Properties

Label 8011.2.a.b.1.15
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 1.15
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61797 q^{2}\) \(+1.26070 q^{3}\) \(+4.85374 q^{4}\) \(+0.306561 q^{5}\) \(-3.30046 q^{6}\) \(-1.43849 q^{7}\) \(-7.47100 q^{8}\) \(-1.41065 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61797 q^{2}\) \(+1.26070 q^{3}\) \(+4.85374 q^{4}\) \(+0.306561 q^{5}\) \(-3.30046 q^{6}\) \(-1.43849 q^{7}\) \(-7.47100 q^{8}\) \(-1.41065 q^{9}\) \(-0.802565 q^{10}\) \(+2.14470 q^{11}\) \(+6.11909 q^{12}\) \(-3.19914 q^{13}\) \(+3.76591 q^{14}\) \(+0.386480 q^{15}\) \(+9.85133 q^{16}\) \(-3.80611 q^{17}\) \(+3.69302 q^{18}\) \(+4.63838 q^{19}\) \(+1.48797 q^{20}\) \(-1.81349 q^{21}\) \(-5.61474 q^{22}\) \(-3.20363 q^{23}\) \(-9.41866 q^{24}\) \(-4.90602 q^{25}\) \(+8.37523 q^{26}\) \(-5.56048 q^{27}\) \(-6.98204 q^{28}\) \(-3.93433 q^{29}\) \(-1.01179 q^{30}\) \(-3.98336 q^{31}\) \(-10.8484 q^{32}\) \(+2.70381 q^{33}\) \(+9.96426 q^{34}\) \(-0.440983 q^{35}\) \(-6.84691 q^{36}\) \(+3.40998 q^{37}\) \(-12.1431 q^{38}\) \(-4.03314 q^{39}\) \(-2.29031 q^{40}\) \(+8.71086 q^{41}\) \(+4.74766 q^{42}\) \(-7.51262 q^{43}\) \(+10.4098 q^{44}\) \(-0.432449 q^{45}\) \(+8.38698 q^{46}\) \(-8.65394 q^{47}\) \(+12.4195 q^{48}\) \(-4.93076 q^{49}\) \(+12.8438 q^{50}\) \(-4.79834 q^{51}\) \(-15.5278 q^{52}\) \(-1.13168 q^{53}\) \(+14.5572 q^{54}\) \(+0.657480 q^{55}\) \(+10.7469 q^{56}\) \(+5.84758 q^{57}\) \(+10.2999 q^{58}\) \(+12.0044 q^{59}\) \(+1.87587 q^{60}\) \(-1.57506 q^{61}\) \(+10.4283 q^{62}\) \(+2.02919 q^{63}\) \(+8.69818 q^{64}\) \(-0.980730 q^{65}\) \(-7.07848 q^{66}\) \(+11.9537 q^{67}\) \(-18.4739 q^{68}\) \(-4.03880 q^{69}\) \(+1.15448 q^{70}\) \(+15.1590 q^{71}\) \(+10.5389 q^{72}\) \(+0.359001 q^{73}\) \(-8.92722 q^{74}\) \(-6.18500 q^{75}\) \(+22.5135 q^{76}\) \(-3.08511 q^{77}\) \(+10.5586 q^{78}\) \(-0.646053 q^{79}\) \(+3.02003 q^{80}\) \(-2.77814 q^{81}\) \(-22.8047 q^{82}\) \(+6.65148 q^{83}\) \(-8.80223 q^{84}\) \(-1.16680 q^{85}\) \(+19.6678 q^{86}\) \(-4.95999 q^{87}\) \(-16.0230 q^{88}\) \(-8.54918 q^{89}\) \(+1.13214 q^{90}\) \(+4.60191 q^{91}\) \(-15.5496 q^{92}\) \(-5.02181 q^{93}\) \(+22.6557 q^{94}\) \(+1.42194 q^{95}\) \(-13.6766 q^{96}\) \(-12.6530 q^{97}\) \(+12.9086 q^{98}\) \(-3.02541 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61797 −1.85118 −0.925590 0.378526i \(-0.876431\pi\)
−0.925590 + 0.378526i \(0.876431\pi\)
\(3\) 1.26070 0.727863 0.363932 0.931426i \(-0.381434\pi\)
0.363932 + 0.931426i \(0.381434\pi\)
\(4\) 4.85374 2.42687
\(5\) 0.306561 0.137098 0.0685491 0.997648i \(-0.478163\pi\)
0.0685491 + 0.997648i \(0.478163\pi\)
\(6\) −3.30046 −1.34741
\(7\) −1.43849 −0.543696 −0.271848 0.962340i \(-0.587635\pi\)
−0.271848 + 0.962340i \(0.587635\pi\)
\(8\) −7.47100 −2.64140
\(9\) −1.41065 −0.470215
\(10\) −0.802565 −0.253793
\(11\) 2.14470 0.646650 0.323325 0.946288i \(-0.395199\pi\)
0.323325 + 0.946288i \(0.395199\pi\)
\(12\) 6.11909 1.76643
\(13\) −3.19914 −0.887281 −0.443641 0.896205i \(-0.646313\pi\)
−0.443641 + 0.896205i \(0.646313\pi\)
\(14\) 3.76591 1.00648
\(15\) 0.386480 0.0997887
\(16\) 9.85133 2.46283
\(17\) −3.80611 −0.923117 −0.461558 0.887110i \(-0.652709\pi\)
−0.461558 + 0.887110i \(0.652709\pi\)
\(18\) 3.69302 0.870454
\(19\) 4.63838 1.06412 0.532058 0.846708i \(-0.321419\pi\)
0.532058 + 0.846708i \(0.321419\pi\)
\(20\) 1.48797 0.332719
\(21\) −1.81349 −0.395737
\(22\) −5.61474 −1.19707
\(23\) −3.20363 −0.668002 −0.334001 0.942573i \(-0.608399\pi\)
−0.334001 + 0.942573i \(0.608399\pi\)
\(24\) −9.41866 −1.92257
\(25\) −4.90602 −0.981204
\(26\) 8.37523 1.64252
\(27\) −5.56048 −1.07012
\(28\) −6.98204 −1.31948
\(29\) −3.93433 −0.730586 −0.365293 0.930893i \(-0.619031\pi\)
−0.365293 + 0.930893i \(0.619031\pi\)
\(30\) −1.01179 −0.184727
\(31\) −3.98336 −0.715433 −0.357716 0.933830i \(-0.616445\pi\)
−0.357716 + 0.933830i \(0.616445\pi\)
\(32\) −10.8484 −1.91775
\(33\) 2.70381 0.470673
\(34\) 9.96426 1.70886
\(35\) −0.440983 −0.0745398
\(36\) −6.84691 −1.14115
\(37\) 3.40998 0.560598 0.280299 0.959913i \(-0.409566\pi\)
0.280299 + 0.959913i \(0.409566\pi\)
\(38\) −12.1431 −1.96987
\(39\) −4.03314 −0.645819
\(40\) −2.29031 −0.362130
\(41\) 8.71086 1.36041 0.680204 0.733023i \(-0.261891\pi\)
0.680204 + 0.733023i \(0.261891\pi\)
\(42\) 4.74766 0.732580
\(43\) −7.51262 −1.14566 −0.572832 0.819673i \(-0.694155\pi\)
−0.572832 + 0.819673i \(0.694155\pi\)
\(44\) 10.4098 1.56934
\(45\) −0.432449 −0.0644656
\(46\) 8.38698 1.23659
\(47\) −8.65394 −1.26231 −0.631153 0.775658i \(-0.717418\pi\)
−0.631153 + 0.775658i \(0.717418\pi\)
\(48\) 12.4195 1.79260
\(49\) −4.93076 −0.704394
\(50\) 12.8438 1.81639
\(51\) −4.79834 −0.671903
\(52\) −15.5278 −2.15332
\(53\) −1.13168 −0.155448 −0.0777238 0.996975i \(-0.524765\pi\)
−0.0777238 + 0.996975i \(0.524765\pi\)
\(54\) 14.5572 1.98098
\(55\) 0.657480 0.0886545
\(56\) 10.7469 1.43612
\(57\) 5.84758 0.774531
\(58\) 10.2999 1.35245
\(59\) 12.0044 1.56284 0.781419 0.624006i \(-0.214496\pi\)
0.781419 + 0.624006i \(0.214496\pi\)
\(60\) 1.87587 0.242174
\(61\) −1.57506 −0.201666 −0.100833 0.994903i \(-0.532151\pi\)
−0.100833 + 0.994903i \(0.532151\pi\)
\(62\) 10.4283 1.32440
\(63\) 2.02919 0.255654
\(64\) 8.69818 1.08727
\(65\) −0.980730 −0.121645
\(66\) −7.07848 −0.871301
\(67\) 11.9537 1.46037 0.730187 0.683247i \(-0.239433\pi\)
0.730187 + 0.683247i \(0.239433\pi\)
\(68\) −18.4739 −2.24029
\(69\) −4.03880 −0.486214
\(70\) 1.15448 0.137987
\(71\) 15.1590 1.79904 0.899522 0.436876i \(-0.143915\pi\)
0.899522 + 0.436876i \(0.143915\pi\)
\(72\) 10.5389 1.24203
\(73\) 0.359001 0.0420179 0.0210090 0.999779i \(-0.493312\pi\)
0.0210090 + 0.999779i \(0.493312\pi\)
\(74\) −8.92722 −1.03777
\(75\) −6.18500 −0.714182
\(76\) 22.5135 2.58247
\(77\) −3.08511 −0.351581
\(78\) 10.5586 1.19553
\(79\) −0.646053 −0.0726866 −0.0363433 0.999339i \(-0.511571\pi\)
−0.0363433 + 0.999339i \(0.511571\pi\)
\(80\) 3.02003 0.337650
\(81\) −2.77814 −0.308682
\(82\) −22.8047 −2.51836
\(83\) 6.65148 0.730095 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(84\) −8.80223 −0.960402
\(85\) −1.16680 −0.126558
\(86\) 19.6678 2.12083
\(87\) −4.95999 −0.531767
\(88\) −16.0230 −1.70806
\(89\) −8.54918 −0.906211 −0.453106 0.891457i \(-0.649684\pi\)
−0.453106 + 0.891457i \(0.649684\pi\)
\(90\) 1.13214 0.119338
\(91\) 4.60191 0.482412
\(92\) −15.5496 −1.62115
\(93\) −5.02181 −0.520737
\(94\) 22.6557 2.33676
\(95\) 1.42194 0.145888
\(96\) −13.6766 −1.39586
\(97\) −12.6530 −1.28472 −0.642360 0.766403i \(-0.722045\pi\)
−0.642360 + 0.766403i \(0.722045\pi\)
\(98\) 12.9086 1.30396
\(99\) −3.02541 −0.304065
\(100\) −23.8126 −2.38126
\(101\) −6.34079 −0.630933 −0.315466 0.948937i \(-0.602161\pi\)
−0.315466 + 0.948937i \(0.602161\pi\)
\(102\) 12.5619 1.24381
\(103\) 11.5248 1.13557 0.567787 0.823175i \(-0.307800\pi\)
0.567787 + 0.823175i \(0.307800\pi\)
\(104\) 23.9008 2.34366
\(105\) −0.555946 −0.0542547
\(106\) 2.96269 0.287762
\(107\) −11.1373 −1.07668 −0.538341 0.842727i \(-0.680949\pi\)
−0.538341 + 0.842727i \(0.680949\pi\)
\(108\) −26.9892 −2.59703
\(109\) 11.5157 1.10301 0.551503 0.834173i \(-0.314054\pi\)
0.551503 + 0.834173i \(0.314054\pi\)
\(110\) −1.72126 −0.164116
\(111\) 4.29895 0.408038
\(112\) −14.1710 −1.33903
\(113\) 2.90877 0.273634 0.136817 0.990596i \(-0.456313\pi\)
0.136817 + 0.990596i \(0.456313\pi\)
\(114\) −15.3088 −1.43380
\(115\) −0.982106 −0.0915818
\(116\) −19.0962 −1.77304
\(117\) 4.51285 0.417213
\(118\) −31.4271 −2.89310
\(119\) 5.47503 0.501895
\(120\) −2.88739 −0.263581
\(121\) −6.40028 −0.581844
\(122\) 4.12346 0.373321
\(123\) 10.9817 0.990191
\(124\) −19.3342 −1.73626
\(125\) −3.03680 −0.271619
\(126\) −5.31236 −0.473263
\(127\) 11.9053 1.05642 0.528212 0.849113i \(-0.322863\pi\)
0.528212 + 0.849113i \(0.322863\pi\)
\(128\) −1.07465 −0.0949866
\(129\) −9.47113 −0.833886
\(130\) 2.56752 0.225186
\(131\) 18.0008 1.57274 0.786369 0.617757i \(-0.211959\pi\)
0.786369 + 0.617757i \(0.211959\pi\)
\(132\) 13.1236 1.14226
\(133\) −6.67224 −0.578556
\(134\) −31.2943 −2.70342
\(135\) −1.70463 −0.146711
\(136\) 28.4354 2.43832
\(137\) 8.19044 0.699757 0.349878 0.936795i \(-0.386223\pi\)
0.349878 + 0.936795i \(0.386223\pi\)
\(138\) 10.5734 0.900070
\(139\) −0.764507 −0.0648446 −0.0324223 0.999474i \(-0.510322\pi\)
−0.0324223 + 0.999474i \(0.510322\pi\)
\(140\) −2.14042 −0.180898
\(141\) −10.9100 −0.918786
\(142\) −39.6858 −3.33035
\(143\) −6.86118 −0.573761
\(144\) −13.8967 −1.15806
\(145\) −1.20611 −0.100162
\(146\) −0.939853 −0.0777828
\(147\) −6.21619 −0.512703
\(148\) 16.5512 1.36050
\(149\) 13.4093 1.09853 0.549266 0.835647i \(-0.314907\pi\)
0.549266 + 0.835647i \(0.314907\pi\)
\(150\) 16.1921 1.32208
\(151\) 0.0304420 0.00247734 0.00123867 0.999999i \(-0.499606\pi\)
0.00123867 + 0.999999i \(0.499606\pi\)
\(152\) −34.6533 −2.81075
\(153\) 5.36907 0.434064
\(154\) 8.07672 0.650841
\(155\) −1.22114 −0.0980845
\(156\) −19.5758 −1.56732
\(157\) −4.61814 −0.368568 −0.184284 0.982873i \(-0.558997\pi\)
−0.184284 + 0.982873i \(0.558997\pi\)
\(158\) 1.69134 0.134556
\(159\) −1.42670 −0.113145
\(160\) −3.32570 −0.262920
\(161\) 4.60837 0.363190
\(162\) 7.27307 0.571427
\(163\) −13.6220 −1.06695 −0.533477 0.845814i \(-0.679115\pi\)
−0.533477 + 0.845814i \(0.679115\pi\)
\(164\) 42.2803 3.30154
\(165\) 0.828882 0.0645284
\(166\) −17.4134 −1.35154
\(167\) 13.6096 1.05314 0.526572 0.850130i \(-0.323477\pi\)
0.526572 + 0.850130i \(0.323477\pi\)
\(168\) 13.5486 1.04530
\(169\) −2.76552 −0.212732
\(170\) 3.05465 0.234281
\(171\) −6.54311 −0.500364
\(172\) −36.4643 −2.78038
\(173\) −17.8627 −1.35807 −0.679037 0.734104i \(-0.737602\pi\)
−0.679037 + 0.734104i \(0.737602\pi\)
\(174\) 12.9851 0.984396
\(175\) 7.05724 0.533477
\(176\) 21.1281 1.59259
\(177\) 15.1339 1.13753
\(178\) 22.3815 1.67756
\(179\) −1.22572 −0.0916148 −0.0458074 0.998950i \(-0.514586\pi\)
−0.0458074 + 0.998950i \(0.514586\pi\)
\(180\) −2.09899 −0.156450
\(181\) 17.3486 1.28951 0.644757 0.764388i \(-0.276959\pi\)
0.644757 + 0.764388i \(0.276959\pi\)
\(182\) −12.0477 −0.893031
\(183\) −1.98568 −0.146785
\(184\) 23.9343 1.76446
\(185\) 1.04537 0.0768569
\(186\) 13.1469 0.963979
\(187\) −8.16294 −0.596934
\(188\) −42.0040 −3.06345
\(189\) 7.99867 0.581818
\(190\) −3.72260 −0.270066
\(191\) 8.04609 0.582194 0.291097 0.956693i \(-0.405980\pi\)
0.291097 + 0.956693i \(0.405980\pi\)
\(192\) 10.9658 0.791385
\(193\) −1.91820 −0.138075 −0.0690377 0.997614i \(-0.521993\pi\)
−0.0690377 + 0.997614i \(0.521993\pi\)
\(194\) 33.1252 2.37825
\(195\) −1.23640 −0.0885406
\(196\) −23.9326 −1.70947
\(197\) 3.97652 0.283315 0.141658 0.989916i \(-0.454757\pi\)
0.141658 + 0.989916i \(0.454757\pi\)
\(198\) 7.92041 0.562879
\(199\) 3.41021 0.241744 0.120872 0.992668i \(-0.461431\pi\)
0.120872 + 0.992668i \(0.461431\pi\)
\(200\) 36.6529 2.59175
\(201\) 15.0700 1.06295
\(202\) 16.6000 1.16797
\(203\) 5.65947 0.397217
\(204\) −23.2899 −1.63062
\(205\) 2.67041 0.186509
\(206\) −30.1716 −2.10215
\(207\) 4.51918 0.314105
\(208\) −31.5158 −2.18522
\(209\) 9.94791 0.688111
\(210\) 1.45545 0.100435
\(211\) 11.1255 0.765911 0.382956 0.923767i \(-0.374906\pi\)
0.382956 + 0.923767i \(0.374906\pi\)
\(212\) −5.49286 −0.377251
\(213\) 19.1109 1.30946
\(214\) 29.1570 1.99313
\(215\) −2.30307 −0.157068
\(216\) 41.5424 2.82660
\(217\) 5.73001 0.388978
\(218\) −30.1478 −2.04186
\(219\) 0.452592 0.0305833
\(220\) 3.19124 0.215153
\(221\) 12.1763 0.819064
\(222\) −11.2545 −0.755353
\(223\) −1.44898 −0.0970311 −0.0485155 0.998822i \(-0.515449\pi\)
−0.0485155 + 0.998822i \(0.515449\pi\)
\(224\) 15.6053 1.04267
\(225\) 6.92066 0.461377
\(226\) −7.61506 −0.506546
\(227\) 16.3369 1.08432 0.542158 0.840277i \(-0.317607\pi\)
0.542158 + 0.840277i \(0.317607\pi\)
\(228\) 28.3827 1.87969
\(229\) 0.826735 0.0546322 0.0273161 0.999627i \(-0.491304\pi\)
0.0273161 + 0.999627i \(0.491304\pi\)
\(230\) 2.57112 0.169535
\(231\) −3.88939 −0.255903
\(232\) 29.3933 1.92977
\(233\) 0.970813 0.0636000 0.0318000 0.999494i \(-0.489876\pi\)
0.0318000 + 0.999494i \(0.489876\pi\)
\(234\) −11.8145 −0.772337
\(235\) −2.65296 −0.173060
\(236\) 58.2662 3.79281
\(237\) −0.814476 −0.0529059
\(238\) −14.3334 −0.929099
\(239\) −15.8436 −1.02484 −0.512418 0.858736i \(-0.671250\pi\)
−0.512418 + 0.858736i \(0.671250\pi\)
\(240\) 3.80734 0.245763
\(241\) −2.58060 −0.166231 −0.0831155 0.996540i \(-0.526487\pi\)
−0.0831155 + 0.996540i \(0.526487\pi\)
\(242\) 16.7557 1.07710
\(243\) 13.1791 0.845437
\(244\) −7.64495 −0.489418
\(245\) −1.51158 −0.0965711
\(246\) −28.7498 −1.83302
\(247\) −14.8388 −0.944171
\(248\) 29.7597 1.88974
\(249\) 8.38550 0.531409
\(250\) 7.95023 0.502817
\(251\) 16.7979 1.06028 0.530138 0.847911i \(-0.322140\pi\)
0.530138 + 0.847911i \(0.322140\pi\)
\(252\) 9.84918 0.620440
\(253\) −6.87080 −0.431964
\(254\) −31.1676 −1.95563
\(255\) −1.47098 −0.0921166
\(256\) −14.5830 −0.911435
\(257\) 16.7370 1.04402 0.522011 0.852939i \(-0.325182\pi\)
0.522011 + 0.852939i \(0.325182\pi\)
\(258\) 24.7951 1.54367
\(259\) −4.90521 −0.304795
\(260\) −4.76021 −0.295216
\(261\) 5.54994 0.343533
\(262\) −47.1255 −2.91142
\(263\) 20.7574 1.27996 0.639978 0.768394i \(-0.278944\pi\)
0.639978 + 0.768394i \(0.278944\pi\)
\(264\) −20.2002 −1.24323
\(265\) −0.346927 −0.0213116
\(266\) 17.4677 1.07101
\(267\) −10.7779 −0.659598
\(268\) 58.0201 3.54414
\(269\) 17.4002 1.06091 0.530455 0.847713i \(-0.322021\pi\)
0.530455 + 0.847713i \(0.322021\pi\)
\(270\) 4.46265 0.271588
\(271\) 7.29446 0.443107 0.221553 0.975148i \(-0.428887\pi\)
0.221553 + 0.975148i \(0.428887\pi\)
\(272\) −37.4952 −2.27348
\(273\) 5.80161 0.351130
\(274\) −21.4423 −1.29538
\(275\) −10.5219 −0.634496
\(276\) −19.6033 −1.17998
\(277\) 29.7651 1.78841 0.894206 0.447655i \(-0.147741\pi\)
0.894206 + 0.447655i \(0.147741\pi\)
\(278\) 2.00145 0.120039
\(279\) 5.61911 0.336407
\(280\) 3.29458 0.196889
\(281\) 8.47562 0.505613 0.252806 0.967517i \(-0.418646\pi\)
0.252806 + 0.967517i \(0.418646\pi\)
\(282\) 28.5620 1.70084
\(283\) −1.62463 −0.0965742 −0.0482871 0.998833i \(-0.515376\pi\)
−0.0482871 + 0.998833i \(0.515376\pi\)
\(284\) 73.5779 4.36605
\(285\) 1.79264 0.106187
\(286\) 17.9623 1.06213
\(287\) −12.5304 −0.739649
\(288\) 15.3033 0.901756
\(289\) −2.51355 −0.147856
\(290\) 3.15755 0.185418
\(291\) −15.9516 −0.935101
\(292\) 1.74250 0.101972
\(293\) −7.82481 −0.457130 −0.228565 0.973529i \(-0.573403\pi\)
−0.228565 + 0.973529i \(0.573403\pi\)
\(294\) 16.2738 0.949105
\(295\) 3.68007 0.214262
\(296\) −25.4760 −1.48076
\(297\) −11.9255 −0.691990
\(298\) −35.1051 −2.03358
\(299\) 10.2488 0.592706
\(300\) −30.0204 −1.73323
\(301\) 10.8068 0.622893
\(302\) −0.0796962 −0.00458600
\(303\) −7.99381 −0.459233
\(304\) 45.6942 2.62074
\(305\) −0.482853 −0.0276481
\(306\) −14.0560 −0.803530
\(307\) −8.32610 −0.475195 −0.237598 0.971364i \(-0.576360\pi\)
−0.237598 + 0.971364i \(0.576360\pi\)
\(308\) −14.9743 −0.853243
\(309\) 14.5293 0.826543
\(310\) 3.19691 0.181572
\(311\) −17.8404 −1.01164 −0.505819 0.862640i \(-0.668810\pi\)
−0.505819 + 0.862640i \(0.668810\pi\)
\(312\) 30.1316 1.70586
\(313\) −10.4731 −0.591973 −0.295986 0.955192i \(-0.595648\pi\)
−0.295986 + 0.955192i \(0.595648\pi\)
\(314\) 12.0901 0.682285
\(315\) 0.622071 0.0350497
\(316\) −3.13577 −0.176401
\(317\) 11.8069 0.663143 0.331572 0.943430i \(-0.392421\pi\)
0.331572 + 0.943430i \(0.392421\pi\)
\(318\) 3.73505 0.209451
\(319\) −8.43793 −0.472434
\(320\) 2.66652 0.149063
\(321\) −14.0407 −0.783677
\(322\) −12.0645 −0.672331
\(323\) −17.6542 −0.982304
\(324\) −13.4844 −0.749132
\(325\) 15.6950 0.870604
\(326\) 35.6618 1.97513
\(327\) 14.5178 0.802838
\(328\) −65.0788 −3.59338
\(329\) 12.4486 0.686312
\(330\) −2.16998 −0.119454
\(331\) −8.82622 −0.485133 −0.242566 0.970135i \(-0.577989\pi\)
−0.242566 + 0.970135i \(0.577989\pi\)
\(332\) 32.2846 1.77185
\(333\) −4.81028 −0.263602
\(334\) −35.6295 −1.94956
\(335\) 3.66453 0.200215
\(336\) −17.8653 −0.974633
\(337\) −18.2774 −0.995633 −0.497817 0.867282i \(-0.665865\pi\)
−0.497817 + 0.867282i \(0.665865\pi\)
\(338\) 7.24002 0.393805
\(339\) 3.66708 0.199168
\(340\) −5.66336 −0.307139
\(341\) −8.54310 −0.462635
\(342\) 17.1296 0.926264
\(343\) 17.1622 0.926673
\(344\) 56.1268 3.02615
\(345\) −1.23814 −0.0666590
\(346\) 46.7638 2.51404
\(347\) 12.1185 0.650555 0.325278 0.945619i \(-0.394542\pi\)
0.325278 + 0.945619i \(0.394542\pi\)
\(348\) −24.0745 −1.29053
\(349\) 31.0920 1.66432 0.832158 0.554539i \(-0.187105\pi\)
0.832158 + 0.554539i \(0.187105\pi\)
\(350\) −18.4756 −0.987563
\(351\) 17.7888 0.949493
\(352\) −23.2666 −1.24011
\(353\) 5.14565 0.273876 0.136938 0.990580i \(-0.456274\pi\)
0.136938 + 0.990580i \(0.456274\pi\)
\(354\) −39.6200 −2.10578
\(355\) 4.64716 0.246645
\(356\) −41.4955 −2.19926
\(357\) 6.90235 0.365311
\(358\) 3.20890 0.169596
\(359\) 13.6632 0.721116 0.360558 0.932737i \(-0.382586\pi\)
0.360558 + 0.932737i \(0.382586\pi\)
\(360\) 3.23082 0.170279
\(361\) 2.51455 0.132345
\(362\) −45.4181 −2.38712
\(363\) −8.06881 −0.423502
\(364\) 22.3365 1.17075
\(365\) 0.110056 0.00576058
\(366\) 5.19843 0.271726
\(367\) −24.2666 −1.26670 −0.633352 0.773864i \(-0.718322\pi\)
−0.633352 + 0.773864i \(0.718322\pi\)
\(368\) −31.5600 −1.64518
\(369\) −12.2879 −0.639685
\(370\) −2.73673 −0.142276
\(371\) 1.62790 0.0845163
\(372\) −24.3746 −1.26376
\(373\) −4.97493 −0.257592 −0.128796 0.991671i \(-0.541111\pi\)
−0.128796 + 0.991671i \(0.541111\pi\)
\(374\) 21.3703 1.10503
\(375\) −3.82848 −0.197702
\(376\) 64.6535 3.33425
\(377\) 12.5865 0.648235
\(378\) −20.9403 −1.07705
\(379\) −10.7244 −0.550876 −0.275438 0.961319i \(-0.588823\pi\)
−0.275438 + 0.961319i \(0.588823\pi\)
\(380\) 6.90175 0.354052
\(381\) 15.0090 0.768932
\(382\) −21.0644 −1.07775
\(383\) 0.642144 0.0328120 0.0164060 0.999865i \(-0.494778\pi\)
0.0164060 + 0.999865i \(0.494778\pi\)
\(384\) −1.35481 −0.0691373
\(385\) −0.945775 −0.0482011
\(386\) 5.02179 0.255602
\(387\) 10.5976 0.538709
\(388\) −61.4145 −3.11785
\(389\) −18.7104 −0.948654 −0.474327 0.880349i \(-0.657309\pi\)
−0.474327 + 0.880349i \(0.657309\pi\)
\(390\) 3.23686 0.163905
\(391\) 12.1933 0.616644
\(392\) 36.8377 1.86058
\(393\) 22.6935 1.14474
\(394\) −10.4104 −0.524468
\(395\) −0.198054 −0.00996520
\(396\) −14.6845 −0.737926
\(397\) −11.6015 −0.582261 −0.291130 0.956683i \(-0.594031\pi\)
−0.291130 + 0.956683i \(0.594031\pi\)
\(398\) −8.92782 −0.447511
\(399\) −8.41166 −0.421110
\(400\) −48.3308 −2.41654
\(401\) 17.3902 0.868427 0.434213 0.900810i \(-0.357026\pi\)
0.434213 + 0.900810i \(0.357026\pi\)
\(402\) −39.4526 −1.96772
\(403\) 12.7433 0.634790
\(404\) −30.7766 −1.53119
\(405\) −0.851669 −0.0423198
\(406\) −14.8163 −0.735320
\(407\) 7.31338 0.362511
\(408\) 35.8484 1.77476
\(409\) −2.54231 −0.125709 −0.0628545 0.998023i \(-0.520020\pi\)
−0.0628545 + 0.998023i \(0.520020\pi\)
\(410\) −6.99104 −0.345263
\(411\) 10.3257 0.509327
\(412\) 55.9385 2.75589
\(413\) −17.2681 −0.849710
\(414\) −11.8311 −0.581465
\(415\) 2.03908 0.100095
\(416\) 34.7056 1.70158
\(417\) −0.963810 −0.0471980
\(418\) −26.0433 −1.27382
\(419\) 11.2979 0.551938 0.275969 0.961166i \(-0.411001\pi\)
0.275969 + 0.961166i \(0.411001\pi\)
\(420\) −2.69842 −0.131669
\(421\) −19.4419 −0.947539 −0.473769 0.880649i \(-0.657107\pi\)
−0.473769 + 0.880649i \(0.657107\pi\)
\(422\) −29.1262 −1.41784
\(423\) 12.2076 0.593556
\(424\) 8.45474 0.410599
\(425\) 18.6728 0.905766
\(426\) −50.0317 −2.42404
\(427\) 2.26571 0.109645
\(428\) −54.0575 −2.61297
\(429\) −8.64986 −0.417619
\(430\) 6.02937 0.290762
\(431\) 30.5031 1.46928 0.734641 0.678456i \(-0.237350\pi\)
0.734641 + 0.678456i \(0.237350\pi\)
\(432\) −54.7781 −2.63551
\(433\) −33.2187 −1.59639 −0.798194 0.602400i \(-0.794211\pi\)
−0.798194 + 0.602400i \(0.794211\pi\)
\(434\) −15.0010 −0.720069
\(435\) −1.52054 −0.0729042
\(436\) 55.8944 2.67685
\(437\) −14.8596 −0.710832
\(438\) −1.18487 −0.0566152
\(439\) 11.2379 0.536357 0.268179 0.963369i \(-0.413578\pi\)
0.268179 + 0.963369i \(0.413578\pi\)
\(440\) −4.91203 −0.234172
\(441\) 6.95556 0.331217
\(442\) −31.8770 −1.51624
\(443\) 20.1855 0.959042 0.479521 0.877530i \(-0.340810\pi\)
0.479521 + 0.877530i \(0.340810\pi\)
\(444\) 20.8660 0.990257
\(445\) −2.62084 −0.124240
\(446\) 3.79339 0.179622
\(447\) 16.9051 0.799582
\(448\) −12.5122 −0.591146
\(449\) −16.3341 −0.770854 −0.385427 0.922738i \(-0.625946\pi\)
−0.385427 + 0.922738i \(0.625946\pi\)
\(450\) −18.1180 −0.854093
\(451\) 18.6822 0.879708
\(452\) 14.1184 0.664075
\(453\) 0.0383781 0.00180316
\(454\) −42.7693 −2.00726
\(455\) 1.41077 0.0661377
\(456\) −43.6873 −2.04584
\(457\) −12.7483 −0.596341 −0.298170 0.954513i \(-0.596376\pi\)
−0.298170 + 0.954513i \(0.596376\pi\)
\(458\) −2.16436 −0.101134
\(459\) 21.1638 0.987841
\(460\) −4.76689 −0.222257
\(461\) −17.1503 −0.798771 −0.399386 0.916783i \(-0.630777\pi\)
−0.399386 + 0.916783i \(0.630777\pi\)
\(462\) 10.1823 0.473723
\(463\) −14.9112 −0.692983 −0.346492 0.938053i \(-0.612627\pi\)
−0.346492 + 0.938053i \(0.612627\pi\)
\(464\) −38.7583 −1.79931
\(465\) −1.53949 −0.0713921
\(466\) −2.54155 −0.117735
\(467\) −26.0415 −1.20506 −0.602528 0.798098i \(-0.705840\pi\)
−0.602528 + 0.798098i \(0.705840\pi\)
\(468\) 21.9042 1.01252
\(469\) −17.1952 −0.794001
\(470\) 6.94535 0.320365
\(471\) −5.82207 −0.268267
\(472\) −89.6848 −4.12808
\(473\) −16.1123 −0.740844
\(474\) 2.13227 0.0979384
\(475\) −22.7560 −1.04412
\(476\) 26.5744 1.21803
\(477\) 1.59639 0.0730938
\(478\) 41.4779 1.89716
\(479\) 20.8625 0.953232 0.476616 0.879112i \(-0.341863\pi\)
0.476616 + 0.879112i \(0.341863\pi\)
\(480\) −4.19270 −0.191370
\(481\) −10.9090 −0.497408
\(482\) 6.75591 0.307723
\(483\) 5.80975 0.264353
\(484\) −31.0653 −1.41206
\(485\) −3.87892 −0.176133
\(486\) −34.5023 −1.56506
\(487\) 28.6657 1.29897 0.649483 0.760376i \(-0.274985\pi\)
0.649483 + 0.760376i \(0.274985\pi\)
\(488\) 11.7673 0.532680
\(489\) −17.1732 −0.776597
\(490\) 3.95726 0.178771
\(491\) −29.8768 −1.34832 −0.674161 0.738585i \(-0.735494\pi\)
−0.674161 + 0.738585i \(0.735494\pi\)
\(492\) 53.3026 2.40307
\(493\) 14.9745 0.674416
\(494\) 38.8475 1.74783
\(495\) −0.927471 −0.0416867
\(496\) −39.2414 −1.76199
\(497\) −21.8060 −0.978133
\(498\) −21.9529 −0.983735
\(499\) 15.9901 0.715814 0.357907 0.933757i \(-0.383491\pi\)
0.357907 + 0.933757i \(0.383491\pi\)
\(500\) −14.7398 −0.659185
\(501\) 17.1576 0.766545
\(502\) −43.9764 −1.96276
\(503\) −9.27556 −0.413577 −0.206788 0.978386i \(-0.566301\pi\)
−0.206788 + 0.978386i \(0.566301\pi\)
\(504\) −15.1601 −0.675285
\(505\) −1.94384 −0.0864997
\(506\) 17.9875 0.799643
\(507\) −3.48647 −0.154840
\(508\) 57.7852 2.56380
\(509\) −18.3968 −0.815425 −0.407713 0.913110i \(-0.633673\pi\)
−0.407713 + 0.913110i \(0.633673\pi\)
\(510\) 3.85098 0.170524
\(511\) −0.516418 −0.0228450
\(512\) 40.3270 1.78222
\(513\) −25.7916 −1.13873
\(514\) −43.8168 −1.93267
\(515\) 3.53306 0.155685
\(516\) −45.9704 −2.02373
\(517\) −18.5601 −0.816271
\(518\) 12.8417 0.564231
\(519\) −22.5194 −0.988492
\(520\) 7.32703 0.321312
\(521\) −3.85217 −0.168766 −0.0843832 0.996433i \(-0.526892\pi\)
−0.0843832 + 0.996433i \(0.526892\pi\)
\(522\) −14.5296 −0.635941
\(523\) 2.26358 0.0989795 0.0494898 0.998775i \(-0.484240\pi\)
0.0494898 + 0.998775i \(0.484240\pi\)
\(524\) 87.3713 3.81683
\(525\) 8.89703 0.388298
\(526\) −54.3421 −2.36943
\(527\) 15.1611 0.660428
\(528\) 26.6361 1.15919
\(529\) −12.7368 −0.553773
\(530\) 0.908243 0.0394516
\(531\) −16.9339 −0.734871
\(532\) −32.3853 −1.40408
\(533\) −27.8673 −1.20706
\(534\) 28.2162 1.22103
\(535\) −3.41425 −0.147611
\(536\) −89.3059 −3.85743
\(537\) −1.54526 −0.0666830
\(538\) −45.5532 −1.96394
\(539\) −10.5750 −0.455497
\(540\) −8.27381 −0.356048
\(541\) −5.51425 −0.237076 −0.118538 0.992949i \(-0.537821\pi\)
−0.118538 + 0.992949i \(0.537821\pi\)
\(542\) −19.0966 −0.820271
\(543\) 21.8713 0.938589
\(544\) 41.2903 1.77031
\(545\) 3.53027 0.151220
\(546\) −15.1884 −0.650005
\(547\) 22.7586 0.973085 0.486543 0.873657i \(-0.338258\pi\)
0.486543 + 0.873657i \(0.338258\pi\)
\(548\) 39.7543 1.69822
\(549\) 2.22186 0.0948265
\(550\) 27.5460 1.17457
\(551\) −18.2489 −0.777429
\(552\) 30.1738 1.28428
\(553\) 0.929337 0.0395194
\(554\) −77.9240 −3.31068
\(555\) 1.31789 0.0559413
\(556\) −3.71072 −0.157370
\(557\) 39.7440 1.68401 0.842003 0.539472i \(-0.181376\pi\)
0.842003 + 0.539472i \(0.181376\pi\)
\(558\) −14.7106 −0.622751
\(559\) 24.0339 1.01653
\(560\) −4.34427 −0.183579
\(561\) −10.2910 −0.434486
\(562\) −22.1889 −0.935981
\(563\) 1.77435 0.0747800 0.0373900 0.999301i \(-0.488096\pi\)
0.0373900 + 0.999301i \(0.488096\pi\)
\(564\) −52.9542 −2.22978
\(565\) 0.891715 0.0375147
\(566\) 4.25323 0.178776
\(567\) 3.99631 0.167829
\(568\) −113.253 −4.75199
\(569\) 28.0634 1.17648 0.588240 0.808687i \(-0.299821\pi\)
0.588240 + 0.808687i \(0.299821\pi\)
\(570\) −4.69307 −0.196571
\(571\) −9.34358 −0.391017 −0.195508 0.980702i \(-0.562636\pi\)
−0.195508 + 0.980702i \(0.562636\pi\)
\(572\) −33.3024 −1.39244
\(573\) 10.1437 0.423758
\(574\) 32.8043 1.36922
\(575\) 15.7171 0.655446
\(576\) −12.2700 −0.511252
\(577\) −2.10749 −0.0877361 −0.0438681 0.999037i \(-0.513968\pi\)
−0.0438681 + 0.999037i \(0.513968\pi\)
\(578\) 6.58038 0.273708
\(579\) −2.41827 −0.100500
\(580\) −5.85414 −0.243080
\(581\) −9.56806 −0.396950
\(582\) 41.7608 1.73104
\(583\) −2.42710 −0.100520
\(584\) −2.68210 −0.110986
\(585\) 1.38346 0.0571991
\(586\) 20.4851 0.846231
\(587\) −32.0162 −1.32145 −0.660726 0.750628i \(-0.729751\pi\)
−0.660726 + 0.750628i \(0.729751\pi\)
\(588\) −30.1718 −1.24426
\(589\) −18.4763 −0.761304
\(590\) −9.63431 −0.396638
\(591\) 5.01318 0.206215
\(592\) 33.5929 1.38066
\(593\) 21.4455 0.880663 0.440331 0.897835i \(-0.354861\pi\)
0.440331 + 0.897835i \(0.354861\pi\)
\(594\) 31.2207 1.28100
\(595\) 1.67843 0.0688089
\(596\) 65.0853 2.66600
\(597\) 4.29924 0.175956
\(598\) −26.8311 −1.09721
\(599\) −12.0350 −0.491737 −0.245869 0.969303i \(-0.579073\pi\)
−0.245869 + 0.969303i \(0.579073\pi\)
\(600\) 46.2081 1.88644
\(601\) −43.5498 −1.77643 −0.888216 0.459426i \(-0.848055\pi\)
−0.888216 + 0.459426i \(0.848055\pi\)
\(602\) −28.2918 −1.15309
\(603\) −16.8624 −0.686691
\(604\) 0.147758 0.00601218
\(605\) −1.96207 −0.0797697
\(606\) 20.9275 0.850123
\(607\) 45.0782 1.82967 0.914833 0.403831i \(-0.132322\pi\)
0.914833 + 0.403831i \(0.132322\pi\)
\(608\) −50.3191 −2.04071
\(609\) 7.13487 0.289120
\(610\) 1.26409 0.0511816
\(611\) 27.6851 1.12002
\(612\) 26.0601 1.05342
\(613\) 0.144746 0.00584622 0.00292311 0.999996i \(-0.499070\pi\)
0.00292311 + 0.999996i \(0.499070\pi\)
\(614\) 21.7974 0.879673
\(615\) 3.36657 0.135753
\(616\) 23.0489 0.928666
\(617\) 30.2069 1.21608 0.608041 0.793905i \(-0.291955\pi\)
0.608041 + 0.793905i \(0.291955\pi\)
\(618\) −38.0372 −1.53008
\(619\) −46.1879 −1.85645 −0.928224 0.372021i \(-0.878665\pi\)
−0.928224 + 0.372021i \(0.878665\pi\)
\(620\) −5.92711 −0.238038
\(621\) 17.8137 0.714839
\(622\) 46.7056 1.87273
\(623\) 12.2979 0.492704
\(624\) −39.7318 −1.59054
\(625\) 23.5991 0.943966
\(626\) 27.4181 1.09585
\(627\) 12.5413 0.500851
\(628\) −22.4153 −0.894466
\(629\) −12.9788 −0.517497
\(630\) −1.62856 −0.0648834
\(631\) −7.18123 −0.285880 −0.142940 0.989731i \(-0.545656\pi\)
−0.142940 + 0.989731i \(0.545656\pi\)
\(632\) 4.82666 0.191994
\(633\) 14.0259 0.557478
\(634\) −30.9101 −1.22760
\(635\) 3.64970 0.144834
\(636\) −6.92483 −0.274587
\(637\) 15.7742 0.624996
\(638\) 22.0902 0.874560
\(639\) −21.3840 −0.845938
\(640\) −0.329446 −0.0130225
\(641\) −9.07665 −0.358506 −0.179253 0.983803i \(-0.557368\pi\)
−0.179253 + 0.983803i \(0.557368\pi\)
\(642\) 36.7581 1.45073
\(643\) 27.2560 1.07487 0.537435 0.843305i \(-0.319393\pi\)
0.537435 + 0.843305i \(0.319393\pi\)
\(644\) 22.3678 0.881416
\(645\) −2.90348 −0.114324
\(646\) 46.2180 1.81842
\(647\) 2.28574 0.0898618 0.0449309 0.998990i \(-0.485693\pi\)
0.0449309 + 0.998990i \(0.485693\pi\)
\(648\) 20.7555 0.815352
\(649\) 25.7458 1.01061
\(650\) −41.0891 −1.61165
\(651\) 7.22380 0.283123
\(652\) −66.1175 −2.58936
\(653\) 18.7175 0.732474 0.366237 0.930522i \(-0.380646\pi\)
0.366237 + 0.930522i \(0.380646\pi\)
\(654\) −38.0072 −1.48620
\(655\) 5.51834 0.215619
\(656\) 85.8136 3.35046
\(657\) −0.506424 −0.0197575
\(658\) −32.5899 −1.27049
\(659\) 32.8968 1.28148 0.640740 0.767758i \(-0.278628\pi\)
0.640740 + 0.767758i \(0.278628\pi\)
\(660\) 4.02318 0.156602
\(661\) 14.8430 0.577327 0.288663 0.957431i \(-0.406789\pi\)
0.288663 + 0.957431i \(0.406789\pi\)
\(662\) 23.1067 0.898069
\(663\) 15.3506 0.596167
\(664\) −49.6932 −1.92847
\(665\) −2.04545 −0.0793190
\(666\) 12.5931 0.487974
\(667\) 12.6041 0.488033
\(668\) 66.0576 2.55585
\(669\) −1.82673 −0.0706253
\(670\) −9.59361 −0.370634
\(671\) −3.37803 −0.130407
\(672\) 19.6736 0.758924
\(673\) −40.3923 −1.55701 −0.778505 0.627639i \(-0.784021\pi\)
−0.778505 + 0.627639i \(0.784021\pi\)
\(674\) 47.8496 1.84310
\(675\) 27.2798 1.05000
\(676\) −13.4231 −0.516273
\(677\) −41.2475 −1.58527 −0.792635 0.609697i \(-0.791291\pi\)
−0.792635 + 0.609697i \(0.791291\pi\)
\(678\) −9.60028 −0.368696
\(679\) 18.2012 0.698498
\(680\) 8.71718 0.334289
\(681\) 20.5958 0.789233
\(682\) 22.3655 0.856421
\(683\) 12.1394 0.464499 0.232250 0.972656i \(-0.425391\pi\)
0.232250 + 0.972656i \(0.425391\pi\)
\(684\) −31.7586 −1.21432
\(685\) 2.51087 0.0959353
\(686\) −44.9301 −1.71544
\(687\) 1.04226 0.0397647
\(688\) −74.0093 −2.82158
\(689\) 3.62039 0.137926
\(690\) 3.24140 0.123398
\(691\) 1.24102 0.0472105 0.0236052 0.999721i \(-0.492486\pi\)
0.0236052 + 0.999721i \(0.492486\pi\)
\(692\) −86.7008 −3.29587
\(693\) 4.35200 0.165319
\(694\) −31.7258 −1.20430
\(695\) −0.234368 −0.00889007
\(696\) 37.0561 1.40461
\(697\) −33.1545 −1.25582
\(698\) −81.3977 −3.08095
\(699\) 1.22390 0.0462921
\(700\) 34.2540 1.29468
\(701\) −25.3081 −0.955874 −0.477937 0.878394i \(-0.658615\pi\)
−0.477937 + 0.878394i \(0.658615\pi\)
\(702\) −46.5703 −1.75768
\(703\) 15.8168 0.596541
\(704\) 18.6549 0.703085
\(705\) −3.34457 −0.125964
\(706\) −13.4711 −0.506993
\(707\) 9.12114 0.343036
\(708\) 73.4560 2.76064
\(709\) 8.94358 0.335883 0.167942 0.985797i \(-0.446288\pi\)
0.167942 + 0.985797i \(0.446288\pi\)
\(710\) −12.1661 −0.456585
\(711\) 0.911352 0.0341784
\(712\) 63.8709 2.39366
\(713\) 12.7612 0.477910
\(714\) −18.0701 −0.676257
\(715\) −2.10337 −0.0786615
\(716\) −5.94934 −0.222337
\(717\) −19.9739 −0.745940
\(718\) −35.7698 −1.33492
\(719\) 26.5539 0.990292 0.495146 0.868810i \(-0.335115\pi\)
0.495146 + 0.868810i \(0.335115\pi\)
\(720\) −4.26019 −0.158768
\(721\) −16.5783 −0.617408
\(722\) −6.58299 −0.244994
\(723\) −3.25335 −0.120993
\(724\) 84.2058 3.12948
\(725\) 19.3019 0.716854
\(726\) 21.1239 0.783980
\(727\) −10.9201 −0.405005 −0.202503 0.979282i \(-0.564907\pi\)
−0.202503 + 0.979282i \(0.564907\pi\)
\(728\) −34.3809 −1.27424
\(729\) 24.9492 0.924045
\(730\) −0.288122 −0.0106639
\(731\) 28.5938 1.05758
\(732\) −9.63796 −0.356229
\(733\) −10.7268 −0.396204 −0.198102 0.980181i \(-0.563478\pi\)
−0.198102 + 0.980181i \(0.563478\pi\)
\(734\) 63.5290 2.34490
\(735\) −1.90564 −0.0702906
\(736\) 34.7543 1.28106
\(737\) 25.6370 0.944352
\(738\) 32.1694 1.18417
\(739\) −12.2472 −0.450520 −0.225260 0.974299i \(-0.572323\pi\)
−0.225260 + 0.974299i \(0.572323\pi\)
\(740\) 5.07394 0.186522
\(741\) −18.7072 −0.687227
\(742\) −4.26178 −0.156455
\(743\) 17.5079 0.642303 0.321151 0.947028i \(-0.395930\pi\)
0.321151 + 0.947028i \(0.395930\pi\)
\(744\) 37.5179 1.37547
\(745\) 4.11077 0.150607
\(746\) 13.0242 0.476850
\(747\) −9.38289 −0.343302
\(748\) −39.6208 −1.44868
\(749\) 16.0208 0.585388
\(750\) 10.0228 0.365982
\(751\) 51.1566 1.86673 0.933366 0.358927i \(-0.116857\pi\)
0.933366 + 0.358927i \(0.116857\pi\)
\(752\) −85.2528 −3.10885
\(753\) 21.1771 0.771736
\(754\) −32.9509 −1.20000
\(755\) 0.00933233 0.000339638 0
\(756\) 38.8235 1.41200
\(757\) 1.70821 0.0620860 0.0310430 0.999518i \(-0.490117\pi\)
0.0310430 + 0.999518i \(0.490117\pi\)
\(758\) 28.0761 1.01977
\(759\) −8.66199 −0.314410
\(760\) −10.6233 −0.385349
\(761\) −30.4614 −1.10422 −0.552112 0.833770i \(-0.686178\pi\)
−0.552112 + 0.833770i \(0.686178\pi\)
\(762\) −39.2929 −1.42343
\(763\) −16.5652 −0.599701
\(764\) 39.0536 1.41291
\(765\) 1.64595 0.0595093
\(766\) −1.68111 −0.0607410
\(767\) −38.4037 −1.38668
\(768\) −18.3847 −0.663400
\(769\) 21.1952 0.764318 0.382159 0.924097i \(-0.375181\pi\)
0.382159 + 0.924097i \(0.375181\pi\)
\(770\) 2.47601 0.0892290
\(771\) 21.1002 0.759905
\(772\) −9.31047 −0.335091
\(773\) 1.45276 0.0522520 0.0261260 0.999659i \(-0.491683\pi\)
0.0261260 + 0.999659i \(0.491683\pi\)
\(774\) −27.7443 −0.997247
\(775\) 19.5424 0.701986
\(776\) 94.5308 3.39346
\(777\) −6.18398 −0.221849
\(778\) 48.9831 1.75613
\(779\) 40.4043 1.44763
\(780\) −6.00118 −0.214877
\(781\) 32.5115 1.16335
\(782\) −31.9217 −1.14152
\(783\) 21.8768 0.781811
\(784\) −48.5745 −1.73480
\(785\) −1.41574 −0.0505299
\(786\) −59.4109 −2.11912
\(787\) 37.5672 1.33913 0.669563 0.742755i \(-0.266481\pi\)
0.669563 + 0.742755i \(0.266481\pi\)
\(788\) 19.3010 0.687569
\(789\) 26.1687 0.931632
\(790\) 0.518499 0.0184474
\(791\) −4.18423 −0.148774
\(792\) 22.6028 0.803156
\(793\) 5.03885 0.178935
\(794\) 30.3722 1.07787
\(795\) −0.437370 −0.0155119
\(796\) 16.5523 0.586680
\(797\) 32.1631 1.13927 0.569637 0.821896i \(-0.307084\pi\)
0.569637 + 0.821896i \(0.307084\pi\)
\(798\) 22.0214 0.779551
\(799\) 32.9378 1.16526
\(800\) 53.2227 1.88171
\(801\) 12.0599 0.426114
\(802\) −45.5270 −1.60761
\(803\) 0.769949 0.0271709
\(804\) 73.1457 2.57965
\(805\) 1.41274 0.0497927
\(806\) −33.3616 −1.17511
\(807\) 21.9364 0.772198
\(808\) 47.3721 1.66654
\(809\) −29.5131 −1.03762 −0.518812 0.854888i \(-0.673625\pi\)
−0.518812 + 0.854888i \(0.673625\pi\)
\(810\) 2.22964 0.0783415
\(811\) 51.2879 1.80096 0.900481 0.434896i \(-0.143215\pi\)
0.900481 + 0.434896i \(0.143215\pi\)
\(812\) 27.4696 0.963994
\(813\) 9.19610 0.322521
\(814\) −19.1462 −0.671073
\(815\) −4.17596 −0.146277
\(816\) −47.2701 −1.65478
\(817\) −34.8464 −1.21912
\(818\) 6.65567 0.232710
\(819\) −6.49167 −0.226837
\(820\) 12.9615 0.452634
\(821\) −34.2790 −1.19634 −0.598172 0.801367i \(-0.704106\pi\)
−0.598172 + 0.801367i \(0.704106\pi\)
\(822\) −27.0322 −0.942857
\(823\) −4.33258 −0.151024 −0.0755122 0.997145i \(-0.524059\pi\)
−0.0755122 + 0.997145i \(0.524059\pi\)
\(824\) −86.1019 −2.99950
\(825\) −13.2649 −0.461826
\(826\) 45.2074 1.57297
\(827\) 27.7728 0.965755 0.482877 0.875688i \(-0.339592\pi\)
0.482877 + 0.875688i \(0.339592\pi\)
\(828\) 21.9349 0.762292
\(829\) 15.3857 0.534368 0.267184 0.963646i \(-0.413907\pi\)
0.267184 + 0.963646i \(0.413907\pi\)
\(830\) −5.33825 −0.185293
\(831\) 37.5248 1.30172
\(832\) −27.8267 −0.964716
\(833\) 18.7670 0.650238
\(834\) 2.52322 0.0873720
\(835\) 4.17218 0.144384
\(836\) 48.2846 1.66996
\(837\) 22.1494 0.765596
\(838\) −29.5775 −1.02174
\(839\) 12.0889 0.417357 0.208678 0.977984i \(-0.433084\pi\)
0.208678 + 0.977984i \(0.433084\pi\)
\(840\) 4.15347 0.143308
\(841\) −13.5211 −0.466244
\(842\) 50.8981 1.75407
\(843\) 10.6852 0.368017
\(844\) 54.0003 1.85877
\(845\) −0.847798 −0.0291651
\(846\) −31.9592 −1.09878
\(847\) 9.20671 0.316346
\(848\) −11.1485 −0.382841
\(849\) −2.04816 −0.0702928
\(850\) −48.8849 −1.67674
\(851\) −10.9243 −0.374480
\(852\) 92.7594 3.17788
\(853\) −11.8908 −0.407132 −0.203566 0.979061i \(-0.565253\pi\)
−0.203566 + 0.979061i \(0.565253\pi\)
\(854\) −5.93154 −0.202973
\(855\) −2.00586 −0.0685990
\(856\) 83.2066 2.84394
\(857\) 24.0313 0.820894 0.410447 0.911884i \(-0.365373\pi\)
0.410447 + 0.911884i \(0.365373\pi\)
\(858\) 22.6450 0.773089
\(859\) −44.1456 −1.50623 −0.753114 0.657890i \(-0.771449\pi\)
−0.753114 + 0.657890i \(0.771449\pi\)
\(860\) −11.1785 −0.381185
\(861\) −15.7971 −0.538363
\(862\) −79.8561 −2.71991
\(863\) 8.85583 0.301456 0.150728 0.988575i \(-0.451838\pi\)
0.150728 + 0.988575i \(0.451838\pi\)
\(864\) 60.3226 2.05221
\(865\) −5.47599 −0.186189
\(866\) 86.9654 2.95520
\(867\) −3.16882 −0.107619
\(868\) 27.8120 0.944000
\(869\) −1.38559 −0.0470028
\(870\) 3.98071 0.134959
\(871\) −38.2415 −1.29576
\(872\) −86.0339 −2.91348
\(873\) 17.8489 0.604095
\(874\) 38.9020 1.31588
\(875\) 4.36839 0.147678
\(876\) 2.19676 0.0742218
\(877\) 30.1102 1.01675 0.508374 0.861137i \(-0.330247\pi\)
0.508374 + 0.861137i \(0.330247\pi\)
\(878\) −29.4205 −0.992894
\(879\) −9.86471 −0.332728
\(880\) 6.47705 0.218341
\(881\) −41.8158 −1.40881 −0.704405 0.709798i \(-0.748786\pi\)
−0.704405 + 0.709798i \(0.748786\pi\)
\(882\) −18.2094 −0.613142
\(883\) −47.6824 −1.60464 −0.802321 0.596893i \(-0.796402\pi\)
−0.802321 + 0.596893i \(0.796402\pi\)
\(884\) 59.1004 1.98776
\(885\) 4.63946 0.155954
\(886\) −52.8450 −1.77536
\(887\) 44.2469 1.48566 0.742832 0.669477i \(-0.233482\pi\)
0.742832 + 0.669477i \(0.233482\pi\)
\(888\) −32.1175 −1.07779
\(889\) −17.1256 −0.574374
\(890\) 6.86128 0.229990
\(891\) −5.95827 −0.199609
\(892\) −7.03299 −0.235482
\(893\) −40.1402 −1.34324
\(894\) −44.2568 −1.48017
\(895\) −0.375758 −0.0125602
\(896\) 1.54587 0.0516439
\(897\) 12.9207 0.431409
\(898\) 42.7621 1.42699
\(899\) 15.6718 0.522685
\(900\) 33.5911 1.11970
\(901\) 4.30728 0.143496
\(902\) −48.9092 −1.62850
\(903\) 13.6241 0.453381
\(904\) −21.7314 −0.722776
\(905\) 5.31841 0.176790
\(906\) −0.100473 −0.00333798
\(907\) −6.89056 −0.228797 −0.114399 0.993435i \(-0.536494\pi\)
−0.114399 + 0.993435i \(0.536494\pi\)
\(908\) 79.2949 2.63149
\(909\) 8.94462 0.296674
\(910\) −3.69334 −0.122433
\(911\) 38.0127 1.25942 0.629708 0.776832i \(-0.283175\pi\)
0.629708 + 0.776832i \(0.283175\pi\)
\(912\) 57.6065 1.90754
\(913\) 14.2654 0.472116
\(914\) 33.3746 1.10393
\(915\) −0.608730 −0.0201240
\(916\) 4.01276 0.132585
\(917\) −25.8939 −0.855092
\(918\) −55.4061 −1.82867
\(919\) 55.0205 1.81496 0.907480 0.420095i \(-0.138003\pi\)
0.907480 + 0.420095i \(0.138003\pi\)
\(920\) 7.33731 0.241904
\(921\) −10.4967 −0.345877
\(922\) 44.8990 1.47867
\(923\) −48.4958 −1.59626
\(924\) −18.8781 −0.621044
\(925\) −16.7294 −0.550061
\(926\) 39.0371 1.28284
\(927\) −16.2574 −0.533965
\(928\) 42.6813 1.40108
\(929\) 37.1759 1.21970 0.609852 0.792516i \(-0.291229\pi\)
0.609852 + 0.792516i \(0.291229\pi\)
\(930\) 4.03033 0.132160
\(931\) −22.8707 −0.749558
\(932\) 4.71207 0.154349
\(933\) −22.4914 −0.736334
\(934\) 68.1757 2.23078
\(935\) −2.50244 −0.0818385
\(936\) −33.7155 −1.10203
\(937\) −7.38376 −0.241217 −0.120608 0.992700i \(-0.538485\pi\)
−0.120608 + 0.992700i \(0.538485\pi\)
\(938\) 45.0164 1.46984
\(939\) −13.2034 −0.430875
\(940\) −12.8768 −0.419994
\(941\) −24.9506 −0.813365 −0.406683 0.913570i \(-0.633314\pi\)
−0.406683 + 0.913570i \(0.633314\pi\)
\(942\) 15.2420 0.496610
\(943\) −27.9063 −0.908755
\(944\) 118.259 3.84901
\(945\) 2.45208 0.0797661
\(946\) 42.1814 1.37144
\(947\) 31.9341 1.03772 0.518859 0.854860i \(-0.326357\pi\)
0.518859 + 0.854860i \(0.326357\pi\)
\(948\) −3.95326 −0.128396
\(949\) −1.14850 −0.0372817
\(950\) 59.5744 1.93285
\(951\) 14.8850 0.482678
\(952\) −40.9039 −1.32570
\(953\) −39.8078 −1.28950 −0.644750 0.764394i \(-0.723039\pi\)
−0.644750 + 0.764394i \(0.723039\pi\)
\(954\) −4.17930 −0.135310
\(955\) 2.46661 0.0798177
\(956\) −76.9006 −2.48714
\(957\) −10.6377 −0.343867
\(958\) −54.6173 −1.76460
\(959\) −11.7818 −0.380455
\(960\) 3.36167 0.108497
\(961\) −15.1328 −0.488156
\(962\) 28.5594 0.920792
\(963\) 15.7108 0.506272
\(964\) −12.5256 −0.403421
\(965\) −0.588046 −0.0189299
\(966\) −15.2097 −0.489365
\(967\) −26.9510 −0.866686 −0.433343 0.901229i \(-0.642666\pi\)
−0.433343 + 0.901229i \(0.642666\pi\)
\(968\) 47.8165 1.53688
\(969\) −22.2565 −0.714983
\(970\) 10.1549 0.326054
\(971\) −22.4582 −0.720719 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(972\) 63.9678 2.05177
\(973\) 1.09973 0.0352558
\(974\) −75.0457 −2.40462
\(975\) 19.7867 0.633681
\(976\) −15.5165 −0.496670
\(977\) 19.9005 0.636674 0.318337 0.947978i \(-0.396876\pi\)
0.318337 + 0.947978i \(0.396876\pi\)
\(978\) 44.9587 1.43762
\(979\) −18.3354 −0.586002
\(980\) −7.33680 −0.234366
\(981\) −16.2446 −0.518650
\(982\) 78.2164 2.49599
\(983\) 12.7730 0.407397 0.203698 0.979034i \(-0.434704\pi\)
0.203698 + 0.979034i \(0.434704\pi\)
\(984\) −82.0446 −2.61549
\(985\) 1.21904 0.0388420
\(986\) −39.2026 −1.24847
\(987\) 15.6939 0.499541
\(988\) −72.0238 −2.29138
\(989\) 24.0676 0.765306
\(990\) 2.42809 0.0771696
\(991\) 57.5291 1.82747 0.913736 0.406307i \(-0.133184\pi\)
0.913736 + 0.406307i \(0.133184\pi\)
\(992\) 43.2132 1.37202
\(993\) −11.1272 −0.353110
\(994\) 57.0874 1.81070
\(995\) 1.04544 0.0331426
\(996\) 40.7010 1.28966
\(997\) 19.0551 0.603481 0.301741 0.953390i \(-0.402432\pi\)
0.301741 + 0.953390i \(0.402432\pi\)
\(998\) −41.8614 −1.32510
\(999\) −18.9612 −0.599904
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 \(a_p\))