Properties

Label 6041.2.a.f.1.16
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32322 q^{2}\) \(+2.41590 q^{3}\) \(+3.39733 q^{4}\) \(+0.249961 q^{5}\) \(-5.61265 q^{6}\) \(+1.00000 q^{7}\) \(-3.24629 q^{8}\) \(+2.83657 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32322 q^{2}\) \(+2.41590 q^{3}\) \(+3.39733 q^{4}\) \(+0.249961 q^{5}\) \(-5.61265 q^{6}\) \(+1.00000 q^{7}\) \(-3.24629 q^{8}\) \(+2.83657 q^{9}\) \(-0.580712 q^{10}\) \(+3.91510 q^{11}\) \(+8.20760 q^{12}\) \(+0.778528 q^{13}\) \(-2.32322 q^{14}\) \(+0.603880 q^{15}\) \(+0.747183 q^{16}\) \(+3.22662 q^{17}\) \(-6.58997 q^{18}\) \(+6.57430 q^{19}\) \(+0.849198 q^{20}\) \(+2.41590 q^{21}\) \(-9.09562 q^{22}\) \(-3.71094 q^{23}\) \(-7.84272 q^{24}\) \(-4.93752 q^{25}\) \(-1.80869 q^{26}\) \(-0.394827 q^{27}\) \(+3.39733 q^{28}\) \(+9.52419 q^{29}\) \(-1.40294 q^{30}\) \(+7.29397 q^{31}\) \(+4.75672 q^{32}\) \(+9.45849 q^{33}\) \(-7.49612 q^{34}\) \(+0.249961 q^{35}\) \(+9.63676 q^{36}\) \(-8.87264 q^{37}\) \(-15.2735 q^{38}\) \(+1.88085 q^{39}\) \(-0.811446 q^{40}\) \(+4.01810 q^{41}\) \(-5.61265 q^{42}\) \(+2.12465 q^{43}\) \(+13.3009 q^{44}\) \(+0.709031 q^{45}\) \(+8.62132 q^{46}\) \(-13.2644 q^{47}\) \(+1.80512 q^{48}\) \(+1.00000 q^{49}\) \(+11.4709 q^{50}\) \(+7.79518 q^{51}\) \(+2.64492 q^{52}\) \(+4.92230 q^{53}\) \(+0.917268 q^{54}\) \(+0.978621 q^{55}\) \(-3.24629 q^{56}\) \(+15.8829 q^{57}\) \(-22.1267 q^{58}\) \(-3.00791 q^{59}\) \(+2.05158 q^{60}\) \(+7.07562 q^{61}\) \(-16.9455 q^{62}\) \(+2.83657 q^{63}\) \(-12.5453 q^{64}\) \(+0.194601 q^{65}\) \(-21.9741 q^{66}\) \(+9.24765 q^{67}\) \(+10.9619 q^{68}\) \(-8.96526 q^{69}\) \(-0.580712 q^{70}\) \(+13.4447 q^{71}\) \(-9.20835 q^{72}\) \(+3.92772 q^{73}\) \(+20.6131 q^{74}\) \(-11.9286 q^{75}\) \(+22.3351 q^{76}\) \(+3.91510 q^{77}\) \(-4.36961 q^{78}\) \(+9.95908 q^{79}\) \(+0.186766 q^{80}\) \(-9.46358 q^{81}\) \(-9.33490 q^{82}\) \(-17.4886 q^{83}\) \(+8.20760 q^{84}\) \(+0.806527 q^{85}\) \(-4.93601 q^{86}\) \(+23.0095 q^{87}\) \(-12.7096 q^{88}\) \(-1.86575 q^{89}\) \(-1.64723 q^{90}\) \(+0.778528 q^{91}\) \(-12.6073 q^{92}\) \(+17.6215 q^{93}\) \(+30.8161 q^{94}\) \(+1.64332 q^{95}\) \(+11.4918 q^{96}\) \(+3.66925 q^{97}\) \(-2.32322 q^{98}\) \(+11.1055 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32322 −1.64276 −0.821381 0.570381i \(-0.806796\pi\)
−0.821381 + 0.570381i \(0.806796\pi\)
\(3\) 2.41590 1.39482 0.697410 0.716672i \(-0.254336\pi\)
0.697410 + 0.716672i \(0.254336\pi\)
\(4\) 3.39733 1.69866
\(5\) 0.249961 0.111786 0.0558929 0.998437i \(-0.482199\pi\)
0.0558929 + 0.998437i \(0.482199\pi\)
\(6\) −5.61265 −2.29136
\(7\) 1.00000 0.377964
\(8\) −3.24629 −1.14774
\(9\) 2.83657 0.945524
\(10\) −0.580712 −0.183637
\(11\) 3.91510 1.18045 0.590224 0.807240i \(-0.299040\pi\)
0.590224 + 0.807240i \(0.299040\pi\)
\(12\) 8.20760 2.36933
\(13\) 0.778528 0.215925 0.107962 0.994155i \(-0.465567\pi\)
0.107962 + 0.994155i \(0.465567\pi\)
\(14\) −2.32322 −0.620905
\(15\) 0.603880 0.155921
\(16\) 0.747183 0.186796
\(17\) 3.22662 0.782569 0.391285 0.920270i \(-0.372031\pi\)
0.391285 + 0.920270i \(0.372031\pi\)
\(18\) −6.58997 −1.55327
\(19\) 6.57430 1.50825 0.754124 0.656732i \(-0.228062\pi\)
0.754124 + 0.656732i \(0.228062\pi\)
\(20\) 0.849198 0.189886
\(21\) 2.41590 0.527193
\(22\) −9.09562 −1.93919
\(23\) −3.71094 −0.773785 −0.386892 0.922125i \(-0.626452\pi\)
−0.386892 + 0.922125i \(0.626452\pi\)
\(24\) −7.84272 −1.60089
\(25\) −4.93752 −0.987504
\(26\) −1.80869 −0.354713
\(27\) −0.394827 −0.0759845
\(28\) 3.39733 0.642035
\(29\) 9.52419 1.76860 0.884299 0.466922i \(-0.154637\pi\)
0.884299 + 0.466922i \(0.154637\pi\)
\(30\) −1.40294 −0.256141
\(31\) 7.29397 1.31004 0.655018 0.755614i \(-0.272661\pi\)
0.655018 + 0.755614i \(0.272661\pi\)
\(32\) 4.75672 0.840878
\(33\) 9.45849 1.64651
\(34\) −7.49612 −1.28557
\(35\) 0.249961 0.0422510
\(36\) 9.63676 1.60613
\(37\) −8.87264 −1.45865 −0.729327 0.684166i \(-0.760166\pi\)
−0.729327 + 0.684166i \(0.760166\pi\)
\(38\) −15.2735 −2.47769
\(39\) 1.88085 0.301177
\(40\) −0.811446 −0.128301
\(41\) 4.01810 0.627521 0.313761 0.949502i \(-0.398411\pi\)
0.313761 + 0.949502i \(0.398411\pi\)
\(42\) −5.61265 −0.866051
\(43\) 2.12465 0.324005 0.162003 0.986790i \(-0.448205\pi\)
0.162003 + 0.986790i \(0.448205\pi\)
\(44\) 13.3009 2.00518
\(45\) 0.709031 0.105696
\(46\) 8.62132 1.27114
\(47\) −13.2644 −1.93482 −0.967408 0.253223i \(-0.918509\pi\)
−0.967408 + 0.253223i \(0.918509\pi\)
\(48\) 1.80512 0.260546
\(49\) 1.00000 0.142857
\(50\) 11.4709 1.62223
\(51\) 7.79518 1.09154
\(52\) 2.64492 0.366784
\(53\) 4.92230 0.676130 0.338065 0.941123i \(-0.390228\pi\)
0.338065 + 0.941123i \(0.390228\pi\)
\(54\) 0.917268 0.124824
\(55\) 0.978621 0.131957
\(56\) −3.24629 −0.433804
\(57\) 15.8829 2.10374
\(58\) −22.1267 −2.90538
\(59\) −3.00791 −0.391596 −0.195798 0.980644i \(-0.562730\pi\)
−0.195798 + 0.980644i \(0.562730\pi\)
\(60\) 2.05158 0.264858
\(61\) 7.07562 0.905941 0.452970 0.891526i \(-0.350364\pi\)
0.452970 + 0.891526i \(0.350364\pi\)
\(62\) −16.9455 −2.15207
\(63\) 2.83657 0.357374
\(64\) −12.5453 −1.56816
\(65\) 0.194601 0.0241373
\(66\) −21.9741 −2.70483
\(67\) 9.24765 1.12978 0.564890 0.825166i \(-0.308918\pi\)
0.564890 + 0.825166i \(0.308918\pi\)
\(68\) 10.9619 1.32932
\(69\) −8.96526 −1.07929
\(70\) −0.580712 −0.0694084
\(71\) 13.4447 1.59559 0.797795 0.602928i \(-0.206000\pi\)
0.797795 + 0.602928i \(0.206000\pi\)
\(72\) −9.20835 −1.08521
\(73\) 3.92772 0.459705 0.229852 0.973226i \(-0.426176\pi\)
0.229852 + 0.973226i \(0.426176\pi\)
\(74\) 20.6131 2.39622
\(75\) −11.9286 −1.37739
\(76\) 22.3351 2.56201
\(77\) 3.91510 0.446167
\(78\) −4.36961 −0.494761
\(79\) 9.95908 1.12048 0.560242 0.828329i \(-0.310708\pi\)
0.560242 + 0.828329i \(0.310708\pi\)
\(80\) 0.186766 0.0208811
\(81\) −9.46358 −1.05151
\(82\) −9.33490 −1.03087
\(83\) −17.4886 −1.91963 −0.959813 0.280639i \(-0.909454\pi\)
−0.959813 + 0.280639i \(0.909454\pi\)
\(84\) 8.20760 0.895523
\(85\) 0.806527 0.0874801
\(86\) −4.93601 −0.532263
\(87\) 23.0095 2.46688
\(88\) −12.7096 −1.35484
\(89\) −1.86575 −0.197769 −0.0988844 0.995099i \(-0.531527\pi\)
−0.0988844 + 0.995099i \(0.531527\pi\)
\(90\) −1.64723 −0.173633
\(91\) 0.778528 0.0816120
\(92\) −12.6073 −1.31440
\(93\) 17.6215 1.82726
\(94\) 30.8161 3.17844
\(95\) 1.64332 0.168601
\(96\) 11.4918 1.17287
\(97\) 3.66925 0.372556 0.186278 0.982497i \(-0.440357\pi\)
0.186278 + 0.982497i \(0.440357\pi\)
\(98\) −2.32322 −0.234680
\(99\) 11.1055 1.11614
\(100\) −16.7744 −1.67744
\(101\) −7.99220 −0.795254 −0.397627 0.917547i \(-0.630166\pi\)
−0.397627 + 0.917547i \(0.630166\pi\)
\(102\) −18.1099 −1.79315
\(103\) −9.14245 −0.900832 −0.450416 0.892819i \(-0.648724\pi\)
−0.450416 + 0.892819i \(0.648724\pi\)
\(104\) −2.52733 −0.247825
\(105\) 0.603880 0.0589326
\(106\) −11.4356 −1.11072
\(107\) 2.38360 0.230431 0.115216 0.993341i \(-0.463244\pi\)
0.115216 + 0.993341i \(0.463244\pi\)
\(108\) −1.34136 −0.129072
\(109\) 1.05016 0.100587 0.0502934 0.998734i \(-0.483984\pi\)
0.0502934 + 0.998734i \(0.483984\pi\)
\(110\) −2.27355 −0.216774
\(111\) −21.4354 −2.03456
\(112\) 0.747183 0.0706021
\(113\) −15.7834 −1.48478 −0.742389 0.669969i \(-0.766307\pi\)
−0.742389 + 0.669969i \(0.766307\pi\)
\(114\) −36.8993 −3.45594
\(115\) −0.927589 −0.0864981
\(116\) 32.3568 3.00425
\(117\) 2.20835 0.204162
\(118\) 6.98802 0.643299
\(119\) 3.22662 0.295783
\(120\) −1.96037 −0.178957
\(121\) 4.32801 0.393455
\(122\) −16.4382 −1.48824
\(123\) 9.70732 0.875279
\(124\) 24.7800 2.22531
\(125\) −2.48399 −0.222175
\(126\) −6.58997 −0.587081
\(127\) −7.24116 −0.642549 −0.321274 0.946986i \(-0.604111\pi\)
−0.321274 + 0.946986i \(0.604111\pi\)
\(128\) 19.6319 1.73523
\(129\) 5.13293 0.451929
\(130\) −0.452101 −0.0396519
\(131\) 20.9396 1.82950 0.914752 0.404016i \(-0.132386\pi\)
0.914752 + 0.404016i \(0.132386\pi\)
\(132\) 32.1336 2.79687
\(133\) 6.57430 0.570064
\(134\) −21.4843 −1.85596
\(135\) −0.0986911 −0.00849398
\(136\) −10.4745 −0.898185
\(137\) −19.9137 −1.70134 −0.850669 0.525701i \(-0.823803\pi\)
−0.850669 + 0.525701i \(0.823803\pi\)
\(138\) 20.8282 1.77302
\(139\) −13.6921 −1.16135 −0.580675 0.814135i \(-0.697211\pi\)
−0.580675 + 0.814135i \(0.697211\pi\)
\(140\) 0.849198 0.0717703
\(141\) −32.0455 −2.69872
\(142\) −31.2349 −2.62117
\(143\) 3.04802 0.254888
\(144\) 2.11944 0.176620
\(145\) 2.38067 0.197704
\(146\) −9.12493 −0.755185
\(147\) 2.41590 0.199260
\(148\) −30.1433 −2.47776
\(149\) 11.9358 0.977819 0.488909 0.872335i \(-0.337395\pi\)
0.488909 + 0.872335i \(0.337395\pi\)
\(150\) 27.7126 2.26272
\(151\) 0.0794979 0.00646945 0.00323472 0.999995i \(-0.498970\pi\)
0.00323472 + 0.999995i \(0.498970\pi\)
\(152\) −21.3421 −1.73107
\(153\) 9.15252 0.739938
\(154\) −9.09562 −0.732946
\(155\) 1.82320 0.146443
\(156\) 6.38985 0.511598
\(157\) −4.64293 −0.370546 −0.185273 0.982687i \(-0.559317\pi\)
−0.185273 + 0.982687i \(0.559317\pi\)
\(158\) −23.1371 −1.84069
\(159\) 11.8918 0.943079
\(160\) 1.18899 0.0939981
\(161\) −3.71094 −0.292463
\(162\) 21.9859 1.72738
\(163\) 16.1775 1.26712 0.633558 0.773695i \(-0.281594\pi\)
0.633558 + 0.773695i \(0.281594\pi\)
\(164\) 13.6508 1.06595
\(165\) 2.36425 0.184057
\(166\) 40.6298 3.15349
\(167\) −6.40110 −0.495332 −0.247666 0.968845i \(-0.579664\pi\)
−0.247666 + 0.968845i \(0.579664\pi\)
\(168\) −7.84272 −0.605079
\(169\) −12.3939 −0.953376
\(170\) −1.87373 −0.143709
\(171\) 18.6485 1.42608
\(172\) 7.21812 0.550376
\(173\) −15.3410 −1.16635 −0.583177 0.812345i \(-0.698191\pi\)
−0.583177 + 0.812345i \(0.698191\pi\)
\(174\) −53.4560 −4.05249
\(175\) −4.93752 −0.373241
\(176\) 2.92530 0.220502
\(177\) −7.26681 −0.546207
\(178\) 4.33453 0.324887
\(179\) 20.0212 1.49645 0.748227 0.663443i \(-0.230905\pi\)
0.748227 + 0.663443i \(0.230905\pi\)
\(180\) 2.40881 0.179542
\(181\) 14.5407 1.08080 0.540402 0.841407i \(-0.318272\pi\)
0.540402 + 0.841407i \(0.318272\pi\)
\(182\) −1.80869 −0.134069
\(183\) 17.0940 1.26362
\(184\) 12.0468 0.888102
\(185\) −2.21781 −0.163057
\(186\) −40.9385 −3.00176
\(187\) 12.6325 0.923781
\(188\) −45.0636 −3.28660
\(189\) −0.394827 −0.0287194
\(190\) −3.81778 −0.276971
\(191\) −8.15118 −0.589799 −0.294899 0.955528i \(-0.595286\pi\)
−0.294899 + 0.955528i \(0.595286\pi\)
\(192\) −30.3081 −2.18730
\(193\) 16.3978 1.18034 0.590168 0.807280i \(-0.299061\pi\)
0.590168 + 0.807280i \(0.299061\pi\)
\(194\) −8.52446 −0.612021
\(195\) 0.470138 0.0336672
\(196\) 3.39733 0.242666
\(197\) 10.7579 0.766472 0.383236 0.923650i \(-0.374810\pi\)
0.383236 + 0.923650i \(0.374810\pi\)
\(198\) −25.8004 −1.83355
\(199\) 26.3198 1.86576 0.932882 0.360182i \(-0.117285\pi\)
0.932882 + 0.360182i \(0.117285\pi\)
\(200\) 16.0286 1.13340
\(201\) 22.3414 1.57584
\(202\) 18.5676 1.30641
\(203\) 9.52419 0.668467
\(204\) 26.4828 1.85417
\(205\) 1.00437 0.0701479
\(206\) 21.2399 1.47985
\(207\) −10.5264 −0.731632
\(208\) 0.581703 0.0403338
\(209\) 25.7391 1.78041
\(210\) −1.40294 −0.0968122
\(211\) −18.4210 −1.26815 −0.634076 0.773271i \(-0.718619\pi\)
−0.634076 + 0.773271i \(0.718619\pi\)
\(212\) 16.7227 1.14852
\(213\) 32.4810 2.22556
\(214\) −5.53761 −0.378543
\(215\) 0.531078 0.0362192
\(216\) 1.28172 0.0872103
\(217\) 7.29397 0.495147
\(218\) −2.43974 −0.165240
\(219\) 9.48897 0.641205
\(220\) 3.32470 0.224151
\(221\) 2.51201 0.168976
\(222\) 49.7991 3.34229
\(223\) −1.18338 −0.0792452 −0.0396226 0.999215i \(-0.512616\pi\)
−0.0396226 + 0.999215i \(0.512616\pi\)
\(224\) 4.75672 0.317822
\(225\) −14.0056 −0.933709
\(226\) 36.6683 2.43914
\(227\) 0.425661 0.0282521 0.0141261 0.999900i \(-0.495503\pi\)
0.0141261 + 0.999900i \(0.495503\pi\)
\(228\) 53.9593 3.57354
\(229\) 17.1475 1.13314 0.566569 0.824015i \(-0.308271\pi\)
0.566569 + 0.824015i \(0.308271\pi\)
\(230\) 2.15499 0.142096
\(231\) 9.45849 0.622323
\(232\) −30.9183 −2.02989
\(233\) −27.5273 −1.80338 −0.901688 0.432387i \(-0.857671\pi\)
−0.901688 + 0.432387i \(0.857671\pi\)
\(234\) −5.13048 −0.335390
\(235\) −3.31558 −0.216285
\(236\) −10.2189 −0.665191
\(237\) 24.0601 1.56287
\(238\) −7.49612 −0.485901
\(239\) −6.62922 −0.428808 −0.214404 0.976745i \(-0.568781\pi\)
−0.214404 + 0.976745i \(0.568781\pi\)
\(240\) 0.451208 0.0291254
\(241\) 20.7738 1.33816 0.669080 0.743190i \(-0.266688\pi\)
0.669080 + 0.743190i \(0.266688\pi\)
\(242\) −10.0549 −0.646353
\(243\) −21.6786 −1.39068
\(244\) 24.0382 1.53889
\(245\) 0.249961 0.0159694
\(246\) −22.5522 −1.43788
\(247\) 5.11828 0.325668
\(248\) −23.6784 −1.50358
\(249\) −42.2508 −2.67753
\(250\) 5.77084 0.364980
\(251\) −22.0828 −1.39386 −0.696928 0.717141i \(-0.745450\pi\)
−0.696928 + 0.717141i \(0.745450\pi\)
\(252\) 9.63676 0.607059
\(253\) −14.5287 −0.913412
\(254\) 16.8228 1.05555
\(255\) 1.94849 0.122019
\(256\) −20.5186 −1.28241
\(257\) −6.24116 −0.389313 −0.194656 0.980872i \(-0.562359\pi\)
−0.194656 + 0.980872i \(0.562359\pi\)
\(258\) −11.9249 −0.742412
\(259\) −8.87264 −0.551319
\(260\) 0.661125 0.0410012
\(261\) 27.0160 1.67225
\(262\) −48.6473 −3.00544
\(263\) −5.24927 −0.323684 −0.161842 0.986817i \(-0.551743\pi\)
−0.161842 + 0.986817i \(0.551743\pi\)
\(264\) −30.7050 −1.88976
\(265\) 1.23038 0.0755817
\(266\) −15.2735 −0.936480
\(267\) −4.50746 −0.275852
\(268\) 31.4173 1.91912
\(269\) 13.0845 0.797779 0.398889 0.916999i \(-0.369396\pi\)
0.398889 + 0.916999i \(0.369396\pi\)
\(270\) 0.229281 0.0139536
\(271\) 6.80852 0.413588 0.206794 0.978384i \(-0.433697\pi\)
0.206794 + 0.978384i \(0.433697\pi\)
\(272\) 2.41087 0.146181
\(273\) 1.88085 0.113834
\(274\) 46.2637 2.79489
\(275\) −19.3309 −1.16570
\(276\) −30.4579 −1.83335
\(277\) 10.0423 0.603386 0.301693 0.953405i \(-0.402448\pi\)
0.301693 + 0.953405i \(0.402448\pi\)
\(278\) 31.8097 1.90782
\(279\) 20.6899 1.23867
\(280\) −0.811446 −0.0484931
\(281\) −5.98701 −0.357155 −0.178578 0.983926i \(-0.557150\pi\)
−0.178578 + 0.983926i \(0.557150\pi\)
\(282\) 74.4487 4.43335
\(283\) −0.833588 −0.0495517 −0.0247758 0.999693i \(-0.507887\pi\)
−0.0247758 + 0.999693i \(0.507887\pi\)
\(284\) 45.6760 2.71037
\(285\) 3.97009 0.235168
\(286\) −7.08120 −0.418720
\(287\) 4.01810 0.237181
\(288\) 13.4928 0.795070
\(289\) −6.58895 −0.387586
\(290\) −5.53081 −0.324781
\(291\) 8.86454 0.519649
\(292\) 13.3437 0.780884
\(293\) −4.29442 −0.250882 −0.125441 0.992101i \(-0.540035\pi\)
−0.125441 + 0.992101i \(0.540035\pi\)
\(294\) −5.61265 −0.327337
\(295\) −0.751859 −0.0437749
\(296\) 28.8032 1.67415
\(297\) −1.54579 −0.0896956
\(298\) −27.7294 −1.60632
\(299\) −2.88907 −0.167079
\(300\) −40.5252 −2.33972
\(301\) 2.12465 0.122463
\(302\) −0.184691 −0.0106278
\(303\) −19.3084 −1.10924
\(304\) 4.91221 0.281734
\(305\) 1.76863 0.101271
\(306\) −21.2633 −1.21554
\(307\) −13.5745 −0.774738 −0.387369 0.921925i \(-0.626616\pi\)
−0.387369 + 0.921925i \(0.626616\pi\)
\(308\) 13.3009 0.757888
\(309\) −22.0872 −1.25650
\(310\) −4.23570 −0.240571
\(311\) −7.87348 −0.446464 −0.223232 0.974765i \(-0.571661\pi\)
−0.223232 + 0.974765i \(0.571661\pi\)
\(312\) −6.10578 −0.345672
\(313\) 6.78714 0.383632 0.191816 0.981431i \(-0.438562\pi\)
0.191816 + 0.981431i \(0.438562\pi\)
\(314\) 10.7865 0.608719
\(315\) 0.709031 0.0399494
\(316\) 33.8343 1.90333
\(317\) 6.98076 0.392079 0.196039 0.980596i \(-0.437192\pi\)
0.196039 + 0.980596i \(0.437192\pi\)
\(318\) −27.6272 −1.54925
\(319\) 37.2882 2.08774
\(320\) −3.13582 −0.175298
\(321\) 5.75854 0.321410
\(322\) 8.62132 0.480447
\(323\) 21.2127 1.18031
\(324\) −32.1509 −1.78616
\(325\) −3.84400 −0.213227
\(326\) −37.5837 −2.08157
\(327\) 2.53707 0.140300
\(328\) −13.0439 −0.720230
\(329\) −13.2644 −0.731292
\(330\) −5.49266 −0.302361
\(331\) −18.4003 −1.01137 −0.505685 0.862718i \(-0.668760\pi\)
−0.505685 + 0.862718i \(0.668760\pi\)
\(332\) −59.4146 −3.26080
\(333\) −25.1679 −1.37919
\(334\) 14.8711 0.813713
\(335\) 2.31155 0.126293
\(336\) 1.80512 0.0984773
\(337\) 11.1747 0.608724 0.304362 0.952556i \(-0.401557\pi\)
0.304362 + 0.952556i \(0.401557\pi\)
\(338\) 28.7937 1.56617
\(339\) −38.1311 −2.07100
\(340\) 2.74004 0.148599
\(341\) 28.5566 1.54643
\(342\) −43.3244 −2.34272
\(343\) 1.00000 0.0539949
\(344\) −6.89722 −0.371873
\(345\) −2.24096 −0.120649
\(346\) 35.6404 1.91604
\(347\) −3.12443 −0.167728 −0.0838642 0.996477i \(-0.526726\pi\)
−0.0838642 + 0.996477i \(0.526726\pi\)
\(348\) 78.1708 4.19039
\(349\) 0.948338 0.0507634 0.0253817 0.999678i \(-0.491920\pi\)
0.0253817 + 0.999678i \(0.491920\pi\)
\(350\) 11.4709 0.613146
\(351\) −0.307384 −0.0164069
\(352\) 18.6230 0.992611
\(353\) −27.6077 −1.46941 −0.734706 0.678386i \(-0.762680\pi\)
−0.734706 + 0.678386i \(0.762680\pi\)
\(354\) 16.8824 0.897287
\(355\) 3.36064 0.178364
\(356\) −6.33855 −0.335943
\(357\) 7.79518 0.412565
\(358\) −46.5135 −2.45832
\(359\) −6.73201 −0.355302 −0.177651 0.984094i \(-0.556850\pi\)
−0.177651 + 0.984094i \(0.556850\pi\)
\(360\) −2.30172 −0.121311
\(361\) 24.2215 1.27481
\(362\) −33.7812 −1.77550
\(363\) 10.4560 0.548800
\(364\) 2.64492 0.138631
\(365\) 0.981774 0.0513884
\(366\) −39.7130 −2.07583
\(367\) 25.3040 1.32086 0.660428 0.750889i \(-0.270375\pi\)
0.660428 + 0.750889i \(0.270375\pi\)
\(368\) −2.77275 −0.144540
\(369\) 11.3976 0.593336
\(370\) 5.15245 0.267863
\(371\) 4.92230 0.255553
\(372\) 59.8660 3.10391
\(373\) −5.91183 −0.306103 −0.153051 0.988218i \(-0.548910\pi\)
−0.153051 + 0.988218i \(0.548910\pi\)
\(374\) −29.3481 −1.51755
\(375\) −6.00107 −0.309894
\(376\) 43.0602 2.22066
\(377\) 7.41485 0.381884
\(378\) 0.917268 0.0471792
\(379\) 3.53866 0.181769 0.0908843 0.995861i \(-0.471031\pi\)
0.0908843 + 0.995861i \(0.471031\pi\)
\(380\) 5.58289 0.286396
\(381\) −17.4939 −0.896240
\(382\) 18.9369 0.968898
\(383\) 23.0661 1.17862 0.589310 0.807907i \(-0.299400\pi\)
0.589310 + 0.807907i \(0.299400\pi\)
\(384\) 47.4286 2.42033
\(385\) 0.978621 0.0498751
\(386\) −38.0955 −1.93901
\(387\) 6.02671 0.306355
\(388\) 12.4657 0.632848
\(389\) 8.30924 0.421295 0.210647 0.977562i \(-0.432443\pi\)
0.210647 + 0.977562i \(0.432443\pi\)
\(390\) −1.09223 −0.0553072
\(391\) −11.9738 −0.605540
\(392\) −3.24629 −0.163963
\(393\) 50.5880 2.55183
\(394\) −24.9930 −1.25913
\(395\) 2.48938 0.125254
\(396\) 37.7289 1.89595
\(397\) 22.9321 1.15093 0.575466 0.817826i \(-0.304821\pi\)
0.575466 + 0.817826i \(0.304821\pi\)
\(398\) −61.1466 −3.06500
\(399\) 15.8829 0.795137
\(400\) −3.68923 −0.184461
\(401\) −12.2159 −0.610031 −0.305016 0.952347i \(-0.598662\pi\)
−0.305016 + 0.952347i \(0.598662\pi\)
\(402\) −51.9039 −2.58873
\(403\) 5.67856 0.282869
\(404\) −27.1521 −1.35087
\(405\) −2.36552 −0.117544
\(406\) −22.1267 −1.09813
\(407\) −34.7373 −1.72186
\(408\) −25.3054 −1.25281
\(409\) 11.5517 0.571195 0.285597 0.958350i \(-0.407808\pi\)
0.285597 + 0.958350i \(0.407808\pi\)
\(410\) −2.33336 −0.115236
\(411\) −48.1094 −2.37306
\(412\) −31.0599 −1.53021
\(413\) −3.00791 −0.148010
\(414\) 24.4550 1.20190
\(415\) −4.37147 −0.214587
\(416\) 3.70324 0.181566
\(417\) −33.0788 −1.61988
\(418\) −59.7974 −2.92478
\(419\) −30.7824 −1.50382 −0.751909 0.659266i \(-0.770867\pi\)
−0.751909 + 0.659266i \(0.770867\pi\)
\(420\) 2.05158 0.100107
\(421\) 0.890721 0.0434111 0.0217056 0.999764i \(-0.493090\pi\)
0.0217056 + 0.999764i \(0.493090\pi\)
\(422\) 42.7959 2.08327
\(423\) −37.6255 −1.82941
\(424\) −15.9792 −0.776020
\(425\) −15.9315 −0.772790
\(426\) −75.4604 −3.65607
\(427\) 7.07562 0.342413
\(428\) 8.09787 0.391425
\(429\) 7.36370 0.355523
\(430\) −1.23381 −0.0594995
\(431\) −22.2770 −1.07304 −0.536521 0.843887i \(-0.680262\pi\)
−0.536521 + 0.843887i \(0.680262\pi\)
\(432\) −0.295008 −0.0141936
\(433\) 4.00513 0.192474 0.0962371 0.995358i \(-0.469319\pi\)
0.0962371 + 0.995358i \(0.469319\pi\)
\(434\) −16.9455 −0.813408
\(435\) 5.75146 0.275762
\(436\) 3.56773 0.170863
\(437\) −24.3969 −1.16706
\(438\) −22.0449 −1.05335
\(439\) −25.6374 −1.22361 −0.611804 0.791009i \(-0.709556\pi\)
−0.611804 + 0.791009i \(0.709556\pi\)
\(440\) −3.17689 −0.151452
\(441\) 2.83657 0.135075
\(442\) −5.83594 −0.277588
\(443\) −3.71944 −0.176716 −0.0883579 0.996089i \(-0.528162\pi\)
−0.0883579 + 0.996089i \(0.528162\pi\)
\(444\) −72.8231 −3.45603
\(445\) −0.466363 −0.0221077
\(446\) 2.74925 0.130181
\(447\) 28.8357 1.36388
\(448\) −12.5453 −0.592708
\(449\) 22.2992 1.05236 0.526182 0.850372i \(-0.323623\pi\)
0.526182 + 0.850372i \(0.323623\pi\)
\(450\) 32.5381 1.53386
\(451\) 15.7313 0.740756
\(452\) −53.6214 −2.52214
\(453\) 0.192059 0.00902372
\(454\) −0.988902 −0.0464115
\(455\) 0.194601 0.00912306
\(456\) −51.5604 −2.41454
\(457\) 1.95251 0.0913345 0.0456672 0.998957i \(-0.485459\pi\)
0.0456672 + 0.998957i \(0.485459\pi\)
\(458\) −39.8373 −1.86147
\(459\) −1.27395 −0.0594631
\(460\) −3.15132 −0.146931
\(461\) −6.21417 −0.289423 −0.144711 0.989474i \(-0.546225\pi\)
−0.144711 + 0.989474i \(0.546225\pi\)
\(462\) −21.9741 −1.02233
\(463\) −2.94314 −0.136779 −0.0683897 0.997659i \(-0.521786\pi\)
−0.0683897 + 0.997659i \(0.521786\pi\)
\(464\) 7.11631 0.330366
\(465\) 4.40468 0.204262
\(466\) 63.9519 2.96252
\(467\) −3.36550 −0.155737 −0.0778683 0.996964i \(-0.524811\pi\)
−0.0778683 + 0.996964i \(0.524811\pi\)
\(468\) 7.50250 0.346803
\(469\) 9.24765 0.427017
\(470\) 7.70282 0.355304
\(471\) −11.2169 −0.516846
\(472\) 9.76456 0.449450
\(473\) 8.31820 0.382471
\(474\) −55.8969 −2.56743
\(475\) −32.4607 −1.48940
\(476\) 10.9619 0.502437
\(477\) 13.9625 0.639297
\(478\) 15.4011 0.704430
\(479\) 6.62083 0.302513 0.151257 0.988495i \(-0.451668\pi\)
0.151257 + 0.988495i \(0.451668\pi\)
\(480\) 2.87249 0.131111
\(481\) −6.90760 −0.314960
\(482\) −48.2621 −2.19828
\(483\) −8.96526 −0.407934
\(484\) 14.7037 0.668348
\(485\) 0.917168 0.0416465
\(486\) 50.3640 2.28456
\(487\) 10.8426 0.491326 0.245663 0.969355i \(-0.420994\pi\)
0.245663 + 0.969355i \(0.420994\pi\)
\(488\) −22.9696 −1.03978
\(489\) 39.0831 1.76740
\(490\) −0.580712 −0.0262339
\(491\) −14.2737 −0.644164 −0.322082 0.946712i \(-0.604383\pi\)
−0.322082 + 0.946712i \(0.604383\pi\)
\(492\) 32.9789 1.48681
\(493\) 30.7309 1.38405
\(494\) −11.8909 −0.534995
\(495\) 2.77593 0.124769
\(496\) 5.44993 0.244709
\(497\) 13.4447 0.603077
\(498\) 98.1576 4.39855
\(499\) −26.4167 −1.18257 −0.591286 0.806462i \(-0.701380\pi\)
−0.591286 + 0.806462i \(0.701380\pi\)
\(500\) −8.43892 −0.377400
\(501\) −15.4644 −0.690900
\(502\) 51.3032 2.28977
\(503\) 16.1977 0.722219 0.361110 0.932523i \(-0.382398\pi\)
0.361110 + 0.932523i \(0.382398\pi\)
\(504\) −9.20835 −0.410172
\(505\) −1.99774 −0.0888981
\(506\) 33.7533 1.50052
\(507\) −29.9424 −1.32979
\(508\) −24.6006 −1.09147
\(509\) 7.46534 0.330895 0.165448 0.986219i \(-0.447093\pi\)
0.165448 + 0.986219i \(0.447093\pi\)
\(510\) −4.52676 −0.200448
\(511\) 3.92772 0.173752
\(512\) 8.40529 0.371465
\(513\) −2.59571 −0.114603
\(514\) 14.4995 0.639548
\(515\) −2.28525 −0.100700
\(516\) 17.4382 0.767676
\(517\) −51.9316 −2.28395
\(518\) 20.6131 0.905686
\(519\) −37.0623 −1.62686
\(520\) −0.631733 −0.0277033
\(521\) −22.5064 −0.986025 −0.493012 0.870022i \(-0.664104\pi\)
−0.493012 + 0.870022i \(0.664104\pi\)
\(522\) −62.7641 −2.74711
\(523\) 6.29048 0.275063 0.137532 0.990497i \(-0.456083\pi\)
0.137532 + 0.990497i \(0.456083\pi\)
\(524\) 71.1388 3.10771
\(525\) −11.9286 −0.520605
\(526\) 12.1952 0.531736
\(527\) 23.5348 1.02519
\(528\) 7.06722 0.307561
\(529\) −9.22891 −0.401257
\(530\) −2.85844 −0.124163
\(531\) −8.53215 −0.370264
\(532\) 22.3351 0.968348
\(533\) 3.12820 0.135497
\(534\) 10.4718 0.453159
\(535\) 0.595806 0.0257589
\(536\) −30.0206 −1.29669
\(537\) 48.3692 2.08728
\(538\) −30.3982 −1.31056
\(539\) 3.91510 0.168635
\(540\) −0.335286 −0.0144284
\(541\) −18.1700 −0.781191 −0.390596 0.920562i \(-0.627731\pi\)
−0.390596 + 0.920562i \(0.627731\pi\)
\(542\) −15.8177 −0.679427
\(543\) 35.1289 1.50753
\(544\) 15.3481 0.658045
\(545\) 0.262498 0.0112442
\(546\) −4.36961 −0.187002
\(547\) 25.8143 1.10374 0.551869 0.833931i \(-0.313915\pi\)
0.551869 + 0.833931i \(0.313915\pi\)
\(548\) −67.6532 −2.89000
\(549\) 20.0705 0.856588
\(550\) 44.9098 1.91496
\(551\) 62.6149 2.66748
\(552\) 29.1039 1.23874
\(553\) 9.95908 0.423503
\(554\) −23.3305 −0.991219
\(555\) −5.35801 −0.227435
\(556\) −46.5166 −1.97274
\(557\) 5.72328 0.242503 0.121252 0.992622i \(-0.461309\pi\)
0.121252 + 0.992622i \(0.461309\pi\)
\(558\) −48.0670 −2.03484
\(559\) 1.65410 0.0699608
\(560\) 0.186766 0.00789231
\(561\) 30.5189 1.28851
\(562\) 13.9091 0.586721
\(563\) 9.19731 0.387620 0.193810 0.981039i \(-0.437915\pi\)
0.193810 + 0.981039i \(0.437915\pi\)
\(564\) −108.869 −4.58422
\(565\) −3.94523 −0.165977
\(566\) 1.93660 0.0814016
\(567\) −9.46358 −0.397433
\(568\) −43.6454 −1.83132
\(569\) −19.1641 −0.803403 −0.401701 0.915771i \(-0.631581\pi\)
−0.401701 + 0.915771i \(0.631581\pi\)
\(570\) −9.22337 −0.386324
\(571\) −12.6880 −0.530975 −0.265487 0.964114i \(-0.585533\pi\)
−0.265487 + 0.964114i \(0.585533\pi\)
\(572\) 10.3551 0.432969
\(573\) −19.6924 −0.822663
\(574\) −9.33490 −0.389631
\(575\) 18.3228 0.764116
\(576\) −35.5855 −1.48273
\(577\) −29.8813 −1.24397 −0.621987 0.783028i \(-0.713674\pi\)
−0.621987 + 0.783028i \(0.713674\pi\)
\(578\) 15.3076 0.636710
\(579\) 39.6153 1.64636
\(580\) 8.08792 0.335833
\(581\) −17.4886 −0.725551
\(582\) −20.5942 −0.853659
\(583\) 19.2713 0.798135
\(584\) −12.7505 −0.527620
\(585\) 0.552001 0.0228224
\(586\) 9.97685 0.412140
\(587\) 33.1092 1.36656 0.683282 0.730155i \(-0.260552\pi\)
0.683282 + 0.730155i \(0.260552\pi\)
\(588\) 8.20760 0.338476
\(589\) 47.9527 1.97586
\(590\) 1.74673 0.0719117
\(591\) 25.9901 1.06909
\(592\) −6.62948 −0.272470
\(593\) 6.38519 0.262208 0.131104 0.991369i \(-0.458148\pi\)
0.131104 + 0.991369i \(0.458148\pi\)
\(594\) 3.59119 0.147348
\(595\) 0.806527 0.0330644
\(596\) 40.5498 1.66099
\(597\) 63.5861 2.60241
\(598\) 6.71194 0.274472
\(599\) −20.2403 −0.826998 −0.413499 0.910505i \(-0.635693\pi\)
−0.413499 + 0.910505i \(0.635693\pi\)
\(600\) 38.7236 1.58088
\(601\) −0.800381 −0.0326482 −0.0163241 0.999867i \(-0.505196\pi\)
−0.0163241 + 0.999867i \(0.505196\pi\)
\(602\) −4.93601 −0.201177
\(603\) 26.2316 1.06823
\(604\) 0.270081 0.0109894
\(605\) 1.08183 0.0439827
\(606\) 44.8575 1.82221
\(607\) 41.9841 1.70408 0.852040 0.523476i \(-0.175365\pi\)
0.852040 + 0.523476i \(0.175365\pi\)
\(608\) 31.2721 1.26825
\(609\) 23.0095 0.932391
\(610\) −4.10890 −0.166365
\(611\) −10.3267 −0.417775
\(612\) 31.0941 1.25691
\(613\) 16.9583 0.684941 0.342470 0.939529i \(-0.388736\pi\)
0.342470 + 0.939529i \(0.388736\pi\)
\(614\) 31.5365 1.27271
\(615\) 2.42645 0.0978438
\(616\) −12.7096 −0.512083
\(617\) −14.9102 −0.600261 −0.300131 0.953898i \(-0.597030\pi\)
−0.300131 + 0.953898i \(0.597030\pi\)
\(618\) 51.3134 2.06413
\(619\) −9.52969 −0.383031 −0.191515 0.981490i \(-0.561340\pi\)
−0.191515 + 0.981490i \(0.561340\pi\)
\(620\) 6.19402 0.248758
\(621\) 1.46518 0.0587956
\(622\) 18.2918 0.733434
\(623\) −1.86575 −0.0747496
\(624\) 1.40534 0.0562585
\(625\) 24.0667 0.962668
\(626\) −15.7680 −0.630215
\(627\) 62.1830 2.48335
\(628\) −15.7736 −0.629434
\(629\) −28.6286 −1.14150
\(630\) −1.64723 −0.0656273
\(631\) −16.6968 −0.664688 −0.332344 0.943158i \(-0.607839\pi\)
−0.332344 + 0.943158i \(0.607839\pi\)
\(632\) −32.3301 −1.28602
\(633\) −44.5032 −1.76884
\(634\) −16.2178 −0.644092
\(635\) −1.81000 −0.0718278
\(636\) 40.4003 1.60198
\(637\) 0.778528 0.0308464
\(638\) −86.6284 −3.42965
\(639\) 38.1368 1.50867
\(640\) 4.90720 0.193974
\(641\) 26.5122 1.04717 0.523585 0.851973i \(-0.324594\pi\)
0.523585 + 0.851973i \(0.324594\pi\)
\(642\) −13.3783 −0.528000
\(643\) 39.4211 1.55462 0.777309 0.629119i \(-0.216584\pi\)
0.777309 + 0.629119i \(0.216584\pi\)
\(644\) −12.6073 −0.496797
\(645\) 1.28303 0.0505193
\(646\) −49.2818 −1.93897
\(647\) −34.4890 −1.35590 −0.677951 0.735107i \(-0.737132\pi\)
−0.677951 + 0.735107i \(0.737132\pi\)
\(648\) 30.7216 1.20686
\(649\) −11.7763 −0.462259
\(650\) 8.93044 0.350281
\(651\) 17.6215 0.690641
\(652\) 54.9601 2.15241
\(653\) 27.1351 1.06188 0.530939 0.847410i \(-0.321839\pi\)
0.530939 + 0.847410i \(0.321839\pi\)
\(654\) −5.89417 −0.230480
\(655\) 5.23408 0.204513
\(656\) 3.00225 0.117218
\(657\) 11.1413 0.434662
\(658\) 30.8161 1.20134
\(659\) 42.3125 1.64826 0.824131 0.566399i \(-0.191664\pi\)
0.824131 + 0.566399i \(0.191664\pi\)
\(660\) 8.03213 0.312650
\(661\) −25.9655 −1.00994 −0.504970 0.863137i \(-0.668497\pi\)
−0.504970 + 0.863137i \(0.668497\pi\)
\(662\) 42.7477 1.66144
\(663\) 6.06877 0.235691
\(664\) 56.7732 2.20323
\(665\) 1.64332 0.0637251
\(666\) 58.4704 2.26568
\(667\) −35.3437 −1.36851
\(668\) −21.7467 −0.841403
\(669\) −2.85894 −0.110533
\(670\) −5.37023 −0.207470
\(671\) 27.7018 1.06941
\(672\) 11.4918 0.443304
\(673\) −5.54953 −0.213919 −0.106959 0.994263i \(-0.534111\pi\)
−0.106959 + 0.994263i \(0.534111\pi\)
\(674\) −25.9612 −0.999988
\(675\) 1.94947 0.0750349
\(676\) −42.1061 −1.61947
\(677\) 38.3481 1.47384 0.736918 0.675982i \(-0.236280\pi\)
0.736918 + 0.675982i \(0.236280\pi\)
\(678\) 88.5868 3.40216
\(679\) 3.66925 0.140813
\(680\) −2.61822 −0.100404
\(681\) 1.02835 0.0394066
\(682\) −66.3431 −2.54041
\(683\) 41.5552 1.59007 0.795033 0.606566i \(-0.207454\pi\)
0.795033 + 0.606566i \(0.207454\pi\)
\(684\) 63.3550 2.42244
\(685\) −4.97763 −0.190185
\(686\) −2.32322 −0.0887008
\(687\) 41.4266 1.58052
\(688\) 1.58750 0.0605228
\(689\) 3.83215 0.145993
\(690\) 5.20624 0.198198
\(691\) 32.4489 1.23441 0.617207 0.786801i \(-0.288264\pi\)
0.617207 + 0.786801i \(0.288264\pi\)
\(692\) −52.1184 −1.98125
\(693\) 11.1055 0.421862
\(694\) 7.25873 0.275538
\(695\) −3.42249 −0.129822
\(696\) −74.6956 −2.83133
\(697\) 12.9649 0.491079
\(698\) −2.20319 −0.0833921
\(699\) −66.5033 −2.51539
\(700\) −16.7744 −0.634012
\(701\) 20.5210 0.775068 0.387534 0.921855i \(-0.373327\pi\)
0.387534 + 0.921855i \(0.373327\pi\)
\(702\) 0.714119 0.0269527
\(703\) −58.3314 −2.20001
\(704\) −49.1159 −1.85113
\(705\) −8.01012 −0.301679
\(706\) 64.1387 2.41389
\(707\) −7.99220 −0.300578
\(708\) −24.6877 −0.927822
\(709\) 25.5778 0.960593 0.480297 0.877106i \(-0.340529\pi\)
0.480297 + 0.877106i \(0.340529\pi\)
\(710\) −7.80749 −0.293010
\(711\) 28.2496 1.05944
\(712\) 6.05676 0.226987
\(713\) −27.0675 −1.01369
\(714\) −18.1099 −0.677745
\(715\) 0.761884 0.0284928
\(716\) 68.0186 2.54197
\(717\) −16.0155 −0.598111
\(718\) 15.6399 0.583676
\(719\) −19.9240 −0.743040 −0.371520 0.928425i \(-0.621163\pi\)
−0.371520 + 0.928425i \(0.621163\pi\)
\(720\) 0.529776 0.0197436
\(721\) −9.14245 −0.340483
\(722\) −56.2716 −2.09421
\(723\) 50.1875 1.86649
\(724\) 49.3996 1.83592
\(725\) −47.0259 −1.74650
\(726\) −24.2916 −0.901546
\(727\) 4.38569 0.162656 0.0813280 0.996687i \(-0.474084\pi\)
0.0813280 + 0.996687i \(0.474084\pi\)
\(728\) −2.52733 −0.0936692
\(729\) −23.9825 −0.888242
\(730\) −2.28087 −0.0844189
\(731\) 6.85541 0.253557
\(732\) 58.0739 2.14647
\(733\) −36.0771 −1.33254 −0.666270 0.745711i \(-0.732110\pi\)
−0.666270 + 0.745711i \(0.732110\pi\)
\(734\) −58.7865 −2.16985
\(735\) 0.603880 0.0222744
\(736\) −17.6519 −0.650658
\(737\) 36.2055 1.33365
\(738\) −26.4791 −0.974710
\(739\) −42.0234 −1.54585 −0.772927 0.634495i \(-0.781208\pi\)
−0.772927 + 0.634495i \(0.781208\pi\)
\(740\) −7.53463 −0.276979
\(741\) 12.3653 0.454249
\(742\) −11.4356 −0.419813
\(743\) −50.9812 −1.87032 −0.935160 0.354225i \(-0.884745\pi\)
−0.935160 + 0.354225i \(0.884745\pi\)
\(744\) −57.2045 −2.09722
\(745\) 2.98348 0.109306
\(746\) 13.7345 0.502854
\(747\) −49.6078 −1.81505
\(748\) 42.9168 1.56919
\(749\) 2.38360 0.0870948
\(750\) 13.9418 0.509081
\(751\) −26.6313 −0.971790 −0.485895 0.874017i \(-0.661506\pi\)
−0.485895 + 0.874017i \(0.661506\pi\)
\(752\) −9.91095 −0.361415
\(753\) −53.3499 −1.94418
\(754\) −17.2263 −0.627345
\(755\) 0.0198713 0.000723192 0
\(756\) −1.34136 −0.0487847
\(757\) 46.4929 1.68981 0.844907 0.534914i \(-0.179656\pi\)
0.844907 + 0.534914i \(0.179656\pi\)
\(758\) −8.22106 −0.298602
\(759\) −35.0999 −1.27405
\(760\) −5.33469 −0.193509
\(761\) −10.3478 −0.375106 −0.187553 0.982254i \(-0.560056\pi\)
−0.187553 + 0.982254i \(0.560056\pi\)
\(762\) 40.6421 1.47231
\(763\) 1.05016 0.0380182
\(764\) −27.6922 −1.00187
\(765\) 2.28777 0.0827145
\(766\) −53.5874 −1.93619
\(767\) −2.34174 −0.0845554
\(768\) −49.5708 −1.78873
\(769\) 41.4044 1.49308 0.746541 0.665340i \(-0.231713\pi\)
0.746541 + 0.665340i \(0.231713\pi\)
\(770\) −2.27355 −0.0819329
\(771\) −15.0780 −0.543021
\(772\) 55.7086 2.00500
\(773\) −22.4816 −0.808605 −0.404303 0.914625i \(-0.632486\pi\)
−0.404303 + 0.914625i \(0.632486\pi\)
\(774\) −14.0013 −0.503268
\(775\) −36.0141 −1.29366
\(776\) −11.9115 −0.427597
\(777\) −21.4354 −0.768991
\(778\) −19.3041 −0.692087
\(779\) 26.4162 0.946458
\(780\) 1.59721 0.0571893
\(781\) 52.6373 1.88351
\(782\) 27.8177 0.994758
\(783\) −3.76041 −0.134386
\(784\) 0.747183 0.0266851
\(785\) −1.16055 −0.0414218
\(786\) −117.527 −4.19205
\(787\) 9.60789 0.342484 0.171242 0.985229i \(-0.445222\pi\)
0.171242 + 0.985229i \(0.445222\pi\)
\(788\) 36.5483 1.30198
\(789\) −12.6817 −0.451481
\(790\) −5.78336 −0.205763
\(791\) −15.7834 −0.561193
\(792\) −36.0516 −1.28104
\(793\) 5.50857 0.195615
\(794\) −53.2763 −1.89071
\(795\) 2.97248 0.105423
\(796\) 89.4171 3.16931
\(797\) 35.9437 1.27319 0.636596 0.771198i \(-0.280342\pi\)
0.636596 + 0.771198i \(0.280342\pi\)
\(798\) −36.8993 −1.30622
\(799\) −42.7992 −1.51413
\(800\) −23.4864 −0.830370
\(801\) −5.29232 −0.186995
\(802\) 28.3801 1.00214
\(803\) 15.3774 0.542657
\(804\) 75.9011 2.67682
\(805\) −0.927589 −0.0326932
\(806\) −13.1925 −0.464687
\(807\) 31.6109 1.11276
\(808\) 25.9450 0.912743
\(809\) 7.44846 0.261874 0.130937 0.991391i \(-0.458201\pi\)
0.130937 + 0.991391i \(0.458201\pi\)
\(810\) 5.49561 0.193096
\(811\) −17.3304 −0.608552 −0.304276 0.952584i \(-0.598414\pi\)
−0.304276 + 0.952584i \(0.598414\pi\)
\(812\) 32.3568 1.13550
\(813\) 16.4487 0.576881
\(814\) 80.7022 2.82861
\(815\) 4.04373 0.141646
\(816\) 5.82442 0.203896
\(817\) 13.9681 0.488681
\(818\) −26.8371 −0.938336
\(819\) 2.20835 0.0771661
\(820\) 3.41216 0.119158
\(821\) −40.4372 −1.41127 −0.705634 0.708577i \(-0.749338\pi\)
−0.705634 + 0.708577i \(0.749338\pi\)
\(822\) 111.768 3.89837
\(823\) −10.8949 −0.379772 −0.189886 0.981806i \(-0.560812\pi\)
−0.189886 + 0.981806i \(0.560812\pi\)
\(824\) 29.6791 1.03392
\(825\) −46.7015 −1.62594
\(826\) 6.98802 0.243144
\(827\) −25.3817 −0.882608 −0.441304 0.897358i \(-0.645484\pi\)
−0.441304 + 0.897358i \(0.645484\pi\)
\(828\) −35.7615 −1.24280
\(829\) 14.4419 0.501587 0.250793 0.968041i \(-0.419309\pi\)
0.250793 + 0.968041i \(0.419309\pi\)
\(830\) 10.1559 0.352515
\(831\) 24.2613 0.841615
\(832\) −9.76684 −0.338604
\(833\) 3.22662 0.111796
\(834\) 76.8492 2.66107
\(835\) −1.60002 −0.0553711
\(836\) 87.4440 3.02431
\(837\) −2.87985 −0.0995423
\(838\) 71.5141 2.47042
\(839\) 36.7760 1.26965 0.634824 0.772657i \(-0.281073\pi\)
0.634824 + 0.772657i \(0.281073\pi\)
\(840\) −1.96037 −0.0676392
\(841\) 61.7102 2.12794
\(842\) −2.06934 −0.0713141
\(843\) −14.4640 −0.498167
\(844\) −62.5821 −2.15417
\(845\) −3.09798 −0.106574
\(846\) 87.4121 3.00529
\(847\) 4.32801 0.148712
\(848\) 3.67786 0.126298
\(849\) −2.01387 −0.0691157
\(850\) 37.0122 1.26951
\(851\) 32.9259 1.12868
\(852\) 110.349 3.78048
\(853\) 22.3193 0.764200 0.382100 0.924121i \(-0.375201\pi\)
0.382100 + 0.924121i \(0.375201\pi\)
\(854\) −16.4382 −0.562503
\(855\) 4.66138 0.159416
\(856\) −7.73786 −0.264475
\(857\) 34.9241 1.19298 0.596491 0.802619i \(-0.296561\pi\)
0.596491 + 0.802619i \(0.296561\pi\)
\(858\) −17.1075 −0.584039
\(859\) −18.2717 −0.623423 −0.311711 0.950177i \(-0.600902\pi\)
−0.311711 + 0.950177i \(0.600902\pi\)
\(860\) 1.80424 0.0615242
\(861\) 9.70732 0.330825
\(862\) 51.7541 1.76275
\(863\) −1.00000 −0.0340404
\(864\) −1.87808 −0.0638936
\(865\) −3.83465 −0.130382
\(866\) −9.30477 −0.316189
\(867\) −15.9183 −0.540612
\(868\) 24.7800 0.841088
\(869\) 38.9908 1.32267
\(870\) −13.3619 −0.453010
\(871\) 7.19956 0.243948
\(872\) −3.40912 −0.115447
\(873\) 10.4081 0.352261
\(874\) 56.6791 1.91720
\(875\) −2.48399 −0.0839741
\(876\) 32.2371 1.08919
\(877\) 45.5877 1.53939 0.769694 0.638413i \(-0.220409\pi\)
0.769694 + 0.638413i \(0.220409\pi\)
\(878\) 59.5613 2.01010
\(879\) −10.3749 −0.349936
\(880\) 0.731208 0.0246490
\(881\) −5.12342 −0.172612 −0.0863062 0.996269i \(-0.527506\pi\)
−0.0863062 + 0.996269i \(0.527506\pi\)
\(882\) −6.58997 −0.221896
\(883\) −9.79563 −0.329649 −0.164825 0.986323i \(-0.552706\pi\)
−0.164825 + 0.986323i \(0.552706\pi\)
\(884\) 8.53413 0.287034
\(885\) −1.81642 −0.0610581
\(886\) 8.64105 0.290302
\(887\) 34.6144 1.16224 0.581119 0.813819i \(-0.302615\pi\)
0.581119 + 0.813819i \(0.302615\pi\)
\(888\) 69.5856 2.33514
\(889\) −7.24116 −0.242861
\(890\) 1.08346 0.0363177
\(891\) −37.0508 −1.24125
\(892\) −4.02034 −0.134611
\(893\) −87.2044 −2.91818
\(894\) −66.9915 −2.24053
\(895\) 5.00451 0.167282
\(896\) 19.6319 0.655855
\(897\) −6.97971 −0.233046
\(898\) −51.8058 −1.72878
\(899\) 69.4691 2.31692
\(900\) −47.5817 −1.58606
\(901\) 15.8824 0.529118
\(902\) −36.5471 −1.21688
\(903\) 5.13293 0.170813
\(904\) 51.2376 1.70414
\(905\) 3.63461 0.120819
\(906\) −0.446194 −0.0148238
\(907\) −8.11052 −0.269305 −0.134653 0.990893i \(-0.542992\pi\)
−0.134653 + 0.990893i \(0.542992\pi\)
\(908\) 1.44611 0.0479909
\(909\) −22.6705 −0.751932
\(910\) −0.452101 −0.0149870
\(911\) −41.5161 −1.37549 −0.687746 0.725952i \(-0.741400\pi\)
−0.687746 + 0.725952i \(0.741400\pi\)
\(912\) 11.8674 0.392969
\(913\) −68.4697 −2.26602
\(914\) −4.53610 −0.150041
\(915\) 4.27282 0.141255
\(916\) 58.2556 1.92482
\(917\) 20.9396 0.691488
\(918\) 2.95967 0.0976836
\(919\) −9.47738 −0.312630 −0.156315 0.987707i \(-0.549961\pi\)
−0.156315 + 0.987707i \(0.549961\pi\)
\(920\) 3.01123 0.0992772
\(921\) −32.7946 −1.08062
\(922\) 14.4369 0.475453
\(923\) 10.4671 0.344528
\(924\) 32.1336 1.05712
\(925\) 43.8088 1.44043
\(926\) 6.83755 0.224696
\(927\) −25.9332 −0.851758
\(928\) 45.3039 1.48717
\(929\) 57.2899 1.87962 0.939810 0.341697i \(-0.111002\pi\)
0.939810 + 0.341697i \(0.111002\pi\)
\(930\) −10.2330 −0.335554
\(931\) 6.57430 0.215464
\(932\) −93.5194 −3.06333
\(933\) −19.0215 −0.622737
\(934\) 7.81877 0.255838
\(935\) 3.15763 0.103266
\(936\) −7.16896 −0.234325
\(937\) 36.7691 1.20119 0.600597 0.799552i \(-0.294930\pi\)
0.600597 + 0.799552i \(0.294930\pi\)
\(938\) −21.4843 −0.701487
\(939\) 16.3970 0.535097
\(940\) −11.2641 −0.367395
\(941\) 51.1660 1.66796 0.833982 0.551792i \(-0.186056\pi\)
0.833982 + 0.551792i \(0.186056\pi\)
\(942\) 26.0592 0.849054
\(943\) −14.9109 −0.485566
\(944\) −2.24746 −0.0731485
\(945\) −0.0986911 −0.00321042
\(946\) −19.3250 −0.628309
\(947\) 54.9177 1.78458 0.892292 0.451459i \(-0.149096\pi\)
0.892292 + 0.451459i \(0.149096\pi\)
\(948\) 81.7402 2.65480
\(949\) 3.05784 0.0992617
\(950\) 75.4133 2.44673
\(951\) 16.8648 0.546879
\(952\) −10.4745 −0.339482
\(953\) 29.9073 0.968792 0.484396 0.874849i \(-0.339039\pi\)
0.484396 + 0.874849i \(0.339039\pi\)
\(954\) −32.4378 −1.05021
\(955\) −2.03747 −0.0659311
\(956\) −22.5216 −0.728401
\(957\) 90.0844 2.91202
\(958\) −15.3816 −0.496957
\(959\) −19.9137 −0.643046
\(960\) −7.57582 −0.244509
\(961\) 22.2020 0.716192
\(962\) 16.0478 0.517403
\(963\) 6.76125 0.217878
\(964\) 70.5755 2.27308
\(965\) 4.09879 0.131945
\(966\) 20.8282 0.670137
\(967\) 48.2573 1.55185 0.775925 0.630825i \(-0.217284\pi\)
0.775925 + 0.630825i \(0.217284\pi\)
\(968\) −14.0500 −0.451584
\(969\) 51.2479 1.64632
\(970\) −2.13078 −0.0684152
\(971\) −21.8317 −0.700612 −0.350306 0.936635i \(-0.613922\pi\)
−0.350306 + 0.936635i \(0.613922\pi\)
\(972\) −73.6492 −2.36230
\(973\) −13.6921 −0.438949
\(974\) −25.1898 −0.807132
\(975\) −9.28672 −0.297413
\(976\) 5.28678 0.169226
\(977\) −50.8131 −1.62566 −0.812828 0.582504i \(-0.802073\pi\)
−0.812828 + 0.582504i \(0.802073\pi\)
\(978\) −90.7985 −2.90342
\(979\) −7.30459 −0.233456
\(980\) 0.849198 0.0271266
\(981\) 2.97884 0.0951072
\(982\) 33.1609 1.05821
\(983\) −62.2006 −1.98389 −0.991945 0.126668i \(-0.959572\pi\)
−0.991945 + 0.126668i \(0.959572\pi\)
\(984\) −31.5128 −1.00459
\(985\) 2.68906 0.0856807
\(986\) −71.3945 −2.27366
\(987\) −32.0455 −1.02002
\(988\) 17.3885 0.553201
\(989\) −7.88443 −0.250710
\(990\) −6.44908 −0.204965
\(991\) 22.4166 0.712088 0.356044 0.934469i \(-0.384125\pi\)
0.356044 + 0.934469i \(0.384125\pi\)
\(992\) 34.6954 1.10158
\(993\) −44.4532 −1.41068
\(994\) −31.2349 −0.990711
\(995\) 6.57892 0.208566
\(996\) −143.540 −4.54823
\(997\) 62.2275 1.97076 0.985382 0.170361i \(-0.0544935\pi\)
0.985382 + 0.170361i \(0.0544935\pi\)
\(998\) 61.3716 1.94268
\(999\) 3.50316 0.110835
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 \(a_p\))