Properties

Label 6041.2.a.f.1.18
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25429 q^{2}\) \(-3.03067 q^{3}\) \(+3.08183 q^{4}\) \(+3.72305 q^{5}\) \(+6.83200 q^{6}\) \(+1.00000 q^{7}\) \(-2.43875 q^{8}\) \(+6.18494 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25429 q^{2}\) \(-3.03067 q^{3}\) \(+3.08183 q^{4}\) \(+3.72305 q^{5}\) \(+6.83200 q^{6}\) \(+1.00000 q^{7}\) \(-2.43875 q^{8}\) \(+6.18494 q^{9}\) \(-8.39284 q^{10}\) \(+4.60514 q^{11}\) \(-9.33999 q^{12}\) \(+6.90097 q^{13}\) \(-2.25429 q^{14}\) \(-11.2833 q^{15}\) \(-0.665999 q^{16}\) \(-2.74488 q^{17}\) \(-13.9427 q^{18}\) \(+4.67145 q^{19}\) \(+11.4738 q^{20}\) \(-3.03067 q^{21}\) \(-10.3813 q^{22}\) \(-1.63794 q^{23}\) \(+7.39104 q^{24}\) \(+8.86112 q^{25}\) \(-15.5568 q^{26}\) \(-9.65250 q^{27}\) \(+3.08183 q^{28}\) \(-8.57376 q^{29}\) \(+25.4359 q^{30}\) \(+7.04253 q^{31}\) \(+6.37886 q^{32}\) \(-13.9567 q^{33}\) \(+6.18776 q^{34}\) \(+3.72305 q^{35}\) \(+19.0609 q^{36}\) \(-9.34078 q^{37}\) \(-10.5308 q^{38}\) \(-20.9145 q^{39}\) \(-9.07960 q^{40}\) \(-0.689890 q^{41}\) \(+6.83200 q^{42}\) \(+3.66860 q^{43}\) \(+14.1923 q^{44}\) \(+23.0269 q^{45}\) \(+3.69239 q^{46}\) \(-4.36195 q^{47}\) \(+2.01842 q^{48}\) \(+1.00000 q^{49}\) \(-19.9755 q^{50}\) \(+8.31882 q^{51}\) \(+21.2676 q^{52}\) \(-4.46864 q^{53}\) \(+21.7596 q^{54}\) \(+17.1452 q^{55}\) \(-2.43875 q^{56}\) \(-14.1576 q^{57}\) \(+19.3278 q^{58}\) \(+2.35520 q^{59}\) \(-34.7733 q^{60}\) \(+5.59282 q^{61}\) \(-15.8759 q^{62}\) \(+6.18494 q^{63}\) \(-13.0478 q^{64}\) \(+25.6927 q^{65}\) \(+31.4624 q^{66}\) \(-5.53840 q^{67}\) \(-8.45924 q^{68}\) \(+4.96405 q^{69}\) \(-8.39284 q^{70}\) \(+13.6336 q^{71}\) \(-15.0835 q^{72}\) \(+3.36845 q^{73}\) \(+21.0568 q^{74}\) \(-26.8551 q^{75}\) \(+14.3966 q^{76}\) \(+4.60514 q^{77}\) \(+47.1475 q^{78}\) \(-7.88014 q^{79}\) \(-2.47955 q^{80}\) \(+10.6987 q^{81}\) \(+1.55521 q^{82}\) \(+13.3384 q^{83}\) \(-9.33999 q^{84}\) \(-10.2193 q^{85}\) \(-8.27009 q^{86}\) \(+25.9842 q^{87}\) \(-11.2308 q^{88}\) \(-9.52845 q^{89}\) \(-51.9093 q^{90}\) \(+6.90097 q^{91}\) \(-5.04784 q^{92}\) \(-21.3436 q^{93}\) \(+9.83311 q^{94}\) \(+17.3921 q^{95}\) \(-19.3322 q^{96}\) \(+10.6575 q^{97}\) \(-2.25429 q^{98}\) \(+28.4826 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25429 −1.59402 −0.797012 0.603963i \(-0.793587\pi\)
−0.797012 + 0.603963i \(0.793587\pi\)
\(3\) −3.03067 −1.74976 −0.874878 0.484343i \(-0.839059\pi\)
−0.874878 + 0.484343i \(0.839059\pi\)
\(4\) 3.08183 1.54091
\(5\) 3.72305 1.66500 0.832500 0.554025i \(-0.186909\pi\)
0.832500 + 0.554025i \(0.186909\pi\)
\(6\) 6.83200 2.78915
\(7\) 1.00000 0.377964
\(8\) −2.43875 −0.862229
\(9\) 6.18494 2.06165
\(10\) −8.39284 −2.65405
\(11\) 4.60514 1.38850 0.694251 0.719733i \(-0.255736\pi\)
0.694251 + 0.719733i \(0.255736\pi\)
\(12\) −9.33999 −2.69622
\(13\) 6.90097 1.91399 0.956993 0.290112i \(-0.0936927\pi\)
0.956993 + 0.290112i \(0.0936927\pi\)
\(14\) −2.25429 −0.602485
\(15\) −11.2833 −2.91334
\(16\) −0.665999 −0.166500
\(17\) −2.74488 −0.665731 −0.332866 0.942974i \(-0.608016\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(18\) −13.9427 −3.28632
\(19\) 4.67145 1.07170 0.535852 0.844312i \(-0.319990\pi\)
0.535852 + 0.844312i \(0.319990\pi\)
\(20\) 11.4738 2.56562
\(21\) −3.03067 −0.661346
\(22\) −10.3813 −2.21331
\(23\) −1.63794 −0.341534 −0.170767 0.985311i \(-0.554625\pi\)
−0.170767 + 0.985311i \(0.554625\pi\)
\(24\) 7.39104 1.50869
\(25\) 8.86112 1.77222
\(26\) −15.5568 −3.05094
\(27\) −9.65250 −1.85763
\(28\) 3.08183 0.582410
\(29\) −8.57376 −1.59211 −0.796054 0.605226i \(-0.793083\pi\)
−0.796054 + 0.605226i \(0.793083\pi\)
\(30\) 25.4359 4.64394
\(31\) 7.04253 1.26488 0.632438 0.774611i \(-0.282054\pi\)
0.632438 + 0.774611i \(0.282054\pi\)
\(32\) 6.37886 1.12763
\(33\) −13.9567 −2.42954
\(34\) 6.18776 1.06119
\(35\) 3.72305 0.629311
\(36\) 19.0609 3.17682
\(37\) −9.34078 −1.53562 −0.767808 0.640680i \(-0.778652\pi\)
−0.767808 + 0.640680i \(0.778652\pi\)
\(38\) −10.5308 −1.70832
\(39\) −20.9145 −3.34901
\(40\) −9.07960 −1.43561
\(41\) −0.689890 −0.107743 −0.0538714 0.998548i \(-0.517156\pi\)
−0.0538714 + 0.998548i \(0.517156\pi\)
\(42\) 6.83200 1.05420
\(43\) 3.66860 0.559457 0.279728 0.960079i \(-0.409756\pi\)
0.279728 + 0.960079i \(0.409756\pi\)
\(44\) 14.1923 2.13956
\(45\) 23.0269 3.43264
\(46\) 3.69239 0.544413
\(47\) −4.36195 −0.636256 −0.318128 0.948048i \(-0.603054\pi\)
−0.318128 + 0.948048i \(0.603054\pi\)
\(48\) 2.01842 0.291334
\(49\) 1.00000 0.142857
\(50\) −19.9755 −2.82497
\(51\) 8.31882 1.16487
\(52\) 21.2676 2.94929
\(53\) −4.46864 −0.613815 −0.306907 0.951739i \(-0.599294\pi\)
−0.306907 + 0.951739i \(0.599294\pi\)
\(54\) 21.7596 2.96110
\(55\) 17.1452 2.31186
\(56\) −2.43875 −0.325892
\(57\) −14.1576 −1.87522
\(58\) 19.3278 2.53786
\(59\) 2.35520 0.306621 0.153310 0.988178i \(-0.451007\pi\)
0.153310 + 0.988178i \(0.451007\pi\)
\(60\) −34.7733 −4.48921
\(61\) 5.59282 0.716088 0.358044 0.933705i \(-0.383444\pi\)
0.358044 + 0.933705i \(0.383444\pi\)
\(62\) −15.8759 −2.01624
\(63\) 6.18494 0.779230
\(64\) −13.0478 −1.63098
\(65\) 25.6927 3.18678
\(66\) 31.4624 3.87275
\(67\) −5.53840 −0.676623 −0.338312 0.941034i \(-0.609856\pi\)
−0.338312 + 0.941034i \(0.609856\pi\)
\(68\) −8.45924 −1.02583
\(69\) 4.96405 0.597601
\(70\) −8.39284 −1.00314
\(71\) 13.6336 1.61801 0.809005 0.587801i \(-0.200006\pi\)
0.809005 + 0.587801i \(0.200006\pi\)
\(72\) −15.0835 −1.77761
\(73\) 3.36845 0.394248 0.197124 0.980379i \(-0.436840\pi\)
0.197124 + 0.980379i \(0.436840\pi\)
\(74\) 21.0568 2.44781
\(75\) −26.8551 −3.10096
\(76\) 14.3966 1.65140
\(77\) 4.60514 0.524805
\(78\) 47.1475 5.33840
\(79\) −7.88014 −0.886585 −0.443293 0.896377i \(-0.646190\pi\)
−0.443293 + 0.896377i \(0.646190\pi\)
\(80\) −2.47955 −0.277222
\(81\) 10.6987 1.18874
\(82\) 1.55521 0.171745
\(83\) 13.3384 1.46408 0.732039 0.681263i \(-0.238569\pi\)
0.732039 + 0.681263i \(0.238569\pi\)
\(84\) −9.33999 −1.01908
\(85\) −10.2193 −1.10844
\(86\) −8.27009 −0.891787
\(87\) 25.9842 2.78580
\(88\) −11.2308 −1.19721
\(89\) −9.52845 −1.01001 −0.505007 0.863115i \(-0.668510\pi\)
−0.505007 + 0.863115i \(0.668510\pi\)
\(90\) −51.9093 −5.47172
\(91\) 6.90097 0.723418
\(92\) −5.04784 −0.526274
\(93\) −21.3436 −2.21322
\(94\) 9.83311 1.01421
\(95\) 17.3921 1.78439
\(96\) −19.3322 −1.97308
\(97\) 10.6575 1.08211 0.541054 0.840988i \(-0.318026\pi\)
0.541054 + 0.840988i \(0.318026\pi\)
\(98\) −2.25429 −0.227718
\(99\) 28.4826 2.86260
\(100\) 27.3084 2.73084
\(101\) 12.4116 1.23500 0.617500 0.786571i \(-0.288146\pi\)
0.617500 + 0.786571i \(0.288146\pi\)
\(102\) −18.7530 −1.85683
\(103\) 10.5713 1.04162 0.520809 0.853673i \(-0.325630\pi\)
0.520809 + 0.853673i \(0.325630\pi\)
\(104\) −16.8298 −1.65029
\(105\) −11.2833 −1.10114
\(106\) 10.0736 0.978436
\(107\) −1.99044 −0.192423 −0.0962115 0.995361i \(-0.530673\pi\)
−0.0962115 + 0.995361i \(0.530673\pi\)
\(108\) −29.7473 −2.86244
\(109\) −12.2011 −1.16866 −0.584328 0.811517i \(-0.698642\pi\)
−0.584328 + 0.811517i \(0.698642\pi\)
\(110\) −38.6502 −3.68516
\(111\) 28.3088 2.68695
\(112\) −0.665999 −0.0629310
\(113\) −1.01925 −0.0958833 −0.0479416 0.998850i \(-0.515266\pi\)
−0.0479416 + 0.998850i \(0.515266\pi\)
\(114\) 31.9154 2.98915
\(115\) −6.09813 −0.568654
\(116\) −26.4228 −2.45330
\(117\) 42.6821 3.94596
\(118\) −5.30930 −0.488761
\(119\) −2.74488 −0.251623
\(120\) 27.5172 2.51197
\(121\) 10.2073 0.927940
\(122\) −12.6078 −1.14146
\(123\) 2.09083 0.188524
\(124\) 21.7039 1.94906
\(125\) 14.3751 1.28575
\(126\) −13.9427 −1.24211
\(127\) 4.26430 0.378395 0.189198 0.981939i \(-0.439411\pi\)
0.189198 + 0.981939i \(0.439411\pi\)
\(128\) 16.6558 1.47218
\(129\) −11.1183 −0.978913
\(130\) −57.9188 −5.07981
\(131\) 10.0596 0.878913 0.439457 0.898264i \(-0.355171\pi\)
0.439457 + 0.898264i \(0.355171\pi\)
\(132\) −43.0120 −3.74371
\(133\) 4.67145 0.405066
\(134\) 12.4852 1.07855
\(135\) −35.9368 −3.09295
\(136\) 6.69408 0.574013
\(137\) −0.638694 −0.0545673 −0.0272836 0.999628i \(-0.508686\pi\)
−0.0272836 + 0.999628i \(0.508686\pi\)
\(138\) −11.1904 −0.952591
\(139\) 8.55547 0.725666 0.362833 0.931854i \(-0.381810\pi\)
0.362833 + 0.931854i \(0.381810\pi\)
\(140\) 11.4738 0.969713
\(141\) 13.2196 1.11329
\(142\) −30.7341 −2.57915
\(143\) 31.7800 2.65757
\(144\) −4.11916 −0.343264
\(145\) −31.9206 −2.65086
\(146\) −7.59347 −0.628440
\(147\) −3.03067 −0.249965
\(148\) −28.7867 −2.36625
\(149\) 14.6962 1.20396 0.601979 0.798512i \(-0.294379\pi\)
0.601979 + 0.798512i \(0.294379\pi\)
\(150\) 60.5392 4.94300
\(151\) 16.0298 1.30449 0.652244 0.758009i \(-0.273828\pi\)
0.652244 + 0.758009i \(0.273828\pi\)
\(152\) −11.3925 −0.924055
\(153\) −16.9769 −1.37250
\(154\) −10.3813 −0.836552
\(155\) 26.2197 2.10602
\(156\) −64.4550 −5.16053
\(157\) −21.9839 −1.75451 −0.877254 0.480027i \(-0.840627\pi\)
−0.877254 + 0.480027i \(0.840627\pi\)
\(158\) 17.7641 1.41324
\(159\) 13.5430 1.07403
\(160\) 23.7488 1.87751
\(161\) −1.63794 −0.129088
\(162\) −24.1180 −1.89489
\(163\) 6.65472 0.521238 0.260619 0.965442i \(-0.416073\pi\)
0.260619 + 0.965442i \(0.416073\pi\)
\(164\) −2.12612 −0.166022
\(165\) −51.9614 −4.04519
\(166\) −30.0686 −2.33378
\(167\) −24.4448 −1.89160 −0.945799 0.324753i \(-0.894719\pi\)
−0.945799 + 0.324753i \(0.894719\pi\)
\(168\) 7.39104 0.570231
\(169\) 34.6234 2.66334
\(170\) 23.0373 1.76688
\(171\) 28.8927 2.20948
\(172\) 11.3060 0.862074
\(173\) −24.0224 −1.82639 −0.913193 0.407527i \(-0.866391\pi\)
−0.913193 + 0.407527i \(0.866391\pi\)
\(174\) −58.5760 −4.44063
\(175\) 8.86112 0.669837
\(176\) −3.06702 −0.231185
\(177\) −7.13783 −0.536512
\(178\) 21.4799 1.60999
\(179\) 7.27705 0.543912 0.271956 0.962310i \(-0.412329\pi\)
0.271956 + 0.962310i \(0.412329\pi\)
\(180\) 70.9648 5.28940
\(181\) 17.6274 1.31024 0.655119 0.755526i \(-0.272619\pi\)
0.655119 + 0.755526i \(0.272619\pi\)
\(182\) −15.5568 −1.15315
\(183\) −16.9500 −1.25298
\(184\) 3.99453 0.294480
\(185\) −34.7762 −2.55680
\(186\) 48.1146 3.52793
\(187\) −12.6406 −0.924370
\(188\) −13.4428 −0.980416
\(189\) −9.65250 −0.702116
\(190\) −39.2068 −2.84436
\(191\) −15.5032 −1.12177 −0.560885 0.827894i \(-0.689539\pi\)
−0.560885 + 0.827894i \(0.689539\pi\)
\(192\) 39.5435 2.85381
\(193\) 3.94362 0.283868 0.141934 0.989876i \(-0.454668\pi\)
0.141934 + 0.989876i \(0.454668\pi\)
\(194\) −24.0252 −1.72491
\(195\) −77.8659 −5.57610
\(196\) 3.08183 0.220130
\(197\) −12.2876 −0.875458 −0.437729 0.899107i \(-0.644217\pi\)
−0.437729 + 0.899107i \(0.644217\pi\)
\(198\) −64.2079 −4.56306
\(199\) −10.6334 −0.753781 −0.376891 0.926258i \(-0.623007\pi\)
−0.376891 + 0.926258i \(0.623007\pi\)
\(200\) −21.6101 −1.52806
\(201\) 16.7850 1.18393
\(202\) −27.9793 −1.96862
\(203\) −8.57376 −0.601760
\(204\) 25.6372 1.79496
\(205\) −2.56850 −0.179392
\(206\) −23.8307 −1.66036
\(207\) −10.1306 −0.704123
\(208\) −4.59604 −0.318678
\(209\) 21.5127 1.48807
\(210\) 25.4359 1.75524
\(211\) 22.9316 1.57867 0.789337 0.613960i \(-0.210424\pi\)
0.789337 + 0.613960i \(0.210424\pi\)
\(212\) −13.7716 −0.945836
\(213\) −41.3189 −2.83112
\(214\) 4.48703 0.306727
\(215\) 13.6584 0.931495
\(216\) 23.5401 1.60170
\(217\) 7.04253 0.478078
\(218\) 27.5049 1.86287
\(219\) −10.2087 −0.689837
\(220\) 52.8385 3.56237
\(221\) −18.9423 −1.27420
\(222\) −63.8163 −4.28307
\(223\) 5.08809 0.340723 0.170362 0.985382i \(-0.445506\pi\)
0.170362 + 0.985382i \(0.445506\pi\)
\(224\) 6.37886 0.426205
\(225\) 54.8055 3.65370
\(226\) 2.29769 0.152840
\(227\) 8.36899 0.555470 0.277735 0.960658i \(-0.410416\pi\)
0.277735 + 0.960658i \(0.410416\pi\)
\(228\) −43.6313 −2.88956
\(229\) −25.7656 −1.70264 −0.851320 0.524646i \(-0.824198\pi\)
−0.851320 + 0.524646i \(0.824198\pi\)
\(230\) 13.7470 0.906448
\(231\) −13.9567 −0.918281
\(232\) 20.9093 1.37276
\(233\) −3.54921 −0.232517 −0.116258 0.993219i \(-0.537090\pi\)
−0.116258 + 0.993219i \(0.537090\pi\)
\(234\) −96.2179 −6.28996
\(235\) −16.2398 −1.05937
\(236\) 7.25832 0.472476
\(237\) 23.8821 1.55131
\(238\) 6.18776 0.401093
\(239\) 3.40779 0.220431 0.110216 0.993908i \(-0.464846\pi\)
0.110216 + 0.993908i \(0.464846\pi\)
\(240\) 7.51468 0.485071
\(241\) −13.7734 −0.887223 −0.443611 0.896219i \(-0.646303\pi\)
−0.443611 + 0.896219i \(0.646303\pi\)
\(242\) −23.0103 −1.47916
\(243\) −3.46668 −0.222387
\(244\) 17.2361 1.10343
\(245\) 3.72305 0.237857
\(246\) −4.71333 −0.300511
\(247\) 32.2376 2.05123
\(248\) −17.1750 −1.09061
\(249\) −40.4242 −2.56178
\(250\) −32.4057 −2.04952
\(251\) 9.39040 0.592717 0.296358 0.955077i \(-0.404228\pi\)
0.296358 + 0.955077i \(0.404228\pi\)
\(252\) 19.0609 1.20073
\(253\) −7.54294 −0.474221
\(254\) −9.61297 −0.603171
\(255\) 30.9714 1.93950
\(256\) −11.4515 −0.715716
\(257\) −11.2074 −0.699100 −0.349550 0.936918i \(-0.613666\pi\)
−0.349550 + 0.936918i \(0.613666\pi\)
\(258\) 25.0639 1.56041
\(259\) −9.34078 −0.580408
\(260\) 79.1804 4.91056
\(261\) −53.0282 −3.28237
\(262\) −22.6773 −1.40101
\(263\) −16.5851 −1.02268 −0.511340 0.859379i \(-0.670851\pi\)
−0.511340 + 0.859379i \(0.670851\pi\)
\(264\) 34.0368 2.09482
\(265\) −16.6370 −1.02200
\(266\) −10.5308 −0.645686
\(267\) 28.8776 1.76728
\(268\) −17.0684 −1.04262
\(269\) −7.57053 −0.461584 −0.230792 0.973003i \(-0.574132\pi\)
−0.230792 + 0.973003i \(0.574132\pi\)
\(270\) 81.0119 4.93023
\(271\) −9.05037 −0.549771 −0.274885 0.961477i \(-0.588640\pi\)
−0.274885 + 0.961477i \(0.588640\pi\)
\(272\) 1.82809 0.110844
\(273\) −20.9145 −1.26581
\(274\) 1.43980 0.0869815
\(275\) 40.8067 2.46074
\(276\) 15.2983 0.920851
\(277\) −11.9485 −0.717916 −0.358958 0.933354i \(-0.616868\pi\)
−0.358958 + 0.933354i \(0.616868\pi\)
\(278\) −19.2865 −1.15673
\(279\) 43.5576 2.60773
\(280\) −9.07960 −0.542610
\(281\) 17.3429 1.03459 0.517295 0.855807i \(-0.326939\pi\)
0.517295 + 0.855807i \(0.326939\pi\)
\(282\) −29.8009 −1.77462
\(283\) 7.10486 0.422340 0.211170 0.977449i \(-0.432273\pi\)
0.211170 + 0.977449i \(0.432273\pi\)
\(284\) 42.0164 2.49321
\(285\) −52.7096 −3.12224
\(286\) −71.6413 −4.23624
\(287\) −0.689890 −0.0407229
\(288\) 39.4529 2.32478
\(289\) −9.46563 −0.556802
\(290\) 71.9582 4.22553
\(291\) −32.2994 −1.89343
\(292\) 10.3810 0.607501
\(293\) 15.2871 0.893080 0.446540 0.894764i \(-0.352656\pi\)
0.446540 + 0.894764i \(0.352656\pi\)
\(294\) 6.83200 0.398451
\(295\) 8.76853 0.510524
\(296\) 22.7798 1.32405
\(297\) −44.4512 −2.57932
\(298\) −33.1294 −1.91914
\(299\) −11.3034 −0.653691
\(300\) −82.7627 −4.77831
\(301\) 3.66860 0.211455
\(302\) −36.1359 −2.07939
\(303\) −37.6154 −2.16095
\(304\) −3.11118 −0.178439
\(305\) 20.8224 1.19229
\(306\) 38.2709 2.18780
\(307\) −28.3238 −1.61652 −0.808262 0.588823i \(-0.799591\pi\)
−0.808262 + 0.588823i \(0.799591\pi\)
\(308\) 14.1923 0.808679
\(309\) −32.0380 −1.82258
\(310\) −59.1068 −3.35704
\(311\) 21.5050 1.21944 0.609718 0.792618i \(-0.291283\pi\)
0.609718 + 0.792618i \(0.291283\pi\)
\(312\) 51.0054 2.88761
\(313\) 20.3159 1.14833 0.574163 0.818741i \(-0.305328\pi\)
0.574163 + 0.818741i \(0.305328\pi\)
\(314\) 49.5581 2.79673
\(315\) 23.0269 1.29742
\(316\) −24.2852 −1.36615
\(317\) 19.3504 1.08683 0.543413 0.839465i \(-0.317132\pi\)
0.543413 + 0.839465i \(0.317132\pi\)
\(318\) −30.5298 −1.71202
\(319\) −39.4834 −2.21065
\(320\) −48.5776 −2.71557
\(321\) 6.03236 0.336693
\(322\) 3.69239 0.205769
\(323\) −12.8226 −0.713467
\(324\) 32.9715 1.83175
\(325\) 61.1503 3.39201
\(326\) −15.0017 −0.830865
\(327\) 36.9776 2.04486
\(328\) 1.68247 0.0928989
\(329\) −4.36195 −0.240482
\(330\) 117.136 6.44812
\(331\) −11.3451 −0.623584 −0.311792 0.950150i \(-0.600929\pi\)
−0.311792 + 0.950150i \(0.600929\pi\)
\(332\) 41.1066 2.25602
\(333\) −57.7722 −3.16590
\(334\) 55.1058 3.01525
\(335\) −20.6197 −1.12658
\(336\) 2.01842 0.110114
\(337\) 2.99034 0.162894 0.0814472 0.996678i \(-0.474046\pi\)
0.0814472 + 0.996678i \(0.474046\pi\)
\(338\) −78.0512 −4.24543
\(339\) 3.08902 0.167772
\(340\) −31.4942 −1.70801
\(341\) 32.4319 1.75628
\(342\) −65.1325 −3.52196
\(343\) 1.00000 0.0539949
\(344\) −8.94681 −0.482379
\(345\) 18.4814 0.995006
\(346\) 54.1534 2.91130
\(347\) 29.7605 1.59763 0.798814 0.601578i \(-0.205461\pi\)
0.798814 + 0.601578i \(0.205461\pi\)
\(348\) 80.0789 4.29268
\(349\) 21.0109 1.12469 0.562344 0.826903i \(-0.309900\pi\)
0.562344 + 0.826903i \(0.309900\pi\)
\(350\) −19.9755 −1.06774
\(351\) −66.6117 −3.55547
\(352\) 29.3756 1.56572
\(353\) 9.94228 0.529174 0.264587 0.964362i \(-0.414764\pi\)
0.264587 + 0.964362i \(0.414764\pi\)
\(354\) 16.0907 0.855213
\(355\) 50.7586 2.69399
\(356\) −29.3650 −1.55634
\(357\) 8.31882 0.440279
\(358\) −16.4046 −0.867009
\(359\) 26.2079 1.38320 0.691600 0.722281i \(-0.256906\pi\)
0.691600 + 0.722281i \(0.256906\pi\)
\(360\) −56.1568 −2.95972
\(361\) 2.82248 0.148551
\(362\) −39.7374 −2.08855
\(363\) −30.9351 −1.62367
\(364\) 21.2676 1.11472
\(365\) 12.5409 0.656422
\(366\) 38.2102 1.99728
\(367\) 14.9036 0.777964 0.388982 0.921245i \(-0.372827\pi\)
0.388982 + 0.921245i \(0.372827\pi\)
\(368\) 1.09087 0.0568653
\(369\) −4.26693 −0.222128
\(370\) 78.3957 4.07560
\(371\) −4.46864 −0.232000
\(372\) −65.7771 −3.41039
\(373\) 23.8075 1.23271 0.616353 0.787470i \(-0.288609\pi\)
0.616353 + 0.787470i \(0.288609\pi\)
\(374\) 28.4955 1.47347
\(375\) −43.5662 −2.24975
\(376\) 10.6377 0.548598
\(377\) −59.1673 −3.04727
\(378\) 21.7596 1.11919
\(379\) −12.3314 −0.633421 −0.316711 0.948522i \(-0.602578\pi\)
−0.316711 + 0.948522i \(0.602578\pi\)
\(380\) 53.5993 2.74959
\(381\) −12.9237 −0.662100
\(382\) 34.9487 1.78813
\(383\) −27.5813 −1.40934 −0.704670 0.709535i \(-0.748905\pi\)
−0.704670 + 0.709535i \(0.748905\pi\)
\(384\) −50.4783 −2.57596
\(385\) 17.1452 0.873800
\(386\) −8.89007 −0.452493
\(387\) 22.6901 1.15340
\(388\) 32.8446 1.66743
\(389\) 26.7330 1.35541 0.677707 0.735332i \(-0.262974\pi\)
0.677707 + 0.735332i \(0.262974\pi\)
\(390\) 175.532 8.88843
\(391\) 4.49595 0.227370
\(392\) −2.43875 −0.123176
\(393\) −30.4874 −1.53788
\(394\) 27.6999 1.39550
\(395\) −29.3382 −1.47616
\(396\) 87.7783 4.41102
\(397\) 28.1100 1.41080 0.705400 0.708809i \(-0.250767\pi\)
0.705400 + 0.708809i \(0.250767\pi\)
\(398\) 23.9708 1.20155
\(399\) −14.1576 −0.708768
\(400\) −5.90149 −0.295075
\(401\) −17.1713 −0.857493 −0.428747 0.903425i \(-0.641045\pi\)
−0.428747 + 0.903425i \(0.641045\pi\)
\(402\) −37.8384 −1.88721
\(403\) 48.6003 2.42095
\(404\) 38.2504 1.90303
\(405\) 39.8318 1.97926
\(406\) 19.3278 0.959220
\(407\) −43.0156 −2.13221
\(408\) −20.2875 −1.00438
\(409\) −7.38916 −0.365371 −0.182685 0.983171i \(-0.558479\pi\)
−0.182685 + 0.983171i \(0.558479\pi\)
\(410\) 5.79014 0.285955
\(411\) 1.93567 0.0954794
\(412\) 32.5788 1.60504
\(413\) 2.35520 0.115892
\(414\) 22.8372 1.12239
\(415\) 49.6595 2.43769
\(416\) 44.0203 2.15827
\(417\) −25.9288 −1.26974
\(418\) −48.4959 −2.37201
\(419\) 36.9104 1.80319 0.901595 0.432582i \(-0.142397\pi\)
0.901595 + 0.432582i \(0.142397\pi\)
\(420\) −34.7733 −1.69676
\(421\) −5.91626 −0.288341 −0.144170 0.989553i \(-0.546051\pi\)
−0.144170 + 0.989553i \(0.546051\pi\)
\(422\) −51.6944 −2.51645
\(423\) −26.9784 −1.31174
\(424\) 10.8979 0.529249
\(425\) −24.3227 −1.17982
\(426\) 93.1448 4.51288
\(427\) 5.59282 0.270656
\(428\) −6.13418 −0.296507
\(429\) −96.3145 −4.65011
\(430\) −30.7900 −1.48483
\(431\) −35.5724 −1.71346 −0.856731 0.515763i \(-0.827508\pi\)
−0.856731 + 0.515763i \(0.827508\pi\)
\(432\) 6.42856 0.309294
\(433\) −27.3652 −1.31509 −0.657543 0.753417i \(-0.728404\pi\)
−0.657543 + 0.753417i \(0.728404\pi\)
\(434\) −15.8759 −0.762068
\(435\) 96.7406 4.63836
\(436\) −37.6018 −1.80080
\(437\) −7.65156 −0.366024
\(438\) 23.0133 1.09962
\(439\) −12.5989 −0.601313 −0.300657 0.953732i \(-0.597206\pi\)
−0.300657 + 0.953732i \(0.597206\pi\)
\(440\) −41.8128 −1.99335
\(441\) 6.18494 0.294521
\(442\) 42.7015 2.03111
\(443\) −31.5810 −1.50046 −0.750229 0.661178i \(-0.770057\pi\)
−0.750229 + 0.661178i \(0.770057\pi\)
\(444\) 87.2428 4.14036
\(445\) −35.4749 −1.68167
\(446\) −11.4700 −0.543121
\(447\) −44.5392 −2.10663
\(448\) −13.0478 −0.616451
\(449\) −20.8281 −0.982940 −0.491470 0.870895i \(-0.663540\pi\)
−0.491470 + 0.870895i \(0.663540\pi\)
\(450\) −123.548 −5.82409
\(451\) −3.17704 −0.149601
\(452\) −3.14116 −0.147748
\(453\) −48.5811 −2.28254
\(454\) −18.8661 −0.885432
\(455\) 25.6927 1.20449
\(456\) 34.5269 1.61687
\(457\) 18.3454 0.858159 0.429080 0.903267i \(-0.358838\pi\)
0.429080 + 0.903267i \(0.358838\pi\)
\(458\) 58.0832 2.71405
\(459\) 26.4950 1.23668
\(460\) −18.7934 −0.876246
\(461\) 26.3289 1.22626 0.613129 0.789983i \(-0.289911\pi\)
0.613129 + 0.789983i \(0.289911\pi\)
\(462\) 31.4624 1.46376
\(463\) −24.1152 −1.12073 −0.560363 0.828247i \(-0.689338\pi\)
−0.560363 + 0.828247i \(0.689338\pi\)
\(464\) 5.71012 0.265085
\(465\) −79.4632 −3.68502
\(466\) 8.00095 0.370637
\(467\) −8.90721 −0.412177 −0.206088 0.978533i \(-0.566073\pi\)
−0.206088 + 0.978533i \(0.566073\pi\)
\(468\) 131.539 6.08039
\(469\) −5.53840 −0.255739
\(470\) 36.6092 1.68866
\(471\) 66.6259 3.06996
\(472\) −5.74375 −0.264377
\(473\) 16.8944 0.776807
\(474\) −53.8372 −2.47282
\(475\) 41.3943 1.89930
\(476\) −8.45924 −0.387729
\(477\) −27.6383 −1.26547
\(478\) −7.68214 −0.351373
\(479\) −37.8103 −1.72760 −0.863799 0.503837i \(-0.831921\pi\)
−0.863799 + 0.503837i \(0.831921\pi\)
\(480\) −71.9748 −3.28518
\(481\) −64.4605 −2.93914
\(482\) 31.0493 1.41425
\(483\) 4.96405 0.225872
\(484\) 31.4573 1.42988
\(485\) 39.6785 1.80171
\(486\) 7.81490 0.354491
\(487\) 14.1828 0.642682 0.321341 0.946964i \(-0.395866\pi\)
0.321341 + 0.946964i \(0.395866\pi\)
\(488\) −13.6395 −0.617431
\(489\) −20.1682 −0.912039
\(490\) −8.39284 −0.379150
\(491\) 4.26214 0.192348 0.0961739 0.995365i \(-0.469339\pi\)
0.0961739 + 0.995365i \(0.469339\pi\)
\(492\) 6.44357 0.290498
\(493\) 23.5340 1.05992
\(494\) −72.6728 −3.26971
\(495\) 106.042 4.76623
\(496\) −4.69032 −0.210601
\(497\) 13.6336 0.611551
\(498\) 91.1279 4.08354
\(499\) 38.3623 1.71733 0.858667 0.512535i \(-0.171293\pi\)
0.858667 + 0.512535i \(0.171293\pi\)
\(500\) 44.3017 1.98123
\(501\) 74.0841 3.30984
\(502\) −21.1687 −0.944805
\(503\) −19.9391 −0.889040 −0.444520 0.895769i \(-0.646626\pi\)
−0.444520 + 0.895769i \(0.646626\pi\)
\(504\) −15.0835 −0.671874
\(505\) 46.2090 2.05627
\(506\) 17.0040 0.755919
\(507\) −104.932 −4.66020
\(508\) 13.1418 0.583074
\(509\) 11.7075 0.518928 0.259464 0.965753i \(-0.416454\pi\)
0.259464 + 0.965753i \(0.416454\pi\)
\(510\) −69.8185 −3.09162
\(511\) 3.36845 0.149012
\(512\) −7.49672 −0.331311
\(513\) −45.0912 −1.99083
\(514\) 25.2648 1.11438
\(515\) 39.3574 1.73429
\(516\) −34.2647 −1.50842
\(517\) −20.0874 −0.883444
\(518\) 21.0568 0.925184
\(519\) 72.8038 3.19573
\(520\) −62.6580 −2.74774
\(521\) 21.9536 0.961805 0.480903 0.876774i \(-0.340309\pi\)
0.480903 + 0.876774i \(0.340309\pi\)
\(522\) 119.541 5.23217
\(523\) 21.2931 0.931081 0.465540 0.885027i \(-0.345860\pi\)
0.465540 + 0.885027i \(0.345860\pi\)
\(524\) 31.0020 1.35433
\(525\) −26.8551 −1.17205
\(526\) 37.3876 1.63018
\(527\) −19.3309 −0.842067
\(528\) 9.29512 0.404518
\(529\) −20.3172 −0.883355
\(530\) 37.5046 1.62910
\(531\) 14.5668 0.632144
\(532\) 14.3966 0.624172
\(533\) −4.76091 −0.206218
\(534\) −65.0984 −2.81708
\(535\) −7.41050 −0.320384
\(536\) 13.5068 0.583404
\(537\) −22.0543 −0.951714
\(538\) 17.0662 0.735775
\(539\) 4.60514 0.198358
\(540\) −110.751 −4.76596
\(541\) 37.4091 1.60834 0.804171 0.594398i \(-0.202609\pi\)
0.804171 + 0.594398i \(0.202609\pi\)
\(542\) 20.4022 0.876348
\(543\) −53.4229 −2.29260
\(544\) −17.5092 −0.750701
\(545\) −45.4254 −1.94581
\(546\) 47.1475 2.01773
\(547\) 24.5552 1.04990 0.524952 0.851132i \(-0.324083\pi\)
0.524952 + 0.851132i \(0.324083\pi\)
\(548\) −1.96834 −0.0840834
\(549\) 34.5913 1.47632
\(550\) −91.9902 −3.92247
\(551\) −40.0519 −1.70627
\(552\) −12.1061 −0.515269
\(553\) −7.88014 −0.335098
\(554\) 26.9354 1.14438
\(555\) 105.395 4.47378
\(556\) 26.3665 1.11819
\(557\) 21.0497 0.891904 0.445952 0.895057i \(-0.352865\pi\)
0.445952 + 0.895057i \(0.352865\pi\)
\(558\) −98.1916 −4.15678
\(559\) 25.3169 1.07079
\(560\) −2.47955 −0.104780
\(561\) 38.3093 1.61742
\(562\) −39.0959 −1.64916
\(563\) −36.1074 −1.52175 −0.760873 0.648901i \(-0.775229\pi\)
−0.760873 + 0.648901i \(0.775229\pi\)
\(564\) 40.7406 1.71549
\(565\) −3.79473 −0.159646
\(566\) −16.0164 −0.673221
\(567\) 10.6987 0.449303
\(568\) −33.2490 −1.39510
\(569\) −20.8710 −0.874956 −0.437478 0.899229i \(-0.644128\pi\)
−0.437478 + 0.899229i \(0.644128\pi\)
\(570\) 118.823 4.97693
\(571\) 21.0708 0.881786 0.440893 0.897560i \(-0.354662\pi\)
0.440893 + 0.897560i \(0.354662\pi\)
\(572\) 97.9403 4.09509
\(573\) 46.9850 1.96283
\(574\) 1.55521 0.0649133
\(575\) −14.5140 −0.605274
\(576\) −80.6999 −3.36250
\(577\) −9.03741 −0.376232 −0.188116 0.982147i \(-0.560238\pi\)
−0.188116 + 0.982147i \(0.560238\pi\)
\(578\) 21.3383 0.887556
\(579\) −11.9518 −0.496700
\(580\) −98.3736 −4.08474
\(581\) 13.3384 0.553369
\(582\) 72.8123 3.01817
\(583\) −20.5787 −0.852284
\(584\) −8.21482 −0.339932
\(585\) 158.908 6.57003
\(586\) −34.4615 −1.42359
\(587\) 11.2515 0.464397 0.232199 0.972668i \(-0.425408\pi\)
0.232199 + 0.972668i \(0.425408\pi\)
\(588\) −9.33999 −0.385175
\(589\) 32.8988 1.35557
\(590\) −19.7668 −0.813787
\(591\) 37.2397 1.53184
\(592\) 6.22095 0.255679
\(593\) −2.67163 −0.109711 −0.0548554 0.998494i \(-0.517470\pi\)
−0.0548554 + 0.998494i \(0.517470\pi\)
\(594\) 100.206 4.11150
\(595\) −10.2193 −0.418952
\(596\) 45.2911 1.85519
\(597\) 32.2263 1.31893
\(598\) 25.4811 1.04200
\(599\) 4.78630 0.195563 0.0977815 0.995208i \(-0.468825\pi\)
0.0977815 + 0.995208i \(0.468825\pi\)
\(600\) 65.4929 2.67374
\(601\) 35.2968 1.43978 0.719892 0.694086i \(-0.244191\pi\)
0.719892 + 0.694086i \(0.244191\pi\)
\(602\) −8.27009 −0.337064
\(603\) −34.2547 −1.39496
\(604\) 49.4011 2.01010
\(605\) 38.0025 1.54502
\(606\) 84.7961 3.44460
\(607\) 26.6218 1.08054 0.540272 0.841490i \(-0.318321\pi\)
0.540272 + 0.841490i \(0.318321\pi\)
\(608\) 29.7985 1.20849
\(609\) 25.9842 1.05293
\(610\) −46.9397 −1.90053
\(611\) −30.1017 −1.21779
\(612\) −52.3199 −2.11491
\(613\) 39.2277 1.58439 0.792195 0.610268i \(-0.208938\pi\)
0.792195 + 0.610268i \(0.208938\pi\)
\(614\) 63.8500 2.57678
\(615\) 7.78426 0.313892
\(616\) −11.2308 −0.452502
\(617\) −28.0508 −1.12928 −0.564641 0.825337i \(-0.690985\pi\)
−0.564641 + 0.825337i \(0.690985\pi\)
\(618\) 72.2230 2.90523
\(619\) −27.9342 −1.12277 −0.561386 0.827554i \(-0.689732\pi\)
−0.561386 + 0.827554i \(0.689732\pi\)
\(620\) 80.8046 3.24519
\(621\) 15.8102 0.634442
\(622\) −48.4785 −1.94381
\(623\) −9.52845 −0.381749
\(624\) 13.9291 0.557609
\(625\) 9.21379 0.368552
\(626\) −45.7980 −1.83046
\(627\) −65.1979 −2.60375
\(628\) −67.7506 −2.70354
\(629\) 25.6393 1.02231
\(630\) −51.9093 −2.06811
\(631\) 38.9245 1.54956 0.774779 0.632232i \(-0.217861\pi\)
0.774779 + 0.632232i \(0.217861\pi\)
\(632\) 19.2177 0.764439
\(633\) −69.4980 −2.76230
\(634\) −43.6214 −1.73243
\(635\) 15.8762 0.630028
\(636\) 41.7371 1.65498
\(637\) 6.90097 0.273426
\(638\) 89.0071 3.52382
\(639\) 84.3230 3.33577
\(640\) 62.0105 2.45118
\(641\) 24.6770 0.974682 0.487341 0.873212i \(-0.337967\pi\)
0.487341 + 0.873212i \(0.337967\pi\)
\(642\) −13.5987 −0.536697
\(643\) −32.9601 −1.29982 −0.649911 0.760011i \(-0.725194\pi\)
−0.649911 + 0.760011i \(0.725194\pi\)
\(644\) −5.04784 −0.198913
\(645\) −41.3940 −1.62989
\(646\) 28.9058 1.13728
\(647\) −40.9674 −1.61060 −0.805298 0.592870i \(-0.797995\pi\)
−0.805298 + 0.592870i \(0.797995\pi\)
\(648\) −26.0915 −1.02497
\(649\) 10.8460 0.425744
\(650\) −137.851 −5.40694
\(651\) −21.3436 −0.836520
\(652\) 20.5087 0.803182
\(653\) −44.7385 −1.75075 −0.875376 0.483442i \(-0.839386\pi\)
−0.875376 + 0.483442i \(0.839386\pi\)
\(654\) −83.3582 −3.25956
\(655\) 37.4525 1.46339
\(656\) 0.459466 0.0179391
\(657\) 20.8337 0.812800
\(658\) 9.83311 0.383335
\(659\) −43.8139 −1.70675 −0.853373 0.521300i \(-0.825447\pi\)
−0.853373 + 0.521300i \(0.825447\pi\)
\(660\) −160.136 −6.23328
\(661\) −6.02501 −0.234346 −0.117173 0.993112i \(-0.537383\pi\)
−0.117173 + 0.993112i \(0.537383\pi\)
\(662\) 25.5752 0.994009
\(663\) 57.4079 2.22954
\(664\) −32.5290 −1.26237
\(665\) 17.3921 0.674435
\(666\) 130.235 5.04652
\(667\) 14.0433 0.543759
\(668\) −75.3347 −2.91479
\(669\) −15.4203 −0.596183
\(670\) 46.4829 1.79579
\(671\) 25.7557 0.994290
\(672\) −19.3322 −0.745756
\(673\) 6.44598 0.248474 0.124237 0.992253i \(-0.460352\pi\)
0.124237 + 0.992253i \(0.460352\pi\)
\(674\) −6.74111 −0.259658
\(675\) −85.5320 −3.29213
\(676\) 106.703 4.10397
\(677\) −7.30889 −0.280903 −0.140452 0.990088i \(-0.544855\pi\)
−0.140452 + 0.990088i \(0.544855\pi\)
\(678\) −6.96354 −0.267433
\(679\) 10.6575 0.408998
\(680\) 24.9224 0.955731
\(681\) −25.3636 −0.971936
\(682\) −73.1108 −2.79956
\(683\) −11.5913 −0.443530 −0.221765 0.975100i \(-0.571182\pi\)
−0.221765 + 0.975100i \(0.571182\pi\)
\(684\) 89.0422 3.40461
\(685\) −2.37789 −0.0908545
\(686\) −2.25429 −0.0860692
\(687\) 78.0871 2.97921
\(688\) −2.44328 −0.0931493
\(689\) −30.8380 −1.17483
\(690\) −41.6625 −1.58606
\(691\) 10.1183 0.384919 0.192459 0.981305i \(-0.438354\pi\)
0.192459 + 0.981305i \(0.438354\pi\)
\(692\) −74.0328 −2.81430
\(693\) 28.4826 1.08196
\(694\) −67.0888 −2.54666
\(695\) 31.8525 1.20823
\(696\) −63.3691 −2.40200
\(697\) 1.89367 0.0717277
\(698\) −47.3647 −1.79278
\(699\) 10.7565 0.406847
\(700\) 27.3084 1.03216
\(701\) 0.686891 0.0259435 0.0129718 0.999916i \(-0.495871\pi\)
0.0129718 + 0.999916i \(0.495871\pi\)
\(702\) 150.162 5.66750
\(703\) −43.6350 −1.64573
\(704\) −60.0870 −2.26461
\(705\) 49.2174 1.85363
\(706\) −22.4128 −0.843516
\(707\) 12.4116 0.466786
\(708\) −21.9975 −0.826718
\(709\) 20.6481 0.775454 0.387727 0.921774i \(-0.373260\pi\)
0.387727 + 0.921774i \(0.373260\pi\)
\(710\) −114.425 −4.29428
\(711\) −48.7382 −1.82783
\(712\) 23.2375 0.870863
\(713\) −11.5352 −0.431998
\(714\) −18.7530 −0.701815
\(715\) 118.318 4.42486
\(716\) 22.4266 0.838121
\(717\) −10.3279 −0.385701
\(718\) −59.0802 −2.20485
\(719\) 17.0181 0.634669 0.317334 0.948314i \(-0.397212\pi\)
0.317334 + 0.948314i \(0.397212\pi\)
\(720\) −15.3359 −0.571534
\(721\) 10.5713 0.393695
\(722\) −6.36268 −0.236795
\(723\) 41.7426 1.55242
\(724\) 54.3247 2.01896
\(725\) −75.9731 −2.82157
\(726\) 69.7366 2.58817
\(727\) 37.6283 1.39556 0.697779 0.716313i \(-0.254172\pi\)
0.697779 + 0.716313i \(0.254172\pi\)
\(728\) −16.8298 −0.623752
\(729\) −21.5897 −0.799620
\(730\) −28.2709 −1.04635
\(731\) −10.0699 −0.372448
\(732\) −52.2369 −1.93073
\(733\) −9.87426 −0.364714 −0.182357 0.983232i \(-0.558373\pi\)
−0.182357 + 0.983232i \(0.558373\pi\)
\(734\) −33.5971 −1.24009
\(735\) −11.2833 −0.416192
\(736\) −10.4482 −0.385125
\(737\) −25.5051 −0.939493
\(738\) 9.61890 0.354077
\(739\) 23.6321 0.869323 0.434661 0.900594i \(-0.356868\pi\)
0.434661 + 0.900594i \(0.356868\pi\)
\(740\) −107.174 −3.93980
\(741\) −97.7013 −3.58915
\(742\) 10.0736 0.369814
\(743\) 29.0739 1.06662 0.533308 0.845921i \(-0.320949\pi\)
0.533308 + 0.845921i \(0.320949\pi\)
\(744\) 52.0516 1.90831
\(745\) 54.7146 2.00459
\(746\) −53.6691 −1.96496
\(747\) 82.4971 3.01841
\(748\) −38.9560 −1.42437
\(749\) −1.99044 −0.0727290
\(750\) 98.2110 3.58616
\(751\) −21.1003 −0.769960 −0.384980 0.922925i \(-0.625792\pi\)
−0.384980 + 0.922925i \(0.625792\pi\)
\(752\) 2.90506 0.105936
\(753\) −28.4592 −1.03711
\(754\) 133.380 4.85742
\(755\) 59.6799 2.17197
\(756\) −29.7473 −1.08190
\(757\) 29.3371 1.06628 0.533138 0.846028i \(-0.321013\pi\)
0.533138 + 0.846028i \(0.321013\pi\)
\(758\) 27.7986 1.00969
\(759\) 22.8602 0.829771
\(760\) −42.4149 −1.53855
\(761\) −52.5553 −1.90513 −0.952563 0.304340i \(-0.901564\pi\)
−0.952563 + 0.304340i \(0.901564\pi\)
\(762\) 29.1337 1.05540
\(763\) −12.2011 −0.441711
\(764\) −47.7781 −1.72855
\(765\) −63.2060 −2.28522
\(766\) 62.1763 2.24652
\(767\) 16.2532 0.586868
\(768\) 34.7056 1.25233
\(769\) −29.7038 −1.07115 −0.535573 0.844489i \(-0.679904\pi\)
−0.535573 + 0.844489i \(0.679904\pi\)
\(770\) −38.6502 −1.39286
\(771\) 33.9660 1.22326
\(772\) 12.1536 0.437416
\(773\) −21.9188 −0.788366 −0.394183 0.919032i \(-0.628972\pi\)
−0.394183 + 0.919032i \(0.628972\pi\)
\(774\) −51.1501 −1.83855
\(775\) 62.4047 2.24164
\(776\) −25.9911 −0.933024
\(777\) 28.3088 1.01557
\(778\) −60.2639 −2.16056
\(779\) −3.22279 −0.115468
\(780\) −239.969 −8.59228
\(781\) 62.7847 2.24661
\(782\) −10.1352 −0.362433
\(783\) 82.7583 2.95754
\(784\) −0.665999 −0.0237857
\(785\) −81.8473 −2.92125
\(786\) 68.7274 2.45143
\(787\) 44.5772 1.58901 0.794503 0.607261i \(-0.207732\pi\)
0.794503 + 0.607261i \(0.207732\pi\)
\(788\) −37.8684 −1.34900
\(789\) 50.2638 1.78944
\(790\) 66.1368 2.35304
\(791\) −1.01925 −0.0362405
\(792\) −69.4619 −2.46822
\(793\) 38.5959 1.37058
\(794\) −63.3681 −2.24885
\(795\) 50.4211 1.78825
\(796\) −32.7703 −1.16151
\(797\) 0.0778664 0.00275817 0.00137909 0.999999i \(-0.499561\pi\)
0.00137909 + 0.999999i \(0.499561\pi\)
\(798\) 31.9154 1.12979
\(799\) 11.9730 0.423576
\(800\) 56.5238 1.99842
\(801\) −58.9329 −2.08229
\(802\) 38.7091 1.36686
\(803\) 15.5122 0.547414
\(804\) 51.7286 1.82433
\(805\) −6.09813 −0.214931
\(806\) −109.559 −3.85906
\(807\) 22.9438 0.807659
\(808\) −30.2688 −1.06485
\(809\) −26.2864 −0.924182 −0.462091 0.886833i \(-0.652901\pi\)
−0.462091 + 0.886833i \(0.652901\pi\)
\(810\) −89.7925 −3.15499
\(811\) −11.0002 −0.386270 −0.193135 0.981172i \(-0.561865\pi\)
−0.193135 + 0.981172i \(0.561865\pi\)
\(812\) −26.4228 −0.927260
\(813\) 27.4286 0.961965
\(814\) 96.9698 3.39879
\(815\) 24.7759 0.867860
\(816\) −5.54032 −0.193950
\(817\) 17.1377 0.599572
\(818\) 16.6573 0.582410
\(819\) 42.6821 1.49143
\(820\) −7.91566 −0.276427
\(821\) −36.9123 −1.28825 −0.644124 0.764921i \(-0.722778\pi\)
−0.644124 + 0.764921i \(0.722778\pi\)
\(822\) −4.36356 −0.152197
\(823\) −18.6814 −0.651194 −0.325597 0.945509i \(-0.605565\pi\)
−0.325597 + 0.945509i \(0.605565\pi\)
\(824\) −25.7807 −0.898113
\(825\) −123.672 −4.30569
\(826\) −5.30930 −0.184734
\(827\) −8.30608 −0.288831 −0.144415 0.989517i \(-0.546130\pi\)
−0.144415 + 0.989517i \(0.546130\pi\)
\(828\) −31.2206 −1.08499
\(829\) −43.6011 −1.51433 −0.757165 0.653224i \(-0.773416\pi\)
−0.757165 + 0.653224i \(0.773416\pi\)
\(830\) −111.947 −3.88573
\(831\) 36.2119 1.25618
\(832\) −90.0425 −3.12166
\(833\) −2.74488 −0.0951045
\(834\) 58.4510 2.02399
\(835\) −91.0094 −3.14951
\(836\) 66.2984 2.29298
\(837\) −67.9780 −2.34966
\(838\) −83.2067 −2.87433
\(839\) 24.2757 0.838089 0.419044 0.907966i \(-0.362365\pi\)
0.419044 + 0.907966i \(0.362365\pi\)
\(840\) 27.5172 0.949435
\(841\) 44.5094 1.53481
\(842\) 13.3370 0.459622
\(843\) −52.5605 −1.81028
\(844\) 70.6711 2.43260
\(845\) 128.905 4.43446
\(846\) 60.8172 2.09094
\(847\) 10.2073 0.350728
\(848\) 2.97611 0.102200
\(849\) −21.5325 −0.738993
\(850\) 54.8304 1.88067
\(851\) 15.2996 0.524465
\(852\) −127.338 −4.36252
\(853\) 15.3152 0.524383 0.262192 0.965016i \(-0.415555\pi\)
0.262192 + 0.965016i \(0.415555\pi\)
\(854\) −12.6078 −0.431432
\(855\) 107.569 3.67878
\(856\) 4.85418 0.165913
\(857\) −14.4846 −0.494786 −0.247393 0.968915i \(-0.579574\pi\)
−0.247393 + 0.968915i \(0.579574\pi\)
\(858\) 217.121 7.41238
\(859\) −25.8375 −0.881564 −0.440782 0.897614i \(-0.645299\pi\)
−0.440782 + 0.897614i \(0.645299\pi\)
\(860\) 42.0928 1.43535
\(861\) 2.09083 0.0712552
\(862\) 80.1905 2.73130
\(863\) −1.00000 −0.0340404
\(864\) −61.5719 −2.09472
\(865\) −89.4365 −3.04093
\(866\) 61.6890 2.09628
\(867\) 28.6872 0.974268
\(868\) 21.7039 0.736677
\(869\) −36.2892 −1.23103
\(870\) −218.081 −7.39365
\(871\) −38.2203 −1.29505
\(872\) 29.7555 1.00765
\(873\) 65.9162 2.23093
\(874\) 17.2488 0.583450
\(875\) 14.3751 0.485968
\(876\) −31.4613 −1.06298
\(877\) −32.6768 −1.10342 −0.551709 0.834037i \(-0.686024\pi\)
−0.551709 + 0.834037i \(0.686024\pi\)
\(878\) 28.4016 0.958508
\(879\) −46.3300 −1.56267
\(880\) −11.4187 −0.384923
\(881\) −56.9219 −1.91775 −0.958873 0.283835i \(-0.908393\pi\)
−0.958873 + 0.283835i \(0.908393\pi\)
\(882\) −13.9427 −0.469474
\(883\) −21.1937 −0.713226 −0.356613 0.934252i \(-0.616068\pi\)
−0.356613 + 0.934252i \(0.616068\pi\)
\(884\) −58.3770 −1.96343
\(885\) −26.5745 −0.893292
\(886\) 71.1927 2.39177
\(887\) 3.67028 0.123236 0.0616180 0.998100i \(-0.480374\pi\)
0.0616180 + 0.998100i \(0.480374\pi\)
\(888\) −69.0381 −2.31677
\(889\) 4.26430 0.143020
\(890\) 79.9708 2.68063
\(891\) 49.2690 1.65057
\(892\) 15.6806 0.525025
\(893\) −20.3767 −0.681879
\(894\) 100.404 3.35802
\(895\) 27.0928 0.905613
\(896\) 16.6558 0.556432
\(897\) 34.2568 1.14380
\(898\) 46.9526 1.56683
\(899\) −60.3810 −2.01382
\(900\) 168.901 5.63003
\(901\) 12.2659 0.408636
\(902\) 7.16198 0.238468
\(903\) −11.1183 −0.369994
\(904\) 2.48571 0.0826733
\(905\) 65.6279 2.18154
\(906\) 109.516 3.63842
\(907\) 10.0018 0.332105 0.166053 0.986117i \(-0.446898\pi\)
0.166053 + 0.986117i \(0.446898\pi\)
\(908\) 25.7918 0.855930
\(909\) 76.7650 2.54613
\(910\) −57.9188 −1.91999
\(911\) 23.6799 0.784550 0.392275 0.919848i \(-0.371688\pi\)
0.392275 + 0.919848i \(0.371688\pi\)
\(912\) 9.42896 0.312224
\(913\) 61.4252 2.03288
\(914\) −41.3558 −1.36793
\(915\) −63.1057 −2.08621
\(916\) −79.4052 −2.62362
\(917\) 10.0596 0.332198
\(918\) −59.7274 −1.97130
\(919\) 22.0085 0.725995 0.362998 0.931790i \(-0.381753\pi\)
0.362998 + 0.931790i \(0.381753\pi\)
\(920\) 14.8718 0.490310
\(921\) 85.8399 2.82852
\(922\) −59.3529 −1.95468
\(923\) 94.0851 3.09685
\(924\) −43.0120 −1.41499
\(925\) −82.7698 −2.72145
\(926\) 54.3626 1.78646
\(927\) 65.3827 2.14745
\(928\) −54.6908 −1.79531
\(929\) −14.4510 −0.474121 −0.237061 0.971495i \(-0.576184\pi\)
−0.237061 + 0.971495i \(0.576184\pi\)
\(930\) 179.133 5.87401
\(931\) 4.67145 0.153101
\(932\) −10.9381 −0.358288
\(933\) −65.1745 −2.13372
\(934\) 20.0794 0.657019
\(935\) −47.0615 −1.53908
\(936\) −104.091 −3.40232
\(937\) 23.2434 0.759328 0.379664 0.925124i \(-0.376040\pi\)
0.379664 + 0.925124i \(0.376040\pi\)
\(938\) 12.4852 0.407655
\(939\) −61.5709 −2.00929
\(940\) −50.0482 −1.63239
\(941\) −60.8281 −1.98294 −0.991470 0.130336i \(-0.958394\pi\)
−0.991470 + 0.130336i \(0.958394\pi\)
\(942\) −150.194 −4.89359
\(943\) 1.13000 0.0367978
\(944\) −1.56856 −0.0510523
\(945\) −35.9368 −1.16902
\(946\) −38.0850 −1.23825
\(947\) −25.4286 −0.826318 −0.413159 0.910659i \(-0.635575\pi\)
−0.413159 + 0.910659i \(0.635575\pi\)
\(948\) 73.6005 2.39043
\(949\) 23.2456 0.754584
\(950\) −93.3148 −3.02753
\(951\) −58.6446 −1.90168
\(952\) 6.69408 0.216956
\(953\) 28.8238 0.933696 0.466848 0.884338i \(-0.345390\pi\)
0.466848 + 0.884338i \(0.345390\pi\)
\(954\) 62.3047 2.01719
\(955\) −57.7191 −1.86775
\(956\) 10.5022 0.339666
\(957\) 119.661 3.86809
\(958\) 85.2354 2.75383
\(959\) −0.638694 −0.0206245
\(960\) 147.223 4.75159
\(961\) 18.5972 0.599910
\(962\) 145.313 4.68507
\(963\) −12.3107 −0.396708
\(964\) −42.4472 −1.36713
\(965\) 14.6823 0.472640
\(966\) −11.1904 −0.360045
\(967\) −26.0562 −0.837911 −0.418955 0.908007i \(-0.637604\pi\)
−0.418955 + 0.908007i \(0.637604\pi\)
\(968\) −24.8932 −0.800097
\(969\) 38.8610 1.24839
\(970\) −89.4469 −2.87197
\(971\) −9.74612 −0.312768 −0.156384 0.987696i \(-0.549984\pi\)
−0.156384 + 0.987696i \(0.549984\pi\)
\(972\) −10.6837 −0.342680
\(973\) 8.55547 0.274276
\(974\) −31.9720 −1.02445
\(975\) −185.326 −5.93519
\(976\) −3.72481 −0.119228
\(977\) −41.5512 −1.32934 −0.664671 0.747137i \(-0.731428\pi\)
−0.664671 + 0.747137i \(0.731428\pi\)
\(978\) 45.4651 1.45381
\(979\) −43.8799 −1.40241
\(980\) 11.4738 0.366517
\(981\) −75.4633 −2.40936
\(982\) −9.60811 −0.306607
\(983\) 27.4507 0.875542 0.437771 0.899087i \(-0.355768\pi\)
0.437771 + 0.899087i \(0.355768\pi\)
\(984\) −5.09901 −0.162550
\(985\) −45.7475 −1.45764
\(986\) −53.0524 −1.68953
\(987\) 13.2196 0.420785
\(988\) 99.3506 3.16076
\(989\) −6.00895 −0.191073
\(990\) −239.050 −7.59749
\(991\) −23.0233 −0.731358 −0.365679 0.930741i \(-0.619163\pi\)
−0.365679 + 0.930741i \(0.619163\pi\)
\(992\) 44.9233 1.42632
\(993\) 34.3833 1.09112
\(994\) −30.7341 −0.974826
\(995\) −39.5887 −1.25505
\(996\) −124.580 −3.94748
\(997\) −52.9713 −1.67762 −0.838809 0.544426i \(-0.816747\pi\)
−0.838809 + 0.544426i \(0.816747\pi\)
\(998\) −86.4798 −2.73747
\(999\) 90.1619 2.85260
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 \(a_p\))