Properties

Label 8035.2.a.e.1.5
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 1.5
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65503 q^{2}\) \(-2.98031 q^{3}\) \(+5.04918 q^{4}\) \(+1.00000 q^{5}\) \(+7.91280 q^{6}\) \(-3.81633 q^{7}\) \(-8.09566 q^{8}\) \(+5.88223 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65503 q^{2}\) \(-2.98031 q^{3}\) \(+5.04918 q^{4}\) \(+1.00000 q^{5}\) \(+7.91280 q^{6}\) \(-3.81633 q^{7}\) \(-8.09566 q^{8}\) \(+5.88223 q^{9}\) \(-2.65503 q^{10}\) \(-5.97342 q^{11}\) \(-15.0481 q^{12}\) \(+2.24489 q^{13}\) \(+10.1325 q^{14}\) \(-2.98031 q^{15}\) \(+11.3958 q^{16}\) \(-1.94879 q^{17}\) \(-15.6175 q^{18}\) \(+0.247485 q^{19}\) \(+5.04918 q^{20}\) \(+11.3739 q^{21}\) \(+15.8596 q^{22}\) \(+2.92599 q^{23}\) \(+24.1275 q^{24}\) \(+1.00000 q^{25}\) \(-5.96024 q^{26}\) \(-8.58993 q^{27}\) \(-19.2694 q^{28}\) \(+10.2141 q^{29}\) \(+7.91280 q^{30}\) \(+4.85592 q^{31}\) \(-14.0650 q^{32}\) \(+17.8026 q^{33}\) \(+5.17410 q^{34}\) \(-3.81633 q^{35}\) \(+29.7004 q^{36}\) \(-8.83263 q^{37}\) \(-0.657079 q^{38}\) \(-6.69045 q^{39}\) \(-8.09566 q^{40}\) \(+11.0506 q^{41}\) \(-30.1979 q^{42}\) \(+7.95994 q^{43}\) \(-30.1609 q^{44}\) \(+5.88223 q^{45}\) \(-7.76858 q^{46}\) \(+8.98985 q^{47}\) \(-33.9631 q^{48}\) \(+7.56441 q^{49}\) \(-2.65503 q^{50}\) \(+5.80800 q^{51}\) \(+11.3348 q^{52}\) \(+3.51176 q^{53}\) \(+22.8065 q^{54}\) \(-5.97342 q^{55}\) \(+30.8957 q^{56}\) \(-0.737580 q^{57}\) \(-27.1187 q^{58}\) \(-8.81620 q^{59}\) \(-15.0481 q^{60}\) \(+3.39339 q^{61}\) \(-12.8926 q^{62}\) \(-22.4486 q^{63}\) \(+14.5513 q^{64}\) \(+2.24489 q^{65}\) \(-47.2665 q^{66}\) \(-8.80481 q^{67}\) \(-9.83980 q^{68}\) \(-8.72034 q^{69}\) \(+10.1325 q^{70}\) \(-5.71246 q^{71}\) \(-47.6205 q^{72}\) \(-10.4008 q^{73}\) \(+23.4509 q^{74}\) \(-2.98031 q^{75}\) \(+1.24959 q^{76}\) \(+22.7966 q^{77}\) \(+17.7633 q^{78}\) \(-11.6445 q^{79}\) \(+11.3958 q^{80}\) \(+7.95395 q^{81}\) \(-29.3396 q^{82}\) \(+4.73389 q^{83}\) \(+57.4286 q^{84}\) \(-1.94879 q^{85}\) \(-21.1339 q^{86}\) \(-30.4411 q^{87}\) \(+48.3588 q^{88}\) \(+12.4396 q^{89}\) \(-15.6175 q^{90}\) \(-8.56723 q^{91}\) \(+14.7738 q^{92}\) \(-14.4721 q^{93}\) \(-23.8683 q^{94}\) \(+0.247485 q^{95}\) \(+41.9180 q^{96}\) \(+7.20990 q^{97}\) \(-20.0837 q^{98}\) \(-35.1370 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65503 −1.87739 −0.938694 0.344750i \(-0.887964\pi\)
−0.938694 + 0.344750i \(0.887964\pi\)
\(3\) −2.98031 −1.72068 −0.860341 0.509720i \(-0.829749\pi\)
−0.860341 + 0.509720i \(0.829749\pi\)
\(4\) 5.04918 2.52459
\(5\) 1.00000 0.447214
\(6\) 7.91280 3.23039
\(7\) −3.81633 −1.44244 −0.721220 0.692707i \(-0.756418\pi\)
−0.721220 + 0.692707i \(0.756418\pi\)
\(8\) −8.09566 −2.86225
\(9\) 5.88223 1.96074
\(10\) −2.65503 −0.839594
\(11\) −5.97342 −1.80105 −0.900527 0.434800i \(-0.856819\pi\)
−0.900527 + 0.434800i \(0.856819\pi\)
\(12\) −15.0481 −4.34401
\(13\) 2.24489 0.622619 0.311310 0.950309i \(-0.399232\pi\)
0.311310 + 0.950309i \(0.399232\pi\)
\(14\) 10.1325 2.70802
\(15\) −2.98031 −0.769512
\(16\) 11.3958 2.84896
\(17\) −1.94879 −0.472652 −0.236326 0.971674i \(-0.575943\pi\)
−0.236326 + 0.971674i \(0.575943\pi\)
\(18\) −15.6175 −3.68108
\(19\) 0.247485 0.0567768 0.0283884 0.999597i \(-0.490962\pi\)
0.0283884 + 0.999597i \(0.490962\pi\)
\(20\) 5.04918 1.12903
\(21\) 11.3739 2.48198
\(22\) 15.8596 3.38128
\(23\) 2.92599 0.610111 0.305055 0.952335i \(-0.401325\pi\)
0.305055 + 0.952335i \(0.401325\pi\)
\(24\) 24.1275 4.92501
\(25\) 1.00000 0.200000
\(26\) −5.96024 −1.16890
\(27\) −8.58993 −1.65313
\(28\) −19.2694 −3.64157
\(29\) 10.2141 1.89671 0.948355 0.317212i \(-0.102747\pi\)
0.948355 + 0.317212i \(0.102747\pi\)
\(30\) 7.91280 1.44467
\(31\) 4.85592 0.872149 0.436075 0.899911i \(-0.356368\pi\)
0.436075 + 0.899911i \(0.356368\pi\)
\(32\) −14.0650 −2.48636
\(33\) 17.8026 3.09904
\(34\) 5.17410 0.887351
\(35\) −3.81633 −0.645078
\(36\) 29.7004 4.95007
\(37\) −8.83263 −1.45208 −0.726038 0.687655i \(-0.758640\pi\)
−0.726038 + 0.687655i \(0.758640\pi\)
\(38\) −0.657079 −0.106592
\(39\) −6.69045 −1.07133
\(40\) −8.09566 −1.28004
\(41\) 11.0506 1.72581 0.862905 0.505366i \(-0.168643\pi\)
0.862905 + 0.505366i \(0.168643\pi\)
\(42\) −30.1979 −4.65964
\(43\) 7.95994 1.21388 0.606940 0.794748i \(-0.292397\pi\)
0.606940 + 0.794748i \(0.292397\pi\)
\(44\) −30.1609 −4.54692
\(45\) 5.88223 0.876871
\(46\) −7.76858 −1.14542
\(47\) 8.98985 1.31130 0.655652 0.755063i \(-0.272394\pi\)
0.655652 + 0.755063i \(0.272394\pi\)
\(48\) −33.9631 −4.90215
\(49\) 7.56441 1.08063
\(50\) −2.65503 −0.375478
\(51\) 5.80800 0.813283
\(52\) 11.3348 1.57186
\(53\) 3.51176 0.482377 0.241189 0.970478i \(-0.422463\pi\)
0.241189 + 0.970478i \(0.422463\pi\)
\(54\) 22.8065 3.10357
\(55\) −5.97342 −0.805456
\(56\) 30.8957 4.12862
\(57\) −0.737580 −0.0976949
\(58\) −27.1187 −3.56086
\(59\) −8.81620 −1.14777 −0.573886 0.818935i \(-0.694565\pi\)
−0.573886 + 0.818935i \(0.694565\pi\)
\(60\) −15.0481 −1.94270
\(61\) 3.39339 0.434479 0.217239 0.976118i \(-0.430295\pi\)
0.217239 + 0.976118i \(0.430295\pi\)
\(62\) −12.8926 −1.63736
\(63\) −22.4486 −2.82825
\(64\) 14.5513 1.81891
\(65\) 2.24489 0.278444
\(66\) −47.2665 −5.81810
\(67\) −8.80481 −1.07568 −0.537839 0.843047i \(-0.680759\pi\)
−0.537839 + 0.843047i \(0.680759\pi\)
\(68\) −9.83980 −1.19325
\(69\) −8.72034 −1.04981
\(70\) 10.1325 1.21106
\(71\) −5.71246 −0.677944 −0.338972 0.940796i \(-0.610079\pi\)
−0.338972 + 0.940796i \(0.610079\pi\)
\(72\) −47.6205 −5.61213
\(73\) −10.4008 −1.21732 −0.608658 0.793433i \(-0.708292\pi\)
−0.608658 + 0.793433i \(0.708292\pi\)
\(74\) 23.4509 2.72611
\(75\) −2.98031 −0.344136
\(76\) 1.24959 0.143338
\(77\) 22.7966 2.59791
\(78\) 17.7633 2.01130
\(79\) −11.6445 −1.31011 −0.655055 0.755581i \(-0.727355\pi\)
−0.655055 + 0.755581i \(0.727355\pi\)
\(80\) 11.3958 1.27409
\(81\) 7.95395 0.883772
\(82\) −29.3396 −3.24002
\(83\) 4.73389 0.519612 0.259806 0.965661i \(-0.416341\pi\)
0.259806 + 0.965661i \(0.416341\pi\)
\(84\) 57.4286 6.26597
\(85\) −1.94879 −0.211376
\(86\) −21.1339 −2.27893
\(87\) −30.4411 −3.26363
\(88\) 48.3588 5.15506
\(89\) 12.4396 1.31860 0.659300 0.751880i \(-0.270853\pi\)
0.659300 + 0.751880i \(0.270853\pi\)
\(90\) −15.6175 −1.64623
\(91\) −8.56723 −0.898090
\(92\) 14.7738 1.54028
\(93\) −14.4721 −1.50069
\(94\) −23.8683 −2.46183
\(95\) 0.247485 0.0253914
\(96\) 41.9180 4.27824
\(97\) 7.20990 0.732054 0.366027 0.930604i \(-0.380718\pi\)
0.366027 + 0.930604i \(0.380718\pi\)
\(98\) −20.0837 −2.02876
\(99\) −35.1370 −3.53141
\(100\) 5.04918 0.504918
\(101\) 8.99297 0.894834 0.447417 0.894325i \(-0.352344\pi\)
0.447417 + 0.894325i \(0.352344\pi\)
\(102\) −15.4204 −1.52685
\(103\) 9.11838 0.898461 0.449230 0.893416i \(-0.351698\pi\)
0.449230 + 0.893416i \(0.351698\pi\)
\(104\) −18.1738 −1.78209
\(105\) 11.3739 1.10997
\(106\) −9.32382 −0.905609
\(107\) −1.44306 −0.139506 −0.0697529 0.997564i \(-0.522221\pi\)
−0.0697529 + 0.997564i \(0.522221\pi\)
\(108\) −43.3721 −4.17348
\(109\) −4.35427 −0.417064 −0.208532 0.978016i \(-0.566869\pi\)
−0.208532 + 0.978016i \(0.566869\pi\)
\(110\) 15.8596 1.51215
\(111\) 26.3239 2.49856
\(112\) −43.4904 −4.10945
\(113\) 4.40957 0.414817 0.207409 0.978254i \(-0.433497\pi\)
0.207409 + 0.978254i \(0.433497\pi\)
\(114\) 1.95830 0.183411
\(115\) 2.92599 0.272850
\(116\) 51.5728 4.78841
\(117\) 13.2049 1.22080
\(118\) 23.4073 2.15481
\(119\) 7.43724 0.681771
\(120\) 24.1275 2.20253
\(121\) 24.6818 2.24380
\(122\) −9.00954 −0.815686
\(123\) −32.9341 −2.96957
\(124\) 24.5184 2.20182
\(125\) 1.00000 0.0894427
\(126\) 59.6016 5.30973
\(127\) −19.3773 −1.71946 −0.859730 0.510749i \(-0.829368\pi\)
−0.859730 + 0.510749i \(0.829368\pi\)
\(128\) −10.5040 −0.928434
\(129\) −23.7231 −2.08870
\(130\) −5.96024 −0.522747
\(131\) 8.00338 0.699258 0.349629 0.936888i \(-0.386308\pi\)
0.349629 + 0.936888i \(0.386308\pi\)
\(132\) 89.8887 7.82380
\(133\) −0.944484 −0.0818971
\(134\) 23.3770 2.01947
\(135\) −8.58993 −0.739304
\(136\) 15.7768 1.35285
\(137\) −18.2210 −1.55672 −0.778362 0.627815i \(-0.783949\pi\)
−0.778362 + 0.627815i \(0.783949\pi\)
\(138\) 23.1528 1.97089
\(139\) −12.2402 −1.03820 −0.519101 0.854713i \(-0.673733\pi\)
−0.519101 + 0.854713i \(0.673733\pi\)
\(140\) −19.2694 −1.62856
\(141\) −26.7925 −2.25634
\(142\) 15.1667 1.27276
\(143\) −13.4096 −1.12137
\(144\) 67.0330 5.58608
\(145\) 10.2141 0.848234
\(146\) 27.6143 2.28538
\(147\) −22.5443 −1.85942
\(148\) −44.5975 −3.66589
\(149\) −23.7952 −1.94938 −0.974691 0.223556i \(-0.928233\pi\)
−0.974691 + 0.223556i \(0.928233\pi\)
\(150\) 7.91280 0.646078
\(151\) −6.96534 −0.566831 −0.283416 0.958997i \(-0.591468\pi\)
−0.283416 + 0.958997i \(0.591468\pi\)
\(152\) −2.00355 −0.162509
\(153\) −11.4632 −0.926748
\(154\) −60.5256 −4.87729
\(155\) 4.85592 0.390037
\(156\) −33.7813 −2.70467
\(157\) 24.3870 1.94630 0.973148 0.230182i \(-0.0739320\pi\)
0.973148 + 0.230182i \(0.0739320\pi\)
\(158\) 30.9165 2.45959
\(159\) −10.4661 −0.830017
\(160\) −14.0650 −1.11193
\(161\) −11.1666 −0.880048
\(162\) −21.1180 −1.65918
\(163\) 9.42925 0.738556 0.369278 0.929319i \(-0.379605\pi\)
0.369278 + 0.929319i \(0.379605\pi\)
\(164\) 55.7963 4.35696
\(165\) 17.8026 1.38593
\(166\) −12.5686 −0.975514
\(167\) 4.62383 0.357802 0.178901 0.983867i \(-0.442746\pi\)
0.178901 + 0.983867i \(0.442746\pi\)
\(168\) −92.0788 −7.10403
\(169\) −7.96049 −0.612345
\(170\) 5.17410 0.396835
\(171\) 1.45576 0.111325
\(172\) 40.1912 3.06455
\(173\) 17.4888 1.32965 0.664825 0.746999i \(-0.268506\pi\)
0.664825 + 0.746999i \(0.268506\pi\)
\(174\) 80.8221 6.12711
\(175\) −3.81633 −0.288488
\(176\) −68.0722 −5.13113
\(177\) 26.2750 1.97495
\(178\) −33.0276 −2.47552
\(179\) −2.04104 −0.152554 −0.0762772 0.997087i \(-0.524303\pi\)
−0.0762772 + 0.997087i \(0.524303\pi\)
\(180\) 29.7004 2.21374
\(181\) −3.94104 −0.292936 −0.146468 0.989215i \(-0.546790\pi\)
−0.146468 + 0.989215i \(0.546790\pi\)
\(182\) 22.7463 1.68606
\(183\) −10.1133 −0.747599
\(184\) −23.6878 −1.74629
\(185\) −8.83263 −0.649388
\(186\) 38.4239 2.81738
\(187\) 11.6410 0.851271
\(188\) 45.3914 3.31051
\(189\) 32.7821 2.38454
\(190\) −0.657079 −0.0476695
\(191\) 22.2647 1.61102 0.805509 0.592583i \(-0.201892\pi\)
0.805509 + 0.592583i \(0.201892\pi\)
\(192\) −43.3672 −3.12976
\(193\) −5.97822 −0.430322 −0.215161 0.976579i \(-0.569028\pi\)
−0.215161 + 0.976579i \(0.569028\pi\)
\(194\) −19.1425 −1.37435
\(195\) −6.69045 −0.479113
\(196\) 38.1941 2.72815
\(197\) 12.1829 0.867998 0.433999 0.900913i \(-0.357102\pi\)
0.433999 + 0.900913i \(0.357102\pi\)
\(198\) 93.2899 6.62982
\(199\) −12.9375 −0.917113 −0.458556 0.888665i \(-0.651633\pi\)
−0.458556 + 0.888665i \(0.651633\pi\)
\(200\) −8.09566 −0.572449
\(201\) 26.2410 1.85090
\(202\) −23.8766 −1.67995
\(203\) −38.9804 −2.73589
\(204\) 29.3256 2.05320
\(205\) 11.0506 0.771806
\(206\) −24.2096 −1.68676
\(207\) 17.2113 1.19627
\(208\) 25.5824 1.77382
\(209\) −1.47833 −0.102258
\(210\) −30.1979 −2.08385
\(211\) 16.4031 1.12923 0.564617 0.825353i \(-0.309024\pi\)
0.564617 + 0.825353i \(0.309024\pi\)
\(212\) 17.7315 1.21780
\(213\) 17.0249 1.16653
\(214\) 3.83137 0.261907
\(215\) 7.95994 0.542864
\(216\) 69.5412 4.73168
\(217\) −18.5318 −1.25802
\(218\) 11.5607 0.782991
\(219\) 30.9974 2.09461
\(220\) −30.1609 −2.03345
\(221\) −4.37481 −0.294282
\(222\) −69.8908 −4.69077
\(223\) −16.1155 −1.07917 −0.539587 0.841930i \(-0.681420\pi\)
−0.539587 + 0.841930i \(0.681420\pi\)
\(224\) 53.6767 3.58643
\(225\) 5.88223 0.392149
\(226\) −11.7075 −0.778774
\(227\) 11.0683 0.734631 0.367316 0.930096i \(-0.380277\pi\)
0.367316 + 0.930096i \(0.380277\pi\)
\(228\) −3.72417 −0.246639
\(229\) −7.68033 −0.507530 −0.253765 0.967266i \(-0.581669\pi\)
−0.253765 + 0.967266i \(0.581669\pi\)
\(230\) −7.76858 −0.512245
\(231\) −67.9408 −4.47018
\(232\) −82.6898 −5.42885
\(233\) −9.02941 −0.591536 −0.295768 0.955260i \(-0.595576\pi\)
−0.295768 + 0.955260i \(0.595576\pi\)
\(234\) −35.0595 −2.29191
\(235\) 8.98985 0.586433
\(236\) −44.5146 −2.89765
\(237\) 34.7042 2.25428
\(238\) −19.7461 −1.27995
\(239\) −4.87072 −0.315061 −0.157530 0.987514i \(-0.550353\pi\)
−0.157530 + 0.987514i \(0.550353\pi\)
\(240\) −33.9631 −2.19231
\(241\) −12.8906 −0.830358 −0.415179 0.909740i \(-0.636281\pi\)
−0.415179 + 0.909740i \(0.636281\pi\)
\(242\) −65.5308 −4.21248
\(243\) 2.06459 0.132444
\(244\) 17.1338 1.09688
\(245\) 7.56441 0.483273
\(246\) 87.4410 5.57504
\(247\) 0.555574 0.0353504
\(248\) −39.3119 −2.49631
\(249\) −14.1085 −0.894087
\(250\) −2.65503 −0.167919
\(251\) 11.8884 0.750387 0.375193 0.926947i \(-0.377576\pi\)
0.375193 + 0.926947i \(0.377576\pi\)
\(252\) −113.347 −7.14018
\(253\) −17.4782 −1.09884
\(254\) 51.4474 3.22810
\(255\) 5.80800 0.363711
\(256\) −1.21401 −0.0758757
\(257\) −29.5639 −1.84415 −0.922074 0.387015i \(-0.873506\pi\)
−0.922074 + 0.387015i \(0.873506\pi\)
\(258\) 62.9855 3.92130
\(259\) 33.7083 2.09453
\(260\) 11.3348 0.702956
\(261\) 60.0817 3.71896
\(262\) −21.2492 −1.31278
\(263\) 18.4930 1.14033 0.570165 0.821531i \(-0.306879\pi\)
0.570165 + 0.821531i \(0.306879\pi\)
\(264\) −144.124 −8.87022
\(265\) 3.51176 0.215726
\(266\) 2.50763 0.153753
\(267\) −37.0740 −2.26889
\(268\) −44.4571 −2.71565
\(269\) −5.61575 −0.342398 −0.171199 0.985236i \(-0.554764\pi\)
−0.171199 + 0.985236i \(0.554764\pi\)
\(270\) 22.8065 1.38796
\(271\) 0.304439 0.0184933 0.00924666 0.999957i \(-0.497057\pi\)
0.00924666 + 0.999957i \(0.497057\pi\)
\(272\) −22.2081 −1.34657
\(273\) 25.5330 1.54533
\(274\) 48.3773 2.92258
\(275\) −5.97342 −0.360211
\(276\) −44.0306 −2.65033
\(277\) −14.2658 −0.857146 −0.428573 0.903507i \(-0.640984\pi\)
−0.428573 + 0.903507i \(0.640984\pi\)
\(278\) 32.4982 1.94911
\(279\) 28.5636 1.71006
\(280\) 30.8957 1.84637
\(281\) 2.57025 0.153328 0.0766640 0.997057i \(-0.475573\pi\)
0.0766640 + 0.997057i \(0.475573\pi\)
\(282\) 71.1349 4.23602
\(283\) 28.1868 1.67553 0.837766 0.546029i \(-0.183861\pi\)
0.837766 + 0.546029i \(0.183861\pi\)
\(284\) −28.8432 −1.71153
\(285\) −0.737580 −0.0436905
\(286\) 35.6030 2.10525
\(287\) −42.1727 −2.48938
\(288\) −82.7335 −4.87512
\(289\) −13.2022 −0.776601
\(290\) −27.1187 −1.59247
\(291\) −21.4877 −1.25963
\(292\) −52.5152 −3.07322
\(293\) −9.49328 −0.554603 −0.277302 0.960783i \(-0.589440\pi\)
−0.277302 + 0.960783i \(0.589440\pi\)
\(294\) 59.8557 3.49086
\(295\) −8.81620 −0.513299
\(296\) 71.5059 4.15620
\(297\) 51.3113 2.97738
\(298\) 63.1770 3.65975
\(299\) 6.56851 0.379867
\(300\) −15.0481 −0.868803
\(301\) −30.3778 −1.75095
\(302\) 18.4932 1.06416
\(303\) −26.8018 −1.53972
\(304\) 2.82030 0.161755
\(305\) 3.39339 0.194305
\(306\) 30.4352 1.73987
\(307\) −5.85040 −0.333900 −0.166950 0.985965i \(-0.553392\pi\)
−0.166950 + 0.985965i \(0.553392\pi\)
\(308\) 115.104 6.55866
\(309\) −27.1756 −1.54596
\(310\) −12.8926 −0.732251
\(311\) 8.35482 0.473758 0.236879 0.971539i \(-0.423875\pi\)
0.236879 + 0.971539i \(0.423875\pi\)
\(312\) 54.1636 3.06641
\(313\) 19.7865 1.11840 0.559199 0.829033i \(-0.311109\pi\)
0.559199 + 0.829033i \(0.311109\pi\)
\(314\) −64.7482 −3.65395
\(315\) −22.4486 −1.26483
\(316\) −58.7952 −3.30749
\(317\) −12.9975 −0.730015 −0.365008 0.931005i \(-0.618934\pi\)
−0.365008 + 0.931005i \(0.618934\pi\)
\(318\) 27.7878 1.55827
\(319\) −61.0131 −3.41608
\(320\) 14.5513 0.813440
\(321\) 4.30076 0.240045
\(322\) 29.6475 1.65219
\(323\) −0.482296 −0.0268357
\(324\) 40.1609 2.23116
\(325\) 2.24489 0.124524
\(326\) −25.0349 −1.38656
\(327\) 12.9771 0.717634
\(328\) −89.4617 −4.93969
\(329\) −34.3083 −1.89148
\(330\) −47.2665 −2.60194
\(331\) −22.6296 −1.24384 −0.621918 0.783083i \(-0.713646\pi\)
−0.621918 + 0.783083i \(0.713646\pi\)
\(332\) 23.9023 1.31181
\(333\) −51.9556 −2.84715
\(334\) −12.2764 −0.671734
\(335\) −8.80481 −0.481058
\(336\) 129.615 7.07106
\(337\) 1.87499 0.102137 0.0510687 0.998695i \(-0.483737\pi\)
0.0510687 + 0.998695i \(0.483737\pi\)
\(338\) 21.1353 1.14961
\(339\) −13.1419 −0.713769
\(340\) −9.83980 −0.533638
\(341\) −29.0065 −1.57079
\(342\) −3.86509 −0.209000
\(343\) −2.15399 −0.116304
\(344\) −64.4410 −3.47442
\(345\) −8.72034 −0.469488
\(346\) −46.4333 −2.49627
\(347\) −14.5547 −0.781339 −0.390670 0.920531i \(-0.627756\pi\)
−0.390670 + 0.920531i \(0.627756\pi\)
\(348\) −153.703 −8.23933
\(349\) 2.61220 0.139828 0.0699138 0.997553i \(-0.477728\pi\)
0.0699138 + 0.997553i \(0.477728\pi\)
\(350\) 10.1325 0.541604
\(351\) −19.2834 −1.02927
\(352\) 84.0161 4.47807
\(353\) −19.7114 −1.04913 −0.524567 0.851369i \(-0.675773\pi\)
−0.524567 + 0.851369i \(0.675773\pi\)
\(354\) −69.7609 −3.70775
\(355\) −5.71246 −0.303186
\(356\) 62.8100 3.32892
\(357\) −22.1653 −1.17311
\(358\) 5.41901 0.286404
\(359\) −4.66104 −0.246000 −0.123000 0.992407i \(-0.539252\pi\)
−0.123000 + 0.992407i \(0.539252\pi\)
\(360\) −47.6205 −2.50982
\(361\) −18.9388 −0.996776
\(362\) 10.4636 0.549954
\(363\) −73.5592 −3.86086
\(364\) −43.2575 −2.26731
\(365\) −10.4008 −0.544400
\(366\) 26.8512 1.40353
\(367\) 13.0740 0.682456 0.341228 0.939981i \(-0.389157\pi\)
0.341228 + 0.939981i \(0.389157\pi\)
\(368\) 33.3441 1.73818
\(369\) 65.0020 3.38387
\(370\) 23.4509 1.21915
\(371\) −13.4020 −0.695800
\(372\) −73.0724 −3.78863
\(373\) 29.7409 1.53993 0.769963 0.638089i \(-0.220275\pi\)
0.769963 + 0.638089i \(0.220275\pi\)
\(374\) −30.9071 −1.59817
\(375\) −2.98031 −0.153902
\(376\) −72.7787 −3.75328
\(377\) 22.9295 1.18093
\(378\) −87.0373 −4.47672
\(379\) 16.7370 0.859722 0.429861 0.902895i \(-0.358563\pi\)
0.429861 + 0.902895i \(0.358563\pi\)
\(380\) 1.24959 0.0641028
\(381\) 57.7504 2.95864
\(382\) −59.1135 −3.02451
\(383\) −24.4848 −1.25111 −0.625557 0.780178i \(-0.715128\pi\)
−0.625557 + 0.780178i \(0.715128\pi\)
\(384\) 31.3052 1.59754
\(385\) 22.7966 1.16182
\(386\) 15.8724 0.807881
\(387\) 46.8222 2.38011
\(388\) 36.4041 1.84814
\(389\) −34.8170 −1.76529 −0.882646 0.470039i \(-0.844240\pi\)
−0.882646 + 0.470039i \(0.844240\pi\)
\(390\) 17.7633 0.899481
\(391\) −5.70214 −0.288370
\(392\) −61.2389 −3.09303
\(393\) −23.8525 −1.20320
\(394\) −32.3460 −1.62957
\(395\) −11.6445 −0.585899
\(396\) −177.413 −8.91535
\(397\) −4.30688 −0.216156 −0.108078 0.994142i \(-0.534470\pi\)
−0.108078 + 0.994142i \(0.534470\pi\)
\(398\) 34.3494 1.72178
\(399\) 2.81485 0.140919
\(400\) 11.3958 0.569792
\(401\) 25.7850 1.28764 0.643820 0.765177i \(-0.277348\pi\)
0.643820 + 0.765177i \(0.277348\pi\)
\(402\) −69.6707 −3.47486
\(403\) 10.9010 0.543017
\(404\) 45.4071 2.25909
\(405\) 7.95395 0.395235
\(406\) 103.494 5.13633
\(407\) 52.7610 2.61527
\(408\) −47.0196 −2.32782
\(409\) −2.22146 −0.109844 −0.0549222 0.998491i \(-0.517491\pi\)
−0.0549222 + 0.998491i \(0.517491\pi\)
\(410\) −29.3396 −1.44898
\(411\) 54.3042 2.67863
\(412\) 46.0403 2.26824
\(413\) 33.6456 1.65559
\(414\) −45.6966 −2.24587
\(415\) 4.73389 0.232378
\(416\) −31.5743 −1.54806
\(417\) 36.4796 1.78642
\(418\) 3.92501 0.191978
\(419\) 10.0287 0.489932 0.244966 0.969532i \(-0.421223\pi\)
0.244966 + 0.969532i \(0.421223\pi\)
\(420\) 57.4286 2.80223
\(421\) −5.81908 −0.283605 −0.141802 0.989895i \(-0.545290\pi\)
−0.141802 + 0.989895i \(0.545290\pi\)
\(422\) −43.5506 −2.12001
\(423\) 52.8804 2.57113
\(424\) −28.4300 −1.38068
\(425\) −1.94879 −0.0945303
\(426\) −45.2016 −2.19002
\(427\) −12.9503 −0.626709
\(428\) −7.28627 −0.352195
\(429\) 39.9649 1.92952
\(430\) −21.1339 −1.01917
\(431\) −12.9347 −0.623044 −0.311522 0.950239i \(-0.600839\pi\)
−0.311522 + 0.950239i \(0.600839\pi\)
\(432\) −97.8896 −4.70971
\(433\) −23.5359 −1.13107 −0.565533 0.824726i \(-0.691329\pi\)
−0.565533 + 0.824726i \(0.691329\pi\)
\(434\) 49.2025 2.36180
\(435\) −30.4411 −1.45954
\(436\) −21.9855 −1.05292
\(437\) 0.724137 0.0346402
\(438\) −82.2991 −3.93240
\(439\) 31.3057 1.49414 0.747071 0.664744i \(-0.231460\pi\)
0.747071 + 0.664744i \(0.231460\pi\)
\(440\) 48.3588 2.30541
\(441\) 44.4956 2.11884
\(442\) 11.6153 0.552482
\(443\) −16.6991 −0.793399 −0.396700 0.917948i \(-0.629845\pi\)
−0.396700 + 0.917948i \(0.629845\pi\)
\(444\) 132.914 6.30783
\(445\) 12.4396 0.589696
\(446\) 42.7871 2.02603
\(447\) 70.9171 3.35426
\(448\) −55.5325 −2.62366
\(449\) 6.56348 0.309750 0.154875 0.987934i \(-0.450503\pi\)
0.154875 + 0.987934i \(0.450503\pi\)
\(450\) −15.6175 −0.736216
\(451\) −66.0097 −3.10828
\(452\) 22.2647 1.04724
\(453\) 20.7588 0.975336
\(454\) −29.3867 −1.37919
\(455\) −8.56723 −0.401638
\(456\) 5.97119 0.279627
\(457\) −36.7531 −1.71924 −0.859618 0.510936i \(-0.829299\pi\)
−0.859618 + 0.510936i \(0.829299\pi\)
\(458\) 20.3915 0.952832
\(459\) 16.7400 0.781356
\(460\) 14.7738 0.688834
\(461\) −1.29772 −0.0604407 −0.0302204 0.999543i \(-0.509621\pi\)
−0.0302204 + 0.999543i \(0.509621\pi\)
\(462\) 180.385 8.39226
\(463\) 28.0446 1.30334 0.651672 0.758501i \(-0.274068\pi\)
0.651672 + 0.758501i \(0.274068\pi\)
\(464\) 116.398 5.40365
\(465\) −14.4721 −0.671129
\(466\) 23.9733 1.11054
\(467\) 12.1619 0.562785 0.281392 0.959593i \(-0.409204\pi\)
0.281392 + 0.959593i \(0.409204\pi\)
\(468\) 66.6741 3.08201
\(469\) 33.6021 1.55160
\(470\) −23.8683 −1.10096
\(471\) −72.6808 −3.34895
\(472\) 71.3730 3.28521
\(473\) −47.5481 −2.18626
\(474\) −92.1407 −4.23216
\(475\) 0.247485 0.0113554
\(476\) 37.5520 1.72119
\(477\) 20.6570 0.945818
\(478\) 12.9319 0.591491
\(479\) 16.9027 0.772302 0.386151 0.922436i \(-0.373804\pi\)
0.386151 + 0.922436i \(0.373804\pi\)
\(480\) 41.9180 1.91329
\(481\) −19.8282 −0.904090
\(482\) 34.2250 1.55891
\(483\) 33.2798 1.51428
\(484\) 124.623 5.66466
\(485\) 7.20990 0.327385
\(486\) −5.48156 −0.248648
\(487\) −33.8959 −1.53597 −0.767986 0.640467i \(-0.778741\pi\)
−0.767986 + 0.640467i \(0.778741\pi\)
\(488\) −27.4717 −1.24359
\(489\) −28.1021 −1.27082
\(490\) −20.0837 −0.907291
\(491\) −12.7427 −0.575071 −0.287535 0.957770i \(-0.592836\pi\)
−0.287535 + 0.957770i \(0.592836\pi\)
\(492\) −166.290 −7.49694
\(493\) −19.9051 −0.896483
\(494\) −1.47507 −0.0663664
\(495\) −35.1370 −1.57929
\(496\) 55.3373 2.48472
\(497\) 21.8007 0.977893
\(498\) 37.4584 1.67855
\(499\) 28.0565 1.25598 0.627991 0.778220i \(-0.283877\pi\)
0.627991 + 0.778220i \(0.283877\pi\)
\(500\) 5.04918 0.225806
\(501\) −13.7804 −0.615664
\(502\) −31.5639 −1.40877
\(503\) −23.7553 −1.05920 −0.529598 0.848249i \(-0.677657\pi\)
−0.529598 + 0.848249i \(0.677657\pi\)
\(504\) 181.736 8.09516
\(505\) 8.99297 0.400182
\(506\) 46.4050 2.06295
\(507\) 23.7247 1.05365
\(508\) −97.8396 −4.34093
\(509\) −3.54301 −0.157041 −0.0785206 0.996912i \(-0.525020\pi\)
−0.0785206 + 0.996912i \(0.525020\pi\)
\(510\) −15.4204 −0.682827
\(511\) 39.6927 1.75590
\(512\) 24.2313 1.07088
\(513\) −2.12588 −0.0938597
\(514\) 78.4931 3.46218
\(515\) 9.11838 0.401804
\(516\) −119.782 −5.27311
\(517\) −53.7002 −2.36173
\(518\) −89.4964 −3.93225
\(519\) −52.1221 −2.28791
\(520\) −18.1738 −0.796975
\(521\) 13.2057 0.578554 0.289277 0.957245i \(-0.406585\pi\)
0.289277 + 0.957245i \(0.406585\pi\)
\(522\) −159.519 −6.98194
\(523\) −31.4058 −1.37328 −0.686640 0.726997i \(-0.740915\pi\)
−0.686640 + 0.726997i \(0.740915\pi\)
\(524\) 40.4105 1.76534
\(525\) 11.3739 0.496396
\(526\) −49.0995 −2.14084
\(527\) −9.46318 −0.412223
\(528\) 202.876 8.82905
\(529\) −14.4386 −0.627765
\(530\) −9.32382 −0.405001
\(531\) −51.8589 −2.25049
\(532\) −4.76887 −0.206757
\(533\) 24.8073 1.07452
\(534\) 98.4324 4.25959
\(535\) −1.44306 −0.0623889
\(536\) 71.2807 3.07886
\(537\) 6.08292 0.262497
\(538\) 14.9100 0.642814
\(539\) −45.1854 −1.94627
\(540\) −43.3721 −1.86644
\(541\) 45.9627 1.97609 0.988046 0.154158i \(-0.0492664\pi\)
0.988046 + 0.154158i \(0.0492664\pi\)
\(542\) −0.808293 −0.0347192
\(543\) 11.7455 0.504049
\(544\) 27.4097 1.17518
\(545\) −4.35427 −0.186517
\(546\) −67.7908 −2.90118
\(547\) 16.4598 0.703772 0.351886 0.936043i \(-0.385541\pi\)
0.351886 + 0.936043i \(0.385541\pi\)
\(548\) −92.0011 −3.93009
\(549\) 19.9607 0.851901
\(550\) 15.8596 0.676256
\(551\) 2.52783 0.107689
\(552\) 70.5969 3.00480
\(553\) 44.4394 1.88975
\(554\) 37.8760 1.60920
\(555\) 26.3239 1.11739
\(556\) −61.8031 −2.62103
\(557\) 34.6230 1.46702 0.733511 0.679677i \(-0.237880\pi\)
0.733511 + 0.679677i \(0.237880\pi\)
\(558\) −75.8373 −3.21045
\(559\) 17.8692 0.755785
\(560\) −43.4904 −1.83780
\(561\) −34.6936 −1.46477
\(562\) −6.82408 −0.287856
\(563\) 10.8938 0.459121 0.229560 0.973294i \(-0.426271\pi\)
0.229560 + 0.973294i \(0.426271\pi\)
\(564\) −135.280 −5.69632
\(565\) 4.40957 0.185512
\(566\) −74.8368 −3.14563
\(567\) −30.3549 −1.27479
\(568\) 46.2461 1.94044
\(569\) −25.7017 −1.07747 −0.538736 0.842474i \(-0.681098\pi\)
−0.538736 + 0.842474i \(0.681098\pi\)
\(570\) 1.95830 0.0820240
\(571\) −17.0004 −0.711443 −0.355722 0.934592i \(-0.615765\pi\)
−0.355722 + 0.934592i \(0.615765\pi\)
\(572\) −67.7077 −2.83100
\(573\) −66.3557 −2.77205
\(574\) 111.970 4.67353
\(575\) 2.92599 0.122022
\(576\) 85.5938 3.56641
\(577\) −3.55652 −0.148060 −0.0740298 0.997256i \(-0.523586\pi\)
−0.0740298 + 0.997256i \(0.523586\pi\)
\(578\) 35.0522 1.45798
\(579\) 17.8169 0.740447
\(580\) 51.5728 2.14144
\(581\) −18.0661 −0.749509
\(582\) 57.0505 2.36482
\(583\) −20.9772 −0.868787
\(584\) 84.2009 3.48426
\(585\) 13.2049 0.545957
\(586\) 25.2049 1.04121
\(587\) 28.8139 1.18928 0.594639 0.803992i \(-0.297295\pi\)
0.594639 + 0.803992i \(0.297295\pi\)
\(588\) −113.830 −4.69427
\(589\) 1.20177 0.0495179
\(590\) 23.4073 0.963662
\(591\) −36.3089 −1.49355
\(592\) −100.655 −4.13691
\(593\) −1.83885 −0.0755123 −0.0377562 0.999287i \(-0.512021\pi\)
−0.0377562 + 0.999287i \(0.512021\pi\)
\(594\) −136.233 −5.58971
\(595\) 7.43724 0.304897
\(596\) −120.146 −4.92139
\(597\) 38.5576 1.57806
\(598\) −17.4396 −0.713157
\(599\) 30.4869 1.24566 0.622831 0.782356i \(-0.285982\pi\)
0.622831 + 0.782356i \(0.285982\pi\)
\(600\) 24.1275 0.985003
\(601\) 21.9983 0.897330 0.448665 0.893700i \(-0.351900\pi\)
0.448665 + 0.893700i \(0.351900\pi\)
\(602\) 80.6540 3.28721
\(603\) −51.7919 −2.10913
\(604\) −35.1692 −1.43102
\(605\) 24.6818 1.00346
\(606\) 71.1596 2.89066
\(607\) 22.9888 0.933087 0.466543 0.884498i \(-0.345499\pi\)
0.466543 + 0.884498i \(0.345499\pi\)
\(608\) −3.48087 −0.141168
\(609\) 116.174 4.70759
\(610\) −9.00954 −0.364786
\(611\) 20.1812 0.816443
\(612\) −57.8800 −2.33966
\(613\) 28.7067 1.15945 0.579726 0.814811i \(-0.303159\pi\)
0.579726 + 0.814811i \(0.303159\pi\)
\(614\) 15.5330 0.626860
\(615\) −32.9341 −1.32803
\(616\) −184.553 −7.43586
\(617\) 32.7294 1.31764 0.658818 0.752302i \(-0.271057\pi\)
0.658818 + 0.752302i \(0.271057\pi\)
\(618\) 72.1519 2.90238
\(619\) −7.96111 −0.319984 −0.159992 0.987118i \(-0.551147\pi\)
−0.159992 + 0.987118i \(0.551147\pi\)
\(620\) 24.5184 0.984683
\(621\) −25.1340 −1.00859
\(622\) −22.1823 −0.889429
\(623\) −47.4739 −1.90200
\(624\) −76.2433 −3.05218
\(625\) 1.00000 0.0400000
\(626\) −52.5337 −2.09967
\(627\) 4.40588 0.175954
\(628\) 123.134 4.91360
\(629\) 17.2130 0.686326
\(630\) 59.6016 2.37458
\(631\) 1.91141 0.0760920 0.0380460 0.999276i \(-0.487887\pi\)
0.0380460 + 0.999276i \(0.487887\pi\)
\(632\) 94.2700 3.74986
\(633\) −48.8862 −1.94305
\(634\) 34.5089 1.37052
\(635\) −19.3773 −0.768966
\(636\) −52.8453 −2.09545
\(637\) 16.9812 0.672821
\(638\) 161.991 6.41330
\(639\) −33.6020 −1.32927
\(640\) −10.5040 −0.415208
\(641\) 7.71540 0.304740 0.152370 0.988324i \(-0.451309\pi\)
0.152370 + 0.988324i \(0.451309\pi\)
\(642\) −11.4186 −0.450658
\(643\) −7.09735 −0.279892 −0.139946 0.990159i \(-0.544693\pi\)
−0.139946 + 0.990159i \(0.544693\pi\)
\(644\) −56.3819 −2.22176
\(645\) −23.7231 −0.934095
\(646\) 1.28051 0.0503810
\(647\) 0.921504 0.0362281 0.0181140 0.999836i \(-0.494234\pi\)
0.0181140 + 0.999836i \(0.494234\pi\)
\(648\) −64.3924 −2.52957
\(649\) 52.6629 2.06720
\(650\) −5.96024 −0.233780
\(651\) 55.2305 2.16465
\(652\) 47.6099 1.86455
\(653\) 11.2155 0.438898 0.219449 0.975624i \(-0.429574\pi\)
0.219449 + 0.975624i \(0.429574\pi\)
\(654\) −34.4545 −1.34728
\(655\) 8.00338 0.312718
\(656\) 125.931 4.91677
\(657\) −61.1796 −2.38684
\(658\) 91.0895 3.55104
\(659\) −10.5720 −0.411825 −0.205912 0.978570i \(-0.566016\pi\)
−0.205912 + 0.978570i \(0.566016\pi\)
\(660\) 89.8887 3.49891
\(661\) 11.4559 0.445584 0.222792 0.974866i \(-0.428483\pi\)
0.222792 + 0.974866i \(0.428483\pi\)
\(662\) 60.0822 2.33516
\(663\) 13.0383 0.506365
\(664\) −38.3240 −1.48726
\(665\) −0.944484 −0.0366255
\(666\) 137.944 5.34520
\(667\) 29.8863 1.15720
\(668\) 23.3465 0.903304
\(669\) 48.0292 1.85691
\(670\) 23.3770 0.903133
\(671\) −20.2701 −0.782520
\(672\) −159.973 −6.17109
\(673\) −4.34984 −0.167674 −0.0838370 0.996479i \(-0.526718\pi\)
−0.0838370 + 0.996479i \(0.526718\pi\)
\(674\) −4.97816 −0.191752
\(675\) −8.58993 −0.330627
\(676\) −40.1939 −1.54592
\(677\) 0.564636 0.0217007 0.0108504 0.999941i \(-0.496546\pi\)
0.0108504 + 0.999941i \(0.496546\pi\)
\(678\) 34.8921 1.34002
\(679\) −27.5154 −1.05594
\(680\) 15.7768 0.605011
\(681\) −32.9870 −1.26407
\(682\) 77.0130 2.94898
\(683\) 30.2367 1.15698 0.578488 0.815691i \(-0.303643\pi\)
0.578488 + 0.815691i \(0.303643\pi\)
\(684\) 7.35040 0.281050
\(685\) −18.2210 −0.696189
\(686\) 5.71890 0.218349
\(687\) 22.8897 0.873298
\(688\) 90.7103 3.45830
\(689\) 7.88349 0.300337
\(690\) 23.1528 0.881411
\(691\) −27.9321 −1.06259 −0.531294 0.847187i \(-0.678294\pi\)
−0.531294 + 0.847187i \(0.678294\pi\)
\(692\) 88.3042 3.35682
\(693\) 134.095 5.09384
\(694\) 38.6432 1.46688
\(695\) −12.2402 −0.464298
\(696\) 246.441 9.34132
\(697\) −21.5353 −0.815707
\(698\) −6.93546 −0.262511
\(699\) 26.9104 1.01784
\(700\) −19.2694 −0.728313
\(701\) 30.5685 1.15456 0.577279 0.816547i \(-0.304115\pi\)
0.577279 + 0.816547i \(0.304115\pi\)
\(702\) 51.1980 1.93235
\(703\) −2.18594 −0.0824443
\(704\) −86.9208 −3.27595
\(705\) −26.7925 −1.00906
\(706\) 52.3344 1.96963
\(707\) −34.3202 −1.29074
\(708\) 132.667 4.98594
\(709\) 29.7823 1.11850 0.559249 0.829000i \(-0.311090\pi\)
0.559249 + 0.829000i \(0.311090\pi\)
\(710\) 15.1667 0.569198
\(711\) −68.4957 −2.56879
\(712\) −100.707 −3.77416
\(713\) 14.2084 0.532108
\(714\) 58.8494 2.20238
\(715\) −13.4096 −0.501492
\(716\) −10.3056 −0.385137
\(717\) 14.5162 0.542119
\(718\) 12.3752 0.461838
\(719\) −43.4163 −1.61915 −0.809577 0.587014i \(-0.800304\pi\)
−0.809577 + 0.587014i \(0.800304\pi\)
\(720\) 67.0330 2.49817
\(721\) −34.7988 −1.29597
\(722\) 50.2829 1.87134
\(723\) 38.4180 1.42878
\(724\) −19.8990 −0.739542
\(725\) 10.2141 0.379342
\(726\) 195.302 7.24833
\(727\) −10.5941 −0.392915 −0.196458 0.980512i \(-0.562944\pi\)
−0.196458 + 0.980512i \(0.562944\pi\)
\(728\) 69.3574 2.57056
\(729\) −30.0150 −1.11167
\(730\) 27.6143 1.02205
\(731\) −15.5123 −0.573742
\(732\) −51.0640 −1.88738
\(733\) −24.7053 −0.912510 −0.456255 0.889849i \(-0.650809\pi\)
−0.456255 + 0.889849i \(0.650809\pi\)
\(734\) −34.7118 −1.28124
\(735\) −22.5443 −0.831558
\(736\) −41.1540 −1.51696
\(737\) 52.5948 1.93736
\(738\) −172.582 −6.35284
\(739\) −41.2265 −1.51654 −0.758270 0.651940i \(-0.773955\pi\)
−0.758270 + 0.651940i \(0.773955\pi\)
\(740\) −44.5975 −1.63944
\(741\) −1.65578 −0.0608267
\(742\) 35.5828 1.30629
\(743\) 40.1936 1.47456 0.737280 0.675587i \(-0.236110\pi\)
0.737280 + 0.675587i \(0.236110\pi\)
\(744\) 117.161 4.29535
\(745\) −23.7952 −0.871790
\(746\) −78.9629 −2.89104
\(747\) 27.8459 1.01883
\(748\) 58.7773 2.14911
\(749\) 5.50720 0.201229
\(750\) 7.91280 0.288935
\(751\) 21.7084 0.792151 0.396076 0.918218i \(-0.370372\pi\)
0.396076 + 0.918218i \(0.370372\pi\)
\(752\) 102.447 3.73586
\(753\) −35.4310 −1.29118
\(754\) −60.8784 −2.21706
\(755\) −6.96534 −0.253495
\(756\) 165.522 6.01999
\(757\) −17.3965 −0.632285 −0.316143 0.948712i \(-0.602388\pi\)
−0.316143 + 0.948712i \(0.602388\pi\)
\(758\) −44.4372 −1.61403
\(759\) 52.0903 1.89076
\(760\) −2.00355 −0.0726764
\(761\) −33.9211 −1.22964 −0.614819 0.788668i \(-0.710771\pi\)
−0.614819 + 0.788668i \(0.710771\pi\)
\(762\) −153.329 −5.55452
\(763\) 16.6174 0.601589
\(764\) 112.419 4.06716
\(765\) −11.4632 −0.414454
\(766\) 65.0078 2.34883
\(767\) −19.7914 −0.714625
\(768\) 3.61812 0.130558
\(769\) −1.47421 −0.0531612 −0.0265806 0.999647i \(-0.508462\pi\)
−0.0265806 + 0.999647i \(0.508462\pi\)
\(770\) −60.5256 −2.18119
\(771\) 88.1096 3.17319
\(772\) −30.1851 −1.08639
\(773\) 42.4065 1.52526 0.762628 0.646838i \(-0.223909\pi\)
0.762628 + 0.646838i \(0.223909\pi\)
\(774\) −124.314 −4.46839
\(775\) 4.85592 0.174430
\(776\) −58.3689 −2.09532
\(777\) −100.461 −3.60402
\(778\) 92.4401 3.31414
\(779\) 2.73485 0.0979861
\(780\) −33.7813 −1.20956
\(781\) 34.1229 1.22101
\(782\) 15.1394 0.541382
\(783\) −87.7384 −3.13551
\(784\) 86.2029 3.07867
\(785\) 24.3870 0.870410
\(786\) 63.3291 2.25888
\(787\) −3.02005 −0.107653 −0.0538266 0.998550i \(-0.517142\pi\)
−0.0538266 + 0.998550i \(0.517142\pi\)
\(788\) 61.5138 2.19134
\(789\) −55.1149 −1.96214
\(790\) 30.9165 1.09996
\(791\) −16.8284 −0.598349
\(792\) 284.457 10.1078
\(793\) 7.61777 0.270515
\(794\) 11.4349 0.405810
\(795\) −10.4661 −0.371195
\(796\) −65.3236 −2.31533
\(797\) −26.3177 −0.932220 −0.466110 0.884727i \(-0.654345\pi\)
−0.466110 + 0.884727i \(0.654345\pi\)
\(798\) −7.47351 −0.264560
\(799\) −17.5193 −0.619790
\(800\) −14.0650 −0.497272
\(801\) 73.1729 2.58544
\(802\) −68.4599 −2.41740
\(803\) 62.1281 2.19245
\(804\) 132.496 4.67276
\(805\) −11.1666 −0.393569
\(806\) −28.9424 −1.01945
\(807\) 16.7366 0.589158
\(808\) −72.8040 −2.56124
\(809\) 15.1560 0.532855 0.266428 0.963855i \(-0.414157\pi\)
0.266428 + 0.963855i \(0.414157\pi\)
\(810\) −21.1180 −0.742009
\(811\) 49.2555 1.72960 0.864798 0.502120i \(-0.167447\pi\)
0.864798 + 0.502120i \(0.167447\pi\)
\(812\) −196.819 −6.90699
\(813\) −0.907320 −0.0318211
\(814\) −140.082 −4.90987
\(815\) 9.42925 0.330292
\(816\) 66.1871 2.31701
\(817\) 1.96996 0.0689203
\(818\) 5.89805 0.206221
\(819\) −50.3945 −1.76092
\(820\) 55.7963 1.94849
\(821\) −11.2850 −0.393850 −0.196925 0.980419i \(-0.563096\pi\)
−0.196925 + 0.980419i \(0.563096\pi\)
\(822\) −144.179 −5.02883
\(823\) 4.08790 0.142495 0.0712477 0.997459i \(-0.477302\pi\)
0.0712477 + 0.997459i \(0.477302\pi\)
\(824\) −73.8193 −2.57162
\(825\) 17.8026 0.619808
\(826\) −89.3300 −3.10819
\(827\) 34.2008 1.18928 0.594639 0.803993i \(-0.297295\pi\)
0.594639 + 0.803993i \(0.297295\pi\)
\(828\) 86.9031 3.02009
\(829\) 33.9772 1.18008 0.590038 0.807375i \(-0.299113\pi\)
0.590038 + 0.807375i \(0.299113\pi\)
\(830\) −12.5686 −0.436263
\(831\) 42.5163 1.47488
\(832\) 32.6659 1.13249
\(833\) −14.7415 −0.510762
\(834\) −96.8545 −3.35380
\(835\) 4.62383 0.160014
\(836\) −7.46435 −0.258160
\(837\) −41.7120 −1.44178
\(838\) −26.6264 −0.919792
\(839\) −31.5023 −1.08758 −0.543789 0.839222i \(-0.683011\pi\)
−0.543789 + 0.839222i \(0.683011\pi\)
\(840\) −92.0788 −3.17702
\(841\) 75.3277 2.59751
\(842\) 15.4498 0.532436
\(843\) −7.66012 −0.263829
\(844\) 82.8220 2.85085
\(845\) −7.96049 −0.273849
\(846\) −140.399 −4.82701
\(847\) −94.1939 −3.23654
\(848\) 40.0195 1.37427
\(849\) −84.0054 −2.88306
\(850\) 5.17410 0.177470
\(851\) −25.8442 −0.885927
\(852\) 85.9617 2.94500
\(853\) 3.39342 0.116189 0.0580943 0.998311i \(-0.481498\pi\)
0.0580943 + 0.998311i \(0.481498\pi\)
\(854\) 34.3834 1.17658
\(855\) 1.45576 0.0497860
\(856\) 11.6825 0.399300
\(857\) 47.4311 1.62022 0.810108 0.586280i \(-0.199408\pi\)
0.810108 + 0.586280i \(0.199408\pi\)
\(858\) −106.108 −3.62246
\(859\) −23.8829 −0.814874 −0.407437 0.913233i \(-0.633577\pi\)
−0.407437 + 0.913233i \(0.633577\pi\)
\(860\) 40.1912 1.37051
\(861\) 125.688 4.28342
\(862\) 34.3421 1.16970
\(863\) 7.72664 0.263018 0.131509 0.991315i \(-0.458018\pi\)
0.131509 + 0.991315i \(0.458018\pi\)
\(864\) 120.817 4.11029
\(865\) 17.4888 0.594638
\(866\) 62.4886 2.12345
\(867\) 39.3466 1.33628
\(868\) −93.5705 −3.17599
\(869\) 69.5576 2.35958
\(870\) 80.8221 2.74013
\(871\) −19.7658 −0.669738
\(872\) 35.2507 1.19374
\(873\) 42.4103 1.43537
\(874\) −1.92260 −0.0650331
\(875\) −3.81633 −0.129016
\(876\) 156.512 5.28804
\(877\) −40.2874 −1.36041 −0.680204 0.733022i \(-0.738109\pi\)
−0.680204 + 0.733022i \(0.738109\pi\)
\(878\) −83.1177 −2.80509
\(879\) 28.2929 0.954295
\(880\) −68.0722 −2.29471
\(881\) 16.1391 0.543739 0.271870 0.962334i \(-0.412358\pi\)
0.271870 + 0.962334i \(0.412358\pi\)
\(882\) −118.137 −3.97789
\(883\) −44.0726 −1.48316 −0.741580 0.670864i \(-0.765923\pi\)
−0.741580 + 0.670864i \(0.765923\pi\)
\(884\) −22.0892 −0.742941
\(885\) 26.2750 0.883224
\(886\) 44.3367 1.48952
\(887\) 4.45959 0.149738 0.0748692 0.997193i \(-0.476146\pi\)
0.0748692 + 0.997193i \(0.476146\pi\)
\(888\) −213.110 −7.15149
\(889\) 73.9504 2.48022
\(890\) −33.0276 −1.10709
\(891\) −47.5123 −1.59172
\(892\) −81.3701 −2.72447
\(893\) 2.22485 0.0744517
\(894\) −188.287 −6.29726
\(895\) −2.04104 −0.0682244
\(896\) 40.0869 1.33921
\(897\) −19.5762 −0.653629
\(898\) −17.4262 −0.581521
\(899\) 49.5988 1.65421
\(900\) 29.7004 0.990014
\(901\) −6.84369 −0.227996
\(902\) 175.258 5.83545
\(903\) 90.5352 3.01282
\(904\) −35.6984 −1.18731
\(905\) −3.94104 −0.131005
\(906\) −55.1153 −1.83108
\(907\) 6.19036 0.205547 0.102774 0.994705i \(-0.467228\pi\)
0.102774 + 0.994705i \(0.467228\pi\)
\(908\) 55.8860 1.85464
\(909\) 52.8987 1.75454
\(910\) 22.7463 0.754031
\(911\) 31.8641 1.05570 0.527852 0.849337i \(-0.322998\pi\)
0.527852 + 0.849337i \(0.322998\pi\)
\(912\) −8.40535 −0.278329
\(913\) −28.2775 −0.935850
\(914\) 97.5805 3.22768
\(915\) −10.1133 −0.334337
\(916\) −38.7794 −1.28131
\(917\) −30.5436 −1.00864
\(918\) −44.4452 −1.46691
\(919\) −20.4431 −0.674354 −0.337177 0.941441i \(-0.609472\pi\)
−0.337177 + 0.941441i \(0.609472\pi\)
\(920\) −23.6878 −0.780964
\(921\) 17.4360 0.574535
\(922\) 3.44548 0.113471
\(923\) −12.8238 −0.422101
\(924\) −343.045 −11.2854
\(925\) −8.83263 −0.290415
\(926\) −74.4593 −2.44688
\(927\) 53.6364 1.76165
\(928\) −143.661 −4.71591
\(929\) −44.5783 −1.46257 −0.731283 0.682074i \(-0.761078\pi\)
−0.731283 + 0.682074i \(0.761078\pi\)
\(930\) 38.4239 1.25997
\(931\) 1.87208 0.0613548
\(932\) −45.5911 −1.49339
\(933\) −24.8999 −0.815187
\(934\) −32.2901 −1.05657
\(935\) 11.6410 0.380700
\(936\) −106.903 −3.49422
\(937\) 32.1595 1.05061 0.525303 0.850915i \(-0.323952\pi\)
0.525303 + 0.850915i \(0.323952\pi\)
\(938\) −89.2146 −2.91296
\(939\) −58.9698 −1.92441
\(940\) 45.3914 1.48050
\(941\) −53.1108 −1.73136 −0.865682 0.500595i \(-0.833115\pi\)
−0.865682 + 0.500595i \(0.833115\pi\)
\(942\) 192.970 6.28729
\(943\) 32.3339 1.05294
\(944\) −100.468 −3.26996
\(945\) 32.7821 1.06640
\(946\) 126.242 4.10447
\(947\) −18.4457 −0.599404 −0.299702 0.954033i \(-0.596887\pi\)
−0.299702 + 0.954033i \(0.596887\pi\)
\(948\) 175.228 5.69113
\(949\) −23.3485 −0.757924
\(950\) −0.657079 −0.0213184
\(951\) 38.7367 1.25612
\(952\) −60.2094 −1.95140
\(953\) −0.334831 −0.0108462 −0.00542312 0.999985i \(-0.501726\pi\)
−0.00542312 + 0.999985i \(0.501726\pi\)
\(954\) −54.8449 −1.77567
\(955\) 22.2647 0.720469
\(956\) −24.5931 −0.795399
\(957\) 181.838 5.87798
\(958\) −44.8770 −1.44991
\(959\) 69.5374 2.24548
\(960\) −43.3672 −1.39967
\(961\) −7.42003 −0.239356
\(962\) 52.6445 1.69733
\(963\) −8.48841 −0.273535
\(964\) −65.0871 −2.09631
\(965\) −5.97822 −0.192446
\(966\) −88.3587 −2.84289
\(967\) −51.4091 −1.65321 −0.826603 0.562785i \(-0.809730\pi\)
−0.826603 + 0.562785i \(0.809730\pi\)
\(968\) −199.815 −6.42230
\(969\) 1.43739 0.0461756
\(970\) −19.1425 −0.614628
\(971\) −56.4309 −1.81096 −0.905478 0.424394i \(-0.860487\pi\)
−0.905478 + 0.424394i \(0.860487\pi\)
\(972\) 10.4245 0.334366
\(973\) 46.7128 1.49754
\(974\) 89.9947 2.88362
\(975\) −6.69045 −0.214266
\(976\) 38.6705 1.23781
\(977\) 0.157554 0.00504059 0.00252030 0.999997i \(-0.499198\pi\)
0.00252030 + 0.999997i \(0.499198\pi\)
\(978\) 74.6118 2.38582
\(979\) −74.3072 −2.37487
\(980\) 38.1941 1.22006
\(981\) −25.6129 −0.817755
\(982\) 33.8323 1.07963
\(983\) 48.1152 1.53464 0.767318 0.641267i \(-0.221591\pi\)
0.767318 + 0.641267i \(0.221591\pi\)
\(984\) 266.623 8.49964
\(985\) 12.1829 0.388181
\(986\) 52.8487 1.68305
\(987\) 102.249 3.25463
\(988\) 2.80519 0.0892451
\(989\) 23.2907 0.740601
\(990\) 93.2899 2.96495
\(991\) −50.8853 −1.61642 −0.808212 0.588892i \(-0.799564\pi\)
−0.808212 + 0.588892i \(0.799564\pi\)
\(992\) −68.2985 −2.16848
\(993\) 67.4432 2.14024
\(994\) −57.8814 −1.83589
\(995\) −12.9375 −0.410145
\(996\) −71.2361 −2.25720
\(997\) −61.0410 −1.93319 −0.966594 0.256312i \(-0.917493\pi\)
−0.966594 + 0.256312i \(0.917493\pi\)
\(998\) −74.4909 −2.35797
\(999\) 75.8717 2.40047
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 \(a_p\))