Properties

Label 6041.2.a.f.1.9
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

Related objects

Downloads

Learn more about

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 1.9
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58774 q^{2}\) \(-2.55272 q^{3}\) \(+4.69637 q^{4}\) \(-0.926438 q^{5}\) \(+6.60577 q^{6}\) \(+1.00000 q^{7}\) \(-6.97750 q^{8}\) \(+3.51640 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58774 q^{2}\) \(-2.55272 q^{3}\) \(+4.69637 q^{4}\) \(-0.926438 q^{5}\) \(+6.60577 q^{6}\) \(+1.00000 q^{7}\) \(-6.97750 q^{8}\) \(+3.51640 q^{9}\) \(+2.39738 q^{10}\) \(-3.56028 q^{11}\) \(-11.9885 q^{12}\) \(+2.87730 q^{13}\) \(-2.58774 q^{14}\) \(+2.36494 q^{15}\) \(+8.66319 q^{16}\) \(-8.21408 q^{17}\) \(-9.09950 q^{18}\) \(+2.16744 q^{19}\) \(-4.35090 q^{20}\) \(-2.55272 q^{21}\) \(+9.21306 q^{22}\) \(-0.335991 q^{23}\) \(+17.8116 q^{24}\) \(-4.14171 q^{25}\) \(-7.44569 q^{26}\) \(-1.31822 q^{27}\) \(+4.69637 q^{28}\) \(+1.26605 q^{29}\) \(-6.11984 q^{30}\) \(-6.32958 q^{31}\) \(-8.46303 q^{32}\) \(+9.08841 q^{33}\) \(+21.2559 q^{34}\) \(-0.926438 q^{35}\) \(+16.5143 q^{36}\) \(-8.90580 q^{37}\) \(-5.60876 q^{38}\) \(-7.34495 q^{39}\) \(+6.46423 q^{40}\) \(-2.02377 q^{41}\) \(+6.60577 q^{42}\) \(-9.40480 q^{43}\) \(-16.7204 q^{44}\) \(-3.25772 q^{45}\) \(+0.869456 q^{46}\) \(-12.9943 q^{47}\) \(-22.1147 q^{48}\) \(+1.00000 q^{49}\) \(+10.7177 q^{50}\) \(+20.9683 q^{51}\) \(+13.5129 q^{52}\) \(+8.89857 q^{53}\) \(+3.41120 q^{54}\) \(+3.29838 q^{55}\) \(-6.97750 q^{56}\) \(-5.53288 q^{57}\) \(-3.27619 q^{58}\) \(-5.37236 q^{59}\) \(+11.1066 q^{60}\) \(+6.49942 q^{61}\) \(+16.3793 q^{62}\) \(+3.51640 q^{63}\) \(+4.57370 q^{64}\) \(-2.66564 q^{65}\) \(-23.5184 q^{66}\) \(+2.20617 q^{67}\) \(-38.5764 q^{68}\) \(+0.857692 q^{69}\) \(+2.39738 q^{70}\) \(-2.33177 q^{71}\) \(-24.5357 q^{72}\) \(-8.74179 q^{73}\) \(+23.0459 q^{74}\) \(+10.5726 q^{75}\) \(+10.1791 q^{76}\) \(-3.56028 q^{77}\) \(+19.0068 q^{78}\) \(+15.8561 q^{79}\) \(-8.02591 q^{80}\) \(-7.18414 q^{81}\) \(+5.23697 q^{82}\) \(-0.914229 q^{83}\) \(-11.9885 q^{84}\) \(+7.60984 q^{85}\) \(+24.3371 q^{86}\) \(-3.23187 q^{87}\) \(+24.8419 q^{88}\) \(-9.19383 q^{89}\) \(+8.43013 q^{90}\) \(+2.87730 q^{91}\) \(-1.57794 q^{92}\) \(+16.1577 q^{93}\) \(+33.6259 q^{94}\) \(-2.00800 q^{95}\) \(+21.6038 q^{96}\) \(+5.49484 q^{97}\) \(-2.58774 q^{98}\) \(-12.5194 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58774 −1.82981 −0.914903 0.403675i \(-0.867733\pi\)
−0.914903 + 0.403675i \(0.867733\pi\)
\(3\) −2.55272 −1.47382 −0.736908 0.675993i \(-0.763715\pi\)
−0.736908 + 0.675993i \(0.763715\pi\)
\(4\) 4.69637 2.34819
\(5\) −0.926438 −0.414316 −0.207158 0.978308i \(-0.566421\pi\)
−0.207158 + 0.978308i \(0.566421\pi\)
\(6\) 6.60577 2.69680
\(7\) 1.00000 0.377964
\(8\) −6.97750 −2.46692
\(9\) 3.51640 1.17213
\(10\) 2.39738 0.758117
\(11\) −3.56028 −1.07346 −0.536732 0.843753i \(-0.680341\pi\)
−0.536732 + 0.843753i \(0.680341\pi\)
\(12\) −11.9885 −3.46080
\(13\) 2.87730 0.798020 0.399010 0.916947i \(-0.369354\pi\)
0.399010 + 0.916947i \(0.369354\pi\)
\(14\) −2.58774 −0.691601
\(15\) 2.36494 0.610625
\(16\) 8.66319 2.16580
\(17\) −8.21408 −1.99221 −0.996104 0.0881900i \(-0.971892\pi\)
−0.996104 + 0.0881900i \(0.971892\pi\)
\(18\) −9.09950 −2.14477
\(19\) 2.16744 0.497245 0.248622 0.968600i \(-0.420022\pi\)
0.248622 + 0.968600i \(0.420022\pi\)
\(20\) −4.35090 −0.972891
\(21\) −2.55272 −0.557050
\(22\) 9.21306 1.96423
\(23\) −0.335991 −0.0700590 −0.0350295 0.999386i \(-0.511153\pi\)
−0.0350295 + 0.999386i \(0.511153\pi\)
\(24\) 17.8116 3.63579
\(25\) −4.14171 −0.828343
\(26\) −7.44569 −1.46022
\(27\) −1.31822 −0.253691
\(28\) 4.69637 0.887531
\(29\) 1.26605 0.235099 0.117549 0.993067i \(-0.462496\pi\)
0.117549 + 0.993067i \(0.462496\pi\)
\(30\) −6.11984 −1.11732
\(31\) −6.32958 −1.13683 −0.568413 0.822743i \(-0.692443\pi\)
−0.568413 + 0.822743i \(0.692443\pi\)
\(32\) −8.46303 −1.49607
\(33\) 9.08841 1.58209
\(34\) 21.2559 3.64535
\(35\) −0.926438 −0.156597
\(36\) 16.5143 2.75239
\(37\) −8.90580 −1.46410 −0.732052 0.681248i \(-0.761437\pi\)
−0.732052 + 0.681248i \(0.761437\pi\)
\(38\) −5.60876 −0.909861
\(39\) −7.34495 −1.17613
\(40\) 6.46423 1.02208
\(41\) −2.02377 −0.316059 −0.158030 0.987434i \(-0.550514\pi\)
−0.158030 + 0.987434i \(0.550514\pi\)
\(42\) 6.60577 1.01929
\(43\) −9.40480 −1.43422 −0.717109 0.696961i \(-0.754535\pi\)
−0.717109 + 0.696961i \(0.754535\pi\)
\(44\) −16.7204 −2.52070
\(45\) −3.25772 −0.485633
\(46\) 0.869456 0.128194
\(47\) −12.9943 −1.89542 −0.947708 0.319138i \(-0.896607\pi\)
−0.947708 + 0.319138i \(0.896607\pi\)
\(48\) −22.1147 −3.19198
\(49\) 1.00000 0.142857
\(50\) 10.7177 1.51571
\(51\) 20.9683 2.93615
\(52\) 13.5129 1.87390
\(53\) 8.89857 1.22231 0.611156 0.791510i \(-0.290705\pi\)
0.611156 + 0.791510i \(0.290705\pi\)
\(54\) 3.41120 0.464205
\(55\) 3.29838 0.444753
\(56\) −6.97750 −0.932408
\(57\) −5.53288 −0.732847
\(58\) −3.27619 −0.430185
\(59\) −5.37236 −0.699422 −0.349711 0.936858i \(-0.613720\pi\)
−0.349711 + 0.936858i \(0.613720\pi\)
\(60\) 11.1066 1.43386
\(61\) 6.49942 0.832165 0.416083 0.909327i \(-0.363403\pi\)
0.416083 + 0.909327i \(0.363403\pi\)
\(62\) 16.3793 2.08017
\(63\) 3.51640 0.443024
\(64\) 4.57370 0.571712
\(65\) −2.66564 −0.330632
\(66\) −23.5184 −2.89491
\(67\) 2.20617 0.269527 0.134763 0.990878i \(-0.456973\pi\)
0.134763 + 0.990878i \(0.456973\pi\)
\(68\) −38.5764 −4.67808
\(69\) 0.857692 0.103254
\(70\) 2.39738 0.286541
\(71\) −2.33177 −0.276730 −0.138365 0.990381i \(-0.544185\pi\)
−0.138365 + 0.990381i \(0.544185\pi\)
\(72\) −24.5357 −2.89156
\(73\) −8.74179 −1.02315 −0.511574 0.859239i \(-0.670938\pi\)
−0.511574 + 0.859239i \(0.670938\pi\)
\(74\) 23.0459 2.67903
\(75\) 10.5726 1.22082
\(76\) 10.1791 1.16762
\(77\) −3.56028 −0.405731
\(78\) 19.0068 2.15210
\(79\) 15.8561 1.78395 0.891975 0.452085i \(-0.149320\pi\)
0.891975 + 0.452085i \(0.149320\pi\)
\(80\) −8.02591 −0.897323
\(81\) −7.18414 −0.798238
\(82\) 5.23697 0.578326
\(83\) −0.914229 −0.100350 −0.0501748 0.998740i \(-0.515978\pi\)
−0.0501748 + 0.998740i \(0.515978\pi\)
\(84\) −11.9885 −1.30806
\(85\) 7.60984 0.825403
\(86\) 24.3371 2.62434
\(87\) −3.23187 −0.346492
\(88\) 24.8419 2.64815
\(89\) −9.19383 −0.974544 −0.487272 0.873250i \(-0.662008\pi\)
−0.487272 + 0.873250i \(0.662008\pi\)
\(90\) 8.43013 0.888613
\(91\) 2.87730 0.301623
\(92\) −1.57794 −0.164512
\(93\) 16.1577 1.67547
\(94\) 33.6259 3.46824
\(95\) −2.00800 −0.206016
\(96\) 21.6038 2.20493
\(97\) 5.49484 0.557916 0.278958 0.960303i \(-0.410011\pi\)
0.278958 + 0.960303i \(0.410011\pi\)
\(98\) −2.58774 −0.261401
\(99\) −12.5194 −1.25824
\(100\) −19.4510 −1.94510
\(101\) −6.85233 −0.681832 −0.340916 0.940094i \(-0.610737\pi\)
−0.340916 + 0.940094i \(0.610737\pi\)
\(102\) −54.2604 −5.37258
\(103\) −6.13127 −0.604132 −0.302066 0.953287i \(-0.597676\pi\)
−0.302066 + 0.953287i \(0.597676\pi\)
\(104\) −20.0764 −1.96865
\(105\) 2.36494 0.230794
\(106\) −23.0271 −2.23659
\(107\) 5.52258 0.533888 0.266944 0.963712i \(-0.413986\pi\)
0.266944 + 0.963712i \(0.413986\pi\)
\(108\) −6.19085 −0.595714
\(109\) 2.59425 0.248484 0.124242 0.992252i \(-0.460350\pi\)
0.124242 + 0.992252i \(0.460350\pi\)
\(110\) −8.53533 −0.813812
\(111\) 22.7340 2.15782
\(112\) 8.66319 0.818594
\(113\) −14.8633 −1.39822 −0.699109 0.715015i \(-0.746420\pi\)
−0.699109 + 0.715015i \(0.746420\pi\)
\(114\) 14.3176 1.34097
\(115\) 0.311275 0.0290265
\(116\) 5.94583 0.552056
\(117\) 10.1177 0.935385
\(118\) 13.9022 1.27981
\(119\) −8.21408 −0.752984
\(120\) −16.5014 −1.50636
\(121\) 1.67558 0.152326
\(122\) −16.8188 −1.52270
\(123\) 5.16611 0.465813
\(124\) −29.7261 −2.66948
\(125\) 8.46923 0.757511
\(126\) −9.09950 −0.810648
\(127\) 21.1131 1.87348 0.936741 0.350022i \(-0.113826\pi\)
0.936741 + 0.350022i \(0.113826\pi\)
\(128\) 5.09053 0.449943
\(129\) 24.0079 2.11377
\(130\) 6.89797 0.604992
\(131\) 10.1180 0.884016 0.442008 0.897011i \(-0.354266\pi\)
0.442008 + 0.897011i \(0.354266\pi\)
\(132\) 42.6826 3.71504
\(133\) 2.16744 0.187941
\(134\) −5.70899 −0.493182
\(135\) 1.22125 0.105108
\(136\) 57.3138 4.91462
\(137\) −9.62283 −0.822134 −0.411067 0.911605i \(-0.634844\pi\)
−0.411067 + 0.911605i \(0.634844\pi\)
\(138\) −2.21948 −0.188935
\(139\) 10.5397 0.893963 0.446982 0.894543i \(-0.352499\pi\)
0.446982 + 0.894543i \(0.352499\pi\)
\(140\) −4.35090 −0.367718
\(141\) 33.1709 2.79349
\(142\) 6.03401 0.506363
\(143\) −10.2440 −0.856646
\(144\) 30.4632 2.53860
\(145\) −1.17291 −0.0974052
\(146\) 22.6214 1.87216
\(147\) −2.55272 −0.210545
\(148\) −41.8250 −3.43799
\(149\) −4.22005 −0.345720 −0.172860 0.984946i \(-0.555301\pi\)
−0.172860 + 0.984946i \(0.555301\pi\)
\(150\) −27.3592 −2.23387
\(151\) 7.25759 0.590614 0.295307 0.955402i \(-0.404578\pi\)
0.295307 + 0.955402i \(0.404578\pi\)
\(152\) −15.1233 −1.22666
\(153\) −28.8840 −2.33513
\(154\) 9.21306 0.742409
\(155\) 5.86397 0.471005
\(156\) −34.4947 −2.76178
\(157\) −1.59949 −0.127653 −0.0638265 0.997961i \(-0.520330\pi\)
−0.0638265 + 0.997961i \(0.520330\pi\)
\(158\) −41.0314 −3.26428
\(159\) −22.7156 −1.80146
\(160\) 7.84047 0.619843
\(161\) −0.335991 −0.0264798
\(162\) 18.5907 1.46062
\(163\) −24.3902 −1.91039 −0.955195 0.295977i \(-0.904355\pi\)
−0.955195 + 0.295977i \(0.904355\pi\)
\(164\) −9.50436 −0.742166
\(165\) −8.41984 −0.655484
\(166\) 2.36578 0.183620
\(167\) −3.20085 −0.247689 −0.123845 0.992302i \(-0.539522\pi\)
−0.123845 + 0.992302i \(0.539522\pi\)
\(168\) 17.8116 1.37420
\(169\) −4.72114 −0.363164
\(170\) −19.6922 −1.51033
\(171\) 7.62158 0.582837
\(172\) −44.1685 −3.36781
\(173\) −4.70033 −0.357359 −0.178680 0.983907i \(-0.557183\pi\)
−0.178680 + 0.983907i \(0.557183\pi\)
\(174\) 8.36322 0.634014
\(175\) −4.14171 −0.313084
\(176\) −30.8434 −2.32491
\(177\) 13.7141 1.03082
\(178\) 23.7912 1.78323
\(179\) −8.21919 −0.614331 −0.307165 0.951656i \(-0.599380\pi\)
−0.307165 + 0.951656i \(0.599380\pi\)
\(180\) −15.2995 −1.14036
\(181\) −22.3162 −1.65875 −0.829375 0.558692i \(-0.811303\pi\)
−0.829375 + 0.558692i \(0.811303\pi\)
\(182\) −7.44569 −0.551912
\(183\) −16.5912 −1.22646
\(184\) 2.34438 0.172830
\(185\) 8.25067 0.606602
\(186\) −41.8118 −3.06579
\(187\) 29.2444 2.13856
\(188\) −61.0262 −4.45079
\(189\) −1.31822 −0.0958863
\(190\) 5.19617 0.376970
\(191\) 3.04677 0.220456 0.110228 0.993906i \(-0.464842\pi\)
0.110228 + 0.993906i \(0.464842\pi\)
\(192\) −11.6754 −0.842599
\(193\) −10.0749 −0.725209 −0.362605 0.931943i \(-0.618112\pi\)
−0.362605 + 0.931943i \(0.618112\pi\)
\(194\) −14.2192 −1.02088
\(195\) 6.80464 0.487291
\(196\) 4.69637 0.335455
\(197\) −9.60675 −0.684453 −0.342226 0.939618i \(-0.611181\pi\)
−0.342226 + 0.939618i \(0.611181\pi\)
\(198\) 32.3968 2.30234
\(199\) −7.47306 −0.529751 −0.264876 0.964283i \(-0.585331\pi\)
−0.264876 + 0.964283i \(0.585331\pi\)
\(200\) 28.8988 2.04346
\(201\) −5.63175 −0.397233
\(202\) 17.7320 1.24762
\(203\) 1.26605 0.0888591
\(204\) 98.4749 6.89462
\(205\) 1.87489 0.130948
\(206\) 15.8661 1.10544
\(207\) −1.18148 −0.0821184
\(208\) 24.9266 1.72835
\(209\) −7.71669 −0.533775
\(210\) −6.11984 −0.422309
\(211\) −28.5278 −1.96393 −0.981966 0.189056i \(-0.939457\pi\)
−0.981966 + 0.189056i \(0.939457\pi\)
\(212\) 41.7910 2.87022
\(213\) 5.95237 0.407850
\(214\) −14.2910 −0.976910
\(215\) 8.71296 0.594219
\(216\) 9.19787 0.625836
\(217\) −6.32958 −0.429680
\(218\) −6.71323 −0.454677
\(219\) 22.3154 1.50793
\(220\) 15.4904 1.04436
\(221\) −23.6344 −1.58982
\(222\) −58.8297 −3.94839
\(223\) −14.0443 −0.940478 −0.470239 0.882539i \(-0.655832\pi\)
−0.470239 + 0.882539i \(0.655832\pi\)
\(224\) −8.46303 −0.565460
\(225\) −14.5639 −0.970927
\(226\) 38.4622 2.55847
\(227\) −16.1290 −1.07052 −0.535259 0.844688i \(-0.679786\pi\)
−0.535259 + 0.844688i \(0.679786\pi\)
\(228\) −25.9845 −1.72086
\(229\) −5.02598 −0.332126 −0.166063 0.986115i \(-0.553106\pi\)
−0.166063 + 0.986115i \(0.553106\pi\)
\(230\) −0.805497 −0.0531129
\(231\) 9.08841 0.597973
\(232\) −8.83385 −0.579970
\(233\) 6.06168 0.397114 0.198557 0.980089i \(-0.436375\pi\)
0.198557 + 0.980089i \(0.436375\pi\)
\(234\) −26.1820 −1.71157
\(235\) 12.0384 0.785301
\(236\) −25.2306 −1.64237
\(237\) −40.4762 −2.62921
\(238\) 21.2559 1.37781
\(239\) −1.09997 −0.0711510 −0.0355755 0.999367i \(-0.511326\pi\)
−0.0355755 + 0.999367i \(0.511326\pi\)
\(240\) 20.4879 1.32249
\(241\) 14.4793 0.932693 0.466347 0.884602i \(-0.345570\pi\)
0.466347 + 0.884602i \(0.345570\pi\)
\(242\) −4.33597 −0.278727
\(243\) 22.2938 1.43015
\(244\) 30.5237 1.95408
\(245\) −0.926438 −0.0591879
\(246\) −13.3685 −0.852347
\(247\) 6.23638 0.396811
\(248\) 44.1647 2.80446
\(249\) 2.33377 0.147897
\(250\) −21.9161 −1.38610
\(251\) 19.2715 1.21641 0.608203 0.793782i \(-0.291891\pi\)
0.608203 + 0.793782i \(0.291891\pi\)
\(252\) 16.5143 1.04030
\(253\) 1.19622 0.0752058
\(254\) −54.6351 −3.42811
\(255\) −19.4258 −1.21649
\(256\) −22.3203 −1.39502
\(257\) 3.97311 0.247836 0.123918 0.992292i \(-0.460454\pi\)
0.123918 + 0.992292i \(0.460454\pi\)
\(258\) −62.1260 −3.86779
\(259\) −8.90580 −0.553380
\(260\) −12.5188 −0.776386
\(261\) 4.45192 0.275567
\(262\) −26.1828 −1.61758
\(263\) −29.0214 −1.78953 −0.894767 0.446534i \(-0.852658\pi\)
−0.894767 + 0.446534i \(0.852658\pi\)
\(264\) −63.4144 −3.90289
\(265\) −8.24397 −0.506423
\(266\) −5.60876 −0.343895
\(267\) 23.4693 1.43630
\(268\) 10.3610 0.632900
\(269\) 11.5057 0.701517 0.350759 0.936466i \(-0.385924\pi\)
0.350759 + 0.936466i \(0.385924\pi\)
\(270\) −3.16026 −0.192328
\(271\) −2.06495 −0.125437 −0.0627184 0.998031i \(-0.519977\pi\)
−0.0627184 + 0.998031i \(0.519977\pi\)
\(272\) −71.1601 −4.31472
\(273\) −7.34495 −0.444537
\(274\) 24.9014 1.50435
\(275\) 14.7457 0.889196
\(276\) 4.02805 0.242460
\(277\) 3.88821 0.233620 0.116810 0.993154i \(-0.462733\pi\)
0.116810 + 0.993154i \(0.462733\pi\)
\(278\) −27.2739 −1.63578
\(279\) −22.2573 −1.33251
\(280\) 6.46423 0.386311
\(281\) 10.5209 0.627625 0.313812 0.949485i \(-0.398394\pi\)
0.313812 + 0.949485i \(0.398394\pi\)
\(282\) −85.8375 −5.11155
\(283\) −3.14605 −0.187013 −0.0935065 0.995619i \(-0.529808\pi\)
−0.0935065 + 0.995619i \(0.529808\pi\)
\(284\) −10.9509 −0.649815
\(285\) 5.12587 0.303630
\(286\) 26.5087 1.56750
\(287\) −2.02377 −0.119459
\(288\) −29.7594 −1.75359
\(289\) 50.4711 2.96889
\(290\) 3.03519 0.178233
\(291\) −14.0268 −0.822265
\(292\) −41.0547 −2.40255
\(293\) −9.96907 −0.582399 −0.291200 0.956662i \(-0.594054\pi\)
−0.291200 + 0.956662i \(0.594054\pi\)
\(294\) 6.60577 0.385256
\(295\) 4.97716 0.289781
\(296\) 62.1403 3.61183
\(297\) 4.69322 0.272328
\(298\) 10.9204 0.632600
\(299\) −0.966748 −0.0559085
\(300\) 49.6531 2.86672
\(301\) −9.40480 −0.542084
\(302\) −18.7807 −1.08071
\(303\) 17.4921 1.00489
\(304\) 18.7769 1.07693
\(305\) −6.02131 −0.344779
\(306\) 74.7441 4.27283
\(307\) −16.4041 −0.936230 −0.468115 0.883667i \(-0.655067\pi\)
−0.468115 + 0.883667i \(0.655067\pi\)
\(308\) −16.7204 −0.952733
\(309\) 15.6514 0.890380
\(310\) −15.1744 −0.861848
\(311\) −26.1687 −1.48389 −0.741944 0.670462i \(-0.766096\pi\)
−0.741944 + 0.670462i \(0.766096\pi\)
\(312\) 51.2495 2.90143
\(313\) 2.60063 0.146996 0.0734981 0.997295i \(-0.476584\pi\)
0.0734981 + 0.997295i \(0.476584\pi\)
\(314\) 4.13905 0.233580
\(315\) −3.25772 −0.183552
\(316\) 74.4662 4.18905
\(317\) −9.53816 −0.535716 −0.267858 0.963458i \(-0.586316\pi\)
−0.267858 + 0.963458i \(0.586316\pi\)
\(318\) 58.7819 3.29633
\(319\) −4.50748 −0.252370
\(320\) −4.23725 −0.236869
\(321\) −14.0976 −0.786852
\(322\) 0.869456 0.0484529
\(323\) −17.8035 −0.990615
\(324\) −33.7394 −1.87441
\(325\) −11.9170 −0.661034
\(326\) 63.1155 3.49564
\(327\) −6.62240 −0.366220
\(328\) 14.1208 0.779692
\(329\) −12.9943 −0.716400
\(330\) 21.7883 1.19941
\(331\) 15.4946 0.851659 0.425829 0.904804i \(-0.359982\pi\)
0.425829 + 0.904804i \(0.359982\pi\)
\(332\) −4.29356 −0.235640
\(333\) −31.3163 −1.71612
\(334\) 8.28295 0.453223
\(335\) −2.04388 −0.111669
\(336\) −22.1147 −1.20646
\(337\) 9.95684 0.542383 0.271192 0.962525i \(-0.412582\pi\)
0.271192 + 0.962525i \(0.412582\pi\)
\(338\) 12.2171 0.664520
\(339\) 37.9418 2.06071
\(340\) 35.7386 1.93820
\(341\) 22.5351 1.22034
\(342\) −19.7226 −1.06648
\(343\) 1.00000 0.0539949
\(344\) 65.6220 3.53810
\(345\) −0.794599 −0.0427798
\(346\) 12.1632 0.653898
\(347\) 11.9186 0.639826 0.319913 0.947447i \(-0.396346\pi\)
0.319913 + 0.947447i \(0.396346\pi\)
\(348\) −15.1781 −0.813629
\(349\) −22.2469 −1.19085 −0.595424 0.803412i \(-0.703016\pi\)
−0.595424 + 0.803412i \(0.703016\pi\)
\(350\) 10.7177 0.572883
\(351\) −3.79291 −0.202451
\(352\) 30.1307 1.60597
\(353\) −7.81816 −0.416119 −0.208059 0.978116i \(-0.566715\pi\)
−0.208059 + 0.978116i \(0.566715\pi\)
\(354\) −35.4886 −1.88620
\(355\) 2.16024 0.114654
\(356\) −43.1777 −2.28841
\(357\) 20.9683 1.10976
\(358\) 21.2691 1.12411
\(359\) 29.2799 1.54533 0.772667 0.634812i \(-0.218922\pi\)
0.772667 + 0.634812i \(0.218922\pi\)
\(360\) 22.7308 1.19802
\(361\) −14.3022 −0.752748
\(362\) 57.7484 3.03519
\(363\) −4.27730 −0.224500
\(364\) 13.5129 0.708268
\(365\) 8.09872 0.423907
\(366\) 42.9337 2.24418
\(367\) −11.7868 −0.615268 −0.307634 0.951505i \(-0.599537\pi\)
−0.307634 + 0.951505i \(0.599537\pi\)
\(368\) −2.91075 −0.151734
\(369\) −7.11636 −0.370463
\(370\) −21.3506 −1.10996
\(371\) 8.89857 0.461991
\(372\) 75.8825 3.93432
\(373\) −30.4904 −1.57873 −0.789367 0.613922i \(-0.789591\pi\)
−0.789367 + 0.613922i \(0.789591\pi\)
\(374\) −75.6768 −3.91316
\(375\) −21.6196 −1.11643
\(376\) 90.6679 4.67584
\(377\) 3.64280 0.187614
\(378\) 3.41120 0.175453
\(379\) −10.1378 −0.520744 −0.260372 0.965508i \(-0.583845\pi\)
−0.260372 + 0.965508i \(0.583845\pi\)
\(380\) −9.43032 −0.483765
\(381\) −53.8959 −2.76117
\(382\) −7.88423 −0.403392
\(383\) −7.41836 −0.379061 −0.189530 0.981875i \(-0.560697\pi\)
−0.189530 + 0.981875i \(0.560697\pi\)
\(384\) −12.9947 −0.663133
\(385\) 3.29838 0.168101
\(386\) 26.0713 1.32699
\(387\) −33.0710 −1.68109
\(388\) 25.8058 1.31009
\(389\) −21.9818 −1.11452 −0.557260 0.830338i \(-0.688147\pi\)
−0.557260 + 0.830338i \(0.688147\pi\)
\(390\) −17.6086 −0.891647
\(391\) 2.75986 0.139572
\(392\) −6.97750 −0.352417
\(393\) −25.8285 −1.30288
\(394\) 24.8597 1.25241
\(395\) −14.6897 −0.739118
\(396\) −58.7956 −2.95459
\(397\) −7.50680 −0.376755 −0.188378 0.982097i \(-0.560323\pi\)
−0.188378 + 0.982097i \(0.560323\pi\)
\(398\) 19.3383 0.969342
\(399\) −5.53288 −0.276990
\(400\) −35.8804 −1.79402
\(401\) 0.144643 0.00722311 0.00361156 0.999993i \(-0.498850\pi\)
0.00361156 + 0.999993i \(0.498850\pi\)
\(402\) 14.5735 0.726859
\(403\) −18.2121 −0.907210
\(404\) −32.1811 −1.60107
\(405\) 6.65566 0.330723
\(406\) −3.27619 −0.162595
\(407\) 31.7071 1.57166
\(408\) −146.306 −7.24324
\(409\) 19.1667 0.947733 0.473867 0.880597i \(-0.342858\pi\)
0.473867 + 0.880597i \(0.342858\pi\)
\(410\) −4.85173 −0.239610
\(411\) 24.5644 1.21167
\(412\) −28.7948 −1.41862
\(413\) −5.37236 −0.264357
\(414\) 3.05735 0.150261
\(415\) 0.846976 0.0415764
\(416\) −24.3507 −1.19389
\(417\) −26.9049 −1.31754
\(418\) 19.9688 0.976704
\(419\) −14.1986 −0.693649 −0.346824 0.937930i \(-0.612740\pi\)
−0.346824 + 0.937930i \(0.612740\pi\)
\(420\) 11.1066 0.541949
\(421\) 32.2411 1.57134 0.785668 0.618648i \(-0.212319\pi\)
0.785668 + 0.618648i \(0.212319\pi\)
\(422\) 73.8223 3.59361
\(423\) −45.6932 −2.22168
\(424\) −62.0898 −3.01535
\(425\) 34.0204 1.65023
\(426\) −15.4032 −0.746285
\(427\) 6.49942 0.314529
\(428\) 25.9361 1.25367
\(429\) 26.1501 1.26254
\(430\) −22.5468 −1.08731
\(431\) 27.1037 1.30554 0.652770 0.757556i \(-0.273607\pi\)
0.652770 + 0.757556i \(0.273607\pi\)
\(432\) −11.4200 −0.549444
\(433\) −18.5978 −0.893752 −0.446876 0.894596i \(-0.647463\pi\)
−0.446876 + 0.894596i \(0.647463\pi\)
\(434\) 16.3793 0.786231
\(435\) 2.99412 0.143557
\(436\) 12.1836 0.583487
\(437\) −0.728241 −0.0348365
\(438\) −57.7463 −2.75922
\(439\) 11.7683 0.561668 0.280834 0.959756i \(-0.409389\pi\)
0.280834 + 0.959756i \(0.409389\pi\)
\(440\) −23.0144 −1.09717
\(441\) 3.51640 0.167447
\(442\) 61.1595 2.90906
\(443\) −26.1449 −1.24218 −0.621090 0.783739i \(-0.713310\pi\)
−0.621090 + 0.783739i \(0.713310\pi\)
\(444\) 106.768 5.06697
\(445\) 8.51751 0.403769
\(446\) 36.3430 1.72089
\(447\) 10.7726 0.509527
\(448\) 4.57370 0.216087
\(449\) −41.4442 −1.95587 −0.977936 0.208906i \(-0.933010\pi\)
−0.977936 + 0.208906i \(0.933010\pi\)
\(450\) 37.6875 1.77661
\(451\) 7.20517 0.339278
\(452\) −69.8034 −3.28328
\(453\) −18.5266 −0.870456
\(454\) 41.7375 1.95884
\(455\) −2.66564 −0.124967
\(456\) 38.6057 1.80788
\(457\) 10.4933 0.490857 0.245429 0.969415i \(-0.421071\pi\)
0.245429 + 0.969415i \(0.421071\pi\)
\(458\) 13.0059 0.607726
\(459\) 10.8280 0.505405
\(460\) 1.46186 0.0681598
\(461\) −6.77599 −0.315589 −0.157795 0.987472i \(-0.550438\pi\)
−0.157795 + 0.987472i \(0.550438\pi\)
\(462\) −23.5184 −1.09417
\(463\) −0.307725 −0.0143012 −0.00715061 0.999974i \(-0.502276\pi\)
−0.00715061 + 0.999974i \(0.502276\pi\)
\(464\) 10.9680 0.509177
\(465\) −14.9691 −0.694175
\(466\) −15.6860 −0.726641
\(467\) 41.3969 1.91562 0.957810 0.287402i \(-0.0927917\pi\)
0.957810 + 0.287402i \(0.0927917\pi\)
\(468\) 47.5167 2.19646
\(469\) 2.20617 0.101872
\(470\) −31.1523 −1.43695
\(471\) 4.08305 0.188137
\(472\) 37.4857 1.72542
\(473\) 33.4837 1.53958
\(474\) 104.742 4.81095
\(475\) −8.97691 −0.411889
\(476\) −38.5764 −1.76815
\(477\) 31.2909 1.43271
\(478\) 2.84642 0.130192
\(479\) 6.38702 0.291830 0.145915 0.989297i \(-0.453387\pi\)
0.145915 + 0.989297i \(0.453387\pi\)
\(480\) −20.0145 −0.913535
\(481\) −25.6247 −1.16838
\(482\) −37.4686 −1.70665
\(483\) 0.857692 0.0390264
\(484\) 7.86917 0.357690
\(485\) −5.09063 −0.231153
\(486\) −57.6904 −2.61689
\(487\) 8.25725 0.374172 0.187086 0.982344i \(-0.440096\pi\)
0.187086 + 0.982344i \(0.440096\pi\)
\(488\) −45.3497 −2.05289
\(489\) 62.2615 2.81556
\(490\) 2.39738 0.108302
\(491\) 11.8967 0.536892 0.268446 0.963295i \(-0.413490\pi\)
0.268446 + 0.963295i \(0.413490\pi\)
\(492\) 24.2620 1.09382
\(493\) −10.3994 −0.468366
\(494\) −16.1381 −0.726087
\(495\) 11.5984 0.521309
\(496\) −54.8344 −2.46214
\(497\) −2.33177 −0.104594
\(498\) −6.03919 −0.270622
\(499\) 8.42778 0.377279 0.188640 0.982046i \(-0.439592\pi\)
0.188640 + 0.982046i \(0.439592\pi\)
\(500\) 39.7747 1.77878
\(501\) 8.17088 0.365048
\(502\) −49.8695 −2.22579
\(503\) 38.8892 1.73398 0.866991 0.498323i \(-0.166051\pi\)
0.866991 + 0.498323i \(0.166051\pi\)
\(504\) −24.5357 −1.09291
\(505\) 6.34826 0.282494
\(506\) −3.09551 −0.137612
\(507\) 12.0518 0.535237
\(508\) 99.1549 4.39929
\(509\) −19.2784 −0.854501 −0.427250 0.904133i \(-0.640518\pi\)
−0.427250 + 0.904133i \(0.640518\pi\)
\(510\) 50.2689 2.22594
\(511\) −8.74179 −0.386714
\(512\) 47.5781 2.10267
\(513\) −2.85716 −0.126147
\(514\) −10.2814 −0.453492
\(515\) 5.68025 0.250302
\(516\) 112.750 4.96354
\(517\) 46.2634 2.03466
\(518\) 23.0459 1.01258
\(519\) 11.9986 0.526682
\(520\) 18.5995 0.815643
\(521\) 24.1563 1.05831 0.529154 0.848526i \(-0.322509\pi\)
0.529154 + 0.848526i \(0.322509\pi\)
\(522\) −11.5204 −0.504234
\(523\) −15.1764 −0.663617 −0.331809 0.943347i \(-0.607659\pi\)
−0.331809 + 0.943347i \(0.607659\pi\)
\(524\) 47.5180 2.07584
\(525\) 10.5726 0.461428
\(526\) 75.0996 3.27450
\(527\) 51.9917 2.26479
\(528\) 78.7346 3.42648
\(529\) −22.8871 −0.995092
\(530\) 21.3332 0.926656
\(531\) −18.8913 −0.819815
\(532\) 10.1791 0.441320
\(533\) −5.82298 −0.252221
\(534\) −60.7324 −2.62815
\(535\) −5.11632 −0.221198
\(536\) −15.3936 −0.664901
\(537\) 20.9813 0.905410
\(538\) −29.7738 −1.28364
\(539\) −3.56028 −0.153352
\(540\) 5.73543 0.246814
\(541\) −20.0158 −0.860546 −0.430273 0.902699i \(-0.641583\pi\)
−0.430273 + 0.902699i \(0.641583\pi\)
\(542\) 5.34355 0.229525
\(543\) 56.9671 2.44469
\(544\) 69.5160 2.98047
\(545\) −2.40341 −0.102951
\(546\) 19.0068 0.813416
\(547\) 25.2533 1.07975 0.539877 0.841744i \(-0.318471\pi\)
0.539877 + 0.841744i \(0.318471\pi\)
\(548\) −45.1924 −1.93053
\(549\) 22.8545 0.975408
\(550\) −38.1578 −1.62706
\(551\) 2.74408 0.116902
\(552\) −5.98455 −0.254719
\(553\) 15.8561 0.674270
\(554\) −10.0617 −0.427479
\(555\) −21.0617 −0.894019
\(556\) 49.4983 2.09919
\(557\) 2.56624 0.108735 0.0543675 0.998521i \(-0.482686\pi\)
0.0543675 + 0.998521i \(0.482686\pi\)
\(558\) 57.5961 2.43824
\(559\) −27.0604 −1.14453
\(560\) −8.02591 −0.339156
\(561\) −74.6529 −3.15185
\(562\) −27.2253 −1.14843
\(563\) −4.29395 −0.180969 −0.0904843 0.995898i \(-0.528841\pi\)
−0.0904843 + 0.995898i \(0.528841\pi\)
\(564\) 155.783 6.55965
\(565\) 13.7699 0.579303
\(566\) 8.14113 0.342197
\(567\) −7.18414 −0.301706
\(568\) 16.2699 0.682672
\(569\) 30.1446 1.26373 0.631864 0.775080i \(-0.282290\pi\)
0.631864 + 0.775080i \(0.282290\pi\)
\(570\) −13.2644 −0.555584
\(571\) −2.79198 −0.116841 −0.0584204 0.998292i \(-0.518606\pi\)
−0.0584204 + 0.998292i \(0.518606\pi\)
\(572\) −48.1096 −2.01156
\(573\) −7.77756 −0.324912
\(574\) 5.23697 0.218587
\(575\) 1.39158 0.0580328
\(576\) 16.0829 0.670123
\(577\) −36.0580 −1.50111 −0.750556 0.660807i \(-0.770214\pi\)
−0.750556 + 0.660807i \(0.770214\pi\)
\(578\) −130.606 −5.43249
\(579\) 25.7185 1.06882
\(580\) −5.50844 −0.228726
\(581\) −0.914229 −0.0379286
\(582\) 36.2976 1.50459
\(583\) −31.6814 −1.31211
\(584\) 60.9959 2.52403
\(585\) −9.37345 −0.387545
\(586\) 25.7973 1.06568
\(587\) −17.2070 −0.710209 −0.355104 0.934827i \(-0.615555\pi\)
−0.355104 + 0.934827i \(0.615555\pi\)
\(588\) −11.9885 −0.494399
\(589\) −13.7190 −0.565281
\(590\) −12.8796 −0.530243
\(591\) 24.5234 1.00876
\(592\) −77.1526 −3.17095
\(593\) −1.90670 −0.0782988 −0.0391494 0.999233i \(-0.512465\pi\)
−0.0391494 + 0.999233i \(0.512465\pi\)
\(594\) −12.1448 −0.498308
\(595\) 7.60984 0.311973
\(596\) −19.8189 −0.811815
\(597\) 19.0767 0.780756
\(598\) 2.50169 0.102302
\(599\) 42.5983 1.74052 0.870260 0.492592i \(-0.163951\pi\)
0.870260 + 0.492592i \(0.163951\pi\)
\(600\) −73.7707 −3.01168
\(601\) 15.9275 0.649695 0.324847 0.945766i \(-0.394687\pi\)
0.324847 + 0.945766i \(0.394687\pi\)
\(602\) 24.3371 0.991908
\(603\) 7.75778 0.315921
\(604\) 34.0843 1.38687
\(605\) −1.55232 −0.0631110
\(606\) −45.2649 −1.83876
\(607\) −37.5467 −1.52398 −0.761988 0.647591i \(-0.775776\pi\)
−0.761988 + 0.647591i \(0.775776\pi\)
\(608\) −18.3431 −0.743911
\(609\) −3.23187 −0.130962
\(610\) 15.5816 0.630879
\(611\) −37.3886 −1.51258
\(612\) −135.650 −5.48332
\(613\) 22.9103 0.925337 0.462669 0.886531i \(-0.346892\pi\)
0.462669 + 0.886531i \(0.346892\pi\)
\(614\) 42.4494 1.71312
\(615\) −4.78608 −0.192993
\(616\) 24.8419 1.00091
\(617\) 26.2985 1.05874 0.529370 0.848391i \(-0.322428\pi\)
0.529370 + 0.848391i \(0.322428\pi\)
\(618\) −40.5018 −1.62922
\(619\) −15.0138 −0.603455 −0.301728 0.953394i \(-0.597563\pi\)
−0.301728 + 0.953394i \(0.597563\pi\)
\(620\) 27.5394 1.10601
\(621\) 0.442910 0.0177733
\(622\) 67.7175 2.71523
\(623\) −9.19383 −0.368343
\(624\) −63.6307 −2.54727
\(625\) 12.8623 0.514494
\(626\) −6.72973 −0.268974
\(627\) 19.6986 0.786685
\(628\) −7.51179 −0.299753
\(629\) 73.1530 2.91680
\(630\) 8.43013 0.335864
\(631\) 35.9330 1.43047 0.715235 0.698884i \(-0.246320\pi\)
0.715235 + 0.698884i \(0.246320\pi\)
\(632\) −110.636 −4.40086
\(633\) 72.8235 2.89447
\(634\) 24.6822 0.980257
\(635\) −19.5600 −0.776213
\(636\) −106.681 −4.23017
\(637\) 2.87730 0.114003
\(638\) 11.6642 0.461789
\(639\) −8.19944 −0.324365
\(640\) −4.71606 −0.186419
\(641\) 46.5780 1.83972 0.919860 0.392246i \(-0.128302\pi\)
0.919860 + 0.392246i \(0.128302\pi\)
\(642\) 36.4809 1.43979
\(643\) 29.5578 1.16565 0.582823 0.812599i \(-0.301948\pi\)
0.582823 + 0.812599i \(0.301948\pi\)
\(644\) −1.57794 −0.0621796
\(645\) −22.2418 −0.875770
\(646\) 46.0708 1.81263
\(647\) 33.0627 1.29983 0.649914 0.760008i \(-0.274805\pi\)
0.649914 + 0.760008i \(0.274805\pi\)
\(648\) 50.1274 1.96919
\(649\) 19.1271 0.750804
\(650\) 30.8379 1.20956
\(651\) 16.1577 0.633269
\(652\) −114.546 −4.48595
\(653\) −24.3924 −0.954547 −0.477273 0.878755i \(-0.658375\pi\)
−0.477273 + 0.878755i \(0.658375\pi\)
\(654\) 17.1370 0.670110
\(655\) −9.37372 −0.366262
\(656\) −17.5323 −0.684520
\(657\) −30.7396 −1.19927
\(658\) 33.6259 1.31087
\(659\) 12.7268 0.495766 0.247883 0.968790i \(-0.420265\pi\)
0.247883 + 0.968790i \(0.420265\pi\)
\(660\) −39.5427 −1.53920
\(661\) −32.1814 −1.25171 −0.625856 0.779939i \(-0.715250\pi\)
−0.625856 + 0.779939i \(0.715250\pi\)
\(662\) −40.0958 −1.55837
\(663\) 60.3321 2.34310
\(664\) 6.37903 0.247555
\(665\) −2.00800 −0.0778669
\(666\) 81.0384 3.14017
\(667\) −0.425380 −0.0164708
\(668\) −15.0324 −0.581621
\(669\) 35.8513 1.38609
\(670\) 5.28903 0.204333
\(671\) −23.1397 −0.893300
\(672\) 21.6038 0.833383
\(673\) 39.5329 1.52388 0.761941 0.647646i \(-0.224247\pi\)
0.761941 + 0.647646i \(0.224247\pi\)
\(674\) −25.7657 −0.992456
\(675\) 5.45968 0.210143
\(676\) −22.1722 −0.852778
\(677\) 9.41019 0.361663 0.180831 0.983514i \(-0.442121\pi\)
0.180831 + 0.983514i \(0.442121\pi\)
\(678\) −98.1833 −3.77071
\(679\) 5.49484 0.210872
\(680\) −53.0977 −2.03620
\(681\) 41.1728 1.57774
\(682\) −58.3148 −2.23299
\(683\) 23.1050 0.884088 0.442044 0.896993i \(-0.354253\pi\)
0.442044 + 0.896993i \(0.354253\pi\)
\(684\) 35.7938 1.36861
\(685\) 8.91496 0.340623
\(686\) −2.58774 −0.0988002
\(687\) 12.8299 0.489493
\(688\) −81.4755 −3.10623
\(689\) 25.6039 0.975429
\(690\) 2.05621 0.0782786
\(691\) 4.43164 0.168587 0.0842937 0.996441i \(-0.473137\pi\)
0.0842937 + 0.996441i \(0.473137\pi\)
\(692\) −22.0745 −0.839146
\(693\) −12.5194 −0.475571
\(694\) −30.8423 −1.17076
\(695\) −9.76435 −0.370383
\(696\) 22.5504 0.854769
\(697\) 16.6234 0.629655
\(698\) 57.5690 2.17902
\(699\) −15.4738 −0.585273
\(700\) −19.4510 −0.735180
\(701\) 31.5133 1.19024 0.595121 0.803636i \(-0.297104\pi\)
0.595121 + 0.803636i \(0.297104\pi\)
\(702\) 9.81505 0.370445
\(703\) −19.3028 −0.728019
\(704\) −16.2836 −0.613713
\(705\) −30.7308 −1.15739
\(706\) 20.2313 0.761416
\(707\) −6.85233 −0.257708
\(708\) 64.4068 2.42056
\(709\) 22.0676 0.828766 0.414383 0.910103i \(-0.363997\pi\)
0.414383 + 0.910103i \(0.363997\pi\)
\(710\) −5.59013 −0.209794
\(711\) 55.7563 2.09103
\(712\) 64.1500 2.40412
\(713\) 2.12668 0.0796449
\(714\) −54.2604 −2.03064
\(715\) 9.49043 0.354922
\(716\) −38.6004 −1.44256
\(717\) 2.80791 0.104863
\(718\) −75.7686 −2.82766
\(719\) −19.9026 −0.742242 −0.371121 0.928585i \(-0.621026\pi\)
−0.371121 + 0.928585i \(0.621026\pi\)
\(720\) −28.2223 −1.05178
\(721\) −6.13127 −0.228341
\(722\) 37.0103 1.37738
\(723\) −36.9616 −1.37462
\(724\) −104.805 −3.89506
\(725\) −5.24360 −0.194742
\(726\) 11.0685 0.410792
\(727\) 31.7129 1.17617 0.588083 0.808801i \(-0.299883\pi\)
0.588083 + 0.808801i \(0.299883\pi\)
\(728\) −20.0764 −0.744080
\(729\) −35.3574 −1.30953
\(730\) −20.9574 −0.775666
\(731\) 77.2518 2.85726
\(732\) −77.9186 −2.87995
\(733\) 0.0386833 0.00142880 0.000714401 1.00000i \(-0.499773\pi\)
0.000714401 1.00000i \(0.499773\pi\)
\(734\) 30.5012 1.12582
\(735\) 2.36494 0.0872321
\(736\) 2.84350 0.104813
\(737\) −7.85459 −0.289328
\(738\) 18.4153 0.677875
\(739\) −6.45203 −0.237342 −0.118671 0.992934i \(-0.537863\pi\)
−0.118671 + 0.992934i \(0.537863\pi\)
\(740\) 38.7483 1.42441
\(741\) −15.9197 −0.584827
\(742\) −23.0271 −0.845353
\(743\) −22.8314 −0.837603 −0.418801 0.908078i \(-0.637550\pi\)
−0.418801 + 0.908078i \(0.637550\pi\)
\(744\) −112.740 −4.13326
\(745\) 3.90961 0.143237
\(746\) 78.9011 2.88877
\(747\) −3.21479 −0.117623
\(748\) 137.343 5.02175
\(749\) 5.52258 0.201791
\(750\) 55.9458 2.04285
\(751\) 18.8441 0.687633 0.343816 0.939037i \(-0.388280\pi\)
0.343816 + 0.939037i \(0.388280\pi\)
\(752\) −112.572 −4.10509
\(753\) −49.1948 −1.79276
\(754\) −9.42660 −0.343296
\(755\) −6.72370 −0.244701
\(756\) −6.19085 −0.225159
\(757\) −32.4425 −1.17914 −0.589572 0.807716i \(-0.700704\pi\)
−0.589572 + 0.807716i \(0.700704\pi\)
\(758\) 26.2339 0.952860
\(759\) −3.05362 −0.110840
\(760\) 14.0108 0.508226
\(761\) −14.7522 −0.534767 −0.267383 0.963590i \(-0.586159\pi\)
−0.267383 + 0.963590i \(0.586159\pi\)
\(762\) 139.468 5.05240
\(763\) 2.59425 0.0939181
\(764\) 14.3088 0.517673
\(765\) 26.7592 0.967481
\(766\) 19.1968 0.693607
\(767\) −15.4579 −0.558152
\(768\) 56.9777 2.05600
\(769\) 19.0848 0.688216 0.344108 0.938930i \(-0.388181\pi\)
0.344108 + 0.938930i \(0.388181\pi\)
\(770\) −8.53533 −0.307592
\(771\) −10.1423 −0.365265
\(772\) −47.3157 −1.70293
\(773\) 5.51555 0.198381 0.0991903 0.995068i \(-0.468375\pi\)
0.0991903 + 0.995068i \(0.468375\pi\)
\(774\) 85.5790 3.07607
\(775\) 26.2153 0.941682
\(776\) −38.3402 −1.37633
\(777\) 22.7340 0.815579
\(778\) 56.8830 2.03936
\(779\) −4.38639 −0.157159
\(780\) 31.9572 1.14425
\(781\) 8.30176 0.297060
\(782\) −7.14178 −0.255390
\(783\) −1.66893 −0.0596425
\(784\) 8.66319 0.309400
\(785\) 1.48182 0.0528886
\(786\) 66.8374 2.38401
\(787\) −54.1255 −1.92936 −0.964682 0.263417i \(-0.915151\pi\)
−0.964682 + 0.263417i \(0.915151\pi\)
\(788\) −45.1169 −1.60722
\(789\) 74.0835 2.63744
\(790\) 38.0130 1.35244
\(791\) −14.8633 −0.528477
\(792\) 87.3538 3.10398
\(793\) 18.7008 0.664084
\(794\) 19.4256 0.689389
\(795\) 21.0446 0.746374
\(796\) −35.0963 −1.24396
\(797\) 21.7229 0.769465 0.384732 0.923028i \(-0.374294\pi\)
0.384732 + 0.923028i \(0.374294\pi\)
\(798\) 14.3176 0.506838
\(799\) 106.736 3.77606
\(800\) 35.0514 1.23925
\(801\) −32.3292 −1.14229
\(802\) −0.374297 −0.0132169
\(803\) 31.1232 1.09831
\(804\) −26.4488 −0.932777
\(805\) 0.311275 0.0109710
\(806\) 47.1281 1.66002
\(807\) −29.3710 −1.03391
\(808\) 47.8121 1.68203
\(809\) −44.5713 −1.56704 −0.783522 0.621364i \(-0.786579\pi\)
−0.783522 + 0.621364i \(0.786579\pi\)
\(810\) −17.2231 −0.605158
\(811\) −23.9069 −0.839486 −0.419743 0.907643i \(-0.637880\pi\)
−0.419743 + 0.907643i \(0.637880\pi\)
\(812\) 5.94583 0.208658
\(813\) 5.27125 0.184871
\(814\) −82.0497 −2.87584
\(815\) 22.5960 0.791504
\(816\) 181.652 6.35910
\(817\) −20.3843 −0.713158
\(818\) −49.5984 −1.73417
\(819\) 10.1177 0.353542
\(820\) 8.80520 0.307491
\(821\) −1.65022 −0.0575929 −0.0287965 0.999585i \(-0.509167\pi\)
−0.0287965 + 0.999585i \(0.509167\pi\)
\(822\) −63.5663 −2.21713
\(823\) 13.3037 0.463739 0.231869 0.972747i \(-0.425516\pi\)
0.231869 + 0.972747i \(0.425516\pi\)
\(824\) 42.7810 1.49035
\(825\) −37.6416 −1.31051
\(826\) 13.9022 0.483721
\(827\) −2.04451 −0.0710946 −0.0355473 0.999368i \(-0.511317\pi\)
−0.0355473 + 0.999368i \(0.511317\pi\)
\(828\) −5.54866 −0.192829
\(829\) 50.8295 1.76538 0.882691 0.469953i \(-0.155729\pi\)
0.882691 + 0.469953i \(0.155729\pi\)
\(830\) −2.19175 −0.0760768
\(831\) −9.92552 −0.344312
\(832\) 13.1599 0.456238
\(833\) −8.21408 −0.284601
\(834\) 69.6227 2.41084
\(835\) 2.96539 0.102621
\(836\) −36.2405 −1.25340
\(837\) 8.34377 0.288403
\(838\) 36.7423 1.26924
\(839\) 34.4263 1.18853 0.594265 0.804270i \(-0.297443\pi\)
0.594265 + 0.804270i \(0.297443\pi\)
\(840\) −16.5014 −0.569352
\(841\) −27.3971 −0.944728
\(842\) −83.4315 −2.87524
\(843\) −26.8570 −0.925003
\(844\) −133.977 −4.61168
\(845\) 4.37384 0.150465
\(846\) 118.242 4.06524
\(847\) 1.67558 0.0575738
\(848\) 77.0899 2.64728
\(849\) 8.03098 0.275623
\(850\) −88.0357 −3.01960
\(851\) 2.99227 0.102574
\(852\) 27.9546 0.957707
\(853\) −54.5516 −1.86781 −0.933906 0.357520i \(-0.883622\pi\)
−0.933906 + 0.357520i \(0.883622\pi\)
\(854\) −16.8188 −0.575527
\(855\) −7.06092 −0.241478
\(856\) −38.5338 −1.31706
\(857\) −32.9574 −1.12580 −0.562901 0.826524i \(-0.690315\pi\)
−0.562901 + 0.826524i \(0.690315\pi\)
\(858\) −67.6695 −2.31020
\(859\) −15.7218 −0.536420 −0.268210 0.963360i \(-0.586432\pi\)
−0.268210 + 0.963360i \(0.586432\pi\)
\(860\) 40.9193 1.39534
\(861\) 5.16611 0.176061
\(862\) −70.1373 −2.38889
\(863\) −1.00000 −0.0340404
\(864\) 11.1561 0.379539
\(865\) 4.35456 0.148060
\(866\) 48.1261 1.63539
\(867\) −128.839 −4.37560
\(868\) −29.7261 −1.00897
\(869\) −56.4521 −1.91501
\(870\) −7.74800 −0.262682
\(871\) 6.34782 0.215088
\(872\) −18.1014 −0.612990
\(873\) 19.3220 0.653951
\(874\) 1.88449 0.0637440
\(875\) 8.46923 0.286312
\(876\) 104.801 3.54091
\(877\) 11.6583 0.393672 0.196836 0.980436i \(-0.436933\pi\)
0.196836 + 0.980436i \(0.436933\pi\)
\(878\) −30.4531 −1.02774
\(879\) 25.4483 0.858349
\(880\) 28.5745 0.963245
\(881\) −25.3140 −0.852852 −0.426426 0.904523i \(-0.640227\pi\)
−0.426426 + 0.904523i \(0.640227\pi\)
\(882\) −9.09950 −0.306396
\(883\) 7.35615 0.247554 0.123777 0.992310i \(-0.460499\pi\)
0.123777 + 0.992310i \(0.460499\pi\)
\(884\) −110.996 −3.73320
\(885\) −12.7053 −0.427084
\(886\) 67.6560 2.27295
\(887\) −26.6486 −0.894774 −0.447387 0.894340i \(-0.647645\pi\)
−0.447387 + 0.894340i \(0.647645\pi\)
\(888\) −158.627 −5.32317
\(889\) 21.1131 0.708110
\(890\) −22.0411 −0.738819
\(891\) 25.5776 0.856880
\(892\) −65.9574 −2.20842
\(893\) −28.1644 −0.942486
\(894\) −27.8767 −0.932336
\(895\) 7.61457 0.254527
\(896\) 5.09053 0.170063
\(897\) 2.46784 0.0823988
\(898\) 107.247 3.57886
\(899\) −8.01355 −0.267267
\(900\) −68.3976 −2.27992
\(901\) −73.0935 −2.43510
\(902\) −18.6451 −0.620813
\(903\) 24.0079 0.798931
\(904\) 103.708 3.44929
\(905\) 20.6746 0.687246
\(906\) 47.9420 1.59277
\(907\) −5.04332 −0.167461 −0.0837304 0.996488i \(-0.526683\pi\)
−0.0837304 + 0.996488i \(0.526683\pi\)
\(908\) −75.7477 −2.51377
\(909\) −24.0955 −0.799197
\(910\) 6.89797 0.228666
\(911\) 48.7189 1.61413 0.807065 0.590463i \(-0.201055\pi\)
0.807065 + 0.590463i \(0.201055\pi\)
\(912\) −47.9323 −1.58720
\(913\) 3.25491 0.107722
\(914\) −27.1540 −0.898173
\(915\) 15.3707 0.508141
\(916\) −23.6039 −0.779895
\(917\) 10.1180 0.334127
\(918\) −28.0199 −0.924794
\(919\) 21.8140 0.719578 0.359789 0.933034i \(-0.382849\pi\)
0.359789 + 0.933034i \(0.382849\pi\)
\(920\) −2.17192 −0.0716062
\(921\) 41.8751 1.37983
\(922\) 17.5345 0.577467
\(923\) −6.70921 −0.220836
\(924\) 42.6826 1.40415
\(925\) 36.8853 1.21278
\(926\) 0.796312 0.0261684
\(927\) −21.5600 −0.708123
\(928\) −10.7146 −0.351724
\(929\) −26.3320 −0.863926 −0.431963 0.901891i \(-0.642179\pi\)
−0.431963 + 0.901891i \(0.642179\pi\)
\(930\) 38.7360 1.27020
\(931\) 2.16744 0.0710350
\(932\) 28.4679 0.932498
\(933\) 66.8013 2.18698
\(934\) −107.124 −3.50521
\(935\) −27.0931 −0.886040
\(936\) −70.5965 −2.30752
\(937\) 14.6705 0.479263 0.239632 0.970864i \(-0.422973\pi\)
0.239632 + 0.970864i \(0.422973\pi\)
\(938\) −5.70899 −0.186405
\(939\) −6.63868 −0.216645
\(940\) 56.5370 1.84403
\(941\) −30.2139 −0.984946 −0.492473 0.870328i \(-0.663907\pi\)
−0.492473 + 0.870328i \(0.663907\pi\)
\(942\) −10.5658 −0.344254
\(943\) 0.679967 0.0221428
\(944\) −46.5418 −1.51481
\(945\) 1.22125 0.0397272
\(946\) −86.6470 −2.81714
\(947\) 46.4017 1.50785 0.753927 0.656958i \(-0.228157\pi\)
0.753927 + 0.656958i \(0.228157\pi\)
\(948\) −190.092 −6.17389
\(949\) −25.1528 −0.816493
\(950\) 23.2299 0.753677
\(951\) 24.3483 0.789547
\(952\) 57.3138 1.85755
\(953\) 14.9037 0.482777 0.241389 0.970429i \(-0.422397\pi\)
0.241389 + 0.970429i \(0.422397\pi\)
\(954\) −80.9725 −2.62158
\(955\) −2.82264 −0.0913386
\(956\) −5.16586 −0.167076
\(957\) 11.5063 0.371947
\(958\) −16.5279 −0.533993
\(959\) −9.62283 −0.310738
\(960\) 10.8165 0.349102
\(961\) 9.06363 0.292375
\(962\) 66.3099 2.13792
\(963\) 19.4196 0.625787
\(964\) 68.0002 2.19014
\(965\) 9.33380 0.300466
\(966\) −2.21948 −0.0714106
\(967\) 43.4998 1.39886 0.699430 0.714701i \(-0.253437\pi\)
0.699430 + 0.714701i \(0.253437\pi\)
\(968\) −11.6914 −0.375776
\(969\) 45.4475 1.45998
\(970\) 13.1732 0.422966
\(971\) −1.24168 −0.0398474 −0.0199237 0.999802i \(-0.506342\pi\)
−0.0199237 + 0.999802i \(0.506342\pi\)
\(972\) 104.700 3.35825
\(973\) 10.5397 0.337886
\(974\) −21.3676 −0.684661
\(975\) 30.4207 0.974242
\(976\) 56.3057 1.80230
\(977\) −52.0623 −1.66562 −0.832810 0.553559i \(-0.813269\pi\)
−0.832810 + 0.553559i \(0.813269\pi\)
\(978\) −161.116 −5.15193
\(979\) 32.7326 1.04614
\(980\) −4.35090 −0.138984
\(981\) 9.12241 0.291256
\(982\) −30.7856 −0.982408
\(983\) 11.8054 0.376533 0.188267 0.982118i \(-0.439713\pi\)
0.188267 + 0.982118i \(0.439713\pi\)
\(984\) −36.0466 −1.14912
\(985\) 8.90006 0.283579
\(986\) 26.9109 0.857018
\(987\) 33.1709 1.05584
\(988\) 29.2884 0.931787
\(989\) 3.15993 0.100480
\(990\) −30.0136 −0.953895
\(991\) 32.2640 1.02490 0.512449 0.858717i \(-0.328738\pi\)
0.512449 + 0.858717i \(0.328738\pi\)
\(992\) 53.5674 1.70077
\(993\) −39.5533 −1.25519
\(994\) 6.03401 0.191387
\(995\) 6.92333 0.219484
\(996\) 10.9603 0.347289
\(997\) −54.2228 −1.71725 −0.858626 0.512602i \(-0.828682\pi\)
−0.858626 + 0.512602i \(0.828682\pi\)
\(998\) −21.8089 −0.690348
\(999\) 11.7398 0.371430
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 \(a_p\))