Properties

Label 6041.2.a.f.1.17
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 1.17
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26422 q^{2}\) \(-1.83534 q^{3}\) \(+3.12671 q^{4}\) \(+1.84374 q^{5}\) \(+4.15563 q^{6}\) \(+1.00000 q^{7}\) \(-2.55113 q^{8}\) \(+0.368489 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.26422 q^{2}\) \(-1.83534 q^{3}\) \(+3.12671 q^{4}\) \(+1.84374 q^{5}\) \(+4.15563 q^{6}\) \(+1.00000 q^{7}\) \(-2.55113 q^{8}\) \(+0.368489 q^{9}\) \(-4.17465 q^{10}\) \(-4.09366 q^{11}\) \(-5.73860 q^{12}\) \(-3.93746 q^{13}\) \(-2.26422 q^{14}\) \(-3.38390 q^{15}\) \(-0.477091 q^{16}\) \(+6.99137 q^{17}\) \(-0.834343 q^{18}\) \(-4.65170 q^{19}\) \(+5.76486 q^{20}\) \(-1.83534 q^{21}\) \(+9.26896 q^{22}\) \(-0.636658 q^{23}\) \(+4.68221 q^{24}\) \(-1.60061 q^{25}\) \(+8.91530 q^{26}\) \(+4.82973 q^{27}\) \(+3.12671 q^{28}\) \(-9.22256 q^{29}\) \(+7.66192 q^{30}\) \(-3.51122 q^{31}\) \(+6.18250 q^{32}\) \(+7.51327 q^{33}\) \(-15.8300 q^{34}\) \(+1.84374 q^{35}\) \(+1.15216 q^{36}\) \(-6.93591 q^{37}\) \(+10.5325 q^{38}\) \(+7.22660 q^{39}\) \(-4.70363 q^{40}\) \(-10.3404 q^{41}\) \(+4.15563 q^{42}\) \(-8.46498 q^{43}\) \(-12.7997 q^{44}\) \(+0.679400 q^{45}\) \(+1.44154 q^{46}\) \(+4.09615 q^{47}\) \(+0.875626 q^{48}\) \(+1.00000 q^{49}\) \(+3.62415 q^{50}\) \(-12.8316 q^{51}\) \(-12.3113 q^{52}\) \(-13.4441 q^{53}\) \(-10.9356 q^{54}\) \(-7.54765 q^{55}\) \(-2.55113 q^{56}\) \(+8.53748 q^{57}\) \(+20.8820 q^{58}\) \(+3.54000 q^{59}\) \(-10.5805 q^{60}\) \(+3.99565 q^{61}\) \(+7.95018 q^{62}\) \(+0.368489 q^{63}\) \(-13.0444 q^{64}\) \(-7.25967 q^{65}\) \(-17.0117 q^{66}\) \(-10.1417 q^{67}\) \(+21.8600 q^{68}\) \(+1.16849 q^{69}\) \(-4.17465 q^{70}\) \(-5.36963 q^{71}\) \(-0.940065 q^{72}\) \(+11.3145 q^{73}\) \(+15.7045 q^{74}\) \(+2.93768 q^{75}\) \(-14.5445 q^{76}\) \(-4.09366 q^{77}\) \(-16.3626 q^{78}\) \(+14.1963 q^{79}\) \(-0.879632 q^{80}\) \(-9.96968 q^{81}\) \(+23.4131 q^{82}\) \(+17.4633 q^{83}\) \(-5.73860 q^{84}\) \(+12.8903 q^{85}\) \(+19.1666 q^{86}\) \(+16.9266 q^{87}\) \(+10.4435 q^{88}\) \(+6.71228 q^{89}\) \(-1.53831 q^{90}\) \(-3.93746 q^{91}\) \(-1.99065 q^{92}\) \(+6.44429 q^{93}\) \(-9.27460 q^{94}\) \(-8.57655 q^{95}\) \(-11.3470 q^{96}\) \(+15.8528 q^{97}\) \(-2.26422 q^{98}\) \(-1.50847 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26422 −1.60105 −0.800524 0.599300i \(-0.795446\pi\)
−0.800524 + 0.599300i \(0.795446\pi\)
\(3\) −1.83534 −1.05964 −0.529818 0.848111i \(-0.677740\pi\)
−0.529818 + 0.848111i \(0.677740\pi\)
\(4\) 3.12671 1.56336
\(5\) 1.84374 0.824547 0.412273 0.911060i \(-0.364735\pi\)
0.412273 + 0.911060i \(0.364735\pi\)
\(6\) 4.15563 1.69653
\(7\) 1.00000 0.377964
\(8\) −2.55113 −0.901961
\(9\) 0.368489 0.122830
\(10\) −4.17465 −1.32014
\(11\) −4.09366 −1.23428 −0.617142 0.786852i \(-0.711710\pi\)
−0.617142 + 0.786852i \(0.711710\pi\)
\(12\) −5.73860 −1.65659
\(13\) −3.93746 −1.09206 −0.546028 0.837767i \(-0.683861\pi\)
−0.546028 + 0.837767i \(0.683861\pi\)
\(14\) −2.26422 −0.605139
\(15\) −3.38390 −0.873720
\(16\) −0.477091 −0.119273
\(17\) 6.99137 1.69566 0.847829 0.530270i \(-0.177910\pi\)
0.847829 + 0.530270i \(0.177910\pi\)
\(18\) −0.834343 −0.196656
\(19\) −4.65170 −1.06717 −0.533587 0.845745i \(-0.679156\pi\)
−0.533587 + 0.845745i \(0.679156\pi\)
\(20\) 5.76486 1.28906
\(21\) −1.83534 −0.400505
\(22\) 9.26896 1.97615
\(23\) −0.636658 −0.132752 −0.0663762 0.997795i \(-0.521144\pi\)
−0.0663762 + 0.997795i \(0.521144\pi\)
\(24\) 4.68221 0.955751
\(25\) −1.60061 −0.320122
\(26\) 8.91530 1.74843
\(27\) 4.82973 0.929482
\(28\) 3.12671 0.590893
\(29\) −9.22256 −1.71259 −0.856293 0.516490i \(-0.827238\pi\)
−0.856293 + 0.516490i \(0.827238\pi\)
\(30\) 7.66192 1.39887
\(31\) −3.51122 −0.630633 −0.315317 0.948987i \(-0.602111\pi\)
−0.315317 + 0.948987i \(0.602111\pi\)
\(32\) 6.18250 1.09292
\(33\) 7.51327 1.30789
\(34\) −15.8300 −2.71483
\(35\) 1.84374 0.311649
\(36\) 1.15216 0.192027
\(37\) −6.93591 −1.14026 −0.570129 0.821556i \(-0.693107\pi\)
−0.570129 + 0.821556i \(0.693107\pi\)
\(38\) 10.5325 1.70860
\(39\) 7.22660 1.15718
\(40\) −4.70363 −0.743709
\(41\) −10.3404 −1.61490 −0.807452 0.589933i \(-0.799154\pi\)
−0.807452 + 0.589933i \(0.799154\pi\)
\(42\) 4.15563 0.641228
\(43\) −8.46498 −1.29090 −0.645449 0.763804i \(-0.723330\pi\)
−0.645449 + 0.763804i \(0.723330\pi\)
\(44\) −12.7997 −1.92963
\(45\) 0.679400 0.101279
\(46\) 1.44154 0.212543
\(47\) 4.09615 0.597485 0.298742 0.954334i \(-0.403433\pi\)
0.298742 + 0.954334i \(0.403433\pi\)
\(48\) 0.875626 0.126386
\(49\) 1.00000 0.142857
\(50\) 3.62415 0.512532
\(51\) −12.8316 −1.79678
\(52\) −12.3113 −1.70727
\(53\) −13.4441 −1.84670 −0.923348 0.383965i \(-0.874558\pi\)
−0.923348 + 0.383965i \(0.874558\pi\)
\(54\) −10.9356 −1.48815
\(55\) −7.54765 −1.01773
\(56\) −2.55113 −0.340909
\(57\) 8.53748 1.13082
\(58\) 20.8820 2.74193
\(59\) 3.54000 0.460869 0.230434 0.973088i \(-0.425985\pi\)
0.230434 + 0.973088i \(0.425985\pi\)
\(60\) −10.5805 −1.36594
\(61\) 3.99565 0.511590 0.255795 0.966731i \(-0.417663\pi\)
0.255795 + 0.966731i \(0.417663\pi\)
\(62\) 7.95018 1.00967
\(63\) 0.368489 0.0464253
\(64\) −13.0444 −1.63055
\(65\) −7.25967 −0.900451
\(66\) −17.0117 −2.09400
\(67\) −10.1417 −1.23901 −0.619503 0.784994i \(-0.712666\pi\)
−0.619503 + 0.784994i \(0.712666\pi\)
\(68\) 21.8600 2.65092
\(69\) 1.16849 0.140669
\(70\) −4.17465 −0.498966
\(71\) −5.36963 −0.637258 −0.318629 0.947879i \(-0.603222\pi\)
−0.318629 + 0.947879i \(0.603222\pi\)
\(72\) −0.940065 −0.110788
\(73\) 11.3145 1.32426 0.662129 0.749390i \(-0.269653\pi\)
0.662129 + 0.749390i \(0.269653\pi\)
\(74\) 15.7045 1.82561
\(75\) 2.93768 0.339213
\(76\) −14.5445 −1.66837
\(77\) −4.09366 −0.466516
\(78\) −16.3626 −1.85271
\(79\) 14.1963 1.59721 0.798606 0.601854i \(-0.205571\pi\)
0.798606 + 0.601854i \(0.205571\pi\)
\(80\) −0.879632 −0.0983459
\(81\) −9.96968 −1.10774
\(82\) 23.4131 2.58554
\(83\) 17.4633 1.91685 0.958425 0.285345i \(-0.0921081\pi\)
0.958425 + 0.285345i \(0.0921081\pi\)
\(84\) −5.73860 −0.626132
\(85\) 12.8903 1.39815
\(86\) 19.1666 2.06679
\(87\) 16.9266 1.81472
\(88\) 10.4435 1.11328
\(89\) 6.71228 0.711500 0.355750 0.934581i \(-0.384225\pi\)
0.355750 + 0.934581i \(0.384225\pi\)
\(90\) −1.53831 −0.162152
\(91\) −3.93746 −0.412758
\(92\) −1.99065 −0.207539
\(93\) 6.44429 0.668242
\(94\) −9.27460 −0.956602
\(95\) −8.57655 −0.879935
\(96\) −11.3470 −1.15810
\(97\) 15.8528 1.60961 0.804806 0.593537i \(-0.202269\pi\)
0.804806 + 0.593537i \(0.202269\pi\)
\(98\) −2.26422 −0.228721
\(99\) −1.50847 −0.151607
\(100\) −5.00466 −0.500466
\(101\) 4.57731 0.455459 0.227730 0.973724i \(-0.426870\pi\)
0.227730 + 0.973724i \(0.426870\pi\)
\(102\) 29.0536 2.87673
\(103\) −17.7433 −1.74830 −0.874152 0.485653i \(-0.838582\pi\)
−0.874152 + 0.485653i \(0.838582\pi\)
\(104\) 10.0450 0.984992
\(105\) −3.38390 −0.330235
\(106\) 30.4406 2.95665
\(107\) −8.27987 −0.800445 −0.400223 0.916418i \(-0.631067\pi\)
−0.400223 + 0.916418i \(0.631067\pi\)
\(108\) 15.1012 1.45311
\(109\) −3.53671 −0.338755 −0.169378 0.985551i \(-0.554176\pi\)
−0.169378 + 0.985551i \(0.554176\pi\)
\(110\) 17.0896 1.62943
\(111\) 12.7298 1.20826
\(112\) −0.477091 −0.0450808
\(113\) 13.2572 1.24713 0.623567 0.781770i \(-0.285683\pi\)
0.623567 + 0.781770i \(0.285683\pi\)
\(114\) −19.3308 −1.81049
\(115\) −1.17383 −0.109461
\(116\) −28.8363 −2.67738
\(117\) −1.45091 −0.134137
\(118\) −8.01535 −0.737873
\(119\) 6.99137 0.640898
\(120\) 8.63278 0.788062
\(121\) 5.75803 0.523458
\(122\) −9.04704 −0.819081
\(123\) 18.9783 1.71121
\(124\) −10.9786 −0.985905
\(125\) −12.1698 −1.08850
\(126\) −0.834343 −0.0743291
\(127\) 12.6340 1.12109 0.560544 0.828125i \(-0.310592\pi\)
0.560544 + 0.828125i \(0.310592\pi\)
\(128\) 17.1704 1.51767
\(129\) 15.5362 1.36788
\(130\) 16.4375 1.44167
\(131\) 5.20058 0.454377 0.227188 0.973851i \(-0.427047\pi\)
0.227188 + 0.973851i \(0.427047\pi\)
\(132\) 23.4918 2.04470
\(133\) −4.65170 −0.403354
\(134\) 22.9631 1.98371
\(135\) 8.90478 0.766401
\(136\) −17.8359 −1.52942
\(137\) −20.8710 −1.78313 −0.891564 0.452895i \(-0.850391\pi\)
−0.891564 + 0.452895i \(0.850391\pi\)
\(138\) −2.64572 −0.225218
\(139\) 23.4092 1.98554 0.992771 0.120024i \(-0.0382973\pi\)
0.992771 + 0.120024i \(0.0382973\pi\)
\(140\) 5.76486 0.487219
\(141\) −7.51784 −0.633117
\(142\) 12.1581 1.02028
\(143\) 16.1186 1.34791
\(144\) −0.175803 −0.0146502
\(145\) −17.0040 −1.41211
\(146\) −25.6185 −2.12020
\(147\) −1.83534 −0.151377
\(148\) −21.6866 −1.78263
\(149\) −6.17957 −0.506250 −0.253125 0.967434i \(-0.581458\pi\)
−0.253125 + 0.967434i \(0.581458\pi\)
\(150\) −6.65156 −0.543097
\(151\) 5.01492 0.408108 0.204054 0.978960i \(-0.434588\pi\)
0.204054 + 0.978960i \(0.434588\pi\)
\(152\) 11.8671 0.962550
\(153\) 2.57625 0.208277
\(154\) 9.26896 0.746914
\(155\) −6.47378 −0.519987
\(156\) 22.5955 1.80909
\(157\) −17.9981 −1.43641 −0.718204 0.695833i \(-0.755035\pi\)
−0.718204 + 0.695833i \(0.755035\pi\)
\(158\) −32.1437 −2.55721
\(159\) 24.6746 1.95683
\(160\) 11.3989 0.901166
\(161\) −0.636658 −0.0501757
\(162\) 22.5736 1.77355
\(163\) 23.5559 1.84504 0.922521 0.385946i \(-0.126125\pi\)
0.922521 + 0.385946i \(0.126125\pi\)
\(164\) −32.3316 −2.52467
\(165\) 13.8525 1.07842
\(166\) −39.5409 −3.06897
\(167\) −0.0505672 −0.00391301 −0.00195650 0.999998i \(-0.500623\pi\)
−0.00195650 + 0.999998i \(0.500623\pi\)
\(168\) 4.68221 0.361240
\(169\) 2.50362 0.192586
\(170\) −29.1865 −2.23850
\(171\) −1.71410 −0.131081
\(172\) −26.4676 −2.01813
\(173\) −18.4878 −1.40560 −0.702800 0.711387i \(-0.748067\pi\)
−0.702800 + 0.711387i \(0.748067\pi\)
\(174\) −38.3256 −2.90545
\(175\) −1.60061 −0.120995
\(176\) 1.95305 0.147216
\(177\) −6.49712 −0.488353
\(178\) −15.1981 −1.13915
\(179\) −13.6924 −1.02341 −0.511707 0.859160i \(-0.670987\pi\)
−0.511707 + 0.859160i \(0.670987\pi\)
\(180\) 2.12429 0.158335
\(181\) 1.42027 0.105568 0.0527839 0.998606i \(-0.483191\pi\)
0.0527839 + 0.998606i \(0.483191\pi\)
\(182\) 8.91530 0.660846
\(183\) −7.33339 −0.542100
\(184\) 1.62420 0.119738
\(185\) −12.7880 −0.940195
\(186\) −14.5913 −1.06989
\(187\) −28.6203 −2.09292
\(188\) 12.8075 0.934082
\(189\) 4.82973 0.351311
\(190\) 19.4192 1.40882
\(191\) 5.68236 0.411161 0.205580 0.978640i \(-0.434092\pi\)
0.205580 + 0.978640i \(0.434092\pi\)
\(192\) 23.9410 1.72779
\(193\) −14.2845 −1.02822 −0.514109 0.857725i \(-0.671877\pi\)
−0.514109 + 0.857725i \(0.671877\pi\)
\(194\) −35.8944 −2.57707
\(195\) 13.3240 0.954151
\(196\) 3.12671 0.223337
\(197\) 21.1914 1.50982 0.754911 0.655827i \(-0.227680\pi\)
0.754911 + 0.655827i \(0.227680\pi\)
\(198\) 3.41551 0.242730
\(199\) 12.6626 0.897628 0.448814 0.893625i \(-0.351846\pi\)
0.448814 + 0.893625i \(0.351846\pi\)
\(200\) 4.08337 0.288738
\(201\) 18.6135 1.31290
\(202\) −10.3641 −0.729212
\(203\) −9.22256 −0.647297
\(204\) −40.1207 −2.80901
\(205\) −19.0651 −1.33156
\(206\) 40.1749 2.79912
\(207\) −0.234602 −0.0163059
\(208\) 1.87853 0.130252
\(209\) 19.0425 1.31720
\(210\) 7.66192 0.528723
\(211\) −0.894265 −0.0615637 −0.0307819 0.999526i \(-0.509800\pi\)
−0.0307819 + 0.999526i \(0.509800\pi\)
\(212\) −42.0360 −2.88704
\(213\) 9.85513 0.675262
\(214\) 18.7475 1.28155
\(215\) −15.6072 −1.06441
\(216\) −12.3213 −0.838357
\(217\) −3.51122 −0.238357
\(218\) 8.00790 0.542363
\(219\) −20.7659 −1.40323
\(220\) −23.5993 −1.59107
\(221\) −27.5283 −1.85175
\(222\) −28.8231 −1.93448
\(223\) 15.1715 1.01596 0.507979 0.861369i \(-0.330393\pi\)
0.507979 + 0.861369i \(0.330393\pi\)
\(224\) 6.18250 0.413086
\(225\) −0.589809 −0.0393206
\(226\) −30.0173 −1.99672
\(227\) −13.1612 −0.873540 −0.436770 0.899573i \(-0.643878\pi\)
−0.436770 + 0.899573i \(0.643878\pi\)
\(228\) 26.6943 1.76787
\(229\) 9.33629 0.616959 0.308480 0.951231i \(-0.400180\pi\)
0.308480 + 0.951231i \(0.400180\pi\)
\(230\) 2.65782 0.175252
\(231\) 7.51327 0.494337
\(232\) 23.5280 1.54469
\(233\) 1.15611 0.0757396 0.0378698 0.999283i \(-0.487943\pi\)
0.0378698 + 0.999283i \(0.487943\pi\)
\(234\) 3.28519 0.214760
\(235\) 7.55224 0.492654
\(236\) 11.0686 0.720502
\(237\) −26.0552 −1.69246
\(238\) −15.8300 −1.02611
\(239\) 0.350693 0.0226844 0.0113422 0.999936i \(-0.496390\pi\)
0.0113422 + 0.999936i \(0.496390\pi\)
\(240\) 1.61443 0.104211
\(241\) 12.8468 0.827532 0.413766 0.910383i \(-0.364213\pi\)
0.413766 + 0.910383i \(0.364213\pi\)
\(242\) −13.0375 −0.838081
\(243\) 3.80862 0.244323
\(244\) 12.4932 0.799798
\(245\) 1.84374 0.117792
\(246\) −42.9711 −2.73973
\(247\) 18.3159 1.16541
\(248\) 8.95758 0.568807
\(249\) −32.0512 −2.03116
\(250\) 27.5552 1.74275
\(251\) −15.5657 −0.982497 −0.491249 0.871019i \(-0.663459\pi\)
−0.491249 + 0.871019i \(0.663459\pi\)
\(252\) 1.15216 0.0725793
\(253\) 2.60626 0.163854
\(254\) −28.6062 −1.79492
\(255\) −23.6581 −1.48153
\(256\) −12.7889 −0.799308
\(257\) −5.03255 −0.313922 −0.156961 0.987605i \(-0.550170\pi\)
−0.156961 + 0.987605i \(0.550170\pi\)
\(258\) −35.1773 −2.19005
\(259\) −6.93591 −0.430977
\(260\) −22.6989 −1.40773
\(261\) −3.39842 −0.210357
\(262\) −11.7753 −0.727479
\(263\) 10.7445 0.662532 0.331266 0.943537i \(-0.392524\pi\)
0.331266 + 0.943537i \(0.392524\pi\)
\(264\) −19.1673 −1.17967
\(265\) −24.7875 −1.52269
\(266\) 10.5325 0.645789
\(267\) −12.3193 −0.753932
\(268\) −31.7102 −1.93701
\(269\) −2.24346 −0.136786 −0.0683932 0.997658i \(-0.521787\pi\)
−0.0683932 + 0.997658i \(0.521787\pi\)
\(270\) −20.1624 −1.22705
\(271\) 13.9892 0.849780 0.424890 0.905245i \(-0.360313\pi\)
0.424890 + 0.905245i \(0.360313\pi\)
\(272\) −3.33552 −0.202246
\(273\) 7.22660 0.437374
\(274\) 47.2566 2.85487
\(275\) 6.55236 0.395122
\(276\) 3.65352 0.219916
\(277\) −13.5539 −0.814376 −0.407188 0.913344i \(-0.633491\pi\)
−0.407188 + 0.913344i \(0.633491\pi\)
\(278\) −53.0037 −3.17895
\(279\) −1.29385 −0.0774605
\(280\) −4.70363 −0.281096
\(281\) 2.27941 0.135978 0.0679892 0.997686i \(-0.478342\pi\)
0.0679892 + 0.997686i \(0.478342\pi\)
\(282\) 17.0221 1.01365
\(283\) 8.42115 0.500585 0.250293 0.968170i \(-0.419473\pi\)
0.250293 + 0.968170i \(0.419473\pi\)
\(284\) −16.7893 −0.996262
\(285\) 15.7409 0.932412
\(286\) −36.4962 −2.15807
\(287\) −10.3404 −0.610377
\(288\) 2.27819 0.134243
\(289\) 31.8793 1.87525
\(290\) 38.5010 2.26085
\(291\) −29.0954 −1.70560
\(292\) 35.3771 2.07029
\(293\) 2.29106 0.133845 0.0669227 0.997758i \(-0.478682\pi\)
0.0669227 + 0.997758i \(0.478682\pi\)
\(294\) 4.15563 0.242361
\(295\) 6.52685 0.380008
\(296\) 17.6944 1.02847
\(297\) −19.7713 −1.14724
\(298\) 13.9919 0.810531
\(299\) 2.50682 0.144973
\(300\) 9.18527 0.530312
\(301\) −8.46498 −0.487913
\(302\) −11.3549 −0.653401
\(303\) −8.40094 −0.482621
\(304\) 2.21928 0.127285
\(305\) 7.36695 0.421830
\(306\) −5.83320 −0.333462
\(307\) −14.4987 −0.827483 −0.413742 0.910394i \(-0.635778\pi\)
−0.413742 + 0.910394i \(0.635778\pi\)
\(308\) −12.7997 −0.729330
\(309\) 32.5651 1.85257
\(310\) 14.6581 0.832524
\(311\) −0.600926 −0.0340754 −0.0170377 0.999855i \(-0.505424\pi\)
−0.0170377 + 0.999855i \(0.505424\pi\)
\(312\) −18.4360 −1.04373
\(313\) −12.3762 −0.699545 −0.349772 0.936835i \(-0.613741\pi\)
−0.349772 + 0.936835i \(0.613741\pi\)
\(314\) 40.7518 2.29976
\(315\) 0.679400 0.0382798
\(316\) 44.3879 2.49701
\(317\) −5.25535 −0.295170 −0.147585 0.989049i \(-0.547150\pi\)
−0.147585 + 0.989049i \(0.547150\pi\)
\(318\) −55.8689 −3.13297
\(319\) 37.7540 2.11382
\(320\) −24.0505 −1.34446
\(321\) 15.1964 0.848181
\(322\) 1.44154 0.0803337
\(323\) −32.5218 −1.80956
\(324\) −31.1723 −1.73180
\(325\) 6.30235 0.349592
\(326\) −53.3359 −2.95400
\(327\) 6.49107 0.358957
\(328\) 26.3798 1.45658
\(329\) 4.09615 0.225828
\(330\) −31.3653 −1.72660
\(331\) 1.45232 0.0798267 0.0399133 0.999203i \(-0.487292\pi\)
0.0399133 + 0.999203i \(0.487292\pi\)
\(332\) 54.6028 2.99672
\(333\) −2.55581 −0.140058
\(334\) 0.114496 0.00626492
\(335\) −18.6987 −1.02162
\(336\) 0.875626 0.0477693
\(337\) −16.7030 −0.909870 −0.454935 0.890525i \(-0.650337\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(338\) −5.66875 −0.308340
\(339\) −24.3316 −1.32151
\(340\) 40.3043 2.18581
\(341\) 14.3737 0.778381
\(342\) 3.88112 0.209867
\(343\) 1.00000 0.0539949
\(344\) 21.5953 1.16434
\(345\) 2.15439 0.115988
\(346\) 41.8605 2.25043
\(347\) −33.5259 −1.79977 −0.899883 0.436132i \(-0.856348\pi\)
−0.899883 + 0.436132i \(0.856348\pi\)
\(348\) 52.9246 2.83705
\(349\) −1.70421 −0.0912242 −0.0456121 0.998959i \(-0.514524\pi\)
−0.0456121 + 0.998959i \(0.514524\pi\)
\(350\) 3.62415 0.193719
\(351\) −19.0169 −1.01505
\(352\) −25.3091 −1.34898
\(353\) 21.0054 1.11800 0.559001 0.829167i \(-0.311185\pi\)
0.559001 + 0.829167i \(0.311185\pi\)
\(354\) 14.7109 0.781877
\(355\) −9.90022 −0.525449
\(356\) 20.9874 1.11233
\(357\) −12.8316 −0.679119
\(358\) 31.0026 1.63854
\(359\) −10.7416 −0.566919 −0.283460 0.958984i \(-0.591482\pi\)
−0.283460 + 0.958984i \(0.591482\pi\)
\(360\) −1.73324 −0.0913497
\(361\) 2.63836 0.138861
\(362\) −3.21581 −0.169019
\(363\) −10.5680 −0.554675
\(364\) −12.3113 −0.645288
\(365\) 20.8610 1.09191
\(366\) 16.6044 0.867928
\(367\) −36.0310 −1.88080 −0.940401 0.340068i \(-0.889550\pi\)
−0.940401 + 0.340068i \(0.889550\pi\)
\(368\) 0.303744 0.0158337
\(369\) −3.81034 −0.198358
\(370\) 28.9550 1.50530
\(371\) −13.4441 −0.697985
\(372\) 20.1495 1.04470
\(373\) 15.2208 0.788102 0.394051 0.919089i \(-0.371073\pi\)
0.394051 + 0.919089i \(0.371073\pi\)
\(374\) 64.8028 3.35087
\(375\) 22.3358 1.15342
\(376\) −10.4498 −0.538908
\(377\) 36.3135 1.87024
\(378\) −10.9356 −0.562466
\(379\) 35.9547 1.84687 0.923434 0.383758i \(-0.125370\pi\)
0.923434 + 0.383758i \(0.125370\pi\)
\(380\) −26.8164 −1.37565
\(381\) −23.1878 −1.18795
\(382\) −12.8661 −0.658288
\(383\) 2.03383 0.103924 0.0519620 0.998649i \(-0.483453\pi\)
0.0519620 + 0.998649i \(0.483453\pi\)
\(384\) −31.5137 −1.60818
\(385\) −7.54765 −0.384664
\(386\) 32.3432 1.64623
\(387\) −3.11926 −0.158561
\(388\) 49.5673 2.51640
\(389\) 7.72004 0.391422 0.195711 0.980662i \(-0.437299\pi\)
0.195711 + 0.980662i \(0.437299\pi\)
\(390\) −30.1685 −1.52764
\(391\) −4.45111 −0.225103
\(392\) −2.55113 −0.128852
\(393\) −9.54485 −0.481474
\(394\) −47.9820 −2.41730
\(395\) 26.1744 1.31698
\(396\) −4.71655 −0.237016
\(397\) 8.69939 0.436610 0.218305 0.975881i \(-0.429947\pi\)
0.218305 + 0.975881i \(0.429947\pi\)
\(398\) −28.6710 −1.43715
\(399\) 8.53748 0.427409
\(400\) 0.763637 0.0381819
\(401\) −24.9235 −1.24462 −0.622311 0.782770i \(-0.713806\pi\)
−0.622311 + 0.782770i \(0.713806\pi\)
\(402\) −42.1452 −2.10201
\(403\) 13.8253 0.688687
\(404\) 14.3119 0.712045
\(405\) −18.3815 −0.913386
\(406\) 20.8820 1.03635
\(407\) 28.3933 1.40740
\(408\) 32.7351 1.62063
\(409\) 22.9581 1.13521 0.567603 0.823302i \(-0.307871\pi\)
0.567603 + 0.823302i \(0.307871\pi\)
\(410\) 43.1677 2.13190
\(411\) 38.3054 1.88947
\(412\) −55.4783 −2.73322
\(413\) 3.54000 0.174192
\(414\) 0.531191 0.0261066
\(415\) 32.1979 1.58053
\(416\) −24.3434 −1.19353
\(417\) −42.9639 −2.10395
\(418\) −43.1165 −2.10890
\(419\) 37.0080 1.80796 0.903979 0.427577i \(-0.140633\pi\)
0.903979 + 0.427577i \(0.140633\pi\)
\(420\) −10.5805 −0.516275
\(421\) 21.0392 1.02539 0.512695 0.858571i \(-0.328647\pi\)
0.512695 + 0.858571i \(0.328647\pi\)
\(422\) 2.02482 0.0985665
\(423\) 1.50939 0.0733889
\(424\) 34.2978 1.66565
\(425\) −11.1905 −0.542818
\(426\) −22.3142 −1.08113
\(427\) 3.99565 0.193363
\(428\) −25.8888 −1.25138
\(429\) −29.5832 −1.42829
\(430\) 35.3383 1.70416
\(431\) 12.1906 0.587200 0.293600 0.955928i \(-0.405147\pi\)
0.293600 + 0.955928i \(0.405147\pi\)
\(432\) −2.30422 −0.110862
\(433\) −1.29556 −0.0622606 −0.0311303 0.999515i \(-0.509911\pi\)
−0.0311303 + 0.999515i \(0.509911\pi\)
\(434\) 7.95018 0.381621
\(435\) 31.2083 1.49632
\(436\) −11.0583 −0.529595
\(437\) 2.96155 0.141670
\(438\) 47.0188 2.24664
\(439\) 6.15175 0.293607 0.146803 0.989166i \(-0.453102\pi\)
0.146803 + 0.989166i \(0.453102\pi\)
\(440\) 19.2551 0.917949
\(441\) 0.368489 0.0175471
\(442\) 62.3302 2.96475
\(443\) 5.27310 0.250532 0.125266 0.992123i \(-0.460021\pi\)
0.125266 + 0.992123i \(0.460021\pi\)
\(444\) 39.8024 1.88894
\(445\) 12.3757 0.586665
\(446\) −34.3517 −1.62660
\(447\) 11.3416 0.536441
\(448\) −13.0444 −0.616290
\(449\) −17.7339 −0.836917 −0.418458 0.908236i \(-0.637429\pi\)
−0.418458 + 0.908236i \(0.637429\pi\)
\(450\) 1.33546 0.0629541
\(451\) 42.3302 1.99325
\(452\) 41.4515 1.94971
\(453\) −9.20410 −0.432446
\(454\) 29.7999 1.39858
\(455\) −7.25967 −0.340339
\(456\) −21.7802 −1.01995
\(457\) 25.7157 1.20293 0.601465 0.798899i \(-0.294584\pi\)
0.601465 + 0.798899i \(0.294584\pi\)
\(458\) −21.1395 −0.987782
\(459\) 33.7664 1.57608
\(460\) −3.67024 −0.171126
\(461\) −28.9624 −1.34891 −0.674456 0.738315i \(-0.735622\pi\)
−0.674456 + 0.738315i \(0.735622\pi\)
\(462\) −17.0117 −0.791458
\(463\) 39.9602 1.85711 0.928555 0.371195i \(-0.121052\pi\)
0.928555 + 0.371195i \(0.121052\pi\)
\(464\) 4.40000 0.204265
\(465\) 11.8816 0.550997
\(466\) −2.61770 −0.121263
\(467\) 22.5022 1.04128 0.520638 0.853777i \(-0.325694\pi\)
0.520638 + 0.853777i \(0.325694\pi\)
\(468\) −4.53659 −0.209704
\(469\) −10.1417 −0.468300
\(470\) −17.1000 −0.788763
\(471\) 33.0328 1.52207
\(472\) −9.03100 −0.415686
\(473\) 34.6527 1.59333
\(474\) 58.9947 2.70972
\(475\) 7.44558 0.341626
\(476\) 21.8600 1.00195
\(477\) −4.95402 −0.226829
\(478\) −0.794048 −0.0363189
\(479\) −6.24138 −0.285176 −0.142588 0.989782i \(-0.545542\pi\)
−0.142588 + 0.989782i \(0.545542\pi\)
\(480\) −20.9210 −0.954908
\(481\) 27.3099 1.24522
\(482\) −29.0879 −1.32492
\(483\) 1.16849 0.0531680
\(484\) 18.0037 0.818351
\(485\) 29.2286 1.32720
\(486\) −8.62357 −0.391173
\(487\) −31.0674 −1.40780 −0.703900 0.710299i \(-0.748560\pi\)
−0.703900 + 0.710299i \(0.748560\pi\)
\(488\) −10.1934 −0.461435
\(489\) −43.2332 −1.95507
\(490\) −4.17465 −0.188591
\(491\) −31.7564 −1.43315 −0.716574 0.697511i \(-0.754291\pi\)
−0.716574 + 0.697511i \(0.754291\pi\)
\(492\) 59.3396 2.67524
\(493\) −64.4784 −2.90396
\(494\) −41.4714 −1.86588
\(495\) −2.78123 −0.125007
\(496\) 1.67517 0.0752173
\(497\) −5.36963 −0.240861
\(498\) 72.5712 3.25199
\(499\) −18.0042 −0.805977 −0.402988 0.915205i \(-0.632029\pi\)
−0.402988 + 0.915205i \(0.632029\pi\)
\(500\) −38.0516 −1.70172
\(501\) 0.0928082 0.00414637
\(502\) 35.2442 1.57303
\(503\) 7.97197 0.355452 0.177726 0.984080i \(-0.443126\pi\)
0.177726 + 0.984080i \(0.443126\pi\)
\(504\) −0.940065 −0.0418738
\(505\) 8.43938 0.375547
\(506\) −5.90116 −0.262338
\(507\) −4.59500 −0.204071
\(508\) 39.5029 1.75266
\(509\) 26.9104 1.19278 0.596391 0.802694i \(-0.296601\pi\)
0.596391 + 0.802694i \(0.296601\pi\)
\(510\) 53.5673 2.37200
\(511\) 11.3145 0.500523
\(512\) −5.38386 −0.237935
\(513\) −22.4665 −0.991919
\(514\) 11.3948 0.502604
\(515\) −32.7142 −1.44156
\(516\) 48.5771 2.13849
\(517\) −16.7682 −0.737466
\(518\) 15.7045 0.690015
\(519\) 33.9315 1.48943
\(520\) 18.5204 0.812172
\(521\) −22.2290 −0.973869 −0.486934 0.873439i \(-0.661885\pi\)
−0.486934 + 0.873439i \(0.661885\pi\)
\(522\) 7.69478 0.336791
\(523\) 8.13677 0.355796 0.177898 0.984049i \(-0.443070\pi\)
0.177898 + 0.984049i \(0.443070\pi\)
\(524\) 16.2607 0.710353
\(525\) 2.93768 0.128211
\(526\) −24.3279 −1.06075
\(527\) −24.5482 −1.06934
\(528\) −3.58451 −0.155996
\(529\) −22.5947 −0.982377
\(530\) 56.1246 2.43790
\(531\) 1.30445 0.0566084
\(532\) −14.5445 −0.630586
\(533\) 40.7151 1.76357
\(534\) 27.8938 1.20708
\(535\) −15.2660 −0.660005
\(536\) 25.8728 1.11754
\(537\) 25.1302 1.08445
\(538\) 5.07970 0.219002
\(539\) −4.09366 −0.176326
\(540\) 27.8427 1.19816
\(541\) −14.1295 −0.607476 −0.303738 0.952756i \(-0.598235\pi\)
−0.303738 + 0.952756i \(0.598235\pi\)
\(542\) −31.6746 −1.36054
\(543\) −2.60668 −0.111864
\(544\) 43.2242 1.85322
\(545\) −6.52078 −0.279319
\(546\) −16.3626 −0.700257
\(547\) 27.6916 1.18401 0.592005 0.805935i \(-0.298337\pi\)
0.592005 + 0.805935i \(0.298337\pi\)
\(548\) −65.2575 −2.78766
\(549\) 1.47235 0.0628385
\(550\) −14.8360 −0.632610
\(551\) 42.9006 1.82763
\(552\) −2.98096 −0.126878
\(553\) 14.1963 0.603689
\(554\) 30.6891 1.30386
\(555\) 23.4705 0.996265
\(556\) 73.1938 3.10411
\(557\) 2.82031 0.119500 0.0597502 0.998213i \(-0.480970\pi\)
0.0597502 + 0.998213i \(0.480970\pi\)
\(558\) 2.92956 0.124018
\(559\) 33.3306 1.40973
\(560\) −0.879632 −0.0371713
\(561\) 52.5281 2.21774
\(562\) −5.16110 −0.217708
\(563\) 5.66128 0.238595 0.119297 0.992859i \(-0.461936\pi\)
0.119297 + 0.992859i \(0.461936\pi\)
\(564\) −23.5061 −0.989787
\(565\) 24.4429 1.02832
\(566\) −19.0674 −0.801461
\(567\) −9.96968 −0.418687
\(568\) 13.6986 0.574782
\(569\) −28.7445 −1.20503 −0.602516 0.798107i \(-0.705835\pi\)
−0.602516 + 0.798107i \(0.705835\pi\)
\(570\) −35.6410 −1.49284
\(571\) −20.8234 −0.871432 −0.435716 0.900084i \(-0.643505\pi\)
−0.435716 + 0.900084i \(0.643505\pi\)
\(572\) 50.3983 2.10726
\(573\) −10.4291 −0.435681
\(574\) 23.4131 0.977243
\(575\) 1.01904 0.0424970
\(576\) −4.80672 −0.200280
\(577\) −13.9613 −0.581217 −0.290609 0.956842i \(-0.593858\pi\)
−0.290609 + 0.956842i \(0.593858\pi\)
\(578\) −72.1819 −3.00237
\(579\) 26.2169 1.08954
\(580\) −53.1667 −2.20763
\(581\) 17.4633 0.724501
\(582\) 65.8786 2.73076
\(583\) 55.0357 2.27935
\(584\) −28.8647 −1.19443
\(585\) −2.67511 −0.110602
\(586\) −5.18748 −0.214293
\(587\) 11.2413 0.463980 0.231990 0.972718i \(-0.425476\pi\)
0.231990 + 0.972718i \(0.425476\pi\)
\(588\) −5.73860 −0.236656
\(589\) 16.3331 0.672995
\(590\) −14.7782 −0.608411
\(591\) −38.8935 −1.59986
\(592\) 3.30906 0.136001
\(593\) −23.1764 −0.951741 −0.475871 0.879515i \(-0.657867\pi\)
−0.475871 + 0.879515i \(0.657867\pi\)
\(594\) 44.7666 1.83679
\(595\) 12.8903 0.528451
\(596\) −19.3217 −0.791450
\(597\) −23.2402 −0.951160
\(598\) −5.67600 −0.232109
\(599\) 40.4613 1.65320 0.826601 0.562788i \(-0.190271\pi\)
0.826601 + 0.562788i \(0.190271\pi\)
\(600\) −7.49440 −0.305957
\(601\) 3.84778 0.156954 0.0784772 0.996916i \(-0.474994\pi\)
0.0784772 + 0.996916i \(0.474994\pi\)
\(602\) 19.1666 0.781173
\(603\) −3.73711 −0.152187
\(604\) 15.6802 0.638018
\(605\) 10.6163 0.431615
\(606\) 19.0216 0.772700
\(607\) 1.50603 0.0611279 0.0305640 0.999533i \(-0.490270\pi\)
0.0305640 + 0.999533i \(0.490270\pi\)
\(608\) −28.7592 −1.16634
\(609\) 16.9266 0.685900
\(610\) −16.6804 −0.675371
\(611\) −16.1284 −0.652487
\(612\) 8.05518 0.325612
\(613\) −37.2836 −1.50587 −0.752935 0.658095i \(-0.771363\pi\)
−0.752935 + 0.658095i \(0.771363\pi\)
\(614\) 32.8283 1.32484
\(615\) 34.9910 1.41097
\(616\) 10.4435 0.420779
\(617\) −15.3056 −0.616182 −0.308091 0.951357i \(-0.599690\pi\)
−0.308091 + 0.951357i \(0.599690\pi\)
\(618\) −73.7348 −2.96605
\(619\) −42.4160 −1.70484 −0.852421 0.522856i \(-0.824867\pi\)
−0.852421 + 0.522856i \(0.824867\pi\)
\(620\) −20.2417 −0.812924
\(621\) −3.07489 −0.123391
\(622\) 1.36063 0.0545563
\(623\) 6.71228 0.268922
\(624\) −3.44774 −0.138020
\(625\) −14.4350 −0.577399
\(626\) 28.0225 1.12000
\(627\) −34.9495 −1.39575
\(628\) −56.2750 −2.24562
\(629\) −48.4916 −1.93349
\(630\) −1.53831 −0.0612879
\(631\) 1.95402 0.0777884 0.0388942 0.999243i \(-0.487616\pi\)
0.0388942 + 0.999243i \(0.487616\pi\)
\(632\) −36.2167 −1.44062
\(633\) 1.64128 0.0652352
\(634\) 11.8993 0.472581
\(635\) 23.2939 0.924389
\(636\) 77.1505 3.05922
\(637\) −3.93746 −0.156008
\(638\) −85.4836 −3.38433
\(639\) −1.97865 −0.0782743
\(640\) 31.6579 1.25139
\(641\) 5.98473 0.236383 0.118191 0.992991i \(-0.462290\pi\)
0.118191 + 0.992991i \(0.462290\pi\)
\(642\) −34.4081 −1.35798
\(643\) −3.02394 −0.119253 −0.0596263 0.998221i \(-0.518991\pi\)
−0.0596263 + 0.998221i \(0.518991\pi\)
\(644\) −1.99065 −0.0784425
\(645\) 28.6447 1.12788
\(646\) 73.6367 2.89720
\(647\) 5.88434 0.231337 0.115669 0.993288i \(-0.463099\pi\)
0.115669 + 0.993288i \(0.463099\pi\)
\(648\) 25.4340 0.999141
\(649\) −14.4915 −0.568843
\(650\) −14.2699 −0.559713
\(651\) 6.44429 0.252572
\(652\) 73.6526 2.88446
\(653\) −29.2544 −1.14481 −0.572407 0.819970i \(-0.693990\pi\)
−0.572407 + 0.819970i \(0.693990\pi\)
\(654\) −14.6973 −0.574708
\(655\) 9.58853 0.374655
\(656\) 4.93333 0.192614
\(657\) 4.16926 0.162658
\(658\) −9.27460 −0.361562
\(659\) −23.3660 −0.910209 −0.455105 0.890438i \(-0.650398\pi\)
−0.455105 + 0.890438i \(0.650398\pi\)
\(660\) 43.3129 1.68595
\(661\) 16.0112 0.622762 0.311381 0.950285i \(-0.399208\pi\)
0.311381 + 0.950285i \(0.399208\pi\)
\(662\) −3.28838 −0.127806
\(663\) 50.5239 1.96218
\(664\) −44.5513 −1.72892
\(665\) −8.57655 −0.332584
\(666\) 5.78693 0.224239
\(667\) 5.87162 0.227350
\(668\) −0.158109 −0.00611743
\(669\) −27.8449 −1.07655
\(670\) 42.3380 1.63566
\(671\) −16.3568 −0.631448
\(672\) −11.3470 −0.437721
\(673\) −0.630073 −0.0242875 −0.0121438 0.999926i \(-0.503866\pi\)
−0.0121438 + 0.999926i \(0.503866\pi\)
\(674\) 37.8193 1.45675
\(675\) −7.73052 −0.297548
\(676\) 7.82809 0.301081
\(677\) 13.6729 0.525491 0.262745 0.964865i \(-0.415372\pi\)
0.262745 + 0.964865i \(0.415372\pi\)
\(678\) 55.0921 2.11580
\(679\) 15.8528 0.608376
\(680\) −32.8848 −1.26108
\(681\) 24.1553 0.925635
\(682\) −32.5453 −1.24623
\(683\) 18.5849 0.711133 0.355566 0.934651i \(-0.384288\pi\)
0.355566 + 0.934651i \(0.384288\pi\)
\(684\) −5.35951 −0.204926
\(685\) −38.4807 −1.47027
\(686\) −2.26422 −0.0864485
\(687\) −17.1353 −0.653753
\(688\) 4.03856 0.153969
\(689\) 52.9358 2.01669
\(690\) −4.87802 −0.185703
\(691\) 31.1894 1.18650 0.593251 0.805018i \(-0.297844\pi\)
0.593251 + 0.805018i \(0.297844\pi\)
\(692\) −57.8060 −2.19745
\(693\) −1.50847 −0.0573020
\(694\) 75.9102 2.88151
\(695\) 43.1605 1.63717
\(696\) −43.1819 −1.63681
\(697\) −72.2939 −2.73833
\(698\) 3.85871 0.146054
\(699\) −2.12187 −0.0802564
\(700\) −5.00466 −0.189158
\(701\) 36.8567 1.39206 0.696029 0.718014i \(-0.254949\pi\)
0.696029 + 0.718014i \(0.254949\pi\)
\(702\) 43.0585 1.62514
\(703\) 32.2638 1.21685
\(704\) 53.3993 2.01256
\(705\) −13.8610 −0.522034
\(706\) −47.5609 −1.78998
\(707\) 4.57731 0.172147
\(708\) −20.3146 −0.763470
\(709\) 26.2784 0.986906 0.493453 0.869772i \(-0.335734\pi\)
0.493453 + 0.869772i \(0.335734\pi\)
\(710\) 22.4163 0.841270
\(711\) 5.23120 0.196185
\(712\) −17.1239 −0.641746
\(713\) 2.23544 0.0837181
\(714\) 29.0536 1.08730
\(715\) 29.7186 1.11141
\(716\) −42.8121 −1.59996
\(717\) −0.643643 −0.0240373
\(718\) 24.3214 0.907665
\(719\) 17.2952 0.645004 0.322502 0.946569i \(-0.395476\pi\)
0.322502 + 0.946569i \(0.395476\pi\)
\(720\) −0.324135 −0.0120798
\(721\) −17.7433 −0.660797
\(722\) −5.97383 −0.222323
\(723\) −23.5782 −0.876883
\(724\) 4.44078 0.165040
\(725\) 14.7617 0.548238
\(726\) 23.9283 0.888061
\(727\) −6.61551 −0.245356 −0.122678 0.992447i \(-0.539148\pi\)
−0.122678 + 0.992447i \(0.539148\pi\)
\(728\) 10.0450 0.372292
\(729\) 22.9189 0.848849
\(730\) −47.2339 −1.74821
\(731\) −59.1818 −2.18892
\(732\) −22.9294 −0.847495
\(733\) 8.65614 0.319722 0.159861 0.987140i \(-0.448895\pi\)
0.159861 + 0.987140i \(0.448895\pi\)
\(734\) 81.5822 3.01126
\(735\) −3.38390 −0.124817
\(736\) −3.93614 −0.145088
\(737\) 41.5167 1.52929
\(738\) 8.62747 0.317581
\(739\) −29.0683 −1.06929 −0.534647 0.845076i \(-0.679555\pi\)
−0.534647 + 0.845076i \(0.679555\pi\)
\(740\) −39.9845 −1.46986
\(741\) −33.6160 −1.23492
\(742\) 30.4406 1.11751
\(743\) −22.8121 −0.836894 −0.418447 0.908241i \(-0.637426\pi\)
−0.418447 + 0.908241i \(0.637426\pi\)
\(744\) −16.4402 −0.602728
\(745\) −11.3935 −0.417427
\(746\) −34.4633 −1.26179
\(747\) 6.43505 0.235446
\(748\) −89.4874 −3.27199
\(749\) −8.27987 −0.302540
\(750\) −50.5733 −1.84668
\(751\) 28.6368 1.04497 0.522485 0.852648i \(-0.325005\pi\)
0.522485 + 0.852648i \(0.325005\pi\)
\(752\) −1.95423 −0.0712636
\(753\) 28.5684 1.04109
\(754\) −82.2219 −2.99435
\(755\) 9.24622 0.336504
\(756\) 15.1012 0.549224
\(757\) −10.8520 −0.394423 −0.197211 0.980361i \(-0.563188\pi\)
−0.197211 + 0.980361i \(0.563188\pi\)
\(758\) −81.4095 −2.95692
\(759\) −4.78338 −0.173626
\(760\) 21.8799 0.793668
\(761\) −21.0205 −0.761993 −0.380997 0.924576i \(-0.624419\pi\)
−0.380997 + 0.924576i \(0.624419\pi\)
\(762\) 52.5023 1.90196
\(763\) −3.53671 −0.128037
\(764\) 17.7671 0.642791
\(765\) 4.74994 0.171734
\(766\) −4.60506 −0.166388
\(767\) −13.9386 −0.503294
\(768\) 23.4721 0.846976
\(769\) 15.9036 0.573497 0.286748 0.958006i \(-0.407426\pi\)
0.286748 + 0.958006i \(0.407426\pi\)
\(770\) 17.0896 0.615866
\(771\) 9.23647 0.332643
\(772\) −44.6634 −1.60747
\(773\) 23.4483 0.843376 0.421688 0.906741i \(-0.361438\pi\)
0.421688 + 0.906741i \(0.361438\pi\)
\(774\) 7.06269 0.253863
\(775\) 5.62010 0.201880
\(776\) −40.4427 −1.45181
\(777\) 12.7298 0.456679
\(778\) −17.4799 −0.626685
\(779\) 48.1007 1.72338
\(780\) 41.6603 1.49168
\(781\) 21.9814 0.786558
\(782\) 10.0783 0.360400
\(783\) −44.5425 −1.59182
\(784\) −0.477091 −0.0170390
\(785\) −33.1839 −1.18439
\(786\) 21.6117 0.770864
\(787\) 41.8206 1.49074 0.745372 0.666649i \(-0.232272\pi\)
0.745372 + 0.666649i \(0.232272\pi\)
\(788\) 66.2593 2.36039
\(789\) −19.7198 −0.702043
\(790\) −59.2647 −2.10854
\(791\) 13.2572 0.471372
\(792\) 3.84830 0.136744
\(793\) −15.7327 −0.558685
\(794\) −19.6974 −0.699034
\(795\) 45.4937 1.61349
\(796\) 39.5923 1.40331
\(797\) 22.9401 0.812579 0.406289 0.913744i \(-0.366822\pi\)
0.406289 + 0.913744i \(0.366822\pi\)
\(798\) −19.3308 −0.684302
\(799\) 28.6377 1.01313
\(800\) −9.89579 −0.349869
\(801\) 2.47340 0.0873934
\(802\) 56.4325 1.99270
\(803\) −46.3176 −1.63451
\(804\) 58.1991 2.05253
\(805\) −1.17383 −0.0413722
\(806\) −31.3036 −1.10262
\(807\) 4.11753 0.144944
\(808\) −11.6773 −0.410807
\(809\) 36.1740 1.27181 0.635905 0.771768i \(-0.280627\pi\)
0.635905 + 0.771768i \(0.280627\pi\)
\(810\) 41.6199 1.46237
\(811\) 33.5614 1.17850 0.589250 0.807951i \(-0.299423\pi\)
0.589250 + 0.807951i \(0.299423\pi\)
\(812\) −28.8363 −1.01196
\(813\) −25.6749 −0.900458
\(814\) −64.2887 −2.25332
\(815\) 43.4311 1.52132
\(816\) 6.12183 0.214307
\(817\) 39.3766 1.37761
\(818\) −51.9823 −1.81752
\(819\) −1.45091 −0.0506990
\(820\) −59.6111 −2.08171
\(821\) −48.2017 −1.68225 −0.841125 0.540840i \(-0.818106\pi\)
−0.841125 + 0.540840i \(0.818106\pi\)
\(822\) −86.7321 −3.02513
\(823\) 35.9918 1.25460 0.627298 0.778780i \(-0.284161\pi\)
0.627298 + 0.778780i \(0.284161\pi\)
\(824\) 45.2656 1.57690
\(825\) −12.0258 −0.418686
\(826\) −8.01535 −0.278890
\(827\) 21.8807 0.760868 0.380434 0.924808i \(-0.375775\pi\)
0.380434 + 0.924808i \(0.375775\pi\)
\(828\) −0.733532 −0.0254920
\(829\) 10.3642 0.359964 0.179982 0.983670i \(-0.442396\pi\)
0.179982 + 0.983670i \(0.442396\pi\)
\(830\) −72.9033 −2.53051
\(831\) 24.8761 0.862943
\(832\) 51.3618 1.78065
\(833\) 6.99137 0.242237
\(834\) 97.2800 3.36853
\(835\) −0.0932329 −0.00322646
\(836\) 59.5404 2.05925
\(837\) −16.9582 −0.586162
\(838\) −83.7944 −2.89463
\(839\) −39.8212 −1.37478 −0.687391 0.726288i \(-0.741244\pi\)
−0.687391 + 0.726288i \(0.741244\pi\)
\(840\) 8.63278 0.297859
\(841\) 56.0557 1.93295
\(842\) −47.6376 −1.64170
\(843\) −4.18351 −0.144088
\(844\) −2.79611 −0.0962461
\(845\) 4.61603 0.158796
\(846\) −3.41759 −0.117499
\(847\) 5.75803 0.197848
\(848\) 6.41408 0.220260
\(849\) −15.4557 −0.530438
\(850\) 25.3378 0.869078
\(851\) 4.41580 0.151372
\(852\) 30.8142 1.05568
\(853\) −1.49025 −0.0510253 −0.0255126 0.999674i \(-0.508122\pi\)
−0.0255126 + 0.999674i \(0.508122\pi\)
\(854\) −9.04704 −0.309583
\(855\) −3.16037 −0.108082
\(856\) 21.1230 0.721971
\(857\) 7.09138 0.242237 0.121119 0.992638i \(-0.461352\pi\)
0.121119 + 0.992638i \(0.461352\pi\)
\(858\) 66.9831 2.28676
\(859\) −10.8869 −0.371457 −0.185728 0.982601i \(-0.559464\pi\)
−0.185728 + 0.982601i \(0.559464\pi\)
\(860\) −48.7994 −1.66405
\(861\) 18.9783 0.646777
\(862\) −27.6022 −0.940135
\(863\) −1.00000 −0.0340404
\(864\) 29.8598 1.01585
\(865\) −34.0867 −1.15898
\(866\) 2.93344 0.0996822
\(867\) −58.5095 −1.98709
\(868\) −10.9786 −0.372637
\(869\) −58.1149 −1.97141
\(870\) −70.6625 −2.39568
\(871\) 39.9326 1.35306
\(872\) 9.02260 0.305544
\(873\) 5.84160 0.197708
\(874\) −6.70560 −0.226820
\(875\) −12.1698 −0.411415
\(876\) −64.9292 −2.19375
\(877\) −25.5673 −0.863347 −0.431674 0.902030i \(-0.642077\pi\)
−0.431674 + 0.902030i \(0.642077\pi\)
\(878\) −13.9289 −0.470079
\(879\) −4.20489 −0.141827
\(880\) 3.60091 0.121387
\(881\) 22.3644 0.753476 0.376738 0.926320i \(-0.377046\pi\)
0.376738 + 0.926320i \(0.377046\pi\)
\(882\) −0.834343 −0.0280938
\(883\) 29.8754 1.00539 0.502694 0.864464i \(-0.332342\pi\)
0.502694 + 0.864464i \(0.332342\pi\)
\(884\) −86.0730 −2.89495
\(885\) −11.9790 −0.402670
\(886\) −11.9395 −0.401115
\(887\) −17.2558 −0.579394 −0.289697 0.957118i \(-0.593555\pi\)
−0.289697 + 0.957118i \(0.593555\pi\)
\(888\) −32.4754 −1.08980
\(889\) 12.6340 0.423731
\(890\) −28.0214 −0.939280
\(891\) 40.8125 1.36727
\(892\) 47.4369 1.58831
\(893\) −19.0541 −0.637620
\(894\) −25.6800 −0.858868
\(895\) −25.2452 −0.843853
\(896\) 17.1704 0.573624
\(897\) −4.60087 −0.153619
\(898\) 40.1536 1.33994
\(899\) 32.3824 1.08001
\(900\) −1.84416 −0.0614721
\(901\) −93.9931 −3.13136
\(902\) −95.8451 −3.19129
\(903\) 15.5362 0.517011
\(904\) −33.8209 −1.12487
\(905\) 2.61861 0.0870456
\(906\) 20.8401 0.692368
\(907\) −14.2245 −0.472318 −0.236159 0.971714i \(-0.575889\pi\)
−0.236159 + 0.971714i \(0.575889\pi\)
\(908\) −41.1513 −1.36565
\(909\) 1.68669 0.0559439
\(910\) 16.4375 0.544899
\(911\) −9.83375 −0.325807 −0.162903 0.986642i \(-0.552086\pi\)
−0.162903 + 0.986642i \(0.552086\pi\)
\(912\) −4.07315 −0.134876
\(913\) −71.4889 −2.36594
\(914\) −58.2262 −1.92595
\(915\) −13.5209 −0.446987
\(916\) 29.1919 0.964527
\(917\) 5.20058 0.171738
\(918\) −76.4548 −2.52338
\(919\) 3.54559 0.116958 0.0584791 0.998289i \(-0.481375\pi\)
0.0584791 + 0.998289i \(0.481375\pi\)
\(920\) 2.99460 0.0987292
\(921\) 26.6101 0.876832
\(922\) 65.5774 2.15968
\(923\) 21.1427 0.695922
\(924\) 23.4918 0.772825
\(925\) 11.1017 0.365022
\(926\) −90.4790 −2.97332
\(927\) −6.53823 −0.214744
\(928\) −57.0185 −1.87173
\(929\) 1.81336 0.0594946 0.0297473 0.999557i \(-0.490530\pi\)
0.0297473 + 0.999557i \(0.490530\pi\)
\(930\) −26.9027 −0.882173
\(931\) −4.65170 −0.152453
\(932\) 3.61484 0.118408
\(933\) 1.10291 0.0361075
\(934\) −50.9500 −1.66713
\(935\) −52.7685 −1.72571
\(936\) 3.70147 0.120986
\(937\) 31.6072 1.03256 0.516281 0.856419i \(-0.327316\pi\)
0.516281 + 0.856419i \(0.327316\pi\)
\(938\) 22.9631 0.749772
\(939\) 22.7146 0.741263
\(940\) 23.6137 0.770194
\(941\) 39.7611 1.29617 0.648087 0.761566i \(-0.275569\pi\)
0.648087 + 0.761566i \(0.275569\pi\)
\(942\) −74.7936 −2.43691
\(943\) 6.58332 0.214382
\(944\) −1.68890 −0.0549690
\(945\) 8.90478 0.289672
\(946\) −78.4616 −2.55101
\(947\) 7.37886 0.239781 0.119890 0.992787i \(-0.461746\pi\)
0.119890 + 0.992787i \(0.461746\pi\)
\(948\) −81.4670 −2.64593
\(949\) −44.5503 −1.44616
\(950\) −16.8585 −0.546961
\(951\) 9.64537 0.312773
\(952\) −17.8359 −0.578065
\(953\) 53.2555 1.72512 0.862558 0.505959i \(-0.168861\pi\)
0.862558 + 0.505959i \(0.168861\pi\)
\(954\) 11.2170 0.363165
\(955\) 10.4768 0.339021
\(956\) 1.09652 0.0354639
\(957\) −69.2916 −2.23988
\(958\) 14.1319 0.456580
\(959\) −20.8710 −0.673959
\(960\) 44.1410 1.42464
\(961\) −18.6714 −0.602302
\(962\) −61.8358 −1.99366
\(963\) −3.05104 −0.0983185
\(964\) 40.1681 1.29373
\(965\) −26.3369 −0.847813
\(966\) −2.64572 −0.0851245
\(967\) 37.7789 1.21489 0.607443 0.794363i \(-0.292195\pi\)
0.607443 + 0.794363i \(0.292195\pi\)
\(968\) −14.6895 −0.472138
\(969\) 59.6887 1.91748
\(970\) −66.1801 −2.12491
\(971\) 49.4932 1.58831 0.794156 0.607714i \(-0.207913\pi\)
0.794156 + 0.607714i \(0.207913\pi\)
\(972\) 11.9085 0.381964
\(973\) 23.4092 0.750464
\(974\) 70.3437 2.25396
\(975\) −11.5670 −0.370440
\(976\) −1.90629 −0.0610187
\(977\) 24.7603 0.792154 0.396077 0.918217i \(-0.370371\pi\)
0.396077 + 0.918217i \(0.370371\pi\)
\(978\) 97.8898 3.13017
\(979\) −27.4778 −0.878194
\(980\) 5.76486 0.184152
\(981\) −1.30324 −0.0416092
\(982\) 71.9037 2.29454
\(983\) −7.25055 −0.231257 −0.115628 0.993293i \(-0.536888\pi\)
−0.115628 + 0.993293i \(0.536888\pi\)
\(984\) −48.4161 −1.54345
\(985\) 39.0714 1.24492
\(986\) 145.994 4.64938
\(987\) −7.51784 −0.239296
\(988\) 57.2686 1.82196
\(989\) 5.38930 0.171370
\(990\) 6.29733 0.200142
\(991\) 23.9449 0.760635 0.380318 0.924856i \(-0.375815\pi\)
0.380318 + 0.924856i \(0.375815\pi\)
\(992\) −21.7081 −0.689233
\(993\) −2.66551 −0.0845873
\(994\) 12.1581 0.385630
\(995\) 23.3466 0.740137
\(996\) −100.215 −3.17543
\(997\) 26.5566 0.841056 0.420528 0.907280i \(-0.361845\pi\)
0.420528 + 0.907280i \(0.361845\pi\)
\(998\) 40.7655 1.29041
\(999\) −33.4986 −1.05985
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 \(a_p\))