Properties

Label 6023.2.a.b.1.17
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 1.17
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.96796 q^{2}\) \(-0.967508 q^{3}\) \(+1.87288 q^{4}\) \(+0.188751 q^{5}\) \(+1.90402 q^{6}\) \(-4.91446 q^{7}\) \(+0.250172 q^{8}\) \(-2.06393 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.96796 q^{2}\) \(-0.967508 q^{3}\) \(+1.87288 q^{4}\) \(+0.188751 q^{5}\) \(+1.90402 q^{6}\) \(-4.91446 q^{7}\) \(+0.250172 q^{8}\) \(-2.06393 q^{9}\) \(-0.371455 q^{10}\) \(-1.60871 q^{11}\) \(-1.81202 q^{12}\) \(+3.63672 q^{13}\) \(+9.67146 q^{14}\) \(-0.182618 q^{15}\) \(-4.23808 q^{16}\) \(+3.34454 q^{17}\) \(+4.06173 q^{18}\) \(-1.00000 q^{19}\) \(+0.353508 q^{20}\) \(+4.75477 q^{21}\) \(+3.16589 q^{22}\) \(+2.14601 q^{23}\) \(-0.242044 q^{24}\) \(-4.96437 q^{25}\) \(-7.15693 q^{26}\) \(+4.89939 q^{27}\) \(-9.20417 q^{28}\) \(-3.45241 q^{29}\) \(+0.359386 q^{30}\) \(+3.44285 q^{31}\) \(+7.84005 q^{32}\) \(+1.55644 q^{33}\) \(-6.58193 q^{34}\) \(-0.927609 q^{35}\) \(-3.86548 q^{36}\) \(-5.13774 q^{37}\) \(+1.96796 q^{38}\) \(-3.51856 q^{39}\) \(+0.0472203 q^{40}\) \(-11.7806 q^{41}\) \(-9.35722 q^{42}\) \(-3.74167 q^{43}\) \(-3.01292 q^{44}\) \(-0.389569 q^{45}\) \(-4.22327 q^{46}\) \(+5.82681 q^{47}\) \(+4.10038 q^{48}\) \(+17.1519 q^{49}\) \(+9.76970 q^{50}\) \(-3.23587 q^{51}\) \(+6.81113 q^{52}\) \(-10.8588 q^{53}\) \(-9.64182 q^{54}\) \(-0.303646 q^{55}\) \(-1.22946 q^{56}\) \(+0.967508 q^{57}\) \(+6.79422 q^{58}\) \(+5.17048 q^{59}\) \(-0.342022 q^{60}\) \(+9.16826 q^{61}\) \(-6.77540 q^{62}\) \(+10.1431 q^{63}\) \(-6.95275 q^{64}\) \(+0.686435 q^{65}\) \(-3.06302 q^{66}\) \(+13.8922 q^{67}\) \(+6.26392 q^{68}\) \(-2.07628 q^{69}\) \(+1.82550 q^{70}\) \(-7.81496 q^{71}\) \(-0.516338 q^{72}\) \(+7.15869 q^{73}\) \(+10.1109 q^{74}\) \(+4.80307 q^{75}\) \(-1.87288 q^{76}\) \(+7.90594 q^{77}\) \(+6.92439 q^{78}\) \(+14.7823 q^{79}\) \(-0.799943 q^{80}\) \(+1.45159 q^{81}\) \(+23.1839 q^{82}\) \(+8.05904 q^{83}\) \(+8.90511 q^{84}\) \(+0.631286 q^{85}\) \(+7.36348 q^{86}\) \(+3.34024 q^{87}\) \(-0.402456 q^{88}\) \(+0.0958099 q^{89}\) \(+0.766657 q^{90}\) \(-17.8725 q^{91}\) \(+4.01921 q^{92}\) \(-3.33098 q^{93}\) \(-11.4670 q^{94}\) \(-0.188751 q^{95}\) \(-7.58531 q^{96}\) \(-3.34440 q^{97}\) \(-33.7542 q^{98}\) \(+3.32027 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96796 −1.39156 −0.695780 0.718255i \(-0.744941\pi\)
−0.695780 + 0.718255i \(0.744941\pi\)
\(3\) −0.967508 −0.558591 −0.279295 0.960205i \(-0.590101\pi\)
−0.279295 + 0.960205i \(0.590101\pi\)
\(4\) 1.87288 0.936439
\(5\) 0.188751 0.0844121 0.0422060 0.999109i \(-0.486561\pi\)
0.0422060 + 0.999109i \(0.486561\pi\)
\(6\) 1.90402 0.777313
\(7\) −4.91446 −1.85749 −0.928745 0.370720i \(-0.879111\pi\)
−0.928745 + 0.370720i \(0.879111\pi\)
\(8\) 0.250172 0.0884493
\(9\) −2.06393 −0.687976
\(10\) −0.371455 −0.117464
\(11\) −1.60871 −0.485045 −0.242522 0.970146i \(-0.577975\pi\)
−0.242522 + 0.970146i \(0.577975\pi\)
\(12\) −1.81202 −0.523086
\(13\) 3.63672 1.00864 0.504322 0.863515i \(-0.331742\pi\)
0.504322 + 0.863515i \(0.331742\pi\)
\(14\) 9.67146 2.58481
\(15\) −0.182618 −0.0471518
\(16\) −4.23808 −1.05952
\(17\) 3.34454 0.811171 0.405585 0.914057i \(-0.367068\pi\)
0.405585 + 0.914057i \(0.367068\pi\)
\(18\) 4.06173 0.957360
\(19\) −1.00000 −0.229416
\(20\) 0.353508 0.0790467
\(21\) 4.75477 1.03758
\(22\) 3.16589 0.674969
\(23\) 2.14601 0.447474 0.223737 0.974650i \(-0.428174\pi\)
0.223737 + 0.974650i \(0.428174\pi\)
\(24\) −0.242044 −0.0494070
\(25\) −4.96437 −0.992875
\(26\) −7.15693 −1.40359
\(27\) 4.89939 0.942888
\(28\) −9.20417 −1.73943
\(29\) −3.45241 −0.641097 −0.320549 0.947232i \(-0.603867\pi\)
−0.320549 + 0.947232i \(0.603867\pi\)
\(30\) 0.359386 0.0656146
\(31\) 3.44285 0.618354 0.309177 0.951005i \(-0.399946\pi\)
0.309177 + 0.951005i \(0.399946\pi\)
\(32\) 7.84005 1.38594
\(33\) 1.55644 0.270942
\(34\) −6.58193 −1.12879
\(35\) −0.927609 −0.156795
\(36\) −3.86548 −0.644247
\(37\) −5.13774 −0.844639 −0.422319 0.906447i \(-0.638784\pi\)
−0.422319 + 0.906447i \(0.638784\pi\)
\(38\) 1.96796 0.319246
\(39\) −3.51856 −0.563420
\(40\) 0.0472203 0.00746619
\(41\) −11.7806 −1.83983 −0.919914 0.392121i \(-0.871741\pi\)
−0.919914 + 0.392121i \(0.871741\pi\)
\(42\) −9.35722 −1.44385
\(43\) −3.74167 −0.570600 −0.285300 0.958438i \(-0.592093\pi\)
−0.285300 + 0.958438i \(0.592093\pi\)
\(44\) −3.01292 −0.454215
\(45\) −0.389569 −0.0580735
\(46\) −4.22327 −0.622687
\(47\) 5.82681 0.849928 0.424964 0.905210i \(-0.360287\pi\)
0.424964 + 0.905210i \(0.360287\pi\)
\(48\) 4.10038 0.591839
\(49\) 17.1519 2.45027
\(50\) 9.76970 1.38164
\(51\) −3.23587 −0.453113
\(52\) 6.81113 0.944534
\(53\) −10.8588 −1.49157 −0.745785 0.666186i \(-0.767926\pi\)
−0.745785 + 0.666186i \(0.767926\pi\)
\(54\) −9.64182 −1.31209
\(55\) −0.303646 −0.0409436
\(56\) −1.22946 −0.164294
\(57\) 0.967508 0.128150
\(58\) 6.79422 0.892125
\(59\) 5.17048 0.673139 0.336569 0.941659i \(-0.390733\pi\)
0.336569 + 0.941659i \(0.390733\pi\)
\(60\) −0.342022 −0.0441548
\(61\) 9.16826 1.17387 0.586937 0.809632i \(-0.300333\pi\)
0.586937 + 0.809632i \(0.300333\pi\)
\(62\) −6.77540 −0.860477
\(63\) 10.1431 1.27791
\(64\) −6.95275 −0.869094
\(65\) 0.686435 0.0851418
\(66\) −3.06302 −0.377032
\(67\) 13.8922 1.69720 0.848601 0.529034i \(-0.177445\pi\)
0.848601 + 0.529034i \(0.177445\pi\)
\(68\) 6.26392 0.759612
\(69\) −2.07628 −0.249955
\(70\) 1.82550 0.218189
\(71\) −7.81496 −0.927465 −0.463733 0.885975i \(-0.653490\pi\)
−0.463733 + 0.885975i \(0.653490\pi\)
\(72\) −0.516338 −0.0608510
\(73\) 7.15869 0.837861 0.418931 0.908018i \(-0.362405\pi\)
0.418931 + 0.908018i \(0.362405\pi\)
\(74\) 10.1109 1.17537
\(75\) 4.80307 0.554611
\(76\) −1.87288 −0.214834
\(77\) 7.90594 0.900966
\(78\) 6.92439 0.784032
\(79\) 14.7823 1.66314 0.831571 0.555419i \(-0.187442\pi\)
0.831571 + 0.555419i \(0.187442\pi\)
\(80\) −0.799943 −0.0894364
\(81\) 1.45159 0.161287
\(82\) 23.1839 2.56023
\(83\) 8.05904 0.884595 0.442297 0.896868i \(-0.354164\pi\)
0.442297 + 0.896868i \(0.354164\pi\)
\(84\) 8.90511 0.971627
\(85\) 0.631286 0.0684726
\(86\) 7.36348 0.794024
\(87\) 3.34024 0.358111
\(88\) −0.402456 −0.0429019
\(89\) 0.0958099 0.0101558 0.00507792 0.999987i \(-0.498384\pi\)
0.00507792 + 0.999987i \(0.498384\pi\)
\(90\) 0.766657 0.0808127
\(91\) −17.8725 −1.87355
\(92\) 4.01921 0.419032
\(93\) −3.33098 −0.345407
\(94\) −11.4670 −1.18273
\(95\) −0.188751 −0.0193655
\(96\) −7.58531 −0.774172
\(97\) −3.34440 −0.339572 −0.169786 0.985481i \(-0.554308\pi\)
−0.169786 + 0.985481i \(0.554308\pi\)
\(98\) −33.7542 −3.40969
\(99\) 3.32027 0.333699
\(100\) −9.29766 −0.929766
\(101\) −5.26784 −0.524170 −0.262085 0.965045i \(-0.584410\pi\)
−0.262085 + 0.965045i \(0.584410\pi\)
\(102\) 6.36807 0.630533
\(103\) 1.78581 0.175961 0.0879805 0.996122i \(-0.471959\pi\)
0.0879805 + 0.996122i \(0.471959\pi\)
\(104\) 0.909807 0.0892139
\(105\) 0.897469 0.0875840
\(106\) 21.3697 2.07561
\(107\) −11.9476 −1.15502 −0.577508 0.816385i \(-0.695975\pi\)
−0.577508 + 0.816385i \(0.695975\pi\)
\(108\) 9.17596 0.882957
\(109\) 10.7995 1.03441 0.517204 0.855862i \(-0.326973\pi\)
0.517204 + 0.855862i \(0.326973\pi\)
\(110\) 0.597564 0.0569755
\(111\) 4.97080 0.471808
\(112\) 20.8279 1.96805
\(113\) 18.0149 1.69470 0.847350 0.531034i \(-0.178197\pi\)
0.847350 + 0.531034i \(0.178197\pi\)
\(114\) −1.90402 −0.178328
\(115\) 0.405062 0.0377722
\(116\) −6.46595 −0.600348
\(117\) −7.50593 −0.693923
\(118\) −10.1753 −0.936713
\(119\) −16.4366 −1.50674
\(120\) −0.0456861 −0.00417055
\(121\) −8.41205 −0.764731
\(122\) −18.0428 −1.63352
\(123\) 11.3979 1.02771
\(124\) 6.44803 0.579051
\(125\) −1.88079 −0.168223
\(126\) −19.9612 −1.77829
\(127\) −14.8043 −1.31367 −0.656836 0.754033i \(-0.728106\pi\)
−0.656836 + 0.754033i \(0.728106\pi\)
\(128\) −1.99734 −0.176541
\(129\) 3.62010 0.318732
\(130\) −1.35088 −0.118480
\(131\) 10.0720 0.879996 0.439998 0.897999i \(-0.354979\pi\)
0.439998 + 0.897999i \(0.354979\pi\)
\(132\) 2.91502 0.253720
\(133\) 4.91446 0.426137
\(134\) −27.3393 −2.36176
\(135\) 0.924765 0.0795911
\(136\) 0.836712 0.0717475
\(137\) 10.9503 0.935543 0.467772 0.883849i \(-0.345057\pi\)
0.467772 + 0.883849i \(0.345057\pi\)
\(138\) 4.08604 0.347827
\(139\) 14.7580 1.25175 0.625877 0.779922i \(-0.284741\pi\)
0.625877 + 0.779922i \(0.284741\pi\)
\(140\) −1.73730 −0.146828
\(141\) −5.63749 −0.474762
\(142\) 15.3796 1.29062
\(143\) −5.85044 −0.489238
\(144\) 8.74710 0.728925
\(145\) −0.651647 −0.0541163
\(146\) −14.0880 −1.16593
\(147\) −16.5946 −1.36870
\(148\) −9.62235 −0.790952
\(149\) 14.6769 1.20238 0.601188 0.799108i \(-0.294694\pi\)
0.601188 + 0.799108i \(0.294694\pi\)
\(150\) −9.45226 −0.771774
\(151\) −9.88759 −0.804641 −0.402320 0.915499i \(-0.631796\pi\)
−0.402320 + 0.915499i \(0.631796\pi\)
\(152\) −0.250172 −0.0202917
\(153\) −6.90290 −0.558066
\(154\) −15.5586 −1.25375
\(155\) 0.649842 0.0521965
\(156\) −6.58982 −0.527608
\(157\) −6.72897 −0.537030 −0.268515 0.963275i \(-0.586533\pi\)
−0.268515 + 0.963275i \(0.586533\pi\)
\(158\) −29.0911 −2.31436
\(159\) 10.5060 0.833178
\(160\) 1.47982 0.116990
\(161\) −10.5465 −0.831178
\(162\) −2.85667 −0.224441
\(163\) −5.75158 −0.450498 −0.225249 0.974301i \(-0.572320\pi\)
−0.225249 + 0.974301i \(0.572320\pi\)
\(164\) −22.0637 −1.72289
\(165\) 0.293780 0.0228708
\(166\) −15.8599 −1.23097
\(167\) 0.849574 0.0657420 0.0328710 0.999460i \(-0.489535\pi\)
0.0328710 + 0.999460i \(0.489535\pi\)
\(168\) 1.18951 0.0917730
\(169\) 0.225734 0.0173641
\(170\) −1.24235 −0.0952837
\(171\) 2.06393 0.157833
\(172\) −7.00770 −0.534332
\(173\) 14.2419 1.08279 0.541395 0.840768i \(-0.317896\pi\)
0.541395 + 0.840768i \(0.317896\pi\)
\(174\) −6.57347 −0.498333
\(175\) 24.3972 1.84425
\(176\) 6.81786 0.513915
\(177\) −5.00248 −0.376009
\(178\) −0.188550 −0.0141324
\(179\) 8.03224 0.600358 0.300179 0.953883i \(-0.402954\pi\)
0.300179 + 0.953883i \(0.402954\pi\)
\(180\) −0.729615 −0.0543823
\(181\) 2.09618 0.155808 0.0779040 0.996961i \(-0.475177\pi\)
0.0779040 + 0.996961i \(0.475177\pi\)
\(182\) 35.1724 2.60715
\(183\) −8.87036 −0.655716
\(184\) 0.536872 0.0395788
\(185\) −0.969754 −0.0712977
\(186\) 6.55525 0.480654
\(187\) −5.38041 −0.393454
\(188\) 10.9129 0.795906
\(189\) −24.0778 −1.75140
\(190\) 0.371455 0.0269482
\(191\) −1.76351 −0.127603 −0.0638014 0.997963i \(-0.520322\pi\)
−0.0638014 + 0.997963i \(0.520322\pi\)
\(192\) 6.72684 0.485468
\(193\) −0.887799 −0.0639052 −0.0319526 0.999489i \(-0.510173\pi\)
−0.0319526 + 0.999489i \(0.510173\pi\)
\(194\) 6.58166 0.472535
\(195\) −0.664131 −0.0475594
\(196\) 32.1233 2.29452
\(197\) 14.4349 1.02844 0.514221 0.857658i \(-0.328081\pi\)
0.514221 + 0.857658i \(0.328081\pi\)
\(198\) −6.53416 −0.464363
\(199\) 0.796173 0.0564392 0.0282196 0.999602i \(-0.491016\pi\)
0.0282196 + 0.999602i \(0.491016\pi\)
\(200\) −1.24195 −0.0878191
\(201\) −13.4408 −0.948042
\(202\) 10.3669 0.729414
\(203\) 16.9667 1.19083
\(204\) −6.06039 −0.424312
\(205\) −2.22361 −0.155304
\(206\) −3.51441 −0.244860
\(207\) −4.42921 −0.307851
\(208\) −15.4127 −1.06868
\(209\) 1.60871 0.111277
\(210\) −1.76619 −0.121878
\(211\) 4.91514 0.338372 0.169186 0.985584i \(-0.445886\pi\)
0.169186 + 0.985584i \(0.445886\pi\)
\(212\) −20.3372 −1.39676
\(213\) 7.56104 0.518074
\(214\) 23.5124 1.60727
\(215\) −0.706245 −0.0481655
\(216\) 1.22569 0.0833978
\(217\) −16.9197 −1.14859
\(218\) −21.2531 −1.43944
\(219\) −6.92609 −0.468022
\(220\) −0.568692 −0.0383412
\(221\) 12.1632 0.818183
\(222\) −9.78235 −0.656548
\(223\) 11.1315 0.745424 0.372712 0.927947i \(-0.378428\pi\)
0.372712 + 0.927947i \(0.378428\pi\)
\(224\) −38.5296 −2.57436
\(225\) 10.2461 0.683074
\(226\) −35.4527 −2.35828
\(227\) −22.8786 −1.51851 −0.759253 0.650796i \(-0.774435\pi\)
−0.759253 + 0.650796i \(0.774435\pi\)
\(228\) 1.81202 0.120004
\(229\) −23.5220 −1.55438 −0.777189 0.629267i \(-0.783355\pi\)
−0.777189 + 0.629267i \(0.783355\pi\)
\(230\) −0.797146 −0.0525623
\(231\) −7.64906 −0.503271
\(232\) −0.863699 −0.0567046
\(233\) −10.1296 −0.663613 −0.331806 0.943347i \(-0.607658\pi\)
−0.331806 + 0.943347i \(0.607658\pi\)
\(234\) 14.7714 0.965636
\(235\) 1.09982 0.0717442
\(236\) 9.68367 0.630353
\(237\) −14.3020 −0.929016
\(238\) 32.3466 2.09672
\(239\) −4.49190 −0.290557 −0.145278 0.989391i \(-0.546408\pi\)
−0.145278 + 0.989391i \(0.546408\pi\)
\(240\) 0.773951 0.0499584
\(241\) −6.25584 −0.402974 −0.201487 0.979491i \(-0.564577\pi\)
−0.201487 + 0.979491i \(0.564577\pi\)
\(242\) 16.5546 1.06417
\(243\) −16.1026 −1.03298
\(244\) 17.1710 1.09926
\(245\) 3.23743 0.206832
\(246\) −22.4306 −1.43012
\(247\) −3.63672 −0.231399
\(248\) 0.861306 0.0546930
\(249\) −7.79719 −0.494127
\(250\) 3.70132 0.234092
\(251\) −7.32121 −0.462111 −0.231055 0.972941i \(-0.574218\pi\)
−0.231055 + 0.972941i \(0.574218\pi\)
\(252\) 18.9968 1.19668
\(253\) −3.45231 −0.217045
\(254\) 29.1344 1.82805
\(255\) −0.610774 −0.0382482
\(256\) 17.8362 1.11476
\(257\) −17.8582 −1.11396 −0.556981 0.830525i \(-0.688040\pi\)
−0.556981 + 0.830525i \(0.688040\pi\)
\(258\) −7.12422 −0.443535
\(259\) 25.2492 1.56891
\(260\) 1.28561 0.0797301
\(261\) 7.12554 0.441060
\(262\) −19.8213 −1.22457
\(263\) 11.6234 0.716728 0.358364 0.933582i \(-0.383335\pi\)
0.358364 + 0.933582i \(0.383335\pi\)
\(264\) 0.389379 0.0239646
\(265\) −2.04961 −0.125907
\(266\) −9.67146 −0.592996
\(267\) −0.0926969 −0.00567296
\(268\) 26.0184 1.58933
\(269\) 21.0073 1.28084 0.640419 0.768025i \(-0.278761\pi\)
0.640419 + 0.768025i \(0.278761\pi\)
\(270\) −1.81990 −0.110756
\(271\) −3.97821 −0.241659 −0.120830 0.992673i \(-0.538555\pi\)
−0.120830 + 0.992673i \(0.538555\pi\)
\(272\) −14.1745 −0.859453
\(273\) 17.2918 1.04655
\(274\) −21.5497 −1.30186
\(275\) 7.98625 0.481589
\(276\) −3.88862 −0.234067
\(277\) −5.35621 −0.321824 −0.160912 0.986969i \(-0.551443\pi\)
−0.160912 + 0.986969i \(0.551443\pi\)
\(278\) −29.0431 −1.74189
\(279\) −7.10579 −0.425413
\(280\) −0.232062 −0.0138684
\(281\) 17.6593 1.05346 0.526732 0.850032i \(-0.323417\pi\)
0.526732 + 0.850032i \(0.323417\pi\)
\(282\) 11.0944 0.660660
\(283\) −3.63125 −0.215856 −0.107928 0.994159i \(-0.534422\pi\)
−0.107928 + 0.994159i \(0.534422\pi\)
\(284\) −14.6365 −0.868514
\(285\) 0.182618 0.0108174
\(286\) 11.5134 0.680804
\(287\) 57.8954 3.41746
\(288\) −16.1813 −0.953492
\(289\) −5.81404 −0.342002
\(290\) 1.28242 0.0753061
\(291\) 3.23573 0.189682
\(292\) 13.4073 0.784606
\(293\) −7.40251 −0.432459 −0.216230 0.976343i \(-0.569376\pi\)
−0.216230 + 0.976343i \(0.569376\pi\)
\(294\) 32.6575 1.90462
\(295\) 0.975933 0.0568210
\(296\) −1.28532 −0.0747077
\(297\) −7.88171 −0.457343
\(298\) −28.8835 −1.67318
\(299\) 7.80443 0.451342
\(300\) 8.99556 0.519359
\(301\) 18.3883 1.05988
\(302\) 19.4584 1.11971
\(303\) 5.09668 0.292797
\(304\) 4.23808 0.243071
\(305\) 1.73052 0.0990892
\(306\) 13.5846 0.776582
\(307\) −13.0501 −0.744807 −0.372404 0.928071i \(-0.621466\pi\)
−0.372404 + 0.928071i \(0.621466\pi\)
\(308\) 14.8069 0.843699
\(309\) −1.72778 −0.0982902
\(310\) −1.27886 −0.0726346
\(311\) 33.5659 1.90335 0.951673 0.307113i \(-0.0993629\pi\)
0.951673 + 0.307113i \(0.0993629\pi\)
\(312\) −0.880246 −0.0498341
\(313\) −19.6588 −1.11118 −0.555592 0.831455i \(-0.687508\pi\)
−0.555592 + 0.831455i \(0.687508\pi\)
\(314\) 13.2424 0.747310
\(315\) 1.91452 0.107871
\(316\) 27.6855 1.55743
\(317\) −1.00000 −0.0561656
\(318\) −20.6754 −1.15942
\(319\) 5.55394 0.310961
\(320\) −1.31234 −0.0733620
\(321\) 11.5594 0.645182
\(322\) 20.7550 1.15663
\(323\) −3.34454 −0.186095
\(324\) 2.71864 0.151036
\(325\) −18.0540 −1.00146
\(326\) 11.3189 0.626895
\(327\) −10.4486 −0.577811
\(328\) −2.94719 −0.162731
\(329\) −28.6356 −1.57873
\(330\) −0.578148 −0.0318260
\(331\) 27.0196 1.48513 0.742565 0.669774i \(-0.233609\pi\)
0.742565 + 0.669774i \(0.233609\pi\)
\(332\) 15.0936 0.828369
\(333\) 10.6039 0.581091
\(334\) −1.67193 −0.0914840
\(335\) 2.62217 0.143264
\(336\) −20.1511 −1.09933
\(337\) −6.55603 −0.357130 −0.178565 0.983928i \(-0.557145\pi\)
−0.178565 + 0.983928i \(0.557145\pi\)
\(338\) −0.444235 −0.0241632
\(339\) −17.4296 −0.946644
\(340\) 1.18232 0.0641204
\(341\) −5.53855 −0.299929
\(342\) −4.06173 −0.219633
\(343\) −49.8909 −2.69386
\(344\) −0.936064 −0.0504692
\(345\) −0.391900 −0.0210992
\(346\) −28.0275 −1.50677
\(347\) −16.5458 −0.888227 −0.444113 0.895971i \(-0.646481\pi\)
−0.444113 + 0.895971i \(0.646481\pi\)
\(348\) 6.25586 0.335349
\(349\) −35.4680 −1.89856 −0.949279 0.314436i \(-0.898184\pi\)
−0.949279 + 0.314436i \(0.898184\pi\)
\(350\) −48.0128 −2.56639
\(351\) 17.8177 0.951039
\(352\) −12.6124 −0.672242
\(353\) −5.82385 −0.309973 −0.154986 0.987917i \(-0.549533\pi\)
−0.154986 + 0.987917i \(0.549533\pi\)
\(354\) 9.84469 0.523239
\(355\) −1.47508 −0.0782893
\(356\) 0.179440 0.00951031
\(357\) 15.9025 0.841652
\(358\) −15.8071 −0.835434
\(359\) 23.3455 1.23213 0.616063 0.787697i \(-0.288727\pi\)
0.616063 + 0.787697i \(0.288727\pi\)
\(360\) −0.0974594 −0.00513656
\(361\) 1.00000 0.0526316
\(362\) −4.12521 −0.216816
\(363\) 8.13872 0.427172
\(364\) −33.4730 −1.75446
\(365\) 1.35121 0.0707256
\(366\) 17.4565 0.912468
\(367\) −0.883059 −0.0460953 −0.0230477 0.999734i \(-0.507337\pi\)
−0.0230477 + 0.999734i \(0.507337\pi\)
\(368\) −9.09497 −0.474108
\(369\) 24.3144 1.26576
\(370\) 1.90844 0.0992150
\(371\) 53.3651 2.77058
\(372\) −6.23852 −0.323452
\(373\) 5.06087 0.262042 0.131021 0.991380i \(-0.458174\pi\)
0.131021 + 0.991380i \(0.458174\pi\)
\(374\) 10.5884 0.547515
\(375\) 1.81968 0.0939677
\(376\) 1.45771 0.0751756
\(377\) −12.5555 −0.646639
\(378\) 47.3843 2.43718
\(379\) 2.77259 0.142418 0.0712092 0.997461i \(-0.477314\pi\)
0.0712092 + 0.997461i \(0.477314\pi\)
\(380\) −0.353508 −0.0181346
\(381\) 14.3233 0.733806
\(382\) 3.47051 0.177567
\(383\) 10.3211 0.527382 0.263691 0.964607i \(-0.415060\pi\)
0.263691 + 0.964607i \(0.415060\pi\)
\(384\) 1.93244 0.0986144
\(385\) 1.49226 0.0760524
\(386\) 1.74716 0.0889279
\(387\) 7.72255 0.392559
\(388\) −6.26365 −0.317989
\(389\) −10.0931 −0.511740 −0.255870 0.966711i \(-0.582362\pi\)
−0.255870 + 0.966711i \(0.582362\pi\)
\(390\) 1.30699 0.0661818
\(391\) 7.17742 0.362978
\(392\) 4.29093 0.216724
\(393\) −9.74475 −0.491558
\(394\) −28.4073 −1.43114
\(395\) 2.79018 0.140389
\(396\) 6.21845 0.312489
\(397\) 4.21868 0.211729 0.105865 0.994381i \(-0.466239\pi\)
0.105865 + 0.994381i \(0.466239\pi\)
\(398\) −1.56684 −0.0785385
\(399\) −4.75477 −0.238036
\(400\) 21.0394 1.05197
\(401\) −22.5470 −1.12594 −0.562971 0.826477i \(-0.690342\pi\)
−0.562971 + 0.826477i \(0.690342\pi\)
\(402\) 26.4510 1.31926
\(403\) 12.5207 0.623699
\(404\) −9.86603 −0.490853
\(405\) 0.273988 0.0136146
\(406\) −33.3899 −1.65711
\(407\) 8.26514 0.409688
\(408\) −0.809526 −0.0400775
\(409\) 28.8575 1.42691 0.713456 0.700700i \(-0.247129\pi\)
0.713456 + 0.700700i \(0.247129\pi\)
\(410\) 4.37598 0.216114
\(411\) −10.5945 −0.522586
\(412\) 3.34460 0.164777
\(413\) −25.4101 −1.25035
\(414\) 8.71652 0.428393
\(415\) 1.52115 0.0746705
\(416\) 28.5121 1.39792
\(417\) −14.2784 −0.699218
\(418\) −3.16589 −0.154849
\(419\) −1.85598 −0.0906707 −0.0453354 0.998972i \(-0.514436\pi\)
−0.0453354 + 0.998972i \(0.514436\pi\)
\(420\) 1.68085 0.0820171
\(421\) −27.4874 −1.33965 −0.669827 0.742517i \(-0.733632\pi\)
−0.669827 + 0.742517i \(0.733632\pi\)
\(422\) −9.67282 −0.470865
\(423\) −12.0261 −0.584730
\(424\) −2.71657 −0.131928
\(425\) −16.6036 −0.805391
\(426\) −14.8798 −0.720931
\(427\) −45.0570 −2.18046
\(428\) −22.3764 −1.08160
\(429\) 5.66034 0.273284
\(430\) 1.38986 0.0670252
\(431\) −12.9904 −0.625727 −0.312863 0.949798i \(-0.601288\pi\)
−0.312863 + 0.949798i \(0.601288\pi\)
\(432\) −20.7640 −0.999010
\(433\) −11.7942 −0.566793 −0.283397 0.959003i \(-0.591461\pi\)
−0.283397 + 0.959003i \(0.591461\pi\)
\(434\) 33.2974 1.59833
\(435\) 0.630474 0.0302289
\(436\) 20.2262 0.968659
\(437\) −2.14601 −0.102658
\(438\) 13.6303 0.651280
\(439\) −6.60344 −0.315165 −0.157582 0.987506i \(-0.550370\pi\)
−0.157582 + 0.987506i \(0.550370\pi\)
\(440\) −0.0759639 −0.00362144
\(441\) −35.4002 −1.68573
\(442\) −23.9367 −1.13855
\(443\) −3.92798 −0.186624 −0.0933120 0.995637i \(-0.529745\pi\)
−0.0933120 + 0.995637i \(0.529745\pi\)
\(444\) 9.30970 0.441819
\(445\) 0.0180842 0.000857275 0
\(446\) −21.9065 −1.03730
\(447\) −14.2000 −0.671637
\(448\) 34.1690 1.61433
\(449\) −13.5326 −0.638644 −0.319322 0.947646i \(-0.603455\pi\)
−0.319322 + 0.947646i \(0.603455\pi\)
\(450\) −20.1640 −0.950538
\(451\) 18.9517 0.892399
\(452\) 33.7397 1.58698
\(453\) 9.56632 0.449465
\(454\) 45.0242 2.11309
\(455\) −3.37345 −0.158150
\(456\) 0.242044 0.0113347
\(457\) 7.58845 0.354973 0.177486 0.984123i \(-0.443203\pi\)
0.177486 + 0.984123i \(0.443203\pi\)
\(458\) 46.2905 2.16301
\(459\) 16.3862 0.764843
\(460\) 0.758631 0.0353713
\(461\) −5.04183 −0.234822 −0.117411 0.993083i \(-0.537459\pi\)
−0.117411 + 0.993083i \(0.537459\pi\)
\(462\) 15.0531 0.700332
\(463\) 10.1341 0.470970 0.235485 0.971878i \(-0.424332\pi\)
0.235485 + 0.971878i \(0.424332\pi\)
\(464\) 14.6316 0.679256
\(465\) −0.628727 −0.0291565
\(466\) 19.9347 0.923457
\(467\) 22.4356 1.03820 0.519098 0.854715i \(-0.326268\pi\)
0.519098 + 0.854715i \(0.326268\pi\)
\(468\) −14.0577 −0.649817
\(469\) −68.2726 −3.15253
\(470\) −2.16440 −0.0998363
\(471\) 6.51033 0.299980
\(472\) 1.29351 0.0595387
\(473\) 6.01928 0.276767
\(474\) 28.1458 1.29278
\(475\) 4.96437 0.227781
\(476\) −30.7837 −1.41097
\(477\) 22.4118 1.02617
\(478\) 8.83990 0.404327
\(479\) −15.6650 −0.715752 −0.357876 0.933769i \(-0.616499\pi\)
−0.357876 + 0.933769i \(0.616499\pi\)
\(480\) −1.43174 −0.0653495
\(481\) −18.6845 −0.851940
\(482\) 12.3113 0.560762
\(483\) 10.2038 0.464288
\(484\) −15.7547 −0.716124
\(485\) −0.631259 −0.0286640
\(486\) 31.6893 1.43746
\(487\) 29.6945 1.34559 0.672793 0.739831i \(-0.265094\pi\)
0.672793 + 0.739831i \(0.265094\pi\)
\(488\) 2.29365 0.103828
\(489\) 5.56470 0.251644
\(490\) −6.37115 −0.287819
\(491\) −6.71702 −0.303135 −0.151567 0.988447i \(-0.548432\pi\)
−0.151567 + 0.988447i \(0.548432\pi\)
\(492\) 21.3468 0.962388
\(493\) −11.5467 −0.520039
\(494\) 7.15693 0.322005
\(495\) 0.626704 0.0281682
\(496\) −14.5911 −0.655159
\(497\) 38.4063 1.72276
\(498\) 15.3446 0.687607
\(499\) 27.2615 1.22039 0.610197 0.792250i \(-0.291090\pi\)
0.610197 + 0.792250i \(0.291090\pi\)
\(500\) −3.52248 −0.157530
\(501\) −0.821970 −0.0367229
\(502\) 14.4079 0.643055
\(503\) −14.3469 −0.639698 −0.319849 0.947469i \(-0.603632\pi\)
−0.319849 + 0.947469i \(0.603632\pi\)
\(504\) 2.53752 0.113030
\(505\) −0.994311 −0.0442463
\(506\) 6.79402 0.302031
\(507\) −0.218399 −0.00969944
\(508\) −27.7267 −1.23017
\(509\) −6.37551 −0.282590 −0.141295 0.989968i \(-0.545127\pi\)
−0.141295 + 0.989968i \(0.545127\pi\)
\(510\) 1.20198 0.0532246
\(511\) −35.1811 −1.55632
\(512\) −31.1063 −1.37472
\(513\) −4.89939 −0.216313
\(514\) 35.1442 1.55015
\(515\) 0.337073 0.0148532
\(516\) 6.78000 0.298473
\(517\) −9.37366 −0.412253
\(518\) −49.6894 −2.18323
\(519\) −13.7791 −0.604837
\(520\) 0.171727 0.00753073
\(521\) −15.5851 −0.682796 −0.341398 0.939919i \(-0.610900\pi\)
−0.341398 + 0.939919i \(0.610900\pi\)
\(522\) −14.0228 −0.613761
\(523\) −26.4795 −1.15787 −0.578933 0.815375i \(-0.696531\pi\)
−0.578933 + 0.815375i \(0.696531\pi\)
\(524\) 18.8636 0.824062
\(525\) −23.6045 −1.03018
\(526\) −22.8744 −0.997370
\(527\) 11.5148 0.501591
\(528\) −6.59633 −0.287069
\(529\) −18.3946 −0.799767
\(530\) 4.03356 0.175207
\(531\) −10.6715 −0.463103
\(532\) 9.20417 0.399051
\(533\) −42.8429 −1.85573
\(534\) 0.182424 0.00789426
\(535\) −2.25512 −0.0974973
\(536\) 3.47545 0.150116
\(537\) −7.77125 −0.335354
\(538\) −41.3416 −1.78236
\(539\) −27.5924 −1.18849
\(540\) 1.73197 0.0745322
\(541\) −9.54249 −0.410264 −0.205132 0.978734i \(-0.565762\pi\)
−0.205132 + 0.978734i \(0.565762\pi\)
\(542\) 7.82898 0.336283
\(543\) −2.02807 −0.0870329
\(544\) 26.2214 1.12423
\(545\) 2.03842 0.0873165
\(546\) −34.0296 −1.45633
\(547\) −18.2343 −0.779641 −0.389820 0.920891i \(-0.627463\pi\)
−0.389820 + 0.920891i \(0.627463\pi\)
\(548\) 20.5085 0.876079
\(549\) −18.9226 −0.807598
\(550\) −15.7166 −0.670160
\(551\) 3.45241 0.147078
\(552\) −0.519428 −0.0221083
\(553\) −72.6471 −3.08927
\(554\) 10.5408 0.447837
\(555\) 0.938244 0.0398263
\(556\) 27.6398 1.17219
\(557\) 6.84967 0.290230 0.145115 0.989415i \(-0.453645\pi\)
0.145115 + 0.989415i \(0.453645\pi\)
\(558\) 13.9839 0.591987
\(559\) −13.6074 −0.575533
\(560\) 3.93129 0.166127
\(561\) 5.20559 0.219780
\(562\) −34.7528 −1.46596
\(563\) −38.4048 −1.61857 −0.809284 0.587418i \(-0.800145\pi\)
−0.809284 + 0.587418i \(0.800145\pi\)
\(564\) −10.5583 −0.444586
\(565\) 3.40033 0.143053
\(566\) 7.14617 0.300376
\(567\) −7.13375 −0.299589
\(568\) −1.95509 −0.0820337
\(569\) −4.08204 −0.171128 −0.0855639 0.996333i \(-0.527269\pi\)
−0.0855639 + 0.996333i \(0.527269\pi\)
\(570\) −0.359386 −0.0150530
\(571\) −1.39252 −0.0582752 −0.0291376 0.999575i \(-0.509276\pi\)
−0.0291376 + 0.999575i \(0.509276\pi\)
\(572\) −10.9571 −0.458141
\(573\) 1.70621 0.0712778
\(574\) −113.936 −4.75560
\(575\) −10.6536 −0.444285
\(576\) 14.3500 0.597916
\(577\) −36.8132 −1.53255 −0.766277 0.642511i \(-0.777893\pi\)
−0.766277 + 0.642511i \(0.777893\pi\)
\(578\) 11.4418 0.475916
\(579\) 0.858952 0.0356968
\(580\) −1.22046 −0.0506766
\(581\) −39.6058 −1.64313
\(582\) −6.36780 −0.263954
\(583\) 17.4687 0.723479
\(584\) 1.79091 0.0741083
\(585\) −1.41675 −0.0585755
\(586\) 14.5679 0.601793
\(587\) 2.29919 0.0948978 0.0474489 0.998874i \(-0.484891\pi\)
0.0474489 + 0.998874i \(0.484891\pi\)
\(588\) −31.0796 −1.28170
\(589\) −3.44285 −0.141860
\(590\) −1.92060 −0.0790699
\(591\) −13.9658 −0.574478
\(592\) 21.7742 0.894913
\(593\) 29.5571 1.21377 0.606883 0.794791i \(-0.292420\pi\)
0.606883 + 0.794791i \(0.292420\pi\)
\(594\) 15.5109 0.636420
\(595\) −3.10243 −0.127187
\(596\) 27.4880 1.12595
\(597\) −0.770304 −0.0315264
\(598\) −15.3588 −0.628069
\(599\) −28.0205 −1.14488 −0.572442 0.819945i \(-0.694004\pi\)
−0.572442 + 0.819945i \(0.694004\pi\)
\(600\) 1.20160 0.0490550
\(601\) −30.6197 −1.24900 −0.624501 0.781024i \(-0.714698\pi\)
−0.624501 + 0.781024i \(0.714698\pi\)
\(602\) −36.1875 −1.47489
\(603\) −28.6725 −1.16763
\(604\) −18.5182 −0.753497
\(605\) −1.58778 −0.0645526
\(606\) −10.0301 −0.407444
\(607\) −0.931814 −0.0378212 −0.0189106 0.999821i \(-0.506020\pi\)
−0.0189106 + 0.999821i \(0.506020\pi\)
\(608\) −7.84005 −0.317956
\(609\) −16.4155 −0.665188
\(610\) −3.40560 −0.137889
\(611\) 21.1905 0.857275
\(612\) −12.9283 −0.522595
\(613\) −46.0062 −1.85817 −0.929086 0.369864i \(-0.879404\pi\)
−0.929086 + 0.369864i \(0.879404\pi\)
\(614\) 25.6821 1.03644
\(615\) 2.15136 0.0867512
\(616\) 1.97785 0.0796898
\(617\) −33.0705 −1.33137 −0.665685 0.746233i \(-0.731861\pi\)
−0.665685 + 0.746233i \(0.731861\pi\)
\(618\) 3.40022 0.136777
\(619\) 9.02535 0.362760 0.181380 0.983413i \(-0.441944\pi\)
0.181380 + 0.983413i \(0.441944\pi\)
\(620\) 1.21707 0.0488789
\(621\) 10.5141 0.421918
\(622\) −66.0564 −2.64862
\(623\) −0.470854 −0.0188644
\(624\) 14.9119 0.596955
\(625\) 24.4669 0.978675
\(626\) 38.6879 1.54628
\(627\) −1.55644 −0.0621583
\(628\) −12.6025 −0.502896
\(629\) −17.1834 −0.685146
\(630\) −3.76770 −0.150109
\(631\) −12.5967 −0.501465 −0.250733 0.968056i \(-0.580672\pi\)
−0.250733 + 0.968056i \(0.580672\pi\)
\(632\) 3.69813 0.147104
\(633\) −4.75544 −0.189012
\(634\) 1.96796 0.0781578
\(635\) −2.79433 −0.110890
\(636\) 19.6764 0.780220
\(637\) 62.3765 2.47145
\(638\) −10.9299 −0.432721
\(639\) 16.1295 0.638074
\(640\) −0.377000 −0.0149022
\(641\) 47.1585 1.86265 0.931324 0.364191i \(-0.118655\pi\)
0.931324 + 0.364191i \(0.118655\pi\)
\(642\) −22.7484 −0.897809
\(643\) −43.1064 −1.69995 −0.849976 0.526821i \(-0.823384\pi\)
−0.849976 + 0.526821i \(0.823384\pi\)
\(644\) −19.7522 −0.778347
\(645\) 0.683298 0.0269048
\(646\) 6.58193 0.258963
\(647\) 46.8352 1.84128 0.920640 0.390412i \(-0.127667\pi\)
0.920640 + 0.390412i \(0.127667\pi\)
\(648\) 0.363147 0.0142657
\(649\) −8.31781 −0.326503
\(650\) 35.5297 1.39359
\(651\) 16.3700 0.641590
\(652\) −10.7720 −0.421864
\(653\) −24.8394 −0.972039 −0.486020 0.873948i \(-0.661552\pi\)
−0.486020 + 0.873948i \(0.661552\pi\)
\(654\) 20.5625 0.804058
\(655\) 1.90110 0.0742823
\(656\) 49.9274 1.94934
\(657\) −14.7750 −0.576428
\(658\) 56.3538 2.19690
\(659\) 40.5713 1.58043 0.790217 0.612827i \(-0.209968\pi\)
0.790217 + 0.612827i \(0.209968\pi\)
\(660\) 0.550214 0.0214171
\(661\) −9.50686 −0.369774 −0.184887 0.982760i \(-0.559192\pi\)
−0.184887 + 0.982760i \(0.559192\pi\)
\(662\) −53.1735 −2.06665
\(663\) −11.7680 −0.457030
\(664\) 2.01615 0.0782418
\(665\) 0.927609 0.0359711
\(666\) −20.8681 −0.808623
\(667\) −7.40891 −0.286874
\(668\) 1.59115 0.0615634
\(669\) −10.7699 −0.416387
\(670\) −5.16033 −0.199361
\(671\) −14.7491 −0.569382
\(672\) 37.2777 1.43802
\(673\) −30.0316 −1.15763 −0.578816 0.815458i \(-0.696485\pi\)
−0.578816 + 0.815458i \(0.696485\pi\)
\(674\) 12.9020 0.496967
\(675\) −24.3224 −0.936170
\(676\) 0.422771 0.0162604
\(677\) −13.3937 −0.514761 −0.257380 0.966310i \(-0.582859\pi\)
−0.257380 + 0.966310i \(0.582859\pi\)
\(678\) 34.3007 1.31731
\(679\) 16.4359 0.630752
\(680\) 0.157930 0.00605635
\(681\) 22.1352 0.848224
\(682\) 10.8997 0.417370
\(683\) −2.22871 −0.0852793 −0.0426396 0.999091i \(-0.513577\pi\)
−0.0426396 + 0.999091i \(0.513577\pi\)
\(684\) 3.86548 0.147801
\(685\) 2.06687 0.0789711
\(686\) 98.1834 3.74866
\(687\) 22.7577 0.868262
\(688\) 15.8575 0.604563
\(689\) −39.4904 −1.50447
\(690\) 0.771245 0.0293608
\(691\) 25.7189 0.978391 0.489196 0.872174i \(-0.337290\pi\)
0.489196 + 0.872174i \(0.337290\pi\)
\(692\) 26.6733 1.01397
\(693\) −16.3173 −0.619843
\(694\) 32.5616 1.23602
\(695\) 2.78558 0.105663
\(696\) 0.835636 0.0316747
\(697\) −39.4009 −1.49241
\(698\) 69.7997 2.64196
\(699\) 9.80048 0.370688
\(700\) 45.6929 1.72703
\(701\) 10.8324 0.409135 0.204567 0.978853i \(-0.434421\pi\)
0.204567 + 0.978853i \(0.434421\pi\)
\(702\) −35.0646 −1.32343
\(703\) 5.13774 0.193773
\(704\) 11.1850 0.421550
\(705\) −1.06408 −0.0400757
\(706\) 11.4611 0.431345
\(707\) 25.8886 0.973640
\(708\) −9.36903 −0.352110
\(709\) −7.60880 −0.285755 −0.142877 0.989740i \(-0.545635\pi\)
−0.142877 + 0.989740i \(0.545635\pi\)
\(710\) 2.90291 0.108944
\(711\) −30.5097 −1.14420
\(712\) 0.0239690 0.000898277 0
\(713\) 7.38838 0.276697
\(714\) −31.2956 −1.17121
\(715\) −1.10428 −0.0412976
\(716\) 15.0434 0.562198
\(717\) 4.34595 0.162303
\(718\) −45.9430 −1.71458
\(719\) −49.0630 −1.82974 −0.914870 0.403749i \(-0.867707\pi\)
−0.914870 + 0.403749i \(0.867707\pi\)
\(720\) 1.65103 0.0615301
\(721\) −8.77628 −0.326846
\(722\) −1.96796 −0.0732400
\(723\) 6.05257 0.225098
\(724\) 3.92589 0.145905
\(725\) 17.1391 0.636529
\(726\) −16.0167 −0.594435
\(727\) −38.6064 −1.43183 −0.715915 0.698187i \(-0.753990\pi\)
−0.715915 + 0.698187i \(0.753990\pi\)
\(728\) −4.47121 −0.165714
\(729\) 11.2246 0.415727
\(730\) −2.65913 −0.0984189
\(731\) −12.5142 −0.462854
\(732\) −16.6131 −0.614038
\(733\) −21.7522 −0.803436 −0.401718 0.915763i \(-0.631587\pi\)
−0.401718 + 0.915763i \(0.631587\pi\)
\(734\) 1.73783 0.0641444
\(735\) −3.13224 −0.115535
\(736\) 16.8248 0.620171
\(737\) −22.3485 −0.823219
\(738\) −47.8498 −1.76138
\(739\) 10.7551 0.395632 0.197816 0.980239i \(-0.436615\pi\)
0.197816 + 0.980239i \(0.436615\pi\)
\(740\) −1.81623 −0.0667659
\(741\) 3.51856 0.129257
\(742\) −105.020 −3.85542
\(743\) 1.46444 0.0537253 0.0268626 0.999639i \(-0.491448\pi\)
0.0268626 + 0.999639i \(0.491448\pi\)
\(744\) −0.833321 −0.0305510
\(745\) 2.77028 0.101495
\(746\) −9.95961 −0.364647
\(747\) −16.6333 −0.608580
\(748\) −10.0768 −0.368446
\(749\) 58.7159 2.14543
\(750\) −3.58105 −0.130762
\(751\) 40.9213 1.49324 0.746619 0.665252i \(-0.231676\pi\)
0.746619 + 0.665252i \(0.231676\pi\)
\(752\) −24.6945 −0.900517
\(753\) 7.08333 0.258131
\(754\) 24.7087 0.899837
\(755\) −1.86629 −0.0679214
\(756\) −45.0948 −1.64008
\(757\) 36.9995 1.34477 0.672384 0.740202i \(-0.265270\pi\)
0.672384 + 0.740202i \(0.265270\pi\)
\(758\) −5.45635 −0.198184
\(759\) 3.34014 0.121239
\(760\) −0.0472203 −0.00171286
\(761\) 51.8764 1.88052 0.940259 0.340460i \(-0.110583\pi\)
0.940259 + 0.340460i \(0.110583\pi\)
\(762\) −28.1877 −1.02113
\(763\) −53.0738 −1.92140
\(764\) −3.30283 −0.119492
\(765\) −1.30293 −0.0471075
\(766\) −20.3115 −0.733884
\(767\) 18.8036 0.678958
\(768\) −17.2567 −0.622696
\(769\) −33.2617 −1.19945 −0.599724 0.800207i \(-0.704723\pi\)
−0.599724 + 0.800207i \(0.704723\pi\)
\(770\) −2.93670 −0.105831
\(771\) 17.2779 0.622249
\(772\) −1.66274 −0.0598433
\(773\) −19.9933 −0.719109 −0.359554 0.933124i \(-0.617071\pi\)
−0.359554 + 0.933124i \(0.617071\pi\)
\(774\) −15.1977 −0.546270
\(775\) −17.0916 −0.613948
\(776\) −0.836677 −0.0300350
\(777\) −24.4288 −0.876378
\(778\) 19.8628 0.712117
\(779\) 11.7806 0.422085
\(780\) −1.24384 −0.0445365
\(781\) 12.5720 0.449862
\(782\) −14.1249 −0.505105
\(783\) −16.9147 −0.604483
\(784\) −72.6911 −2.59611
\(785\) −1.27010 −0.0453318
\(786\) 19.1773 0.684032
\(787\) 54.5076 1.94299 0.971493 0.237066i \(-0.0761859\pi\)
0.971493 + 0.237066i \(0.0761859\pi\)
\(788\) 27.0347 0.963072
\(789\) −11.2457 −0.400358
\(790\) −5.49097 −0.195360
\(791\) −88.5335 −3.14789
\(792\) 0.830639 0.0295155
\(793\) 33.3424 1.18402
\(794\) −8.30220 −0.294634
\(795\) 1.98301 0.0703303
\(796\) 1.49113 0.0528519
\(797\) −41.5152 −1.47055 −0.735273 0.677772i \(-0.762946\pi\)
−0.735273 + 0.677772i \(0.762946\pi\)
\(798\) 9.35722 0.331242
\(799\) 19.4880 0.689437
\(800\) −38.9209 −1.37606
\(801\) −0.197745 −0.00698697
\(802\) 44.3716 1.56682
\(803\) −11.5163 −0.406400
\(804\) −25.1730 −0.887783
\(805\) −1.99066 −0.0701614
\(806\) −24.6402 −0.867915
\(807\) −20.3247 −0.715465
\(808\) −1.31787 −0.0463625
\(809\) 36.3019 1.27631 0.638154 0.769909i \(-0.279698\pi\)
0.638154 + 0.769909i \(0.279698\pi\)
\(810\) −0.539199 −0.0189455
\(811\) −7.54260 −0.264856 −0.132428 0.991193i \(-0.542277\pi\)
−0.132428 + 0.991193i \(0.542277\pi\)
\(812\) 31.7766 1.11514
\(813\) 3.84895 0.134989
\(814\) −16.2655 −0.570105
\(815\) −1.08562 −0.0380275
\(816\) 13.7139 0.480082
\(817\) 3.74167 0.130905
\(818\) −56.7905 −1.98563
\(819\) 36.8876 1.28896
\(820\) −4.16455 −0.145432
\(821\) −46.0521 −1.60723 −0.803614 0.595151i \(-0.797092\pi\)
−0.803614 + 0.595151i \(0.797092\pi\)
\(822\) 20.8495 0.727210
\(823\) −23.4774 −0.818370 −0.409185 0.912451i \(-0.634187\pi\)
−0.409185 + 0.912451i \(0.634187\pi\)
\(824\) 0.446760 0.0155636
\(825\) −7.72676 −0.269011
\(826\) 50.0061 1.73993
\(827\) −5.68901 −0.197826 −0.0989132 0.995096i \(-0.531537\pi\)
−0.0989132 + 0.995096i \(0.531537\pi\)
\(828\) −8.29536 −0.288284
\(829\) −0.0641062 −0.00222650 −0.00111325 0.999999i \(-0.500354\pi\)
−0.00111325 + 0.999999i \(0.500354\pi\)
\(830\) −2.99357 −0.103908
\(831\) 5.18218 0.179768
\(832\) −25.2852 −0.876607
\(833\) 57.3652 1.98758
\(834\) 28.0994 0.973004
\(835\) 0.160358 0.00554942
\(836\) 3.01292 0.104204
\(837\) 16.8679 0.583039
\(838\) 3.65251 0.126174
\(839\) −27.8242 −0.960599 −0.480300 0.877104i \(-0.659472\pi\)
−0.480300 + 0.877104i \(0.659472\pi\)
\(840\) 0.224522 0.00774675
\(841\) −17.0808 −0.588994
\(842\) 54.0942 1.86421
\(843\) −17.0855 −0.588455
\(844\) 9.20546 0.316865
\(845\) 0.0426075 0.00146574
\(846\) 23.6670 0.813687
\(847\) 41.3406 1.42048
\(848\) 46.0205 1.58035
\(849\) 3.51327 0.120575
\(850\) 32.6752 1.12075
\(851\) −11.0256 −0.377954
\(852\) 14.1609 0.485144
\(853\) −40.4409 −1.38467 −0.692335 0.721577i \(-0.743418\pi\)
−0.692335 + 0.721577i \(0.743418\pi\)
\(854\) 88.6705 3.03424
\(855\) 0.389569 0.0133230
\(856\) −2.98896 −0.102160
\(857\) −48.8738 −1.66950 −0.834749 0.550631i \(-0.814387\pi\)
−0.834749 + 0.550631i \(0.814387\pi\)
\(858\) −11.1393 −0.380291
\(859\) −9.65359 −0.329376 −0.164688 0.986346i \(-0.552662\pi\)
−0.164688 + 0.986346i \(0.552662\pi\)
\(860\) −1.32271 −0.0451041
\(861\) −56.0143 −1.90896
\(862\) 25.5647 0.870736
\(863\) 50.9009 1.73269 0.866344 0.499448i \(-0.166464\pi\)
0.866344 + 0.499448i \(0.166464\pi\)
\(864\) 38.4115 1.30678
\(865\) 2.68817 0.0914006
\(866\) 23.2105 0.788726
\(867\) 5.62513 0.191039
\(868\) −31.6886 −1.07558
\(869\) −23.7805 −0.806698
\(870\) −1.24075 −0.0420653
\(871\) 50.5220 1.71187
\(872\) 2.70175 0.0914927
\(873\) 6.90260 0.233618
\(874\) 4.22327 0.142854
\(875\) 9.24304 0.312472
\(876\) −12.9717 −0.438274
\(877\) −33.6231 −1.13537 −0.567686 0.823245i \(-0.692161\pi\)
−0.567686 + 0.823245i \(0.692161\pi\)
\(878\) 12.9953 0.438571
\(879\) 7.16198 0.241568
\(880\) 1.28688 0.0433807
\(881\) 3.15075 0.106151 0.0530757 0.998590i \(-0.483098\pi\)
0.0530757 + 0.998590i \(0.483098\pi\)
\(882\) 69.6663 2.34579
\(883\) −48.8822 −1.64502 −0.822508 0.568753i \(-0.807426\pi\)
−0.822508 + 0.568753i \(0.807426\pi\)
\(884\) 22.7801 0.766178
\(885\) −0.944223 −0.0317397
\(886\) 7.73012 0.259698
\(887\) 16.2806 0.546648 0.273324 0.961922i \(-0.411877\pi\)
0.273324 + 0.961922i \(0.411877\pi\)
\(888\) 1.24356 0.0417311
\(889\) 72.7552 2.44013
\(890\) −0.0355891 −0.00119295
\(891\) −2.33518 −0.0782316
\(892\) 20.8480 0.698044
\(893\) −5.82681 −0.194987
\(894\) 27.9451 0.934622
\(895\) 1.51609 0.0506774
\(896\) 9.81582 0.327924
\(897\) −7.55085 −0.252116
\(898\) 26.6317 0.888711
\(899\) −11.8861 −0.396425
\(900\) 19.1897 0.639657
\(901\) −36.3177 −1.20992
\(902\) −37.2962 −1.24183
\(903\) −17.7908 −0.592041
\(904\) 4.50684 0.149895
\(905\) 0.395657 0.0131521
\(906\) −18.8262 −0.625457
\(907\) 31.3658 1.04148 0.520742 0.853714i \(-0.325655\pi\)
0.520742 + 0.853714i \(0.325655\pi\)
\(908\) −42.8488 −1.42199
\(909\) 10.8725 0.360616
\(910\) 6.63883 0.220075
\(911\) −3.23866 −0.107302 −0.0536509 0.998560i \(-0.517086\pi\)
−0.0536509 + 0.998560i \(0.517086\pi\)
\(912\) −4.10038 −0.135777
\(913\) −12.9647 −0.429068
\(914\) −14.9338 −0.493965
\(915\) −1.67429 −0.0553503
\(916\) −44.0539 −1.45558
\(917\) −49.4985 −1.63458
\(918\) −32.2475 −1.06433
\(919\) 44.9041 1.48125 0.740625 0.671918i \(-0.234529\pi\)
0.740625 + 0.671918i \(0.234529\pi\)
\(920\) 0.101335 0.00334092
\(921\) 12.6261 0.416043
\(922\) 9.92214 0.326768
\(923\) −28.4208 −0.935483
\(924\) −14.3258 −0.471283
\(925\) 25.5056 0.838620
\(926\) −19.9435 −0.655383
\(927\) −3.68578 −0.121057
\(928\) −27.0671 −0.888521
\(929\) 43.0558 1.41261 0.706307 0.707906i \(-0.250360\pi\)
0.706307 + 0.707906i \(0.250360\pi\)
\(930\) 1.23731 0.0405730
\(931\) −17.1519 −0.562130
\(932\) −18.9715 −0.621433
\(933\) −32.4753 −1.06319
\(934\) −44.1524 −1.44471
\(935\) −1.01556 −0.0332123
\(936\) −1.87778 −0.0613771
\(937\) 21.2253 0.693399 0.346699 0.937976i \(-0.387302\pi\)
0.346699 + 0.937976i \(0.387302\pi\)
\(938\) 134.358 4.38694
\(939\) 19.0201 0.620697
\(940\) 2.05982 0.0671840
\(941\) 9.73246 0.317269 0.158635 0.987337i \(-0.449291\pi\)
0.158635 + 0.987337i \(0.449291\pi\)
\(942\) −12.8121 −0.417440
\(943\) −25.2814 −0.823274
\(944\) −21.9129 −0.713205
\(945\) −4.54472 −0.147840
\(946\) −11.8457 −0.385137
\(947\) −36.0309 −1.17085 −0.585423 0.810728i \(-0.699071\pi\)
−0.585423 + 0.810728i \(0.699071\pi\)
\(948\) −26.7859 −0.869967
\(949\) 26.0341 0.845104
\(950\) −9.76970 −0.316971
\(951\) 0.967508 0.0313736
\(952\) −4.11199 −0.133270
\(953\) 17.6960 0.573228 0.286614 0.958046i \(-0.407470\pi\)
0.286614 + 0.958046i \(0.407470\pi\)
\(954\) −44.1056 −1.42797
\(955\) −0.332864 −0.0107712
\(956\) −8.41278 −0.272089
\(957\) −5.37348 −0.173700
\(958\) 30.8281 0.996012
\(959\) −53.8145 −1.73776
\(960\) 1.26970 0.0409794
\(961\) −19.1468 −0.617638
\(962\) 36.7704 1.18553
\(963\) 24.6590 0.794624
\(964\) −11.7164 −0.377360
\(965\) −0.167573 −0.00539437
\(966\) −20.0807 −0.646085
\(967\) 1.36674 0.0439515 0.0219757 0.999759i \(-0.493004\pi\)
0.0219757 + 0.999759i \(0.493004\pi\)
\(968\) −2.10446 −0.0676400
\(969\) 3.23587 0.103951
\(970\) 1.24229 0.0398877
\(971\) 43.9793 1.41136 0.705682 0.708529i \(-0.250641\pi\)
0.705682 + 0.708529i \(0.250641\pi\)
\(972\) −30.1582 −0.967324
\(973\) −72.5273 −2.32512
\(974\) −58.4377 −1.87246
\(975\) 17.4674 0.559405
\(976\) −38.8558 −1.24375
\(977\) 14.0611 0.449854 0.224927 0.974376i \(-0.427786\pi\)
0.224927 + 0.974376i \(0.427786\pi\)
\(978\) −10.9511 −0.350178
\(979\) −0.154131 −0.00492603
\(980\) 6.06332 0.193686
\(981\) −22.2895 −0.711648
\(982\) 13.2188 0.421830
\(983\) −56.3939 −1.79869 −0.899344 0.437242i \(-0.855955\pi\)
−0.899344 + 0.437242i \(0.855955\pi\)
\(984\) 2.85143 0.0909003
\(985\) 2.72460 0.0868129
\(986\) 22.7236 0.723666
\(987\) 27.7052 0.881866
\(988\) −6.81113 −0.216691
\(989\) −8.02967 −0.255329
\(990\) −1.23333 −0.0391978
\(991\) 24.6063 0.781644 0.390822 0.920466i \(-0.372191\pi\)
0.390822 + 0.920466i \(0.372191\pi\)
\(992\) 26.9921 0.857000
\(993\) −26.1416 −0.829580
\(994\) −75.5821 −2.39732
\(995\) 0.150279 0.00476415
\(996\) −14.6032 −0.462719
\(997\) 39.5072 1.25120 0.625602 0.780142i \(-0.284853\pi\)
0.625602 + 0.780142i \(0.284853\pi\)
\(998\) −53.6497 −1.69825
\(999\) −25.1718 −0.796400
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 \(a_p\))