Properties

Label 6019.2.a.c.1.14
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 1.14
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26345 q^{2}\) \(+2.92995 q^{3}\) \(+3.12323 q^{4}\) \(+0.680242 q^{5}\) \(-6.63181 q^{6}\) \(-3.22192 q^{7}\) \(-2.54237 q^{8}\) \(+5.58462 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.26345 q^{2}\) \(+2.92995 q^{3}\) \(+3.12323 q^{4}\) \(+0.680242 q^{5}\) \(-6.63181 q^{6}\) \(-3.22192 q^{7}\) \(-2.54237 q^{8}\) \(+5.58462 q^{9}\) \(-1.53970 q^{10}\) \(+3.31025 q^{11}\) \(+9.15090 q^{12}\) \(-1.00000 q^{13}\) \(+7.29267 q^{14}\) \(+1.99308 q^{15}\) \(-0.491910 q^{16}\) \(-1.52177 q^{17}\) \(-12.6405 q^{18}\) \(+1.11243 q^{19}\) \(+2.12455 q^{20}\) \(-9.44007 q^{21}\) \(-7.49260 q^{22}\) \(+3.23019 q^{23}\) \(-7.44903 q^{24}\) \(-4.53727 q^{25}\) \(+2.26345 q^{26}\) \(+7.57280 q^{27}\) \(-10.0628 q^{28}\) \(+0.0198701 q^{29}\) \(-4.51124 q^{30}\) \(-7.73083 q^{31}\) \(+6.19816 q^{32}\) \(+9.69887 q^{33}\) \(+3.44447 q^{34}\) \(-2.19169 q^{35}\) \(+17.4420 q^{36}\) \(-9.89082 q^{37}\) \(-2.51793 q^{38}\) \(-2.92995 q^{39}\) \(-1.72943 q^{40}\) \(-5.18027 q^{41}\) \(+21.3672 q^{42}\) \(+3.84001 q^{43}\) \(+10.3387 q^{44}\) \(+3.79889 q^{45}\) \(-7.31139 q^{46}\) \(-9.40407 q^{47}\) \(-1.44127 q^{48}\) \(+3.38078 q^{49}\) \(+10.2699 q^{50}\) \(-4.45873 q^{51}\) \(-3.12323 q^{52}\) \(-6.20709 q^{53}\) \(-17.1407 q^{54}\) \(+2.25177 q^{55}\) \(+8.19132 q^{56}\) \(+3.25936 q^{57}\) \(-0.0449750 q^{58}\) \(-1.12786 q^{59}\) \(+6.22483 q^{60}\) \(-10.9419 q^{61}\) \(+17.4984 q^{62}\) \(-17.9932 q^{63}\) \(-13.0454 q^{64}\) \(-0.680242 q^{65}\) \(-21.9530 q^{66}\) \(-7.88697 q^{67}\) \(-4.75285 q^{68}\) \(+9.46431 q^{69}\) \(+4.96078 q^{70}\) \(-4.66354 q^{71}\) \(-14.1982 q^{72}\) \(+2.12653 q^{73}\) \(+22.3874 q^{74}\) \(-13.2940 q^{75}\) \(+3.47437 q^{76}\) \(-10.6654 q^{77}\) \(+6.63181 q^{78}\) \(-7.87136 q^{79}\) \(-0.334618 q^{80}\) \(+5.43410 q^{81}\) \(+11.7253 q^{82}\) \(+5.81401 q^{83}\) \(-29.4835 q^{84}\) \(-1.03518 q^{85}\) \(-8.69170 q^{86}\) \(+0.0582184 q^{87}\) \(-8.41589 q^{88}\) \(-5.39332 q^{89}\) \(-8.59862 q^{90}\) \(+3.22192 q^{91}\) \(+10.0886 q^{92}\) \(-22.6509 q^{93}\) \(+21.2857 q^{94}\) \(+0.756722 q^{95}\) \(+18.1603 q^{96}\) \(+4.09432 q^{97}\) \(-7.65223 q^{98}\) \(+18.4865 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26345 −1.60050 −0.800252 0.599664i \(-0.795301\pi\)
−0.800252 + 0.599664i \(0.795301\pi\)
\(3\) 2.92995 1.69161 0.845804 0.533493i \(-0.179121\pi\)
0.845804 + 0.533493i \(0.179121\pi\)
\(4\) 3.12323 1.56161
\(5\) 0.680242 0.304214 0.152107 0.988364i \(-0.451394\pi\)
0.152107 + 0.988364i \(0.451394\pi\)
\(6\) −6.63181 −2.70743
\(7\) −3.22192 −1.21777 −0.608886 0.793258i \(-0.708383\pi\)
−0.608886 + 0.793258i \(0.708383\pi\)
\(8\) −2.54237 −0.898864
\(9\) 5.58462 1.86154
\(10\) −1.53970 −0.486895
\(11\) 3.31025 0.998078 0.499039 0.866580i \(-0.333686\pi\)
0.499039 + 0.866580i \(0.333686\pi\)
\(12\) 9.15090 2.64164
\(13\) −1.00000 −0.277350
\(14\) 7.29267 1.94905
\(15\) 1.99308 0.514610
\(16\) −0.491910 −0.122977
\(17\) −1.52177 −0.369085 −0.184542 0.982825i \(-0.559080\pi\)
−0.184542 + 0.982825i \(0.559080\pi\)
\(18\) −12.6405 −2.97940
\(19\) 1.11243 0.255209 0.127604 0.991825i \(-0.459271\pi\)
0.127604 + 0.991825i \(0.459271\pi\)
\(20\) 2.12455 0.475064
\(21\) −9.44007 −2.05999
\(22\) −7.49260 −1.59743
\(23\) 3.23019 0.673542 0.336771 0.941587i \(-0.390665\pi\)
0.336771 + 0.941587i \(0.390665\pi\)
\(24\) −7.44903 −1.52053
\(25\) −4.53727 −0.907454
\(26\) 2.26345 0.443900
\(27\) 7.57280 1.45739
\(28\) −10.0628 −1.90169
\(29\) 0.0198701 0.00368978 0.00184489 0.999998i \(-0.499413\pi\)
0.00184489 + 0.999998i \(0.499413\pi\)
\(30\) −4.51124 −0.823636
\(31\) −7.73083 −1.38850 −0.694249 0.719735i \(-0.744263\pi\)
−0.694249 + 0.719735i \(0.744263\pi\)
\(32\) 6.19816 1.09569
\(33\) 9.69887 1.68836
\(34\) 3.44447 0.590721
\(35\) −2.19169 −0.370463
\(36\) 17.4420 2.90700
\(37\) −9.89082 −1.62604 −0.813020 0.582235i \(-0.802178\pi\)
−0.813020 + 0.582235i \(0.802178\pi\)
\(38\) −2.51793 −0.408463
\(39\) −2.92995 −0.469168
\(40\) −1.72943 −0.273447
\(41\) −5.18027 −0.809023 −0.404511 0.914533i \(-0.632558\pi\)
−0.404511 + 0.914533i \(0.632558\pi\)
\(42\) 21.3672 3.29703
\(43\) 3.84001 0.585597 0.292798 0.956174i \(-0.405414\pi\)
0.292798 + 0.956174i \(0.405414\pi\)
\(44\) 10.3387 1.55861
\(45\) 3.79889 0.566306
\(46\) −7.31139 −1.07801
\(47\) −9.40407 −1.37172 −0.685862 0.727731i \(-0.740575\pi\)
−0.685862 + 0.727731i \(0.740575\pi\)
\(48\) −1.44127 −0.208030
\(49\) 3.38078 0.482968
\(50\) 10.2699 1.45238
\(51\) −4.45873 −0.624347
\(52\) −3.12323 −0.433114
\(53\) −6.20709 −0.852609 −0.426305 0.904580i \(-0.640185\pi\)
−0.426305 + 0.904580i \(0.640185\pi\)
\(54\) −17.1407 −2.33255
\(55\) 2.25177 0.303629
\(56\) 8.19132 1.09461
\(57\) 3.25936 0.431713
\(58\) −0.0449750 −0.00590551
\(59\) −1.12786 −0.146835 −0.0734176 0.997301i \(-0.523391\pi\)
−0.0734176 + 0.997301i \(0.523391\pi\)
\(60\) 6.22483 0.803622
\(61\) −10.9419 −1.40096 −0.700481 0.713671i \(-0.747031\pi\)
−0.700481 + 0.713671i \(0.747031\pi\)
\(62\) 17.4984 2.22230
\(63\) −17.9932 −2.26693
\(64\) −13.0454 −1.63068
\(65\) −0.680242 −0.0843737
\(66\) −21.9530 −2.70222
\(67\) −7.88697 −0.963546 −0.481773 0.876296i \(-0.660007\pi\)
−0.481773 + 0.876296i \(0.660007\pi\)
\(68\) −4.75285 −0.576367
\(69\) 9.46431 1.13937
\(70\) 4.96078 0.592927
\(71\) −4.66354 −0.553460 −0.276730 0.960948i \(-0.589251\pi\)
−0.276730 + 0.960948i \(0.589251\pi\)
\(72\) −14.1982 −1.67327
\(73\) 2.12653 0.248891 0.124446 0.992226i \(-0.460285\pi\)
0.124446 + 0.992226i \(0.460285\pi\)
\(74\) 22.3874 2.60248
\(75\) −13.2940 −1.53506
\(76\) 3.47437 0.398537
\(77\) −10.6654 −1.21543
\(78\) 6.63181 0.750905
\(79\) −7.87136 −0.885597 −0.442799 0.896621i \(-0.646014\pi\)
−0.442799 + 0.896621i \(0.646014\pi\)
\(80\) −0.334618 −0.0374114
\(81\) 5.43410 0.603789
\(82\) 11.7253 1.29484
\(83\) 5.81401 0.638170 0.319085 0.947726i \(-0.396624\pi\)
0.319085 + 0.947726i \(0.396624\pi\)
\(84\) −29.4835 −3.21691
\(85\) −1.03518 −0.112281
\(86\) −8.69170 −0.937250
\(87\) 0.0582184 0.00624166
\(88\) −8.41589 −0.897137
\(89\) −5.39332 −0.571691 −0.285845 0.958276i \(-0.592274\pi\)
−0.285845 + 0.958276i \(0.592274\pi\)
\(90\) −8.59862 −0.906374
\(91\) 3.22192 0.337749
\(92\) 10.0886 1.05181
\(93\) −22.6509 −2.34879
\(94\) 21.2857 2.19545
\(95\) 0.756722 0.0776380
\(96\) 18.1603 1.85348
\(97\) 4.09432 0.415715 0.207857 0.978159i \(-0.433351\pi\)
0.207857 + 0.978159i \(0.433351\pi\)
\(98\) −7.65223 −0.772992
\(99\) 18.4865 1.85796
\(100\) −14.1709 −1.41709
\(101\) 15.2432 1.51675 0.758377 0.651817i \(-0.225993\pi\)
0.758377 + 0.651817i \(0.225993\pi\)
\(102\) 10.0921 0.999269
\(103\) 7.63389 0.752190 0.376095 0.926581i \(-0.377267\pi\)
0.376095 + 0.926581i \(0.377267\pi\)
\(104\) 2.54237 0.249300
\(105\) −6.42154 −0.626678
\(106\) 14.0495 1.36460
\(107\) −2.30101 −0.222447 −0.111224 0.993795i \(-0.535477\pi\)
−0.111224 + 0.993795i \(0.535477\pi\)
\(108\) 23.6516 2.27587
\(109\) −5.94139 −0.569082 −0.284541 0.958664i \(-0.591841\pi\)
−0.284541 + 0.958664i \(0.591841\pi\)
\(110\) −5.09678 −0.485959
\(111\) −28.9796 −2.75062
\(112\) 1.58489 0.149758
\(113\) 14.7339 1.38605 0.693027 0.720912i \(-0.256277\pi\)
0.693027 + 0.720912i \(0.256277\pi\)
\(114\) −7.37742 −0.690959
\(115\) 2.19731 0.204901
\(116\) 0.0620587 0.00576201
\(117\) −5.58462 −0.516298
\(118\) 2.55286 0.235010
\(119\) 4.90304 0.449461
\(120\) −5.06714 −0.462565
\(121\) −0.0422420 −0.00384018
\(122\) 24.7664 2.24224
\(123\) −15.1779 −1.36855
\(124\) −24.1451 −2.16830
\(125\) −6.48766 −0.580274
\(126\) 40.7268 3.62823
\(127\) 19.4666 1.72738 0.863689 0.504025i \(-0.168148\pi\)
0.863689 + 0.504025i \(0.168148\pi\)
\(128\) 17.1314 1.51422
\(129\) 11.2511 0.990600
\(130\) 1.53970 0.135040
\(131\) 5.62875 0.491786 0.245893 0.969297i \(-0.420919\pi\)
0.245893 + 0.969297i \(0.420919\pi\)
\(132\) 30.2918 2.63656
\(133\) −3.58416 −0.310786
\(134\) 17.8518 1.54216
\(135\) 5.15134 0.443357
\(136\) 3.86892 0.331757
\(137\) −3.05008 −0.260586 −0.130293 0.991476i \(-0.541592\pi\)
−0.130293 + 0.991476i \(0.541592\pi\)
\(138\) −21.4220 −1.82356
\(139\) 11.5692 0.981288 0.490644 0.871360i \(-0.336762\pi\)
0.490644 + 0.871360i \(0.336762\pi\)
\(140\) −6.84514 −0.578520
\(141\) −27.5535 −2.32042
\(142\) 10.5557 0.885816
\(143\) −3.31025 −0.276817
\(144\) −2.74713 −0.228927
\(145\) 0.0135165 0.00112248
\(146\) −4.81330 −0.398352
\(147\) 9.90551 0.816993
\(148\) −30.8913 −2.53925
\(149\) 17.5796 1.44018 0.720090 0.693881i \(-0.244101\pi\)
0.720090 + 0.693881i \(0.244101\pi\)
\(150\) 30.0903 2.45686
\(151\) −16.3004 −1.32651 −0.663255 0.748394i \(-0.730825\pi\)
−0.663255 + 0.748394i \(0.730825\pi\)
\(152\) −2.82821 −0.229398
\(153\) −8.49853 −0.687065
\(154\) 24.1406 1.94530
\(155\) −5.25884 −0.422400
\(156\) −9.15090 −0.732659
\(157\) 8.12772 0.648663 0.324331 0.945944i \(-0.394861\pi\)
0.324331 + 0.945944i \(0.394861\pi\)
\(158\) 17.8165 1.41740
\(159\) −18.1865 −1.44228
\(160\) 4.21625 0.333324
\(161\) −10.4074 −0.820220
\(162\) −12.2998 −0.966366
\(163\) −13.2504 −1.03785 −0.518927 0.854818i \(-0.673668\pi\)
−0.518927 + 0.854818i \(0.673668\pi\)
\(164\) −16.1792 −1.26338
\(165\) 6.59759 0.513621
\(166\) −13.1597 −1.02139
\(167\) −19.2393 −1.48878 −0.744392 0.667742i \(-0.767261\pi\)
−0.744392 + 0.667742i \(0.767261\pi\)
\(168\) 24.0002 1.85165
\(169\) 1.00000 0.0769231
\(170\) 2.34307 0.179705
\(171\) 6.21249 0.475081
\(172\) 11.9932 0.914475
\(173\) 8.19152 0.622790 0.311395 0.950281i \(-0.399204\pi\)
0.311395 + 0.950281i \(0.399204\pi\)
\(174\) −0.131775 −0.00998981
\(175\) 14.6187 1.10507
\(176\) −1.62834 −0.122741
\(177\) −3.30458 −0.248388
\(178\) 12.2075 0.914993
\(179\) 18.3696 1.37301 0.686506 0.727124i \(-0.259144\pi\)
0.686506 + 0.727124i \(0.259144\pi\)
\(180\) 11.8648 0.884350
\(181\) 12.9027 0.959051 0.479525 0.877528i \(-0.340809\pi\)
0.479525 + 0.877528i \(0.340809\pi\)
\(182\) −7.29267 −0.540569
\(183\) −32.0591 −2.36988
\(184\) −8.21235 −0.605423
\(185\) −6.72815 −0.494664
\(186\) 51.2694 3.75925
\(187\) −5.03746 −0.368375
\(188\) −29.3710 −2.14210
\(189\) −24.3990 −1.77476
\(190\) −1.71280 −0.124260
\(191\) −5.03605 −0.364395 −0.182198 0.983262i \(-0.558321\pi\)
−0.182198 + 0.983262i \(0.558321\pi\)
\(192\) −38.2225 −2.75847
\(193\) 6.61862 0.476419 0.238210 0.971214i \(-0.423440\pi\)
0.238210 + 0.971214i \(0.423440\pi\)
\(194\) −9.26730 −0.665353
\(195\) −1.99308 −0.142727
\(196\) 10.5589 0.754209
\(197\) −4.22401 −0.300948 −0.150474 0.988614i \(-0.548080\pi\)
−0.150474 + 0.988614i \(0.548080\pi\)
\(198\) −41.8433 −2.97367
\(199\) −17.5872 −1.24673 −0.623363 0.781932i \(-0.714234\pi\)
−0.623363 + 0.781932i \(0.714234\pi\)
\(200\) 11.5354 0.815678
\(201\) −23.1084 −1.62994
\(202\) −34.5022 −2.42757
\(203\) −0.0640198 −0.00449331
\(204\) −13.9256 −0.974988
\(205\) −3.52384 −0.246116
\(206\) −17.2790 −1.20388
\(207\) 18.0394 1.25382
\(208\) 0.491910 0.0341078
\(209\) 3.68242 0.254718
\(210\) 14.5349 1.00300
\(211\) −27.5650 −1.89765 −0.948826 0.315798i \(-0.897728\pi\)
−0.948826 + 0.315798i \(0.897728\pi\)
\(212\) −19.3861 −1.33145
\(213\) −13.6639 −0.936238
\(214\) 5.20823 0.356028
\(215\) 2.61214 0.178146
\(216\) −19.2529 −1.30999
\(217\) 24.9081 1.69087
\(218\) 13.4481 0.910818
\(219\) 6.23063 0.421027
\(220\) 7.03280 0.474151
\(221\) 1.52177 0.102366
\(222\) 65.5940 4.40238
\(223\) −10.3303 −0.691768 −0.345884 0.938277i \(-0.612421\pi\)
−0.345884 + 0.938277i \(0.612421\pi\)
\(224\) −19.9700 −1.33430
\(225\) −25.3389 −1.68926
\(226\) −33.3496 −2.21838
\(227\) −18.1916 −1.20742 −0.603709 0.797204i \(-0.706311\pi\)
−0.603709 + 0.797204i \(0.706311\pi\)
\(228\) 10.1797 0.674169
\(229\) 11.4352 0.755661 0.377831 0.925875i \(-0.376670\pi\)
0.377831 + 0.925875i \(0.376670\pi\)
\(230\) −4.97352 −0.327944
\(231\) −31.2490 −2.05603
\(232\) −0.0505171 −0.00331661
\(233\) 15.2638 0.999965 0.499982 0.866036i \(-0.333340\pi\)
0.499982 + 0.866036i \(0.333340\pi\)
\(234\) 12.6405 0.826337
\(235\) −6.39705 −0.417297
\(236\) −3.52257 −0.229300
\(237\) −23.0627 −1.49808
\(238\) −11.0978 −0.719364
\(239\) 4.99955 0.323394 0.161697 0.986840i \(-0.448303\pi\)
0.161697 + 0.986840i \(0.448303\pi\)
\(240\) −0.980414 −0.0632855
\(241\) 8.77763 0.565417 0.282709 0.959206i \(-0.408767\pi\)
0.282709 + 0.959206i \(0.408767\pi\)
\(242\) 0.0956128 0.00614623
\(243\) −6.79677 −0.436013
\(244\) −34.1739 −2.18776
\(245\) 2.29975 0.146925
\(246\) 34.3546 2.19037
\(247\) −1.11243 −0.0707822
\(248\) 19.6546 1.24807
\(249\) 17.0348 1.07953
\(250\) 14.6845 0.928730
\(251\) −12.4897 −0.788342 −0.394171 0.919037i \(-0.628968\pi\)
−0.394171 + 0.919037i \(0.628968\pi\)
\(252\) −56.1968 −3.54007
\(253\) 10.6927 0.672247
\(254\) −44.0617 −2.76468
\(255\) −3.03301 −0.189935
\(256\) −12.6853 −0.792833
\(257\) −4.48320 −0.279654 −0.139827 0.990176i \(-0.544655\pi\)
−0.139827 + 0.990176i \(0.544655\pi\)
\(258\) −25.4663 −1.58546
\(259\) 31.8674 1.98015
\(260\) −2.12455 −0.131759
\(261\) 0.110967 0.00686867
\(262\) −12.7404 −0.787106
\(263\) −10.1282 −0.624533 −0.312267 0.949995i \(-0.601088\pi\)
−0.312267 + 0.949995i \(0.601088\pi\)
\(264\) −24.6581 −1.51760
\(265\) −4.22232 −0.259375
\(266\) 8.11258 0.497414
\(267\) −15.8022 −0.967077
\(268\) −24.6328 −1.50469
\(269\) −31.0037 −1.89033 −0.945164 0.326597i \(-0.894098\pi\)
−0.945164 + 0.326597i \(0.894098\pi\)
\(270\) −11.6598 −0.709595
\(271\) 3.81442 0.231709 0.115855 0.993266i \(-0.463039\pi\)
0.115855 + 0.993266i \(0.463039\pi\)
\(272\) 0.748576 0.0453891
\(273\) 9.44007 0.571339
\(274\) 6.90372 0.417069
\(275\) −15.0195 −0.905710
\(276\) 29.5592 1.77925
\(277\) −8.61452 −0.517596 −0.258798 0.965931i \(-0.583326\pi\)
−0.258798 + 0.965931i \(0.583326\pi\)
\(278\) −26.1864 −1.57056
\(279\) −43.1737 −2.58474
\(280\) 5.57208 0.332996
\(281\) −22.3342 −1.33234 −0.666172 0.745798i \(-0.732068\pi\)
−0.666172 + 0.745798i \(0.732068\pi\)
\(282\) 62.3660 3.71384
\(283\) 9.83432 0.584590 0.292295 0.956328i \(-0.405581\pi\)
0.292295 + 0.956328i \(0.405581\pi\)
\(284\) −14.5653 −0.864291
\(285\) 2.21716 0.131333
\(286\) 7.49260 0.443047
\(287\) 16.6904 0.985205
\(288\) 34.6143 2.03967
\(289\) −14.6842 −0.863777
\(290\) −0.0305939 −0.00179654
\(291\) 11.9962 0.703227
\(292\) 6.64163 0.388672
\(293\) 0.481581 0.0281343 0.0140671 0.999901i \(-0.495522\pi\)
0.0140671 + 0.999901i \(0.495522\pi\)
\(294\) −22.4207 −1.30760
\(295\) −0.767219 −0.0446692
\(296\) 25.1461 1.46159
\(297\) 25.0679 1.45459
\(298\) −39.7907 −2.30501
\(299\) −3.23019 −0.186807
\(300\) −41.5201 −2.39717
\(301\) −12.3722 −0.713123
\(302\) 36.8953 2.12308
\(303\) 44.6618 2.56575
\(304\) −0.547215 −0.0313849
\(305\) −7.44311 −0.426191
\(306\) 19.2360 1.09965
\(307\) 31.4914 1.79731 0.898653 0.438660i \(-0.144547\pi\)
0.898653 + 0.438660i \(0.144547\pi\)
\(308\) −33.3104 −1.89803
\(309\) 22.3669 1.27241
\(310\) 11.9031 0.676053
\(311\) −8.55557 −0.485142 −0.242571 0.970134i \(-0.577991\pi\)
−0.242571 + 0.970134i \(0.577991\pi\)
\(312\) 7.44903 0.421718
\(313\) 3.07349 0.173724 0.0868620 0.996220i \(-0.472316\pi\)
0.0868620 + 0.996220i \(0.472316\pi\)
\(314\) −18.3967 −1.03819
\(315\) −12.2397 −0.689631
\(316\) −24.5840 −1.38296
\(317\) −9.56879 −0.537437 −0.268718 0.963219i \(-0.586600\pi\)
−0.268718 + 0.963219i \(0.586600\pi\)
\(318\) 41.1642 2.30838
\(319\) 0.0657749 0.00368269
\(320\) −8.87406 −0.496075
\(321\) −6.74185 −0.376293
\(322\) 23.5567 1.31277
\(323\) −1.69287 −0.0941936
\(324\) 16.9719 0.942884
\(325\) 4.53727 0.251682
\(326\) 29.9918 1.66109
\(327\) −17.4080 −0.962664
\(328\) 13.1702 0.727201
\(329\) 30.2992 1.67045
\(330\) −14.9333 −0.822053
\(331\) 3.20415 0.176116 0.0880580 0.996115i \(-0.471934\pi\)
0.0880580 + 0.996115i \(0.471934\pi\)
\(332\) 18.1585 0.996575
\(333\) −55.2364 −3.02694
\(334\) 43.5474 2.38281
\(335\) −5.36505 −0.293124
\(336\) 4.64366 0.253333
\(337\) 21.3352 1.16220 0.581102 0.813831i \(-0.302622\pi\)
0.581102 + 0.813831i \(0.302622\pi\)
\(338\) −2.26345 −0.123116
\(339\) 43.1698 2.34466
\(340\) −3.23309 −0.175339
\(341\) −25.5910 −1.38583
\(342\) −14.0617 −0.760369
\(343\) 11.6609 0.629627
\(344\) −9.76274 −0.526372
\(345\) 6.43802 0.346612
\(346\) −18.5411 −0.996778
\(347\) −12.3745 −0.664296 −0.332148 0.943227i \(-0.607773\pi\)
−0.332148 + 0.943227i \(0.607773\pi\)
\(348\) 0.181829 0.00974706
\(349\) −2.30594 −0.123434 −0.0617171 0.998094i \(-0.519658\pi\)
−0.0617171 + 0.998094i \(0.519658\pi\)
\(350\) −33.0888 −1.76867
\(351\) −7.57280 −0.404206
\(352\) 20.5175 1.09358
\(353\) 1.40002 0.0745153 0.0372577 0.999306i \(-0.488138\pi\)
0.0372577 + 0.999306i \(0.488138\pi\)
\(354\) 7.47977 0.397545
\(355\) −3.17234 −0.168370
\(356\) −16.8446 −0.892760
\(357\) 14.3657 0.760312
\(358\) −41.5789 −2.19751
\(359\) −9.27979 −0.489769 −0.244884 0.969552i \(-0.578750\pi\)
−0.244884 + 0.969552i \(0.578750\pi\)
\(360\) −9.65820 −0.509032
\(361\) −17.7625 −0.934868
\(362\) −29.2047 −1.53496
\(363\) −0.123767 −0.00649608
\(364\) 10.0628 0.527433
\(365\) 1.44656 0.0757162
\(366\) 72.5643 3.79300
\(367\) 4.55669 0.237857 0.118929 0.992903i \(-0.462054\pi\)
0.118929 + 0.992903i \(0.462054\pi\)
\(368\) −1.58896 −0.0828304
\(369\) −28.9298 −1.50603
\(370\) 15.2289 0.791711
\(371\) 19.9987 1.03828
\(372\) −70.7440 −3.66791
\(373\) 33.2759 1.72296 0.861480 0.507792i \(-0.169538\pi\)
0.861480 + 0.507792i \(0.169538\pi\)
\(374\) 11.4021 0.589586
\(375\) −19.0085 −0.981596
\(376\) 23.9086 1.23299
\(377\) −0.0198701 −0.00102336
\(378\) 55.2260 2.84052
\(379\) −29.2480 −1.50237 −0.751183 0.660094i \(-0.770517\pi\)
−0.751183 + 0.660094i \(0.770517\pi\)
\(380\) 2.36341 0.121241
\(381\) 57.0361 2.92205
\(382\) 11.3989 0.583216
\(383\) 0.595444 0.0304258 0.0152129 0.999884i \(-0.495157\pi\)
0.0152129 + 0.999884i \(0.495157\pi\)
\(384\) 50.1942 2.56146
\(385\) −7.25503 −0.369751
\(386\) −14.9810 −0.762511
\(387\) 21.4450 1.09011
\(388\) 12.7875 0.649186
\(389\) −0.417898 −0.0211883 −0.0105941 0.999944i \(-0.503372\pi\)
−0.0105941 + 0.999944i \(0.503372\pi\)
\(390\) 4.51124 0.228436
\(391\) −4.91563 −0.248594
\(392\) −8.59519 −0.434123
\(393\) 16.4920 0.831909
\(394\) 9.56086 0.481669
\(395\) −5.35443 −0.269411
\(396\) 57.7375 2.90142
\(397\) −2.78884 −0.139968 −0.0699839 0.997548i \(-0.522295\pi\)
−0.0699839 + 0.997548i \(0.522295\pi\)
\(398\) 39.8079 1.99539
\(399\) −10.5014 −0.525728
\(400\) 2.23193 0.111596
\(401\) 15.7666 0.787346 0.393673 0.919250i \(-0.371204\pi\)
0.393673 + 0.919250i \(0.371204\pi\)
\(402\) 52.3049 2.60873
\(403\) 7.73083 0.385100
\(404\) 47.6079 2.36858
\(405\) 3.69650 0.183681
\(406\) 0.144906 0.00719156
\(407\) −32.7411 −1.62292
\(408\) 11.3357 0.561203
\(409\) 23.4720 1.16062 0.580308 0.814397i \(-0.302932\pi\)
0.580308 + 0.814397i \(0.302932\pi\)
\(410\) 7.97605 0.393909
\(411\) −8.93659 −0.440809
\(412\) 23.8424 1.17463
\(413\) 3.63388 0.178812
\(414\) −40.8313 −2.00675
\(415\) 3.95493 0.194140
\(416\) −6.19816 −0.303890
\(417\) 33.8973 1.65996
\(418\) −8.33499 −0.407678
\(419\) −9.97494 −0.487308 −0.243654 0.969862i \(-0.578346\pi\)
−0.243654 + 0.969862i \(0.578346\pi\)
\(420\) −20.0559 −0.978629
\(421\) 7.59287 0.370054 0.185027 0.982733i \(-0.440763\pi\)
0.185027 + 0.982733i \(0.440763\pi\)
\(422\) 62.3921 3.03720
\(423\) −52.5181 −2.55352
\(424\) 15.7807 0.766380
\(425\) 6.90470 0.334927
\(426\) 30.9277 1.49845
\(427\) 35.2538 1.70605
\(428\) −7.18658 −0.347376
\(429\) −9.69887 −0.468266
\(430\) −5.91246 −0.285124
\(431\) −2.04736 −0.0986180 −0.0493090 0.998784i \(-0.515702\pi\)
−0.0493090 + 0.998784i \(0.515702\pi\)
\(432\) −3.72514 −0.179226
\(433\) 18.4577 0.887023 0.443511 0.896269i \(-0.353733\pi\)
0.443511 + 0.896269i \(0.353733\pi\)
\(434\) −56.3784 −2.70625
\(435\) 0.0396026 0.00189880
\(436\) −18.5563 −0.888686
\(437\) 3.59336 0.171894
\(438\) −14.1027 −0.673855
\(439\) 6.53771 0.312028 0.156014 0.987755i \(-0.450136\pi\)
0.156014 + 0.987755i \(0.450136\pi\)
\(440\) −5.72484 −0.272921
\(441\) 18.8803 0.899064
\(442\) −3.44447 −0.163837
\(443\) −7.98030 −0.379155 −0.189578 0.981866i \(-0.560712\pi\)
−0.189578 + 0.981866i \(0.560712\pi\)
\(444\) −90.5099 −4.29541
\(445\) −3.66877 −0.173916
\(446\) 23.3821 1.10718
\(447\) 51.5075 2.43622
\(448\) 42.0314 1.98579
\(449\) 15.9321 0.751883 0.375942 0.926643i \(-0.377319\pi\)
0.375942 + 0.926643i \(0.377319\pi\)
\(450\) 57.3535 2.70367
\(451\) −17.1480 −0.807468
\(452\) 46.0175 2.16448
\(453\) −47.7595 −2.24394
\(454\) 41.1759 1.93248
\(455\) 2.19169 0.102748
\(456\) −8.28652 −0.388052
\(457\) 26.8148 1.25435 0.627173 0.778880i \(-0.284212\pi\)
0.627173 + 0.778880i \(0.284212\pi\)
\(458\) −25.8831 −1.20944
\(459\) −11.5241 −0.537899
\(460\) 6.86271 0.319975
\(461\) −28.2264 −1.31464 −0.657318 0.753614i \(-0.728309\pi\)
−0.657318 + 0.753614i \(0.728309\pi\)
\(462\) 70.7307 3.29069
\(463\) −1.00000 −0.0464739
\(464\) −0.00977428 −0.000453760 0
\(465\) −15.4081 −0.714535
\(466\) −34.5489 −1.60045
\(467\) −6.81840 −0.315518 −0.157759 0.987478i \(-0.550427\pi\)
−0.157759 + 0.987478i \(0.550427\pi\)
\(468\) −17.4420 −0.806258
\(469\) 25.4112 1.17338
\(470\) 14.4794 0.667886
\(471\) 23.8138 1.09728
\(472\) 2.86744 0.131985
\(473\) 12.7114 0.584471
\(474\) 52.2014 2.39769
\(475\) −5.04739 −0.231590
\(476\) 15.3133 0.701884
\(477\) −34.6642 −1.58717
\(478\) −11.3163 −0.517593
\(479\) −6.04125 −0.276032 −0.138016 0.990430i \(-0.544072\pi\)
−0.138016 + 0.990430i \(0.544072\pi\)
\(480\) 12.3534 0.563853
\(481\) 9.89082 0.450982
\(482\) −19.8678 −0.904952
\(483\) −30.4933 −1.38749
\(484\) −0.131931 −0.00599688
\(485\) 2.78513 0.126466
\(486\) 15.3842 0.697840
\(487\) 13.3627 0.605522 0.302761 0.953067i \(-0.402092\pi\)
0.302761 + 0.953067i \(0.402092\pi\)
\(488\) 27.8183 1.25927
\(489\) −38.8231 −1.75564
\(490\) −5.20537 −0.235155
\(491\) −24.2079 −1.09249 −0.546243 0.837627i \(-0.683942\pi\)
−0.546243 + 0.837627i \(0.683942\pi\)
\(492\) −47.4042 −2.13715
\(493\) −0.0302378 −0.00136184
\(494\) 2.51793 0.113287
\(495\) 12.5753 0.565217
\(496\) 3.80287 0.170754
\(497\) 15.0256 0.673988
\(498\) −38.5574 −1.72780
\(499\) −5.66497 −0.253599 −0.126799 0.991928i \(-0.540470\pi\)
−0.126799 + 0.991928i \(0.540470\pi\)
\(500\) −20.2624 −0.906163
\(501\) −56.3703 −2.51844
\(502\) 28.2698 1.26174
\(503\) −25.3285 −1.12934 −0.564671 0.825316i \(-0.690997\pi\)
−0.564671 + 0.825316i \(0.690997\pi\)
\(504\) 45.7454 2.03766
\(505\) 10.3691 0.461417
\(506\) −24.2025 −1.07593
\(507\) 2.92995 0.130124
\(508\) 60.7985 2.69750
\(509\) 6.13399 0.271884 0.135942 0.990717i \(-0.456594\pi\)
0.135942 + 0.990717i \(0.456594\pi\)
\(510\) 6.86509 0.303991
\(511\) −6.85151 −0.303093
\(512\) −5.55017 −0.245285
\(513\) 8.42421 0.371938
\(514\) 10.1475 0.447588
\(515\) 5.19290 0.228826
\(516\) 35.1396 1.54693
\(517\) −31.1298 −1.36909
\(518\) −72.1305 −3.16923
\(519\) 24.0008 1.05352
\(520\) 1.72943 0.0758405
\(521\) 26.5921 1.16502 0.582510 0.812823i \(-0.302071\pi\)
0.582510 + 0.812823i \(0.302071\pi\)
\(522\) −0.251168 −0.0109933
\(523\) 1.77660 0.0776854 0.0388427 0.999245i \(-0.487633\pi\)
0.0388427 + 0.999245i \(0.487633\pi\)
\(524\) 17.5799 0.767980
\(525\) 42.8322 1.86935
\(526\) 22.9248 0.999568
\(527\) 11.7646 0.512473
\(528\) −4.77097 −0.207630
\(529\) −12.5659 −0.546342
\(530\) 9.55704 0.415131
\(531\) −6.29868 −0.273339
\(532\) −11.1941 −0.485328
\(533\) 5.18027 0.224383
\(534\) 35.7675 1.54781
\(535\) −1.56525 −0.0676715
\(536\) 20.0516 0.866097
\(537\) 53.8222 2.32260
\(538\) 70.1754 3.02548
\(539\) 11.1912 0.482040
\(540\) 16.0888 0.692352
\(541\) 35.1097 1.50948 0.754741 0.656022i \(-0.227762\pi\)
0.754741 + 0.656022i \(0.227762\pi\)
\(542\) −8.63376 −0.370852
\(543\) 37.8043 1.62234
\(544\) −9.43220 −0.404402
\(545\) −4.04159 −0.173123
\(546\) −21.3672 −0.914431
\(547\) 31.7831 1.35895 0.679474 0.733699i \(-0.262208\pi\)
0.679474 + 0.733699i \(0.262208\pi\)
\(548\) −9.52609 −0.406934
\(549\) −61.1061 −2.60794
\(550\) 33.9960 1.44959
\(551\) 0.0221041 0.000941664 0
\(552\) −24.0618 −1.02414
\(553\) 25.3609 1.07846
\(554\) 19.4986 0.828415
\(555\) −19.7132 −0.836777
\(556\) 36.1333 1.53239
\(557\) −13.4753 −0.570968 −0.285484 0.958383i \(-0.592154\pi\)
−0.285484 + 0.958383i \(0.592154\pi\)
\(558\) 97.7217 4.13689
\(559\) −3.84001 −0.162415
\(560\) 1.07811 0.0455586
\(561\) −14.7595 −0.623147
\(562\) 50.5524 2.13242
\(563\) 3.92036 0.165223 0.0826117 0.996582i \(-0.473674\pi\)
0.0826117 + 0.996582i \(0.473674\pi\)
\(564\) −86.0557 −3.62360
\(565\) 10.0227 0.421656
\(566\) −22.2595 −0.935638
\(567\) −17.5082 −0.735277
\(568\) 11.8565 0.497486
\(569\) −8.68954 −0.364284 −0.182142 0.983272i \(-0.558303\pi\)
−0.182142 + 0.983272i \(0.558303\pi\)
\(570\) −5.01844 −0.210199
\(571\) −33.5234 −1.40291 −0.701456 0.712713i \(-0.747466\pi\)
−0.701456 + 0.712713i \(0.747466\pi\)
\(572\) −10.3387 −0.432281
\(573\) −14.7554 −0.616414
\(574\) −37.7780 −1.57682
\(575\) −14.6563 −0.611208
\(576\) −72.8537 −3.03557
\(577\) −9.89383 −0.411885 −0.205943 0.978564i \(-0.566026\pi\)
−0.205943 + 0.978564i \(0.566026\pi\)
\(578\) 33.2370 1.38248
\(579\) 19.3923 0.805914
\(580\) 0.0422150 0.00175288
\(581\) −18.7323 −0.777146
\(582\) −27.1527 −1.12552
\(583\) −20.5470 −0.850970
\(584\) −5.40643 −0.223720
\(585\) −3.79889 −0.157065
\(586\) −1.09004 −0.0450290
\(587\) 18.5916 0.767356 0.383678 0.923467i \(-0.374657\pi\)
0.383678 + 0.923467i \(0.374657\pi\)
\(588\) 30.9372 1.27583
\(589\) −8.60000 −0.354357
\(590\) 1.73657 0.0714933
\(591\) −12.3762 −0.509087
\(592\) 4.86539 0.199966
\(593\) −7.01602 −0.288113 −0.144057 0.989569i \(-0.546015\pi\)
−0.144057 + 0.989569i \(0.546015\pi\)
\(594\) −56.7400 −2.32807
\(595\) 3.33525 0.136732
\(596\) 54.9052 2.24900
\(597\) −51.5298 −2.10897
\(598\) 7.31139 0.298985
\(599\) −18.7944 −0.767917 −0.383958 0.923350i \(-0.625439\pi\)
−0.383958 + 0.923350i \(0.625439\pi\)
\(600\) 33.7982 1.37981
\(601\) −42.5969 −1.73756 −0.868782 0.495195i \(-0.835097\pi\)
−0.868782 + 0.495195i \(0.835097\pi\)
\(602\) 28.0040 1.14136
\(603\) −44.0457 −1.79368
\(604\) −50.9099 −2.07150
\(605\) −0.0287348 −0.00116824
\(606\) −101.090 −4.10650
\(607\) −23.9555 −0.972323 −0.486162 0.873869i \(-0.661603\pi\)
−0.486162 + 0.873869i \(0.661603\pi\)
\(608\) 6.89501 0.279630
\(609\) −0.187575 −0.00760092
\(610\) 16.8472 0.682121
\(611\) 9.40407 0.380448
\(612\) −26.5428 −1.07293
\(613\) −38.3699 −1.54974 −0.774872 0.632118i \(-0.782186\pi\)
−0.774872 + 0.632118i \(0.782186\pi\)
\(614\) −71.2792 −2.87660
\(615\) −10.3247 −0.416331
\(616\) 27.1153 1.09251
\(617\) 44.7158 1.80019 0.900095 0.435694i \(-0.143497\pi\)
0.900095 + 0.435694i \(0.143497\pi\)
\(618\) −50.6265 −2.03650
\(619\) 4.28944 0.172407 0.0862035 0.996278i \(-0.472526\pi\)
0.0862035 + 0.996278i \(0.472526\pi\)
\(620\) −16.4245 −0.659625
\(621\) 24.4616 0.981611
\(622\) 19.3651 0.776472
\(623\) 17.3769 0.696189
\(624\) 1.44127 0.0576970
\(625\) 18.2732 0.730927
\(626\) −6.95671 −0.278046
\(627\) 10.7893 0.430884
\(628\) 25.3847 1.01296
\(629\) 15.0516 0.600146
\(630\) 27.7041 1.10376
\(631\) −26.9827 −1.07416 −0.537081 0.843531i \(-0.680473\pi\)
−0.537081 + 0.843531i \(0.680473\pi\)
\(632\) 20.0119 0.796032
\(633\) −80.7641 −3.21009
\(634\) 21.6585 0.860170
\(635\) 13.2420 0.525492
\(636\) −56.8005 −2.25228
\(637\) −3.38078 −0.133951
\(638\) −0.148879 −0.00589416
\(639\) −26.0441 −1.03029
\(640\) 11.6535 0.460646
\(641\) −43.0590 −1.70073 −0.850363 0.526196i \(-0.823618\pi\)
−0.850363 + 0.526196i \(0.823618\pi\)
\(642\) 15.2599 0.602259
\(643\) −18.5205 −0.730378 −0.365189 0.930933i \(-0.618996\pi\)
−0.365189 + 0.930933i \(0.618996\pi\)
\(644\) −32.5047 −1.28087
\(645\) 7.65344 0.301354
\(646\) 3.83173 0.150757
\(647\) 38.2908 1.50537 0.752683 0.658383i \(-0.228759\pi\)
0.752683 + 0.658383i \(0.228759\pi\)
\(648\) −13.8155 −0.542724
\(649\) −3.73351 −0.146553
\(650\) −10.2699 −0.402819
\(651\) 72.9796 2.86029
\(652\) −41.3841 −1.62073
\(653\) −41.0021 −1.60454 −0.802268 0.596964i \(-0.796374\pi\)
−0.802268 + 0.596964i \(0.796374\pi\)
\(654\) 39.4022 1.54075
\(655\) 3.82891 0.149608
\(656\) 2.54823 0.0994915
\(657\) 11.8759 0.463321
\(658\) −68.5808 −2.67356
\(659\) 28.4933 1.10994 0.554970 0.831870i \(-0.312730\pi\)
0.554970 + 0.831870i \(0.312730\pi\)
\(660\) 20.6058 0.802078
\(661\) −5.34830 −0.208025 −0.104012 0.994576i \(-0.533168\pi\)
−0.104012 + 0.994576i \(0.533168\pi\)
\(662\) −7.25245 −0.281874
\(663\) 4.45873 0.173163
\(664\) −14.7814 −0.573628
\(665\) −2.43810 −0.0945454
\(666\) 125.025 4.84463
\(667\) 0.0641842 0.00248522
\(668\) −60.0888 −2.32491
\(669\) −30.2673 −1.17020
\(670\) 12.1435 0.469146
\(671\) −36.2203 −1.39827
\(672\) −58.5111 −2.25711
\(673\) −27.1439 −1.04632 −0.523161 0.852234i \(-0.675247\pi\)
−0.523161 + 0.852234i \(0.675247\pi\)
\(674\) −48.2913 −1.86011
\(675\) −34.3599 −1.32251
\(676\) 3.12323 0.120124
\(677\) 16.6676 0.640586 0.320293 0.947318i \(-0.396219\pi\)
0.320293 + 0.947318i \(0.396219\pi\)
\(678\) −97.7128 −3.75264
\(679\) −13.1916 −0.506246
\(680\) 2.63180 0.100925
\(681\) −53.3005 −2.04248
\(682\) 57.9240 2.21802
\(683\) 24.9502 0.954693 0.477346 0.878715i \(-0.341599\pi\)
0.477346 + 0.878715i \(0.341599\pi\)
\(684\) 19.4030 0.741893
\(685\) −2.07479 −0.0792738
\(686\) −26.3938 −1.00772
\(687\) 33.5047 1.27828
\(688\) −1.88894 −0.0720152
\(689\) 6.20709 0.236471
\(690\) −14.5722 −0.554753
\(691\) 37.4324 1.42400 0.711998 0.702182i \(-0.247791\pi\)
0.711998 + 0.702182i \(0.247791\pi\)
\(692\) 25.5840 0.972557
\(693\) −59.5620 −2.26257
\(694\) 28.0090 1.06321
\(695\) 7.86987 0.298521
\(696\) −0.148013 −0.00561041
\(697\) 7.88321 0.298598
\(698\) 5.21939 0.197557
\(699\) 44.7222 1.69155
\(700\) 45.6576 1.72569
\(701\) 27.0410 1.02132 0.510662 0.859782i \(-0.329400\pi\)
0.510662 + 0.859782i \(0.329400\pi\)
\(702\) 17.1407 0.646934
\(703\) −11.0028 −0.414980
\(704\) −43.1836 −1.62754
\(705\) −18.7430 −0.705904
\(706\) −3.16887 −0.119262
\(707\) −49.1123 −1.84706
\(708\) −10.3210 −0.387885
\(709\) −16.7139 −0.627703 −0.313851 0.949472i \(-0.601619\pi\)
−0.313851 + 0.949472i \(0.601619\pi\)
\(710\) 7.18044 0.269477
\(711\) −43.9585 −1.64857
\(712\) 13.7118 0.513872
\(713\) −24.9721 −0.935211
\(714\) −32.5160 −1.21688
\(715\) −2.25177 −0.0842115
\(716\) 57.3726 2.14411
\(717\) 14.6484 0.547056
\(718\) 21.0044 0.783877
\(719\) 0.727067 0.0271150 0.0135575 0.999908i \(-0.495684\pi\)
0.0135575 + 0.999908i \(0.495684\pi\)
\(720\) −1.86871 −0.0696428
\(721\) −24.5958 −0.915995
\(722\) 40.2046 1.49626
\(723\) 25.7180 0.956464
\(724\) 40.2981 1.49767
\(725\) −0.0901559 −0.00334831
\(726\) 0.280141 0.0103970
\(727\) −29.9195 −1.10965 −0.554826 0.831966i \(-0.687215\pi\)
−0.554826 + 0.831966i \(0.687215\pi\)
\(728\) −8.19132 −0.303591
\(729\) −36.2165 −1.34135
\(730\) −3.27421 −0.121184
\(731\) −5.84364 −0.216135
\(732\) −100.128 −3.70083
\(733\) 31.8668 1.17703 0.588514 0.808487i \(-0.299713\pi\)
0.588514 + 0.808487i \(0.299713\pi\)
\(734\) −10.3139 −0.380692
\(735\) 6.73815 0.248540
\(736\) 20.0212 0.737993
\(737\) −26.1078 −0.961694
\(738\) 65.4814 2.41040
\(739\) −4.89026 −0.179891 −0.0899455 0.995947i \(-0.528669\pi\)
−0.0899455 + 0.995947i \(0.528669\pi\)
\(740\) −21.0135 −0.772473
\(741\) −3.25936 −0.119736
\(742\) −45.2663 −1.66178
\(743\) −9.94066 −0.364687 −0.182344 0.983235i \(-0.558368\pi\)
−0.182344 + 0.983235i \(0.558368\pi\)
\(744\) 57.5871 2.11125
\(745\) 11.9584 0.438122
\(746\) −75.3184 −2.75760
\(747\) 32.4690 1.18798
\(748\) −15.7331 −0.575260
\(749\) 7.41368 0.270890
\(750\) 43.0249 1.57105
\(751\) 15.9747 0.582925 0.291462 0.956582i \(-0.405858\pi\)
0.291462 + 0.956582i \(0.405858\pi\)
\(752\) 4.62595 0.168691
\(753\) −36.5942 −1.33357
\(754\) 0.0449750 0.00163789
\(755\) −11.0882 −0.403542
\(756\) −76.2035 −2.77150
\(757\) 9.47230 0.344277 0.172138 0.985073i \(-0.444932\pi\)
0.172138 + 0.985073i \(0.444932\pi\)
\(758\) 66.2014 2.40454
\(759\) 31.3292 1.13718
\(760\) −1.92387 −0.0697860
\(761\) −42.5489 −1.54240 −0.771198 0.636595i \(-0.780342\pi\)
−0.771198 + 0.636595i \(0.780342\pi\)
\(762\) −129.099 −4.67675
\(763\) 19.1427 0.693012
\(764\) −15.7287 −0.569045
\(765\) −5.78106 −0.209015
\(766\) −1.34776 −0.0486966
\(767\) 1.12786 0.0407247
\(768\) −37.1674 −1.34116
\(769\) −21.9542 −0.791687 −0.395844 0.918318i \(-0.629548\pi\)
−0.395844 + 0.918318i \(0.629548\pi\)
\(770\) 16.4214 0.591788
\(771\) −13.1355 −0.473065
\(772\) 20.6715 0.743982
\(773\) −38.0044 −1.36692 −0.683462 0.729986i \(-0.739526\pi\)
−0.683462 + 0.729986i \(0.739526\pi\)
\(774\) −48.5398 −1.74473
\(775\) 35.0768 1.26000
\(776\) −10.4093 −0.373671
\(777\) 93.3700 3.34963
\(778\) 0.945892 0.0339119
\(779\) −5.76269 −0.206470
\(780\) −6.22483 −0.222885
\(781\) −15.4375 −0.552397
\(782\) 11.1263 0.397875
\(783\) 0.150472 0.00537744
\(784\) −1.66304 −0.0593942
\(785\) 5.52882 0.197332
\(786\) −37.3288 −1.33147
\(787\) −7.41197 −0.264208 −0.132104 0.991236i \(-0.542173\pi\)
−0.132104 + 0.991236i \(0.542173\pi\)
\(788\) −13.1925 −0.469965
\(789\) −29.6752 −1.05647
\(790\) 12.1195 0.431193
\(791\) −47.4716 −1.68790
\(792\) −46.9995 −1.67005
\(793\) 10.9419 0.388557
\(794\) 6.31241 0.224019
\(795\) −12.3712 −0.438761
\(796\) −54.9289 −1.94690
\(797\) −20.2593 −0.717623 −0.358811 0.933410i \(-0.616818\pi\)
−0.358811 + 0.933410i \(0.616818\pi\)
\(798\) 23.7695 0.841430
\(799\) 14.3109 0.506282
\(800\) −28.1227 −0.994288
\(801\) −30.1196 −1.06422
\(802\) −35.6870 −1.26015
\(803\) 7.03935 0.248413
\(804\) −72.1729 −2.54534
\(805\) −7.07957 −0.249522
\(806\) −17.4984 −0.616354
\(807\) −90.8393 −3.19769
\(808\) −38.7538 −1.36336
\(809\) −30.8077 −1.08314 −0.541570 0.840655i \(-0.682170\pi\)
−0.541570 + 0.840655i \(0.682170\pi\)
\(810\) −8.36687 −0.293982
\(811\) 54.5747 1.91638 0.958189 0.286135i \(-0.0923707\pi\)
0.958189 + 0.286135i \(0.0923707\pi\)
\(812\) −0.199948 −0.00701681
\(813\) 11.1761 0.391962
\(814\) 74.1080 2.59748
\(815\) −9.01351 −0.315729
\(816\) 2.19329 0.0767805
\(817\) 4.27174 0.149449
\(818\) −53.1278 −1.85757
\(819\) 17.9932 0.628733
\(820\) −11.0058 −0.384338
\(821\) 44.9502 1.56877 0.784386 0.620273i \(-0.212978\pi\)
0.784386 + 0.620273i \(0.212978\pi\)
\(822\) 20.2276 0.705517
\(823\) 15.1747 0.528956 0.264478 0.964392i \(-0.414800\pi\)
0.264478 + 0.964392i \(0.414800\pi\)
\(824\) −19.4082 −0.676116
\(825\) −44.0064 −1.53211
\(826\) −8.22513 −0.286189
\(827\) 16.7141 0.581206 0.290603 0.956844i \(-0.406144\pi\)
0.290603 + 0.956844i \(0.406144\pi\)
\(828\) 56.3411 1.95799
\(829\) 8.89578 0.308963 0.154482 0.987996i \(-0.450629\pi\)
0.154482 + 0.987996i \(0.450629\pi\)
\(830\) −8.95181 −0.310722
\(831\) −25.2401 −0.875570
\(832\) 13.0454 0.452269
\(833\) −5.14478 −0.178256
\(834\) −76.7249 −2.65677
\(835\) −13.0874 −0.452909
\(836\) 11.5010 0.397771
\(837\) −58.5440 −2.02358
\(838\) 22.5778 0.779938
\(839\) 51.4877 1.77755 0.888777 0.458340i \(-0.151556\pi\)
0.888777 + 0.458340i \(0.151556\pi\)
\(840\) 16.3259 0.563298
\(841\) −28.9996 −0.999986
\(842\) −17.1861 −0.592273
\(843\) −65.4380 −2.25380
\(844\) −86.0917 −2.96340
\(845\) 0.680242 0.0234010
\(846\) 118.872 4.08692
\(847\) 0.136100 0.00467646
\(848\) 3.05333 0.104852
\(849\) 28.8141 0.988897
\(850\) −15.6285 −0.536052
\(851\) −31.9492 −1.09521
\(852\) −42.6756 −1.46204
\(853\) 0.272071 0.00931553 0.00465776 0.999989i \(-0.498517\pi\)
0.00465776 + 0.999989i \(0.498517\pi\)
\(854\) −79.7954 −2.73054
\(855\) 4.22600 0.144526
\(856\) 5.85003 0.199950
\(857\) −35.1209 −1.19971 −0.599853 0.800110i \(-0.704774\pi\)
−0.599853 + 0.800110i \(0.704774\pi\)
\(858\) 21.9530 0.749462
\(859\) 40.4413 1.37984 0.689919 0.723886i \(-0.257646\pi\)
0.689919 + 0.723886i \(0.257646\pi\)
\(860\) 8.15831 0.278196
\(861\) 48.9022 1.66658
\(862\) 4.63411 0.157838
\(863\) −13.2307 −0.450378 −0.225189 0.974315i \(-0.572300\pi\)
−0.225189 + 0.974315i \(0.572300\pi\)
\(864\) 46.9374 1.59684
\(865\) 5.57222 0.189461
\(866\) −41.7783 −1.41968
\(867\) −43.0240 −1.46117
\(868\) 77.7937 2.64049
\(869\) −26.0562 −0.883895
\(870\) −0.0896387 −0.00303904
\(871\) 7.88697 0.267240
\(872\) 15.1052 0.511528
\(873\) 22.8652 0.773870
\(874\) −8.13341 −0.275117
\(875\) 20.9027 0.706641
\(876\) 19.4597 0.657481
\(877\) 16.4901 0.556830 0.278415 0.960461i \(-0.410191\pi\)
0.278415 + 0.960461i \(0.410191\pi\)
\(878\) −14.7978 −0.499402
\(879\) 1.41101 0.0475921
\(880\) −1.10767 −0.0373395
\(881\) −42.5574 −1.43380 −0.716898 0.697179i \(-0.754438\pi\)
−0.716898 + 0.697179i \(0.754438\pi\)
\(882\) −42.7348 −1.43896
\(883\) 39.9087 1.34304 0.671518 0.740989i \(-0.265643\pi\)
0.671518 + 0.740989i \(0.265643\pi\)
\(884\) 4.75285 0.159856
\(885\) −2.24792 −0.0755629
\(886\) 18.0630 0.606840
\(887\) 46.3137 1.55506 0.777530 0.628845i \(-0.216472\pi\)
0.777530 + 0.628845i \(0.216472\pi\)
\(888\) 73.6770 2.47244
\(889\) −62.7197 −2.10355
\(890\) 8.30408 0.278353
\(891\) 17.9882 0.602628
\(892\) −32.2638 −1.08027
\(893\) −10.4614 −0.350076
\(894\) −116.585 −3.89918
\(895\) 12.4958 0.417689
\(896\) −55.1961 −1.84397
\(897\) −9.46431 −0.316004
\(898\) −36.0616 −1.20339
\(899\) −0.153612 −0.00512325
\(900\) −79.1392 −2.63797
\(901\) 9.44579 0.314685
\(902\) 38.8137 1.29236
\(903\) −36.2500 −1.20632
\(904\) −37.4592 −1.24587
\(905\) 8.77697 0.291756
\(906\) 108.101 3.59143
\(907\) −1.75416 −0.0582459 −0.0291230 0.999576i \(-0.509271\pi\)
−0.0291230 + 0.999576i \(0.509271\pi\)
\(908\) −56.8165 −1.88552
\(909\) 85.1273 2.82350
\(910\) −4.96078 −0.164448
\(911\) 41.3414 1.36970 0.684851 0.728683i \(-0.259867\pi\)
0.684851 + 0.728683i \(0.259867\pi\)
\(912\) −1.60331 −0.0530910
\(913\) 19.2458 0.636944
\(914\) −60.6942 −2.00758
\(915\) −21.8080 −0.720949
\(916\) 35.7148 1.18005
\(917\) −18.1354 −0.598883
\(918\) 26.0843 0.860910
\(919\) 2.02434 0.0667768 0.0333884 0.999442i \(-0.489370\pi\)
0.0333884 + 0.999442i \(0.489370\pi\)
\(920\) −5.58639 −0.184178
\(921\) 92.2681 3.04034
\(922\) 63.8892 2.10408
\(923\) 4.66354 0.153502
\(924\) −97.5977 −3.21073
\(925\) 44.8773 1.47556
\(926\) 2.26345 0.0743817
\(927\) 42.6324 1.40023
\(928\) 0.123158 0.00404286
\(929\) 12.8983 0.423179 0.211590 0.977359i \(-0.432136\pi\)
0.211590 + 0.977359i \(0.432136\pi\)
\(930\) 34.8756 1.14362
\(931\) 3.76087 0.123258
\(932\) 47.6723 1.56156
\(933\) −25.0674 −0.820670
\(934\) 15.4331 0.504988
\(935\) −3.42669 −0.112065
\(936\) 14.1982 0.464082
\(937\) −2.31855 −0.0757437 −0.0378719 0.999283i \(-0.512058\pi\)
−0.0378719 + 0.999283i \(0.512058\pi\)
\(938\) −57.5171 −1.87800
\(939\) 9.00518 0.293873
\(940\) −19.9794 −0.651657
\(941\) −28.4465 −0.927328 −0.463664 0.886011i \(-0.653466\pi\)
−0.463664 + 0.886011i \(0.653466\pi\)
\(942\) −53.9015 −1.75621
\(943\) −16.7333 −0.544911
\(944\) 0.554806 0.0180574
\(945\) −16.5972 −0.539908
\(946\) −28.7717 −0.935448
\(947\) 55.7179 1.81059 0.905294 0.424785i \(-0.139650\pi\)
0.905294 + 0.424785i \(0.139650\pi\)
\(948\) −72.0300 −2.33943
\(949\) −2.12653 −0.0690301
\(950\) 11.4245 0.370661
\(951\) −28.0361 −0.909133
\(952\) −12.4653 −0.404004
\(953\) 35.7883 1.15930 0.579648 0.814867i \(-0.303190\pi\)
0.579648 + 0.814867i \(0.303190\pi\)
\(954\) 78.4609 2.54026
\(955\) −3.42573 −0.110854
\(956\) 15.6147 0.505016
\(957\) 0.192717 0.00622967
\(958\) 13.6741 0.441790
\(959\) 9.82712 0.317334
\(960\) −26.0006 −0.839164
\(961\) 28.7657 0.927925
\(962\) −22.3874 −0.721799
\(963\) −12.8503 −0.414094
\(964\) 27.4145 0.882963
\(965\) 4.50227 0.144933
\(966\) 69.0201 2.22069
\(967\) 14.1750 0.455837 0.227918 0.973680i \(-0.426808\pi\)
0.227918 + 0.973680i \(0.426808\pi\)
\(968\) 0.107395 0.00345180
\(969\) −4.96002 −0.159339
\(970\) −6.30401 −0.202410
\(971\) 20.7926 0.667267 0.333633 0.942703i \(-0.391725\pi\)
0.333633 + 0.942703i \(0.391725\pi\)
\(972\) −21.2278 −0.680883
\(973\) −37.2751 −1.19499
\(974\) −30.2459 −0.969140
\(975\) 13.2940 0.425748
\(976\) 5.38241 0.172287
\(977\) 14.2968 0.457395 0.228697 0.973498i \(-0.426553\pi\)
0.228697 + 0.973498i \(0.426553\pi\)
\(978\) 87.8744 2.80991
\(979\) −17.8532 −0.570592
\(980\) 7.18263 0.229441
\(981\) −33.1804 −1.05937
\(982\) 54.7934 1.74853
\(983\) −13.4566 −0.429199 −0.214599 0.976702i \(-0.568845\pi\)
−0.214599 + 0.976702i \(0.568845\pi\)
\(984\) 38.5880 1.23014
\(985\) −2.87335 −0.0915526
\(986\) 0.0684418 0.00217963
\(987\) 88.7751 2.82574
\(988\) −3.47437 −0.110534
\(989\) 12.4040 0.394424
\(990\) −28.4636 −0.904632
\(991\) −1.60509 −0.0509874 −0.0254937 0.999675i \(-0.508116\pi\)
−0.0254937 + 0.999675i \(0.508116\pi\)
\(992\) −47.9169 −1.52136
\(993\) 9.38800 0.297919
\(994\) −34.0097 −1.07872
\(995\) −11.9636 −0.379271
\(996\) 53.2034 1.68581
\(997\) −60.8447 −1.92697 −0.963486 0.267760i \(-0.913716\pi\)
−0.963486 + 0.267760i \(0.913716\pi\)
\(998\) 12.8224 0.405886
\(999\) −74.9012 −2.36977
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 \(a_p\))