Properties

Label 8011.2.a.b.1.18
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 1.18
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56990 q^{2}\) \(+3.01881 q^{3}\) \(+4.60437 q^{4}\) \(+3.51758 q^{5}\) \(-7.75803 q^{6}\) \(-1.89430 q^{7}\) \(-6.69296 q^{8}\) \(+6.11321 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56990 q^{2}\) \(+3.01881 q^{3}\) \(+4.60437 q^{4}\) \(+3.51758 q^{5}\) \(-7.75803 q^{6}\) \(-1.89430 q^{7}\) \(-6.69296 q^{8}\) \(+6.11321 q^{9}\) \(-9.03981 q^{10}\) \(-2.04327 q^{11}\) \(+13.8997 q^{12}\) \(+5.52430 q^{13}\) \(+4.86814 q^{14}\) \(+10.6189 q^{15}\) \(+7.99147 q^{16}\) \(+5.58761 q^{17}\) \(-15.7103 q^{18}\) \(-2.18252 q^{19}\) \(+16.1962 q^{20}\) \(-5.71852 q^{21}\) \(+5.25099 q^{22}\) \(-0.824846 q^{23}\) \(-20.2048 q^{24}\) \(+7.37336 q^{25}\) \(-14.1969 q^{26}\) \(+9.39820 q^{27}\) \(-8.72204 q^{28}\) \(+0.760452 q^{29}\) \(-27.2895 q^{30}\) \(-6.60621 q^{31}\) \(-7.15133 q^{32}\) \(-6.16824 q^{33}\) \(-14.3596 q^{34}\) \(-6.66334 q^{35}\) \(+28.1475 q^{36}\) \(-0.863836 q^{37}\) \(+5.60884 q^{38}\) \(+16.6768 q^{39}\) \(-23.5430 q^{40}\) \(+1.16868 q^{41}\) \(+14.6960 q^{42}\) \(+3.90466 q^{43}\) \(-9.40796 q^{44}\) \(+21.5037 q^{45}\) \(+2.11977 q^{46}\) \(-6.31336 q^{47}\) \(+24.1247 q^{48}\) \(-3.41164 q^{49}\) \(-18.9488 q^{50}\) \(+16.8679 q^{51}\) \(+25.4359 q^{52}\) \(+2.65911 q^{53}\) \(-24.1524 q^{54}\) \(-7.18736 q^{55}\) \(+12.6784 q^{56}\) \(-6.58861 q^{57}\) \(-1.95428 q^{58}\) \(-7.22794 q^{59}\) \(+48.8933 q^{60}\) \(+14.0967 q^{61}\) \(+16.9773 q^{62}\) \(-11.5802 q^{63}\) \(+2.39525 q^{64}\) \(+19.4322 q^{65}\) \(+15.8517 q^{66}\) \(-2.05388 q^{67}\) \(+25.7274 q^{68}\) \(-2.49005 q^{69}\) \(+17.1241 q^{70}\) \(+2.82818 q^{71}\) \(-40.9155 q^{72}\) \(+14.4041 q^{73}\) \(+2.21997 q^{74}\) \(+22.2588 q^{75}\) \(-10.0491 q^{76}\) \(+3.87056 q^{77}\) \(-42.8577 q^{78}\) \(+11.7023 q^{79}\) \(+28.1106 q^{80}\) \(+10.0317 q^{81}\) \(-3.00340 q^{82}\) \(+14.0093 q^{83}\) \(-26.3302 q^{84}\) \(+19.6549 q^{85}\) \(-10.0346 q^{86}\) \(+2.29566 q^{87}\) \(+13.6755 q^{88}\) \(-0.766249 q^{89}\) \(-55.2623 q^{90}\) \(-10.4647 q^{91}\) \(-3.79790 q^{92}\) \(-19.9429 q^{93}\) \(+16.2247 q^{94}\) \(-7.67718 q^{95}\) \(-21.5885 q^{96}\) \(-13.1703 q^{97}\) \(+8.76757 q^{98}\) \(-12.4909 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56990 −1.81719 −0.908596 0.417677i \(-0.862844\pi\)
−0.908596 + 0.417677i \(0.862844\pi\)
\(3\) 3.01881 1.74291 0.871455 0.490475i \(-0.163177\pi\)
0.871455 + 0.490475i \(0.163177\pi\)
\(4\) 4.60437 2.30218
\(5\) 3.51758 1.57311 0.786554 0.617521i \(-0.211863\pi\)
0.786554 + 0.617521i \(0.211863\pi\)
\(6\) −7.75803 −3.16720
\(7\) −1.89430 −0.715977 −0.357988 0.933726i \(-0.616537\pi\)
−0.357988 + 0.933726i \(0.616537\pi\)
\(8\) −6.69296 −2.36632
\(9\) 6.11321 2.03774
\(10\) −9.03981 −2.85864
\(11\) −2.04327 −0.616069 −0.308034 0.951375i \(-0.599671\pi\)
−0.308034 + 0.951375i \(0.599671\pi\)
\(12\) 13.8997 4.01250
\(13\) 5.52430 1.53217 0.766083 0.642742i \(-0.222203\pi\)
0.766083 + 0.642742i \(0.222203\pi\)
\(14\) 4.86814 1.30107
\(15\) 10.6189 2.74179
\(16\) 7.99147 1.99787
\(17\) 5.58761 1.35519 0.677597 0.735433i \(-0.263021\pi\)
0.677597 + 0.735433i \(0.263021\pi\)
\(18\) −15.7103 −3.70296
\(19\) −2.18252 −0.500704 −0.250352 0.968155i \(-0.580546\pi\)
−0.250352 + 0.968155i \(0.580546\pi\)
\(20\) 16.1962 3.62159
\(21\) −5.71852 −1.24788
\(22\) 5.25099 1.11951
\(23\) −0.824846 −0.171992 −0.0859962 0.996295i \(-0.527407\pi\)
−0.0859962 + 0.996295i \(0.527407\pi\)
\(24\) −20.2048 −4.12428
\(25\) 7.37336 1.47467
\(26\) −14.1969 −2.78424
\(27\) 9.39820 1.80868
\(28\) −8.72204 −1.64831
\(29\) 0.760452 0.141212 0.0706062 0.997504i \(-0.477507\pi\)
0.0706062 + 0.997504i \(0.477507\pi\)
\(30\) −27.2895 −4.98235
\(31\) −6.60621 −1.18651 −0.593255 0.805015i \(-0.702157\pi\)
−0.593255 + 0.805015i \(0.702157\pi\)
\(32\) −7.15133 −1.26419
\(33\) −6.16824 −1.07375
\(34\) −14.3596 −2.46265
\(35\) −6.66334 −1.12631
\(36\) 28.1475 4.69125
\(37\) −0.863836 −0.142014 −0.0710069 0.997476i \(-0.522621\pi\)
−0.0710069 + 0.997476i \(0.522621\pi\)
\(38\) 5.60884 0.909875
\(39\) 16.6768 2.67043
\(40\) −23.5430 −3.72247
\(41\) 1.16868 0.182518 0.0912589 0.995827i \(-0.470911\pi\)
0.0912589 + 0.995827i \(0.470911\pi\)
\(42\) 14.6960 2.26764
\(43\) 3.90466 0.595455 0.297727 0.954651i \(-0.403771\pi\)
0.297727 + 0.954651i \(0.403771\pi\)
\(44\) −9.40796 −1.41830
\(45\) 21.5037 3.20558
\(46\) 2.11977 0.312543
\(47\) −6.31336 −0.920898 −0.460449 0.887686i \(-0.652312\pi\)
−0.460449 + 0.887686i \(0.652312\pi\)
\(48\) 24.1247 3.48210
\(49\) −3.41164 −0.487378
\(50\) −18.9488 −2.67976
\(51\) 16.8679 2.36198
\(52\) 25.4359 3.52733
\(53\) 2.65911 0.365256 0.182628 0.983182i \(-0.441540\pi\)
0.182628 + 0.983182i \(0.441540\pi\)
\(54\) −24.1524 −3.28673
\(55\) −7.18736 −0.969143
\(56\) 12.6784 1.69423
\(57\) −6.58861 −0.872682
\(58\) −1.95428 −0.256610
\(59\) −7.22794 −0.940997 −0.470499 0.882401i \(-0.655926\pi\)
−0.470499 + 0.882401i \(0.655926\pi\)
\(60\) 48.8933 6.31210
\(61\) 14.0967 1.80490 0.902451 0.430793i \(-0.141766\pi\)
0.902451 + 0.430793i \(0.141766\pi\)
\(62\) 16.9773 2.15612
\(63\) −11.5802 −1.45897
\(64\) 2.39525 0.299406
\(65\) 19.4322 2.41026
\(66\) 15.8517 1.95121
\(67\) −2.05388 −0.250921 −0.125461 0.992099i \(-0.540041\pi\)
−0.125461 + 0.992099i \(0.540041\pi\)
\(68\) 25.7274 3.11991
\(69\) −2.49005 −0.299767
\(70\) 17.1241 2.04672
\(71\) 2.82818 0.335643 0.167822 0.985817i \(-0.446327\pi\)
0.167822 + 0.985817i \(0.446327\pi\)
\(72\) −40.9155 −4.82193
\(73\) 14.4041 1.68587 0.842937 0.538012i \(-0.180825\pi\)
0.842937 + 0.538012i \(0.180825\pi\)
\(74\) 2.21997 0.258066
\(75\) 22.2588 2.57022
\(76\) −10.0491 −1.15271
\(77\) 3.87056 0.441091
\(78\) −42.8577 −4.85268
\(79\) 11.7023 1.31661 0.658307 0.752750i \(-0.271273\pi\)
0.658307 + 0.752750i \(0.271273\pi\)
\(80\) 28.1106 3.14286
\(81\) 10.0317 1.11464
\(82\) −3.00340 −0.331670
\(83\) 14.0093 1.53772 0.768862 0.639415i \(-0.220824\pi\)
0.768862 + 0.639415i \(0.220824\pi\)
\(84\) −26.3302 −2.87286
\(85\) 19.6549 2.13187
\(86\) −10.0346 −1.08206
\(87\) 2.29566 0.246121
\(88\) 13.6755 1.45781
\(89\) −0.766249 −0.0812222 −0.0406111 0.999175i \(-0.512930\pi\)
−0.0406111 + 0.999175i \(0.512930\pi\)
\(90\) −55.2623 −5.82516
\(91\) −10.4647 −1.09700
\(92\) −3.79790 −0.395958
\(93\) −19.9429 −2.06798
\(94\) 16.2247 1.67345
\(95\) −7.67718 −0.787662
\(96\) −21.5885 −2.20337
\(97\) −13.1703 −1.33724 −0.668622 0.743603i \(-0.733116\pi\)
−0.668622 + 0.743603i \(0.733116\pi\)
\(98\) 8.76757 0.885658
\(99\) −12.4909 −1.25539
\(100\) 33.9497 3.39497
\(101\) −10.2772 −1.02262 −0.511308 0.859398i \(-0.670839\pi\)
−0.511308 + 0.859398i \(0.670839\pi\)
\(102\) −43.3488 −4.29217
\(103\) 14.1916 1.39834 0.699171 0.714954i \(-0.253553\pi\)
0.699171 + 0.714954i \(0.253553\pi\)
\(104\) −36.9739 −3.62559
\(105\) −20.1153 −1.96306
\(106\) −6.83363 −0.663741
\(107\) 2.85494 0.275998 0.137999 0.990432i \(-0.455933\pi\)
0.137999 + 0.990432i \(0.455933\pi\)
\(108\) 43.2728 4.16392
\(109\) 12.1418 1.16297 0.581485 0.813557i \(-0.302472\pi\)
0.581485 + 0.813557i \(0.302472\pi\)
\(110\) 18.4708 1.76112
\(111\) −2.60776 −0.247517
\(112\) −15.1382 −1.43043
\(113\) 3.71863 0.349819 0.174909 0.984585i \(-0.444037\pi\)
0.174909 + 0.984585i \(0.444037\pi\)
\(114\) 16.9320 1.58583
\(115\) −2.90146 −0.270563
\(116\) 3.50140 0.325097
\(117\) 33.7712 3.12215
\(118\) 18.5751 1.70997
\(119\) −10.5846 −0.970287
\(120\) −71.0718 −6.48794
\(121\) −6.82505 −0.620459
\(122\) −36.2271 −3.27985
\(123\) 3.52804 0.318112
\(124\) −30.4174 −2.73156
\(125\) 8.34848 0.746711
\(126\) 29.7600 2.65123
\(127\) −14.9468 −1.32631 −0.663155 0.748482i \(-0.730783\pi\)
−0.663155 + 0.748482i \(0.730783\pi\)
\(128\) 8.14713 0.720111
\(129\) 11.7874 1.03782
\(130\) −49.9387 −4.37991
\(131\) 8.20622 0.716981 0.358490 0.933533i \(-0.383292\pi\)
0.358490 + 0.933533i \(0.383292\pi\)
\(132\) −28.4008 −2.47198
\(133\) 4.13433 0.358492
\(134\) 5.27826 0.455972
\(135\) 33.0589 2.84526
\(136\) −37.3976 −3.20682
\(137\) 12.5563 1.07276 0.536380 0.843977i \(-0.319791\pi\)
0.536380 + 0.843977i \(0.319791\pi\)
\(138\) 6.39918 0.544734
\(139\) −6.34030 −0.537777 −0.268889 0.963171i \(-0.586656\pi\)
−0.268889 + 0.963171i \(0.586656\pi\)
\(140\) −30.6804 −2.59297
\(141\) −19.0588 −1.60504
\(142\) −7.26813 −0.609928
\(143\) −11.2876 −0.943920
\(144\) 48.8535 4.07113
\(145\) 2.67495 0.222143
\(146\) −37.0171 −3.06356
\(147\) −10.2991 −0.849455
\(148\) −3.97742 −0.326942
\(149\) 5.38553 0.441199 0.220600 0.975364i \(-0.429199\pi\)
0.220600 + 0.975364i \(0.429199\pi\)
\(150\) −57.2027 −4.67058
\(151\) −19.7706 −1.60891 −0.804456 0.594013i \(-0.797543\pi\)
−0.804456 + 0.594013i \(0.797543\pi\)
\(152\) 14.6075 1.18482
\(153\) 34.1582 2.76153
\(154\) −9.94693 −0.801546
\(155\) −23.2379 −1.86651
\(156\) 76.7862 6.14782
\(157\) −10.4282 −0.832262 −0.416131 0.909305i \(-0.636614\pi\)
−0.416131 + 0.909305i \(0.636614\pi\)
\(158\) −30.0737 −2.39254
\(159\) 8.02734 0.636609
\(160\) −25.1554 −1.98871
\(161\) 1.56250 0.123142
\(162\) −25.7805 −2.02551
\(163\) 4.14566 0.324713 0.162357 0.986732i \(-0.448091\pi\)
0.162357 + 0.986732i \(0.448091\pi\)
\(164\) 5.38105 0.420190
\(165\) −21.6973 −1.68913
\(166\) −36.0025 −2.79434
\(167\) 4.98845 0.386018 0.193009 0.981197i \(-0.438175\pi\)
0.193009 + 0.981197i \(0.438175\pi\)
\(168\) 38.2738 2.95289
\(169\) 17.5179 1.34753
\(170\) −50.5109 −3.87401
\(171\) −13.3422 −1.02030
\(172\) 17.9785 1.37085
\(173\) −4.24557 −0.322784 −0.161392 0.986890i \(-0.551598\pi\)
−0.161392 + 0.986890i \(0.551598\pi\)
\(174\) −5.89961 −0.447248
\(175\) −13.9673 −1.05583
\(176\) −16.3287 −1.23082
\(177\) −21.8198 −1.64007
\(178\) 1.96918 0.147596
\(179\) 8.63074 0.645092 0.322546 0.946554i \(-0.395461\pi\)
0.322546 + 0.946554i \(0.395461\pi\)
\(180\) 99.0110 7.37984
\(181\) 11.1512 0.828864 0.414432 0.910080i \(-0.363980\pi\)
0.414432 + 0.910080i \(0.363980\pi\)
\(182\) 26.8931 1.99345
\(183\) 42.5554 3.14578
\(184\) 5.52066 0.406988
\(185\) −3.03861 −0.223403
\(186\) 51.2512 3.75792
\(187\) −11.4170 −0.834893
\(188\) −29.0690 −2.12008
\(189\) −17.8030 −1.29498
\(190\) 19.7295 1.43133
\(191\) 2.20824 0.159783 0.0798914 0.996804i \(-0.474543\pi\)
0.0798914 + 0.996804i \(0.474543\pi\)
\(192\) 7.23079 0.521838
\(193\) −9.97999 −0.718375 −0.359188 0.933265i \(-0.616946\pi\)
−0.359188 + 0.933265i \(0.616946\pi\)
\(194\) 33.8464 2.43003
\(195\) 58.6620 4.20088
\(196\) −15.7085 −1.12203
\(197\) 10.0406 0.715366 0.357683 0.933843i \(-0.383567\pi\)
0.357683 + 0.933843i \(0.383567\pi\)
\(198\) 32.1004 2.28128
\(199\) 0.481253 0.0341151 0.0170576 0.999855i \(-0.494570\pi\)
0.0170576 + 0.999855i \(0.494570\pi\)
\(200\) −49.3496 −3.48954
\(201\) −6.20027 −0.437333
\(202\) 26.4112 1.85829
\(203\) −1.44052 −0.101105
\(204\) 77.6661 5.43772
\(205\) 4.11094 0.287120
\(206\) −36.4710 −2.54106
\(207\) −5.04246 −0.350475
\(208\) 44.1473 3.06106
\(209\) 4.45947 0.308468
\(210\) 51.6943 3.56725
\(211\) 9.90262 0.681724 0.340862 0.940113i \(-0.389281\pi\)
0.340862 + 0.940113i \(0.389281\pi\)
\(212\) 12.2435 0.840887
\(213\) 8.53774 0.584996
\(214\) −7.33691 −0.501541
\(215\) 13.7349 0.936716
\(216\) −62.9017 −4.27992
\(217\) 12.5141 0.849513
\(218\) −31.2031 −2.11334
\(219\) 43.4833 2.93833
\(220\) −33.0932 −2.23115
\(221\) 30.8676 2.07638
\(222\) 6.70167 0.449786
\(223\) 13.3722 0.895471 0.447736 0.894166i \(-0.352231\pi\)
0.447736 + 0.894166i \(0.352231\pi\)
\(224\) 13.5467 0.905129
\(225\) 45.0749 3.00499
\(226\) −9.55648 −0.635688
\(227\) 3.15449 0.209371 0.104685 0.994505i \(-0.466616\pi\)
0.104685 + 0.994505i \(0.466616\pi\)
\(228\) −30.3364 −2.00907
\(229\) −7.61781 −0.503399 −0.251700 0.967805i \(-0.580989\pi\)
−0.251700 + 0.967805i \(0.580989\pi\)
\(230\) 7.45646 0.491664
\(231\) 11.6845 0.768782
\(232\) −5.08967 −0.334153
\(233\) −12.4080 −0.812875 −0.406438 0.913679i \(-0.633229\pi\)
−0.406438 + 0.913679i \(0.633229\pi\)
\(234\) −86.7886 −5.67355
\(235\) −22.2077 −1.44867
\(236\) −33.2801 −2.16635
\(237\) 35.3271 2.29474
\(238\) 27.2013 1.76320
\(239\) −16.1930 −1.04744 −0.523719 0.851891i \(-0.675456\pi\)
−0.523719 + 0.851891i \(0.675456\pi\)
\(240\) 84.8606 5.47773
\(241\) −12.3741 −0.797085 −0.398543 0.917150i \(-0.630484\pi\)
−0.398543 + 0.917150i \(0.630484\pi\)
\(242\) 17.5397 1.12749
\(243\) 2.08931 0.134030
\(244\) 64.9065 4.15522
\(245\) −12.0007 −0.766698
\(246\) −9.06669 −0.578071
\(247\) −12.0569 −0.767161
\(248\) 44.2151 2.80766
\(249\) 42.2915 2.68011
\(250\) −21.4547 −1.35692
\(251\) −6.67493 −0.421318 −0.210659 0.977560i \(-0.567561\pi\)
−0.210659 + 0.977560i \(0.567561\pi\)
\(252\) −53.3197 −3.35882
\(253\) 1.68538 0.105959
\(254\) 38.4116 2.41016
\(255\) 59.3343 3.71566
\(256\) −25.7278 −1.60799
\(257\) 8.65730 0.540028 0.270014 0.962856i \(-0.412972\pi\)
0.270014 + 0.962856i \(0.412972\pi\)
\(258\) −30.2925 −1.88593
\(259\) 1.63636 0.101679
\(260\) 89.4729 5.54887
\(261\) 4.64881 0.287754
\(262\) −21.0891 −1.30289
\(263\) 19.2664 1.18802 0.594009 0.804459i \(-0.297545\pi\)
0.594009 + 0.804459i \(0.297545\pi\)
\(264\) 41.2838 2.54084
\(265\) 9.35362 0.574588
\(266\) −10.6248 −0.651449
\(267\) −2.31316 −0.141563
\(268\) −9.45681 −0.577667
\(269\) 14.6977 0.896136 0.448068 0.894000i \(-0.352112\pi\)
0.448068 + 0.894000i \(0.352112\pi\)
\(270\) −84.9580 −5.17038
\(271\) −22.0532 −1.33963 −0.669817 0.742526i \(-0.733628\pi\)
−0.669817 + 0.742526i \(0.733628\pi\)
\(272\) 44.6532 2.70750
\(273\) −31.5908 −1.91196
\(274\) −32.2685 −1.94941
\(275\) −15.0658 −0.908499
\(276\) −11.4651 −0.690119
\(277\) −20.3509 −1.22277 −0.611383 0.791335i \(-0.709387\pi\)
−0.611383 + 0.791335i \(0.709387\pi\)
\(278\) 16.2939 0.977244
\(279\) −40.3852 −2.41780
\(280\) 44.5974 2.66520
\(281\) −1.18888 −0.0709225 −0.0354613 0.999371i \(-0.511290\pi\)
−0.0354613 + 0.999371i \(0.511290\pi\)
\(282\) 48.9792 2.91667
\(283\) 30.2210 1.79645 0.898225 0.439537i \(-0.144857\pi\)
0.898225 + 0.439537i \(0.144857\pi\)
\(284\) 13.0220 0.772713
\(285\) −23.1759 −1.37282
\(286\) 29.0081 1.71528
\(287\) −2.21383 −0.130679
\(288\) −43.7176 −2.57609
\(289\) 14.2214 0.836551
\(290\) −6.87435 −0.403676
\(291\) −39.7587 −2.33070
\(292\) 66.3218 3.88119
\(293\) −7.32755 −0.428080 −0.214040 0.976825i \(-0.568662\pi\)
−0.214040 + 0.976825i \(0.568662\pi\)
\(294\) 26.4676 1.54362
\(295\) −25.4248 −1.48029
\(296\) 5.78162 0.336050
\(297\) −19.2030 −1.11427
\(298\) −13.8402 −0.801744
\(299\) −4.55670 −0.263521
\(300\) 102.488 5.91712
\(301\) −7.39658 −0.426332
\(302\) 50.8085 2.92370
\(303\) −31.0248 −1.78233
\(304\) −17.4415 −1.00034
\(305\) 49.5864 2.83931
\(306\) −87.7831 −5.01823
\(307\) 6.20288 0.354017 0.177009 0.984209i \(-0.443358\pi\)
0.177009 + 0.984209i \(0.443358\pi\)
\(308\) 17.8215 1.01547
\(309\) 42.8418 2.43719
\(310\) 59.7189 3.39180
\(311\) 21.0085 1.19129 0.595643 0.803250i \(-0.296897\pi\)
0.595643 + 0.803250i \(0.296897\pi\)
\(312\) −111.617 −6.31908
\(313\) 15.2706 0.863148 0.431574 0.902078i \(-0.357958\pi\)
0.431574 + 0.902078i \(0.357958\pi\)
\(314\) 26.7994 1.51238
\(315\) −40.7344 −2.29512
\(316\) 53.8818 3.03109
\(317\) 9.46137 0.531404 0.265702 0.964055i \(-0.414396\pi\)
0.265702 + 0.964055i \(0.414396\pi\)
\(318\) −20.6294 −1.15684
\(319\) −1.55381 −0.0869966
\(320\) 8.42547 0.470998
\(321\) 8.61853 0.481039
\(322\) −4.01547 −0.223773
\(323\) −12.1951 −0.678551
\(324\) 46.1898 2.56610
\(325\) 40.7327 2.25944
\(326\) −10.6539 −0.590066
\(327\) 36.6536 2.02695
\(328\) −7.82195 −0.431895
\(329\) 11.9594 0.659342
\(330\) 55.7597 3.06947
\(331\) −35.3503 −1.94303 −0.971515 0.236978i \(-0.923843\pi\)
−0.971515 + 0.236978i \(0.923843\pi\)
\(332\) 64.5041 3.54012
\(333\) −5.28081 −0.289387
\(334\) −12.8198 −0.701468
\(335\) −7.22468 −0.394726
\(336\) −45.6994 −2.49310
\(337\) 2.31746 0.126240 0.0631200 0.998006i \(-0.479895\pi\)
0.0631200 + 0.998006i \(0.479895\pi\)
\(338\) −45.0193 −2.44873
\(339\) 11.2258 0.609703
\(340\) 90.4982 4.90795
\(341\) 13.4983 0.730972
\(342\) 34.2881 1.85409
\(343\) 19.7227 1.06493
\(344\) −26.1337 −1.40904
\(345\) −8.75896 −0.471567
\(346\) 10.9107 0.586561
\(347\) −25.2643 −1.35626 −0.678131 0.734941i \(-0.737210\pi\)
−0.678131 + 0.734941i \(0.737210\pi\)
\(348\) 10.5701 0.566615
\(349\) −19.0097 −1.01757 −0.508783 0.860895i \(-0.669905\pi\)
−0.508783 + 0.860895i \(0.669905\pi\)
\(350\) 35.8946 1.91865
\(351\) 51.9185 2.77120
\(352\) 14.6121 0.778827
\(353\) −31.5377 −1.67858 −0.839291 0.543683i \(-0.817029\pi\)
−0.839291 + 0.543683i \(0.817029\pi\)
\(354\) 56.0745 2.98033
\(355\) 9.94835 0.528004
\(356\) −3.52809 −0.186988
\(357\) −31.9528 −1.69112
\(358\) −22.1801 −1.17226
\(359\) 16.8660 0.890155 0.445077 0.895492i \(-0.353176\pi\)
0.445077 + 0.895492i \(0.353176\pi\)
\(360\) −143.923 −7.58543
\(361\) −14.2366 −0.749296
\(362\) −28.6575 −1.50620
\(363\) −20.6035 −1.08141
\(364\) −48.1832 −2.52548
\(365\) 50.6676 2.65206
\(366\) −109.363 −5.71649
\(367\) 20.2590 1.05751 0.528756 0.848774i \(-0.322658\pi\)
0.528756 + 0.848774i \(0.322658\pi\)
\(368\) −6.59173 −0.343618
\(369\) 7.14442 0.371924
\(370\) 7.80892 0.405966
\(371\) −5.03713 −0.261515
\(372\) −91.8244 −4.76087
\(373\) −21.6332 −1.12012 −0.560061 0.828451i \(-0.689222\pi\)
−0.560061 + 0.828451i \(0.689222\pi\)
\(374\) 29.3405 1.51716
\(375\) 25.2025 1.30145
\(376\) 42.2550 2.17914
\(377\) 4.20097 0.216361
\(378\) 45.7518 2.35322
\(379\) 1.63918 0.0841992 0.0420996 0.999113i \(-0.486595\pi\)
0.0420996 + 0.999113i \(0.486595\pi\)
\(380\) −35.3485 −1.81334
\(381\) −45.1214 −2.31164
\(382\) −5.67495 −0.290356
\(383\) −8.24395 −0.421246 −0.210623 0.977567i \(-0.567549\pi\)
−0.210623 + 0.977567i \(0.567549\pi\)
\(384\) 24.5946 1.25509
\(385\) 13.6150 0.693884
\(386\) 25.6475 1.30543
\(387\) 23.8700 1.21338
\(388\) −60.6410 −3.07858
\(389\) −31.0594 −1.57477 −0.787386 0.616460i \(-0.788566\pi\)
−0.787386 + 0.616460i \(0.788566\pi\)
\(390\) −150.755 −7.63379
\(391\) −4.60892 −0.233083
\(392\) 22.8340 1.15329
\(393\) 24.7730 1.24963
\(394\) −25.8034 −1.29996
\(395\) 41.1638 2.07118
\(396\) −57.5129 −2.89013
\(397\) 23.3629 1.17255 0.586275 0.810112i \(-0.300594\pi\)
0.586275 + 0.810112i \(0.300594\pi\)
\(398\) −1.23677 −0.0619937
\(399\) 12.4808 0.624820
\(400\) 58.9240 2.94620
\(401\) −26.7606 −1.33636 −0.668181 0.743998i \(-0.732927\pi\)
−0.668181 + 0.743998i \(0.732927\pi\)
\(402\) 15.9340 0.794718
\(403\) −36.4947 −1.81793
\(404\) −47.3198 −2.35425
\(405\) 35.2874 1.75345
\(406\) 3.70199 0.183727
\(407\) 1.76505 0.0874903
\(408\) −112.896 −5.58920
\(409\) −20.2225 −0.999939 −0.499970 0.866043i \(-0.666656\pi\)
−0.499970 + 0.866043i \(0.666656\pi\)
\(410\) −10.5647 −0.521753
\(411\) 37.9052 1.86972
\(412\) 65.3435 3.21924
\(413\) 13.6919 0.673732
\(414\) 12.9586 0.636881
\(415\) 49.2789 2.41901
\(416\) −39.5061 −1.93695
\(417\) −19.1402 −0.937298
\(418\) −11.4604 −0.560545
\(419\) −1.17122 −0.0572180 −0.0286090 0.999591i \(-0.509108\pi\)
−0.0286090 + 0.999591i \(0.509108\pi\)
\(420\) −92.6184 −4.51932
\(421\) −12.5250 −0.610430 −0.305215 0.952283i \(-0.598728\pi\)
−0.305215 + 0.952283i \(0.598728\pi\)
\(422\) −25.4487 −1.23882
\(423\) −38.5949 −1.87655
\(424\) −17.7973 −0.864312
\(425\) 41.1994 1.99847
\(426\) −21.9411 −1.06305
\(427\) −26.7034 −1.29227
\(428\) 13.1452 0.635397
\(429\) −34.0752 −1.64517
\(430\) −35.2974 −1.70219
\(431\) 13.3825 0.644614 0.322307 0.946635i \(-0.395542\pi\)
0.322307 + 0.946635i \(0.395542\pi\)
\(432\) 75.1054 3.61351
\(433\) 12.8323 0.616681 0.308341 0.951276i \(-0.400226\pi\)
0.308341 + 0.951276i \(0.400226\pi\)
\(434\) −32.1600 −1.54373
\(435\) 8.07517 0.387175
\(436\) 55.9051 2.67737
\(437\) 1.80024 0.0861172
\(438\) −111.748 −5.33950
\(439\) −18.6686 −0.891004 −0.445502 0.895281i \(-0.646975\pi\)
−0.445502 + 0.895281i \(0.646975\pi\)
\(440\) 48.1047 2.29330
\(441\) −20.8561 −0.993148
\(442\) −79.3266 −3.77318
\(443\) −0.0814150 −0.00386814 −0.00193407 0.999998i \(-0.500616\pi\)
−0.00193407 + 0.999998i \(0.500616\pi\)
\(444\) −12.0071 −0.569830
\(445\) −2.69534 −0.127771
\(446\) −34.3653 −1.62724
\(447\) 16.2579 0.768971
\(448\) −4.53731 −0.214368
\(449\) 29.2926 1.38240 0.691202 0.722661i \(-0.257081\pi\)
0.691202 + 0.722661i \(0.257081\pi\)
\(450\) −115.838 −5.46065
\(451\) −2.38794 −0.112444
\(452\) 17.1219 0.805347
\(453\) −59.6838 −2.80419
\(454\) −8.10672 −0.380467
\(455\) −36.8103 −1.72569
\(456\) 44.0972 2.06504
\(457\) −0.339229 −0.0158684 −0.00793422 0.999969i \(-0.502526\pi\)
−0.00793422 + 0.999969i \(0.502526\pi\)
\(458\) 19.5770 0.914773
\(459\) 52.5135 2.45112
\(460\) −13.3594 −0.622885
\(461\) −35.3400 −1.64595 −0.822975 0.568078i \(-0.807687\pi\)
−0.822975 + 0.568078i \(0.807687\pi\)
\(462\) −30.0279 −1.39702
\(463\) 19.4823 0.905417 0.452709 0.891659i \(-0.350458\pi\)
0.452709 + 0.891659i \(0.350458\pi\)
\(464\) 6.07713 0.282124
\(465\) −70.1507 −3.25316
\(466\) 31.8873 1.47715
\(467\) −30.0671 −1.39134 −0.695669 0.718363i \(-0.744892\pi\)
−0.695669 + 0.718363i \(0.744892\pi\)
\(468\) 155.495 7.18777
\(469\) 3.89065 0.179654
\(470\) 57.0716 2.63252
\(471\) −31.4808 −1.45056
\(472\) 48.3763 2.22670
\(473\) −7.97827 −0.366841
\(474\) −90.7869 −4.16998
\(475\) −16.0925 −0.738374
\(476\) −48.7353 −2.23378
\(477\) 16.2557 0.744297
\(478\) 41.6143 1.90340
\(479\) −8.66647 −0.395981 −0.197990 0.980204i \(-0.563442\pi\)
−0.197990 + 0.980204i \(0.563442\pi\)
\(480\) −75.9393 −3.46614
\(481\) −4.77209 −0.217589
\(482\) 31.8001 1.44846
\(483\) 4.71690 0.214626
\(484\) −31.4251 −1.42841
\(485\) −46.3277 −2.10363
\(486\) −5.36932 −0.243557
\(487\) −42.5089 −1.92626 −0.963132 0.269030i \(-0.913297\pi\)
−0.963132 + 0.269030i \(0.913297\pi\)
\(488\) −94.3488 −4.27097
\(489\) 12.5150 0.565946
\(490\) 30.8406 1.39324
\(491\) −33.8321 −1.52682 −0.763411 0.645913i \(-0.776477\pi\)
−0.763411 + 0.645913i \(0.776477\pi\)
\(492\) 16.2444 0.732353
\(493\) 4.24911 0.191370
\(494\) 30.9850 1.39408
\(495\) −43.9379 −1.97486
\(496\) −52.7933 −2.37049
\(497\) −5.35741 −0.240313
\(498\) −108.685 −4.87028
\(499\) −16.9601 −0.759238 −0.379619 0.925143i \(-0.623945\pi\)
−0.379619 + 0.925143i \(0.623945\pi\)
\(500\) 38.4395 1.71907
\(501\) 15.0592 0.672795
\(502\) 17.1539 0.765615
\(503\) 19.8394 0.884597 0.442298 0.896868i \(-0.354163\pi\)
0.442298 + 0.896868i \(0.354163\pi\)
\(504\) 77.5060 3.45239
\(505\) −36.1507 −1.60869
\(506\) −4.33126 −0.192548
\(507\) 52.8833 2.34863
\(508\) −68.8204 −3.05341
\(509\) 22.5274 0.998511 0.499256 0.866455i \(-0.333607\pi\)
0.499256 + 0.866455i \(0.333607\pi\)
\(510\) −152.483 −6.75206
\(511\) −27.2857 −1.20705
\(512\) 49.8234 2.20191
\(513\) −20.5117 −0.905615
\(514\) −22.2484 −0.981334
\(515\) 49.9202 2.19974
\(516\) 54.2736 2.38926
\(517\) 12.8999 0.567337
\(518\) −4.20528 −0.184769
\(519\) −12.8166 −0.562584
\(520\) −130.059 −5.70345
\(521\) 41.4955 1.81795 0.908976 0.416849i \(-0.136866\pi\)
0.908976 + 0.416849i \(0.136866\pi\)
\(522\) −11.9470 −0.522904
\(523\) −27.3310 −1.19510 −0.597551 0.801831i \(-0.703860\pi\)
−0.597551 + 0.801831i \(0.703860\pi\)
\(524\) 37.7845 1.65062
\(525\) −42.1647 −1.84022
\(526\) −49.5126 −2.15885
\(527\) −36.9129 −1.60795
\(528\) −49.2933 −2.14521
\(529\) −22.3196 −0.970419
\(530\) −24.0378 −1.04414
\(531\) −44.1859 −1.91751
\(532\) 19.0360 0.825315
\(533\) 6.45617 0.279648
\(534\) 5.94458 0.257247
\(535\) 10.0425 0.434174
\(536\) 13.7465 0.593759
\(537\) 26.0546 1.12434
\(538\) −37.7716 −1.62845
\(539\) 6.97090 0.300258
\(540\) 152.215 6.55031
\(541\) 38.6036 1.65970 0.829849 0.557989i \(-0.188427\pi\)
0.829849 + 0.557989i \(0.188427\pi\)
\(542\) 56.6744 2.43437
\(543\) 33.6634 1.44464
\(544\) −39.9588 −1.71322
\(545\) 42.7096 1.82948
\(546\) 81.1852 3.47441
\(547\) 8.31600 0.355567 0.177783 0.984070i \(-0.443107\pi\)
0.177783 + 0.984070i \(0.443107\pi\)
\(548\) 57.8140 2.46969
\(549\) 86.1763 3.67792
\(550\) 38.7174 1.65092
\(551\) −1.65970 −0.0707056
\(552\) 16.6658 0.709344
\(553\) −22.1677 −0.942664
\(554\) 52.2997 2.22200
\(555\) −9.17299 −0.389372
\(556\) −29.1931 −1.23806
\(557\) 34.1127 1.44540 0.722701 0.691160i \(-0.242900\pi\)
0.722701 + 0.691160i \(0.242900\pi\)
\(558\) 103.786 4.39360
\(559\) 21.5705 0.912336
\(560\) −53.2498 −2.25022
\(561\) −34.4657 −1.45514
\(562\) 3.05529 0.128880
\(563\) 2.89073 0.121830 0.0609149 0.998143i \(-0.480598\pi\)
0.0609149 + 0.998143i \(0.480598\pi\)
\(564\) −87.7539 −3.69510
\(565\) 13.0806 0.550303
\(566\) −77.6647 −3.26449
\(567\) −19.0031 −0.798054
\(568\) −18.9289 −0.794239
\(569\) −7.28200 −0.305278 −0.152639 0.988282i \(-0.548777\pi\)
−0.152639 + 0.988282i \(0.548777\pi\)
\(570\) 59.5598 2.49468
\(571\) 11.5500 0.483351 0.241675 0.970357i \(-0.422303\pi\)
0.241675 + 0.970357i \(0.422303\pi\)
\(572\) −51.9724 −2.17308
\(573\) 6.66626 0.278487
\(574\) 5.68933 0.237468
\(575\) −6.08189 −0.253632
\(576\) 14.6427 0.610111
\(577\) −36.5194 −1.52032 −0.760161 0.649735i \(-0.774880\pi\)
−0.760161 + 0.649735i \(0.774880\pi\)
\(578\) −36.5474 −1.52017
\(579\) −30.1277 −1.25206
\(580\) 12.3165 0.511413
\(581\) −26.5378 −1.10097
\(582\) 102.176 4.23532
\(583\) −5.43327 −0.225023
\(584\) −96.4061 −3.98931
\(585\) 118.793 4.91149
\(586\) 18.8310 0.777903
\(587\) 21.2612 0.877543 0.438771 0.898599i \(-0.355414\pi\)
0.438771 + 0.898599i \(0.355414\pi\)
\(588\) −47.4208 −1.95560
\(589\) 14.4182 0.594090
\(590\) 65.3392 2.68997
\(591\) 30.3108 1.24682
\(592\) −6.90332 −0.283725
\(593\) 34.3543 1.41076 0.705381 0.708828i \(-0.250776\pi\)
0.705381 + 0.708828i \(0.250776\pi\)
\(594\) 49.3498 2.02485
\(595\) −37.2321 −1.52637
\(596\) 24.7969 1.01572
\(597\) 1.45281 0.0594596
\(598\) 11.7102 0.478868
\(599\) 9.32891 0.381169 0.190584 0.981671i \(-0.438962\pi\)
0.190584 + 0.981671i \(0.438962\pi\)
\(600\) −148.977 −6.08196
\(601\) 4.73396 0.193102 0.0965510 0.995328i \(-0.469219\pi\)
0.0965510 + 0.995328i \(0.469219\pi\)
\(602\) 19.0084 0.774726
\(603\) −12.5558 −0.511312
\(604\) −91.0313 −3.70401
\(605\) −24.0077 −0.976050
\(606\) 79.7305 3.23883
\(607\) −38.3477 −1.55648 −0.778242 0.627965i \(-0.783888\pi\)
−0.778242 + 0.627965i \(0.783888\pi\)
\(608\) 15.6079 0.632984
\(609\) −4.34866 −0.176217
\(610\) −127.432 −5.15956
\(611\) −34.8769 −1.41097
\(612\) 157.277 6.35755
\(613\) 10.9044 0.440424 0.220212 0.975452i \(-0.429325\pi\)
0.220212 + 0.975452i \(0.429325\pi\)
\(614\) −15.9408 −0.643317
\(615\) 12.4101 0.500425
\(616\) −25.9055 −1.04376
\(617\) 38.4179 1.54664 0.773322 0.634013i \(-0.218593\pi\)
0.773322 + 0.634013i \(0.218593\pi\)
\(618\) −110.099 −4.42883
\(619\) 25.3912 1.02056 0.510279 0.860009i \(-0.329542\pi\)
0.510279 + 0.860009i \(0.329542\pi\)
\(620\) −106.996 −4.29705
\(621\) −7.75207 −0.311080
\(622\) −53.9898 −2.16479
\(623\) 1.45150 0.0581532
\(624\) 133.272 5.33516
\(625\) −7.50037 −0.300015
\(626\) −39.2440 −1.56850
\(627\) 13.4623 0.537632
\(628\) −48.0153 −1.91602
\(629\) −4.82678 −0.192456
\(630\) 104.683 4.17068
\(631\) −28.4641 −1.13314 −0.566569 0.824014i \(-0.691730\pi\)
−0.566569 + 0.824014i \(0.691730\pi\)
\(632\) −78.3231 −3.11552
\(633\) 29.8941 1.18818
\(634\) −24.3148 −0.965662
\(635\) −52.5764 −2.08643
\(636\) 36.9608 1.46559
\(637\) −18.8469 −0.746743
\(638\) 3.99313 0.158089
\(639\) 17.2893 0.683953
\(640\) 28.6582 1.13281
\(641\) 1.57817 0.0623341 0.0311671 0.999514i \(-0.490078\pi\)
0.0311671 + 0.999514i \(0.490078\pi\)
\(642\) −22.1487 −0.874140
\(643\) −14.2118 −0.560459 −0.280230 0.959933i \(-0.590411\pi\)
−0.280230 + 0.959933i \(0.590411\pi\)
\(644\) 7.19434 0.283497
\(645\) 41.4632 1.63261
\(646\) 31.3400 1.23306
\(647\) −1.42495 −0.0560207 −0.0280104 0.999608i \(-0.508917\pi\)
−0.0280104 + 0.999608i \(0.508917\pi\)
\(648\) −67.1420 −2.63759
\(649\) 14.7686 0.579719
\(650\) −104.679 −4.10584
\(651\) 37.7777 1.48063
\(652\) 19.0881 0.747549
\(653\) 35.1520 1.37560 0.687801 0.725899i \(-0.258576\pi\)
0.687801 + 0.725899i \(0.258576\pi\)
\(654\) −94.1961 −3.68336
\(655\) 28.8660 1.12789
\(656\) 9.33950 0.364646
\(657\) 88.0554 3.43537
\(658\) −30.7343 −1.19815
\(659\) 14.0381 0.546848 0.273424 0.961894i \(-0.411844\pi\)
0.273424 + 0.961894i \(0.411844\pi\)
\(660\) −99.9022 −3.88869
\(661\) 27.1013 1.05412 0.527059 0.849829i \(-0.323295\pi\)
0.527059 + 0.849829i \(0.323295\pi\)
\(662\) 90.8467 3.53086
\(663\) 93.1836 3.61895
\(664\) −93.7638 −3.63874
\(665\) 14.5428 0.563947
\(666\) 13.5711 0.525871
\(667\) −0.627256 −0.0242875
\(668\) 22.9687 0.888684
\(669\) 40.3682 1.56073
\(670\) 18.5667 0.717293
\(671\) −28.8034 −1.11194
\(672\) 40.8950 1.57756
\(673\) −1.03078 −0.0397336 −0.0198668 0.999803i \(-0.506324\pi\)
−0.0198668 + 0.999803i \(0.506324\pi\)
\(674\) −5.95562 −0.229402
\(675\) 69.2963 2.66722
\(676\) 80.6590 3.10227
\(677\) −28.2590 −1.08608 −0.543041 0.839706i \(-0.682727\pi\)
−0.543041 + 0.839706i \(0.682727\pi\)
\(678\) −28.8492 −1.10795
\(679\) 24.9485 0.957435
\(680\) −131.549 −5.04468
\(681\) 9.52281 0.364915
\(682\) −34.6891 −1.32832
\(683\) 6.89001 0.263639 0.131819 0.991274i \(-0.457918\pi\)
0.131819 + 0.991274i \(0.457918\pi\)
\(684\) −61.4324 −2.34893
\(685\) 44.1679 1.68757
\(686\) −50.6854 −1.93518
\(687\) −22.9967 −0.877380
\(688\) 31.2040 1.18964
\(689\) 14.6897 0.559633
\(690\) 22.5096 0.856927
\(691\) −36.6174 −1.39299 −0.696495 0.717561i \(-0.745258\pi\)
−0.696495 + 0.717561i \(0.745258\pi\)
\(692\) −19.5481 −0.743109
\(693\) 23.6615 0.898827
\(694\) 64.9268 2.46459
\(695\) −22.3025 −0.845982
\(696\) −15.3648 −0.582400
\(697\) 6.53015 0.247347
\(698\) 48.8530 1.84911
\(699\) −37.4574 −1.41677
\(700\) −64.3107 −2.43072
\(701\) −21.4128 −0.808752 −0.404376 0.914593i \(-0.632511\pi\)
−0.404376 + 0.914593i \(0.632511\pi\)
\(702\) −133.425 −5.03581
\(703\) 1.88534 0.0711069
\(704\) −4.89413 −0.184455
\(705\) −67.0409 −2.52491
\(706\) 81.0486 3.05030
\(707\) 19.4680 0.732169
\(708\) −100.466 −3.77575
\(709\) −9.75922 −0.366515 −0.183258 0.983065i \(-0.558664\pi\)
−0.183258 + 0.983065i \(0.558664\pi\)
\(710\) −25.5662 −0.959483
\(711\) 71.5388 2.68291
\(712\) 5.12847 0.192197
\(713\) 5.44911 0.204071
\(714\) 82.1155 3.07310
\(715\) −39.7051 −1.48489
\(716\) 39.7391 1.48512
\(717\) −48.8836 −1.82559
\(718\) −43.3439 −1.61758
\(719\) −26.7330 −0.996974 −0.498487 0.866897i \(-0.666111\pi\)
−0.498487 + 0.866897i \(0.666111\pi\)
\(720\) 171.846 6.40433
\(721\) −26.8831 −1.00118
\(722\) 36.5866 1.36161
\(723\) −37.3550 −1.38925
\(724\) 51.3443 1.90820
\(725\) 5.60709 0.208242
\(726\) 52.9490 1.96512
\(727\) 10.1609 0.376847 0.188424 0.982088i \(-0.439662\pi\)
0.188424 + 0.982088i \(0.439662\pi\)
\(728\) 70.0395 2.59584
\(729\) −23.7880 −0.881036
\(730\) −130.210 −4.81931
\(731\) 21.8177 0.806957
\(732\) 195.940 7.24217
\(733\) 23.1531 0.855179 0.427590 0.903973i \(-0.359363\pi\)
0.427590 + 0.903973i \(0.359363\pi\)
\(734\) −52.0636 −1.92170
\(735\) −36.2279 −1.33629
\(736\) 5.89875 0.217431
\(737\) 4.19663 0.154585
\(738\) −18.3604 −0.675856
\(739\) 48.8067 1.79538 0.897692 0.440624i \(-0.145243\pi\)
0.897692 + 0.440624i \(0.145243\pi\)
\(740\) −13.9909 −0.514315
\(741\) −36.3975 −1.33709
\(742\) 12.9449 0.475223
\(743\) −40.6906 −1.49279 −0.746396 0.665502i \(-0.768218\pi\)
−0.746396 + 0.665502i \(0.768218\pi\)
\(744\) 133.477 4.89350
\(745\) 18.9440 0.694055
\(746\) 55.5950 2.03548
\(747\) 85.6420 3.13348
\(748\) −52.5680 −1.92208
\(749\) −5.40811 −0.197608
\(750\) −64.7677 −2.36498
\(751\) 38.2044 1.39410 0.697049 0.717024i \(-0.254496\pi\)
0.697049 + 0.717024i \(0.254496\pi\)
\(752\) −50.4530 −1.83983
\(753\) −20.1503 −0.734319
\(754\) −10.7961 −0.393169
\(755\) −69.5448 −2.53099
\(756\) −81.9714 −2.98127
\(757\) −43.6832 −1.58769 −0.793847 0.608117i \(-0.791925\pi\)
−0.793847 + 0.608117i \(0.791925\pi\)
\(758\) −4.21253 −0.153006
\(759\) 5.08785 0.184677
\(760\) 51.3830 1.86386
\(761\) −4.52727 −0.164113 −0.0820567 0.996628i \(-0.526149\pi\)
−0.0820567 + 0.996628i \(0.526149\pi\)
\(762\) 115.957 4.20069
\(763\) −23.0001 −0.832659
\(764\) 10.1676 0.367849
\(765\) 120.154 4.34419
\(766\) 21.1861 0.765484
\(767\) −39.9293 −1.44176
\(768\) −77.6672 −2.80257
\(769\) 27.1105 0.977629 0.488814 0.872388i \(-0.337429\pi\)
0.488814 + 0.872388i \(0.337429\pi\)
\(770\) −34.9891 −1.26092
\(771\) 26.1348 0.941220
\(772\) −45.9515 −1.65383
\(773\) −40.6488 −1.46203 −0.731017 0.682359i \(-0.760954\pi\)
−0.731017 + 0.682359i \(0.760954\pi\)
\(774\) −61.3435 −2.20495
\(775\) −48.7099 −1.74971
\(776\) 88.1484 3.16434
\(777\) 4.93986 0.177217
\(778\) 79.8194 2.86166
\(779\) −2.55067 −0.0913874
\(780\) 270.102 9.67119
\(781\) −5.77873 −0.206779
\(782\) 11.8444 0.423556
\(783\) 7.14688 0.255409
\(784\) −27.2640 −0.973715
\(785\) −36.6821 −1.30924
\(786\) −63.6641 −2.27082
\(787\) −43.9994 −1.56841 −0.784205 0.620502i \(-0.786929\pi\)
−0.784205 + 0.620502i \(0.786929\pi\)
\(788\) 46.2308 1.64690
\(789\) 58.1616 2.07061
\(790\) −105.787 −3.76372
\(791\) −7.04418 −0.250462
\(792\) 83.6013 2.97064
\(793\) 77.8746 2.76541
\(794\) −60.0403 −2.13075
\(795\) 28.2368 1.00146
\(796\) 2.21587 0.0785393
\(797\) 11.5233 0.408176 0.204088 0.978953i \(-0.434577\pi\)
0.204088 + 0.978953i \(0.434577\pi\)
\(798\) −32.0743 −1.13542
\(799\) −35.2766 −1.24800
\(800\) −52.7293 −1.86426
\(801\) −4.68424 −0.165510
\(802\) 68.7721 2.42843
\(803\) −29.4315 −1.03861
\(804\) −28.5483 −1.00682
\(805\) 5.49623 0.193717
\(806\) 93.7876 3.30353
\(807\) 44.3696 1.56188
\(808\) 68.7846 2.41983
\(809\) 25.5818 0.899406 0.449703 0.893178i \(-0.351530\pi\)
0.449703 + 0.893178i \(0.351530\pi\)
\(810\) −90.6850 −3.18635
\(811\) −27.1884 −0.954713 −0.477356 0.878710i \(-0.658405\pi\)
−0.477356 + 0.878710i \(0.658405\pi\)
\(812\) −6.63269 −0.232762
\(813\) −66.5743 −2.33486
\(814\) −4.53599 −0.158987
\(815\) 14.5827 0.510809
\(816\) 134.799 4.71893
\(817\) −8.52199 −0.298147
\(818\) 51.9698 1.81708
\(819\) −63.9727 −2.23539
\(820\) 18.9283 0.661004
\(821\) 20.1045 0.701651 0.350825 0.936441i \(-0.385901\pi\)
0.350825 + 0.936441i \(0.385901\pi\)
\(822\) −97.4124 −3.39765
\(823\) −53.9432 −1.88034 −0.940171 0.340702i \(-0.889335\pi\)
−0.940171 + 0.340702i \(0.889335\pi\)
\(824\) −94.9839 −3.30892
\(825\) −45.4807 −1.58343
\(826\) −35.1866 −1.22430
\(827\) 25.0946 0.872624 0.436312 0.899795i \(-0.356284\pi\)
0.436312 + 0.899795i \(0.356284\pi\)
\(828\) −23.2173 −0.806859
\(829\) −43.3820 −1.50672 −0.753359 0.657609i \(-0.771568\pi\)
−0.753359 + 0.657609i \(0.771568\pi\)
\(830\) −126.642 −4.39580
\(831\) −61.4354 −2.13117
\(832\) 13.2321 0.458739
\(833\) −19.0629 −0.660491
\(834\) 49.1882 1.70325
\(835\) 17.5473 0.607248
\(836\) 20.5330 0.710150
\(837\) −62.0865 −2.14602
\(838\) 3.00992 0.103976
\(839\) −19.8241 −0.684404 −0.342202 0.939626i \(-0.611173\pi\)
−0.342202 + 0.939626i \(0.611173\pi\)
\(840\) 134.631 4.64521
\(841\) −28.4217 −0.980059
\(842\) 32.1879 1.10927
\(843\) −3.58900 −0.123612
\(844\) 45.5953 1.56945
\(845\) 61.6207 2.11982
\(846\) 99.1849 3.41005
\(847\) 12.9287 0.444234
\(848\) 21.2502 0.729734
\(849\) 91.2313 3.13105
\(850\) −105.878 −3.63160
\(851\) 0.712532 0.0244253
\(852\) 39.3109 1.34677
\(853\) −56.0377 −1.91869 −0.959347 0.282230i \(-0.908926\pi\)
−0.959347 + 0.282230i \(0.908926\pi\)
\(854\) 68.6249 2.34830
\(855\) −46.9322 −1.60505
\(856\) −19.1080 −0.653098
\(857\) 38.4961 1.31500 0.657500 0.753454i \(-0.271614\pi\)
0.657500 + 0.753454i \(0.271614\pi\)
\(858\) 87.5698 2.98958
\(859\) −5.49647 −0.187537 −0.0937686 0.995594i \(-0.529891\pi\)
−0.0937686 + 0.995594i \(0.529891\pi\)
\(860\) 63.2407 2.15649
\(861\) −6.68315 −0.227761
\(862\) −34.3917 −1.17139
\(863\) 8.64293 0.294209 0.147104 0.989121i \(-0.453005\pi\)
0.147104 + 0.989121i \(0.453005\pi\)
\(864\) −67.2096 −2.28652
\(865\) −14.9341 −0.507775
\(866\) −32.9777 −1.12063
\(867\) 42.9316 1.45803
\(868\) 57.6196 1.95574
\(869\) −23.9110 −0.811124
\(870\) −20.7523 −0.703570
\(871\) −11.3462 −0.384453
\(872\) −81.2642 −2.75195
\(873\) −80.5130 −2.72495
\(874\) −4.62643 −0.156491
\(875\) −15.8145 −0.534627
\(876\) 200.213 6.76457
\(877\) 20.4661 0.691091 0.345545 0.938402i \(-0.387694\pi\)
0.345545 + 0.938402i \(0.387694\pi\)
\(878\) 47.9764 1.61912
\(879\) −22.1205 −0.746105
\(880\) −57.4375 −1.93622
\(881\) 24.0686 0.810890 0.405445 0.914119i \(-0.367117\pi\)
0.405445 + 0.914119i \(0.367117\pi\)
\(882\) 53.5980 1.80474
\(883\) 16.5981 0.558571 0.279286 0.960208i \(-0.409902\pi\)
0.279286 + 0.960208i \(0.409902\pi\)
\(884\) 142.126 4.78021
\(885\) −76.7528 −2.58002
\(886\) 0.209228 0.00702916
\(887\) −42.1194 −1.41423 −0.707115 0.707098i \(-0.750004\pi\)
−0.707115 + 0.707098i \(0.750004\pi\)
\(888\) 17.4536 0.585705
\(889\) 28.3136 0.949608
\(890\) 6.92674 0.232185
\(891\) −20.4975 −0.686693
\(892\) 61.5707 2.06154
\(893\) 13.7790 0.461097
\(894\) −41.7811 −1.39737
\(895\) 30.3593 1.01480
\(896\) −15.4331 −0.515583
\(897\) −13.7558 −0.459293
\(898\) −75.2790 −2.51209
\(899\) −5.02371 −0.167550
\(900\) 207.542 6.91805
\(901\) 14.8580 0.494993
\(902\) 6.13675 0.204331
\(903\) −22.3289 −0.743058
\(904\) −24.8886 −0.827782
\(905\) 39.2253 1.30389
\(906\) 153.381 5.09575
\(907\) −53.9890 −1.79268 −0.896338 0.443371i \(-0.853783\pi\)
−0.896338 + 0.443371i \(0.853783\pi\)
\(908\) 14.5244 0.482010
\(909\) −62.8265 −2.08382
\(910\) 94.5986 3.13591
\(911\) 53.7788 1.78177 0.890885 0.454229i \(-0.150085\pi\)
0.890885 + 0.454229i \(0.150085\pi\)
\(912\) −52.6526 −1.74350
\(913\) −28.6248 −0.947343
\(914\) 0.871782 0.0288360
\(915\) 149.692 4.94866
\(916\) −35.0752 −1.15892
\(917\) −15.5450 −0.513342
\(918\) −134.954 −4.45415
\(919\) 53.2122 1.75531 0.877654 0.479294i \(-0.159107\pi\)
0.877654 + 0.479294i \(0.159107\pi\)
\(920\) 19.4194 0.640237
\(921\) 18.7253 0.617021
\(922\) 90.8203 2.99101
\(923\) 15.6237 0.514261
\(924\) 53.7996 1.76988
\(925\) −6.36937 −0.209424
\(926\) −50.0674 −1.64532
\(927\) 86.7564 2.84945
\(928\) −5.43825 −0.178519
\(929\) −8.01410 −0.262934 −0.131467 0.991321i \(-0.541969\pi\)
−0.131467 + 0.991321i \(0.541969\pi\)
\(930\) 180.280 5.91161
\(931\) 7.44597 0.244032
\(932\) −57.1310 −1.87139
\(933\) 63.4208 2.07630
\(934\) 77.2692 2.52833
\(935\) −40.1601 −1.31338
\(936\) −226.029 −7.38800
\(937\) −41.4302 −1.35346 −0.676732 0.736229i \(-0.736605\pi\)
−0.676732 + 0.736229i \(0.736605\pi\)
\(938\) −9.99858 −0.326465
\(939\) 46.0992 1.50439
\(940\) −102.253 −3.33511
\(941\) −51.0635 −1.66462 −0.832311 0.554309i \(-0.812983\pi\)
−0.832311 + 0.554309i \(0.812983\pi\)
\(942\) 80.9024 2.63594
\(943\) −0.963985 −0.0313917
\(944\) −57.7618 −1.87999
\(945\) −62.6234 −2.03714
\(946\) 20.5033 0.666621
\(947\) −19.7931 −0.643191 −0.321595 0.946877i \(-0.604219\pi\)
−0.321595 + 0.946877i \(0.604219\pi\)
\(948\) 162.659 5.28291
\(949\) 79.5727 2.58304
\(950\) 41.3560 1.34177
\(951\) 28.5621 0.926189
\(952\) 70.8421 2.29601
\(953\) −16.1670 −0.523701 −0.261850 0.965109i \(-0.584333\pi\)
−0.261850 + 0.965109i \(0.584333\pi\)
\(954\) −41.7754 −1.35253
\(955\) 7.76767 0.251356
\(956\) −74.5586 −2.41140
\(957\) −4.69065 −0.151627
\(958\) 22.2719 0.719573
\(959\) −23.7854 −0.768071
\(960\) 25.4349 0.820907
\(961\) 12.6420 0.407806
\(962\) 12.2638 0.395400
\(963\) 17.4529 0.562411
\(964\) −56.9748 −1.83504
\(965\) −35.1054 −1.13008
\(966\) −12.1219 −0.390017
\(967\) −43.9246 −1.41252 −0.706259 0.707953i \(-0.749619\pi\)
−0.706259 + 0.707953i \(0.749619\pi\)
\(968\) 45.6798 1.46820
\(969\) −36.8145 −1.18265
\(970\) 119.057 3.82270
\(971\) 55.8870 1.79350 0.896749 0.442540i \(-0.145922\pi\)
0.896749 + 0.442540i \(0.145922\pi\)
\(972\) 9.61997 0.308561
\(973\) 12.0104 0.385036
\(974\) 109.244 3.50039
\(975\) 122.964 3.93801
\(976\) 112.654 3.60595
\(977\) −53.0278 −1.69651 −0.848255 0.529587i \(-0.822347\pi\)
−0.848255 + 0.529587i \(0.822347\pi\)
\(978\) −32.1621 −1.02843
\(979\) 1.56565 0.0500385
\(980\) −55.2557 −1.76508
\(981\) 74.2251 2.36983
\(982\) 86.9450 2.77453
\(983\) 47.1222 1.50296 0.751482 0.659753i \(-0.229339\pi\)
0.751482 + 0.659753i \(0.229339\pi\)
\(984\) −23.6130 −0.752755
\(985\) 35.3188 1.12535
\(986\) −10.9198 −0.347756
\(987\) 36.1031 1.14917
\(988\) −55.5144 −1.76615
\(989\) −3.22074 −0.102414
\(990\) 112.916 3.58870
\(991\) −52.7595 −1.67596 −0.837980 0.545701i \(-0.816263\pi\)
−0.837980 + 0.545701i \(0.816263\pi\)
\(992\) 47.2432 1.49997
\(993\) −106.716 −3.38653
\(994\) 13.7680 0.436694
\(995\) 1.69285 0.0536668
\(996\) 194.726 6.17012
\(997\) 35.2757 1.11719 0.558597 0.829439i \(-0.311340\pi\)
0.558597 + 0.829439i \(0.311340\pi\)
\(998\) 43.5857 1.37968
\(999\) −8.11850 −0.256858
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 \(a_p\))