Properties

Label 4009.2.a.c.1.13
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.08913 q^{2}\) \(+2.53881 q^{3}\) \(+2.36446 q^{4}\) \(+0.545075 q^{5}\) \(-5.30390 q^{6}\) \(+0.502260 q^{7}\) \(-0.761409 q^{8}\) \(+3.44555 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.08913 q^{2}\) \(+2.53881 q^{3}\) \(+2.36446 q^{4}\) \(+0.545075 q^{5}\) \(-5.30390 q^{6}\) \(+0.502260 q^{7}\) \(-0.761409 q^{8}\) \(+3.44555 q^{9}\) \(-1.13873 q^{10}\) \(-0.886428 q^{11}\) \(+6.00292 q^{12}\) \(-1.49726 q^{13}\) \(-1.04929 q^{14}\) \(+1.38384 q^{15}\) \(-3.13824 q^{16}\) \(-7.27823 q^{17}\) \(-7.19820 q^{18}\) \(+1.00000 q^{19}\) \(+1.28881 q^{20}\) \(+1.27514 q^{21}\) \(+1.85186 q^{22}\) \(-3.29382 q^{23}\) \(-1.93307 q^{24}\) \(-4.70289 q^{25}\) \(+3.12796 q^{26}\) \(+1.13117 q^{27}\) \(+1.18758 q^{28}\) \(+1.34373 q^{29}\) \(-2.89103 q^{30}\) \(+10.9986 q^{31}\) \(+8.07901 q^{32}\) \(-2.25047 q^{33}\) \(+15.2052 q^{34}\) \(+0.273770 q^{35}\) \(+8.14688 q^{36}\) \(+7.35907 q^{37}\) \(-2.08913 q^{38}\) \(-3.80125 q^{39}\) \(-0.415026 q^{40}\) \(-12.1447 q^{41}\) \(-2.66394 q^{42}\) \(-6.10178 q^{43}\) \(-2.09593 q^{44}\) \(+1.87809 q^{45}\) \(+6.88122 q^{46}\) \(-7.55200 q^{47}\) \(-7.96740 q^{48}\) \(-6.74773 q^{49}\) \(+9.82495 q^{50}\) \(-18.4780 q^{51}\) \(-3.54021 q^{52}\) \(+2.77691 q^{53}\) \(-2.36316 q^{54}\) \(-0.483170 q^{55}\) \(-0.382426 q^{56}\) \(+2.53881 q^{57}\) \(-2.80722 q^{58}\) \(+10.6355 q^{59}\) \(+3.27204 q^{60}\) \(-13.0361 q^{61}\) \(-22.9775 q^{62}\) \(+1.73056 q^{63}\) \(-10.6016 q^{64}\) \(-0.816118 q^{65}\) \(+4.70153 q^{66}\) \(-4.04620 q^{67}\) \(-17.2091 q^{68}\) \(-8.36238 q^{69}\) \(-0.571940 q^{70}\) \(-4.91131 q^{71}\) \(-2.62348 q^{72}\) \(+1.17251 q^{73}\) \(-15.3740 q^{74}\) \(-11.9397 q^{75}\) \(+2.36446 q^{76}\) \(-0.445218 q^{77}\) \(+7.94130 q^{78}\) \(+6.89393 q^{79}\) \(-1.71058 q^{80}\) \(-7.46483 q^{81}\) \(+25.3718 q^{82}\) \(+4.36066 q^{83}\) \(+3.01503 q^{84}\) \(-3.96719 q^{85}\) \(+12.7474 q^{86}\) \(+3.41147 q^{87}\) \(+0.674935 q^{88}\) \(-6.11709 q^{89}\) \(-3.92356 q^{90}\) \(-0.752013 q^{91}\) \(-7.78811 q^{92}\) \(+27.9233 q^{93}\) \(+15.7771 q^{94}\) \(+0.545075 q^{95}\) \(+20.5111 q^{96}\) \(+2.25721 q^{97}\) \(+14.0969 q^{98}\) \(-3.05424 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08913 −1.47724 −0.738619 0.674123i \(-0.764522\pi\)
−0.738619 + 0.674123i \(0.764522\pi\)
\(3\) 2.53881 1.46578 0.732891 0.680346i \(-0.238170\pi\)
0.732891 + 0.680346i \(0.238170\pi\)
\(4\) 2.36446 1.18223
\(5\) 0.545075 0.243765 0.121883 0.992545i \(-0.461107\pi\)
0.121883 + 0.992545i \(0.461107\pi\)
\(6\) −5.30390 −2.16531
\(7\) 0.502260 0.189837 0.0949183 0.995485i \(-0.469741\pi\)
0.0949183 + 0.995485i \(0.469741\pi\)
\(8\) −0.761409 −0.269199
\(9\) 3.44555 1.14852
\(10\) −1.13873 −0.360099
\(11\) −0.886428 −0.267268 −0.133634 0.991031i \(-0.542665\pi\)
−0.133634 + 0.991031i \(0.542665\pi\)
\(12\) 6.00292 1.73289
\(13\) −1.49726 −0.415264 −0.207632 0.978207i \(-0.566576\pi\)
−0.207632 + 0.978207i \(0.566576\pi\)
\(14\) −1.04929 −0.280434
\(15\) 1.38384 0.357307
\(16\) −3.13824 −0.784561
\(17\) −7.27823 −1.76523 −0.882615 0.470096i \(-0.844219\pi\)
−0.882615 + 0.470096i \(0.844219\pi\)
\(18\) −7.19820 −1.69663
\(19\) 1.00000 0.229416
\(20\) 1.28881 0.288187
\(21\) 1.27514 0.278259
\(22\) 1.85186 0.394819
\(23\) −3.29382 −0.686809 −0.343404 0.939188i \(-0.611580\pi\)
−0.343404 + 0.939188i \(0.611580\pi\)
\(24\) −1.93307 −0.394587
\(25\) −4.70289 −0.940579
\(26\) 3.12796 0.613444
\(27\) 1.13117 0.217694
\(28\) 1.18758 0.224431
\(29\) 1.34373 0.249524 0.124762 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(30\) −2.89103 −0.527827
\(31\) 10.9986 1.97540 0.987702 0.156348i \(-0.0499721\pi\)
0.987702 + 0.156348i \(0.0499721\pi\)
\(32\) 8.07901 1.42818
\(33\) −2.25047 −0.391757
\(34\) 15.2052 2.60767
\(35\) 0.273770 0.0462755
\(36\) 8.14688 1.35781
\(37\) 7.35907 1.20982 0.604912 0.796293i \(-0.293208\pi\)
0.604912 + 0.796293i \(0.293208\pi\)
\(38\) −2.08913 −0.338902
\(39\) −3.80125 −0.608687
\(40\) −0.415026 −0.0656213
\(41\) −12.1447 −1.89668 −0.948341 0.317252i \(-0.897240\pi\)
−0.948341 + 0.317252i \(0.897240\pi\)
\(42\) −2.66394 −0.411055
\(43\) −6.10178 −0.930512 −0.465256 0.885176i \(-0.654038\pi\)
−0.465256 + 0.885176i \(0.654038\pi\)
\(44\) −2.09593 −0.315973
\(45\) 1.87809 0.279968
\(46\) 6.88122 1.01458
\(47\) −7.55200 −1.10157 −0.550786 0.834646i \(-0.685672\pi\)
−0.550786 + 0.834646i \(0.685672\pi\)
\(48\) −7.96740 −1.14999
\(49\) −6.74773 −0.963962
\(50\) 9.82495 1.38946
\(51\) −18.4780 −2.58744
\(52\) −3.54021 −0.490939
\(53\) 2.77691 0.381438 0.190719 0.981645i \(-0.438918\pi\)
0.190719 + 0.981645i \(0.438918\pi\)
\(54\) −2.36316 −0.321586
\(55\) −0.483170 −0.0651507
\(56\) −0.382426 −0.0511038
\(57\) 2.53881 0.336273
\(58\) −2.80722 −0.368607
\(59\) 10.6355 1.38463 0.692313 0.721598i \(-0.256592\pi\)
0.692313 + 0.721598i \(0.256592\pi\)
\(60\) 3.27204 0.422419
\(61\) −13.0361 −1.66910 −0.834548 0.550935i \(-0.814271\pi\)
−0.834548 + 0.550935i \(0.814271\pi\)
\(62\) −22.9775 −2.91814
\(63\) 1.73056 0.218031
\(64\) −10.6016 −1.32520
\(65\) −0.816118 −0.101227
\(66\) 4.70153 0.578718
\(67\) −4.04620 −0.494322 −0.247161 0.968974i \(-0.579498\pi\)
−0.247161 + 0.968974i \(0.579498\pi\)
\(68\) −17.2091 −2.08691
\(69\) −8.36238 −1.00671
\(70\) −0.571940 −0.0683600
\(71\) −4.91131 −0.582866 −0.291433 0.956591i \(-0.594132\pi\)
−0.291433 + 0.956591i \(0.594132\pi\)
\(72\) −2.62348 −0.309180
\(73\) 1.17251 0.137232 0.0686161 0.997643i \(-0.478142\pi\)
0.0686161 + 0.997643i \(0.478142\pi\)
\(74\) −15.3740 −1.78720
\(75\) −11.9397 −1.37868
\(76\) 2.36446 0.271222
\(77\) −0.445218 −0.0507373
\(78\) 7.94130 0.899176
\(79\) 6.89393 0.775628 0.387814 0.921738i \(-0.373230\pi\)
0.387814 + 0.921738i \(0.373230\pi\)
\(80\) −1.71058 −0.191249
\(81\) −7.46483 −0.829425
\(82\) 25.3718 2.80185
\(83\) 4.36066 0.478645 0.239323 0.970940i \(-0.423075\pi\)
0.239323 + 0.970940i \(0.423075\pi\)
\(84\) 3.01503 0.328967
\(85\) −3.96719 −0.430302
\(86\) 12.7474 1.37459
\(87\) 3.41147 0.365748
\(88\) 0.674935 0.0719483
\(89\) −6.11709 −0.648410 −0.324205 0.945987i \(-0.605097\pi\)
−0.324205 + 0.945987i \(0.605097\pi\)
\(90\) −3.92356 −0.413580
\(91\) −0.752013 −0.0788324
\(92\) −7.78811 −0.811967
\(93\) 27.9233 2.89551
\(94\) 15.7771 1.62728
\(95\) 0.545075 0.0559236
\(96\) 20.5111 2.09340
\(97\) 2.25721 0.229185 0.114592 0.993413i \(-0.463444\pi\)
0.114592 + 0.993413i \(0.463444\pi\)
\(98\) 14.0969 1.42400
\(99\) −3.05424 −0.306962
\(100\) −11.1198 −1.11198
\(101\) −14.0586 −1.39888 −0.699441 0.714690i \(-0.746568\pi\)
−0.699441 + 0.714690i \(0.746568\pi\)
\(102\) 38.6030 3.82227
\(103\) −2.33696 −0.230268 −0.115134 0.993350i \(-0.536730\pi\)
−0.115134 + 0.993350i \(0.536730\pi\)
\(104\) 1.14003 0.111789
\(105\) 0.695049 0.0678298
\(106\) −5.80133 −0.563475
\(107\) 0.971779 0.0939454 0.0469727 0.998896i \(-0.485043\pi\)
0.0469727 + 0.998896i \(0.485043\pi\)
\(108\) 2.67461 0.257364
\(109\) −5.34939 −0.512378 −0.256189 0.966627i \(-0.582467\pi\)
−0.256189 + 0.966627i \(0.582467\pi\)
\(110\) 1.00941 0.0962430
\(111\) 18.6833 1.77334
\(112\) −1.57621 −0.148938
\(113\) 9.49763 0.893462 0.446731 0.894668i \(-0.352588\pi\)
0.446731 + 0.894668i \(0.352588\pi\)
\(114\) −5.30390 −0.496756
\(115\) −1.79538 −0.167420
\(116\) 3.17720 0.294995
\(117\) −5.15888 −0.476938
\(118\) −22.2190 −2.04542
\(119\) −3.65557 −0.335105
\(120\) −1.05367 −0.0961865
\(121\) −10.2142 −0.928568
\(122\) 27.2340 2.46565
\(123\) −30.8331 −2.78012
\(124\) 26.0057 2.33538
\(125\) −5.28881 −0.473045
\(126\) −3.61537 −0.322083
\(127\) −7.72323 −0.685326 −0.342663 0.939458i \(-0.611329\pi\)
−0.342663 + 0.939458i \(0.611329\pi\)
\(128\) 5.99013 0.529458
\(129\) −15.4912 −1.36393
\(130\) 1.70498 0.149536
\(131\) −14.6723 −1.28193 −0.640963 0.767572i \(-0.721465\pi\)
−0.640963 + 0.767572i \(0.721465\pi\)
\(132\) −5.32116 −0.463147
\(133\) 0.502260 0.0435515
\(134\) 8.45304 0.730231
\(135\) 0.616573 0.0530662
\(136\) 5.54171 0.475198
\(137\) −9.76110 −0.833947 −0.416974 0.908919i \(-0.636909\pi\)
−0.416974 + 0.908919i \(0.636909\pi\)
\(138\) 17.4701 1.48715
\(139\) 8.22954 0.698021 0.349010 0.937119i \(-0.386518\pi\)
0.349010 + 0.937119i \(0.386518\pi\)
\(140\) 0.647318 0.0547084
\(141\) −19.1731 −1.61467
\(142\) 10.2604 0.861031
\(143\) 1.32721 0.110987
\(144\) −10.8130 −0.901081
\(145\) 0.732434 0.0608253
\(146\) −2.44953 −0.202724
\(147\) −17.1312 −1.41296
\(148\) 17.4002 1.43029
\(149\) 7.50461 0.614802 0.307401 0.951580i \(-0.400541\pi\)
0.307401 + 0.951580i \(0.400541\pi\)
\(150\) 24.9437 2.03664
\(151\) 0.650776 0.0529594 0.0264797 0.999649i \(-0.491570\pi\)
0.0264797 + 0.999649i \(0.491570\pi\)
\(152\) −0.761409 −0.0617585
\(153\) −25.0775 −2.02740
\(154\) 0.930118 0.0749510
\(155\) 5.99506 0.481535
\(156\) −8.98791 −0.719609
\(157\) 2.24450 0.179131 0.0895653 0.995981i \(-0.471452\pi\)
0.0895653 + 0.995981i \(0.471452\pi\)
\(158\) −14.4023 −1.14579
\(159\) 7.05005 0.559106
\(160\) 4.40367 0.348141
\(161\) −1.65435 −0.130381
\(162\) 15.5950 1.22526
\(163\) 16.7436 1.31146 0.655730 0.754995i \(-0.272361\pi\)
0.655730 + 0.754995i \(0.272361\pi\)
\(164\) −28.7157 −2.24232
\(165\) −1.22668 −0.0954967
\(166\) −9.10999 −0.707073
\(167\) 7.19056 0.556422 0.278211 0.960520i \(-0.410259\pi\)
0.278211 + 0.960520i \(0.410259\pi\)
\(168\) −0.970906 −0.0749070
\(169\) −10.7582 −0.827555
\(170\) 8.28797 0.635658
\(171\) 3.44555 0.263488
\(172\) −14.4274 −1.10008
\(173\) −7.21645 −0.548657 −0.274328 0.961636i \(-0.588455\pi\)
−0.274328 + 0.961636i \(0.588455\pi\)
\(174\) −7.12701 −0.540297
\(175\) −2.36208 −0.178556
\(176\) 2.78183 0.209688
\(177\) 27.0015 2.02956
\(178\) 12.7794 0.957856
\(179\) 1.92293 0.143727 0.0718633 0.997414i \(-0.477105\pi\)
0.0718633 + 0.997414i \(0.477105\pi\)
\(180\) 4.44066 0.330987
\(181\) 11.7533 0.873618 0.436809 0.899554i \(-0.356109\pi\)
0.436809 + 0.899554i \(0.356109\pi\)
\(182\) 1.57105 0.116454
\(183\) −33.0961 −2.44653
\(184\) 2.50794 0.184888
\(185\) 4.01125 0.294913
\(186\) −58.3354 −4.27736
\(187\) 6.45163 0.471790
\(188\) −17.8564 −1.30231
\(189\) 0.568142 0.0413262
\(190\) −1.13873 −0.0826124
\(191\) 3.58319 0.259270 0.129635 0.991562i \(-0.458619\pi\)
0.129635 + 0.991562i \(0.458619\pi\)
\(192\) −26.9155 −1.94246
\(193\) 11.1120 0.799860 0.399930 0.916546i \(-0.369034\pi\)
0.399930 + 0.916546i \(0.369034\pi\)
\(194\) −4.71560 −0.338561
\(195\) −2.07197 −0.148377
\(196\) −15.9548 −1.13963
\(197\) 0.415089 0.0295739 0.0147869 0.999891i \(-0.495293\pi\)
0.0147869 + 0.999891i \(0.495293\pi\)
\(198\) 6.38069 0.453456
\(199\) −7.11252 −0.504193 −0.252096 0.967702i \(-0.581120\pi\)
−0.252096 + 0.967702i \(0.581120\pi\)
\(200\) 3.58083 0.253203
\(201\) −10.2725 −0.724568
\(202\) 29.3702 2.06648
\(203\) 0.674902 0.0473688
\(204\) −43.6906 −3.05896
\(205\) −6.61977 −0.462345
\(206\) 4.88222 0.340160
\(207\) −11.3490 −0.788812
\(208\) 4.69876 0.325800
\(209\) −0.886428 −0.0613155
\(210\) −1.45205 −0.100201
\(211\) 1.00000 0.0688428
\(212\) 6.56591 0.450948
\(213\) −12.4689 −0.854354
\(214\) −2.03017 −0.138780
\(215\) −3.32593 −0.226826
\(216\) −0.861284 −0.0586029
\(217\) 5.52415 0.375004
\(218\) 11.1756 0.756905
\(219\) 2.97678 0.201152
\(220\) −1.14244 −0.0770232
\(221\) 10.8974 0.733038
\(222\) −39.0318 −2.61964
\(223\) 15.6045 1.04495 0.522477 0.852653i \(-0.325008\pi\)
0.522477 + 0.852653i \(0.325008\pi\)
\(224\) 4.05777 0.271121
\(225\) −16.2041 −1.08027
\(226\) −19.8418 −1.31986
\(227\) 0.643938 0.0427396 0.0213698 0.999772i \(-0.493197\pi\)
0.0213698 + 0.999772i \(0.493197\pi\)
\(228\) 6.00292 0.397553
\(229\) −16.6315 −1.09904 −0.549519 0.835481i \(-0.685189\pi\)
−0.549519 + 0.835481i \(0.685189\pi\)
\(230\) 3.75078 0.247319
\(231\) −1.13032 −0.0743698
\(232\) −1.02313 −0.0671716
\(233\) −16.6602 −1.09145 −0.545724 0.837965i \(-0.683745\pi\)
−0.545724 + 0.837965i \(0.683745\pi\)
\(234\) 10.7776 0.704551
\(235\) −4.11641 −0.268525
\(236\) 25.1473 1.63695
\(237\) 17.5024 1.13690
\(238\) 7.63695 0.495030
\(239\) 16.5726 1.07199 0.535995 0.844221i \(-0.319937\pi\)
0.535995 + 0.844221i \(0.319937\pi\)
\(240\) −4.34283 −0.280329
\(241\) −9.26176 −0.596603 −0.298301 0.954472i \(-0.596420\pi\)
−0.298301 + 0.954472i \(0.596420\pi\)
\(242\) 21.3389 1.37172
\(243\) −22.3453 −1.43345
\(244\) −30.8233 −1.97326
\(245\) −3.67802 −0.234980
\(246\) 64.4143 4.10690
\(247\) −1.49726 −0.0952682
\(248\) −8.37443 −0.531777
\(249\) 11.0709 0.701589
\(250\) 11.0490 0.698801
\(251\) −9.06799 −0.572366 −0.286183 0.958175i \(-0.592387\pi\)
−0.286183 + 0.958175i \(0.592387\pi\)
\(252\) 4.09185 0.257763
\(253\) 2.91974 0.183562
\(254\) 16.1348 1.01239
\(255\) −10.0719 −0.630729
\(256\) 8.68908 0.543067
\(257\) 3.44022 0.214595 0.107298 0.994227i \(-0.465780\pi\)
0.107298 + 0.994227i \(0.465780\pi\)
\(258\) 32.3632 2.01485
\(259\) 3.69617 0.229669
\(260\) −1.92968 −0.119674
\(261\) 4.62989 0.286583
\(262\) 30.6524 1.89371
\(263\) 10.2535 0.632255 0.316128 0.948717i \(-0.397617\pi\)
0.316128 + 0.948717i \(0.397617\pi\)
\(264\) 1.71353 0.105461
\(265\) 1.51363 0.0929814
\(266\) −1.04929 −0.0643359
\(267\) −15.5301 −0.950428
\(268\) −9.56709 −0.584403
\(269\) −6.94192 −0.423257 −0.211628 0.977350i \(-0.567877\pi\)
−0.211628 + 0.977350i \(0.567877\pi\)
\(270\) −1.28810 −0.0783913
\(271\) 20.7920 1.26302 0.631512 0.775366i \(-0.282435\pi\)
0.631512 + 0.775366i \(0.282435\pi\)
\(272\) 22.8409 1.38493
\(273\) −1.90922 −0.115551
\(274\) 20.3922 1.23194
\(275\) 4.16878 0.251387
\(276\) −19.7725 −1.19017
\(277\) −2.59446 −0.155886 −0.0779431 0.996958i \(-0.524835\pi\)
−0.0779431 + 0.996958i \(0.524835\pi\)
\(278\) −17.1926 −1.03114
\(279\) 37.8962 2.26879
\(280\) −0.208451 −0.0124573
\(281\) −30.7993 −1.83733 −0.918666 0.395036i \(-0.870732\pi\)
−0.918666 + 0.395036i \(0.870732\pi\)
\(282\) 40.0551 2.38525
\(283\) 0.0995144 0.00591552 0.00295776 0.999996i \(-0.499059\pi\)
0.00295776 + 0.999996i \(0.499059\pi\)
\(284\) −11.6126 −0.689082
\(285\) 1.38384 0.0819718
\(286\) −2.77272 −0.163954
\(287\) −6.09980 −0.360060
\(288\) 27.8367 1.64029
\(289\) 35.9727 2.11604
\(290\) −1.53015 −0.0898534
\(291\) 5.73062 0.335935
\(292\) 2.77236 0.162240
\(293\) −11.8654 −0.693184 −0.346592 0.938016i \(-0.612661\pi\)
−0.346592 + 0.938016i \(0.612661\pi\)
\(294\) 35.7893 2.08728
\(295\) 5.79715 0.337523
\(296\) −5.60326 −0.325683
\(297\) −1.00270 −0.0581826
\(298\) −15.6781 −0.908208
\(299\) 4.93170 0.285207
\(300\) −28.2311 −1.62992
\(301\) −3.06468 −0.176645
\(302\) −1.35956 −0.0782336
\(303\) −35.6921 −2.05046
\(304\) −3.13824 −0.179991
\(305\) −7.10564 −0.406867
\(306\) 52.3902 2.99495
\(307\) 27.8816 1.59129 0.795643 0.605766i \(-0.207133\pi\)
0.795643 + 0.605766i \(0.207133\pi\)
\(308\) −1.05270 −0.0599832
\(309\) −5.93310 −0.337522
\(310\) −12.5245 −0.711341
\(311\) 16.9851 0.963139 0.481570 0.876408i \(-0.340067\pi\)
0.481570 + 0.876408i \(0.340067\pi\)
\(312\) 2.89431 0.163858
\(313\) 30.5752 1.72821 0.864107 0.503309i \(-0.167884\pi\)
0.864107 + 0.503309i \(0.167884\pi\)
\(314\) −4.68905 −0.264618
\(315\) 0.943288 0.0531482
\(316\) 16.3004 0.916971
\(317\) −5.64859 −0.317257 −0.158628 0.987338i \(-0.550707\pi\)
−0.158628 + 0.987338i \(0.550707\pi\)
\(318\) −14.7285 −0.825932
\(319\) −1.19112 −0.0666899
\(320\) −5.77868 −0.323038
\(321\) 2.46716 0.137704
\(322\) 3.45616 0.192604
\(323\) −7.27823 −0.404972
\(324\) −17.6503 −0.980573
\(325\) 7.04144 0.390589
\(326\) −34.9796 −1.93734
\(327\) −13.5811 −0.751035
\(328\) 9.24708 0.510585
\(329\) −3.79307 −0.209119
\(330\) 2.56269 0.141071
\(331\) −18.9675 −1.04255 −0.521274 0.853389i \(-0.674543\pi\)
−0.521274 + 0.853389i \(0.674543\pi\)
\(332\) 10.3106 0.565869
\(333\) 25.3560 1.38950
\(334\) −15.0220 −0.821967
\(335\) −2.20548 −0.120498
\(336\) −4.00171 −0.218311
\(337\) −11.1788 −0.608945 −0.304473 0.952521i \(-0.598480\pi\)
−0.304473 + 0.952521i \(0.598480\pi\)
\(338\) 22.4753 1.22250
\(339\) 24.1127 1.30962
\(340\) −9.38026 −0.508716
\(341\) −9.74946 −0.527963
\(342\) −7.19820 −0.389234
\(343\) −6.90494 −0.372832
\(344\) 4.64595 0.250493
\(345\) −4.55813 −0.245401
\(346\) 15.0761 0.810496
\(347\) −20.2523 −1.08720 −0.543599 0.839345i \(-0.682939\pi\)
−0.543599 + 0.839345i \(0.682939\pi\)
\(348\) 8.06630 0.432399
\(349\) 31.4396 1.68292 0.841461 0.540317i \(-0.181696\pi\)
0.841461 + 0.540317i \(0.181696\pi\)
\(350\) 4.93468 0.263770
\(351\) −1.69365 −0.0904005
\(352\) −7.16147 −0.381707
\(353\) −35.7646 −1.90356 −0.951779 0.306785i \(-0.900747\pi\)
−0.951779 + 0.306785i \(0.900747\pi\)
\(354\) −56.4097 −2.99814
\(355\) −2.67704 −0.142082
\(356\) −14.4636 −0.766571
\(357\) −9.28079 −0.491191
\(358\) −4.01725 −0.212318
\(359\) 6.68138 0.352630 0.176315 0.984334i \(-0.443582\pi\)
0.176315 + 0.984334i \(0.443582\pi\)
\(360\) −1.42999 −0.0753672
\(361\) 1.00000 0.0526316
\(362\) −24.5542 −1.29054
\(363\) −25.9320 −1.36108
\(364\) −1.77811 −0.0931981
\(365\) 0.639107 0.0334524
\(366\) 69.1420 3.61411
\(367\) 37.6971 1.96777 0.983887 0.178792i \(-0.0572189\pi\)
0.983887 + 0.178792i \(0.0572189\pi\)
\(368\) 10.3368 0.538843
\(369\) −41.8452 −2.17837
\(370\) −8.38001 −0.435656
\(371\) 1.39473 0.0724110
\(372\) 66.0236 3.42316
\(373\) −7.11293 −0.368293 −0.184147 0.982899i \(-0.558952\pi\)
−0.184147 + 0.982899i \(0.558952\pi\)
\(374\) −13.4783 −0.696946
\(375\) −13.4273 −0.693381
\(376\) 5.75017 0.296542
\(377\) −2.01191 −0.103619
\(378\) −1.18692 −0.0610487
\(379\) −16.5868 −0.852007 −0.426003 0.904722i \(-0.640079\pi\)
−0.426003 + 0.904722i \(0.640079\pi\)
\(380\) 1.28881 0.0661146
\(381\) −19.6078 −1.00454
\(382\) −7.48574 −0.383004
\(383\) −7.11316 −0.363466 −0.181733 0.983348i \(-0.558171\pi\)
−0.181733 + 0.983348i \(0.558171\pi\)
\(384\) 15.2078 0.776070
\(385\) −0.242677 −0.0123680
\(386\) −23.2144 −1.18158
\(387\) −21.0240 −1.06871
\(388\) 5.33709 0.270950
\(389\) 23.9956 1.21663 0.608314 0.793697i \(-0.291846\pi\)
0.608314 + 0.793697i \(0.291846\pi\)
\(390\) 4.32861 0.219188
\(391\) 23.9732 1.21238
\(392\) 5.13779 0.259497
\(393\) −37.2502 −1.87902
\(394\) −0.867174 −0.0436876
\(395\) 3.75771 0.189071
\(396\) −7.22162 −0.362900
\(397\) −23.4761 −1.17823 −0.589115 0.808049i \(-0.700524\pi\)
−0.589115 + 0.808049i \(0.700524\pi\)
\(398\) 14.8590 0.744813
\(399\) 1.27514 0.0638370
\(400\) 14.7588 0.737941
\(401\) 22.4420 1.12070 0.560350 0.828256i \(-0.310666\pi\)
0.560350 + 0.828256i \(0.310666\pi\)
\(402\) 21.4606 1.07036
\(403\) −16.4677 −0.820315
\(404\) −33.2410 −1.65380
\(405\) −4.06889 −0.202185
\(406\) −1.40996 −0.0699750
\(407\) −6.52329 −0.323347
\(408\) 14.0694 0.696537
\(409\) 8.20578 0.405750 0.202875 0.979205i \(-0.434972\pi\)
0.202875 + 0.979205i \(0.434972\pi\)
\(410\) 13.8296 0.682994
\(411\) −24.7816 −1.22238
\(412\) −5.52566 −0.272230
\(413\) 5.34179 0.262852
\(414\) 23.7096 1.16526
\(415\) 2.37689 0.116677
\(416\) −12.0964 −0.593073
\(417\) 20.8932 1.02315
\(418\) 1.85186 0.0905776
\(419\) −7.02038 −0.342968 −0.171484 0.985187i \(-0.554856\pi\)
−0.171484 + 0.985187i \(0.554856\pi\)
\(420\) 1.64342 0.0801906
\(421\) 6.72465 0.327739 0.163870 0.986482i \(-0.447602\pi\)
0.163870 + 0.986482i \(0.447602\pi\)
\(422\) −2.08913 −0.101697
\(423\) −26.0208 −1.26518
\(424\) −2.11437 −0.102683
\(425\) 34.2288 1.66034
\(426\) 26.0491 1.26208
\(427\) −6.54749 −0.316855
\(428\) 2.29774 0.111065
\(429\) 3.36954 0.162683
\(430\) 6.94830 0.335077
\(431\) 24.4434 1.17740 0.588699 0.808352i \(-0.299640\pi\)
0.588699 + 0.808352i \(0.299640\pi\)
\(432\) −3.54989 −0.170794
\(433\) −15.8218 −0.760345 −0.380172 0.924916i \(-0.624135\pi\)
−0.380172 + 0.924916i \(0.624135\pi\)
\(434\) −11.5407 −0.553970
\(435\) 1.85951 0.0891566
\(436\) −12.6484 −0.605750
\(437\) −3.29382 −0.157565
\(438\) −6.21889 −0.297150
\(439\) −10.8332 −0.517041 −0.258520 0.966006i \(-0.583235\pi\)
−0.258520 + 0.966006i \(0.583235\pi\)
\(440\) 0.367890 0.0175385
\(441\) −23.2497 −1.10713
\(442\) −22.7661 −1.08287
\(443\) −13.0347 −0.619299 −0.309650 0.950851i \(-0.600212\pi\)
−0.309650 + 0.950851i \(0.600212\pi\)
\(444\) 44.1759 2.09649
\(445\) −3.33428 −0.158060
\(446\) −32.5998 −1.54365
\(447\) 19.0528 0.901165
\(448\) −5.32477 −0.251572
\(449\) −1.11968 −0.0528409 −0.0264205 0.999651i \(-0.508411\pi\)
−0.0264205 + 0.999651i \(0.508411\pi\)
\(450\) 33.8524 1.59582
\(451\) 10.7654 0.506923
\(452\) 22.4568 1.05628
\(453\) 1.65220 0.0776270
\(454\) −1.34527 −0.0631366
\(455\) −0.409904 −0.0192166
\(456\) −1.93307 −0.0905244
\(457\) 8.39294 0.392605 0.196303 0.980543i \(-0.437107\pi\)
0.196303 + 0.980543i \(0.437107\pi\)
\(458\) 34.7453 1.62354
\(459\) −8.23292 −0.384280
\(460\) −4.24511 −0.197929
\(461\) −14.7600 −0.687442 −0.343721 0.939072i \(-0.611688\pi\)
−0.343721 + 0.939072i \(0.611688\pi\)
\(462\) 2.36139 0.109862
\(463\) −10.4446 −0.485403 −0.242701 0.970101i \(-0.578033\pi\)
−0.242701 + 0.970101i \(0.578033\pi\)
\(464\) −4.21695 −0.195767
\(465\) 15.2203 0.705825
\(466\) 34.8053 1.61233
\(467\) 19.9157 0.921588 0.460794 0.887507i \(-0.347565\pi\)
0.460794 + 0.887507i \(0.347565\pi\)
\(468\) −12.1980 −0.563851
\(469\) −2.03225 −0.0938404
\(470\) 8.59972 0.396675
\(471\) 5.69835 0.262566
\(472\) −8.09798 −0.372740
\(473\) 5.40879 0.248696
\(474\) −36.5647 −1.67947
\(475\) −4.70289 −0.215784
\(476\) −8.64345 −0.396172
\(477\) 9.56800 0.438089
\(478\) −34.6222 −1.58358
\(479\) −39.4253 −1.80139 −0.900694 0.434453i \(-0.856942\pi\)
−0.900694 + 0.434453i \(0.856942\pi\)
\(480\) 11.1801 0.510299
\(481\) −11.0184 −0.502397
\(482\) 19.3490 0.881324
\(483\) −4.20009 −0.191111
\(484\) −24.1512 −1.09778
\(485\) 1.23035 0.0558673
\(486\) 46.6822 2.11755
\(487\) 26.9105 1.21943 0.609716 0.792620i \(-0.291284\pi\)
0.609716 + 0.792620i \(0.291284\pi\)
\(488\) 9.92578 0.449319
\(489\) 42.5088 1.92232
\(490\) 7.68387 0.347122
\(491\) −28.1432 −1.27009 −0.635043 0.772477i \(-0.719018\pi\)
−0.635043 + 0.772477i \(0.719018\pi\)
\(492\) −72.9036 −3.28675
\(493\) −9.77997 −0.440468
\(494\) 3.12796 0.140734
\(495\) −1.66479 −0.0748267
\(496\) −34.5162 −1.54982
\(497\) −2.46676 −0.110649
\(498\) −23.1285 −1.03641
\(499\) 5.60279 0.250815 0.125408 0.992105i \(-0.459976\pi\)
0.125408 + 0.992105i \(0.459976\pi\)
\(500\) −12.5052 −0.559249
\(501\) 18.2554 0.815593
\(502\) 18.9442 0.845521
\(503\) −4.67738 −0.208554 −0.104277 0.994548i \(-0.533253\pi\)
−0.104277 + 0.994548i \(0.533253\pi\)
\(504\) −1.31767 −0.0586936
\(505\) −7.66299 −0.340999
\(506\) −6.09971 −0.271165
\(507\) −27.3131 −1.21302
\(508\) −18.2613 −0.810213
\(509\) −32.3575 −1.43422 −0.717111 0.696959i \(-0.754536\pi\)
−0.717111 + 0.696959i \(0.754536\pi\)
\(510\) 21.0416 0.931736
\(511\) 0.588906 0.0260517
\(512\) −30.1329 −1.33170
\(513\) 1.13117 0.0499424
\(514\) −7.18707 −0.317008
\(515\) −1.27382 −0.0561313
\(516\) −36.6285 −1.61248
\(517\) 6.69431 0.294415
\(518\) −7.72177 −0.339275
\(519\) −18.3212 −0.804211
\(520\) 0.621400 0.0272502
\(521\) −12.6607 −0.554676 −0.277338 0.960772i \(-0.589452\pi\)
−0.277338 + 0.960772i \(0.589452\pi\)
\(522\) −9.67243 −0.423351
\(523\) −6.30642 −0.275761 −0.137880 0.990449i \(-0.544029\pi\)
−0.137880 + 0.990449i \(0.544029\pi\)
\(524\) −34.6921 −1.51553
\(525\) −5.99686 −0.261724
\(526\) −21.4208 −0.933992
\(527\) −80.0503 −3.48704
\(528\) 7.06253 0.307357
\(529\) −12.1508 −0.528294
\(530\) −3.16216 −0.137356
\(531\) 36.6452 1.59027
\(532\) 1.18758 0.0514879
\(533\) 18.1837 0.787625
\(534\) 32.4444 1.40401
\(535\) 0.529693 0.0229006
\(536\) 3.08081 0.133071
\(537\) 4.88195 0.210672
\(538\) 14.5026 0.625251
\(539\) 5.98138 0.257636
\(540\) 1.45786 0.0627365
\(541\) −2.25820 −0.0970876 −0.0485438 0.998821i \(-0.515458\pi\)
−0.0485438 + 0.998821i \(0.515458\pi\)
\(542\) −43.4372 −1.86579
\(543\) 29.8394 1.28053
\(544\) −58.8009 −2.52107
\(545\) −2.91582 −0.124900
\(546\) 3.98860 0.170696
\(547\) 5.45943 0.233428 0.116714 0.993166i \(-0.462764\pi\)
0.116714 + 0.993166i \(0.462764\pi\)
\(548\) −23.0798 −0.985918
\(549\) −44.9164 −1.91699
\(550\) −8.70912 −0.371358
\(551\) 1.34373 0.0572448
\(552\) 6.36719 0.271006
\(553\) 3.46255 0.147242
\(554\) 5.42017 0.230281
\(555\) 10.1838 0.432278
\(556\) 19.4584 0.825222
\(557\) −29.7576 −1.26087 −0.630436 0.776241i \(-0.717124\pi\)
−0.630436 + 0.776241i \(0.717124\pi\)
\(558\) −79.1701 −3.35154
\(559\) 9.13593 0.386409
\(560\) −0.859156 −0.0363060
\(561\) 16.3795 0.691542
\(562\) 64.3437 2.71417
\(563\) 0.0442812 0.00186623 0.000933115 1.00000i \(-0.499703\pi\)
0.000933115 1.00000i \(0.499703\pi\)
\(564\) −45.3341 −1.90891
\(565\) 5.17693 0.217795
\(566\) −0.207899 −0.00873863
\(567\) −3.74929 −0.157455
\(568\) 3.73952 0.156907
\(569\) −10.1196 −0.424234 −0.212117 0.977244i \(-0.568036\pi\)
−0.212117 + 0.977244i \(0.568036\pi\)
\(570\) −2.89103 −0.121092
\(571\) −36.7464 −1.53779 −0.768895 0.639375i \(-0.779193\pi\)
−0.768895 + 0.639375i \(0.779193\pi\)
\(572\) 3.13814 0.131212
\(573\) 9.09703 0.380034
\(574\) 12.7433 0.531894
\(575\) 15.4905 0.645998
\(576\) −36.5284 −1.52202
\(577\) 30.3548 1.26369 0.631843 0.775097i \(-0.282299\pi\)
0.631843 + 0.775097i \(0.282299\pi\)
\(578\) −75.1516 −3.12589
\(579\) 28.2113 1.17242
\(580\) 1.73181 0.0719096
\(581\) 2.19019 0.0908643
\(582\) −11.9720 −0.496256
\(583\) −2.46154 −0.101946
\(584\) −0.892761 −0.0369427
\(585\) −2.81198 −0.116261
\(586\) 24.7884 1.02400
\(587\) −25.9241 −1.07000 −0.535002 0.844851i \(-0.679689\pi\)
−0.535002 + 0.844851i \(0.679689\pi\)
\(588\) −40.5061 −1.67044
\(589\) 10.9986 0.453189
\(590\) −12.1110 −0.498602
\(591\) 1.05383 0.0433488
\(592\) −23.0945 −0.949179
\(593\) 25.0174 1.02734 0.513671 0.857987i \(-0.328285\pi\)
0.513671 + 0.857987i \(0.328285\pi\)
\(594\) 2.09477 0.0859496
\(595\) −1.99256 −0.0816870
\(596\) 17.7444 0.726838
\(597\) −18.0573 −0.739037
\(598\) −10.3030 −0.421319
\(599\) 18.1978 0.743544 0.371772 0.928324i \(-0.378750\pi\)
0.371772 + 0.928324i \(0.378750\pi\)
\(600\) 9.09103 0.371140
\(601\) −0.434167 −0.0177100 −0.00885501 0.999961i \(-0.502819\pi\)
−0.00885501 + 0.999961i \(0.502819\pi\)
\(602\) 6.40251 0.260947
\(603\) −13.9414 −0.567737
\(604\) 1.53874 0.0626103
\(605\) −5.56753 −0.226352
\(606\) 74.5654 3.02901
\(607\) 31.7084 1.28700 0.643501 0.765445i \(-0.277481\pi\)
0.643501 + 0.765445i \(0.277481\pi\)
\(608\) 8.07901 0.327647
\(609\) 1.71345 0.0694324
\(610\) 14.8446 0.601040
\(611\) 11.3073 0.457444
\(612\) −59.2949 −2.39685
\(613\) 1.83790 0.0742322 0.0371161 0.999311i \(-0.488183\pi\)
0.0371161 + 0.999311i \(0.488183\pi\)
\(614\) −58.2482 −2.35071
\(615\) −16.8063 −0.677697
\(616\) 0.338993 0.0136584
\(617\) −9.43200 −0.379718 −0.189859 0.981811i \(-0.560803\pi\)
−0.189859 + 0.981811i \(0.560803\pi\)
\(618\) 12.3950 0.498601
\(619\) 5.84887 0.235086 0.117543 0.993068i \(-0.462498\pi\)
0.117543 + 0.993068i \(0.462498\pi\)
\(620\) 14.1751 0.569285
\(621\) −3.72587 −0.149514
\(622\) −35.4842 −1.42279
\(623\) −3.07237 −0.123092
\(624\) 11.9292 0.477552
\(625\) 20.6317 0.825267
\(626\) −63.8756 −2.55298
\(627\) −2.25047 −0.0898752
\(628\) 5.30703 0.211774
\(629\) −53.5610 −2.13562
\(630\) −1.97065 −0.0785126
\(631\) −31.8250 −1.26693 −0.633467 0.773770i \(-0.718369\pi\)
−0.633467 + 0.773770i \(0.718369\pi\)
\(632\) −5.24910 −0.208798
\(633\) 2.53881 0.100909
\(634\) 11.8006 0.468663
\(635\) −4.20974 −0.167058
\(636\) 16.6696 0.660992
\(637\) 10.1031 0.400299
\(638\) 2.48840 0.0985168
\(639\) −16.9222 −0.669431
\(640\) 3.26508 0.129063
\(641\) 10.8364 0.428011 0.214006 0.976832i \(-0.431349\pi\)
0.214006 + 0.976832i \(0.431349\pi\)
\(642\) −5.15422 −0.203421
\(643\) 10.0693 0.397093 0.198546 0.980091i \(-0.436378\pi\)
0.198546 + 0.980091i \(0.436378\pi\)
\(644\) −3.91166 −0.154141
\(645\) −8.44390 −0.332478
\(646\) 15.2052 0.598240
\(647\) −14.8226 −0.582736 −0.291368 0.956611i \(-0.594110\pi\)
−0.291368 + 0.956611i \(0.594110\pi\)
\(648\) 5.68379 0.223280
\(649\) −9.42762 −0.370066
\(650\) −14.7105 −0.576993
\(651\) 14.0248 0.549674
\(652\) 39.5896 1.55045
\(653\) −31.7293 −1.24167 −0.620833 0.783943i \(-0.713205\pi\)
−0.620833 + 0.783943i \(0.713205\pi\)
\(654\) 28.3726 1.10946
\(655\) −7.99752 −0.312489
\(656\) 38.1130 1.48806
\(657\) 4.03995 0.157613
\(658\) 7.92422 0.308918
\(659\) −46.7350 −1.82054 −0.910269 0.414018i \(-0.864125\pi\)
−0.910269 + 0.414018i \(0.864125\pi\)
\(660\) −2.90043 −0.112899
\(661\) 31.0533 1.20783 0.603916 0.797048i \(-0.293606\pi\)
0.603916 + 0.797048i \(0.293606\pi\)
\(662\) 39.6256 1.54009
\(663\) 27.6664 1.07447
\(664\) −3.32025 −0.128851
\(665\) 0.273770 0.0106163
\(666\) −52.9721 −2.05263
\(667\) −4.42600 −0.171375
\(668\) 17.0018 0.657819
\(669\) 39.6168 1.53168
\(670\) 4.60754 0.178005
\(671\) 11.5555 0.446096
\(672\) 10.3019 0.397404
\(673\) 21.4003 0.824920 0.412460 0.910976i \(-0.364670\pi\)
0.412460 + 0.910976i \(0.364670\pi\)
\(674\) 23.3539 0.899557
\(675\) −5.31977 −0.204758
\(676\) −25.4374 −0.978362
\(677\) −34.0647 −1.30921 −0.654606 0.755971i \(-0.727165\pi\)
−0.654606 + 0.755971i \(0.727165\pi\)
\(678\) −50.3745 −1.93462
\(679\) 1.13371 0.0435077
\(680\) 3.02065 0.115837
\(681\) 1.63483 0.0626470
\(682\) 20.3679 0.779927
\(683\) 31.9822 1.22376 0.611882 0.790949i \(-0.290413\pi\)
0.611882 + 0.790949i \(0.290413\pi\)
\(684\) 8.14688 0.311504
\(685\) −5.32054 −0.203287
\(686\) 14.4253 0.550761
\(687\) −42.2241 −1.61095
\(688\) 19.1489 0.730043
\(689\) −4.15775 −0.158398
\(690\) 9.52252 0.362516
\(691\) 3.43283 0.130591 0.0652955 0.997866i \(-0.479201\pi\)
0.0652955 + 0.997866i \(0.479201\pi\)
\(692\) −17.0630 −0.648639
\(693\) −1.53402 −0.0582726
\(694\) 42.3096 1.60605
\(695\) 4.48572 0.170153
\(696\) −2.59753 −0.0984590
\(697\) 88.3919 3.34808
\(698\) −65.6814 −2.48608
\(699\) −42.2971 −1.59982
\(700\) −5.58504 −0.211095
\(701\) −8.09290 −0.305665 −0.152832 0.988252i \(-0.548839\pi\)
−0.152832 + 0.988252i \(0.548839\pi\)
\(702\) 3.53826 0.133543
\(703\) 7.35907 0.277552
\(704\) 9.39758 0.354185
\(705\) −10.4508 −0.393599
\(706\) 74.7169 2.81201
\(707\) −7.06107 −0.265559
\(708\) 63.8441 2.39941
\(709\) 22.1547 0.832037 0.416018 0.909356i \(-0.363425\pi\)
0.416018 + 0.909356i \(0.363425\pi\)
\(710\) 5.59268 0.209889
\(711\) 23.7534 0.890822
\(712\) 4.65761 0.174551
\(713\) −36.2274 −1.35672
\(714\) 19.3888 0.725606
\(715\) 0.723430 0.0270548
\(716\) 4.54670 0.169918
\(717\) 42.0745 1.57130
\(718\) −13.9583 −0.520918
\(719\) −30.7062 −1.14515 −0.572574 0.819853i \(-0.694055\pi\)
−0.572574 + 0.819853i \(0.694055\pi\)
\(720\) −5.89389 −0.219652
\(721\) −1.17376 −0.0437132
\(722\) −2.08913 −0.0777494
\(723\) −23.5139 −0.874490
\(724\) 27.7903 1.03282
\(725\) −6.31941 −0.234697
\(726\) 54.1753 2.01064
\(727\) −47.6134 −1.76588 −0.882942 0.469482i \(-0.844441\pi\)
−0.882942 + 0.469482i \(0.844441\pi\)
\(728\) 0.572590 0.0212216
\(729\) −34.3359 −1.27170
\(730\) −1.33518 −0.0494172
\(731\) 44.4102 1.64257
\(732\) −78.2544 −2.89237
\(733\) −41.3484 −1.52724 −0.763619 0.645667i \(-0.776580\pi\)
−0.763619 + 0.645667i \(0.776580\pi\)
\(734\) −78.7542 −2.90687
\(735\) −9.33780 −0.344430
\(736\) −26.6108 −0.980888
\(737\) 3.58667 0.132117
\(738\) 87.4200 3.21797
\(739\) 11.4151 0.419910 0.209955 0.977711i \(-0.432668\pi\)
0.209955 + 0.977711i \(0.432668\pi\)
\(740\) 9.48444 0.348655
\(741\) −3.80125 −0.139642
\(742\) −2.91378 −0.106968
\(743\) 43.8005 1.60689 0.803443 0.595382i \(-0.202999\pi\)
0.803443 + 0.595382i \(0.202999\pi\)
\(744\) −21.2611 −0.779469
\(745\) 4.09058 0.149867
\(746\) 14.8598 0.544057
\(747\) 15.0249 0.549732
\(748\) 15.2546 0.557765
\(749\) 0.488086 0.0178343
\(750\) 28.0513 1.02429
\(751\) 44.0727 1.60823 0.804117 0.594471i \(-0.202638\pi\)
0.804117 + 0.594471i \(0.202638\pi\)
\(752\) 23.7000 0.864251
\(753\) −23.0219 −0.838965
\(754\) 4.20314 0.153069
\(755\) 0.354722 0.0129097
\(756\) 1.34335 0.0488572
\(757\) −25.9109 −0.941749 −0.470875 0.882200i \(-0.656062\pi\)
−0.470875 + 0.882200i \(0.656062\pi\)
\(758\) 34.6520 1.25862
\(759\) 7.41265 0.269062
\(760\) −0.415026 −0.0150546
\(761\) 12.9657 0.470005 0.235002 0.971995i \(-0.424490\pi\)
0.235002 + 0.971995i \(0.424490\pi\)
\(762\) 40.9632 1.48394
\(763\) −2.68679 −0.0972682
\(764\) 8.47231 0.306517
\(765\) −13.6691 −0.494209
\(766\) 14.8603 0.536925
\(767\) −15.9241 −0.574986
\(768\) 22.0599 0.796018
\(769\) −16.6009 −0.598645 −0.299322 0.954152i \(-0.596761\pi\)
−0.299322 + 0.954152i \(0.596761\pi\)
\(770\) 0.506984 0.0182704
\(771\) 8.73406 0.314550
\(772\) 26.2739 0.945620
\(773\) 21.5445 0.774901 0.387450 0.921891i \(-0.373356\pi\)
0.387450 + 0.921891i \(0.373356\pi\)
\(774\) 43.9218 1.57874
\(775\) −51.7252 −1.85802
\(776\) −1.71866 −0.0616963
\(777\) 9.38386 0.336644
\(778\) −50.1300 −1.79725
\(779\) −12.1447 −0.435129
\(780\) −4.89909 −0.175416
\(781\) 4.35353 0.155782
\(782\) −50.0831 −1.79097
\(783\) 1.51999 0.0543199
\(784\) 21.1760 0.756287
\(785\) 1.22342 0.0436658
\(786\) 77.8205 2.77576
\(787\) −4.22340 −0.150548 −0.0752740 0.997163i \(-0.523983\pi\)
−0.0752740 + 0.997163i \(0.523983\pi\)
\(788\) 0.981462 0.0349631
\(789\) 26.0316 0.926749
\(790\) −7.85035 −0.279303
\(791\) 4.77028 0.169612
\(792\) 2.32552 0.0826339
\(793\) 19.5183 0.693116
\(794\) 49.0446 1.74053
\(795\) 3.84281 0.136290
\(796\) −16.8173 −0.596073
\(797\) 5.28169 0.187087 0.0935436 0.995615i \(-0.470181\pi\)
0.0935436 + 0.995615i \(0.470181\pi\)
\(798\) −2.66394 −0.0943024
\(799\) 54.9652 1.94453
\(800\) −37.9947 −1.34332
\(801\) −21.0767 −0.744710
\(802\) −46.8843 −1.65554
\(803\) −1.03935 −0.0366778
\(804\) −24.2890 −0.856607
\(805\) −0.901748 −0.0317824
\(806\) 34.4032 1.21180
\(807\) −17.6242 −0.620402
\(808\) 10.7043 0.376578
\(809\) 2.96467 0.104232 0.0521161 0.998641i \(-0.483403\pi\)
0.0521161 + 0.998641i \(0.483403\pi\)
\(810\) 8.50045 0.298675
\(811\) 30.9700 1.08750 0.543751 0.839246i \(-0.317003\pi\)
0.543751 + 0.839246i \(0.317003\pi\)
\(812\) 1.59578 0.0560009
\(813\) 52.7869 1.85132
\(814\) 13.6280 0.477661
\(815\) 9.12653 0.319688
\(816\) 57.9886 2.03001
\(817\) −6.10178 −0.213474
\(818\) −17.1429 −0.599388
\(819\) −2.59110 −0.0905403
\(820\) −15.6522 −0.546599
\(821\) 13.4230 0.468468 0.234234 0.972180i \(-0.424742\pi\)
0.234234 + 0.972180i \(0.424742\pi\)
\(822\) 51.7719 1.80575
\(823\) 12.3681 0.431124 0.215562 0.976490i \(-0.430842\pi\)
0.215562 + 0.976490i \(0.430842\pi\)
\(824\) 1.77939 0.0619878
\(825\) 10.5837 0.368478
\(826\) −11.1597 −0.388296
\(827\) 23.0041 0.799931 0.399966 0.916530i \(-0.369022\pi\)
0.399966 + 0.916530i \(0.369022\pi\)
\(828\) −26.8343 −0.932558
\(829\) 20.9002 0.725893 0.362946 0.931810i \(-0.381771\pi\)
0.362946 + 0.931810i \(0.381771\pi\)
\(830\) −4.96563 −0.172360
\(831\) −6.58685 −0.228495
\(832\) 15.8734 0.550310
\(833\) 49.1116 1.70162
\(834\) −43.6487 −1.51143
\(835\) 3.91940 0.135636
\(836\) −2.09593 −0.0724891
\(837\) 12.4413 0.430033
\(838\) 14.6665 0.506645
\(839\) −2.64740 −0.0913985 −0.0456993 0.998955i \(-0.514552\pi\)
−0.0456993 + 0.998955i \(0.514552\pi\)
\(840\) −0.529217 −0.0182597
\(841\) −27.1944 −0.937738
\(842\) −14.0487 −0.484149
\(843\) −78.1935 −2.69313
\(844\) 2.36446 0.0813882
\(845\) −5.86404 −0.201729
\(846\) 54.3609 1.86896
\(847\) −5.13021 −0.176276
\(848\) −8.71463 −0.299262
\(849\) 0.252648 0.00867086
\(850\) −71.5083 −2.45271
\(851\) −24.2394 −0.830917
\(852\) −29.4822 −1.01004
\(853\) −20.9211 −0.716324 −0.358162 0.933659i \(-0.616596\pi\)
−0.358162 + 0.933659i \(0.616596\pi\)
\(854\) 13.6786 0.468071
\(855\) 1.87809 0.0642292
\(856\) −0.739922 −0.0252900
\(857\) 36.8618 1.25918 0.629588 0.776929i \(-0.283224\pi\)
0.629588 + 0.776929i \(0.283224\pi\)
\(858\) −7.03940 −0.240321
\(859\) 25.4407 0.868024 0.434012 0.900907i \(-0.357098\pi\)
0.434012 + 0.900907i \(0.357098\pi\)
\(860\) −7.86403 −0.268161
\(861\) −15.4862 −0.527769
\(862\) −51.0655 −1.73930
\(863\) −26.2705 −0.894258 −0.447129 0.894470i \(-0.647553\pi\)
−0.447129 + 0.894470i \(0.647553\pi\)
\(864\) 9.13874 0.310906
\(865\) −3.93351 −0.133743
\(866\) 33.0537 1.12321
\(867\) 91.3278 3.10165
\(868\) 13.0617 0.443341
\(869\) −6.11097 −0.207301
\(870\) −3.88476 −0.131706
\(871\) 6.05820 0.205274
\(872\) 4.07307 0.137932
\(873\) 7.77733 0.263223
\(874\) 6.88122 0.232761
\(875\) −2.65636 −0.0898013
\(876\) 7.03849 0.237809
\(877\) 16.0157 0.540812 0.270406 0.962746i \(-0.412842\pi\)
0.270406 + 0.962746i \(0.412842\pi\)
\(878\) 22.6320 0.763792
\(879\) −30.1240 −1.01606
\(880\) 1.51631 0.0511147
\(881\) −19.8350 −0.668257 −0.334128 0.942528i \(-0.608442\pi\)
−0.334128 + 0.942528i \(0.608442\pi\)
\(882\) 48.5716 1.63549
\(883\) −3.38233 −0.113825 −0.0569123 0.998379i \(-0.518126\pi\)
−0.0569123 + 0.998379i \(0.518126\pi\)
\(884\) 25.7665 0.866620
\(885\) 14.7179 0.494736
\(886\) 27.2313 0.914852
\(887\) −8.29322 −0.278459 −0.139230 0.990260i \(-0.544463\pi\)
−0.139230 + 0.990260i \(0.544463\pi\)
\(888\) −14.2256 −0.477380
\(889\) −3.87907 −0.130100
\(890\) 6.96573 0.233492
\(891\) 6.61704 0.221679
\(892\) 36.8962 1.23538
\(893\) −7.55200 −0.252718
\(894\) −39.8037 −1.33124
\(895\) 1.04814 0.0350355
\(896\) 3.00861 0.100510
\(897\) 12.5206 0.418052
\(898\) 2.33915 0.0780586
\(899\) 14.7791 0.492911
\(900\) −38.3139 −1.27713
\(901\) −20.2110 −0.673327
\(902\) −22.4903 −0.748846
\(903\) −7.78064 −0.258923
\(904\) −7.23159 −0.240519
\(905\) 6.40645 0.212958
\(906\) −3.45165 −0.114673
\(907\) −40.6705 −1.35044 −0.675221 0.737615i \(-0.735952\pi\)
−0.675221 + 0.737615i \(0.735952\pi\)
\(908\) 1.52257 0.0505281
\(909\) −48.4396 −1.60664
\(910\) 0.856342 0.0283875
\(911\) 30.5709 1.01286 0.506430 0.862281i \(-0.330965\pi\)
0.506430 + 0.862281i \(0.330965\pi\)
\(912\) −7.96740 −0.263827
\(913\) −3.86542 −0.127927
\(914\) −17.5339 −0.579971
\(915\) −18.0399 −0.596379
\(916\) −39.3245 −1.29932
\(917\) −7.36932 −0.243356
\(918\) 17.1996 0.567673
\(919\) −53.9539 −1.77978 −0.889888 0.456179i \(-0.849218\pi\)
−0.889888 + 0.456179i \(0.849218\pi\)
\(920\) 1.36702 0.0450693
\(921\) 70.7860 2.33248
\(922\) 30.8356 1.01552
\(923\) 7.35350 0.242043
\(924\) −2.67261 −0.0879223
\(925\) −34.6089 −1.13793
\(926\) 21.8202 0.717055
\(927\) −8.05213 −0.264467
\(928\) 10.8560 0.356366
\(929\) −55.6887 −1.82709 −0.913543 0.406742i \(-0.866665\pi\)
−0.913543 + 0.406742i \(0.866665\pi\)
\(930\) −31.7972 −1.04267
\(931\) −6.74773 −0.221148
\(932\) −39.3925 −1.29034
\(933\) 43.1221 1.41175
\(934\) −41.6064 −1.36140
\(935\) 3.51663 0.115006
\(936\) 3.92802 0.128391
\(937\) 60.9497 1.99114 0.995569 0.0940297i \(-0.0299749\pi\)
0.995569 + 0.0940297i \(0.0299749\pi\)
\(938\) 4.24562 0.138625
\(939\) 77.6246 2.53318
\(940\) −9.73310 −0.317459
\(941\) 21.0671 0.686768 0.343384 0.939195i \(-0.388427\pi\)
0.343384 + 0.939195i \(0.388427\pi\)
\(942\) −11.9046 −0.387873
\(943\) 40.0024 1.30266
\(944\) −33.3768 −1.08632
\(945\) 0.309680 0.0100739
\(946\) −11.2997 −0.367384
\(947\) 38.9283 1.26500 0.632500 0.774560i \(-0.282029\pi\)
0.632500 + 0.774560i \(0.282029\pi\)
\(948\) 41.3837 1.34408
\(949\) −1.75555 −0.0569876
\(950\) 9.82495 0.318764
\(951\) −14.3407 −0.465029
\(952\) 2.78338 0.0902100
\(953\) 10.8572 0.351701 0.175850 0.984417i \(-0.443733\pi\)
0.175850 + 0.984417i \(0.443733\pi\)
\(954\) −19.9888 −0.647161
\(955\) 1.95311 0.0632010
\(956\) 39.1852 1.26734
\(957\) −3.02403 −0.0977529
\(958\) 82.3646 2.66108
\(959\) −4.90261 −0.158314
\(960\) −14.6710 −0.473504
\(961\) 89.9689 2.90222
\(962\) 23.0189 0.742159
\(963\) 3.34832 0.107898
\(964\) −21.8991 −0.705322
\(965\) 6.05689 0.194978
\(966\) 8.77453 0.282316
\(967\) −14.1288 −0.454350 −0.227175 0.973854i \(-0.572949\pi\)
−0.227175 + 0.973854i \(0.572949\pi\)
\(968\) 7.77722 0.249969
\(969\) −18.4780 −0.593600
\(970\) −2.57036 −0.0825293
\(971\) 41.3006 1.32540 0.662700 0.748885i \(-0.269411\pi\)
0.662700 + 0.748885i \(0.269411\pi\)
\(972\) −52.8346 −1.69467
\(973\) 4.13337 0.132510
\(974\) −56.2195 −1.80139
\(975\) 17.8769 0.572518
\(976\) 40.9103 1.30951
\(977\) 32.7177 1.04673 0.523367 0.852108i \(-0.324676\pi\)
0.523367 + 0.852108i \(0.324676\pi\)
\(978\) −88.8065 −2.83972
\(979\) 5.42236 0.173299
\(980\) −8.69655 −0.277801
\(981\) −18.4316 −0.588475
\(982\) 58.7948 1.87622
\(983\) −6.59906 −0.210477 −0.105239 0.994447i \(-0.533561\pi\)
−0.105239 + 0.994447i \(0.533561\pi\)
\(984\) 23.4766 0.748406
\(985\) 0.226255 0.00720907
\(986\) 20.4316 0.650676
\(987\) −9.62988 −0.306523
\(988\) −3.54021 −0.112629
\(989\) 20.0982 0.639084
\(990\) 3.47796 0.110537
\(991\) 40.6842 1.29238 0.646188 0.763178i \(-0.276362\pi\)
0.646188 + 0.763178i \(0.276362\pi\)
\(992\) 88.8577 2.82124
\(993\) −48.1549 −1.52815
\(994\) 5.15338 0.163455
\(995\) −3.87686 −0.122905
\(996\) 26.1767 0.829441
\(997\) 15.7544 0.498946 0.249473 0.968382i \(-0.419743\pi\)
0.249473 + 0.968382i \(0.419743\pi\)
\(998\) −11.7049 −0.370514
\(999\) 8.32436 0.263371
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 \(a_p\))