Properties

Label 8018.2.a.f.1.10
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.04582 q^{3}\) \(+1.00000 q^{4}\) \(-4.09434 q^{5}\) \(+2.04582 q^{6}\) \(+1.49846 q^{7}\) \(-1.00000 q^{8}\) \(+1.18539 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.04582 q^{3}\) \(+1.00000 q^{4}\) \(-4.09434 q^{5}\) \(+2.04582 q^{6}\) \(+1.49846 q^{7}\) \(-1.00000 q^{8}\) \(+1.18539 q^{9}\) \(+4.09434 q^{10}\) \(+4.36668 q^{11}\) \(-2.04582 q^{12}\) \(-2.07746 q^{13}\) \(-1.49846 q^{14}\) \(+8.37630 q^{15}\) \(+1.00000 q^{16}\) \(+2.71655 q^{17}\) \(-1.18539 q^{18}\) \(-1.00000 q^{19}\) \(-4.09434 q^{20}\) \(-3.06558 q^{21}\) \(-4.36668 q^{22}\) \(-8.72662 q^{23}\) \(+2.04582 q^{24}\) \(+11.7636 q^{25}\) \(+2.07746 q^{26}\) \(+3.71237 q^{27}\) \(+1.49846 q^{28}\) \(+1.76891 q^{29}\) \(-8.37630 q^{30}\) \(-3.93079 q^{31}\) \(-1.00000 q^{32}\) \(-8.93345 q^{33}\) \(-2.71655 q^{34}\) \(-6.13520 q^{35}\) \(+1.18539 q^{36}\) \(-9.86688 q^{37}\) \(+1.00000 q^{38}\) \(+4.25010 q^{39}\) \(+4.09434 q^{40}\) \(+5.20665 q^{41}\) \(+3.06558 q^{42}\) \(+4.35112 q^{43}\) \(+4.36668 q^{44}\) \(-4.85339 q^{45}\) \(+8.72662 q^{46}\) \(-5.27226 q^{47}\) \(-2.04582 q^{48}\) \(-4.75463 q^{49}\) \(-11.7636 q^{50}\) \(-5.55758 q^{51}\) \(-2.07746 q^{52}\) \(-2.90552 q^{53}\) \(-3.71237 q^{54}\) \(-17.8787 q^{55}\) \(-1.49846 q^{56}\) \(+2.04582 q^{57}\) \(-1.76891 q^{58}\) \(+7.50249 q^{59}\) \(+8.37630 q^{60}\) \(-4.68551 q^{61}\) \(+3.93079 q^{62}\) \(+1.77626 q^{63}\) \(+1.00000 q^{64}\) \(+8.50581 q^{65}\) \(+8.93345 q^{66}\) \(-8.57101 q^{67}\) \(+2.71655 q^{68}\) \(+17.8531 q^{69}\) \(+6.13520 q^{70}\) \(+1.09328 q^{71}\) \(-1.18539 q^{72}\) \(+11.3584 q^{73}\) \(+9.86688 q^{74}\) \(-24.0663 q^{75}\) \(-1.00000 q^{76}\) \(+6.54328 q^{77}\) \(-4.25010 q^{78}\) \(+7.46127 q^{79}\) \(-4.09434 q^{80}\) \(-11.1510 q^{81}\) \(-5.20665 q^{82}\) \(+15.3359 q^{83}\) \(-3.06558 q^{84}\) \(-11.1225 q^{85}\) \(-4.35112 q^{86}\) \(-3.61887 q^{87}\) \(-4.36668 q^{88}\) \(+7.24142 q^{89}\) \(+4.85339 q^{90}\) \(-3.11298 q^{91}\) \(-8.72662 q^{92}\) \(+8.04171 q^{93}\) \(+5.27226 q^{94}\) \(+4.09434 q^{95}\) \(+2.04582 q^{96}\) \(-16.3302 q^{97}\) \(+4.75463 q^{98}\) \(+5.17622 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.04582 −1.18116 −0.590578 0.806980i \(-0.701100\pi\)
−0.590578 + 0.806980i \(0.701100\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.09434 −1.83105 −0.915523 0.402266i \(-0.868223\pi\)
−0.915523 + 0.402266i \(0.868223\pi\)
\(6\) 2.04582 0.835204
\(7\) 1.49846 0.566363 0.283182 0.959066i \(-0.408610\pi\)
0.283182 + 0.959066i \(0.408610\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.18539 0.395130
\(10\) 4.09434 1.29474
\(11\) 4.36668 1.31660 0.658302 0.752754i \(-0.271275\pi\)
0.658302 + 0.752754i \(0.271275\pi\)
\(12\) −2.04582 −0.590578
\(13\) −2.07746 −0.576182 −0.288091 0.957603i \(-0.593021\pi\)
−0.288091 + 0.957603i \(0.593021\pi\)
\(14\) −1.49846 −0.400479
\(15\) 8.37630 2.16275
\(16\) 1.00000 0.250000
\(17\) 2.71655 0.658861 0.329430 0.944180i \(-0.393143\pi\)
0.329430 + 0.944180i \(0.393143\pi\)
\(18\) −1.18539 −0.279399
\(19\) −1.00000 −0.229416
\(20\) −4.09434 −0.915523
\(21\) −3.06558 −0.668964
\(22\) −4.36668 −0.930979
\(23\) −8.72662 −1.81963 −0.909813 0.415017i \(-0.863776\pi\)
−0.909813 + 0.415017i \(0.863776\pi\)
\(24\) 2.04582 0.417602
\(25\) 11.7636 2.35273
\(26\) 2.07746 0.407422
\(27\) 3.71237 0.714446
\(28\) 1.49846 0.283182
\(29\) 1.76891 0.328478 0.164239 0.986421i \(-0.447483\pi\)
0.164239 + 0.986421i \(0.447483\pi\)
\(30\) −8.37630 −1.52930
\(31\) −3.93079 −0.705991 −0.352996 0.935625i \(-0.614837\pi\)
−0.352996 + 0.935625i \(0.614837\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.93345 −1.55511
\(34\) −2.71655 −0.465885
\(35\) −6.13520 −1.03704
\(36\) 1.18539 0.197565
\(37\) −9.86688 −1.62210 −0.811052 0.584973i \(-0.801105\pi\)
−0.811052 + 0.584973i \(0.801105\pi\)
\(38\) 1.00000 0.162221
\(39\) 4.25010 0.680561
\(40\) 4.09434 0.647372
\(41\) 5.20665 0.813142 0.406571 0.913619i \(-0.366724\pi\)
0.406571 + 0.913619i \(0.366724\pi\)
\(42\) 3.06558 0.473029
\(43\) 4.35112 0.663539 0.331769 0.943361i \(-0.392354\pi\)
0.331769 + 0.943361i \(0.392354\pi\)
\(44\) 4.36668 0.658302
\(45\) −4.85339 −0.723501
\(46\) 8.72662 1.28667
\(47\) −5.27226 −0.769039 −0.384519 0.923117i \(-0.625633\pi\)
−0.384519 + 0.923117i \(0.625633\pi\)
\(48\) −2.04582 −0.295289
\(49\) −4.75463 −0.679232
\(50\) −11.7636 −1.66363
\(51\) −5.55758 −0.778218
\(52\) −2.07746 −0.288091
\(53\) −2.90552 −0.399104 −0.199552 0.979887i \(-0.563949\pi\)
−0.199552 + 0.979887i \(0.563949\pi\)
\(54\) −3.71237 −0.505190
\(55\) −17.8787 −2.41076
\(56\) −1.49846 −0.200240
\(57\) 2.04582 0.270976
\(58\) −1.76891 −0.232269
\(59\) 7.50249 0.976741 0.488371 0.872636i \(-0.337591\pi\)
0.488371 + 0.872636i \(0.337591\pi\)
\(60\) 8.37630 1.08138
\(61\) −4.68551 −0.599918 −0.299959 0.953952i \(-0.596973\pi\)
−0.299959 + 0.953952i \(0.596973\pi\)
\(62\) 3.93079 0.499211
\(63\) 1.77626 0.223787
\(64\) 1.00000 0.125000
\(65\) 8.50581 1.05502
\(66\) 8.93345 1.09963
\(67\) −8.57101 −1.04712 −0.523558 0.851990i \(-0.675396\pi\)
−0.523558 + 0.851990i \(0.675396\pi\)
\(68\) 2.71655 0.329430
\(69\) 17.8531 2.14926
\(70\) 6.13520 0.733296
\(71\) 1.09328 0.129748 0.0648741 0.997893i \(-0.479335\pi\)
0.0648741 + 0.997893i \(0.479335\pi\)
\(72\) −1.18539 −0.139700
\(73\) 11.3584 1.32940 0.664700 0.747111i \(-0.268560\pi\)
0.664700 + 0.747111i \(0.268560\pi\)
\(74\) 9.86688 1.14700
\(75\) −24.0663 −2.77894
\(76\) −1.00000 −0.114708
\(77\) 6.54328 0.745676
\(78\) −4.25010 −0.481230
\(79\) 7.46127 0.839458 0.419729 0.907649i \(-0.362125\pi\)
0.419729 + 0.907649i \(0.362125\pi\)
\(80\) −4.09434 −0.457761
\(81\) −11.1510 −1.23900
\(82\) −5.20665 −0.574978
\(83\) 15.3359 1.68333 0.841666 0.539999i \(-0.181575\pi\)
0.841666 + 0.539999i \(0.181575\pi\)
\(84\) −3.06558 −0.334482
\(85\) −11.1225 −1.20640
\(86\) −4.35112 −0.469193
\(87\) −3.61887 −0.387983
\(88\) −4.36668 −0.465490
\(89\) 7.24142 0.767589 0.383795 0.923418i \(-0.374617\pi\)
0.383795 + 0.923418i \(0.374617\pi\)
\(90\) 4.85339 0.511593
\(91\) −3.11298 −0.326329
\(92\) −8.72662 −0.909813
\(93\) 8.04171 0.833886
\(94\) 5.27226 0.543792
\(95\) 4.09434 0.420071
\(96\) 2.04582 0.208801
\(97\) −16.3302 −1.65808 −0.829042 0.559186i \(-0.811114\pi\)
−0.829042 + 0.559186i \(0.811114\pi\)
\(98\) 4.75463 0.480290
\(99\) 5.17622 0.520230
\(100\) 11.7636 1.17636
\(101\) 1.31063 0.130413 0.0652063 0.997872i \(-0.479229\pi\)
0.0652063 + 0.997872i \(0.479229\pi\)
\(102\) 5.55758 0.550283
\(103\) −0.646222 −0.0636742 −0.0318371 0.999493i \(-0.510136\pi\)
−0.0318371 + 0.999493i \(0.510136\pi\)
\(104\) 2.07746 0.203711
\(105\) 12.5515 1.22490
\(106\) 2.90552 0.282209
\(107\) 17.4634 1.68825 0.844125 0.536147i \(-0.180121\pi\)
0.844125 + 0.536147i \(0.180121\pi\)
\(108\) 3.71237 0.357223
\(109\) 13.5424 1.29713 0.648565 0.761160i \(-0.275370\pi\)
0.648565 + 0.761160i \(0.275370\pi\)
\(110\) 17.8787 1.70467
\(111\) 20.1859 1.91596
\(112\) 1.49846 0.141591
\(113\) −10.1385 −0.953747 −0.476874 0.878972i \(-0.658230\pi\)
−0.476874 + 0.878972i \(0.658230\pi\)
\(114\) −2.04582 −0.191609
\(115\) 35.7298 3.33182
\(116\) 1.76891 0.164239
\(117\) −2.46259 −0.227667
\(118\) −7.50249 −0.690660
\(119\) 4.07064 0.373155
\(120\) −8.37630 −0.764648
\(121\) 8.06789 0.733445
\(122\) 4.68551 0.424206
\(123\) −10.6519 −0.960447
\(124\) −3.93079 −0.352996
\(125\) −27.6927 −2.47691
\(126\) −1.77626 −0.158241
\(127\) −11.5486 −1.02477 −0.512385 0.858756i \(-0.671238\pi\)
−0.512385 + 0.858756i \(0.671238\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.90161 −0.783743
\(130\) −8.50581 −0.746009
\(131\) −2.24440 −0.196094 −0.0980469 0.995182i \(-0.531260\pi\)
−0.0980469 + 0.995182i \(0.531260\pi\)
\(132\) −8.93345 −0.777557
\(133\) −1.49846 −0.129933
\(134\) 8.57101 0.740423
\(135\) −15.1997 −1.30818
\(136\) −2.71655 −0.232942
\(137\) 0.788239 0.0673438 0.0336719 0.999433i \(-0.489280\pi\)
0.0336719 + 0.999433i \(0.489280\pi\)
\(138\) −17.8531 −1.51976
\(139\) 0.0659961 0.00559771 0.00279886 0.999996i \(-0.499109\pi\)
0.00279886 + 0.999996i \(0.499109\pi\)
\(140\) −6.13520 −0.518519
\(141\) 10.7861 0.908355
\(142\) −1.09328 −0.0917458
\(143\) −9.07158 −0.758604
\(144\) 1.18539 0.0987825
\(145\) −7.24251 −0.601458
\(146\) −11.3584 −0.940027
\(147\) 9.72712 0.802280
\(148\) −9.86688 −0.811052
\(149\) 21.7928 1.78533 0.892666 0.450718i \(-0.148832\pi\)
0.892666 + 0.450718i \(0.148832\pi\)
\(150\) 24.0663 1.96501
\(151\) 3.76642 0.306507 0.153254 0.988187i \(-0.451025\pi\)
0.153254 + 0.988187i \(0.451025\pi\)
\(152\) 1.00000 0.0811107
\(153\) 3.22017 0.260336
\(154\) −6.54328 −0.527273
\(155\) 16.0940 1.29270
\(156\) 4.25010 0.340281
\(157\) 1.35547 0.108178 0.0540892 0.998536i \(-0.482774\pi\)
0.0540892 + 0.998536i \(0.482774\pi\)
\(158\) −7.46127 −0.593586
\(159\) 5.94419 0.471405
\(160\) 4.09434 0.323686
\(161\) −13.0765 −1.03057
\(162\) 11.1510 0.876107
\(163\) −3.10546 −0.243238 −0.121619 0.992577i \(-0.538809\pi\)
−0.121619 + 0.992577i \(0.538809\pi\)
\(164\) 5.20665 0.406571
\(165\) 36.5766 2.84749
\(166\) −15.3359 −1.19029
\(167\) 20.7368 1.60466 0.802331 0.596879i \(-0.203593\pi\)
0.802331 + 0.596879i \(0.203593\pi\)
\(168\) 3.06558 0.236514
\(169\) −8.68418 −0.668014
\(170\) 11.1225 0.853057
\(171\) −1.18539 −0.0906490
\(172\) 4.35112 0.331769
\(173\) 15.9654 1.21382 0.606912 0.794769i \(-0.292408\pi\)
0.606912 + 0.794769i \(0.292408\pi\)
\(174\) 3.61887 0.274346
\(175\) 17.6273 1.33250
\(176\) 4.36668 0.329151
\(177\) −15.3488 −1.15368
\(178\) −7.24142 −0.542768
\(179\) 6.73294 0.503244 0.251622 0.967826i \(-0.419036\pi\)
0.251622 + 0.967826i \(0.419036\pi\)
\(180\) −4.85339 −0.361751
\(181\) −11.4281 −0.849445 −0.424723 0.905323i \(-0.639628\pi\)
−0.424723 + 0.905323i \(0.639628\pi\)
\(182\) 3.11298 0.230749
\(183\) 9.58572 0.708596
\(184\) 8.72662 0.643335
\(185\) 40.3984 2.97015
\(186\) −8.04171 −0.589646
\(187\) 11.8623 0.867458
\(188\) −5.27226 −0.384519
\(189\) 5.56283 0.404636
\(190\) −4.09434 −0.297035
\(191\) 22.8164 1.65093 0.825467 0.564450i \(-0.190912\pi\)
0.825467 + 0.564450i \(0.190912\pi\)
\(192\) −2.04582 −0.147645
\(193\) −3.66905 −0.264104 −0.132052 0.991243i \(-0.542157\pi\)
−0.132052 + 0.991243i \(0.542157\pi\)
\(194\) 16.3302 1.17244
\(195\) −17.4014 −1.24614
\(196\) −4.75463 −0.339616
\(197\) −2.93118 −0.208838 −0.104419 0.994533i \(-0.533298\pi\)
−0.104419 + 0.994533i \(0.533298\pi\)
\(198\) −5.17622 −0.367858
\(199\) 12.3039 0.872201 0.436100 0.899898i \(-0.356359\pi\)
0.436100 + 0.899898i \(0.356359\pi\)
\(200\) −11.7636 −0.831815
\(201\) 17.5348 1.23681
\(202\) −1.31063 −0.0922157
\(203\) 2.65063 0.186038
\(204\) −5.55758 −0.389109
\(205\) −21.3178 −1.48890
\(206\) 0.646222 0.0450244
\(207\) −10.3445 −0.718989
\(208\) −2.07746 −0.144046
\(209\) −4.36668 −0.302050
\(210\) −12.5515 −0.866137
\(211\) −1.00000 −0.0688428
\(212\) −2.90552 −0.199552
\(213\) −2.23665 −0.153253
\(214\) −17.4634 −1.19377
\(215\) −17.8150 −1.21497
\(216\) −3.71237 −0.252595
\(217\) −5.89012 −0.399848
\(218\) −13.5424 −0.917209
\(219\) −23.2373 −1.57023
\(220\) −17.8787 −1.20538
\(221\) −5.64352 −0.379624
\(222\) −20.1859 −1.35479
\(223\) −15.1165 −1.01228 −0.506138 0.862453i \(-0.668927\pi\)
−0.506138 + 0.862453i \(0.668927\pi\)
\(224\) −1.49846 −0.100120
\(225\) 13.9445 0.929634
\(226\) 10.1385 0.674401
\(227\) 5.52236 0.366532 0.183266 0.983063i \(-0.441333\pi\)
0.183266 + 0.983063i \(0.441333\pi\)
\(228\) 2.04582 0.135488
\(229\) 8.47458 0.560016 0.280008 0.959998i \(-0.409663\pi\)
0.280008 + 0.959998i \(0.409663\pi\)
\(230\) −35.7298 −2.35595
\(231\) −13.3864 −0.880760
\(232\) −1.76891 −0.116134
\(233\) 11.7599 0.770415 0.385208 0.922830i \(-0.374130\pi\)
0.385208 + 0.922830i \(0.374130\pi\)
\(234\) 2.46259 0.160985
\(235\) 21.5865 1.40814
\(236\) 7.50249 0.488371
\(237\) −15.2644 −0.991531
\(238\) −4.07064 −0.263860
\(239\) −2.68897 −0.173935 −0.0869676 0.996211i \(-0.527718\pi\)
−0.0869676 + 0.996211i \(0.527718\pi\)
\(240\) 8.37630 0.540688
\(241\) 0.0708398 0.00456319 0.00228160 0.999997i \(-0.499274\pi\)
0.00228160 + 0.999997i \(0.499274\pi\)
\(242\) −8.06789 −0.518624
\(243\) 11.6759 0.749009
\(244\) −4.68551 −0.299959
\(245\) 19.4671 1.24371
\(246\) 10.6519 0.679139
\(247\) 2.07746 0.132185
\(248\) 3.93079 0.249606
\(249\) −31.3745 −1.98828
\(250\) 27.6927 1.75144
\(251\) 28.0554 1.77084 0.885420 0.464792i \(-0.153871\pi\)
0.885420 + 0.464792i \(0.153871\pi\)
\(252\) 1.77626 0.111894
\(253\) −38.1064 −2.39573
\(254\) 11.5486 0.724621
\(255\) 22.7547 1.42495
\(256\) 1.00000 0.0625000
\(257\) −11.4019 −0.711230 −0.355615 0.934633i \(-0.615729\pi\)
−0.355615 + 0.934633i \(0.615729\pi\)
\(258\) 8.90161 0.554190
\(259\) −14.7851 −0.918701
\(260\) 8.50581 0.527508
\(261\) 2.09684 0.129791
\(262\) 2.24440 0.138659
\(263\) −32.2678 −1.98972 −0.994859 0.101272i \(-0.967709\pi\)
−0.994859 + 0.101272i \(0.967709\pi\)
\(264\) 8.93345 0.549816
\(265\) 11.8962 0.730779
\(266\) 1.49846 0.0918763
\(267\) −14.8147 −0.906643
\(268\) −8.57101 −0.523558
\(269\) −25.3155 −1.54351 −0.771756 0.635918i \(-0.780621\pi\)
−0.771756 + 0.635918i \(0.780621\pi\)
\(270\) 15.1997 0.925025
\(271\) −7.88294 −0.478855 −0.239427 0.970914i \(-0.576960\pi\)
−0.239427 + 0.970914i \(0.576960\pi\)
\(272\) 2.71655 0.164715
\(273\) 6.36860 0.385445
\(274\) −0.788239 −0.0476193
\(275\) 51.3681 3.09761
\(276\) 17.8531 1.07463
\(277\) 6.05207 0.363634 0.181817 0.983332i \(-0.441802\pi\)
0.181817 + 0.983332i \(0.441802\pi\)
\(278\) −0.0659961 −0.00395818
\(279\) −4.65952 −0.278958
\(280\) 6.13520 0.366648
\(281\) −23.4655 −1.39984 −0.699918 0.714223i \(-0.746780\pi\)
−0.699918 + 0.714223i \(0.746780\pi\)
\(282\) −10.7861 −0.642304
\(283\) 31.9526 1.89938 0.949691 0.313188i \(-0.101397\pi\)
0.949691 + 0.313188i \(0.101397\pi\)
\(284\) 1.09328 0.0648741
\(285\) −8.37630 −0.496169
\(286\) 9.07158 0.536414
\(287\) 7.80193 0.460534
\(288\) −1.18539 −0.0698498
\(289\) −9.62034 −0.565902
\(290\) 7.24251 0.425295
\(291\) 33.4088 1.95846
\(292\) 11.3584 0.664700
\(293\) −0.530799 −0.0310096 −0.0155048 0.999880i \(-0.504936\pi\)
−0.0155048 + 0.999880i \(0.504936\pi\)
\(294\) −9.72712 −0.567297
\(295\) −30.7178 −1.78846
\(296\) 9.86688 0.573501
\(297\) 16.2107 0.940642
\(298\) −21.7928 −1.26242
\(299\) 18.1292 1.04844
\(300\) −24.0663 −1.38947
\(301\) 6.51996 0.375804
\(302\) −3.76642 −0.216733
\(303\) −2.68132 −0.154038
\(304\) −1.00000 −0.0573539
\(305\) 19.1841 1.09848
\(306\) −3.22017 −0.184085
\(307\) 12.2045 0.696546 0.348273 0.937393i \(-0.386768\pi\)
0.348273 + 0.937393i \(0.386768\pi\)
\(308\) 6.54328 0.372838
\(309\) 1.32206 0.0752092
\(310\) −16.0940 −0.914079
\(311\) 20.4475 1.15947 0.579736 0.814804i \(-0.303156\pi\)
0.579736 + 0.814804i \(0.303156\pi\)
\(312\) −4.25010 −0.240615
\(313\) 32.5985 1.84258 0.921288 0.388881i \(-0.127138\pi\)
0.921288 + 0.388881i \(0.127138\pi\)
\(314\) −1.35547 −0.0764937
\(315\) −7.27260 −0.409765
\(316\) 7.46127 0.419729
\(317\) −26.8916 −1.51038 −0.755190 0.655505i \(-0.772456\pi\)
−0.755190 + 0.655505i \(0.772456\pi\)
\(318\) −5.94419 −0.333333
\(319\) 7.72425 0.432475
\(320\) −4.09434 −0.228881
\(321\) −35.7270 −1.99409
\(322\) 13.0765 0.728723
\(323\) −2.71655 −0.151153
\(324\) −11.1510 −0.619501
\(325\) −24.4384 −1.35560
\(326\) 3.10546 0.171996
\(327\) −27.7054 −1.53211
\(328\) −5.20665 −0.287489
\(329\) −7.90026 −0.435555
\(330\) −36.5766 −2.01348
\(331\) −28.2584 −1.55322 −0.776610 0.629982i \(-0.783062\pi\)
−0.776610 + 0.629982i \(0.783062\pi\)
\(332\) 15.3359 0.841666
\(333\) −11.6961 −0.640942
\(334\) −20.7368 −1.13467
\(335\) 35.0927 1.91732
\(336\) −3.06558 −0.167241
\(337\) −19.2134 −1.04662 −0.523310 0.852142i \(-0.675303\pi\)
−0.523310 + 0.852142i \(0.675303\pi\)
\(338\) 8.68418 0.472357
\(339\) 20.7415 1.12652
\(340\) −11.1225 −0.603202
\(341\) −17.1645 −0.929511
\(342\) 1.18539 0.0640986
\(343\) −17.6138 −0.951056
\(344\) −4.35112 −0.234596
\(345\) −73.0968 −3.93540
\(346\) −15.9654 −0.858303
\(347\) −16.9938 −0.912277 −0.456139 0.889909i \(-0.650768\pi\)
−0.456139 + 0.889909i \(0.650768\pi\)
\(348\) −3.61887 −0.193992
\(349\) −11.9704 −0.640761 −0.320381 0.947289i \(-0.603811\pi\)
−0.320381 + 0.947289i \(0.603811\pi\)
\(350\) −17.6273 −0.942220
\(351\) −7.71228 −0.411651
\(352\) −4.36668 −0.232745
\(353\) 30.9605 1.64786 0.823931 0.566691i \(-0.191777\pi\)
0.823931 + 0.566691i \(0.191777\pi\)
\(354\) 15.3488 0.815778
\(355\) −4.47625 −0.237575
\(356\) 7.24142 0.383795
\(357\) −8.32780 −0.440754
\(358\) −6.73294 −0.355847
\(359\) −30.9264 −1.63223 −0.816117 0.577887i \(-0.803877\pi\)
−0.816117 + 0.577887i \(0.803877\pi\)
\(360\) 4.85339 0.255796
\(361\) 1.00000 0.0526316
\(362\) 11.4281 0.600649
\(363\) −16.5055 −0.866313
\(364\) −3.11298 −0.163164
\(365\) −46.5052 −2.43419
\(366\) −9.58572 −0.501053
\(367\) −36.5323 −1.90697 −0.953484 0.301443i \(-0.902532\pi\)
−0.953484 + 0.301443i \(0.902532\pi\)
\(368\) −8.72662 −0.454907
\(369\) 6.17191 0.321297
\(370\) −40.3984 −2.10021
\(371\) −4.35380 −0.226038
\(372\) 8.04171 0.416943
\(373\) 14.1511 0.732718 0.366359 0.930474i \(-0.380604\pi\)
0.366359 + 0.930474i \(0.380604\pi\)
\(374\) −11.8623 −0.613386
\(375\) 56.6543 2.92562
\(376\) 5.27226 0.271896
\(377\) −3.67482 −0.189263
\(378\) −5.56283 −0.286121
\(379\) 7.71892 0.396495 0.198247 0.980152i \(-0.436475\pi\)
0.198247 + 0.980152i \(0.436475\pi\)
\(380\) 4.09434 0.210035
\(381\) 23.6263 1.21041
\(382\) −22.8164 −1.16739
\(383\) 12.3725 0.632207 0.316104 0.948725i \(-0.397625\pi\)
0.316104 + 0.948725i \(0.397625\pi\)
\(384\) 2.04582 0.104400
\(385\) −26.7904 −1.36537
\(386\) 3.66905 0.186750
\(387\) 5.15777 0.262184
\(388\) −16.3302 −0.829042
\(389\) −25.4546 −1.29060 −0.645299 0.763930i \(-0.723267\pi\)
−0.645299 + 0.763930i \(0.723267\pi\)
\(390\) 17.4014 0.881153
\(391\) −23.7063 −1.19888
\(392\) 4.75463 0.240145
\(393\) 4.59163 0.231617
\(394\) 2.93118 0.147671
\(395\) −30.5490 −1.53709
\(396\) 5.17622 0.260115
\(397\) 12.6444 0.634605 0.317302 0.948324i \(-0.397223\pi\)
0.317302 + 0.948324i \(0.397223\pi\)
\(398\) −12.3039 −0.616739
\(399\) 3.06558 0.153471
\(400\) 11.7636 0.588182
\(401\) −14.7905 −0.738605 −0.369302 0.929309i \(-0.620403\pi\)
−0.369302 + 0.929309i \(0.620403\pi\)
\(402\) −17.5348 −0.874555
\(403\) 8.16605 0.406780
\(404\) 1.31063 0.0652063
\(405\) 45.6561 2.26867
\(406\) −2.65063 −0.131548
\(407\) −43.0855 −2.13567
\(408\) 5.55758 0.275141
\(409\) −7.91564 −0.391403 −0.195702 0.980663i \(-0.562698\pi\)
−0.195702 + 0.980663i \(0.562698\pi\)
\(410\) 21.3178 1.05281
\(411\) −1.61260 −0.0795436
\(412\) −0.646222 −0.0318371
\(413\) 11.2422 0.553191
\(414\) 10.3445 0.508402
\(415\) −62.7903 −3.08226
\(416\) 2.07746 0.101856
\(417\) −0.135016 −0.00661177
\(418\) 4.36668 0.213581
\(419\) 3.22411 0.157508 0.0787540 0.996894i \(-0.474906\pi\)
0.0787540 + 0.996894i \(0.474906\pi\)
\(420\) 12.5515 0.612452
\(421\) 26.3204 1.28278 0.641389 0.767216i \(-0.278358\pi\)
0.641389 + 0.767216i \(0.278358\pi\)
\(422\) 1.00000 0.0486792
\(423\) −6.24969 −0.303870
\(424\) 2.90552 0.141105
\(425\) 31.9566 1.55012
\(426\) 2.23665 0.108366
\(427\) −7.02103 −0.339771
\(428\) 17.4634 0.844125
\(429\) 18.5588 0.896030
\(430\) 17.8150 0.859114
\(431\) −2.92758 −0.141016 −0.0705082 0.997511i \(-0.522462\pi\)
−0.0705082 + 0.997511i \(0.522462\pi\)
\(432\) 3.71237 0.178611
\(433\) −15.5142 −0.745567 −0.372784 0.927918i \(-0.621597\pi\)
−0.372784 + 0.927918i \(0.621597\pi\)
\(434\) 5.89012 0.282735
\(435\) 14.8169 0.710415
\(436\) 13.5424 0.648565
\(437\) 8.72662 0.417451
\(438\) 23.2373 1.11032
\(439\) 25.6971 1.22645 0.613227 0.789906i \(-0.289871\pi\)
0.613227 + 0.789906i \(0.289871\pi\)
\(440\) 17.8787 0.852333
\(441\) −5.63609 −0.268385
\(442\) 5.64352 0.268435
\(443\) −4.35774 −0.207042 −0.103521 0.994627i \(-0.533011\pi\)
−0.103521 + 0.994627i \(0.533011\pi\)
\(444\) 20.1859 0.957980
\(445\) −29.6489 −1.40549
\(446\) 15.1165 0.715787
\(447\) −44.5841 −2.10876
\(448\) 1.49846 0.0707954
\(449\) −13.8264 −0.652509 −0.326254 0.945282i \(-0.605787\pi\)
−0.326254 + 0.945282i \(0.605787\pi\)
\(450\) −13.9445 −0.657350
\(451\) 22.7358 1.07059
\(452\) −10.1385 −0.476874
\(453\) −7.70544 −0.362033
\(454\) −5.52236 −0.259177
\(455\) 12.7456 0.597523
\(456\) −2.04582 −0.0958044
\(457\) 11.6026 0.542748 0.271374 0.962474i \(-0.412522\pi\)
0.271374 + 0.962474i \(0.412522\pi\)
\(458\) −8.47458 −0.395991
\(459\) 10.0848 0.470720
\(460\) 35.7298 1.66591
\(461\) 19.3868 0.902934 0.451467 0.892288i \(-0.350901\pi\)
0.451467 + 0.892288i \(0.350901\pi\)
\(462\) 13.3864 0.622791
\(463\) 30.5402 1.41932 0.709662 0.704543i \(-0.248848\pi\)
0.709662 + 0.704543i \(0.248848\pi\)
\(464\) 1.76891 0.0821194
\(465\) −32.9255 −1.52688
\(466\) −11.7599 −0.544766
\(467\) −23.8146 −1.10201 −0.551003 0.834503i \(-0.685755\pi\)
−0.551003 + 0.834503i \(0.685755\pi\)
\(468\) −2.46259 −0.113833
\(469\) −12.8433 −0.593048
\(470\) −21.5865 −0.995709
\(471\) −2.77306 −0.127776
\(472\) −7.50249 −0.345330
\(473\) 18.9999 0.873618
\(474\) 15.2644 0.701118
\(475\) −11.7636 −0.539753
\(476\) 4.07064 0.186577
\(477\) −3.44418 −0.157698
\(478\) 2.68897 0.122991
\(479\) −31.5928 −1.44351 −0.721755 0.692148i \(-0.756664\pi\)
−0.721755 + 0.692148i \(0.756664\pi\)
\(480\) −8.37630 −0.382324
\(481\) 20.4980 0.934628
\(482\) −0.0708398 −0.00322667
\(483\) 26.7521 1.21726
\(484\) 8.06789 0.366722
\(485\) 66.8616 3.03603
\(486\) −11.6759 −0.529630
\(487\) −43.3546 −1.96459 −0.982293 0.187351i \(-0.940010\pi\)
−0.982293 + 0.187351i \(0.940010\pi\)
\(488\) 4.68551 0.212103
\(489\) 6.35322 0.287303
\(490\) −19.4671 −0.879433
\(491\) 11.7792 0.531589 0.265794 0.964030i \(-0.414366\pi\)
0.265794 + 0.964030i \(0.414366\pi\)
\(492\) −10.6519 −0.480224
\(493\) 4.80533 0.216421
\(494\) −2.07746 −0.0934691
\(495\) −21.1932 −0.952564
\(496\) −3.93079 −0.176498
\(497\) 1.63823 0.0734846
\(498\) 31.3745 1.40592
\(499\) −14.9516 −0.669325 −0.334663 0.942338i \(-0.608622\pi\)
−0.334663 + 0.942338i \(0.608622\pi\)
\(500\) −27.6927 −1.23845
\(501\) −42.4238 −1.89536
\(502\) −28.0554 −1.25217
\(503\) −11.3813 −0.507469 −0.253734 0.967274i \(-0.581659\pi\)
−0.253734 + 0.967274i \(0.581659\pi\)
\(504\) −1.77626 −0.0791207
\(505\) −5.36617 −0.238792
\(506\) 38.1064 1.69404
\(507\) 17.7663 0.789029
\(508\) −11.5486 −0.512385
\(509\) −8.22872 −0.364732 −0.182366 0.983231i \(-0.558376\pi\)
−0.182366 + 0.983231i \(0.558376\pi\)
\(510\) −22.7547 −1.00759
\(511\) 17.0201 0.752923
\(512\) −1.00000 −0.0441942
\(513\) −3.71237 −0.163905
\(514\) 11.4019 0.502915
\(515\) 2.64586 0.116590
\(516\) −8.90161 −0.391872
\(517\) −23.0223 −1.01252
\(518\) 14.7851 0.649620
\(519\) −32.6623 −1.43371
\(520\) −8.50581 −0.373005
\(521\) 14.5267 0.636428 0.318214 0.948019i \(-0.396917\pi\)
0.318214 + 0.948019i \(0.396917\pi\)
\(522\) −2.09684 −0.0917763
\(523\) 43.6760 1.90982 0.954909 0.296898i \(-0.0959521\pi\)
0.954909 + 0.296898i \(0.0959521\pi\)
\(524\) −2.24440 −0.0980469
\(525\) −36.0624 −1.57389
\(526\) 32.2678 1.40694
\(527\) −10.6782 −0.465150
\(528\) −8.93345 −0.388779
\(529\) 53.1540 2.31104
\(530\) −11.8962 −0.516738
\(531\) 8.89338 0.385940
\(532\) −1.49846 −0.0649663
\(533\) −10.8166 −0.468518
\(534\) 14.8147 0.641093
\(535\) −71.5011 −3.09126
\(536\) 8.57101 0.370211
\(537\) −13.7744 −0.594409
\(538\) 25.3155 1.09143
\(539\) −20.7619 −0.894280
\(540\) −15.1997 −0.654092
\(541\) −24.4618 −1.05170 −0.525848 0.850578i \(-0.676252\pi\)
−0.525848 + 0.850578i \(0.676252\pi\)
\(542\) 7.88294 0.338601
\(543\) 23.3799 1.00333
\(544\) −2.71655 −0.116471
\(545\) −55.4473 −2.37510
\(546\) −6.36860 −0.272551
\(547\) −5.66493 −0.242215 −0.121107 0.992639i \(-0.538645\pi\)
−0.121107 + 0.992639i \(0.538645\pi\)
\(548\) 0.788239 0.0336719
\(549\) −5.55415 −0.237045
\(550\) −51.3681 −2.19034
\(551\) −1.76891 −0.0753579
\(552\) −17.8531 −0.759879
\(553\) 11.1804 0.475438
\(554\) −6.05207 −0.257128
\(555\) −82.6479 −3.50821
\(556\) 0.0659961 0.00279886
\(557\) 11.5574 0.489703 0.244852 0.969561i \(-0.421261\pi\)
0.244852 + 0.969561i \(0.421261\pi\)
\(558\) 4.65952 0.197253
\(559\) −9.03925 −0.382319
\(560\) −6.13520 −0.259259
\(561\) −24.2682 −1.02460
\(562\) 23.4655 0.989833
\(563\) −10.8222 −0.456100 −0.228050 0.973649i \(-0.573235\pi\)
−0.228050 + 0.973649i \(0.573235\pi\)
\(564\) 10.7861 0.454177
\(565\) 41.5104 1.74635
\(566\) −31.9526 −1.34307
\(567\) −16.7093 −0.701726
\(568\) −1.09328 −0.0458729
\(569\) 6.77462 0.284007 0.142003 0.989866i \(-0.454646\pi\)
0.142003 + 0.989866i \(0.454646\pi\)
\(570\) 8.37630 0.350845
\(571\) 2.24551 0.0939718 0.0469859 0.998896i \(-0.485038\pi\)
0.0469859 + 0.998896i \(0.485038\pi\)
\(572\) −9.07158 −0.379302
\(573\) −46.6782 −1.95001
\(574\) −7.80193 −0.325646
\(575\) −102.657 −4.28109
\(576\) 1.18539 0.0493913
\(577\) 0.473162 0.0196980 0.00984899 0.999951i \(-0.496865\pi\)
0.00984899 + 0.999951i \(0.496865\pi\)
\(578\) 9.62034 0.400153
\(579\) 7.50623 0.311948
\(580\) −7.24251 −0.300729
\(581\) 22.9801 0.953377
\(582\) −33.4088 −1.38484
\(583\) −12.6875 −0.525462
\(584\) −11.3584 −0.470014
\(585\) 10.0827 0.416869
\(586\) 0.530799 0.0219271
\(587\) 18.2336 0.752581 0.376291 0.926502i \(-0.377199\pi\)
0.376291 + 0.926502i \(0.377199\pi\)
\(588\) 9.72712 0.401140
\(589\) 3.93079 0.161966
\(590\) 30.7178 1.26463
\(591\) 5.99667 0.246670
\(592\) −9.86688 −0.405526
\(593\) −32.4418 −1.33223 −0.666113 0.745850i \(-0.732043\pi\)
−0.666113 + 0.745850i \(0.732043\pi\)
\(594\) −16.2107 −0.665134
\(595\) −16.6666 −0.683263
\(596\) 21.7928 0.892666
\(597\) −25.1716 −1.03021
\(598\) −18.1292 −0.741357
\(599\) 1.69293 0.0691714 0.0345857 0.999402i \(-0.488989\pi\)
0.0345857 + 0.999402i \(0.488989\pi\)
\(600\) 24.0663 0.982504
\(601\) −36.2204 −1.47746 −0.738731 0.674000i \(-0.764575\pi\)
−0.738731 + 0.674000i \(0.764575\pi\)
\(602\) −6.51996 −0.265734
\(603\) −10.1600 −0.413747
\(604\) 3.76642 0.153254
\(605\) −33.0327 −1.34297
\(606\) 2.68132 0.108921
\(607\) 22.6619 0.919819 0.459910 0.887966i \(-0.347882\pi\)
0.459910 + 0.887966i \(0.347882\pi\)
\(608\) 1.00000 0.0405554
\(609\) −5.42272 −0.219740
\(610\) −19.1841 −0.776740
\(611\) 10.9529 0.443106
\(612\) 3.22017 0.130168
\(613\) −33.5176 −1.35376 −0.676881 0.736092i \(-0.736669\pi\)
−0.676881 + 0.736092i \(0.736669\pi\)
\(614\) −12.2045 −0.492532
\(615\) 43.6124 1.75862
\(616\) −6.54328 −0.263636
\(617\) −41.9273 −1.68793 −0.843965 0.536399i \(-0.819784\pi\)
−0.843965 + 0.536399i \(0.819784\pi\)
\(618\) −1.32206 −0.0531809
\(619\) 15.7090 0.631398 0.315699 0.948859i \(-0.397761\pi\)
0.315699 + 0.948859i \(0.397761\pi\)
\(620\) 16.0940 0.646351
\(621\) −32.3965 −1.30003
\(622\) −20.4475 −0.819871
\(623\) 10.8510 0.434734
\(624\) 4.25010 0.170140
\(625\) 54.5651 2.18261
\(626\) −32.5985 −1.30290
\(627\) 8.93345 0.356768
\(628\) 1.35547 0.0540892
\(629\) −26.8039 −1.06874
\(630\) 7.27260 0.289747
\(631\) 41.4461 1.64994 0.824972 0.565174i \(-0.191191\pi\)
0.824972 + 0.565174i \(0.191191\pi\)
\(632\) −7.46127 −0.296793
\(633\) 2.04582 0.0813141
\(634\) 26.8916 1.06800
\(635\) 47.2838 1.87640
\(636\) 5.94419 0.235702
\(637\) 9.87753 0.391362
\(638\) −7.72425 −0.305806
\(639\) 1.29596 0.0512674
\(640\) 4.09434 0.161843
\(641\) 38.9245 1.53742 0.768712 0.639595i \(-0.220898\pi\)
0.768712 + 0.639595i \(0.220898\pi\)
\(642\) 35.7270 1.41003
\(643\) −4.98299 −0.196510 −0.0982550 0.995161i \(-0.531326\pi\)
−0.0982550 + 0.995161i \(0.531326\pi\)
\(644\) −13.0765 −0.515285
\(645\) 36.4462 1.43507
\(646\) 2.71655 0.106881
\(647\) −12.8205 −0.504024 −0.252012 0.967724i \(-0.581092\pi\)
−0.252012 + 0.967724i \(0.581092\pi\)
\(648\) 11.1510 0.438053
\(649\) 32.7610 1.28598
\(650\) 24.4384 0.958555
\(651\) 12.0501 0.472282
\(652\) −3.10546 −0.121619
\(653\) 41.3605 1.61856 0.809281 0.587422i \(-0.199857\pi\)
0.809281 + 0.587422i \(0.199857\pi\)
\(654\) 27.7054 1.08337
\(655\) 9.18932 0.359057
\(656\) 5.20665 0.203285
\(657\) 13.4641 0.525286
\(658\) 7.90026 0.307984
\(659\) −23.9235 −0.931926 −0.465963 0.884804i \(-0.654292\pi\)
−0.465963 + 0.884804i \(0.654292\pi\)
\(660\) 36.5766 1.42374
\(661\) 48.5286 1.88754 0.943771 0.330599i \(-0.107251\pi\)
0.943771 + 0.330599i \(0.107251\pi\)
\(662\) 28.2584 1.09829
\(663\) 11.5456 0.448395
\(664\) −15.3359 −0.595147
\(665\) 6.13520 0.237913
\(666\) 11.6961 0.453215
\(667\) −15.4366 −0.597707
\(668\) 20.7368 0.802331
\(669\) 30.9257 1.19566
\(670\) −35.0927 −1.35575
\(671\) −20.4601 −0.789854
\(672\) 3.06558 0.118257
\(673\) −41.8990 −1.61509 −0.807545 0.589806i \(-0.799204\pi\)
−0.807545 + 0.589806i \(0.799204\pi\)
\(674\) 19.2134 0.740072
\(675\) 43.6710 1.68090
\(676\) −8.68418 −0.334007
\(677\) −14.1658 −0.544438 −0.272219 0.962235i \(-0.587757\pi\)
−0.272219 + 0.962235i \(0.587757\pi\)
\(678\) −20.7415 −0.796573
\(679\) −24.4701 −0.939078
\(680\) 11.1225 0.426528
\(681\) −11.2978 −0.432931
\(682\) 17.1645 0.657263
\(683\) −1.01076 −0.0386757 −0.0193378 0.999813i \(-0.506156\pi\)
−0.0193378 + 0.999813i \(0.506156\pi\)
\(684\) −1.18539 −0.0453245
\(685\) −3.22732 −0.123310
\(686\) 17.6138 0.672498
\(687\) −17.3375 −0.661467
\(688\) 4.35112 0.165885
\(689\) 6.03610 0.229957
\(690\) 73.0968 2.78275
\(691\) 0.825563 0.0314059 0.0157030 0.999877i \(-0.495001\pi\)
0.0157030 + 0.999877i \(0.495001\pi\)
\(692\) 15.9654 0.606912
\(693\) 7.75634 0.294639
\(694\) 16.9938 0.645077
\(695\) −0.270211 −0.0102497
\(696\) 3.61887 0.137173
\(697\) 14.1441 0.535747
\(698\) 11.9704 0.453087
\(699\) −24.0586 −0.909981
\(700\) 17.6273 0.666250
\(701\) −38.0743 −1.43805 −0.719024 0.694985i \(-0.755411\pi\)
−0.719024 + 0.694985i \(0.755411\pi\)
\(702\) 7.71228 0.291081
\(703\) 9.86688 0.372136
\(704\) 4.36668 0.164575
\(705\) −44.1621 −1.66324
\(706\) −30.9605 −1.16521
\(707\) 1.96392 0.0738610
\(708\) −15.3488 −0.576842
\(709\) −7.04075 −0.264421 −0.132211 0.991222i \(-0.542207\pi\)
−0.132211 + 0.991222i \(0.542207\pi\)
\(710\) 4.47625 0.167991
\(711\) 8.84451 0.331695
\(712\) −7.24142 −0.271384
\(713\) 34.3026 1.28464
\(714\) 8.32780 0.311660
\(715\) 37.1422 1.38904
\(716\) 6.73294 0.251622
\(717\) 5.50116 0.205445
\(718\) 30.9264 1.15416
\(719\) −47.0755 −1.75562 −0.877810 0.479009i \(-0.840996\pi\)
−0.877810 + 0.479009i \(0.840996\pi\)
\(720\) −4.85339 −0.180875
\(721\) −0.968336 −0.0360627
\(722\) −1.00000 −0.0372161
\(723\) −0.144926 −0.00538985
\(724\) −11.4281 −0.424723
\(725\) 20.8088 0.772819
\(726\) 16.5055 0.612576
\(727\) −38.1337 −1.41430 −0.707151 0.707062i \(-0.750020\pi\)
−0.707151 + 0.707062i \(0.750020\pi\)
\(728\) 3.11298 0.115375
\(729\) 9.56624 0.354305
\(730\) 46.5052 1.72123
\(731\) 11.8200 0.437180
\(732\) 9.58572 0.354298
\(733\) −12.9104 −0.476856 −0.238428 0.971160i \(-0.576632\pi\)
−0.238428 + 0.971160i \(0.576632\pi\)
\(734\) 36.5323 1.34843
\(735\) −39.8262 −1.46901
\(736\) 8.72662 0.321668
\(737\) −37.4269 −1.37864
\(738\) −6.17191 −0.227191
\(739\) 9.26237 0.340722 0.170361 0.985382i \(-0.445507\pi\)
0.170361 + 0.985382i \(0.445507\pi\)
\(740\) 40.3984 1.48507
\(741\) −4.25010 −0.156131
\(742\) 4.35380 0.159833
\(743\) −8.65339 −0.317462 −0.158731 0.987322i \(-0.550740\pi\)
−0.158731 + 0.987322i \(0.550740\pi\)
\(744\) −8.04171 −0.294823
\(745\) −89.2270 −3.26903
\(746\) −14.1511 −0.518110
\(747\) 18.1790 0.665135
\(748\) 11.8623 0.433729
\(749\) 26.1681 0.956162
\(750\) −56.6543 −2.06872
\(751\) −39.3621 −1.43634 −0.718172 0.695865i \(-0.755021\pi\)
−0.718172 + 0.695865i \(0.755021\pi\)
\(752\) −5.27226 −0.192260
\(753\) −57.3963 −2.09164
\(754\) 3.67482 0.133829
\(755\) −15.4210 −0.561229
\(756\) 5.56283 0.202318
\(757\) −30.3091 −1.10160 −0.550802 0.834636i \(-0.685678\pi\)
−0.550802 + 0.834636i \(0.685678\pi\)
\(758\) −7.71892 −0.280364
\(759\) 77.9589 2.82973
\(760\) −4.09434 −0.148517
\(761\) 16.7137 0.605871 0.302936 0.953011i \(-0.402033\pi\)
0.302936 + 0.953011i \(0.402033\pi\)
\(762\) −23.6263 −0.855891
\(763\) 20.2927 0.734647
\(764\) 22.8164 0.825467
\(765\) −13.1845 −0.476687
\(766\) −12.3725 −0.447038
\(767\) −15.5861 −0.562781
\(768\) −2.04582 −0.0738223
\(769\) 37.2199 1.34218 0.671092 0.741374i \(-0.265825\pi\)
0.671092 + 0.741374i \(0.265825\pi\)
\(770\) 26.7904 0.965460
\(771\) 23.3262 0.840074
\(772\) −3.66905 −0.132052
\(773\) −42.1269 −1.51520 −0.757599 0.652720i \(-0.773628\pi\)
−0.757599 + 0.652720i \(0.773628\pi\)
\(774\) −5.15777 −0.185392
\(775\) −46.2405 −1.66101
\(776\) 16.3302 0.586221
\(777\) 30.2477 1.08513
\(778\) 25.4546 0.912591
\(779\) −5.20665 −0.186547
\(780\) −17.4014 −0.623070
\(781\) 4.77399 0.170827
\(782\) 23.7063 0.847737
\(783\) 6.56683 0.234679
\(784\) −4.75463 −0.169808
\(785\) −5.54977 −0.198080
\(786\) −4.59163 −0.163778
\(787\) −27.6128 −0.984291 −0.492146 0.870513i \(-0.663787\pi\)
−0.492146 + 0.870513i \(0.663787\pi\)
\(788\) −2.93118 −0.104419
\(789\) 66.0142 2.35017
\(790\) 30.5490 1.08688
\(791\) −15.1921 −0.540168
\(792\) −5.17622 −0.183929
\(793\) 9.73393 0.345662
\(794\) −12.6444 −0.448733
\(795\) −24.3375 −0.863164
\(796\) 12.3039 0.436100
\(797\) −44.7859 −1.58640 −0.793200 0.608962i \(-0.791586\pi\)
−0.793200 + 0.608962i \(0.791586\pi\)
\(798\) −3.06558 −0.108520
\(799\) −14.3224 −0.506689
\(800\) −11.7636 −0.415908
\(801\) 8.58391 0.303298
\(802\) 14.7905 0.522272
\(803\) 49.5985 1.75029
\(804\) 17.5348 0.618404
\(805\) 53.5396 1.88702
\(806\) −8.16605 −0.287637
\(807\) 51.7910 1.82313
\(808\) −1.31063 −0.0461078
\(809\) 37.4511 1.31671 0.658355 0.752708i \(-0.271253\pi\)
0.658355 + 0.752708i \(0.271253\pi\)
\(810\) −45.6561 −1.60419
\(811\) −38.7566 −1.36093 −0.680464 0.732782i \(-0.738222\pi\)
−0.680464 + 0.732782i \(0.738222\pi\)
\(812\) 2.65063 0.0930188
\(813\) 16.1271 0.565602
\(814\) 43.0855 1.51015
\(815\) 12.7148 0.445381
\(816\) −5.55758 −0.194554
\(817\) −4.35112 −0.152226
\(818\) 7.91564 0.276764
\(819\) −3.69009 −0.128942
\(820\) −21.3178 −0.744450
\(821\) 28.0920 0.980417 0.490208 0.871605i \(-0.336921\pi\)
0.490208 + 0.871605i \(0.336921\pi\)
\(822\) 1.61260 0.0562458
\(823\) 32.8455 1.14492 0.572461 0.819932i \(-0.305989\pi\)
0.572461 + 0.819932i \(0.305989\pi\)
\(824\) 0.646222 0.0225122
\(825\) −105.090 −3.65876
\(826\) −11.2422 −0.391165
\(827\) −7.59414 −0.264074 −0.132037 0.991245i \(-0.542152\pi\)
−0.132037 + 0.991245i \(0.542152\pi\)
\(828\) −10.3445 −0.359495
\(829\) −24.7291 −0.858878 −0.429439 0.903096i \(-0.641289\pi\)
−0.429439 + 0.903096i \(0.641289\pi\)
\(830\) 62.7903 2.17948
\(831\) −12.3815 −0.429508
\(832\) −2.07746 −0.0720228
\(833\) −12.9162 −0.447520
\(834\) 0.135016 0.00467523
\(835\) −84.9036 −2.93821
\(836\) −4.36668 −0.151025
\(837\) −14.5926 −0.504393
\(838\) −3.22411 −0.111375
\(839\) −14.8366 −0.512215 −0.256107 0.966648i \(-0.582440\pi\)
−0.256107 + 0.966648i \(0.582440\pi\)
\(840\) −12.5515 −0.433069
\(841\) −25.8710 −0.892102
\(842\) −26.3204 −0.907061
\(843\) 48.0063 1.65342
\(844\) −1.00000 −0.0344214
\(845\) 35.5560 1.22316
\(846\) 6.24969 0.214869
\(847\) 12.0894 0.415396
\(848\) −2.90552 −0.0997761
\(849\) −65.3693 −2.24347
\(850\) −31.9566 −1.09610
\(851\) 86.1045 2.95163
\(852\) −2.23665 −0.0766264
\(853\) 46.3414 1.58670 0.793350 0.608766i \(-0.208335\pi\)
0.793350 + 0.608766i \(0.208335\pi\)
\(854\) 7.02103 0.240255
\(855\) 4.85339 0.165983
\(856\) −17.4634 −0.596886
\(857\) 38.8509 1.32712 0.663561 0.748122i \(-0.269044\pi\)
0.663561 + 0.748122i \(0.269044\pi\)
\(858\) −18.5588 −0.633589
\(859\) −9.96164 −0.339887 −0.169943 0.985454i \(-0.554358\pi\)
−0.169943 + 0.985454i \(0.554358\pi\)
\(860\) −17.8150 −0.607485
\(861\) −15.9614 −0.543962
\(862\) 2.92758 0.0997136
\(863\) −9.72885 −0.331174 −0.165587 0.986195i \(-0.552952\pi\)
−0.165587 + 0.986195i \(0.552952\pi\)
\(864\) −3.71237 −0.126297
\(865\) −65.3676 −2.22257
\(866\) 15.5142 0.527196
\(867\) 19.6815 0.668419
\(868\) −5.89012 −0.199924
\(869\) 32.5810 1.10523
\(870\) −14.8169 −0.502339
\(871\) 17.8059 0.603330
\(872\) −13.5424 −0.458604
\(873\) −19.3577 −0.655159
\(874\) −8.72662 −0.295182
\(875\) −41.4963 −1.40283
\(876\) −23.2373 −0.785114
\(877\) −41.7847 −1.41097 −0.705484 0.708726i \(-0.749270\pi\)
−0.705484 + 0.708726i \(0.749270\pi\)
\(878\) −25.6971 −0.867234
\(879\) 1.08592 0.0366272
\(880\) −17.8787 −0.602690
\(881\) 36.0925 1.21599 0.607993 0.793942i \(-0.291975\pi\)
0.607993 + 0.793942i \(0.291975\pi\)
\(882\) 5.63609 0.189777
\(883\) 11.4951 0.386841 0.193421 0.981116i \(-0.438042\pi\)
0.193421 + 0.981116i \(0.438042\pi\)
\(884\) −5.64352 −0.189812
\(885\) 62.8431 2.11245
\(886\) 4.35774 0.146401
\(887\) 38.3961 1.28921 0.644607 0.764514i \(-0.277021\pi\)
0.644607 + 0.764514i \(0.277021\pi\)
\(888\) −20.1859 −0.677394
\(889\) −17.3050 −0.580392
\(890\) 29.6489 0.993832
\(891\) −48.6929 −1.63127
\(892\) −15.1165 −0.506138
\(893\) 5.27226 0.176430
\(894\) 44.5841 1.49112
\(895\) −27.5670 −0.921462
\(896\) −1.49846 −0.0500599
\(897\) −37.0891 −1.23837
\(898\) 13.8264 0.461393
\(899\) −6.95320 −0.231902
\(900\) 13.9445 0.464817
\(901\) −7.89301 −0.262954
\(902\) −22.7358 −0.757018
\(903\) −13.3387 −0.443883
\(904\) 10.1385 0.337201
\(905\) 46.7906 1.55537
\(906\) 7.70544 0.255996
\(907\) −41.2826 −1.37077 −0.685383 0.728183i \(-0.740365\pi\)
−0.685383 + 0.728183i \(0.740365\pi\)
\(908\) 5.52236 0.183266
\(909\) 1.55361 0.0515300
\(910\) −12.7456 −0.422512
\(911\) 22.5764 0.747991 0.373995 0.927431i \(-0.377988\pi\)
0.373995 + 0.927431i \(0.377988\pi\)
\(912\) 2.04582 0.0677440
\(913\) 66.9669 2.21628
\(914\) −11.6026 −0.383781
\(915\) −39.2472 −1.29747
\(916\) 8.47458 0.280008
\(917\) −3.36313 −0.111060
\(918\) −10.0848 −0.332850
\(919\) −5.67769 −0.187290 −0.0936449 0.995606i \(-0.529852\pi\)
−0.0936449 + 0.995606i \(0.529852\pi\)
\(920\) −35.7298 −1.17798
\(921\) −24.9682 −0.822729
\(922\) −19.3868 −0.638471
\(923\) −2.27124 −0.0747586
\(924\) −13.3864 −0.440380
\(925\) −116.070 −3.81637
\(926\) −30.5402 −1.00361
\(927\) −0.766026 −0.0251596
\(928\) −1.76891 −0.0580672
\(929\) −24.6134 −0.807540 −0.403770 0.914860i \(-0.632300\pi\)
−0.403770 + 0.914860i \(0.632300\pi\)
\(930\) 32.9255 1.07967
\(931\) 4.75463 0.155827
\(932\) 11.7599 0.385208
\(933\) −41.8320 −1.36952
\(934\) 23.8146 0.779236
\(935\) −48.5684 −1.58836
\(936\) 2.46259 0.0804924
\(937\) −20.7073 −0.676477 −0.338239 0.941060i \(-0.609831\pi\)
−0.338239 + 0.941060i \(0.609831\pi\)
\(938\) 12.8433 0.419348
\(939\) −66.6907 −2.17637
\(940\) 21.5865 0.704072
\(941\) 7.68290 0.250455 0.125228 0.992128i \(-0.460034\pi\)
0.125228 + 0.992128i \(0.460034\pi\)
\(942\) 2.77306 0.0903510
\(943\) −45.4365 −1.47961
\(944\) 7.50249 0.244185
\(945\) −22.7761 −0.740907
\(946\) −18.9999 −0.617741
\(947\) −30.5206 −0.991787 −0.495894 0.868383i \(-0.665159\pi\)
−0.495894 + 0.868383i \(0.665159\pi\)
\(948\) −15.2644 −0.495766
\(949\) −23.5966 −0.765976
\(950\) 11.7636 0.381663
\(951\) 55.0154 1.78400
\(952\) −4.07064 −0.131930
\(953\) −7.70126 −0.249468 −0.124734 0.992190i \(-0.539808\pi\)
−0.124734 + 0.992190i \(0.539808\pi\)
\(954\) 3.44418 0.111509
\(955\) −93.4181 −3.02294
\(956\) −2.68897 −0.0869676
\(957\) −15.8024 −0.510820
\(958\) 31.5928 1.02072
\(959\) 1.18114 0.0381411
\(960\) 8.37630 0.270344
\(961\) −15.5489 −0.501576
\(962\) −20.4980 −0.660882
\(963\) 20.7009 0.667078
\(964\) 0.0708398 0.00228160
\(965\) 15.0224 0.483587
\(966\) −26.7521 −0.860736
\(967\) 10.0243 0.322358 0.161179 0.986925i \(-0.448470\pi\)
0.161179 + 0.986925i \(0.448470\pi\)
\(968\) −8.06789 −0.259312
\(969\) 5.55758 0.178535
\(970\) −66.8616 −2.14680
\(971\) 25.6509 0.823177 0.411589 0.911370i \(-0.364974\pi\)
0.411589 + 0.911370i \(0.364974\pi\)
\(972\) 11.6759 0.374505
\(973\) 0.0988922 0.00317034
\(974\) 43.3546 1.38917
\(975\) 49.9967 1.60118
\(976\) −4.68551 −0.149979
\(977\) 35.3621 1.13133 0.565667 0.824634i \(-0.308619\pi\)
0.565667 + 0.824634i \(0.308619\pi\)
\(978\) −6.35322 −0.203154
\(979\) 31.6210 1.01061
\(980\) 19.4671 0.621853
\(981\) 16.0531 0.512535
\(982\) −11.7792 −0.375890
\(983\) −30.7198 −0.979809 −0.489904 0.871776i \(-0.662968\pi\)
−0.489904 + 0.871776i \(0.662968\pi\)
\(984\) 10.6519 0.339569
\(985\) 12.0013 0.382392
\(986\) −4.80533 −0.153033
\(987\) 16.1625 0.514459
\(988\) 2.07746 0.0660927
\(989\) −37.9705 −1.20739
\(990\) 21.1932 0.673565
\(991\) −22.4415 −0.712877 −0.356439 0.934319i \(-0.616009\pi\)
−0.356439 + 0.934319i \(0.616009\pi\)
\(992\) 3.93079 0.124803
\(993\) 57.8116 1.83460
\(994\) −1.63823 −0.0519615
\(995\) −50.3764 −1.59704
\(996\) −31.3745 −0.994139
\(997\) −22.9174 −0.725803 −0.362901 0.931828i \(-0.618214\pi\)
−0.362901 + 0.931828i \(0.618214\pi\)
\(998\) 14.9516 0.473284
\(999\) −36.6295 −1.15891
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 \(a_p\))