Properties

Label 6019.2.a.c.1.7
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60952 q^{2}\) \(+3.26666 q^{3}\) \(+4.80961 q^{4}\) \(-2.76749 q^{5}\) \(-8.52442 q^{6}\) \(-0.615812 q^{7}\) \(-7.33173 q^{8}\) \(+7.67107 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60952 q^{2}\) \(+3.26666 q^{3}\) \(+4.80961 q^{4}\) \(-2.76749 q^{5}\) \(-8.52442 q^{6}\) \(-0.615812 q^{7}\) \(-7.33173 q^{8}\) \(+7.67107 q^{9}\) \(+7.22184 q^{10}\) \(-2.51197 q^{11}\) \(+15.7114 q^{12}\) \(-1.00000 q^{13}\) \(+1.60698 q^{14}\) \(-9.04046 q^{15}\) \(+9.51309 q^{16}\) \(+2.40142 q^{17}\) \(-20.0178 q^{18}\) \(-0.0503723 q^{19}\) \(-13.3106 q^{20}\) \(-2.01165 q^{21}\) \(+6.55503 q^{22}\) \(-3.59072 q^{23}\) \(-23.9503 q^{24}\) \(+2.65902 q^{25}\) \(+2.60952 q^{26}\) \(+15.2588 q^{27}\) \(-2.96181 q^{28}\) \(-5.79202 q^{29}\) \(+23.5913 q^{30}\) \(+3.35869 q^{31}\) \(-10.1612 q^{32}\) \(-8.20575 q^{33}\) \(-6.26655 q^{34}\) \(+1.70426 q^{35}\) \(+36.8948 q^{36}\) \(-3.26030 q^{37}\) \(+0.131448 q^{38}\) \(-3.26666 q^{39}\) \(+20.2905 q^{40}\) \(+7.71689 q^{41}\) \(+5.24945 q^{42}\) \(+10.4913 q^{43}\) \(-12.0816 q^{44}\) \(-21.2296 q^{45}\) \(+9.37005 q^{46}\) \(+6.11194 q^{47}\) \(+31.0761 q^{48}\) \(-6.62078 q^{49}\) \(-6.93877 q^{50}\) \(+7.84462 q^{51}\) \(-4.80961 q^{52}\) \(-6.99504 q^{53}\) \(-39.8182 q^{54}\) \(+6.95185 q^{55}\) \(+4.51497 q^{56}\) \(-0.164549 q^{57}\) \(+15.1144 q^{58}\) \(-4.10455 q^{59}\) \(-43.4811 q^{60}\) \(-6.39430 q^{61}\) \(-8.76458 q^{62}\) \(-4.72394 q^{63}\) \(+7.48962 q^{64}\) \(+2.76749 q^{65}\) \(+21.4131 q^{66}\) \(+1.21688 q^{67}\) \(+11.5499 q^{68}\) \(-11.7297 q^{69}\) \(-4.44730 q^{70}\) \(-12.1196 q^{71}\) \(-56.2422 q^{72}\) \(+8.15155 q^{73}\) \(+8.50782 q^{74}\) \(+8.68612 q^{75}\) \(-0.242271 q^{76}\) \(+1.54690 q^{77}\) \(+8.52442 q^{78}\) \(+2.11639 q^{79}\) \(-26.3274 q^{80}\) \(+26.8322 q^{81}\) \(-20.1374 q^{82}\) \(-16.3133 q^{83}\) \(-9.67524 q^{84}\) \(-6.64591 q^{85}\) \(-27.3772 q^{86}\) \(-18.9206 q^{87}\) \(+18.4171 q^{88}\) \(+6.90629 q^{89}\) \(+55.3992 q^{90}\) \(+0.615812 q^{91}\) \(-17.2699 q^{92}\) \(+10.9717 q^{93}\) \(-15.9493 q^{94}\) \(+0.139405 q^{95}\) \(-33.1931 q^{96}\) \(-17.3241 q^{97}\) \(+17.2771 q^{98}\) \(-19.2695 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60952 −1.84521 −0.922605 0.385745i \(-0.873944\pi\)
−0.922605 + 0.385745i \(0.873944\pi\)
\(3\) 3.26666 1.88601 0.943004 0.332782i \(-0.107987\pi\)
0.943004 + 0.332782i \(0.107987\pi\)
\(4\) 4.80961 2.40480
\(5\) −2.76749 −1.23766 −0.618830 0.785525i \(-0.712393\pi\)
−0.618830 + 0.785525i \(0.712393\pi\)
\(6\) −8.52442 −3.48008
\(7\) −0.615812 −0.232755 −0.116378 0.993205i \(-0.537128\pi\)
−0.116378 + 0.993205i \(0.537128\pi\)
\(8\) −7.33173 −2.59216
\(9\) 7.67107 2.55702
\(10\) 7.22184 2.28374
\(11\) −2.51197 −0.757387 −0.378693 0.925522i \(-0.623626\pi\)
−0.378693 + 0.925522i \(0.623626\pi\)
\(12\) 15.7114 4.53548
\(13\) −1.00000 −0.277350
\(14\) 1.60698 0.429482
\(15\) −9.04046 −2.33424
\(16\) 9.51309 2.37827
\(17\) 2.40142 0.582430 0.291215 0.956658i \(-0.405941\pi\)
0.291215 + 0.956658i \(0.405941\pi\)
\(18\) −20.0178 −4.71825
\(19\) −0.0503723 −0.0115562 −0.00577810 0.999983i \(-0.501839\pi\)
−0.00577810 + 0.999983i \(0.501839\pi\)
\(20\) −13.3106 −2.97633
\(21\) −2.01165 −0.438978
\(22\) 6.55503 1.39754
\(23\) −3.59072 −0.748716 −0.374358 0.927284i \(-0.622137\pi\)
−0.374358 + 0.927284i \(0.622137\pi\)
\(24\) −23.9503 −4.88883
\(25\) 2.65902 0.531804
\(26\) 2.60952 0.511769
\(27\) 15.2588 2.93656
\(28\) −2.96181 −0.559730
\(29\) −5.79202 −1.07555 −0.537776 0.843088i \(-0.680735\pi\)
−0.537776 + 0.843088i \(0.680735\pi\)
\(30\) 23.5913 4.30716
\(31\) 3.35869 0.603239 0.301620 0.953428i \(-0.402473\pi\)
0.301620 + 0.953428i \(0.402473\pi\)
\(32\) −10.1612 −1.79626
\(33\) −8.20575 −1.42844
\(34\) −6.26655 −1.07471
\(35\) 1.70426 0.288072
\(36\) 36.8948 6.14914
\(37\) −3.26030 −0.535990 −0.267995 0.963420i \(-0.586361\pi\)
−0.267995 + 0.963420i \(0.586361\pi\)
\(38\) 0.131448 0.0213236
\(39\) −3.26666 −0.523084
\(40\) 20.2905 3.20821
\(41\) 7.71689 1.20518 0.602588 0.798052i \(-0.294136\pi\)
0.602588 + 0.798052i \(0.294136\pi\)
\(42\) 5.24945 0.810007
\(43\) 10.4913 1.59990 0.799951 0.600065i \(-0.204859\pi\)
0.799951 + 0.600065i \(0.204859\pi\)
\(44\) −12.0816 −1.82137
\(45\) −21.2296 −3.16473
\(46\) 9.37005 1.38154
\(47\) 6.11194 0.891519 0.445759 0.895153i \(-0.352934\pi\)
0.445759 + 0.895153i \(0.352934\pi\)
\(48\) 31.0761 4.48544
\(49\) −6.62078 −0.945825
\(50\) −6.93877 −0.981290
\(51\) 7.84462 1.09847
\(52\) −4.80961 −0.666972
\(53\) −6.99504 −0.960843 −0.480421 0.877038i \(-0.659516\pi\)
−0.480421 + 0.877038i \(0.659516\pi\)
\(54\) −39.8182 −5.41857
\(55\) 6.95185 0.937388
\(56\) 4.51497 0.603338
\(57\) −0.164549 −0.0217951
\(58\) 15.1144 1.98462
\(59\) −4.10455 −0.534367 −0.267183 0.963646i \(-0.586093\pi\)
−0.267183 + 0.963646i \(0.586093\pi\)
\(60\) −43.4811 −5.61338
\(61\) −6.39430 −0.818706 −0.409353 0.912376i \(-0.634246\pi\)
−0.409353 + 0.912376i \(0.634246\pi\)
\(62\) −8.76458 −1.11310
\(63\) −4.72394 −0.595161
\(64\) 7.48962 0.936202
\(65\) 2.76749 0.343265
\(66\) 21.4131 2.63577
\(67\) 1.21688 0.148665 0.0743327 0.997233i \(-0.476317\pi\)
0.0743327 + 0.997233i \(0.476317\pi\)
\(68\) 11.5499 1.40063
\(69\) −11.7297 −1.41208
\(70\) −4.44730 −0.531553
\(71\) −12.1196 −1.43833 −0.719164 0.694840i \(-0.755475\pi\)
−0.719164 + 0.694840i \(0.755475\pi\)
\(72\) −56.2422 −6.62821
\(73\) 8.15155 0.954067 0.477034 0.878885i \(-0.341712\pi\)
0.477034 + 0.878885i \(0.341712\pi\)
\(74\) 8.50782 0.989014
\(75\) 8.68612 1.00299
\(76\) −0.242271 −0.0277904
\(77\) 1.54690 0.176286
\(78\) 8.52442 0.965201
\(79\) 2.11639 0.238112 0.119056 0.992888i \(-0.462013\pi\)
0.119056 + 0.992888i \(0.462013\pi\)
\(80\) −26.3274 −2.94350
\(81\) 26.8322 2.98135
\(82\) −20.1374 −2.22380
\(83\) −16.3133 −1.79062 −0.895311 0.445442i \(-0.853047\pi\)
−0.895311 + 0.445442i \(0.853047\pi\)
\(84\) −9.67524 −1.05566
\(85\) −6.64591 −0.720850
\(86\) −27.3772 −2.95216
\(87\) −18.9206 −2.02850
\(88\) 18.4171 1.96327
\(89\) 6.90629 0.732065 0.366032 0.930602i \(-0.380716\pi\)
0.366032 + 0.930602i \(0.380716\pi\)
\(90\) 55.3992 5.83959
\(91\) 0.615812 0.0645547
\(92\) −17.2699 −1.80051
\(93\) 10.9717 1.13771
\(94\) −15.9493 −1.64504
\(95\) 0.139405 0.0143027
\(96\) −33.1931 −3.38776
\(97\) −17.3241 −1.75900 −0.879499 0.475901i \(-0.842122\pi\)
−0.879499 + 0.475901i \(0.842122\pi\)
\(98\) 17.2771 1.74525
\(99\) −19.2695 −1.93666
\(100\) 12.7888 1.27888
\(101\) 5.91189 0.588255 0.294127 0.955766i \(-0.404971\pi\)
0.294127 + 0.955766i \(0.404971\pi\)
\(102\) −20.4707 −2.02690
\(103\) 1.17555 0.115830 0.0579152 0.998322i \(-0.481555\pi\)
0.0579152 + 0.998322i \(0.481555\pi\)
\(104\) 7.33173 0.718935
\(105\) 5.56723 0.543306
\(106\) 18.2537 1.77296
\(107\) −17.3840 −1.68058 −0.840290 0.542138i \(-0.817615\pi\)
−0.840290 + 0.542138i \(0.817615\pi\)
\(108\) 73.3889 7.06185
\(109\) 19.1539 1.83461 0.917306 0.398182i \(-0.130359\pi\)
0.917306 + 0.398182i \(0.130359\pi\)
\(110\) −18.1410 −1.72968
\(111\) −10.6503 −1.01088
\(112\) −5.85828 −0.553556
\(113\) −4.95444 −0.466075 −0.233037 0.972468i \(-0.574866\pi\)
−0.233037 + 0.972468i \(0.574866\pi\)
\(114\) 0.429395 0.0402165
\(115\) 9.93728 0.926656
\(116\) −27.8574 −2.58649
\(117\) −7.67107 −0.709191
\(118\) 10.7109 0.986020
\(119\) −1.47882 −0.135564
\(120\) 66.2822 6.05071
\(121\) −4.69002 −0.426366
\(122\) 16.6861 1.51069
\(123\) 25.2085 2.27297
\(124\) 16.1540 1.45067
\(125\) 6.47865 0.579468
\(126\) 12.3272 1.09820
\(127\) −2.22713 −0.197626 −0.0988130 0.995106i \(-0.531505\pi\)
−0.0988130 + 0.995106i \(0.531505\pi\)
\(128\) 0.778024 0.0687683
\(129\) 34.2714 3.01743
\(130\) −7.22184 −0.633397
\(131\) −13.8689 −1.21174 −0.605868 0.795566i \(-0.707174\pi\)
−0.605868 + 0.795566i \(0.707174\pi\)
\(132\) −39.4664 −3.43511
\(133\) 0.0310199 0.00268977
\(134\) −3.17547 −0.274319
\(135\) −42.2287 −3.63447
\(136\) −17.6065 −1.50975
\(137\) 4.90087 0.418710 0.209355 0.977840i \(-0.432864\pi\)
0.209355 + 0.977840i \(0.432864\pi\)
\(138\) 30.6088 2.60559
\(139\) 10.2827 0.872171 0.436086 0.899905i \(-0.356364\pi\)
0.436086 + 0.899905i \(0.356364\pi\)
\(140\) 8.19680 0.692756
\(141\) 19.9656 1.68141
\(142\) 31.6263 2.65402
\(143\) 2.51197 0.210061
\(144\) 72.9756 6.08130
\(145\) 16.0294 1.33117
\(146\) −21.2717 −1.76046
\(147\) −21.6278 −1.78383
\(148\) −15.6807 −1.28895
\(149\) −16.3214 −1.33710 −0.668552 0.743665i \(-0.733086\pi\)
−0.668552 + 0.743665i \(0.733086\pi\)
\(150\) −22.6666 −1.85072
\(151\) 3.97750 0.323684 0.161842 0.986817i \(-0.448256\pi\)
0.161842 + 0.986817i \(0.448256\pi\)
\(152\) 0.369316 0.0299555
\(153\) 18.4215 1.48929
\(154\) −4.03667 −0.325284
\(155\) −9.29516 −0.746605
\(156\) −15.7114 −1.25791
\(157\) −7.56584 −0.603820 −0.301910 0.953336i \(-0.597624\pi\)
−0.301910 + 0.953336i \(0.597624\pi\)
\(158\) −5.52276 −0.439367
\(159\) −22.8504 −1.81216
\(160\) 28.1210 2.22316
\(161\) 2.21121 0.174268
\(162\) −70.0191 −5.50122
\(163\) 1.68690 0.132128 0.0660642 0.997815i \(-0.478956\pi\)
0.0660642 + 0.997815i \(0.478956\pi\)
\(164\) 37.1152 2.89821
\(165\) 22.7093 1.76792
\(166\) 42.5700 3.30407
\(167\) −11.4356 −0.884915 −0.442457 0.896790i \(-0.645893\pi\)
−0.442457 + 0.896790i \(0.645893\pi\)
\(168\) 14.7489 1.13790
\(169\) 1.00000 0.0769231
\(170\) 17.3426 1.33012
\(171\) −0.386410 −0.0295495
\(172\) 50.4588 3.84745
\(173\) −3.56830 −0.271292 −0.135646 0.990757i \(-0.543311\pi\)
−0.135646 + 0.990757i \(0.543311\pi\)
\(174\) 49.3737 3.74301
\(175\) −1.63746 −0.123780
\(176\) −23.8966 −1.80127
\(177\) −13.4082 −1.00782
\(178\) −18.0221 −1.35081
\(179\) 8.50720 0.635858 0.317929 0.948114i \(-0.397013\pi\)
0.317929 + 0.948114i \(0.397013\pi\)
\(180\) −102.106 −7.61055
\(181\) −20.7162 −1.53982 −0.769912 0.638150i \(-0.779700\pi\)
−0.769912 + 0.638150i \(0.779700\pi\)
\(182\) −1.60698 −0.119117
\(183\) −20.8880 −1.54409
\(184\) 26.3261 1.94079
\(185\) 9.02285 0.663373
\(186\) −28.6309 −2.09932
\(187\) −6.03228 −0.441124
\(188\) 29.3960 2.14393
\(189\) −9.39657 −0.683500
\(190\) −0.363781 −0.0263914
\(191\) 3.85826 0.279174 0.139587 0.990210i \(-0.455423\pi\)
0.139587 + 0.990210i \(0.455423\pi\)
\(192\) 24.4660 1.76568
\(193\) 16.5723 1.19290 0.596451 0.802649i \(-0.296577\pi\)
0.596451 + 0.802649i \(0.296577\pi\)
\(194\) 45.2077 3.24572
\(195\) 9.04046 0.647401
\(196\) −31.8433 −2.27452
\(197\) −9.90716 −0.705856 −0.352928 0.935651i \(-0.614814\pi\)
−0.352928 + 0.935651i \(0.614814\pi\)
\(198\) 50.2842 3.57354
\(199\) −2.28664 −0.162095 −0.0810477 0.996710i \(-0.525827\pi\)
−0.0810477 + 0.996710i \(0.525827\pi\)
\(200\) −19.4952 −1.37852
\(201\) 3.97513 0.280384
\(202\) −15.4272 −1.08545
\(203\) 3.56680 0.250340
\(204\) 37.7295 2.64160
\(205\) −21.3564 −1.49160
\(206\) −3.06762 −0.213731
\(207\) −27.5446 −1.91449
\(208\) −9.51309 −0.659614
\(209\) 0.126534 0.00875251
\(210\) −14.5278 −1.00251
\(211\) −9.32687 −0.642088 −0.321044 0.947064i \(-0.604034\pi\)
−0.321044 + 0.947064i \(0.604034\pi\)
\(212\) −33.6434 −2.31064
\(213\) −39.5905 −2.71270
\(214\) 45.3640 3.10102
\(215\) −29.0345 −1.98014
\(216\) −111.873 −7.61203
\(217\) −2.06832 −0.140407
\(218\) −49.9826 −3.38525
\(219\) 26.6284 1.79938
\(220\) 33.4357 2.25423
\(221\) −2.40142 −0.161537
\(222\) 27.7922 1.86529
\(223\) −24.0372 −1.60965 −0.804825 0.593512i \(-0.797741\pi\)
−0.804825 + 0.593512i \(0.797741\pi\)
\(224\) 6.25738 0.418089
\(225\) 20.3975 1.35984
\(226\) 12.9287 0.860006
\(227\) −1.22477 −0.0812907 −0.0406453 0.999174i \(-0.512941\pi\)
−0.0406453 + 0.999174i \(0.512941\pi\)
\(228\) −0.791417 −0.0524129
\(229\) −15.8136 −1.04499 −0.522495 0.852643i \(-0.674999\pi\)
−0.522495 + 0.852643i \(0.674999\pi\)
\(230\) −25.9316 −1.70988
\(231\) 5.05320 0.332476
\(232\) 42.4655 2.78800
\(233\) −22.1219 −1.44925 −0.724626 0.689143i \(-0.757987\pi\)
−0.724626 + 0.689143i \(0.757987\pi\)
\(234\) 20.0178 1.30861
\(235\) −16.9148 −1.10340
\(236\) −19.7413 −1.28505
\(237\) 6.91352 0.449082
\(238\) 3.85902 0.250143
\(239\) −16.2539 −1.05138 −0.525690 0.850676i \(-0.676193\pi\)
−0.525690 + 0.850676i \(0.676193\pi\)
\(240\) −86.0028 −5.55145
\(241\) −17.1531 −1.10493 −0.552464 0.833537i \(-0.686312\pi\)
−0.552464 + 0.833537i \(0.686312\pi\)
\(242\) 12.2387 0.786734
\(243\) 41.8751 2.68629
\(244\) −30.7541 −1.96883
\(245\) 18.3230 1.17061
\(246\) −65.7821 −4.19411
\(247\) 0.0503723 0.00320511
\(248\) −24.6250 −1.56369
\(249\) −53.2902 −3.37713
\(250\) −16.9062 −1.06924
\(251\) −13.8074 −0.871517 −0.435758 0.900064i \(-0.643520\pi\)
−0.435758 + 0.900064i \(0.643520\pi\)
\(252\) −22.7203 −1.43124
\(253\) 9.01976 0.567067
\(254\) 5.81175 0.364662
\(255\) −21.7099 −1.35953
\(256\) −17.0095 −1.06309
\(257\) 8.44661 0.526885 0.263442 0.964675i \(-0.415142\pi\)
0.263442 + 0.964675i \(0.415142\pi\)
\(258\) −89.4320 −5.56779
\(259\) 2.00773 0.124754
\(260\) 13.3106 0.825485
\(261\) −44.4311 −2.75021
\(262\) 36.1913 2.23591
\(263\) −6.02822 −0.371716 −0.185858 0.982577i \(-0.559506\pi\)
−0.185858 + 0.982577i \(0.559506\pi\)
\(264\) 60.1623 3.70273
\(265\) 19.3587 1.18920
\(266\) −0.0809471 −0.00496319
\(267\) 22.5605 1.38068
\(268\) 5.85271 0.357511
\(269\) −25.3720 −1.54696 −0.773479 0.633822i \(-0.781485\pi\)
−0.773479 + 0.633822i \(0.781485\pi\)
\(270\) 110.197 6.70636
\(271\) −0.766798 −0.0465797 −0.0232898 0.999729i \(-0.507414\pi\)
−0.0232898 + 0.999729i \(0.507414\pi\)
\(272\) 22.8449 1.38518
\(273\) 2.01165 0.121751
\(274\) −12.7889 −0.772608
\(275\) −6.67937 −0.402781
\(276\) −56.4150 −3.39578
\(277\) 15.6890 0.942659 0.471330 0.881957i \(-0.343774\pi\)
0.471330 + 0.881957i \(0.343774\pi\)
\(278\) −26.8331 −1.60934
\(279\) 25.7648 1.54250
\(280\) −12.4951 −0.746728
\(281\) 14.7101 0.877530 0.438765 0.898602i \(-0.355416\pi\)
0.438765 + 0.898602i \(0.355416\pi\)
\(282\) −52.1008 −3.10256
\(283\) 3.78484 0.224985 0.112493 0.993653i \(-0.464117\pi\)
0.112493 + 0.993653i \(0.464117\pi\)
\(284\) −58.2904 −3.45890
\(285\) 0.455389 0.0269749
\(286\) −6.55503 −0.387607
\(287\) −4.75216 −0.280511
\(288\) −77.9471 −4.59308
\(289\) −11.2332 −0.660776
\(290\) −41.8290 −2.45629
\(291\) −56.5920 −3.31748
\(292\) 39.2058 2.29434
\(293\) −17.4072 −1.01694 −0.508469 0.861080i \(-0.669788\pi\)
−0.508469 + 0.861080i \(0.669788\pi\)
\(294\) 56.4383 3.29155
\(295\) 11.3593 0.661365
\(296\) 23.9036 1.38937
\(297\) −38.3296 −2.22411
\(298\) 42.5912 2.46724
\(299\) 3.59072 0.207656
\(300\) 41.7768 2.41198
\(301\) −6.46065 −0.372386
\(302\) −10.3794 −0.597265
\(303\) 19.3121 1.10945
\(304\) −0.479197 −0.0274838
\(305\) 17.6962 1.01328
\(306\) −48.0712 −2.74805
\(307\) −11.8849 −0.678305 −0.339153 0.940731i \(-0.610140\pi\)
−0.339153 + 0.940731i \(0.610140\pi\)
\(308\) 7.43998 0.423932
\(309\) 3.84012 0.218457
\(310\) 24.2559 1.37764
\(311\) 18.7705 1.06438 0.532190 0.846625i \(-0.321369\pi\)
0.532190 + 0.846625i \(0.321369\pi\)
\(312\) 23.9503 1.35592
\(313\) 19.8757 1.12344 0.561719 0.827328i \(-0.310140\pi\)
0.561719 + 0.827328i \(0.310140\pi\)
\(314\) 19.7432 1.11417
\(315\) 13.0735 0.736607
\(316\) 10.1790 0.572613
\(317\) −3.92209 −0.220286 −0.110143 0.993916i \(-0.535131\pi\)
−0.110143 + 0.993916i \(0.535131\pi\)
\(318\) 59.6287 3.34381
\(319\) 14.5494 0.814609
\(320\) −20.7275 −1.15870
\(321\) −56.7878 −3.16958
\(322\) −5.77019 −0.321560
\(323\) −0.120965 −0.00673067
\(324\) 129.052 7.16956
\(325\) −2.65902 −0.147496
\(326\) −4.40201 −0.243805
\(327\) 62.5694 3.46009
\(328\) −56.5781 −3.12401
\(329\) −3.76381 −0.207506
\(330\) −59.2605 −3.26219
\(331\) 17.1731 0.943917 0.471959 0.881621i \(-0.343547\pi\)
0.471959 + 0.881621i \(0.343547\pi\)
\(332\) −78.4607 −4.30609
\(333\) −25.0100 −1.37054
\(334\) 29.8415 1.63285
\(335\) −3.36771 −0.183997
\(336\) −19.1370 −1.04401
\(337\) 13.1360 0.715561 0.357781 0.933806i \(-0.383534\pi\)
0.357781 + 0.933806i \(0.383534\pi\)
\(338\) −2.60952 −0.141939
\(339\) −16.1845 −0.879020
\(340\) −31.9642 −1.73350
\(341\) −8.43693 −0.456885
\(342\) 1.00835 0.0545251
\(343\) 8.38784 0.452901
\(344\) −76.9191 −4.14720
\(345\) 32.4617 1.74768
\(346\) 9.31155 0.500592
\(347\) 21.1558 1.13570 0.567852 0.823131i \(-0.307775\pi\)
0.567852 + 0.823131i \(0.307775\pi\)
\(348\) −91.0005 −4.87814
\(349\) 21.7016 1.16166 0.580830 0.814025i \(-0.302728\pi\)
0.580830 + 0.814025i \(0.302728\pi\)
\(350\) 4.27298 0.228400
\(351\) −15.2588 −0.814455
\(352\) 25.5245 1.36046
\(353\) 34.9332 1.85931 0.929653 0.368437i \(-0.120107\pi\)
0.929653 + 0.368437i \(0.120107\pi\)
\(354\) 34.9889 1.85964
\(355\) 33.5408 1.78016
\(356\) 33.2165 1.76047
\(357\) −4.83081 −0.255674
\(358\) −22.1997 −1.17329
\(359\) −20.1761 −1.06485 −0.532427 0.846476i \(-0.678720\pi\)
−0.532427 + 0.846476i \(0.678720\pi\)
\(360\) 155.650 8.20347
\(361\) −18.9975 −0.999866
\(362\) 54.0594 2.84130
\(363\) −15.3207 −0.804129
\(364\) 2.96181 0.155241
\(365\) −22.5594 −1.18081
\(366\) 54.5077 2.84916
\(367\) −20.2178 −1.05536 −0.527679 0.849444i \(-0.676938\pi\)
−0.527679 + 0.849444i \(0.676938\pi\)
\(368\) −34.1588 −1.78065
\(369\) 59.1969 3.08167
\(370\) −23.5453 −1.22406
\(371\) 4.30763 0.223641
\(372\) 52.7696 2.73598
\(373\) −6.74751 −0.349373 −0.174686 0.984624i \(-0.555891\pi\)
−0.174686 + 0.984624i \(0.555891\pi\)
\(374\) 15.7414 0.813967
\(375\) 21.1635 1.09288
\(376\) −44.8111 −2.31096
\(377\) 5.79202 0.298304
\(378\) 24.5206 1.26120
\(379\) 3.83115 0.196793 0.0983964 0.995147i \(-0.468629\pi\)
0.0983964 + 0.995147i \(0.468629\pi\)
\(380\) 0.670483 0.0343951
\(381\) −7.27529 −0.372724
\(382\) −10.0682 −0.515134
\(383\) 19.9158 1.01765 0.508824 0.860870i \(-0.330080\pi\)
0.508824 + 0.860870i \(0.330080\pi\)
\(384\) 2.54154 0.129697
\(385\) −4.28104 −0.218182
\(386\) −43.2458 −2.20116
\(387\) 80.4792 4.09099
\(388\) −83.3222 −4.23004
\(389\) 0.904447 0.0458573 0.0229286 0.999737i \(-0.492701\pi\)
0.0229286 + 0.999737i \(0.492701\pi\)
\(390\) −23.5913 −1.19459
\(391\) −8.62281 −0.436074
\(392\) 48.5417 2.45173
\(393\) −45.3051 −2.28534
\(394\) 25.8529 1.30245
\(395\) −5.85709 −0.294702
\(396\) −92.6786 −4.65728
\(397\) −14.1047 −0.707897 −0.353949 0.935265i \(-0.615161\pi\)
−0.353949 + 0.935265i \(0.615161\pi\)
\(398\) 5.96703 0.299100
\(399\) 0.101332 0.00507292
\(400\) 25.2955 1.26478
\(401\) −7.03623 −0.351372 −0.175686 0.984446i \(-0.556214\pi\)
−0.175686 + 0.984446i \(0.556214\pi\)
\(402\) −10.3732 −0.517368
\(403\) −3.35869 −0.167308
\(404\) 28.4338 1.41464
\(405\) −74.2578 −3.68990
\(406\) −9.30765 −0.461931
\(407\) 8.18976 0.405951
\(408\) −57.5146 −2.84740
\(409\) −26.2638 −1.29866 −0.649331 0.760506i \(-0.724951\pi\)
−0.649331 + 0.760506i \(0.724951\pi\)
\(410\) 55.7301 2.75231
\(411\) 16.0095 0.789690
\(412\) 5.65393 0.278549
\(413\) 2.52763 0.124377
\(414\) 71.8784 3.53263
\(415\) 45.1471 2.21618
\(416\) 10.1612 0.498192
\(417\) 33.5903 1.64492
\(418\) −0.330192 −0.0161502
\(419\) −12.3762 −0.604617 −0.302308 0.953210i \(-0.597757\pi\)
−0.302308 + 0.953210i \(0.597757\pi\)
\(420\) 26.7762 1.30654
\(421\) −35.8535 −1.74739 −0.873697 0.486470i \(-0.838284\pi\)
−0.873697 + 0.486470i \(0.838284\pi\)
\(422\) 24.3387 1.18479
\(423\) 46.8852 2.27963
\(424\) 51.2857 2.49066
\(425\) 6.38542 0.309738
\(426\) 103.312 5.00550
\(427\) 3.93769 0.190558
\(428\) −83.6104 −4.04146
\(429\) 8.20575 0.396177
\(430\) 75.7662 3.65377
\(431\) −4.09900 −0.197442 −0.0987209 0.995115i \(-0.531475\pi\)
−0.0987209 + 0.995115i \(0.531475\pi\)
\(432\) 145.159 6.98394
\(433\) 26.8547 1.29056 0.645278 0.763948i \(-0.276742\pi\)
0.645278 + 0.763948i \(0.276742\pi\)
\(434\) 5.39734 0.259081
\(435\) 52.3626 2.51059
\(436\) 92.1228 4.41188
\(437\) 0.180873 0.00865231
\(438\) −69.4873 −3.32023
\(439\) 19.8292 0.946396 0.473198 0.880956i \(-0.343100\pi\)
0.473198 + 0.880956i \(0.343100\pi\)
\(440\) −50.9691 −2.42986
\(441\) −50.7885 −2.41850
\(442\) 6.26655 0.298070
\(443\) −15.5489 −0.738751 −0.369376 0.929280i \(-0.620428\pi\)
−0.369376 + 0.929280i \(0.620428\pi\)
\(444\) −51.2237 −2.43097
\(445\) −19.1131 −0.906048
\(446\) 62.7256 2.97014
\(447\) −53.3166 −2.52179
\(448\) −4.61220 −0.217906
\(449\) −17.8517 −0.842475 −0.421238 0.906950i \(-0.638404\pi\)
−0.421238 + 0.906950i \(0.638404\pi\)
\(450\) −53.2278 −2.50918
\(451\) −19.3846 −0.912784
\(452\) −23.8289 −1.12082
\(453\) 12.9931 0.610471
\(454\) 3.19606 0.149998
\(455\) −1.70426 −0.0798968
\(456\) 1.20643 0.0564963
\(457\) 0.611560 0.0286076 0.0143038 0.999898i \(-0.495447\pi\)
0.0143038 + 0.999898i \(0.495447\pi\)
\(458\) 41.2658 1.92823
\(459\) 36.6428 1.71034
\(460\) 47.7944 2.22843
\(461\) 23.3553 1.08776 0.543882 0.839162i \(-0.316954\pi\)
0.543882 + 0.839162i \(0.316954\pi\)
\(462\) −13.1864 −0.613489
\(463\) −1.00000 −0.0464739
\(464\) −55.1001 −2.55796
\(465\) −30.3641 −1.40810
\(466\) 57.7275 2.67417
\(467\) −28.3940 −1.31392 −0.656959 0.753926i \(-0.728158\pi\)
−0.656959 + 0.753926i \(0.728158\pi\)
\(468\) −36.8948 −1.70546
\(469\) −0.749369 −0.0346027
\(470\) 44.1394 2.03600
\(471\) −24.7150 −1.13881
\(472\) 30.0934 1.38516
\(473\) −26.3537 −1.21174
\(474\) −18.0410 −0.828650
\(475\) −0.133941 −0.00614563
\(476\) −7.11256 −0.326004
\(477\) −53.6595 −2.45690
\(478\) 42.4150 1.94002
\(479\) 18.1246 0.828132 0.414066 0.910247i \(-0.364108\pi\)
0.414066 + 0.910247i \(0.364108\pi\)
\(480\) 91.8617 4.19289
\(481\) 3.26030 0.148657
\(482\) 44.7614 2.03883
\(483\) 7.22326 0.328670
\(484\) −22.5571 −1.02532
\(485\) 47.9444 2.17704
\(486\) −109.274 −4.95677
\(487\) −2.82231 −0.127891 −0.0639455 0.997953i \(-0.520368\pi\)
−0.0639455 + 0.997953i \(0.520368\pi\)
\(488\) 46.8813 2.12222
\(489\) 5.51054 0.249195
\(490\) −47.8141 −2.16002
\(491\) 39.0553 1.76254 0.881272 0.472610i \(-0.156688\pi\)
0.881272 + 0.472610i \(0.156688\pi\)
\(492\) 121.243 5.46605
\(493\) −13.9091 −0.626433
\(494\) −0.131448 −0.00591411
\(495\) 53.3282 2.39692
\(496\) 31.9516 1.43467
\(497\) 7.46338 0.334779
\(498\) 139.062 6.23151
\(499\) −19.8755 −0.889751 −0.444876 0.895592i \(-0.646752\pi\)
−0.444876 + 0.895592i \(0.646752\pi\)
\(500\) 31.1597 1.39351
\(501\) −37.3563 −1.66896
\(502\) 36.0308 1.60813
\(503\) −15.2846 −0.681509 −0.340754 0.940152i \(-0.610682\pi\)
−0.340754 + 0.940152i \(0.610682\pi\)
\(504\) 34.6347 1.54275
\(505\) −16.3611 −0.728060
\(506\) −23.5373 −1.04636
\(507\) 3.26666 0.145078
\(508\) −10.7116 −0.475252
\(509\) 13.9304 0.617454 0.308727 0.951151i \(-0.400097\pi\)
0.308727 + 0.951151i \(0.400097\pi\)
\(510\) 56.6526 2.50862
\(511\) −5.01983 −0.222064
\(512\) 42.8306 1.89286
\(513\) −0.768622 −0.0339355
\(514\) −22.0416 −0.972214
\(515\) −3.25333 −0.143359
\(516\) 164.832 7.25632
\(517\) −15.3530 −0.675224
\(518\) −5.23922 −0.230198
\(519\) −11.6564 −0.511660
\(520\) −20.2905 −0.889798
\(521\) −21.0940 −0.924146 −0.462073 0.886842i \(-0.652894\pi\)
−0.462073 + 0.886842i \(0.652894\pi\)
\(522\) 115.944 5.07472
\(523\) −14.8324 −0.648576 −0.324288 0.945958i \(-0.605125\pi\)
−0.324288 + 0.945958i \(0.605125\pi\)
\(524\) −66.7041 −2.91398
\(525\) −5.34902 −0.233450
\(526\) 15.7308 0.685895
\(527\) 8.06563 0.351344
\(528\) −78.0620 −3.39721
\(529\) −10.1068 −0.439424
\(530\) −50.5170 −2.19432
\(531\) −31.4863 −1.36639
\(532\) 0.149193 0.00646836
\(533\) −7.71689 −0.334256
\(534\) −58.8721 −2.54765
\(535\) 48.1102 2.07999
\(536\) −8.92183 −0.385364
\(537\) 27.7902 1.19923
\(538\) 66.2088 2.85446
\(539\) 16.6312 0.716355
\(540\) −203.103 −8.74017
\(541\) −27.0274 −1.16200 −0.580999 0.813904i \(-0.697338\pi\)
−0.580999 + 0.813904i \(0.697338\pi\)
\(542\) 2.00098 0.0859493
\(543\) −67.6729 −2.90412
\(544\) −24.4012 −1.04619
\(545\) −53.0083 −2.27063
\(546\) −5.24945 −0.224656
\(547\) 20.7389 0.886729 0.443365 0.896341i \(-0.353785\pi\)
0.443365 + 0.896341i \(0.353785\pi\)
\(548\) 23.5713 1.00691
\(549\) −49.0512 −2.09345
\(550\) 17.4300 0.743216
\(551\) 0.291758 0.0124293
\(552\) 85.9986 3.66034
\(553\) −1.30330 −0.0554219
\(554\) −40.9407 −1.73940
\(555\) 29.4746 1.25113
\(556\) 49.4560 2.09740
\(557\) 10.6497 0.451241 0.225621 0.974215i \(-0.427559\pi\)
0.225621 + 0.974215i \(0.427559\pi\)
\(558\) −67.2338 −2.84623
\(559\) −10.4913 −0.443733
\(560\) 16.2128 0.685114
\(561\) −19.7054 −0.831964
\(562\) −38.3863 −1.61923
\(563\) 30.4639 1.28390 0.641950 0.766746i \(-0.278125\pi\)
0.641950 + 0.766746i \(0.278125\pi\)
\(564\) 96.0269 4.04346
\(565\) 13.7114 0.576842
\(566\) −9.87662 −0.415145
\(567\) −16.5236 −0.693925
\(568\) 88.8574 3.72837
\(569\) 30.1392 1.26350 0.631750 0.775172i \(-0.282337\pi\)
0.631750 + 0.775172i \(0.282337\pi\)
\(570\) −1.18835 −0.0497744
\(571\) −1.53762 −0.0643473 −0.0321736 0.999482i \(-0.510243\pi\)
−0.0321736 + 0.999482i \(0.510243\pi\)
\(572\) 12.0816 0.505156
\(573\) 12.6036 0.526524
\(574\) 12.4009 0.517602
\(575\) −9.54778 −0.398170
\(576\) 57.4534 2.39389
\(577\) −28.6279 −1.19180 −0.595898 0.803060i \(-0.703204\pi\)
−0.595898 + 0.803060i \(0.703204\pi\)
\(578\) 29.3133 1.21927
\(579\) 54.1362 2.24982
\(580\) 77.0950 3.20120
\(581\) 10.0460 0.416777
\(582\) 147.678 6.12145
\(583\) 17.5713 0.727730
\(584\) −59.7650 −2.47309
\(585\) 21.2296 0.877738
\(586\) 45.4244 1.87646
\(587\) −35.9026 −1.48186 −0.740930 0.671582i \(-0.765615\pi\)
−0.740930 + 0.671582i \(0.765615\pi\)
\(588\) −104.021 −4.28977
\(589\) −0.169185 −0.00697115
\(590\) −29.6424 −1.22036
\(591\) −32.3633 −1.33125
\(592\) −31.0155 −1.27473
\(593\) 30.3410 1.24596 0.622978 0.782239i \(-0.285922\pi\)
0.622978 + 0.782239i \(0.285922\pi\)
\(594\) 100.022 4.10396
\(595\) 4.09263 0.167782
\(596\) −78.4997 −3.21547
\(597\) −7.46967 −0.305713
\(598\) −9.37005 −0.383170
\(599\) 27.3815 1.11878 0.559389 0.828905i \(-0.311036\pi\)
0.559389 + 0.828905i \(0.311036\pi\)
\(600\) −63.6842 −2.59990
\(601\) −4.51174 −0.184038 −0.0920189 0.995757i \(-0.529332\pi\)
−0.0920189 + 0.995757i \(0.529332\pi\)
\(602\) 16.8592 0.687130
\(603\) 9.33477 0.380141
\(604\) 19.1302 0.778396
\(605\) 12.9796 0.527696
\(606\) −50.3954 −2.04717
\(607\) 9.67083 0.392527 0.196263 0.980551i \(-0.437119\pi\)
0.196263 + 0.980551i \(0.437119\pi\)
\(608\) 0.511842 0.0207579
\(609\) 11.6515 0.472144
\(610\) −46.1786 −1.86972
\(611\) −6.11194 −0.247263
\(612\) 88.6000 3.58144
\(613\) 30.2232 1.22071 0.610353 0.792130i \(-0.291028\pi\)
0.610353 + 0.792130i \(0.291028\pi\)
\(614\) 31.0138 1.25162
\(615\) −69.7643 −2.81317
\(616\) −11.3415 −0.456960
\(617\) −25.8703 −1.04150 −0.520750 0.853709i \(-0.674348\pi\)
−0.520750 + 0.853709i \(0.674348\pi\)
\(618\) −10.0209 −0.403099
\(619\) −11.8793 −0.477468 −0.238734 0.971085i \(-0.576732\pi\)
−0.238734 + 0.971085i \(0.576732\pi\)
\(620\) −44.7061 −1.79544
\(621\) −54.7901 −2.19865
\(622\) −48.9821 −1.96400
\(623\) −4.25298 −0.170392
\(624\) −31.0761 −1.24404
\(625\) −31.2247 −1.24899
\(626\) −51.8660 −2.07298
\(627\) 0.413342 0.0165073
\(628\) −36.3887 −1.45207
\(629\) −7.82934 −0.312176
\(630\) −34.1155 −1.35920
\(631\) −2.17469 −0.0865730 −0.0432865 0.999063i \(-0.513783\pi\)
−0.0432865 + 0.999063i \(0.513783\pi\)
\(632\) −15.5168 −0.617224
\(633\) −30.4677 −1.21098
\(634\) 10.2348 0.406475
\(635\) 6.16357 0.244594
\(636\) −109.902 −4.35788
\(637\) 6.62078 0.262325
\(638\) −37.9669 −1.50312
\(639\) −92.9702 −3.67784
\(640\) −2.15318 −0.0851118
\(641\) 31.5362 1.24561 0.622803 0.782379i \(-0.285994\pi\)
0.622803 + 0.782379i \(0.285994\pi\)
\(642\) 148.189 5.84855
\(643\) −27.2396 −1.07423 −0.537113 0.843510i \(-0.680485\pi\)
−0.537113 + 0.843510i \(0.680485\pi\)
\(644\) 10.6350 0.419079
\(645\) −94.8458 −3.73455
\(646\) 0.315661 0.0124195
\(647\) 15.1717 0.596461 0.298230 0.954494i \(-0.403604\pi\)
0.298230 + 0.954494i \(0.403604\pi\)
\(648\) −196.726 −7.72813
\(649\) 10.3105 0.404722
\(650\) 6.93877 0.272161
\(651\) −6.75652 −0.264809
\(652\) 8.11333 0.317743
\(653\) 23.9750 0.938215 0.469107 0.883141i \(-0.344576\pi\)
0.469107 + 0.883141i \(0.344576\pi\)
\(654\) −163.276 −6.38460
\(655\) 38.3822 1.49972
\(656\) 73.4115 2.86624
\(657\) 62.5312 2.43957
\(658\) 9.82175 0.382892
\(659\) −35.1953 −1.37102 −0.685508 0.728065i \(-0.740420\pi\)
−0.685508 + 0.728065i \(0.740420\pi\)
\(660\) 109.223 4.25150
\(661\) −15.2007 −0.591238 −0.295619 0.955306i \(-0.595526\pi\)
−0.295619 + 0.955306i \(0.595526\pi\)
\(662\) −44.8135 −1.74173
\(663\) −7.84462 −0.304660
\(664\) 119.605 4.64157
\(665\) −0.0858474 −0.00332902
\(666\) 65.2641 2.52893
\(667\) 20.7975 0.805283
\(668\) −55.0008 −2.12805
\(669\) −78.5214 −3.03581
\(670\) 8.78810 0.339514
\(671\) 16.0623 0.620077
\(672\) 20.4407 0.788518
\(673\) 24.5823 0.947580 0.473790 0.880638i \(-0.342886\pi\)
0.473790 + 0.880638i \(0.342886\pi\)
\(674\) −34.2786 −1.32036
\(675\) 40.5735 1.56167
\(676\) 4.80961 0.184985
\(677\) 46.3490 1.78134 0.890669 0.454653i \(-0.150237\pi\)
0.890669 + 0.454653i \(0.150237\pi\)
\(678\) 42.2337 1.62198
\(679\) 10.6684 0.409416
\(680\) 48.7260 1.86856
\(681\) −4.00090 −0.153315
\(682\) 22.0163 0.843049
\(683\) −26.8348 −1.02681 −0.513403 0.858148i \(-0.671615\pi\)
−0.513403 + 0.858148i \(0.671615\pi\)
\(684\) −1.85848 −0.0710607
\(685\) −13.5631 −0.518221
\(686\) −21.8883 −0.835698
\(687\) −51.6575 −1.97086
\(688\) 99.8043 3.80500
\(689\) 6.99504 0.266490
\(690\) −84.7096 −3.22484
\(691\) 4.79554 0.182431 0.0912155 0.995831i \(-0.470925\pi\)
0.0912155 + 0.995831i \(0.470925\pi\)
\(692\) −17.1621 −0.652405
\(693\) 11.8664 0.450767
\(694\) −55.2066 −2.09561
\(695\) −28.4574 −1.07945
\(696\) 138.721 5.25819
\(697\) 18.5315 0.701930
\(698\) −56.6308 −2.14351
\(699\) −72.2646 −2.73330
\(700\) −7.87552 −0.297667
\(701\) −9.24177 −0.349057 −0.174528 0.984652i \(-0.555840\pi\)
−0.174528 + 0.984652i \(0.555840\pi\)
\(702\) 39.8182 1.50284
\(703\) 0.164229 0.00619400
\(704\) −18.8137 −0.709067
\(705\) −55.2548 −2.08102
\(706\) −91.1589 −3.43081
\(707\) −3.64061 −0.136919
\(708\) −64.4880 −2.42361
\(709\) −42.8216 −1.60820 −0.804100 0.594494i \(-0.797352\pi\)
−0.804100 + 0.594494i \(0.797352\pi\)
\(710\) −87.5256 −3.28478
\(711\) 16.2350 0.608859
\(712\) −50.6350 −1.89763
\(713\) −12.0601 −0.451655
\(714\) 12.6061 0.471772
\(715\) −6.95185 −0.259985
\(716\) 40.9163 1.52911
\(717\) −53.0961 −1.98291
\(718\) 52.6500 1.96488
\(719\) 11.1499 0.415821 0.207911 0.978148i \(-0.433334\pi\)
0.207911 + 0.978148i \(0.433334\pi\)
\(720\) −201.960 −7.52659
\(721\) −0.723918 −0.0269601
\(722\) 49.5743 1.84496
\(723\) −56.0334 −2.08390
\(724\) −99.6368 −3.70297
\(725\) −15.4011 −0.571983
\(726\) 39.9797 1.48379
\(727\) −12.3545 −0.458203 −0.229101 0.973403i \(-0.573579\pi\)
−0.229101 + 0.973403i \(0.573579\pi\)
\(728\) −4.51497 −0.167336
\(729\) 56.2954 2.08501
\(730\) 58.8692 2.17885
\(731\) 25.1939 0.931830
\(732\) −100.463 −3.71322
\(733\) −0.603646 −0.0222962 −0.0111481 0.999938i \(-0.503549\pi\)
−0.0111481 + 0.999938i \(0.503549\pi\)
\(734\) 52.7587 1.94736
\(735\) 59.8549 2.20778
\(736\) 36.4859 1.34489
\(737\) −3.05676 −0.112597
\(738\) −154.476 −5.68632
\(739\) −14.4452 −0.531374 −0.265687 0.964059i \(-0.585599\pi\)
−0.265687 + 0.964059i \(0.585599\pi\)
\(740\) 43.3964 1.59528
\(741\) 0.164549 0.00604487
\(742\) −11.2409 −0.412665
\(743\) −8.15550 −0.299196 −0.149598 0.988747i \(-0.547798\pi\)
−0.149598 + 0.988747i \(0.547798\pi\)
\(744\) −80.4416 −2.94913
\(745\) 45.1695 1.65488
\(746\) 17.6078 0.644666
\(747\) −125.141 −4.57866
\(748\) −29.0129 −1.06082
\(749\) 10.7053 0.391164
\(750\) −55.2267 −2.01660
\(751\) −3.75818 −0.137138 −0.0685690 0.997646i \(-0.521843\pi\)
−0.0685690 + 0.997646i \(0.521843\pi\)
\(752\) 58.1435 2.12027
\(753\) −45.1042 −1.64369
\(754\) −15.1144 −0.550435
\(755\) −11.0077 −0.400611
\(756\) −45.1938 −1.64368
\(757\) −21.0061 −0.763481 −0.381741 0.924270i \(-0.624675\pi\)
−0.381741 + 0.924270i \(0.624675\pi\)
\(758\) −9.99746 −0.363124
\(759\) 29.4645 1.06949
\(760\) −1.02208 −0.0370747
\(761\) −31.4829 −1.14126 −0.570628 0.821209i \(-0.693300\pi\)
−0.570628 + 0.821209i \(0.693300\pi\)
\(762\) 18.9850 0.687755
\(763\) −11.7952 −0.427016
\(764\) 18.5567 0.671358
\(765\) −50.9813 −1.84323
\(766\) −51.9707 −1.87778
\(767\) 4.10455 0.148207
\(768\) −55.5643 −2.00500
\(769\) 32.2935 1.16453 0.582266 0.812998i \(-0.302166\pi\)
0.582266 + 0.812998i \(0.302166\pi\)
\(770\) 11.1715 0.402591
\(771\) 27.5922 0.993709
\(772\) 79.7063 2.86869
\(773\) 41.5918 1.49595 0.747976 0.663726i \(-0.231026\pi\)
0.747976 + 0.663726i \(0.231026\pi\)
\(774\) −210.012 −7.54874
\(775\) 8.93083 0.320805
\(776\) 127.016 4.55960
\(777\) 6.55858 0.235288
\(778\) −2.36017 −0.0846163
\(779\) −0.388718 −0.0139273
\(780\) 43.4811 1.55687
\(781\) 30.4440 1.08937
\(782\) 22.5014 0.804649
\(783\) −88.3795 −3.15842
\(784\) −62.9841 −2.24943
\(785\) 20.9384 0.747324
\(786\) 118.225 4.21694
\(787\) 17.3676 0.619088 0.309544 0.950885i \(-0.399824\pi\)
0.309544 + 0.950885i \(0.399824\pi\)
\(788\) −47.6495 −1.69744
\(789\) −19.6922 −0.701060
\(790\) 15.2842 0.543788
\(791\) 3.05101 0.108481
\(792\) 141.279 5.02012
\(793\) 6.39430 0.227068
\(794\) 36.8067 1.30622
\(795\) 63.2384 2.24284
\(796\) −10.9978 −0.389807
\(797\) −40.9934 −1.45206 −0.726031 0.687662i \(-0.758637\pi\)
−0.726031 + 0.687662i \(0.758637\pi\)
\(798\) −0.264427 −0.00936061
\(799\) 14.6773 0.519247
\(800\) −27.0188 −0.955257
\(801\) 52.9786 1.87191
\(802\) 18.3612 0.648356
\(803\) −20.4764 −0.722598
\(804\) 19.1188 0.674269
\(805\) −6.11950 −0.215684
\(806\) 8.76458 0.308719
\(807\) −82.8817 −2.91757
\(808\) −43.3443 −1.52485
\(809\) 1.99775 0.0702373 0.0351186 0.999383i \(-0.488819\pi\)
0.0351186 + 0.999383i \(0.488819\pi\)
\(810\) 193.777 6.80865
\(811\) 31.4712 1.10510 0.552552 0.833479i \(-0.313654\pi\)
0.552552 + 0.833479i \(0.313654\pi\)
\(812\) 17.1549 0.602019
\(813\) −2.50487 −0.0878496
\(814\) −21.3714 −0.749066
\(815\) −4.66849 −0.163530
\(816\) 74.6266 2.61245
\(817\) −0.528469 −0.0184888
\(818\) 68.5360 2.39631
\(819\) 4.72394 0.165068
\(820\) −102.716 −3.58700
\(821\) −50.5937 −1.76573 −0.882867 0.469623i \(-0.844390\pi\)
−0.882867 + 0.469623i \(0.844390\pi\)
\(822\) −41.7771 −1.45714
\(823\) 24.3057 0.847243 0.423622 0.905839i \(-0.360759\pi\)
0.423622 + 0.905839i \(0.360759\pi\)
\(824\) −8.61881 −0.300250
\(825\) −21.8192 −0.759648
\(826\) −6.59591 −0.229501
\(827\) 49.4208 1.71853 0.859265 0.511530i \(-0.170921\pi\)
0.859265 + 0.511530i \(0.170921\pi\)
\(828\) −132.479 −4.60396
\(829\) −26.2785 −0.912690 −0.456345 0.889803i \(-0.650842\pi\)
−0.456345 + 0.889803i \(0.650842\pi\)
\(830\) −117.812 −4.08932
\(831\) 51.2506 1.77786
\(832\) −7.48962 −0.259656
\(833\) −15.8993 −0.550876
\(834\) −87.6545 −3.03523
\(835\) 31.6480 1.09522
\(836\) 0.608577 0.0210481
\(837\) 51.2497 1.77145
\(838\) 32.2960 1.11565
\(839\) 7.79347 0.269060 0.134530 0.990909i \(-0.457047\pi\)
0.134530 + 0.990909i \(0.457047\pi\)
\(840\) −40.8174 −1.40833
\(841\) 4.54755 0.156812
\(842\) 93.5606 3.22431
\(843\) 48.0529 1.65503
\(844\) −44.8586 −1.54410
\(845\) −2.76749 −0.0952047
\(846\) −122.348 −4.20641
\(847\) 2.88817 0.0992388
\(848\) −66.5445 −2.28515
\(849\) 12.3638 0.424324
\(850\) −16.6629 −0.571533
\(851\) 11.7068 0.401304
\(852\) −190.415 −6.52351
\(853\) 49.0249 1.67858 0.839290 0.543684i \(-0.182971\pi\)
0.839290 + 0.543684i \(0.182971\pi\)
\(854\) −10.2755 −0.351620
\(855\) 1.06939 0.0365723
\(856\) 127.455 4.35632
\(857\) 20.2675 0.692323 0.346162 0.938175i \(-0.387485\pi\)
0.346162 + 0.938175i \(0.387485\pi\)
\(858\) −21.4131 −0.731030
\(859\) 7.07694 0.241462 0.120731 0.992685i \(-0.461476\pi\)
0.120731 + 0.992685i \(0.461476\pi\)
\(860\) −139.644 −4.76184
\(861\) −15.5237 −0.529046
\(862\) 10.6964 0.364322
\(863\) −35.3743 −1.20415 −0.602077 0.798438i \(-0.705660\pi\)
−0.602077 + 0.798438i \(0.705660\pi\)
\(864\) −155.047 −5.27482
\(865\) 9.87523 0.335768
\(866\) −70.0780 −2.38135
\(867\) −36.6950 −1.24623
\(868\) −9.94782 −0.337651
\(869\) −5.31630 −0.180343
\(870\) −136.641 −4.63257
\(871\) −1.21688 −0.0412324
\(872\) −140.431 −4.75560
\(873\) −132.895 −4.49780
\(874\) −0.471991 −0.0159653
\(875\) −3.98963 −0.134874
\(876\) 128.072 4.32715
\(877\) 50.8543 1.71723 0.858614 0.512622i \(-0.171326\pi\)
0.858614 + 0.512622i \(0.171326\pi\)
\(878\) −51.7447 −1.74630
\(879\) −56.8633 −1.91795
\(880\) 66.1336 2.22936
\(881\) 54.3883 1.83239 0.916193 0.400736i \(-0.131246\pi\)
0.916193 + 0.400736i \(0.131246\pi\)
\(882\) 132.534 4.46264
\(883\) 52.8574 1.77879 0.889397 0.457137i \(-0.151125\pi\)
0.889397 + 0.457137i \(0.151125\pi\)
\(884\) −11.5499 −0.388464
\(885\) 37.1070 1.24734
\(886\) 40.5752 1.36315
\(887\) −27.7353 −0.931259 −0.465630 0.884980i \(-0.654172\pi\)
−0.465630 + 0.884980i \(0.654172\pi\)
\(888\) 78.0850 2.62036
\(889\) 1.37150 0.0459985
\(890\) 49.8761 1.67185
\(891\) −67.4015 −2.25804
\(892\) −115.609 −3.87089
\(893\) −0.307873 −0.0103026
\(894\) 139.131 4.65323
\(895\) −23.5436 −0.786977
\(896\) −0.479117 −0.0160062
\(897\) 11.7297 0.391642
\(898\) 46.5845 1.55454
\(899\) −19.4536 −0.648815
\(900\) 98.1041 3.27014
\(901\) −16.7980 −0.559623
\(902\) 50.5845 1.68428
\(903\) −21.1047 −0.702322
\(904\) 36.3246 1.20814
\(905\) 57.3320 1.90578
\(906\) −33.9059 −1.12645
\(907\) −16.5779 −0.550459 −0.275229 0.961379i \(-0.588754\pi\)
−0.275229 + 0.961379i \(0.588754\pi\)
\(908\) −5.89065 −0.195488
\(909\) 45.3505 1.50418
\(910\) 4.44730 0.147426
\(911\) −49.3067 −1.63360 −0.816802 0.576918i \(-0.804255\pi\)
−0.816802 + 0.576918i \(0.804255\pi\)
\(912\) −1.56537 −0.0518347
\(913\) 40.9786 1.35619
\(914\) −1.59588 −0.0527870
\(915\) 57.8074 1.91105
\(916\) −76.0570 −2.51299
\(917\) 8.54067 0.282038
\(918\) −95.6202 −3.15594
\(919\) −28.3388 −0.934810 −0.467405 0.884043i \(-0.654811\pi\)
−0.467405 + 0.884043i \(0.654811\pi\)
\(920\) −72.8574 −2.40204
\(921\) −38.8238 −1.27929
\(922\) −60.9462 −2.00715
\(923\) 12.1196 0.398921
\(924\) 24.3039 0.799540
\(925\) −8.66919 −0.285041
\(926\) 2.60952 0.0857542
\(927\) 9.01773 0.296181
\(928\) 58.8538 1.93197
\(929\) 50.2592 1.64895 0.824476 0.565897i \(-0.191470\pi\)
0.824476 + 0.565897i \(0.191470\pi\)
\(930\) 79.2359 2.59825
\(931\) 0.333504 0.0109301
\(932\) −106.397 −3.48516
\(933\) 61.3170 2.00743
\(934\) 74.0948 2.42446
\(935\) 16.6943 0.545962
\(936\) 56.2422 1.83833
\(937\) −54.2013 −1.77068 −0.885339 0.464945i \(-0.846074\pi\)
−0.885339 + 0.464945i \(0.846074\pi\)
\(938\) 1.95550 0.0638492
\(939\) 64.9270 2.11881
\(940\) −81.3533 −2.65345
\(941\) −27.6544 −0.901509 −0.450755 0.892648i \(-0.648845\pi\)
−0.450755 + 0.892648i \(0.648845\pi\)
\(942\) 64.4944 2.10134
\(943\) −27.7092 −0.902335
\(944\) −39.0470 −1.27087
\(945\) 26.0049 0.845941
\(946\) 68.7706 2.23592
\(947\) 54.6218 1.77497 0.887485 0.460837i \(-0.152451\pi\)
0.887485 + 0.460837i \(0.152451\pi\)
\(948\) 33.2513 1.07995
\(949\) −8.15155 −0.264611
\(950\) 0.349522 0.0113400
\(951\) −12.8121 −0.415462
\(952\) 10.8423 0.351402
\(953\) −20.0508 −0.649508 −0.324754 0.945799i \(-0.605281\pi\)
−0.324754 + 0.945799i \(0.605281\pi\)
\(954\) 140.026 4.53350
\(955\) −10.6777 −0.345522
\(956\) −78.1751 −2.52836
\(957\) 47.5279 1.53636
\(958\) −47.2964 −1.52808
\(959\) −3.01802 −0.0974569
\(960\) −67.7096 −2.18532
\(961\) −19.7192 −0.636103
\(962\) −8.50782 −0.274303
\(963\) −133.354 −4.29728
\(964\) −82.4996 −2.65713
\(965\) −45.8638 −1.47641
\(966\) −18.8493 −0.606465
\(967\) −22.7688 −0.732195 −0.366097 0.930577i \(-0.619306\pi\)
−0.366097 + 0.930577i \(0.619306\pi\)
\(968\) 34.3860 1.10521
\(969\) −0.395152 −0.0126941
\(970\) −125.112 −4.01710
\(971\) −43.9279 −1.40971 −0.704857 0.709350i \(-0.748989\pi\)
−0.704857 + 0.709350i \(0.748989\pi\)
\(972\) 201.403 6.46000
\(973\) −6.33224 −0.203002
\(974\) 7.36487 0.235986
\(975\) −8.68612 −0.278178
\(976\) −60.8296 −1.94711
\(977\) 44.5207 1.42434 0.712172 0.702005i \(-0.247711\pi\)
0.712172 + 0.702005i \(0.247711\pi\)
\(978\) −14.3799 −0.459818
\(979\) −17.3484 −0.554456
\(980\) 88.1262 2.81509
\(981\) 146.931 4.69115
\(982\) −101.916 −3.25226
\(983\) −14.0394 −0.447787 −0.223894 0.974614i \(-0.571877\pi\)
−0.223894 + 0.974614i \(0.571877\pi\)
\(984\) −184.822 −5.89190
\(985\) 27.4180 0.873610
\(986\) 36.2960 1.15590
\(987\) −12.2951 −0.391357
\(988\) 0.242271 0.00770767
\(989\) −37.6711 −1.19787
\(990\) −139.161 −4.42283
\(991\) 19.6219 0.623310 0.311655 0.950195i \(-0.399117\pi\)
0.311655 + 0.950195i \(0.399117\pi\)
\(992\) −34.1283 −1.08357
\(993\) 56.0986 1.78023
\(994\) −19.4759 −0.617737
\(995\) 6.32825 0.200619
\(996\) −256.305 −8.12132
\(997\) −4.48042 −0.141896 −0.0709482 0.997480i \(-0.522602\pi\)
−0.0709482 + 0.997480i \(0.522602\pi\)
\(998\) 51.8656 1.64178
\(999\) −49.7483 −1.57397
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 \(a_p\))