Properties

Label 8011.2.a.b.1.2
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79741 q^{2}\) \(+3.22245 q^{3}\) \(+5.82553 q^{4}\) \(-0.295886 q^{5}\) \(-9.01452 q^{6}\) \(+1.71950 q^{7}\) \(-10.7016 q^{8}\) \(+7.38416 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79741 q^{2}\) \(+3.22245 q^{3}\) \(+5.82553 q^{4}\) \(-0.295886 q^{5}\) \(-9.01452 q^{6}\) \(+1.71950 q^{7}\) \(-10.7016 q^{8}\) \(+7.38416 q^{9}\) \(+0.827715 q^{10}\) \(+4.76010 q^{11}\) \(+18.7725 q^{12}\) \(-0.569413 q^{13}\) \(-4.81015 q^{14}\) \(-0.953476 q^{15}\) \(+18.2857 q^{16}\) \(+2.37635 q^{17}\) \(-20.6566 q^{18}\) \(+4.95583 q^{19}\) \(-1.72369 q^{20}\) \(+5.54099 q^{21}\) \(-13.3160 q^{22}\) \(+6.53282 q^{23}\) \(-34.4853 q^{24}\) \(-4.91245 q^{25}\) \(+1.59289 q^{26}\) \(+14.1277 q^{27}\) \(+10.0170 q^{28}\) \(+9.48955 q^{29}\) \(+2.66727 q^{30}\) \(-5.25196 q^{31}\) \(-29.7496 q^{32}\) \(+15.3392 q^{33}\) \(-6.64765 q^{34}\) \(-0.508775 q^{35}\) \(+43.0167 q^{36}\) \(+2.25957 q^{37}\) \(-13.8635 q^{38}\) \(-1.83490 q^{39}\) \(+3.16645 q^{40}\) \(-2.41689 q^{41}\) \(-15.5005 q^{42}\) \(-6.28325 q^{43}\) \(+27.7301 q^{44}\) \(-2.18487 q^{45}\) \(-18.2750 q^{46}\) \(+3.48677 q^{47}\) \(+58.9248 q^{48}\) \(-4.04333 q^{49}\) \(+13.7422 q^{50}\) \(+7.65768 q^{51}\) \(-3.31713 q^{52}\) \(-12.6934 q^{53}\) \(-39.5211 q^{54}\) \(-1.40845 q^{55}\) \(-18.4014 q^{56}\) \(+15.9699 q^{57}\) \(-26.5462 q^{58}\) \(+13.6200 q^{59}\) \(-5.55450 q^{60}\) \(+6.78837 q^{61}\) \(+14.6919 q^{62}\) \(+12.6971 q^{63}\) \(+46.6505 q^{64}\) \(+0.168481 q^{65}\) \(-42.9100 q^{66}\) \(-12.4057 q^{67}\) \(+13.8435 q^{68}\) \(+21.0517 q^{69}\) \(+1.42325 q^{70}\) \(-6.95038 q^{71}\) \(-79.0223 q^{72}\) \(+9.90863 q^{73}\) \(-6.32097 q^{74}\) \(-15.8301 q^{75}\) \(+28.8704 q^{76}\) \(+8.18499 q^{77}\) \(+5.13299 q^{78}\) \(-1.84979 q^{79}\) \(-5.41049 q^{80}\) \(+23.3734 q^{81}\) \(+6.76103 q^{82}\) \(+8.47139 q^{83}\) \(+32.2792 q^{84}\) \(-0.703129 q^{85}\) \(+17.5769 q^{86}\) \(+30.5796 q^{87}\) \(-50.9407 q^{88}\) \(+2.21152 q^{89}\) \(+6.11198 q^{90}\) \(-0.979105 q^{91}\) \(+38.0572 q^{92}\) \(-16.9242 q^{93}\) \(-9.75396 q^{94}\) \(-1.46636 q^{95}\) \(-95.8665 q^{96}\) \(-4.85889 q^{97}\) \(+11.3109 q^{98}\) \(+35.1494 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79741 −1.97807 −0.989036 0.147678i \(-0.952820\pi\)
−0.989036 + 0.147678i \(0.952820\pi\)
\(3\) 3.22245 1.86048 0.930240 0.366951i \(-0.119598\pi\)
0.930240 + 0.366951i \(0.119598\pi\)
\(4\) 5.82553 2.91276
\(5\) −0.295886 −0.132324 −0.0661620 0.997809i \(-0.521075\pi\)
−0.0661620 + 0.997809i \(0.521075\pi\)
\(6\) −9.01452 −3.68016
\(7\) 1.71950 0.649909 0.324955 0.945730i \(-0.394651\pi\)
0.324955 + 0.945730i \(0.394651\pi\)
\(8\) −10.7016 −3.78358
\(9\) 7.38416 2.46139
\(10\) 0.827715 0.261746
\(11\) 4.76010 1.43522 0.717612 0.696443i \(-0.245235\pi\)
0.717612 + 0.696443i \(0.245235\pi\)
\(12\) 18.7725 5.41914
\(13\) −0.569413 −0.157927 −0.0789634 0.996878i \(-0.525161\pi\)
−0.0789634 + 0.996878i \(0.525161\pi\)
\(14\) −4.81015 −1.28557
\(15\) −0.953476 −0.246186
\(16\) 18.2857 4.57143
\(17\) 2.37635 0.576351 0.288175 0.957578i \(-0.406951\pi\)
0.288175 + 0.957578i \(0.406951\pi\)
\(18\) −20.6566 −4.86880
\(19\) 4.95583 1.13695 0.568473 0.822702i \(-0.307534\pi\)
0.568473 + 0.822702i \(0.307534\pi\)
\(20\) −1.72369 −0.385429
\(21\) 5.54099 1.20914
\(22\) −13.3160 −2.83898
\(23\) 6.53282 1.36219 0.681094 0.732196i \(-0.261505\pi\)
0.681094 + 0.732196i \(0.261505\pi\)
\(24\) −34.4853 −7.03929
\(25\) −4.91245 −0.982490
\(26\) 1.59289 0.312391
\(27\) 14.1277 2.71888
\(28\) 10.0170 1.89303
\(29\) 9.48955 1.76217 0.881083 0.472962i \(-0.156815\pi\)
0.881083 + 0.472962i \(0.156815\pi\)
\(30\) 2.66727 0.486974
\(31\) −5.25196 −0.943280 −0.471640 0.881791i \(-0.656338\pi\)
−0.471640 + 0.881791i \(0.656338\pi\)
\(32\) −29.7496 −5.25904
\(33\) 15.3392 2.67021
\(34\) −6.64765 −1.14006
\(35\) −0.508775 −0.0859986
\(36\) 43.0167 7.16944
\(37\) 2.25957 0.371472 0.185736 0.982600i \(-0.440533\pi\)
0.185736 + 0.982600i \(0.440533\pi\)
\(38\) −13.8635 −2.24896
\(39\) −1.83490 −0.293820
\(40\) 3.16645 0.500659
\(41\) −2.41689 −0.377454 −0.188727 0.982030i \(-0.560436\pi\)
−0.188727 + 0.982030i \(0.560436\pi\)
\(42\) −15.5005 −2.39177
\(43\) −6.28325 −0.958187 −0.479094 0.877764i \(-0.659035\pi\)
−0.479094 + 0.877764i \(0.659035\pi\)
\(44\) 27.7301 4.18047
\(45\) −2.18487 −0.325701
\(46\) −18.2750 −2.69450
\(47\) 3.48677 0.508598 0.254299 0.967126i \(-0.418155\pi\)
0.254299 + 0.967126i \(0.418155\pi\)
\(48\) 58.9248 8.50506
\(49\) −4.04333 −0.577618
\(50\) 13.7422 1.94344
\(51\) 7.65768 1.07229
\(52\) −3.31713 −0.460004
\(53\) −12.6934 −1.74357 −0.871787 0.489884i \(-0.837039\pi\)
−0.871787 + 0.489884i \(0.837039\pi\)
\(54\) −39.5211 −5.37814
\(55\) −1.40845 −0.189915
\(56\) −18.4014 −2.45899
\(57\) 15.9699 2.11527
\(58\) −26.5462 −3.48569
\(59\) 13.6200 1.77317 0.886584 0.462567i \(-0.153072\pi\)
0.886584 + 0.462567i \(0.153072\pi\)
\(60\) −5.55450 −0.717083
\(61\) 6.78837 0.869162 0.434581 0.900633i \(-0.356896\pi\)
0.434581 + 0.900633i \(0.356896\pi\)
\(62\) 14.6919 1.86588
\(63\) 12.6971 1.59968
\(64\) 46.6505 5.83131
\(65\) 0.168481 0.0208975
\(66\) −42.9100 −5.28186
\(67\) −12.4057 −1.51560 −0.757799 0.652488i \(-0.773725\pi\)
−0.757799 + 0.652488i \(0.773725\pi\)
\(68\) 13.8435 1.67877
\(69\) 21.0517 2.53432
\(70\) 1.42325 0.170111
\(71\) −6.95038 −0.824858 −0.412429 0.910990i \(-0.635320\pi\)
−0.412429 + 0.910990i \(0.635320\pi\)
\(72\) −79.0223 −9.31287
\(73\) 9.90863 1.15972 0.579859 0.814717i \(-0.303108\pi\)
0.579859 + 0.814717i \(0.303108\pi\)
\(74\) −6.32097 −0.734798
\(75\) −15.8301 −1.82790
\(76\) 28.8704 3.31166
\(77\) 8.18499 0.932766
\(78\) 5.13299 0.581197
\(79\) −1.84979 −0.208118 −0.104059 0.994571i \(-0.533183\pi\)
−0.104059 + 0.994571i \(0.533183\pi\)
\(80\) −5.41049 −0.604911
\(81\) 23.3734 2.59704
\(82\) 6.76103 0.746631
\(83\) 8.47139 0.929856 0.464928 0.885349i \(-0.346080\pi\)
0.464928 + 0.885349i \(0.346080\pi\)
\(84\) 32.2792 3.52195
\(85\) −0.703129 −0.0762651
\(86\) 17.5769 1.89536
\(87\) 30.5796 3.27847
\(88\) −50.9407 −5.43029
\(89\) 2.21152 0.234421 0.117210 0.993107i \(-0.462605\pi\)
0.117210 + 0.993107i \(0.462605\pi\)
\(90\) 6.11198 0.644259
\(91\) −0.979105 −0.102638
\(92\) 38.0572 3.96773
\(93\) −16.9242 −1.75495
\(94\) −9.75396 −1.00604
\(95\) −1.46636 −0.150445
\(96\) −95.8665 −9.78434
\(97\) −4.85889 −0.493346 −0.246673 0.969099i \(-0.579337\pi\)
−0.246673 + 0.969099i \(0.579337\pi\)
\(98\) 11.3109 1.14257
\(99\) 35.1494 3.53264
\(100\) −28.6176 −2.86176
\(101\) 7.18760 0.715193 0.357597 0.933876i \(-0.383596\pi\)
0.357597 + 0.933876i \(0.383596\pi\)
\(102\) −21.4217 −2.12106
\(103\) 9.39259 0.925480 0.462740 0.886494i \(-0.346866\pi\)
0.462740 + 0.886494i \(0.346866\pi\)
\(104\) 6.09363 0.597530
\(105\) −1.63950 −0.159999
\(106\) 35.5087 3.44891
\(107\) −15.3956 −1.48834 −0.744172 0.667988i \(-0.767156\pi\)
−0.744172 + 0.667988i \(0.767156\pi\)
\(108\) 82.3015 7.91946
\(109\) −8.19652 −0.785084 −0.392542 0.919734i \(-0.628404\pi\)
−0.392542 + 0.919734i \(0.628404\pi\)
\(110\) 3.94001 0.375665
\(111\) 7.28136 0.691116
\(112\) 31.4423 2.97102
\(113\) −8.19462 −0.770885 −0.385443 0.922732i \(-0.625951\pi\)
−0.385443 + 0.922732i \(0.625951\pi\)
\(114\) −44.6745 −4.18415
\(115\) −1.93297 −0.180250
\(116\) 55.2817 5.13277
\(117\) −4.20464 −0.388719
\(118\) −38.1007 −3.50745
\(119\) 4.08614 0.374576
\(120\) 10.2037 0.931467
\(121\) 11.6586 1.05987
\(122\) −18.9899 −1.71926
\(123\) −7.78828 −0.702246
\(124\) −30.5955 −2.74755
\(125\) 2.93295 0.262331
\(126\) −35.5189 −3.16428
\(127\) 9.45115 0.838654 0.419327 0.907835i \(-0.362266\pi\)
0.419327 + 0.907835i \(0.362266\pi\)
\(128\) −71.0016 −6.27572
\(129\) −20.2475 −1.78269
\(130\) −0.471312 −0.0413368
\(131\) 1.36787 0.119512 0.0597558 0.998213i \(-0.480968\pi\)
0.0597558 + 0.998213i \(0.480968\pi\)
\(132\) 89.3588 7.77769
\(133\) 8.52155 0.738912
\(134\) 34.7039 2.99796
\(135\) −4.18019 −0.359774
\(136\) −25.4308 −2.18067
\(137\) −20.0197 −1.71040 −0.855199 0.518300i \(-0.826565\pi\)
−0.855199 + 0.518300i \(0.826565\pi\)
\(138\) −58.8903 −5.01307
\(139\) −0.356925 −0.0302740 −0.0151370 0.999885i \(-0.504818\pi\)
−0.0151370 + 0.999885i \(0.504818\pi\)
\(140\) −2.96388 −0.250494
\(141\) 11.2359 0.946237
\(142\) 19.4431 1.63163
\(143\) −2.71047 −0.226661
\(144\) 135.025 11.2521
\(145\) −2.80782 −0.233177
\(146\) −27.7186 −2.29400
\(147\) −13.0294 −1.07465
\(148\) 13.1632 1.08201
\(149\) 0.411045 0.0336741 0.0168370 0.999858i \(-0.494640\pi\)
0.0168370 + 0.999858i \(0.494640\pi\)
\(150\) 44.2834 3.61572
\(151\) −13.2413 −1.07756 −0.538780 0.842447i \(-0.681115\pi\)
−0.538780 + 0.842447i \(0.681115\pi\)
\(152\) −53.0353 −4.30173
\(153\) 17.5474 1.41862
\(154\) −22.8968 −1.84508
\(155\) 1.55398 0.124819
\(156\) −10.6893 −0.855828
\(157\) −13.2152 −1.05469 −0.527345 0.849651i \(-0.676812\pi\)
−0.527345 + 0.849651i \(0.676812\pi\)
\(158\) 5.17464 0.411672
\(159\) −40.9039 −3.24389
\(160\) 8.80248 0.695897
\(161\) 11.2332 0.885299
\(162\) −65.3850 −5.13713
\(163\) −24.1635 −1.89263 −0.946317 0.323241i \(-0.895228\pi\)
−0.946317 + 0.323241i \(0.895228\pi\)
\(164\) −14.0796 −1.09943
\(165\) −4.53864 −0.353333
\(166\) −23.6980 −1.83932
\(167\) −18.9667 −1.46768 −0.733842 0.679320i \(-0.762275\pi\)
−0.733842 + 0.679320i \(0.762275\pi\)
\(168\) −59.2974 −4.57490
\(169\) −12.6758 −0.975059
\(170\) 1.96694 0.150858
\(171\) 36.5947 2.79847
\(172\) −36.6033 −2.79097
\(173\) 23.9198 1.81859 0.909293 0.416156i \(-0.136623\pi\)
0.909293 + 0.416156i \(0.136623\pi\)
\(174\) −85.5437 −6.48505
\(175\) −8.44695 −0.638530
\(176\) 87.0420 6.56104
\(177\) 43.8896 3.29895
\(178\) −6.18654 −0.463701
\(179\) 0.794507 0.0593843 0.0296921 0.999559i \(-0.490547\pi\)
0.0296921 + 0.999559i \(0.490547\pi\)
\(180\) −12.7280 −0.948690
\(181\) −11.9035 −0.884781 −0.442390 0.896823i \(-0.645869\pi\)
−0.442390 + 0.896823i \(0.645869\pi\)
\(182\) 2.73896 0.203026
\(183\) 21.8752 1.61706
\(184\) −69.9116 −5.15395
\(185\) −0.668576 −0.0491547
\(186\) 47.3439 3.47142
\(187\) 11.3117 0.827193
\(188\) 20.3123 1.48143
\(189\) 24.2926 1.76703
\(190\) 4.10202 0.297592
\(191\) 10.0934 0.730333 0.365166 0.930942i \(-0.381012\pi\)
0.365166 + 0.930942i \(0.381012\pi\)
\(192\) 150.329 10.8490
\(193\) −1.57834 −0.113612 −0.0568058 0.998385i \(-0.518092\pi\)
−0.0568058 + 0.998385i \(0.518092\pi\)
\(194\) 13.5923 0.975873
\(195\) 0.542922 0.0388794
\(196\) −23.5545 −1.68247
\(197\) −5.31119 −0.378407 −0.189203 0.981938i \(-0.560591\pi\)
−0.189203 + 0.981938i \(0.560591\pi\)
\(198\) −98.3273 −6.98782
\(199\) −15.9935 −1.13375 −0.566875 0.823804i \(-0.691848\pi\)
−0.566875 + 0.823804i \(0.691848\pi\)
\(200\) 52.5711 3.71734
\(201\) −39.9767 −2.81974
\(202\) −20.1067 −1.41470
\(203\) 16.3173 1.14525
\(204\) 44.6100 3.12333
\(205\) 0.715122 0.0499463
\(206\) −26.2750 −1.83066
\(207\) 48.2394 3.35287
\(208\) −10.4121 −0.721952
\(209\) 23.5903 1.63177
\(210\) 4.58636 0.316489
\(211\) −10.6108 −0.730477 −0.365239 0.930914i \(-0.619013\pi\)
−0.365239 + 0.930914i \(0.619013\pi\)
\(212\) −73.9459 −5.07862
\(213\) −22.3972 −1.53463
\(214\) 43.0678 2.94405
\(215\) 1.85912 0.126791
\(216\) −151.189 −10.2871
\(217\) −9.03074 −0.613047
\(218\) 22.9291 1.55295
\(219\) 31.9300 2.15763
\(220\) −8.20494 −0.553177
\(221\) −1.35313 −0.0910213
\(222\) −20.3690 −1.36708
\(223\) 9.82366 0.657841 0.328921 0.944358i \(-0.393315\pi\)
0.328921 + 0.944358i \(0.393315\pi\)
\(224\) −51.1544 −3.41790
\(225\) −36.2743 −2.41829
\(226\) 22.9238 1.52487
\(227\) −17.8725 −1.18624 −0.593118 0.805115i \(-0.702103\pi\)
−0.593118 + 0.805115i \(0.702103\pi\)
\(228\) 93.0332 6.16127
\(229\) −26.3659 −1.74231 −0.871153 0.491012i \(-0.836627\pi\)
−0.871153 + 0.491012i \(0.836627\pi\)
\(230\) 5.40731 0.356548
\(231\) 26.3757 1.73539
\(232\) −101.553 −6.66730
\(233\) 16.6028 1.08768 0.543842 0.839187i \(-0.316969\pi\)
0.543842 + 0.839187i \(0.316969\pi\)
\(234\) 11.7621 0.768914
\(235\) −1.03169 −0.0672998
\(236\) 79.3435 5.16482
\(237\) −5.96086 −0.387199
\(238\) −11.4306 −0.740937
\(239\) −8.62053 −0.557616 −0.278808 0.960347i \(-0.589939\pi\)
−0.278808 + 0.960347i \(0.589939\pi\)
\(240\) −17.4350 −1.12542
\(241\) 8.51174 0.548289 0.274145 0.961688i \(-0.411605\pi\)
0.274145 + 0.961688i \(0.411605\pi\)
\(242\) −32.6139 −2.09650
\(243\) 32.9362 2.11286
\(244\) 39.5459 2.53166
\(245\) 1.19636 0.0764328
\(246\) 21.7871 1.38909
\(247\) −2.82192 −0.179554
\(248\) 56.2044 3.56898
\(249\) 27.2986 1.72998
\(250\) −8.20468 −0.518910
\(251\) −11.7387 −0.740938 −0.370469 0.928845i \(-0.620803\pi\)
−0.370469 + 0.928845i \(0.620803\pi\)
\(252\) 73.9671 4.65949
\(253\) 31.0969 1.95505
\(254\) −26.4388 −1.65892
\(255\) −2.26580 −0.141890
\(256\) 105.320 6.58250
\(257\) −9.19620 −0.573643 −0.286822 0.957984i \(-0.592599\pi\)
−0.286822 + 0.957984i \(0.592599\pi\)
\(258\) 56.6405 3.52628
\(259\) 3.88534 0.241423
\(260\) 0.981492 0.0608696
\(261\) 70.0724 4.33737
\(262\) −3.82650 −0.236402
\(263\) 21.2195 1.30845 0.654225 0.756300i \(-0.272995\pi\)
0.654225 + 0.756300i \(0.272995\pi\)
\(264\) −164.154 −10.1030
\(265\) 3.75580 0.230717
\(266\) −23.8383 −1.46162
\(267\) 7.12651 0.436135
\(268\) −72.2698 −4.41458
\(269\) 21.2646 1.29652 0.648261 0.761418i \(-0.275496\pi\)
0.648261 + 0.761418i \(0.275496\pi\)
\(270\) 11.6937 0.711658
\(271\) 13.0106 0.790336 0.395168 0.918609i \(-0.370686\pi\)
0.395168 + 0.918609i \(0.370686\pi\)
\(272\) 43.4534 2.63475
\(273\) −3.15511 −0.190956
\(274\) 56.0034 3.38329
\(275\) −23.3838 −1.41009
\(276\) 122.637 7.38189
\(277\) 16.6991 1.00335 0.501677 0.865055i \(-0.332717\pi\)
0.501677 + 0.865055i \(0.332717\pi\)
\(278\) 0.998468 0.0598841
\(279\) −38.7813 −2.32178
\(280\) 5.44470 0.325383
\(281\) −9.93377 −0.592599 −0.296299 0.955095i \(-0.595753\pi\)
−0.296299 + 0.955095i \(0.595753\pi\)
\(282\) −31.4316 −1.87172
\(283\) 0.728183 0.0432860 0.0216430 0.999766i \(-0.493110\pi\)
0.0216430 + 0.999766i \(0.493110\pi\)
\(284\) −40.4896 −2.40262
\(285\) −4.72527 −0.279901
\(286\) 7.58230 0.448351
\(287\) −4.15583 −0.245311
\(288\) −219.676 −12.9445
\(289\) −11.3529 −0.667820
\(290\) 7.85464 0.461240
\(291\) −15.6575 −0.917861
\(292\) 57.7230 3.37799
\(293\) 16.7529 0.978715 0.489358 0.872083i \(-0.337231\pi\)
0.489358 + 0.872083i \(0.337231\pi\)
\(294\) 36.4486 2.12573
\(295\) −4.02995 −0.234633
\(296\) −24.1811 −1.40550
\(297\) 67.2494 3.90221
\(298\) −1.14986 −0.0666097
\(299\) −3.71988 −0.215126
\(300\) −92.2188 −5.32425
\(301\) −10.8040 −0.622735
\(302\) 37.0413 2.13149
\(303\) 23.1617 1.33060
\(304\) 90.6211 5.19748
\(305\) −2.00858 −0.115011
\(306\) −49.0873 −2.80614
\(307\) 7.32258 0.417922 0.208961 0.977924i \(-0.432992\pi\)
0.208961 + 0.977924i \(0.432992\pi\)
\(308\) 47.6819 2.71693
\(309\) 30.2671 1.72184
\(310\) −4.34713 −0.246900
\(311\) 19.9093 1.12895 0.564475 0.825450i \(-0.309079\pi\)
0.564475 + 0.825450i \(0.309079\pi\)
\(312\) 19.6364 1.11169
\(313\) −0.567200 −0.0320600 −0.0160300 0.999872i \(-0.505103\pi\)
−0.0160300 + 0.999872i \(0.505103\pi\)
\(314\) 36.9684 2.08625
\(315\) −3.75688 −0.211676
\(316\) −10.7760 −0.606199
\(317\) −0.427611 −0.0240170 −0.0120085 0.999928i \(-0.503823\pi\)
−0.0120085 + 0.999928i \(0.503823\pi\)
\(318\) 114.425 6.41664
\(319\) 45.1712 2.52910
\(320\) −13.8032 −0.771623
\(321\) −49.6114 −2.76904
\(322\) −31.4239 −1.75118
\(323\) 11.7768 0.655280
\(324\) 136.162 7.56456
\(325\) 2.79722 0.155162
\(326\) 67.5954 3.74376
\(327\) −26.4129 −1.46063
\(328\) 25.8645 1.42813
\(329\) 5.99550 0.330543
\(330\) 12.6965 0.698917
\(331\) −9.46313 −0.520141 −0.260070 0.965590i \(-0.583746\pi\)
−0.260070 + 0.965590i \(0.583746\pi\)
\(332\) 49.3503 2.70845
\(333\) 16.6851 0.914336
\(334\) 53.0576 2.90318
\(335\) 3.67067 0.200550
\(336\) 101.321 5.52752
\(337\) −10.2290 −0.557209 −0.278604 0.960406i \(-0.589872\pi\)
−0.278604 + 0.960406i \(0.589872\pi\)
\(338\) 35.4594 1.92874
\(339\) −26.4067 −1.43422
\(340\) −4.09610 −0.222142
\(341\) −24.9999 −1.35382
\(342\) −102.371 −5.53556
\(343\) −18.9890 −1.02531
\(344\) 67.2408 3.62538
\(345\) −6.22889 −0.335352
\(346\) −66.9135 −3.59729
\(347\) −12.8192 −0.688169 −0.344084 0.938939i \(-0.611811\pi\)
−0.344084 + 0.938939i \(0.611811\pi\)
\(348\) 178.142 9.54942
\(349\) −26.4986 −1.41844 −0.709218 0.704989i \(-0.750952\pi\)
−0.709218 + 0.704989i \(0.750952\pi\)
\(350\) 23.6296 1.26306
\(351\) −8.04452 −0.429385
\(352\) −141.611 −7.54790
\(353\) −24.2714 −1.29184 −0.645919 0.763406i \(-0.723526\pi\)
−0.645919 + 0.763406i \(0.723526\pi\)
\(354\) −122.777 −6.52555
\(355\) 2.05652 0.109149
\(356\) 12.8833 0.682812
\(357\) 13.1674 0.696891
\(358\) −2.22257 −0.117466
\(359\) 18.8896 0.996954 0.498477 0.866903i \(-0.333893\pi\)
0.498477 + 0.866903i \(0.333893\pi\)
\(360\) 23.3816 1.23232
\(361\) 5.56030 0.292647
\(362\) 33.2990 1.75016
\(363\) 37.5691 1.97187
\(364\) −5.70381 −0.298961
\(365\) −2.93182 −0.153459
\(366\) −61.1939 −3.19866
\(367\) −4.58029 −0.239089 −0.119545 0.992829i \(-0.538143\pi\)
−0.119545 + 0.992829i \(0.538143\pi\)
\(368\) 119.457 6.22715
\(369\) −17.8467 −0.929060
\(370\) 1.87028 0.0972314
\(371\) −21.8263 −1.13317
\(372\) −98.5922 −5.11177
\(373\) −22.7896 −1.18000 −0.590002 0.807402i \(-0.700873\pi\)
−0.590002 + 0.807402i \(0.700873\pi\)
\(374\) −31.6435 −1.63625
\(375\) 9.45128 0.488062
\(376\) −37.3140 −1.92433
\(377\) −5.40348 −0.278293
\(378\) −67.9565 −3.49530
\(379\) 5.56494 0.285852 0.142926 0.989733i \(-0.454349\pi\)
0.142926 + 0.989733i \(0.454349\pi\)
\(380\) −8.54232 −0.438212
\(381\) 30.4558 1.56030
\(382\) −28.2354 −1.44465
\(383\) 2.56511 0.131071 0.0655355 0.997850i \(-0.479124\pi\)
0.0655355 + 0.997850i \(0.479124\pi\)
\(384\) −228.799 −11.6758
\(385\) −2.42182 −0.123427
\(386\) 4.41528 0.224732
\(387\) −46.3966 −2.35847
\(388\) −28.3056 −1.43700
\(389\) 25.0265 1.26889 0.634447 0.772966i \(-0.281228\pi\)
0.634447 + 0.772966i \(0.281228\pi\)
\(390\) −1.51878 −0.0769063
\(391\) 15.5243 0.785098
\(392\) 43.2700 2.18547
\(393\) 4.40789 0.222349
\(394\) 14.8576 0.748515
\(395\) 0.547327 0.0275390
\(396\) 204.764 10.2898
\(397\) −32.4397 −1.62810 −0.814050 0.580795i \(-0.802742\pi\)
−0.814050 + 0.580795i \(0.802742\pi\)
\(398\) 44.7405 2.24264
\(399\) 27.4602 1.37473
\(400\) −89.8278 −4.49139
\(401\) −35.4524 −1.77041 −0.885204 0.465202i \(-0.845982\pi\)
−0.885204 + 0.465202i \(0.845982\pi\)
\(402\) 111.831 5.57764
\(403\) 2.99054 0.148969
\(404\) 41.8716 2.08319
\(405\) −6.91584 −0.343651
\(406\) −45.6462 −2.26538
\(407\) 10.7558 0.533146
\(408\) −81.9493 −4.05710
\(409\) 25.4003 1.25596 0.627982 0.778228i \(-0.283881\pi\)
0.627982 + 0.778228i \(0.283881\pi\)
\(410\) −2.00049 −0.0987972
\(411\) −64.5124 −3.18216
\(412\) 54.7168 2.69571
\(413\) 23.4195 1.15240
\(414\) −134.946 −6.63222
\(415\) −2.50656 −0.123042
\(416\) 16.9398 0.830543
\(417\) −1.15017 −0.0563242
\(418\) −65.9918 −3.22776
\(419\) 26.0223 1.27127 0.635637 0.771988i \(-0.280737\pi\)
0.635637 + 0.771988i \(0.280737\pi\)
\(420\) −9.55095 −0.466039
\(421\) 32.0370 1.56139 0.780694 0.624913i \(-0.214866\pi\)
0.780694 + 0.624913i \(0.214866\pi\)
\(422\) 29.6828 1.44494
\(423\) 25.7469 1.25186
\(424\) 135.840 6.59696
\(425\) −11.6737 −0.566259
\(426\) 62.6543 3.03561
\(427\) 11.6726 0.564876
\(428\) −89.6873 −4.33520
\(429\) −8.73433 −0.421698
\(430\) −5.20074 −0.250802
\(431\) 5.74291 0.276626 0.138313 0.990389i \(-0.455832\pi\)
0.138313 + 0.990389i \(0.455832\pi\)
\(432\) 258.336 12.4292
\(433\) 0.125801 0.00604559 0.00302280 0.999995i \(-0.499038\pi\)
0.00302280 + 0.999995i \(0.499038\pi\)
\(434\) 25.2627 1.21265
\(435\) −9.04805 −0.433821
\(436\) −47.7491 −2.28677
\(437\) 32.3756 1.54873
\(438\) −89.3216 −4.26795
\(439\) 26.4347 1.26166 0.630829 0.775922i \(-0.282715\pi\)
0.630829 + 0.775922i \(0.282715\pi\)
\(440\) 15.0726 0.718559
\(441\) −29.8566 −1.42174
\(442\) 3.78526 0.180047
\(443\) 12.5625 0.596864 0.298432 0.954431i \(-0.403536\pi\)
0.298432 + 0.954431i \(0.403536\pi\)
\(444\) 42.4178 2.01306
\(445\) −0.654357 −0.0310195
\(446\) −27.4809 −1.30126
\(447\) 1.32457 0.0626500
\(448\) 80.2155 3.78983
\(449\) −30.2232 −1.42632 −0.713161 0.701000i \(-0.752737\pi\)
−0.713161 + 0.701000i \(0.752737\pi\)
\(450\) 101.474 4.78355
\(451\) −11.5046 −0.541731
\(452\) −47.7380 −2.24541
\(453\) −42.6693 −2.00478
\(454\) 49.9967 2.34646
\(455\) 0.289703 0.0135815
\(456\) −170.904 −8.00329
\(457\) −33.5684 −1.57026 −0.785131 0.619330i \(-0.787404\pi\)
−0.785131 + 0.619330i \(0.787404\pi\)
\(458\) 73.7563 3.44640
\(459\) 33.5725 1.56703
\(460\) −11.2606 −0.525027
\(461\) 37.7660 1.75894 0.879469 0.475955i \(-0.157898\pi\)
0.879469 + 0.475955i \(0.157898\pi\)
\(462\) −73.7837 −3.43273
\(463\) −22.4431 −1.04302 −0.521510 0.853245i \(-0.674631\pi\)
−0.521510 + 0.853245i \(0.674631\pi\)
\(464\) 173.523 8.05562
\(465\) 5.00762 0.232223
\(466\) −46.4449 −2.15152
\(467\) 18.9509 0.876945 0.438473 0.898745i \(-0.355520\pi\)
0.438473 + 0.898745i \(0.355520\pi\)
\(468\) −24.4943 −1.13225
\(469\) −21.3316 −0.985001
\(470\) 2.88605 0.133124
\(471\) −42.5853 −1.96223
\(472\) −145.755 −6.70893
\(473\) −29.9089 −1.37521
\(474\) 16.6750 0.765908
\(475\) −24.3453 −1.11704
\(476\) 23.8039 1.09105
\(477\) −93.7302 −4.29161
\(478\) 24.1152 1.10300
\(479\) 7.22302 0.330028 0.165014 0.986291i \(-0.447233\pi\)
0.165014 + 0.986291i \(0.447233\pi\)
\(480\) 28.3655 1.29470
\(481\) −1.28663 −0.0586654
\(482\) −23.8109 −1.08456
\(483\) 36.1983 1.64708
\(484\) 67.9174 3.08715
\(485\) 1.43768 0.0652815
\(486\) −92.1362 −4.17938
\(487\) 17.4232 0.789519 0.394760 0.918784i \(-0.370828\pi\)
0.394760 + 0.918784i \(0.370828\pi\)
\(488\) −72.6464 −3.28855
\(489\) −77.8657 −3.52121
\(490\) −3.34672 −0.151189
\(491\) −12.8614 −0.580425 −0.290213 0.956962i \(-0.593726\pi\)
−0.290213 + 0.956962i \(0.593726\pi\)
\(492\) −45.3709 −2.04548
\(493\) 22.5505 1.01563
\(494\) 7.89408 0.355171
\(495\) −10.4002 −0.467454
\(496\) −96.0360 −4.31214
\(497\) −11.9512 −0.536083
\(498\) −76.3655 −3.42202
\(499\) 7.21194 0.322851 0.161425 0.986885i \(-0.448391\pi\)
0.161425 + 0.986885i \(0.448391\pi\)
\(500\) 17.0860 0.764109
\(501\) −61.1190 −2.73060
\(502\) 32.8379 1.46563
\(503\) −11.0130 −0.491046 −0.245523 0.969391i \(-0.578960\pi\)
−0.245523 + 0.969391i \(0.578960\pi\)
\(504\) −135.879 −6.05252
\(505\) −2.12671 −0.0946373
\(506\) −86.9909 −3.86722
\(507\) −40.8470 −1.81408
\(508\) 55.0579 2.44280
\(509\) 26.1184 1.15768 0.578839 0.815442i \(-0.303506\pi\)
0.578839 + 0.815442i \(0.303506\pi\)
\(510\) 6.33837 0.280668
\(511\) 17.0379 0.753711
\(512\) −152.620 −6.74493
\(513\) 70.0147 3.09122
\(514\) 25.7256 1.13471
\(515\) −2.77913 −0.122463
\(516\) −117.952 −5.19255
\(517\) 16.5974 0.729953
\(518\) −10.8689 −0.477552
\(519\) 77.0802 3.38345
\(520\) −1.80302 −0.0790676
\(521\) −39.7475 −1.74137 −0.870684 0.491842i \(-0.836324\pi\)
−0.870684 + 0.491842i \(0.836324\pi\)
\(522\) −196.021 −8.57963
\(523\) −13.0059 −0.568707 −0.284353 0.958720i \(-0.591779\pi\)
−0.284353 + 0.958720i \(0.591779\pi\)
\(524\) 7.96858 0.348109
\(525\) −27.2199 −1.18797
\(526\) −59.3597 −2.58821
\(527\) −12.4805 −0.543660
\(528\) 280.488 12.2067
\(529\) 19.6778 0.855556
\(530\) −10.5065 −0.456374
\(531\) 100.572 4.36445
\(532\) 49.6425 2.15228
\(533\) 1.37621 0.0596101
\(534\) −19.9358 −0.862706
\(535\) 4.55532 0.196944
\(536\) 132.761 5.73439
\(537\) 2.56026 0.110483
\(538\) −59.4858 −2.56461
\(539\) −19.2466 −0.829012
\(540\) −24.3518 −1.04794
\(541\) 15.1102 0.649640 0.324820 0.945776i \(-0.394696\pi\)
0.324820 + 0.945776i \(0.394696\pi\)
\(542\) −36.3960 −1.56334
\(543\) −38.3584 −1.64612
\(544\) −70.6956 −3.03105
\(545\) 2.42523 0.103886
\(546\) 8.82617 0.377725
\(547\) 29.5247 1.26238 0.631192 0.775626i \(-0.282566\pi\)
0.631192 + 0.775626i \(0.282566\pi\)
\(548\) −116.625 −4.98199
\(549\) 50.1264 2.13934
\(550\) 65.4141 2.78927
\(551\) 47.0286 2.00349
\(552\) −225.286 −9.58883
\(553\) −3.18072 −0.135258
\(554\) −46.7144 −1.98471
\(555\) −2.15445 −0.0914513
\(556\) −2.07928 −0.0881811
\(557\) −38.6394 −1.63720 −0.818602 0.574361i \(-0.805251\pi\)
−0.818602 + 0.574361i \(0.805251\pi\)
\(558\) 108.487 4.59264
\(559\) 3.57777 0.151324
\(560\) −9.30332 −0.393137
\(561\) 36.4513 1.53898
\(562\) 27.7889 1.17220
\(563\) −6.83895 −0.288227 −0.144114 0.989561i \(-0.546033\pi\)
−0.144114 + 0.989561i \(0.546033\pi\)
\(564\) 65.4553 2.75617
\(565\) 2.42467 0.102007
\(566\) −2.03703 −0.0856227
\(567\) 40.1904 1.68784
\(568\) 74.3801 3.12092
\(569\) 37.6671 1.57909 0.789543 0.613696i \(-0.210318\pi\)
0.789543 + 0.613696i \(0.210318\pi\)
\(570\) 13.2185 0.553663
\(571\) −39.8856 −1.66916 −0.834581 0.550885i \(-0.814290\pi\)
−0.834581 + 0.550885i \(0.814290\pi\)
\(572\) −15.7899 −0.660209
\(573\) 32.5254 1.35877
\(574\) 11.6256 0.485242
\(575\) −32.0922 −1.33834
\(576\) 344.475 14.3531
\(577\) 36.2466 1.50896 0.754482 0.656320i \(-0.227888\pi\)
0.754482 + 0.656320i \(0.227888\pi\)
\(578\) 31.7589 1.32100
\(579\) −5.08613 −0.211372
\(580\) −16.3570 −0.679189
\(581\) 14.5665 0.604322
\(582\) 43.8006 1.81559
\(583\) −60.4220 −2.50242
\(584\) −106.038 −4.38789
\(585\) 1.24409 0.0514369
\(586\) −46.8648 −1.93597
\(587\) 6.83881 0.282268 0.141134 0.989991i \(-0.454925\pi\)
0.141134 + 0.989991i \(0.454925\pi\)
\(588\) −75.9032 −3.13019
\(589\) −26.0279 −1.07246
\(590\) 11.2734 0.464120
\(591\) −17.1150 −0.704018
\(592\) 41.3180 1.69816
\(593\) −28.5848 −1.17384 −0.586919 0.809646i \(-0.699659\pi\)
−0.586919 + 0.809646i \(0.699659\pi\)
\(594\) −188.125 −7.71884
\(595\) −1.20903 −0.0495654
\(596\) 2.39455 0.0980847
\(597\) −51.5382 −2.10932
\(598\) 10.4060 0.425535
\(599\) −34.1841 −1.39673 −0.698363 0.715744i \(-0.746088\pi\)
−0.698363 + 0.715744i \(0.746088\pi\)
\(600\) 169.407 6.91603
\(601\) 19.6808 0.802798 0.401399 0.915903i \(-0.368524\pi\)
0.401399 + 0.915903i \(0.368524\pi\)
\(602\) 30.2234 1.23181
\(603\) −91.6057 −3.73047
\(604\) −77.1374 −3.13868
\(605\) −3.44960 −0.140246
\(606\) −64.7928 −2.63203
\(607\) −15.8421 −0.643010 −0.321505 0.946908i \(-0.604189\pi\)
−0.321505 + 0.946908i \(0.604189\pi\)
\(608\) −147.434 −5.97924
\(609\) 52.5815 2.13071
\(610\) 5.61884 0.227500
\(611\) −1.98542 −0.0803213
\(612\) 102.223 4.13211
\(613\) −16.4098 −0.662785 −0.331393 0.943493i \(-0.607519\pi\)
−0.331393 + 0.943493i \(0.607519\pi\)
\(614\) −20.4843 −0.826679
\(615\) 2.30444 0.0929240
\(616\) −87.5924 −3.52920
\(617\) 7.90787 0.318359 0.159179 0.987250i \(-0.449115\pi\)
0.159179 + 0.987250i \(0.449115\pi\)
\(618\) −84.6697 −3.40592
\(619\) −8.42971 −0.338819 −0.169409 0.985546i \(-0.554186\pi\)
−0.169409 + 0.985546i \(0.554186\pi\)
\(620\) 9.05276 0.363567
\(621\) 92.2939 3.70363
\(622\) −55.6944 −2.23314
\(623\) 3.80271 0.152352
\(624\) −33.5526 −1.34318
\(625\) 23.6944 0.947778
\(626\) 1.58669 0.0634170
\(627\) 76.0184 3.03588
\(628\) −76.9856 −3.07206
\(629\) 5.36955 0.214098
\(630\) 10.5095 0.418710
\(631\) 11.2052 0.446070 0.223035 0.974810i \(-0.428404\pi\)
0.223035 + 0.974810i \(0.428404\pi\)
\(632\) 19.7957 0.787432
\(633\) −34.1927 −1.35904
\(634\) 1.19621 0.0475074
\(635\) −2.79646 −0.110974
\(636\) −238.287 −9.44868
\(637\) 2.30232 0.0912214
\(638\) −126.363 −5.00275
\(639\) −51.3227 −2.03029
\(640\) 21.0084 0.830428
\(641\) −15.1899 −0.599965 −0.299982 0.953945i \(-0.596981\pi\)
−0.299982 + 0.953945i \(0.596981\pi\)
\(642\) 138.784 5.47735
\(643\) 29.7505 1.17325 0.586623 0.809860i \(-0.300457\pi\)
0.586623 + 0.809860i \(0.300457\pi\)
\(644\) 65.4392 2.57867
\(645\) 5.99093 0.235893
\(646\) −32.9447 −1.29619
\(647\) −1.57306 −0.0618435 −0.0309218 0.999522i \(-0.509844\pi\)
−0.0309218 + 0.999522i \(0.509844\pi\)
\(648\) −250.132 −9.82612
\(649\) 64.8324 2.54490
\(650\) −7.82497 −0.306921
\(651\) −29.1011 −1.14056
\(652\) −140.765 −5.51280
\(653\) 17.8432 0.698259 0.349130 0.937074i \(-0.386477\pi\)
0.349130 + 0.937074i \(0.386477\pi\)
\(654\) 73.8877 2.88924
\(655\) −0.404734 −0.0158142
\(656\) −44.1945 −1.72551
\(657\) 73.1669 2.85451
\(658\) −16.7719 −0.653837
\(659\) −18.3868 −0.716250 −0.358125 0.933674i \(-0.616584\pi\)
−0.358125 + 0.933674i \(0.616584\pi\)
\(660\) −26.4400 −1.02918
\(661\) −42.3139 −1.64582 −0.822909 0.568173i \(-0.807651\pi\)
−0.822909 + 0.568173i \(0.807651\pi\)
\(662\) 26.4723 1.02888
\(663\) −4.36038 −0.169343
\(664\) −90.6573 −3.51819
\(665\) −2.52140 −0.0977758
\(666\) −46.6750 −1.80862
\(667\) 61.9936 2.40040
\(668\) −110.491 −4.27502
\(669\) 31.6562 1.22390
\(670\) −10.2684 −0.396702
\(671\) 32.3133 1.24744
\(672\) −164.842 −6.35893
\(673\) −0.406318 −0.0156624 −0.00783120 0.999969i \(-0.502493\pi\)
−0.00783120 + 0.999969i \(0.502493\pi\)
\(674\) 28.6147 1.10220
\(675\) −69.4018 −2.67128
\(676\) −73.8431 −2.84012
\(677\) 1.18167 0.0454151 0.0227076 0.999742i \(-0.492771\pi\)
0.0227076 + 0.999742i \(0.492771\pi\)
\(678\) 73.8706 2.83698
\(679\) −8.35486 −0.320630
\(680\) 7.52460 0.288555
\(681\) −57.5930 −2.20697
\(682\) 69.9350 2.67795
\(683\) −24.5351 −0.938808 −0.469404 0.882983i \(-0.655531\pi\)
−0.469404 + 0.882983i \(0.655531\pi\)
\(684\) 213.183 8.15127
\(685\) 5.92354 0.226327
\(686\) 53.1201 2.02813
\(687\) −84.9626 −3.24152
\(688\) −114.894 −4.38029
\(689\) 7.22780 0.275357
\(690\) 17.4248 0.663350
\(691\) 29.6416 1.12762 0.563809 0.825905i \(-0.309335\pi\)
0.563809 + 0.825905i \(0.309335\pi\)
\(692\) 139.345 5.29712
\(693\) 60.4393 2.29590
\(694\) 35.8605 1.36125
\(695\) 0.105609 0.00400598
\(696\) −327.250 −12.4044
\(697\) −5.74338 −0.217546
\(698\) 74.1275 2.80577
\(699\) 53.5016 2.02362
\(700\) −49.2080 −1.85989
\(701\) 25.1416 0.949586 0.474793 0.880098i \(-0.342523\pi\)
0.474793 + 0.880098i \(0.342523\pi\)
\(702\) 22.5038 0.849353
\(703\) 11.1981 0.422344
\(704\) 222.061 8.36925
\(705\) −3.32455 −0.125210
\(706\) 67.8973 2.55535
\(707\) 12.3591 0.464811
\(708\) 255.680 9.60905
\(709\) 18.8533 0.708052 0.354026 0.935236i \(-0.384812\pi\)
0.354026 + 0.935236i \(0.384812\pi\)
\(710\) −5.75293 −0.215904
\(711\) −13.6592 −0.512259
\(712\) −23.6668 −0.886951
\(713\) −34.3101 −1.28492
\(714\) −36.8346 −1.37850
\(715\) 0.801988 0.0299926
\(716\) 4.62843 0.172972
\(717\) −27.7792 −1.03743
\(718\) −52.8420 −1.97205
\(719\) −10.5637 −0.393961 −0.196981 0.980407i \(-0.563114\pi\)
−0.196981 + 0.980407i \(0.563114\pi\)
\(720\) −39.9519 −1.48892
\(721\) 16.1506 0.601478
\(722\) −15.5545 −0.578877
\(723\) 27.4286 1.02008
\(724\) −69.3442 −2.57716
\(725\) −46.6170 −1.73131
\(726\) −105.096 −3.90049
\(727\) 37.2633 1.38202 0.691009 0.722846i \(-0.257166\pi\)
0.691009 + 0.722846i \(0.257166\pi\)
\(728\) 10.4780 0.388340
\(729\) 36.0151 1.33389
\(730\) 8.20152 0.303552
\(731\) −14.9312 −0.552252
\(732\) 127.434 4.71011
\(733\) −46.5415 −1.71905 −0.859525 0.511094i \(-0.829240\pi\)
−0.859525 + 0.511094i \(0.829240\pi\)
\(734\) 12.8130 0.472936
\(735\) 3.85521 0.142202
\(736\) −194.349 −7.16380
\(737\) −59.0524 −2.17522
\(738\) 49.9245 1.83775
\(739\) 28.3079 1.04132 0.520661 0.853763i \(-0.325685\pi\)
0.520661 + 0.853763i \(0.325685\pi\)
\(740\) −3.89481 −0.143176
\(741\) −9.09348 −0.334057
\(742\) 61.0572 2.24148
\(743\) 12.2210 0.448346 0.224173 0.974549i \(-0.428032\pi\)
0.224173 + 0.974549i \(0.428032\pi\)
\(744\) 181.116 6.64002
\(745\) −0.121622 −0.00445589
\(746\) 63.7521 2.33413
\(747\) 62.5541 2.28873
\(748\) 65.8966 2.40942
\(749\) −26.4726 −0.967289
\(750\) −26.4392 −0.965421
\(751\) 24.7590 0.903470 0.451735 0.892152i \(-0.350805\pi\)
0.451735 + 0.892152i \(0.350805\pi\)
\(752\) 63.7582 2.32502
\(753\) −37.8272 −1.37850
\(754\) 15.1158 0.550484
\(755\) 3.91790 0.142587
\(756\) 141.517 5.14693
\(757\) −11.2940 −0.410487 −0.205243 0.978711i \(-0.565799\pi\)
−0.205243 + 0.978711i \(0.565799\pi\)
\(758\) −15.5674 −0.565435
\(759\) 100.208 3.63732
\(760\) 15.6924 0.569223
\(761\) −29.7177 −1.07726 −0.538632 0.842541i \(-0.681059\pi\)
−0.538632 + 0.842541i \(0.681059\pi\)
\(762\) −85.1975 −3.08638
\(763\) −14.0939 −0.510234
\(764\) 58.7994 2.12729
\(765\) −5.19202 −0.187718
\(766\) −7.17568 −0.259268
\(767\) −7.75539 −0.280031
\(768\) 339.388 12.2466
\(769\) 16.8909 0.609102 0.304551 0.952496i \(-0.401494\pi\)
0.304551 + 0.952496i \(0.401494\pi\)
\(770\) 6.77484 0.244148
\(771\) −29.6343 −1.06725
\(772\) −9.19469 −0.330924
\(773\) 1.52842 0.0549733 0.0274866 0.999622i \(-0.491250\pi\)
0.0274866 + 0.999622i \(0.491250\pi\)
\(774\) 129.790 4.66522
\(775\) 25.8000 0.926764
\(776\) 51.9979 1.86662
\(777\) 12.5203 0.449163
\(778\) −70.0095 −2.50996
\(779\) −11.9777 −0.429145
\(780\) 3.16281 0.113247
\(781\) −33.0845 −1.18386
\(782\) −43.4279 −1.55298
\(783\) 134.066 4.79112
\(784\) −73.9352 −2.64054
\(785\) 3.91019 0.139561
\(786\) −12.3307 −0.439822
\(787\) 15.9095 0.567113 0.283556 0.958956i \(-0.408486\pi\)
0.283556 + 0.958956i \(0.408486\pi\)
\(788\) −30.9405 −1.10221
\(789\) 68.3787 2.43434
\(790\) −1.53110 −0.0544741
\(791\) −14.0906 −0.501006
\(792\) −376.154 −13.3661
\(793\) −3.86539 −0.137264
\(794\) 90.7472 3.22050
\(795\) 12.1029 0.429244
\(796\) −93.1706 −3.30235
\(797\) −10.8307 −0.383644 −0.191822 0.981430i \(-0.561440\pi\)
−0.191822 + 0.981430i \(0.561440\pi\)
\(798\) −76.8177 −2.71932
\(799\) 8.28581 0.293131
\(800\) 146.144 5.16695
\(801\) 16.3302 0.577000
\(802\) 99.1751 3.50199
\(803\) 47.1661 1.66446
\(804\) −232.885 −8.21324
\(805\) −3.32374 −0.117146
\(806\) −8.36577 −0.294672
\(807\) 68.5239 2.41216
\(808\) −76.9188 −2.70599
\(809\) 36.6948 1.29012 0.645059 0.764132i \(-0.276833\pi\)
0.645059 + 0.764132i \(0.276833\pi\)
\(810\) 19.3465 0.679766
\(811\) −6.32762 −0.222193 −0.111096 0.993810i \(-0.535436\pi\)
−0.111096 + 0.993810i \(0.535436\pi\)
\(812\) 95.0567 3.33584
\(813\) 41.9259 1.47041
\(814\) −30.0885 −1.05460
\(815\) 7.14964 0.250441
\(816\) 140.026 4.90190
\(817\) −31.1388 −1.08941
\(818\) −71.0552 −2.48439
\(819\) −7.22987 −0.252632
\(820\) 4.16596 0.145482
\(821\) 22.1814 0.774135 0.387068 0.922051i \(-0.373488\pi\)
0.387068 + 0.922051i \(0.373488\pi\)
\(822\) 180.468 6.29454
\(823\) 6.55122 0.228361 0.114181 0.993460i \(-0.463576\pi\)
0.114181 + 0.993460i \(0.463576\pi\)
\(824\) −100.516 −3.50163
\(825\) −75.3530 −2.62345
\(826\) −65.5141 −2.27953
\(827\) 26.9579 0.937419 0.468710 0.883352i \(-0.344719\pi\)
0.468710 + 0.883352i \(0.344719\pi\)
\(828\) 281.020 9.76613
\(829\) 18.4142 0.639550 0.319775 0.947493i \(-0.396393\pi\)
0.319775 + 0.947493i \(0.396393\pi\)
\(830\) 7.01189 0.243386
\(831\) 53.8121 1.86672
\(832\) −26.5634 −0.920921
\(833\) −9.60837 −0.332910
\(834\) 3.21751 0.111413
\(835\) 5.61196 0.194210
\(836\) 137.426 4.75297
\(837\) −74.1983 −2.56467
\(838\) −72.7953 −2.51467
\(839\) −20.9821 −0.724382 −0.362191 0.932104i \(-0.617971\pi\)
−0.362191 + 0.932104i \(0.617971\pi\)
\(840\) 17.5453 0.605369
\(841\) 61.0516 2.10523
\(842\) −89.6208 −3.08854
\(843\) −32.0110 −1.10252
\(844\) −61.8135 −2.12771
\(845\) 3.75058 0.129024
\(846\) −72.0248 −2.47626
\(847\) 20.0469 0.688820
\(848\) −232.108 −7.97064
\(849\) 2.34653 0.0805327
\(850\) 32.6563 1.12010
\(851\) 14.7614 0.506014
\(852\) −130.476 −4.47002
\(853\) 25.7414 0.881368 0.440684 0.897662i \(-0.354736\pi\)
0.440684 + 0.897662i \(0.354736\pi\)
\(854\) −32.6531 −1.11737
\(855\) −10.8278 −0.370304
\(856\) 164.757 5.63128
\(857\) 40.3727 1.37911 0.689553 0.724236i \(-0.257807\pi\)
0.689553 + 0.724236i \(0.257807\pi\)
\(858\) 24.4336 0.834148
\(859\) 40.0981 1.36813 0.684065 0.729421i \(-0.260210\pi\)
0.684065 + 0.729421i \(0.260210\pi\)
\(860\) 10.8304 0.369313
\(861\) −13.3919 −0.456396
\(862\) −16.0653 −0.547186
\(863\) 40.7029 1.38554 0.692771 0.721157i \(-0.256390\pi\)
0.692771 + 0.721157i \(0.256390\pi\)
\(864\) −420.294 −14.2987
\(865\) −7.07752 −0.240643
\(866\) −0.351916 −0.0119586
\(867\) −36.5842 −1.24247
\(868\) −52.6088 −1.78566
\(869\) −8.80520 −0.298696
\(870\) 25.3112 0.858129
\(871\) 7.06397 0.239354
\(872\) 87.7159 2.97043
\(873\) −35.8789 −1.21432
\(874\) −90.5680 −3.06351
\(875\) 5.04321 0.170491
\(876\) 186.009 6.28467
\(877\) −24.9584 −0.842787 −0.421393 0.906878i \(-0.638459\pi\)
−0.421393 + 0.906878i \(0.638459\pi\)
\(878\) −73.9488 −2.49565
\(879\) 53.9853 1.82088
\(880\) −25.7545 −0.868183
\(881\) 38.0745 1.28276 0.641382 0.767222i \(-0.278362\pi\)
0.641382 + 0.767222i \(0.278362\pi\)
\(882\) 83.5212 2.81231
\(883\) 58.9922 1.98525 0.992623 0.121242i \(-0.0386877\pi\)
0.992623 + 0.121242i \(0.0386877\pi\)
\(884\) −7.88269 −0.265124
\(885\) −12.9863 −0.436530
\(886\) −35.1426 −1.18064
\(887\) −1.20170 −0.0403492 −0.0201746 0.999796i \(-0.506422\pi\)
−0.0201746 + 0.999796i \(0.506422\pi\)
\(888\) −77.9221 −2.61490
\(889\) 16.2512 0.545049
\(890\) 1.83051 0.0613588
\(891\) 111.260 3.72734
\(892\) 57.2280 1.91614
\(893\) 17.2799 0.578249
\(894\) −3.70537 −0.123926
\(895\) −0.235083 −0.00785797
\(896\) −122.087 −4.07865
\(897\) −11.9871 −0.400238
\(898\) 84.5469 2.82137
\(899\) −49.8388 −1.66222
\(900\) −211.317 −7.04391
\(901\) −30.1641 −1.00491
\(902\) 32.1832 1.07158
\(903\) −34.8155 −1.15859
\(904\) 87.6955 2.91671
\(905\) 3.52208 0.117078
\(906\) 119.364 3.96559
\(907\) 9.69436 0.321896 0.160948 0.986963i \(-0.448545\pi\)
0.160948 + 0.986963i \(0.448545\pi\)
\(908\) −104.117 −3.45523
\(909\) 53.0744 1.76037
\(910\) −0.810420 −0.0268652
\(911\) −17.4515 −0.578194 −0.289097 0.957300i \(-0.593355\pi\)
−0.289097 + 0.957300i \(0.593355\pi\)
\(912\) 292.022 9.66980
\(913\) 40.3247 1.33455
\(914\) 93.9046 3.10609
\(915\) −6.47255 −0.213976
\(916\) −153.595 −5.07493
\(917\) 2.35205 0.0776716
\(918\) −93.9162 −3.09970
\(919\) 17.5880 0.580174 0.290087 0.957000i \(-0.406316\pi\)
0.290087 + 0.957000i \(0.406316\pi\)
\(920\) 20.6858 0.681992
\(921\) 23.5966 0.777535
\(922\) −105.647 −3.47931
\(923\) 3.95764 0.130267
\(924\) 153.652 5.05479
\(925\) −11.1001 −0.364967
\(926\) 62.7827 2.06317
\(927\) 69.3564 2.27796
\(928\) −282.310 −9.26729
\(929\) 27.6489 0.907129 0.453565 0.891223i \(-0.350152\pi\)
0.453565 + 0.891223i \(0.350152\pi\)
\(930\) −14.0084 −0.459353
\(931\) −20.0381 −0.656721
\(932\) 96.7200 3.16817
\(933\) 64.1565 2.10039
\(934\) −53.0137 −1.73466
\(935\) −3.34697 −0.109458
\(936\) 44.9964 1.47075
\(937\) −19.5903 −0.639988 −0.319994 0.947420i \(-0.603681\pi\)
−0.319994 + 0.947420i \(0.603681\pi\)
\(938\) 59.6733 1.94840
\(939\) −1.82777 −0.0596471
\(940\) −6.01012 −0.196029
\(941\) −27.4102 −0.893547 −0.446773 0.894647i \(-0.647427\pi\)
−0.446773 + 0.894647i \(0.647427\pi\)
\(942\) 119.129 3.88143
\(943\) −15.7891 −0.514163
\(944\) 249.051 8.10592
\(945\) −7.18783 −0.233820
\(946\) 83.6677 2.72027
\(947\) −25.5165 −0.829173 −0.414587 0.910010i \(-0.636074\pi\)
−0.414587 + 0.910010i \(0.636074\pi\)
\(948\) −34.7252 −1.12782
\(949\) −5.64211 −0.183151
\(950\) 68.1039 2.20958
\(951\) −1.37795 −0.0446832
\(952\) −43.7282 −1.41724
\(953\) 27.3734 0.886710 0.443355 0.896346i \(-0.353788\pi\)
0.443355 + 0.896346i \(0.353788\pi\)
\(954\) 262.202 8.48911
\(955\) −2.98649 −0.0966406
\(956\) −50.2192 −1.62420
\(957\) 145.562 4.70535
\(958\) −20.2058 −0.652820
\(959\) −34.4238 −1.11160
\(960\) −44.4801 −1.43559
\(961\) −3.41689 −0.110222
\(962\) 3.59924 0.116044
\(963\) −113.683 −3.66339
\(964\) 49.5854 1.59704
\(965\) 0.467009 0.0150336
\(966\) −101.262 −3.25804
\(967\) −52.5651 −1.69038 −0.845189 0.534467i \(-0.820512\pi\)
−0.845189 + 0.534467i \(0.820512\pi\)
\(968\) −124.765 −4.01011
\(969\) 37.9502 1.21914
\(970\) −4.02178 −0.129132
\(971\) 1.44469 0.0463622 0.0231811 0.999731i \(-0.492621\pi\)
0.0231811 + 0.999731i \(0.492621\pi\)
\(972\) 191.871 6.15426
\(973\) −0.613733 −0.0196754
\(974\) −48.7399 −1.56173
\(975\) 9.01388 0.288675
\(976\) 124.130 3.97332
\(977\) −10.9340 −0.349810 −0.174905 0.984585i \(-0.555962\pi\)
−0.174905 + 0.984585i \(0.555962\pi\)
\(978\) 217.823 6.96520
\(979\) 10.5271 0.336446
\(980\) 6.96944 0.222631
\(981\) −60.5244 −1.93240
\(982\) 35.9786 1.14812
\(983\) −11.1197 −0.354663 −0.177331 0.984151i \(-0.556746\pi\)
−0.177331 + 0.984151i \(0.556746\pi\)
\(984\) 83.3470 2.65701
\(985\) 1.57150 0.0500723
\(986\) −63.0832 −2.00898
\(987\) 19.3202 0.614968
\(988\) −16.4392 −0.523000
\(989\) −41.0474 −1.30523
\(990\) 29.0936 0.924657
\(991\) 27.7737 0.882261 0.441131 0.897443i \(-0.354578\pi\)
0.441131 + 0.897443i \(0.354578\pi\)
\(992\) 156.244 4.96075
\(993\) −30.4944 −0.967712
\(994\) 33.4324 1.06041
\(995\) 4.73225 0.150022
\(996\) 159.029 5.03902
\(997\) 34.8657 1.10421 0.552104 0.833775i \(-0.313825\pi\)
0.552104 + 0.833775i \(0.313825\pi\)
\(998\) −20.1748 −0.638622
\(999\) 31.9227 1.00999
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 \(a_p\))