Properties

Label 6010.2.a.c.1.11
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(1.52769\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.527686 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.527686 q^{6}\) \(-1.45681 q^{7}\) \(+1.00000 q^{8}\) \(-2.72155 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.527686 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.527686 q^{6}\) \(-1.45681 q^{7}\) \(+1.00000 q^{8}\) \(-2.72155 q^{9}\) \(+1.00000 q^{10}\) \(-2.62149 q^{11}\) \(+0.527686 q^{12}\) \(+1.24353 q^{13}\) \(-1.45681 q^{14}\) \(+0.527686 q^{15}\) \(+1.00000 q^{16}\) \(+2.45768 q^{17}\) \(-2.72155 q^{18}\) \(-1.20341 q^{19}\) \(+1.00000 q^{20}\) \(-0.768738 q^{21}\) \(-2.62149 q^{22}\) \(-1.35625 q^{23}\) \(+0.527686 q^{24}\) \(+1.00000 q^{25}\) \(+1.24353 q^{26}\) \(-3.01918 q^{27}\) \(-1.45681 q^{28}\) \(+0.521590 q^{29}\) \(+0.527686 q^{30}\) \(-2.53028 q^{31}\) \(+1.00000 q^{32}\) \(-1.38333 q^{33}\) \(+2.45768 q^{34}\) \(-1.45681 q^{35}\) \(-2.72155 q^{36}\) \(-10.7002 q^{37}\) \(-1.20341 q^{38}\) \(+0.656195 q^{39}\) \(+1.00000 q^{40}\) \(-4.79988 q^{41}\) \(-0.768738 q^{42}\) \(-6.82716 q^{43}\) \(-2.62149 q^{44}\) \(-2.72155 q^{45}\) \(-1.35625 q^{46}\) \(+7.76806 q^{47}\) \(+0.527686 q^{48}\) \(-4.87771 q^{49}\) \(+1.00000 q^{50}\) \(+1.29688 q^{51}\) \(+1.24353 q^{52}\) \(+2.85206 q^{53}\) \(-3.01918 q^{54}\) \(-2.62149 q^{55}\) \(-1.45681 q^{56}\) \(-0.635024 q^{57}\) \(+0.521590 q^{58}\) \(+4.64954 q^{59}\) \(+0.527686 q^{60}\) \(-5.90552 q^{61}\) \(-2.53028 q^{62}\) \(+3.96477 q^{63}\) \(+1.00000 q^{64}\) \(+1.24353 q^{65}\) \(-1.38333 q^{66}\) \(-2.08902 q^{67}\) \(+2.45768 q^{68}\) \(-0.715675 q^{69}\) \(-1.45681 q^{70}\) \(+9.96266 q^{71}\) \(-2.72155 q^{72}\) \(-5.44302 q^{73}\) \(-10.7002 q^{74}\) \(+0.527686 q^{75}\) \(-1.20341 q^{76}\) \(+3.81902 q^{77}\) \(+0.656195 q^{78}\) \(-9.71634 q^{79}\) \(+1.00000 q^{80}\) \(+6.57146 q^{81}\) \(-4.79988 q^{82}\) \(-17.4608 q^{83}\) \(-0.768738 q^{84}\) \(+2.45768 q^{85}\) \(-6.82716 q^{86}\) \(+0.275236 q^{87}\) \(-2.62149 q^{88}\) \(+5.36866 q^{89}\) \(-2.72155 q^{90}\) \(-1.81159 q^{91}\) \(-1.35625 q^{92}\) \(-1.33519 q^{93}\) \(+7.76806 q^{94}\) \(-1.20341 q^{95}\) \(+0.527686 q^{96}\) \(-13.4933 q^{97}\) \(-4.87771 q^{98}\) \(+7.13452 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.527686 0.304660 0.152330 0.988330i \(-0.451322\pi\)
0.152330 + 0.988330i \(0.451322\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.527686 0.215427
\(7\) −1.45681 −0.550622 −0.275311 0.961355i \(-0.588781\pi\)
−0.275311 + 0.961355i \(0.588781\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.72155 −0.907182
\(10\) 1.00000 0.316228
\(11\) −2.62149 −0.790410 −0.395205 0.918593i \(-0.629327\pi\)
−0.395205 + 0.918593i \(0.629327\pi\)
\(12\) 0.527686 0.152330
\(13\) 1.24353 0.344894 0.172447 0.985019i \(-0.444833\pi\)
0.172447 + 0.985019i \(0.444833\pi\)
\(14\) −1.45681 −0.389348
\(15\) 0.527686 0.136248
\(16\) 1.00000 0.250000
\(17\) 2.45768 0.596074 0.298037 0.954554i \(-0.403668\pi\)
0.298037 + 0.954554i \(0.403668\pi\)
\(18\) −2.72155 −0.641475
\(19\) −1.20341 −0.276081 −0.138041 0.990427i \(-0.544080\pi\)
−0.138041 + 0.990427i \(0.544080\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.768738 −0.167752
\(22\) −2.62149 −0.558905
\(23\) −1.35625 −0.282798 −0.141399 0.989953i \(-0.545160\pi\)
−0.141399 + 0.989953i \(0.545160\pi\)
\(24\) 0.527686 0.107714
\(25\) 1.00000 0.200000
\(26\) 1.24353 0.243877
\(27\) −3.01918 −0.581042
\(28\) −1.45681 −0.275311
\(29\) 0.521590 0.0968568 0.0484284 0.998827i \(-0.484579\pi\)
0.0484284 + 0.998827i \(0.484579\pi\)
\(30\) 0.527686 0.0963419
\(31\) −2.53028 −0.454452 −0.227226 0.973842i \(-0.572966\pi\)
−0.227226 + 0.973842i \(0.572966\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.38333 −0.240806
\(34\) 2.45768 0.421488
\(35\) −1.45681 −0.246246
\(36\) −2.72155 −0.453591
\(37\) −10.7002 −1.75910 −0.879552 0.475803i \(-0.842158\pi\)
−0.879552 + 0.475803i \(0.842158\pi\)
\(38\) −1.20341 −0.195219
\(39\) 0.656195 0.105075
\(40\) 1.00000 0.158114
\(41\) −4.79988 −0.749616 −0.374808 0.927103i \(-0.622291\pi\)
−0.374808 + 0.927103i \(0.622291\pi\)
\(42\) −0.768738 −0.118619
\(43\) −6.82716 −1.04113 −0.520566 0.853822i \(-0.674279\pi\)
−0.520566 + 0.853822i \(0.674279\pi\)
\(44\) −2.62149 −0.395205
\(45\) −2.72155 −0.405704
\(46\) −1.35625 −0.199968
\(47\) 7.76806 1.13309 0.566544 0.824031i \(-0.308280\pi\)
0.566544 + 0.824031i \(0.308280\pi\)
\(48\) 0.527686 0.0761650
\(49\) −4.87771 −0.696816
\(50\) 1.00000 0.141421
\(51\) 1.29688 0.181600
\(52\) 1.24353 0.172447
\(53\) 2.85206 0.391761 0.195880 0.980628i \(-0.437244\pi\)
0.195880 + 0.980628i \(0.437244\pi\)
\(54\) −3.01918 −0.410859
\(55\) −2.62149 −0.353482
\(56\) −1.45681 −0.194674
\(57\) −0.635024 −0.0841110
\(58\) 0.521590 0.0684881
\(59\) 4.64954 0.605318 0.302659 0.953099i \(-0.402126\pi\)
0.302659 + 0.953099i \(0.402126\pi\)
\(60\) 0.527686 0.0681240
\(61\) −5.90552 −0.756124 −0.378062 0.925780i \(-0.623409\pi\)
−0.378062 + 0.925780i \(0.623409\pi\)
\(62\) −2.53028 −0.321346
\(63\) 3.96477 0.499514
\(64\) 1.00000 0.125000
\(65\) 1.24353 0.154241
\(66\) −1.38333 −0.170276
\(67\) −2.08902 −0.255214 −0.127607 0.991825i \(-0.540730\pi\)
−0.127607 + 0.991825i \(0.540730\pi\)
\(68\) 2.45768 0.298037
\(69\) −0.715675 −0.0861571
\(70\) −1.45681 −0.174122
\(71\) 9.96266 1.18235 0.591175 0.806543i \(-0.298664\pi\)
0.591175 + 0.806543i \(0.298664\pi\)
\(72\) −2.72155 −0.320737
\(73\) −5.44302 −0.637057 −0.318529 0.947913i \(-0.603189\pi\)
−0.318529 + 0.947913i \(0.603189\pi\)
\(74\) −10.7002 −1.24387
\(75\) 0.527686 0.0609320
\(76\) −1.20341 −0.138041
\(77\) 3.81902 0.435217
\(78\) 0.656195 0.0742995
\(79\) −9.71634 −1.09317 −0.546587 0.837402i \(-0.684073\pi\)
−0.546587 + 0.837402i \(0.684073\pi\)
\(80\) 1.00000 0.111803
\(81\) 6.57146 0.730162
\(82\) −4.79988 −0.530058
\(83\) −17.4608 −1.91657 −0.958284 0.285816i \(-0.907735\pi\)
−0.958284 + 0.285816i \(0.907735\pi\)
\(84\) −0.768738 −0.0838762
\(85\) 2.45768 0.266572
\(86\) −6.82716 −0.736191
\(87\) 0.275236 0.0295084
\(88\) −2.62149 −0.279452
\(89\) 5.36866 0.569077 0.284538 0.958665i \(-0.408160\pi\)
0.284538 + 0.958665i \(0.408160\pi\)
\(90\) −2.72155 −0.286876
\(91\) −1.81159 −0.189906
\(92\) −1.35625 −0.141399
\(93\) −1.33519 −0.138453
\(94\) 7.76806 0.801214
\(95\) −1.20341 −0.123467
\(96\) 0.527686 0.0538568
\(97\) −13.4933 −1.37003 −0.685017 0.728527i \(-0.740205\pi\)
−0.685017 + 0.728527i \(0.740205\pi\)
\(98\) −4.87771 −0.492723
\(99\) 7.13452 0.717046
\(100\) 1.00000 0.100000
\(101\) 5.06770 0.504255 0.252127 0.967694i \(-0.418870\pi\)
0.252127 + 0.967694i \(0.418870\pi\)
\(102\) 1.29688 0.128410
\(103\) 9.02142 0.888907 0.444453 0.895802i \(-0.353398\pi\)
0.444453 + 0.895802i \(0.353398\pi\)
\(104\) 1.24353 0.121938
\(105\) −0.768738 −0.0750212
\(106\) 2.85206 0.277017
\(107\) 6.53561 0.631822 0.315911 0.948789i \(-0.397690\pi\)
0.315911 + 0.948789i \(0.397690\pi\)
\(108\) −3.01918 −0.290521
\(109\) −1.18883 −0.113869 −0.0569345 0.998378i \(-0.518133\pi\)
−0.0569345 + 0.998378i \(0.518133\pi\)
\(110\) −2.62149 −0.249950
\(111\) −5.64636 −0.535929
\(112\) −1.45681 −0.137655
\(113\) −4.78861 −0.450474 −0.225237 0.974304i \(-0.572316\pi\)
−0.225237 + 0.974304i \(0.572316\pi\)
\(114\) −0.635024 −0.0594754
\(115\) −1.35625 −0.126471
\(116\) 0.521590 0.0484284
\(117\) −3.38433 −0.312882
\(118\) 4.64954 0.428025
\(119\) −3.58036 −0.328211
\(120\) 0.527686 0.0481710
\(121\) −4.12777 −0.375251
\(122\) −5.90552 −0.534661
\(123\) −2.53283 −0.228378
\(124\) −2.53028 −0.227226
\(125\) 1.00000 0.0894427
\(126\) 3.96477 0.353210
\(127\) −3.81154 −0.338219 −0.169110 0.985597i \(-0.554089\pi\)
−0.169110 + 0.985597i \(0.554089\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.60260 −0.317191
\(130\) 1.24353 0.109065
\(131\) 2.67702 0.233892 0.116946 0.993138i \(-0.462690\pi\)
0.116946 + 0.993138i \(0.462690\pi\)
\(132\) −1.38333 −0.120403
\(133\) 1.75314 0.152017
\(134\) −2.08902 −0.180464
\(135\) −3.01918 −0.259850
\(136\) 2.45768 0.210744
\(137\) −13.4125 −1.14591 −0.572954 0.819588i \(-0.694203\pi\)
−0.572954 + 0.819588i \(0.694203\pi\)
\(138\) −0.715675 −0.0609223
\(139\) −17.3453 −1.47121 −0.735603 0.677413i \(-0.763101\pi\)
−0.735603 + 0.677413i \(0.763101\pi\)
\(140\) −1.45681 −0.123123
\(141\) 4.09910 0.345207
\(142\) 9.96266 0.836048
\(143\) −3.25991 −0.272608
\(144\) −2.72155 −0.226796
\(145\) 0.521590 0.0433157
\(146\) −5.44302 −0.450468
\(147\) −2.57390 −0.212292
\(148\) −10.7002 −0.879552
\(149\) −20.3630 −1.66820 −0.834101 0.551612i \(-0.814013\pi\)
−0.834101 + 0.551612i \(0.814013\pi\)
\(150\) 0.527686 0.0430854
\(151\) −9.03664 −0.735391 −0.367696 0.929946i \(-0.619853\pi\)
−0.367696 + 0.929946i \(0.619853\pi\)
\(152\) −1.20341 −0.0976095
\(153\) −6.68868 −0.540748
\(154\) 3.81902 0.307745
\(155\) −2.53028 −0.203237
\(156\) 0.656195 0.0525377
\(157\) 7.93990 0.633673 0.316836 0.948480i \(-0.397379\pi\)
0.316836 + 0.948480i \(0.397379\pi\)
\(158\) −9.71634 −0.772991
\(159\) 1.50499 0.119354
\(160\) 1.00000 0.0790569
\(161\) 1.97580 0.155715
\(162\) 6.57146 0.516303
\(163\) 17.2900 1.35426 0.677130 0.735863i \(-0.263223\pi\)
0.677130 + 0.735863i \(0.263223\pi\)
\(164\) −4.79988 −0.374808
\(165\) −1.38333 −0.107692
\(166\) −17.4608 −1.35522
\(167\) −9.42282 −0.729160 −0.364580 0.931172i \(-0.618787\pi\)
−0.364580 + 0.931172i \(0.618787\pi\)
\(168\) −0.768738 −0.0593094
\(169\) −11.4536 −0.881048
\(170\) 2.45768 0.188495
\(171\) 3.27514 0.250456
\(172\) −6.82716 −0.520566
\(173\) 1.86070 0.141466 0.0707331 0.997495i \(-0.477466\pi\)
0.0707331 + 0.997495i \(0.477466\pi\)
\(174\) 0.275236 0.0208656
\(175\) −1.45681 −0.110124
\(176\) −2.62149 −0.197603
\(177\) 2.45350 0.184416
\(178\) 5.36866 0.402398
\(179\) 10.0718 0.752805 0.376402 0.926456i \(-0.377161\pi\)
0.376402 + 0.926456i \(0.377161\pi\)
\(180\) −2.72155 −0.202852
\(181\) −0.752269 −0.0559157 −0.0279579 0.999609i \(-0.508900\pi\)
−0.0279579 + 0.999609i \(0.508900\pi\)
\(182\) −1.81159 −0.134284
\(183\) −3.11626 −0.230361
\(184\) −1.35625 −0.0999841
\(185\) −10.7002 −0.786695
\(186\) −1.33519 −0.0979012
\(187\) −6.44278 −0.471143
\(188\) 7.76806 0.566544
\(189\) 4.39837 0.319934
\(190\) −1.20341 −0.0873046
\(191\) −3.15540 −0.228317 −0.114158 0.993463i \(-0.536417\pi\)
−0.114158 + 0.993463i \(0.536417\pi\)
\(192\) 0.527686 0.0380825
\(193\) −7.76219 −0.558734 −0.279367 0.960184i \(-0.590125\pi\)
−0.279367 + 0.960184i \(0.590125\pi\)
\(194\) −13.4933 −0.968760
\(195\) 0.656195 0.0469911
\(196\) −4.87771 −0.348408
\(197\) −14.2092 −1.01237 −0.506183 0.862426i \(-0.668944\pi\)
−0.506183 + 0.862426i \(0.668944\pi\)
\(198\) 7.13452 0.507028
\(199\) 8.59075 0.608982 0.304491 0.952515i \(-0.401514\pi\)
0.304491 + 0.952515i \(0.401514\pi\)
\(200\) 1.00000 0.0707107
\(201\) −1.10235 −0.0777535
\(202\) 5.06770 0.356562
\(203\) −0.759857 −0.0533315
\(204\) 1.29688 0.0907999
\(205\) −4.79988 −0.335238
\(206\) 9.02142 0.628552
\(207\) 3.69110 0.256549
\(208\) 1.24353 0.0862235
\(209\) 3.15474 0.218218
\(210\) −0.768738 −0.0530480
\(211\) 27.1324 1.86787 0.933937 0.357438i \(-0.116350\pi\)
0.933937 + 0.357438i \(0.116350\pi\)
\(212\) 2.85206 0.195880
\(213\) 5.25716 0.360215
\(214\) 6.53561 0.446765
\(215\) −6.82716 −0.465608
\(216\) −3.01918 −0.205429
\(217\) 3.68613 0.250231
\(218\) −1.18883 −0.0805175
\(219\) −2.87221 −0.194086
\(220\) −2.62149 −0.176741
\(221\) 3.05620 0.205582
\(222\) −5.64636 −0.378959
\(223\) 23.7152 1.58809 0.794044 0.607860i \(-0.207972\pi\)
0.794044 + 0.607860i \(0.207972\pi\)
\(224\) −1.45681 −0.0973371
\(225\) −2.72155 −0.181436
\(226\) −4.78861 −0.318534
\(227\) 11.4333 0.758857 0.379429 0.925221i \(-0.376121\pi\)
0.379429 + 0.925221i \(0.376121\pi\)
\(228\) −0.635024 −0.0420555
\(229\) −4.78887 −0.316457 −0.158229 0.987402i \(-0.550578\pi\)
−0.158229 + 0.987402i \(0.550578\pi\)
\(230\) −1.35625 −0.0894285
\(231\) 2.01524 0.132593
\(232\) 0.521590 0.0342441
\(233\) −28.5022 −1.86724 −0.933621 0.358262i \(-0.883369\pi\)
−0.933621 + 0.358262i \(0.883369\pi\)
\(234\) −3.38433 −0.221241
\(235\) 7.76806 0.506733
\(236\) 4.64954 0.302659
\(237\) −5.12718 −0.333046
\(238\) −3.58036 −0.232080
\(239\) 17.5347 1.13423 0.567114 0.823639i \(-0.308060\pi\)
0.567114 + 0.823639i \(0.308060\pi\)
\(240\) 0.527686 0.0340620
\(241\) 17.6740 1.13848 0.569241 0.822171i \(-0.307237\pi\)
0.569241 + 0.822171i \(0.307237\pi\)
\(242\) −4.12777 −0.265343
\(243\) 12.5252 0.803493
\(244\) −5.90552 −0.378062
\(245\) −4.87771 −0.311625
\(246\) −2.53283 −0.161488
\(247\) −1.49648 −0.0952188
\(248\) −2.53028 −0.160673
\(249\) −9.21381 −0.583902
\(250\) 1.00000 0.0632456
\(251\) 22.0973 1.39477 0.697386 0.716696i \(-0.254347\pi\)
0.697386 + 0.716696i \(0.254347\pi\)
\(252\) 3.96477 0.249757
\(253\) 3.55540 0.223526
\(254\) −3.81154 −0.239157
\(255\) 1.29688 0.0812139
\(256\) 1.00000 0.0625000
\(257\) −25.0526 −1.56274 −0.781369 0.624069i \(-0.785478\pi\)
−0.781369 + 0.624069i \(0.785478\pi\)
\(258\) −3.60260 −0.224288
\(259\) 15.5882 0.968601
\(260\) 1.24353 0.0771206
\(261\) −1.41953 −0.0878668
\(262\) 2.67702 0.165387
\(263\) −26.5018 −1.63417 −0.817086 0.576516i \(-0.804412\pi\)
−0.817086 + 0.576516i \(0.804412\pi\)
\(264\) −1.38333 −0.0851379
\(265\) 2.85206 0.175201
\(266\) 1.75314 0.107492
\(267\) 2.83297 0.173375
\(268\) −2.08902 −0.127607
\(269\) 13.0978 0.798584 0.399292 0.916824i \(-0.369256\pi\)
0.399292 + 0.916824i \(0.369256\pi\)
\(270\) −3.01918 −0.183742
\(271\) −10.8390 −0.658420 −0.329210 0.944257i \(-0.606782\pi\)
−0.329210 + 0.944257i \(0.606782\pi\)
\(272\) 2.45768 0.149018
\(273\) −0.955951 −0.0578568
\(274\) −13.4125 −0.810279
\(275\) −2.62149 −0.158082
\(276\) −0.715675 −0.0430786
\(277\) 2.62756 0.157875 0.0789374 0.996880i \(-0.474847\pi\)
0.0789374 + 0.996880i \(0.474847\pi\)
\(278\) −17.3453 −1.04030
\(279\) 6.88628 0.412271
\(280\) −1.45681 −0.0870610
\(281\) 14.3946 0.858713 0.429356 0.903135i \(-0.358740\pi\)
0.429356 + 0.903135i \(0.358740\pi\)
\(282\) 4.09910 0.244098
\(283\) −10.7074 −0.636488 −0.318244 0.948009i \(-0.603093\pi\)
−0.318244 + 0.948009i \(0.603093\pi\)
\(284\) 9.96266 0.591175
\(285\) −0.635024 −0.0376156
\(286\) −3.25991 −0.192763
\(287\) 6.99251 0.412755
\(288\) −2.72155 −0.160369
\(289\) −10.9598 −0.644696
\(290\) 0.521590 0.0306288
\(291\) −7.12021 −0.417394
\(292\) −5.44302 −0.318529
\(293\) 10.1084 0.590536 0.295268 0.955414i \(-0.404591\pi\)
0.295268 + 0.955414i \(0.404591\pi\)
\(294\) −2.57390 −0.150113
\(295\) 4.64954 0.270707
\(296\) −10.7002 −0.621937
\(297\) 7.91477 0.459262
\(298\) −20.3630 −1.17960
\(299\) −1.68654 −0.0975352
\(300\) 0.527686 0.0304660
\(301\) 9.94586 0.573270
\(302\) −9.03664 −0.520000
\(303\) 2.67416 0.153626
\(304\) −1.20341 −0.0690204
\(305\) −5.90552 −0.338149
\(306\) −6.68868 −0.382366
\(307\) −32.0679 −1.83021 −0.915105 0.403216i \(-0.867892\pi\)
−0.915105 + 0.403216i \(0.867892\pi\)
\(308\) 3.81902 0.217609
\(309\) 4.76048 0.270814
\(310\) −2.53028 −0.143710
\(311\) 0.533714 0.0302642 0.0151321 0.999886i \(-0.495183\pi\)
0.0151321 + 0.999886i \(0.495183\pi\)
\(312\) 0.656195 0.0371497
\(313\) 23.4850 1.32745 0.663725 0.747977i \(-0.268975\pi\)
0.663725 + 0.747977i \(0.268975\pi\)
\(314\) 7.93990 0.448074
\(315\) 3.96477 0.223390
\(316\) −9.71634 −0.546587
\(317\) 30.0676 1.68877 0.844383 0.535740i \(-0.179967\pi\)
0.844383 + 0.535740i \(0.179967\pi\)
\(318\) 1.50499 0.0843959
\(319\) −1.36735 −0.0765566
\(320\) 1.00000 0.0559017
\(321\) 3.44875 0.192491
\(322\) 1.97580 0.110107
\(323\) −2.95759 −0.164565
\(324\) 6.57146 0.365081
\(325\) 1.24353 0.0689788
\(326\) 17.2900 0.957607
\(327\) −0.627328 −0.0346913
\(328\) −4.79988 −0.265029
\(329\) −11.3166 −0.623903
\(330\) −1.38333 −0.0761497
\(331\) 9.77668 0.537375 0.268687 0.963227i \(-0.413410\pi\)
0.268687 + 0.963227i \(0.413410\pi\)
\(332\) −17.4608 −0.958284
\(333\) 29.1211 1.59583
\(334\) −9.42282 −0.515594
\(335\) −2.08902 −0.114135
\(336\) −0.768738 −0.0419381
\(337\) −14.5929 −0.794925 −0.397463 0.917618i \(-0.630109\pi\)
−0.397463 + 0.917618i \(0.630109\pi\)
\(338\) −11.4536 −0.622995
\(339\) −2.52688 −0.137242
\(340\) 2.45768 0.133286
\(341\) 6.63312 0.359203
\(342\) 3.27514 0.177099
\(343\) 17.3035 0.934304
\(344\) −6.82716 −0.368096
\(345\) −0.715675 −0.0385306
\(346\) 1.86070 0.100032
\(347\) −19.4971 −1.04666 −0.523330 0.852130i \(-0.675310\pi\)
−0.523330 + 0.852130i \(0.675310\pi\)
\(348\) 0.275236 0.0147542
\(349\) −6.24943 −0.334524 −0.167262 0.985912i \(-0.553493\pi\)
−0.167262 + 0.985912i \(0.553493\pi\)
\(350\) −1.45681 −0.0778697
\(351\) −3.75445 −0.200398
\(352\) −2.62149 −0.139726
\(353\) 8.57783 0.456552 0.228276 0.973596i \(-0.426691\pi\)
0.228276 + 0.973596i \(0.426691\pi\)
\(354\) 2.45350 0.130402
\(355\) 9.96266 0.528763
\(356\) 5.36866 0.284538
\(357\) −1.88931 −0.0999928
\(358\) 10.0718 0.532313
\(359\) 9.90321 0.522671 0.261336 0.965248i \(-0.415837\pi\)
0.261336 + 0.965248i \(0.415837\pi\)
\(360\) −2.72155 −0.143438
\(361\) −17.5518 −0.923779
\(362\) −0.752269 −0.0395384
\(363\) −2.17817 −0.114324
\(364\) −1.81159 −0.0949531
\(365\) −5.44302 −0.284901
\(366\) −3.11626 −0.162890
\(367\) 32.8695 1.71577 0.857886 0.513840i \(-0.171777\pi\)
0.857886 + 0.513840i \(0.171777\pi\)
\(368\) −1.35625 −0.0706994
\(369\) 13.0631 0.680038
\(370\) −10.7002 −0.556278
\(371\) −4.15491 −0.215712
\(372\) −1.33519 −0.0692266
\(373\) 6.77078 0.350577 0.175289 0.984517i \(-0.443914\pi\)
0.175289 + 0.984517i \(0.443914\pi\)
\(374\) −6.44278 −0.333148
\(375\) 0.527686 0.0272496
\(376\) 7.76806 0.400607
\(377\) 0.648614 0.0334053
\(378\) 4.39837 0.226228
\(379\) 34.9977 1.79771 0.898857 0.438242i \(-0.144399\pi\)
0.898857 + 0.438242i \(0.144399\pi\)
\(380\) −1.20341 −0.0617337
\(381\) −2.01130 −0.103042
\(382\) −3.15540 −0.161444
\(383\) −1.92123 −0.0981701 −0.0490851 0.998795i \(-0.515631\pi\)
−0.0490851 + 0.998795i \(0.515631\pi\)
\(384\) 0.527686 0.0269284
\(385\) 3.81902 0.194635
\(386\) −7.76219 −0.395085
\(387\) 18.5804 0.944496
\(388\) −13.4933 −0.685017
\(389\) −19.8128 −1.00455 −0.502274 0.864709i \(-0.667503\pi\)
−0.502274 + 0.864709i \(0.667503\pi\)
\(390\) 0.656195 0.0332277
\(391\) −3.33322 −0.168568
\(392\) −4.87771 −0.246361
\(393\) 1.41263 0.0712575
\(394\) −14.2092 −0.715851
\(395\) −9.71634 −0.488882
\(396\) 7.13452 0.358523
\(397\) 24.4796 1.22860 0.614299 0.789073i \(-0.289439\pi\)
0.614299 + 0.789073i \(0.289439\pi\)
\(398\) 8.59075 0.430616
\(399\) 0.925108 0.0463133
\(400\) 1.00000 0.0500000
\(401\) −6.26064 −0.312641 −0.156321 0.987706i \(-0.549963\pi\)
−0.156321 + 0.987706i \(0.549963\pi\)
\(402\) −1.10235 −0.0549800
\(403\) −3.14649 −0.156738
\(404\) 5.06770 0.252127
\(405\) 6.57146 0.326538
\(406\) −0.759857 −0.0377111
\(407\) 28.0506 1.39041
\(408\) 1.29688 0.0642052
\(409\) 17.3216 0.856499 0.428250 0.903661i \(-0.359130\pi\)
0.428250 + 0.903661i \(0.359130\pi\)
\(410\) −4.79988 −0.237049
\(411\) −7.07760 −0.349112
\(412\) 9.02142 0.444453
\(413\) −6.77349 −0.333302
\(414\) 3.69110 0.181408
\(415\) −17.4608 −0.857116
\(416\) 1.24353 0.0609692
\(417\) −9.15286 −0.448218
\(418\) 3.15474 0.154303
\(419\) −24.5868 −1.20114 −0.600572 0.799571i \(-0.705060\pi\)
−0.600572 + 0.799571i \(0.705060\pi\)
\(420\) −0.768738 −0.0375106
\(421\) −37.1346 −1.80983 −0.904916 0.425591i \(-0.860066\pi\)
−0.904916 + 0.425591i \(0.860066\pi\)
\(422\) 27.1324 1.32079
\(423\) −21.1411 −1.02792
\(424\) 2.85206 0.138508
\(425\) 2.45768 0.119215
\(426\) 5.25716 0.254710
\(427\) 8.60321 0.416339
\(428\) 6.53561 0.315911
\(429\) −1.72021 −0.0830526
\(430\) −6.82716 −0.329235
\(431\) 15.0911 0.726911 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(432\) −3.01918 −0.145261
\(433\) 29.4439 1.41498 0.707492 0.706722i \(-0.249827\pi\)
0.707492 + 0.706722i \(0.249827\pi\)
\(434\) 3.68613 0.176940
\(435\) 0.275236 0.0131966
\(436\) −1.18883 −0.0569345
\(437\) 1.63213 0.0780752
\(438\) −2.87221 −0.137239
\(439\) −12.8585 −0.613702 −0.306851 0.951758i \(-0.599275\pi\)
−0.306851 + 0.951758i \(0.599275\pi\)
\(440\) −2.62149 −0.124975
\(441\) 13.2749 0.632139
\(442\) 3.05620 0.145369
\(443\) 8.99480 0.427356 0.213678 0.976904i \(-0.431456\pi\)
0.213678 + 0.976904i \(0.431456\pi\)
\(444\) −5.64636 −0.267964
\(445\) 5.36866 0.254499
\(446\) 23.7152 1.12295
\(447\) −10.7453 −0.508234
\(448\) −1.45681 −0.0688277
\(449\) 2.15083 0.101504 0.0507519 0.998711i \(-0.483838\pi\)
0.0507519 + 0.998711i \(0.483838\pi\)
\(450\) −2.72155 −0.128295
\(451\) 12.5829 0.592504
\(452\) −4.78861 −0.225237
\(453\) −4.76851 −0.224044
\(454\) 11.4333 0.536593
\(455\) −1.81159 −0.0849286
\(456\) −0.635024 −0.0297377
\(457\) 33.5887 1.57121 0.785606 0.618728i \(-0.212352\pi\)
0.785606 + 0.618728i \(0.212352\pi\)
\(458\) −4.78887 −0.223769
\(459\) −7.42017 −0.346344
\(460\) −1.35625 −0.0632355
\(461\) −30.9832 −1.44303 −0.721515 0.692398i \(-0.756554\pi\)
−0.721515 + 0.692398i \(0.756554\pi\)
\(462\) 2.01524 0.0937576
\(463\) −17.2054 −0.799602 −0.399801 0.916602i \(-0.630921\pi\)
−0.399801 + 0.916602i \(0.630921\pi\)
\(464\) 0.521590 0.0242142
\(465\) −1.33519 −0.0619182
\(466\) −28.5022 −1.32034
\(467\) 2.17888 0.100826 0.0504132 0.998728i \(-0.483946\pi\)
0.0504132 + 0.998728i \(0.483946\pi\)
\(468\) −3.38433 −0.156441
\(469\) 3.04330 0.140526
\(470\) 7.76806 0.358314
\(471\) 4.18978 0.193055
\(472\) 4.64954 0.214012
\(473\) 17.8974 0.822921
\(474\) −5.12718 −0.235499
\(475\) −1.20341 −0.0552163
\(476\) −3.58036 −0.164106
\(477\) −7.76202 −0.355399
\(478\) 17.5347 0.802020
\(479\) 29.3115 1.33928 0.669639 0.742687i \(-0.266449\pi\)
0.669639 + 0.742687i \(0.266449\pi\)
\(480\) 0.527686 0.0240855
\(481\) −13.3061 −0.606704
\(482\) 17.6740 0.805028
\(483\) 1.04260 0.0474400
\(484\) −4.12777 −0.187626
\(485\) −13.4933 −0.612697
\(486\) 12.5252 0.568155
\(487\) −2.85069 −0.129177 −0.0645884 0.997912i \(-0.520573\pi\)
−0.0645884 + 0.997912i \(0.520573\pi\)
\(488\) −5.90552 −0.267330
\(489\) 9.12372 0.412589
\(490\) −4.87771 −0.220352
\(491\) −22.3198 −1.00728 −0.503638 0.863915i \(-0.668006\pi\)
−0.503638 + 0.863915i \(0.668006\pi\)
\(492\) −2.53283 −0.114189
\(493\) 1.28190 0.0577338
\(494\) −1.49648 −0.0673299
\(495\) 7.13452 0.320673
\(496\) −2.53028 −0.113613
\(497\) −14.5137 −0.651028
\(498\) −9.21381 −0.412881
\(499\) −39.3315 −1.76072 −0.880361 0.474305i \(-0.842699\pi\)
−0.880361 + 0.474305i \(0.842699\pi\)
\(500\) 1.00000 0.0447214
\(501\) −4.97229 −0.222146
\(502\) 22.0973 0.986252
\(503\) 22.7238 1.01320 0.506602 0.862180i \(-0.330902\pi\)
0.506602 + 0.862180i \(0.330902\pi\)
\(504\) 3.96477 0.176605
\(505\) 5.06770 0.225510
\(506\) 3.55540 0.158057
\(507\) −6.04392 −0.268420
\(508\) −3.81154 −0.169110
\(509\) −4.55005 −0.201677 −0.100839 0.994903i \(-0.532153\pi\)
−0.100839 + 0.994903i \(0.532153\pi\)
\(510\) 1.29688 0.0574269
\(511\) 7.92944 0.350778
\(512\) 1.00000 0.0441942
\(513\) 3.63332 0.160415
\(514\) −25.0526 −1.10502
\(515\) 9.02142 0.397531
\(516\) −3.60260 −0.158596
\(517\) −20.3639 −0.895605
\(518\) 15.5882 0.684905
\(519\) 0.981865 0.0430991
\(520\) 1.24353 0.0545325
\(521\) 27.4148 1.20106 0.600531 0.799601i \(-0.294956\pi\)
0.600531 + 0.799601i \(0.294956\pi\)
\(522\) −1.41953 −0.0621312
\(523\) 29.8544 1.30544 0.652720 0.757599i \(-0.273628\pi\)
0.652720 + 0.757599i \(0.273628\pi\)
\(524\) 2.67702 0.116946
\(525\) −0.768738 −0.0335505
\(526\) −26.5018 −1.15553
\(527\) −6.21861 −0.270887
\(528\) −1.38333 −0.0602016
\(529\) −21.1606 −0.920025
\(530\) 2.85206 0.123886
\(531\) −12.6539 −0.549134
\(532\) 1.75314 0.0760083
\(533\) −5.96881 −0.258538
\(534\) 2.83297 0.122595
\(535\) 6.53561 0.282559
\(536\) −2.08902 −0.0902318
\(537\) 5.31478 0.229349
\(538\) 13.0978 0.564685
\(539\) 12.7869 0.550770
\(540\) −3.01918 −0.129925
\(541\) −36.0471 −1.54978 −0.774892 0.632094i \(-0.782196\pi\)
−0.774892 + 0.632094i \(0.782196\pi\)
\(542\) −10.8390 −0.465573
\(543\) −0.396962 −0.0170353
\(544\) 2.45768 0.105372
\(545\) −1.18883 −0.0509237
\(546\) −0.955951 −0.0409109
\(547\) 5.24440 0.224235 0.112117 0.993695i \(-0.464237\pi\)
0.112117 + 0.993695i \(0.464237\pi\)
\(548\) −13.4125 −0.572954
\(549\) 16.0721 0.685943
\(550\) −2.62149 −0.111781
\(551\) −0.627687 −0.0267404
\(552\) −0.715675 −0.0304612
\(553\) 14.1549 0.601925
\(554\) 2.62756 0.111634
\(555\) −5.64636 −0.239675
\(556\) −17.3453 −0.735603
\(557\) 21.1447 0.895930 0.447965 0.894051i \(-0.352149\pi\)
0.447965 + 0.894051i \(0.352149\pi\)
\(558\) 6.88628 0.291519
\(559\) −8.48979 −0.359080
\(560\) −1.45681 −0.0615614
\(561\) −3.39977 −0.143538
\(562\) 14.3946 0.607202
\(563\) 15.0001 0.632177 0.316089 0.948730i \(-0.397630\pi\)
0.316089 + 0.948730i \(0.397630\pi\)
\(564\) 4.09910 0.172603
\(565\) −4.78861 −0.201458
\(566\) −10.7074 −0.450065
\(567\) −9.57336 −0.402043
\(568\) 9.96266 0.418024
\(569\) 38.6940 1.62214 0.811069 0.584950i \(-0.198886\pi\)
0.811069 + 0.584950i \(0.198886\pi\)
\(570\) −0.635024 −0.0265982
\(571\) 9.73147 0.407249 0.203625 0.979049i \(-0.434728\pi\)
0.203625 + 0.979049i \(0.434728\pi\)
\(572\) −3.25991 −0.136304
\(573\) −1.66506 −0.0695590
\(574\) 6.99251 0.291862
\(575\) −1.35625 −0.0565596
\(576\) −2.72155 −0.113398
\(577\) −19.5085 −0.812148 −0.406074 0.913840i \(-0.633102\pi\)
−0.406074 + 0.913840i \(0.633102\pi\)
\(578\) −10.9598 −0.455869
\(579\) −4.09600 −0.170224
\(580\) 0.521590 0.0216578
\(581\) 25.4370 1.05530
\(582\) −7.12021 −0.295142
\(583\) −7.47667 −0.309652
\(584\) −5.44302 −0.225234
\(585\) −3.38433 −0.139925
\(586\) 10.1084 0.417572
\(587\) 14.7817 0.610106 0.305053 0.952335i \(-0.401326\pi\)
0.305053 + 0.952335i \(0.401326\pi\)
\(588\) −2.57390 −0.106146
\(589\) 3.04497 0.125466
\(590\) 4.64954 0.191419
\(591\) −7.49802 −0.308427
\(592\) −10.7002 −0.439776
\(593\) 3.20171 0.131478 0.0657392 0.997837i \(-0.479059\pi\)
0.0657392 + 0.997837i \(0.479059\pi\)
\(594\) 7.91477 0.324747
\(595\) −3.58036 −0.146781
\(596\) −20.3630 −0.834101
\(597\) 4.53322 0.185533
\(598\) −1.68654 −0.0689678
\(599\) −41.1127 −1.67982 −0.839910 0.542726i \(-0.817392\pi\)
−0.839910 + 0.542726i \(0.817392\pi\)
\(600\) 0.527686 0.0215427
\(601\) −1.00000 −0.0407909
\(602\) 9.94586 0.405363
\(603\) 5.68536 0.231526
\(604\) −9.03664 −0.367696
\(605\) −4.12777 −0.167818
\(606\) 2.67416 0.108630
\(607\) −32.6049 −1.32339 −0.661696 0.749772i \(-0.730163\pi\)
−0.661696 + 0.749772i \(0.730163\pi\)
\(608\) −1.20341 −0.0488048
\(609\) −0.400966 −0.0162480
\(610\) −5.90552 −0.239107
\(611\) 9.65984 0.390795
\(612\) −6.68868 −0.270374
\(613\) 38.4767 1.55406 0.777030 0.629464i \(-0.216725\pi\)
0.777030 + 0.629464i \(0.216725\pi\)
\(614\) −32.0679 −1.29415
\(615\) −2.53283 −0.102134
\(616\) 3.81902 0.153873
\(617\) −44.5065 −1.79176 −0.895882 0.444293i \(-0.853455\pi\)
−0.895882 + 0.444293i \(0.853455\pi\)
\(618\) 4.76048 0.191495
\(619\) −47.8908 −1.92489 −0.962447 0.271471i \(-0.912490\pi\)
−0.962447 + 0.271471i \(0.912490\pi\)
\(620\) −2.53028 −0.101619
\(621\) 4.09477 0.164317
\(622\) 0.533714 0.0214000
\(623\) −7.82111 −0.313346
\(624\) 0.656195 0.0262688
\(625\) 1.00000 0.0400000
\(626\) 23.4850 0.938649
\(627\) 1.66471 0.0664822
\(628\) 7.93990 0.316836
\(629\) −26.2977 −1.04856
\(630\) 3.96477 0.157960
\(631\) −36.4674 −1.45174 −0.725872 0.687830i \(-0.758564\pi\)
−0.725872 + 0.687830i \(0.758564\pi\)
\(632\) −9.71634 −0.386495
\(633\) 14.3174 0.569066
\(634\) 30.0676 1.19414
\(635\) −3.81154 −0.151256
\(636\) 1.50499 0.0596769
\(637\) −6.06559 −0.240327
\(638\) −1.36735 −0.0541337
\(639\) −27.1139 −1.07261
\(640\) 1.00000 0.0395285
\(641\) −4.68407 −0.185010 −0.0925048 0.995712i \(-0.529487\pi\)
−0.0925048 + 0.995712i \(0.529487\pi\)
\(642\) 3.44875 0.136112
\(643\) −6.04543 −0.238409 −0.119204 0.992870i \(-0.538034\pi\)
−0.119204 + 0.992870i \(0.538034\pi\)
\(644\) 1.97580 0.0778573
\(645\) −3.60260 −0.141852
\(646\) −2.95759 −0.116365
\(647\) −34.4331 −1.35370 −0.676852 0.736120i \(-0.736656\pi\)
−0.676852 + 0.736120i \(0.736656\pi\)
\(648\) 6.57146 0.258151
\(649\) −12.1887 −0.478450
\(650\) 1.24353 0.0487754
\(651\) 1.94512 0.0762354
\(652\) 17.2900 0.677130
\(653\) −2.60127 −0.101796 −0.0508978 0.998704i \(-0.516208\pi\)
−0.0508978 + 0.998704i \(0.516208\pi\)
\(654\) −0.627328 −0.0245305
\(655\) 2.67702 0.104600
\(656\) −4.79988 −0.187404
\(657\) 14.8134 0.577927
\(658\) −11.3166 −0.441166
\(659\) −27.1201 −1.05645 −0.528225 0.849105i \(-0.677142\pi\)
−0.528225 + 0.849105i \(0.677142\pi\)
\(660\) −1.38333 −0.0538459
\(661\) 36.9919 1.43882 0.719409 0.694586i \(-0.244413\pi\)
0.719409 + 0.694586i \(0.244413\pi\)
\(662\) 9.77668 0.379981
\(663\) 1.61272 0.0626327
\(664\) −17.4608 −0.677609
\(665\) 1.75314 0.0679839
\(666\) 29.1211 1.12842
\(667\) −0.707407 −0.0273909
\(668\) −9.42282 −0.364580
\(669\) 12.5142 0.483827
\(670\) −2.08902 −0.0807058
\(671\) 15.4813 0.597648
\(672\) −0.768738 −0.0296547
\(673\) 8.65152 0.333491 0.166746 0.986000i \(-0.446674\pi\)
0.166746 + 0.986000i \(0.446674\pi\)
\(674\) −14.5929 −0.562097
\(675\) −3.01918 −0.116208
\(676\) −11.4536 −0.440524
\(677\) 33.6014 1.29141 0.645703 0.763589i \(-0.276564\pi\)
0.645703 + 0.763589i \(0.276564\pi\)
\(678\) −2.52688 −0.0970444
\(679\) 19.6571 0.754370
\(680\) 2.45768 0.0942476
\(681\) 6.03322 0.231193
\(682\) 6.63312 0.253995
\(683\) −6.53157 −0.249924 −0.124962 0.992162i \(-0.539881\pi\)
−0.124962 + 0.992162i \(0.539881\pi\)
\(684\) 3.27514 0.125228
\(685\) −13.4125 −0.512466
\(686\) 17.3035 0.660653
\(687\) −2.52702 −0.0964119
\(688\) −6.82716 −0.260283
\(689\) 3.54663 0.135116
\(690\) −0.715675 −0.0272453
\(691\) 45.6707 1.73740 0.868698 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(692\) 1.86070 0.0707331
\(693\) −10.3936 −0.394821
\(694\) −19.4971 −0.740100
\(695\) −17.3453 −0.657944
\(696\) 0.275236 0.0104328
\(697\) −11.7966 −0.446826
\(698\) −6.24943 −0.236544
\(699\) −15.0402 −0.568874
\(700\) −1.45681 −0.0550622
\(701\) −34.5577 −1.30523 −0.652614 0.757690i \(-0.726328\pi\)
−0.652614 + 0.757690i \(0.726328\pi\)
\(702\) −3.75445 −0.141703
\(703\) 12.8768 0.485656
\(704\) −2.62149 −0.0988013
\(705\) 4.09910 0.154381
\(706\) 8.57783 0.322831
\(707\) −7.38267 −0.277654
\(708\) 2.45350 0.0922081
\(709\) 43.1652 1.62110 0.810551 0.585668i \(-0.199168\pi\)
0.810551 + 0.585668i \(0.199168\pi\)
\(710\) 9.96266 0.373892
\(711\) 26.4435 0.991708
\(712\) 5.36866 0.201199
\(713\) 3.43169 0.128518
\(714\) −1.88931 −0.0707056
\(715\) −3.25991 −0.121914
\(716\) 10.0718 0.376402
\(717\) 9.25284 0.345554
\(718\) 9.90321 0.369584
\(719\) 3.40341 0.126926 0.0634628 0.997984i \(-0.479786\pi\)
0.0634628 + 0.997984i \(0.479786\pi\)
\(720\) −2.72155 −0.101426
\(721\) −13.1425 −0.489451
\(722\) −17.5518 −0.653210
\(723\) 9.32633 0.346850
\(724\) −0.752269 −0.0279579
\(725\) 0.521590 0.0193714
\(726\) −2.17817 −0.0808393
\(727\) 32.4078 1.20194 0.600969 0.799272i \(-0.294782\pi\)
0.600969 + 0.799272i \(0.294782\pi\)
\(728\) −1.81159 −0.0671420
\(729\) −13.1050 −0.485370
\(730\) −5.44302 −0.201455
\(731\) −16.7789 −0.620591
\(732\) −3.11626 −0.115180
\(733\) −6.04603 −0.223315 −0.111658 0.993747i \(-0.535616\pi\)
−0.111658 + 0.993747i \(0.535616\pi\)
\(734\) 32.8695 1.21323
\(735\) −2.57390 −0.0949398
\(736\) −1.35625 −0.0499921
\(737\) 5.47635 0.201724
\(738\) 13.0631 0.480859
\(739\) 25.4319 0.935526 0.467763 0.883854i \(-0.345060\pi\)
0.467763 + 0.883854i \(0.345060\pi\)
\(740\) −10.7002 −0.393348
\(741\) −0.789673 −0.0290094
\(742\) −4.15491 −0.152532
\(743\) 30.5313 1.12008 0.560042 0.828464i \(-0.310785\pi\)
0.560042 + 0.828464i \(0.310785\pi\)
\(744\) −1.33519 −0.0489506
\(745\) −20.3630 −0.746042
\(746\) 6.77078 0.247896
\(747\) 47.5203 1.73868
\(748\) −6.44278 −0.235571
\(749\) −9.52114 −0.347895
\(750\) 0.527686 0.0192684
\(751\) 17.7883 0.649106 0.324553 0.945867i \(-0.394786\pi\)
0.324553 + 0.945867i \(0.394786\pi\)
\(752\) 7.76806 0.283272
\(753\) 11.6605 0.424931
\(754\) 0.648614 0.0236211
\(755\) −9.03664 −0.328877
\(756\) 4.39837 0.159967
\(757\) −45.4058 −1.65030 −0.825151 0.564913i \(-0.808910\pi\)
−0.825151 + 0.564913i \(0.808910\pi\)
\(758\) 34.9977 1.27118
\(759\) 1.87614 0.0680995
\(760\) −1.20341 −0.0436523
\(761\) 25.8410 0.936735 0.468367 0.883534i \(-0.344842\pi\)
0.468367 + 0.883534i \(0.344842\pi\)
\(762\) −2.01130 −0.0728616
\(763\) 1.73189 0.0626987
\(764\) −3.15540 −0.114158
\(765\) −6.68868 −0.241830
\(766\) −1.92123 −0.0694168
\(767\) 5.78185 0.208771
\(768\) 0.527686 0.0190412
\(769\) 29.3539 1.05853 0.529264 0.848457i \(-0.322468\pi\)
0.529264 + 0.848457i \(0.322468\pi\)
\(770\) 3.81902 0.137628
\(771\) −13.2199 −0.476104
\(772\) −7.76219 −0.279367
\(773\) 13.7170 0.493366 0.246683 0.969096i \(-0.420659\pi\)
0.246683 + 0.969096i \(0.420659\pi\)
\(774\) 18.5804 0.667860
\(775\) −2.53028 −0.0908904
\(776\) −13.4933 −0.484380
\(777\) 8.22566 0.295094
\(778\) −19.8128 −0.710323
\(779\) 5.77623 0.206955
\(780\) 0.656195 0.0234956
\(781\) −26.1171 −0.934542
\(782\) −3.33322 −0.119196
\(783\) −1.57478 −0.0562779
\(784\) −4.87771 −0.174204
\(785\) 7.93990 0.283387
\(786\) 1.41263 0.0503867
\(787\) −40.2677 −1.43539 −0.717695 0.696358i \(-0.754803\pi\)
−0.717695 + 0.696358i \(0.754803\pi\)
\(788\) −14.2092 −0.506183
\(789\) −13.9846 −0.497867
\(790\) −9.71634 −0.345692
\(791\) 6.97609 0.248041
\(792\) 7.13452 0.253514
\(793\) −7.34371 −0.260783
\(794\) 24.4796 0.868750
\(795\) 1.50499 0.0533767
\(796\) 8.59075 0.304491
\(797\) −20.0391 −0.709821 −0.354910 0.934900i \(-0.615489\pi\)
−0.354910 + 0.934900i \(0.615489\pi\)
\(798\) 0.925108 0.0327485
\(799\) 19.0914 0.675404
\(800\) 1.00000 0.0353553
\(801\) −14.6111 −0.516257
\(802\) −6.26064 −0.221071
\(803\) 14.2689 0.503537
\(804\) −1.10235 −0.0388768
\(805\) 1.97580 0.0696377
\(806\) −3.14649 −0.110830
\(807\) 6.91151 0.243297
\(808\) 5.06770 0.178281
\(809\) −48.4907 −1.70484 −0.852422 0.522855i \(-0.824867\pi\)
−0.852422 + 0.522855i \(0.824867\pi\)
\(810\) 6.57146 0.230898
\(811\) 38.1208 1.33860 0.669301 0.742992i \(-0.266594\pi\)
0.669301 + 0.742992i \(0.266594\pi\)
\(812\) −0.759857 −0.0266657
\(813\) −5.71957 −0.200594
\(814\) 28.0506 0.983171
\(815\) 17.2900 0.605644
\(816\) 1.29688 0.0454000
\(817\) 8.21588 0.287437
\(818\) 17.3216 0.605636
\(819\) 4.93032 0.172279
\(820\) −4.79988 −0.167619
\(821\) −20.7438 −0.723964 −0.361982 0.932185i \(-0.617900\pi\)
−0.361982 + 0.932185i \(0.617900\pi\)
\(822\) −7.07760 −0.246860
\(823\) 49.2294 1.71603 0.858015 0.513625i \(-0.171698\pi\)
0.858015 + 0.513625i \(0.171698\pi\)
\(824\) 9.02142 0.314276
\(825\) −1.38333 −0.0481613
\(826\) −6.77349 −0.235680
\(827\) 32.5946 1.13343 0.566713 0.823915i \(-0.308215\pi\)
0.566713 + 0.823915i \(0.308215\pi\)
\(828\) 3.69110 0.128275
\(829\) −0.215824 −0.00749589 −0.00374795 0.999993i \(-0.501193\pi\)
−0.00374795 + 0.999993i \(0.501193\pi\)
\(830\) −17.4608 −0.606072
\(831\) 1.38653 0.0480981
\(832\) 1.24353 0.0431117
\(833\) −11.9878 −0.415354
\(834\) −9.15286 −0.316938
\(835\) −9.42282 −0.326090
\(836\) 3.15474 0.109109
\(837\) 7.63938 0.264056
\(838\) −24.5868 −0.849337
\(839\) 13.6258 0.470413 0.235207 0.971945i \(-0.424423\pi\)
0.235207 + 0.971945i \(0.424423\pi\)
\(840\) −0.768738 −0.0265240
\(841\) −28.7279 −0.990619
\(842\) −37.1346 −1.27974
\(843\) 7.59586 0.261615
\(844\) 27.1324 0.933937
\(845\) −11.4536 −0.394017
\(846\) −21.1411 −0.726848
\(847\) 6.01336 0.206622
\(848\) 2.85206 0.0979402
\(849\) −5.65014 −0.193912
\(850\) 2.45768 0.0842976
\(851\) 14.5122 0.497471
\(852\) 5.25716 0.180107
\(853\) −41.4481 −1.41916 −0.709578 0.704627i \(-0.751114\pi\)
−0.709578 + 0.704627i \(0.751114\pi\)
\(854\) 8.60321 0.294396
\(855\) 3.27514 0.112007
\(856\) 6.53561 0.223383
\(857\) −56.5055 −1.93019 −0.965095 0.261900i \(-0.915651\pi\)
−0.965095 + 0.261900i \(0.915651\pi\)
\(858\) −1.72021 −0.0587271
\(859\) −25.9645 −0.885899 −0.442949 0.896547i \(-0.646068\pi\)
−0.442949 + 0.896547i \(0.646068\pi\)
\(860\) −6.82716 −0.232804
\(861\) 3.68985 0.125750
\(862\) 15.0911 0.514004
\(863\) 1.50224 0.0511368 0.0255684 0.999673i \(-0.491860\pi\)
0.0255684 + 0.999673i \(0.491860\pi\)
\(864\) −3.01918 −0.102715
\(865\) 1.86070 0.0632656
\(866\) 29.4439 1.00054
\(867\) −5.78335 −0.196413
\(868\) 3.68613 0.125116
\(869\) 25.4713 0.864056
\(870\) 0.275236 0.00933137
\(871\) −2.59776 −0.0880218
\(872\) −1.18883 −0.0402588
\(873\) 36.7225 1.24287
\(874\) 1.63213 0.0552075
\(875\) −1.45681 −0.0492491
\(876\) −2.87221 −0.0970429
\(877\) 57.2813 1.93425 0.967126 0.254299i \(-0.0818448\pi\)
0.967126 + 0.254299i \(0.0818448\pi\)
\(878\) −12.8585 −0.433953
\(879\) 5.33404 0.179913
\(880\) −2.62149 −0.0883706
\(881\) 20.1691 0.679513 0.339757 0.940513i \(-0.389655\pi\)
0.339757 + 0.940513i \(0.389655\pi\)
\(882\) 13.2749 0.446990
\(883\) −21.0001 −0.706710 −0.353355 0.935489i \(-0.614959\pi\)
−0.353355 + 0.935489i \(0.614959\pi\)
\(884\) 3.05620 0.102791
\(885\) 2.45350 0.0824735
\(886\) 8.99480 0.302186
\(887\) 34.3226 1.15244 0.576220 0.817295i \(-0.304527\pi\)
0.576220 + 0.817295i \(0.304527\pi\)
\(888\) −5.64636 −0.189479
\(889\) 5.55268 0.186231
\(890\) 5.36866 0.179958
\(891\) −17.2270 −0.577128
\(892\) 23.7152 0.794044
\(893\) −9.34817 −0.312825
\(894\) −10.7453 −0.359376
\(895\) 10.0718 0.336665
\(896\) −1.45681 −0.0486686
\(897\) −0.889965 −0.0297151
\(898\) 2.15083 0.0717740
\(899\) −1.31977 −0.0440168
\(900\) −2.72155 −0.0907182
\(901\) 7.00944 0.233518
\(902\) 12.5829 0.418964
\(903\) 5.24829 0.174652
\(904\) −4.78861 −0.159267
\(905\) −0.752269 −0.0250063
\(906\) −4.76851 −0.158423
\(907\) −23.1385 −0.768302 −0.384151 0.923270i \(-0.625506\pi\)
−0.384151 + 0.923270i \(0.625506\pi\)
\(908\) 11.4333 0.379429
\(909\) −13.7920 −0.457451
\(910\) −1.81159 −0.0600536
\(911\) 34.2913 1.13612 0.568060 0.822987i \(-0.307694\pi\)
0.568060 + 0.822987i \(0.307694\pi\)
\(912\) −0.635024 −0.0210277
\(913\) 45.7733 1.51488
\(914\) 33.5887 1.11101
\(915\) −3.11626 −0.103020
\(916\) −4.78887 −0.158229
\(917\) −3.89990 −0.128786
\(918\) −7.42017 −0.244902
\(919\) −53.1213 −1.75231 −0.876155 0.482030i \(-0.839900\pi\)
−0.876155 + 0.482030i \(0.839900\pi\)
\(920\) −1.35625 −0.0447143
\(921\) −16.9218 −0.557591
\(922\) −30.9832 −1.02038
\(923\) 12.3889 0.407785
\(924\) 2.01524 0.0662966
\(925\) −10.7002 −0.351821
\(926\) −17.2054 −0.565404
\(927\) −24.5522 −0.806400
\(928\) 0.521590 0.0171220
\(929\) 25.6258 0.840755 0.420377 0.907349i \(-0.361898\pi\)
0.420377 + 0.907349i \(0.361898\pi\)
\(930\) −1.33519 −0.0437828
\(931\) 5.86989 0.192378
\(932\) −28.5022 −0.933621
\(933\) 0.281634 0.00922028
\(934\) 2.17888 0.0712950
\(935\) −6.44278 −0.210702
\(936\) −3.38433 −0.110620
\(937\) −15.3419 −0.501199 −0.250600 0.968091i \(-0.580628\pi\)
−0.250600 + 0.968091i \(0.580628\pi\)
\(938\) 3.04330 0.0993672
\(939\) 12.3927 0.404421
\(940\) 7.76806 0.253366
\(941\) −12.9629 −0.422577 −0.211289 0.977424i \(-0.567766\pi\)
−0.211289 + 0.977424i \(0.567766\pi\)
\(942\) 4.18978 0.136510
\(943\) 6.50984 0.211990
\(944\) 4.64954 0.151330
\(945\) 4.39837 0.143079
\(946\) 17.8974 0.581893
\(947\) −34.3424 −1.11598 −0.557988 0.829849i \(-0.688427\pi\)
−0.557988 + 0.829849i \(0.688427\pi\)
\(948\) −5.12718 −0.166523
\(949\) −6.76857 −0.219717
\(950\) −1.20341 −0.0390438
\(951\) 15.8663 0.514499
\(952\) −3.58036 −0.116040
\(953\) 56.7450 1.83815 0.919076 0.394080i \(-0.128937\pi\)
0.919076 + 0.394080i \(0.128937\pi\)
\(954\) −7.76202 −0.251305
\(955\) −3.15540 −0.102106
\(956\) 17.5347 0.567114
\(957\) −0.721530 −0.0233237
\(958\) 29.3115 0.947012
\(959\) 19.5395 0.630962
\(960\) 0.527686 0.0170310
\(961\) −24.5977 −0.793474
\(962\) −13.3061 −0.429005
\(963\) −17.7870 −0.573177
\(964\) 17.6740 0.569241
\(965\) −7.76219 −0.249874
\(966\) 1.04260 0.0335452
\(967\) 39.3646 1.26588 0.632940 0.774200i \(-0.281848\pi\)
0.632940 + 0.774200i \(0.281848\pi\)
\(968\) −4.12777 −0.132671
\(969\) −1.56068 −0.0501363
\(970\) −13.4933 −0.433243
\(971\) −15.2564 −0.489601 −0.244801 0.969573i \(-0.578722\pi\)
−0.244801 + 0.969573i \(0.578722\pi\)
\(972\) 12.5252 0.401747
\(973\) 25.2687 0.810079
\(974\) −2.85069 −0.0913418
\(975\) 0.656195 0.0210151
\(976\) −5.90552 −0.189031
\(977\) −14.6568 −0.468914 −0.234457 0.972126i \(-0.575331\pi\)
−0.234457 + 0.972126i \(0.575331\pi\)
\(978\) 9.12372 0.291744
\(979\) −14.0739 −0.449804
\(980\) −4.87771 −0.155813
\(981\) 3.23545 0.103300
\(982\) −22.3198 −0.712252
\(983\) 36.2154 1.15509 0.577546 0.816358i \(-0.304010\pi\)
0.577546 + 0.816358i \(0.304010\pi\)
\(984\) −2.53283 −0.0807438
\(985\) −14.2092 −0.452744
\(986\) 1.28190 0.0408240
\(987\) −5.97161 −0.190078
\(988\) −1.49648 −0.0476094
\(989\) 9.25933 0.294430
\(990\) 7.13452 0.226750
\(991\) 24.9078 0.791223 0.395612 0.918418i \(-0.370533\pi\)
0.395612 + 0.918418i \(0.370533\pi\)
\(992\) −2.53028 −0.0803365
\(993\) 5.15902 0.163717
\(994\) −14.5137 −0.460346
\(995\) 8.59075 0.272345
\(996\) −9.21381 −0.291951
\(997\) −57.8545 −1.83227 −0.916135 0.400870i \(-0.868708\pi\)
−0.916135 + 0.400870i \(0.868708\pi\)
\(998\) −39.3315 −1.24502
\(999\) 32.3059 1.02211
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 \(a_p\))