Properties

Label 6017.2.a.c.1.11
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.42329 q^{2}\) \(-0.918445 q^{3}\) \(+3.87233 q^{4}\) \(-2.10804 q^{5}\) \(+2.22566 q^{6}\) \(-2.69568 q^{7}\) \(-4.53719 q^{8}\) \(-2.15646 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.42329 q^{2}\) \(-0.918445 q^{3}\) \(+3.87233 q^{4}\) \(-2.10804 q^{5}\) \(+2.22566 q^{6}\) \(-2.69568 q^{7}\) \(-4.53719 q^{8}\) \(-2.15646 q^{9}\) \(+5.10839 q^{10}\) \(+1.00000 q^{11}\) \(-3.55652 q^{12}\) \(-1.31790 q^{13}\) \(+6.53241 q^{14}\) \(+1.93612 q^{15}\) \(+3.25026 q^{16}\) \(-1.02624 q^{17}\) \(+5.22572 q^{18}\) \(+1.40367 q^{19}\) \(-8.16302 q^{20}\) \(+2.47583 q^{21}\) \(-2.42329 q^{22}\) \(-7.47517 q^{23}\) \(+4.16716 q^{24}\) \(-0.556169 q^{25}\) \(+3.19364 q^{26}\) \(+4.73592 q^{27}\) \(-10.4386 q^{28}\) \(+4.75007 q^{29}\) \(-4.69177 q^{30}\) \(+4.78215 q^{31}\) \(+1.19805 q^{32}\) \(-0.918445 q^{33}\) \(+2.48687 q^{34}\) \(+5.68260 q^{35}\) \(-8.35052 q^{36}\) \(-7.86278 q^{37}\) \(-3.40149 q^{38}\) \(+1.21042 q^{39}\) \(+9.56457 q^{40}\) \(+8.85425 q^{41}\) \(-5.99966 q^{42}\) \(-3.78885 q^{43}\) \(+3.87233 q^{44}\) \(+4.54590 q^{45}\) \(+18.1145 q^{46}\) \(-12.0893 q^{47}\) \(-2.98519 q^{48}\) \(+0.266696 q^{49}\) \(+1.34776 q^{50}\) \(+0.942544 q^{51}\) \(-5.10333 q^{52}\) \(+3.68886 q^{53}\) \(-11.4765 q^{54}\) \(-2.10804 q^{55}\) \(+12.2308 q^{56}\) \(-1.28919 q^{57}\) \(-11.5108 q^{58}\) \(+7.33831 q^{59}\) \(+7.49728 q^{60}\) \(+3.68949 q^{61}\) \(-11.5885 q^{62}\) \(+5.81313 q^{63}\) \(-9.40375 q^{64}\) \(+2.77818 q^{65}\) \(+2.22566 q^{66}\) \(-3.00896 q^{67}\) \(-3.97393 q^{68}\) \(+6.86553 q^{69}\) \(-13.7706 q^{70}\) \(+4.85676 q^{71}\) \(+9.78426 q^{72}\) \(+13.9945 q^{73}\) \(+19.0538 q^{74}\) \(+0.510810 q^{75}\) \(+5.43546 q^{76}\) \(-2.69568 q^{77}\) \(-2.93319 q^{78}\) \(-11.2438 q^{79}\) \(-6.85168 q^{80}\) \(+2.11969 q^{81}\) \(-21.4564 q^{82}\) \(+15.9306 q^{83}\) \(+9.58724 q^{84}\) \(+2.16335 q^{85}\) \(+9.18148 q^{86}\) \(-4.36268 q^{87}\) \(-4.53719 q^{88}\) \(+8.85401 q^{89}\) \(-11.0160 q^{90}\) \(+3.55263 q^{91}\) \(-28.9463 q^{92}\) \(-4.39214 q^{93}\) \(+29.2958 q^{94}\) \(-2.95899 q^{95}\) \(-1.10034 q^{96}\) \(+6.42119 q^{97}\) \(-0.646282 q^{98}\) \(-2.15646 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42329 −1.71352 −0.856762 0.515712i \(-0.827527\pi\)
−0.856762 + 0.515712i \(0.827527\pi\)
\(3\) −0.918445 −0.530264 −0.265132 0.964212i \(-0.585416\pi\)
−0.265132 + 0.964212i \(0.585416\pi\)
\(4\) 3.87233 1.93616
\(5\) −2.10804 −0.942744 −0.471372 0.881934i \(-0.656241\pi\)
−0.471372 + 0.881934i \(0.656241\pi\)
\(6\) 2.22566 0.908621
\(7\) −2.69568 −1.01887 −0.509436 0.860509i \(-0.670146\pi\)
−0.509436 + 0.860509i \(0.670146\pi\)
\(8\) −4.53719 −1.60414
\(9\) −2.15646 −0.718820
\(10\) 5.10839 1.61541
\(11\) 1.00000 0.301511
\(12\) −3.55652 −1.02668
\(13\) −1.31790 −0.365519 −0.182759 0.983158i \(-0.558503\pi\)
−0.182759 + 0.983158i \(0.558503\pi\)
\(14\) 6.53241 1.74586
\(15\) 1.93612 0.499904
\(16\) 3.25026 0.812566
\(17\) −1.02624 −0.248900 −0.124450 0.992226i \(-0.539717\pi\)
−0.124450 + 0.992226i \(0.539717\pi\)
\(18\) 5.22572 1.23171
\(19\) 1.40367 0.322023 0.161012 0.986953i \(-0.448524\pi\)
0.161012 + 0.986953i \(0.448524\pi\)
\(20\) −8.16302 −1.82531
\(21\) 2.47583 0.540271
\(22\) −2.42329 −0.516647
\(23\) −7.47517 −1.55868 −0.779340 0.626601i \(-0.784445\pi\)
−0.779340 + 0.626601i \(0.784445\pi\)
\(24\) 4.16716 0.850618
\(25\) −0.556169 −0.111234
\(26\) 3.19364 0.626325
\(27\) 4.73592 0.911429
\(28\) −10.4386 −1.97270
\(29\) 4.75007 0.882066 0.441033 0.897491i \(-0.354612\pi\)
0.441033 + 0.897491i \(0.354612\pi\)
\(30\) −4.69177 −0.856597
\(31\) 4.78215 0.858899 0.429450 0.903091i \(-0.358708\pi\)
0.429450 + 0.903091i \(0.358708\pi\)
\(32\) 1.19805 0.211788
\(33\) −0.918445 −0.159881
\(34\) 2.48687 0.426495
\(35\) 5.68260 0.960535
\(36\) −8.35052 −1.39175
\(37\) −7.86278 −1.29263 −0.646317 0.763069i \(-0.723691\pi\)
−0.646317 + 0.763069i \(0.723691\pi\)
\(38\) −3.40149 −0.551795
\(39\) 1.21042 0.193822
\(40\) 9.56457 1.51229
\(41\) 8.85425 1.38280 0.691401 0.722471i \(-0.256994\pi\)
0.691401 + 0.722471i \(0.256994\pi\)
\(42\) −5.99966 −0.925768
\(43\) −3.78885 −0.577794 −0.288897 0.957360i \(-0.593289\pi\)
−0.288897 + 0.957360i \(0.593289\pi\)
\(44\) 3.87233 0.583775
\(45\) 4.54590 0.677663
\(46\) 18.1145 2.67083
\(47\) −12.0893 −1.76340 −0.881702 0.471807i \(-0.843602\pi\)
−0.881702 + 0.471807i \(0.843602\pi\)
\(48\) −2.98519 −0.430875
\(49\) 0.266696 0.0380995
\(50\) 1.34776 0.190602
\(51\) 0.942544 0.131983
\(52\) −5.10333 −0.707704
\(53\) 3.68886 0.506704 0.253352 0.967374i \(-0.418467\pi\)
0.253352 + 0.967374i \(0.418467\pi\)
\(54\) −11.4765 −1.56175
\(55\) −2.10804 −0.284248
\(56\) 12.2308 1.63441
\(57\) −1.28919 −0.170758
\(58\) −11.5108 −1.51144
\(59\) 7.33831 0.955366 0.477683 0.878532i \(-0.341477\pi\)
0.477683 + 0.878532i \(0.341477\pi\)
\(60\) 7.49728 0.967895
\(61\) 3.68949 0.472391 0.236195 0.971706i \(-0.424100\pi\)
0.236195 + 0.971706i \(0.424100\pi\)
\(62\) −11.5885 −1.47174
\(63\) 5.81313 0.732385
\(64\) −9.40375 −1.17547
\(65\) 2.77818 0.344591
\(66\) 2.22566 0.273959
\(67\) −3.00896 −0.367603 −0.183801 0.982963i \(-0.558840\pi\)
−0.183801 + 0.982963i \(0.558840\pi\)
\(68\) −3.97393 −0.481910
\(69\) 6.86553 0.826512
\(70\) −13.7706 −1.64590
\(71\) 4.85676 0.576391 0.288196 0.957572i \(-0.406945\pi\)
0.288196 + 0.957572i \(0.406945\pi\)
\(72\) 9.78426 1.15309
\(73\) 13.9945 1.63794 0.818968 0.573839i \(-0.194546\pi\)
0.818968 + 0.573839i \(0.194546\pi\)
\(74\) 19.0538 2.21496
\(75\) 0.510810 0.0589833
\(76\) 5.43546 0.623490
\(77\) −2.69568 −0.307201
\(78\) −2.93319 −0.332118
\(79\) −11.2438 −1.26503 −0.632516 0.774548i \(-0.717978\pi\)
−0.632516 + 0.774548i \(0.717978\pi\)
\(80\) −6.85168 −0.766042
\(81\) 2.11969 0.235521
\(82\) −21.4564 −2.36946
\(83\) 15.9306 1.74862 0.874308 0.485372i \(-0.161316\pi\)
0.874308 + 0.485372i \(0.161316\pi\)
\(84\) 9.58724 1.04605
\(85\) 2.16335 0.234649
\(86\) 9.18148 0.990064
\(87\) −4.36268 −0.467728
\(88\) −4.53719 −0.483666
\(89\) 8.85401 0.938524 0.469262 0.883059i \(-0.344520\pi\)
0.469262 + 0.883059i \(0.344520\pi\)
\(90\) −11.0160 −1.16119
\(91\) 3.55263 0.372417
\(92\) −28.9463 −3.01786
\(93\) −4.39214 −0.455444
\(94\) 29.2958 3.02163
\(95\) −2.95899 −0.303586
\(96\) −1.10034 −0.112303
\(97\) 6.42119 0.651973 0.325987 0.945374i \(-0.394304\pi\)
0.325987 + 0.945374i \(0.394304\pi\)
\(98\) −0.646282 −0.0652843
\(99\) −2.15646 −0.216732
\(100\) −2.15367 −0.215367
\(101\) −15.5113 −1.54343 −0.771716 0.635968i \(-0.780601\pi\)
−0.771716 + 0.635968i \(0.780601\pi\)
\(102\) −2.28406 −0.226155
\(103\) 11.6308 1.14602 0.573008 0.819549i \(-0.305776\pi\)
0.573008 + 0.819549i \(0.305776\pi\)
\(104\) 5.97955 0.586343
\(105\) −5.21916 −0.509338
\(106\) −8.93917 −0.868249
\(107\) −15.2861 −1.47776 −0.738881 0.673836i \(-0.764646\pi\)
−0.738881 + 0.673836i \(0.764646\pi\)
\(108\) 18.3390 1.76468
\(109\) −1.18087 −0.113107 −0.0565533 0.998400i \(-0.518011\pi\)
−0.0565533 + 0.998400i \(0.518011\pi\)
\(110\) 5.10839 0.487066
\(111\) 7.22153 0.685437
\(112\) −8.76167 −0.827900
\(113\) 10.0801 0.948254 0.474127 0.880456i \(-0.342764\pi\)
0.474127 + 0.880456i \(0.342764\pi\)
\(114\) 3.12408 0.292597
\(115\) 15.7579 1.46944
\(116\) 18.3938 1.70782
\(117\) 2.84199 0.262742
\(118\) −17.7828 −1.63704
\(119\) 2.76641 0.253597
\(120\) −8.78453 −0.801915
\(121\) 1.00000 0.0909091
\(122\) −8.94069 −0.809452
\(123\) −8.13214 −0.733251
\(124\) 18.5180 1.66297
\(125\) 11.7126 1.04761
\(126\) −14.0869 −1.25496
\(127\) 1.53610 0.136307 0.0681533 0.997675i \(-0.478289\pi\)
0.0681533 + 0.997675i \(0.478289\pi\)
\(128\) 20.3919 1.80241
\(129\) 3.47985 0.306384
\(130\) −6.73233 −0.590464
\(131\) 1.09698 0.0958435 0.0479218 0.998851i \(-0.484740\pi\)
0.0479218 + 0.998851i \(0.484740\pi\)
\(132\) −3.55652 −0.309555
\(133\) −3.78384 −0.328100
\(134\) 7.29157 0.629896
\(135\) −9.98351 −0.859244
\(136\) 4.65624 0.399269
\(137\) 8.42685 0.719954 0.359977 0.932961i \(-0.382784\pi\)
0.359977 + 0.932961i \(0.382784\pi\)
\(138\) −16.6372 −1.41625
\(139\) −6.46863 −0.548662 −0.274331 0.961635i \(-0.588456\pi\)
−0.274331 + 0.961635i \(0.588456\pi\)
\(140\) 22.0049 1.85975
\(141\) 11.1033 0.935070
\(142\) −11.7693 −0.987660
\(143\) −1.31790 −0.110208
\(144\) −7.00906 −0.584088
\(145\) −10.0133 −0.831562
\(146\) −33.9128 −2.80664
\(147\) −0.244946 −0.0202028
\(148\) −30.4473 −2.50275
\(149\) 7.03937 0.576688 0.288344 0.957527i \(-0.406895\pi\)
0.288344 + 0.957527i \(0.406895\pi\)
\(150\) −1.23784 −0.101069
\(151\) 4.48252 0.364782 0.182391 0.983226i \(-0.441616\pi\)
0.182391 + 0.983226i \(0.441616\pi\)
\(152\) −6.36870 −0.516570
\(153\) 2.21304 0.178914
\(154\) 6.53241 0.526397
\(155\) −10.0810 −0.809722
\(156\) 4.68712 0.375270
\(157\) −3.92980 −0.313632 −0.156816 0.987628i \(-0.550123\pi\)
−0.156816 + 0.987628i \(0.550123\pi\)
\(158\) 27.2471 2.16766
\(159\) −3.38802 −0.268687
\(160\) −2.52554 −0.199661
\(161\) 20.1507 1.58809
\(162\) −5.13663 −0.403572
\(163\) 13.9010 1.08881 0.544406 0.838822i \(-0.316755\pi\)
0.544406 + 0.838822i \(0.316755\pi\)
\(164\) 34.2866 2.67733
\(165\) 1.93612 0.150727
\(166\) −38.6046 −2.99629
\(167\) 1.96335 0.151929 0.0759645 0.997111i \(-0.475796\pi\)
0.0759645 + 0.997111i \(0.475796\pi\)
\(168\) −11.2333 −0.866670
\(169\) −11.2631 −0.866396
\(170\) −5.24243 −0.402076
\(171\) −3.02695 −0.231477
\(172\) −14.6717 −1.11870
\(173\) −8.60803 −0.654457 −0.327228 0.944945i \(-0.606115\pi\)
−0.327228 + 0.944945i \(0.606115\pi\)
\(174\) 10.5720 0.801463
\(175\) 1.49925 0.113333
\(176\) 3.25026 0.244998
\(177\) −6.73983 −0.506597
\(178\) −21.4558 −1.60818
\(179\) 15.5556 1.16268 0.581340 0.813660i \(-0.302528\pi\)
0.581340 + 0.813660i \(0.302528\pi\)
\(180\) 17.6032 1.31207
\(181\) −8.95677 −0.665752 −0.332876 0.942971i \(-0.608019\pi\)
−0.332876 + 0.942971i \(0.608019\pi\)
\(182\) −8.60904 −0.638145
\(183\) −3.38859 −0.250492
\(184\) 33.9162 2.50034
\(185\) 16.5751 1.21862
\(186\) 10.6434 0.780414
\(187\) −1.02624 −0.0750461
\(188\) −46.8137 −3.41424
\(189\) −12.7665 −0.928629
\(190\) 7.17048 0.520201
\(191\) 23.1298 1.67361 0.836806 0.547499i \(-0.184420\pi\)
0.836806 + 0.547499i \(0.184420\pi\)
\(192\) 8.63683 0.623309
\(193\) −26.7959 −1.92881 −0.964405 0.264431i \(-0.914816\pi\)
−0.964405 + 0.264431i \(0.914816\pi\)
\(194\) −15.5604 −1.11717
\(195\) −2.55160 −0.182724
\(196\) 1.03273 0.0737668
\(197\) −1.59916 −0.113935 −0.0569676 0.998376i \(-0.518143\pi\)
−0.0569676 + 0.998376i \(0.518143\pi\)
\(198\) 5.22572 0.371376
\(199\) 12.0933 0.857271 0.428636 0.903477i \(-0.358994\pi\)
0.428636 + 0.903477i \(0.358994\pi\)
\(200\) 2.52344 0.178434
\(201\) 2.76356 0.194927
\(202\) 37.5883 2.64471
\(203\) −12.8047 −0.898712
\(204\) 3.64984 0.255540
\(205\) −18.6651 −1.30363
\(206\) −28.1848 −1.96373
\(207\) 16.1199 1.12041
\(208\) −4.28351 −0.297008
\(209\) 1.40367 0.0970937
\(210\) 12.6475 0.872762
\(211\) −8.61138 −0.592832 −0.296416 0.955059i \(-0.595791\pi\)
−0.296416 + 0.955059i \(0.595791\pi\)
\(212\) 14.2845 0.981062
\(213\) −4.46066 −0.305640
\(214\) 37.0426 2.53218
\(215\) 7.98705 0.544712
\(216\) −21.4878 −1.46206
\(217\) −12.8911 −0.875108
\(218\) 2.86158 0.193811
\(219\) −12.8532 −0.868539
\(220\) −8.16302 −0.550351
\(221\) 1.35248 0.0909775
\(222\) −17.4999 −1.17451
\(223\) −5.52585 −0.370038 −0.185019 0.982735i \(-0.559235\pi\)
−0.185019 + 0.982735i \(0.559235\pi\)
\(224\) −3.22956 −0.215784
\(225\) 1.19936 0.0799570
\(226\) −24.4269 −1.62486
\(227\) −7.32329 −0.486064 −0.243032 0.970018i \(-0.578142\pi\)
−0.243032 + 0.970018i \(0.578142\pi\)
\(228\) −4.99217 −0.330614
\(229\) −1.07543 −0.0710664 −0.0355332 0.999368i \(-0.511313\pi\)
−0.0355332 + 0.999368i \(0.511313\pi\)
\(230\) −38.1860 −2.51791
\(231\) 2.47583 0.162898
\(232\) −21.5520 −1.41496
\(233\) −1.67722 −0.109879 −0.0549393 0.998490i \(-0.517497\pi\)
−0.0549393 + 0.998490i \(0.517497\pi\)
\(234\) −6.88696 −0.450215
\(235\) 25.4847 1.66244
\(236\) 28.4163 1.84975
\(237\) 10.3268 0.670801
\(238\) −6.70382 −0.434544
\(239\) −10.8477 −0.701682 −0.350841 0.936435i \(-0.614104\pi\)
−0.350841 + 0.936435i \(0.614104\pi\)
\(240\) 6.29289 0.406205
\(241\) −7.48950 −0.482441 −0.241221 0.970470i \(-0.577548\pi\)
−0.241221 + 0.970470i \(0.577548\pi\)
\(242\) −2.42329 −0.155775
\(243\) −16.1546 −1.03632
\(244\) 14.2869 0.914625
\(245\) −0.562206 −0.0359180
\(246\) 19.7065 1.25644
\(247\) −1.84989 −0.117706
\(248\) −21.6975 −1.37779
\(249\) −14.6314 −0.927229
\(250\) −28.3831 −1.79510
\(251\) 27.7115 1.74914 0.874568 0.484903i \(-0.161145\pi\)
0.874568 + 0.484903i \(0.161145\pi\)
\(252\) 22.5103 1.41802
\(253\) −7.47517 −0.469960
\(254\) −3.72241 −0.233565
\(255\) −1.98692 −0.124426
\(256\) −30.6080 −1.91300
\(257\) 9.95515 0.620985 0.310492 0.950576i \(-0.399506\pi\)
0.310492 + 0.950576i \(0.399506\pi\)
\(258\) −8.43268 −0.524996
\(259\) 21.1956 1.31703
\(260\) 10.7580 0.667184
\(261\) −10.2433 −0.634046
\(262\) −2.65830 −0.164230
\(263\) −17.1976 −1.06045 −0.530225 0.847857i \(-0.677892\pi\)
−0.530225 + 0.847857i \(0.677892\pi\)
\(264\) 4.16716 0.256471
\(265\) −7.77627 −0.477692
\(266\) 9.16933 0.562208
\(267\) −8.13192 −0.497666
\(268\) −11.6517 −0.711739
\(269\) −2.54516 −0.155181 −0.0775904 0.996985i \(-0.524723\pi\)
−0.0775904 + 0.996985i \(0.524723\pi\)
\(270\) 24.1929 1.47234
\(271\) −2.92557 −0.177716 −0.0888580 0.996044i \(-0.528322\pi\)
−0.0888580 + 0.996044i \(0.528322\pi\)
\(272\) −3.33555 −0.202247
\(273\) −3.26289 −0.197479
\(274\) −20.4207 −1.23366
\(275\) −0.556169 −0.0335382
\(276\) 26.5856 1.60026
\(277\) 8.69420 0.522384 0.261192 0.965287i \(-0.415884\pi\)
0.261192 + 0.965287i \(0.415884\pi\)
\(278\) 15.6753 0.940145
\(279\) −10.3125 −0.617394
\(280\) −25.7830 −1.54083
\(281\) 23.3912 1.39540 0.697701 0.716389i \(-0.254207\pi\)
0.697701 + 0.716389i \(0.254207\pi\)
\(282\) −26.9066 −1.60227
\(283\) 24.8099 1.47479 0.737397 0.675459i \(-0.236055\pi\)
0.737397 + 0.675459i \(0.236055\pi\)
\(284\) 18.8070 1.11599
\(285\) 2.71767 0.160981
\(286\) 3.19364 0.188844
\(287\) −23.8682 −1.40890
\(288\) −2.58355 −0.152237
\(289\) −15.9468 −0.938049
\(290\) 24.2652 1.42490
\(291\) −5.89751 −0.345718
\(292\) 54.1914 3.17131
\(293\) 9.94455 0.580967 0.290483 0.956880i \(-0.406184\pi\)
0.290483 + 0.956880i \(0.406184\pi\)
\(294\) 0.593574 0.0346180
\(295\) −15.4694 −0.900666
\(296\) 35.6749 2.07356
\(297\) 4.73592 0.274806
\(298\) −17.0584 −0.988168
\(299\) 9.85149 0.569727
\(300\) 1.97803 0.114201
\(301\) 10.2135 0.588698
\(302\) −10.8624 −0.625063
\(303\) 14.2463 0.818427
\(304\) 4.56229 0.261665
\(305\) −7.77759 −0.445343
\(306\) −5.36284 −0.306573
\(307\) 11.2560 0.642414 0.321207 0.947009i \(-0.395912\pi\)
0.321207 + 0.947009i \(0.395912\pi\)
\(308\) −10.4386 −0.594792
\(309\) −10.6823 −0.607692
\(310\) 24.4291 1.38748
\(311\) 12.4455 0.705721 0.352861 0.935676i \(-0.385209\pi\)
0.352861 + 0.935676i \(0.385209\pi\)
\(312\) −5.49188 −0.310917
\(313\) −3.16794 −0.179062 −0.0895312 0.995984i \(-0.528537\pi\)
−0.0895312 + 0.995984i \(0.528537\pi\)
\(314\) 9.52305 0.537417
\(315\) −12.2543 −0.690452
\(316\) −43.5398 −2.44931
\(317\) −2.69488 −0.151360 −0.0756798 0.997132i \(-0.524113\pi\)
−0.0756798 + 0.997132i \(0.524113\pi\)
\(318\) 8.21014 0.460402
\(319\) 4.75007 0.265953
\(320\) 19.8235 1.10817
\(321\) 14.0394 0.783605
\(322\) −48.8309 −2.72124
\(323\) −1.44050 −0.0801515
\(324\) 8.20814 0.456008
\(325\) 0.732973 0.0406580
\(326\) −33.6862 −1.86571
\(327\) 1.08456 0.0599764
\(328\) −40.1734 −2.21821
\(329\) 32.5889 1.79668
\(330\) −4.69177 −0.258274
\(331\) 14.0372 0.771553 0.385777 0.922592i \(-0.373934\pi\)
0.385777 + 0.922592i \(0.373934\pi\)
\(332\) 61.6887 3.38561
\(333\) 16.9558 0.929170
\(334\) −4.75777 −0.260334
\(335\) 6.34300 0.346555
\(336\) 8.04711 0.439006
\(337\) 21.0536 1.14686 0.573430 0.819255i \(-0.305612\pi\)
0.573430 + 0.819255i \(0.305612\pi\)
\(338\) 27.2939 1.48459
\(339\) −9.25800 −0.502825
\(340\) 8.37721 0.454318
\(341\) 4.78215 0.258968
\(342\) 7.33518 0.396641
\(343\) 18.1508 0.980053
\(344\) 17.1907 0.926862
\(345\) −14.4728 −0.779190
\(346\) 20.8597 1.12143
\(347\) 35.7373 1.91848 0.959239 0.282595i \(-0.0911954\pi\)
0.959239 + 0.282595i \(0.0911954\pi\)
\(348\) −16.8937 −0.905598
\(349\) −15.1078 −0.808701 −0.404351 0.914604i \(-0.632502\pi\)
−0.404351 + 0.914604i \(0.632502\pi\)
\(350\) −3.63312 −0.194199
\(351\) −6.24146 −0.333144
\(352\) 1.19805 0.0638564
\(353\) −2.53152 −0.134739 −0.0673696 0.997728i \(-0.521461\pi\)
−0.0673696 + 0.997728i \(0.521461\pi\)
\(354\) 16.3326 0.868065
\(355\) −10.2382 −0.543389
\(356\) 34.2856 1.81714
\(357\) −2.54080 −0.134473
\(358\) −37.6957 −1.99228
\(359\) −5.30166 −0.279811 −0.139905 0.990165i \(-0.544680\pi\)
−0.139905 + 0.990165i \(0.544680\pi\)
\(360\) −20.6256 −1.08707
\(361\) −17.0297 −0.896301
\(362\) 21.7048 1.14078
\(363\) −0.918445 −0.0482059
\(364\) 13.7569 0.721060
\(365\) −29.5010 −1.54415
\(366\) 8.21153 0.429224
\(367\) 9.13428 0.476806 0.238403 0.971166i \(-0.423376\pi\)
0.238403 + 0.971166i \(0.423376\pi\)
\(368\) −24.2963 −1.26653
\(369\) −19.0938 −0.993985
\(370\) −40.1661 −2.08814
\(371\) −9.94399 −0.516266
\(372\) −17.0078 −0.881813
\(373\) 6.53079 0.338151 0.169076 0.985603i \(-0.445922\pi\)
0.169076 + 0.985603i \(0.445922\pi\)
\(374\) 2.48687 0.128593
\(375\) −10.7574 −0.555510
\(376\) 54.8514 2.82874
\(377\) −6.26010 −0.322411
\(378\) 30.9370 1.59123
\(379\) −19.6425 −1.00897 −0.504485 0.863421i \(-0.668318\pi\)
−0.504485 + 0.863421i \(0.668318\pi\)
\(380\) −11.4582 −0.587791
\(381\) −1.41082 −0.0722785
\(382\) −56.0502 −2.86778
\(383\) −28.0869 −1.43517 −0.717586 0.696470i \(-0.754753\pi\)
−0.717586 + 0.696470i \(0.754753\pi\)
\(384\) −18.7288 −0.955752
\(385\) 5.68260 0.289612
\(386\) 64.9341 3.30506
\(387\) 8.17050 0.415330
\(388\) 24.8650 1.26233
\(389\) 14.8286 0.751841 0.375921 0.926652i \(-0.377327\pi\)
0.375921 + 0.926652i \(0.377327\pi\)
\(390\) 6.18327 0.313102
\(391\) 7.67131 0.387955
\(392\) −1.21005 −0.0611168
\(393\) −1.00752 −0.0508224
\(394\) 3.87522 0.195231
\(395\) 23.7025 1.19260
\(396\) −8.35052 −0.419629
\(397\) 0.513142 0.0257539 0.0128769 0.999917i \(-0.495901\pi\)
0.0128769 + 0.999917i \(0.495901\pi\)
\(398\) −29.3056 −1.46895
\(399\) 3.47525 0.173980
\(400\) −1.80770 −0.0903848
\(401\) 33.4550 1.67066 0.835332 0.549746i \(-0.185276\pi\)
0.835332 + 0.549746i \(0.185276\pi\)
\(402\) −6.69690 −0.334011
\(403\) −6.30238 −0.313944
\(404\) −60.0648 −2.98834
\(405\) −4.46840 −0.222036
\(406\) 31.0294 1.53996
\(407\) −7.86278 −0.389744
\(408\) −4.27650 −0.211718
\(409\) −2.57499 −0.127325 −0.0636625 0.997971i \(-0.520278\pi\)
−0.0636625 + 0.997971i \(0.520278\pi\)
\(410\) 45.2310 2.23380
\(411\) −7.73960 −0.381766
\(412\) 45.0383 2.21888
\(413\) −19.7817 −0.973395
\(414\) −39.0631 −1.91985
\(415\) −33.5824 −1.64850
\(416\) −1.57891 −0.0774123
\(417\) 5.94108 0.290936
\(418\) −3.40149 −0.166372
\(419\) 24.7432 1.20879 0.604393 0.796687i \(-0.293416\pi\)
0.604393 + 0.796687i \(0.293416\pi\)
\(420\) −20.2103 −0.986161
\(421\) −22.4123 −1.09231 −0.546154 0.837685i \(-0.683909\pi\)
−0.546154 + 0.837685i \(0.683909\pi\)
\(422\) 20.8678 1.01583
\(423\) 26.0701 1.26757
\(424\) −16.7371 −0.812823
\(425\) 0.570762 0.0276860
\(426\) 10.8095 0.523721
\(427\) −9.94568 −0.481305
\(428\) −59.1928 −2.86119
\(429\) 1.21042 0.0584394
\(430\) −19.3549 −0.933377
\(431\) −3.30159 −0.159032 −0.0795161 0.996834i \(-0.525338\pi\)
−0.0795161 + 0.996834i \(0.525338\pi\)
\(432\) 15.3930 0.740596
\(433\) 6.45790 0.310347 0.155174 0.987887i \(-0.450406\pi\)
0.155174 + 0.987887i \(0.450406\pi\)
\(434\) 31.2390 1.49952
\(435\) 9.19669 0.440948
\(436\) −4.57270 −0.218993
\(437\) −10.4926 −0.501931
\(438\) 31.1470 1.48826
\(439\) −16.7949 −0.801577 −0.400788 0.916171i \(-0.631264\pi\)
−0.400788 + 0.916171i \(0.631264\pi\)
\(440\) 9.56457 0.455973
\(441\) −0.575119 −0.0273866
\(442\) −3.27744 −0.155892
\(443\) −30.6915 −1.45820 −0.729098 0.684409i \(-0.760060\pi\)
−0.729098 + 0.684409i \(0.760060\pi\)
\(444\) 27.9641 1.32712
\(445\) −18.6646 −0.884788
\(446\) 13.3907 0.634069
\(447\) −6.46528 −0.305797
\(448\) 25.3495 1.19765
\(449\) −1.56946 −0.0740674 −0.0370337 0.999314i \(-0.511791\pi\)
−0.0370337 + 0.999314i \(0.511791\pi\)
\(450\) −2.90638 −0.137008
\(451\) 8.85425 0.416930
\(452\) 39.0334 1.83598
\(453\) −4.11695 −0.193431
\(454\) 17.7464 0.832882
\(455\) −7.48908 −0.351094
\(456\) 5.84930 0.273919
\(457\) −34.5254 −1.61503 −0.807516 0.589845i \(-0.799189\pi\)
−0.807516 + 0.589845i \(0.799189\pi\)
\(458\) 2.60608 0.121774
\(459\) −4.86019 −0.226854
\(460\) 61.0199 2.84507
\(461\) 27.4203 1.27709 0.638544 0.769585i \(-0.279537\pi\)
0.638544 + 0.769585i \(0.279537\pi\)
\(462\) −5.99966 −0.279129
\(463\) −3.61913 −0.168195 −0.0840976 0.996458i \(-0.526801\pi\)
−0.0840976 + 0.996458i \(0.526801\pi\)
\(464\) 15.4390 0.716736
\(465\) 9.25880 0.429367
\(466\) 4.06440 0.188280
\(467\) 2.56468 0.118679 0.0593397 0.998238i \(-0.481100\pi\)
0.0593397 + 0.998238i \(0.481100\pi\)
\(468\) 11.0051 0.508712
\(469\) 8.11119 0.374540
\(470\) −61.7568 −2.84863
\(471\) 3.60931 0.166308
\(472\) −33.2953 −1.53254
\(473\) −3.78885 −0.174212
\(474\) −25.0249 −1.14943
\(475\) −0.780676 −0.0358199
\(476\) 10.7125 0.491005
\(477\) −7.95488 −0.364229
\(478\) 26.2872 1.20235
\(479\) −2.93213 −0.133973 −0.0669863 0.997754i \(-0.521338\pi\)
−0.0669863 + 0.997754i \(0.521338\pi\)
\(480\) 2.31957 0.105873
\(481\) 10.3623 0.472482
\(482\) 18.1492 0.826674
\(483\) −18.5073 −0.842110
\(484\) 3.87233 0.176015
\(485\) −13.5361 −0.614644
\(486\) 39.1472 1.77575
\(487\) −10.3197 −0.467628 −0.233814 0.972281i \(-0.575121\pi\)
−0.233814 + 0.972281i \(0.575121\pi\)
\(488\) −16.7399 −0.757780
\(489\) −12.7673 −0.577358
\(490\) 1.36239 0.0615464
\(491\) −17.6388 −0.796027 −0.398014 0.917380i \(-0.630300\pi\)
−0.398014 + 0.917380i \(0.630300\pi\)
\(492\) −31.4903 −1.41969
\(493\) −4.87471 −0.219546
\(494\) 4.48281 0.201691
\(495\) 4.54590 0.204323
\(496\) 15.5432 0.697912
\(497\) −13.0923 −0.587269
\(498\) 35.4562 1.58883
\(499\) −26.2776 −1.17635 −0.588175 0.808734i \(-0.700153\pi\)
−0.588175 + 0.808734i \(0.700153\pi\)
\(500\) 45.3551 2.02834
\(501\) −1.80323 −0.0805625
\(502\) −67.1530 −2.99719
\(503\) −36.6836 −1.63564 −0.817819 0.575475i \(-0.804817\pi\)
−0.817819 + 0.575475i \(0.804817\pi\)
\(504\) −26.3753 −1.17485
\(505\) 32.6984 1.45506
\(506\) 18.1145 0.805287
\(507\) 10.3446 0.459419
\(508\) 5.94827 0.263912
\(509\) −22.0754 −0.978473 −0.489236 0.872151i \(-0.662724\pi\)
−0.489236 + 0.872151i \(0.662724\pi\)
\(510\) 4.81488 0.213207
\(511\) −37.7248 −1.66885
\(512\) 33.3881 1.47556
\(513\) 6.64766 0.293501
\(514\) −24.1242 −1.06407
\(515\) −24.5182 −1.08040
\(516\) 13.4751 0.593209
\(517\) −12.0893 −0.531686
\(518\) −51.3629 −2.25676
\(519\) 7.90600 0.347035
\(520\) −12.6051 −0.552771
\(521\) −26.7323 −1.17116 −0.585581 0.810614i \(-0.699133\pi\)
−0.585581 + 0.810614i \(0.699133\pi\)
\(522\) 24.8225 1.08645
\(523\) 2.28156 0.0997655 0.0498827 0.998755i \(-0.484115\pi\)
0.0498827 + 0.998755i \(0.484115\pi\)
\(524\) 4.24786 0.185569
\(525\) −1.37698 −0.0600964
\(526\) 41.6747 1.81711
\(527\) −4.90763 −0.213780
\(528\) −2.98519 −0.129914
\(529\) 32.8781 1.42948
\(530\) 18.8441 0.818537
\(531\) −15.8248 −0.686736
\(532\) −14.6523 −0.635256
\(533\) −11.6690 −0.505440
\(534\) 19.7060 0.852762
\(535\) 32.2237 1.39315
\(536\) 13.6522 0.589685
\(537\) −14.2870 −0.616528
\(538\) 6.16765 0.265906
\(539\) 0.266696 0.0114874
\(540\) −38.6594 −1.66364
\(541\) −27.4207 −1.17891 −0.589455 0.807801i \(-0.700657\pi\)
−0.589455 + 0.807801i \(0.700657\pi\)
\(542\) 7.08951 0.304520
\(543\) 8.22630 0.353024
\(544\) −1.22949 −0.0527138
\(545\) 2.48931 0.106631
\(546\) 7.90693 0.338385
\(547\) 1.00000 0.0427569
\(548\) 32.6315 1.39395
\(549\) −7.95623 −0.339564
\(550\) 1.34776 0.0574686
\(551\) 6.66752 0.284046
\(552\) −31.1502 −1.32584
\(553\) 30.3098 1.28890
\(554\) −21.0686 −0.895118
\(555\) −15.2233 −0.646192
\(556\) −25.0486 −1.06230
\(557\) −41.1637 −1.74416 −0.872081 0.489362i \(-0.837230\pi\)
−0.872081 + 0.489362i \(0.837230\pi\)
\(558\) 24.9902 1.05792
\(559\) 4.99331 0.211195
\(560\) 18.4700 0.780498
\(561\) 0.942544 0.0397942
\(562\) −56.6836 −2.39105
\(563\) −41.9675 −1.76872 −0.884360 0.466806i \(-0.845405\pi\)
−0.884360 + 0.466806i \(0.845405\pi\)
\(564\) 42.9958 1.81045
\(565\) −21.2492 −0.893961
\(566\) −60.1215 −2.52710
\(567\) −5.71402 −0.239966
\(568\) −22.0360 −0.924611
\(569\) −15.5916 −0.653636 −0.326818 0.945087i \(-0.605976\pi\)
−0.326818 + 0.945087i \(0.605976\pi\)
\(570\) −6.58569 −0.275844
\(571\) −30.3166 −1.26871 −0.634355 0.773042i \(-0.718734\pi\)
−0.634355 + 0.773042i \(0.718734\pi\)
\(572\) −5.10333 −0.213381
\(573\) −21.2434 −0.887457
\(574\) 57.8396 2.41418
\(575\) 4.15745 0.173378
\(576\) 20.2788 0.844950
\(577\) 35.9008 1.49457 0.747285 0.664504i \(-0.231357\pi\)
0.747285 + 0.664504i \(0.231357\pi\)
\(578\) 38.6438 1.60737
\(579\) 24.6105 1.02278
\(580\) −38.7749 −1.61004
\(581\) −42.9439 −1.78162
\(582\) 14.2914 0.592396
\(583\) 3.68886 0.152777
\(584\) −63.4958 −2.62748
\(585\) −5.99103 −0.247698
\(586\) −24.0985 −0.995501
\(587\) 8.33164 0.343884 0.171942 0.985107i \(-0.444996\pi\)
0.171942 + 0.985107i \(0.444996\pi\)
\(588\) −0.948510 −0.0391159
\(589\) 6.71254 0.276586
\(590\) 37.4869 1.54331
\(591\) 1.46874 0.0604158
\(592\) −25.5561 −1.05035
\(593\) −10.7932 −0.443225 −0.221613 0.975135i \(-0.571132\pi\)
−0.221613 + 0.975135i \(0.571132\pi\)
\(594\) −11.4765 −0.470887
\(595\) −5.83171 −0.239077
\(596\) 27.2588 1.11656
\(597\) −11.1070 −0.454580
\(598\) −23.8730 −0.976240
\(599\) −18.5253 −0.756924 −0.378462 0.925617i \(-0.623547\pi\)
−0.378462 + 0.925617i \(0.623547\pi\)
\(600\) −2.31764 −0.0946174
\(601\) 44.5411 1.81687 0.908435 0.418027i \(-0.137278\pi\)
0.908435 + 0.418027i \(0.137278\pi\)
\(602\) −24.7503 −1.00875
\(603\) 6.48869 0.264240
\(604\) 17.3578 0.706278
\(605\) −2.10804 −0.0857040
\(606\) −34.5228 −1.40239
\(607\) −22.1435 −0.898775 −0.449388 0.893337i \(-0.648358\pi\)
−0.449388 + 0.893337i \(0.648358\pi\)
\(608\) 1.68167 0.0682005
\(609\) 11.7604 0.476555
\(610\) 18.8473 0.763106
\(611\) 15.9324 0.644557
\(612\) 8.56963 0.346407
\(613\) −22.7573 −0.919157 −0.459578 0.888137i \(-0.651999\pi\)
−0.459578 + 0.888137i \(0.651999\pi\)
\(614\) −27.2765 −1.10079
\(615\) 17.1429 0.691268
\(616\) 12.2308 0.492794
\(617\) −5.65514 −0.227667 −0.113834 0.993500i \(-0.536313\pi\)
−0.113834 + 0.993500i \(0.536313\pi\)
\(618\) 25.8862 1.04129
\(619\) −8.76926 −0.352466 −0.176233 0.984348i \(-0.556391\pi\)
−0.176233 + 0.984348i \(0.556391\pi\)
\(620\) −39.0368 −1.56775
\(621\) −35.4018 −1.42063
\(622\) −30.1591 −1.20927
\(623\) −23.8676 −0.956235
\(624\) 3.93417 0.157493
\(625\) −21.9098 −0.876393
\(626\) 7.67682 0.306828
\(627\) −1.28919 −0.0514853
\(628\) −15.2175 −0.607244
\(629\) 8.06910 0.321736
\(630\) 29.6957 1.18311
\(631\) −0.148030 −0.00589297 −0.00294649 0.999996i \(-0.500938\pi\)
−0.00294649 + 0.999996i \(0.500938\pi\)
\(632\) 51.0154 2.02929
\(633\) 7.90907 0.314357
\(634\) 6.53048 0.259358
\(635\) −3.23815 −0.128502
\(636\) −13.1195 −0.520222
\(637\) −0.351478 −0.0139261
\(638\) −11.5108 −0.455716
\(639\) −10.4734 −0.414321
\(640\) −42.9869 −1.69921
\(641\) −11.8264 −0.467115 −0.233557 0.972343i \(-0.575037\pi\)
−0.233557 + 0.972343i \(0.575037\pi\)
\(642\) −34.0216 −1.34273
\(643\) −14.1666 −0.558676 −0.279338 0.960193i \(-0.590115\pi\)
−0.279338 + 0.960193i \(0.590115\pi\)
\(644\) 78.0300 3.07481
\(645\) −7.33566 −0.288841
\(646\) 3.49074 0.137341
\(647\) 19.0243 0.747923 0.373962 0.927444i \(-0.377999\pi\)
0.373962 + 0.927444i \(0.377999\pi\)
\(648\) −9.61745 −0.377809
\(649\) 7.33831 0.288054
\(650\) −1.77621 −0.0696685
\(651\) 11.8398 0.464039
\(652\) 53.8293 2.10812
\(653\) 8.26613 0.323479 0.161739 0.986834i \(-0.448290\pi\)
0.161739 + 0.986834i \(0.448290\pi\)
\(654\) −2.62820 −0.102771
\(655\) −2.31248 −0.0903559
\(656\) 28.7787 1.12362
\(657\) −30.1786 −1.17738
\(658\) −78.9722 −3.07866
\(659\) −35.7654 −1.39322 −0.696612 0.717448i \(-0.745310\pi\)
−0.696612 + 0.717448i \(0.745310\pi\)
\(660\) 7.49728 0.291831
\(661\) 1.30544 0.0507757 0.0253879 0.999678i \(-0.491918\pi\)
0.0253879 + 0.999678i \(0.491918\pi\)
\(662\) −34.0161 −1.32207
\(663\) −1.24218 −0.0482421
\(664\) −72.2804 −2.80502
\(665\) 7.97648 0.309315
\(666\) −41.0887 −1.59216
\(667\) −35.5075 −1.37486
\(668\) 7.60275 0.294159
\(669\) 5.07518 0.196218
\(670\) −15.3709 −0.593830
\(671\) 3.68949 0.142431
\(672\) 2.96618 0.114423
\(673\) 14.6344 0.564115 0.282057 0.959398i \(-0.408983\pi\)
0.282057 + 0.959398i \(0.408983\pi\)
\(674\) −51.0188 −1.96517
\(675\) −2.63397 −0.101382
\(676\) −43.6146 −1.67748
\(677\) −8.61393 −0.331060 −0.165530 0.986205i \(-0.552934\pi\)
−0.165530 + 0.986205i \(0.552934\pi\)
\(678\) 22.4348 0.861603
\(679\) −17.3095 −0.664277
\(680\) −9.81554 −0.376409
\(681\) 6.72604 0.257742
\(682\) −11.5885 −0.443748
\(683\) 6.50361 0.248854 0.124427 0.992229i \(-0.460291\pi\)
0.124427 + 0.992229i \(0.460291\pi\)
\(684\) −11.7213 −0.448177
\(685\) −17.7641 −0.678733
\(686\) −43.9847 −1.67934
\(687\) 0.987723 0.0376840
\(688\) −12.3148 −0.469496
\(689\) −4.86154 −0.185210
\(690\) 35.0718 1.33516
\(691\) −33.1087 −1.25952 −0.629758 0.776791i \(-0.716846\pi\)
−0.629758 + 0.776791i \(0.716846\pi\)
\(692\) −33.3331 −1.26714
\(693\) 5.81313 0.220822
\(694\) −86.6018 −3.28736
\(695\) 13.6361 0.517248
\(696\) 19.7943 0.750300
\(697\) −9.08658 −0.344179
\(698\) 36.6105 1.38573
\(699\) 1.54044 0.0582647
\(700\) 5.80560 0.219431
\(701\) 33.0709 1.24907 0.624535 0.780997i \(-0.285288\pi\)
0.624535 + 0.780997i \(0.285288\pi\)
\(702\) 15.1248 0.570851
\(703\) −11.0367 −0.416258
\(704\) −9.40375 −0.354417
\(705\) −23.4063 −0.881532
\(706\) 6.13460 0.230879
\(707\) 41.8135 1.57256
\(708\) −26.0988 −0.980854
\(709\) −34.6498 −1.30130 −0.650650 0.759378i \(-0.725503\pi\)
−0.650650 + 0.759378i \(0.725503\pi\)
\(710\) 24.8102 0.931110
\(711\) 24.2469 0.909329
\(712\) −40.1723 −1.50552
\(713\) −35.7474 −1.33875
\(714\) 6.15709 0.230423
\(715\) 2.77818 0.103898
\(716\) 60.2364 2.25114
\(717\) 9.96306 0.372077
\(718\) 12.8475 0.479463
\(719\) 3.76103 0.140263 0.0701315 0.997538i \(-0.477658\pi\)
0.0701315 + 0.997538i \(0.477658\pi\)
\(720\) 14.7754 0.550646
\(721\) −31.3529 −1.16764
\(722\) 41.2679 1.53583
\(723\) 6.87869 0.255821
\(724\) −34.6836 −1.28900
\(725\) −2.64184 −0.0981155
\(726\) 2.22566 0.0826019
\(727\) 42.9574 1.59320 0.796602 0.604505i \(-0.206629\pi\)
0.796602 + 0.604505i \(0.206629\pi\)
\(728\) −16.1189 −0.597408
\(729\) 8.47802 0.314001
\(730\) 71.4895 2.64595
\(731\) 3.88827 0.143813
\(732\) −13.1217 −0.484993
\(733\) 32.5724 1.20309 0.601545 0.798839i \(-0.294552\pi\)
0.601545 + 0.798839i \(0.294552\pi\)
\(734\) −22.1350 −0.817018
\(735\) 0.516355 0.0190461
\(736\) −8.95563 −0.330109
\(737\) −3.00896 −0.110836
\(738\) 46.2699 1.70322
\(739\) −30.1478 −1.10900 −0.554502 0.832183i \(-0.687091\pi\)
−0.554502 + 0.832183i \(0.687091\pi\)
\(740\) 64.1840 2.35945
\(741\) 1.69902 0.0624151
\(742\) 24.0972 0.884635
\(743\) 27.1034 0.994328 0.497164 0.867657i \(-0.334375\pi\)
0.497164 + 0.867657i \(0.334375\pi\)
\(744\) 19.9280 0.730595
\(745\) −14.8393 −0.543669
\(746\) −15.8260 −0.579431
\(747\) −34.3538 −1.25694
\(748\) −3.97393 −0.145301
\(749\) 41.2064 1.50565
\(750\) 26.0683 0.951879
\(751\) −23.9887 −0.875359 −0.437680 0.899131i \(-0.644200\pi\)
−0.437680 + 0.899131i \(0.644200\pi\)
\(752\) −39.2934 −1.43288
\(753\) −25.4515 −0.927505
\(754\) 15.1700 0.552460
\(755\) −9.44933 −0.343896
\(756\) −49.4362 −1.79798
\(757\) −20.4233 −0.742297 −0.371149 0.928573i \(-0.621036\pi\)
−0.371149 + 0.928573i \(0.621036\pi\)
\(758\) 47.5996 1.72889
\(759\) 6.86553 0.249203
\(760\) 13.4255 0.486993
\(761\) 26.0309 0.943619 0.471810 0.881701i \(-0.343601\pi\)
0.471810 + 0.881701i \(0.343601\pi\)
\(762\) 3.41882 0.123851
\(763\) 3.18324 0.115241
\(764\) 89.5661 3.24039
\(765\) −4.66518 −0.168670
\(766\) 68.0626 2.45920
\(767\) −9.67113 −0.349204
\(768\) 28.1117 1.01439
\(769\) 32.7648 1.18153 0.590765 0.806844i \(-0.298826\pi\)
0.590765 + 0.806844i \(0.298826\pi\)
\(770\) −13.7706 −0.496257
\(771\) −9.14325 −0.329286
\(772\) −103.762 −3.73449
\(773\) −14.4067 −0.518175 −0.259087 0.965854i \(-0.583422\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(774\) −19.7995 −0.711678
\(775\) −2.65968 −0.0955386
\(776\) −29.1342 −1.04586
\(777\) −19.4669 −0.698373
\(778\) −35.9340 −1.28830
\(779\) 12.4284 0.445295
\(780\) −9.88064 −0.353784
\(781\) 4.85676 0.173788
\(782\) −18.5898 −0.664770
\(783\) 22.4960 0.803940
\(784\) 0.866833 0.0309583
\(785\) 8.28418 0.295675
\(786\) 2.44150 0.0870854
\(787\) −45.9728 −1.63875 −0.819377 0.573254i \(-0.805681\pi\)
−0.819377 + 0.573254i \(0.805681\pi\)
\(788\) −6.19246 −0.220597
\(789\) 15.7950 0.562319
\(790\) −57.4379 −2.04355
\(791\) −27.1727 −0.966149
\(792\) 9.78426 0.347669
\(793\) −4.86236 −0.172668
\(794\) −1.24349 −0.0441298
\(795\) 7.14207 0.253303
\(796\) 46.8292 1.65982
\(797\) −24.0229 −0.850935 −0.425467 0.904974i \(-0.639890\pi\)
−0.425467 + 0.904974i \(0.639890\pi\)
\(798\) −8.42153 −0.298119
\(799\) 12.4065 0.438911
\(800\) −0.666319 −0.0235579
\(801\) −19.0933 −0.674629
\(802\) −81.0711 −2.86272
\(803\) 13.9945 0.493856
\(804\) 10.7014 0.377410
\(805\) −42.4784 −1.49717
\(806\) 15.2725 0.537950
\(807\) 2.33758 0.0822869
\(808\) 70.3777 2.47588
\(809\) 40.7641 1.43319 0.716595 0.697490i \(-0.245700\pi\)
0.716595 + 0.697490i \(0.245700\pi\)
\(810\) 10.8282 0.380465
\(811\) −54.1288 −1.90072 −0.950360 0.311151i \(-0.899285\pi\)
−0.950360 + 0.311151i \(0.899285\pi\)
\(812\) −49.5839 −1.74005
\(813\) 2.68698 0.0942364
\(814\) 19.0538 0.667835
\(815\) −29.3039 −1.02647
\(816\) 3.06352 0.107245
\(817\) −5.31829 −0.186063
\(818\) 6.23994 0.218174
\(819\) −7.66110 −0.267700
\(820\) −72.2774 −2.52404
\(821\) −52.1354 −1.81954 −0.909768 0.415116i \(-0.863741\pi\)
−0.909768 + 0.415116i \(0.863741\pi\)
\(822\) 18.7553 0.654165
\(823\) 47.7734 1.66528 0.832638 0.553817i \(-0.186829\pi\)
0.832638 + 0.553817i \(0.186829\pi\)
\(824\) −52.7711 −1.83837
\(825\) 0.510810 0.0177841
\(826\) 47.9368 1.66794
\(827\) −14.3208 −0.497984 −0.248992 0.968505i \(-0.580099\pi\)
−0.248992 + 0.968505i \(0.580099\pi\)
\(828\) 62.4215 2.16930
\(829\) 33.8554 1.17585 0.587924 0.808916i \(-0.299945\pi\)
0.587924 + 0.808916i \(0.299945\pi\)
\(830\) 81.3799 2.82474
\(831\) −7.98515 −0.277002
\(832\) 12.3932 0.429656
\(833\) −0.273694 −0.00948294
\(834\) −14.3969 −0.498525
\(835\) −4.13883 −0.143230
\(836\) 5.43546 0.187989
\(837\) 22.6479 0.782826
\(838\) −59.9600 −2.07128
\(839\) 8.09662 0.279526 0.139763 0.990185i \(-0.455366\pi\)
0.139763 + 0.990185i \(0.455366\pi\)
\(840\) 23.6803 0.817048
\(841\) −6.43685 −0.221960
\(842\) 54.3114 1.87170
\(843\) −21.4835 −0.739932
\(844\) −33.3461 −1.14782
\(845\) 23.7432 0.816790
\(846\) −63.1753 −2.17201
\(847\) −2.69568 −0.0926247
\(848\) 11.9898 0.411730
\(849\) −22.7865 −0.782031
\(850\) −1.38312 −0.0474407
\(851\) 58.7756 2.01480
\(852\) −17.2732 −0.591768
\(853\) 20.7415 0.710176 0.355088 0.934833i \(-0.384451\pi\)
0.355088 + 0.934833i \(0.384451\pi\)
\(854\) 24.1013 0.824728
\(855\) 6.38093 0.218223
\(856\) 69.3559 2.37054
\(857\) 6.04129 0.206367 0.103183 0.994662i \(-0.467097\pi\)
0.103183 + 0.994662i \(0.467097\pi\)
\(858\) −2.93319 −0.100137
\(859\) −5.01431 −0.171086 −0.0855431 0.996334i \(-0.527263\pi\)
−0.0855431 + 0.996334i \(0.527263\pi\)
\(860\) 30.9285 1.05465
\(861\) 21.9217 0.747088
\(862\) 8.00072 0.272506
\(863\) 7.10321 0.241796 0.120898 0.992665i \(-0.461423\pi\)
0.120898 + 0.992665i \(0.461423\pi\)
\(864\) 5.67388 0.193029
\(865\) 18.1461 0.616985
\(866\) −15.6494 −0.531787
\(867\) 14.6463 0.497414
\(868\) −49.9187 −1.69435
\(869\) −11.2438 −0.381421
\(870\) −22.2862 −0.755574
\(871\) 3.96549 0.134366
\(872\) 5.35782 0.181439
\(873\) −13.8470 −0.468651
\(874\) 25.4267 0.860071
\(875\) −31.5735 −1.06738
\(876\) −49.7718 −1.68163
\(877\) −8.19348 −0.276674 −0.138337 0.990385i \(-0.544176\pi\)
−0.138337 + 0.990385i \(0.544176\pi\)
\(878\) 40.6989 1.37352
\(879\) −9.13352 −0.308066
\(880\) −6.85168 −0.230970
\(881\) 21.0986 0.710831 0.355416 0.934708i \(-0.384339\pi\)
0.355416 + 0.934708i \(0.384339\pi\)
\(882\) 1.39368 0.0469277
\(883\) 41.3137 1.39032 0.695159 0.718856i \(-0.255334\pi\)
0.695159 + 0.718856i \(0.255334\pi\)
\(884\) 5.23723 0.176147
\(885\) 14.2078 0.477591
\(886\) 74.3743 2.49865
\(887\) 10.9280 0.366925 0.183462 0.983027i \(-0.441269\pi\)
0.183462 + 0.983027i \(0.441269\pi\)
\(888\) −32.7655 −1.09954
\(889\) −4.14083 −0.138879
\(890\) 45.2297 1.51610
\(891\) 2.11969 0.0710124
\(892\) −21.3979 −0.716454
\(893\) −16.9693 −0.567857
\(894\) 15.6672 0.523990
\(895\) −32.7918 −1.09611
\(896\) −54.9701 −1.83642
\(897\) −9.04805 −0.302106
\(898\) 3.80326 0.126916
\(899\) 22.7155 0.757605
\(900\) 4.64430 0.154810
\(901\) −3.78565 −0.126118
\(902\) −21.4564 −0.714420
\(903\) −9.38057 −0.312166
\(904\) −45.7352 −1.52113
\(905\) 18.8812 0.627633
\(906\) 9.97655 0.331449
\(907\) −7.61973 −0.253009 −0.126504 0.991966i \(-0.540376\pi\)
−0.126504 + 0.991966i \(0.540376\pi\)
\(908\) −28.3582 −0.941099
\(909\) 33.4495 1.10945
\(910\) 18.1482 0.601607
\(911\) 11.0538 0.366228 0.183114 0.983092i \(-0.441382\pi\)
0.183114 + 0.983092i \(0.441382\pi\)
\(912\) −4.19021 −0.138752
\(913\) 15.9306 0.527228
\(914\) 83.6651 2.76740
\(915\) 7.14328 0.236150
\(916\) −4.16441 −0.137596
\(917\) −2.95711 −0.0976523
\(918\) 11.7776 0.388720
\(919\) 25.4030 0.837968 0.418984 0.907994i \(-0.362386\pi\)
0.418984 + 0.907994i \(0.362386\pi\)
\(920\) −71.4968 −2.35718
\(921\) −10.3380 −0.340649
\(922\) −66.4472 −2.18832
\(923\) −6.40070 −0.210682
\(924\) 9.58724 0.315397
\(925\) 4.37303 0.143784
\(926\) 8.77019 0.288206
\(927\) −25.0813 −0.823780
\(928\) 5.69083 0.186811
\(929\) 0.877180 0.0287793 0.0143897 0.999896i \(-0.495419\pi\)
0.0143897 + 0.999896i \(0.495419\pi\)
\(930\) −22.4368 −0.735730
\(931\) 0.374353 0.0122689
\(932\) −6.49476 −0.212743
\(933\) −11.4305 −0.374219
\(934\) −6.21497 −0.203360
\(935\) 2.16335 0.0707492
\(936\) −12.8946 −0.421475
\(937\) 13.5802 0.443646 0.221823 0.975087i \(-0.428799\pi\)
0.221823 + 0.975087i \(0.428799\pi\)
\(938\) −19.6557 −0.641783
\(939\) 2.90958 0.0949504
\(940\) 98.6851 3.21875
\(941\) −6.10609 −0.199053 −0.0995265 0.995035i \(-0.531733\pi\)
−0.0995265 + 0.995035i \(0.531733\pi\)
\(942\) −8.74639 −0.284973
\(943\) −66.1870 −2.15535
\(944\) 23.8514 0.776298
\(945\) 26.9124 0.875459
\(946\) 9.18148 0.298516
\(947\) 42.2325 1.37237 0.686187 0.727425i \(-0.259283\pi\)
0.686187 + 0.727425i \(0.259283\pi\)
\(948\) 39.9889 1.29878
\(949\) −18.4433 −0.598696
\(950\) 1.89180 0.0613782
\(951\) 2.47510 0.0802607
\(952\) −12.5517 −0.406804
\(953\) 18.7654 0.607870 0.303935 0.952693i \(-0.401699\pi\)
0.303935 + 0.952693i \(0.401699\pi\)
\(954\) 19.2770 0.624115
\(955\) −48.7585 −1.57779
\(956\) −42.0060 −1.35857
\(957\) −4.36268 −0.141025
\(958\) 7.10541 0.229565
\(959\) −22.7161 −0.733541
\(960\) −18.2068 −0.587621
\(961\) −8.13106 −0.262292
\(962\) −25.1109 −0.809609
\(963\) 32.9638 1.06224
\(964\) −29.0018 −0.934085
\(965\) 56.4868 1.81837
\(966\) 44.8485 1.44298
\(967\) −39.6513 −1.27510 −0.637550 0.770409i \(-0.720052\pi\)
−0.637550 + 0.770409i \(0.720052\pi\)
\(968\) −4.53719 −0.145831
\(969\) 1.32302 0.0425015
\(970\) 32.8019 1.05321
\(971\) −38.9569 −1.25019 −0.625093 0.780550i \(-0.714939\pi\)
−0.625093 + 0.780550i \(0.714939\pi\)
\(972\) −62.5559 −2.00648
\(973\) 17.4374 0.559016
\(974\) 25.0075 0.801292
\(975\) −0.673195 −0.0215595
\(976\) 11.9918 0.383848
\(977\) 27.6929 0.885973 0.442986 0.896528i \(-0.353919\pi\)
0.442986 + 0.896528i \(0.353919\pi\)
\(978\) 30.9389 0.989317
\(979\) 8.85401 0.282976
\(980\) −2.17705 −0.0695432
\(981\) 2.54649 0.0813032
\(982\) 42.7439 1.36401
\(983\) −39.7200 −1.26687 −0.633436 0.773795i \(-0.718356\pi\)
−0.633436 + 0.773795i \(0.718356\pi\)
\(984\) 36.8971 1.17624
\(985\) 3.37108 0.107412
\(986\) 11.8128 0.376197
\(987\) −29.9311 −0.952717
\(988\) −7.16337 −0.227897
\(989\) 28.3223 0.900596
\(990\) −11.0160 −0.350112
\(991\) 14.2432 0.452452 0.226226 0.974075i \(-0.427361\pi\)
0.226226 + 0.974075i \(0.427361\pi\)
\(992\) 5.72926 0.181904
\(993\) −12.8924 −0.409127
\(994\) 31.7263 1.00630
\(995\) −25.4932 −0.808187
\(996\) −56.6577 −1.79527
\(997\) 15.4930 0.490667 0.245334 0.969439i \(-0.421103\pi\)
0.245334 + 0.969439i \(0.421103\pi\)
\(998\) 63.6783 2.01570
\(999\) −37.2375 −1.17814
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 \(a_p\))