Properties

Label 8002.2.a.d.1.7
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.87355 q^{3}\) \(+1.00000 q^{4}\) \(+2.00628 q^{5}\) \(-2.87355 q^{6}\) \(+0.474155 q^{7}\) \(+1.00000 q^{8}\) \(+5.25731 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.87355 q^{3}\) \(+1.00000 q^{4}\) \(+2.00628 q^{5}\) \(-2.87355 q^{6}\) \(+0.474155 q^{7}\) \(+1.00000 q^{8}\) \(+5.25731 q^{9}\) \(+2.00628 q^{10}\) \(+3.13649 q^{11}\) \(-2.87355 q^{12}\) \(+5.27734 q^{13}\) \(+0.474155 q^{14}\) \(-5.76514 q^{15}\) \(+1.00000 q^{16}\) \(-4.17091 q^{17}\) \(+5.25731 q^{18}\) \(-7.51640 q^{19}\) \(+2.00628 q^{20}\) \(-1.36251 q^{21}\) \(+3.13649 q^{22}\) \(+5.06333 q^{23}\) \(-2.87355 q^{24}\) \(-0.974857 q^{25}\) \(+5.27734 q^{26}\) \(-6.48651 q^{27}\) \(+0.474155 q^{28}\) \(-7.99676 q^{29}\) \(-5.76514 q^{30}\) \(-2.39818 q^{31}\) \(+1.00000 q^{32}\) \(-9.01288 q^{33}\) \(-4.17091 q^{34}\) \(+0.951285 q^{35}\) \(+5.25731 q^{36}\) \(-0.569544 q^{37}\) \(-7.51640 q^{38}\) \(-15.1647 q^{39}\) \(+2.00628 q^{40}\) \(-11.4748 q^{41}\) \(-1.36251 q^{42}\) \(+0.986101 q^{43}\) \(+3.13649 q^{44}\) \(+10.5476 q^{45}\) \(+5.06333 q^{46}\) \(-12.5668 q^{47}\) \(-2.87355 q^{48}\) \(-6.77518 q^{49}\) \(-0.974857 q^{50}\) \(+11.9853 q^{51}\) \(+5.27734 q^{52}\) \(-3.91121 q^{53}\) \(-6.48651 q^{54}\) \(+6.29267 q^{55}\) \(+0.474155 q^{56}\) \(+21.5988 q^{57}\) \(-7.99676 q^{58}\) \(-14.7429 q^{59}\) \(-5.76514 q^{60}\) \(-2.93433 q^{61}\) \(-2.39818 q^{62}\) \(+2.49278 q^{63}\) \(+1.00000 q^{64}\) \(+10.5878 q^{65}\) \(-9.01288 q^{66}\) \(+15.4928 q^{67}\) \(-4.17091 q^{68}\) \(-14.5497 q^{69}\) \(+0.951285 q^{70}\) \(-3.47675 q^{71}\) \(+5.25731 q^{72}\) \(-15.9455 q^{73}\) \(-0.569544 q^{74}\) \(+2.80130 q^{75}\) \(-7.51640 q^{76}\) \(+1.48718 q^{77}\) \(-15.1647 q^{78}\) \(+12.4960 q^{79}\) \(+2.00628 q^{80}\) \(+2.86741 q^{81}\) \(-11.4748 q^{82}\) \(+4.50846 q^{83}\) \(-1.36251 q^{84}\) \(-8.36799 q^{85}\) \(+0.986101 q^{86}\) \(+22.9791 q^{87}\) \(+3.13649 q^{88}\) \(-11.7024 q^{89}\) \(+10.5476 q^{90}\) \(+2.50228 q^{91}\) \(+5.06333 q^{92}\) \(+6.89130 q^{93}\) \(-12.5668 q^{94}\) \(-15.0800 q^{95}\) \(-2.87355 q^{96}\) \(+8.57923 q^{97}\) \(-6.77518 q^{98}\) \(+16.4895 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.87355 −1.65905 −0.829524 0.558472i \(-0.811388\pi\)
−0.829524 + 0.558472i \(0.811388\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00628 0.897234 0.448617 0.893724i \(-0.351917\pi\)
0.448617 + 0.893724i \(0.351917\pi\)
\(6\) −2.87355 −1.17312
\(7\) 0.474155 0.179214 0.0896068 0.995977i \(-0.471439\pi\)
0.0896068 + 0.995977i \(0.471439\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.25731 1.75244
\(10\) 2.00628 0.634440
\(11\) 3.13649 0.945688 0.472844 0.881146i \(-0.343227\pi\)
0.472844 + 0.881146i \(0.343227\pi\)
\(12\) −2.87355 −0.829524
\(13\) 5.27734 1.46367 0.731836 0.681481i \(-0.238664\pi\)
0.731836 + 0.681481i \(0.238664\pi\)
\(14\) 0.474155 0.126723
\(15\) −5.76514 −1.48855
\(16\) 1.00000 0.250000
\(17\) −4.17091 −1.01159 −0.505797 0.862653i \(-0.668801\pi\)
−0.505797 + 0.862653i \(0.668801\pi\)
\(18\) 5.25731 1.23916
\(19\) −7.51640 −1.72438 −0.862190 0.506585i \(-0.830907\pi\)
−0.862190 + 0.506585i \(0.830907\pi\)
\(20\) 2.00628 0.448617
\(21\) −1.36251 −0.297324
\(22\) 3.13649 0.668702
\(23\) 5.06333 1.05578 0.527888 0.849314i \(-0.322984\pi\)
0.527888 + 0.849314i \(0.322984\pi\)
\(24\) −2.87355 −0.586562
\(25\) −0.974857 −0.194971
\(26\) 5.27734 1.03497
\(27\) −6.48651 −1.24833
\(28\) 0.474155 0.0896068
\(29\) −7.99676 −1.48496 −0.742481 0.669867i \(-0.766351\pi\)
−0.742481 + 0.669867i \(0.766351\pi\)
\(30\) −5.76514 −1.05257
\(31\) −2.39818 −0.430726 −0.215363 0.976534i \(-0.569093\pi\)
−0.215363 + 0.976534i \(0.569093\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.01288 −1.56894
\(34\) −4.17091 −0.715304
\(35\) 0.951285 0.160797
\(36\) 5.25731 0.876219
\(37\) −0.569544 −0.0936325 −0.0468163 0.998904i \(-0.514908\pi\)
−0.0468163 + 0.998904i \(0.514908\pi\)
\(38\) −7.51640 −1.21932
\(39\) −15.1647 −2.42830
\(40\) 2.00628 0.317220
\(41\) −11.4748 −1.79206 −0.896030 0.443994i \(-0.853561\pi\)
−0.896030 + 0.443994i \(0.853561\pi\)
\(42\) −1.36251 −0.210240
\(43\) 0.986101 0.150379 0.0751895 0.997169i \(-0.476044\pi\)
0.0751895 + 0.997169i \(0.476044\pi\)
\(44\) 3.13649 0.472844
\(45\) 10.5476 1.57235
\(46\) 5.06333 0.746547
\(47\) −12.5668 −1.83305 −0.916525 0.399978i \(-0.869018\pi\)
−0.916525 + 0.399978i \(0.869018\pi\)
\(48\) −2.87355 −0.414762
\(49\) −6.77518 −0.967882
\(50\) −0.974857 −0.137866
\(51\) 11.9853 1.67828
\(52\) 5.27734 0.731836
\(53\) −3.91121 −0.537246 −0.268623 0.963245i \(-0.586569\pi\)
−0.268623 + 0.963245i \(0.586569\pi\)
\(54\) −6.48651 −0.882703
\(55\) 6.29267 0.848503
\(56\) 0.474155 0.0633616
\(57\) 21.5988 2.86083
\(58\) −7.99676 −1.05003
\(59\) −14.7429 −1.91936 −0.959679 0.281098i \(-0.909301\pi\)
−0.959679 + 0.281098i \(0.909301\pi\)
\(60\) −5.76514 −0.744277
\(61\) −2.93433 −0.375702 −0.187851 0.982197i \(-0.560152\pi\)
−0.187851 + 0.982197i \(0.560152\pi\)
\(62\) −2.39818 −0.304569
\(63\) 2.49278 0.314061
\(64\) 1.00000 0.125000
\(65\) 10.5878 1.31326
\(66\) −9.01288 −1.10941
\(67\) 15.4928 1.89275 0.946373 0.323077i \(-0.104717\pi\)
0.946373 + 0.323077i \(0.104717\pi\)
\(68\) −4.17091 −0.505797
\(69\) −14.5497 −1.75158
\(70\) 0.951285 0.113700
\(71\) −3.47675 −0.412614 −0.206307 0.978487i \(-0.566145\pi\)
−0.206307 + 0.978487i \(0.566145\pi\)
\(72\) 5.25731 0.619580
\(73\) −15.9455 −1.86628 −0.933140 0.359513i \(-0.882943\pi\)
−0.933140 + 0.359513i \(0.882943\pi\)
\(74\) −0.569544 −0.0662082
\(75\) 2.80130 0.323467
\(76\) −7.51640 −0.862190
\(77\) 1.48718 0.169480
\(78\) −15.1647 −1.71707
\(79\) 12.4960 1.40590 0.702952 0.711237i \(-0.251865\pi\)
0.702952 + 0.711237i \(0.251865\pi\)
\(80\) 2.00628 0.224308
\(81\) 2.86741 0.318601
\(82\) −11.4748 −1.26718
\(83\) 4.50846 0.494868 0.247434 0.968905i \(-0.420413\pi\)
0.247434 + 0.968905i \(0.420413\pi\)
\(84\) −1.36251 −0.148662
\(85\) −8.36799 −0.907636
\(86\) 0.986101 0.106334
\(87\) 22.9791 2.46362
\(88\) 3.13649 0.334351
\(89\) −11.7024 −1.24045 −0.620227 0.784422i \(-0.712960\pi\)
−0.620227 + 0.784422i \(0.712960\pi\)
\(90\) 10.5476 1.11182
\(91\) 2.50228 0.262310
\(92\) 5.06333 0.527888
\(93\) 6.89130 0.714594
\(94\) −12.5668 −1.29616
\(95\) −15.0800 −1.54717
\(96\) −2.87355 −0.293281
\(97\) 8.57923 0.871089 0.435544 0.900167i \(-0.356556\pi\)
0.435544 + 0.900167i \(0.356556\pi\)
\(98\) −6.77518 −0.684396
\(99\) 16.4895 1.65726
\(100\) −0.974857 −0.0974857
\(101\) 0.137329 0.0136647 0.00683236 0.999977i \(-0.497825\pi\)
0.00683236 + 0.999977i \(0.497825\pi\)
\(102\) 11.9853 1.18672
\(103\) −3.54690 −0.349486 −0.174743 0.984614i \(-0.555909\pi\)
−0.174743 + 0.984614i \(0.555909\pi\)
\(104\) 5.27734 0.517486
\(105\) −2.73357 −0.266769
\(106\) −3.91121 −0.379890
\(107\) 8.85259 0.855812 0.427906 0.903823i \(-0.359251\pi\)
0.427906 + 0.903823i \(0.359251\pi\)
\(108\) −6.48651 −0.624165
\(109\) −18.9773 −1.81770 −0.908848 0.417127i \(-0.863037\pi\)
−0.908848 + 0.417127i \(0.863037\pi\)
\(110\) 6.29267 0.599982
\(111\) 1.63662 0.155341
\(112\) 0.474155 0.0448034
\(113\) −7.64564 −0.719242 −0.359621 0.933099i \(-0.617094\pi\)
−0.359621 + 0.933099i \(0.617094\pi\)
\(114\) 21.5988 2.02291
\(115\) 10.1584 0.947279
\(116\) −7.99676 −0.742481
\(117\) 27.7447 2.56499
\(118\) −14.7429 −1.35719
\(119\) −1.97766 −0.181291
\(120\) −5.76514 −0.526283
\(121\) −1.16241 −0.105674
\(122\) −2.93433 −0.265662
\(123\) 32.9734 2.97311
\(124\) −2.39818 −0.215363
\(125\) −11.9872 −1.07217
\(126\) 2.49278 0.222075
\(127\) 8.05309 0.714596 0.357298 0.933990i \(-0.383698\pi\)
0.357298 + 0.933990i \(0.383698\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.83362 −0.249486
\(130\) 10.5878 0.928612
\(131\) 0.752333 0.0657316 0.0328658 0.999460i \(-0.489537\pi\)
0.0328658 + 0.999460i \(0.489537\pi\)
\(132\) −9.01288 −0.784471
\(133\) −3.56394 −0.309032
\(134\) 15.4928 1.33837
\(135\) −13.0137 −1.12004
\(136\) −4.17091 −0.357652
\(137\) −10.8307 −0.925332 −0.462666 0.886533i \(-0.653107\pi\)
−0.462666 + 0.886533i \(0.653107\pi\)
\(138\) −14.5497 −1.23856
\(139\) 8.73015 0.740482 0.370241 0.928936i \(-0.379275\pi\)
0.370241 + 0.928936i \(0.379275\pi\)
\(140\) 0.951285 0.0803983
\(141\) 36.1113 3.04112
\(142\) −3.47675 −0.291762
\(143\) 16.5524 1.38418
\(144\) 5.25731 0.438109
\(145\) −16.0437 −1.33236
\(146\) −15.9455 −1.31966
\(147\) 19.4688 1.60576
\(148\) −0.569544 −0.0468163
\(149\) 9.85012 0.806953 0.403477 0.914990i \(-0.367802\pi\)
0.403477 + 0.914990i \(0.367802\pi\)
\(150\) 2.80130 0.228726
\(151\) 6.45762 0.525514 0.262757 0.964862i \(-0.415368\pi\)
0.262757 + 0.964862i \(0.415368\pi\)
\(152\) −7.51640 −0.609660
\(153\) −21.9278 −1.77275
\(154\) 1.48718 0.119841
\(155\) −4.81141 −0.386462
\(156\) −15.1647 −1.21415
\(157\) 14.5023 1.15741 0.578704 0.815538i \(-0.303559\pi\)
0.578704 + 0.815538i \(0.303559\pi\)
\(158\) 12.4960 0.994125
\(159\) 11.2391 0.891316
\(160\) 2.00628 0.158610
\(161\) 2.40080 0.189210
\(162\) 2.86741 0.225285
\(163\) 5.38961 0.422147 0.211073 0.977470i \(-0.432304\pi\)
0.211073 + 0.977470i \(0.432304\pi\)
\(164\) −11.4748 −0.896030
\(165\) −18.0823 −1.40771
\(166\) 4.50846 0.349924
\(167\) 6.36959 0.492894 0.246447 0.969156i \(-0.420737\pi\)
0.246447 + 0.969156i \(0.420737\pi\)
\(168\) −1.36251 −0.105120
\(169\) 14.8504 1.14234
\(170\) −8.36799 −0.641795
\(171\) −39.5161 −3.02187
\(172\) 0.986101 0.0751895
\(173\) 7.81112 0.593868 0.296934 0.954898i \(-0.404036\pi\)
0.296934 + 0.954898i \(0.404036\pi\)
\(174\) 22.9791 1.74204
\(175\) −0.462233 −0.0349415
\(176\) 3.13649 0.236422
\(177\) 42.3644 3.18431
\(178\) −11.7024 −0.877134
\(179\) 15.4458 1.15447 0.577237 0.816576i \(-0.304131\pi\)
0.577237 + 0.816576i \(0.304131\pi\)
\(180\) 10.5476 0.786173
\(181\) −11.0557 −0.821766 −0.410883 0.911688i \(-0.634780\pi\)
−0.410883 + 0.911688i \(0.634780\pi\)
\(182\) 2.50228 0.185481
\(183\) 8.43196 0.623308
\(184\) 5.06333 0.373273
\(185\) −1.14266 −0.0840102
\(186\) 6.89130 0.505294
\(187\) −13.0820 −0.956652
\(188\) −12.5668 −0.916525
\(189\) −3.07561 −0.223718
\(190\) −15.0800 −1.09402
\(191\) 0.561071 0.0405977 0.0202988 0.999794i \(-0.493538\pi\)
0.0202988 + 0.999794i \(0.493538\pi\)
\(192\) −2.87355 −0.207381
\(193\) −12.0776 −0.869368 −0.434684 0.900583i \(-0.643140\pi\)
−0.434684 + 0.900583i \(0.643140\pi\)
\(194\) 8.57923 0.615953
\(195\) −30.4246 −2.17875
\(196\) −6.77518 −0.483941
\(197\) 3.06465 0.218347 0.109173 0.994023i \(-0.465180\pi\)
0.109173 + 0.994023i \(0.465180\pi\)
\(198\) 16.4895 1.17186
\(199\) 22.3326 1.58312 0.791560 0.611092i \(-0.209269\pi\)
0.791560 + 0.611092i \(0.209269\pi\)
\(200\) −0.974857 −0.0689328
\(201\) −44.5194 −3.14015
\(202\) 0.137329 0.00966241
\(203\) −3.79170 −0.266125
\(204\) 11.9853 0.839141
\(205\) −23.0216 −1.60790
\(206\) −3.54690 −0.247124
\(207\) 26.6195 1.85018
\(208\) 5.27734 0.365918
\(209\) −23.5751 −1.63073
\(210\) −2.73357 −0.188634
\(211\) −12.4694 −0.858426 −0.429213 0.903203i \(-0.641209\pi\)
−0.429213 + 0.903203i \(0.641209\pi\)
\(212\) −3.91121 −0.268623
\(213\) 9.99063 0.684547
\(214\) 8.85259 0.605151
\(215\) 1.97839 0.134925
\(216\) −6.48651 −0.441351
\(217\) −1.13711 −0.0771919
\(218\) −18.9773 −1.28531
\(219\) 45.8203 3.09625
\(220\) 6.29267 0.424252
\(221\) −22.0113 −1.48064
\(222\) 1.63662 0.109842
\(223\) 0.373646 0.0250212 0.0125106 0.999922i \(-0.496018\pi\)
0.0125106 + 0.999922i \(0.496018\pi\)
\(224\) 0.474155 0.0316808
\(225\) −5.12513 −0.341675
\(226\) −7.64564 −0.508581
\(227\) −24.1798 −1.60487 −0.802434 0.596741i \(-0.796462\pi\)
−0.802434 + 0.596741i \(0.796462\pi\)
\(228\) 21.5988 1.43041
\(229\) −6.68006 −0.441431 −0.220715 0.975338i \(-0.570839\pi\)
−0.220715 + 0.975338i \(0.570839\pi\)
\(230\) 10.1584 0.669827
\(231\) −4.27350 −0.281176
\(232\) −7.99676 −0.525013
\(233\) −11.6049 −0.760259 −0.380130 0.924933i \(-0.624121\pi\)
−0.380130 + 0.924933i \(0.624121\pi\)
\(234\) 27.7447 1.81372
\(235\) −25.2124 −1.64467
\(236\) −14.7429 −0.959679
\(237\) −35.9078 −2.33246
\(238\) −1.97766 −0.128192
\(239\) 8.85678 0.572897 0.286449 0.958096i \(-0.407525\pi\)
0.286449 + 0.958096i \(0.407525\pi\)
\(240\) −5.76514 −0.372138
\(241\) 9.26722 0.596954 0.298477 0.954417i \(-0.403521\pi\)
0.298477 + 0.954417i \(0.403521\pi\)
\(242\) −1.16241 −0.0747228
\(243\) 11.2199 0.719756
\(244\) −2.93433 −0.187851
\(245\) −13.5929 −0.868417
\(246\) 32.9734 2.10231
\(247\) −39.6666 −2.52393
\(248\) −2.39818 −0.152285
\(249\) −12.9553 −0.821009
\(250\) −11.9872 −0.758138
\(251\) 6.32352 0.399137 0.199569 0.979884i \(-0.436046\pi\)
0.199569 + 0.979884i \(0.436046\pi\)
\(252\) 2.49278 0.157030
\(253\) 15.8811 0.998435
\(254\) 8.05309 0.505296
\(255\) 24.0459 1.50581
\(256\) 1.00000 0.0625000
\(257\) 23.3014 1.45350 0.726750 0.686902i \(-0.241030\pi\)
0.726750 + 0.686902i \(0.241030\pi\)
\(258\) −2.83362 −0.176413
\(259\) −0.270052 −0.0167802
\(260\) 10.5878 0.656628
\(261\) −42.0415 −2.60230
\(262\) 0.752333 0.0464793
\(263\) −32.2528 −1.98879 −0.994397 0.105709i \(-0.966289\pi\)
−0.994397 + 0.105709i \(0.966289\pi\)
\(264\) −9.01288 −0.554705
\(265\) −7.84696 −0.482035
\(266\) −3.56394 −0.218519
\(267\) 33.6276 2.05797
\(268\) 15.4928 0.946373
\(269\) −9.79631 −0.597292 −0.298646 0.954364i \(-0.596535\pi\)
−0.298646 + 0.954364i \(0.596535\pi\)
\(270\) −13.0137 −0.791991
\(271\) 10.6748 0.648451 0.324225 0.945980i \(-0.394896\pi\)
0.324225 + 0.945980i \(0.394896\pi\)
\(272\) −4.17091 −0.252898
\(273\) −7.19043 −0.435185
\(274\) −10.8307 −0.654308
\(275\) −3.05763 −0.184382
\(276\) −14.5497 −0.875792
\(277\) 18.6153 1.11849 0.559243 0.829004i \(-0.311092\pi\)
0.559243 + 0.829004i \(0.311092\pi\)
\(278\) 8.73015 0.523600
\(279\) −12.6080 −0.754820
\(280\) 0.951285 0.0568502
\(281\) 26.5735 1.58524 0.792622 0.609714i \(-0.208716\pi\)
0.792622 + 0.609714i \(0.208716\pi\)
\(282\) 36.1113 2.15039
\(283\) −23.3476 −1.38787 −0.693935 0.720037i \(-0.744125\pi\)
−0.693935 + 0.720037i \(0.744125\pi\)
\(284\) −3.47675 −0.206307
\(285\) 43.3331 2.56683
\(286\) 16.5524 0.978761
\(287\) −5.44082 −0.321162
\(288\) 5.25731 0.309790
\(289\) 0.396457 0.0233210
\(290\) −16.0437 −0.942119
\(291\) −24.6529 −1.44518
\(292\) −15.9455 −0.933140
\(293\) 10.9773 0.641301 0.320651 0.947198i \(-0.396098\pi\)
0.320651 + 0.947198i \(0.396098\pi\)
\(294\) 19.4688 1.13545
\(295\) −29.5783 −1.72211
\(296\) −0.569544 −0.0331041
\(297\) −20.3449 −1.18053
\(298\) 9.85012 0.570602
\(299\) 26.7209 1.54531
\(300\) 2.80130 0.161733
\(301\) 0.467565 0.0269500
\(302\) 6.45762 0.371594
\(303\) −0.394621 −0.0226704
\(304\) −7.51640 −0.431095
\(305\) −5.88708 −0.337093
\(306\) −21.9278 −1.25353
\(307\) −25.7684 −1.47068 −0.735340 0.677699i \(-0.762977\pi\)
−0.735340 + 0.677699i \(0.762977\pi\)
\(308\) 1.48718 0.0847401
\(309\) 10.1922 0.579814
\(310\) −4.81141 −0.273270
\(311\) 7.77395 0.440820 0.220410 0.975407i \(-0.429260\pi\)
0.220410 + 0.975407i \(0.429260\pi\)
\(312\) −15.1647 −0.858534
\(313\) −14.1309 −0.798727 −0.399363 0.916793i \(-0.630769\pi\)
−0.399363 + 0.916793i \(0.630769\pi\)
\(314\) 14.5023 0.818411
\(315\) 5.00121 0.281786
\(316\) 12.4960 0.702952
\(317\) 12.4982 0.701969 0.350984 0.936381i \(-0.385847\pi\)
0.350984 + 0.936381i \(0.385847\pi\)
\(318\) 11.2391 0.630256
\(319\) −25.0818 −1.40431
\(320\) 2.00628 0.112154
\(321\) −25.4384 −1.41983
\(322\) 2.40080 0.133791
\(323\) 31.3502 1.74437
\(324\) 2.86741 0.159300
\(325\) −5.14466 −0.285374
\(326\) 5.38961 0.298503
\(327\) 54.5323 3.01564
\(328\) −11.4748 −0.633589
\(329\) −5.95859 −0.328508
\(330\) −18.0823 −0.995399
\(331\) −22.5909 −1.24171 −0.620854 0.783926i \(-0.713214\pi\)
−0.620854 + 0.783926i \(0.713214\pi\)
\(332\) 4.50846 0.247434
\(333\) −2.99427 −0.164085
\(334\) 6.36959 0.348529
\(335\) 31.0828 1.69823
\(336\) −1.36251 −0.0743310
\(337\) 22.9344 1.24932 0.624658 0.780899i \(-0.285239\pi\)
0.624658 + 0.780899i \(0.285239\pi\)
\(338\) 14.8504 0.807754
\(339\) 21.9702 1.19326
\(340\) −8.36799 −0.453818
\(341\) −7.52187 −0.407332
\(342\) −39.5161 −2.13678
\(343\) −6.53157 −0.352671
\(344\) 0.986101 0.0531670
\(345\) −29.1908 −1.57158
\(346\) 7.81112 0.419928
\(347\) −20.7794 −1.11550 −0.557749 0.830010i \(-0.688335\pi\)
−0.557749 + 0.830010i \(0.688335\pi\)
\(348\) 22.9791 1.23181
\(349\) 20.9301 1.12036 0.560181 0.828370i \(-0.310732\pi\)
0.560181 + 0.828370i \(0.310732\pi\)
\(350\) −0.462233 −0.0247074
\(351\) −34.2316 −1.82715
\(352\) 3.13649 0.167176
\(353\) −25.8437 −1.37552 −0.687761 0.725937i \(-0.741406\pi\)
−0.687761 + 0.725937i \(0.741406\pi\)
\(354\) 42.3644 2.25164
\(355\) −6.97532 −0.370211
\(356\) −11.7024 −0.620227
\(357\) 5.68290 0.300771
\(358\) 15.4458 0.816337
\(359\) −16.6639 −0.879488 −0.439744 0.898123i \(-0.644931\pi\)
−0.439744 + 0.898123i \(0.644931\pi\)
\(360\) 10.5476 0.555908
\(361\) 37.4962 1.97348
\(362\) −11.0557 −0.581077
\(363\) 3.34026 0.175318
\(364\) 2.50228 0.131155
\(365\) −31.9911 −1.67449
\(366\) 8.43196 0.440745
\(367\) −0.0793847 −0.00414385 −0.00207192 0.999998i \(-0.500660\pi\)
−0.00207192 + 0.999998i \(0.500660\pi\)
\(368\) 5.06333 0.263944
\(369\) −60.3265 −3.14047
\(370\) −1.14266 −0.0594042
\(371\) −1.85452 −0.0962818
\(372\) 6.89130 0.357297
\(373\) −14.5444 −0.753078 −0.376539 0.926401i \(-0.622886\pi\)
−0.376539 + 0.926401i \(0.622886\pi\)
\(374\) −13.0820 −0.676455
\(375\) 34.4459 1.77878
\(376\) −12.5668 −0.648081
\(377\) −42.2017 −2.17350
\(378\) −3.07561 −0.158192
\(379\) −5.02379 −0.258055 −0.129027 0.991641i \(-0.541186\pi\)
−0.129027 + 0.991641i \(0.541186\pi\)
\(380\) −15.0800 −0.773586
\(381\) −23.1410 −1.18555
\(382\) 0.561071 0.0287069
\(383\) 30.2657 1.54650 0.773252 0.634099i \(-0.218629\pi\)
0.773252 + 0.634099i \(0.218629\pi\)
\(384\) −2.87355 −0.146640
\(385\) 2.98370 0.152063
\(386\) −12.0776 −0.614736
\(387\) 5.18424 0.263530
\(388\) 8.57923 0.435544
\(389\) 33.7613 1.71177 0.855884 0.517168i \(-0.173014\pi\)
0.855884 + 0.517168i \(0.173014\pi\)
\(390\) −30.4246 −1.54061
\(391\) −21.1187 −1.06802
\(392\) −6.77518 −0.342198
\(393\) −2.16187 −0.109052
\(394\) 3.06465 0.154395
\(395\) 25.0703 1.26143
\(396\) 16.4895 0.828630
\(397\) −12.1085 −0.607706 −0.303853 0.952719i \(-0.598273\pi\)
−0.303853 + 0.952719i \(0.598273\pi\)
\(398\) 22.3326 1.11943
\(399\) 10.2412 0.512699
\(400\) −0.974857 −0.0487429
\(401\) 39.6423 1.97964 0.989821 0.142318i \(-0.0454554\pi\)
0.989821 + 0.142318i \(0.0454554\pi\)
\(402\) −44.5194 −2.22042
\(403\) −12.6560 −0.630441
\(404\) 0.137329 0.00683236
\(405\) 5.75281 0.285859
\(406\) −3.79170 −0.188179
\(407\) −1.78637 −0.0885471
\(408\) 11.9853 0.593362
\(409\) 1.71914 0.0850059 0.0425029 0.999096i \(-0.486467\pi\)
0.0425029 + 0.999096i \(0.486467\pi\)
\(410\) −23.0216 −1.13695
\(411\) 31.1227 1.53517
\(412\) −3.54690 −0.174743
\(413\) −6.99040 −0.343975
\(414\) 26.6195 1.30828
\(415\) 9.04521 0.444012
\(416\) 5.27734 0.258743
\(417\) −25.0866 −1.22849
\(418\) −23.5751 −1.15310
\(419\) −9.23743 −0.451278 −0.225639 0.974211i \(-0.572447\pi\)
−0.225639 + 0.974211i \(0.572447\pi\)
\(420\) −2.73357 −0.133385
\(421\) 29.7368 1.44928 0.724641 0.689127i \(-0.242006\pi\)
0.724641 + 0.689127i \(0.242006\pi\)
\(422\) −12.4694 −0.606999
\(423\) −66.0674 −3.21231
\(424\) −3.91121 −0.189945
\(425\) 4.06604 0.197232
\(426\) 9.99063 0.484047
\(427\) −1.39133 −0.0673310
\(428\) 8.85259 0.427906
\(429\) −47.5641 −2.29642
\(430\) 1.97839 0.0954065
\(431\) −34.9712 −1.68450 −0.842252 0.539083i \(-0.818771\pi\)
−0.842252 + 0.539083i \(0.818771\pi\)
\(432\) −6.48651 −0.312083
\(433\) −2.66594 −0.128117 −0.0640584 0.997946i \(-0.520404\pi\)
−0.0640584 + 0.997946i \(0.520404\pi\)
\(434\) −1.13711 −0.0545829
\(435\) 46.1025 2.21044
\(436\) −18.9773 −0.908848
\(437\) −38.0580 −1.82056
\(438\) 45.8203 2.18938
\(439\) −8.69016 −0.414759 −0.207379 0.978261i \(-0.566493\pi\)
−0.207379 + 0.978261i \(0.566493\pi\)
\(440\) 6.29267 0.299991
\(441\) −35.6192 −1.69615
\(442\) −22.0113 −1.04697
\(443\) −23.0163 −1.09354 −0.546768 0.837284i \(-0.684142\pi\)
−0.546768 + 0.837284i \(0.684142\pi\)
\(444\) 1.63662 0.0776704
\(445\) −23.4783 −1.11298
\(446\) 0.373646 0.0176927
\(447\) −28.3049 −1.33877
\(448\) 0.474155 0.0224017
\(449\) 18.6419 0.879764 0.439882 0.898056i \(-0.355020\pi\)
0.439882 + 0.898056i \(0.355020\pi\)
\(450\) −5.12513 −0.241601
\(451\) −35.9906 −1.69473
\(452\) −7.64564 −0.359621
\(453\) −18.5563 −0.871852
\(454\) −24.1798 −1.13481
\(455\) 5.02026 0.235353
\(456\) 21.5988 1.01146
\(457\) −11.6584 −0.545358 −0.272679 0.962105i \(-0.587910\pi\)
−0.272679 + 0.962105i \(0.587910\pi\)
\(458\) −6.68006 −0.312139
\(459\) 27.0546 1.26280
\(460\) 10.1584 0.473639
\(461\) 29.5786 1.37761 0.688806 0.724946i \(-0.258135\pi\)
0.688806 + 0.724946i \(0.258135\pi\)
\(462\) −4.27350 −0.198821
\(463\) −34.6632 −1.61094 −0.805469 0.592639i \(-0.798086\pi\)
−0.805469 + 0.592639i \(0.798086\pi\)
\(464\) −7.99676 −0.371240
\(465\) 13.8258 0.641158
\(466\) −11.6049 −0.537585
\(467\) −5.43995 −0.251731 −0.125866 0.992047i \(-0.540171\pi\)
−0.125866 + 0.992047i \(0.540171\pi\)
\(468\) 27.7447 1.28250
\(469\) 7.34598 0.339206
\(470\) −25.2124 −1.16296
\(471\) −41.6731 −1.92019
\(472\) −14.7429 −0.678595
\(473\) 3.09290 0.142212
\(474\) −35.9078 −1.64930
\(475\) 7.32741 0.336205
\(476\) −1.97766 −0.0906457
\(477\) −20.5625 −0.941490
\(478\) 8.85678 0.405100
\(479\) 5.97601 0.273051 0.136525 0.990637i \(-0.456406\pi\)
0.136525 + 0.990637i \(0.456406\pi\)
\(480\) −5.76514 −0.263142
\(481\) −3.00568 −0.137047
\(482\) 9.26722 0.422110
\(483\) −6.89883 −0.313908
\(484\) −1.16241 −0.0528370
\(485\) 17.2123 0.781570
\(486\) 11.2199 0.508945
\(487\) 23.8893 1.08253 0.541264 0.840853i \(-0.317946\pi\)
0.541264 + 0.840853i \(0.317946\pi\)
\(488\) −2.93433 −0.132831
\(489\) −15.4873 −0.700362
\(490\) −13.5929 −0.614063
\(491\) 17.3083 0.781111 0.390556 0.920579i \(-0.372283\pi\)
0.390556 + 0.920579i \(0.372283\pi\)
\(492\) 32.9734 1.48656
\(493\) 33.3537 1.50218
\(494\) −39.6666 −1.78469
\(495\) 33.0825 1.48695
\(496\) −2.39818 −0.107681
\(497\) −1.64852 −0.0739461
\(498\) −12.9553 −0.580541
\(499\) −22.6110 −1.01221 −0.506104 0.862472i \(-0.668915\pi\)
−0.506104 + 0.862472i \(0.668915\pi\)
\(500\) −11.9872 −0.536084
\(501\) −18.3034 −0.817734
\(502\) 6.32352 0.282233
\(503\) −5.34781 −0.238447 −0.119223 0.992867i \(-0.538040\pi\)
−0.119223 + 0.992867i \(0.538040\pi\)
\(504\) 2.49278 0.111037
\(505\) 0.275519 0.0122604
\(506\) 15.8811 0.706000
\(507\) −42.6733 −1.89519
\(508\) 8.05309 0.357298
\(509\) −31.4902 −1.39578 −0.697889 0.716206i \(-0.745877\pi\)
−0.697889 + 0.716206i \(0.745877\pi\)
\(510\) 24.0459 1.06477
\(511\) −7.56064 −0.334463
\(512\) 1.00000 0.0441942
\(513\) 48.7552 2.15259
\(514\) 23.3014 1.02778
\(515\) −7.11605 −0.313571
\(516\) −2.83362 −0.124743
\(517\) −39.4155 −1.73349
\(518\) −0.270052 −0.0118654
\(519\) −22.4457 −0.985255
\(520\) 10.5878 0.464306
\(521\) 22.5914 0.989749 0.494874 0.868965i \(-0.335214\pi\)
0.494874 + 0.868965i \(0.335214\pi\)
\(522\) −42.0415 −1.84011
\(523\) 32.8113 1.43474 0.717369 0.696694i \(-0.245346\pi\)
0.717369 + 0.696694i \(0.245346\pi\)
\(524\) 0.752333 0.0328658
\(525\) 1.32825 0.0579697
\(526\) −32.2528 −1.40629
\(527\) 10.0026 0.435719
\(528\) −9.01288 −0.392235
\(529\) 2.63728 0.114664
\(530\) −7.84696 −0.340850
\(531\) −77.5079 −3.36356
\(532\) −3.56394 −0.154516
\(533\) −60.5564 −2.62299
\(534\) 33.6276 1.45521
\(535\) 17.7607 0.767864
\(536\) 15.4928 0.669186
\(537\) −44.3844 −1.91533
\(538\) −9.79631 −0.422349
\(539\) −21.2503 −0.915315
\(540\) −13.0137 −0.560022
\(541\) −12.0832 −0.519497 −0.259748 0.965676i \(-0.583640\pi\)
−0.259748 + 0.965676i \(0.583640\pi\)
\(542\) 10.6748 0.458524
\(543\) 31.7693 1.36335
\(544\) −4.17091 −0.178826
\(545\) −38.0737 −1.63090
\(546\) −7.19043 −0.307722
\(547\) 13.1188 0.560919 0.280459 0.959866i \(-0.409513\pi\)
0.280459 + 0.959866i \(0.409513\pi\)
\(548\) −10.8307 −0.462666
\(549\) −15.4267 −0.658395
\(550\) −3.05763 −0.130378
\(551\) 60.1068 2.56064
\(552\) −14.5497 −0.619278
\(553\) 5.92502 0.251957
\(554\) 18.6153 0.790889
\(555\) 3.28350 0.139377
\(556\) 8.73015 0.370241
\(557\) −18.2352 −0.772649 −0.386324 0.922363i \(-0.626255\pi\)
−0.386324 + 0.922363i \(0.626255\pi\)
\(558\) −12.6080 −0.533738
\(559\) 5.20400 0.220106
\(560\) 0.951285 0.0401991
\(561\) 37.5919 1.58713
\(562\) 26.5735 1.12094
\(563\) 10.1351 0.427145 0.213573 0.976927i \(-0.431490\pi\)
0.213573 + 0.976927i \(0.431490\pi\)
\(564\) 36.1113 1.52056
\(565\) −15.3393 −0.645328
\(566\) −23.3476 −0.981373
\(567\) 1.35959 0.0570976
\(568\) −3.47675 −0.145881
\(569\) 9.95090 0.417163 0.208582 0.978005i \(-0.433115\pi\)
0.208582 + 0.978005i \(0.433115\pi\)
\(570\) 43.3331 1.81502
\(571\) 41.1917 1.72382 0.861909 0.507063i \(-0.169269\pi\)
0.861909 + 0.507063i \(0.169269\pi\)
\(572\) 16.5524 0.692089
\(573\) −1.61227 −0.0673535
\(574\) −5.44082 −0.227096
\(575\) −4.93602 −0.205846
\(576\) 5.25731 0.219055
\(577\) 3.91645 0.163044 0.0815219 0.996672i \(-0.474022\pi\)
0.0815219 + 0.996672i \(0.474022\pi\)
\(578\) 0.396457 0.0164904
\(579\) 34.7058 1.44232
\(580\) −16.0437 −0.666179
\(581\) 2.13771 0.0886871
\(582\) −24.6529 −1.02189
\(583\) −12.2675 −0.508067
\(584\) −15.9455 −0.659830
\(585\) 55.6634 2.30140
\(586\) 10.9773 0.453468
\(587\) 14.6065 0.602873 0.301437 0.953486i \(-0.402534\pi\)
0.301437 + 0.953486i \(0.402534\pi\)
\(588\) 19.4688 0.802881
\(589\) 18.0257 0.742734
\(590\) −29.5783 −1.21772
\(591\) −8.80642 −0.362248
\(592\) −0.569544 −0.0234081
\(593\) 4.28773 0.176076 0.0880380 0.996117i \(-0.471940\pi\)
0.0880380 + 0.996117i \(0.471940\pi\)
\(594\) −20.3449 −0.834761
\(595\) −3.96772 −0.162661
\(596\) 9.85012 0.403477
\(597\) −64.1741 −2.62647
\(598\) 26.7209 1.09270
\(599\) −30.4161 −1.24277 −0.621385 0.783505i \(-0.713430\pi\)
−0.621385 + 0.783505i \(0.713430\pi\)
\(600\) 2.80130 0.114363
\(601\) 19.7703 0.806449 0.403224 0.915101i \(-0.367889\pi\)
0.403224 + 0.915101i \(0.367889\pi\)
\(602\) 0.467565 0.0190565
\(603\) 81.4504 3.31692
\(604\) 6.45762 0.262757
\(605\) −2.33212 −0.0948143
\(606\) −0.394621 −0.0160304
\(607\) −3.52900 −0.143238 −0.0716188 0.997432i \(-0.522817\pi\)
−0.0716188 + 0.997432i \(0.522817\pi\)
\(608\) −7.51640 −0.304830
\(609\) 10.8957 0.441515
\(610\) −5.88708 −0.238361
\(611\) −66.3191 −2.68298
\(612\) −21.9278 −0.886377
\(613\) −45.4906 −1.83735 −0.918673 0.395018i \(-0.870738\pi\)
−0.918673 + 0.395018i \(0.870738\pi\)
\(614\) −25.7684 −1.03993
\(615\) 66.1537 2.66758
\(616\) 1.48718 0.0599203
\(617\) −7.29572 −0.293715 −0.146857 0.989158i \(-0.546916\pi\)
−0.146857 + 0.989158i \(0.546916\pi\)
\(618\) 10.1922 0.409990
\(619\) 19.3059 0.775970 0.387985 0.921666i \(-0.373171\pi\)
0.387985 + 0.921666i \(0.373171\pi\)
\(620\) −4.81141 −0.193231
\(621\) −32.8433 −1.31796
\(622\) 7.77395 0.311707
\(623\) −5.54876 −0.222306
\(624\) −15.1647 −0.607075
\(625\) −19.1754 −0.767015
\(626\) −14.1309 −0.564785
\(627\) 67.7444 2.70545
\(628\) 14.5023 0.578704
\(629\) 2.37552 0.0947180
\(630\) 5.00121 0.199253
\(631\) 11.8848 0.473126 0.236563 0.971616i \(-0.423979\pi\)
0.236563 + 0.971616i \(0.423979\pi\)
\(632\) 12.4960 0.497062
\(633\) 35.8314 1.42417
\(634\) 12.4982 0.496367
\(635\) 16.1567 0.641160
\(636\) 11.2391 0.445658
\(637\) −35.7549 −1.41666
\(638\) −25.0818 −0.992997
\(639\) −18.2784 −0.723081
\(640\) 2.00628 0.0793050
\(641\) −28.6778 −1.13271 −0.566353 0.824163i \(-0.691646\pi\)
−0.566353 + 0.824163i \(0.691646\pi\)
\(642\) −25.4384 −1.00397
\(643\) 2.10027 0.0828265 0.0414133 0.999142i \(-0.486814\pi\)
0.0414133 + 0.999142i \(0.486814\pi\)
\(644\) 2.40080 0.0946048
\(645\) −5.68501 −0.223847
\(646\) 31.3502 1.23346
\(647\) −3.63405 −0.142869 −0.0714345 0.997445i \(-0.522758\pi\)
−0.0714345 + 0.997445i \(0.522758\pi\)
\(648\) 2.86741 0.112642
\(649\) −46.2409 −1.81511
\(650\) −5.14466 −0.201790
\(651\) 3.26754 0.128065
\(652\) 5.38961 0.211073
\(653\) 23.0756 0.903019 0.451510 0.892266i \(-0.350886\pi\)
0.451510 + 0.892266i \(0.350886\pi\)
\(654\) 54.5323 2.13238
\(655\) 1.50939 0.0589766
\(656\) −11.4748 −0.448015
\(657\) −83.8305 −3.27054
\(658\) −5.95859 −0.232290
\(659\) −32.7884 −1.27726 −0.638628 0.769516i \(-0.720498\pi\)
−0.638628 + 0.769516i \(0.720498\pi\)
\(660\) −18.0823 −0.703854
\(661\) −8.78604 −0.341737 −0.170869 0.985294i \(-0.554657\pi\)
−0.170869 + 0.985294i \(0.554657\pi\)
\(662\) −22.5909 −0.878021
\(663\) 63.2507 2.45645
\(664\) 4.50846 0.174962
\(665\) −7.15024 −0.277274
\(666\) −2.99427 −0.116026
\(667\) −40.4902 −1.56779
\(668\) 6.36959 0.246447
\(669\) −1.07369 −0.0415113
\(670\) 31.0828 1.20083
\(671\) −9.20350 −0.355297
\(672\) −1.36251 −0.0525600
\(673\) −21.7062 −0.836712 −0.418356 0.908283i \(-0.637394\pi\)
−0.418356 + 0.908283i \(0.637394\pi\)
\(674\) 22.9344 0.883399
\(675\) 6.32342 0.243389
\(676\) 14.8504 0.571168
\(677\) 7.79013 0.299399 0.149700 0.988732i \(-0.452169\pi\)
0.149700 + 0.988732i \(0.452169\pi\)
\(678\) 21.9702 0.843759
\(679\) 4.06788 0.156111
\(680\) −8.36799 −0.320898
\(681\) 69.4819 2.66255
\(682\) −7.52187 −0.288027
\(683\) −9.95393 −0.380877 −0.190438 0.981699i \(-0.560991\pi\)
−0.190438 + 0.981699i \(0.560991\pi\)
\(684\) −39.5161 −1.51093
\(685\) −21.7294 −0.830239
\(686\) −6.53157 −0.249376
\(687\) 19.1955 0.732354
\(688\) 0.986101 0.0375948
\(689\) −20.6408 −0.786352
\(690\) −29.1908 −1.11127
\(691\) 19.8504 0.755145 0.377572 0.925980i \(-0.376759\pi\)
0.377572 + 0.925980i \(0.376759\pi\)
\(692\) 7.81112 0.296934
\(693\) 7.81859 0.297004
\(694\) −20.7794 −0.788776
\(695\) 17.5151 0.664385
\(696\) 22.9791 0.871022
\(697\) 47.8602 1.81284
\(698\) 20.9301 0.792216
\(699\) 33.3472 1.26131
\(700\) −0.462233 −0.0174708
\(701\) 10.8325 0.409138 0.204569 0.978852i \(-0.434421\pi\)
0.204569 + 0.978852i \(0.434421\pi\)
\(702\) −34.2316 −1.29199
\(703\) 4.28092 0.161458
\(704\) 3.13649 0.118211
\(705\) 72.4491 2.72859
\(706\) −25.8437 −0.972641
\(707\) 0.0651151 0.00244890
\(708\) 42.3644 1.59215
\(709\) 7.46164 0.280228 0.140114 0.990135i \(-0.455253\pi\)
0.140114 + 0.990135i \(0.455253\pi\)
\(710\) −6.97532 −0.261779
\(711\) 65.6951 2.46376
\(712\) −11.7024 −0.438567
\(713\) −12.1428 −0.454750
\(714\) 5.68290 0.212677
\(715\) 33.2086 1.24193
\(716\) 15.4458 0.577237
\(717\) −25.4504 −0.950464
\(718\) −16.6639 −0.621892
\(719\) 32.8904 1.22660 0.613302 0.789848i \(-0.289841\pi\)
0.613302 + 0.789848i \(0.289841\pi\)
\(720\) 10.5476 0.393087
\(721\) −1.68178 −0.0626327
\(722\) 37.4962 1.39546
\(723\) −26.6298 −0.990375
\(724\) −11.0557 −0.410883
\(725\) 7.79570 0.289525
\(726\) 3.34026 0.123969
\(727\) 8.15963 0.302624 0.151312 0.988486i \(-0.451650\pi\)
0.151312 + 0.988486i \(0.451650\pi\)
\(728\) 2.50228 0.0927406
\(729\) −40.8432 −1.51271
\(730\) −31.9911 −1.18404
\(731\) −4.11294 −0.152122
\(732\) 8.43196 0.311654
\(733\) −47.1494 −1.74150 −0.870752 0.491723i \(-0.836367\pi\)
−0.870752 + 0.491723i \(0.836367\pi\)
\(734\) −0.0793847 −0.00293014
\(735\) 39.0599 1.44074
\(736\) 5.06333 0.186637
\(737\) 48.5930 1.78995
\(738\) −60.3265 −2.22065
\(739\) 7.20872 0.265177 0.132589 0.991171i \(-0.457671\pi\)
0.132589 + 0.991171i \(0.457671\pi\)
\(740\) −1.14266 −0.0420051
\(741\) 113.984 4.18731
\(742\) −1.85452 −0.0680815
\(743\) −3.81638 −0.140009 −0.0700047 0.997547i \(-0.522301\pi\)
−0.0700047 + 0.997547i \(0.522301\pi\)
\(744\) 6.89130 0.252647
\(745\) 19.7621 0.724026
\(746\) −14.5444 −0.532507
\(747\) 23.7024 0.867225
\(748\) −13.0820 −0.478326
\(749\) 4.19750 0.153373
\(750\) 34.4459 1.25779
\(751\) 25.1095 0.916260 0.458130 0.888885i \(-0.348519\pi\)
0.458130 + 0.888885i \(0.348519\pi\)
\(752\) −12.5668 −0.458262
\(753\) −18.1710 −0.662187
\(754\) −42.2017 −1.53689
\(755\) 12.9558 0.471509
\(756\) −3.07561 −0.111859
\(757\) −27.7020 −1.00685 −0.503423 0.864040i \(-0.667926\pi\)
−0.503423 + 0.864040i \(0.667926\pi\)
\(758\) −5.02379 −0.182472
\(759\) −45.6352 −1.65645
\(760\) −15.0800 −0.547008
\(761\) −15.8264 −0.573708 −0.286854 0.957974i \(-0.592609\pi\)
−0.286854 + 0.957974i \(0.592609\pi\)
\(762\) −23.1410 −0.838309
\(763\) −8.99818 −0.325756
\(764\) 0.561071 0.0202988
\(765\) −43.9931 −1.59058
\(766\) 30.2657 1.09354
\(767\) −77.8032 −2.80931
\(768\) −2.87355 −0.103690
\(769\) 31.2360 1.12640 0.563200 0.826321i \(-0.309570\pi\)
0.563200 + 0.826321i \(0.309570\pi\)
\(770\) 2.98370 0.107525
\(771\) −66.9578 −2.41143
\(772\) −12.0776 −0.434684
\(773\) 28.4596 1.02362 0.511811 0.859098i \(-0.328975\pi\)
0.511811 + 0.859098i \(0.328975\pi\)
\(774\) 5.18424 0.186344
\(775\) 2.33788 0.0839792
\(776\) 8.57923 0.307976
\(777\) 0.776010 0.0278392
\(778\) 33.7613 1.21040
\(779\) 86.2490 3.09019
\(780\) −30.4246 −1.08938
\(781\) −10.9048 −0.390204
\(782\) −21.1187 −0.755202
\(783\) 51.8711 1.85372
\(784\) −6.77518 −0.241971
\(785\) 29.0956 1.03847
\(786\) −2.16187 −0.0771113
\(787\) 20.1144 0.717001 0.358501 0.933530i \(-0.383288\pi\)
0.358501 + 0.933530i \(0.383288\pi\)
\(788\) 3.06465 0.109173
\(789\) 92.6802 3.29950
\(790\) 25.0703 0.891962
\(791\) −3.62522 −0.128898
\(792\) 16.4895 0.585930
\(793\) −15.4855 −0.549905
\(794\) −12.1085 −0.429713
\(795\) 22.5487 0.799719
\(796\) 22.3326 0.791560
\(797\) −56.2427 −1.99222 −0.996110 0.0881204i \(-0.971914\pi\)
−0.996110 + 0.0881204i \(0.971914\pi\)
\(798\) 10.2412 0.362533
\(799\) 52.4148 1.85430
\(800\) −0.974857 −0.0344664
\(801\) −61.5233 −2.17382
\(802\) 39.6423 1.39982
\(803\) −50.0130 −1.76492
\(804\) −44.5194 −1.57008
\(805\) 4.81667 0.169765
\(806\) −12.6560 −0.445789
\(807\) 28.1502 0.990935
\(808\) 0.137329 0.00483121
\(809\) 14.2122 0.499676 0.249838 0.968288i \(-0.419623\pi\)
0.249838 + 0.968288i \(0.419623\pi\)
\(810\) 5.75281 0.202133
\(811\) 44.7633 1.57185 0.785925 0.618321i \(-0.212187\pi\)
0.785925 + 0.618321i \(0.212187\pi\)
\(812\) −3.79170 −0.133063
\(813\) −30.6748 −1.07581
\(814\) −1.78637 −0.0626123
\(815\) 10.8130 0.378765
\(816\) 11.9853 0.419570
\(817\) −7.41193 −0.259311
\(818\) 1.71914 0.0601082
\(819\) 13.1553 0.459682
\(820\) −23.0216 −0.803948
\(821\) 23.3131 0.813633 0.406816 0.913510i \(-0.366639\pi\)
0.406816 + 0.913510i \(0.366639\pi\)
\(822\) 31.1227 1.08553
\(823\) 16.8012 0.585651 0.292826 0.956166i \(-0.405404\pi\)
0.292826 + 0.956166i \(0.405404\pi\)
\(824\) −3.54690 −0.123562
\(825\) 8.78627 0.305899
\(826\) −6.99040 −0.243227
\(827\) −27.9958 −0.973508 −0.486754 0.873539i \(-0.661819\pi\)
−0.486754 + 0.873539i \(0.661819\pi\)
\(828\) 26.6195 0.925092
\(829\) −17.8763 −0.620869 −0.310434 0.950595i \(-0.600474\pi\)
−0.310434 + 0.950595i \(0.600474\pi\)
\(830\) 9.04521 0.313964
\(831\) −53.4921 −1.85562
\(832\) 5.27734 0.182959
\(833\) 28.2586 0.979103
\(834\) −25.0866 −0.868677
\(835\) 12.7792 0.442241
\(836\) −23.5751 −0.815363
\(837\) 15.5558 0.537688
\(838\) −9.23743 −0.319102
\(839\) 17.9502 0.619709 0.309855 0.950784i \(-0.399720\pi\)
0.309855 + 0.950784i \(0.399720\pi\)
\(840\) −2.73357 −0.0943171
\(841\) 34.9482 1.20511
\(842\) 29.7368 1.02480
\(843\) −76.3604 −2.62999
\(844\) −12.4694 −0.429213
\(845\) 29.7939 1.02494
\(846\) −66.0674 −2.27144
\(847\) −0.551164 −0.0189382
\(848\) −3.91121 −0.134311
\(849\) 67.0906 2.30254
\(850\) 4.06604 0.139464
\(851\) −2.88379 −0.0988550
\(852\) 9.99063 0.342273
\(853\) −2.16305 −0.0740614 −0.0370307 0.999314i \(-0.511790\pi\)
−0.0370307 + 0.999314i \(0.511790\pi\)
\(854\) −1.39133 −0.0476102
\(855\) −79.2801 −2.71132
\(856\) 8.85259 0.302575
\(857\) 34.8072 1.18899 0.594496 0.804098i \(-0.297352\pi\)
0.594496 + 0.804098i \(0.297352\pi\)
\(858\) −47.5641 −1.62381
\(859\) 18.7338 0.639190 0.319595 0.947554i \(-0.396453\pi\)
0.319595 + 0.947554i \(0.396453\pi\)
\(860\) 1.97839 0.0674626
\(861\) 15.6345 0.532822
\(862\) −34.9712 −1.19112
\(863\) −40.8284 −1.38981 −0.694907 0.719099i \(-0.744555\pi\)
−0.694907 + 0.719099i \(0.744555\pi\)
\(864\) −6.48651 −0.220676
\(865\) 15.6713 0.532839
\(866\) −2.66594 −0.0905922
\(867\) −1.13924 −0.0386906
\(868\) −1.13711 −0.0385960
\(869\) 39.1935 1.32955
\(870\) 46.1025 1.56302
\(871\) 81.7608 2.77036
\(872\) −18.9773 −0.642653
\(873\) 45.1037 1.52653
\(874\) −38.0580 −1.28733
\(875\) −5.68379 −0.192147
\(876\) 45.8203 1.54812
\(877\) 12.8278 0.433165 0.216583 0.976264i \(-0.430509\pi\)
0.216583 + 0.976264i \(0.430509\pi\)
\(878\) −8.69016 −0.293279
\(879\) −31.5439 −1.06395
\(880\) 6.29267 0.212126
\(881\) −12.4564 −0.419666 −0.209833 0.977737i \(-0.567292\pi\)
−0.209833 + 0.977737i \(0.567292\pi\)
\(882\) −35.6192 −1.19936
\(883\) 46.4232 1.56226 0.781132 0.624366i \(-0.214642\pi\)
0.781132 + 0.624366i \(0.214642\pi\)
\(884\) −22.0113 −0.740320
\(885\) 84.9947 2.85707
\(886\) −23.0163 −0.773247
\(887\) −26.8689 −0.902169 −0.451085 0.892481i \(-0.648963\pi\)
−0.451085 + 0.892481i \(0.648963\pi\)
\(888\) 1.63662 0.0549212
\(889\) 3.81841 0.128065
\(890\) −23.4783 −0.786994
\(891\) 8.99360 0.301297
\(892\) 0.373646 0.0125106
\(893\) 94.4567 3.16087
\(894\) −28.3049 −0.946656
\(895\) 30.9886 1.03583
\(896\) 0.474155 0.0158404
\(897\) −76.7840 −2.56374
\(898\) 18.6419 0.622087
\(899\) 19.1777 0.639611
\(900\) −5.12513 −0.170838
\(901\) 16.3133 0.543474
\(902\) −35.9906 −1.19835
\(903\) −1.34357 −0.0447113
\(904\) −7.64564 −0.254290
\(905\) −22.1809 −0.737317
\(906\) −18.5563 −0.616492
\(907\) −11.9869 −0.398017 −0.199009 0.979998i \(-0.563772\pi\)
−0.199009 + 0.979998i \(0.563772\pi\)
\(908\) −24.1798 −0.802434
\(909\) 0.721980 0.0239466
\(910\) 5.02026 0.166420
\(911\) 6.41774 0.212629 0.106315 0.994333i \(-0.466095\pi\)
0.106315 + 0.994333i \(0.466095\pi\)
\(912\) 21.5988 0.715207
\(913\) 14.1407 0.467990
\(914\) −11.6584 −0.385626
\(915\) 16.9168 0.559253
\(916\) −6.68006 −0.220715
\(917\) 0.356722 0.0117800
\(918\) 27.0546 0.892936
\(919\) −13.8151 −0.455717 −0.227858 0.973694i \(-0.573172\pi\)
−0.227858 + 0.973694i \(0.573172\pi\)
\(920\) 10.1584 0.334914
\(921\) 74.0469 2.43993
\(922\) 29.5786 0.974118
\(923\) −18.3480 −0.603932
\(924\) −4.27350 −0.140588
\(925\) 0.555224 0.0182557
\(926\) −34.6632 −1.13910
\(927\) −18.6471 −0.612453
\(928\) −7.99676 −0.262507
\(929\) −32.6475 −1.07113 −0.535565 0.844494i \(-0.679901\pi\)
−0.535565 + 0.844494i \(0.679901\pi\)
\(930\) 13.8258 0.453367
\(931\) 50.9249 1.66900
\(932\) −11.6049 −0.380130
\(933\) −22.3389 −0.731341
\(934\) −5.43995 −0.178001
\(935\) −26.2461 −0.858340
\(936\) 27.7447 0.906862
\(937\) 52.4364 1.71302 0.856511 0.516129i \(-0.172628\pi\)
0.856511 + 0.516129i \(0.172628\pi\)
\(938\) 7.34598 0.239855
\(939\) 40.6059 1.32513
\(940\) −25.2124 −0.822337
\(941\) −36.5728 −1.19224 −0.596119 0.802896i \(-0.703292\pi\)
−0.596119 + 0.802896i \(0.703292\pi\)
\(942\) −41.6731 −1.35778
\(943\) −58.1006 −1.89201
\(944\) −14.7429 −0.479839
\(945\) −6.17053 −0.200727
\(946\) 3.09290 0.100559
\(947\) 40.2995 1.30956 0.654779 0.755820i \(-0.272762\pi\)
0.654779 + 0.755820i \(0.272762\pi\)
\(948\) −35.9078 −1.16623
\(949\) −84.1499 −2.73162
\(950\) 7.32741 0.237733
\(951\) −35.9143 −1.16460
\(952\) −1.97766 −0.0640962
\(953\) 34.4306 1.11532 0.557659 0.830070i \(-0.311700\pi\)
0.557659 + 0.830070i \(0.311700\pi\)
\(954\) −20.5625 −0.665734
\(955\) 1.12566 0.0364256
\(956\) 8.85678 0.286449
\(957\) 72.0739 2.32982
\(958\) 5.97601 0.193076
\(959\) −5.13544 −0.165832
\(960\) −5.76514 −0.186069
\(961\) −25.2487 −0.814475
\(962\) −3.00568 −0.0969071
\(963\) 46.5409 1.49976
\(964\) 9.26722 0.298477
\(965\) −24.2311 −0.780026
\(966\) −6.89883 −0.221966
\(967\) 30.7935 0.990252 0.495126 0.868821i \(-0.335122\pi\)
0.495126 + 0.868821i \(0.335122\pi\)
\(968\) −1.16241 −0.0373614
\(969\) −90.0864 −2.89399
\(970\) 17.2123 0.552654
\(971\) −19.9214 −0.639310 −0.319655 0.947534i \(-0.603567\pi\)
−0.319655 + 0.947534i \(0.603567\pi\)
\(972\) 11.2199 0.359878
\(973\) 4.13944 0.132704
\(974\) 23.8893 0.765463
\(975\) 14.7835 0.473449
\(976\) −2.93433 −0.0939256
\(977\) −53.1745 −1.70120 −0.850602 0.525811i \(-0.823762\pi\)
−0.850602 + 0.525811i \(0.823762\pi\)
\(978\) −15.4873 −0.495231
\(979\) −36.7046 −1.17308
\(980\) −13.5929 −0.434208
\(981\) −99.7697 −3.18540
\(982\) 17.3083 0.552329
\(983\) −9.79688 −0.312472 −0.156236 0.987720i \(-0.549936\pi\)
−0.156236 + 0.987720i \(0.549936\pi\)
\(984\) 32.9734 1.05115
\(985\) 6.14852 0.195908
\(986\) 33.3537 1.06220
\(987\) 17.1223 0.545010
\(988\) −39.6666 −1.26196
\(989\) 4.99295 0.158767
\(990\) 33.0825 1.05143
\(991\) −5.64566 −0.179340 −0.0896702 0.995972i \(-0.528581\pi\)
−0.0896702 + 0.995972i \(0.528581\pi\)
\(992\) −2.39818 −0.0761423
\(993\) 64.9162 2.06005
\(994\) −1.64852 −0.0522878
\(995\) 44.8055 1.42043
\(996\) −12.9553 −0.410504
\(997\) 10.2970 0.326109 0.163055 0.986617i \(-0.447865\pi\)
0.163055 + 0.986617i \(0.447865\pi\)
\(998\) −22.6110 −0.715739
\(999\) 3.69436 0.116884
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 \(a_p\))