Properties

Label 8042.2.a.a.1.12
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.22608 q^{3}\) \(+1.00000 q^{4}\) \(+1.44593 q^{5}\) \(-2.22608 q^{6}\) \(+1.32066 q^{7}\) \(+1.00000 q^{8}\) \(+1.95543 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.22608 q^{3}\) \(+1.00000 q^{4}\) \(+1.44593 q^{5}\) \(-2.22608 q^{6}\) \(+1.32066 q^{7}\) \(+1.00000 q^{8}\) \(+1.95543 q^{9}\) \(+1.44593 q^{10}\) \(-4.69336 q^{11}\) \(-2.22608 q^{12}\) \(+1.27986 q^{13}\) \(+1.32066 q^{14}\) \(-3.21876 q^{15}\) \(+1.00000 q^{16}\) \(-1.75842 q^{17}\) \(+1.95543 q^{18}\) \(-1.83542 q^{19}\) \(+1.44593 q^{20}\) \(-2.93990 q^{21}\) \(-4.69336 q^{22}\) \(+1.61507 q^{23}\) \(-2.22608 q^{24}\) \(-2.90928 q^{25}\) \(+1.27986 q^{26}\) \(+2.32529 q^{27}\) \(+1.32066 q^{28}\) \(+5.04102 q^{29}\) \(-3.21876 q^{30}\) \(+4.04230 q^{31}\) \(+1.00000 q^{32}\) \(+10.4478 q^{33}\) \(-1.75842 q^{34}\) \(+1.90959 q^{35}\) \(+1.95543 q^{36}\) \(-1.67445 q^{37}\) \(-1.83542 q^{38}\) \(-2.84906 q^{39}\) \(+1.44593 q^{40}\) \(-3.00389 q^{41}\) \(-2.93990 q^{42}\) \(-3.28239 q^{43}\) \(-4.69336 q^{44}\) \(+2.82742 q^{45}\) \(+1.61507 q^{46}\) \(+6.32528 q^{47}\) \(-2.22608 q^{48}\) \(-5.25585 q^{49}\) \(-2.90928 q^{50}\) \(+3.91438 q^{51}\) \(+1.27986 q^{52}\) \(-6.43256 q^{53}\) \(+2.32529 q^{54}\) \(-6.78628 q^{55}\) \(+1.32066 q^{56}\) \(+4.08579 q^{57}\) \(+5.04102 q^{58}\) \(+1.32811 q^{59}\) \(-3.21876 q^{60}\) \(-2.36183 q^{61}\) \(+4.04230 q^{62}\) \(+2.58247 q^{63}\) \(+1.00000 q^{64}\) \(+1.85059 q^{65}\) \(+10.4478 q^{66}\) \(+8.01836 q^{67}\) \(-1.75842 q^{68}\) \(-3.59527 q^{69}\) \(+1.90959 q^{70}\) \(-11.2422 q^{71}\) \(+1.95543 q^{72}\) \(-0.908233 q^{73}\) \(-1.67445 q^{74}\) \(+6.47629 q^{75}\) \(-1.83542 q^{76}\) \(-6.19835 q^{77}\) \(-2.84906 q^{78}\) \(-4.37488 q^{79}\) \(+1.44593 q^{80}\) \(-11.0426 q^{81}\) \(-3.00389 q^{82}\) \(+12.7989 q^{83}\) \(-2.93990 q^{84}\) \(-2.54256 q^{85}\) \(-3.28239 q^{86}\) \(-11.2217 q^{87}\) \(-4.69336 q^{88}\) \(-12.9009 q^{89}\) \(+2.82742 q^{90}\) \(+1.69026 q^{91}\) \(+1.61507 q^{92}\) \(-8.99849 q^{93}\) \(+6.32528 q^{94}\) \(-2.65389 q^{95}\) \(-2.22608 q^{96}\) \(-9.16110 q^{97}\) \(-5.25585 q^{98}\) \(-9.17755 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.22608 −1.28523 −0.642614 0.766190i \(-0.722150\pi\)
−0.642614 + 0.766190i \(0.722150\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.44593 0.646641 0.323320 0.946290i \(-0.395201\pi\)
0.323320 + 0.946290i \(0.395201\pi\)
\(6\) −2.22608 −0.908793
\(7\) 1.32066 0.499164 0.249582 0.968354i \(-0.419707\pi\)
0.249582 + 0.968354i \(0.419707\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.95543 0.651811
\(10\) 1.44593 0.457244
\(11\) −4.69336 −1.41510 −0.707551 0.706662i \(-0.750200\pi\)
−0.707551 + 0.706662i \(0.750200\pi\)
\(12\) −2.22608 −0.642614
\(13\) 1.27986 0.354968 0.177484 0.984124i \(-0.443204\pi\)
0.177484 + 0.984124i \(0.443204\pi\)
\(14\) 1.32066 0.352962
\(15\) −3.21876 −0.831080
\(16\) 1.00000 0.250000
\(17\) −1.75842 −0.426480 −0.213240 0.977000i \(-0.568402\pi\)
−0.213240 + 0.977000i \(0.568402\pi\)
\(18\) 1.95543 0.460900
\(19\) −1.83542 −0.421075 −0.210537 0.977586i \(-0.567521\pi\)
−0.210537 + 0.977586i \(0.567521\pi\)
\(20\) 1.44593 0.323320
\(21\) −2.93990 −0.641539
\(22\) −4.69336 −1.00063
\(23\) 1.61507 0.336765 0.168383 0.985722i \(-0.446146\pi\)
0.168383 + 0.985722i \(0.446146\pi\)
\(24\) −2.22608 −0.454397
\(25\) −2.90928 −0.581856
\(26\) 1.27986 0.251001
\(27\) 2.32529 0.447502
\(28\) 1.32066 0.249582
\(29\) 5.04102 0.936095 0.468047 0.883703i \(-0.344958\pi\)
0.468047 + 0.883703i \(0.344958\pi\)
\(30\) −3.21876 −0.587663
\(31\) 4.04230 0.726019 0.363010 0.931785i \(-0.381749\pi\)
0.363010 + 0.931785i \(0.381749\pi\)
\(32\) 1.00000 0.176777
\(33\) 10.4478 1.81873
\(34\) −1.75842 −0.301567
\(35\) 1.90959 0.322779
\(36\) 1.95543 0.325905
\(37\) −1.67445 −0.275278 −0.137639 0.990482i \(-0.543951\pi\)
−0.137639 + 0.990482i \(0.543951\pi\)
\(38\) −1.83542 −0.297745
\(39\) −2.84906 −0.456215
\(40\) 1.44593 0.228622
\(41\) −3.00389 −0.469130 −0.234565 0.972100i \(-0.575366\pi\)
−0.234565 + 0.972100i \(0.575366\pi\)
\(42\) −2.93990 −0.453636
\(43\) −3.28239 −0.500561 −0.250280 0.968173i \(-0.580523\pi\)
−0.250280 + 0.968173i \(0.580523\pi\)
\(44\) −4.69336 −0.707551
\(45\) 2.82742 0.421487
\(46\) 1.61507 0.238129
\(47\) 6.32528 0.922637 0.461318 0.887235i \(-0.347377\pi\)
0.461318 + 0.887235i \(0.347377\pi\)
\(48\) −2.22608 −0.321307
\(49\) −5.25585 −0.750836
\(50\) −2.90928 −0.411434
\(51\) 3.91438 0.548124
\(52\) 1.27986 0.177484
\(53\) −6.43256 −0.883580 −0.441790 0.897119i \(-0.645656\pi\)
−0.441790 + 0.897119i \(0.645656\pi\)
\(54\) 2.32529 0.316432
\(55\) −6.78628 −0.915062
\(56\) 1.32066 0.176481
\(57\) 4.08579 0.541177
\(58\) 5.04102 0.661919
\(59\) 1.32811 0.172905 0.0864524 0.996256i \(-0.472447\pi\)
0.0864524 + 0.996256i \(0.472447\pi\)
\(60\) −3.21876 −0.415540
\(61\) −2.36183 −0.302401 −0.151201 0.988503i \(-0.548314\pi\)
−0.151201 + 0.988503i \(0.548314\pi\)
\(62\) 4.04230 0.513373
\(63\) 2.58247 0.325360
\(64\) 1.00000 0.125000
\(65\) 1.85059 0.229537
\(66\) 10.4478 1.28604
\(67\) 8.01836 0.979599 0.489799 0.871835i \(-0.337070\pi\)
0.489799 + 0.871835i \(0.337070\pi\)
\(68\) −1.75842 −0.213240
\(69\) −3.59527 −0.432820
\(70\) 1.90959 0.228239
\(71\) −11.2422 −1.33420 −0.667100 0.744968i \(-0.732465\pi\)
−0.667100 + 0.744968i \(0.732465\pi\)
\(72\) 1.95543 0.230450
\(73\) −0.908233 −0.106301 −0.0531503 0.998587i \(-0.516926\pi\)
−0.0531503 + 0.998587i \(0.516926\pi\)
\(74\) −1.67445 −0.194651
\(75\) 6.47629 0.747818
\(76\) −1.83542 −0.210537
\(77\) −6.19835 −0.706367
\(78\) −2.84906 −0.322593
\(79\) −4.37488 −0.492212 −0.246106 0.969243i \(-0.579151\pi\)
−0.246106 + 0.969243i \(0.579151\pi\)
\(80\) 1.44593 0.161660
\(81\) −11.0426 −1.22695
\(82\) −3.00389 −0.331725
\(83\) 12.7989 1.40486 0.702429 0.711753i \(-0.252099\pi\)
0.702429 + 0.711753i \(0.252099\pi\)
\(84\) −2.93990 −0.320769
\(85\) −2.54256 −0.275779
\(86\) −3.28239 −0.353950
\(87\) −11.2217 −1.20309
\(88\) −4.69336 −0.500314
\(89\) −12.9009 −1.36749 −0.683745 0.729721i \(-0.739650\pi\)
−0.683745 + 0.729721i \(0.739650\pi\)
\(90\) 2.82742 0.298037
\(91\) 1.69026 0.177187
\(92\) 1.61507 0.168383
\(93\) −8.99849 −0.933100
\(94\) 6.32528 0.652403
\(95\) −2.65389 −0.272284
\(96\) −2.22608 −0.227198
\(97\) −9.16110 −0.930169 −0.465085 0.885266i \(-0.653976\pi\)
−0.465085 + 0.885266i \(0.653976\pi\)
\(98\) −5.25585 −0.530921
\(99\) −9.17755 −0.922379
\(100\) −2.90928 −0.290928
\(101\) −9.75684 −0.970842 −0.485421 0.874281i \(-0.661334\pi\)
−0.485421 + 0.874281i \(0.661334\pi\)
\(102\) 3.91438 0.387582
\(103\) −13.9265 −1.37222 −0.686112 0.727496i \(-0.740684\pi\)
−0.686112 + 0.727496i \(0.740684\pi\)
\(104\) 1.27986 0.125500
\(105\) −4.25090 −0.414845
\(106\) −6.43256 −0.624785
\(107\) 0.0699806 0.00676528 0.00338264 0.999994i \(-0.498923\pi\)
0.00338264 + 0.999994i \(0.498923\pi\)
\(108\) 2.32529 0.223751
\(109\) 7.14893 0.684743 0.342372 0.939565i \(-0.388770\pi\)
0.342372 + 0.939565i \(0.388770\pi\)
\(110\) −6.78628 −0.647047
\(111\) 3.72746 0.353795
\(112\) 1.32066 0.124791
\(113\) 18.1278 1.70532 0.852662 0.522463i \(-0.174987\pi\)
0.852662 + 0.522463i \(0.174987\pi\)
\(114\) 4.08579 0.382670
\(115\) 2.33528 0.217766
\(116\) 5.04102 0.468047
\(117\) 2.50267 0.231372
\(118\) 1.32811 0.122262
\(119\) −2.32228 −0.212883
\(120\) −3.21876 −0.293831
\(121\) 11.0277 1.00251
\(122\) −2.36183 −0.213830
\(123\) 6.68691 0.602938
\(124\) 4.04230 0.363010
\(125\) −11.4363 −1.02289
\(126\) 2.58247 0.230064
\(127\) 15.1331 1.34285 0.671425 0.741073i \(-0.265683\pi\)
0.671425 + 0.741073i \(0.265683\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.30687 0.643334
\(130\) 1.85059 0.162307
\(131\) −5.41604 −0.473201 −0.236601 0.971607i \(-0.576033\pi\)
−0.236601 + 0.971607i \(0.576033\pi\)
\(132\) 10.4478 0.909364
\(133\) −2.42397 −0.210185
\(134\) 8.01836 0.692681
\(135\) 3.36221 0.289373
\(136\) −1.75842 −0.150783
\(137\) −16.3466 −1.39658 −0.698291 0.715814i \(-0.746056\pi\)
−0.698291 + 0.715814i \(0.746056\pi\)
\(138\) −3.59527 −0.306050
\(139\) −9.63523 −0.817250 −0.408625 0.912702i \(-0.633992\pi\)
−0.408625 + 0.912702i \(0.633992\pi\)
\(140\) 1.90959 0.161390
\(141\) −14.0806 −1.18580
\(142\) −11.2422 −0.943422
\(143\) −6.00683 −0.502316
\(144\) 1.95543 0.162953
\(145\) 7.28898 0.605317
\(146\) −0.908233 −0.0751659
\(147\) 11.6999 0.964995
\(148\) −1.67445 −0.137639
\(149\) 3.55096 0.290906 0.145453 0.989365i \(-0.453536\pi\)
0.145453 + 0.989365i \(0.453536\pi\)
\(150\) 6.47629 0.528787
\(151\) 8.65736 0.704526 0.352263 0.935901i \(-0.385412\pi\)
0.352263 + 0.935901i \(0.385412\pi\)
\(152\) −1.83542 −0.148872
\(153\) −3.43847 −0.277984
\(154\) −6.19835 −0.499477
\(155\) 5.84490 0.469474
\(156\) −2.84906 −0.228108
\(157\) −18.1654 −1.44975 −0.724877 0.688878i \(-0.758103\pi\)
−0.724877 + 0.688878i \(0.758103\pi\)
\(158\) −4.37488 −0.348047
\(159\) 14.3194 1.13560
\(160\) 1.44593 0.114311
\(161\) 2.13296 0.168101
\(162\) −11.0426 −0.867587
\(163\) −14.1560 −1.10879 −0.554393 0.832255i \(-0.687050\pi\)
−0.554393 + 0.832255i \(0.687050\pi\)
\(164\) −3.00389 −0.234565
\(165\) 15.1068 1.17606
\(166\) 12.7989 0.993385
\(167\) 8.75105 0.677176 0.338588 0.940935i \(-0.390051\pi\)
0.338588 + 0.940935i \(0.390051\pi\)
\(168\) −2.93990 −0.226818
\(169\) −11.3620 −0.873997
\(170\) −2.54256 −0.195005
\(171\) −3.58904 −0.274461
\(172\) −3.28239 −0.250280
\(173\) −20.5300 −1.56087 −0.780433 0.625239i \(-0.785001\pi\)
−0.780433 + 0.625239i \(0.785001\pi\)
\(174\) −11.2217 −0.850717
\(175\) −3.84218 −0.290441
\(176\) −4.69336 −0.353776
\(177\) −2.95647 −0.222222
\(178\) −12.9009 −0.966961
\(179\) −7.14274 −0.533874 −0.266937 0.963714i \(-0.586012\pi\)
−0.266937 + 0.963714i \(0.586012\pi\)
\(180\) 2.82742 0.210744
\(181\) −4.22490 −0.314034 −0.157017 0.987596i \(-0.550188\pi\)
−0.157017 + 0.987596i \(0.550188\pi\)
\(182\) 1.69026 0.125290
\(183\) 5.25762 0.388655
\(184\) 1.61507 0.119065
\(185\) −2.42114 −0.178006
\(186\) −8.99849 −0.659802
\(187\) 8.25291 0.603512
\(188\) 6.32528 0.461318
\(189\) 3.07092 0.223377
\(190\) −2.65389 −0.192534
\(191\) 5.89653 0.426658 0.213329 0.976980i \(-0.431569\pi\)
0.213329 + 0.976980i \(0.431569\pi\)
\(192\) −2.22608 −0.160653
\(193\) 22.3976 1.61222 0.806108 0.591768i \(-0.201570\pi\)
0.806108 + 0.591768i \(0.201570\pi\)
\(194\) −9.16110 −0.657729
\(195\) −4.11955 −0.295007
\(196\) −5.25585 −0.375418
\(197\) −11.9420 −0.850833 −0.425417 0.904998i \(-0.639872\pi\)
−0.425417 + 0.904998i \(0.639872\pi\)
\(198\) −9.17755 −0.652220
\(199\) −2.13617 −0.151429 −0.0757147 0.997130i \(-0.524124\pi\)
−0.0757147 + 0.997130i \(0.524124\pi\)
\(200\) −2.90928 −0.205717
\(201\) −17.8495 −1.25901
\(202\) −9.75684 −0.686489
\(203\) 6.65749 0.467264
\(204\) 3.91438 0.274062
\(205\) −4.34343 −0.303358
\(206\) −13.9265 −0.970308
\(207\) 3.15816 0.219507
\(208\) 1.27986 0.0887421
\(209\) 8.61430 0.595864
\(210\) −4.25090 −0.293340
\(211\) 9.83082 0.676781 0.338391 0.941006i \(-0.390117\pi\)
0.338391 + 0.941006i \(0.390117\pi\)
\(212\) −6.43256 −0.441790
\(213\) 25.0260 1.71475
\(214\) 0.0699806 0.00478377
\(215\) −4.74612 −0.323683
\(216\) 2.32529 0.158216
\(217\) 5.33852 0.362402
\(218\) 7.14893 0.484187
\(219\) 2.02180 0.136621
\(220\) −6.78628 −0.457531
\(221\) −2.25053 −0.151387
\(222\) 3.72746 0.250171
\(223\) −17.5616 −1.17601 −0.588005 0.808857i \(-0.700087\pi\)
−0.588005 + 0.808857i \(0.700087\pi\)
\(224\) 1.32066 0.0882405
\(225\) −5.68890 −0.379260
\(226\) 18.1278 1.20585
\(227\) −4.98834 −0.331088 −0.165544 0.986202i \(-0.552938\pi\)
−0.165544 + 0.986202i \(0.552938\pi\)
\(228\) 4.08579 0.270588
\(229\) −4.96024 −0.327782 −0.163891 0.986478i \(-0.552405\pi\)
−0.163891 + 0.986478i \(0.552405\pi\)
\(230\) 2.33528 0.153984
\(231\) 13.7980 0.907843
\(232\) 5.04102 0.330959
\(233\) 3.88242 0.254346 0.127173 0.991881i \(-0.459410\pi\)
0.127173 + 0.991881i \(0.459410\pi\)
\(234\) 2.50267 0.163605
\(235\) 9.14593 0.596614
\(236\) 1.32811 0.0864524
\(237\) 9.73883 0.632605
\(238\) −2.32228 −0.150531
\(239\) 19.0246 1.23060 0.615299 0.788294i \(-0.289035\pi\)
0.615299 + 0.788294i \(0.289035\pi\)
\(240\) −3.21876 −0.207770
\(241\) 8.14953 0.524957 0.262479 0.964938i \(-0.415460\pi\)
0.262479 + 0.964938i \(0.415460\pi\)
\(242\) 11.0277 0.708885
\(243\) 17.6058 1.12941
\(244\) −2.36183 −0.151201
\(245\) −7.59960 −0.485521
\(246\) 6.68691 0.426342
\(247\) −2.34908 −0.149468
\(248\) 4.04230 0.256687
\(249\) −28.4913 −1.80556
\(250\) −11.4363 −0.723294
\(251\) 1.16166 0.0733236 0.0366618 0.999328i \(-0.488328\pi\)
0.0366618 + 0.999328i \(0.488328\pi\)
\(252\) 2.58247 0.162680
\(253\) −7.58011 −0.476557
\(254\) 15.1331 0.949538
\(255\) 5.65994 0.354439
\(256\) 1.00000 0.0625000
\(257\) 25.1089 1.56625 0.783126 0.621863i \(-0.213624\pi\)
0.783126 + 0.621863i \(0.213624\pi\)
\(258\) 7.30687 0.454906
\(259\) −2.21138 −0.137409
\(260\) 1.85059 0.114768
\(261\) 9.85738 0.610157
\(262\) −5.41604 −0.334604
\(263\) 6.73112 0.415058 0.207529 0.978229i \(-0.433458\pi\)
0.207529 + 0.978229i \(0.433458\pi\)
\(264\) 10.4478 0.643018
\(265\) −9.30104 −0.571359
\(266\) −2.42397 −0.148623
\(267\) 28.7184 1.75754
\(268\) 8.01836 0.489799
\(269\) −6.39523 −0.389924 −0.194962 0.980811i \(-0.562458\pi\)
−0.194962 + 0.980811i \(0.562458\pi\)
\(270\) 3.36221 0.204618
\(271\) 9.50505 0.577390 0.288695 0.957421i \(-0.406779\pi\)
0.288695 + 0.957421i \(0.406779\pi\)
\(272\) −1.75842 −0.106620
\(273\) −3.76265 −0.227726
\(274\) −16.3466 −0.987533
\(275\) 13.6543 0.823386
\(276\) −3.59527 −0.216410
\(277\) −22.0202 −1.32307 −0.661533 0.749916i \(-0.730094\pi\)
−0.661533 + 0.749916i \(0.730094\pi\)
\(278\) −9.63523 −0.577883
\(279\) 7.90445 0.473227
\(280\) 1.90959 0.114120
\(281\) −30.9873 −1.84855 −0.924275 0.381728i \(-0.875329\pi\)
−0.924275 + 0.381728i \(0.875329\pi\)
\(282\) −14.0806 −0.838486
\(283\) 16.6965 0.992505 0.496253 0.868178i \(-0.334709\pi\)
0.496253 + 0.868178i \(0.334709\pi\)
\(284\) −11.2422 −0.667100
\(285\) 5.90778 0.349947
\(286\) −6.00683 −0.355191
\(287\) −3.96713 −0.234172
\(288\) 1.95543 0.115225
\(289\) −13.9080 −0.818115
\(290\) 7.28898 0.428024
\(291\) 20.3933 1.19548
\(292\) −0.908233 −0.0531503
\(293\) 6.92641 0.404645 0.202322 0.979319i \(-0.435151\pi\)
0.202322 + 0.979319i \(0.435151\pi\)
\(294\) 11.6999 0.682355
\(295\) 1.92035 0.111807
\(296\) −1.67445 −0.0973254
\(297\) −10.9134 −0.633262
\(298\) 3.55096 0.205702
\(299\) 2.06706 0.119541
\(300\) 6.47629 0.373909
\(301\) −4.33494 −0.249862
\(302\) 8.65736 0.498175
\(303\) 21.7195 1.24775
\(304\) −1.83542 −0.105269
\(305\) −3.41505 −0.195545
\(306\) −3.43847 −0.196564
\(307\) 6.50377 0.371190 0.185595 0.982626i \(-0.440579\pi\)
0.185595 + 0.982626i \(0.440579\pi\)
\(308\) −6.19835 −0.353184
\(309\) 31.0016 1.76362
\(310\) 5.84490 0.331968
\(311\) −29.7435 −1.68660 −0.843300 0.537444i \(-0.819390\pi\)
−0.843300 + 0.537444i \(0.819390\pi\)
\(312\) −2.84906 −0.161296
\(313\) −10.7975 −0.610313 −0.305156 0.952302i \(-0.598709\pi\)
−0.305156 + 0.952302i \(0.598709\pi\)
\(314\) −18.1654 −1.02513
\(315\) 3.73407 0.210391
\(316\) −4.37488 −0.246106
\(317\) −2.34579 −0.131753 −0.0658765 0.997828i \(-0.520984\pi\)
−0.0658765 + 0.997828i \(0.520984\pi\)
\(318\) 14.3194 0.802992
\(319\) −23.6594 −1.32467
\(320\) 1.44593 0.0808301
\(321\) −0.155782 −0.00869492
\(322\) 2.13296 0.118865
\(323\) 3.22744 0.179580
\(324\) −11.0426 −0.613477
\(325\) −3.72346 −0.206540
\(326\) −14.1560 −0.784030
\(327\) −15.9141 −0.880051
\(328\) −3.00389 −0.165862
\(329\) 8.35356 0.460547
\(330\) 15.1068 0.831603
\(331\) 0.327186 0.0179837 0.00899187 0.999960i \(-0.497138\pi\)
0.00899187 + 0.999960i \(0.497138\pi\)
\(332\) 12.7989 0.702429
\(333\) −3.27427 −0.179429
\(334\) 8.75105 0.478836
\(335\) 11.5940 0.633448
\(336\) −2.93990 −0.160385
\(337\) −6.08028 −0.331214 −0.165607 0.986192i \(-0.552958\pi\)
−0.165607 + 0.986192i \(0.552958\pi\)
\(338\) −11.3620 −0.618010
\(339\) −40.3540 −2.19173
\(340\) −2.54256 −0.137890
\(341\) −18.9720 −1.02739
\(342\) −3.58904 −0.194073
\(343\) −16.1858 −0.873953
\(344\) −3.28239 −0.176975
\(345\) −5.19852 −0.279879
\(346\) −20.5300 −1.10370
\(347\) −11.3965 −0.611794 −0.305897 0.952065i \(-0.598956\pi\)
−0.305897 + 0.952065i \(0.598956\pi\)
\(348\) −11.2217 −0.601547
\(349\) 10.3551 0.554293 0.277147 0.960828i \(-0.410611\pi\)
0.277147 + 0.960828i \(0.410611\pi\)
\(350\) −3.84218 −0.205373
\(351\) 2.97604 0.158849
\(352\) −4.69336 −0.250157
\(353\) −11.2397 −0.598230 −0.299115 0.954217i \(-0.596691\pi\)
−0.299115 + 0.954217i \(0.596691\pi\)
\(354\) −2.95647 −0.157135
\(355\) −16.2554 −0.862748
\(356\) −12.9009 −0.683745
\(357\) 5.16958 0.273603
\(358\) −7.14274 −0.377506
\(359\) −5.87584 −0.310115 −0.155057 0.987905i \(-0.549556\pi\)
−0.155057 + 0.987905i \(0.549556\pi\)
\(360\) 2.82742 0.149018
\(361\) −15.6312 −0.822696
\(362\) −4.22490 −0.222056
\(363\) −24.5484 −1.28846
\(364\) 1.69026 0.0885936
\(365\) −1.31324 −0.0687383
\(366\) 5.25762 0.274820
\(367\) −13.3605 −0.697415 −0.348707 0.937232i \(-0.613379\pi\)
−0.348707 + 0.937232i \(0.613379\pi\)
\(368\) 1.61507 0.0841913
\(369\) −5.87391 −0.305784
\(370\) −2.42114 −0.125869
\(371\) −8.49524 −0.441051
\(372\) −8.99849 −0.466550
\(373\) 34.0479 1.76293 0.881467 0.472245i \(-0.156556\pi\)
0.881467 + 0.472245i \(0.156556\pi\)
\(374\) 8.25291 0.426748
\(375\) 25.4581 1.31465
\(376\) 6.32528 0.326201
\(377\) 6.45179 0.332284
\(378\) 3.07092 0.157951
\(379\) −25.2972 −1.29943 −0.649715 0.760178i \(-0.725112\pi\)
−0.649715 + 0.760178i \(0.725112\pi\)
\(380\) −2.65389 −0.136142
\(381\) −33.6876 −1.72587
\(382\) 5.89653 0.301693
\(383\) 17.0415 0.870782 0.435391 0.900241i \(-0.356610\pi\)
0.435391 + 0.900241i \(0.356610\pi\)
\(384\) −2.22608 −0.113599
\(385\) −8.96239 −0.456766
\(386\) 22.3976 1.14001
\(387\) −6.41850 −0.326271
\(388\) −9.16110 −0.465085
\(389\) 18.9159 0.959074 0.479537 0.877522i \(-0.340805\pi\)
0.479537 + 0.877522i \(0.340805\pi\)
\(390\) −4.11955 −0.208602
\(391\) −2.83997 −0.143624
\(392\) −5.25585 −0.265461
\(393\) 12.0565 0.608172
\(394\) −11.9420 −0.601630
\(395\) −6.32578 −0.318284
\(396\) −9.17755 −0.461189
\(397\) −8.33504 −0.418323 −0.209162 0.977881i \(-0.567074\pi\)
−0.209162 + 0.977881i \(0.567074\pi\)
\(398\) −2.13617 −0.107077
\(399\) 5.39596 0.270136
\(400\) −2.90928 −0.145464
\(401\) −15.2801 −0.763054 −0.381527 0.924358i \(-0.624602\pi\)
−0.381527 + 0.924358i \(0.624602\pi\)
\(402\) −17.8495 −0.890253
\(403\) 5.17357 0.257714
\(404\) −9.75684 −0.485421
\(405\) −15.9668 −0.793398
\(406\) 6.65749 0.330406
\(407\) 7.85880 0.389546
\(408\) 3.91438 0.193791
\(409\) −12.4078 −0.613527 −0.306764 0.951786i \(-0.599246\pi\)
−0.306764 + 0.951786i \(0.599246\pi\)
\(410\) −4.34343 −0.214507
\(411\) 36.3888 1.79493
\(412\) −13.9265 −0.686112
\(413\) 1.75398 0.0863078
\(414\) 3.15816 0.155215
\(415\) 18.5063 0.908439
\(416\) 1.27986 0.0627501
\(417\) 21.4488 1.05035
\(418\) 8.61430 0.421339
\(419\) −19.6693 −0.960907 −0.480453 0.877020i \(-0.659528\pi\)
−0.480453 + 0.877020i \(0.659528\pi\)
\(420\) −4.25090 −0.207423
\(421\) −14.0490 −0.684704 −0.342352 0.939572i \(-0.611224\pi\)
−0.342352 + 0.939572i \(0.611224\pi\)
\(422\) 9.83082 0.478557
\(423\) 12.3687 0.601385
\(424\) −6.43256 −0.312393
\(425\) 5.11574 0.248150
\(426\) 25.0260 1.21251
\(427\) −3.11918 −0.150948
\(428\) 0.0699806 0.00338264
\(429\) 13.3717 0.645591
\(430\) −4.74612 −0.228878
\(431\) 15.8254 0.762283 0.381142 0.924517i \(-0.375531\pi\)
0.381142 + 0.924517i \(0.375531\pi\)
\(432\) 2.32529 0.111876
\(433\) −3.72748 −0.179131 −0.0895657 0.995981i \(-0.528548\pi\)
−0.0895657 + 0.995981i \(0.528548\pi\)
\(434\) 5.33852 0.256257
\(435\) −16.2258 −0.777970
\(436\) 7.14893 0.342372
\(437\) −2.96433 −0.141803
\(438\) 2.02180 0.0966053
\(439\) 2.55266 0.121832 0.0609160 0.998143i \(-0.480598\pi\)
0.0609160 + 0.998143i \(0.480598\pi\)
\(440\) −6.78628 −0.323523
\(441\) −10.2775 −0.489403
\(442\) −2.25053 −0.107047
\(443\) −7.30889 −0.347256 −0.173628 0.984811i \(-0.555549\pi\)
−0.173628 + 0.984811i \(0.555549\pi\)
\(444\) 3.72746 0.176897
\(445\) −18.6538 −0.884274
\(446\) −17.5616 −0.831565
\(447\) −7.90473 −0.373881
\(448\) 1.32066 0.0623954
\(449\) 5.87689 0.277347 0.138674 0.990338i \(-0.455716\pi\)
0.138674 + 0.990338i \(0.455716\pi\)
\(450\) −5.68890 −0.268177
\(451\) 14.0984 0.663866
\(452\) 18.1278 0.852662
\(453\) −19.2720 −0.905476
\(454\) −4.98834 −0.234114
\(455\) 2.44400 0.114576
\(456\) 4.08579 0.191335
\(457\) −28.3939 −1.32821 −0.664105 0.747639i \(-0.731187\pi\)
−0.664105 + 0.747639i \(0.731187\pi\)
\(458\) −4.96024 −0.231777
\(459\) −4.08884 −0.190851
\(460\) 2.33528 0.108883
\(461\) −26.7478 −1.24577 −0.622885 0.782313i \(-0.714040\pi\)
−0.622885 + 0.782313i \(0.714040\pi\)
\(462\) 13.7980 0.641942
\(463\) −36.7289 −1.70694 −0.853468 0.521145i \(-0.825505\pi\)
−0.853468 + 0.521145i \(0.825505\pi\)
\(464\) 5.04102 0.234024
\(465\) −13.0112 −0.603381
\(466\) 3.88242 0.179850
\(467\) −7.38286 −0.341638 −0.170819 0.985302i \(-0.554641\pi\)
−0.170819 + 0.985302i \(0.554641\pi\)
\(468\) 2.50267 0.115686
\(469\) 10.5896 0.488980
\(470\) 9.14593 0.421870
\(471\) 40.4376 1.86326
\(472\) 1.32811 0.0611311
\(473\) 15.4055 0.708344
\(474\) 9.73883 0.447319
\(475\) 5.33975 0.245005
\(476\) −2.32228 −0.106442
\(477\) −12.5784 −0.575927
\(478\) 19.0246 0.870164
\(479\) −11.6682 −0.533132 −0.266566 0.963817i \(-0.585889\pi\)
−0.266566 + 0.963817i \(0.585889\pi\)
\(480\) −3.21876 −0.146916
\(481\) −2.14306 −0.0977149
\(482\) 8.14953 0.371201
\(483\) −4.74814 −0.216048
\(484\) 11.0277 0.501257
\(485\) −13.2463 −0.601485
\(486\) 17.6058 0.798615
\(487\) −19.5412 −0.885495 −0.442748 0.896646i \(-0.645996\pi\)
−0.442748 + 0.896646i \(0.645996\pi\)
\(488\) −2.36183 −0.106915
\(489\) 31.5125 1.42504
\(490\) −7.59960 −0.343315
\(491\) 1.52840 0.0689757 0.0344879 0.999405i \(-0.489020\pi\)
0.0344879 + 0.999405i \(0.489020\pi\)
\(492\) 6.68691 0.301469
\(493\) −8.86424 −0.399225
\(494\) −2.34908 −0.105690
\(495\) −13.2701 −0.596448
\(496\) 4.04230 0.181505
\(497\) −14.8471 −0.665984
\(498\) −28.4913 −1.27673
\(499\) −42.1288 −1.88595 −0.942973 0.332870i \(-0.891983\pi\)
−0.942973 + 0.332870i \(0.891983\pi\)
\(500\) −11.4363 −0.511446
\(501\) −19.4805 −0.870326
\(502\) 1.16166 0.0518476
\(503\) 12.3148 0.549088 0.274544 0.961575i \(-0.411473\pi\)
0.274544 + 0.961575i \(0.411473\pi\)
\(504\) 2.58247 0.115032
\(505\) −14.1077 −0.627786
\(506\) −7.58011 −0.336977
\(507\) 25.2926 1.12329
\(508\) 15.1331 0.671425
\(509\) 12.1132 0.536909 0.268455 0.963292i \(-0.413487\pi\)
0.268455 + 0.963292i \(0.413487\pi\)
\(510\) 5.65994 0.250626
\(511\) −1.19947 −0.0530614
\(512\) 1.00000 0.0441942
\(513\) −4.26789 −0.188432
\(514\) 25.1089 1.10751
\(515\) −20.1368 −0.887335
\(516\) 7.30687 0.321667
\(517\) −29.6868 −1.30563
\(518\) −2.21138 −0.0971626
\(519\) 45.7014 2.00607
\(520\) 1.85059 0.0811536
\(521\) −26.4763 −1.15995 −0.579974 0.814635i \(-0.696937\pi\)
−0.579974 + 0.814635i \(0.696937\pi\)
\(522\) 9.85738 0.431446
\(523\) 10.3520 0.452660 0.226330 0.974051i \(-0.427327\pi\)
0.226330 + 0.974051i \(0.427327\pi\)
\(524\) −5.41604 −0.236601
\(525\) 8.55299 0.373283
\(526\) 6.73112 0.293491
\(527\) −7.10807 −0.309632
\(528\) 10.4478 0.454682
\(529\) −20.3916 −0.886589
\(530\) −9.30104 −0.404012
\(531\) 2.59702 0.112701
\(532\) −2.42397 −0.105093
\(533\) −3.84455 −0.166526
\(534\) 28.7184 1.24277
\(535\) 0.101187 0.00437470
\(536\) 8.01836 0.346341
\(537\) 15.9003 0.686149
\(538\) −6.39523 −0.275718
\(539\) 24.6676 1.06251
\(540\) 3.36221 0.144687
\(541\) 27.3982 1.17794 0.588971 0.808154i \(-0.299533\pi\)
0.588971 + 0.808154i \(0.299533\pi\)
\(542\) 9.50505 0.408277
\(543\) 9.40496 0.403606
\(544\) −1.75842 −0.0753917
\(545\) 10.3369 0.442783
\(546\) −3.76265 −0.161027
\(547\) −30.1829 −1.29053 −0.645264 0.763959i \(-0.723253\pi\)
−0.645264 + 0.763959i \(0.723253\pi\)
\(548\) −16.3466 −0.698291
\(549\) −4.61840 −0.197108
\(550\) 13.6543 0.582222
\(551\) −9.25240 −0.394166
\(552\) −3.59527 −0.153025
\(553\) −5.77774 −0.245694
\(554\) −22.0202 −0.935549
\(555\) 5.38965 0.228778
\(556\) −9.63523 −0.408625
\(557\) 7.68484 0.325617 0.162809 0.986658i \(-0.447945\pi\)
0.162809 + 0.986658i \(0.447945\pi\)
\(558\) 7.90445 0.334622
\(559\) −4.20099 −0.177683
\(560\) 1.90959 0.0806948
\(561\) −18.3716 −0.775651
\(562\) −30.9873 −1.30712
\(563\) 27.6489 1.16526 0.582631 0.812737i \(-0.302023\pi\)
0.582631 + 0.812737i \(0.302023\pi\)
\(564\) −14.0806 −0.592899
\(565\) 26.2116 1.10273
\(566\) 16.6965 0.701807
\(567\) −14.5835 −0.612450
\(568\) −11.2422 −0.471711
\(569\) −29.8901 −1.25306 −0.626530 0.779398i \(-0.715525\pi\)
−0.626530 + 0.779398i \(0.715525\pi\)
\(570\) 5.90778 0.247450
\(571\) −3.17758 −0.132978 −0.0664888 0.997787i \(-0.521180\pi\)
−0.0664888 + 0.997787i \(0.521180\pi\)
\(572\) −6.00683 −0.251158
\(573\) −13.1262 −0.548353
\(574\) −3.96713 −0.165585
\(575\) −4.69869 −0.195949
\(576\) 1.95543 0.0814763
\(577\) −15.8826 −0.661202 −0.330601 0.943771i \(-0.607251\pi\)
−0.330601 + 0.943771i \(0.607251\pi\)
\(578\) −13.9080 −0.578495
\(579\) −49.8589 −2.07207
\(580\) 7.28898 0.302658
\(581\) 16.9030 0.701254
\(582\) 20.3933 0.845332
\(583\) 30.1903 1.25036
\(584\) −0.908233 −0.0375829
\(585\) 3.61870 0.149615
\(586\) 6.92641 0.286127
\(587\) 18.2326 0.752540 0.376270 0.926510i \(-0.377207\pi\)
0.376270 + 0.926510i \(0.377207\pi\)
\(588\) 11.6999 0.482498
\(589\) −7.41933 −0.305708
\(590\) 1.92035 0.0790597
\(591\) 26.5839 1.09351
\(592\) −1.67445 −0.0688195
\(593\) 8.27513 0.339819 0.169909 0.985460i \(-0.445652\pi\)
0.169909 + 0.985460i \(0.445652\pi\)
\(594\) −10.9134 −0.447784
\(595\) −3.35786 −0.137659
\(596\) 3.55096 0.145453
\(597\) 4.75529 0.194621
\(598\) 2.06706 0.0845283
\(599\) −5.06788 −0.207068 −0.103534 0.994626i \(-0.533015\pi\)
−0.103534 + 0.994626i \(0.533015\pi\)
\(600\) 6.47629 0.264393
\(601\) −23.3877 −0.954004 −0.477002 0.878902i \(-0.658277\pi\)
−0.477002 + 0.878902i \(0.658277\pi\)
\(602\) −4.33494 −0.176679
\(603\) 15.6794 0.638513
\(604\) 8.65736 0.352263
\(605\) 15.9452 0.648266
\(606\) 21.7195 0.882295
\(607\) 20.6447 0.837941 0.418971 0.908000i \(-0.362391\pi\)
0.418971 + 0.908000i \(0.362391\pi\)
\(608\) −1.83542 −0.0744362
\(609\) −14.8201 −0.600541
\(610\) −3.41505 −0.138271
\(611\) 8.09545 0.327507
\(612\) −3.43847 −0.138992
\(613\) −11.4334 −0.461790 −0.230895 0.972979i \(-0.574165\pi\)
−0.230895 + 0.972979i \(0.574165\pi\)
\(614\) 6.50377 0.262471
\(615\) 9.66882 0.389884
\(616\) −6.19835 −0.249739
\(617\) 2.24546 0.0903986 0.0451993 0.998978i \(-0.485608\pi\)
0.0451993 + 0.998978i \(0.485608\pi\)
\(618\) 31.0016 1.24707
\(619\) 15.7379 0.632562 0.316281 0.948666i \(-0.397566\pi\)
0.316281 + 0.948666i \(0.397566\pi\)
\(620\) 5.84490 0.234737
\(621\) 3.75551 0.150703
\(622\) −29.7435 −1.19261
\(623\) −17.0377 −0.682601
\(624\) −2.84906 −0.114054
\(625\) −1.98969 −0.0795876
\(626\) −10.7975 −0.431556
\(627\) −19.1761 −0.765820
\(628\) −18.1654 −0.724877
\(629\) 2.94439 0.117400
\(630\) 3.73407 0.148769
\(631\) −27.0675 −1.07754 −0.538770 0.842453i \(-0.681111\pi\)
−0.538770 + 0.842453i \(0.681111\pi\)
\(632\) −4.37488 −0.174023
\(633\) −21.8842 −0.869818
\(634\) −2.34579 −0.0931634
\(635\) 21.8815 0.868341
\(636\) 14.3194 0.567801
\(637\) −6.72673 −0.266523
\(638\) −23.6594 −0.936683
\(639\) −21.9833 −0.869646
\(640\) 1.44593 0.0571555
\(641\) 18.1861 0.718309 0.359154 0.933278i \(-0.383065\pi\)
0.359154 + 0.933278i \(0.383065\pi\)
\(642\) −0.155782 −0.00614824
\(643\) 25.3873 1.00118 0.500588 0.865686i \(-0.333117\pi\)
0.500588 + 0.865686i \(0.333117\pi\)
\(644\) 2.13296 0.0840505
\(645\) 10.5652 0.416006
\(646\) 3.22744 0.126982
\(647\) −25.7397 −1.01193 −0.505967 0.862553i \(-0.668864\pi\)
−0.505967 + 0.862553i \(0.668864\pi\)
\(648\) −11.0426 −0.433794
\(649\) −6.23329 −0.244678
\(650\) −3.72346 −0.146046
\(651\) −11.8840 −0.465770
\(652\) −14.1560 −0.554393
\(653\) 16.3795 0.640981 0.320491 0.947252i \(-0.396152\pi\)
0.320491 + 0.947252i \(0.396152\pi\)
\(654\) −15.9141 −0.622290
\(655\) −7.83122 −0.305991
\(656\) −3.00389 −0.117282
\(657\) −1.77599 −0.0692879
\(658\) 8.35356 0.325656
\(659\) 33.4879 1.30450 0.652251 0.758003i \(-0.273825\pi\)
0.652251 + 0.758003i \(0.273825\pi\)
\(660\) 15.1068 0.588032
\(661\) 14.0937 0.548180 0.274090 0.961704i \(-0.411623\pi\)
0.274090 + 0.961704i \(0.411623\pi\)
\(662\) 0.327186 0.0127164
\(663\) 5.00985 0.194566
\(664\) 12.7989 0.496693
\(665\) −3.50490 −0.135914
\(666\) −3.27427 −0.126876
\(667\) 8.14160 0.315244
\(668\) 8.75105 0.338588
\(669\) 39.0935 1.51144
\(670\) 11.5940 0.447916
\(671\) 11.0849 0.427929
\(672\) −2.93990 −0.113409
\(673\) −16.8891 −0.651025 −0.325513 0.945538i \(-0.605537\pi\)
−0.325513 + 0.945538i \(0.605537\pi\)
\(674\) −6.08028 −0.234204
\(675\) −6.76492 −0.260382
\(676\) −11.3620 −0.436999
\(677\) 49.3306 1.89593 0.947965 0.318374i \(-0.103137\pi\)
0.947965 + 0.318374i \(0.103137\pi\)
\(678\) −40.3540 −1.54979
\(679\) −12.0987 −0.464306
\(680\) −2.54256 −0.0975026
\(681\) 11.1044 0.425523
\(682\) −18.9720 −0.726476
\(683\) −44.9875 −1.72140 −0.860700 0.509112i \(-0.829974\pi\)
−0.860700 + 0.509112i \(0.829974\pi\)
\(684\) −3.58904 −0.137230
\(685\) −23.6360 −0.903087
\(686\) −16.1858 −0.617978
\(687\) 11.0419 0.421275
\(688\) −3.28239 −0.125140
\(689\) −8.23275 −0.313643
\(690\) −5.19852 −0.197904
\(691\) 14.5597 0.553876 0.276938 0.960888i \(-0.410680\pi\)
0.276938 + 0.960888i \(0.410680\pi\)
\(692\) −20.5300 −0.780433
\(693\) −12.1205 −0.460418
\(694\) −11.3965 −0.432604
\(695\) −13.9319 −0.528467
\(696\) −11.2217 −0.425358
\(697\) 5.28211 0.200074
\(698\) 10.3551 0.391945
\(699\) −8.64258 −0.326892
\(700\) −3.84218 −0.145221
\(701\) 32.9733 1.24538 0.622692 0.782467i \(-0.286039\pi\)
0.622692 + 0.782467i \(0.286039\pi\)
\(702\) 2.97604 0.112323
\(703\) 3.07332 0.115912
\(704\) −4.69336 −0.176888
\(705\) −20.3596 −0.766786
\(706\) −11.2397 −0.423013
\(707\) −12.8855 −0.484609
\(708\) −2.95647 −0.111111
\(709\) −29.3855 −1.10360 −0.551798 0.833978i \(-0.686058\pi\)
−0.551798 + 0.833978i \(0.686058\pi\)
\(710\) −16.2554 −0.610055
\(711\) −8.55478 −0.320829
\(712\) −12.9009 −0.483481
\(713\) 6.52860 0.244498
\(714\) 5.16958 0.193467
\(715\) −8.68547 −0.324818
\(716\) −7.14274 −0.266937
\(717\) −42.3502 −1.58160
\(718\) −5.87584 −0.219284
\(719\) 37.5592 1.40072 0.700362 0.713788i \(-0.253022\pi\)
0.700362 + 0.713788i \(0.253022\pi\)
\(720\) 2.82742 0.105372
\(721\) −18.3923 −0.684964
\(722\) −15.6312 −0.581734
\(723\) −18.1415 −0.674690
\(724\) −4.22490 −0.157017
\(725\) −14.6657 −0.544672
\(726\) −24.5484 −0.911078
\(727\) −52.2273 −1.93700 −0.968501 0.249009i \(-0.919895\pi\)
−0.968501 + 0.249009i \(0.919895\pi\)
\(728\) 1.69026 0.0626451
\(729\) −6.06417 −0.224599
\(730\) −1.31324 −0.0486053
\(731\) 5.77183 0.213479
\(732\) 5.25762 0.194327
\(733\) 44.4111 1.64036 0.820181 0.572104i \(-0.193873\pi\)
0.820181 + 0.572104i \(0.193873\pi\)
\(734\) −13.3605 −0.493147
\(735\) 16.9173 0.624005
\(736\) 1.61507 0.0595323
\(737\) −37.6331 −1.38623
\(738\) −5.87391 −0.216222
\(739\) 34.6183 1.27346 0.636728 0.771088i \(-0.280287\pi\)
0.636728 + 0.771088i \(0.280287\pi\)
\(740\) −2.42114 −0.0890029
\(741\) 5.22923 0.192101
\(742\) −8.49524 −0.311870
\(743\) −15.8354 −0.580945 −0.290473 0.956883i \(-0.593813\pi\)
−0.290473 + 0.956883i \(0.593813\pi\)
\(744\) −8.99849 −0.329901
\(745\) 5.13445 0.188112
\(746\) 34.0479 1.24658
\(747\) 25.0273 0.915702
\(748\) 8.25291 0.301756
\(749\) 0.0924207 0.00337698
\(750\) 25.4581 0.929598
\(751\) 10.9417 0.399268 0.199634 0.979871i \(-0.436025\pi\)
0.199634 + 0.979871i \(0.436025\pi\)
\(752\) 6.32528 0.230659
\(753\) −2.58596 −0.0942375
\(754\) 6.45179 0.234960
\(755\) 12.5180 0.455575
\(756\) 3.07092 0.111688
\(757\) −5.70389 −0.207311 −0.103656 0.994613i \(-0.533054\pi\)
−0.103656 + 0.994613i \(0.533054\pi\)
\(758\) −25.2972 −0.918836
\(759\) 16.8739 0.612485
\(760\) −2.65389 −0.0962669
\(761\) 50.8699 1.84403 0.922016 0.387151i \(-0.126541\pi\)
0.922016 + 0.387151i \(0.126541\pi\)
\(762\) −33.6876 −1.22037
\(763\) 9.44132 0.341799
\(764\) 5.89653 0.213329
\(765\) −4.97180 −0.179756
\(766\) 17.0415 0.615736
\(767\) 1.69979 0.0613757
\(768\) −2.22608 −0.0803267
\(769\) −12.7091 −0.458301 −0.229150 0.973391i \(-0.573595\pi\)
−0.229150 + 0.973391i \(0.573595\pi\)
\(770\) −8.96239 −0.322982
\(771\) −55.8945 −2.01299
\(772\) 22.3976 0.806108
\(773\) 17.6765 0.635781 0.317890 0.948127i \(-0.397026\pi\)
0.317890 + 0.948127i \(0.397026\pi\)
\(774\) −6.41850 −0.230708
\(775\) −11.7602 −0.422439
\(776\) −9.16110 −0.328864
\(777\) 4.92272 0.176601
\(778\) 18.9159 0.678168
\(779\) 5.51341 0.197538
\(780\) −4.11955 −0.147504
\(781\) 52.7636 1.88803
\(782\) −2.83997 −0.101557
\(783\) 11.7218 0.418905
\(784\) −5.25585 −0.187709
\(785\) −26.2659 −0.937470
\(786\) 12.0565 0.430042
\(787\) 9.34658 0.333170 0.166585 0.986027i \(-0.446726\pi\)
0.166585 + 0.986027i \(0.446726\pi\)
\(788\) −11.9420 −0.425417
\(789\) −14.9840 −0.533445
\(790\) −6.32578 −0.225061
\(791\) 23.9408 0.851236
\(792\) −9.17755 −0.326110
\(793\) −3.02280 −0.107343
\(794\) −8.33504 −0.295799
\(795\) 20.7049 0.734326
\(796\) −2.13617 −0.0757147
\(797\) 26.9195 0.953539 0.476769 0.879028i \(-0.341808\pi\)
0.476769 + 0.879028i \(0.341808\pi\)
\(798\) 5.39596 0.191015
\(799\) −11.1225 −0.393486
\(800\) −2.90928 −0.102859
\(801\) −25.2268 −0.891345
\(802\) −15.2801 −0.539561
\(803\) 4.26267 0.150426
\(804\) −17.8495 −0.629504
\(805\) 3.08412 0.108701
\(806\) 5.17357 0.182231
\(807\) 14.2363 0.501141
\(808\) −9.75684 −0.343244
\(809\) −5.77202 −0.202934 −0.101467 0.994839i \(-0.532354\pi\)
−0.101467 + 0.994839i \(0.532354\pi\)
\(810\) −15.9668 −0.561017
\(811\) 9.12700 0.320492 0.160246 0.987077i \(-0.448771\pi\)
0.160246 + 0.987077i \(0.448771\pi\)
\(812\) 6.65749 0.233632
\(813\) −21.1590 −0.742078
\(814\) 7.85880 0.275451
\(815\) −20.4687 −0.716986
\(816\) 3.91438 0.137031
\(817\) 6.02458 0.210773
\(818\) −12.4078 −0.433829
\(819\) 3.30519 0.115493
\(820\) −4.34343 −0.151679
\(821\) 19.2026 0.670174 0.335087 0.942187i \(-0.391234\pi\)
0.335087 + 0.942187i \(0.391234\pi\)
\(822\) 36.3888 1.26920
\(823\) −9.99020 −0.348236 −0.174118 0.984725i \(-0.555707\pi\)
−0.174118 + 0.984725i \(0.555707\pi\)
\(824\) −13.9265 −0.485154
\(825\) −30.3956 −1.05824
\(826\) 1.75398 0.0610288
\(827\) 33.1679 1.15336 0.576680 0.816970i \(-0.304348\pi\)
0.576680 + 0.816970i \(0.304348\pi\)
\(828\) 3.15816 0.109754
\(829\) −11.5001 −0.399416 −0.199708 0.979855i \(-0.563999\pi\)
−0.199708 + 0.979855i \(0.563999\pi\)
\(830\) 18.5063 0.642363
\(831\) 49.0187 1.70044
\(832\) 1.27986 0.0443710
\(833\) 9.24200 0.320216
\(834\) 21.4488 0.742711
\(835\) 12.6534 0.437890
\(836\) 8.61430 0.297932
\(837\) 9.39954 0.324895
\(838\) −19.6693 −0.679464
\(839\) −30.4146 −1.05003 −0.525015 0.851093i \(-0.675940\pi\)
−0.525015 + 0.851093i \(0.675940\pi\)
\(840\) −4.25090 −0.146670
\(841\) −3.58808 −0.123727
\(842\) −14.0490 −0.484159
\(843\) 68.9803 2.37581
\(844\) 9.83082 0.338391
\(845\) −16.4286 −0.565162
\(846\) 12.3687 0.425243
\(847\) 14.5638 0.500419
\(848\) −6.43256 −0.220895
\(849\) −37.1678 −1.27560
\(850\) 5.11574 0.175468
\(851\) −2.70435 −0.0927040
\(852\) 25.0260 0.857375
\(853\) 23.9854 0.821246 0.410623 0.911805i \(-0.365311\pi\)
0.410623 + 0.911805i \(0.365311\pi\)
\(854\) −3.11918 −0.106736
\(855\) −5.18951 −0.177478
\(856\) 0.0699806 0.00239189
\(857\) −12.2807 −0.419501 −0.209750 0.977755i \(-0.567265\pi\)
−0.209750 + 0.977755i \(0.567265\pi\)
\(858\) 13.3717 0.456502
\(859\) −28.9811 −0.988822 −0.494411 0.869228i \(-0.664616\pi\)
−0.494411 + 0.869228i \(0.664616\pi\)
\(860\) −4.74612 −0.161841
\(861\) 8.83115 0.300965
\(862\) 15.8254 0.539016
\(863\) 26.6918 0.908598 0.454299 0.890849i \(-0.349890\pi\)
0.454299 + 0.890849i \(0.349890\pi\)
\(864\) 2.32529 0.0791080
\(865\) −29.6850 −1.00932
\(866\) −3.72748 −0.126665
\(867\) 30.9602 1.05146
\(868\) 5.33852 0.181201
\(869\) 20.5329 0.696531
\(870\) −16.2258 −0.550108
\(871\) 10.2624 0.347727
\(872\) 7.14893 0.242093
\(873\) −17.9139 −0.606294
\(874\) −2.96433 −0.100270
\(875\) −15.1035 −0.510590
\(876\) 2.02180 0.0683103
\(877\) 16.4113 0.554171 0.277086 0.960845i \(-0.410631\pi\)
0.277086 + 0.960845i \(0.410631\pi\)
\(878\) 2.55266 0.0861482
\(879\) −15.4187 −0.520061
\(880\) −6.78628 −0.228766
\(881\) −30.3579 −1.02278 −0.511391 0.859348i \(-0.670870\pi\)
−0.511391 + 0.859348i \(0.670870\pi\)
\(882\) −10.2775 −0.346060
\(883\) 36.0715 1.21390 0.606951 0.794739i \(-0.292392\pi\)
0.606951 + 0.794739i \(0.292392\pi\)
\(884\) −2.25053 −0.0756934
\(885\) −4.27486 −0.143698
\(886\) −7.30889 −0.245547
\(887\) −16.2250 −0.544782 −0.272391 0.962187i \(-0.587814\pi\)
−0.272391 + 0.962187i \(0.587814\pi\)
\(888\) 3.72746 0.125085
\(889\) 19.9858 0.670301
\(890\) −18.6538 −0.625276
\(891\) 51.8268 1.73626
\(892\) −17.5616 −0.588005
\(893\) −11.6096 −0.388499
\(894\) −7.90473 −0.264374
\(895\) −10.3279 −0.345224
\(896\) 1.32066 0.0441202
\(897\) −4.60144 −0.153637
\(898\) 5.87689 0.196114
\(899\) 20.3774 0.679623
\(900\) −5.68890 −0.189630
\(901\) 11.3111 0.376829
\(902\) 14.0984 0.469424
\(903\) 9.64991 0.321129
\(904\) 18.1278 0.602923
\(905\) −6.10892 −0.203067
\(906\) −19.2720 −0.640268
\(907\) −43.8409 −1.45571 −0.727857 0.685729i \(-0.759484\pi\)
−0.727857 + 0.685729i \(0.759484\pi\)
\(908\) −4.98834 −0.165544
\(909\) −19.0788 −0.632805
\(910\) 2.44400 0.0810178
\(911\) 44.3590 1.46968 0.734840 0.678241i \(-0.237257\pi\)
0.734840 + 0.678241i \(0.237257\pi\)
\(912\) 4.08579 0.135294
\(913\) −60.0698 −1.98802
\(914\) −28.3939 −0.939187
\(915\) 7.60217 0.251320
\(916\) −4.96024 −0.163891
\(917\) −7.15276 −0.236205
\(918\) −4.08884 −0.134952
\(919\) 52.9228 1.74576 0.872882 0.487932i \(-0.162249\pi\)
0.872882 + 0.487932i \(0.162249\pi\)
\(920\) 2.33528 0.0769919
\(921\) −14.4779 −0.477064
\(922\) −26.7478 −0.880893
\(923\) −14.3884 −0.473599
\(924\) 13.7980 0.453922
\(925\) 4.87144 0.160172
\(926\) −36.7289 −1.20699
\(927\) −27.2324 −0.894430
\(928\) 5.04102 0.165480
\(929\) −33.9073 −1.11246 −0.556232 0.831027i \(-0.687753\pi\)
−0.556232 + 0.831027i \(0.687753\pi\)
\(930\) −13.0112 −0.426654
\(931\) 9.64670 0.316158
\(932\) 3.88242 0.127173
\(933\) 66.2114 2.16766
\(934\) −7.38286 −0.241575
\(935\) 11.9331 0.390256
\(936\) 2.50267 0.0818024
\(937\) 31.5868 1.03190 0.515948 0.856620i \(-0.327440\pi\)
0.515948 + 0.856620i \(0.327440\pi\)
\(938\) 10.5896 0.345761
\(939\) 24.0362 0.784391
\(940\) 9.14593 0.298307
\(941\) 6.89053 0.224625 0.112312 0.993673i \(-0.464174\pi\)
0.112312 + 0.993673i \(0.464174\pi\)
\(942\) 40.4376 1.31753
\(943\) −4.85150 −0.157987
\(944\) 1.32811 0.0432262
\(945\) 4.44035 0.144445
\(946\) 15.4055 0.500875
\(947\) 10.0686 0.327184 0.163592 0.986528i \(-0.447692\pi\)
0.163592 + 0.986528i \(0.447692\pi\)
\(948\) 9.73883 0.316302
\(949\) −1.16241 −0.0377334
\(950\) 5.33975 0.173245
\(951\) 5.22193 0.169333
\(952\) −2.32228 −0.0752655
\(953\) −6.39412 −0.207126 −0.103563 0.994623i \(-0.533024\pi\)
−0.103563 + 0.994623i \(0.533024\pi\)
\(954\) −12.5784 −0.407242
\(955\) 8.52599 0.275895
\(956\) 19.0246 0.615299
\(957\) 52.6676 1.70250
\(958\) −11.6682 −0.376981
\(959\) −21.5883 −0.697123
\(960\) −3.21876 −0.103885
\(961\) −14.6598 −0.472896
\(962\) −2.14306 −0.0690949
\(963\) 0.136842 0.00440968
\(964\) 8.14953 0.262479
\(965\) 32.3854 1.04252
\(966\) −4.74814 −0.152769
\(967\) −32.0285 −1.02997 −0.514984 0.857200i \(-0.672202\pi\)
−0.514984 + 0.857200i \(0.672202\pi\)
\(968\) 11.0277 0.354442
\(969\) −7.18455 −0.230801
\(970\) −13.2463 −0.425314
\(971\) 37.6530 1.20834 0.604171 0.796854i \(-0.293504\pi\)
0.604171 + 0.796854i \(0.293504\pi\)
\(972\) 17.6058 0.564706
\(973\) −12.7249 −0.407941
\(974\) −19.5412 −0.626140
\(975\) 8.28872 0.265452
\(976\) −2.36183 −0.0756003
\(977\) −59.4357 −1.90152 −0.950759 0.309931i \(-0.899694\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(978\) 31.5125 1.00766
\(979\) 60.5485 1.93514
\(980\) −7.59960 −0.242760
\(981\) 13.9792 0.446323
\(982\) 1.52840 0.0487732
\(983\) 51.6959 1.64884 0.824422 0.565975i \(-0.191500\pi\)
0.824422 + 0.565975i \(0.191500\pi\)
\(984\) 6.68691 0.213171
\(985\) −17.2673 −0.550183
\(986\) −8.86424 −0.282295
\(987\) −18.5957 −0.591907
\(988\) −2.34908 −0.0747341
\(989\) −5.30130 −0.168571
\(990\) −13.2701 −0.421752
\(991\) 30.2304 0.960299 0.480149 0.877187i \(-0.340582\pi\)
0.480149 + 0.877187i \(0.340582\pi\)
\(992\) 4.04230 0.128343
\(993\) −0.728341 −0.0231132
\(994\) −14.8471 −0.470922
\(995\) −3.08876 −0.0979204
\(996\) −28.4913 −0.902782
\(997\) −6.31333 −0.199945 −0.0999725 0.994990i \(-0.531875\pi\)
−0.0999725 + 0.994990i \(0.531875\pi\)
\(998\) −42.1288 −1.33356
\(999\) −3.89358 −0.123188
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 \(a_p\))