Properties

Label 8035.2.a.e.1.19
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28006 q^{2}\) \(+1.15086 q^{3}\) \(+3.19869 q^{4}\) \(+1.00000 q^{5}\) \(-2.62404 q^{6}\) \(-0.851041 q^{7}\) \(-2.73309 q^{8}\) \(-1.67552 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.28006 q^{2}\) \(+1.15086 q^{3}\) \(+3.19869 q^{4}\) \(+1.00000 q^{5}\) \(-2.62404 q^{6}\) \(-0.851041 q^{7}\) \(-2.73309 q^{8}\) \(-1.67552 q^{9}\) \(-2.28006 q^{10}\) \(-4.47426 q^{11}\) \(+3.68125 q^{12}\) \(-5.96077 q^{13}\) \(+1.94043 q^{14}\) \(+1.15086 q^{15}\) \(-0.165768 q^{16}\) \(-7.60594 q^{17}\) \(+3.82028 q^{18}\) \(+3.98204 q^{19}\) \(+3.19869 q^{20}\) \(-0.979430 q^{21}\) \(+10.2016 q^{22}\) \(-8.96149 q^{23}\) \(-3.14541 q^{24}\) \(+1.00000 q^{25}\) \(+13.5909 q^{26}\) \(-5.38087 q^{27}\) \(-2.72221 q^{28}\) \(+7.44110 q^{29}\) \(-2.62404 q^{30}\) \(-4.02401 q^{31}\) \(+5.84413 q^{32}\) \(-5.14926 q^{33}\) \(+17.3420 q^{34}\) \(-0.851041 q^{35}\) \(-5.35946 q^{36}\) \(+6.29845 q^{37}\) \(-9.07931 q^{38}\) \(-6.86003 q^{39}\) \(-2.73309 q^{40}\) \(+10.1364 q^{41}\) \(+2.23316 q^{42}\) \(-5.50881 q^{43}\) \(-14.3118 q^{44}\) \(-1.67552 q^{45}\) \(+20.4328 q^{46}\) \(-5.34036 q^{47}\) \(-0.190776 q^{48}\) \(-6.27573 q^{49}\) \(-2.28006 q^{50}\) \(-8.75339 q^{51}\) \(-19.0667 q^{52}\) \(+10.5970 q^{53}\) \(+12.2687 q^{54}\) \(-4.47426 q^{55}\) \(+2.32597 q^{56}\) \(+4.58278 q^{57}\) \(-16.9662 q^{58}\) \(-1.91943 q^{59}\) \(+3.68125 q^{60}\) \(-10.6988 q^{61}\) \(+9.17500 q^{62}\) \(+1.42593 q^{63}\) \(-12.9935 q^{64}\) \(-5.96077 q^{65}\) \(+11.7406 q^{66}\) \(-1.14548 q^{67}\) \(-24.3290 q^{68}\) \(-10.3134 q^{69}\) \(+1.94043 q^{70}\) \(+2.44211 q^{71}\) \(+4.57933 q^{72}\) \(+0.585835 q^{73}\) \(-14.3609 q^{74}\) \(+1.15086 q^{75}\) \(+12.7373 q^{76}\) \(+3.80778 q^{77}\) \(+15.6413 q^{78}\) \(-8.15531 q^{79}\) \(-0.165768 q^{80}\) \(-1.16609 q^{81}\) \(-23.1116 q^{82}\) \(-11.0014 q^{83}\) \(-3.13289 q^{84}\) \(-7.60594 q^{85}\) \(+12.5604 q^{86}\) \(+8.56368 q^{87}\) \(+12.2286 q^{88}\) \(+14.6865 q^{89}\) \(+3.82028 q^{90}\) \(+5.07286 q^{91}\) \(-28.6650 q^{92}\) \(-4.63108 q^{93}\) \(+12.1764 q^{94}\) \(+3.98204 q^{95}\) \(+6.72579 q^{96}\) \(+10.1915 q^{97}\) \(+14.3091 q^{98}\) \(+7.49670 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28006 −1.61225 −0.806124 0.591746i \(-0.798439\pi\)
−0.806124 + 0.591746i \(0.798439\pi\)
\(3\) 1.15086 0.664450 0.332225 0.943200i \(-0.392201\pi\)
0.332225 + 0.943200i \(0.392201\pi\)
\(4\) 3.19869 1.59934
\(5\) 1.00000 0.447214
\(6\) −2.62404 −1.07126
\(7\) −0.851041 −0.321663 −0.160832 0.986982i \(-0.551418\pi\)
−0.160832 + 0.986982i \(0.551418\pi\)
\(8\) −2.73309 −0.966292
\(9\) −1.67552 −0.558506
\(10\) −2.28006 −0.721019
\(11\) −4.47426 −1.34904 −0.674521 0.738256i \(-0.735650\pi\)
−0.674521 + 0.738256i \(0.735650\pi\)
\(12\) 3.68125 1.06269
\(13\) −5.96077 −1.65322 −0.826611 0.562774i \(-0.809734\pi\)
−0.826611 + 0.562774i \(0.809734\pi\)
\(14\) 1.94043 0.518601
\(15\) 1.15086 0.297151
\(16\) −0.165768 −0.0414419
\(17\) −7.60594 −1.84471 −0.922356 0.386342i \(-0.873739\pi\)
−0.922356 + 0.386342i \(0.873739\pi\)
\(18\) 3.82028 0.900450
\(19\) 3.98204 0.913544 0.456772 0.889584i \(-0.349006\pi\)
0.456772 + 0.889584i \(0.349006\pi\)
\(20\) 3.19869 0.715249
\(21\) −0.979430 −0.213729
\(22\) 10.2016 2.17499
\(23\) −8.96149 −1.86860 −0.934300 0.356487i \(-0.883974\pi\)
−0.934300 + 0.356487i \(0.883974\pi\)
\(24\) −3.14541 −0.642053
\(25\) 1.00000 0.200000
\(26\) 13.5909 2.66540
\(27\) −5.38087 −1.03555
\(28\) −2.72221 −0.514450
\(29\) 7.44110 1.38178 0.690889 0.722961i \(-0.257219\pi\)
0.690889 + 0.722961i \(0.257219\pi\)
\(30\) −2.62404 −0.479082
\(31\) −4.02401 −0.722733 −0.361367 0.932424i \(-0.617690\pi\)
−0.361367 + 0.932424i \(0.617690\pi\)
\(32\) 5.84413 1.03311
\(33\) −5.14926 −0.896371
\(34\) 17.3420 2.97413
\(35\) −0.851041 −0.143852
\(36\) −5.35946 −0.893243
\(37\) 6.29845 1.03546 0.517730 0.855544i \(-0.326777\pi\)
0.517730 + 0.855544i \(0.326777\pi\)
\(38\) −9.07931 −1.47286
\(39\) −6.86003 −1.09848
\(40\) −2.73309 −0.432139
\(41\) 10.1364 1.58304 0.791518 0.611146i \(-0.209291\pi\)
0.791518 + 0.611146i \(0.209291\pi\)
\(42\) 2.23316 0.344585
\(43\) −5.50881 −0.840086 −0.420043 0.907504i \(-0.637985\pi\)
−0.420043 + 0.907504i \(0.637985\pi\)
\(44\) −14.3118 −2.15758
\(45\) −1.67552 −0.249771
\(46\) 20.4328 3.01265
\(47\) −5.34036 −0.778971 −0.389486 0.921033i \(-0.627347\pi\)
−0.389486 + 0.921033i \(0.627347\pi\)
\(48\) −0.190776 −0.0275361
\(49\) −6.27573 −0.896533
\(50\) −2.28006 −0.322450
\(51\) −8.75339 −1.22572
\(52\) −19.0667 −2.64407
\(53\) 10.5970 1.45560 0.727802 0.685787i \(-0.240542\pi\)
0.727802 + 0.685787i \(0.240542\pi\)
\(54\) 12.2687 1.66956
\(55\) −4.47426 −0.603310
\(56\) 2.32597 0.310820
\(57\) 4.58278 0.607005
\(58\) −16.9662 −2.22777
\(59\) −1.91943 −0.249888 −0.124944 0.992164i \(-0.539875\pi\)
−0.124944 + 0.992164i \(0.539875\pi\)
\(60\) 3.68125 0.475247
\(61\) −10.6988 −1.36984 −0.684919 0.728620i \(-0.740162\pi\)
−0.684919 + 0.728620i \(0.740162\pi\)
\(62\) 9.17500 1.16523
\(63\) 1.42593 0.179651
\(64\) −12.9935 −1.62418
\(65\) −5.96077 −0.739343
\(66\) 11.7406 1.44517
\(67\) −1.14548 −0.139942 −0.0699712 0.997549i \(-0.522291\pi\)
−0.0699712 + 0.997549i \(0.522291\pi\)
\(68\) −24.3290 −2.95033
\(69\) −10.3134 −1.24159
\(70\) 1.94043 0.231925
\(71\) 2.44211 0.289825 0.144913 0.989444i \(-0.453710\pi\)
0.144913 + 0.989444i \(0.453710\pi\)
\(72\) 4.57933 0.539679
\(73\) 0.585835 0.0685668 0.0342834 0.999412i \(-0.489085\pi\)
0.0342834 + 0.999412i \(0.489085\pi\)
\(74\) −14.3609 −1.66942
\(75\) 1.15086 0.132890
\(76\) 12.7373 1.46107
\(77\) 3.80778 0.433937
\(78\) 15.6413 1.77103
\(79\) −8.15531 −0.917544 −0.458772 0.888554i \(-0.651710\pi\)
−0.458772 + 0.888554i \(0.651710\pi\)
\(80\) −0.165768 −0.0185334
\(81\) −1.16609 −0.129566
\(82\) −23.1116 −2.55225
\(83\) −11.0014 −1.20756 −0.603781 0.797150i \(-0.706340\pi\)
−0.603781 + 0.797150i \(0.706340\pi\)
\(84\) −3.13289 −0.341827
\(85\) −7.60594 −0.824980
\(86\) 12.5604 1.35443
\(87\) 8.56368 0.918123
\(88\) 12.2286 1.30357
\(89\) 14.6865 1.55677 0.778383 0.627789i \(-0.216040\pi\)
0.778383 + 0.627789i \(0.216040\pi\)
\(90\) 3.82028 0.402693
\(91\) 5.07286 0.531780
\(92\) −28.6650 −2.98854
\(93\) −4.63108 −0.480221
\(94\) 12.1764 1.25589
\(95\) 3.98204 0.408549
\(96\) 6.72579 0.686448
\(97\) 10.1915 1.03479 0.517394 0.855747i \(-0.326902\pi\)
0.517394 + 0.855747i \(0.326902\pi\)
\(98\) 14.3091 1.44543
\(99\) 7.49670 0.753447
\(100\) 3.19869 0.319869
\(101\) −1.69842 −0.169000 −0.0844998 0.996423i \(-0.526929\pi\)
−0.0844998 + 0.996423i \(0.526929\pi\)
\(102\) 19.9583 1.97616
\(103\) −3.19745 −0.315054 −0.157527 0.987515i \(-0.550352\pi\)
−0.157527 + 0.987515i \(0.550352\pi\)
\(104\) 16.2913 1.59749
\(105\) −0.979430 −0.0955826
\(106\) −24.1617 −2.34680
\(107\) 1.90224 0.183897 0.0919484 0.995764i \(-0.470691\pi\)
0.0919484 + 0.995764i \(0.470691\pi\)
\(108\) −17.2117 −1.65620
\(109\) −18.9596 −1.81600 −0.907998 0.418974i \(-0.862390\pi\)
−0.907998 + 0.418974i \(0.862390\pi\)
\(110\) 10.2016 0.972685
\(111\) 7.24865 0.688012
\(112\) 0.141075 0.0133303
\(113\) −17.2936 −1.62684 −0.813422 0.581674i \(-0.802398\pi\)
−0.813422 + 0.581674i \(0.802398\pi\)
\(114\) −10.4490 −0.978642
\(115\) −8.96149 −0.835663
\(116\) 23.8018 2.20994
\(117\) 9.98737 0.923333
\(118\) 4.37641 0.402881
\(119\) 6.47296 0.593376
\(120\) −3.14541 −0.287135
\(121\) 9.01904 0.819913
\(122\) 24.3939 2.20852
\(123\) 11.6656 1.05185
\(124\) −12.8716 −1.15590
\(125\) 1.00000 0.0894427
\(126\) −3.25122 −0.289641
\(127\) −8.08267 −0.717221 −0.358610 0.933487i \(-0.616749\pi\)
−0.358610 + 0.933487i \(0.616749\pi\)
\(128\) 17.9376 1.58548
\(129\) −6.33988 −0.558195
\(130\) 13.5909 1.19200
\(131\) 2.52746 0.220825 0.110413 0.993886i \(-0.464783\pi\)
0.110413 + 0.993886i \(0.464783\pi\)
\(132\) −16.4709 −1.43361
\(133\) −3.38888 −0.293853
\(134\) 2.61176 0.225622
\(135\) −5.38087 −0.463112
\(136\) 20.7877 1.78253
\(137\) −10.1491 −0.867095 −0.433548 0.901131i \(-0.642738\pi\)
−0.433548 + 0.901131i \(0.642738\pi\)
\(138\) 23.5153 2.00176
\(139\) −11.4921 −0.974744 −0.487372 0.873195i \(-0.662044\pi\)
−0.487372 + 0.873195i \(0.662044\pi\)
\(140\) −2.72221 −0.230069
\(141\) −6.14601 −0.517588
\(142\) −5.56817 −0.467270
\(143\) 26.6701 2.23026
\(144\) 0.277746 0.0231455
\(145\) 7.44110 0.617950
\(146\) −1.33574 −0.110547
\(147\) −7.22250 −0.595702
\(148\) 20.1468 1.65606
\(149\) 20.2394 1.65808 0.829040 0.559190i \(-0.188888\pi\)
0.829040 + 0.559190i \(0.188888\pi\)
\(150\) −2.62404 −0.214252
\(151\) 17.8074 1.44915 0.724573 0.689198i \(-0.242037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(152\) −10.8833 −0.882750
\(153\) 12.7439 1.03028
\(154\) −8.68198 −0.699614
\(155\) −4.02401 −0.323216
\(156\) −21.9431 −1.75685
\(157\) −3.64311 −0.290752 −0.145376 0.989376i \(-0.546439\pi\)
−0.145376 + 0.989376i \(0.546439\pi\)
\(158\) 18.5946 1.47931
\(159\) 12.1956 0.967177
\(160\) 5.84413 0.462019
\(161\) 7.62659 0.601060
\(162\) 2.65877 0.208893
\(163\) 17.2437 1.35063 0.675316 0.737528i \(-0.264007\pi\)
0.675316 + 0.737528i \(0.264007\pi\)
\(164\) 32.4231 2.53182
\(165\) −5.14926 −0.400869
\(166\) 25.0839 1.94689
\(167\) −23.1080 −1.78815 −0.894077 0.447914i \(-0.852167\pi\)
−0.894077 + 0.447914i \(0.852167\pi\)
\(168\) 2.67687 0.206525
\(169\) 22.5308 1.73314
\(170\) 17.3420 1.33007
\(171\) −6.67198 −0.510219
\(172\) −17.6210 −1.34359
\(173\) 5.02692 0.382189 0.191095 0.981572i \(-0.438796\pi\)
0.191095 + 0.981572i \(0.438796\pi\)
\(174\) −19.5257 −1.48024
\(175\) −0.851041 −0.0643326
\(176\) 0.741688 0.0559068
\(177\) −2.20899 −0.166038
\(178\) −33.4862 −2.50989
\(179\) −8.87136 −0.663077 −0.331538 0.943442i \(-0.607568\pi\)
−0.331538 + 0.943442i \(0.607568\pi\)
\(180\) −5.35946 −0.399470
\(181\) −0.590912 −0.0439221 −0.0219611 0.999759i \(-0.506991\pi\)
−0.0219611 + 0.999759i \(0.506991\pi\)
\(182\) −11.5664 −0.857362
\(183\) −12.3128 −0.910189
\(184\) 24.4925 1.80561
\(185\) 6.29845 0.463072
\(186\) 10.5592 0.774235
\(187\) 34.0310 2.48859
\(188\) −17.0821 −1.24584
\(189\) 4.57934 0.333098
\(190\) −9.07931 −0.658683
\(191\) 4.56601 0.330385 0.165192 0.986261i \(-0.447176\pi\)
0.165192 + 0.986261i \(0.447176\pi\)
\(192\) −14.9537 −1.07919
\(193\) 15.5989 1.12283 0.561417 0.827533i \(-0.310256\pi\)
0.561417 + 0.827533i \(0.310256\pi\)
\(194\) −23.2372 −1.66833
\(195\) −6.86003 −0.491257
\(196\) −20.0741 −1.43386
\(197\) 19.8507 1.41430 0.707152 0.707062i \(-0.249980\pi\)
0.707152 + 0.707062i \(0.249980\pi\)
\(198\) −17.0930 −1.21474
\(199\) −10.7219 −0.760056 −0.380028 0.924975i \(-0.624086\pi\)
−0.380028 + 0.924975i \(0.624086\pi\)
\(200\) −2.73309 −0.193258
\(201\) −1.31829 −0.0929848
\(202\) 3.87251 0.272469
\(203\) −6.33268 −0.444467
\(204\) −27.9994 −1.96035
\(205\) 10.1364 0.707955
\(206\) 7.29039 0.507945
\(207\) 15.0151 1.04362
\(208\) 0.988103 0.0685126
\(209\) −17.8167 −1.23241
\(210\) 2.23316 0.154103
\(211\) −9.10373 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(212\) 33.8964 2.32801
\(213\) 2.81053 0.192575
\(214\) −4.33723 −0.296487
\(215\) −5.50881 −0.375698
\(216\) 14.7064 1.00064
\(217\) 3.42460 0.232477
\(218\) 43.2290 2.92784
\(219\) 0.674216 0.0455593
\(220\) −14.3118 −0.964900
\(221\) 45.3373 3.04972
\(222\) −16.5274 −1.10925
\(223\) −13.0519 −0.874017 −0.437009 0.899457i \(-0.643962\pi\)
−0.437009 + 0.899457i \(0.643962\pi\)
\(224\) −4.97359 −0.332312
\(225\) −1.67552 −0.111701
\(226\) 39.4305 2.62288
\(227\) 10.5108 0.697623 0.348812 0.937193i \(-0.386585\pi\)
0.348812 + 0.937193i \(0.386585\pi\)
\(228\) 14.6589 0.970809
\(229\) 14.6567 0.968543 0.484271 0.874918i \(-0.339085\pi\)
0.484271 + 0.874918i \(0.339085\pi\)
\(230\) 20.4328 1.34730
\(231\) 4.38223 0.288330
\(232\) −20.3372 −1.33520
\(233\) −17.9965 −1.17899 −0.589495 0.807772i \(-0.700673\pi\)
−0.589495 + 0.807772i \(0.700673\pi\)
\(234\) −22.7718 −1.48864
\(235\) −5.34036 −0.348366
\(236\) −6.13964 −0.399657
\(237\) −9.38563 −0.609662
\(238\) −14.7588 −0.956669
\(239\) 18.2297 1.17918 0.589592 0.807701i \(-0.299288\pi\)
0.589592 + 0.807701i \(0.299288\pi\)
\(240\) −0.190776 −0.0123145
\(241\) 3.14810 0.202787 0.101393 0.994846i \(-0.467670\pi\)
0.101393 + 0.994846i \(0.467670\pi\)
\(242\) −20.5640 −1.32190
\(243\) 14.8006 0.949460
\(244\) −34.2220 −2.19084
\(245\) −6.27573 −0.400942
\(246\) −26.5982 −1.69584
\(247\) −23.7361 −1.51029
\(248\) 10.9980 0.698371
\(249\) −12.6611 −0.802365
\(250\) −2.28006 −0.144204
\(251\) −10.8307 −0.683629 −0.341814 0.939767i \(-0.611041\pi\)
−0.341814 + 0.939767i \(0.611041\pi\)
\(252\) 4.56111 0.287323
\(253\) 40.0961 2.52082
\(254\) 18.4290 1.15634
\(255\) −8.75339 −0.548158
\(256\) −14.9120 −0.932003
\(257\) 23.6306 1.47404 0.737018 0.675873i \(-0.236233\pi\)
0.737018 + 0.675873i \(0.236233\pi\)
\(258\) 14.4553 0.899950
\(259\) −5.36024 −0.333069
\(260\) −19.0667 −1.18246
\(261\) −12.4677 −0.771731
\(262\) −5.76277 −0.356025
\(263\) 2.76852 0.170714 0.0853572 0.996350i \(-0.472797\pi\)
0.0853572 + 0.996350i \(0.472797\pi\)
\(264\) 14.0734 0.866156
\(265\) 10.5970 0.650966
\(266\) 7.72686 0.473764
\(267\) 16.9021 1.03439
\(268\) −3.66403 −0.223816
\(269\) −26.5828 −1.62078 −0.810390 0.585891i \(-0.800745\pi\)
−0.810390 + 0.585891i \(0.800745\pi\)
\(270\) 12.2687 0.746651
\(271\) 6.19227 0.376153 0.188077 0.982154i \(-0.439775\pi\)
0.188077 + 0.982154i \(0.439775\pi\)
\(272\) 1.26082 0.0764484
\(273\) 5.83816 0.353342
\(274\) 23.1406 1.39797
\(275\) −4.47426 −0.269808
\(276\) −32.9895 −1.98573
\(277\) 6.77737 0.407213 0.203606 0.979053i \(-0.434734\pi\)
0.203606 + 0.979053i \(0.434734\pi\)
\(278\) 26.2026 1.57153
\(279\) 6.74229 0.403651
\(280\) 2.32597 0.139003
\(281\) 24.5927 1.46708 0.733538 0.679649i \(-0.237868\pi\)
0.733538 + 0.679649i \(0.237868\pi\)
\(282\) 14.0133 0.834480
\(283\) 4.64584 0.276167 0.138083 0.990421i \(-0.455906\pi\)
0.138083 + 0.990421i \(0.455906\pi\)
\(284\) 7.81155 0.463530
\(285\) 4.58278 0.271461
\(286\) −60.8095 −3.59574
\(287\) −8.62646 −0.509204
\(288\) −9.79194 −0.576996
\(289\) 40.8503 2.40296
\(290\) −16.9662 −0.996289
\(291\) 11.7290 0.687565
\(292\) 1.87390 0.109662
\(293\) 30.2073 1.76473 0.882365 0.470566i \(-0.155950\pi\)
0.882365 + 0.470566i \(0.155950\pi\)
\(294\) 16.4678 0.960419
\(295\) −1.91943 −0.111753
\(296\) −17.2142 −1.00056
\(297\) 24.0755 1.39700
\(298\) −46.1472 −2.67324
\(299\) 53.4174 3.08921
\(300\) 3.68125 0.212537
\(301\) 4.68822 0.270225
\(302\) −40.6020 −2.33638
\(303\) −1.95465 −0.112292
\(304\) −0.660094 −0.0378590
\(305\) −10.6988 −0.612610
\(306\) −29.0569 −1.66107
\(307\) 3.89479 0.222288 0.111144 0.993804i \(-0.464549\pi\)
0.111144 + 0.993804i \(0.464549\pi\)
\(308\) 12.1799 0.694014
\(309\) −3.67982 −0.209338
\(310\) 9.17500 0.521105
\(311\) 17.0374 0.966100 0.483050 0.875593i \(-0.339529\pi\)
0.483050 + 0.875593i \(0.339529\pi\)
\(312\) 18.7490 1.06146
\(313\) −19.1541 −1.08266 −0.541328 0.840812i \(-0.682078\pi\)
−0.541328 + 0.840812i \(0.682078\pi\)
\(314\) 8.30653 0.468765
\(315\) 1.42593 0.0803422
\(316\) −26.0863 −1.46747
\(317\) 8.27307 0.464662 0.232331 0.972637i \(-0.425365\pi\)
0.232331 + 0.972637i \(0.425365\pi\)
\(318\) −27.8068 −1.55933
\(319\) −33.2935 −1.86408
\(320\) −12.9935 −0.726356
\(321\) 2.18922 0.122190
\(322\) −17.3891 −0.969058
\(323\) −30.2872 −1.68522
\(324\) −3.72997 −0.207221
\(325\) −5.96077 −0.330644
\(326\) −39.3168 −2.17756
\(327\) −21.8198 −1.20664
\(328\) −27.7036 −1.52967
\(329\) 4.54486 0.250566
\(330\) 11.7406 0.646301
\(331\) −18.2283 −1.00192 −0.500960 0.865470i \(-0.667020\pi\)
−0.500960 + 0.865470i \(0.667020\pi\)
\(332\) −35.1901 −1.93131
\(333\) −10.5532 −0.578310
\(334\) 52.6878 2.88295
\(335\) −1.14548 −0.0625842
\(336\) 0.162358 0.00885734
\(337\) −12.1404 −0.661332 −0.330666 0.943748i \(-0.607273\pi\)
−0.330666 + 0.943748i \(0.607273\pi\)
\(338\) −51.3717 −2.79425
\(339\) −19.9025 −1.08096
\(340\) −24.3290 −1.31943
\(341\) 18.0045 0.974997
\(342\) 15.2125 0.822600
\(343\) 11.2982 0.610045
\(344\) 15.0561 0.811768
\(345\) −10.3134 −0.555257
\(346\) −11.4617 −0.616184
\(347\) −8.03659 −0.431427 −0.215713 0.976457i \(-0.569208\pi\)
−0.215713 + 0.976457i \(0.569208\pi\)
\(348\) 27.3926 1.46840
\(349\) 0.856938 0.0458708 0.0229354 0.999737i \(-0.492699\pi\)
0.0229354 + 0.999737i \(0.492699\pi\)
\(350\) 1.94043 0.103720
\(351\) 32.0742 1.71199
\(352\) −26.1482 −1.39370
\(353\) −15.0983 −0.803599 −0.401800 0.915728i \(-0.631615\pi\)
−0.401800 + 0.915728i \(0.631615\pi\)
\(354\) 5.03665 0.267695
\(355\) 2.44211 0.129614
\(356\) 46.9776 2.48981
\(357\) 7.44949 0.394269
\(358\) 20.2273 1.06904
\(359\) −16.6800 −0.880335 −0.440167 0.897916i \(-0.645081\pi\)
−0.440167 + 0.897916i \(0.645081\pi\)
\(360\) 4.57933 0.241352
\(361\) −3.14332 −0.165438
\(362\) 1.34732 0.0708134
\(363\) 10.3797 0.544791
\(364\) 16.2265 0.850500
\(365\) 0.585835 0.0306640
\(366\) 28.0740 1.46745
\(367\) −1.25576 −0.0655499 −0.0327749 0.999463i \(-0.510434\pi\)
−0.0327749 + 0.999463i \(0.510434\pi\)
\(368\) 1.48553 0.0774384
\(369\) −16.9837 −0.884134
\(370\) −14.3609 −0.746586
\(371\) −9.01844 −0.468214
\(372\) −14.8134 −0.768038
\(373\) 9.23550 0.478196 0.239098 0.970995i \(-0.423148\pi\)
0.239098 + 0.970995i \(0.423148\pi\)
\(374\) −77.5928 −4.01223
\(375\) 1.15086 0.0594303
\(376\) 14.5957 0.752713
\(377\) −44.3547 −2.28439
\(378\) −10.4412 −0.537037
\(379\) 5.00757 0.257221 0.128611 0.991695i \(-0.458948\pi\)
0.128611 + 0.991695i \(0.458948\pi\)
\(380\) 12.7373 0.653411
\(381\) −9.30204 −0.476558
\(382\) −10.4108 −0.532662
\(383\) 28.3321 1.44770 0.723851 0.689957i \(-0.242370\pi\)
0.723851 + 0.689957i \(0.242370\pi\)
\(384\) 20.6438 1.05347
\(385\) 3.80778 0.194062
\(386\) −35.5665 −1.81029
\(387\) 9.23010 0.469193
\(388\) 32.5994 1.65498
\(389\) 15.4718 0.784450 0.392225 0.919869i \(-0.371706\pi\)
0.392225 + 0.919869i \(0.371706\pi\)
\(390\) 15.6413 0.792028
\(391\) 68.1606 3.44703
\(392\) 17.1521 0.866312
\(393\) 2.90876 0.146728
\(394\) −45.2608 −2.28021
\(395\) −8.15531 −0.410338
\(396\) 23.9796 1.20502
\(397\) 21.9553 1.10190 0.550952 0.834537i \(-0.314265\pi\)
0.550952 + 0.834537i \(0.314265\pi\)
\(398\) 24.4466 1.22540
\(399\) −3.90013 −0.195251
\(400\) −0.165768 −0.00828838
\(401\) 6.54841 0.327012 0.163506 0.986542i \(-0.447720\pi\)
0.163506 + 0.986542i \(0.447720\pi\)
\(402\) 3.00578 0.149915
\(403\) 23.9862 1.19484
\(404\) −5.43273 −0.270288
\(405\) −1.16609 −0.0579437
\(406\) 14.4389 0.716591
\(407\) −28.1810 −1.39688
\(408\) 23.9238 1.18440
\(409\) 2.58117 0.127631 0.0638154 0.997962i \(-0.479673\pi\)
0.0638154 + 0.997962i \(0.479673\pi\)
\(410\) −23.1116 −1.14140
\(411\) −11.6802 −0.576142
\(412\) −10.2276 −0.503880
\(413\) 1.63351 0.0803797
\(414\) −34.2354 −1.68258
\(415\) −11.0014 −0.540038
\(416\) −34.8356 −1.70795
\(417\) −13.2258 −0.647669
\(418\) 40.6232 1.98695
\(419\) 21.6954 1.05989 0.529944 0.848033i \(-0.322213\pi\)
0.529944 + 0.848033i \(0.322213\pi\)
\(420\) −3.13289 −0.152869
\(421\) −29.7689 −1.45085 −0.725424 0.688303i \(-0.758356\pi\)
−0.725424 + 0.688303i \(0.758356\pi\)
\(422\) 20.7571 1.01044
\(423\) 8.94786 0.435060
\(424\) −28.9624 −1.40654
\(425\) −7.60594 −0.368942
\(426\) −6.40819 −0.310478
\(427\) 9.10509 0.440626
\(428\) 6.08468 0.294114
\(429\) 30.6936 1.48190
\(430\) 12.5604 0.605718
\(431\) 5.88079 0.283267 0.141634 0.989919i \(-0.454764\pi\)
0.141634 + 0.989919i \(0.454764\pi\)
\(432\) 0.891975 0.0429152
\(433\) −16.9070 −0.812500 −0.406250 0.913762i \(-0.633164\pi\)
−0.406250 + 0.913762i \(0.633164\pi\)
\(434\) −7.80829 −0.374810
\(435\) 8.56368 0.410597
\(436\) −60.6457 −2.90440
\(437\) −35.6851 −1.70705
\(438\) −1.53725 −0.0734529
\(439\) 9.13729 0.436099 0.218050 0.975938i \(-0.430031\pi\)
0.218050 + 0.975938i \(0.430031\pi\)
\(440\) 12.2286 0.582973
\(441\) 10.5151 0.500719
\(442\) −103.372 −4.91690
\(443\) −29.7050 −1.41132 −0.705662 0.708548i \(-0.749350\pi\)
−0.705662 + 0.708548i \(0.749350\pi\)
\(444\) 23.1862 1.10037
\(445\) 14.6865 0.696207
\(446\) 29.7591 1.40913
\(447\) 23.2928 1.10171
\(448\) 11.0580 0.522440
\(449\) −2.64872 −0.125001 −0.0625004 0.998045i \(-0.519907\pi\)
−0.0625004 + 0.998045i \(0.519907\pi\)
\(450\) 3.82028 0.180090
\(451\) −45.3528 −2.13558
\(452\) −55.3168 −2.60188
\(453\) 20.4939 0.962886
\(454\) −23.9652 −1.12474
\(455\) 5.07286 0.237819
\(456\) −12.5251 −0.586544
\(457\) 1.77245 0.0829115 0.0414558 0.999140i \(-0.486800\pi\)
0.0414558 + 0.999140i \(0.486800\pi\)
\(458\) −33.4182 −1.56153
\(459\) 40.9266 1.91029
\(460\) −28.6650 −1.33651
\(461\) 1.50816 0.0702419 0.0351210 0.999383i \(-0.488818\pi\)
0.0351210 + 0.999383i \(0.488818\pi\)
\(462\) −9.99176 −0.464859
\(463\) −28.7937 −1.33816 −0.669078 0.743192i \(-0.733311\pi\)
−0.669078 + 0.743192i \(0.733311\pi\)
\(464\) −1.23349 −0.0572635
\(465\) −4.63108 −0.214761
\(466\) 41.0332 1.90082
\(467\) −16.4285 −0.760220 −0.380110 0.924941i \(-0.624114\pi\)
−0.380110 + 0.924941i \(0.624114\pi\)
\(468\) 31.9465 1.47673
\(469\) 0.974849 0.0450143
\(470\) 12.1764 0.561653
\(471\) −4.19272 −0.193190
\(472\) 5.24596 0.241465
\(473\) 24.6479 1.13331
\(474\) 21.3998 0.982927
\(475\) 3.98204 0.182709
\(476\) 20.7050 0.949012
\(477\) −17.7554 −0.812963
\(478\) −41.5650 −1.90114
\(479\) −9.47171 −0.432773 −0.216387 0.976308i \(-0.569427\pi\)
−0.216387 + 0.976308i \(0.569427\pi\)
\(480\) 6.72579 0.306989
\(481\) −37.5437 −1.71184
\(482\) −7.17786 −0.326943
\(483\) 8.77716 0.399374
\(484\) 28.8491 1.31132
\(485\) 10.1915 0.462771
\(486\) −33.7463 −1.53076
\(487\) 11.0766 0.501929 0.250964 0.967996i \(-0.419252\pi\)
0.250964 + 0.967996i \(0.419252\pi\)
\(488\) 29.2407 1.32366
\(489\) 19.8451 0.897429
\(490\) 14.3091 0.646418
\(491\) 38.8335 1.75253 0.876267 0.481826i \(-0.160026\pi\)
0.876267 + 0.481826i \(0.160026\pi\)
\(492\) 37.3145 1.68227
\(493\) −56.5966 −2.54898
\(494\) 54.1197 2.43496
\(495\) 7.49670 0.336952
\(496\) 0.667050 0.0299514
\(497\) −2.07834 −0.0932261
\(498\) 28.8681 1.29361
\(499\) 2.43635 0.109066 0.0545330 0.998512i \(-0.482633\pi\)
0.0545330 + 0.998512i \(0.482633\pi\)
\(500\) 3.19869 0.143050
\(501\) −26.5942 −1.18814
\(502\) 24.6947 1.10218
\(503\) 17.7347 0.790752 0.395376 0.918519i \(-0.370614\pi\)
0.395376 + 0.918519i \(0.370614\pi\)
\(504\) −3.89720 −0.173595
\(505\) −1.69842 −0.0755789
\(506\) −91.4216 −4.06419
\(507\) 25.9299 1.15159
\(508\) −25.8539 −1.14708
\(509\) −32.7436 −1.45134 −0.725668 0.688045i \(-0.758469\pi\)
−0.725668 + 0.688045i \(0.758469\pi\)
\(510\) 19.9583 0.883767
\(511\) −0.498570 −0.0220554
\(512\) −1.87488 −0.0828589
\(513\) −21.4269 −0.946020
\(514\) −53.8793 −2.37651
\(515\) −3.19745 −0.140896
\(516\) −20.2793 −0.892747
\(517\) 23.8942 1.05086
\(518\) 12.2217 0.536990
\(519\) 5.78529 0.253946
\(520\) 16.2913 0.714421
\(521\) −1.29770 −0.0568532 −0.0284266 0.999596i \(-0.509050\pi\)
−0.0284266 + 0.999596i \(0.509050\pi\)
\(522\) 28.4271 1.24422
\(523\) 29.8560 1.30551 0.652755 0.757569i \(-0.273613\pi\)
0.652755 + 0.757569i \(0.273613\pi\)
\(524\) 8.08457 0.353176
\(525\) −0.979430 −0.0427458
\(526\) −6.31241 −0.275234
\(527\) 30.6064 1.33323
\(528\) 0.853581 0.0371473
\(529\) 57.3083 2.49167
\(530\) −24.1617 −1.04952
\(531\) 3.21603 0.139564
\(532\) −10.8400 −0.469973
\(533\) −60.4206 −2.61711
\(534\) −38.5380 −1.66770
\(535\) 1.90224 0.0822411
\(536\) 3.13069 0.135225
\(537\) −10.2097 −0.440582
\(538\) 60.6104 2.61310
\(539\) 28.0793 1.20946
\(540\) −17.2117 −0.740675
\(541\) 13.7272 0.590180 0.295090 0.955470i \(-0.404650\pi\)
0.295090 + 0.955470i \(0.404650\pi\)
\(542\) −14.1188 −0.606453
\(543\) −0.680058 −0.0291841
\(544\) −44.4501 −1.90578
\(545\) −18.9596 −0.812138
\(546\) −13.3114 −0.569674
\(547\) −34.3003 −1.46658 −0.733288 0.679918i \(-0.762015\pi\)
−0.733288 + 0.679918i \(0.762015\pi\)
\(548\) −32.4638 −1.38678
\(549\) 17.9260 0.765062
\(550\) 10.2016 0.434998
\(551\) 29.6308 1.26232
\(552\) 28.1875 1.19974
\(553\) 6.94050 0.295140
\(554\) −15.4528 −0.656528
\(555\) 7.24865 0.307688
\(556\) −36.7595 −1.55895
\(557\) −5.33307 −0.225969 −0.112985 0.993597i \(-0.536041\pi\)
−0.112985 + 0.993597i \(0.536041\pi\)
\(558\) −15.3729 −0.650785
\(559\) 32.8368 1.38885
\(560\) 0.141075 0.00596150
\(561\) 39.1650 1.65355
\(562\) −56.0728 −2.36529
\(563\) 39.5053 1.66495 0.832475 0.554062i \(-0.186923\pi\)
0.832475 + 0.554062i \(0.186923\pi\)
\(564\) −19.6592 −0.827801
\(565\) −17.2936 −0.727546
\(566\) −10.5928 −0.445249
\(567\) 0.992393 0.0416766
\(568\) −6.67450 −0.280056
\(569\) 21.3177 0.893685 0.446842 0.894613i \(-0.352548\pi\)
0.446842 + 0.894613i \(0.352548\pi\)
\(570\) −10.4490 −0.437662
\(571\) −9.95790 −0.416725 −0.208363 0.978052i \(-0.566813\pi\)
−0.208363 + 0.978052i \(0.566813\pi\)
\(572\) 85.3093 3.56696
\(573\) 5.25484 0.219524
\(574\) 19.6689 0.820963
\(575\) −8.96149 −0.373720
\(576\) 21.7708 0.907115
\(577\) 10.6056 0.441518 0.220759 0.975328i \(-0.429147\pi\)
0.220759 + 0.975328i \(0.429147\pi\)
\(578\) −93.1413 −3.87417
\(579\) 17.9522 0.746068
\(580\) 23.8018 0.988315
\(581\) 9.36265 0.388428
\(582\) −26.7428 −1.10853
\(583\) −47.4136 −1.96367
\(584\) −1.60114 −0.0662556
\(585\) 9.98737 0.412927
\(586\) −68.8746 −2.84518
\(587\) −18.3736 −0.758361 −0.379180 0.925323i \(-0.623794\pi\)
−0.379180 + 0.925323i \(0.623794\pi\)
\(588\) −23.1025 −0.952732
\(589\) −16.0238 −0.660249
\(590\) 4.37641 0.180174
\(591\) 22.8454 0.939735
\(592\) −1.04408 −0.0429114
\(593\) −7.84694 −0.322235 −0.161118 0.986935i \(-0.551510\pi\)
−0.161118 + 0.986935i \(0.551510\pi\)
\(594\) −54.8936 −2.25231
\(595\) 6.47296 0.265366
\(596\) 64.7397 2.65184
\(597\) −12.3394 −0.505020
\(598\) −121.795 −4.98057
\(599\) 3.43399 0.140309 0.0701545 0.997536i \(-0.477651\pi\)
0.0701545 + 0.997536i \(0.477651\pi\)
\(600\) −3.14541 −0.128411
\(601\) 3.77224 0.153873 0.0769365 0.997036i \(-0.475486\pi\)
0.0769365 + 0.997036i \(0.475486\pi\)
\(602\) −10.6894 −0.435669
\(603\) 1.91927 0.0781586
\(604\) 56.9604 2.31768
\(605\) 9.01904 0.366676
\(606\) 4.45673 0.181042
\(607\) −23.5666 −0.956540 −0.478270 0.878213i \(-0.658736\pi\)
−0.478270 + 0.878213i \(0.658736\pi\)
\(608\) 23.2716 0.943788
\(609\) −7.28804 −0.295326
\(610\) 24.3939 0.987679
\(611\) 31.8327 1.28781
\(612\) 40.7637 1.64778
\(613\) −9.88640 −0.399308 −0.199654 0.979866i \(-0.563982\pi\)
−0.199654 + 0.979866i \(0.563982\pi\)
\(614\) −8.88038 −0.358383
\(615\) 11.6656 0.470401
\(616\) −10.4070 −0.419310
\(617\) −33.2682 −1.33933 −0.669664 0.742664i \(-0.733562\pi\)
−0.669664 + 0.742664i \(0.733562\pi\)
\(618\) 8.39023 0.337504
\(619\) 22.3304 0.897534 0.448767 0.893649i \(-0.351863\pi\)
0.448767 + 0.893649i \(0.351863\pi\)
\(620\) −12.8716 −0.516934
\(621\) 48.2207 1.93503
\(622\) −38.8463 −1.55759
\(623\) −12.4988 −0.500754
\(624\) 1.13717 0.0455232
\(625\) 1.00000 0.0400000
\(626\) 43.6726 1.74551
\(627\) −20.5046 −0.818874
\(628\) −11.6532 −0.465013
\(629\) −47.9057 −1.91012
\(630\) −3.25122 −0.129532
\(631\) 4.50741 0.179437 0.0897187 0.995967i \(-0.471403\pi\)
0.0897187 + 0.995967i \(0.471403\pi\)
\(632\) 22.2892 0.886615
\(633\) −10.4771 −0.416429
\(634\) −18.8631 −0.749151
\(635\) −8.08267 −0.320751
\(636\) 39.0101 1.54685
\(637\) 37.4082 1.48217
\(638\) 75.9112 3.00535
\(639\) −4.09180 −0.161869
\(640\) 17.9376 0.709048
\(641\) 34.4693 1.36146 0.680729 0.732536i \(-0.261663\pi\)
0.680729 + 0.732536i \(0.261663\pi\)
\(642\) −4.99156 −0.197001
\(643\) −2.52205 −0.0994600 −0.0497300 0.998763i \(-0.515836\pi\)
−0.0497300 + 0.998763i \(0.515836\pi\)
\(644\) 24.3951 0.961302
\(645\) −6.33988 −0.249633
\(646\) 69.0567 2.71700
\(647\) −6.34952 −0.249626 −0.124813 0.992180i \(-0.539833\pi\)
−0.124813 + 0.992180i \(0.539833\pi\)
\(648\) 3.18704 0.125199
\(649\) 8.58802 0.337109
\(650\) 13.5909 0.533081
\(651\) 3.94124 0.154469
\(652\) 55.1573 2.16013
\(653\) 48.3184 1.89084 0.945422 0.325847i \(-0.105649\pi\)
0.945422 + 0.325847i \(0.105649\pi\)
\(654\) 49.7506 1.94540
\(655\) 2.52746 0.0987561
\(656\) −1.68028 −0.0656040
\(657\) −0.981577 −0.0382950
\(658\) −10.3626 −0.403975
\(659\) 6.11791 0.238320 0.119160 0.992875i \(-0.461980\pi\)
0.119160 + 0.992875i \(0.461980\pi\)
\(660\) −16.4709 −0.641128
\(661\) −25.2321 −0.981416 −0.490708 0.871324i \(-0.663262\pi\)
−0.490708 + 0.871324i \(0.663262\pi\)
\(662\) 41.5618 1.61534
\(663\) 52.1770 2.02639
\(664\) 30.0678 1.16686
\(665\) −3.38888 −0.131415
\(666\) 24.0619 0.932379
\(667\) −66.6834 −2.58199
\(668\) −73.9154 −2.85987
\(669\) −15.0209 −0.580741
\(670\) 2.61176 0.100901
\(671\) 47.8691 1.84797
\(672\) −5.72392 −0.220805
\(673\) −46.2002 −1.78089 −0.890443 0.455094i \(-0.849606\pi\)
−0.890443 + 0.455094i \(0.849606\pi\)
\(674\) 27.6810 1.06623
\(675\) −5.38087 −0.207110
\(676\) 72.0691 2.77189
\(677\) −40.3289 −1.54997 −0.774983 0.631982i \(-0.782242\pi\)
−0.774983 + 0.631982i \(0.782242\pi\)
\(678\) 45.3790 1.74277
\(679\) −8.67336 −0.332853
\(680\) 20.7877 0.797172
\(681\) 12.0964 0.463536
\(682\) −41.0514 −1.57194
\(683\) 8.76492 0.335380 0.167690 0.985840i \(-0.446369\pi\)
0.167690 + 0.985840i \(0.446369\pi\)
\(684\) −21.3416 −0.816016
\(685\) −10.1491 −0.387777
\(686\) −25.7606 −0.983543
\(687\) 16.8679 0.643549
\(688\) 0.913182 0.0348148
\(689\) −63.1661 −2.40644
\(690\) 23.5153 0.895212
\(691\) −17.9806 −0.684013 −0.342006 0.939698i \(-0.611106\pi\)
−0.342006 + 0.939698i \(0.611106\pi\)
\(692\) 16.0795 0.611252
\(693\) −6.38000 −0.242356
\(694\) 18.3239 0.695567
\(695\) −11.4921 −0.435919
\(696\) −23.4053 −0.887175
\(697\) −77.0966 −2.92024
\(698\) −1.95387 −0.0739552
\(699\) −20.7115 −0.783380
\(700\) −2.72221 −0.102890
\(701\) 28.5781 1.07938 0.539690 0.841864i \(-0.318541\pi\)
0.539690 + 0.841864i \(0.318541\pi\)
\(702\) −73.1311 −2.76016
\(703\) 25.0807 0.945938
\(704\) 58.1362 2.19109
\(705\) −6.14601 −0.231472
\(706\) 34.4250 1.29560
\(707\) 1.44543 0.0543609
\(708\) −7.06588 −0.265552
\(709\) 3.08152 0.115729 0.0578644 0.998324i \(-0.481571\pi\)
0.0578644 + 0.998324i \(0.481571\pi\)
\(710\) −5.56817 −0.208970
\(711\) 13.6644 0.512453
\(712\) −40.1395 −1.50429
\(713\) 36.0611 1.35050
\(714\) −16.9853 −0.635659
\(715\) 26.6701 0.997404
\(716\) −28.3767 −1.06049
\(717\) 20.9799 0.783510
\(718\) 38.0314 1.41932
\(719\) −37.3606 −1.39331 −0.696657 0.717404i \(-0.745330\pi\)
−0.696657 + 0.717404i \(0.745330\pi\)
\(720\) 0.277746 0.0103510
\(721\) 2.72116 0.101341
\(722\) 7.16697 0.266727
\(723\) 3.62303 0.134742
\(724\) −1.89014 −0.0702466
\(725\) 7.44110 0.276356
\(726\) −23.6663 −0.878339
\(727\) 15.8784 0.588897 0.294449 0.955667i \(-0.404864\pi\)
0.294449 + 0.955667i \(0.404864\pi\)
\(728\) −13.8646 −0.513855
\(729\) 20.5317 0.760435
\(730\) −1.33574 −0.0494380
\(731\) 41.8997 1.54972
\(732\) −39.3848 −1.45571
\(733\) −38.2749 −1.41372 −0.706858 0.707356i \(-0.749888\pi\)
−0.706858 + 0.707356i \(0.749888\pi\)
\(734\) 2.86320 0.105683
\(735\) −7.22250 −0.266406
\(736\) −52.3722 −1.93046
\(737\) 5.12517 0.188788
\(738\) 38.7238 1.42544
\(739\) −42.2068 −1.55260 −0.776301 0.630363i \(-0.782906\pi\)
−0.776301 + 0.630363i \(0.782906\pi\)
\(740\) 20.1468 0.740611
\(741\) −27.3169 −1.00351
\(742\) 20.5626 0.754877
\(743\) 25.9945 0.953647 0.476824 0.878999i \(-0.341788\pi\)
0.476824 + 0.878999i \(0.341788\pi\)
\(744\) 12.6571 0.464033
\(745\) 20.2394 0.741516
\(746\) −21.0575 −0.770971
\(747\) 18.4331 0.674430
\(748\) 108.855 3.98012
\(749\) −1.61889 −0.0591528
\(750\) −2.62404 −0.0958163
\(751\) −40.6898 −1.48479 −0.742396 0.669961i \(-0.766311\pi\)
−0.742396 + 0.669961i \(0.766311\pi\)
\(752\) 0.885258 0.0322820
\(753\) −12.4647 −0.454237
\(754\) 101.132 3.68300
\(755\) 17.8074 0.648078
\(756\) 14.6479 0.532739
\(757\) −15.3374 −0.557448 −0.278724 0.960371i \(-0.589911\pi\)
−0.278724 + 0.960371i \(0.589911\pi\)
\(758\) −11.4176 −0.414705
\(759\) 46.1451 1.67496
\(760\) −10.8833 −0.394778
\(761\) 37.3320 1.35329 0.676643 0.736312i \(-0.263434\pi\)
0.676643 + 0.736312i \(0.263434\pi\)
\(762\) 21.2092 0.768329
\(763\) 16.1354 0.584139
\(764\) 14.6052 0.528399
\(765\) 12.7439 0.460756
\(766\) −64.5989 −2.33405
\(767\) 11.4413 0.413120
\(768\) −17.1617 −0.619270
\(769\) 36.2014 1.30546 0.652728 0.757593i \(-0.273625\pi\)
0.652728 + 0.757593i \(0.273625\pi\)
\(770\) −8.68198 −0.312877
\(771\) 27.1956 0.979424
\(772\) 49.8961 1.79580
\(773\) −16.5850 −0.596520 −0.298260 0.954485i \(-0.596406\pi\)
−0.298260 + 0.954485i \(0.596406\pi\)
\(774\) −21.0452 −0.756455
\(775\) −4.02401 −0.144547
\(776\) −27.8542 −0.999907
\(777\) −6.16890 −0.221308
\(778\) −35.2766 −1.26473
\(779\) 40.3635 1.44617
\(780\) −21.9431 −0.785689
\(781\) −10.9267 −0.390986
\(782\) −155.410 −5.55747
\(783\) −40.0397 −1.43090
\(784\) 1.04031 0.0371540
\(785\) −3.64311 −0.130028
\(786\) −6.63216 −0.236561
\(787\) −43.3720 −1.54605 −0.773023 0.634378i \(-0.781256\pi\)
−0.773023 + 0.634378i \(0.781256\pi\)
\(788\) 63.4962 2.26196
\(789\) 3.18619 0.113431
\(790\) 18.5946 0.661567
\(791\) 14.7175 0.523295
\(792\) −20.4891 −0.728050
\(793\) 63.7729 2.26464
\(794\) −50.0595 −1.77654
\(795\) 12.1956 0.432535
\(796\) −34.2961 −1.21559
\(797\) −40.5342 −1.43580 −0.717898 0.696148i \(-0.754896\pi\)
−0.717898 + 0.696148i \(0.754896\pi\)
\(798\) 8.89255 0.314793
\(799\) 40.6184 1.43698
\(800\) 5.84413 0.206621
\(801\) −24.6075 −0.869463
\(802\) −14.9308 −0.527225
\(803\) −2.62118 −0.0924995
\(804\) −4.21679 −0.148715
\(805\) 7.62659 0.268802
\(806\) −54.6901 −1.92638
\(807\) −30.5931 −1.07693
\(808\) 4.64194 0.163303
\(809\) 18.3441 0.644945 0.322472 0.946579i \(-0.395486\pi\)
0.322472 + 0.946579i \(0.395486\pi\)
\(810\) 2.65877 0.0934196
\(811\) 39.9941 1.40438 0.702192 0.711988i \(-0.252205\pi\)
0.702192 + 0.711988i \(0.252205\pi\)
\(812\) −20.2563 −0.710856
\(813\) 7.12644 0.249935
\(814\) 64.2544 2.25211
\(815\) 17.2437 0.604021
\(816\) 1.45103 0.0507961
\(817\) −21.9363 −0.767455
\(818\) −5.88524 −0.205773
\(819\) −8.49966 −0.297002
\(820\) 32.4231 1.13226
\(821\) 0.520721 0.0181733 0.00908664 0.999959i \(-0.497108\pi\)
0.00908664 + 0.999959i \(0.497108\pi\)
\(822\) 26.6316 0.928883
\(823\) 50.5973 1.76371 0.881856 0.471519i \(-0.156294\pi\)
0.881856 + 0.471519i \(0.156294\pi\)
\(824\) 8.73890 0.304434
\(825\) −5.14926 −0.179274
\(826\) −3.72450 −0.129592
\(827\) 16.0127 0.556817 0.278409 0.960463i \(-0.410193\pi\)
0.278409 + 0.960463i \(0.410193\pi\)
\(828\) 48.0287 1.66911
\(829\) 14.7812 0.513372 0.256686 0.966495i \(-0.417369\pi\)
0.256686 + 0.966495i \(0.417369\pi\)
\(830\) 25.0839 0.870676
\(831\) 7.79982 0.270573
\(832\) 77.4511 2.68513
\(833\) 47.7328 1.65384
\(834\) 30.1556 1.04420
\(835\) −23.1080 −0.799687
\(836\) −56.9901 −1.97105
\(837\) 21.6527 0.748426
\(838\) −49.4668 −1.70880
\(839\) −25.0577 −0.865087 −0.432543 0.901613i \(-0.642384\pi\)
−0.432543 + 0.901613i \(0.642384\pi\)
\(840\) 2.67687 0.0923607
\(841\) 26.3700 0.909312
\(842\) 67.8750 2.33913
\(843\) 28.3028 0.974799
\(844\) −29.1200 −1.00235
\(845\) 22.5308 0.775084
\(846\) −20.4017 −0.701424
\(847\) −7.67557 −0.263736
\(848\) −1.75663 −0.0603230
\(849\) 5.34672 0.183499
\(850\) 17.3420 0.594827
\(851\) −56.4436 −1.93486
\(852\) 8.99002 0.307993
\(853\) −26.0015 −0.890276 −0.445138 0.895462i \(-0.646845\pi\)
−0.445138 + 0.895462i \(0.646845\pi\)
\(854\) −20.7602 −0.710399
\(855\) −6.67198 −0.228177
\(856\) −5.19899 −0.177698
\(857\) −23.9697 −0.818791 −0.409395 0.912357i \(-0.634260\pi\)
−0.409395 + 0.912357i \(0.634260\pi\)
\(858\) −69.9833 −2.38919
\(859\) 42.2242 1.44067 0.720336 0.693626i \(-0.243988\pi\)
0.720336 + 0.693626i \(0.243988\pi\)
\(860\) −17.6210 −0.600870
\(861\) −9.92787 −0.338341
\(862\) −13.4086 −0.456697
\(863\) 10.9708 0.373450 0.186725 0.982412i \(-0.440213\pi\)
0.186725 + 0.982412i \(0.440213\pi\)
\(864\) −31.4465 −1.06983
\(865\) 5.02692 0.170920
\(866\) 38.5491 1.30995
\(867\) 47.0131 1.59665
\(868\) 10.9542 0.371810
\(869\) 36.4890 1.23780
\(870\) −19.5257 −0.661985
\(871\) 6.82794 0.231356
\(872\) 51.8181 1.75478
\(873\) −17.0760 −0.577935
\(874\) 81.3642 2.75219
\(875\) −0.851041 −0.0287704
\(876\) 2.15661 0.0728650
\(877\) −36.0358 −1.21684 −0.608422 0.793614i \(-0.708197\pi\)
−0.608422 + 0.793614i \(0.708197\pi\)
\(878\) −20.8336 −0.703100
\(879\) 34.7644 1.17258
\(880\) 0.741688 0.0250023
\(881\) −16.6108 −0.559633 −0.279816 0.960054i \(-0.590274\pi\)
−0.279816 + 0.960054i \(0.590274\pi\)
\(882\) −23.9751 −0.807283
\(883\) 4.52130 0.152154 0.0760769 0.997102i \(-0.475761\pi\)
0.0760769 + 0.997102i \(0.475761\pi\)
\(884\) 145.020 4.87755
\(885\) −2.20899 −0.0742545
\(886\) 67.7292 2.27541
\(887\) −27.7457 −0.931608 −0.465804 0.884888i \(-0.654235\pi\)
−0.465804 + 0.884888i \(0.654235\pi\)
\(888\) −19.8112 −0.664820
\(889\) 6.87868 0.230703
\(890\) −33.4862 −1.12246
\(891\) 5.21741 0.174790
\(892\) −41.7488 −1.39785
\(893\) −21.2655 −0.711624
\(894\) −53.1091 −1.77623
\(895\) −8.87136 −0.296537
\(896\) −15.2657 −0.509990
\(897\) 61.4761 2.05263
\(898\) 6.03925 0.201532
\(899\) −29.9431 −0.998657
\(900\) −5.35946 −0.178649
\(901\) −80.5998 −2.68517
\(902\) 103.407 3.44309
\(903\) 5.39550 0.179551
\(904\) 47.2649 1.57201
\(905\) −0.590912 −0.0196426
\(906\) −46.7273 −1.55241
\(907\) −7.92585 −0.263173 −0.131587 0.991305i \(-0.542007\pi\)
−0.131587 + 0.991305i \(0.542007\pi\)
\(908\) 33.6206 1.11574
\(909\) 2.84574 0.0943872
\(910\) −11.5664 −0.383424
\(911\) 14.6839 0.486498 0.243249 0.969964i \(-0.421787\pi\)
0.243249 + 0.969964i \(0.421787\pi\)
\(912\) −0.759677 −0.0251554
\(913\) 49.2232 1.62905
\(914\) −4.04129 −0.133674
\(915\) −12.3128 −0.407049
\(916\) 46.8823 1.54903
\(917\) −2.15097 −0.0710314
\(918\) −93.3153 −3.07986
\(919\) 20.2561 0.668186 0.334093 0.942540i \(-0.391570\pi\)
0.334093 + 0.942540i \(0.391570\pi\)
\(920\) 24.4925 0.807495
\(921\) 4.48237 0.147699
\(922\) −3.43870 −0.113247
\(923\) −14.5569 −0.479145
\(924\) 14.0174 0.461138
\(925\) 6.29845 0.207092
\(926\) 65.6514 2.15744
\(927\) 5.35738 0.175959
\(928\) 43.4868 1.42752
\(929\) 44.5280 1.46092 0.730458 0.682958i \(-0.239307\pi\)
0.730458 + 0.682958i \(0.239307\pi\)
\(930\) 10.5592 0.346248
\(931\) −24.9902 −0.819022
\(932\) −57.5652 −1.88561
\(933\) 19.6076 0.641926
\(934\) 37.4580 1.22566
\(935\) 34.0310 1.11293
\(936\) −27.2964 −0.892209
\(937\) −26.6782 −0.871538 −0.435769 0.900059i \(-0.643524\pi\)
−0.435769 + 0.900059i \(0.643524\pi\)
\(938\) −2.22272 −0.0725743
\(939\) −22.0438 −0.719371
\(940\) −17.0821 −0.557158
\(941\) 11.0343 0.359708 0.179854 0.983693i \(-0.442438\pi\)
0.179854 + 0.983693i \(0.442438\pi\)
\(942\) 9.55967 0.311471
\(943\) −90.8370 −2.95806
\(944\) 0.318179 0.0103558
\(945\) 4.57934 0.148966
\(946\) −56.1987 −1.82718
\(947\) −8.38953 −0.272623 −0.136312 0.990666i \(-0.543525\pi\)
−0.136312 + 0.990666i \(0.543525\pi\)
\(948\) −30.0217 −0.975060
\(949\) −3.49203 −0.113356
\(950\) −9.07931 −0.294572
\(951\) 9.52117 0.308745
\(952\) −17.6912 −0.573374
\(953\) −7.66315 −0.248234 −0.124117 0.992268i \(-0.539610\pi\)
−0.124117 + 0.992268i \(0.539610\pi\)
\(954\) 40.4834 1.31070
\(955\) 4.56601 0.147752
\(956\) 58.3113 1.88592
\(957\) −38.3162 −1.23859
\(958\) 21.5961 0.697738
\(959\) 8.63728 0.278912
\(960\) −14.9537 −0.482628
\(961\) −14.8073 −0.477656
\(962\) 85.6019 2.75992
\(963\) −3.18724 −0.102707
\(964\) 10.0698 0.324326
\(965\) 15.5989 0.502147
\(966\) −20.0125 −0.643891
\(967\) −11.0863 −0.356512 −0.178256 0.983984i \(-0.557046\pi\)
−0.178256 + 0.983984i \(0.557046\pi\)
\(968\) −24.6498 −0.792275
\(969\) −34.8564 −1.11975
\(970\) −23.2372 −0.746102
\(971\) 47.7547 1.53252 0.766260 0.642530i \(-0.222115\pi\)
0.766260 + 0.642530i \(0.222115\pi\)
\(972\) 47.3425 1.51851
\(973\) 9.78021 0.313539
\(974\) −25.2554 −0.809234
\(975\) −6.86003 −0.219697
\(976\) 1.77351 0.0567687
\(977\) −53.4877 −1.71122 −0.855612 0.517617i \(-0.826819\pi\)
−0.855612 + 0.517617i \(0.826819\pi\)
\(978\) −45.2482 −1.44688
\(979\) −65.7113 −2.10014
\(980\) −20.0741 −0.641244
\(981\) 31.7671 1.01424
\(982\) −88.5429 −2.82552
\(983\) 48.3581 1.54238 0.771192 0.636603i \(-0.219661\pi\)
0.771192 + 0.636603i \(0.219661\pi\)
\(984\) −31.8830 −1.01639
\(985\) 19.8507 0.632496
\(986\) 129.044 4.10959
\(987\) 5.23051 0.166489
\(988\) −75.9243 −2.41547
\(989\) 49.3672 1.56978
\(990\) −17.0930 −0.543250
\(991\) 51.3019 1.62966 0.814829 0.579701i \(-0.196831\pi\)
0.814829 + 0.579701i \(0.196831\pi\)
\(992\) −23.5168 −0.746661
\(993\) −20.9783 −0.665726
\(994\) 4.73874 0.150304
\(995\) −10.7219 −0.339908
\(996\) −40.4989 −1.28326
\(997\) 33.2743 1.05381 0.526903 0.849925i \(-0.323353\pi\)
0.526903 + 0.849925i \(0.323353\pi\)
\(998\) −5.55503 −0.175841
\(999\) −33.8912 −1.07227
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 \(a_p\))