Properties

Label 6013.2.a.e.1.1
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.71096 q^{2}\) \(+3.20670 q^{3}\) \(+5.34933 q^{4}\) \(+3.06653 q^{5}\) \(-8.69325 q^{6}\) \(+1.00000 q^{7}\) \(-9.07991 q^{8}\) \(+7.28293 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.71096 q^{2}\) \(+3.20670 q^{3}\) \(+5.34933 q^{4}\) \(+3.06653 q^{5}\) \(-8.69325 q^{6}\) \(+1.00000 q^{7}\) \(-9.07991 q^{8}\) \(+7.28293 q^{9}\) \(-8.31326 q^{10}\) \(-0.601902 q^{11}\) \(+17.1537 q^{12}\) \(-1.91242 q^{13}\) \(-2.71096 q^{14}\) \(+9.83345 q^{15}\) \(+13.9166 q^{16}\) \(+2.21291 q^{17}\) \(-19.7438 q^{18}\) \(-1.88875 q^{19}\) \(+16.4039 q^{20}\) \(+3.20670 q^{21}\) \(+1.63173 q^{22}\) \(+0.548445 q^{23}\) \(-29.1165 q^{24}\) \(+4.40363 q^{25}\) \(+5.18452 q^{26}\) \(+13.7341 q^{27}\) \(+5.34933 q^{28}\) \(-4.40627 q^{29}\) \(-26.6581 q^{30}\) \(-0.578064 q^{31}\) \(-19.5677 q^{32}\) \(-1.93012 q^{33}\) \(-5.99912 q^{34}\) \(+3.06653 q^{35}\) \(+38.9588 q^{36}\) \(+2.37183 q^{37}\) \(+5.12032 q^{38}\) \(-6.13257 q^{39}\) \(-27.8438 q^{40}\) \(+12.1364 q^{41}\) \(-8.69325 q^{42}\) \(+9.96651 q^{43}\) \(-3.21977 q^{44}\) \(+22.3333 q^{45}\) \(-1.48681 q^{46}\) \(-2.52239 q^{47}\) \(+44.6265 q^{48}\) \(+1.00000 q^{49}\) \(-11.9381 q^{50}\) \(+7.09614 q^{51}\) \(-10.2302 q^{52}\) \(+1.66466 q^{53}\) \(-37.2326 q^{54}\) \(-1.84575 q^{55}\) \(-9.07991 q^{56}\) \(-6.05664 q^{57}\) \(+11.9452 q^{58}\) \(+10.0741 q^{59}\) \(+52.6024 q^{60}\) \(-4.42119 q^{61}\) \(+1.56711 q^{62}\) \(+7.28293 q^{63}\) \(+25.2141 q^{64}\) \(-5.86452 q^{65}\) \(+5.23248 q^{66}\) \(+4.37369 q^{67}\) \(+11.8376 q^{68}\) \(+1.75870 q^{69}\) \(-8.31326 q^{70}\) \(-6.11918 q^{71}\) \(-66.1283 q^{72}\) \(-12.4692 q^{73}\) \(-6.42994 q^{74}\) \(+14.1211 q^{75}\) \(-10.1035 q^{76}\) \(-0.601902 q^{77}\) \(+16.6252 q^{78}\) \(-9.20628 q^{79}\) \(+42.6759 q^{80}\) \(+22.1923 q^{81}\) \(-32.9014 q^{82}\) \(+4.25325 q^{83}\) \(+17.1537 q^{84}\) \(+6.78597 q^{85}\) \(-27.0189 q^{86}\) \(-14.1296 q^{87}\) \(+5.46521 q^{88}\) \(+15.0841 q^{89}\) \(-60.5449 q^{90}\) \(-1.91242 q^{91}\) \(+2.93381 q^{92}\) \(-1.85368 q^{93}\) \(+6.83811 q^{94}\) \(-5.79190 q^{95}\) \(-62.7478 q^{96}\) \(-2.26710 q^{97}\) \(-2.71096 q^{98}\) \(-4.38361 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71096 −1.91694 −0.958471 0.285191i \(-0.907943\pi\)
−0.958471 + 0.285191i \(0.907943\pi\)
\(3\) 3.20670 1.85139 0.925695 0.378272i \(-0.123481\pi\)
0.925695 + 0.378272i \(0.123481\pi\)
\(4\) 5.34933 2.67466
\(5\) 3.06653 1.37140 0.685698 0.727886i \(-0.259497\pi\)
0.685698 + 0.727886i \(0.259497\pi\)
\(6\) −8.69325 −3.54900
\(7\) 1.00000 0.377964
\(8\) −9.07991 −3.21023
\(9\) 7.28293 2.42764
\(10\) −8.31326 −2.62888
\(11\) −0.601902 −0.181480 −0.0907401 0.995875i \(-0.528923\pi\)
−0.0907401 + 0.995875i \(0.528923\pi\)
\(12\) 17.1537 4.95184
\(13\) −1.91242 −0.530411 −0.265206 0.964192i \(-0.585440\pi\)
−0.265206 + 0.964192i \(0.585440\pi\)
\(14\) −2.71096 −0.724536
\(15\) 9.83345 2.53899
\(16\) 13.9166 3.47916
\(17\) 2.21291 0.536710 0.268355 0.963320i \(-0.413520\pi\)
0.268355 + 0.963320i \(0.413520\pi\)
\(18\) −19.7438 −4.65365
\(19\) −1.88875 −0.433308 −0.216654 0.976248i \(-0.569514\pi\)
−0.216654 + 0.976248i \(0.569514\pi\)
\(20\) 16.4039 3.66802
\(21\) 3.20670 0.699759
\(22\) 1.63173 0.347887
\(23\) 0.548445 0.114359 0.0571793 0.998364i \(-0.481789\pi\)
0.0571793 + 0.998364i \(0.481789\pi\)
\(24\) −29.1165 −5.94339
\(25\) 4.40363 0.880725
\(26\) 5.18452 1.01677
\(27\) 13.7341 2.64312
\(28\) 5.34933 1.01093
\(29\) −4.40627 −0.818223 −0.409112 0.912484i \(-0.634161\pi\)
−0.409112 + 0.912484i \(0.634161\pi\)
\(30\) −26.6581 −4.86709
\(31\) −0.578064 −0.103823 −0.0519117 0.998652i \(-0.516531\pi\)
−0.0519117 + 0.998652i \(0.516531\pi\)
\(32\) −19.5677 −3.45912
\(33\) −1.93012 −0.335991
\(34\) −5.99912 −1.02884
\(35\) 3.06653 0.518339
\(36\) 38.9588 6.49313
\(37\) 2.37183 0.389926 0.194963 0.980811i \(-0.437541\pi\)
0.194963 + 0.980811i \(0.437541\pi\)
\(38\) 5.12032 0.830626
\(39\) −6.13257 −0.981998
\(40\) −27.8438 −4.40250
\(41\) 12.1364 1.89539 0.947696 0.319174i \(-0.103406\pi\)
0.947696 + 0.319174i \(0.103406\pi\)
\(42\) −8.69325 −1.34140
\(43\) 9.96651 1.51988 0.759940 0.649994i \(-0.225229\pi\)
0.759940 + 0.649994i \(0.225229\pi\)
\(44\) −3.21977 −0.485398
\(45\) 22.3333 3.32926
\(46\) −1.48681 −0.219219
\(47\) −2.52239 −0.367928 −0.183964 0.982933i \(-0.558893\pi\)
−0.183964 + 0.982933i \(0.558893\pi\)
\(48\) 44.6265 6.44128
\(49\) 1.00000 0.142857
\(50\) −11.9381 −1.68830
\(51\) 7.09614 0.993659
\(52\) −10.2302 −1.41867
\(53\) 1.66466 0.228658 0.114329 0.993443i \(-0.463528\pi\)
0.114329 + 0.993443i \(0.463528\pi\)
\(54\) −37.2326 −5.06671
\(55\) −1.84575 −0.248881
\(56\) −9.07991 −1.21335
\(57\) −6.05664 −0.802222
\(58\) 11.9452 1.56849
\(59\) 10.0741 1.31153 0.655765 0.754965i \(-0.272346\pi\)
0.655765 + 0.754965i \(0.272346\pi\)
\(60\) 52.6024 6.79094
\(61\) −4.42119 −0.566075 −0.283038 0.959109i \(-0.591342\pi\)
−0.283038 + 0.959109i \(0.591342\pi\)
\(62\) 1.56711 0.199023
\(63\) 7.28293 0.917563
\(64\) 25.2141 3.15176
\(65\) −5.86452 −0.727404
\(66\) 5.23248 0.644074
\(67\) 4.37369 0.534331 0.267166 0.963651i \(-0.413913\pi\)
0.267166 + 0.963651i \(0.413913\pi\)
\(68\) 11.8376 1.43552
\(69\) 1.75870 0.211722
\(70\) −8.31326 −0.993625
\(71\) −6.11918 −0.726213 −0.363106 0.931748i \(-0.618284\pi\)
−0.363106 + 0.931748i \(0.618284\pi\)
\(72\) −66.1283 −7.79329
\(73\) −12.4692 −1.45941 −0.729707 0.683760i \(-0.760344\pi\)
−0.729707 + 0.683760i \(0.760344\pi\)
\(74\) −6.42994 −0.747465
\(75\) 14.1211 1.63057
\(76\) −10.1035 −1.15895
\(77\) −0.601902 −0.0685931
\(78\) 16.6252 1.88243
\(79\) −9.20628 −1.03579 −0.517894 0.855445i \(-0.673284\pi\)
−0.517894 + 0.855445i \(0.673284\pi\)
\(80\) 42.6759 4.77131
\(81\) 22.1923 2.46581
\(82\) −32.9014 −3.63335
\(83\) 4.25325 0.466854 0.233427 0.972374i \(-0.425006\pi\)
0.233427 + 0.972374i \(0.425006\pi\)
\(84\) 17.1537 1.87162
\(85\) 6.78597 0.736041
\(86\) −27.0189 −2.91352
\(87\) −14.1296 −1.51485
\(88\) 5.46521 0.582593
\(89\) 15.0841 1.59891 0.799457 0.600724i \(-0.205121\pi\)
0.799457 + 0.600724i \(0.205121\pi\)
\(90\) −60.5449 −6.38199
\(91\) −1.91242 −0.200477
\(92\) 2.93381 0.305871
\(93\) −1.85368 −0.192218
\(94\) 6.83811 0.705297
\(95\) −5.79190 −0.594237
\(96\) −62.7478 −6.40417
\(97\) −2.26710 −0.230189 −0.115095 0.993355i \(-0.536717\pi\)
−0.115095 + 0.993355i \(0.536717\pi\)
\(98\) −2.71096 −0.273849
\(99\) −4.38361 −0.440569
\(100\) 23.5564 2.35564
\(101\) −12.3078 −1.22467 −0.612334 0.790600i \(-0.709769\pi\)
−0.612334 + 0.790600i \(0.709769\pi\)
\(102\) −19.2374 −1.90479
\(103\) −9.85490 −0.971032 −0.485516 0.874228i \(-0.661368\pi\)
−0.485516 + 0.874228i \(0.661368\pi\)
\(104\) 17.3646 1.70274
\(105\) 9.83345 0.959647
\(106\) −4.51283 −0.438325
\(107\) 5.13480 0.496400 0.248200 0.968709i \(-0.420161\pi\)
0.248200 + 0.968709i \(0.420161\pi\)
\(108\) 73.4680 7.06946
\(109\) 11.8051 1.13072 0.565362 0.824843i \(-0.308736\pi\)
0.565362 + 0.824843i \(0.308736\pi\)
\(110\) 5.00377 0.477090
\(111\) 7.60574 0.721905
\(112\) 13.9166 1.31500
\(113\) −0.284477 −0.0267613 −0.0133807 0.999910i \(-0.504259\pi\)
−0.0133807 + 0.999910i \(0.504259\pi\)
\(114\) 16.4193 1.53781
\(115\) 1.68182 0.156831
\(116\) −23.5706 −2.18847
\(117\) −13.9281 −1.28765
\(118\) −27.3104 −2.51413
\(119\) 2.21291 0.202857
\(120\) −89.2868 −8.15074
\(121\) −10.6377 −0.967065
\(122\) 11.9857 1.08513
\(123\) 38.9179 3.50911
\(124\) −3.09226 −0.277693
\(125\) −1.82880 −0.163573
\(126\) −19.7438 −1.75891
\(127\) −13.3238 −1.18230 −0.591148 0.806563i \(-0.701325\pi\)
−0.591148 + 0.806563i \(0.701325\pi\)
\(128\) −29.2191 −2.58262
\(129\) 31.9596 2.81389
\(130\) 15.8985 1.39439
\(131\) −13.1087 −1.14531 −0.572657 0.819795i \(-0.694087\pi\)
−0.572657 + 0.819795i \(0.694087\pi\)
\(132\) −10.3248 −0.898662
\(133\) −1.88875 −0.163775
\(134\) −11.8569 −1.02428
\(135\) 42.1160 3.62477
\(136\) −20.0930 −1.72296
\(137\) 6.14328 0.524856 0.262428 0.964952i \(-0.415477\pi\)
0.262428 + 0.964952i \(0.415477\pi\)
\(138\) −4.76777 −0.405859
\(139\) 17.2355 1.46190 0.730949 0.682432i \(-0.239078\pi\)
0.730949 + 0.682432i \(0.239078\pi\)
\(140\) 16.4039 1.38638
\(141\) −8.08855 −0.681179
\(142\) 16.5889 1.39211
\(143\) 1.15109 0.0962591
\(144\) 101.354 8.44616
\(145\) −13.5120 −1.12211
\(146\) 33.8037 2.79761
\(147\) 3.20670 0.264484
\(148\) 12.6877 1.04292
\(149\) 1.86756 0.152996 0.0764982 0.997070i \(-0.475626\pi\)
0.0764982 + 0.997070i \(0.475626\pi\)
\(150\) −38.2818 −3.12570
\(151\) −1.07693 −0.0876396 −0.0438198 0.999039i \(-0.513953\pi\)
−0.0438198 + 0.999039i \(0.513953\pi\)
\(152\) 17.1496 1.39102
\(153\) 16.1165 1.30294
\(154\) 1.63173 0.131489
\(155\) −1.77265 −0.142383
\(156\) −32.8051 −2.62651
\(157\) 15.8541 1.26530 0.632649 0.774439i \(-0.281968\pi\)
0.632649 + 0.774439i \(0.281968\pi\)
\(158\) 24.9579 1.98554
\(159\) 5.33806 0.423336
\(160\) −60.0051 −4.74382
\(161\) 0.548445 0.0432235
\(162\) −60.1624 −4.72681
\(163\) 18.3107 1.43421 0.717103 0.696967i \(-0.245468\pi\)
0.717103 + 0.696967i \(0.245468\pi\)
\(164\) 64.9217 5.06954
\(165\) −5.91877 −0.460776
\(166\) −11.5304 −0.894933
\(167\) 4.09051 0.316533 0.158267 0.987396i \(-0.449409\pi\)
0.158267 + 0.987396i \(0.449409\pi\)
\(168\) −29.1165 −2.24639
\(169\) −9.34263 −0.718664
\(170\) −18.3965 −1.41095
\(171\) −13.7556 −1.05192
\(172\) 53.3141 4.06517
\(173\) −17.9424 −1.36414 −0.682069 0.731288i \(-0.738920\pi\)
−0.682069 + 0.731288i \(0.738920\pi\)
\(174\) 38.3048 2.90388
\(175\) 4.40363 0.332883
\(176\) −8.37645 −0.631399
\(177\) 32.3045 2.42815
\(178\) −40.8925 −3.06502
\(179\) 12.7114 0.950092 0.475046 0.879961i \(-0.342431\pi\)
0.475046 + 0.879961i \(0.342431\pi\)
\(180\) 119.468 8.90465
\(181\) −7.53782 −0.560282 −0.280141 0.959959i \(-0.590381\pi\)
−0.280141 + 0.959959i \(0.590381\pi\)
\(182\) 5.18452 0.384302
\(183\) −14.1774 −1.04803
\(184\) −4.97983 −0.367118
\(185\) 7.27329 0.534743
\(186\) 5.02526 0.368470
\(187\) −1.33195 −0.0974022
\(188\) −13.4931 −0.984084
\(189\) 13.7341 0.999006
\(190\) 15.7016 1.13912
\(191\) 19.7380 1.42819 0.714095 0.700049i \(-0.246839\pi\)
0.714095 + 0.700049i \(0.246839\pi\)
\(192\) 80.8540 5.83514
\(193\) 7.44244 0.535719 0.267859 0.963458i \(-0.413684\pi\)
0.267859 + 0.963458i \(0.413684\pi\)
\(194\) 6.14602 0.441259
\(195\) −18.8057 −1.34671
\(196\) 5.34933 0.382095
\(197\) −7.04214 −0.501731 −0.250866 0.968022i \(-0.580715\pi\)
−0.250866 + 0.968022i \(0.580715\pi\)
\(198\) 11.8838 0.844545
\(199\) −23.2970 −1.65148 −0.825741 0.564049i \(-0.809243\pi\)
−0.825741 + 0.564049i \(0.809243\pi\)
\(200\) −39.9845 −2.82733
\(201\) 14.0251 0.989255
\(202\) 33.3659 2.34761
\(203\) −4.40627 −0.309259
\(204\) 37.9596 2.65770
\(205\) 37.2168 2.59933
\(206\) 26.7163 1.86141
\(207\) 3.99428 0.277622
\(208\) −26.6145 −1.84539
\(209\) 1.13684 0.0786369
\(210\) −26.6581 −1.83959
\(211\) −28.1411 −1.93732 −0.968658 0.248399i \(-0.920095\pi\)
−0.968658 + 0.248399i \(0.920095\pi\)
\(212\) 8.90480 0.611584
\(213\) −19.6224 −1.34450
\(214\) −13.9203 −0.951569
\(215\) 30.5626 2.08436
\(216\) −124.704 −8.48503
\(217\) −0.578064 −0.0392416
\(218\) −32.0032 −2.16753
\(219\) −39.9851 −2.70194
\(220\) −9.87353 −0.665673
\(221\) −4.23203 −0.284677
\(222\) −20.6189 −1.38385
\(223\) 6.51775 0.436461 0.218230 0.975897i \(-0.429972\pi\)
0.218230 + 0.975897i \(0.429972\pi\)
\(224\) −19.5677 −1.30742
\(225\) 32.0713 2.13809
\(226\) 0.771207 0.0512999
\(227\) −1.43071 −0.0949593 −0.0474796 0.998872i \(-0.515119\pi\)
−0.0474796 + 0.998872i \(0.515119\pi\)
\(228\) −32.3990 −2.14567
\(229\) −1.22533 −0.0809721 −0.0404861 0.999180i \(-0.512891\pi\)
−0.0404861 + 0.999180i \(0.512891\pi\)
\(230\) −4.55936 −0.300636
\(231\) −1.93012 −0.126992
\(232\) 40.0085 2.62669
\(233\) 28.8004 1.88677 0.943387 0.331693i \(-0.107620\pi\)
0.943387 + 0.331693i \(0.107620\pi\)
\(234\) 37.7585 2.46835
\(235\) −7.73499 −0.504575
\(236\) 53.8894 3.50790
\(237\) −29.5218 −1.91765
\(238\) −5.99912 −0.388865
\(239\) 9.63367 0.623150 0.311575 0.950222i \(-0.399143\pi\)
0.311575 + 0.950222i \(0.399143\pi\)
\(240\) 136.849 8.83355
\(241\) 29.5302 1.90221 0.951103 0.308873i \(-0.0999517\pi\)
0.951103 + 0.308873i \(0.0999517\pi\)
\(242\) 28.8385 1.85381
\(243\) 29.9617 1.92204
\(244\) −23.6504 −1.51406
\(245\) 3.06653 0.195914
\(246\) −105.505 −6.72675
\(247\) 3.61209 0.229832
\(248\) 5.24877 0.333297
\(249\) 13.6389 0.864329
\(250\) 4.95780 0.313559
\(251\) 17.5915 1.11036 0.555182 0.831729i \(-0.312649\pi\)
0.555182 + 0.831729i \(0.312649\pi\)
\(252\) 38.9588 2.45417
\(253\) −0.330110 −0.0207538
\(254\) 36.1204 2.26639
\(255\) 21.7606 1.36270
\(256\) 28.7837 1.79898
\(257\) −15.1458 −0.944767 −0.472383 0.881393i \(-0.656606\pi\)
−0.472383 + 0.881393i \(0.656606\pi\)
\(258\) −86.6414 −5.39406
\(259\) 2.37183 0.147378
\(260\) −31.3712 −1.94556
\(261\) −32.0905 −1.98635
\(262\) 35.5373 2.19550
\(263\) −17.4901 −1.07848 −0.539242 0.842151i \(-0.681289\pi\)
−0.539242 + 0.842151i \(0.681289\pi\)
\(264\) 17.5253 1.07861
\(265\) 5.10473 0.313581
\(266\) 5.12032 0.313947
\(267\) 48.3703 2.96021
\(268\) 23.3963 1.42916
\(269\) 22.2887 1.35897 0.679483 0.733692i \(-0.262204\pi\)
0.679483 + 0.733692i \(0.262204\pi\)
\(270\) −114.175 −6.94846
\(271\) −1.39582 −0.0847901 −0.0423951 0.999101i \(-0.513499\pi\)
−0.0423951 + 0.999101i \(0.513499\pi\)
\(272\) 30.7963 1.86730
\(273\) −6.13257 −0.371160
\(274\) −16.6542 −1.00612
\(275\) −2.65055 −0.159834
\(276\) 9.40785 0.566286
\(277\) −8.76458 −0.526612 −0.263306 0.964712i \(-0.584813\pi\)
−0.263306 + 0.964712i \(0.584813\pi\)
\(278\) −46.7249 −2.80237
\(279\) −4.21000 −0.252046
\(280\) −27.8438 −1.66399
\(281\) 9.67768 0.577322 0.288661 0.957431i \(-0.406790\pi\)
0.288661 + 0.957431i \(0.406790\pi\)
\(282\) 21.9278 1.30578
\(283\) 13.2583 0.788127 0.394063 0.919083i \(-0.371069\pi\)
0.394063 + 0.919083i \(0.371069\pi\)
\(284\) −32.7335 −1.94237
\(285\) −18.5729 −1.10016
\(286\) −3.12057 −0.184523
\(287\) 12.1364 0.716391
\(288\) −142.510 −8.39750
\(289\) −12.1030 −0.711943
\(290\) 36.6304 2.15101
\(291\) −7.26991 −0.426170
\(292\) −66.7020 −3.90344
\(293\) 7.82011 0.456856 0.228428 0.973561i \(-0.426642\pi\)
0.228428 + 0.973561i \(0.426642\pi\)
\(294\) −8.69325 −0.507001
\(295\) 30.8924 1.79863
\(296\) −21.5360 −1.25175
\(297\) −8.26656 −0.479674
\(298\) −5.06289 −0.293285
\(299\) −1.04886 −0.0606571
\(300\) 75.5385 4.36121
\(301\) 9.96651 0.574460
\(302\) 2.91953 0.168000
\(303\) −39.4673 −2.26734
\(304\) −26.2850 −1.50755
\(305\) −13.5577 −0.776313
\(306\) −43.6912 −2.49766
\(307\) 26.5077 1.51287 0.756437 0.654066i \(-0.226938\pi\)
0.756437 + 0.654066i \(0.226938\pi\)
\(308\) −3.21977 −0.183463
\(309\) −31.6017 −1.79776
\(310\) 4.80560 0.272940
\(311\) 9.58095 0.543286 0.271643 0.962398i \(-0.412433\pi\)
0.271643 + 0.962398i \(0.412433\pi\)
\(312\) 55.6832 3.15244
\(313\) −9.00853 −0.509192 −0.254596 0.967047i \(-0.581943\pi\)
−0.254596 + 0.967047i \(0.581943\pi\)
\(314\) −42.9800 −2.42550
\(315\) 22.3333 1.25834
\(316\) −49.2474 −2.77038
\(317\) 11.6484 0.654238 0.327119 0.944983i \(-0.393922\pi\)
0.327119 + 0.944983i \(0.393922\pi\)
\(318\) −14.4713 −0.811509
\(319\) 2.65214 0.148491
\(320\) 77.3199 4.32231
\(321\) 16.4658 0.919029
\(322\) −1.48681 −0.0828569
\(323\) −4.17963 −0.232561
\(324\) 118.714 6.59520
\(325\) −8.42161 −0.467147
\(326\) −49.6397 −2.74929
\(327\) 37.8555 2.09341
\(328\) −110.198 −6.08465
\(329\) −2.52239 −0.139064
\(330\) 16.0456 0.883280
\(331\) −29.9465 −1.64601 −0.823005 0.568034i \(-0.807704\pi\)
−0.823005 + 0.568034i \(0.807704\pi\)
\(332\) 22.7520 1.24868
\(333\) 17.2738 0.946601
\(334\) −11.0892 −0.606775
\(335\) 13.4121 0.732779
\(336\) 44.6265 2.43458
\(337\) −21.9141 −1.19374 −0.596869 0.802338i \(-0.703589\pi\)
−0.596869 + 0.802338i \(0.703589\pi\)
\(338\) 25.3275 1.37764
\(339\) −0.912232 −0.0495457
\(340\) 36.3003 1.96866
\(341\) 0.347938 0.0188419
\(342\) 37.2910 2.01646
\(343\) 1.00000 0.0539949
\(344\) −90.4950 −4.87916
\(345\) 5.39311 0.290355
\(346\) 48.6413 2.61497
\(347\) −21.8573 −1.17336 −0.586679 0.809819i \(-0.699565\pi\)
−0.586679 + 0.809819i \(0.699565\pi\)
\(348\) −75.5837 −4.05171
\(349\) −26.1942 −1.40214 −0.701071 0.713092i \(-0.747294\pi\)
−0.701071 + 0.713092i \(0.747294\pi\)
\(350\) −11.9381 −0.638117
\(351\) −26.2654 −1.40194
\(352\) 11.7778 0.627761
\(353\) −29.4961 −1.56992 −0.784959 0.619548i \(-0.787316\pi\)
−0.784959 + 0.619548i \(0.787316\pi\)
\(354\) −87.5763 −4.65463
\(355\) −18.7647 −0.995925
\(356\) 80.6899 4.27656
\(357\) 7.09614 0.375568
\(358\) −34.4601 −1.82127
\(359\) 13.2883 0.701329 0.350664 0.936501i \(-0.385956\pi\)
0.350664 + 0.936501i \(0.385956\pi\)
\(360\) −202.785 −10.6877
\(361\) −15.4326 −0.812244
\(362\) 20.4348 1.07403
\(363\) −34.1120 −1.79041
\(364\) −10.2302 −0.536207
\(365\) −38.2373 −2.00143
\(366\) 38.4345 2.00900
\(367\) −30.8137 −1.60846 −0.804231 0.594317i \(-0.797423\pi\)
−0.804231 + 0.594317i \(0.797423\pi\)
\(368\) 7.63251 0.397872
\(369\) 88.3887 4.60133
\(370\) −19.7176 −1.02507
\(371\) 1.66466 0.0864247
\(372\) −9.91594 −0.514117
\(373\) −12.9802 −0.672088 −0.336044 0.941846i \(-0.609089\pi\)
−0.336044 + 0.941846i \(0.609089\pi\)
\(374\) 3.61088 0.186714
\(375\) −5.86440 −0.302836
\(376\) 22.9031 1.18114
\(377\) 8.42665 0.433995
\(378\) −37.2326 −1.91504
\(379\) 1.72719 0.0887198 0.0443599 0.999016i \(-0.485875\pi\)
0.0443599 + 0.999016i \(0.485875\pi\)
\(380\) −30.9828 −1.58938
\(381\) −42.7255 −2.18889
\(382\) −53.5089 −2.73775
\(383\) −1.19820 −0.0612251 −0.0306125 0.999531i \(-0.509746\pi\)
−0.0306125 + 0.999531i \(0.509746\pi\)
\(384\) −93.6968 −4.78144
\(385\) −1.84575 −0.0940682
\(386\) −20.1762 −1.02694
\(387\) 72.5854 3.68972
\(388\) −12.1275 −0.615678
\(389\) 18.8931 0.957916 0.478958 0.877838i \(-0.341015\pi\)
0.478958 + 0.877838i \(0.341015\pi\)
\(390\) 50.9817 2.58156
\(391\) 1.21366 0.0613774
\(392\) −9.07991 −0.458605
\(393\) −42.0358 −2.12042
\(394\) 19.0910 0.961790
\(395\) −28.2314 −1.42047
\(396\) −23.4493 −1.17837
\(397\) −15.8486 −0.795420 −0.397710 0.917511i \(-0.630195\pi\)
−0.397710 + 0.917511i \(0.630195\pi\)
\(398\) 63.1574 3.16579
\(399\) −6.05664 −0.303211
\(400\) 61.2837 3.06419
\(401\) −36.6445 −1.82994 −0.914970 0.403522i \(-0.867786\pi\)
−0.914970 + 0.403522i \(0.867786\pi\)
\(402\) −38.0216 −1.89634
\(403\) 1.10550 0.0550691
\(404\) −65.8382 −3.27557
\(405\) 68.0533 3.38160
\(406\) 11.9452 0.592832
\(407\) −1.42761 −0.0707638
\(408\) −64.4323 −3.18987
\(409\) 12.0856 0.597597 0.298798 0.954316i \(-0.403414\pi\)
0.298798 + 0.954316i \(0.403414\pi\)
\(410\) −100.893 −4.98277
\(411\) 19.6996 0.971712
\(412\) −52.7171 −2.59718
\(413\) 10.0741 0.495712
\(414\) −10.8284 −0.532185
\(415\) 13.0427 0.640242
\(416\) 37.4218 1.83475
\(417\) 55.2692 2.70654
\(418\) −3.08193 −0.150742
\(419\) −38.1018 −1.86139 −0.930697 0.365791i \(-0.880798\pi\)
−0.930697 + 0.365791i \(0.880798\pi\)
\(420\) 52.6024 2.56673
\(421\) −24.5812 −1.19801 −0.599007 0.800744i \(-0.704438\pi\)
−0.599007 + 0.800744i \(0.704438\pi\)
\(422\) 76.2896 3.71372
\(423\) −18.3704 −0.893198
\(424\) −15.1149 −0.734046
\(425\) 9.74484 0.472694
\(426\) 53.1955 2.57733
\(427\) −4.42119 −0.213956
\(428\) 27.4677 1.32770
\(429\) 3.69121 0.178213
\(430\) −82.8542 −3.99559
\(431\) 41.3162 1.99013 0.995066 0.0992107i \(-0.0316318\pi\)
0.995066 + 0.0992107i \(0.0316318\pi\)
\(432\) 191.132 9.19585
\(433\) 25.7438 1.23717 0.618584 0.785719i \(-0.287707\pi\)
0.618584 + 0.785719i \(0.287707\pi\)
\(434\) 1.56711 0.0752238
\(435\) −43.3288 −2.07746
\(436\) 63.1494 3.02431
\(437\) −1.03587 −0.0495525
\(438\) 108.398 5.17947
\(439\) −3.01761 −0.144023 −0.0720113 0.997404i \(-0.522942\pi\)
−0.0720113 + 0.997404i \(0.522942\pi\)
\(440\) 16.7593 0.798966
\(441\) 7.28293 0.346806
\(442\) 11.4729 0.545709
\(443\) −26.9062 −1.27835 −0.639177 0.769060i \(-0.720725\pi\)
−0.639177 + 0.769060i \(0.720725\pi\)
\(444\) 40.6856 1.93085
\(445\) 46.2560 2.19274
\(446\) −17.6694 −0.836670
\(447\) 5.98871 0.283256
\(448\) 25.2141 1.19125
\(449\) 36.7009 1.73202 0.866012 0.500023i \(-0.166675\pi\)
0.866012 + 0.500023i \(0.166675\pi\)
\(450\) −86.9441 −4.09859
\(451\) −7.30494 −0.343976
\(452\) −1.52176 −0.0715776
\(453\) −3.45340 −0.162255
\(454\) 3.87859 0.182031
\(455\) −5.86452 −0.274933
\(456\) 54.9938 2.57532
\(457\) 4.66643 0.218286 0.109143 0.994026i \(-0.465189\pi\)
0.109143 + 0.994026i \(0.465189\pi\)
\(458\) 3.32183 0.155219
\(459\) 30.3923 1.41859
\(460\) 8.99663 0.419470
\(461\) −9.94352 −0.463116 −0.231558 0.972821i \(-0.574382\pi\)
−0.231558 + 0.972821i \(0.574382\pi\)
\(462\) 5.23248 0.243437
\(463\) −1.46888 −0.0682645 −0.0341322 0.999417i \(-0.510867\pi\)
−0.0341322 + 0.999417i \(0.510867\pi\)
\(464\) −61.3205 −2.84673
\(465\) −5.68437 −0.263606
\(466\) −78.0768 −3.61684
\(467\) −29.1967 −1.35106 −0.675531 0.737332i \(-0.736085\pi\)
−0.675531 + 0.737332i \(0.736085\pi\)
\(468\) −74.5057 −3.44403
\(469\) 4.37369 0.201958
\(470\) 20.9693 0.967241
\(471\) 50.8395 2.34256
\(472\) −91.4715 −4.21032
\(473\) −5.99886 −0.275828
\(474\) 80.0325 3.67601
\(475\) −8.31734 −0.381626
\(476\) 11.8376 0.542575
\(477\) 12.1236 0.555101
\(478\) −26.1165 −1.19454
\(479\) −36.8990 −1.68596 −0.842980 0.537945i \(-0.819201\pi\)
−0.842980 + 0.537945i \(0.819201\pi\)
\(480\) −192.418 −8.78265
\(481\) −4.53594 −0.206821
\(482\) −80.0553 −3.64642
\(483\) 1.75870 0.0800235
\(484\) −56.9046 −2.58657
\(485\) −6.95213 −0.315680
\(486\) −81.2251 −3.68445
\(487\) 4.33836 0.196590 0.0982949 0.995157i \(-0.468661\pi\)
0.0982949 + 0.995157i \(0.468661\pi\)
\(488\) 40.1440 1.81723
\(489\) 58.7170 2.65527
\(490\) −8.31326 −0.375555
\(491\) −17.5659 −0.792739 −0.396370 0.918091i \(-0.629730\pi\)
−0.396370 + 0.918091i \(0.629730\pi\)
\(492\) 208.185 9.38568
\(493\) −9.75068 −0.439148
\(494\) −9.79224 −0.440574
\(495\) −13.4425 −0.604194
\(496\) −8.04472 −0.361218
\(497\) −6.11918 −0.274483
\(498\) −36.9745 −1.65687
\(499\) −35.8314 −1.60403 −0.802017 0.597301i \(-0.796240\pi\)
−0.802017 + 0.597301i \(0.796240\pi\)
\(500\) −9.78283 −0.437502
\(501\) 13.1170 0.586026
\(502\) −47.6898 −2.12850
\(503\) 24.9407 1.11205 0.556026 0.831165i \(-0.312326\pi\)
0.556026 + 0.831165i \(0.312326\pi\)
\(504\) −66.1283 −2.94559
\(505\) −37.7421 −1.67950
\(506\) 0.894916 0.0397839
\(507\) −29.9590 −1.33053
\(508\) −71.2734 −3.16225
\(509\) −7.26986 −0.322231 −0.161116 0.986936i \(-0.551509\pi\)
−0.161116 + 0.986936i \(0.551509\pi\)
\(510\) −58.9921 −2.61221
\(511\) −12.4692 −0.551607
\(512\) −19.5933 −0.865911
\(513\) −25.9402 −1.14529
\(514\) 41.0596 1.81106
\(515\) −30.2204 −1.33167
\(516\) 170.962 7.52620
\(517\) 1.51823 0.0667717
\(518\) −6.42994 −0.282515
\(519\) −57.5360 −2.52555
\(520\) 53.2492 2.33513
\(521\) 17.4924 0.766356 0.383178 0.923675i \(-0.374830\pi\)
0.383178 + 0.923675i \(0.374830\pi\)
\(522\) 86.9963 3.80772
\(523\) 39.4369 1.72446 0.862228 0.506521i \(-0.169069\pi\)
0.862228 + 0.506521i \(0.169069\pi\)
\(524\) −70.1229 −3.06333
\(525\) 14.1211 0.616296
\(526\) 47.4149 2.06739
\(527\) −1.27920 −0.0557230
\(528\) −26.8608 −1.16897
\(529\) −22.6992 −0.986922
\(530\) −13.8387 −0.601116
\(531\) 73.3686 3.18393
\(532\) −10.1035 −0.438043
\(533\) −23.2100 −1.00534
\(534\) −131.130 −5.67455
\(535\) 15.7460 0.680760
\(536\) −39.7127 −1.71533
\(537\) 40.7615 1.75899
\(538\) −60.4238 −2.60506
\(539\) −0.601902 −0.0259257
\(540\) 225.292 9.69503
\(541\) −29.3765 −1.26300 −0.631498 0.775377i \(-0.717560\pi\)
−0.631498 + 0.775377i \(0.717560\pi\)
\(542\) 3.78402 0.162538
\(543\) −24.1715 −1.03730
\(544\) −43.3016 −1.85654
\(545\) 36.2008 1.55067
\(546\) 16.6252 0.711492
\(547\) 23.3507 0.998402 0.499201 0.866486i \(-0.333627\pi\)
0.499201 + 0.866486i \(0.333627\pi\)
\(548\) 32.8624 1.40381
\(549\) −32.1992 −1.37423
\(550\) 7.18555 0.306393
\(551\) 8.32232 0.354543
\(552\) −15.9688 −0.679678
\(553\) −9.20628 −0.391491
\(554\) 23.7605 1.00949
\(555\) 23.3233 0.990017
\(556\) 92.1985 3.91009
\(557\) −18.7893 −0.796127 −0.398063 0.917358i \(-0.630318\pi\)
−0.398063 + 0.917358i \(0.630318\pi\)
\(558\) 11.4132 0.483158
\(559\) −19.0602 −0.806161
\(560\) 42.6759 1.80338
\(561\) −4.27118 −0.180329
\(562\) −26.2359 −1.10669
\(563\) 36.2316 1.52698 0.763489 0.645820i \(-0.223485\pi\)
0.763489 + 0.645820i \(0.223485\pi\)
\(564\) −43.2683 −1.82192
\(565\) −0.872358 −0.0367004
\(566\) −35.9429 −1.51079
\(567\) 22.1923 0.931987
\(568\) 55.5616 2.33131
\(569\) 6.51409 0.273085 0.136542 0.990634i \(-0.456401\pi\)
0.136542 + 0.990634i \(0.456401\pi\)
\(570\) 50.3505 2.10895
\(571\) −39.6208 −1.65808 −0.829040 0.559190i \(-0.811112\pi\)
−0.829040 + 0.559190i \(0.811112\pi\)
\(572\) 6.15757 0.257461
\(573\) 63.2937 2.64413
\(574\) −32.9014 −1.37328
\(575\) 2.41515 0.100719
\(576\) 183.632 7.65135
\(577\) 34.5277 1.43741 0.718703 0.695317i \(-0.244736\pi\)
0.718703 + 0.695317i \(0.244736\pi\)
\(578\) 32.8109 1.36475
\(579\) 23.8657 0.991824
\(580\) −72.2799 −3.00126
\(581\) 4.25325 0.176454
\(582\) 19.7085 0.816942
\(583\) −1.00196 −0.0414970
\(584\) 113.220 4.68506
\(585\) −42.7108 −1.76588
\(586\) −21.2000 −0.875765
\(587\) −5.02385 −0.207356 −0.103678 0.994611i \(-0.533061\pi\)
−0.103678 + 0.994611i \(0.533061\pi\)
\(588\) 17.1537 0.707406
\(589\) 1.09182 0.0449875
\(590\) −83.7483 −3.44786
\(591\) −22.5820 −0.928900
\(592\) 33.0079 1.35662
\(593\) −8.08190 −0.331884 −0.165942 0.986136i \(-0.553066\pi\)
−0.165942 + 0.986136i \(0.553066\pi\)
\(594\) 22.4103 0.919508
\(595\) 6.78597 0.278197
\(596\) 9.99019 0.409214
\(597\) −74.7066 −3.05754
\(598\) 2.84342 0.116276
\(599\) 8.53728 0.348824 0.174412 0.984673i \(-0.444198\pi\)
0.174412 + 0.984673i \(0.444198\pi\)
\(600\) −128.218 −5.23449
\(601\) −43.3785 −1.76945 −0.884724 0.466115i \(-0.845653\pi\)
−0.884724 + 0.466115i \(0.845653\pi\)
\(602\) −27.0189 −1.10121
\(603\) 31.8533 1.29717
\(604\) −5.76087 −0.234406
\(605\) −32.6209 −1.32623
\(606\) 106.994 4.34635
\(607\) 13.8624 0.562659 0.281329 0.959611i \(-0.409225\pi\)
0.281329 + 0.959611i \(0.409225\pi\)
\(608\) 36.9585 1.49886
\(609\) −14.1296 −0.572559
\(610\) 36.7545 1.48815
\(611\) 4.82388 0.195153
\(612\) 86.2123 3.48492
\(613\) −11.5877 −0.468021 −0.234011 0.972234i \(-0.575185\pi\)
−0.234011 + 0.972234i \(0.575185\pi\)
\(614\) −71.8614 −2.90009
\(615\) 119.343 4.81238
\(616\) 5.46521 0.220200
\(617\) 8.24646 0.331990 0.165995 0.986127i \(-0.446916\pi\)
0.165995 + 0.986127i \(0.446916\pi\)
\(618\) 85.6711 3.44620
\(619\) −19.0552 −0.765892 −0.382946 0.923771i \(-0.625091\pi\)
−0.382946 + 0.923771i \(0.625091\pi\)
\(620\) −9.48250 −0.380827
\(621\) 7.53238 0.302264
\(622\) −25.9736 −1.04145
\(623\) 15.0841 0.604333
\(624\) −85.3449 −3.41653
\(625\) −27.6262 −1.10505
\(626\) 24.4218 0.976092
\(627\) 3.64550 0.145587
\(628\) 84.8090 3.38425
\(629\) 5.24864 0.209277
\(630\) −60.5449 −2.41217
\(631\) 26.4779 1.05407 0.527034 0.849844i \(-0.323304\pi\)
0.527034 + 0.849844i \(0.323304\pi\)
\(632\) 83.5921 3.32512
\(633\) −90.2402 −3.58673
\(634\) −31.5783 −1.25414
\(635\) −40.8579 −1.62140
\(636\) 28.5550 1.13228
\(637\) −1.91242 −0.0757730
\(638\) −7.18986 −0.284649
\(639\) −44.5655 −1.76299
\(640\) −89.6012 −3.54180
\(641\) −8.68284 −0.342952 −0.171476 0.985188i \(-0.554854\pi\)
−0.171476 + 0.985188i \(0.554854\pi\)
\(642\) −44.6381 −1.76173
\(643\) −0.267433 −0.0105465 −0.00527327 0.999986i \(-0.501679\pi\)
−0.00527327 + 0.999986i \(0.501679\pi\)
\(644\) 2.93381 0.115608
\(645\) 98.0053 3.85895
\(646\) 11.3308 0.445805
\(647\) 30.0226 1.18031 0.590154 0.807291i \(-0.299067\pi\)
0.590154 + 0.807291i \(0.299067\pi\)
\(648\) −201.504 −7.91581
\(649\) −6.06359 −0.238017
\(650\) 22.8307 0.895493
\(651\) −1.85368 −0.0726514
\(652\) 97.9500 3.83602
\(653\) −0.661776 −0.0258973 −0.0129487 0.999916i \(-0.504122\pi\)
−0.0129487 + 0.999916i \(0.504122\pi\)
\(654\) −102.625 −4.01295
\(655\) −40.1984 −1.57068
\(656\) 168.898 6.59437
\(657\) −90.8126 −3.54294
\(658\) 6.83811 0.266577
\(659\) −6.77978 −0.264103 −0.132051 0.991243i \(-0.542156\pi\)
−0.132051 + 0.991243i \(0.542156\pi\)
\(660\) −31.6615 −1.23242
\(661\) −11.1445 −0.433471 −0.216735 0.976230i \(-0.569541\pi\)
−0.216735 + 0.976230i \(0.569541\pi\)
\(662\) 81.1840 3.15531
\(663\) −13.5708 −0.527048
\(664\) −38.6191 −1.49871
\(665\) −5.79190 −0.224600
\(666\) −46.8288 −1.81458
\(667\) −2.41659 −0.0935709
\(668\) 21.8815 0.846620
\(669\) 20.9005 0.808059
\(670\) −36.3596 −1.40470
\(671\) 2.66112 0.102731
\(672\) −62.7478 −2.42055
\(673\) 16.4967 0.635900 0.317950 0.948108i \(-0.397006\pi\)
0.317950 + 0.948108i \(0.397006\pi\)
\(674\) 59.4084 2.28833
\(675\) 60.4797 2.32787
\(676\) −49.9768 −1.92218
\(677\) 9.29907 0.357392 0.178696 0.983904i \(-0.442812\pi\)
0.178696 + 0.983904i \(0.442812\pi\)
\(678\) 2.47303 0.0949761
\(679\) −2.26710 −0.0870033
\(680\) −61.6159 −2.36286
\(681\) −4.58784 −0.175807
\(682\) −0.943247 −0.0361188
\(683\) 34.2106 1.30903 0.654517 0.756047i \(-0.272872\pi\)
0.654517 + 0.756047i \(0.272872\pi\)
\(684\) −73.5832 −2.81353
\(685\) 18.8386 0.719784
\(686\) −2.71096 −0.103505
\(687\) −3.92927 −0.149911
\(688\) 138.700 5.28790
\(689\) −3.18353 −0.121283
\(690\) −14.6205 −0.556594
\(691\) −33.5702 −1.27707 −0.638535 0.769592i \(-0.720459\pi\)
−0.638535 + 0.769592i \(0.720459\pi\)
\(692\) −95.9799 −3.64861
\(693\) −4.38361 −0.166519
\(694\) 59.2542 2.24926
\(695\) 52.8533 2.00484
\(696\) 128.295 4.86302
\(697\) 26.8568 1.01728
\(698\) 71.0115 2.68782
\(699\) 92.3541 3.49315
\(700\) 23.5564 0.890350
\(701\) −17.6438 −0.666397 −0.333199 0.942857i \(-0.608128\pi\)
−0.333199 + 0.942857i \(0.608128\pi\)
\(702\) 71.2045 2.68744
\(703\) −4.47978 −0.168958
\(704\) −15.1764 −0.571982
\(705\) −24.8038 −0.934165
\(706\) 79.9628 3.00944
\(707\) −12.3078 −0.462881
\(708\) 172.807 6.49449
\(709\) −6.24030 −0.234359 −0.117180 0.993111i \(-0.537385\pi\)
−0.117180 + 0.993111i \(0.537385\pi\)
\(710\) 50.8703 1.90913
\(711\) −67.0487 −2.51452
\(712\) −136.962 −5.13288
\(713\) −0.317036 −0.0118731
\(714\) −19.2374 −0.719941
\(715\) 3.52986 0.132009
\(716\) 67.9972 2.54118
\(717\) 30.8923 1.15369
\(718\) −36.0241 −1.34441
\(719\) 15.2834 0.569974 0.284987 0.958531i \(-0.408011\pi\)
0.284987 + 0.958531i \(0.408011\pi\)
\(720\) 310.805 11.5830
\(721\) −9.85490 −0.367016
\(722\) 41.8373 1.55702
\(723\) 94.6945 3.52173
\(724\) −40.3223 −1.49857
\(725\) −19.4036 −0.720630
\(726\) 92.4763 3.43212
\(727\) 34.8340 1.29192 0.645961 0.763370i \(-0.276457\pi\)
0.645961 + 0.763370i \(0.276457\pi\)
\(728\) 17.3646 0.643576
\(729\) 29.5015 1.09265
\(730\) 103.660 3.83663
\(731\) 22.0550 0.815734
\(732\) −75.8397 −2.80312
\(733\) −11.1026 −0.410084 −0.205042 0.978753i \(-0.565733\pi\)
−0.205042 + 0.978753i \(0.565733\pi\)
\(734\) 83.5348 3.08333
\(735\) 9.83345 0.362712
\(736\) −10.7318 −0.395580
\(737\) −2.63253 −0.0969705
\(738\) −239.619 −8.82049
\(739\) −5.17889 −0.190509 −0.0952543 0.995453i \(-0.530366\pi\)
−0.0952543 + 0.995453i \(0.530366\pi\)
\(740\) 38.9072 1.43026
\(741\) 11.5829 0.425508
\(742\) −4.51283 −0.165671
\(743\) 31.7879 1.16618 0.583092 0.812406i \(-0.301843\pi\)
0.583092 + 0.812406i \(0.301843\pi\)
\(744\) 16.8312 0.617063
\(745\) 5.72693 0.209819
\(746\) 35.1888 1.28835
\(747\) 30.9761 1.13336
\(748\) −7.12506 −0.260518
\(749\) 5.13480 0.187622
\(750\) 15.8982 0.580520
\(751\) −37.4767 −1.36755 −0.683773 0.729695i \(-0.739662\pi\)
−0.683773 + 0.729695i \(0.739662\pi\)
\(752\) −35.1032 −1.28008
\(753\) 56.4106 2.05572
\(754\) −22.8444 −0.831942
\(755\) −3.30245 −0.120188
\(756\) 73.4680 2.67201
\(757\) 28.3676 1.03104 0.515519 0.856878i \(-0.327599\pi\)
0.515519 + 0.856878i \(0.327599\pi\)
\(758\) −4.68235 −0.170071
\(759\) −1.05856 −0.0384234
\(760\) 52.5899 1.90764
\(761\) 13.4009 0.485784 0.242892 0.970053i \(-0.421904\pi\)
0.242892 + 0.970053i \(0.421904\pi\)
\(762\) 115.827 4.19598
\(763\) 11.8051 0.427374
\(764\) 105.585 3.81993
\(765\) 49.4217 1.78685
\(766\) 3.24827 0.117365
\(767\) −19.2659 −0.695650
\(768\) 92.3006 3.33061
\(769\) −33.4525 −1.20633 −0.603163 0.797618i \(-0.706093\pi\)
−0.603163 + 0.797618i \(0.706093\pi\)
\(770\) 5.00377 0.180323
\(771\) −48.5679 −1.74913
\(772\) 39.8120 1.43287
\(773\) −20.4101 −0.734101 −0.367050 0.930201i \(-0.619632\pi\)
−0.367050 + 0.930201i \(0.619632\pi\)
\(774\) −196.776 −7.07298
\(775\) −2.54558 −0.0914399
\(776\) 20.5850 0.738960
\(777\) 7.60574 0.272854
\(778\) −51.2184 −1.83627
\(779\) −22.9226 −0.821289
\(780\) −100.598 −3.60199
\(781\) 3.68314 0.131793
\(782\) −3.29019 −0.117657
\(783\) −60.5160 −2.16266
\(784\) 13.9166 0.497023
\(785\) 48.6172 1.73522
\(786\) 113.957 4.06473
\(787\) 30.8722 1.10048 0.550238 0.835008i \(-0.314537\pi\)
0.550238 + 0.835008i \(0.314537\pi\)
\(788\) −37.6707 −1.34196
\(789\) −56.0854 −1.99669
\(790\) 76.5342 2.72297
\(791\) −0.284477 −0.0101148
\(792\) 39.8027 1.41433
\(793\) 8.45519 0.300253
\(794\) 42.9651 1.52477
\(795\) 16.3693 0.580560
\(796\) −124.623 −4.41716
\(797\) 14.9883 0.530911 0.265456 0.964123i \(-0.414478\pi\)
0.265456 + 0.964123i \(0.414478\pi\)
\(798\) 16.4193 0.581239
\(799\) −5.58182 −0.197471
\(800\) −86.1689 −3.04653
\(801\) 109.857 3.88159
\(802\) 99.3420 3.50789
\(803\) 7.50526 0.264855
\(804\) 75.0249 2.64592
\(805\) 1.68182 0.0592765
\(806\) −2.99698 −0.105564
\(807\) 71.4731 2.51597
\(808\) 111.753 3.93147
\(809\) −23.7519 −0.835072 −0.417536 0.908660i \(-0.637106\pi\)
−0.417536 + 0.908660i \(0.637106\pi\)
\(810\) −184.490 −6.48232
\(811\) 35.7034 1.25372 0.626858 0.779134i \(-0.284341\pi\)
0.626858 + 0.779134i \(0.284341\pi\)
\(812\) −23.5706 −0.827165
\(813\) −4.47598 −0.156980
\(814\) 3.87019 0.135650
\(815\) 56.1504 1.96686
\(816\) 98.7545 3.45710
\(817\) −18.8242 −0.658576
\(818\) −32.7638 −1.14556
\(819\) −13.9281 −0.486686
\(820\) 199.085 6.95234
\(821\) 0.845604 0.0295118 0.0147559 0.999891i \(-0.495303\pi\)
0.0147559 + 0.999891i \(0.495303\pi\)
\(822\) −53.4050 −1.86271
\(823\) 49.7219 1.73320 0.866599 0.499005i \(-0.166301\pi\)
0.866599 + 0.499005i \(0.166301\pi\)
\(824\) 89.4816 3.11724
\(825\) −8.49952 −0.295915
\(826\) −27.3104 −0.950251
\(827\) −46.3319 −1.61112 −0.805559 0.592516i \(-0.798135\pi\)
−0.805559 + 0.592516i \(0.798135\pi\)
\(828\) 21.3667 0.742545
\(829\) −45.0333 −1.56407 −0.782035 0.623235i \(-0.785818\pi\)
−0.782035 + 0.623235i \(0.785818\pi\)
\(830\) −35.3584 −1.22731
\(831\) −28.1054 −0.974965
\(832\) −48.2201 −1.67173
\(833\) 2.21291 0.0766728
\(834\) −149.833 −5.18828
\(835\) 12.5437 0.434092
\(836\) 6.08133 0.210327
\(837\) −7.93917 −0.274418
\(838\) 103.293 3.56818
\(839\) −26.6191 −0.918994 −0.459497 0.888179i \(-0.651970\pi\)
−0.459497 + 0.888179i \(0.651970\pi\)
\(840\) −89.2868 −3.08069
\(841\) −9.58482 −0.330511
\(842\) 66.6387 2.29652
\(843\) 31.0334 1.06885
\(844\) −150.536 −5.18167
\(845\) −28.6495 −0.985572
\(846\) 49.8014 1.71221
\(847\) −10.6377 −0.365516
\(848\) 23.1665 0.795539
\(849\) 42.5155 1.45913
\(850\) −26.4179 −0.906126
\(851\) 1.30082 0.0445914
\(852\) −104.966 −3.59609
\(853\) −14.5421 −0.497911 −0.248956 0.968515i \(-0.580087\pi\)
−0.248956 + 0.968515i \(0.580087\pi\)
\(854\) 11.9857 0.410142
\(855\) −42.1820 −1.44259
\(856\) −46.6235 −1.59356
\(857\) 3.56813 0.121885 0.0609425 0.998141i \(-0.480589\pi\)
0.0609425 + 0.998141i \(0.480589\pi\)
\(858\) −10.0067 −0.341624
\(859\) −1.00000 −0.0341196
\(860\) 163.490 5.57495
\(861\) 38.9179 1.32632
\(862\) −112.007 −3.81497
\(863\) −8.63542 −0.293953 −0.146977 0.989140i \(-0.546954\pi\)
−0.146977 + 0.989140i \(0.546954\pi\)
\(864\) −268.744 −9.14287
\(865\) −55.0211 −1.87077
\(866\) −69.7905 −2.37158
\(867\) −38.8108 −1.31808
\(868\) −3.09226 −0.104958
\(869\) 5.54128 0.187975
\(870\) 117.463 3.98236
\(871\) −8.36435 −0.283415
\(872\) −107.189 −3.62989
\(873\) −16.5111 −0.558817
\(874\) 2.80821 0.0949893
\(875\) −1.82880 −0.0618246
\(876\) −213.893 −7.22679
\(877\) 4.42770 0.149513 0.0747564 0.997202i \(-0.476182\pi\)
0.0747564 + 0.997202i \(0.476182\pi\)
\(878\) 8.18063 0.276083
\(879\) 25.0767 0.845817
\(880\) −25.6867 −0.865898
\(881\) 33.2611 1.12060 0.560298 0.828291i \(-0.310687\pi\)
0.560298 + 0.828291i \(0.310687\pi\)
\(882\) −19.7438 −0.664807
\(883\) −26.5866 −0.894712 −0.447356 0.894356i \(-0.647634\pi\)
−0.447356 + 0.894356i \(0.647634\pi\)
\(884\) −22.6385 −0.761415
\(885\) 99.0628 3.32996
\(886\) 72.9419 2.45053
\(887\) −27.1995 −0.913272 −0.456636 0.889654i \(-0.650946\pi\)
−0.456636 + 0.889654i \(0.650946\pi\)
\(888\) −69.0594 −2.31748
\(889\) −13.3238 −0.446866
\(890\) −125.398 −4.20336
\(891\) −13.3576 −0.447495
\(892\) 34.8656 1.16739
\(893\) 4.76415 0.159426
\(894\) −16.2352 −0.542985
\(895\) 38.9798 1.30295
\(896\) −29.2191 −0.976140
\(897\) −3.36338 −0.112300
\(898\) −99.4949 −3.32019
\(899\) 2.54711 0.0849507
\(900\) 171.560 5.71866
\(901\) 3.68374 0.122723
\(902\) 19.8034 0.659382
\(903\) 31.9596 1.06355
\(904\) 2.58302 0.0859101
\(905\) −23.1150 −0.768368
\(906\) 9.36205 0.311033
\(907\) −37.5501 −1.24683 −0.623415 0.781892i \(-0.714255\pi\)
−0.623415 + 0.781892i \(0.714255\pi\)
\(908\) −7.65331 −0.253984
\(909\) −89.6365 −2.97305
\(910\) 15.8985 0.527030
\(911\) −23.6806 −0.784574 −0.392287 0.919843i \(-0.628316\pi\)
−0.392287 + 0.919843i \(0.628316\pi\)
\(912\) −84.2882 −2.79106
\(913\) −2.56004 −0.0847248
\(914\) −12.6505 −0.418442
\(915\) −43.4756 −1.43726
\(916\) −6.55469 −0.216573
\(917\) −13.1087 −0.432888
\(918\) −82.3923 −2.71935
\(919\) 22.2342 0.733440 0.366720 0.930331i \(-0.380481\pi\)
0.366720 + 0.930331i \(0.380481\pi\)
\(920\) −15.2708 −0.503463
\(921\) 85.0023 2.80092
\(922\) 26.9565 0.887766
\(923\) 11.7025 0.385191
\(924\) −10.3248 −0.339662
\(925\) 10.4446 0.343418
\(926\) 3.98207 0.130859
\(927\) −71.7725 −2.35732
\(928\) 86.2206 2.83033
\(929\) −37.0580 −1.21583 −0.607917 0.794001i \(-0.707995\pi\)
−0.607917 + 0.794001i \(0.707995\pi\)
\(930\) 15.4101 0.505318
\(931\) −1.88875 −0.0619012
\(932\) 154.063 5.04649
\(933\) 30.7232 1.00583
\(934\) 79.1512 2.58991
\(935\) −4.08448 −0.133577
\(936\) 126.465 4.13365
\(937\) −35.5139 −1.16019 −0.580095 0.814549i \(-0.696984\pi\)
−0.580095 + 0.814549i \(0.696984\pi\)
\(938\) −11.8569 −0.387142
\(939\) −28.8877 −0.942713
\(940\) −41.3770 −1.34957
\(941\) 9.05383 0.295146 0.147573 0.989051i \(-0.452854\pi\)
0.147573 + 0.989051i \(0.452854\pi\)
\(942\) −137.824 −4.49055
\(943\) 6.65616 0.216754
\(944\) 140.197 4.56303
\(945\) 42.1160 1.37003
\(946\) 16.2627 0.528746
\(947\) 16.0623 0.521955 0.260977 0.965345i \(-0.415955\pi\)
0.260977 + 0.965345i \(0.415955\pi\)
\(948\) −157.922 −5.12906
\(949\) 23.8465 0.774090
\(950\) 22.5480 0.731554
\(951\) 37.3528 1.21125
\(952\) −20.0930 −0.651219
\(953\) −0.642797 −0.0208222 −0.0104111 0.999946i \(-0.503314\pi\)
−0.0104111 + 0.999946i \(0.503314\pi\)
\(954\) −32.8666 −1.06410
\(955\) 60.5271 1.95861
\(956\) 51.5336 1.66672
\(957\) 8.50462 0.274915
\(958\) 100.032 3.23189
\(959\) 6.14328 0.198377
\(960\) 247.942 8.00228
\(961\) −30.6658 −0.989221
\(962\) 12.2968 0.396464
\(963\) 37.3964 1.20508
\(964\) 157.967 5.08776
\(965\) 22.8225 0.734682
\(966\) −4.76777 −0.153400
\(967\) −48.4275 −1.55732 −0.778661 0.627445i \(-0.784101\pi\)
−0.778661 + 0.627445i \(0.784101\pi\)
\(968\) 96.5894 3.10450
\(969\) −13.4028 −0.430560
\(970\) 18.8470 0.605140
\(971\) 44.9491 1.44249 0.721243 0.692683i \(-0.243571\pi\)
0.721243 + 0.692683i \(0.243571\pi\)
\(972\) 160.275 5.14082
\(973\) 17.2355 0.552546
\(974\) −11.7611 −0.376851
\(975\) −27.0056 −0.864870
\(976\) −61.5281 −1.96947
\(977\) −9.18954 −0.293999 −0.147000 0.989137i \(-0.546962\pi\)
−0.147000 + 0.989137i \(0.546962\pi\)
\(978\) −159.180 −5.09000
\(979\) −9.07916 −0.290171
\(980\) 16.4039 0.524003
\(981\) 85.9758 2.74500
\(982\) 47.6206 1.51963
\(983\) −12.3371 −0.393493 −0.196746 0.980454i \(-0.563038\pi\)
−0.196746 + 0.980454i \(0.563038\pi\)
\(984\) −353.371 −11.2651
\(985\) −21.5949 −0.688072
\(986\) 26.4337 0.841822
\(987\) −8.08855 −0.257461
\(988\) 19.3222 0.614722
\(989\) 5.46608 0.173811
\(990\) 36.4421 1.15821
\(991\) 11.9780 0.380493 0.190246 0.981736i \(-0.439071\pi\)
0.190246 + 0.981736i \(0.439071\pi\)
\(992\) 11.3114 0.359137
\(993\) −96.0296 −3.04741
\(994\) 16.5889 0.526167
\(995\) −71.4411 −2.26484
\(996\) 72.9589 2.31179
\(997\) 17.8541 0.565445 0.282722 0.959202i \(-0.408762\pi\)
0.282722 + 0.959202i \(0.408762\pi\)
\(998\) 97.1377 3.07484
\(999\) 32.5748 1.03062
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 \(a_p\))