) −11.0713 −0.460906 −0.230453 0.973083i \(-0.574021\pi\)
−0.230453 + 0.973083i \(0.574021\pi\)
\(578\) 19.4523 0.809111
\(579\) 14.9409 0.620923
\(580\) −69.5085 −2.88618
\(581\) 4.59660 0.190699
\(582\) −13.0447 −0.540721
\(583\) −36.5557 −1.51398
\(584\) 10.5956 0.438450
\(585\) −0.977184 −0.0404016
\(586\) 20.2936 0.838319
\(587\) −15.4232 −0.636582 −0.318291 0.947993i \(-0.603109\pi\)
−0.318291 + 0.947993i \(0.603109\pi\)
\(588\) 28.6995 1.18355
\(589\) −9.31539 −0.383834
\(590\) −28.1009 −1.15689
\(591\) 11.3606 0.467313
\(592\) −5.54423 −0.227866
\(593\) −35.7808 −1.46934 −0.734670 0.678425i \(-0.762663\pi\)
−0.734670 + 0.678425i \(0.762663\pi\)
\(594\) −55.0027 −2.25679
\(595\) −8.14962 −0.334102
\(596\) 3.15737 0.129331
\(597\) −7.36358 −0.301371
\(598\) 15.1679 0.620261
\(599\) 26.4128 1.07920 0.539598 0.841923i \(-0.318576\pi\)
0.539598 + 0.841923i \(0.318576\pi\)
\(600\) 10.1340 0.413717
\(601\) 9.40049 0.383454 0.191727 0.981448i \(-0.438591\pi\)
0.191727 + 0.981448i \(0.438591\pi\)
\(602\) −22.9461 −0.935213
\(603\) −2.29445 −0.0934371
\(604\) 63.2885 2.57517
\(605\) 30.0878 1.22325
\(606\) 11.7237 0.476244
\(607\) 37.0366 1.50327 0.751634 0.659580i \(-0.229266\pi\)
0.751634 + 0.659580i \(0.229266\pi\)
\(608\) −7.16140 −0.290433
\(609\) −14.0629 −0.569856
\(610\) −4.28140 −0.173349
\(611\) −15.9571 −0.645555
\(612\) −1.85667 −0.0750516
\(613\) −14.8900 −0.601400 −0.300700 0.953719i \(-0.597220\pi\)
−0.300700 + 0.953719i \(0.597220\pi\)
\(614\) −55.7163 −2.24853
\(615\) −19.8990 −0.802406
\(616\) 8.85842 0.356916
\(617\) 0.394863 0.0158966 0.00794830 0.999968i \(-0.497470\pi\)
0.00794830 + 0.999968i \(0.497470\pi\)
\(618\) −25.0301 −1.00686
\(619\) −25.5070 −1.02521 −0.512607 0.858623i \(-0.671320\pi\)
−0.512607 + 0.858623i \(0.671320\pi\)
\(620\) 76.4027 3.06841
\(621\) −24.4521 −0.981230
\(622\) −42.1109 −1.68849
\(623\) 6.50714 0.260703
\(624\) 3.79513 0.151927
\(625\) −30.7943 −1.23177
\(626\) 3.32165 0.132760
\(627\) 7.72657 0.308569
\(628\) −65.6182 −2.61845
\(629\) 10.5141 0.419224
\(630\) −1.42215 −0.0566598
\(631\) −20.9015 −0.832075 −0.416038 0.909347i \(-0.636581\pi\)
−0.416038 + 0.909347i \(0.636581\pi\)
\(632\) 18.2306 0.725172
\(633\) −16.0267 −0.637002
\(634\) 2.20648 0.0876305
\(635\) 7.65551 0.303799
\(636\) 37.6442 1.49269
\(637\) −9.07443 −0.359542
\(638\) 86.7527 3.43457
\(639\) 0.294999 0.0116700
\(640\) 39.7023 1.56937
\(641\) −4.44033 −0.175383 −0.0876913 0.996148i \(-0.527949\pi\)
−0.0876913 + 0.996148i \(0.527949\pi\)
\(642\) −36.1118 −1.42522
\(643\) −37.3499 −1.47294 −0.736468 0.676472i \(-0.763508\pi\)
−0.736468 + 0.676472i \(0.763508\pi\)
\(644\) 13.0064 0.512524
\(645\) 49.7025 1.95704
\(646\) 6.31222 0.248351
\(647\) 39.7561 1.56297 0.781487 0.623921i \(-0.214461\pi\)
0.781487 + 0.623921i \(0.214461\pi\)
\(648\) 15.8490 0.622608
\(649\) 20.6646 0.811157
\(650\) −10.5826 −0.415083
\(651\) 15.4577 0.605834
\(652\) 33.4025 1.30814
\(653\) 16.2165 0.634603 0.317301 0.948325i \(-0.397223\pi\)
0.317301 + 0.948325i \(0.397223\pi\)
\(654\) −53.5342 −2.09335
\(655\) −10.0407 −0.392323
\(656\) −6.30384 −0.246124
\(657\) 1.25090 0.0488023
\(658\) −23.2233 −0.905337
\(659\) −1.23004 −0.0479155 −0.0239577 0.999713i \(-0.507627\pi\)
−0.0239577 + 0.999713i \(0.507627\pi\)
\(660\) −63.3715 −2.46673
\(661\) −7.46481 −0.290347 −0.145174 0.989406i \(-0.546374\pi\)
−0.145174 + 0.989406i \(0.546374\pi\)
\(662\) 57.7999 2.24646
\(663\) −7.19708 −0.279511
\(664\) 8.84140 0.343113
\(665\) 2.84875 0.110470
\(666\) 1.83476 0.0710955
\(667\) 38.5670 1.49332
\(668\) −4.85955 −0.188022
\(669\) 9.36537 0.362086
\(670\) −63.9782 −2.47169
\(671\) 3.14842 0.121544
\(672\) 11.8834 0.458412
\(673\) −37.0945 −1.42989 −0.714943 0.699183i \(-0.753547\pi\)
−0.714943 + 0.699183i \(0.753547\pi\)
\(674\) −73.4790 −2.83031
\(675\) 17.0602 0.656647
\(676\) −30.7456 −1.18252
\(677\) −6.67528 −0.256552 −0.128276 0.991739i \(-0.540944\pi\)
−0.128276 + 0.991739i \(0.540944\pi\)
\(678\) −19.8860 −0.763717
\(679\) 3.53680 0.135730
\(680\) −15.6755 −0.601129
\(681\) −23.4721 −0.899452
\(682\) −95.3573 −3.65142
\(683\) 15.0637 0.576398 0.288199 0.957571i \(-0.406944\pi\)
0.288199 + 0.957571i \(0.406944\pi\)
\(684\) 0.649012 0.0248156
\(685\) −22.6120 −0.863959
\(686\) −28.5954 −1.09178
\(687\) −24.1325 −0.920711
\(688\) 15.7453 0.600286
\(689\) −11.9026 −0.453453
\(690\) −47.8150 −1.82028
\(691\) −44.5274 −1.69390 −0.846951 0.531671i \(-0.821564\pi\)
−0.846951 + 0.531671i \(0.821564\pi\)
\(692\) −14.4453 −0.549126
\(693\) 1.04581 0.0397271
\(694\) 4.26958 0.162071
\(695\) −39.8475 −1.51150
\(696\) −27.0494 −1.02531
\(697\) 11.9546 0.452813
\(698\) 17.9453 0.679240
\(699\) −28.4803 −1.07723
\(700\) −9.07452 −0.342985
\(701\) −0.767459 −0.0289865 −0.0144933 0.999895i \(-0.504614\pi\)
−0.0144933 + 0.999895i \(0.504614\pi\)
\(702\) −17.9090 −0.675932
\(703\) −3.67526 −0.138615
\(704\) −59.3108 −2.23536
\(705\) 50.3029 1.89452
\(706\) −28.0859 −1.05703
\(707\) −3.17864 −0.119545
\(708\) −21.2799 −0.799749
\(709\) 38.0543 1.42916 0.714580 0.699553i \(-0.246618\pi\)
0.714580 + 0.699553i \(0.246618\pi\)
\(710\) 8.22574 0.308706
\(711\) 2.15227 0.0807164
\(712\) 12.5162 0.469066
\(713\) −42.3922 −1.58760
\(714\) −10.4743 −0.391991
\(715\) 20.0373 0.749351
\(716\) 32.1271 1.20065
\(717\) −39.4806 −1.47443
\(718\) −55.2423 −2.06163
\(719\) 24.9985 0.932288 0.466144 0.884709i \(-0.345643\pi\)
0.466144 + 0.884709i \(0.345643\pi\)
\(720\) 0.975863 0.0363683
\(721\) 6.78638 0.252738
\(722\) −2.20648 −0.0821166
\(723\) −43.4427 −1.61565
\(724\) 61.2205 2.27524
\(725\) −26.9081 −0.999340
\(726\) 38.6704 1.43519
\(727\) −14.8519 −0.550827 −0.275413 0.961326i \(-0.588815\pi\)
−0.275413 + 0.961326i \(0.588815\pi\)
\(728\) 2.88432 0.106900
\(729\) 28.7175 1.06361
\(730\) 34.8801 1.29097
\(731\) −29.8595 −1.10439
\(732\) −3.24217 −0.119834
\(733\) −28.9854 −1.07060 −0.535300 0.844662i \(-0.679801\pi\)
−0.535300 + 0.844662i \(0.679801\pi\)
\(734\) 71.0732 2.62336
\(735\) 28.6061 1.05515
\(736\) −32.5899 −1.20128
\(737\) 47.0479 1.73303
\(738\) 2.08614 0.0767919
\(739\) −9.66230 −0.355434 −0.177717 0.984082i \(-0.556871\pi\)
−0.177717 + 0.984082i \(0.556871\pi\)
\(740\) 30.1437 1.10810
\(741\) 2.51579 0.0924197
\(742\) −17.3225 −0.635930
\(743\) 43.4995 1.59584 0.797922 0.602761i \(-0.205933\pi\)
0.797922 + 0.602761i \(0.205933\pi\)
\(744\) 29.7323 1.09004
\(745\) 3.14709 0.115300
\(746\) 75.0018 2.74601
\(747\) 1.04380 0.0381907
\(748\) 38.0713 1.39202
\(749\) 9.79096 0.357754
\(750\) −19.1747 −0.700160
\(751\) 22.0101 0.803159 0.401580 0.915824i \(-0.368461\pi\)
0.401580 + 0.915824i \(0.368461\pi\)
\(752\) 15.9355 0.581109
\(753\) −7.34649 −0.267721
\(754\) 28.2469 1.02869
\(755\) 63.0823 2.29580
\(756\) −15.3569 −0.558525
\(757\) −26.2899 −0.955521 −0.477761 0.878490i \(-0.658551\pi\)
−0.477761 + 0.878490i \(0.658551\pi\)
\(758\) 45.6857 1.65938
\(759\) 35.1618 1.27629
\(760\) 5.47948 0.198762
\(761\) 48.1510 1.74547 0.872736 0.488193i \(-0.162344\pi\)
0.872736 + 0.488193i \(0.162344\pi\)
\(762\) 9.83925 0.356438
\(763\) 14.5147 0.525467
\(764\) −56.8954 −2.05840
\(765\) −1.85063 −0.0669095
\(766\) 7.68228 0.277572
\(767\) 6.72844 0.242950
\(768\) 8.44352 0.304679
\(769\) −0.670309 −0.0241720 −0.0120860 0.999927i \(-0.503847\pi\)
−0.0120860 + 0.999927i \(0.503847\pi\)
\(770\) 29.1614 1.05090
\(771\) 37.2563 1.34175
\(772\) −25.7339 −0.926184
\(773\) −26.1415 −0.940243 −0.470122 0.882602i \(-0.655790\pi\)
−0.470122 + 0.882602i \(0.655790\pi\)
\(774\) −5.21063 −0.187292
\(775\) 29.5769 1.06243
\(776\) 6.80292 0.244211
\(777\) 6.09862 0.218787
\(778\) −75.7217 −2.71476
\(779\) −4.17881 −0.149721
\(780\) −20.6339 −0.738812
\(781\) −6.04899 −0.216450
\(782\) 28.7255 1.02722
\(783\) −45.5368 −1.62735
\(784\) 9.06216 0.323649
\(785\) −65.4045 −2.33439
\(786\) −12.9048 −0.460300
\(787\) 21.9967 0.784097 0.392049 0.919945i \(-0.371767\pi\)
0.392049 + 0.919945i \(0.371767\pi\)
\(788\) −19.5673 −0.697055
\(789\) 11.1243 0.396036
\(790\) 60.0138 2.13520
\(791\) 5.39168 0.191706
\(792\) 2.01158 0.0714784
\(793\) 1.02513 0.0364036
\(794\) 41.8319 1.48456
\(795\) 37.5216 1.33075
\(796\) 12.6829 0.449533
\(797\) −17.2647 −0.611548 −0.305774 0.952104i \(-0.598915\pi\)
−0.305774 + 0.952104i \(0.598915\pi\)
\(798\) 3.66136 0.129611
\(799\) −30.2201 −1.06911
\(800\) 22.7379 0.803905
\(801\) 1.47765 0.0522101
\(802\) 24.6274 0.869623
\(803\) −25.6499 −0.905165
\(804\) −48.4488 −1.70866
\(805\) 12.9640 0.456922
\(806\) −31.0485 −1.09364
\(807\) 9.88896 0.348108
\(808\) −6.11401 −0.215090
\(809\) 44.4877 1.56411 0.782053 0.623212i \(-0.214173\pi\)
0.782053 + 0.623212i \(0.214173\pi\)
\(810\) 52.1739 1.83321
\(811\) −40.3191 −1.41580 −0.707898 0.706315i \(-0.750356\pi\)
−0.707898 + 0.706315i \(0.750356\pi\)
\(812\) 24.2216 0.850010
\(813\) 46.9671 1.64721
\(814\) −37.6219 −1.31865
\(815\) 33.2937 1.16623
\(816\) 7.18735 0.251608
\(817\) 10.4376 0.365164
\(818\) 71.2107 2.48982
\(819\) 0.340518 0.0118987
\(820\) 34.2737 1.19689
\(821\) 3.49194 0.121869 0.0609347 0.998142i \(-0.480592\pi\)
0.0609347 + 0.998142i \(0.480592\pi\)
\(822\) −29.0620 −1.01366
\(823\) −11.3787 −0.396636 −0.198318 0.980138i \(-0.563548\pi\)
−0.198318 + 0.980138i \(0.563548\pi\)
\(824\) 13.0534 0.454736
\(825\) −24.5323 −0.854105
\(826\) 9.79228 0.340717
\(827\) −25.2499 −0.878025 −0.439012 0.898481i \(-0.644672\pi\)
−0.439012 + 0.898481i \(0.644672\pi\)
\(828\) 2.95351 0.102641
\(829\) −25.8734 −0.898620 −0.449310 0.893376i \(-0.648330\pi\)
−0.449310 + 0.893376i \(0.648330\pi\)
\(830\) 29.1053 1.01026
\(831\) −19.1874 −0.665604
\(832\) −19.3117 −0.669514
\(833\) −17.1855 −0.595442
\(834\) −51.2140 −1.77340
\(835\) −4.84373 −0.167624
\(836\) −13.3081 −0.460269
\(837\) 50.0533 1.73010
\(838\) −40.9977 −1.41624
\(839\) 48.0672 1.65946 0.829732 0.558162i \(-0.188493\pi\)
0.829732 + 0.558162i \(0.188493\pi\)
\(840\) −9.09248 −0.313720
\(841\) 42.8226 1.47664
\(842\) −44.5966 −1.53690
\(843\) −10.4170 −0.358779
\(844\) 27.6040 0.950168
\(845\) −30.6455 −1.05424
\(846\) −5.27357 −0.181309
\(847\) −10.4847 −0.360258
\(848\) 11.8865 0.408185
\(849\) −44.3080 −1.52065
\(850\) −20.0417 −0.687424
\(851\) −16.7253 −0.573335
\(852\) 6.22910 0.213406
\(853\) −4.01704 −0.137541 −0.0687704 0.997633i \(-0.521908\pi\)
−0.0687704 + 0.997633i \(0.521908\pi\)
\(854\) 1.49193 0.0510530
\(855\) 0.646899 0.0221235
\(856\) 18.8326 0.643684
\(857\) 5.40918 0.184774 0.0923870 0.995723i \(-0.470550\pi\)
0.0923870 + 0.995723i \(0.470550\pi\)
\(858\) 25.7529 0.879190
\(859\) 34.5560 1.17904 0.589518 0.807755i \(-0.299318\pi\)
0.589518 + 0.807755i \(0.299318\pi\)
\(860\) −85.6066 −2.91916
\(861\) 6.93419 0.236317
\(862\) −45.6319 −1.55423
\(863\) 19.5155 0.664316 0.332158 0.943224i \(-0.392223\pi\)
0.332158 + 0.943224i \(0.392223\pi\)
\(864\) 38.4795 1.30910
\(865\) −14.3982 −0.489554
\(866\) 75.4696 2.56456
\(867\) 14.6827 0.498650
\(868\) −26.6240 −0.903677
\(869\) −44.1325 −1.49709
\(870\) −89.0449 −3.01891
\(871\) 15.3189 0.519061
\(872\) 27.9185 0.945440
\(873\) 0.803142 0.0271822
\(874\) −10.0412 −0.339648
\(875\) 5.19881 0.175752
\(876\) 26.4136 0.892434
\(877\) 9.27680 0.313255 0.156628 0.987658i \(-0.449938\pi\)
0.156628 + 0.987658i \(0.449938\pi\)
\(878\) −10.9219 −0.368596
\(879\) 15.3176 0.516651
\(880\) −20.0102 −0.674543
\(881\) −12.5957 −0.424359 −0.212179 0.977231i \(-0.568056\pi\)
−0.212179 + 0.977231i \(0.568056\pi\)
\(882\) −2.99895 −0.100980
\(883\) −22.2634 −0.749224 −0.374612 0.927182i \(-0.622224\pi\)
−0.374612 + 0.927182i \(0.622224\pi\)
\(884\) 12.3961 0.416926
\(885\) −21.2106 −0.712987
\(886\) −33.4880 −1.12505
\(887\) −25.6123 −0.859978 −0.429989 0.902834i \(-0.641483\pi\)
−0.429989 + 0.902834i \(0.641483\pi\)
\(888\) 11.7305 0.393649
\(889\) −2.66771 −0.0894720
\(890\) 41.2027 1.38112
\(891\) −38.3673 −1.28535
\(892\) −16.1307 −0.540096
\(893\) 10.5636 0.353499
\(894\) 4.04480 0.135278
\(895\) 32.0225 1.07039
\(896\) −13.8350 −0.462195
\(897\) 11.4488 0.382263
\(898\) −34.4939 −1.15108
\(899\) −78.9463 −2.63301
\(900\) −2.06065 −0.0686884
\(901\) −22.5416 −0.750969
\(902\) −42.7765 −1.42430
\(903\) −17.3198 −0.576367
\(904\) 10.3707 0.344924
\(905\) 61.0211 2.02841
\(906\) 81.0766 2.69359
\(907\) 11.8235 0.392594 0.196297 0.980544i \(-0.437108\pi\)
0.196297 + 0.980544i \(0.437108\pi\)
\(908\) 40.4278 1.34164
\(909\) −0.721810 −0.0239409
\(910\) 9.49500 0.314756
\(911\) −33.8940 −1.12296 −0.561479 0.827491i \(-0.689767\pi\)
−0.561479 + 0.827491i \(0.689767\pi\)
\(912\) −2.51239 −0.0831934
\(913\) −21.4033 −0.708345
\(914\) 43.2883 1.43185
\(915\) −3.23161 −0.106834
\(916\) 41.5652 1.37335
\(917\) 3.49888 0.115543
\(918\) −33.9167 −1.11942
\(919\) 49.0190 1.61699 0.808493 0.588505i \(-0.200283\pi\)
0.808493 + 0.588505i \(0.200283\pi\)
\(920\) 24.9359 0.822111
\(921\) −42.0548 −1.38575
\(922\) 42.4472 1.39792
\(923\) −1.96956 −0.0648290
\(924\) 22.0830 0.726478
\(925\) 11.6692 0.383680
\(926\) −71.2369 −2.34099
\(927\) 1.54106 0.0506151
\(928\) −60.6916 −1.99230
\(929\) −34.9824 −1.14774 −0.573868 0.818948i \(-0.694558\pi\)
−0.573868 + 0.818948i \(0.694558\pi\)
\(930\) 97.8769 3.20951
\(931\) 6.00730 0.196881
\(932\) 49.0539 1.60681
\(933\) −31.7855 −1.04061
\(934\) 48.4851 1.58648
\(935\) 37.9473 1.24101
\(936\) 0.654975 0.0214085
\(937\) 60.6607 1.98170 0.990849 0.134973i \(-0.0430946\pi\)
0.990849 + 0.134973i \(0.0430946\pi\)
\(938\) 22.2944 0.727939
\(939\) 2.50719 0.0818192
\(940\) −86.6406 −2.82591
\(941\) −25.9431 −0.845722 −0.422861 0.906194i \(-0.638974\pi\)
−0.422861 + 0.906194i \(0.638974\pi\)
\(942\) −84.0611 −2.73886
\(943\) −19.0168 −0.619273
\(944\) −6.71935 −0.218696
\(945\) −15.3069 −0.497933
\(946\) 106.844 3.47381
\(947\) 5.97264 0.194085 0.0970423 0.995280i \(-0.469062\pi\)
0.0970423 + 0.995280i \(0.469062\pi\)
\(948\) 45.4466 1.47604
\(949\) −8.35166 −0.271106
\(950\) 7.00570 0.227295
\(951\) 1.66546 0.0540062
\(952\) 5.46243 0.177038
\(953\) −25.9103 −0.839317 −0.419658 0.907682i \(-0.637850\pi\)
−0.419658 + 0.907682i \(0.637850\pi\)
\(954\) −3.93362 −0.127356
\(955\) −56.7101 −1.83510
\(956\) 68.0005 2.19929
\(957\) 65.4812 2.11671
\(958\) 1.40537 0.0454053
\(959\) 7.87957 0.254445
\(960\) 60.8780 1.96483
\(961\) 55.7766 1.79924
\(962\) −12.2498 −0.394949
\(963\) 2.22334 0.0716462
\(964\) 74.8247 2.40994
\(965\) −25.6501 −0.825706
\(966\) 16.6620 0.536092
\(967\) 32.1479 1.03381 0.516904 0.856043i \(-0.327084\pi\)
0.516904 + 0.856043i \(0.327084\pi\)
\(968\) −20.1669 −0.648189
\(969\) 4.76449 0.153057
\(970\) 22.3948 0.719053
\(971\) −48.5836 −1.55912 −0.779561 0.626327i \(-0.784558\pi\)
−0.779561 + 0.626327i \(0.784558\pi\)
\(972\) −6.72997 −0.215864
\(973\) 13.8856 0.445152
\(974\) 47.5578 1.52385
\(975\) −7.98777 −0.255813
\(976\) −1.02375 −0.0327694
\(977\) −21.2550 −0.680009 −0.340004 0.940424i \(-0.610429\pi\)
−0.340004 + 0.940424i \(0.610429\pi\)
\(978\) 42.7908 1.36830
\(979\) −30.2993 −0.968371
\(980\) −49.2705 −1.57389
\(981\) 3.29601 0.105234
\(982\) −31.3086 −0.999099
\(983\) 37.4467 1.19436 0.597181 0.802106i \(-0.296287\pi\)
0.597181 + 0.802106i \(0.296287\pi\)
\(984\) 13.3377 0.425190
\(985\) −19.5035 −0.621434
\(986\) 53.4949 1.70363
\(987\) −17.5290 −0.557954
\(988\) −4.33314 −0.137855
\(989\) 47.4990 1.51038
\(990\) 6.62200 0.210461
\(991\) 48.0090 1.52506 0.762528 0.646956i \(-0.223958\pi\)
0.762528 + 0.646956i \(0.223958\pi\)
\(992\) 66.7113 2.11808
\(993\) 43.6275 1.38448
\(994\) −2.86641 −0.0909172
\(995\) 12.6416 0.400765
\(996\) 22.0406 0.698383
\(997\) −47.6187 −1.50810 −0.754050 0.656817i \(-0.771902\pi\)
−0.754050 + 0.656817i \(0.771902\pi\)
\(998\) 20.7110 0.655594
\(999\) 19.7479 0.624795
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 \(a_p\))