Properties

Label 6001.2.a.b.1.17
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.18122 q^{2}\) \(+1.64876 q^{3}\) \(+2.75771 q^{4}\) \(-2.64324 q^{5}\) \(-3.59630 q^{6}\) \(-4.67385 q^{7}\) \(-1.65274 q^{8}\) \(-0.281605 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.18122 q^{2}\) \(+1.64876 q^{3}\) \(+2.75771 q^{4}\) \(-2.64324 q^{5}\) \(-3.59630 q^{6}\) \(-4.67385 q^{7}\) \(-1.65274 q^{8}\) \(-0.281605 q^{9}\) \(+5.76549 q^{10}\) \(+5.50049 q^{11}\) \(+4.54680 q^{12}\) \(-1.10509 q^{13}\) \(+10.1947 q^{14}\) \(-4.35806 q^{15}\) \(-1.91044 q^{16}\) \(+1.00000 q^{17}\) \(+0.614241 q^{18}\) \(-7.14625 q^{19}\) \(-7.28931 q^{20}\) \(-7.70604 q^{21}\) \(-11.9978 q^{22}\) \(+4.56494 q^{23}\) \(-2.72496 q^{24}\) \(+1.98674 q^{25}\) \(+2.41044 q^{26}\) \(-5.41056 q^{27}\) \(-12.8891 q^{28}\) \(+5.65182 q^{29}\) \(+9.50589 q^{30}\) \(+7.52303 q^{31}\) \(+7.47257 q^{32}\) \(+9.06897 q^{33}\) \(-2.18122 q^{34}\) \(+12.3541 q^{35}\) \(-0.776585 q^{36}\) \(-9.88532 q^{37}\) \(+15.5875 q^{38}\) \(-1.82202 q^{39}\) \(+4.36859 q^{40}\) \(+9.71363 q^{41}\) \(+16.8086 q^{42}\) \(+6.36697 q^{43}\) \(+15.1688 q^{44}\) \(+0.744350 q^{45}\) \(-9.95713 q^{46}\) \(-10.8208 q^{47}\) \(-3.14985 q^{48}\) \(+14.8449 q^{49}\) \(-4.33351 q^{50}\) \(+1.64876 q^{51}\) \(-3.04752 q^{52}\) \(+8.76412 q^{53}\) \(+11.8016 q^{54}\) \(-14.5391 q^{55}\) \(+7.72466 q^{56}\) \(-11.7824 q^{57}\) \(-12.3278 q^{58}\) \(-9.82363 q^{59}\) \(-12.0183 q^{60}\) \(+1.13872 q^{61}\) \(-16.4094 q^{62}\) \(+1.31618 q^{63}\) \(-12.4784 q^{64}\) \(+2.92102 q^{65}\) \(-19.7814 q^{66}\) \(+12.9490 q^{67}\) \(+2.75771 q^{68}\) \(+7.52647 q^{69}\) \(-26.9471 q^{70}\) \(+3.21895 q^{71}\) \(+0.465419 q^{72}\) \(+9.53275 q^{73}\) \(+21.5620 q^{74}\) \(+3.27565 q^{75}\) \(-19.7073 q^{76}\) \(-25.7085 q^{77}\) \(+3.97423 q^{78}\) \(-7.90519 q^{79}\) \(+5.04976 q^{80}\) \(-8.07588 q^{81}\) \(-21.1875 q^{82}\) \(-4.89734 q^{83}\) \(-21.2510 q^{84}\) \(-2.64324 q^{85}\) \(-13.8877 q^{86}\) \(+9.31846 q^{87}\) \(-9.09088 q^{88}\) \(-13.7981 q^{89}\) \(-1.62359 q^{90}\) \(+5.16503 q^{91}\) \(+12.5888 q^{92}\) \(+12.4036 q^{93}\) \(+23.6026 q^{94}\) \(+18.8893 q^{95}\) \(+12.3204 q^{96}\) \(+11.6986 q^{97}\) \(-32.3799 q^{98}\) \(-1.54896 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18122 −1.54235 −0.771177 0.636621i \(-0.780332\pi\)
−0.771177 + 0.636621i \(0.780332\pi\)
\(3\) 1.64876 0.951910 0.475955 0.879470i \(-0.342103\pi\)
0.475955 + 0.879470i \(0.342103\pi\)
\(4\) 2.75771 1.37886
\(5\) −2.64324 −1.18209 −0.591047 0.806637i \(-0.701285\pi\)
−0.591047 + 0.806637i \(0.701285\pi\)
\(6\) −3.59630 −1.46818
\(7\) −4.67385 −1.76655 −0.883275 0.468856i \(-0.844666\pi\)
−0.883275 + 0.468856i \(0.844666\pi\)
\(8\) −1.65274 −0.584332
\(9\) −0.281605 −0.0938682
\(10\) 5.76549 1.82321
\(11\) 5.50049 1.65846 0.829231 0.558907i \(-0.188779\pi\)
0.829231 + 0.558907i \(0.188779\pi\)
\(12\) 4.54680 1.31255
\(13\) −1.10509 −0.306497 −0.153248 0.988188i \(-0.548973\pi\)
−0.153248 + 0.988188i \(0.548973\pi\)
\(14\) 10.1947 2.72465
\(15\) −4.35806 −1.12525
\(16\) −1.91044 −0.477610
\(17\) 1.00000 0.242536
\(18\) 0.614241 0.144778
\(19\) −7.14625 −1.63946 −0.819731 0.572748i \(-0.805877\pi\)
−0.819731 + 0.572748i \(0.805877\pi\)
\(20\) −7.28931 −1.62994
\(21\) −7.70604 −1.68160
\(22\) −11.9978 −2.55793
\(23\) 4.56494 0.951856 0.475928 0.879484i \(-0.342112\pi\)
0.475928 + 0.879484i \(0.342112\pi\)
\(24\) −2.72496 −0.556231
\(25\) 1.98674 0.397348
\(26\) 2.41044 0.472727
\(27\) −5.41056 −1.04126
\(28\) −12.8891 −2.43582
\(29\) 5.65182 1.04952 0.524758 0.851252i \(-0.324156\pi\)
0.524758 + 0.851252i \(0.324156\pi\)
\(30\) 9.50589 1.73553
\(31\) 7.52303 1.35118 0.675588 0.737280i \(-0.263890\pi\)
0.675588 + 0.737280i \(0.263890\pi\)
\(32\) 7.47257 1.32098
\(33\) 9.06897 1.57870
\(34\) −2.18122 −0.374076
\(35\) 12.3541 2.08823
\(36\) −0.776585 −0.129431
\(37\) −9.88532 −1.62514 −0.812568 0.582866i \(-0.801931\pi\)
−0.812568 + 0.582866i \(0.801931\pi\)
\(38\) 15.5875 2.52863
\(39\) −1.82202 −0.291757
\(40\) 4.36859 0.690735
\(41\) 9.71363 1.51701 0.758507 0.651665i \(-0.225929\pi\)
0.758507 + 0.651665i \(0.225929\pi\)
\(42\) 16.8086 2.59362
\(43\) 6.36697 0.970954 0.485477 0.874250i \(-0.338646\pi\)
0.485477 + 0.874250i \(0.338646\pi\)
\(44\) 15.1688 2.28678
\(45\) 0.744350 0.110961
\(46\) −9.95713 −1.46810
\(47\) −10.8208 −1.57838 −0.789189 0.614151i \(-0.789499\pi\)
−0.789189 + 0.614151i \(0.789499\pi\)
\(48\) −3.14985 −0.454642
\(49\) 14.8449 2.12070
\(50\) −4.33351 −0.612851
\(51\) 1.64876 0.230872
\(52\) −3.04752 −0.422615
\(53\) 8.76412 1.20385 0.601923 0.798554i \(-0.294402\pi\)
0.601923 + 0.798554i \(0.294402\pi\)
\(54\) 11.8016 1.60600
\(55\) −14.5391 −1.96046
\(56\) 7.72466 1.03225
\(57\) −11.7824 −1.56062
\(58\) −12.3278 −1.61873
\(59\) −9.82363 −1.27893 −0.639464 0.768821i \(-0.720844\pi\)
−0.639464 + 0.768821i \(0.720844\pi\)
\(60\) −12.0183 −1.55155
\(61\) 1.13872 0.145799 0.0728993 0.997339i \(-0.476775\pi\)
0.0728993 + 0.997339i \(0.476775\pi\)
\(62\) −16.4094 −2.08399
\(63\) 1.31618 0.165823
\(64\) −12.4784 −1.55980
\(65\) 2.92102 0.362308
\(66\) −19.7814 −2.43492
\(67\) 12.9490 1.58197 0.790983 0.611838i \(-0.209569\pi\)
0.790983 + 0.611838i \(0.209569\pi\)
\(68\) 2.75771 0.334422
\(69\) 7.52647 0.906080
\(70\) −26.9471 −3.22079
\(71\) 3.21895 0.382019 0.191010 0.981588i \(-0.438824\pi\)
0.191010 + 0.981588i \(0.438824\pi\)
\(72\) 0.465419 0.0548502
\(73\) 9.53275 1.11572 0.557862 0.829934i \(-0.311622\pi\)
0.557862 + 0.829934i \(0.311622\pi\)
\(74\) 21.5620 2.50654
\(75\) 3.27565 0.378239
\(76\) −19.7073 −2.26058
\(77\) −25.7085 −2.92975
\(78\) 3.97423 0.449993
\(79\) −7.90519 −0.889404 −0.444702 0.895679i \(-0.646690\pi\)
−0.444702 + 0.895679i \(0.646690\pi\)
\(80\) 5.04976 0.564581
\(81\) −8.07588 −0.897321
\(82\) −21.1875 −2.33977
\(83\) −4.89734 −0.537552 −0.268776 0.963203i \(-0.586619\pi\)
−0.268776 + 0.963203i \(0.586619\pi\)
\(84\) −21.2510 −2.31868
\(85\) −2.64324 −0.286700
\(86\) −13.8877 −1.49755
\(87\) 9.31846 0.999044
\(88\) −9.09088 −0.969091
\(89\) −13.7981 −1.46259 −0.731295 0.682061i \(-0.761084\pi\)
−0.731295 + 0.682061i \(0.761084\pi\)
\(90\) −1.62359 −0.171141
\(91\) 5.16503 0.541442
\(92\) 12.5888 1.31247
\(93\) 12.4036 1.28620
\(94\) 23.6026 2.43442
\(95\) 18.8893 1.93800
\(96\) 12.3204 1.25745
\(97\) 11.6986 1.18782 0.593909 0.804532i \(-0.297584\pi\)
0.593909 + 0.804532i \(0.297584\pi\)
\(98\) −32.3799 −3.27087
\(99\) −1.54896 −0.155677
\(100\) 5.47886 0.547886
\(101\) −11.4408 −1.13841 −0.569203 0.822197i \(-0.692748\pi\)
−0.569203 + 0.822197i \(0.692748\pi\)
\(102\) −3.59630 −0.356086
\(103\) −0.169037 −0.0166557 −0.00832787 0.999965i \(-0.502651\pi\)
−0.00832787 + 0.999965i \(0.502651\pi\)
\(104\) 1.82643 0.179096
\(105\) 20.3689 1.98781
\(106\) −19.1165 −1.85676
\(107\) 8.09262 0.782343 0.391171 0.920318i \(-0.372070\pi\)
0.391171 + 0.920318i \(0.372070\pi\)
\(108\) −14.9208 −1.43575
\(109\) −13.0366 −1.24868 −0.624342 0.781151i \(-0.714633\pi\)
−0.624342 + 0.781151i \(0.714633\pi\)
\(110\) 31.7131 3.02372
\(111\) −16.2985 −1.54698
\(112\) 8.92912 0.843723
\(113\) 9.19528 0.865020 0.432510 0.901629i \(-0.357628\pi\)
0.432510 + 0.901629i \(0.357628\pi\)
\(114\) 25.7000 2.40703
\(115\) −12.0662 −1.12518
\(116\) 15.5861 1.44713
\(117\) 0.311199 0.0287703
\(118\) 21.4275 1.97256
\(119\) −4.67385 −0.428451
\(120\) 7.20274 0.657518
\(121\) 19.2554 1.75049
\(122\) −2.48381 −0.224873
\(123\) 16.0154 1.44406
\(124\) 20.7464 1.86308
\(125\) 7.96478 0.712392
\(126\) −2.87087 −0.255758
\(127\) 0.175459 0.0155695 0.00778474 0.999970i \(-0.497522\pi\)
0.00778474 + 0.999970i \(0.497522\pi\)
\(128\) 12.2730 1.08479
\(129\) 10.4976 0.924260
\(130\) −6.37139 −0.558808
\(131\) 9.63318 0.841655 0.420827 0.907141i \(-0.361740\pi\)
0.420827 + 0.907141i \(0.361740\pi\)
\(132\) 25.0096 2.17681
\(133\) 33.4005 2.89619
\(134\) −28.2445 −2.43995
\(135\) 14.3014 1.23087
\(136\) −1.65274 −0.141721
\(137\) 15.7231 1.34332 0.671658 0.740861i \(-0.265582\pi\)
0.671658 + 0.740861i \(0.265582\pi\)
\(138\) −16.4169 −1.39750
\(139\) −11.9971 −1.01758 −0.508789 0.860891i \(-0.669907\pi\)
−0.508789 + 0.860891i \(0.669907\pi\)
\(140\) 34.0692 2.87937
\(141\) −17.8409 −1.50247
\(142\) −7.02124 −0.589209
\(143\) −6.07854 −0.508313
\(144\) 0.537989 0.0448324
\(145\) −14.9391 −1.24063
\(146\) −20.7930 −1.72084
\(147\) 24.4756 2.01871
\(148\) −27.2609 −2.24083
\(149\) −2.56632 −0.210241 −0.105120 0.994459i \(-0.533523\pi\)
−0.105120 + 0.994459i \(0.533523\pi\)
\(150\) −7.14490 −0.583379
\(151\) −18.9500 −1.54213 −0.771065 0.636756i \(-0.780276\pi\)
−0.771065 + 0.636756i \(0.780276\pi\)
\(152\) 11.8109 0.957990
\(153\) −0.281605 −0.0227664
\(154\) 56.0758 4.51872
\(155\) −19.8852 −1.59722
\(156\) −5.02462 −0.402292
\(157\) 6.29363 0.502287 0.251143 0.967950i \(-0.419193\pi\)
0.251143 + 0.967950i \(0.419193\pi\)
\(158\) 17.2430 1.37178
\(159\) 14.4499 1.14595
\(160\) −19.7518 −1.56152
\(161\) −21.3358 −1.68150
\(162\) 17.6153 1.38399
\(163\) −11.1721 −0.875066 −0.437533 0.899202i \(-0.644148\pi\)
−0.437533 + 0.899202i \(0.644148\pi\)
\(164\) 26.7874 2.09174
\(165\) −23.9715 −1.86618
\(166\) 10.6822 0.829096
\(167\) 14.1528 1.09518 0.547589 0.836748i \(-0.315546\pi\)
0.547589 + 0.836748i \(0.315546\pi\)
\(168\) 12.7361 0.982610
\(169\) −11.7788 −0.906060
\(170\) 5.76549 0.442193
\(171\) 2.01242 0.153894
\(172\) 17.5583 1.33881
\(173\) 18.4078 1.39952 0.699761 0.714377i \(-0.253290\pi\)
0.699761 + 0.714377i \(0.253290\pi\)
\(174\) −20.3256 −1.54088
\(175\) −9.28572 −0.701935
\(176\) −10.5084 −0.792098
\(177\) −16.1968 −1.21742
\(178\) 30.0966 2.25583
\(179\) −18.7020 −1.39785 −0.698927 0.715193i \(-0.746339\pi\)
−0.698927 + 0.715193i \(0.746339\pi\)
\(180\) 2.05270 0.153000
\(181\) −11.6832 −0.868403 −0.434201 0.900816i \(-0.642969\pi\)
−0.434201 + 0.900816i \(0.642969\pi\)
\(182\) −11.2661 −0.835096
\(183\) 1.87748 0.138787
\(184\) −7.54466 −0.556199
\(185\) 26.1293 1.92107
\(186\) −27.0550 −1.98377
\(187\) 5.50049 0.402236
\(188\) −29.8407 −2.17636
\(189\) 25.2882 1.83944
\(190\) −41.2017 −2.98908
\(191\) −7.32065 −0.529704 −0.264852 0.964289i \(-0.585323\pi\)
−0.264852 + 0.964289i \(0.585323\pi\)
\(192\) −20.5739 −1.48479
\(193\) −0.631958 −0.0454894 −0.0227447 0.999741i \(-0.507240\pi\)
−0.0227447 + 0.999741i \(0.507240\pi\)
\(194\) −25.5173 −1.83204
\(195\) 4.81605 0.344885
\(196\) 40.9379 2.92414
\(197\) 10.9726 0.781762 0.390881 0.920441i \(-0.372170\pi\)
0.390881 + 0.920441i \(0.372170\pi\)
\(198\) 3.37863 0.240109
\(199\) 14.9202 1.05766 0.528832 0.848727i \(-0.322630\pi\)
0.528832 + 0.848727i \(0.322630\pi\)
\(200\) −3.28356 −0.232183
\(201\) 21.3497 1.50589
\(202\) 24.9549 1.75582
\(203\) −26.4157 −1.85402
\(204\) 4.54680 0.318339
\(205\) −25.6755 −1.79325
\(206\) 0.368707 0.0256891
\(207\) −1.28551 −0.0893490
\(208\) 2.11121 0.146386
\(209\) −39.3079 −2.71899
\(210\) −44.4291 −3.06590
\(211\) −11.8753 −0.817532 −0.408766 0.912639i \(-0.634041\pi\)
−0.408766 + 0.912639i \(0.634041\pi\)
\(212\) 24.1689 1.65993
\(213\) 5.30726 0.363648
\(214\) −17.6518 −1.20665
\(215\) −16.8295 −1.14776
\(216\) 8.94225 0.608443
\(217\) −35.1615 −2.38692
\(218\) 28.4358 1.92591
\(219\) 15.7172 1.06207
\(220\) −40.0948 −2.70319
\(221\) −1.10509 −0.0743364
\(222\) 35.5505 2.38600
\(223\) −2.17541 −0.145676 −0.0728382 0.997344i \(-0.523206\pi\)
−0.0728382 + 0.997344i \(0.523206\pi\)
\(224\) −34.9257 −2.33357
\(225\) −0.559475 −0.0372983
\(226\) −20.0569 −1.33417
\(227\) −15.6433 −1.03828 −0.519141 0.854689i \(-0.673748\pi\)
−0.519141 + 0.854689i \(0.673748\pi\)
\(228\) −32.4926 −2.15187
\(229\) −14.9613 −0.988671 −0.494336 0.869271i \(-0.664589\pi\)
−0.494336 + 0.869271i \(0.664589\pi\)
\(230\) 26.3191 1.73543
\(231\) −42.3870 −2.78886
\(232\) −9.34098 −0.613265
\(233\) −21.2252 −1.39051 −0.695254 0.718764i \(-0.744708\pi\)
−0.695254 + 0.718764i \(0.744708\pi\)
\(234\) −0.678792 −0.0443740
\(235\) 28.6020 1.86579
\(236\) −27.0908 −1.76346
\(237\) −13.0337 −0.846632
\(238\) 10.1947 0.660824
\(239\) 3.36650 0.217761 0.108880 0.994055i \(-0.465273\pi\)
0.108880 + 0.994055i \(0.465273\pi\)
\(240\) 8.32583 0.537430
\(241\) −11.0635 −0.712661 −0.356331 0.934360i \(-0.615972\pi\)
−0.356331 + 0.934360i \(0.615972\pi\)
\(242\) −42.0003 −2.69988
\(243\) 2.91653 0.187096
\(244\) 3.14028 0.201036
\(245\) −39.2387 −2.50687
\(246\) −34.9331 −2.22725
\(247\) 7.89726 0.502490
\(248\) −12.4336 −0.789535
\(249\) −8.07451 −0.511701
\(250\) −17.3729 −1.09876
\(251\) 17.3055 1.09231 0.546157 0.837683i \(-0.316090\pi\)
0.546157 + 0.837683i \(0.316090\pi\)
\(252\) 3.62964 0.228646
\(253\) 25.1094 1.57862
\(254\) −0.382715 −0.0240137
\(255\) −4.35806 −0.272913
\(256\) −1.81331 −0.113332
\(257\) −9.41460 −0.587266 −0.293633 0.955918i \(-0.594864\pi\)
−0.293633 + 0.955918i \(0.594864\pi\)
\(258\) −22.8975 −1.42554
\(259\) 46.2025 2.87088
\(260\) 8.05535 0.499572
\(261\) −1.59158 −0.0985162
\(262\) −21.0121 −1.29813
\(263\) −11.3323 −0.698781 −0.349391 0.936977i \(-0.613611\pi\)
−0.349391 + 0.936977i \(0.613611\pi\)
\(264\) −14.9886 −0.922487
\(265\) −23.1657 −1.42306
\(266\) −72.8538 −4.46696
\(267\) −22.7496 −1.39225
\(268\) 35.7095 2.18131
\(269\) 2.26739 0.138245 0.0691225 0.997608i \(-0.477980\pi\)
0.0691225 + 0.997608i \(0.477980\pi\)
\(270\) −31.1946 −1.89844
\(271\) −23.7134 −1.44049 −0.720243 0.693721i \(-0.755970\pi\)
−0.720243 + 0.693721i \(0.755970\pi\)
\(272\) −1.91044 −0.115838
\(273\) 8.51587 0.515404
\(274\) −34.2956 −2.07187
\(275\) 10.9280 0.658986
\(276\) 20.7558 1.24936
\(277\) 28.0322 1.68429 0.842147 0.539249i \(-0.181292\pi\)
0.842147 + 0.539249i \(0.181292\pi\)
\(278\) 26.1682 1.56947
\(279\) −2.11852 −0.126832
\(280\) −20.4182 −1.22022
\(281\) −19.0212 −1.13471 −0.567354 0.823474i \(-0.692033\pi\)
−0.567354 + 0.823474i \(0.692033\pi\)
\(282\) 38.9148 2.31735
\(283\) −3.08146 −0.183174 −0.0915869 0.995797i \(-0.529194\pi\)
−0.0915869 + 0.995797i \(0.529194\pi\)
\(284\) 8.87695 0.526750
\(285\) 31.1438 1.84480
\(286\) 13.2586 0.783999
\(287\) −45.4000 −2.67988
\(288\) −2.10431 −0.123998
\(289\) 1.00000 0.0588235
\(290\) 32.5855 1.91349
\(291\) 19.2882 1.13069
\(292\) 26.2886 1.53842
\(293\) −29.5383 −1.72565 −0.862824 0.505504i \(-0.831307\pi\)
−0.862824 + 0.505504i \(0.831307\pi\)
\(294\) −53.3866 −3.11357
\(295\) 25.9662 1.51181
\(296\) 16.3379 0.949619
\(297\) −29.7608 −1.72690
\(298\) 5.59770 0.324266
\(299\) −5.04467 −0.291741
\(300\) 9.03330 0.521538
\(301\) −29.7583 −1.71524
\(302\) 41.3341 2.37851
\(303\) −18.8631 −1.08366
\(304\) 13.6525 0.783025
\(305\) −3.00993 −0.172348
\(306\) 0.614241 0.0351138
\(307\) 18.4904 1.05530 0.527651 0.849461i \(-0.323073\pi\)
0.527651 + 0.849461i \(0.323073\pi\)
\(308\) −70.8966 −4.03971
\(309\) −0.278701 −0.0158548
\(310\) 43.3739 2.46347
\(311\) −24.0884 −1.36593 −0.682963 0.730453i \(-0.739309\pi\)
−0.682963 + 0.730453i \(0.739309\pi\)
\(312\) 3.01133 0.170483
\(313\) 11.7331 0.663195 0.331597 0.943421i \(-0.392412\pi\)
0.331597 + 0.943421i \(0.392412\pi\)
\(314\) −13.7278 −0.774704
\(315\) −3.47898 −0.196018
\(316\) −21.8003 −1.22636
\(317\) −30.4121 −1.70811 −0.854056 0.520180i \(-0.825865\pi\)
−0.854056 + 0.520180i \(0.825865\pi\)
\(318\) −31.5184 −1.76746
\(319\) 31.0878 1.74058
\(320\) 32.9835 1.84383
\(321\) 13.3428 0.744720
\(322\) 46.5381 2.59347
\(323\) −7.14625 −0.397628
\(324\) −22.2710 −1.23728
\(325\) −2.19553 −0.121786
\(326\) 24.3688 1.34966
\(327\) −21.4942 −1.18863
\(328\) −16.0541 −0.886439
\(329\) 50.5749 2.78828
\(330\) 52.2871 2.87831
\(331\) 24.1752 1.32879 0.664395 0.747381i \(-0.268689\pi\)
0.664395 + 0.747381i \(0.268689\pi\)
\(332\) −13.5055 −0.741208
\(333\) 2.78375 0.152549
\(334\) −30.8704 −1.68915
\(335\) −34.2272 −1.87003
\(336\) 14.7219 0.803148
\(337\) 23.3202 1.27033 0.635166 0.772376i \(-0.280932\pi\)
0.635166 + 0.772376i \(0.280932\pi\)
\(338\) 25.6921 1.39746
\(339\) 15.1608 0.823420
\(340\) −7.28931 −0.395318
\(341\) 41.3803 2.24087
\(342\) −4.38952 −0.237358
\(343\) −36.6658 −1.97977
\(344\) −10.5229 −0.567359
\(345\) −19.8943 −1.07107
\(346\) −40.1515 −2.15856
\(347\) −1.03700 −0.0556693 −0.0278346 0.999613i \(-0.508861\pi\)
−0.0278346 + 0.999613i \(0.508861\pi\)
\(348\) 25.6977 1.37754
\(349\) 6.92713 0.370801 0.185400 0.982663i \(-0.440642\pi\)
0.185400 + 0.982663i \(0.440642\pi\)
\(350\) 20.2542 1.08263
\(351\) 5.97916 0.319144
\(352\) 41.1028 2.19079
\(353\) 1.00000 0.0532246
\(354\) 35.3287 1.87770
\(355\) −8.50847 −0.451583
\(356\) −38.0511 −2.01670
\(357\) −7.70604 −0.407847
\(358\) 40.7932 2.15599
\(359\) −11.1618 −0.589095 −0.294547 0.955637i \(-0.595169\pi\)
−0.294547 + 0.955637i \(0.595169\pi\)
\(360\) −1.23022 −0.0648381
\(361\) 32.0689 1.68784
\(362\) 25.4835 1.33938
\(363\) 31.7475 1.66631
\(364\) 14.2437 0.746571
\(365\) −25.1974 −1.31889
\(366\) −4.09519 −0.214059
\(367\) −24.9662 −1.30323 −0.651613 0.758552i \(-0.725907\pi\)
−0.651613 + 0.758552i \(0.725907\pi\)
\(368\) −8.72105 −0.454616
\(369\) −2.73540 −0.142399
\(370\) −56.9937 −2.96296
\(371\) −40.9622 −2.12665
\(372\) 34.2057 1.77348
\(373\) 3.45430 0.178857 0.0894285 0.995993i \(-0.471496\pi\)
0.0894285 + 0.995993i \(0.471496\pi\)
\(374\) −11.9978 −0.620390
\(375\) 13.1320 0.678133
\(376\) 17.8840 0.922296
\(377\) −6.24577 −0.321673
\(378\) −55.1590 −2.83707
\(379\) 21.7587 1.11767 0.558833 0.829280i \(-0.311249\pi\)
0.558833 + 0.829280i \(0.311249\pi\)
\(380\) 52.0913 2.67223
\(381\) 0.289289 0.0148207
\(382\) 15.9679 0.816991
\(383\) −19.4263 −0.992639 −0.496320 0.868140i \(-0.665316\pi\)
−0.496320 + 0.868140i \(0.665316\pi\)
\(384\) 20.2352 1.03262
\(385\) 67.9538 3.46325
\(386\) 1.37844 0.0701607
\(387\) −1.79297 −0.0911417
\(388\) 32.2615 1.63783
\(389\) −23.4435 −1.18863 −0.594316 0.804231i \(-0.702577\pi\)
−0.594316 + 0.804231i \(0.702577\pi\)
\(390\) −10.5049 −0.531935
\(391\) 4.56494 0.230859
\(392\) −24.5347 −1.23919
\(393\) 15.8828 0.801179
\(394\) −23.9335 −1.20575
\(395\) 20.8954 1.05136
\(396\) −4.27160 −0.214656
\(397\) −20.9917 −1.05355 −0.526773 0.850006i \(-0.676598\pi\)
−0.526773 + 0.850006i \(0.676598\pi\)
\(398\) −32.5442 −1.63129
\(399\) 55.0693 2.75691
\(400\) −3.79555 −0.189777
\(401\) 18.1974 0.908736 0.454368 0.890814i \(-0.349865\pi\)
0.454368 + 0.890814i \(0.349865\pi\)
\(402\) −46.5683 −2.32261
\(403\) −8.31362 −0.414131
\(404\) −31.5505 −1.56970
\(405\) 21.3465 1.06072
\(406\) 57.6185 2.85956
\(407\) −54.3741 −2.69523
\(408\) −2.72496 −0.134906
\(409\) −11.3284 −0.560151 −0.280076 0.959978i \(-0.590360\pi\)
−0.280076 + 0.959978i \(0.590360\pi\)
\(410\) 56.0038 2.76583
\(411\) 25.9236 1.27872
\(412\) −0.466157 −0.0229659
\(413\) 45.9142 2.25929
\(414\) 2.80397 0.137808
\(415\) 12.9449 0.635438
\(416\) −8.25787 −0.404875
\(417\) −19.7803 −0.968643
\(418\) 85.7392 4.19364
\(419\) 12.1615 0.594128 0.297064 0.954858i \(-0.403993\pi\)
0.297064 + 0.954858i \(0.403993\pi\)
\(420\) 56.1717 2.74090
\(421\) 1.35865 0.0662168 0.0331084 0.999452i \(-0.489459\pi\)
0.0331084 + 0.999452i \(0.489459\pi\)
\(422\) 25.9027 1.26092
\(423\) 3.04719 0.148160
\(424\) −14.4848 −0.703445
\(425\) 1.98674 0.0963710
\(426\) −11.5763 −0.560874
\(427\) −5.32223 −0.257561
\(428\) 22.3171 1.07874
\(429\) −10.0220 −0.483868
\(430\) 36.7087 1.77025
\(431\) −2.82202 −0.135932 −0.0679660 0.997688i \(-0.521651\pi\)
−0.0679660 + 0.997688i \(0.521651\pi\)
\(432\) 10.3366 0.497318
\(433\) −34.6263 −1.66403 −0.832017 0.554750i \(-0.812814\pi\)
−0.832017 + 0.554750i \(0.812814\pi\)
\(434\) 76.6949 3.68147
\(435\) −24.6310 −1.18096
\(436\) −35.9513 −1.72176
\(437\) −32.6222 −1.56053
\(438\) −34.2826 −1.63809
\(439\) 4.69435 0.224049 0.112025 0.993705i \(-0.464266\pi\)
0.112025 + 0.993705i \(0.464266\pi\)
\(440\) 24.0294 1.14556
\(441\) −4.18039 −0.199066
\(442\) 2.41044 0.114653
\(443\) 11.4305 0.543080 0.271540 0.962427i \(-0.412467\pi\)
0.271540 + 0.962427i \(0.412467\pi\)
\(444\) −44.9465 −2.13307
\(445\) 36.4716 1.72892
\(446\) 4.74505 0.224685
\(447\) −4.23123 −0.200130
\(448\) 58.3223 2.75547
\(449\) −16.7634 −0.791114 −0.395557 0.918441i \(-0.629448\pi\)
−0.395557 + 0.918441i \(0.629448\pi\)
\(450\) 1.22034 0.0575273
\(451\) 53.4297 2.51591
\(452\) 25.3580 1.19274
\(453\) −31.2440 −1.46797
\(454\) 34.1215 1.60140
\(455\) −13.6524 −0.640036
\(456\) 19.4733 0.911920
\(457\) −30.3576 −1.42007 −0.710035 0.704166i \(-0.751321\pi\)
−0.710035 + 0.704166i \(0.751321\pi\)
\(458\) 32.6339 1.52488
\(459\) −5.41056 −0.252544
\(460\) −33.2753 −1.55147
\(461\) 7.70326 0.358777 0.179388 0.983778i \(-0.442588\pi\)
0.179388 + 0.983778i \(0.442588\pi\)
\(462\) 92.4553 4.30141
\(463\) −2.81145 −0.130659 −0.0653296 0.997864i \(-0.520810\pi\)
−0.0653296 + 0.997864i \(0.520810\pi\)
\(464\) −10.7975 −0.501260
\(465\) −32.7858 −1.52041
\(466\) 46.2968 2.14466
\(467\) 16.1892 0.749149 0.374574 0.927197i \(-0.377789\pi\)
0.374574 + 0.927197i \(0.377789\pi\)
\(468\) 0.858197 0.0396702
\(469\) −60.5215 −2.79462
\(470\) −62.3873 −2.87771
\(471\) 10.3767 0.478131
\(472\) 16.2359 0.747318
\(473\) 35.0215 1.61029
\(474\) 28.4294 1.30581
\(475\) −14.1977 −0.651437
\(476\) −12.8891 −0.590773
\(477\) −2.46802 −0.113003
\(478\) −7.34307 −0.335864
\(479\) −0.523321 −0.0239111 −0.0119556 0.999929i \(-0.503806\pi\)
−0.0119556 + 0.999929i \(0.503806\pi\)
\(480\) −32.5659 −1.48642
\(481\) 10.9242 0.498099
\(482\) 24.1319 1.09918
\(483\) −35.1776 −1.60064
\(484\) 53.1009 2.41368
\(485\) −30.9224 −1.40411
\(486\) −6.36159 −0.288568
\(487\) 21.5007 0.974288 0.487144 0.873322i \(-0.338039\pi\)
0.487144 + 0.873322i \(0.338039\pi\)
\(488\) −1.88201 −0.0851948
\(489\) −18.4201 −0.832984
\(490\) 85.5881 3.86647
\(491\) −30.3021 −1.36752 −0.683758 0.729709i \(-0.739656\pi\)
−0.683758 + 0.729709i \(0.739656\pi\)
\(492\) 44.1659 1.99115
\(493\) 5.65182 0.254545
\(494\) −17.2256 −0.775018
\(495\) 4.09429 0.184025
\(496\) −14.3723 −0.645335
\(497\) −15.0449 −0.674856
\(498\) 17.6123 0.789225
\(499\) −16.3743 −0.733016 −0.366508 0.930415i \(-0.619447\pi\)
−0.366508 + 0.930415i \(0.619447\pi\)
\(500\) 21.9646 0.982287
\(501\) 23.3345 1.04251
\(502\) −37.7471 −1.68474
\(503\) −9.66908 −0.431123 −0.215562 0.976490i \(-0.569158\pi\)
−0.215562 + 0.976490i \(0.569158\pi\)
\(504\) −2.17530 −0.0968956
\(505\) 30.2409 1.34570
\(506\) −54.7691 −2.43478
\(507\) −19.4203 −0.862487
\(508\) 0.483866 0.0214681
\(509\) 8.29485 0.367663 0.183831 0.982958i \(-0.441150\pi\)
0.183831 + 0.982958i \(0.441150\pi\)
\(510\) 9.50589 0.420928
\(511\) −44.5547 −1.97098
\(512\) −20.5908 −0.909995
\(513\) 38.6653 1.70711
\(514\) 20.5353 0.905773
\(515\) 0.446807 0.0196887
\(516\) 28.9493 1.27442
\(517\) −59.5198 −2.61768
\(518\) −100.778 −4.42792
\(519\) 30.3500 1.33222
\(520\) −4.82769 −0.211708
\(521\) 19.4041 0.850110 0.425055 0.905168i \(-0.360255\pi\)
0.425055 + 0.905168i \(0.360255\pi\)
\(522\) 3.47158 0.151947
\(523\) 5.33776 0.233404 0.116702 0.993167i \(-0.462768\pi\)
0.116702 + 0.993167i \(0.462768\pi\)
\(524\) 26.5655 1.16052
\(525\) −15.3099 −0.668178
\(526\) 24.7183 1.07777
\(527\) 7.52303 0.327708
\(528\) −17.3257 −0.754006
\(529\) −2.16133 −0.0939710
\(530\) 50.5295 2.19486
\(531\) 2.76638 0.120051
\(532\) 92.1091 3.99344
\(533\) −10.7344 −0.464960
\(534\) 49.6219 2.14735
\(535\) −21.3908 −0.924803
\(536\) −21.4013 −0.924393
\(537\) −30.8350 −1.33063
\(538\) −4.94566 −0.213223
\(539\) 81.6542 3.51709
\(540\) 39.4393 1.69720
\(541\) −6.81084 −0.292821 −0.146410 0.989224i \(-0.546772\pi\)
−0.146410 + 0.989224i \(0.546772\pi\)
\(542\) 51.7241 2.22174
\(543\) −19.2627 −0.826641
\(544\) 7.47257 0.320384
\(545\) 34.4590 1.47606
\(546\) −18.5750 −0.794935
\(547\) −21.9443 −0.938269 −0.469135 0.883127i \(-0.655434\pi\)
−0.469135 + 0.883127i \(0.655434\pi\)
\(548\) 43.3599 1.85224
\(549\) −0.320670 −0.0136859
\(550\) −23.8365 −1.01639
\(551\) −40.3893 −1.72064
\(552\) −12.4393 −0.529451
\(553\) 36.9477 1.57118
\(554\) −61.1444 −2.59778
\(555\) 43.0808 1.82868
\(556\) −33.0845 −1.40310
\(557\) 2.23207 0.0945757 0.0472879 0.998881i \(-0.484942\pi\)
0.0472879 + 0.998881i \(0.484942\pi\)
\(558\) 4.62095 0.195621
\(559\) −7.03608 −0.297594
\(560\) −23.6018 −0.997360
\(561\) 9.06897 0.382892
\(562\) 41.4894 1.75012
\(563\) 32.3468 1.36326 0.681628 0.731699i \(-0.261272\pi\)
0.681628 + 0.731699i \(0.261272\pi\)
\(564\) −49.2000 −2.07169
\(565\) −24.3054 −1.02254
\(566\) 6.72134 0.282519
\(567\) 37.7455 1.58516
\(568\) −5.32009 −0.223226
\(569\) −16.7498 −0.702189 −0.351094 0.936340i \(-0.614190\pi\)
−0.351094 + 0.936340i \(0.614190\pi\)
\(570\) −67.9315 −2.84534
\(571\) −16.9115 −0.707725 −0.353863 0.935297i \(-0.615132\pi\)
−0.353863 + 0.935297i \(0.615132\pi\)
\(572\) −16.7629 −0.700891
\(573\) −12.0700 −0.504230
\(574\) 99.0274 4.13332
\(575\) 9.06934 0.378218
\(576\) 3.51398 0.146416
\(577\) −42.4968 −1.76916 −0.884582 0.466386i \(-0.845556\pi\)
−0.884582 + 0.466386i \(0.845556\pi\)
\(578\) −2.18122 −0.0907267
\(579\) −1.04195 −0.0433018
\(580\) −41.1978 −1.71065
\(581\) 22.8894 0.949613
\(582\) −42.0718 −1.74393
\(583\) 48.2070 1.99653
\(584\) −15.7552 −0.651953
\(585\) −0.822574 −0.0340093
\(586\) 64.4296 2.66156
\(587\) −44.0400 −1.81773 −0.908863 0.417096i \(-0.863048\pi\)
−0.908863 + 0.417096i \(0.863048\pi\)
\(588\) 67.4967 2.78352
\(589\) −53.7614 −2.21520
\(590\) −56.6381 −2.33175
\(591\) 18.0911 0.744167
\(592\) 18.8853 0.776182
\(593\) 26.3240 1.08100 0.540499 0.841344i \(-0.318235\pi\)
0.540499 + 0.841344i \(0.318235\pi\)
\(594\) 64.9147 2.66348
\(595\) 12.3541 0.506470
\(596\) −7.07717 −0.289892
\(597\) 24.5997 1.00680
\(598\) 11.0035 0.449968
\(599\) −41.3234 −1.68843 −0.844214 0.536006i \(-0.819932\pi\)
−0.844214 + 0.536006i \(0.819932\pi\)
\(600\) −5.41379 −0.221017
\(601\) −14.2454 −0.581080 −0.290540 0.956863i \(-0.593835\pi\)
−0.290540 + 0.956863i \(0.593835\pi\)
\(602\) 64.9093 2.64550
\(603\) −3.64649 −0.148496
\(604\) −52.2587 −2.12638
\(605\) −50.8968 −2.06925
\(606\) 41.1446 1.67139
\(607\) −25.9277 −1.05237 −0.526186 0.850369i \(-0.676379\pi\)
−0.526186 + 0.850369i \(0.676379\pi\)
\(608\) −53.4009 −2.16569
\(609\) −43.5531 −1.76486
\(610\) 6.56530 0.265821
\(611\) 11.9580 0.483768
\(612\) −0.776585 −0.0313916
\(613\) 7.06578 0.285384 0.142692 0.989767i \(-0.454424\pi\)
0.142692 + 0.989767i \(0.454424\pi\)
\(614\) −40.3316 −1.62765
\(615\) −42.3326 −1.70702
\(616\) 42.4894 1.71195
\(617\) −5.05958 −0.203691 −0.101845 0.994800i \(-0.532475\pi\)
−0.101845 + 0.994800i \(0.532475\pi\)
\(618\) 0.607908 0.0244537
\(619\) −0.790826 −0.0317860 −0.0158930 0.999874i \(-0.505059\pi\)
−0.0158930 + 0.999874i \(0.505059\pi\)
\(620\) −54.8377 −2.20233
\(621\) −24.6989 −0.991133
\(622\) 52.5420 2.10674
\(623\) 64.4901 2.58374
\(624\) 3.48087 0.139346
\(625\) −30.9866 −1.23946
\(626\) −25.5925 −1.02288
\(627\) −64.8092 −2.58823
\(628\) 17.3560 0.692582
\(629\) −9.88532 −0.394153
\(630\) 7.58842 0.302330
\(631\) −13.1303 −0.522708 −0.261354 0.965243i \(-0.584169\pi\)
−0.261354 + 0.965243i \(0.584169\pi\)
\(632\) 13.0652 0.519707
\(633\) −19.5795 −0.778216
\(634\) 66.3354 2.63452
\(635\) −0.463781 −0.0184046
\(636\) 39.8487 1.58010
\(637\) −16.4049 −0.649987
\(638\) −67.8092 −2.68459
\(639\) −0.906472 −0.0358595
\(640\) −32.4406 −1.28233
\(641\) 20.1518 0.795949 0.397974 0.917397i \(-0.369713\pi\)
0.397974 + 0.917397i \(0.369713\pi\)
\(642\) −29.1035 −1.14862
\(643\) 25.0807 0.989085 0.494543 0.869153i \(-0.335336\pi\)
0.494543 + 0.869153i \(0.335336\pi\)
\(644\) −58.8382 −2.31855
\(645\) −27.7477 −1.09256
\(646\) 15.5875 0.613284
\(647\) −20.6832 −0.813142 −0.406571 0.913619i \(-0.633276\pi\)
−0.406571 + 0.913619i \(0.633276\pi\)
\(648\) 13.3473 0.524333
\(649\) −54.0348 −2.12105
\(650\) 4.78892 0.187837
\(651\) −57.9727 −2.27213
\(652\) −30.8095 −1.20659
\(653\) −23.5925 −0.923246 −0.461623 0.887076i \(-0.652733\pi\)
−0.461623 + 0.887076i \(0.652733\pi\)
\(654\) 46.8836 1.83330
\(655\) −25.4628 −0.994915
\(656\) −18.5573 −0.724542
\(657\) −2.68447 −0.104731
\(658\) −110.315 −4.30052
\(659\) 26.1511 1.01870 0.509352 0.860558i \(-0.329885\pi\)
0.509352 + 0.860558i \(0.329885\pi\)
\(660\) −66.1065 −2.57319
\(661\) −25.4722 −0.990752 −0.495376 0.868679i \(-0.664970\pi\)
−0.495376 + 0.868679i \(0.664970\pi\)
\(662\) −52.7315 −2.04947
\(663\) −1.82202 −0.0707616
\(664\) 8.09402 0.314109
\(665\) −88.2857 −3.42357
\(666\) −6.07197 −0.235284
\(667\) 25.8002 0.998987
\(668\) 39.0294 1.51009
\(669\) −3.58672 −0.138671
\(670\) 74.6571 2.88426
\(671\) 6.26354 0.241801
\(672\) −57.5839 −2.22135
\(673\) 28.0645 1.08181 0.540903 0.841085i \(-0.318083\pi\)
0.540903 + 0.841085i \(0.318083\pi\)
\(674\) −50.8664 −1.95930
\(675\) −10.7494 −0.413744
\(676\) −32.4825 −1.24933
\(677\) 28.2970 1.08754 0.543771 0.839234i \(-0.316996\pi\)
0.543771 + 0.839234i \(0.316996\pi\)
\(678\) −33.0690 −1.27001
\(679\) −54.6777 −2.09834
\(680\) 4.36859 0.167528
\(681\) −25.7920 −0.988351
\(682\) −90.2596 −3.45622
\(683\) −21.8896 −0.837582 −0.418791 0.908083i \(-0.637546\pi\)
−0.418791 + 0.908083i \(0.637546\pi\)
\(684\) 5.54968 0.212197
\(685\) −41.5600 −1.58793
\(686\) 79.9762 3.05350
\(687\) −24.6675 −0.941125
\(688\) −12.1637 −0.463738
\(689\) −9.68515 −0.368975
\(690\) 43.3938 1.65197
\(691\) 34.5680 1.31503 0.657514 0.753442i \(-0.271608\pi\)
0.657514 + 0.753442i \(0.271608\pi\)
\(692\) 50.7635 1.92974
\(693\) 7.23963 0.275011
\(694\) 2.26193 0.0858617
\(695\) 31.7112 1.20287
\(696\) −15.4010 −0.583773
\(697\) 9.71363 0.367930
\(698\) −15.1096 −0.571906
\(699\) −34.9951 −1.32364
\(700\) −25.6074 −0.967867
\(701\) 22.7657 0.859849 0.429925 0.902865i \(-0.358540\pi\)
0.429925 + 0.902865i \(0.358540\pi\)
\(702\) −13.0419 −0.492233
\(703\) 70.6430 2.66435
\(704\) −68.6375 −2.58687
\(705\) 47.1578 1.77606
\(706\) −2.18122 −0.0820912
\(707\) 53.4727 2.01105
\(708\) −44.6660 −1.67865
\(709\) 15.3999 0.578356 0.289178 0.957275i \(-0.406618\pi\)
0.289178 + 0.957275i \(0.406618\pi\)
\(710\) 18.5588 0.696501
\(711\) 2.22614 0.0834868
\(712\) 22.8046 0.854638
\(713\) 34.3422 1.28612
\(714\) 16.8086 0.629044
\(715\) 16.0671 0.600874
\(716\) −51.5748 −1.92744
\(717\) 5.55053 0.207288
\(718\) 24.3462 0.908593
\(719\) −35.2080 −1.31304 −0.656519 0.754310i \(-0.727972\pi\)
−0.656519 + 0.754310i \(0.727972\pi\)
\(720\) −1.42204 −0.0529962
\(721\) 0.790055 0.0294232
\(722\) −69.9494 −2.60325
\(723\) −18.2410 −0.678389
\(724\) −32.2188 −1.19740
\(725\) 11.2287 0.417023
\(726\) −69.2482 −2.57004
\(727\) 8.14471 0.302071 0.151035 0.988528i \(-0.451739\pi\)
0.151035 + 0.988528i \(0.451739\pi\)
\(728\) −8.53645 −0.316382
\(729\) 29.0363 1.07542
\(730\) 54.9610 2.03420
\(731\) 6.36697 0.235491
\(732\) 5.17755 0.191368
\(733\) −35.9498 −1.32783 −0.663917 0.747806i \(-0.731107\pi\)
−0.663917 + 0.747806i \(0.731107\pi\)
\(734\) 54.4568 2.01004
\(735\) −64.6949 −2.38631
\(736\) 34.1118 1.25738
\(737\) 71.2256 2.62363
\(738\) 5.96651 0.219630
\(739\) −0.647430 −0.0238161 −0.0119080 0.999929i \(-0.503791\pi\)
−0.0119080 + 0.999929i \(0.503791\pi\)
\(740\) 72.0572 2.64887
\(741\) 13.0206 0.478325
\(742\) 89.3475 3.28005
\(743\) 2.03924 0.0748125 0.0374063 0.999300i \(-0.488090\pi\)
0.0374063 + 0.999300i \(0.488090\pi\)
\(744\) −20.5000 −0.751565
\(745\) 6.78340 0.248525
\(746\) −7.53459 −0.275861
\(747\) 1.37911 0.0504591
\(748\) 15.1688 0.554626
\(749\) −37.8237 −1.38205
\(750\) −28.6437 −1.04592
\(751\) 19.2799 0.703534 0.351767 0.936088i \(-0.385581\pi\)
0.351767 + 0.936088i \(0.385581\pi\)
\(752\) 20.6725 0.753850
\(753\) 28.5326 1.03978
\(754\) 13.6234 0.496134
\(755\) 50.0895 1.82294
\(756\) 69.7375 2.53633
\(757\) −48.7157 −1.77060 −0.885302 0.465017i \(-0.846048\pi\)
−0.885302 + 0.465017i \(0.846048\pi\)
\(758\) −47.4604 −1.72384
\(759\) 41.3993 1.50270
\(760\) −31.2191 −1.13244
\(761\) −8.89585 −0.322474 −0.161237 0.986916i \(-0.551548\pi\)
−0.161237 + 0.986916i \(0.551548\pi\)
\(762\) −0.631003 −0.0228588
\(763\) 60.9313 2.20586
\(764\) −20.1883 −0.730385
\(765\) 0.744350 0.0269120
\(766\) 42.3731 1.53100
\(767\) 10.8560 0.391987
\(768\) −2.98970 −0.107882
\(769\) −0.859414 −0.0309913 −0.0154956 0.999880i \(-0.504933\pi\)
−0.0154956 + 0.999880i \(0.504933\pi\)
\(770\) −148.222 −5.34155
\(771\) −15.5224 −0.559024
\(772\) −1.74276 −0.0627233
\(773\) −23.5183 −0.845894 −0.422947 0.906154i \(-0.639004\pi\)
−0.422947 + 0.906154i \(0.639004\pi\)
\(774\) 3.91086 0.140573
\(775\) 14.9463 0.536887
\(776\) −19.3348 −0.694079
\(777\) 76.1766 2.73282
\(778\) 51.1354 1.83329
\(779\) −69.4160 −2.48709
\(780\) 13.2813 0.475547
\(781\) 17.7058 0.633564
\(782\) −9.95713 −0.356066
\(783\) −30.5795 −1.09282
\(784\) −28.3603 −1.01287
\(785\) −16.6356 −0.593750
\(786\) −34.6438 −1.23570
\(787\) 29.8587 1.06435 0.532174 0.846635i \(-0.321375\pi\)
0.532174 + 0.846635i \(0.321375\pi\)
\(788\) 30.2592 1.07794
\(789\) −18.6842 −0.665177
\(790\) −45.5773 −1.62157
\(791\) −42.9774 −1.52810
\(792\) 2.56004 0.0909669
\(793\) −1.25839 −0.0446868
\(794\) 45.7876 1.62494
\(795\) −38.1946 −1.35462
\(796\) 41.1456 1.45837
\(797\) 2.50267 0.0886493 0.0443246 0.999017i \(-0.485886\pi\)
0.0443246 + 0.999017i \(0.485886\pi\)
\(798\) −120.118 −4.25214
\(799\) −10.8208 −0.382813
\(800\) 14.8460 0.524887
\(801\) 3.88560 0.137291
\(802\) −39.6926 −1.40159
\(803\) 52.4348 1.85039
\(804\) 58.8763 2.07641
\(805\) 56.3958 1.98769
\(806\) 18.1338 0.638737
\(807\) 3.73836 0.131597
\(808\) 18.9087 0.665206
\(809\) 50.5059 1.77569 0.887847 0.460139i \(-0.152200\pi\)
0.887847 + 0.460139i \(0.152200\pi\)
\(810\) −46.5615 −1.63600
\(811\) −49.3818 −1.73403 −0.867015 0.498281i \(-0.833965\pi\)
−0.867015 + 0.498281i \(0.833965\pi\)
\(812\) −72.8471 −2.55643
\(813\) −39.0976 −1.37121
\(814\) 118.602 4.15699
\(815\) 29.5306 1.03441
\(816\) −3.14985 −0.110267
\(817\) −45.5000 −1.59184
\(818\) 24.7096 0.863952
\(819\) −1.45450 −0.0508242
\(820\) −70.8056 −2.47264
\(821\) 19.4132 0.677524 0.338762 0.940872i \(-0.389992\pi\)
0.338762 + 0.940872i \(0.389992\pi\)
\(822\) −56.5450 −1.97223
\(823\) 3.75774 0.130987 0.0654933 0.997853i \(-0.479138\pi\)
0.0654933 + 0.997853i \(0.479138\pi\)
\(824\) 0.279375 0.00973248
\(825\) 18.0177 0.627295
\(826\) −100.149 −3.48462
\(827\) −27.8959 −0.970036 −0.485018 0.874504i \(-0.661187\pi\)
−0.485018 + 0.874504i \(0.661187\pi\)
\(828\) −3.54506 −0.123200
\(829\) −4.67155 −0.162250 −0.0811248 0.996704i \(-0.525851\pi\)
−0.0811248 + 0.996704i \(0.525851\pi\)
\(830\) −28.2356 −0.980070
\(831\) 46.2183 1.60329
\(832\) 13.7898 0.478075
\(833\) 14.8449 0.514345
\(834\) 43.1450 1.49399
\(835\) −37.4093 −1.29460
\(836\) −108.400 −3.74909
\(837\) −40.7038 −1.40693
\(838\) −26.5269 −0.916356
\(839\) −0.528468 −0.0182448 −0.00912238 0.999958i \(-0.502904\pi\)
−0.00912238 + 0.999958i \(0.502904\pi\)
\(840\) −33.6646 −1.16154
\(841\) 2.94302 0.101483
\(842\) −2.96352 −0.102130
\(843\) −31.3613 −1.08014
\(844\) −32.7488 −1.12726
\(845\) 31.1342 1.07105
\(846\) −6.64659 −0.228514
\(847\) −89.9970 −3.09233
\(848\) −16.7433 −0.574969
\(849\) −5.08058 −0.174365
\(850\) −4.33351 −0.148638
\(851\) −45.1259 −1.54690
\(852\) 14.6359 0.501418
\(853\) 45.5367 1.55915 0.779573 0.626311i \(-0.215436\pi\)
0.779573 + 0.626311i \(0.215436\pi\)
\(854\) 11.6089 0.397250
\(855\) −5.31931 −0.181917
\(856\) −13.3750 −0.457148
\(857\) −7.14436 −0.244047 −0.122023 0.992527i \(-0.538938\pi\)
−0.122023 + 0.992527i \(0.538938\pi\)
\(858\) 21.8602 0.746296
\(859\) 5.22864 0.178399 0.0891994 0.996014i \(-0.471569\pi\)
0.0891994 + 0.996014i \(0.471569\pi\)
\(860\) −46.4108 −1.58260
\(861\) −74.8536 −2.55100
\(862\) 6.15545 0.209655
\(863\) 17.1660 0.584337 0.292169 0.956367i \(-0.405623\pi\)
0.292169 + 0.956367i \(0.405623\pi\)
\(864\) −40.4308 −1.37548
\(865\) −48.6564 −1.65437
\(866\) 75.5275 2.56653
\(867\) 1.64876 0.0559947
\(868\) −96.9654 −3.29122
\(869\) −43.4825 −1.47504
\(870\) 53.7255 1.82147
\(871\) −14.3098 −0.484868
\(872\) 21.5462 0.729646
\(873\) −3.29439 −0.111498
\(874\) 71.1562 2.40689
\(875\) −37.2262 −1.25848
\(876\) 43.3435 1.46444
\(877\) 29.6336 1.00065 0.500327 0.865836i \(-0.333213\pi\)
0.500327 + 0.865836i \(0.333213\pi\)
\(878\) −10.2394 −0.345563
\(879\) −48.7015 −1.64266
\(880\) 27.7762 0.936335
\(881\) −7.52513 −0.253528 −0.126764 0.991933i \(-0.540459\pi\)
−0.126764 + 0.991933i \(0.540459\pi\)
\(882\) 9.11834 0.307031
\(883\) 42.5541 1.43206 0.716030 0.698070i \(-0.245957\pi\)
0.716030 + 0.698070i \(0.245957\pi\)
\(884\) −3.04752 −0.102499
\(885\) 42.8120 1.43911
\(886\) −24.9324 −0.837622
\(887\) 32.0265 1.07534 0.537672 0.843154i \(-0.319304\pi\)
0.537672 + 0.843154i \(0.319304\pi\)
\(888\) 26.9371 0.903951
\(889\) −0.820070 −0.0275043
\(890\) −79.5526 −2.66661
\(891\) −44.4213 −1.48817
\(892\) −5.99917 −0.200867
\(893\) 77.3283 2.58769
\(894\) 9.22924 0.308672
\(895\) 49.4340 1.65240
\(896\) −57.3623 −1.91634
\(897\) −8.31743 −0.277711
\(898\) 36.5646 1.22018
\(899\) 42.5188 1.41808
\(900\) −1.54287 −0.0514291
\(901\) 8.76412 0.291975
\(902\) −116.542 −3.88042
\(903\) −49.0641 −1.63275
\(904\) −15.1974 −0.505458
\(905\) 30.8814 1.02653
\(906\) 68.1499 2.26413
\(907\) −30.2403 −1.00411 −0.502056 0.864835i \(-0.667423\pi\)
−0.502056 + 0.864835i \(0.667423\pi\)
\(908\) −43.1397 −1.43164
\(909\) 3.22179 0.106860
\(910\) 29.7789 0.987162
\(911\) −19.7051 −0.652859 −0.326429 0.945222i \(-0.605846\pi\)
−0.326429 + 0.945222i \(0.605846\pi\)
\(912\) 22.5096 0.745369
\(913\) −26.9378 −0.891510
\(914\) 66.2166 2.19025
\(915\) −4.96263 −0.164060
\(916\) −41.2590 −1.36324
\(917\) −45.0240 −1.48682
\(918\) 11.8016 0.389512
\(919\) 26.3134 0.868000 0.434000 0.900913i \(-0.357102\pi\)
0.434000 + 0.900913i \(0.357102\pi\)
\(920\) 19.9424 0.657480
\(921\) 30.4861 1.00455
\(922\) −16.8025 −0.553361
\(923\) −3.55723 −0.117088
\(924\) −116.891 −3.84544
\(925\) −19.6395 −0.645744
\(926\) 6.13239 0.201523
\(927\) 0.0476017 0.00156345
\(928\) 42.2336 1.38639
\(929\) 22.5947 0.741308 0.370654 0.928771i \(-0.379134\pi\)
0.370654 + 0.928771i \(0.379134\pi\)
\(930\) 71.5130 2.34501
\(931\) −106.085 −3.47681
\(932\) −58.5330 −1.91731
\(933\) −39.7158 −1.30024
\(934\) −35.3123 −1.15545
\(935\) −14.5391 −0.475481
\(936\) −0.514330 −0.0168114
\(937\) −5.19506 −0.169715 −0.0848576 0.996393i \(-0.527044\pi\)
−0.0848576 + 0.996393i \(0.527044\pi\)
\(938\) 132.011 4.31030
\(939\) 19.3450 0.631301
\(940\) 78.8763 2.57266
\(941\) 12.6686 0.412984 0.206492 0.978448i \(-0.433795\pi\)
0.206492 + 0.978448i \(0.433795\pi\)
\(942\) −22.6338 −0.737448
\(943\) 44.3421 1.44398
\(944\) 18.7675 0.610829
\(945\) −66.8428 −2.17440
\(946\) −76.3895 −2.48364
\(947\) −21.7199 −0.705802 −0.352901 0.935661i \(-0.614805\pi\)
−0.352901 + 0.935661i \(0.614805\pi\)
\(948\) −35.9433 −1.16738
\(949\) −10.5346 −0.341966
\(950\) 30.9684 1.00475
\(951\) −50.1421 −1.62597
\(952\) 7.72466 0.250358
\(953\) −12.5369 −0.406110 −0.203055 0.979167i \(-0.565087\pi\)
−0.203055 + 0.979167i \(0.565087\pi\)
\(954\) 5.38329 0.174290
\(955\) 19.3503 0.626160
\(956\) 9.28384 0.300261
\(957\) 51.2561 1.65688
\(958\) 1.14148 0.0368794
\(959\) −73.4875 −2.37304
\(960\) 54.3818 1.75516
\(961\) 25.5959 0.825675
\(962\) −23.8280 −0.768246
\(963\) −2.27892 −0.0734372
\(964\) −30.5099 −0.982658
\(965\) 1.67042 0.0537727
\(966\) 76.7300 2.46875
\(967\) 32.3634 1.04074 0.520369 0.853942i \(-0.325795\pi\)
0.520369 + 0.853942i \(0.325795\pi\)
\(968\) −31.8242 −1.02287
\(969\) −11.7824 −0.378506
\(970\) 67.4484 2.16564
\(971\) −42.8684 −1.37571 −0.687856 0.725847i \(-0.741448\pi\)
−0.687856 + 0.725847i \(0.741448\pi\)
\(972\) 8.04296 0.257978
\(973\) 56.0726 1.79760
\(974\) −46.8976 −1.50270
\(975\) −3.61989 −0.115929
\(976\) −2.17547 −0.0696350
\(977\) 25.3736 0.811772 0.405886 0.913924i \(-0.366963\pi\)
0.405886 + 0.913924i \(0.366963\pi\)
\(978\) 40.1782 1.28476
\(979\) −75.8961 −2.42565
\(980\) −108.209 −3.45661
\(981\) 3.67118 0.117212
\(982\) 66.0956 2.10919
\(983\) −17.1070 −0.545627 −0.272814 0.962067i \(-0.587954\pi\)
−0.272814 + 0.962067i \(0.587954\pi\)
\(984\) −26.4693 −0.843810
\(985\) −29.0032 −0.924117
\(986\) −12.3278 −0.392599
\(987\) 83.3856 2.65419
\(988\) 21.7784 0.692862
\(989\) 29.0648 0.924208
\(990\) −8.93055 −0.283831
\(991\) 21.2800 0.675981 0.337991 0.941149i \(-0.390253\pi\)
0.337991 + 0.941149i \(0.390253\pi\)
\(992\) 56.2163 1.78487
\(993\) 39.8590 1.26489
\(994\) 32.8162 1.04087
\(995\) −39.4377 −1.25026
\(996\) −22.2672 −0.705563
\(997\) 53.0334 1.67958 0.839792 0.542908i \(-0.182677\pi\)
0.839792 + 0.542908i \(0.182677\pi\)
\(998\) 35.7160 1.13057
\(999\) 53.4852 1.69220
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 \(a_p\))