Properties

Label 6023.2.a.b.1.6
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56636 q^{2}\) \(+2.86321 q^{3}\) \(+4.58620 q^{4}\) \(-1.49629 q^{5}\) \(-7.34803 q^{6}\) \(-1.31440 q^{7}\) \(-6.63713 q^{8}\) \(+5.19797 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56636 q^{2}\) \(+2.86321 q^{3}\) \(+4.58620 q^{4}\) \(-1.49629 q^{5}\) \(-7.34803 q^{6}\) \(-1.31440 q^{7}\) \(-6.63713 q^{8}\) \(+5.19797 q^{9}\) \(+3.84001 q^{10}\) \(+5.98208 q^{11}\) \(+13.1313 q^{12}\) \(+1.85013 q^{13}\) \(+3.37322 q^{14}\) \(-4.28419 q^{15}\) \(+7.86086 q^{16}\) \(-3.46147 q^{17}\) \(-13.3399 q^{18}\) \(-1.00000 q^{19}\) \(-6.86228 q^{20}\) \(-3.76340 q^{21}\) \(-15.3522 q^{22}\) \(+0.442595 q^{23}\) \(-19.0035 q^{24}\) \(-2.76112 q^{25}\) \(-4.74811 q^{26}\) \(+6.29324 q^{27}\) \(-6.02810 q^{28}\) \(-2.74531 q^{29}\) \(+10.9948 q^{30}\) \(+0.0954084 q^{31}\) \(-6.89954 q^{32}\) \(+17.1279 q^{33}\) \(+8.88339 q^{34}\) \(+1.96672 q^{35}\) \(+23.8389 q^{36}\) \(-10.1880 q^{37}\) \(+2.56636 q^{38}\) \(+5.29732 q^{39}\) \(+9.93106 q^{40}\) \(-2.51996 q^{41}\) \(+9.65824 q^{42}\) \(-7.29343 q^{43}\) \(+27.4350 q^{44}\) \(-7.77765 q^{45}\) \(-1.13586 q^{46}\) \(-3.12300 q^{47}\) \(+22.5073 q^{48}\) \(-5.27235 q^{49}\) \(+7.08603 q^{50}\) \(-9.91092 q^{51}\) \(+8.48509 q^{52}\) \(-10.9108 q^{53}\) \(-16.1507 q^{54}\) \(-8.95091 q^{55}\) \(+8.72384 q^{56}\) \(-2.86321 q^{57}\) \(+7.04545 q^{58}\) \(-4.29096 q^{59}\) \(-19.6481 q^{60}\) \(-0.761735 q^{61}\) \(-0.244852 q^{62}\) \(-6.83220 q^{63}\) \(+1.98498 q^{64}\) \(-2.76833 q^{65}\) \(-43.9565 q^{66}\) \(-8.54232 q^{67}\) \(-15.8750 q^{68}\) \(+1.26724 q^{69}\) \(-5.04731 q^{70}\) \(+6.58317 q^{71}\) \(-34.4996 q^{72}\) \(-2.57828 q^{73}\) \(+26.1461 q^{74}\) \(-7.90567 q^{75}\) \(-4.58620 q^{76}\) \(-7.86284 q^{77}\) \(-13.5948 q^{78}\) \(+0.758087 q^{79}\) \(-11.7621 q^{80}\) \(+2.42495 q^{81}\) \(+6.46713 q^{82}\) \(-11.7656 q^{83}\) \(-17.2597 q^{84}\) \(+5.17936 q^{85}\) \(+18.7176 q^{86}\) \(-7.86040 q^{87}\) \(-39.7039 q^{88}\) \(+1.41961 q^{89}\) \(+19.9603 q^{90}\) \(-2.43181 q^{91}\) \(+2.02983 q^{92}\) \(+0.273174 q^{93}\) \(+8.01475 q^{94}\) \(+1.49629 q^{95}\) \(-19.7548 q^{96}\) \(-14.5041 q^{97}\) \(+13.5308 q^{98}\) \(+31.0946 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56636 −1.81469 −0.907345 0.420386i \(-0.861895\pi\)
−0.907345 + 0.420386i \(0.861895\pi\)
\(3\) 2.86321 1.65307 0.826537 0.562882i \(-0.190307\pi\)
0.826537 + 0.562882i \(0.190307\pi\)
\(4\) 4.58620 2.29310
\(5\) −1.49629 −0.669160 −0.334580 0.942367i \(-0.608594\pi\)
−0.334580 + 0.942367i \(0.608594\pi\)
\(6\) −7.34803 −2.99982
\(7\) −1.31440 −0.496796 −0.248398 0.968658i \(-0.579904\pi\)
−0.248398 + 0.968658i \(0.579904\pi\)
\(8\) −6.63713 −2.34658
\(9\) 5.19797 1.73266
\(10\) 3.84001 1.21432
\(11\) 5.98208 1.80367 0.901833 0.432086i \(-0.142222\pi\)
0.901833 + 0.432086i \(0.142222\pi\)
\(12\) 13.1313 3.79067
\(13\) 1.85013 0.513135 0.256567 0.966526i \(-0.417408\pi\)
0.256567 + 0.966526i \(0.417408\pi\)
\(14\) 3.37322 0.901531
\(15\) −4.28419 −1.10617
\(16\) 7.86086 1.96522
\(17\) −3.46147 −0.839531 −0.419765 0.907633i \(-0.637888\pi\)
−0.419765 + 0.907633i \(0.637888\pi\)
\(18\) −13.3399 −3.14423
\(19\) −1.00000 −0.229416
\(20\) −6.86228 −1.53445
\(21\) −3.76340 −0.821241
\(22\) −15.3522 −3.27309
\(23\) 0.442595 0.0922874 0.0461437 0.998935i \(-0.485307\pi\)
0.0461437 + 0.998935i \(0.485307\pi\)
\(24\) −19.0035 −3.87907
\(25\) −2.76112 −0.552224
\(26\) −4.74811 −0.931181
\(27\) 6.29324 1.21113
\(28\) −6.02810 −1.13920
\(29\) −2.74531 −0.509791 −0.254896 0.966969i \(-0.582041\pi\)
−0.254896 + 0.966969i \(0.582041\pi\)
\(30\) 10.9948 2.00736
\(31\) 0.0954084 0.0171359 0.00856793 0.999963i \(-0.497273\pi\)
0.00856793 + 0.999963i \(0.497273\pi\)
\(32\) −6.89954 −1.21968
\(33\) 17.1279 2.98159
\(34\) 8.88339 1.52349
\(35\) 1.96672 0.332436
\(36\) 23.8389 3.97316
\(37\) −10.1880 −1.67490 −0.837450 0.546514i \(-0.815955\pi\)
−0.837450 + 0.546514i \(0.815955\pi\)
\(38\) 2.56636 0.416319
\(39\) 5.29732 0.848250
\(40\) 9.93106 1.57024
\(41\) −2.51996 −0.393552 −0.196776 0.980448i \(-0.563047\pi\)
−0.196776 + 0.980448i \(0.563047\pi\)
\(42\) 9.65824 1.49030
\(43\) −7.29343 −1.11224 −0.556119 0.831103i \(-0.687710\pi\)
−0.556119 + 0.831103i \(0.687710\pi\)
\(44\) 27.4350 4.13599
\(45\) −7.77765 −1.15942
\(46\) −1.13586 −0.167473
\(47\) −3.12300 −0.455537 −0.227768 0.973715i \(-0.573143\pi\)
−0.227768 + 0.973715i \(0.573143\pi\)
\(48\) 22.5073 3.24865
\(49\) −5.27235 −0.753194
\(50\) 7.08603 1.00212
\(51\) −9.91092 −1.38781
\(52\) 8.48509 1.17667
\(53\) −10.9108 −1.49871 −0.749354 0.662170i \(-0.769636\pi\)
−0.749354 + 0.662170i \(0.769636\pi\)
\(54\) −16.1507 −2.19783
\(55\) −8.95091 −1.20694
\(56\) 8.72384 1.16577
\(57\) −2.86321 −0.379241
\(58\) 7.04545 0.925114
\(59\) −4.29096 −0.558636 −0.279318 0.960199i \(-0.590108\pi\)
−0.279318 + 0.960199i \(0.590108\pi\)
\(60\) −19.6481 −2.53657
\(61\) −0.761735 −0.0975302 −0.0487651 0.998810i \(-0.515529\pi\)
−0.0487651 + 0.998810i \(0.515529\pi\)
\(62\) −0.244852 −0.0310963
\(63\) −6.83220 −0.860777
\(64\) 1.98498 0.248122
\(65\) −2.76833 −0.343369
\(66\) −43.9565 −5.41067
\(67\) −8.54232 −1.04361 −0.521805 0.853065i \(-0.674741\pi\)
−0.521805 + 0.853065i \(0.674741\pi\)
\(68\) −15.8750 −1.92513
\(69\) 1.26724 0.152558
\(70\) −5.04731 −0.603269
\(71\) 6.58317 0.781279 0.390639 0.920544i \(-0.372254\pi\)
0.390639 + 0.920544i \(0.372254\pi\)
\(72\) −34.4996 −4.06581
\(73\) −2.57828 −0.301765 −0.150883 0.988552i \(-0.548212\pi\)
−0.150883 + 0.988552i \(0.548212\pi\)
\(74\) 26.1461 3.03943
\(75\) −7.90567 −0.912868
\(76\) −4.58620 −0.526074
\(77\) −7.86284 −0.896054
\(78\) −13.5948 −1.53931
\(79\) 0.758087 0.0852915 0.0426457 0.999090i \(-0.486421\pi\)
0.0426457 + 0.999090i \(0.486421\pi\)
\(80\) −11.7621 −1.31504
\(81\) 2.42495 0.269439
\(82\) 6.46713 0.714176
\(83\) −11.7656 −1.29145 −0.645723 0.763571i \(-0.723444\pi\)
−0.645723 + 0.763571i \(0.723444\pi\)
\(84\) −17.2597 −1.88319
\(85\) 5.17936 0.561781
\(86\) 18.7176 2.01837
\(87\) −7.86040 −0.842723
\(88\) −39.7039 −4.23245
\(89\) 1.41961 0.150479 0.0752394 0.997165i \(-0.476028\pi\)
0.0752394 + 0.997165i \(0.476028\pi\)
\(90\) 19.9603 2.10400
\(91\) −2.43181 −0.254923
\(92\) 2.02983 0.211624
\(93\) 0.273174 0.0283268
\(94\) 8.01475 0.826658
\(95\) 1.49629 0.153516
\(96\) −19.7548 −2.01622
\(97\) −14.5041 −1.47267 −0.736335 0.676617i \(-0.763445\pi\)
−0.736335 + 0.676617i \(0.763445\pi\)
\(98\) 13.5308 1.36681
\(99\) 31.0946 3.12513
\(100\) −12.6631 −1.26631
\(101\) −0.875507 −0.0871162 −0.0435581 0.999051i \(-0.513869\pi\)
−0.0435581 + 0.999051i \(0.513869\pi\)
\(102\) 25.4350 2.51844
\(103\) 17.3091 1.70551 0.852757 0.522308i \(-0.174929\pi\)
0.852757 + 0.522308i \(0.174929\pi\)
\(104\) −12.2796 −1.20411
\(105\) 5.63113 0.549542
\(106\) 28.0009 2.71969
\(107\) 3.86462 0.373607 0.186804 0.982397i \(-0.440187\pi\)
0.186804 + 0.982397i \(0.440187\pi\)
\(108\) 28.8621 2.77725
\(109\) 13.7614 1.31811 0.659053 0.752096i \(-0.270957\pi\)
0.659053 + 0.752096i \(0.270957\pi\)
\(110\) 22.9713 2.19022
\(111\) −29.1704 −2.76874
\(112\) −10.3323 −0.976312
\(113\) −6.56733 −0.617802 −0.308901 0.951094i \(-0.599961\pi\)
−0.308901 + 0.951094i \(0.599961\pi\)
\(114\) 7.34803 0.688206
\(115\) −0.662249 −0.0617551
\(116\) −12.5906 −1.16900
\(117\) 9.61693 0.889086
\(118\) 11.0122 1.01375
\(119\) 4.54976 0.417076
\(120\) 28.4347 2.59572
\(121\) 24.7853 2.25321
\(122\) 1.95489 0.176987
\(123\) −7.21518 −0.650571
\(124\) 0.437562 0.0392943
\(125\) 11.6129 1.03869
\(126\) 17.5339 1.56204
\(127\) −1.98474 −0.176117 −0.0880584 0.996115i \(-0.528066\pi\)
−0.0880584 + 0.996115i \(0.528066\pi\)
\(128\) 8.70491 0.769413
\(129\) −20.8826 −1.83861
\(130\) 7.10454 0.623109
\(131\) −4.35732 −0.380701 −0.190350 0.981716i \(-0.560962\pi\)
−0.190350 + 0.981716i \(0.560962\pi\)
\(132\) 78.5523 6.83710
\(133\) 1.31440 0.113973
\(134\) 21.9227 1.89383
\(135\) −9.41649 −0.810443
\(136\) 22.9743 1.97003
\(137\) 6.45791 0.551737 0.275868 0.961195i \(-0.411035\pi\)
0.275868 + 0.961195i \(0.411035\pi\)
\(138\) −3.25220 −0.276846
\(139\) −6.89376 −0.584721 −0.292360 0.956308i \(-0.594441\pi\)
−0.292360 + 0.956308i \(0.594441\pi\)
\(140\) 9.01978 0.762310
\(141\) −8.94181 −0.753036
\(142\) −16.8948 −1.41778
\(143\) 11.0676 0.925523
\(144\) 40.8605 3.40504
\(145\) 4.10777 0.341132
\(146\) 6.61680 0.547610
\(147\) −15.0959 −1.24509
\(148\) −46.7244 −3.84072
\(149\) 19.8092 1.62283 0.811416 0.584468i \(-0.198697\pi\)
0.811416 + 0.584468i \(0.198697\pi\)
\(150\) 20.2888 1.65657
\(151\) 15.8862 1.29280 0.646399 0.763000i \(-0.276274\pi\)
0.646399 + 0.763000i \(0.276274\pi\)
\(152\) 6.63713 0.538342
\(153\) −17.9926 −1.45462
\(154\) 20.1789 1.62606
\(155\) −0.142758 −0.0114666
\(156\) 24.2946 1.94512
\(157\) 5.68950 0.454072 0.227036 0.973886i \(-0.427097\pi\)
0.227036 + 0.973886i \(0.427097\pi\)
\(158\) −1.94552 −0.154778
\(159\) −31.2398 −2.47748
\(160\) 10.3237 0.816160
\(161\) −0.581746 −0.0458480
\(162\) −6.22330 −0.488948
\(163\) −12.1043 −0.948084 −0.474042 0.880502i \(-0.657206\pi\)
−0.474042 + 0.880502i \(0.657206\pi\)
\(164\) −11.5571 −0.902455
\(165\) −25.6283 −1.99516
\(166\) 30.1949 2.34358
\(167\) 3.61094 0.279423 0.139712 0.990192i \(-0.455382\pi\)
0.139712 + 0.990192i \(0.455382\pi\)
\(168\) 24.9782 1.92711
\(169\) −9.57701 −0.736693
\(170\) −13.2921 −1.01946
\(171\) −5.19797 −0.397498
\(172\) −33.4491 −2.55047
\(173\) 21.9374 1.66787 0.833934 0.551864i \(-0.186083\pi\)
0.833934 + 0.551864i \(0.186083\pi\)
\(174\) 20.1726 1.52928
\(175\) 3.62922 0.274343
\(176\) 47.0243 3.54459
\(177\) −12.2859 −0.923466
\(178\) −3.64324 −0.273073
\(179\) −3.58063 −0.267629 −0.133814 0.991006i \(-0.542723\pi\)
−0.133814 + 0.991006i \(0.542723\pi\)
\(180\) −35.6699 −2.65868
\(181\) −24.7806 −1.84193 −0.920964 0.389647i \(-0.872597\pi\)
−0.920964 + 0.389647i \(0.872597\pi\)
\(182\) 6.24091 0.462607
\(183\) −2.18101 −0.161225
\(184\) −2.93756 −0.216560
\(185\) 15.2442 1.12078
\(186\) −0.701063 −0.0514045
\(187\) −20.7068 −1.51423
\(188\) −14.3227 −1.04459
\(189\) −8.27182 −0.601687
\(190\) −3.84001 −0.278584
\(191\) −3.32468 −0.240565 −0.120283 0.992740i \(-0.538380\pi\)
−0.120283 + 0.992740i \(0.538380\pi\)
\(192\) 5.68340 0.410164
\(193\) −16.1728 −1.16414 −0.582071 0.813138i \(-0.697757\pi\)
−0.582071 + 0.813138i \(0.697757\pi\)
\(194\) 37.2228 2.67244
\(195\) −7.92631 −0.567615
\(196\) −24.1801 −1.72715
\(197\) 18.6870 1.33140 0.665698 0.746221i \(-0.268134\pi\)
0.665698 + 0.746221i \(0.268134\pi\)
\(198\) −79.8001 −5.67114
\(199\) −15.2624 −1.08192 −0.540962 0.841047i \(-0.681940\pi\)
−0.540962 + 0.841047i \(0.681940\pi\)
\(200\) 18.3259 1.29584
\(201\) −24.4585 −1.72517
\(202\) 2.24687 0.158089
\(203\) 3.60843 0.253262
\(204\) −45.4535 −3.18238
\(205\) 3.77059 0.263350
\(206\) −44.4213 −3.09498
\(207\) 2.30059 0.159902
\(208\) 14.5436 1.00842
\(209\) −5.98208 −0.413789
\(210\) −14.4515 −0.997249
\(211\) 3.43041 0.236159 0.118080 0.993004i \(-0.462326\pi\)
0.118080 + 0.993004i \(0.462326\pi\)
\(212\) −50.0390 −3.43669
\(213\) 18.8490 1.29151
\(214\) −9.91802 −0.677982
\(215\) 10.9131 0.744265
\(216\) −41.7690 −2.84202
\(217\) −0.125405 −0.00851303
\(218\) −35.3168 −2.39196
\(219\) −7.38216 −0.498840
\(220\) −41.0507 −2.76764
\(221\) −6.40419 −0.430792
\(222\) 74.8618 5.02440
\(223\) −0.693707 −0.0464541 −0.0232270 0.999730i \(-0.507394\pi\)
−0.0232270 + 0.999730i \(0.507394\pi\)
\(224\) 9.06875 0.605931
\(225\) −14.3522 −0.956815
\(226\) 16.8541 1.12112
\(227\) 9.65783 0.641013 0.320506 0.947246i \(-0.396147\pi\)
0.320506 + 0.947246i \(0.396147\pi\)
\(228\) −13.1313 −0.869639
\(229\) 1.06564 0.0704193 0.0352096 0.999380i \(-0.488790\pi\)
0.0352096 + 0.999380i \(0.488790\pi\)
\(230\) 1.69957 0.112066
\(231\) −22.5130 −1.48124
\(232\) 18.2210 1.19627
\(233\) 23.5170 1.54065 0.770324 0.637653i \(-0.220095\pi\)
0.770324 + 0.637653i \(0.220095\pi\)
\(234\) −24.6805 −1.61342
\(235\) 4.67291 0.304827
\(236\) −19.6792 −1.28101
\(237\) 2.17056 0.140993
\(238\) −11.6763 −0.756863
\(239\) −11.0307 −0.713516 −0.356758 0.934197i \(-0.616118\pi\)
−0.356758 + 0.934197i \(0.616118\pi\)
\(240\) −33.6774 −2.17387
\(241\) −15.0306 −0.968208 −0.484104 0.875010i \(-0.660854\pi\)
−0.484104 + 0.875010i \(0.660854\pi\)
\(242\) −63.6080 −4.08888
\(243\) −11.9366 −0.765731
\(244\) −3.49347 −0.223647
\(245\) 7.88896 0.504007
\(246\) 18.5168 1.18059
\(247\) −1.85013 −0.117721
\(248\) −0.633238 −0.0402107
\(249\) −33.6875 −2.13486
\(250\) −29.8028 −1.88490
\(251\) 28.6078 1.80571 0.902855 0.429944i \(-0.141467\pi\)
0.902855 + 0.429944i \(0.141467\pi\)
\(252\) −31.3339 −1.97385
\(253\) 2.64764 0.166456
\(254\) 5.09355 0.319598
\(255\) 14.8296 0.928665
\(256\) −26.3099 −1.64437
\(257\) −13.6738 −0.852949 −0.426474 0.904500i \(-0.640245\pi\)
−0.426474 + 0.904500i \(0.640245\pi\)
\(258\) 53.5923 3.33651
\(259\) 13.3911 0.832084
\(260\) −12.6961 −0.787381
\(261\) −14.2700 −0.883293
\(262\) 11.1824 0.690854
\(263\) −6.92100 −0.426767 −0.213384 0.976969i \(-0.568448\pi\)
−0.213384 + 0.976969i \(0.568448\pi\)
\(264\) −113.680 −6.99655
\(265\) 16.3256 1.00288
\(266\) −3.37322 −0.206825
\(267\) 4.06465 0.248753
\(268\) −39.1768 −2.39311
\(269\) −6.23030 −0.379868 −0.189934 0.981797i \(-0.560827\pi\)
−0.189934 + 0.981797i \(0.560827\pi\)
\(270\) 24.1661 1.47070
\(271\) −14.1717 −0.860871 −0.430436 0.902621i \(-0.641640\pi\)
−0.430436 + 0.902621i \(0.641640\pi\)
\(272\) −27.2102 −1.64986
\(273\) −6.96279 −0.421407
\(274\) −16.5733 −1.00123
\(275\) −16.5173 −0.996028
\(276\) 5.81183 0.349831
\(277\) −28.0618 −1.68607 −0.843035 0.537859i \(-0.819233\pi\)
−0.843035 + 0.537859i \(0.819233\pi\)
\(278\) 17.6919 1.06109
\(279\) 0.495930 0.0296905
\(280\) −13.0534 −0.780088
\(281\) 25.3189 1.51040 0.755199 0.655495i \(-0.227540\pi\)
0.755199 + 0.655495i \(0.227540\pi\)
\(282\) 22.9479 1.36653
\(283\) 2.35984 0.140278 0.0701389 0.997537i \(-0.477656\pi\)
0.0701389 + 0.997537i \(0.477656\pi\)
\(284\) 30.1918 1.79155
\(285\) 4.28419 0.253773
\(286\) −28.4036 −1.67954
\(287\) 3.31224 0.195515
\(288\) −35.8636 −2.11328
\(289\) −5.01820 −0.295188
\(290\) −10.5420 −0.619049
\(291\) −41.5283 −2.43443
\(292\) −11.8245 −0.691978
\(293\) 28.0673 1.63971 0.819854 0.572572i \(-0.194054\pi\)
0.819854 + 0.572572i \(0.194054\pi\)
\(294\) 38.7414 2.25944
\(295\) 6.42051 0.373817
\(296\) 67.6192 3.93029
\(297\) 37.6466 2.18448
\(298\) −50.8375 −2.94494
\(299\) 0.818860 0.0473559
\(300\) −36.2570 −2.09330
\(301\) 9.58647 0.552555
\(302\) −40.7696 −2.34603
\(303\) −2.50676 −0.144010
\(304\) −7.86086 −0.450851
\(305\) 1.13978 0.0652633
\(306\) 46.1756 2.63968
\(307\) −9.12746 −0.520932 −0.260466 0.965483i \(-0.583876\pi\)
−0.260466 + 0.965483i \(0.583876\pi\)
\(308\) −36.0606 −2.05474
\(309\) 49.5595 2.81934
\(310\) 0.366370 0.0208084
\(311\) 15.1187 0.857302 0.428651 0.903470i \(-0.358989\pi\)
0.428651 + 0.903470i \(0.358989\pi\)
\(312\) −35.1590 −1.99049
\(313\) −7.05095 −0.398543 −0.199272 0.979944i \(-0.563858\pi\)
−0.199272 + 0.979944i \(0.563858\pi\)
\(314\) −14.6013 −0.824000
\(315\) 10.2229 0.575997
\(316\) 3.47674 0.195582
\(317\) −1.00000 −0.0561656
\(318\) 80.1725 4.49585
\(319\) −16.4227 −0.919493
\(320\) −2.97010 −0.166033
\(321\) 11.0652 0.617601
\(322\) 1.49297 0.0832000
\(323\) 3.46147 0.192602
\(324\) 11.1213 0.617851
\(325\) −5.10845 −0.283366
\(326\) 31.0641 1.72048
\(327\) 39.4019 2.17893
\(328\) 16.7253 0.923502
\(329\) 4.10487 0.226309
\(330\) 65.7715 3.62060
\(331\) −21.3182 −1.17175 −0.585877 0.810400i \(-0.699250\pi\)
−0.585877 + 0.810400i \(0.699250\pi\)
\(332\) −53.9596 −2.96142
\(333\) −52.9570 −2.90203
\(334\) −9.26698 −0.507066
\(335\) 12.7818 0.698343
\(336\) −29.5836 −1.61392
\(337\) 10.7426 0.585187 0.292593 0.956237i \(-0.405482\pi\)
0.292593 + 0.956237i \(0.405482\pi\)
\(338\) 24.5780 1.33687
\(339\) −18.8036 −1.02127
\(340\) 23.7536 1.28822
\(341\) 0.570741 0.0309073
\(342\) 13.3399 0.721337
\(343\) 16.1308 0.870980
\(344\) 48.4074 2.60995
\(345\) −1.89616 −0.102086
\(346\) −56.2992 −3.02666
\(347\) −30.2575 −1.62431 −0.812153 0.583444i \(-0.801705\pi\)
−0.812153 + 0.583444i \(0.801705\pi\)
\(348\) −36.0494 −1.93245
\(349\) 4.24882 0.227434 0.113717 0.993513i \(-0.463724\pi\)
0.113717 + 0.993513i \(0.463724\pi\)
\(350\) −9.31388 −0.497848
\(351\) 11.6433 0.621475
\(352\) −41.2736 −2.19989
\(353\) −2.32893 −0.123957 −0.0619783 0.998077i \(-0.519741\pi\)
−0.0619783 + 0.998077i \(0.519741\pi\)
\(354\) 31.5301 1.67581
\(355\) −9.85032 −0.522801
\(356\) 6.51064 0.345063
\(357\) 13.0269 0.689457
\(358\) 9.18918 0.485663
\(359\) −13.3658 −0.705420 −0.352710 0.935733i \(-0.614740\pi\)
−0.352710 + 0.935733i \(0.614740\pi\)
\(360\) 51.6213 2.72068
\(361\) 1.00000 0.0526316
\(362\) 63.5960 3.34253
\(363\) 70.9655 3.72472
\(364\) −11.1528 −0.584565
\(365\) 3.85785 0.201929
\(366\) 5.59725 0.292573
\(367\) −25.2979 −1.32054 −0.660271 0.751028i \(-0.729559\pi\)
−0.660271 + 0.751028i \(0.729559\pi\)
\(368\) 3.47918 0.181365
\(369\) −13.0987 −0.681890
\(370\) −39.1221 −2.03386
\(371\) 14.3411 0.744552
\(372\) 1.25283 0.0649564
\(373\) −11.7457 −0.608167 −0.304084 0.952645i \(-0.598350\pi\)
−0.304084 + 0.952645i \(0.598350\pi\)
\(374\) 53.1412 2.74786
\(375\) 33.2501 1.71703
\(376\) 20.7278 1.06895
\(377\) −5.07919 −0.261592
\(378\) 21.2285 1.09188
\(379\) 36.9167 1.89629 0.948143 0.317844i \(-0.102959\pi\)
0.948143 + 0.317844i \(0.102959\pi\)
\(380\) 6.86228 0.352028
\(381\) −5.68271 −0.291134
\(382\) 8.53232 0.436551
\(383\) −8.62707 −0.440823 −0.220411 0.975407i \(-0.570740\pi\)
−0.220411 + 0.975407i \(0.570740\pi\)
\(384\) 24.9240 1.27190
\(385\) 11.7651 0.599604
\(386\) 41.5051 2.11256
\(387\) −37.9110 −1.92712
\(388\) −66.5189 −3.37698
\(389\) −11.8358 −0.600097 −0.300049 0.953924i \(-0.597003\pi\)
−0.300049 + 0.953924i \(0.597003\pi\)
\(390\) 20.3418 1.03005
\(391\) −1.53203 −0.0774781
\(392\) 34.9933 1.76743
\(393\) −12.4759 −0.629327
\(394\) −47.9577 −2.41607
\(395\) −1.13432 −0.0570737
\(396\) 142.606 7.16624
\(397\) 12.7775 0.641284 0.320642 0.947200i \(-0.396101\pi\)
0.320642 + 0.947200i \(0.396101\pi\)
\(398\) 39.1689 1.96336
\(399\) 3.76340 0.188406
\(400\) −21.7048 −1.08524
\(401\) −27.8859 −1.39256 −0.696278 0.717772i \(-0.745162\pi\)
−0.696278 + 0.717772i \(0.745162\pi\)
\(402\) 62.7692 3.13064
\(403\) 0.176518 0.00879300
\(404\) −4.01526 −0.199766
\(405\) −3.62842 −0.180298
\(406\) −9.26054 −0.459593
\(407\) −60.9456 −3.02096
\(408\) 65.7801 3.25660
\(409\) 27.7163 1.37048 0.685240 0.728317i \(-0.259697\pi\)
0.685240 + 0.728317i \(0.259697\pi\)
\(410\) −9.67670 −0.477898
\(411\) 18.4904 0.912062
\(412\) 79.3829 3.91092
\(413\) 5.64004 0.277528
\(414\) −5.90415 −0.290173
\(415\) 17.6048 0.864185
\(416\) −12.7651 −0.625859
\(417\) −19.7383 −0.966587
\(418\) 15.3522 0.750899
\(419\) 27.3216 1.33475 0.667374 0.744723i \(-0.267418\pi\)
0.667374 + 0.744723i \(0.267418\pi\)
\(420\) 25.8255 1.26016
\(421\) 9.11114 0.444050 0.222025 0.975041i \(-0.428733\pi\)
0.222025 + 0.975041i \(0.428733\pi\)
\(422\) −8.80366 −0.428556
\(423\) −16.2333 −0.789288
\(424\) 72.4162 3.51684
\(425\) 9.55755 0.463609
\(426\) −48.3733 −2.34369
\(427\) 1.00122 0.0484526
\(428\) 17.7240 0.856720
\(429\) 31.6890 1.52996
\(430\) −28.0069 −1.35061
\(431\) −24.3199 −1.17145 −0.585725 0.810510i \(-0.699190\pi\)
−0.585725 + 0.810510i \(0.699190\pi\)
\(432\) 49.4703 2.38014
\(433\) −8.86237 −0.425898 −0.212949 0.977063i \(-0.568307\pi\)
−0.212949 + 0.977063i \(0.568307\pi\)
\(434\) 0.321834 0.0154485
\(435\) 11.7614 0.563917
\(436\) 63.1128 3.02255
\(437\) −0.442595 −0.0211722
\(438\) 18.9453 0.905241
\(439\) −0.791614 −0.0377817 −0.0188908 0.999822i \(-0.506013\pi\)
−0.0188908 + 0.999822i \(0.506013\pi\)
\(440\) 59.4084 2.83218
\(441\) −27.4055 −1.30502
\(442\) 16.4355 0.781755
\(443\) 11.3287 0.538241 0.269121 0.963106i \(-0.413267\pi\)
0.269121 + 0.963106i \(0.413267\pi\)
\(444\) −133.782 −6.34899
\(445\) −2.12415 −0.100694
\(446\) 1.78030 0.0842998
\(447\) 56.7179 2.68266
\(448\) −2.60905 −0.123266
\(449\) 9.19039 0.433721 0.216861 0.976203i \(-0.430418\pi\)
0.216861 + 0.976203i \(0.430418\pi\)
\(450\) 36.8330 1.73632
\(451\) −15.0746 −0.709836
\(452\) −30.1191 −1.41668
\(453\) 45.4854 2.13709
\(454\) −24.7855 −1.16324
\(455\) 3.63869 0.170585
\(456\) 19.0035 0.889920
\(457\) −26.7160 −1.24972 −0.624860 0.780737i \(-0.714844\pi\)
−0.624860 + 0.780737i \(0.714844\pi\)
\(458\) −2.73481 −0.127789
\(459\) −21.7839 −1.01678
\(460\) −3.03721 −0.141611
\(461\) 6.37718 0.297015 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(462\) 57.7764 2.68800
\(463\) 20.0954 0.933910 0.466955 0.884281i \(-0.345351\pi\)
0.466955 + 0.884281i \(0.345351\pi\)
\(464\) −21.5805 −1.00185
\(465\) −0.408747 −0.0189552
\(466\) −60.3530 −2.79580
\(467\) −31.4372 −1.45474 −0.727369 0.686246i \(-0.759257\pi\)
−0.727369 + 0.686246i \(0.759257\pi\)
\(468\) 44.1052 2.03876
\(469\) 11.2280 0.518462
\(470\) −11.9924 −0.553167
\(471\) 16.2902 0.750615
\(472\) 28.4797 1.31088
\(473\) −43.6299 −2.00610
\(474\) −5.57044 −0.255859
\(475\) 2.76112 0.126689
\(476\) 20.8661 0.956397
\(477\) −56.7138 −2.59674
\(478\) 28.3087 1.29481
\(479\) 9.44859 0.431717 0.215858 0.976425i \(-0.430745\pi\)
0.215858 + 0.976425i \(0.430745\pi\)
\(480\) 29.5589 1.34917
\(481\) −18.8492 −0.859450
\(482\) 38.5740 1.75700
\(483\) −1.66566 −0.0757902
\(484\) 113.670 5.16684
\(485\) 21.7023 0.985453
\(486\) 30.6335 1.38956
\(487\) 26.0689 1.18129 0.590647 0.806930i \(-0.298872\pi\)
0.590647 + 0.806930i \(0.298872\pi\)
\(488\) 5.05574 0.228862
\(489\) −34.6572 −1.56725
\(490\) −20.2459 −0.914617
\(491\) −28.8172 −1.30050 −0.650250 0.759720i \(-0.725336\pi\)
−0.650250 + 0.759720i \(0.725336\pi\)
\(492\) −33.0903 −1.49183
\(493\) 9.50282 0.427986
\(494\) 4.74811 0.213628
\(495\) −46.5265 −2.09121
\(496\) 0.749992 0.0336756
\(497\) −8.65291 −0.388136
\(498\) 86.4542 3.87411
\(499\) 29.3483 1.31381 0.656906 0.753973i \(-0.271865\pi\)
0.656906 + 0.753973i \(0.271865\pi\)
\(500\) 53.2590 2.38182
\(501\) 10.3389 0.461907
\(502\) −73.4180 −3.27681
\(503\) −9.35889 −0.417292 −0.208646 0.977991i \(-0.566906\pi\)
−0.208646 + 0.977991i \(0.566906\pi\)
\(504\) 45.3462 2.01988
\(505\) 1.31001 0.0582947
\(506\) −6.79479 −0.302065
\(507\) −27.4210 −1.21781
\(508\) −9.10240 −0.403854
\(509\) 16.5734 0.734603 0.367301 0.930102i \(-0.380282\pi\)
0.367301 + 0.930102i \(0.380282\pi\)
\(510\) −38.0581 −1.68524
\(511\) 3.38889 0.149916
\(512\) 50.1108 2.21461
\(513\) −6.29324 −0.277853
\(514\) 35.0919 1.54784
\(515\) −25.8994 −1.14126
\(516\) −95.7719 −4.21612
\(517\) −18.6821 −0.821636
\(518\) −34.3665 −1.50998
\(519\) 62.8113 2.75711
\(520\) 18.3738 0.805744
\(521\) 15.1454 0.663530 0.331765 0.943362i \(-0.392356\pi\)
0.331765 + 0.943362i \(0.392356\pi\)
\(522\) 36.6220 1.60290
\(523\) −7.95709 −0.347939 −0.173970 0.984751i \(-0.555659\pi\)
−0.173970 + 0.984751i \(0.555659\pi\)
\(524\) −19.9836 −0.872985
\(525\) 10.3912 0.453509
\(526\) 17.7618 0.774450
\(527\) −0.330254 −0.0143861
\(528\) 134.640 5.85947
\(529\) −22.8041 −0.991483
\(530\) −41.8975 −1.81991
\(531\) −22.3043 −0.967923
\(532\) 6.02810 0.261351
\(533\) −4.66227 −0.201945
\(534\) −10.4314 −0.451409
\(535\) −5.78259 −0.250003
\(536\) 56.6965 2.44892
\(537\) −10.2521 −0.442410
\(538\) 15.9892 0.689343
\(539\) −31.5397 −1.35851
\(540\) −43.1860 −1.85843
\(541\) 26.1488 1.12422 0.562112 0.827061i \(-0.309989\pi\)
0.562112 + 0.827061i \(0.309989\pi\)
\(542\) 36.3698 1.56222
\(543\) −70.9521 −3.04484
\(544\) 23.8826 1.02396
\(545\) −20.5911 −0.882025
\(546\) 17.8690 0.764724
\(547\) −16.0755 −0.687338 −0.343669 0.939091i \(-0.611670\pi\)
−0.343669 + 0.939091i \(0.611670\pi\)
\(548\) 29.6173 1.26519
\(549\) −3.95947 −0.168986
\(550\) 42.3892 1.80748
\(551\) 2.74531 0.116954
\(552\) −8.41085 −0.357990
\(553\) −0.996429 −0.0423725
\(554\) 72.0167 3.05970
\(555\) 43.6474 1.85273
\(556\) −31.6162 −1.34082
\(557\) −17.1493 −0.726641 −0.363320 0.931664i \(-0.618357\pi\)
−0.363320 + 0.931664i \(0.618357\pi\)
\(558\) −1.27273 −0.0538791
\(559\) −13.4938 −0.570728
\(560\) 15.4601 0.653309
\(561\) −59.2879 −2.50314
\(562\) −64.9774 −2.74091
\(563\) 18.1791 0.766158 0.383079 0.923716i \(-0.374864\pi\)
0.383079 + 0.923716i \(0.374864\pi\)
\(564\) −41.0090 −1.72679
\(565\) 9.82661 0.413409
\(566\) −6.05620 −0.254561
\(567\) −3.18735 −0.133856
\(568\) −43.6934 −1.83333
\(569\) −2.43407 −0.102041 −0.0510207 0.998698i \(-0.516247\pi\)
−0.0510207 + 0.998698i \(0.516247\pi\)
\(570\) −10.9948 −0.460520
\(571\) 11.4311 0.478375 0.239188 0.970973i \(-0.423119\pi\)
0.239188 + 0.970973i \(0.423119\pi\)
\(572\) 50.7585 2.12232
\(573\) −9.51925 −0.397672
\(574\) −8.50040 −0.354800
\(575\) −1.22206 −0.0509634
\(576\) 10.3178 0.429910
\(577\) −24.7817 −1.03167 −0.515837 0.856687i \(-0.672519\pi\)
−0.515837 + 0.856687i \(0.672519\pi\)
\(578\) 12.8785 0.535675
\(579\) −46.3060 −1.92441
\(580\) 18.8391 0.782251
\(581\) 15.4647 0.641586
\(582\) 106.577 4.41774
\(583\) −65.2690 −2.70317
\(584\) 17.1124 0.708116
\(585\) −14.3897 −0.594941
\(586\) −72.0308 −2.97556
\(587\) −40.7999 −1.68399 −0.841996 0.539485i \(-0.818619\pi\)
−0.841996 + 0.539485i \(0.818619\pi\)
\(588\) −69.2327 −2.85511
\(589\) −0.0954084 −0.00393124
\(590\) −16.4774 −0.678362
\(591\) 53.5049 2.20090
\(592\) −80.0866 −3.29154
\(593\) −6.91800 −0.284088 −0.142044 0.989860i \(-0.545368\pi\)
−0.142044 + 0.989860i \(0.545368\pi\)
\(594\) −96.6148 −3.96415
\(595\) −6.80775 −0.279091
\(596\) 90.8490 3.72132
\(597\) −43.6995 −1.78850
\(598\) −2.10149 −0.0859363
\(599\) −24.8997 −1.01737 −0.508687 0.860951i \(-0.669869\pi\)
−0.508687 + 0.860951i \(0.669869\pi\)
\(600\) 52.4710 2.14212
\(601\) −22.3530 −0.911796 −0.455898 0.890032i \(-0.650682\pi\)
−0.455898 + 0.890032i \(0.650682\pi\)
\(602\) −24.6023 −1.00272
\(603\) −44.4027 −1.80822
\(604\) 72.8572 2.96452
\(605\) −37.0859 −1.50776
\(606\) 6.43325 0.261333
\(607\) 14.7877 0.600213 0.300106 0.953906i \(-0.402978\pi\)
0.300106 + 0.953906i \(0.402978\pi\)
\(608\) 6.89954 0.279813
\(609\) 10.3317 0.418662
\(610\) −2.92507 −0.118433
\(611\) −5.77797 −0.233752
\(612\) −82.5179 −3.33559
\(613\) 26.6884 1.07793 0.538967 0.842327i \(-0.318815\pi\)
0.538967 + 0.842327i \(0.318815\pi\)
\(614\) 23.4243 0.945330
\(615\) 10.7960 0.435336
\(616\) 52.1867 2.10266
\(617\) −12.3279 −0.496301 −0.248151 0.968721i \(-0.579823\pi\)
−0.248151 + 0.968721i \(0.579823\pi\)
\(618\) −127.187 −5.11623
\(619\) 19.4973 0.783664 0.391832 0.920037i \(-0.371841\pi\)
0.391832 + 0.920037i \(0.371841\pi\)
\(620\) −0.654719 −0.0262942
\(621\) 2.78535 0.111772
\(622\) −38.8000 −1.55574
\(623\) −1.86594 −0.0747573
\(624\) 41.6415 1.66699
\(625\) −3.57059 −0.142824
\(626\) 18.0953 0.723233
\(627\) −17.1279 −0.684024
\(628\) 26.0932 1.04123
\(629\) 35.2656 1.40613
\(630\) −26.2357 −1.04526
\(631\) −21.9021 −0.871907 −0.435954 0.899969i \(-0.643589\pi\)
−0.435954 + 0.899969i \(0.643589\pi\)
\(632\) −5.03153 −0.200143
\(633\) 9.82198 0.390389
\(634\) 2.56636 0.101923
\(635\) 2.96974 0.117850
\(636\) −143.272 −5.68111
\(637\) −9.75456 −0.386490
\(638\) 42.1465 1.66860
\(639\) 34.2191 1.35369
\(640\) −13.0251 −0.514860
\(641\) 28.6660 1.13224 0.566120 0.824323i \(-0.308444\pi\)
0.566120 + 0.824323i \(0.308444\pi\)
\(642\) −28.3974 −1.12075
\(643\) 13.4375 0.529923 0.264961 0.964259i \(-0.414641\pi\)
0.264961 + 0.964259i \(0.414641\pi\)
\(644\) −2.66801 −0.105134
\(645\) 31.2464 1.23033
\(646\) −8.88339 −0.349512
\(647\) −24.3150 −0.955922 −0.477961 0.878381i \(-0.658624\pi\)
−0.477961 + 0.878381i \(0.658624\pi\)
\(648\) −16.0947 −0.632260
\(649\) −25.6689 −1.00759
\(650\) 13.1101 0.514221
\(651\) −0.359060 −0.0140727
\(652\) −55.5129 −2.17405
\(653\) 37.2541 1.45787 0.728933 0.684585i \(-0.240016\pi\)
0.728933 + 0.684585i \(0.240016\pi\)
\(654\) −101.119 −3.95408
\(655\) 6.51980 0.254750
\(656\) −19.8091 −0.773415
\(657\) −13.4018 −0.522855
\(658\) −10.5346 −0.410681
\(659\) −15.4699 −0.602620 −0.301310 0.953526i \(-0.597424\pi\)
−0.301310 + 0.953526i \(0.597424\pi\)
\(660\) −117.537 −4.57511
\(661\) −13.8542 −0.538867 −0.269433 0.963019i \(-0.586836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(662\) 54.7102 2.12637
\(663\) −18.3365 −0.712132
\(664\) 78.0901 3.03048
\(665\) −1.96672 −0.0762661
\(666\) 135.907 5.26628
\(667\) −1.21506 −0.0470473
\(668\) 16.5605 0.640746
\(669\) −1.98623 −0.0767920
\(670\) −32.8026 −1.26728
\(671\) −4.55676 −0.175912
\(672\) 25.9657 1.00165
\(673\) −14.0871 −0.543016 −0.271508 0.962436i \(-0.587522\pi\)
−0.271508 + 0.962436i \(0.587522\pi\)
\(674\) −27.5694 −1.06193
\(675\) −17.3764 −0.668818
\(676\) −43.9221 −1.68931
\(677\) 33.5710 1.29024 0.645119 0.764082i \(-0.276808\pi\)
0.645119 + 0.764082i \(0.276808\pi\)
\(678\) 48.2569 1.85329
\(679\) 19.0642 0.731617
\(680\) −34.3761 −1.31826
\(681\) 27.6524 1.05964
\(682\) −1.46473 −0.0560873
\(683\) −37.4025 −1.43117 −0.715584 0.698526i \(-0.753839\pi\)
−0.715584 + 0.698526i \(0.753839\pi\)
\(684\) −23.8389 −0.911504
\(685\) −9.66290 −0.369200
\(686\) −41.3974 −1.58056
\(687\) 3.05114 0.116408
\(688\) −57.3326 −2.18579
\(689\) −20.1864 −0.769039
\(690\) 4.86623 0.185254
\(691\) 17.4251 0.662884 0.331442 0.943476i \(-0.392465\pi\)
0.331442 + 0.943476i \(0.392465\pi\)
\(692\) 100.609 3.82459
\(693\) −40.8708 −1.55255
\(694\) 77.6516 2.94761
\(695\) 10.3150 0.391272
\(696\) 52.1705 1.97752
\(697\) 8.72279 0.330399
\(698\) −10.9040 −0.412722
\(699\) 67.3340 2.54680
\(700\) 16.6443 0.629097
\(701\) −4.78410 −0.180693 −0.0903465 0.995910i \(-0.528797\pi\)
−0.0903465 + 0.995910i \(0.528797\pi\)
\(702\) −29.8810 −1.12778
\(703\) 10.1880 0.384249
\(704\) 11.8743 0.447529
\(705\) 13.3795 0.503902
\(706\) 5.97688 0.224943
\(707\) 1.15077 0.0432790
\(708\) −56.3457 −2.11760
\(709\) 42.3685 1.59118 0.795592 0.605833i \(-0.207160\pi\)
0.795592 + 0.605833i \(0.207160\pi\)
\(710\) 25.2795 0.948721
\(711\) 3.94051 0.147781
\(712\) −9.42217 −0.353111
\(713\) 0.0422273 0.00158142
\(714\) −33.4317 −1.25115
\(715\) −16.5604 −0.619323
\(716\) −16.4215 −0.613700
\(717\) −31.5831 −1.17949
\(718\) 34.3015 1.28012
\(719\) 41.0988 1.53273 0.766364 0.642407i \(-0.222064\pi\)
0.766364 + 0.642407i \(0.222064\pi\)
\(720\) −61.1391 −2.27852
\(721\) −22.7510 −0.847293
\(722\) −2.56636 −0.0955100
\(723\) −43.0358 −1.60052
\(724\) −113.649 −4.22373
\(725\) 7.58014 0.281519
\(726\) −182.123 −6.75922
\(727\) −3.81832 −0.141614 −0.0708069 0.997490i \(-0.522557\pi\)
−0.0708069 + 0.997490i \(0.522557\pi\)
\(728\) 16.1403 0.598198
\(729\) −41.4517 −1.53525
\(730\) −9.90064 −0.366439
\(731\) 25.2460 0.933757
\(732\) −10.0025 −0.369705
\(733\) 6.99734 0.258452 0.129226 0.991615i \(-0.458751\pi\)
0.129226 + 0.991615i \(0.458751\pi\)
\(734\) 64.9236 2.39637
\(735\) 22.5877 0.833161
\(736\) −3.05370 −0.112561
\(737\) −51.1009 −1.88232
\(738\) 33.6159 1.23742
\(739\) 29.1231 1.07131 0.535656 0.844436i \(-0.320064\pi\)
0.535656 + 0.844436i \(0.320064\pi\)
\(740\) 69.9131 2.57006
\(741\) −5.29732 −0.194602
\(742\) −36.8044 −1.35113
\(743\) −0.0682136 −0.00250252 −0.00125126 0.999999i \(-0.500398\pi\)
−0.00125126 + 0.999999i \(0.500398\pi\)
\(744\) −1.81309 −0.0664712
\(745\) −29.6403 −1.08594
\(746\) 30.1436 1.10364
\(747\) −61.1574 −2.23763
\(748\) −94.9657 −3.47229
\(749\) −5.07966 −0.185607
\(750\) −85.3317 −3.11587
\(751\) −18.4564 −0.673485 −0.336743 0.941597i \(-0.609325\pi\)
−0.336743 + 0.941597i \(0.609325\pi\)
\(752\) −24.5495 −0.895228
\(753\) 81.9102 2.98497
\(754\) 13.0350 0.474708
\(755\) −23.7703 −0.865089
\(756\) −37.9363 −1.37973
\(757\) 39.0394 1.41891 0.709456 0.704750i \(-0.248941\pi\)
0.709456 + 0.704750i \(0.248941\pi\)
\(758\) −94.7417 −3.44117
\(759\) 7.58074 0.275163
\(760\) −9.93106 −0.360237
\(761\) 13.8369 0.501586 0.250793 0.968041i \(-0.419309\pi\)
0.250793 + 0.968041i \(0.419309\pi\)
\(762\) 14.5839 0.528319
\(763\) −18.0880 −0.654830
\(764\) −15.2476 −0.551641
\(765\) 26.9221 0.973372
\(766\) 22.1402 0.799957
\(767\) −7.93885 −0.286655
\(768\) −75.3307 −2.71826
\(769\) 33.7081 1.21555 0.607773 0.794111i \(-0.292063\pi\)
0.607773 + 0.794111i \(0.292063\pi\)
\(770\) −30.1934 −1.08810
\(771\) −39.1510 −1.40999
\(772\) −74.1716 −2.66949
\(773\) −9.19751 −0.330812 −0.165406 0.986226i \(-0.552893\pi\)
−0.165406 + 0.986226i \(0.552893\pi\)
\(774\) 97.2932 3.49713
\(775\) −0.263434 −0.00946284
\(776\) 96.2658 3.45574
\(777\) 38.3416 1.37550
\(778\) 30.3748 1.08899
\(779\) 2.51996 0.0902871
\(780\) −36.3517 −1.30160
\(781\) 39.3811 1.40917
\(782\) 3.93174 0.140599
\(783\) −17.2769 −0.617425
\(784\) −41.4453 −1.48019
\(785\) −8.51314 −0.303847
\(786\) 32.0177 1.14203
\(787\) 36.2607 1.29255 0.646277 0.763103i \(-0.276325\pi\)
0.646277 + 0.763103i \(0.276325\pi\)
\(788\) 85.7025 3.05303
\(789\) −19.8163 −0.705478
\(790\) 2.91107 0.103571
\(791\) 8.63209 0.306922
\(792\) −206.379 −7.33337
\(793\) −1.40931 −0.0500461
\(794\) −32.7916 −1.16373
\(795\) 46.7437 1.65783
\(796\) −69.9966 −2.48096
\(797\) 17.5761 0.622576 0.311288 0.950316i \(-0.399240\pi\)
0.311288 + 0.950316i \(0.399240\pi\)
\(798\) −9.65824 −0.341898
\(799\) 10.8102 0.382437
\(800\) 19.0505 0.673536
\(801\) 7.37911 0.260728
\(802\) 71.5653 2.52706
\(803\) −15.4235 −0.544283
\(804\) −112.171 −3.95598
\(805\) 0.870460 0.0306797
\(806\) −0.453010 −0.0159566
\(807\) −17.8387 −0.627950
\(808\) 5.81086 0.204425
\(809\) −9.09040 −0.319601 −0.159801 0.987149i \(-0.551085\pi\)
−0.159801 + 0.987149i \(0.551085\pi\)
\(810\) 9.31184 0.327185
\(811\) −28.6532 −1.00615 −0.503074 0.864243i \(-0.667798\pi\)
−0.503074 + 0.864243i \(0.667798\pi\)
\(812\) 16.5490 0.580757
\(813\) −40.5766 −1.42308
\(814\) 156.408 5.48211
\(815\) 18.1116 0.634420
\(816\) −77.9084 −2.72734
\(817\) 7.29343 0.255165
\(818\) −71.1299 −2.48700
\(819\) −12.6405 −0.441694
\(820\) 17.2927 0.603887
\(821\) −16.3321 −0.569993 −0.284997 0.958529i \(-0.591992\pi\)
−0.284997 + 0.958529i \(0.591992\pi\)
\(822\) −47.4529 −1.65511
\(823\) 29.1737 1.01693 0.508465 0.861082i \(-0.330213\pi\)
0.508465 + 0.861082i \(0.330213\pi\)
\(824\) −114.883 −4.00212
\(825\) −47.2924 −1.64651
\(826\) −14.4744 −0.503628
\(827\) 26.8841 0.934850 0.467425 0.884033i \(-0.345182\pi\)
0.467425 + 0.884033i \(0.345182\pi\)
\(828\) 10.5510 0.366672
\(829\) −42.5353 −1.47731 −0.738656 0.674083i \(-0.764539\pi\)
−0.738656 + 0.674083i \(0.764539\pi\)
\(830\) −45.1802 −1.56823
\(831\) −80.3468 −2.78720
\(832\) 3.67247 0.127320
\(833\) 18.2501 0.632329
\(834\) 50.6555 1.75406
\(835\) −5.40301 −0.186979
\(836\) −27.4350 −0.948861
\(837\) 0.600428 0.0207538
\(838\) −70.1171 −2.42215
\(839\) 0.618499 0.0213530 0.0106765 0.999943i \(-0.496602\pi\)
0.0106765 + 0.999943i \(0.496602\pi\)
\(840\) −37.3745 −1.28954
\(841\) −21.4633 −0.740113
\(842\) −23.3825 −0.805813
\(843\) 72.4933 2.49680
\(844\) 15.7326 0.541537
\(845\) 14.3300 0.492966
\(846\) 41.6604 1.43231
\(847\) −32.5778 −1.11939
\(848\) −85.7680 −2.94528
\(849\) 6.75671 0.231890
\(850\) −24.5281 −0.841308
\(851\) −4.50917 −0.154572
\(852\) 86.4453 2.96157
\(853\) −8.51838 −0.291664 −0.145832 0.989309i \(-0.546586\pi\)
−0.145832 + 0.989309i \(0.546586\pi\)
\(854\) −2.56950 −0.0879265
\(855\) 7.77765 0.265990
\(856\) −25.6500 −0.876699
\(857\) 39.6183 1.35334 0.676668 0.736288i \(-0.263423\pi\)
0.676668 + 0.736288i \(0.263423\pi\)
\(858\) −81.3254 −2.77640
\(859\) −31.0116 −1.05810 −0.529052 0.848590i \(-0.677452\pi\)
−0.529052 + 0.848590i \(0.677452\pi\)
\(860\) 50.0496 1.70668
\(861\) 9.48363 0.323201
\(862\) 62.4137 2.12582
\(863\) 39.6641 1.35018 0.675091 0.737735i \(-0.264104\pi\)
0.675091 + 0.737735i \(0.264104\pi\)
\(864\) −43.4204 −1.47719
\(865\) −32.8246 −1.11607
\(866\) 22.7440 0.772873
\(867\) −14.3681 −0.487968
\(868\) −0.575132 −0.0195212
\(869\) 4.53494 0.153837
\(870\) −30.1840 −1.02333
\(871\) −15.8044 −0.535513
\(872\) −91.3365 −3.09304
\(873\) −75.3919 −2.55163
\(874\) 1.13586 0.0384210
\(875\) −15.2640 −0.516016
\(876\) −33.8561 −1.14389
\(877\) 2.90897 0.0982288 0.0491144 0.998793i \(-0.484360\pi\)
0.0491144 + 0.998793i \(0.484360\pi\)
\(878\) 2.03157 0.0685620
\(879\) 80.3625 2.71056
\(880\) −70.3619 −2.37190
\(881\) −22.7326 −0.765882 −0.382941 0.923773i \(-0.625089\pi\)
−0.382941 + 0.923773i \(0.625089\pi\)
\(882\) 70.3324 2.36822
\(883\) 0.716750 0.0241205 0.0120603 0.999927i \(-0.496161\pi\)
0.0120603 + 0.999927i \(0.496161\pi\)
\(884\) −29.3709 −0.987851
\(885\) 18.3833 0.617947
\(886\) −29.0734 −0.976742
\(887\) 26.8965 0.903095 0.451548 0.892247i \(-0.350872\pi\)
0.451548 + 0.892247i \(0.350872\pi\)
\(888\) 193.608 6.49706
\(889\) 2.60874 0.0874942
\(890\) 5.45134 0.182729
\(891\) 14.5063 0.485978
\(892\) −3.18148 −0.106524
\(893\) 3.12300 0.104507
\(894\) −145.559 −4.86820
\(895\) 5.35765 0.179086
\(896\) −11.4417 −0.382241
\(897\) 2.34457 0.0782828
\(898\) −23.5858 −0.787070
\(899\) −0.261926 −0.00873571
\(900\) −65.8222 −2.19407
\(901\) 37.7673 1.25821
\(902\) 38.6869 1.28813
\(903\) 27.4481 0.913415
\(904\) 43.5882 1.44972
\(905\) 37.0789 1.23255
\(906\) −116.732 −3.87816
\(907\) −10.5602 −0.350645 −0.175323 0.984511i \(-0.556097\pi\)
−0.175323 + 0.984511i \(0.556097\pi\)
\(908\) 44.2928 1.46991
\(909\) −4.55086 −0.150942
\(910\) −9.33820 −0.309558
\(911\) −30.8567 −1.02233 −0.511164 0.859483i \(-0.670785\pi\)
−0.511164 + 0.859483i \(0.670785\pi\)
\(912\) −22.5073 −0.745291
\(913\) −70.3830 −2.32934
\(914\) 68.5628 2.26786
\(915\) 3.26341 0.107885
\(916\) 4.88723 0.161479
\(917\) 5.72726 0.189131
\(918\) 55.9053 1.84515
\(919\) −34.7982 −1.14789 −0.573944 0.818895i \(-0.694587\pi\)
−0.573944 + 0.818895i \(0.694587\pi\)
\(920\) 4.39544 0.144913
\(921\) −26.1338 −0.861139
\(922\) −16.3661 −0.538990
\(923\) 12.1797 0.400901
\(924\) −103.249 −3.39664
\(925\) 28.1304 0.924921
\(926\) −51.5719 −1.69476
\(927\) 89.9720 2.95507
\(928\) 18.9414 0.621781
\(929\) 25.3258 0.830911 0.415456 0.909613i \(-0.363622\pi\)
0.415456 + 0.909613i \(0.363622\pi\)
\(930\) 1.04899 0.0343978
\(931\) 5.27235 0.172794
\(932\) 107.854 3.53286
\(933\) 43.2879 1.41718
\(934\) 80.6791 2.63990
\(935\) 30.9834 1.01326
\(936\) −63.8288 −2.08631
\(937\) −1.07542 −0.0351324 −0.0175662 0.999846i \(-0.505592\pi\)
−0.0175662 + 0.999846i \(0.505592\pi\)
\(938\) −28.8151 −0.940848
\(939\) −20.1884 −0.658822
\(940\) 21.4309 0.699000
\(941\) −46.5173 −1.51642 −0.758210 0.652011i \(-0.773926\pi\)
−0.758210 + 0.652011i \(0.773926\pi\)
\(942\) −41.8066 −1.36213
\(943\) −1.11532 −0.0363199
\(944\) −33.7307 −1.09784
\(945\) 12.3770 0.402625
\(946\) 111.970 3.64046
\(947\) −40.5378 −1.31730 −0.658651 0.752448i \(-0.728873\pi\)
−0.658651 + 0.752448i \(0.728873\pi\)
\(948\) 9.95464 0.323312
\(949\) −4.77017 −0.154846
\(950\) −7.08603 −0.229901
\(951\) −2.86321 −0.0928459
\(952\) −30.1973 −0.978702
\(953\) −1.92904 −0.0624879 −0.0312439 0.999512i \(-0.509947\pi\)
−0.0312439 + 0.999512i \(0.509947\pi\)
\(954\) 145.548 4.71229
\(955\) 4.97467 0.160977
\(956\) −50.5890 −1.63616
\(957\) −47.0215 −1.51999
\(958\) −24.2485 −0.783433
\(959\) −8.48828 −0.274101
\(960\) −8.50401 −0.274466
\(961\) −30.9909 −0.999706
\(962\) 48.3738 1.55964
\(963\) 20.0882 0.647333
\(964\) −68.9336 −2.22020
\(965\) 24.1991 0.778997
\(966\) 4.27469 0.137536
\(967\) 28.4008 0.913308 0.456654 0.889644i \(-0.349048\pi\)
0.456654 + 0.889644i \(0.349048\pi\)
\(968\) −164.503 −5.28733
\(969\) 9.91092 0.318385
\(970\) −55.6960 −1.78829
\(971\) −35.4842 −1.13874 −0.569371 0.822081i \(-0.692813\pi\)
−0.569371 + 0.822081i \(0.692813\pi\)
\(972\) −54.7435 −1.75590
\(973\) 9.06115 0.290487
\(974\) −66.9022 −2.14368
\(975\) −14.6265 −0.468424
\(976\) −5.98789 −0.191668
\(977\) 32.7689 1.04837 0.524185 0.851604i \(-0.324370\pi\)
0.524185 + 0.851604i \(0.324370\pi\)
\(978\) 88.9429 2.84408
\(979\) 8.49225 0.271414
\(980\) 36.1804 1.15574
\(981\) 71.5315 2.28382
\(982\) 73.9552 2.36001
\(983\) 57.7029 1.84044 0.920218 0.391405i \(-0.128011\pi\)
0.920218 + 0.391405i \(0.128011\pi\)
\(984\) 47.8881 1.52662
\(985\) −27.9612 −0.890917
\(986\) −24.3877 −0.776661
\(987\) 11.7531 0.374106
\(988\) −8.48509 −0.269947
\(989\) −3.22803 −0.102645
\(990\) 119.404 3.79490
\(991\) 25.8703 0.821796 0.410898 0.911681i \(-0.365215\pi\)
0.410898 + 0.911681i \(0.365215\pi\)
\(992\) −0.658274 −0.0209002
\(993\) −61.0384 −1.93700
\(994\) 22.2065 0.704347
\(995\) 22.8370 0.723981
\(996\) −154.498 −4.89545
\(997\) −62.9735 −1.99439 −0.997195 0.0748476i \(-0.976153\pi\)
−0.997195 + 0.0748476i \(0.976153\pi\)
\(998\) −75.3184 −2.38416
\(999\) −64.1156 −2.02853
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 \(a_p\))