Properties

Label 8011.2.a.b.1.1
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 1.1
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.81343 q^{2}\) \(+0.884173 q^{3}\) \(+5.91537 q^{4}\) \(+1.61259 q^{5}\) \(-2.48756 q^{6}\) \(-3.94545 q^{7}\) \(-11.0156 q^{8}\) \(-2.21824 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.81343 q^{2}\) \(+0.884173 q^{3}\) \(+5.91537 q^{4}\) \(+1.61259 q^{5}\) \(-2.48756 q^{6}\) \(-3.94545 q^{7}\) \(-11.0156 q^{8}\) \(-2.21824 q^{9}\) \(-4.53689 q^{10}\) \(+0.390921 q^{11}\) \(+5.23021 q^{12}\) \(-0.126530 q^{13}\) \(+11.1002 q^{14}\) \(+1.42581 q^{15}\) \(+19.1609 q^{16}\) \(-1.86142 q^{17}\) \(+6.24085 q^{18}\) \(-1.54940 q^{19}\) \(+9.53904 q^{20}\) \(-3.48846 q^{21}\) \(-1.09983 q^{22}\) \(-3.99053 q^{23}\) \(-9.73970 q^{24}\) \(-2.39957 q^{25}\) \(+0.355983 q^{26}\) \(-4.61383 q^{27}\) \(-23.3388 q^{28}\) \(+1.53628 q^{29}\) \(-4.01140 q^{30}\) \(-4.00381 q^{31}\) \(-31.8765 q^{32}\) \(+0.345642 q^{33}\) \(+5.23698 q^{34}\) \(-6.36238 q^{35}\) \(-13.1217 q^{36}\) \(-4.51815 q^{37}\) \(+4.35913 q^{38}\) \(-0.111875 q^{39}\) \(-17.7636 q^{40}\) \(+7.57481 q^{41}\) \(+9.81454 q^{42}\) \(+0.336469 q^{43}\) \(+2.31244 q^{44}\) \(-3.57710 q^{45}\) \(+11.2271 q^{46}\) \(+9.11906 q^{47}\) \(+16.9415 q^{48}\) \(+8.56660 q^{49}\) \(+6.75100 q^{50}\) \(-1.64582 q^{51}\) \(-0.748472 q^{52}\) \(-9.02746 q^{53}\) \(+12.9807 q^{54}\) \(+0.630394 q^{55}\) \(+43.4615 q^{56}\) \(-1.36994 q^{57}\) \(-4.32222 q^{58}\) \(-10.7196 q^{59}\) \(+8.43417 q^{60}\) \(+14.9612 q^{61}\) \(+11.2644 q^{62}\) \(+8.75195 q^{63}\) \(+51.3604 q^{64}\) \(-0.204041 q^{65}\) \(-0.972439 q^{66}\) \(-10.2282 q^{67}\) \(-11.0110 q^{68}\) \(-3.52832 q^{69}\) \(+17.9001 q^{70}\) \(-8.96853 q^{71}\) \(+24.4352 q^{72}\) \(+4.69345 q^{73}\) \(+12.7115 q^{74}\) \(-2.12163 q^{75}\) \(-9.16528 q^{76}\) \(-1.54236 q^{77}\) \(+0.314751 q^{78}\) \(+3.20308 q^{79}\) \(+30.8985 q^{80}\) \(+2.57529 q^{81}\) \(-21.3112 q^{82}\) \(-2.42325 q^{83}\) \(-20.6355 q^{84}\) \(-3.00171 q^{85}\) \(-0.946630 q^{86}\) \(+1.35834 q^{87}\) \(-4.30624 q^{88}\) \(-0.0683005 q^{89}\) \(+10.0639 q^{90}\) \(+0.499219 q^{91}\) \(-23.6055 q^{92}\) \(-3.54007 q^{93}\) \(-25.6558 q^{94}\) \(-2.49854 q^{95}\) \(-28.1843 q^{96}\) \(+7.36358 q^{97}\) \(-24.1015 q^{98}\) \(-0.867157 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81343 −1.98939 −0.994697 0.102853i \(-0.967203\pi\)
−0.994697 + 0.102853i \(0.967203\pi\)
\(3\) 0.884173 0.510478 0.255239 0.966878i \(-0.417846\pi\)
0.255239 + 0.966878i \(0.417846\pi\)
\(4\) 5.91537 2.95768
\(5\) 1.61259 0.721170 0.360585 0.932726i \(-0.382577\pi\)
0.360585 + 0.932726i \(0.382577\pi\)
\(6\) −2.48756 −1.01554
\(7\) −3.94545 −1.49124 −0.745620 0.666371i \(-0.767847\pi\)
−0.745620 + 0.666371i \(0.767847\pi\)
\(8\) −11.0156 −3.89460
\(9\) −2.21824 −0.739413
\(10\) −4.53689 −1.43469
\(11\) 0.390921 0.117867 0.0589336 0.998262i \(-0.481230\pi\)
0.0589336 + 0.998262i \(0.481230\pi\)
\(12\) 5.23021 1.50983
\(13\) −0.126530 −0.0350931 −0.0175466 0.999846i \(-0.505586\pi\)
−0.0175466 + 0.999846i \(0.505586\pi\)
\(14\) 11.1002 2.96666
\(15\) 1.42581 0.368141
\(16\) 19.1609 4.79021
\(17\) −1.86142 −0.451461 −0.225731 0.974190i \(-0.572477\pi\)
−0.225731 + 0.974190i \(0.572477\pi\)
\(18\) 6.24085 1.47098
\(19\) −1.54940 −0.355457 −0.177729 0.984080i \(-0.556875\pi\)
−0.177729 + 0.984080i \(0.556875\pi\)
\(20\) 9.53904 2.13299
\(21\) −3.48846 −0.761245
\(22\) −1.09983 −0.234484
\(23\) −3.99053 −0.832083 −0.416042 0.909346i \(-0.636583\pi\)
−0.416042 + 0.909346i \(0.636583\pi\)
\(24\) −9.73970 −1.98811
\(25\) −2.39957 −0.479913
\(26\) 0.355983 0.0698141
\(27\) −4.61383 −0.887931
\(28\) −23.3388 −4.41062
\(29\) 1.53628 0.285281 0.142640 0.989775i \(-0.454441\pi\)
0.142640 + 0.989775i \(0.454441\pi\)
\(30\) −4.01140 −0.732378
\(31\) −4.00381 −0.719106 −0.359553 0.933125i \(-0.617071\pi\)
−0.359553 + 0.933125i \(0.617071\pi\)
\(32\) −31.8765 −5.63501
\(33\) 0.345642 0.0601686
\(34\) 5.23698 0.898134
\(35\) −6.36238 −1.07544
\(36\) −13.1217 −2.18695
\(37\) −4.51815 −0.742779 −0.371389 0.928477i \(-0.621118\pi\)
−0.371389 + 0.928477i \(0.621118\pi\)
\(38\) 4.35913 0.707144
\(39\) −0.111875 −0.0179143
\(40\) −17.7636 −2.80867
\(41\) 7.57481 1.18299 0.591493 0.806310i \(-0.298539\pi\)
0.591493 + 0.806310i \(0.298539\pi\)
\(42\) 9.81454 1.51442
\(43\) 0.336469 0.0513110 0.0256555 0.999671i \(-0.491833\pi\)
0.0256555 + 0.999671i \(0.491833\pi\)
\(44\) 2.31244 0.348614
\(45\) −3.57710 −0.533243
\(46\) 11.2271 1.65534
\(47\) 9.11906 1.33015 0.665076 0.746776i \(-0.268399\pi\)
0.665076 + 0.746776i \(0.268399\pi\)
\(48\) 16.9415 2.44530
\(49\) 8.56660 1.22380
\(50\) 6.75100 0.954736
\(51\) −1.64582 −0.230461
\(52\) −0.748472 −0.103794
\(53\) −9.02746 −1.24002 −0.620009 0.784595i \(-0.712871\pi\)
−0.620009 + 0.784595i \(0.712871\pi\)
\(54\) 12.9807 1.76644
\(55\) 0.630394 0.0850024
\(56\) 43.4615 5.80779
\(57\) −1.36994 −0.181453
\(58\) −4.32222 −0.567536
\(59\) −10.7196 −1.39557 −0.697787 0.716305i \(-0.745832\pi\)
−0.697787 + 0.716305i \(0.745832\pi\)
\(60\) 8.43417 1.08885
\(61\) 14.9612 1.91559 0.957794 0.287456i \(-0.0928096\pi\)
0.957794 + 0.287456i \(0.0928096\pi\)
\(62\) 11.2644 1.43059
\(63\) 8.75195 1.10264
\(64\) 51.3604 6.42004
\(65\) −0.204041 −0.0253081
\(66\) −0.972439 −0.119699
\(67\) −10.2282 −1.24958 −0.624790 0.780793i \(-0.714815\pi\)
−0.624790 + 0.780793i \(0.714815\pi\)
\(68\) −11.0110 −1.33528
\(69\) −3.52832 −0.424760
\(70\) 17.9001 2.13947
\(71\) −8.96853 −1.06437 −0.532184 0.846629i \(-0.678629\pi\)
−0.532184 + 0.846629i \(0.678629\pi\)
\(72\) 24.4352 2.87972
\(73\) 4.69345 0.549327 0.274663 0.961540i \(-0.411434\pi\)
0.274663 + 0.961540i \(0.411434\pi\)
\(74\) 12.7115 1.47768
\(75\) −2.12163 −0.244985
\(76\) −9.16528 −1.05133
\(77\) −1.54236 −0.175768
\(78\) 0.314751 0.0356385
\(79\) 3.20308 0.360374 0.180187 0.983632i \(-0.442330\pi\)
0.180187 + 0.983632i \(0.442330\pi\)
\(80\) 30.8985 3.45456
\(81\) 2.57529 0.286144
\(82\) −21.3112 −2.35343
\(83\) −2.42325 −0.265986 −0.132993 0.991117i \(-0.542459\pi\)
−0.132993 + 0.991117i \(0.542459\pi\)
\(84\) −20.6355 −2.25152
\(85\) −3.00171 −0.325581
\(86\) −0.946630 −0.102078
\(87\) 1.35834 0.145629
\(88\) −4.30624 −0.459046
\(89\) −0.0683005 −0.00723983 −0.00361992 0.999993i \(-0.501152\pi\)
−0.00361992 + 0.999993i \(0.501152\pi\)
\(90\) 10.0639 1.06083
\(91\) 0.499219 0.0523323
\(92\) −23.6055 −2.46104
\(93\) −3.54007 −0.367088
\(94\) −25.6558 −2.64619
\(95\) −2.49854 −0.256345
\(96\) −28.1843 −2.87655
\(97\) 7.36358 0.747658 0.373829 0.927498i \(-0.378045\pi\)
0.373829 + 0.927498i \(0.378045\pi\)
\(98\) −24.1015 −2.43462
\(99\) −0.867157 −0.0871525
\(100\) −14.1943 −1.41943
\(101\) 2.03271 0.202263 0.101131 0.994873i \(-0.467754\pi\)
0.101131 + 0.994873i \(0.467754\pi\)
\(102\) 4.63040 0.458477
\(103\) −17.2655 −1.70122 −0.850608 0.525800i \(-0.823766\pi\)
−0.850608 + 0.525800i \(0.823766\pi\)
\(104\) 1.39381 0.136674
\(105\) −5.62545 −0.548987
\(106\) 25.3981 2.46688
\(107\) 8.01791 0.775121 0.387560 0.921844i \(-0.373318\pi\)
0.387560 + 0.921844i \(0.373318\pi\)
\(108\) −27.2925 −2.62622
\(109\) −4.07365 −0.390185 −0.195092 0.980785i \(-0.562501\pi\)
−0.195092 + 0.980785i \(0.562501\pi\)
\(110\) −1.77357 −0.169103
\(111\) −3.99482 −0.379172
\(112\) −75.5983 −7.14336
\(113\) 9.55468 0.898829 0.449414 0.893323i \(-0.351633\pi\)
0.449414 + 0.893323i \(0.351633\pi\)
\(114\) 3.85422 0.360981
\(115\) −6.43508 −0.600074
\(116\) 9.08769 0.843771
\(117\) 0.280674 0.0259483
\(118\) 30.1588 2.77635
\(119\) 7.34416 0.673238
\(120\) −15.7061 −1.43376
\(121\) −10.8472 −0.986107
\(122\) −42.0923 −3.81086
\(123\) 6.69744 0.603888
\(124\) −23.6840 −2.12689
\(125\) −11.9324 −1.06727
\(126\) −24.6230 −2.19359
\(127\) −9.53618 −0.846199 −0.423099 0.906083i \(-0.639058\pi\)
−0.423099 + 0.906083i \(0.639058\pi\)
\(128\) −80.7457 −7.13698
\(129\) 0.297497 0.0261931
\(130\) 0.574054 0.0503478
\(131\) −2.40272 −0.209926 −0.104963 0.994476i \(-0.533472\pi\)
−0.104963 + 0.994476i \(0.533472\pi\)
\(132\) 2.04460 0.177960
\(133\) 6.11309 0.530072
\(134\) 28.7764 2.48590
\(135\) −7.44019 −0.640350
\(136\) 20.5047 1.75826
\(137\) 18.9525 1.61922 0.809611 0.586967i \(-0.199678\pi\)
0.809611 + 0.586967i \(0.199678\pi\)
\(138\) 9.92667 0.845014
\(139\) 12.8476 1.08972 0.544858 0.838528i \(-0.316584\pi\)
0.544858 + 0.838528i \(0.316584\pi\)
\(140\) −37.6358 −3.18081
\(141\) 8.06283 0.679013
\(142\) 25.2323 2.11745
\(143\) −0.0494633 −0.00413633
\(144\) −42.5033 −3.54194
\(145\) 2.47739 0.205736
\(146\) −13.2047 −1.09283
\(147\) 7.57435 0.624722
\(148\) −26.7265 −2.19690
\(149\) −0.753234 −0.0617073 −0.0308537 0.999524i \(-0.509823\pi\)
−0.0308537 + 0.999524i \(0.509823\pi\)
\(150\) 5.96906 0.487371
\(151\) 9.98767 0.812785 0.406393 0.913699i \(-0.366787\pi\)
0.406393 + 0.913699i \(0.366787\pi\)
\(152\) 17.0676 1.38436
\(153\) 4.12908 0.333816
\(154\) 4.33932 0.349673
\(155\) −6.45650 −0.518598
\(156\) −0.661779 −0.0529847
\(157\) −2.82307 −0.225305 −0.112653 0.993634i \(-0.535935\pi\)
−0.112653 + 0.993634i \(0.535935\pi\)
\(158\) −9.01162 −0.716926
\(159\) −7.98184 −0.633001
\(160\) −51.4035 −4.06381
\(161\) 15.7445 1.24084
\(162\) −7.24540 −0.569252
\(163\) −16.5065 −1.29289 −0.646446 0.762960i \(-0.723745\pi\)
−0.646446 + 0.762960i \(0.723745\pi\)
\(164\) 44.8078 3.49890
\(165\) 0.557378 0.0433918
\(166\) 6.81763 0.529151
\(167\) −2.09423 −0.162056 −0.0810281 0.996712i \(-0.525820\pi\)
−0.0810281 + 0.996712i \(0.525820\pi\)
\(168\) 38.4275 2.96475
\(169\) −12.9840 −0.998768
\(170\) 8.44508 0.647708
\(171\) 3.43694 0.262829
\(172\) 1.99034 0.151762
\(173\) 10.6545 0.810046 0.405023 0.914306i \(-0.367263\pi\)
0.405023 + 0.914306i \(0.367263\pi\)
\(174\) −3.82159 −0.289714
\(175\) 9.46737 0.715666
\(176\) 7.49039 0.564609
\(177\) −9.47799 −0.712409
\(178\) 0.192158 0.0144029
\(179\) 11.2140 0.838174 0.419087 0.907946i \(-0.362350\pi\)
0.419087 + 0.907946i \(0.362350\pi\)
\(180\) −21.1599 −1.57716
\(181\) −3.67663 −0.273282 −0.136641 0.990621i \(-0.543631\pi\)
−0.136641 + 0.990621i \(0.543631\pi\)
\(182\) −1.40451 −0.104110
\(183\) 13.2283 0.977864
\(184\) 43.9581 3.24064
\(185\) −7.28590 −0.535670
\(186\) 9.95971 0.730282
\(187\) −0.727670 −0.0532125
\(188\) 53.9426 3.93417
\(189\) 18.2036 1.32412
\(190\) 7.02947 0.509971
\(191\) 9.67436 0.700012 0.350006 0.936747i \(-0.386180\pi\)
0.350006 + 0.936747i \(0.386180\pi\)
\(192\) 45.4114 3.27729
\(193\) 11.6414 0.837964 0.418982 0.907995i \(-0.362387\pi\)
0.418982 + 0.907995i \(0.362387\pi\)
\(194\) −20.7169 −1.48739
\(195\) −0.180407 −0.0129192
\(196\) 50.6746 3.61961
\(197\) 19.6763 1.40188 0.700941 0.713219i \(-0.252764\pi\)
0.700941 + 0.713219i \(0.252764\pi\)
\(198\) 2.43968 0.173381
\(199\) 3.20793 0.227404 0.113702 0.993515i \(-0.463729\pi\)
0.113702 + 0.993515i \(0.463729\pi\)
\(200\) 26.4327 1.86907
\(201\) −9.04354 −0.637882
\(202\) −5.71889 −0.402380
\(203\) −6.06134 −0.425422
\(204\) −9.73564 −0.681631
\(205\) 12.2150 0.853135
\(206\) 48.5751 3.38439
\(207\) 8.85195 0.615253
\(208\) −2.42443 −0.168104
\(209\) −0.605694 −0.0418967
\(210\) 15.8268 1.09215
\(211\) −9.71904 −0.669086 −0.334543 0.942380i \(-0.608582\pi\)
−0.334543 + 0.942380i \(0.608582\pi\)
\(212\) −53.4008 −3.66758
\(213\) −7.92973 −0.543336
\(214\) −22.5578 −1.54202
\(215\) 0.542585 0.0370040
\(216\) 50.8241 3.45814
\(217\) 15.7969 1.07236
\(218\) 11.4609 0.776231
\(219\) 4.14982 0.280419
\(220\) 3.72902 0.251410
\(221\) 0.235526 0.0158432
\(222\) 11.2391 0.754322
\(223\) −18.4358 −1.23455 −0.617276 0.786747i \(-0.711764\pi\)
−0.617276 + 0.786747i \(0.711764\pi\)
\(224\) 125.767 8.40316
\(225\) 5.32281 0.354854
\(226\) −26.8814 −1.78812
\(227\) 2.87943 0.191115 0.0955573 0.995424i \(-0.469537\pi\)
0.0955573 + 0.995424i \(0.469537\pi\)
\(228\) −8.10369 −0.536680
\(229\) 17.2424 1.13941 0.569706 0.821848i \(-0.307057\pi\)
0.569706 + 0.821848i \(0.307057\pi\)
\(230\) 18.1046 1.19378
\(231\) −1.36371 −0.0897259
\(232\) −16.9231 −1.11106
\(233\) −2.71881 −0.178115 −0.0890577 0.996026i \(-0.528386\pi\)
−0.0890577 + 0.996026i \(0.528386\pi\)
\(234\) −0.789655 −0.0516214
\(235\) 14.7053 0.959266
\(236\) −63.4104 −4.12767
\(237\) 2.83207 0.183963
\(238\) −20.6622 −1.33933
\(239\) 14.4753 0.936331 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(240\) 27.3197 1.76348
\(241\) −27.6393 −1.78040 −0.890201 0.455568i \(-0.849436\pi\)
−0.890201 + 0.455568i \(0.849436\pi\)
\(242\) 30.5177 1.96176
\(243\) 16.1185 1.03400
\(244\) 88.5011 5.66570
\(245\) 13.8144 0.882568
\(246\) −18.8428 −1.20137
\(247\) 0.196046 0.0124741
\(248\) 44.1044 2.80063
\(249\) −2.14257 −0.135780
\(250\) 33.5710 2.12322
\(251\) 15.5819 0.983519 0.491760 0.870731i \(-0.336354\pi\)
0.491760 + 0.870731i \(0.336354\pi\)
\(252\) 51.7710 3.26127
\(253\) −1.55998 −0.0980754
\(254\) 26.8293 1.68342
\(255\) −2.65403 −0.166202
\(256\) 124.451 7.77821
\(257\) −2.57588 −0.160679 −0.0803394 0.996768i \(-0.525600\pi\)
−0.0803394 + 0.996768i \(0.525600\pi\)
\(258\) −0.836985 −0.0521084
\(259\) 17.8261 1.10766
\(260\) −1.20698 −0.0748535
\(261\) −3.40784 −0.210940
\(262\) 6.75987 0.417626
\(263\) −20.9693 −1.29302 −0.646511 0.762904i \(-0.723773\pi\)
−0.646511 + 0.762904i \(0.723773\pi\)
\(264\) −3.80746 −0.234333
\(265\) −14.5576 −0.894264
\(266\) −17.1987 −1.05452
\(267\) −0.0603894 −0.00369577
\(268\) −60.5039 −3.69586
\(269\) −3.54376 −0.216067 −0.108034 0.994147i \(-0.534455\pi\)
−0.108034 + 0.994147i \(0.534455\pi\)
\(270\) 20.9324 1.27391
\(271\) 21.3475 1.29677 0.648384 0.761314i \(-0.275445\pi\)
0.648384 + 0.761314i \(0.275445\pi\)
\(272\) −35.6665 −2.16260
\(273\) 0.441396 0.0267145
\(274\) −53.3215 −3.22127
\(275\) −0.938042 −0.0565660
\(276\) −20.8713 −1.25631
\(277\) 7.28123 0.437487 0.218743 0.975782i \(-0.429804\pi\)
0.218743 + 0.975782i \(0.429804\pi\)
\(278\) −36.1457 −2.16787
\(279\) 8.88141 0.531716
\(280\) 70.0855 4.18841
\(281\) −6.66001 −0.397303 −0.198651 0.980070i \(-0.563656\pi\)
−0.198651 + 0.980070i \(0.563656\pi\)
\(282\) −22.6842 −1.35082
\(283\) 22.0653 1.31165 0.655823 0.754914i \(-0.272322\pi\)
0.655823 + 0.754914i \(0.272322\pi\)
\(284\) −53.0522 −3.14807
\(285\) −2.20914 −0.130858
\(286\) 0.139161 0.00822879
\(287\) −29.8861 −1.76412
\(288\) 70.7096 4.16660
\(289\) −13.5351 −0.796183
\(290\) −6.96996 −0.409290
\(291\) 6.51068 0.381663
\(292\) 27.7635 1.62473
\(293\) 20.1266 1.17581 0.587903 0.808931i \(-0.299954\pi\)
0.587903 + 0.808931i \(0.299954\pi\)
\(294\) −21.3099 −1.24282
\(295\) −17.2863 −1.00645
\(296\) 49.7701 2.89283
\(297\) −1.80364 −0.104658
\(298\) 2.11917 0.122760
\(299\) 0.504922 0.0292004
\(300\) −12.5502 −0.724588
\(301\) −1.32752 −0.0765171
\(302\) −28.0996 −1.61695
\(303\) 1.79727 0.103250
\(304\) −29.6879 −1.70272
\(305\) 24.1263 1.38147
\(306\) −11.6169 −0.664092
\(307\) −29.2677 −1.67039 −0.835197 0.549950i \(-0.814647\pi\)
−0.835197 + 0.549950i \(0.814647\pi\)
\(308\) −9.12364 −0.519868
\(309\) −15.2657 −0.868433
\(310\) 18.1649 1.03170
\(311\) 31.4536 1.78357 0.891786 0.452457i \(-0.149452\pi\)
0.891786 + 0.452457i \(0.149452\pi\)
\(312\) 1.23237 0.0697690
\(313\) 4.26139 0.240868 0.120434 0.992721i \(-0.461571\pi\)
0.120434 + 0.992721i \(0.461571\pi\)
\(314\) 7.94250 0.448221
\(315\) 14.1133 0.795193
\(316\) 18.9474 1.06587
\(317\) 12.8686 0.722775 0.361387 0.932416i \(-0.382303\pi\)
0.361387 + 0.932416i \(0.382303\pi\)
\(318\) 22.4563 1.25929
\(319\) 0.600566 0.0336253
\(320\) 82.8230 4.62995
\(321\) 7.08922 0.395682
\(322\) −44.2959 −2.46851
\(323\) 2.88409 0.160475
\(324\) 15.2338 0.846323
\(325\) 0.303617 0.0168417
\(326\) 46.4399 2.57207
\(327\) −3.60181 −0.199181
\(328\) −83.4411 −4.60726
\(329\) −35.9788 −1.98358
\(330\) −1.56814 −0.0863233
\(331\) 16.3653 0.899519 0.449759 0.893150i \(-0.351510\pi\)
0.449759 + 0.893150i \(0.351510\pi\)
\(332\) −14.3344 −0.786703
\(333\) 10.0223 0.549220
\(334\) 5.89195 0.322393
\(335\) −16.4939 −0.901160
\(336\) −66.8419 −3.64653
\(337\) −4.66200 −0.253956 −0.126978 0.991906i \(-0.540528\pi\)
−0.126978 + 0.991906i \(0.540528\pi\)
\(338\) 36.5295 1.98694
\(339\) 8.44799 0.458832
\(340\) −17.7562 −0.962965
\(341\) −1.56518 −0.0847591
\(342\) −9.66958 −0.522871
\(343\) −6.18093 −0.333739
\(344\) −3.70641 −0.199836
\(345\) −5.68972 −0.306324
\(346\) −29.9756 −1.61150
\(347\) 29.8831 1.60421 0.802104 0.597184i \(-0.203714\pi\)
0.802104 + 0.597184i \(0.203714\pi\)
\(348\) 8.03509 0.430726
\(349\) 26.9773 1.44406 0.722030 0.691861i \(-0.243209\pi\)
0.722030 + 0.691861i \(0.243209\pi\)
\(350\) −26.6358 −1.42374
\(351\) 0.583788 0.0311603
\(352\) −12.4612 −0.664184
\(353\) −7.73863 −0.411886 −0.205943 0.978564i \(-0.566026\pi\)
−0.205943 + 0.978564i \(0.566026\pi\)
\(354\) 26.6656 1.41726
\(355\) −14.4625 −0.767591
\(356\) −0.404022 −0.0214131
\(357\) 6.49351 0.343673
\(358\) −31.5498 −1.66746
\(359\) 14.7919 0.780686 0.390343 0.920670i \(-0.372356\pi\)
0.390343 + 0.920670i \(0.372356\pi\)
\(360\) 39.4039 2.07677
\(361\) −16.5994 −0.873650
\(362\) 10.3439 0.543665
\(363\) −9.59079 −0.503386
\(364\) 2.95306 0.154783
\(365\) 7.56859 0.396158
\(366\) −37.2169 −1.94536
\(367\) −5.80421 −0.302977 −0.151489 0.988459i \(-0.548407\pi\)
−0.151489 + 0.988459i \(0.548407\pi\)
\(368\) −76.4620 −3.98586
\(369\) −16.8027 −0.874715
\(370\) 20.4983 1.06566
\(371\) 35.6174 1.84916
\(372\) −20.9408 −1.08573
\(373\) −7.20400 −0.373009 −0.186504 0.982454i \(-0.559716\pi\)
−0.186504 + 0.982454i \(0.559716\pi\)
\(374\) 2.04725 0.105861
\(375\) −10.5503 −0.544817
\(376\) −100.452 −5.18042
\(377\) −0.194386 −0.0100114
\(378\) −51.2146 −2.63419
\(379\) 7.80856 0.401099 0.200550 0.979684i \(-0.435727\pi\)
0.200550 + 0.979684i \(0.435727\pi\)
\(380\) −14.7798 −0.758188
\(381\) −8.43163 −0.431966
\(382\) −27.2181 −1.39260
\(383\) −16.6763 −0.852120 −0.426060 0.904695i \(-0.640099\pi\)
−0.426060 + 0.904695i \(0.640099\pi\)
\(384\) −71.3932 −3.64327
\(385\) −2.48719 −0.126759
\(386\) −32.7521 −1.66704
\(387\) −0.746368 −0.0379400
\(388\) 43.5583 2.21134
\(389\) 30.4984 1.54633 0.773164 0.634206i \(-0.218673\pi\)
0.773164 + 0.634206i \(0.218673\pi\)
\(390\) 0.507563 0.0257014
\(391\) 7.42807 0.375654
\(392\) −94.3662 −4.76621
\(393\) −2.12442 −0.107163
\(394\) −55.3580 −2.78889
\(395\) 5.16523 0.259891
\(396\) −5.12955 −0.257770
\(397\) 14.9238 0.749004 0.374502 0.927226i \(-0.377814\pi\)
0.374502 + 0.927226i \(0.377814\pi\)
\(398\) −9.02528 −0.452397
\(399\) 5.40503 0.270590
\(400\) −45.9777 −2.29889
\(401\) 8.16449 0.407715 0.203858 0.979001i \(-0.434652\pi\)
0.203858 + 0.979001i \(0.434652\pi\)
\(402\) 25.4433 1.26900
\(403\) 0.506603 0.0252357
\(404\) 12.0242 0.598229
\(405\) 4.15288 0.206358
\(406\) 17.0531 0.846332
\(407\) −1.76624 −0.0875493
\(408\) 18.1297 0.897554
\(409\) −13.5052 −0.667787 −0.333893 0.942611i \(-0.608363\pi\)
−0.333893 + 0.942611i \(0.608363\pi\)
\(410\) −34.3661 −1.69722
\(411\) 16.7573 0.826577
\(412\) −102.132 −5.03166
\(413\) 42.2937 2.08114
\(414\) −24.9043 −1.22398
\(415\) −3.90770 −0.191821
\(416\) 4.03333 0.197750
\(417\) 11.3595 0.556275
\(418\) 1.70408 0.0833491
\(419\) −17.3975 −0.849925 −0.424963 0.905211i \(-0.639713\pi\)
−0.424963 + 0.905211i \(0.639713\pi\)
\(420\) −33.2766 −1.62373
\(421\) 5.80649 0.282991 0.141495 0.989939i \(-0.454809\pi\)
0.141495 + 0.989939i \(0.454809\pi\)
\(422\) 27.3438 1.33108
\(423\) −20.2282 −0.983531
\(424\) 99.4429 4.82938
\(425\) 4.46661 0.216662
\(426\) 22.3097 1.08091
\(427\) −59.0288 −2.85660
\(428\) 47.4289 2.29256
\(429\) −0.0437341 −0.00211150
\(430\) −1.52652 −0.0736155
\(431\) −22.1690 −1.06784 −0.533921 0.845534i \(-0.679282\pi\)
−0.533921 + 0.845534i \(0.679282\pi\)
\(432\) −88.4049 −4.25338
\(433\) 37.3633 1.79556 0.897782 0.440440i \(-0.145178\pi\)
0.897782 + 0.440440i \(0.145178\pi\)
\(434\) −44.4433 −2.13335
\(435\) 2.19044 0.105024
\(436\) −24.0972 −1.15404
\(437\) 6.18293 0.295770
\(438\) −11.6752 −0.557863
\(439\) −18.5749 −0.886529 −0.443265 0.896391i \(-0.646180\pi\)
−0.443265 + 0.896391i \(0.646180\pi\)
\(440\) −6.94418 −0.331051
\(441\) −19.0027 −0.904893
\(442\) −0.662636 −0.0315184
\(443\) −5.64796 −0.268343 −0.134171 0.990958i \(-0.542837\pi\)
−0.134171 + 0.990958i \(0.542837\pi\)
\(444\) −23.6309 −1.12147
\(445\) −0.110140 −0.00522115
\(446\) 51.8677 2.45601
\(447\) −0.665989 −0.0315002
\(448\) −202.640 −9.57383
\(449\) −6.81914 −0.321815 −0.160908 0.986969i \(-0.551442\pi\)
−0.160908 + 0.986969i \(0.551442\pi\)
\(450\) −14.9753 −0.705944
\(451\) 2.96116 0.139435
\(452\) 56.5195 2.65845
\(453\) 8.83083 0.414909
\(454\) −8.10107 −0.380202
\(455\) 0.805033 0.0377405
\(456\) 15.0907 0.706687
\(457\) −36.9089 −1.72653 −0.863264 0.504754i \(-0.831583\pi\)
−0.863264 + 0.504754i \(0.831583\pi\)
\(458\) −48.5103 −2.26674
\(459\) 8.58828 0.400867
\(460\) −38.0658 −1.77483
\(461\) 1.85794 0.0865327 0.0432663 0.999064i \(-0.486224\pi\)
0.0432663 + 0.999064i \(0.486224\pi\)
\(462\) 3.83671 0.178500
\(463\) 19.6895 0.915051 0.457525 0.889197i \(-0.348736\pi\)
0.457525 + 0.889197i \(0.348736\pi\)
\(464\) 29.4365 1.36656
\(465\) −5.70866 −0.264733
\(466\) 7.64918 0.354342
\(467\) 31.2075 1.44411 0.722056 0.691834i \(-0.243197\pi\)
0.722056 + 0.691834i \(0.243197\pi\)
\(468\) 1.66029 0.0767469
\(469\) 40.3551 1.86342
\(470\) −41.3722 −1.90836
\(471\) −2.49608 −0.115013
\(472\) 118.083 5.43521
\(473\) 0.131533 0.00604789
\(474\) −7.96783 −0.365975
\(475\) 3.71789 0.170589
\(476\) 43.4434 1.99123
\(477\) 20.0251 0.916884
\(478\) −40.7253 −1.86273
\(479\) 13.6101 0.621861 0.310930 0.950433i \(-0.399359\pi\)
0.310930 + 0.950433i \(0.399359\pi\)
\(480\) −45.4496 −2.07448
\(481\) 0.571682 0.0260664
\(482\) 77.7611 3.54192
\(483\) 13.9208 0.633419
\(484\) −64.1651 −2.91659
\(485\) 11.8744 0.539189
\(486\) −45.3482 −2.05703
\(487\) 24.8324 1.12526 0.562631 0.826708i \(-0.309789\pi\)
0.562631 + 0.826708i \(0.309789\pi\)
\(488\) −164.807 −7.46046
\(489\) −14.5946 −0.659992
\(490\) −38.8657 −1.75577
\(491\) 26.1882 1.18186 0.590928 0.806725i \(-0.298762\pi\)
0.590928 + 0.806725i \(0.298762\pi\)
\(492\) 39.6179 1.78611
\(493\) −2.85968 −0.128793
\(494\) −0.551561 −0.0248159
\(495\) −1.39836 −0.0628518
\(496\) −76.7165 −3.44467
\(497\) 35.3849 1.58723
\(498\) 6.02797 0.270120
\(499\) −29.6741 −1.32840 −0.664198 0.747557i \(-0.731227\pi\)
−0.664198 + 0.747557i \(0.731227\pi\)
\(500\) −70.5848 −3.15665
\(501\) −1.85166 −0.0827260
\(502\) −43.8385 −1.95661
\(503\) −18.2098 −0.811934 −0.405967 0.913888i \(-0.633065\pi\)
−0.405967 + 0.913888i \(0.633065\pi\)
\(504\) −96.4080 −4.29436
\(505\) 3.27792 0.145866
\(506\) 4.38890 0.195110
\(507\) −11.4801 −0.509849
\(508\) −56.4100 −2.50279
\(509\) −15.5052 −0.687254 −0.343627 0.939106i \(-0.611656\pi\)
−0.343627 + 0.939106i \(0.611656\pi\)
\(510\) 7.46691 0.330640
\(511\) −18.5178 −0.819178
\(512\) −188.643 −8.33694
\(513\) 7.14867 0.315621
\(514\) 7.24704 0.319653
\(515\) −27.8420 −1.22687
\(516\) 1.75980 0.0774710
\(517\) 3.56484 0.156781
\(518\) −50.1525 −2.20357
\(519\) 9.42042 0.413510
\(520\) 2.24763 0.0985652
\(521\) 24.4901 1.07293 0.536466 0.843922i \(-0.319759\pi\)
0.536466 + 0.843922i \(0.319759\pi\)
\(522\) 9.58772 0.419643
\(523\) 40.6091 1.77571 0.887855 0.460123i \(-0.152195\pi\)
0.887855 + 0.460123i \(0.152195\pi\)
\(524\) −14.2130 −0.620896
\(525\) 8.37080 0.365332
\(526\) 58.9956 2.57233
\(527\) 7.45279 0.324649
\(528\) 6.62280 0.288220
\(529\) −7.07566 −0.307637
\(530\) 40.9566 1.77904
\(531\) 23.7786 1.03191
\(532\) 36.1612 1.56779
\(533\) −0.958442 −0.0415147
\(534\) 0.169901 0.00735234
\(535\) 12.9296 0.558994
\(536\) 112.670 4.86662
\(537\) 9.91512 0.427869
\(538\) 9.97012 0.429842
\(539\) 3.34887 0.144246
\(540\) −44.0115 −1.89395
\(541\) −41.0190 −1.76355 −0.881773 0.471674i \(-0.843650\pi\)
−0.881773 + 0.471674i \(0.843650\pi\)
\(542\) −60.0596 −2.57978
\(543\) −3.25078 −0.139504
\(544\) 59.3356 2.54399
\(545\) −6.56911 −0.281390
\(546\) −1.24183 −0.0531456
\(547\) 10.1663 0.434681 0.217340 0.976096i \(-0.430262\pi\)
0.217340 + 0.976096i \(0.430262\pi\)
\(548\) 112.111 4.78915
\(549\) −33.1875 −1.41641
\(550\) 2.63911 0.112532
\(551\) −2.38032 −0.101405
\(552\) 38.8666 1.65427
\(553\) −12.6376 −0.537405
\(554\) −20.4852 −0.870333
\(555\) −6.44200 −0.273448
\(556\) 75.9981 3.22304
\(557\) 8.44343 0.357760 0.178880 0.983871i \(-0.442753\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(558\) −24.9872 −1.05779
\(559\) −0.0425734 −0.00180066
\(560\) −121.909 −5.15158
\(561\) −0.643386 −0.0271638
\(562\) 18.7375 0.790392
\(563\) −27.2697 −1.14928 −0.574641 0.818405i \(-0.694858\pi\)
−0.574641 + 0.818405i \(0.694858\pi\)
\(564\) 47.6946 2.00831
\(565\) 15.4077 0.648209
\(566\) −62.0791 −2.60938
\(567\) −10.1607 −0.426709
\(568\) 98.7938 4.14529
\(569\) 38.5614 1.61658 0.808288 0.588787i \(-0.200394\pi\)
0.808288 + 0.588787i \(0.200394\pi\)
\(570\) 6.21527 0.260329
\(571\) −2.46267 −0.103060 −0.0515299 0.998671i \(-0.516410\pi\)
−0.0515299 + 0.998671i \(0.516410\pi\)
\(572\) −0.292594 −0.0122340
\(573\) 8.55381 0.357340
\(574\) 84.0822 3.50952
\(575\) 9.57554 0.399328
\(576\) −113.929 −4.74706
\(577\) 8.36280 0.348148 0.174074 0.984733i \(-0.444307\pi\)
0.174074 + 0.984733i \(0.444307\pi\)
\(578\) 38.0800 1.58392
\(579\) 10.2930 0.427762
\(580\) 14.6547 0.608502
\(581\) 9.56081 0.396649
\(582\) −18.3173 −0.759277
\(583\) −3.52903 −0.146157
\(584\) −51.7012 −2.13941
\(585\) 0.452611 0.0187132
\(586\) −56.6246 −2.33914
\(587\) 10.8802 0.449072 0.224536 0.974466i \(-0.427913\pi\)
0.224536 + 0.974466i \(0.427913\pi\)
\(588\) 44.8051 1.84773
\(589\) 6.20352 0.255611
\(590\) 48.6337 2.00222
\(591\) 17.3973 0.715629
\(592\) −86.5715 −3.55807
\(593\) −7.67066 −0.314996 −0.157498 0.987519i \(-0.550343\pi\)
−0.157498 + 0.987519i \(0.550343\pi\)
\(594\) 5.07442 0.208206
\(595\) 11.8431 0.485519
\(596\) −4.45566 −0.182511
\(597\) 2.83637 0.116085
\(598\) −1.42056 −0.0580911
\(599\) 41.9413 1.71368 0.856838 0.515585i \(-0.172425\pi\)
0.856838 + 0.515585i \(0.172425\pi\)
\(600\) 23.3711 0.954119
\(601\) 41.8772 1.70821 0.854103 0.520104i \(-0.174107\pi\)
0.854103 + 0.520104i \(0.174107\pi\)
\(602\) 3.73488 0.152223
\(603\) 22.6887 0.923955
\(604\) 59.0808 2.40396
\(605\) −17.4920 −0.711151
\(606\) −5.05649 −0.205406
\(607\) 20.3926 0.827711 0.413855 0.910343i \(-0.364182\pi\)
0.413855 + 0.910343i \(0.364182\pi\)
\(608\) 49.3894 2.00301
\(609\) −5.35927 −0.217169
\(610\) −67.8774 −2.74828
\(611\) −1.15384 −0.0466792
\(612\) 24.4250 0.987323
\(613\) −38.3502 −1.54895 −0.774475 0.632604i \(-0.781986\pi\)
−0.774475 + 0.632604i \(0.781986\pi\)
\(614\) 82.3425 3.32307
\(615\) 10.8002 0.435506
\(616\) 16.9900 0.684549
\(617\) 24.1188 0.970988 0.485494 0.874240i \(-0.338640\pi\)
0.485494 + 0.874240i \(0.338640\pi\)
\(618\) 42.9488 1.72765
\(619\) 20.7080 0.832324 0.416162 0.909291i \(-0.363375\pi\)
0.416162 + 0.909291i \(0.363375\pi\)
\(620\) −38.1926 −1.53385
\(621\) 18.4116 0.738833
\(622\) −88.4925 −3.54823
\(623\) 0.269476 0.0107963
\(624\) −2.14361 −0.0858132
\(625\) −7.24425 −0.289770
\(626\) −11.9891 −0.479182
\(627\) −0.535538 −0.0213873
\(628\) −16.6995 −0.666382
\(629\) 8.41018 0.335336
\(630\) −39.7067 −1.58195
\(631\) −42.0281 −1.67311 −0.836556 0.547881i \(-0.815435\pi\)
−0.836556 + 0.547881i \(0.815435\pi\)
\(632\) −35.2838 −1.40351
\(633\) −8.59331 −0.341554
\(634\) −36.2050 −1.43788
\(635\) −15.3779 −0.610254
\(636\) −47.2155 −1.87222
\(637\) −1.08393 −0.0429470
\(638\) −1.68965 −0.0668939
\(639\) 19.8943 0.787008
\(640\) −130.209 −5.14698
\(641\) −24.2811 −0.959046 −0.479523 0.877529i \(-0.659190\pi\)
−0.479523 + 0.877529i \(0.659190\pi\)
\(642\) −19.9450 −0.787167
\(643\) 7.94360 0.313265 0.156633 0.987657i \(-0.449936\pi\)
0.156633 + 0.987657i \(0.449936\pi\)
\(644\) 93.1343 3.67000
\(645\) 0.479739 0.0188897
\(646\) −8.11418 −0.319248
\(647\) 14.0235 0.551321 0.275660 0.961255i \(-0.411103\pi\)
0.275660 + 0.961255i \(0.411103\pi\)
\(648\) −28.3684 −1.11442
\(649\) −4.19052 −0.164492
\(650\) −0.854205 −0.0335047
\(651\) 13.9672 0.547416
\(652\) −97.6422 −3.82397
\(653\) −12.6197 −0.493848 −0.246924 0.969035i \(-0.579420\pi\)
−0.246924 + 0.969035i \(0.579420\pi\)
\(654\) 10.1334 0.396249
\(655\) −3.87459 −0.151393
\(656\) 145.140 5.66676
\(657\) −10.4112 −0.406179
\(658\) 101.224 3.94611
\(659\) −16.6361 −0.648051 −0.324026 0.946048i \(-0.605036\pi\)
−0.324026 + 0.946048i \(0.605036\pi\)
\(660\) 3.29710 0.128339
\(661\) −48.2312 −1.87598 −0.937988 0.346667i \(-0.887313\pi\)
−0.937988 + 0.346667i \(0.887313\pi\)
\(662\) −46.0426 −1.78950
\(663\) 0.208246 0.00808760
\(664\) 26.6935 1.03591
\(665\) 9.85788 0.382272
\(666\) −28.1971 −1.09261
\(667\) −6.13059 −0.237377
\(668\) −12.3881 −0.479311
\(669\) −16.3004 −0.630211
\(670\) 46.4045 1.79276
\(671\) 5.84866 0.225785
\(672\) 111.200 4.28963
\(673\) −11.1206 −0.428669 −0.214335 0.976760i \(-0.568758\pi\)
−0.214335 + 0.976760i \(0.568758\pi\)
\(674\) 13.1162 0.505217
\(675\) 11.0712 0.426130
\(676\) −76.8051 −2.95404
\(677\) −7.69090 −0.295585 −0.147793 0.989018i \(-0.547217\pi\)
−0.147793 + 0.989018i \(0.547217\pi\)
\(678\) −23.7678 −0.912797
\(679\) −29.0526 −1.11494
\(680\) 33.0656 1.26801
\(681\) 2.54592 0.0975597
\(682\) 4.40351 0.168619
\(683\) 22.7599 0.870884 0.435442 0.900217i \(-0.356592\pi\)
0.435442 + 0.900217i \(0.356592\pi\)
\(684\) 20.3308 0.777366
\(685\) 30.5625 1.16774
\(686\) 17.3896 0.663938
\(687\) 15.2453 0.581645
\(688\) 6.44703 0.245791
\(689\) 1.14225 0.0435161
\(690\) 16.0076 0.609399
\(691\) −28.5847 −1.08741 −0.543707 0.839275i \(-0.682980\pi\)
−0.543707 + 0.839275i \(0.682980\pi\)
\(692\) 63.0253 2.39586
\(693\) 3.42133 0.129965
\(694\) −84.0739 −3.19140
\(695\) 20.7178 0.785871
\(696\) −14.9629 −0.567169
\(697\) −14.0999 −0.534073
\(698\) −75.8986 −2.87280
\(699\) −2.40390 −0.0909239
\(700\) 56.0030 2.11672
\(701\) 18.1689 0.686231 0.343116 0.939293i \(-0.388518\pi\)
0.343116 + 0.939293i \(0.388518\pi\)
\(702\) −1.64244 −0.0619901
\(703\) 7.00042 0.264026
\(704\) 20.0779 0.756713
\(705\) 13.0020 0.489684
\(706\) 21.7721 0.819403
\(707\) −8.01997 −0.301622
\(708\) −56.0658 −2.10708
\(709\) −3.28712 −0.123450 −0.0617252 0.998093i \(-0.519660\pi\)
−0.0617252 + 0.998093i \(0.519660\pi\)
\(710\) 40.6893 1.52704
\(711\) −7.10518 −0.266465
\(712\) 0.752371 0.0281963
\(713\) 15.9773 0.598356
\(714\) −18.2690 −0.683700
\(715\) −0.0797639 −0.00298300
\(716\) 66.3350 2.47905
\(717\) 12.7987 0.477976
\(718\) −41.6159 −1.55309
\(719\) 9.44679 0.352306 0.176153 0.984363i \(-0.443635\pi\)
0.176153 + 0.984363i \(0.443635\pi\)
\(720\) −68.5403 −2.55435
\(721\) 68.1200 2.53692
\(722\) 46.7011 1.73803
\(723\) −24.4379 −0.908855
\(724\) −21.7486 −0.808282
\(725\) −3.68641 −0.136910
\(726\) 26.9830 1.00143
\(727\) 19.4189 0.720206 0.360103 0.932913i \(-0.382742\pi\)
0.360103 + 0.932913i \(0.382742\pi\)
\(728\) −5.49919 −0.203814
\(729\) 6.52565 0.241691
\(730\) −21.2937 −0.788114
\(731\) −0.626311 −0.0231649
\(732\) 78.2503 2.89221
\(733\) 4.74560 0.175283 0.0876414 0.996152i \(-0.472067\pi\)
0.0876414 + 0.996152i \(0.472067\pi\)
\(734\) 16.3297 0.602741
\(735\) 12.2143 0.450531
\(736\) 127.204 4.68880
\(737\) −3.99844 −0.147284
\(738\) 47.2733 1.74015
\(739\) −31.1655 −1.14644 −0.573221 0.819401i \(-0.694306\pi\)
−0.573221 + 0.819401i \(0.694306\pi\)
\(740\) −43.0988 −1.58434
\(741\) 0.173339 0.00636775
\(742\) −100.207 −3.67871
\(743\) −10.9849 −0.402998 −0.201499 0.979489i \(-0.564581\pi\)
−0.201499 + 0.979489i \(0.564581\pi\)
\(744\) 38.9960 1.42966
\(745\) −1.21465 −0.0445015
\(746\) 20.2679 0.742061
\(747\) 5.37534 0.196673
\(748\) −4.30444 −0.157386
\(749\) −31.6343 −1.15589
\(750\) 29.6826 1.08386
\(751\) 14.9883 0.546930 0.273465 0.961882i \(-0.411830\pi\)
0.273465 + 0.961882i \(0.411830\pi\)
\(752\) 174.729 6.37171
\(753\) 13.7771 0.502065
\(754\) 0.546891 0.0199166
\(755\) 16.1060 0.586157
\(756\) 107.681 3.91633
\(757\) −38.0463 −1.38282 −0.691409 0.722464i \(-0.743010\pi\)
−0.691409 + 0.722464i \(0.743010\pi\)
\(758\) −21.9688 −0.797944
\(759\) −1.37930 −0.0500653
\(760\) 27.5230 0.998363
\(761\) −11.6748 −0.423212 −0.211606 0.977355i \(-0.567869\pi\)
−0.211606 + 0.977355i \(0.567869\pi\)
\(762\) 23.7218 0.859349
\(763\) 16.0724 0.581860
\(764\) 57.2274 2.07041
\(765\) 6.65850 0.240738
\(766\) 46.9176 1.69520
\(767\) 1.35635 0.0489751
\(768\) 110.037 3.97060
\(769\) −12.3601 −0.445716 −0.222858 0.974851i \(-0.571539\pi\)
−0.222858 + 0.974851i \(0.571539\pi\)
\(770\) 6.99753 0.252173
\(771\) −2.27752 −0.0820229
\(772\) 68.8630 2.47843
\(773\) −29.6115 −1.06505 −0.532525 0.846414i \(-0.678757\pi\)
−0.532525 + 0.846414i \(0.678757\pi\)
\(774\) 2.09985 0.0754776
\(775\) 9.60742 0.345109
\(776\) −81.1143 −2.91183
\(777\) 15.7614 0.565437
\(778\) −85.8049 −3.07626
\(779\) −11.7364 −0.420501
\(780\) −1.06718 −0.0382110
\(781\) −3.50599 −0.125454
\(782\) −20.8983 −0.747323
\(783\) −7.08815 −0.253310
\(784\) 164.143 5.86226
\(785\) −4.55244 −0.162484
\(786\) 5.97690 0.213189
\(787\) 35.1337 1.25238 0.626190 0.779671i \(-0.284614\pi\)
0.626190 + 0.779671i \(0.284614\pi\)
\(788\) 116.393 4.14632
\(789\) −18.5405 −0.660059
\(790\) −14.5320 −0.517026
\(791\) −37.6975 −1.34037
\(792\) 9.55225 0.339425
\(793\) −1.89304 −0.0672240
\(794\) −41.9870 −1.49006
\(795\) −12.8714 −0.456502
\(796\) 18.9761 0.672590
\(797\) 16.5353 0.585710 0.292855 0.956157i \(-0.405395\pi\)
0.292855 + 0.956157i \(0.405395\pi\)
\(798\) −15.2067 −0.538310
\(799\) −16.9744 −0.600512
\(800\) 76.4897 2.70432
\(801\) 0.151507 0.00535322
\(802\) −22.9702 −0.811106
\(803\) 1.83477 0.0647476
\(804\) −53.4959 −1.88665
\(805\) 25.3893 0.894855
\(806\) −1.42529 −0.0502037
\(807\) −3.13330 −0.110297
\(808\) −22.3916 −0.787732
\(809\) 28.3862 0.998005 0.499002 0.866601i \(-0.333700\pi\)
0.499002 + 0.866601i \(0.333700\pi\)
\(810\) −11.6838 −0.410528
\(811\) −4.17265 −0.146522 −0.0732608 0.997313i \(-0.523341\pi\)
−0.0732608 + 0.997313i \(0.523341\pi\)
\(812\) −35.8550 −1.25827
\(813\) 18.8749 0.661971
\(814\) 4.96919 0.174170
\(815\) −26.6182 −0.932395
\(816\) −31.5353 −1.10396
\(817\) −0.521325 −0.0182389
\(818\) 37.9958 1.32849
\(819\) −1.10739 −0.0386952
\(820\) 72.2564 2.52330
\(821\) −11.6144 −0.405346 −0.202673 0.979246i \(-0.564963\pi\)
−0.202673 + 0.979246i \(0.564963\pi\)
\(822\) −47.1454 −1.64439
\(823\) −36.2902 −1.26500 −0.632498 0.774562i \(-0.717971\pi\)
−0.632498 + 0.774562i \(0.717971\pi\)
\(824\) 190.189 6.62556
\(825\) −0.829391 −0.0288757
\(826\) −118.990 −4.14020
\(827\) −45.8109 −1.59300 −0.796501 0.604637i \(-0.793318\pi\)
−0.796501 + 0.604637i \(0.793318\pi\)
\(828\) 52.3625 1.81972
\(829\) 17.1152 0.594434 0.297217 0.954810i \(-0.403941\pi\)
0.297217 + 0.954810i \(0.403941\pi\)
\(830\) 10.9940 0.381608
\(831\) 6.43787 0.223327
\(832\) −6.49863 −0.225300
\(833\) −15.9461 −0.552498
\(834\) −31.9590 −1.10665
\(835\) −3.37712 −0.116870
\(836\) −3.58290 −0.123917
\(837\) 18.4729 0.638517
\(838\) 48.9467 1.69084
\(839\) 12.3289 0.425642 0.212821 0.977091i \(-0.431735\pi\)
0.212821 + 0.977091i \(0.431735\pi\)
\(840\) 61.9677 2.13809
\(841\) −26.6398 −0.918615
\(842\) −16.3361 −0.562980
\(843\) −5.88860 −0.202814
\(844\) −57.4917 −1.97895
\(845\) −20.9378 −0.720282
\(846\) 56.9107 1.95663
\(847\) 42.7970 1.47052
\(848\) −172.974 −5.93995
\(849\) 19.5096 0.669566
\(850\) −12.5665 −0.431027
\(851\) 18.0298 0.618054
\(852\) −46.9073 −1.60702
\(853\) 46.1452 1.57998 0.789991 0.613119i \(-0.210085\pi\)
0.789991 + 0.613119i \(0.210085\pi\)
\(854\) 166.073 5.68291
\(855\) 5.54236 0.189545
\(856\) −88.3221 −3.01879
\(857\) 50.0472 1.70958 0.854790 0.518974i \(-0.173686\pi\)
0.854790 + 0.518974i \(0.173686\pi\)
\(858\) 0.123043 0.00420061
\(859\) −11.7176 −0.399798 −0.199899 0.979817i \(-0.564061\pi\)
−0.199899 + 0.979817i \(0.564061\pi\)
\(860\) 3.20959 0.109446
\(861\) −26.4244 −0.900543
\(862\) 62.3708 2.12436
\(863\) 10.1759 0.346391 0.173196 0.984887i \(-0.444591\pi\)
0.173196 + 0.984887i \(0.444591\pi\)
\(864\) 147.072 5.00351
\(865\) 17.1813 0.584181
\(866\) −105.119 −3.57208
\(867\) −11.9674 −0.406433
\(868\) 93.4443 3.17171
\(869\) 1.25215 0.0424763
\(870\) −6.16265 −0.208933
\(871\) 1.29418 0.0438517
\(872\) 44.8737 1.51962
\(873\) −16.3342 −0.552828
\(874\) −17.3952 −0.588402
\(875\) 47.0789 1.59156
\(876\) 24.5477 0.829391
\(877\) 42.1026 1.42170 0.710852 0.703342i \(-0.248310\pi\)
0.710852 + 0.703342i \(0.248310\pi\)
\(878\) 52.2590 1.76366
\(879\) 17.7954 0.600223
\(880\) 12.0789 0.407180
\(881\) 19.4872 0.656540 0.328270 0.944584i \(-0.393534\pi\)
0.328270 + 0.944584i \(0.393534\pi\)
\(882\) 53.4628 1.80019
\(883\) −57.5957 −1.93825 −0.969125 0.246569i \(-0.920697\pi\)
−0.969125 + 0.246569i \(0.920697\pi\)
\(884\) 1.39322 0.0468592
\(885\) −15.2841 −0.513768
\(886\) 15.8901 0.533839
\(887\) −35.1840 −1.18136 −0.590682 0.806904i \(-0.701141\pi\)
−0.590682 + 0.806904i \(0.701141\pi\)
\(888\) 44.0054 1.47672
\(889\) 37.6245 1.26189
\(890\) 0.309872 0.0103869
\(891\) 1.00674 0.0337270
\(892\) −109.054 −3.65141
\(893\) −14.1291 −0.472812
\(894\) 1.87371 0.0626663
\(895\) 18.0835 0.604466
\(896\) 318.578 10.6430
\(897\) 0.446439 0.0149062
\(898\) 19.1851 0.640217
\(899\) −6.15100 −0.205147
\(900\) 31.4864 1.04955
\(901\) 16.8039 0.559820
\(902\) −8.33099 −0.277392
\(903\) −1.17376 −0.0390603
\(904\) −105.251 −3.50058
\(905\) −5.92889 −0.197083
\(906\) −24.8449 −0.825416
\(907\) 6.36743 0.211427 0.105713 0.994397i \(-0.466287\pi\)
0.105713 + 0.994397i \(0.466287\pi\)
\(908\) 17.0329 0.565257
\(909\) −4.50904 −0.149555
\(910\) −2.26490 −0.0750807
\(911\) −19.5154 −0.646573 −0.323286 0.946301i \(-0.604788\pi\)
−0.323286 + 0.946301i \(0.604788\pi\)
\(912\) −26.2492 −0.869198
\(913\) −0.947300 −0.0313510
\(914\) 103.841 3.43474
\(915\) 21.3318 0.705207
\(916\) 101.995 3.37002
\(917\) 9.47981 0.313051
\(918\) −24.1625 −0.797481
\(919\) 46.7587 1.54243 0.771213 0.636577i \(-0.219650\pi\)
0.771213 + 0.636577i \(0.219650\pi\)
\(920\) 70.8862 2.33705
\(921\) −25.8777 −0.852699
\(922\) −5.22717 −0.172148
\(923\) 1.13479 0.0373520
\(924\) −8.06688 −0.265381
\(925\) 10.8416 0.356469
\(926\) −55.3951 −1.82040
\(927\) 38.2989 1.25790
\(928\) −48.9713 −1.60756
\(929\) 22.8271 0.748933 0.374467 0.927240i \(-0.377826\pi\)
0.374467 + 0.927240i \(0.377826\pi\)
\(930\) 16.0609 0.526658
\(931\) −13.2731 −0.435008
\(932\) −16.0828 −0.526809
\(933\) 27.8105 0.910474
\(934\) −87.8001 −2.87291
\(935\) −1.17343 −0.0383753
\(936\) −3.09179 −0.101058
\(937\) −9.50808 −0.310615 −0.155308 0.987866i \(-0.549637\pi\)
−0.155308 + 0.987866i \(0.549637\pi\)
\(938\) −113.536 −3.70708
\(939\) 3.76781 0.122958
\(940\) 86.9871 2.83721
\(941\) −33.6117 −1.09571 −0.547855 0.836573i \(-0.684555\pi\)
−0.547855 + 0.836573i \(0.684555\pi\)
\(942\) 7.02254 0.228807
\(943\) −30.2275 −0.984343
\(944\) −205.397 −6.68510
\(945\) 29.3549 0.954916
\(946\) −0.370058 −0.0120316
\(947\) −20.7879 −0.675516 −0.337758 0.941233i \(-0.609669\pi\)
−0.337758 + 0.941233i \(0.609669\pi\)
\(948\) 16.7528 0.544104
\(949\) −0.593863 −0.0192776
\(950\) −10.4600 −0.339368
\(951\) 11.3781 0.368960
\(952\) −80.9003 −2.62200
\(953\) −29.5520 −0.957284 −0.478642 0.878010i \(-0.658871\pi\)
−0.478642 + 0.878010i \(0.658871\pi\)
\(954\) −56.3390 −1.82404
\(955\) 15.6007 0.504828
\(956\) 85.6269 2.76937
\(957\) 0.531005 0.0171649
\(958\) −38.2910 −1.23713
\(959\) −74.7762 −2.41465
\(960\) 73.2299 2.36348
\(961\) −14.9695 −0.482886
\(962\) −1.60838 −0.0518564
\(963\) −17.7856 −0.573134
\(964\) −163.497 −5.26587
\(965\) 18.7727 0.604315
\(966\) −39.1652 −1.26012
\(967\) 13.1018 0.421326 0.210663 0.977559i \(-0.432438\pi\)
0.210663 + 0.977559i \(0.432438\pi\)
\(968\) 119.488 3.84050
\(969\) 2.55004 0.0819190
\(970\) −33.4078 −1.07266
\(971\) −17.8334 −0.572301 −0.286151 0.958185i \(-0.592376\pi\)
−0.286151 + 0.958185i \(0.592376\pi\)
\(972\) 95.3468 3.05825
\(973\) −50.6894 −1.62503
\(974\) −69.8640 −2.23859
\(975\) 0.268450 0.00859729
\(976\) 286.670 9.17607
\(977\) −2.44557 −0.0782407 −0.0391204 0.999235i \(-0.512456\pi\)
−0.0391204 + 0.999235i \(0.512456\pi\)
\(978\) 41.0609 1.31298
\(979\) −0.0267001 −0.000853339 0
\(980\) 81.7171 2.61036
\(981\) 9.03633 0.288508
\(982\) −73.6785 −2.35117
\(983\) −33.0866 −1.05530 −0.527649 0.849462i \(-0.676927\pi\)
−0.527649 + 0.849462i \(0.676927\pi\)
\(984\) −73.7764 −2.35191
\(985\) 31.7298 1.01100
\(986\) 8.04549 0.256220
\(987\) −31.8115 −1.01257
\(988\) 1.15968 0.0368945
\(989\) −1.34269 −0.0426950
\(990\) 3.93420 0.125037
\(991\) −2.93415 −0.0932063 −0.0466032 0.998913i \(-0.514840\pi\)
−0.0466032 + 0.998913i \(0.514840\pi\)
\(992\) 127.627 4.05217
\(993\) 14.4698 0.459184
\(994\) −99.5528 −3.15762
\(995\) 5.17307 0.163997
\(996\) −12.6741 −0.401594
\(997\) 12.1169 0.383747 0.191874 0.981420i \(-0.438544\pi\)
0.191874 + 0.981420i \(0.438544\pi\)
\(998\) 83.4859 2.64270
\(999\) 20.8459 0.659536
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 \(a_p\))