Properties

Label 4026.2.a.bc.1.1
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.23292\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.23292 q^{5}\) \(+1.00000 q^{6}\) \(+4.29240 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.23292 q^{5}\) \(+1.00000 q^{6}\) \(+4.29240 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-3.23292 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+2.88047 q^{13}\) \(+4.29240 q^{14}\) \(-3.23292 q^{15}\) \(+1.00000 q^{16}\) \(-1.40871 q^{17}\) \(+1.00000 q^{18}\) \(+3.85835 q^{19}\) \(-3.23292 q^{20}\) \(+4.29240 q^{21}\) \(+1.00000 q^{22}\) \(+2.00280 q^{23}\) \(+1.00000 q^{24}\) \(+5.45180 q^{25}\) \(+2.88047 q^{26}\) \(+1.00000 q^{27}\) \(+4.29240 q^{28}\) \(-1.66491 q^{29}\) \(-3.23292 q^{30}\) \(+0.769881 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(-1.40871 q^{34}\) \(-13.8770 q^{35}\) \(+1.00000 q^{36}\) \(+6.59775 q^{37}\) \(+3.85835 q^{38}\) \(+2.88047 q^{39}\) \(-3.23292 q^{40}\) \(-7.18702 q^{41}\) \(+4.29240 q^{42}\) \(-11.7343 q^{43}\) \(+1.00000 q^{44}\) \(-3.23292 q^{45}\) \(+2.00280 q^{46}\) \(+0.896639 q^{47}\) \(+1.00000 q^{48}\) \(+11.4247 q^{49}\) \(+5.45180 q^{50}\) \(-1.40871 q^{51}\) \(+2.88047 q^{52}\) \(-12.1997 q^{53}\) \(+1.00000 q^{54}\) \(-3.23292 q^{55}\) \(+4.29240 q^{56}\) \(+3.85835 q^{57}\) \(-1.66491 q^{58}\) \(+8.74700 q^{59}\) \(-3.23292 q^{60}\) \(-1.00000 q^{61}\) \(+0.769881 q^{62}\) \(+4.29240 q^{63}\) \(+1.00000 q^{64}\) \(-9.31234 q^{65}\) \(+1.00000 q^{66}\) \(+6.74484 q^{67}\) \(-1.40871 q^{68}\) \(+2.00280 q^{69}\) \(-13.8770 q^{70}\) \(+3.73137 q^{71}\) \(+1.00000 q^{72}\) \(+0.751328 q^{73}\) \(+6.59775 q^{74}\) \(+5.45180 q^{75}\) \(+3.85835 q^{76}\) \(+4.29240 q^{77}\) \(+2.88047 q^{78}\) \(+0.132373 q^{79}\) \(-3.23292 q^{80}\) \(+1.00000 q^{81}\) \(-7.18702 q^{82}\) \(+15.9513 q^{83}\) \(+4.29240 q^{84}\) \(+4.55426 q^{85}\) \(-11.7343 q^{86}\) \(-1.66491 q^{87}\) \(+1.00000 q^{88}\) \(+2.50051 q^{89}\) \(-3.23292 q^{90}\) \(+12.3641 q^{91}\) \(+2.00280 q^{92}\) \(+0.769881 q^{93}\) \(+0.896639 q^{94}\) \(-12.4737 q^{95}\) \(+1.00000 q^{96}\) \(+13.2106 q^{97}\) \(+11.4247 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −3.23292 −1.44581 −0.722904 0.690949i \(-0.757193\pi\)
−0.722904 + 0.690949i \(0.757193\pi\)
\(6\) 1.00000 0.408248
\(7\) 4.29240 1.62237 0.811187 0.584787i \(-0.198822\pi\)
0.811187 + 0.584787i \(0.198822\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −3.23292 −1.02234
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 2.88047 0.798898 0.399449 0.916755i \(-0.369201\pi\)
0.399449 + 0.916755i \(0.369201\pi\)
\(14\) 4.29240 1.14719
\(15\) −3.23292 −0.834737
\(16\) 1.00000 0.250000
\(17\) −1.40871 −0.341663 −0.170831 0.985300i \(-0.554645\pi\)
−0.170831 + 0.985300i \(0.554645\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.85835 0.885165 0.442583 0.896728i \(-0.354062\pi\)
0.442583 + 0.896728i \(0.354062\pi\)
\(20\) −3.23292 −0.722904
\(21\) 4.29240 0.936678
\(22\) 1.00000 0.213201
\(23\) 2.00280 0.417614 0.208807 0.977957i \(-0.433042\pi\)
0.208807 + 0.977957i \(0.433042\pi\)
\(24\) 1.00000 0.204124
\(25\) 5.45180 1.09036
\(26\) 2.88047 0.564906
\(27\) 1.00000 0.192450
\(28\) 4.29240 0.811187
\(29\) −1.66491 −0.309167 −0.154583 0.987980i \(-0.549403\pi\)
−0.154583 + 0.987980i \(0.549403\pi\)
\(30\) −3.23292 −0.590248
\(31\) 0.769881 0.138275 0.0691373 0.997607i \(-0.477975\pi\)
0.0691373 + 0.997607i \(0.477975\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −1.40871 −0.241592
\(35\) −13.8770 −2.34564
\(36\) 1.00000 0.166667
\(37\) 6.59775 1.08466 0.542332 0.840164i \(-0.317542\pi\)
0.542332 + 0.840164i \(0.317542\pi\)
\(38\) 3.85835 0.625906
\(39\) 2.88047 0.461244
\(40\) −3.23292 −0.511170
\(41\) −7.18702 −1.12242 −0.561212 0.827672i \(-0.689665\pi\)
−0.561212 + 0.827672i \(0.689665\pi\)
\(42\) 4.29240 0.662332
\(43\) −11.7343 −1.78946 −0.894729 0.446609i \(-0.852632\pi\)
−0.894729 + 0.446609i \(0.852632\pi\)
\(44\) 1.00000 0.150756
\(45\) −3.23292 −0.481936
\(46\) 2.00280 0.295297
\(47\) 0.896639 0.130788 0.0653941 0.997860i \(-0.479170\pi\)
0.0653941 + 0.997860i \(0.479170\pi\)
\(48\) 1.00000 0.144338
\(49\) 11.4247 1.63210
\(50\) 5.45180 0.771001
\(51\) −1.40871 −0.197259
\(52\) 2.88047 0.399449
\(53\) −12.1997 −1.67576 −0.837881 0.545854i \(-0.816205\pi\)
−0.837881 + 0.545854i \(0.816205\pi\)
\(54\) 1.00000 0.136083
\(55\) −3.23292 −0.435927
\(56\) 4.29240 0.573596
\(57\) 3.85835 0.511050
\(58\) −1.66491 −0.218614
\(59\) 8.74700 1.13876 0.569381 0.822074i \(-0.307183\pi\)
0.569381 + 0.822074i \(0.307183\pi\)
\(60\) −3.23292 −0.417369
\(61\) −1.00000 −0.128037
\(62\) 0.769881 0.0977749
\(63\) 4.29240 0.540791
\(64\) 1.00000 0.125000
\(65\) −9.31234 −1.15505
\(66\) 1.00000 0.123091
\(67\) 6.74484 0.824013 0.412007 0.911181i \(-0.364828\pi\)
0.412007 + 0.911181i \(0.364828\pi\)
\(68\) −1.40871 −0.170831
\(69\) 2.00280 0.241109
\(70\) −13.8770 −1.65862
\(71\) 3.73137 0.442832 0.221416 0.975179i \(-0.428932\pi\)
0.221416 + 0.975179i \(0.428932\pi\)
\(72\) 1.00000 0.117851
\(73\) 0.751328 0.0879362 0.0439681 0.999033i \(-0.486000\pi\)
0.0439681 + 0.999033i \(0.486000\pi\)
\(74\) 6.59775 0.766973
\(75\) 5.45180 0.629519
\(76\) 3.85835 0.442583
\(77\) 4.29240 0.489164
\(78\) 2.88047 0.326149
\(79\) 0.132373 0.0148932 0.00744659 0.999972i \(-0.497630\pi\)
0.00744659 + 0.999972i \(0.497630\pi\)
\(80\) −3.23292 −0.361452
\(81\) 1.00000 0.111111
\(82\) −7.18702 −0.793673
\(83\) 15.9513 1.75088 0.875440 0.483327i \(-0.160572\pi\)
0.875440 + 0.483327i \(0.160572\pi\)
\(84\) 4.29240 0.468339
\(85\) 4.55426 0.493979
\(86\) −11.7343 −1.26534
\(87\) −1.66491 −0.178497
\(88\) 1.00000 0.106600
\(89\) 2.50051 0.265053 0.132527 0.991179i \(-0.457691\pi\)
0.132527 + 0.991179i \(0.457691\pi\)
\(90\) −3.23292 −0.340780
\(91\) 12.3641 1.29611
\(92\) 2.00280 0.208807
\(93\) 0.769881 0.0798329
\(94\) 0.896639 0.0924813
\(95\) −12.4737 −1.27978
\(96\) 1.00000 0.102062
\(97\) 13.2106 1.34133 0.670664 0.741761i \(-0.266009\pi\)
0.670664 + 0.741761i \(0.266009\pi\)
\(98\) 11.4247 1.15407
\(99\) 1.00000 0.100504
\(100\) 5.45180 0.545180
\(101\) 12.3663 1.23049 0.615246 0.788335i \(-0.289057\pi\)
0.615246 + 0.788335i \(0.289057\pi\)
\(102\) −1.40871 −0.139483
\(103\) −8.44990 −0.832594 −0.416297 0.909229i \(-0.636672\pi\)
−0.416297 + 0.909229i \(0.636672\pi\)
\(104\) 2.88047 0.282453
\(105\) −13.8770 −1.35426
\(106\) −12.1997 −1.18494
\(107\) 12.8377 1.24107 0.620533 0.784180i \(-0.286916\pi\)
0.620533 + 0.784180i \(0.286916\pi\)
\(108\) 1.00000 0.0962250
\(109\) 7.85123 0.752011 0.376006 0.926617i \(-0.377297\pi\)
0.376006 + 0.926617i \(0.377297\pi\)
\(110\) −3.23292 −0.308247
\(111\) 6.59775 0.626231
\(112\) 4.29240 0.405594
\(113\) −3.68244 −0.346415 −0.173208 0.984885i \(-0.555413\pi\)
−0.173208 + 0.984885i \(0.555413\pi\)
\(114\) 3.85835 0.361367
\(115\) −6.47491 −0.603789
\(116\) −1.66491 −0.154583
\(117\) 2.88047 0.266299
\(118\) 8.74700 0.805227
\(119\) −6.04675 −0.554305
\(120\) −3.23292 −0.295124
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −7.18702 −0.648032
\(124\) 0.769881 0.0691373
\(125\) −1.46063 −0.130642
\(126\) 4.29240 0.382397
\(127\) 20.5720 1.82547 0.912733 0.408557i \(-0.133968\pi\)
0.912733 + 0.408557i \(0.133968\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.7343 −1.03314
\(130\) −9.31234 −0.816746
\(131\) −0.892502 −0.0779783 −0.0389891 0.999240i \(-0.512414\pi\)
−0.0389891 + 0.999240i \(0.512414\pi\)
\(132\) 1.00000 0.0870388
\(133\) 16.5616 1.43607
\(134\) 6.74484 0.582665
\(135\) −3.23292 −0.278246
\(136\) −1.40871 −0.120796
\(137\) −6.13837 −0.524436 −0.262218 0.965009i \(-0.584454\pi\)
−0.262218 + 0.965009i \(0.584454\pi\)
\(138\) 2.00280 0.170490
\(139\) −3.56248 −0.302166 −0.151083 0.988521i \(-0.548276\pi\)
−0.151083 + 0.988521i \(0.548276\pi\)
\(140\) −13.8770 −1.17282
\(141\) 0.896639 0.0755106
\(142\) 3.73137 0.313129
\(143\) 2.88047 0.240877
\(144\) 1.00000 0.0833333
\(145\) 5.38254 0.446995
\(146\) 0.751328 0.0621803
\(147\) 11.4247 0.942293
\(148\) 6.59775 0.542332
\(149\) −5.57250 −0.456517 −0.228258 0.973601i \(-0.573303\pi\)
−0.228258 + 0.973601i \(0.573303\pi\)
\(150\) 5.45180 0.445137
\(151\) 9.29629 0.756521 0.378261 0.925699i \(-0.376522\pi\)
0.378261 + 0.925699i \(0.376522\pi\)
\(152\) 3.85835 0.312953
\(153\) −1.40871 −0.113888
\(154\) 4.29240 0.345891
\(155\) −2.48897 −0.199919
\(156\) 2.88047 0.230622
\(157\) −21.7347 −1.73462 −0.867308 0.497771i \(-0.834152\pi\)
−0.867308 + 0.497771i \(0.834152\pi\)
\(158\) 0.132373 0.0105311
\(159\) −12.1997 −0.967501
\(160\) −3.23292 −0.255585
\(161\) 8.59684 0.677526
\(162\) 1.00000 0.0785674
\(163\) −9.29178 −0.727788 −0.363894 0.931440i \(-0.618553\pi\)
−0.363894 + 0.931440i \(0.618553\pi\)
\(164\) −7.18702 −0.561212
\(165\) −3.23292 −0.251683
\(166\) 15.9513 1.23806
\(167\) −12.9130 −0.999239 −0.499620 0.866245i \(-0.666527\pi\)
−0.499620 + 0.866245i \(0.666527\pi\)
\(168\) 4.29240 0.331166
\(169\) −4.70290 −0.361762
\(170\) 4.55426 0.349296
\(171\) 3.85835 0.295055
\(172\) −11.7343 −0.894729
\(173\) −23.3606 −1.77607 −0.888037 0.459771i \(-0.847931\pi\)
−0.888037 + 0.459771i \(0.847931\pi\)
\(174\) −1.66491 −0.126217
\(175\) 23.4013 1.76897
\(176\) 1.00000 0.0753778
\(177\) 8.74700 0.657465
\(178\) 2.50051 0.187421
\(179\) −4.01612 −0.300179 −0.150090 0.988672i \(-0.547956\pi\)
−0.150090 + 0.988672i \(0.547956\pi\)
\(180\) −3.23292 −0.240968
\(181\) −16.5937 −1.23340 −0.616699 0.787199i \(-0.711530\pi\)
−0.616699 + 0.787199i \(0.711530\pi\)
\(182\) 12.3641 0.916490
\(183\) −1.00000 −0.0739221
\(184\) 2.00280 0.147649
\(185\) −21.3300 −1.56821
\(186\) 0.769881 0.0564504
\(187\) −1.40871 −0.103015
\(188\) 0.896639 0.0653941
\(189\) 4.29240 0.312226
\(190\) −12.4737 −0.904940
\(191\) 7.04645 0.509863 0.254932 0.966959i \(-0.417947\pi\)
0.254932 + 0.966959i \(0.417947\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.26409 −0.306936 −0.153468 0.988154i \(-0.549044\pi\)
−0.153468 + 0.988154i \(0.549044\pi\)
\(194\) 13.2106 0.948463
\(195\) −9.31234 −0.666870
\(196\) 11.4247 0.816049
\(197\) −3.05152 −0.217412 −0.108706 0.994074i \(-0.534671\pi\)
−0.108706 + 0.994074i \(0.534671\pi\)
\(198\) 1.00000 0.0710669
\(199\) 22.6750 1.60739 0.803696 0.595041i \(-0.202864\pi\)
0.803696 + 0.595041i \(0.202864\pi\)
\(200\) 5.45180 0.385500
\(201\) 6.74484 0.475744
\(202\) 12.3663 0.870089
\(203\) −7.14647 −0.501584
\(204\) −1.40871 −0.0986296
\(205\) 23.2351 1.62281
\(206\) −8.44990 −0.588733
\(207\) 2.00280 0.139205
\(208\) 2.88047 0.199725
\(209\) 3.85835 0.266887
\(210\) −13.8770 −0.957604
\(211\) 2.07496 0.142846 0.0714231 0.997446i \(-0.477246\pi\)
0.0714231 + 0.997446i \(0.477246\pi\)
\(212\) −12.1997 −0.837881
\(213\) 3.73137 0.255669
\(214\) 12.8377 0.877566
\(215\) 37.9360 2.58721
\(216\) 1.00000 0.0680414
\(217\) 3.30464 0.224333
\(218\) 7.85123 0.531752
\(219\) 0.751328 0.0507700
\(220\) −3.23292 −0.217964
\(221\) −4.05775 −0.272954
\(222\) 6.59775 0.442812
\(223\) −4.87062 −0.326161 −0.163080 0.986613i \(-0.552143\pi\)
−0.163080 + 0.986613i \(0.552143\pi\)
\(224\) 4.29240 0.286798
\(225\) 5.45180 0.363453
\(226\) −3.68244 −0.244952
\(227\) 22.1378 1.46934 0.734670 0.678425i \(-0.237337\pi\)
0.734670 + 0.678425i \(0.237337\pi\)
\(228\) 3.85835 0.255525
\(229\) −21.5095 −1.42139 −0.710695 0.703500i \(-0.751620\pi\)
−0.710695 + 0.703500i \(0.751620\pi\)
\(230\) −6.47491 −0.426943
\(231\) 4.29240 0.282419
\(232\) −1.66491 −0.109307
\(233\) −13.9601 −0.914554 −0.457277 0.889324i \(-0.651175\pi\)
−0.457277 + 0.889324i \(0.651175\pi\)
\(234\) 2.88047 0.188302
\(235\) −2.89877 −0.189095
\(236\) 8.74700 0.569381
\(237\) 0.132373 0.00859858
\(238\) −6.04675 −0.391953
\(239\) 4.12106 0.266569 0.133284 0.991078i \(-0.457448\pi\)
0.133284 + 0.991078i \(0.457448\pi\)
\(240\) −3.23292 −0.208684
\(241\) 6.60585 0.425520 0.212760 0.977104i \(-0.431755\pi\)
0.212760 + 0.977104i \(0.431755\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −36.9352 −2.35970
\(246\) −7.18702 −0.458227
\(247\) 11.1138 0.707157
\(248\) 0.769881 0.0488875
\(249\) 15.9513 1.01087
\(250\) −1.46063 −0.0923781
\(251\) −25.8066 −1.62890 −0.814449 0.580235i \(-0.802961\pi\)
−0.814449 + 0.580235i \(0.802961\pi\)
\(252\) 4.29240 0.270396
\(253\) 2.00280 0.125915
\(254\) 20.5720 1.29080
\(255\) 4.55426 0.285199
\(256\) 1.00000 0.0625000
\(257\) −21.8807 −1.36488 −0.682441 0.730940i \(-0.739082\pi\)
−0.682441 + 0.730940i \(0.739082\pi\)
\(258\) −11.7343 −0.730543
\(259\) 28.3202 1.75973
\(260\) −9.31234 −0.577527
\(261\) −1.66491 −0.103056
\(262\) −0.892502 −0.0551390
\(263\) 21.7683 1.34229 0.671147 0.741325i \(-0.265802\pi\)
0.671147 + 0.741325i \(0.265802\pi\)
\(264\) 1.00000 0.0615457
\(265\) 39.4408 2.42283
\(266\) 16.5616 1.01545
\(267\) 2.50051 0.153029
\(268\) 6.74484 0.412007
\(269\) 4.86810 0.296813 0.148407 0.988926i \(-0.452586\pi\)
0.148407 + 0.988926i \(0.452586\pi\)
\(270\) −3.23292 −0.196749
\(271\) 19.8242 1.20424 0.602118 0.798407i \(-0.294324\pi\)
0.602118 + 0.798407i \(0.294324\pi\)
\(272\) −1.40871 −0.0854157
\(273\) 12.3641 0.748311
\(274\) −6.13837 −0.370833
\(275\) 5.45180 0.328756
\(276\) 2.00280 0.120555
\(277\) −6.99143 −0.420075 −0.210037 0.977693i \(-0.567359\pi\)
−0.210037 + 0.977693i \(0.567359\pi\)
\(278\) −3.56248 −0.213663
\(279\) 0.769881 0.0460916
\(280\) −13.8770 −0.829309
\(281\) −13.9571 −0.832609 −0.416305 0.909225i \(-0.636675\pi\)
−0.416305 + 0.909225i \(0.636675\pi\)
\(282\) 0.896639 0.0533941
\(283\) −7.59877 −0.451700 −0.225850 0.974162i \(-0.572516\pi\)
−0.225850 + 0.974162i \(0.572516\pi\)
\(284\) 3.73137 0.221416
\(285\) −12.4737 −0.738880
\(286\) 2.88047 0.170326
\(287\) −30.8495 −1.82099
\(288\) 1.00000 0.0589256
\(289\) −15.0155 −0.883267
\(290\) 5.38254 0.316073
\(291\) 13.2106 0.774416
\(292\) 0.751328 0.0439681
\(293\) 18.0763 1.05603 0.528013 0.849236i \(-0.322937\pi\)
0.528013 + 0.849236i \(0.322937\pi\)
\(294\) 11.4247 0.666301
\(295\) −28.2784 −1.64643
\(296\) 6.59775 0.383486
\(297\) 1.00000 0.0580259
\(298\) −5.57250 −0.322806
\(299\) 5.76902 0.333631
\(300\) 5.45180 0.314760
\(301\) −50.3681 −2.90317
\(302\) 9.29629 0.534941
\(303\) 12.3663 0.710424
\(304\) 3.85835 0.221291
\(305\) 3.23292 0.185117
\(306\) −1.40871 −0.0805307
\(307\) −10.1292 −0.578104 −0.289052 0.957313i \(-0.593340\pi\)
−0.289052 + 0.957313i \(0.593340\pi\)
\(308\) 4.29240 0.244582
\(309\) −8.44990 −0.480698
\(310\) −2.48897 −0.141364
\(311\) 9.70940 0.550570 0.275285 0.961363i \(-0.411228\pi\)
0.275285 + 0.961363i \(0.411228\pi\)
\(312\) 2.88047 0.163074
\(313\) −3.60353 −0.203683 −0.101842 0.994801i \(-0.532474\pi\)
−0.101842 + 0.994801i \(0.532474\pi\)
\(314\) −21.7347 −1.22656
\(315\) −13.8770 −0.781880
\(316\) 0.132373 0.00744659
\(317\) −24.8688 −1.39677 −0.698386 0.715722i \(-0.746098\pi\)
−0.698386 + 0.715722i \(0.746098\pi\)
\(318\) −12.1997 −0.684127
\(319\) −1.66491 −0.0932172
\(320\) −3.23292 −0.180726
\(321\) 12.8377 0.716530
\(322\) 8.59684 0.479083
\(323\) −5.43530 −0.302428
\(324\) 1.00000 0.0555556
\(325\) 15.7037 0.871086
\(326\) −9.29178 −0.514624
\(327\) 7.85123 0.434174
\(328\) −7.18702 −0.396837
\(329\) 3.84873 0.212188
\(330\) −3.23292 −0.177967
\(331\) 34.3670 1.88898 0.944490 0.328541i \(-0.106557\pi\)
0.944490 + 0.328541i \(0.106557\pi\)
\(332\) 15.9513 0.875440
\(333\) 6.59775 0.361554
\(334\) −12.9130 −0.706569
\(335\) −21.8055 −1.19136
\(336\) 4.29240 0.234170
\(337\) −19.8632 −1.08202 −0.541008 0.841018i \(-0.681957\pi\)
−0.541008 + 0.841018i \(0.681957\pi\)
\(338\) −4.70290 −0.255804
\(339\) −3.68244 −0.200003
\(340\) 4.55426 0.246989
\(341\) 0.769881 0.0416914
\(342\) 3.85835 0.208635
\(343\) 18.9925 1.02550
\(344\) −11.7343 −0.632669
\(345\) −6.47491 −0.348598
\(346\) −23.3606 −1.25587
\(347\) 2.88427 0.154836 0.0774180 0.996999i \(-0.475332\pi\)
0.0774180 + 0.996999i \(0.475332\pi\)
\(348\) −1.66491 −0.0892487
\(349\) −9.43788 −0.505198 −0.252599 0.967571i \(-0.581285\pi\)
−0.252599 + 0.967571i \(0.581285\pi\)
\(350\) 23.4013 1.25085
\(351\) 2.88047 0.153748
\(352\) 1.00000 0.0533002
\(353\) 32.1549 1.71143 0.855717 0.517445i \(-0.173117\pi\)
0.855717 + 0.517445i \(0.173117\pi\)
\(354\) 8.74700 0.464898
\(355\) −12.0632 −0.640250
\(356\) 2.50051 0.132527
\(357\) −6.04675 −0.320028
\(358\) −4.01612 −0.212259
\(359\) −27.2400 −1.43767 −0.718835 0.695180i \(-0.755325\pi\)
−0.718835 + 0.695180i \(0.755325\pi\)
\(360\) −3.23292 −0.170390
\(361\) −4.11317 −0.216483
\(362\) −16.5937 −0.872144
\(363\) 1.00000 0.0524864
\(364\) 12.3641 0.648056
\(365\) −2.42898 −0.127139
\(366\) −1.00000 −0.0522708
\(367\) 21.4924 1.12189 0.560947 0.827852i \(-0.310437\pi\)
0.560947 + 0.827852i \(0.310437\pi\)
\(368\) 2.00280 0.104403
\(369\) −7.18702 −0.374141
\(370\) −21.3300 −1.10890
\(371\) −52.3661 −2.71871
\(372\) 0.769881 0.0399165
\(373\) 5.71898 0.296118 0.148059 0.988979i \(-0.452698\pi\)
0.148059 + 0.988979i \(0.452698\pi\)
\(374\) −1.40871 −0.0728428
\(375\) −1.46063 −0.0754264
\(376\) 0.896639 0.0462406
\(377\) −4.79573 −0.246993
\(378\) 4.29240 0.220777
\(379\) −6.50559 −0.334169 −0.167085 0.985943i \(-0.553435\pi\)
−0.167085 + 0.985943i \(0.553435\pi\)
\(380\) −12.4737 −0.639889
\(381\) 20.5720 1.05393
\(382\) 7.04645 0.360528
\(383\) 20.2446 1.03445 0.517226 0.855849i \(-0.326965\pi\)
0.517226 + 0.855849i \(0.326965\pi\)
\(384\) 1.00000 0.0510310
\(385\) −13.8770 −0.707237
\(386\) −4.26409 −0.217037
\(387\) −11.7343 −0.596486
\(388\) 13.2106 0.670664
\(389\) −29.9629 −1.51918 −0.759589 0.650403i \(-0.774600\pi\)
−0.759589 + 0.650403i \(0.774600\pi\)
\(390\) −9.31234 −0.471548
\(391\) −2.82137 −0.142683
\(392\) 11.4247 0.577034
\(393\) −0.892502 −0.0450208
\(394\) −3.05152 −0.153734
\(395\) −0.427953 −0.0215327
\(396\) 1.00000 0.0502519
\(397\) −9.15525 −0.459489 −0.229744 0.973251i \(-0.573789\pi\)
−0.229744 + 0.973251i \(0.573789\pi\)
\(398\) 22.6750 1.13660
\(399\) 16.5616 0.829115
\(400\) 5.45180 0.272590
\(401\) 37.5872 1.87701 0.938506 0.345262i \(-0.112210\pi\)
0.938506 + 0.345262i \(0.112210\pi\)
\(402\) 6.74484 0.336402
\(403\) 2.21762 0.110467
\(404\) 12.3663 0.615246
\(405\) −3.23292 −0.160645
\(406\) −7.14647 −0.354673
\(407\) 6.59775 0.327038
\(408\) −1.40871 −0.0697416
\(409\) −21.3450 −1.05544 −0.527722 0.849417i \(-0.676954\pi\)
−0.527722 + 0.849417i \(0.676954\pi\)
\(410\) 23.2351 1.14750
\(411\) −6.13837 −0.302784
\(412\) −8.44990 −0.416297
\(413\) 37.5456 1.84750
\(414\) 2.00280 0.0984325
\(415\) −51.5693 −2.53144
\(416\) 2.88047 0.141227
\(417\) −3.56248 −0.174455
\(418\) 3.85835 0.188718
\(419\) −0.827299 −0.0404162 −0.0202081 0.999796i \(-0.506433\pi\)
−0.0202081 + 0.999796i \(0.506433\pi\)
\(420\) −13.8770 −0.677128
\(421\) −24.3906 −1.18872 −0.594362 0.804198i \(-0.702595\pi\)
−0.594362 + 0.804198i \(0.702595\pi\)
\(422\) 2.07496 0.101007
\(423\) 0.896639 0.0435961
\(424\) −12.1997 −0.592471
\(425\) −7.68001 −0.372535
\(426\) 3.73137 0.180785
\(427\) −4.29240 −0.207724
\(428\) 12.8377 0.620533
\(429\) 2.88047 0.139070
\(430\) 37.9360 1.82944
\(431\) −15.7849 −0.760331 −0.380165 0.924919i \(-0.624133\pi\)
−0.380165 + 0.924919i \(0.624133\pi\)
\(432\) 1.00000 0.0481125
\(433\) −29.7369 −1.42906 −0.714531 0.699604i \(-0.753360\pi\)
−0.714531 + 0.699604i \(0.753360\pi\)
\(434\) 3.30464 0.158628
\(435\) 5.38254 0.258073
\(436\) 7.85123 0.376006
\(437\) 7.72751 0.369657
\(438\) 0.751328 0.0358998
\(439\) −20.5160 −0.979173 −0.489587 0.871955i \(-0.662852\pi\)
−0.489587 + 0.871955i \(0.662852\pi\)
\(440\) −3.23292 −0.154124
\(441\) 11.4247 0.544033
\(442\) −4.05775 −0.193008
\(443\) −17.3896 −0.826204 −0.413102 0.910685i \(-0.635555\pi\)
−0.413102 + 0.910685i \(0.635555\pi\)
\(444\) 6.59775 0.313115
\(445\) −8.08395 −0.383216
\(446\) −4.87062 −0.230631
\(447\) −5.57250 −0.263570
\(448\) 4.29240 0.202797
\(449\) −4.56127 −0.215260 −0.107630 0.994191i \(-0.534326\pi\)
−0.107630 + 0.994191i \(0.534326\pi\)
\(450\) 5.45180 0.257000
\(451\) −7.18702 −0.338423
\(452\) −3.68244 −0.173208
\(453\) 9.29629 0.436778
\(454\) 22.1378 1.03898
\(455\) −39.9723 −1.87393
\(456\) 3.85835 0.180684
\(457\) 28.9963 1.35639 0.678196 0.734881i \(-0.262762\pi\)
0.678196 + 0.734881i \(0.262762\pi\)
\(458\) −21.5095 −1.00508
\(459\) −1.40871 −0.0657530
\(460\) −6.47491 −0.301894
\(461\) −9.76692 −0.454891 −0.227445 0.973791i \(-0.573037\pi\)
−0.227445 + 0.973791i \(0.573037\pi\)
\(462\) 4.29240 0.199700
\(463\) 16.4463 0.764326 0.382163 0.924095i \(-0.375179\pi\)
0.382163 + 0.924095i \(0.375179\pi\)
\(464\) −1.66491 −0.0772916
\(465\) −2.48897 −0.115423
\(466\) −13.9601 −0.646687
\(467\) −16.9538 −0.784528 −0.392264 0.919853i \(-0.628308\pi\)
−0.392264 + 0.919853i \(0.628308\pi\)
\(468\) 2.88047 0.133150
\(469\) 28.9515 1.33686
\(470\) −2.89877 −0.133710
\(471\) −21.7347 −1.00148
\(472\) 8.74700 0.402613
\(473\) −11.7343 −0.539542
\(474\) 0.132373 0.00608011
\(475\) 21.0349 0.965148
\(476\) −6.04675 −0.277152
\(477\) −12.1997 −0.558587
\(478\) 4.12106 0.188493
\(479\) 19.0297 0.869487 0.434744 0.900554i \(-0.356839\pi\)
0.434744 + 0.900554i \(0.356839\pi\)
\(480\) −3.23292 −0.147562
\(481\) 19.0046 0.866536
\(482\) 6.60585 0.300888
\(483\) 8.59684 0.391170
\(484\) 1.00000 0.0454545
\(485\) −42.7087 −1.93930
\(486\) 1.00000 0.0453609
\(487\) −5.55083 −0.251532 −0.125766 0.992060i \(-0.540139\pi\)
−0.125766 + 0.992060i \(0.540139\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −9.29178 −0.420189
\(490\) −36.9352 −1.66856
\(491\) −8.75305 −0.395020 −0.197510 0.980301i \(-0.563285\pi\)
−0.197510 + 0.980301i \(0.563285\pi\)
\(492\) −7.18702 −0.324016
\(493\) 2.34538 0.105631
\(494\) 11.1138 0.500035
\(495\) −3.23292 −0.145309
\(496\) 0.769881 0.0345687
\(497\) 16.0165 0.718439
\(498\) 15.9513 0.714794
\(499\) −5.13148 −0.229716 −0.114858 0.993382i \(-0.536641\pi\)
−0.114858 + 0.993382i \(0.536641\pi\)
\(500\) −1.46063 −0.0653211
\(501\) −12.9130 −0.576911
\(502\) −25.8066 −1.15181
\(503\) 20.5428 0.915957 0.457979 0.888963i \(-0.348574\pi\)
0.457979 + 0.888963i \(0.348574\pi\)
\(504\) 4.29240 0.191199
\(505\) −39.9793 −1.77905
\(506\) 2.00280 0.0890355
\(507\) −4.70290 −0.208863
\(508\) 20.5720 0.912733
\(509\) 30.3874 1.34690 0.673449 0.739233i \(-0.264812\pi\)
0.673449 + 0.739233i \(0.264812\pi\)
\(510\) 4.55426 0.201666
\(511\) 3.22500 0.142665
\(512\) 1.00000 0.0441942
\(513\) 3.85835 0.170350
\(514\) −21.8807 −0.965118
\(515\) 27.3179 1.20377
\(516\) −11.7343 −0.516572
\(517\) 0.896639 0.0394341
\(518\) 28.3202 1.24432
\(519\) −23.3606 −1.02542
\(520\) −9.31234 −0.408373
\(521\) 21.4870 0.941364 0.470682 0.882303i \(-0.344008\pi\)
0.470682 + 0.882303i \(0.344008\pi\)
\(522\) −1.66491 −0.0728713
\(523\) −41.4608 −1.81295 −0.906477 0.422256i \(-0.861238\pi\)
−0.906477 + 0.422256i \(0.861238\pi\)
\(524\) −0.892502 −0.0389891
\(525\) 23.4013 1.02132
\(526\) 21.7683 0.949145
\(527\) −1.08454 −0.0472433
\(528\) 1.00000 0.0435194
\(529\) −18.9888 −0.825599
\(530\) 39.4408 1.71320
\(531\) 8.74700 0.379587
\(532\) 16.5616 0.718035
\(533\) −20.7020 −0.896702
\(534\) 2.50051 0.108208
\(535\) −41.5033 −1.79434
\(536\) 6.74484 0.291333
\(537\) −4.01612 −0.173309
\(538\) 4.86810 0.209879
\(539\) 11.4247 0.492096
\(540\) −3.23292 −0.139123
\(541\) −7.56723 −0.325341 −0.162670 0.986680i \(-0.552011\pi\)
−0.162670 + 0.986680i \(0.552011\pi\)
\(542\) 19.8242 0.851523
\(543\) −16.5937 −0.712103
\(544\) −1.40871 −0.0603980
\(545\) −25.3824 −1.08726
\(546\) 12.3641 0.529136
\(547\) −11.8607 −0.507126 −0.253563 0.967319i \(-0.581603\pi\)
−0.253563 + 0.967319i \(0.581603\pi\)
\(548\) −6.13837 −0.262218
\(549\) −1.00000 −0.0426790
\(550\) 5.45180 0.232465
\(551\) −6.42381 −0.273663
\(552\) 2.00280 0.0852450
\(553\) 0.568200 0.0241623
\(554\) −6.99143 −0.297038
\(555\) −21.3300 −0.905409
\(556\) −3.56248 −0.151083
\(557\) −40.6138 −1.72086 −0.860430 0.509569i \(-0.829805\pi\)
−0.860430 + 0.509569i \(0.829805\pi\)
\(558\) 0.769881 0.0325916
\(559\) −33.8002 −1.42960
\(560\) −13.8770 −0.586410
\(561\) −1.40871 −0.0594759
\(562\) −13.9571 −0.588744
\(563\) 13.7241 0.578401 0.289201 0.957269i \(-0.406611\pi\)
0.289201 + 0.957269i \(0.406611\pi\)
\(564\) 0.896639 0.0377553
\(565\) 11.9051 0.500850
\(566\) −7.59877 −0.319400
\(567\) 4.29240 0.180264
\(568\) 3.73137 0.156565
\(569\) −8.21441 −0.344366 −0.172183 0.985065i \(-0.555082\pi\)
−0.172183 + 0.985065i \(0.555082\pi\)
\(570\) −12.4737 −0.522467
\(571\) 8.58722 0.359364 0.179682 0.983725i \(-0.442493\pi\)
0.179682 + 0.983725i \(0.442493\pi\)
\(572\) 2.88047 0.120438
\(573\) 7.04645 0.294370
\(574\) −30.8495 −1.28764
\(575\) 10.9189 0.455349
\(576\) 1.00000 0.0416667
\(577\) 24.6285 1.02530 0.512650 0.858598i \(-0.328664\pi\)
0.512650 + 0.858598i \(0.328664\pi\)
\(578\) −15.0155 −0.624564
\(579\) −4.26409 −0.177210
\(580\) 5.38254 0.223498
\(581\) 68.4692 2.84058
\(582\) 13.2106 0.547595
\(583\) −12.1997 −0.505261
\(584\) 0.751328 0.0310902
\(585\) −9.31234 −0.385018
\(586\) 18.0763 0.746723
\(587\) 17.7655 0.733261 0.366631 0.930367i \(-0.380511\pi\)
0.366631 + 0.930367i \(0.380511\pi\)
\(588\) 11.4247 0.471146
\(589\) 2.97047 0.122396
\(590\) −28.2784 −1.16420
\(591\) −3.05152 −0.125523
\(592\) 6.59775 0.271166
\(593\) −21.9965 −0.903289 −0.451644 0.892198i \(-0.649162\pi\)
−0.451644 + 0.892198i \(0.649162\pi\)
\(594\) 1.00000 0.0410305
\(595\) 19.5487 0.801418
\(596\) −5.57250 −0.228258
\(597\) 22.6750 0.928028
\(598\) 5.76902 0.235913
\(599\) 7.42717 0.303466 0.151733 0.988422i \(-0.451515\pi\)
0.151733 + 0.988422i \(0.451515\pi\)
\(600\) 5.45180 0.222569
\(601\) −12.1774 −0.496725 −0.248363 0.968667i \(-0.579892\pi\)
−0.248363 + 0.968667i \(0.579892\pi\)
\(602\) −50.3681 −2.05285
\(603\) 6.74484 0.274671
\(604\) 9.29629 0.378261
\(605\) −3.23292 −0.131437
\(606\) 12.3663 0.502346
\(607\) −30.0402 −1.21930 −0.609648 0.792672i \(-0.708689\pi\)
−0.609648 + 0.792672i \(0.708689\pi\)
\(608\) 3.85835 0.156477
\(609\) −7.14647 −0.289590
\(610\) 3.23292 0.130897
\(611\) 2.58274 0.104487
\(612\) −1.40871 −0.0569438
\(613\) −37.9027 −1.53088 −0.765438 0.643509i \(-0.777478\pi\)
−0.765438 + 0.643509i \(0.777478\pi\)
\(614\) −10.1292 −0.408781
\(615\) 23.2351 0.936929
\(616\) 4.29240 0.172946
\(617\) −4.14439 −0.166847 −0.0834234 0.996514i \(-0.526585\pi\)
−0.0834234 + 0.996514i \(0.526585\pi\)
\(618\) −8.44990 −0.339905
\(619\) 5.59655 0.224945 0.112472 0.993655i \(-0.464123\pi\)
0.112472 + 0.993655i \(0.464123\pi\)
\(620\) −2.48897 −0.0999593
\(621\) 2.00280 0.0803698
\(622\) 9.70940 0.389312
\(623\) 10.7332 0.430016
\(624\) 2.88047 0.115311
\(625\) −22.5369 −0.901476
\(626\) −3.60353 −0.144026
\(627\) 3.85835 0.154087
\(628\) −21.7347 −0.867308
\(629\) −9.29433 −0.370589
\(630\) −13.8770 −0.552873
\(631\) −11.5182 −0.458532 −0.229266 0.973364i \(-0.573633\pi\)
−0.229266 + 0.973364i \(0.573633\pi\)
\(632\) 0.132373 0.00526553
\(633\) 2.07496 0.0824723
\(634\) −24.8688 −0.987667
\(635\) −66.5076 −2.63927
\(636\) −12.1997 −0.483751
\(637\) 32.9085 1.30388
\(638\) −1.66491 −0.0659145
\(639\) 3.73137 0.147611
\(640\) −3.23292 −0.127793
\(641\) −25.8167 −1.01970 −0.509849 0.860264i \(-0.670299\pi\)
−0.509849 + 0.860264i \(0.670299\pi\)
\(642\) 12.8377 0.506663
\(643\) −13.2625 −0.523021 −0.261511 0.965201i \(-0.584221\pi\)
−0.261511 + 0.965201i \(0.584221\pi\)
\(644\) 8.59684 0.338763
\(645\) 37.9360 1.49373
\(646\) −5.43530 −0.213849
\(647\) −0.908404 −0.0357130 −0.0178565 0.999841i \(-0.505684\pi\)
−0.0178565 + 0.999841i \(0.505684\pi\)
\(648\) 1.00000 0.0392837
\(649\) 8.74700 0.343350
\(650\) 15.7037 0.615951
\(651\) 3.30464 0.129519
\(652\) −9.29178 −0.363894
\(653\) −18.4193 −0.720804 −0.360402 0.932797i \(-0.617360\pi\)
−0.360402 + 0.932797i \(0.617360\pi\)
\(654\) 7.85123 0.307007
\(655\) 2.88539 0.112742
\(656\) −7.18702 −0.280606
\(657\) 0.751328 0.0293121
\(658\) 3.84873 0.150039
\(659\) 14.8161 0.577152 0.288576 0.957457i \(-0.406818\pi\)
0.288576 + 0.957457i \(0.406818\pi\)
\(660\) −3.23292 −0.125841
\(661\) −30.8685 −1.20065 −0.600323 0.799758i \(-0.704961\pi\)
−0.600323 + 0.799758i \(0.704961\pi\)
\(662\) 34.3670 1.33571
\(663\) −4.05775 −0.157590
\(664\) 15.9513 0.619030
\(665\) −53.5423 −2.07628
\(666\) 6.59775 0.255658
\(667\) −3.33450 −0.129112
\(668\) −12.9130 −0.499620
\(669\) −4.87062 −0.188309
\(670\) −21.8055 −0.842422
\(671\) −1.00000 −0.0386046
\(672\) 4.29240 0.165583
\(673\) −33.2381 −1.28124 −0.640618 0.767860i \(-0.721322\pi\)
−0.640618 + 0.767860i \(0.721322\pi\)
\(674\) −19.8632 −0.765100
\(675\) 5.45180 0.209840
\(676\) −4.70290 −0.180881
\(677\) 31.6218 1.21532 0.607662 0.794196i \(-0.292108\pi\)
0.607662 + 0.794196i \(0.292108\pi\)
\(678\) −3.68244 −0.141423
\(679\) 56.7050 2.17614
\(680\) 4.55426 0.174648
\(681\) 22.1378 0.848324
\(682\) 0.769881 0.0294803
\(683\) −38.2580 −1.46390 −0.731950 0.681358i \(-0.761390\pi\)
−0.731950 + 0.681358i \(0.761390\pi\)
\(684\) 3.85835 0.147528
\(685\) 19.8449 0.758234
\(686\) 18.9925 0.725138
\(687\) −21.5095 −0.820640
\(688\) −11.7343 −0.447365
\(689\) −35.1409 −1.33876
\(690\) −6.47491 −0.246496
\(691\) 8.49250 0.323070 0.161535 0.986867i \(-0.448356\pi\)
0.161535 + 0.986867i \(0.448356\pi\)
\(692\) −23.3606 −0.888037
\(693\) 4.29240 0.163055
\(694\) 2.88427 0.109486
\(695\) 11.5172 0.436873
\(696\) −1.66491 −0.0631084
\(697\) 10.1244 0.383490
\(698\) −9.43788 −0.357229
\(699\) −13.9601 −0.528018
\(700\) 23.4013 0.884486
\(701\) −38.7814 −1.46475 −0.732376 0.680901i \(-0.761589\pi\)
−0.732376 + 0.680901i \(0.761589\pi\)
\(702\) 2.88047 0.108716
\(703\) 25.4564 0.960106
\(704\) 1.00000 0.0376889
\(705\) −2.89877 −0.109174
\(706\) 32.1549 1.21017
\(707\) 53.0810 1.99632
\(708\) 8.74700 0.328732
\(709\) 45.2752 1.70034 0.850172 0.526505i \(-0.176498\pi\)
0.850172 + 0.526505i \(0.176498\pi\)
\(710\) −12.0632 −0.452725
\(711\) 0.132373 0.00496439
\(712\) 2.50051 0.0937105
\(713\) 1.54192 0.0577454
\(714\) −6.04675 −0.226294
\(715\) −9.31234 −0.348262
\(716\) −4.01612 −0.150090
\(717\) 4.12106 0.153904
\(718\) −27.2400 −1.01659
\(719\) 29.6250 1.10483 0.552413 0.833570i \(-0.313707\pi\)
0.552413 + 0.833570i \(0.313707\pi\)
\(720\) −3.23292 −0.120484
\(721\) −36.2704 −1.35078
\(722\) −4.11317 −0.153076
\(723\) 6.60585 0.245674
\(724\) −16.5937 −0.616699
\(725\) −9.07677 −0.337103
\(726\) 1.00000 0.0371135
\(727\) 26.9803 1.00064 0.500322 0.865839i \(-0.333215\pi\)
0.500322 + 0.865839i \(0.333215\pi\)
\(728\) 12.3641 0.458245
\(729\) 1.00000 0.0370370
\(730\) −2.42898 −0.0899008
\(731\) 16.5302 0.611391
\(732\) −1.00000 −0.0369611
\(733\) 21.5038 0.794261 0.397131 0.917762i \(-0.370006\pi\)
0.397131 + 0.917762i \(0.370006\pi\)
\(734\) 21.4924 0.793299
\(735\) −36.9352 −1.36237
\(736\) 2.00280 0.0738244
\(737\) 6.74484 0.248449
\(738\) −7.18702 −0.264558
\(739\) 0.737726 0.0271377 0.0135688 0.999908i \(-0.495681\pi\)
0.0135688 + 0.999908i \(0.495681\pi\)
\(740\) −21.3300 −0.784107
\(741\) 11.1138 0.408277
\(742\) −52.3661 −1.92242
\(743\) 20.2496 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(744\) 0.769881 0.0282252
\(745\) 18.0155 0.660036
\(746\) 5.71898 0.209387
\(747\) 15.9513 0.583627
\(748\) −1.40871 −0.0515076
\(749\) 55.1045 2.01347
\(750\) −1.46063 −0.0533345
\(751\) −20.2016 −0.737167 −0.368584 0.929595i \(-0.620157\pi\)
−0.368584 + 0.929595i \(0.620157\pi\)
\(752\) 0.896639 0.0326971
\(753\) −25.8066 −0.940445
\(754\) −4.79573 −0.174650
\(755\) −30.0542 −1.09378
\(756\) 4.29240 0.156113
\(757\) 11.2010 0.407108 0.203554 0.979064i \(-0.434751\pi\)
0.203554 + 0.979064i \(0.434751\pi\)
\(758\) −6.50559 −0.236293
\(759\) 2.00280 0.0726972
\(760\) −12.4737 −0.452470
\(761\) 8.72882 0.316420 0.158210 0.987406i \(-0.449428\pi\)
0.158210 + 0.987406i \(0.449428\pi\)
\(762\) 20.5720 0.745243
\(763\) 33.7006 1.22004
\(764\) 7.04645 0.254932
\(765\) 4.55426 0.164660
\(766\) 20.2446 0.731468
\(767\) 25.1955 0.909755
\(768\) 1.00000 0.0360844
\(769\) 6.64734 0.239709 0.119855 0.992791i \(-0.461757\pi\)
0.119855 + 0.992791i \(0.461757\pi\)
\(770\) −13.8770 −0.500092
\(771\) −21.8807 −0.788016
\(772\) −4.26409 −0.153468
\(773\) 51.9468 1.86840 0.934199 0.356753i \(-0.116116\pi\)
0.934199 + 0.356753i \(0.116116\pi\)
\(774\) −11.7343 −0.421779
\(775\) 4.19723 0.150769
\(776\) 13.2106 0.474231
\(777\) 28.3202 1.01598
\(778\) −29.9629 −1.07422
\(779\) −27.7300 −0.993530
\(780\) −9.31234 −0.333435
\(781\) 3.73137 0.133519
\(782\) −2.82137 −0.100892
\(783\) −1.66491 −0.0594991
\(784\) 11.4247 0.408025
\(785\) 70.2666 2.50792
\(786\) −0.892502 −0.0318345
\(787\) −46.3543 −1.65235 −0.826177 0.563411i \(-0.809489\pi\)
−0.826177 + 0.563411i \(0.809489\pi\)
\(788\) −3.05152 −0.108706
\(789\) 21.7683 0.774973
\(790\) −0.427953 −0.0152259
\(791\) −15.8065 −0.562015
\(792\) 1.00000 0.0355335
\(793\) −2.88047 −0.102288
\(794\) −9.15525 −0.324908
\(795\) 39.4408 1.39882
\(796\) 22.6750 0.803696
\(797\) 27.4104 0.970926 0.485463 0.874257i \(-0.338651\pi\)
0.485463 + 0.874257i \(0.338651\pi\)
\(798\) 16.5616 0.586273
\(799\) −1.26311 −0.0446855
\(800\) 5.45180 0.192750
\(801\) 2.50051 0.0883511
\(802\) 37.5872 1.32725
\(803\) 0.751328 0.0265138
\(804\) 6.74484 0.237872
\(805\) −27.7929 −0.979572
\(806\) 2.21762 0.0781122
\(807\) 4.86810 0.171365
\(808\) 12.3663 0.435044
\(809\) −54.3029 −1.90919 −0.954594 0.297909i \(-0.903711\pi\)
−0.954594 + 0.297909i \(0.903711\pi\)
\(810\) −3.23292 −0.113593
\(811\) 6.19540 0.217550 0.108775 0.994066i \(-0.465307\pi\)
0.108775 + 0.994066i \(0.465307\pi\)
\(812\) −7.14647 −0.250792
\(813\) 19.8242 0.695265
\(814\) 6.59775 0.231251
\(815\) 30.0396 1.05224
\(816\) −1.40871 −0.0493148
\(817\) −45.2749 −1.58397
\(818\) −21.3450 −0.746311
\(819\) 12.3641 0.432037
\(820\) 23.2351 0.811404
\(821\) −24.7144 −0.862540 −0.431270 0.902223i \(-0.641934\pi\)
−0.431270 + 0.902223i \(0.641934\pi\)
\(822\) −6.13837 −0.214100
\(823\) 1.01775 0.0354766 0.0177383 0.999843i \(-0.494353\pi\)
0.0177383 + 0.999843i \(0.494353\pi\)
\(824\) −8.44990 −0.294366
\(825\) 5.45180 0.189807
\(826\) 37.5456 1.30638
\(827\) −13.5282 −0.470423 −0.235211 0.971944i \(-0.575578\pi\)
−0.235211 + 0.971944i \(0.575578\pi\)
\(828\) 2.00280 0.0696023
\(829\) 4.89375 0.169967 0.0849834 0.996382i \(-0.472916\pi\)
0.0849834 + 0.996382i \(0.472916\pi\)
\(830\) −51.5693 −1.79000
\(831\) −6.99143 −0.242530
\(832\) 2.88047 0.0998623
\(833\) −16.0941 −0.557627
\(834\) −3.56248 −0.123359
\(835\) 41.7468 1.44471
\(836\) 3.85835 0.133444
\(837\) 0.769881 0.0266110
\(838\) −0.827299 −0.0285786
\(839\) 30.9029 1.06689 0.533443 0.845836i \(-0.320898\pi\)
0.533443 + 0.845836i \(0.320898\pi\)
\(840\) −13.8770 −0.478802
\(841\) −26.2281 −0.904416
\(842\) −24.3906 −0.840555
\(843\) −13.9571 −0.480707
\(844\) 2.07496 0.0714231
\(845\) 15.2041 0.523038
\(846\) 0.896639 0.0308271
\(847\) 4.29240 0.147489
\(848\) −12.1997 −0.418940
\(849\) −7.59877 −0.260789
\(850\) −7.68001 −0.263422
\(851\) 13.2140 0.452970
\(852\) 3.73137 0.127835
\(853\) 30.6601 1.04978 0.524891 0.851169i \(-0.324106\pi\)
0.524891 + 0.851169i \(0.324106\pi\)
\(854\) −4.29240 −0.146883
\(855\) −12.4737 −0.426593
\(856\) 12.8377 0.438783
\(857\) −23.2917 −0.795628 −0.397814 0.917466i \(-0.630231\pi\)
−0.397814 + 0.917466i \(0.630231\pi\)
\(858\) 2.88047 0.0983376
\(859\) 1.00051 0.0341369 0.0170685 0.999854i \(-0.494567\pi\)
0.0170685 + 0.999854i \(0.494567\pi\)
\(860\) 37.9360 1.29361
\(861\) −30.8495 −1.05135
\(862\) −15.7849 −0.537635
\(863\) 31.7341 1.08024 0.540121 0.841587i \(-0.318378\pi\)
0.540121 + 0.841587i \(0.318378\pi\)
\(864\) 1.00000 0.0340207
\(865\) 75.5231 2.56786
\(866\) −29.7369 −1.01050
\(867\) −15.0155 −0.509954
\(868\) 3.30464 0.112167
\(869\) 0.132373 0.00449046
\(870\) 5.38254 0.182485
\(871\) 19.4283 0.658303
\(872\) 7.85123 0.265876
\(873\) 13.2106 0.447110
\(874\) 7.72751 0.261387
\(875\) −6.26959 −0.211951
\(876\) 0.751328 0.0253850
\(877\) 38.1898 1.28958 0.644790 0.764360i \(-0.276945\pi\)
0.644790 + 0.764360i \(0.276945\pi\)
\(878\) −20.5160 −0.692380
\(879\) 18.0763 0.609697
\(880\) −3.23292 −0.108982
\(881\) 17.4629 0.588339 0.294169 0.955753i \(-0.404957\pi\)
0.294169 + 0.955753i \(0.404957\pi\)
\(882\) 11.4247 0.384689
\(883\) −6.75763 −0.227412 −0.113706 0.993514i \(-0.536272\pi\)
−0.113706 + 0.993514i \(0.536272\pi\)
\(884\) −4.05775 −0.136477
\(885\) −28.2784 −0.950568
\(886\) −17.3896 −0.584214
\(887\) 14.6558 0.492092 0.246046 0.969258i \(-0.420869\pi\)
0.246046 + 0.969258i \(0.420869\pi\)
\(888\) 6.59775 0.221406
\(889\) 88.3030 2.96159
\(890\) −8.08395 −0.270975
\(891\) 1.00000 0.0335013
\(892\) −4.87062 −0.163080
\(893\) 3.45954 0.115769
\(894\) −5.57250 −0.186372
\(895\) 12.9838 0.434001
\(896\) 4.29240 0.143399
\(897\) 5.76902 0.192622
\(898\) −4.56127 −0.152212
\(899\) −1.28178 −0.0427499
\(900\) 5.45180 0.181727
\(901\) 17.1859 0.572545
\(902\) −7.18702 −0.239301
\(903\) −50.3681 −1.67615
\(904\) −3.68244 −0.122476
\(905\) 53.6461 1.78326
\(906\) 9.29629 0.308849
\(907\) −49.0950 −1.63017 −0.815086 0.579340i \(-0.803311\pi\)
−0.815086 + 0.579340i \(0.803311\pi\)
\(908\) 22.1378 0.734670
\(909\) 12.3663 0.410164
\(910\) −39.9723 −1.32507
\(911\) −35.7518 −1.18451 −0.592255 0.805751i \(-0.701762\pi\)
−0.592255 + 0.805751i \(0.701762\pi\)
\(912\) 3.85835 0.127763
\(913\) 15.9513 0.527910
\(914\) 28.9963 0.959114
\(915\) 3.23292 0.106877
\(916\) −21.5095 −0.710695
\(917\) −3.83098 −0.126510
\(918\) −1.40871 −0.0464944
\(919\) 53.5791 1.76741 0.883705 0.468043i \(-0.155041\pi\)
0.883705 + 0.468043i \(0.155041\pi\)
\(920\) −6.47491 −0.213472
\(921\) −10.1292 −0.333768
\(922\) −9.76692 −0.321656
\(923\) 10.7481 0.353778
\(924\) 4.29240 0.141210
\(925\) 35.9696 1.18267
\(926\) 16.4463 0.540460
\(927\) −8.44990 −0.277531
\(928\) −1.66491 −0.0546534
\(929\) 11.8727 0.389532 0.194766 0.980850i \(-0.437605\pi\)
0.194766 + 0.980850i \(0.437605\pi\)
\(930\) −2.48897 −0.0816164
\(931\) 44.0804 1.44468
\(932\) −13.9601 −0.457277
\(933\) 9.70940 0.317872
\(934\) −16.9538 −0.554745
\(935\) 4.55426 0.148940
\(936\) 2.88047 0.0941511
\(937\) 9.72156 0.317589 0.158795 0.987312i \(-0.449239\pi\)
0.158795 + 0.987312i \(0.449239\pi\)
\(938\) 28.9515 0.945301
\(939\) −3.60353 −0.117597
\(940\) −2.89877 −0.0945473
\(941\) −52.7256 −1.71881 −0.859403 0.511299i \(-0.829164\pi\)
−0.859403 + 0.511299i \(0.829164\pi\)
\(942\) −21.7347 −0.708154
\(943\) −14.3942 −0.468739
\(944\) 8.74700 0.284691
\(945\) −13.8770 −0.451419
\(946\) −11.7343 −0.381514
\(947\) 18.1553 0.589968 0.294984 0.955502i \(-0.404686\pi\)
0.294984 + 0.955502i \(0.404686\pi\)
\(948\) 0.132373 0.00429929
\(949\) 2.16418 0.0702521
\(950\) 21.0349 0.682463
\(951\) −24.8688 −0.806426
\(952\) −6.04675 −0.195976
\(953\) 7.25700 0.235077 0.117539 0.993068i \(-0.462500\pi\)
0.117539 + 0.993068i \(0.462500\pi\)
\(954\) −12.1997 −0.394981
\(955\) −22.7806 −0.737164
\(956\) 4.12106 0.133284
\(957\) −1.66491 −0.0538190
\(958\) 19.0297 0.614820
\(959\) −26.3483 −0.850832
\(960\) −3.23292 −0.104342
\(961\) −30.4073 −0.980880
\(962\) 19.0046 0.612733
\(963\) 12.8377 0.413689
\(964\) 6.60585 0.212760
\(965\) 13.7855 0.443771
\(966\) 8.59684 0.276599
\(967\) 13.9900 0.449887 0.224944 0.974372i \(-0.427780\pi\)
0.224944 + 0.974372i \(0.427780\pi\)
\(968\) 1.00000 0.0321412
\(969\) −5.43530 −0.174607
\(970\) −42.7087 −1.37129
\(971\) −61.8624 −1.98526 −0.992630 0.121183i \(-0.961331\pi\)
−0.992630 + 0.121183i \(0.961331\pi\)
\(972\) 1.00000 0.0320750
\(973\) −15.2916 −0.490226
\(974\) −5.55083 −0.177860
\(975\) 15.7037 0.502922
\(976\) −1.00000 −0.0320092
\(977\) −29.1513 −0.932634 −0.466317 0.884618i \(-0.654419\pi\)
−0.466317 + 0.884618i \(0.654419\pi\)
\(978\) −9.29178 −0.297118
\(979\) 2.50051 0.0799166
\(980\) −36.9352 −1.17985
\(981\) 7.85123 0.250670
\(982\) −8.75305 −0.279321
\(983\) −30.2008 −0.963255 −0.481628 0.876376i \(-0.659954\pi\)
−0.481628 + 0.876376i \(0.659954\pi\)
\(984\) −7.18702 −0.229114
\(985\) 9.86535 0.314336
\(986\) 2.34538 0.0746922
\(987\) 3.84873 0.122507
\(988\) 11.1138 0.353578
\(989\) −23.5014 −0.747302
\(990\) −3.23292 −0.102749
\(991\) 2.64881 0.0841423 0.0420711 0.999115i \(-0.486604\pi\)
0.0420711 + 0.999115i \(0.486604\pi\)
\(992\) 0.769881 0.0244437
\(993\) 34.3670 1.09060
\(994\) 16.0165 0.508013
\(995\) −73.3067 −2.32398
\(996\) 15.9513 0.505435
\(997\) 48.7450 1.54377 0.771886 0.635762i \(-0.219314\pi\)
0.771886 + 0.635762i \(0.219314\pi\)
\(998\) −5.13148 −0.162434
\(999\) 6.59775 0.208744
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 \(a_p\))