Properties

Label 6023.2.a.b.1.4
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 1.4
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62992 q^{2}\) \(+1.18387 q^{3}\) \(+4.91650 q^{4}\) \(+1.04484 q^{5}\) \(-3.11349 q^{6}\) \(+0.263404 q^{7}\) \(-7.67017 q^{8}\) \(-1.59845 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62992 q^{2}\) \(+1.18387 q^{3}\) \(+4.91650 q^{4}\) \(+1.04484 q^{5}\) \(-3.11349 q^{6}\) \(+0.263404 q^{7}\) \(-7.67017 q^{8}\) \(-1.59845 q^{9}\) \(-2.74784 q^{10}\) \(+0.251144 q^{11}\) \(+5.82050 q^{12}\) \(+1.19133 q^{13}\) \(-0.692732 q^{14}\) \(+1.23695 q^{15}\) \(+10.3390 q^{16}\) \(+4.91921 q^{17}\) \(+4.20380 q^{18}\) \(-1.00000 q^{19}\) \(+5.13694 q^{20}\) \(+0.311836 q^{21}\) \(-0.660490 q^{22}\) \(+5.60894 q^{23}\) \(-9.08049 q^{24}\) \(-3.90831 q^{25}\) \(-3.13310 q^{26}\) \(-5.44397 q^{27}\) \(+1.29502 q^{28}\) \(-5.30224 q^{29}\) \(-3.25310 q^{30}\) \(-0.922586 q^{31}\) \(-11.8503 q^{32}\) \(+0.297322 q^{33}\) \(-12.9371 q^{34}\) \(+0.275214 q^{35}\) \(-7.85877 q^{36}\) \(+3.52815 q^{37}\) \(+2.62992 q^{38}\) \(+1.41038 q^{39}\) \(-8.01408 q^{40}\) \(-0.747366 q^{41}\) \(-0.820106 q^{42}\) \(-8.78366 q^{43}\) \(+1.23475 q^{44}\) \(-1.67012 q^{45}\) \(-14.7511 q^{46}\) \(-10.2885 q^{47}\) \(+12.2400 q^{48}\) \(-6.93062 q^{49}\) \(+10.2786 q^{50}\) \(+5.82371 q^{51}\) \(+5.85715 q^{52}\) \(-1.54648 q^{53}\) \(+14.3172 q^{54}\) \(+0.262405 q^{55}\) \(-2.02035 q^{56}\) \(-1.18387 q^{57}\) \(+13.9445 q^{58}\) \(-11.8987 q^{59}\) \(+6.08148 q^{60}\) \(-7.30658 q^{61}\) \(+2.42633 q^{62}\) \(-0.421037 q^{63}\) \(+10.4875 q^{64}\) \(+1.24474 q^{65}\) \(-0.781935 q^{66}\) \(+12.3676 q^{67}\) \(+24.1853 q^{68}\) \(+6.64027 q^{69}\) \(-0.723793 q^{70}\) \(-4.68121 q^{71}\) \(+12.2604 q^{72}\) \(-13.7773 q^{73}\) \(-9.27876 q^{74}\) \(-4.62694 q^{75}\) \(-4.91650 q^{76}\) \(+0.0661523 q^{77}\) \(-3.70918 q^{78}\) \(+9.84399 q^{79}\) \(+10.8025 q^{80}\) \(-1.64962 q^{81}\) \(+1.96552 q^{82}\) \(-2.19820 q^{83}\) \(+1.53314 q^{84}\) \(+5.13977 q^{85}\) \(+23.1004 q^{86}\) \(-6.27717 q^{87}\) \(-1.92632 q^{88}\) \(+6.15320 q^{89}\) \(+4.39229 q^{90}\) \(+0.313800 q^{91}\) \(+27.5764 q^{92}\) \(-1.09222 q^{93}\) \(+27.0580 q^{94}\) \(-1.04484 q^{95}\) \(-14.0293 q^{96}\) \(+9.44861 q^{97}\) \(+18.2270 q^{98}\) \(-0.401441 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62992 −1.85964 −0.929818 0.368019i \(-0.880036\pi\)
−0.929818 + 0.368019i \(0.880036\pi\)
\(3\) 1.18387 0.683509 0.341754 0.939789i \(-0.388979\pi\)
0.341754 + 0.939789i \(0.388979\pi\)
\(4\) 4.91650 2.45825
\(5\) 1.04484 0.467266 0.233633 0.972325i \(-0.424939\pi\)
0.233633 + 0.972325i \(0.424939\pi\)
\(6\) −3.11349 −1.27108
\(7\) 0.263404 0.0995573 0.0497787 0.998760i \(-0.484148\pi\)
0.0497787 + 0.998760i \(0.484148\pi\)
\(8\) −7.67017 −2.71181
\(9\) −1.59845 −0.532816
\(10\) −2.74784 −0.868945
\(11\) 0.251144 0.0757228 0.0378614 0.999283i \(-0.487945\pi\)
0.0378614 + 0.999283i \(0.487945\pi\)
\(12\) 5.82050 1.68023
\(13\) 1.19133 0.330414 0.165207 0.986259i \(-0.447171\pi\)
0.165207 + 0.986259i \(0.447171\pi\)
\(14\) −0.692732 −0.185140
\(15\) 1.23695 0.319380
\(16\) 10.3390 2.58474
\(17\) 4.91921 1.19308 0.596541 0.802582i \(-0.296541\pi\)
0.596541 + 0.802582i \(0.296541\pi\)
\(18\) 4.20380 0.990844
\(19\) −1.00000 −0.229416
\(20\) 5.13694 1.14866
\(21\) 0.311836 0.0680483
\(22\) −0.660490 −0.140817
\(23\) 5.60894 1.16955 0.584773 0.811197i \(-0.301184\pi\)
0.584773 + 0.811197i \(0.301184\pi\)
\(24\) −9.08049 −1.85355
\(25\) −3.90831 −0.781663
\(26\) −3.13310 −0.614451
\(27\) −5.44397 −1.04769
\(28\) 1.29502 0.244737
\(29\) −5.30224 −0.984602 −0.492301 0.870425i \(-0.663844\pi\)
−0.492301 + 0.870425i \(0.663844\pi\)
\(30\) −3.25310 −0.593931
\(31\) −0.922586 −0.165701 −0.0828506 0.996562i \(-0.526402\pi\)
−0.0828506 + 0.996562i \(0.526402\pi\)
\(32\) −11.8503 −2.09486
\(33\) 0.297322 0.0517572
\(34\) −12.9371 −2.21870
\(35\) 0.275214 0.0465197
\(36\) −7.85877 −1.30979
\(37\) 3.52815 0.580024 0.290012 0.957023i \(-0.406341\pi\)
0.290012 + 0.957023i \(0.406341\pi\)
\(38\) 2.62992 0.426630
\(39\) 1.41038 0.225841
\(40\) −8.01408 −1.26714
\(41\) −0.747366 −0.116719 −0.0583595 0.998296i \(-0.518587\pi\)
−0.0583595 + 0.998296i \(0.518587\pi\)
\(42\) −0.820106 −0.126545
\(43\) −8.78366 −1.33950 −0.669748 0.742588i \(-0.733598\pi\)
−0.669748 + 0.742588i \(0.733598\pi\)
\(44\) 1.23475 0.186146
\(45\) −1.67012 −0.248967
\(46\) −14.7511 −2.17493
\(47\) −10.2885 −1.50073 −0.750366 0.661023i \(-0.770123\pi\)
−0.750366 + 0.661023i \(0.770123\pi\)
\(48\) 12.2400 1.76669
\(49\) −6.93062 −0.990088
\(50\) 10.2786 1.45361
\(51\) 5.82371 0.815482
\(52\) 5.85715 0.812241
\(53\) −1.54648 −0.212425 −0.106212 0.994343i \(-0.533872\pi\)
−0.106212 + 0.994343i \(0.533872\pi\)
\(54\) 14.3172 1.94833
\(55\) 0.262405 0.0353827
\(56\) −2.02035 −0.269981
\(57\) −1.18387 −0.156808
\(58\) 13.9445 1.83100
\(59\) −11.8987 −1.54908 −0.774542 0.632523i \(-0.782019\pi\)
−0.774542 + 0.632523i \(0.782019\pi\)
\(60\) 6.08148 0.785116
\(61\) −7.30658 −0.935512 −0.467756 0.883858i \(-0.654937\pi\)
−0.467756 + 0.883858i \(0.654937\pi\)
\(62\) 2.42633 0.308144
\(63\) −0.421037 −0.0530457
\(64\) 10.4875 1.31094
\(65\) 1.24474 0.154391
\(66\) −0.781935 −0.0962496
\(67\) 12.3676 1.51094 0.755472 0.655181i \(-0.227408\pi\)
0.755472 + 0.655181i \(0.227408\pi\)
\(68\) 24.1853 2.93289
\(69\) 6.64027 0.799395
\(70\) −0.723793 −0.0865098
\(71\) −4.68121 −0.555557 −0.277779 0.960645i \(-0.589598\pi\)
−0.277779 + 0.960645i \(0.589598\pi\)
\(72\) 12.2604 1.44490
\(73\) −13.7773 −1.61251 −0.806254 0.591570i \(-0.798508\pi\)
−0.806254 + 0.591570i \(0.798508\pi\)
\(74\) −9.27876 −1.07863
\(75\) −4.62694 −0.534273
\(76\) −4.91650 −0.563961
\(77\) 0.0661523 0.00753876
\(78\) −3.70918 −0.419982
\(79\) 9.84399 1.10754 0.553768 0.832671i \(-0.313190\pi\)
0.553768 + 0.832671i \(0.313190\pi\)
\(80\) 10.8025 1.20776
\(81\) −1.64962 −0.183291
\(82\) 1.96552 0.217055
\(83\) −2.19820 −0.241284 −0.120642 0.992696i \(-0.538495\pi\)
−0.120642 + 0.992696i \(0.538495\pi\)
\(84\) 1.53314 0.167280
\(85\) 5.13977 0.557487
\(86\) 23.1004 2.49098
\(87\) −6.27717 −0.672984
\(88\) −1.92632 −0.205346
\(89\) 6.15320 0.652238 0.326119 0.945329i \(-0.394259\pi\)
0.326119 + 0.945329i \(0.394259\pi\)
\(90\) 4.39229 0.462988
\(91\) 0.313800 0.0328952
\(92\) 27.5764 2.87503
\(93\) −1.09222 −0.113258
\(94\) 27.0580 2.79082
\(95\) −1.04484 −0.107198
\(96\) −14.0293 −1.43186
\(97\) 9.44861 0.959361 0.479680 0.877443i \(-0.340753\pi\)
0.479680 + 0.877443i \(0.340753\pi\)
\(98\) 18.2270 1.84120
\(99\) −0.401441 −0.0403463
\(100\) −19.2152 −1.92152
\(101\) 0.0480356 0.00477972 0.00238986 0.999997i \(-0.499239\pi\)
0.00238986 + 0.999997i \(0.499239\pi\)
\(102\) −15.3159 −1.51650
\(103\) −8.09539 −0.797663 −0.398831 0.917024i \(-0.630584\pi\)
−0.398831 + 0.917024i \(0.630584\pi\)
\(104\) −9.13767 −0.896022
\(105\) 0.325819 0.0317966
\(106\) 4.06711 0.395033
\(107\) 4.80385 0.464406 0.232203 0.972667i \(-0.425407\pi\)
0.232203 + 0.972667i \(0.425407\pi\)
\(108\) −26.7653 −2.57549
\(109\) −1.08309 −0.103741 −0.0518704 0.998654i \(-0.516518\pi\)
−0.0518704 + 0.998654i \(0.516518\pi\)
\(110\) −0.690105 −0.0657989
\(111\) 4.17687 0.396451
\(112\) 2.72332 0.257330
\(113\) 14.9802 1.40922 0.704611 0.709594i \(-0.251121\pi\)
0.704611 + 0.709594i \(0.251121\pi\)
\(114\) 3.11349 0.291605
\(115\) 5.86044 0.546489
\(116\) −26.0685 −2.42040
\(117\) −1.90427 −0.176050
\(118\) 31.2928 2.88073
\(119\) 1.29574 0.118780
\(120\) −9.48764 −0.866100
\(121\) −10.9369 −0.994266
\(122\) 19.2158 1.73971
\(123\) −0.884786 −0.0797784
\(124\) −4.53589 −0.407335
\(125\) −9.30775 −0.832510
\(126\) 1.10730 0.0986458
\(127\) 1.58374 0.140534 0.0702671 0.997528i \(-0.477615\pi\)
0.0702671 + 0.997528i \(0.477615\pi\)
\(128\) −3.88079 −0.343016
\(129\) −10.3987 −0.915557
\(130\) −3.27358 −0.287112
\(131\) 2.77274 0.242255 0.121128 0.992637i \(-0.461349\pi\)
0.121128 + 0.992637i \(0.461349\pi\)
\(132\) 1.46179 0.127232
\(133\) −0.263404 −0.0228400
\(134\) −32.5259 −2.80981
\(135\) −5.68807 −0.489551
\(136\) −37.7311 −3.23542
\(137\) −8.24803 −0.704676 −0.352338 0.935873i \(-0.614613\pi\)
−0.352338 + 0.935873i \(0.614613\pi\)
\(138\) −17.4634 −1.48658
\(139\) 1.23571 0.104812 0.0524059 0.998626i \(-0.483311\pi\)
0.0524059 + 0.998626i \(0.483311\pi\)
\(140\) 1.35309 0.114357
\(141\) −12.1803 −1.02576
\(142\) 12.3112 1.03313
\(143\) 0.299195 0.0250199
\(144\) −16.5263 −1.37719
\(145\) −5.53999 −0.460071
\(146\) 36.2332 2.99868
\(147\) −8.20496 −0.676734
\(148\) 17.3461 1.42584
\(149\) 9.80519 0.803272 0.401636 0.915799i \(-0.368442\pi\)
0.401636 + 0.915799i \(0.368442\pi\)
\(150\) 12.1685 0.993554
\(151\) −13.7343 −1.11768 −0.558840 0.829275i \(-0.688754\pi\)
−0.558840 + 0.829275i \(0.688754\pi\)
\(152\) 7.67017 0.622133
\(153\) −7.86309 −0.635693
\(154\) −0.173976 −0.0140194
\(155\) −0.963953 −0.0774265
\(156\) 6.93412 0.555174
\(157\) −13.4602 −1.07424 −0.537118 0.843507i \(-0.680487\pi\)
−0.537118 + 0.843507i \(0.680487\pi\)
\(158\) −25.8889 −2.05961
\(159\) −1.83083 −0.145194
\(160\) −12.3817 −0.978857
\(161\) 1.47742 0.116437
\(162\) 4.33838 0.340855
\(163\) −16.0892 −1.26020 −0.630101 0.776513i \(-0.716986\pi\)
−0.630101 + 0.776513i \(0.716986\pi\)
\(164\) −3.67442 −0.286924
\(165\) 0.310654 0.0241844
\(166\) 5.78110 0.448700
\(167\) −1.97454 −0.152794 −0.0763972 0.997077i \(-0.524342\pi\)
−0.0763972 + 0.997077i \(0.524342\pi\)
\(168\) −2.39184 −0.184534
\(169\) −11.5807 −0.890826
\(170\) −13.5172 −1.03672
\(171\) 1.59845 0.122236
\(172\) −43.1849 −3.29281
\(173\) −7.69374 −0.584944 −0.292472 0.956274i \(-0.594478\pi\)
−0.292472 + 0.956274i \(0.594478\pi\)
\(174\) 16.5085 1.25151
\(175\) −1.02946 −0.0778202
\(176\) 2.59657 0.195724
\(177\) −14.0866 −1.05881
\(178\) −16.1824 −1.21293
\(179\) −3.35718 −0.250927 −0.125464 0.992098i \(-0.540042\pi\)
−0.125464 + 0.992098i \(0.540042\pi\)
\(180\) −8.21114 −0.612022
\(181\) −4.91319 −0.365195 −0.182597 0.983188i \(-0.558450\pi\)
−0.182597 + 0.983188i \(0.558450\pi\)
\(182\) −0.825270 −0.0611731
\(183\) −8.65006 −0.639431
\(184\) −43.0215 −3.17159
\(185\) 3.68634 0.271025
\(186\) 2.87246 0.210619
\(187\) 1.23543 0.0903436
\(188\) −50.5834 −3.68917
\(189\) −1.43396 −0.104305
\(190\) 2.74784 0.199350
\(191\) 19.1241 1.38377 0.691886 0.722007i \(-0.256780\pi\)
0.691886 + 0.722007i \(0.256780\pi\)
\(192\) 12.4159 0.896041
\(193\) 13.4331 0.966939 0.483469 0.875361i \(-0.339376\pi\)
0.483469 + 0.875361i \(0.339376\pi\)
\(194\) −24.8491 −1.78406
\(195\) 1.47362 0.105528
\(196\) −34.0744 −2.43388
\(197\) 14.0759 1.00287 0.501433 0.865196i \(-0.332806\pi\)
0.501433 + 0.865196i \(0.332806\pi\)
\(198\) 1.05576 0.0750295
\(199\) −5.02687 −0.356345 −0.178173 0.983999i \(-0.557019\pi\)
−0.178173 + 0.983999i \(0.557019\pi\)
\(200\) 29.9774 2.11972
\(201\) 14.6417 1.03274
\(202\) −0.126330 −0.00888854
\(203\) −1.39663 −0.0980243
\(204\) 28.6322 2.00466
\(205\) −0.780877 −0.0545388
\(206\) 21.2903 1.48336
\(207\) −8.96560 −0.623153
\(208\) 12.3171 0.854035
\(209\) −0.251144 −0.0173720
\(210\) −0.856878 −0.0591302
\(211\) −3.09624 −0.213154 −0.106577 0.994304i \(-0.533989\pi\)
−0.106577 + 0.994304i \(0.533989\pi\)
\(212\) −7.60324 −0.522193
\(213\) −5.54195 −0.379728
\(214\) −12.6338 −0.863626
\(215\) −9.17751 −0.625901
\(216\) 41.7562 2.84115
\(217\) −0.243013 −0.0164968
\(218\) 2.84844 0.192920
\(219\) −16.3105 −1.10216
\(220\) 1.29011 0.0869794
\(221\) 5.86038 0.394212
\(222\) −10.9849 −0.737255
\(223\) −18.1100 −1.21274 −0.606369 0.795184i \(-0.707374\pi\)
−0.606369 + 0.795184i \(0.707374\pi\)
\(224\) −3.12142 −0.208559
\(225\) 6.24723 0.416482
\(226\) −39.3969 −2.62064
\(227\) 10.5126 0.697745 0.348873 0.937170i \(-0.386565\pi\)
0.348873 + 0.937170i \(0.386565\pi\)
\(228\) −5.82050 −0.385472
\(229\) −19.4814 −1.28737 −0.643684 0.765291i \(-0.722595\pi\)
−0.643684 + 0.765291i \(0.722595\pi\)
\(230\) −15.4125 −1.01627
\(231\) 0.0783159 0.00515281
\(232\) 40.6691 2.67006
\(233\) −23.6833 −1.55154 −0.775772 0.631014i \(-0.782639\pi\)
−0.775772 + 0.631014i \(0.782639\pi\)
\(234\) 5.00809 0.327389
\(235\) −10.7498 −0.701241
\(236\) −58.5001 −3.80803
\(237\) 11.6540 0.757010
\(238\) −3.40769 −0.220888
\(239\) 25.9761 1.68025 0.840127 0.542390i \(-0.182480\pi\)
0.840127 + 0.542390i \(0.182480\pi\)
\(240\) 12.7888 0.825514
\(241\) 24.9048 1.60426 0.802129 0.597150i \(-0.203700\pi\)
0.802129 + 0.597150i \(0.203700\pi\)
\(242\) 28.7633 1.84897
\(243\) 14.3790 0.922412
\(244\) −35.9228 −2.29972
\(245\) −7.24138 −0.462634
\(246\) 2.32692 0.148359
\(247\) −1.19133 −0.0758023
\(248\) 7.07638 0.449351
\(249\) −2.60239 −0.164919
\(250\) 24.4787 1.54817
\(251\) 19.1757 1.21036 0.605180 0.796089i \(-0.293101\pi\)
0.605180 + 0.796089i \(0.293101\pi\)
\(252\) −2.07003 −0.130400
\(253\) 1.40865 0.0885613
\(254\) −4.16512 −0.261343
\(255\) 6.08483 0.381047
\(256\) −10.7689 −0.673057
\(257\) 13.9965 0.873081 0.436540 0.899685i \(-0.356204\pi\)
0.436540 + 0.899685i \(0.356204\pi\)
\(258\) 27.3479 1.70260
\(259\) 0.929327 0.0577456
\(260\) 6.11978 0.379532
\(261\) 8.47536 0.524612
\(262\) −7.29209 −0.450507
\(263\) 10.6748 0.658238 0.329119 0.944288i \(-0.393248\pi\)
0.329119 + 0.944288i \(0.393248\pi\)
\(264\) −2.28051 −0.140356
\(265\) −1.61582 −0.0992588
\(266\) 0.692732 0.0424741
\(267\) 7.28460 0.445810
\(268\) 60.8053 3.71428
\(269\) 17.4146 1.06179 0.530894 0.847439i \(-0.321856\pi\)
0.530894 + 0.847439i \(0.321856\pi\)
\(270\) 14.9592 0.910387
\(271\) 11.1057 0.674621 0.337311 0.941393i \(-0.390483\pi\)
0.337311 + 0.941393i \(0.390483\pi\)
\(272\) 50.8594 3.08381
\(273\) 0.371499 0.0224841
\(274\) 21.6917 1.31044
\(275\) −0.981550 −0.0591897
\(276\) 32.6469 1.96511
\(277\) −24.2518 −1.45715 −0.728574 0.684968i \(-0.759816\pi\)
−0.728574 + 0.684968i \(0.759816\pi\)
\(278\) −3.24983 −0.194912
\(279\) 1.47470 0.0882883
\(280\) −2.11094 −0.126153
\(281\) −10.7604 −0.641911 −0.320956 0.947094i \(-0.604004\pi\)
−0.320956 + 0.947094i \(0.604004\pi\)
\(282\) 32.0332 1.90755
\(283\) −16.1672 −0.961039 −0.480519 0.876984i \(-0.659552\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(284\) −23.0151 −1.36570
\(285\) −1.23695 −0.0732709
\(286\) −0.786859 −0.0465279
\(287\) −0.196859 −0.0116202
\(288\) 18.9421 1.11618
\(289\) 7.19859 0.423446
\(290\) 14.5697 0.855565
\(291\) 11.1859 0.655731
\(292\) −67.7359 −3.96394
\(293\) −10.8454 −0.633598 −0.316799 0.948493i \(-0.602608\pi\)
−0.316799 + 0.948493i \(0.602608\pi\)
\(294\) 21.5784 1.25848
\(295\) −12.4323 −0.723834
\(296\) −27.0615 −1.57292
\(297\) −1.36722 −0.0793343
\(298\) −25.7869 −1.49380
\(299\) 6.68208 0.386435
\(300\) −22.7483 −1.31338
\(301\) −2.31365 −0.133357
\(302\) 36.1201 2.07848
\(303\) 0.0568680 0.00326698
\(304\) −10.3390 −0.592980
\(305\) −7.63420 −0.437133
\(306\) 20.6793 1.18216
\(307\) −20.0165 −1.14240 −0.571202 0.820809i \(-0.693523\pi\)
−0.571202 + 0.820809i \(0.693523\pi\)
\(308\) 0.325238 0.0185321
\(309\) −9.58391 −0.545209
\(310\) 2.53512 0.143985
\(311\) −29.7462 −1.68675 −0.843377 0.537322i \(-0.819436\pi\)
−0.843377 + 0.537322i \(0.819436\pi\)
\(312\) −10.8178 −0.612439
\(313\) 5.87567 0.332113 0.166056 0.986116i \(-0.446897\pi\)
0.166056 + 0.986116i \(0.446897\pi\)
\(314\) 35.3992 1.99769
\(315\) −0.439916 −0.0247865
\(316\) 48.3979 2.72260
\(317\) −1.00000 −0.0561656
\(318\) 4.81494 0.270008
\(319\) −1.33163 −0.0745568
\(320\) 10.9578 0.612559
\(321\) 5.68714 0.317425
\(322\) −3.88549 −0.216530
\(323\) −4.91921 −0.273712
\(324\) −8.11036 −0.450575
\(325\) −4.65607 −0.258273
\(326\) 42.3133 2.34352
\(327\) −1.28224 −0.0709078
\(328\) 5.73242 0.316520
\(329\) −2.71003 −0.149409
\(330\) −0.816996 −0.0449741
\(331\) −26.5504 −1.45934 −0.729670 0.683799i \(-0.760326\pi\)
−0.729670 + 0.683799i \(0.760326\pi\)
\(332\) −10.8074 −0.593135
\(333\) −5.63956 −0.309046
\(334\) 5.19289 0.284142
\(335\) 12.9221 0.706012
\(336\) 3.22406 0.175887
\(337\) −27.6144 −1.50425 −0.752125 0.659021i \(-0.770971\pi\)
−0.752125 + 0.659021i \(0.770971\pi\)
\(338\) 30.4565 1.65661
\(339\) 17.7347 0.963215
\(340\) 25.2697 1.37044
\(341\) −0.231702 −0.0125474
\(342\) −4.20380 −0.227315
\(343\) −3.66938 −0.198128
\(344\) 67.3721 3.63246
\(345\) 6.93801 0.373530
\(346\) 20.2339 1.08778
\(347\) 34.0857 1.82981 0.914907 0.403664i \(-0.132264\pi\)
0.914907 + 0.403664i \(0.132264\pi\)
\(348\) −30.8617 −1.65436
\(349\) 23.5853 1.26249 0.631246 0.775583i \(-0.282544\pi\)
0.631246 + 0.775583i \(0.282544\pi\)
\(350\) 2.70741 0.144717
\(351\) −6.48555 −0.346173
\(352\) −2.97614 −0.158629
\(353\) 29.6211 1.57657 0.788285 0.615310i \(-0.210969\pi\)
0.788285 + 0.615310i \(0.210969\pi\)
\(354\) 37.0466 1.96901
\(355\) −4.89110 −0.259593
\(356\) 30.2522 1.60336
\(357\) 1.53399 0.0811872
\(358\) 8.82913 0.466634
\(359\) −20.0543 −1.05842 −0.529212 0.848490i \(-0.677512\pi\)
−0.529212 + 0.848490i \(0.677512\pi\)
\(360\) 12.8101 0.675151
\(361\) 1.00000 0.0526316
\(362\) 12.9213 0.679129
\(363\) −12.9479 −0.679589
\(364\) 1.54280 0.0808645
\(365\) −14.3950 −0.753470
\(366\) 22.7490 1.18911
\(367\) −29.9243 −1.56204 −0.781019 0.624508i \(-0.785300\pi\)
−0.781019 + 0.624508i \(0.785300\pi\)
\(368\) 57.9906 3.02297
\(369\) 1.19463 0.0621897
\(370\) −9.69480 −0.504009
\(371\) −0.407347 −0.0211484
\(372\) −5.36991 −0.278417
\(373\) −5.42931 −0.281119 −0.140560 0.990072i \(-0.544890\pi\)
−0.140560 + 0.990072i \(0.544890\pi\)
\(374\) −3.24909 −0.168006
\(375\) −11.0192 −0.569028
\(376\) 78.9145 4.06971
\(377\) −6.31670 −0.325327
\(378\) 3.77121 0.193970
\(379\) 21.7451 1.11697 0.558484 0.829515i \(-0.311383\pi\)
0.558484 + 0.829515i \(0.311383\pi\)
\(380\) −5.13694 −0.263520
\(381\) 1.87495 0.0960564
\(382\) −50.2949 −2.57331
\(383\) 10.9241 0.558194 0.279097 0.960263i \(-0.409965\pi\)
0.279097 + 0.960263i \(0.409965\pi\)
\(384\) −4.59435 −0.234455
\(385\) 0.0691185 0.00352260
\(386\) −35.3281 −1.79815
\(387\) 14.0402 0.713705
\(388\) 46.4540 2.35835
\(389\) −27.8001 −1.40952 −0.704760 0.709446i \(-0.748945\pi\)
−0.704760 + 0.709446i \(0.748945\pi\)
\(390\) −3.87550 −0.196243
\(391\) 27.5915 1.39536
\(392\) 53.1590 2.68493
\(393\) 3.28257 0.165584
\(394\) −37.0186 −1.86497
\(395\) 10.2854 0.517513
\(396\) −1.97368 −0.0991813
\(397\) 22.9605 1.15236 0.576178 0.817324i \(-0.304543\pi\)
0.576178 + 0.817324i \(0.304543\pi\)
\(398\) 13.2203 0.662673
\(399\) −0.311836 −0.0156113
\(400\) −40.4079 −2.02039
\(401\) 0.770767 0.0384902 0.0192451 0.999815i \(-0.493874\pi\)
0.0192451 + 0.999815i \(0.493874\pi\)
\(402\) −38.5064 −1.92053
\(403\) −1.09910 −0.0547501
\(404\) 0.236167 0.0117497
\(405\) −1.72359 −0.0856457
\(406\) 3.67303 0.182290
\(407\) 0.886073 0.0439210
\(408\) −44.6688 −2.21144
\(409\) −13.6104 −0.672992 −0.336496 0.941685i \(-0.609242\pi\)
−0.336496 + 0.941685i \(0.609242\pi\)
\(410\) 2.05365 0.101422
\(411\) −9.76460 −0.481652
\(412\) −39.8010 −1.96085
\(413\) −3.13417 −0.154223
\(414\) 23.5789 1.15884
\(415\) −2.29676 −0.112744
\(416\) −14.1176 −0.692172
\(417\) 1.46293 0.0716398
\(418\) 0.660490 0.0323056
\(419\) 18.2406 0.891111 0.445556 0.895254i \(-0.353006\pi\)
0.445556 + 0.895254i \(0.353006\pi\)
\(420\) 1.60189 0.0781640
\(421\) −1.05245 −0.0512932 −0.0256466 0.999671i \(-0.508164\pi\)
−0.0256466 + 0.999671i \(0.508164\pi\)
\(422\) 8.14287 0.396389
\(423\) 16.4456 0.799614
\(424\) 11.8617 0.576056
\(425\) −19.2258 −0.932588
\(426\) 14.5749 0.706156
\(427\) −1.92458 −0.0931371
\(428\) 23.6181 1.14163
\(429\) 0.354208 0.0171013
\(430\) 24.1361 1.16395
\(431\) −23.5803 −1.13582 −0.567911 0.823090i \(-0.692248\pi\)
−0.567911 + 0.823090i \(0.692248\pi\)
\(432\) −56.2850 −2.70801
\(433\) 35.6289 1.71222 0.856108 0.516796i \(-0.172876\pi\)
0.856108 + 0.516796i \(0.172876\pi\)
\(434\) 0.639105 0.0306780
\(435\) −6.55863 −0.314462
\(436\) −5.32499 −0.255021
\(437\) −5.60894 −0.268312
\(438\) 42.8954 2.04962
\(439\) 0.502882 0.0240012 0.0120006 0.999928i \(-0.496180\pi\)
0.0120006 + 0.999928i \(0.496180\pi\)
\(440\) −2.01269 −0.0959512
\(441\) 11.0782 0.527535
\(442\) −15.4123 −0.733090
\(443\) −39.7468 −1.88843 −0.944214 0.329332i \(-0.893177\pi\)
−0.944214 + 0.329332i \(0.893177\pi\)
\(444\) 20.5356 0.974576
\(445\) 6.42910 0.304769
\(446\) 47.6280 2.25525
\(447\) 11.6081 0.549044
\(448\) 2.76246 0.130514
\(449\) −12.3946 −0.584939 −0.292469 0.956275i \(-0.594477\pi\)
−0.292469 + 0.956275i \(0.594477\pi\)
\(450\) −16.4297 −0.774506
\(451\) −0.187697 −0.00883829
\(452\) 73.6503 3.46422
\(453\) −16.2596 −0.763944
\(454\) −27.6473 −1.29755
\(455\) 0.327870 0.0153708
\(456\) 9.08049 0.425233
\(457\) −5.43254 −0.254124 −0.127062 0.991895i \(-0.540555\pi\)
−0.127062 + 0.991895i \(0.540555\pi\)
\(458\) 51.2346 2.39404
\(459\) −26.7800 −1.24998
\(460\) 28.8128 1.34341
\(461\) 18.9032 0.880410 0.440205 0.897897i \(-0.354906\pi\)
0.440205 + 0.897897i \(0.354906\pi\)
\(462\) −0.205965 −0.00958235
\(463\) −12.4173 −0.577080 −0.288540 0.957468i \(-0.593170\pi\)
−0.288540 + 0.957468i \(0.593170\pi\)
\(464\) −54.8196 −2.54494
\(465\) −1.14120 −0.0529217
\(466\) 62.2852 2.88531
\(467\) 0.632894 0.0292868 0.0146434 0.999893i \(-0.495339\pi\)
0.0146434 + 0.999893i \(0.495339\pi\)
\(468\) −9.36235 −0.432775
\(469\) 3.25768 0.150425
\(470\) 28.2712 1.30405
\(471\) −15.9351 −0.734250
\(472\) 91.2653 4.20082
\(473\) −2.20597 −0.101430
\(474\) −30.6492 −1.40776
\(475\) 3.90831 0.179326
\(476\) 6.37049 0.291991
\(477\) 2.47196 0.113183
\(478\) −68.3151 −3.12466
\(479\) 5.91138 0.270098 0.135049 0.990839i \(-0.456881\pi\)
0.135049 + 0.990839i \(0.456881\pi\)
\(480\) −14.6583 −0.669057
\(481\) 4.20317 0.191648
\(482\) −65.4977 −2.98334
\(483\) 1.74907 0.0795856
\(484\) −53.7714 −2.44415
\(485\) 9.87226 0.448276
\(486\) −37.8156 −1.71535
\(487\) −28.6003 −1.29600 −0.648001 0.761640i \(-0.724395\pi\)
−0.648001 + 0.761640i \(0.724395\pi\)
\(488\) 56.0427 2.53693
\(489\) −19.0475 −0.861358
\(490\) 19.0443 0.860332
\(491\) −2.89299 −0.130559 −0.0652794 0.997867i \(-0.520794\pi\)
−0.0652794 + 0.997867i \(0.520794\pi\)
\(492\) −4.35005 −0.196115
\(493\) −26.0828 −1.17471
\(494\) 3.13310 0.140965
\(495\) −0.419441 −0.0188525
\(496\) −9.53857 −0.428294
\(497\) −1.23305 −0.0553098
\(498\) 6.84408 0.306690
\(499\) 17.5882 0.787355 0.393677 0.919249i \(-0.371203\pi\)
0.393677 + 0.919249i \(0.371203\pi\)
\(500\) −45.7615 −2.04652
\(501\) −2.33760 −0.104436
\(502\) −50.4306 −2.25083
\(503\) −5.30064 −0.236344 −0.118172 0.992993i \(-0.537703\pi\)
−0.118172 + 0.992993i \(0.537703\pi\)
\(504\) 3.22943 0.143850
\(505\) 0.0501894 0.00223340
\(506\) −3.70465 −0.164692
\(507\) −13.7101 −0.608887
\(508\) 7.78646 0.345468
\(509\) −29.0533 −1.28777 −0.643883 0.765124i \(-0.722678\pi\)
−0.643883 + 0.765124i \(0.722678\pi\)
\(510\) −16.0026 −0.708609
\(511\) −3.62899 −0.160537
\(512\) 36.0830 1.59466
\(513\) 5.44397 0.240357
\(514\) −36.8098 −1.62361
\(515\) −8.45838 −0.372721
\(516\) −51.1253 −2.25067
\(517\) −2.58390 −0.113640
\(518\) −2.44406 −0.107386
\(519\) −9.10840 −0.399814
\(520\) −9.54738 −0.418680
\(521\) −2.23914 −0.0980985 −0.0490493 0.998796i \(-0.515619\pi\)
−0.0490493 + 0.998796i \(0.515619\pi\)
\(522\) −22.2895 −0.975587
\(523\) −1.56898 −0.0686066 −0.0343033 0.999411i \(-0.510921\pi\)
−0.0343033 + 0.999411i \(0.510921\pi\)
\(524\) 13.6322 0.595524
\(525\) −1.21875 −0.0531908
\(526\) −28.0740 −1.22408
\(527\) −4.53839 −0.197695
\(528\) 3.07400 0.133779
\(529\) 8.46025 0.367837
\(530\) 4.24947 0.184585
\(531\) 19.0195 0.825376
\(532\) −1.29502 −0.0561464
\(533\) −0.890357 −0.0385656
\(534\) −19.1579 −0.829045
\(535\) 5.01925 0.217001
\(536\) −94.8616 −4.09740
\(537\) −3.97447 −0.171511
\(538\) −45.7991 −1.97454
\(539\) −1.74058 −0.0749723
\(540\) −27.9654 −1.20344
\(541\) 20.2731 0.871610 0.435805 0.900041i \(-0.356464\pi\)
0.435805 + 0.900041i \(0.356464\pi\)
\(542\) −29.2071 −1.25455
\(543\) −5.81659 −0.249614
\(544\) −58.2942 −2.49934
\(545\) −1.13165 −0.0484746
\(546\) −0.977013 −0.0418123
\(547\) −21.4156 −0.915663 −0.457832 0.889039i \(-0.651374\pi\)
−0.457832 + 0.889039i \(0.651374\pi\)
\(548\) −40.5514 −1.73227
\(549\) 11.6792 0.498456
\(550\) 2.58140 0.110071
\(551\) 5.30224 0.225883
\(552\) −50.9320 −2.16781
\(553\) 2.59294 0.110263
\(554\) 63.7803 2.70976
\(555\) 4.36416 0.185248
\(556\) 6.07538 0.257654
\(557\) 16.5201 0.699978 0.349989 0.936754i \(-0.386185\pi\)
0.349989 + 0.936754i \(0.386185\pi\)
\(558\) −3.87836 −0.164184
\(559\) −10.4642 −0.442589
\(560\) 2.84543 0.120241
\(561\) 1.46259 0.0617506
\(562\) 28.2990 1.19372
\(563\) 37.2558 1.57015 0.785073 0.619403i \(-0.212625\pi\)
0.785073 + 0.619403i \(0.212625\pi\)
\(564\) −59.8842 −2.52158
\(565\) 15.6519 0.658481
\(566\) 42.5184 1.78718
\(567\) −0.434516 −0.0182480
\(568\) 35.9056 1.50657
\(569\) 22.8853 0.959402 0.479701 0.877432i \(-0.340745\pi\)
0.479701 + 0.877432i \(0.340745\pi\)
\(570\) 3.25310 0.136257
\(571\) 5.33216 0.223144 0.111572 0.993756i \(-0.464411\pi\)
0.111572 + 0.993756i \(0.464411\pi\)
\(572\) 1.47099 0.0615051
\(573\) 22.6405 0.945820
\(574\) 0.517725 0.0216094
\(575\) −21.9215 −0.914190
\(576\) −16.7638 −0.698491
\(577\) −25.6445 −1.06759 −0.533797 0.845613i \(-0.679235\pi\)
−0.533797 + 0.845613i \(0.679235\pi\)
\(578\) −18.9317 −0.787456
\(579\) 15.9031 0.660911
\(580\) −27.2373 −1.13097
\(581\) −0.579014 −0.0240216
\(582\) −29.4182 −1.21942
\(583\) −0.388388 −0.0160854
\(584\) 105.674 4.37282
\(585\) −1.98966 −0.0822622
\(586\) 28.5227 1.17826
\(587\) −1.87937 −0.0775699 −0.0387849 0.999248i \(-0.512349\pi\)
−0.0387849 + 0.999248i \(0.512349\pi\)
\(588\) −40.3397 −1.66358
\(589\) 0.922586 0.0380145
\(590\) 32.6959 1.34607
\(591\) 16.6641 0.685468
\(592\) 36.4773 1.49921
\(593\) −40.3955 −1.65885 −0.829423 0.558621i \(-0.811331\pi\)
−0.829423 + 0.558621i \(0.811331\pi\)
\(594\) 3.59569 0.147533
\(595\) 1.35384 0.0555019
\(596\) 48.2072 1.97464
\(597\) −5.95117 −0.243565
\(598\) −17.5734 −0.718628
\(599\) 29.2214 1.19395 0.596977 0.802258i \(-0.296368\pi\)
0.596977 + 0.802258i \(0.296368\pi\)
\(600\) 35.4894 1.44885
\(601\) −20.7180 −0.845104 −0.422552 0.906339i \(-0.638866\pi\)
−0.422552 + 0.906339i \(0.638866\pi\)
\(602\) 6.08472 0.247995
\(603\) −19.7690 −0.805055
\(604\) −67.5246 −2.74754
\(605\) −11.4273 −0.464587
\(606\) −0.149558 −0.00607539
\(607\) −4.37730 −0.177669 −0.0888346 0.996046i \(-0.528314\pi\)
−0.0888346 + 0.996046i \(0.528314\pi\)
\(608\) 11.8503 0.480594
\(609\) −1.65343 −0.0670004
\(610\) 20.0774 0.812909
\(611\) −12.2570 −0.495863
\(612\) −38.6589 −1.56269
\(613\) −34.7607 −1.40397 −0.701985 0.712191i \(-0.747703\pi\)
−0.701985 + 0.712191i \(0.747703\pi\)
\(614\) 52.6420 2.12446
\(615\) −0.924458 −0.0372777
\(616\) −0.507399 −0.0204437
\(617\) −44.1300 −1.77661 −0.888304 0.459255i \(-0.848116\pi\)
−0.888304 + 0.459255i \(0.848116\pi\)
\(618\) 25.2049 1.01389
\(619\) −20.2820 −0.815203 −0.407602 0.913160i \(-0.633635\pi\)
−0.407602 + 0.913160i \(0.633635\pi\)
\(620\) −4.73927 −0.190334
\(621\) −30.5349 −1.22532
\(622\) 78.2303 3.13675
\(623\) 1.62078 0.0649351
\(624\) 14.5818 0.583740
\(625\) 9.81648 0.392659
\(626\) −15.4526 −0.617609
\(627\) −0.297322 −0.0118739
\(628\) −66.1768 −2.64074
\(629\) 17.3557 0.692016
\(630\) 1.15695 0.0460938
\(631\) 22.0725 0.878692 0.439346 0.898318i \(-0.355210\pi\)
0.439346 + 0.898318i \(0.355210\pi\)
\(632\) −75.5050 −3.00343
\(633\) −3.66555 −0.145692
\(634\) 2.62992 0.104448
\(635\) 1.65475 0.0656669
\(636\) −9.00126 −0.356923
\(637\) −8.25663 −0.327139
\(638\) 3.50208 0.138649
\(639\) 7.48267 0.296010
\(640\) −4.05479 −0.160280
\(641\) −32.5323 −1.28495 −0.642473 0.766308i \(-0.722092\pi\)
−0.642473 + 0.766308i \(0.722092\pi\)
\(642\) −14.9568 −0.590296
\(643\) −4.51285 −0.177970 −0.0889848 0.996033i \(-0.528362\pi\)
−0.0889848 + 0.996033i \(0.528362\pi\)
\(644\) 7.26372 0.286231
\(645\) −10.8650 −0.427809
\(646\) 12.9371 0.509005
\(647\) −3.53958 −0.139155 −0.0695776 0.997577i \(-0.522165\pi\)
−0.0695776 + 0.997577i \(0.522165\pi\)
\(648\) 12.6529 0.497051
\(649\) −2.98830 −0.117301
\(650\) 12.2451 0.480293
\(651\) −0.287696 −0.0112757
\(652\) −79.1024 −3.09789
\(653\) −43.2427 −1.69222 −0.846110 0.533009i \(-0.821061\pi\)
−0.846110 + 0.533009i \(0.821061\pi\)
\(654\) 3.37218 0.131863
\(655\) 2.89706 0.113198
\(656\) −7.72699 −0.301688
\(657\) 22.0222 0.859170
\(658\) 7.12717 0.277846
\(659\) 18.9540 0.738344 0.369172 0.929361i \(-0.379641\pi\)
0.369172 + 0.929361i \(0.379641\pi\)
\(660\) 1.52733 0.0594512
\(661\) 25.2018 0.980235 0.490117 0.871657i \(-0.336954\pi\)
0.490117 + 0.871657i \(0.336954\pi\)
\(662\) 69.8255 2.71384
\(663\) 6.93793 0.269447
\(664\) 16.8606 0.654316
\(665\) −0.275214 −0.0106724
\(666\) 14.8316 0.574713
\(667\) −29.7400 −1.15154
\(668\) −9.70782 −0.375607
\(669\) −21.4399 −0.828916
\(670\) −33.9843 −1.31293
\(671\) −1.83501 −0.0708396
\(672\) −3.69536 −0.142552
\(673\) −0.0694157 −0.00267578 −0.00133789 0.999999i \(-0.500426\pi\)
−0.00133789 + 0.999999i \(0.500426\pi\)
\(674\) 72.6236 2.79736
\(675\) 21.2767 0.818942
\(676\) −56.9367 −2.18987
\(677\) 3.90032 0.149901 0.0749507 0.997187i \(-0.476120\pi\)
0.0749507 + 0.997187i \(0.476120\pi\)
\(678\) −46.6408 −1.79123
\(679\) 2.48880 0.0955113
\(680\) −39.4229 −1.51180
\(681\) 12.4456 0.476915
\(682\) 0.609358 0.0233335
\(683\) −16.6897 −0.638614 −0.319307 0.947651i \(-0.603450\pi\)
−0.319307 + 0.947651i \(0.603450\pi\)
\(684\) 7.85877 0.300487
\(685\) −8.61785 −0.329271
\(686\) 9.65019 0.368446
\(687\) −23.0635 −0.879927
\(688\) −90.8139 −3.46225
\(689\) −1.84236 −0.0701882
\(690\) −18.2464 −0.694630
\(691\) 21.7352 0.826847 0.413424 0.910539i \(-0.364333\pi\)
0.413424 + 0.910539i \(0.364333\pi\)
\(692\) −37.8262 −1.43794
\(693\) −0.105741 −0.00401677
\(694\) −89.6427 −3.40279
\(695\) 1.29112 0.0489750
\(696\) 48.1470 1.82501
\(697\) −3.67645 −0.139255
\(698\) −62.0275 −2.34778
\(699\) −28.0380 −1.06049
\(700\) −5.06136 −0.191301
\(701\) −42.8313 −1.61771 −0.808857 0.588005i \(-0.799914\pi\)
−0.808857 + 0.588005i \(0.799914\pi\)
\(702\) 17.0565 0.643756
\(703\) −3.52815 −0.133067
\(704\) 2.63389 0.0992683
\(705\) −12.7264 −0.479304
\(706\) −77.9012 −2.93185
\(707\) 0.0126528 0.000475856 0
\(708\) −69.2566 −2.60282
\(709\) −19.0320 −0.714762 −0.357381 0.933959i \(-0.616330\pi\)
−0.357381 + 0.933959i \(0.616330\pi\)
\(710\) 12.8632 0.482748
\(711\) −15.7351 −0.590112
\(712\) −47.1961 −1.76875
\(713\) −5.17473 −0.193795
\(714\) −4.03427 −0.150979
\(715\) 0.312610 0.0116909
\(716\) −16.5056 −0.616842
\(717\) 30.7524 1.14847
\(718\) 52.7412 1.96828
\(719\) 18.2726 0.681452 0.340726 0.940163i \(-0.389327\pi\)
0.340726 + 0.940163i \(0.389327\pi\)
\(720\) −17.2673 −0.643514
\(721\) −2.13236 −0.0794132
\(722\) −2.62992 −0.0978756
\(723\) 29.4841 1.09652
\(724\) −24.1557 −0.897739
\(725\) 20.7228 0.769626
\(726\) 34.0520 1.26379
\(727\) −10.7757 −0.399649 −0.199824 0.979832i \(-0.564037\pi\)
−0.199824 + 0.979832i \(0.564037\pi\)
\(728\) −2.40690 −0.0892055
\(729\) 21.9717 0.813768
\(730\) 37.8578 1.40118
\(731\) −43.2086 −1.59813
\(732\) −42.5280 −1.57188
\(733\) 46.7699 1.72748 0.863742 0.503934i \(-0.168115\pi\)
0.863742 + 0.503934i \(0.168115\pi\)
\(734\) 78.6987 2.90482
\(735\) −8.57286 −0.316215
\(736\) −66.4678 −2.45004
\(737\) 3.10605 0.114413
\(738\) −3.14178 −0.115650
\(739\) 1.15395 0.0424489 0.0212245 0.999775i \(-0.493244\pi\)
0.0212245 + 0.999775i \(0.493244\pi\)
\(740\) 18.1239 0.666248
\(741\) −1.41038 −0.0518115
\(742\) 1.07129 0.0393284
\(743\) 28.7073 1.05317 0.526585 0.850123i \(-0.323472\pi\)
0.526585 + 0.850123i \(0.323472\pi\)
\(744\) 8.37753 0.307135
\(745\) 10.2448 0.375342
\(746\) 14.2787 0.522779
\(747\) 3.51371 0.128560
\(748\) 6.07399 0.222087
\(749\) 1.26535 0.0462350
\(750\) 28.9796 1.05819
\(751\) −40.0982 −1.46321 −0.731603 0.681731i \(-0.761227\pi\)
−0.731603 + 0.681731i \(0.761227\pi\)
\(752\) −106.372 −3.87900
\(753\) 22.7016 0.827291
\(754\) 16.6124 0.604989
\(755\) −14.3501 −0.522254
\(756\) −7.05008 −0.256409
\(757\) 21.7046 0.788866 0.394433 0.918925i \(-0.370941\pi\)
0.394433 + 0.918925i \(0.370941\pi\)
\(758\) −57.1878 −2.07716
\(759\) 1.66766 0.0605324
\(760\) 8.01408 0.290701
\(761\) −7.97656 −0.289150 −0.144575 0.989494i \(-0.546181\pi\)
−0.144575 + 0.989494i \(0.546181\pi\)
\(762\) −4.93096 −0.178630
\(763\) −0.285289 −0.0103282
\(764\) 94.0236 3.40165
\(765\) −8.21566 −0.297038
\(766\) −28.7295 −1.03804
\(767\) −14.1753 −0.511839
\(768\) −12.7490 −0.460041
\(769\) 29.3837 1.05960 0.529802 0.848121i \(-0.322266\pi\)
0.529802 + 0.848121i \(0.322266\pi\)
\(770\) −0.181776 −0.00655076
\(771\) 16.5701 0.596758
\(772\) 66.0440 2.37698
\(773\) −24.3509 −0.875841 −0.437920 0.899014i \(-0.644285\pi\)
−0.437920 + 0.899014i \(0.644285\pi\)
\(774\) −36.9247 −1.32723
\(775\) 3.60575 0.129522
\(776\) −72.4724 −2.60161
\(777\) 1.10020 0.0394696
\(778\) 73.1121 2.62120
\(779\) 0.747366 0.0267772
\(780\) 7.24503 0.259414
\(781\) −1.17566 −0.0420683
\(782\) −72.5637 −2.59487
\(783\) 28.8653 1.03156
\(784\) −71.6553 −2.55912
\(785\) −14.0637 −0.501954
\(786\) −8.63290 −0.307925
\(787\) 40.7835 1.45377 0.726887 0.686758i \(-0.240967\pi\)
0.726887 + 0.686758i \(0.240967\pi\)
\(788\) 69.2042 2.46530
\(789\) 12.6376 0.449911
\(790\) −27.0497 −0.962387
\(791\) 3.94585 0.140298
\(792\) 3.07912 0.109412
\(793\) −8.70452 −0.309107
\(794\) −60.3845 −2.14296
\(795\) −1.91292 −0.0678442
\(796\) −24.7146 −0.875985
\(797\) −2.21305 −0.0783903 −0.0391952 0.999232i \(-0.512479\pi\)
−0.0391952 + 0.999232i \(0.512479\pi\)
\(798\) 0.820106 0.0290314
\(799\) −50.6113 −1.79050
\(800\) 46.3148 1.63747
\(801\) −9.83557 −0.347523
\(802\) −2.02706 −0.0715779
\(803\) −3.46008 −0.122104
\(804\) 71.9857 2.53874
\(805\) 1.54366 0.0544069
\(806\) 2.89055 0.101815
\(807\) 20.6167 0.725741
\(808\) −0.368441 −0.0129617
\(809\) 22.3825 0.786927 0.393463 0.919340i \(-0.371277\pi\)
0.393463 + 0.919340i \(0.371277\pi\)
\(810\) 4.53290 0.159270
\(811\) 15.9590 0.560395 0.280198 0.959942i \(-0.409600\pi\)
0.280198 + 0.959942i \(0.409600\pi\)
\(812\) −6.86653 −0.240968
\(813\) 13.1477 0.461110
\(814\) −2.33031 −0.0816772
\(815\) −16.8106 −0.588849
\(816\) 60.2111 2.10781
\(817\) 8.78366 0.307301
\(818\) 35.7943 1.25152
\(819\) −0.501593 −0.0175271
\(820\) −3.83918 −0.134070
\(821\) 27.4173 0.956871 0.478435 0.878123i \(-0.341204\pi\)
0.478435 + 0.878123i \(0.341204\pi\)
\(822\) 25.6802 0.895698
\(823\) −13.0830 −0.456045 −0.228022 0.973656i \(-0.573226\pi\)
−0.228022 + 0.973656i \(0.573226\pi\)
\(824\) 62.0930 2.16311
\(825\) −1.16203 −0.0404567
\(826\) 8.24263 0.286798
\(827\) 23.9751 0.833696 0.416848 0.908976i \(-0.363135\pi\)
0.416848 + 0.908976i \(0.363135\pi\)
\(828\) −44.0794 −1.53186
\(829\) 0.260194 0.00903692 0.00451846 0.999990i \(-0.498562\pi\)
0.00451846 + 0.999990i \(0.498562\pi\)
\(830\) 6.04031 0.209662
\(831\) −28.7110 −0.995973
\(832\) 12.4941 0.433154
\(833\) −34.0931 −1.18126
\(834\) −3.84738 −0.133224
\(835\) −2.06307 −0.0713956
\(836\) −1.23475 −0.0427047
\(837\) 5.02253 0.173604
\(838\) −47.9714 −1.65714
\(839\) −16.6983 −0.576489 −0.288245 0.957557i \(-0.593072\pi\)
−0.288245 + 0.957557i \(0.593072\pi\)
\(840\) −2.49908 −0.0862265
\(841\) −0.886223 −0.0305594
\(842\) 2.76786 0.0953868
\(843\) −12.7389 −0.438752
\(844\) −15.2226 −0.523985
\(845\) −12.1000 −0.416253
\(846\) −43.2508 −1.48699
\(847\) −2.88083 −0.0989864
\(848\) −15.9889 −0.549062
\(849\) −19.1399 −0.656878
\(850\) 50.5624 1.73428
\(851\) 19.7892 0.678364
\(852\) −27.2470 −0.933466
\(853\) −27.5458 −0.943149 −0.471575 0.881826i \(-0.656314\pi\)
−0.471575 + 0.881826i \(0.656314\pi\)
\(854\) 5.06151 0.173201
\(855\) 1.67012 0.0571169
\(856\) −36.8463 −1.25938
\(857\) −25.1205 −0.858099 −0.429050 0.903281i \(-0.641151\pi\)
−0.429050 + 0.903281i \(0.641151\pi\)
\(858\) −0.931540 −0.0318022
\(859\) 14.6868 0.501106 0.250553 0.968103i \(-0.419388\pi\)
0.250553 + 0.968103i \(0.419388\pi\)
\(860\) −45.1212 −1.53862
\(861\) −0.233056 −0.00794253
\(862\) 62.0144 2.11222
\(863\) −43.8691 −1.49332 −0.746661 0.665205i \(-0.768344\pi\)
−0.746661 + 0.665205i \(0.768344\pi\)
\(864\) 64.5128 2.19477
\(865\) −8.03871 −0.273324
\(866\) −93.7013 −3.18410
\(867\) 8.52220 0.289429
\(868\) −1.19477 −0.0405532
\(869\) 2.47226 0.0838657
\(870\) 17.2487 0.584786
\(871\) 14.7339 0.499238
\(872\) 8.30745 0.281326
\(873\) −15.1031 −0.511163
\(874\) 14.7511 0.498963
\(875\) −2.45170 −0.0828825
\(876\) −80.1906 −2.70939
\(877\) 13.0008 0.439005 0.219503 0.975612i \(-0.429557\pi\)
0.219503 + 0.975612i \(0.429557\pi\)
\(878\) −1.32254 −0.0446336
\(879\) −12.8396 −0.433069
\(880\) 2.71299 0.0914550
\(881\) −39.8300 −1.34191 −0.670954 0.741499i \(-0.734115\pi\)
−0.670954 + 0.741499i \(0.734115\pi\)
\(882\) −29.1349 −0.981023
\(883\) 2.66769 0.0897750 0.0448875 0.998992i \(-0.485707\pi\)
0.0448875 + 0.998992i \(0.485707\pi\)
\(884\) 28.8125 0.969070
\(885\) −14.7182 −0.494747
\(886\) 104.531 3.51179
\(887\) −25.6166 −0.860123 −0.430061 0.902800i \(-0.641508\pi\)
−0.430061 + 0.902800i \(0.641508\pi\)
\(888\) −32.0373 −1.07510
\(889\) 0.417163 0.0139912
\(890\) −16.9080 −0.566759
\(891\) −0.414293 −0.0138793
\(892\) −89.0379 −2.98121
\(893\) 10.2885 0.344292
\(894\) −30.5284 −1.02102
\(895\) −3.50771 −0.117250
\(896\) −1.02221 −0.0341498
\(897\) 7.91073 0.264131
\(898\) 32.5969 1.08777
\(899\) 4.89177 0.163150
\(900\) 30.7145 1.02382
\(901\) −7.60743 −0.253440
\(902\) 0.493628 0.0164360
\(903\) −2.73907 −0.0911504
\(904\) −114.901 −3.82155
\(905\) −5.13349 −0.170643
\(906\) 42.7616 1.42066
\(907\) −8.73472 −0.290032 −0.145016 0.989429i \(-0.546323\pi\)
−0.145016 + 0.989429i \(0.546323\pi\)
\(908\) 51.6851 1.71523
\(909\) −0.0767824 −0.00254671
\(910\) −0.862273 −0.0285841
\(911\) 42.1382 1.39610 0.698051 0.716048i \(-0.254051\pi\)
0.698051 + 0.716048i \(0.254051\pi\)
\(912\) −12.2400 −0.405307
\(913\) −0.552065 −0.0182707
\(914\) 14.2872 0.472577
\(915\) −9.03791 −0.298784
\(916\) −95.7803 −3.16467
\(917\) 0.730350 0.0241183
\(918\) 70.4294 2.32452
\(919\) 20.0060 0.659936 0.329968 0.943992i \(-0.392962\pi\)
0.329968 + 0.943992i \(0.392962\pi\)
\(920\) −44.9505 −1.48198
\(921\) −23.6970 −0.780843
\(922\) −49.7140 −1.63724
\(923\) −5.57684 −0.183564
\(924\) 0.385040 0.0126669
\(925\) −13.7891 −0.453383
\(926\) 32.6565 1.07316
\(927\) 12.9401 0.425007
\(928\) 62.8333 2.06260
\(929\) 41.5578 1.36347 0.681733 0.731601i \(-0.261227\pi\)
0.681733 + 0.731601i \(0.261227\pi\)
\(930\) 3.00126 0.0984152
\(931\) 6.93062 0.227142
\(932\) −116.439 −3.81408
\(933\) −35.2157 −1.15291
\(934\) −1.66446 −0.0544629
\(935\) 1.29082 0.0422145
\(936\) 14.6061 0.477415
\(937\) −17.5115 −0.572075 −0.286038 0.958218i \(-0.592338\pi\)
−0.286038 + 0.958218i \(0.592338\pi\)
\(938\) −8.56744 −0.279737
\(939\) 6.95604 0.227002
\(940\) −52.8515 −1.72382
\(941\) −53.3300 −1.73851 −0.869254 0.494365i \(-0.835401\pi\)
−0.869254 + 0.494365i \(0.835401\pi\)
\(942\) 41.9081 1.36544
\(943\) −4.19194 −0.136508
\(944\) −123.020 −4.00397
\(945\) −1.49826 −0.0487384
\(946\) 5.80152 0.188624
\(947\) −19.6566 −0.638755 −0.319377 0.947628i \(-0.603474\pi\)
−0.319377 + 0.947628i \(0.603474\pi\)
\(948\) 57.2970 1.86092
\(949\) −16.4132 −0.532796
\(950\) −10.2786 −0.333481
\(951\) −1.18387 −0.0383897
\(952\) −9.93852 −0.322109
\(953\) −9.14726 −0.296309 −0.148154 0.988964i \(-0.547333\pi\)
−0.148154 + 0.988964i \(0.547333\pi\)
\(954\) −6.50106 −0.210480
\(955\) 19.9816 0.646589
\(956\) 127.711 4.13048
\(957\) −1.57648 −0.0509602
\(958\) −15.5465 −0.502284
\(959\) −2.17256 −0.0701557
\(960\) 12.9726 0.418689
\(961\) −30.1488 −0.972543
\(962\) −11.0540 −0.356396
\(963\) −7.67871 −0.247443
\(964\) 122.444 3.94367
\(965\) 14.0355 0.451817
\(966\) −4.59993 −0.148000
\(967\) −5.89343 −0.189520 −0.0947599 0.995500i \(-0.530208\pi\)
−0.0947599 + 0.995500i \(0.530208\pi\)
\(968\) 83.8880 2.69626
\(969\) −5.82371 −0.187084
\(970\) −25.9633 −0.833631
\(971\) −30.5805 −0.981376 −0.490688 0.871335i \(-0.663255\pi\)
−0.490688 + 0.871335i \(0.663255\pi\)
\(972\) 70.6942 2.26752
\(973\) 0.325492 0.0104348
\(974\) 75.2165 2.41009
\(975\) −5.51219 −0.176532
\(976\) −75.5424 −2.41805
\(977\) 40.5759 1.29814 0.649069 0.760729i \(-0.275159\pi\)
0.649069 + 0.760729i \(0.275159\pi\)
\(978\) 50.0935 1.60181
\(979\) 1.54534 0.0493893
\(980\) −35.6022 −1.13727
\(981\) 1.73126 0.0552748
\(982\) 7.60834 0.242792
\(983\) −41.5123 −1.32404 −0.662018 0.749488i \(-0.730300\pi\)
−0.662018 + 0.749488i \(0.730300\pi\)
\(984\) 6.78645 0.216344
\(985\) 14.7070 0.468605
\(986\) 68.5958 2.18454
\(987\) −3.20833 −0.102122
\(988\) −5.85715 −0.186341
\(989\) −49.2671 −1.56660
\(990\) 1.10310 0.0350587
\(991\) −50.9193 −1.61750 −0.808752 0.588150i \(-0.799856\pi\)
−0.808752 + 0.588150i \(0.799856\pi\)
\(992\) 10.9329 0.347121
\(993\) −31.4322 −0.997472
\(994\) 3.24282 0.102856
\(995\) −5.25226 −0.166508
\(996\) −12.7946 −0.405413
\(997\) 26.1999 0.829760 0.414880 0.909876i \(-0.363824\pi\)
0.414880 + 0.909876i \(0.363824\pi\)
\(998\) −46.2555 −1.46419
\(999\) −19.2071 −0.607687
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 \(a_p\))