Properties

Label 6041.2.a.f.1.4
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 1.4
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75252 q^{2}\) \(-2.26942 q^{3}\) \(+5.57639 q^{4}\) \(+4.03697 q^{5}\) \(+6.24664 q^{6}\) \(+1.00000 q^{7}\) \(-9.84409 q^{8}\) \(+2.15028 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75252 q^{2}\) \(-2.26942 q^{3}\) \(+5.57639 q^{4}\) \(+4.03697 q^{5}\) \(+6.24664 q^{6}\) \(+1.00000 q^{7}\) \(-9.84409 q^{8}\) \(+2.15028 q^{9}\) \(-11.1119 q^{10}\) \(+5.59978 q^{11}\) \(-12.6552 q^{12}\) \(-6.36706 q^{13}\) \(-2.75252 q^{14}\) \(-9.16159 q^{15}\) \(+15.9433 q^{16}\) \(+3.68559 q^{17}\) \(-5.91869 q^{18}\) \(+0.306021 q^{19}\) \(+22.5117 q^{20}\) \(-2.26942 q^{21}\) \(-15.4135 q^{22}\) \(+4.37544 q^{23}\) \(+22.3404 q^{24}\) \(+11.2971 q^{25}\) \(+17.5255 q^{26}\) \(+1.92838 q^{27}\) \(+5.57639 q^{28}\) \(+3.33467 q^{29}\) \(+25.2175 q^{30}\) \(-5.49463 q^{31}\) \(-24.1962 q^{32}\) \(-12.7083 q^{33}\) \(-10.1447 q^{34}\) \(+4.03697 q^{35}\) \(+11.9908 q^{36}\) \(+0.873713 q^{37}\) \(-0.842329 q^{38}\) \(+14.4496 q^{39}\) \(-39.7403 q^{40}\) \(-6.95623 q^{41}\) \(+6.24664 q^{42}\) \(-8.46973 q^{43}\) \(+31.2265 q^{44}\) \(+8.68061 q^{45}\) \(-12.0435 q^{46}\) \(-13.4609 q^{47}\) \(-36.1821 q^{48}\) \(+1.00000 q^{49}\) \(-31.0956 q^{50}\) \(-8.36416 q^{51}\) \(-35.5052 q^{52}\) \(+12.2196 q^{53}\) \(-5.30791 q^{54}\) \(+22.6061 q^{55}\) \(-9.84409 q^{56}\) \(-0.694490 q^{57}\) \(-9.17876 q^{58}\) \(+9.57366 q^{59}\) \(-51.0886 q^{60}\) \(-7.33583 q^{61}\) \(+15.1241 q^{62}\) \(+2.15028 q^{63}\) \(+34.7140 q^{64}\) \(-25.7036 q^{65}\) \(+34.9798 q^{66}\) \(+12.9283 q^{67}\) \(+20.5523 q^{68}\) \(-9.92971 q^{69}\) \(-11.1119 q^{70}\) \(-1.49753 q^{71}\) \(-21.1675 q^{72}\) \(+5.95771 q^{73}\) \(-2.40492 q^{74}\) \(-25.6380 q^{75}\) \(+1.70649 q^{76}\) \(+5.59978 q^{77}\) \(-39.7727 q^{78}\) \(+5.78081 q^{79}\) \(+64.3628 q^{80}\) \(-10.8271 q^{81}\) \(+19.1472 q^{82}\) \(+0.537141 q^{83}\) \(-12.6552 q^{84}\) \(+14.8786 q^{85}\) \(+23.3131 q^{86}\) \(-7.56778 q^{87}\) \(-55.1247 q^{88}\) \(+3.53672 q^{89}\) \(-23.8936 q^{90}\) \(-6.36706 q^{91}\) \(+24.3991 q^{92}\) \(+12.4696 q^{93}\) \(+37.0514 q^{94}\) \(+1.23540 q^{95}\) \(+54.9114 q^{96}\) \(-9.25815 q^{97}\) \(-2.75252 q^{98}\) \(+12.0411 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75252 −1.94633 −0.973164 0.230112i \(-0.926091\pi\)
−0.973164 + 0.230112i \(0.926091\pi\)
\(3\) −2.26942 −1.31025 −0.655126 0.755520i \(-0.727384\pi\)
−0.655126 + 0.755520i \(0.727384\pi\)
\(4\) 5.57639 2.78819
\(5\) 4.03697 1.80539 0.902694 0.430283i \(-0.141586\pi\)
0.902694 + 0.430283i \(0.141586\pi\)
\(6\) 6.24664 2.55018
\(7\) 1.00000 0.377964
\(8\) −9.84409 −3.48041
\(9\) 2.15028 0.716759
\(10\) −11.1119 −3.51388
\(11\) 5.59978 1.68840 0.844198 0.536031i \(-0.180077\pi\)
0.844198 + 0.536031i \(0.180077\pi\)
\(12\) −12.6552 −3.65324
\(13\) −6.36706 −1.76591 −0.882953 0.469462i \(-0.844448\pi\)
−0.882953 + 0.469462i \(0.844448\pi\)
\(14\) −2.75252 −0.735643
\(15\) −9.16159 −2.36551
\(16\) 15.9433 3.98583
\(17\) 3.68559 0.893887 0.446943 0.894562i \(-0.352513\pi\)
0.446943 + 0.894562i \(0.352513\pi\)
\(18\) −5.91869 −1.39505
\(19\) 0.306021 0.0702059 0.0351030 0.999384i \(-0.488824\pi\)
0.0351030 + 0.999384i \(0.488824\pi\)
\(20\) 22.5117 5.03377
\(21\) −2.26942 −0.495229
\(22\) −15.4135 −3.28617
\(23\) 4.37544 0.912342 0.456171 0.889892i \(-0.349221\pi\)
0.456171 + 0.889892i \(0.349221\pi\)
\(24\) 22.3404 4.56022
\(25\) 11.2971 2.25943
\(26\) 17.5255 3.43703
\(27\) 1.92838 0.371117
\(28\) 5.57639 1.05384
\(29\) 3.33467 0.619233 0.309617 0.950862i \(-0.399799\pi\)
0.309617 + 0.950862i \(0.399799\pi\)
\(30\) 25.2175 4.60406
\(31\) −5.49463 −0.986864 −0.493432 0.869784i \(-0.664258\pi\)
−0.493432 + 0.869784i \(0.664258\pi\)
\(32\) −24.1962 −4.27733
\(33\) −12.7083 −2.21222
\(34\) −10.1447 −1.73980
\(35\) 4.03697 0.682373
\(36\) 11.9908 1.99846
\(37\) 0.873713 0.143638 0.0718188 0.997418i \(-0.477120\pi\)
0.0718188 + 0.997418i \(0.477120\pi\)
\(38\) −0.842329 −0.136644
\(39\) 14.4496 2.31378
\(40\) −39.7403 −6.28350
\(41\) −6.95623 −1.08638 −0.543190 0.839610i \(-0.682784\pi\)
−0.543190 + 0.839610i \(0.682784\pi\)
\(42\) 6.24664 0.963877
\(43\) −8.46973 −1.29162 −0.645811 0.763498i \(-0.723480\pi\)
−0.645811 + 0.763498i \(0.723480\pi\)
\(44\) 31.2265 4.70758
\(45\) 8.68061 1.29403
\(46\) −12.0435 −1.77572
\(47\) −13.4609 −1.96347 −0.981737 0.190245i \(-0.939072\pi\)
−0.981737 + 0.190245i \(0.939072\pi\)
\(48\) −36.1821 −5.22244
\(49\) 1.00000 0.142857
\(50\) −31.0956 −4.39759
\(51\) −8.36416 −1.17122
\(52\) −35.5052 −4.92369
\(53\) 12.2196 1.67849 0.839244 0.543755i \(-0.182998\pi\)
0.839244 + 0.543755i \(0.182998\pi\)
\(54\) −5.30791 −0.722315
\(55\) 22.6061 3.04821
\(56\) −9.84409 −1.31547
\(57\) −0.694490 −0.0919874
\(58\) −9.17876 −1.20523
\(59\) 9.57366 1.24638 0.623192 0.782069i \(-0.285835\pi\)
0.623192 + 0.782069i \(0.285835\pi\)
\(60\) −51.0886 −6.59551
\(61\) −7.33583 −0.939256 −0.469628 0.882864i \(-0.655612\pi\)
−0.469628 + 0.882864i \(0.655612\pi\)
\(62\) 15.1241 1.92076
\(63\) 2.15028 0.270910
\(64\) 34.7140 4.33925
\(65\) −25.7036 −3.18814
\(66\) 34.9798 4.30571
\(67\) 12.9283 1.57944 0.789720 0.613467i \(-0.210226\pi\)
0.789720 + 0.613467i \(0.210226\pi\)
\(68\) 20.5523 2.49233
\(69\) −9.92971 −1.19540
\(70\) −11.1119 −1.32812
\(71\) −1.49753 −0.177724 −0.0888621 0.996044i \(-0.528323\pi\)
−0.0888621 + 0.996044i \(0.528323\pi\)
\(72\) −21.1675 −2.49462
\(73\) 5.95771 0.697297 0.348649 0.937253i \(-0.386641\pi\)
0.348649 + 0.937253i \(0.386641\pi\)
\(74\) −2.40492 −0.279566
\(75\) −25.6380 −2.96042
\(76\) 1.70649 0.195748
\(77\) 5.59978 0.638154
\(78\) −39.7727 −4.50338
\(79\) 5.78081 0.650392 0.325196 0.945647i \(-0.394570\pi\)
0.325196 + 0.945647i \(0.394570\pi\)
\(80\) 64.3628 7.19597
\(81\) −10.8271 −1.20302
\(82\) 19.1472 2.11445
\(83\) 0.537141 0.0589589 0.0294794 0.999565i \(-0.490615\pi\)
0.0294794 + 0.999565i \(0.490615\pi\)
\(84\) −12.6552 −1.38079
\(85\) 14.8786 1.61381
\(86\) 23.3131 2.51392
\(87\) −7.56778 −0.811351
\(88\) −55.1247 −5.87632
\(89\) 3.53672 0.374891 0.187446 0.982275i \(-0.439979\pi\)
0.187446 + 0.982275i \(0.439979\pi\)
\(90\) −23.8936 −2.51861
\(91\) −6.36706 −0.667449
\(92\) 24.3991 2.54379
\(93\) 12.4696 1.29304
\(94\) 37.0514 3.82156
\(95\) 1.23540 0.126749
\(96\) 54.9114 5.60437
\(97\) −9.25815 −0.940022 −0.470011 0.882660i \(-0.655750\pi\)
−0.470011 + 0.882660i \(0.655750\pi\)
\(98\) −2.75252 −0.278047
\(99\) 12.0411 1.21017
\(100\) 62.9972 6.29972
\(101\) 6.53574 0.650330 0.325165 0.945657i \(-0.394580\pi\)
0.325165 + 0.945657i \(0.394580\pi\)
\(102\) 23.0225 2.27957
\(103\) −3.41180 −0.336174 −0.168087 0.985772i \(-0.553759\pi\)
−0.168087 + 0.985772i \(0.553759\pi\)
\(104\) 62.6780 6.14608
\(105\) −9.16159 −0.894080
\(106\) −33.6347 −3.26689
\(107\) 9.31172 0.900197 0.450099 0.892979i \(-0.351389\pi\)
0.450099 + 0.892979i \(0.351389\pi\)
\(108\) 10.7534 1.03475
\(109\) 11.3959 1.09153 0.545766 0.837938i \(-0.316239\pi\)
0.545766 + 0.837938i \(0.316239\pi\)
\(110\) −62.2239 −5.93282
\(111\) −1.98282 −0.188201
\(112\) 15.9433 1.50650
\(113\) −15.4706 −1.45535 −0.727673 0.685924i \(-0.759398\pi\)
−0.727673 + 0.685924i \(0.759398\pi\)
\(114\) 1.91160 0.179038
\(115\) 17.6635 1.64713
\(116\) 18.5954 1.72654
\(117\) −13.6910 −1.26573
\(118\) −26.3517 −2.42587
\(119\) 3.68559 0.337857
\(120\) 90.1876 8.23296
\(121\) 20.3575 1.85068
\(122\) 20.1920 1.82810
\(123\) 15.7866 1.42343
\(124\) −30.6402 −2.75157
\(125\) 25.4213 2.27375
\(126\) −5.91869 −0.527279
\(127\) 15.9098 1.41176 0.705882 0.708330i \(-0.250551\pi\)
0.705882 + 0.708330i \(0.250551\pi\)
\(128\) −47.1587 −4.16828
\(129\) 19.2214 1.69235
\(130\) 70.7499 6.20518
\(131\) −2.26496 −0.197891 −0.0989454 0.995093i \(-0.531547\pi\)
−0.0989454 + 0.995093i \(0.531547\pi\)
\(132\) −70.8662 −6.16811
\(133\) 0.306021 0.0265353
\(134\) −35.5854 −3.07411
\(135\) 7.78481 0.670009
\(136\) −36.2813 −3.11110
\(137\) −0.336057 −0.0287113 −0.0143557 0.999897i \(-0.504570\pi\)
−0.0143557 + 0.999897i \(0.504570\pi\)
\(138\) 27.3318 2.32663
\(139\) −0.0807869 −0.00685226 −0.00342613 0.999994i \(-0.501091\pi\)
−0.00342613 + 0.999994i \(0.501091\pi\)
\(140\) 22.5117 1.90259
\(141\) 30.5485 2.57264
\(142\) 4.12199 0.345910
\(143\) −35.6541 −2.98155
\(144\) 34.2826 2.85688
\(145\) 13.4620 1.11796
\(146\) −16.3987 −1.35717
\(147\) −2.26942 −0.187179
\(148\) 4.87216 0.400489
\(149\) 13.8693 1.13622 0.568109 0.822954i \(-0.307675\pi\)
0.568109 + 0.822954i \(0.307675\pi\)
\(150\) 70.5691 5.76194
\(151\) 4.05473 0.329969 0.164984 0.986296i \(-0.447243\pi\)
0.164984 + 0.986296i \(0.447243\pi\)
\(152\) −3.01249 −0.244346
\(153\) 7.92504 0.640702
\(154\) −15.4135 −1.24206
\(155\) −22.1817 −1.78167
\(156\) 80.5763 6.45127
\(157\) −13.9466 −1.11306 −0.556531 0.830827i \(-0.687868\pi\)
−0.556531 + 0.830827i \(0.687868\pi\)
\(158\) −15.9118 −1.26588
\(159\) −27.7314 −2.19924
\(160\) −97.6794 −7.72223
\(161\) 4.37544 0.344833
\(162\) 29.8020 2.34146
\(163\) 6.82129 0.534284 0.267142 0.963657i \(-0.413921\pi\)
0.267142 + 0.963657i \(0.413921\pi\)
\(164\) −38.7906 −3.02904
\(165\) −51.3029 −3.99392
\(166\) −1.47849 −0.114753
\(167\) −10.8806 −0.841967 −0.420983 0.907068i \(-0.638315\pi\)
−0.420983 + 0.907068i \(0.638315\pi\)
\(168\) 22.3404 1.72360
\(169\) 27.5395 2.11842
\(170\) −40.9538 −3.14101
\(171\) 0.658029 0.0503208
\(172\) −47.2305 −3.60129
\(173\) 12.7630 0.970353 0.485176 0.874416i \(-0.338755\pi\)
0.485176 + 0.874416i \(0.338755\pi\)
\(174\) 20.8305 1.57916
\(175\) 11.2971 0.853983
\(176\) 89.2791 6.72966
\(177\) −21.7267 −1.63308
\(178\) −9.73490 −0.729662
\(179\) 8.17347 0.610914 0.305457 0.952206i \(-0.401191\pi\)
0.305457 + 0.952206i \(0.401191\pi\)
\(180\) 48.4064 3.60800
\(181\) 14.5821 1.08388 0.541940 0.840417i \(-0.317690\pi\)
0.541940 + 0.840417i \(0.317690\pi\)
\(182\) 17.5255 1.29908
\(183\) 16.6481 1.23066
\(184\) −43.0722 −3.17533
\(185\) 3.52715 0.259322
\(186\) −34.3230 −2.51668
\(187\) 20.6385 1.50923
\(188\) −75.0632 −5.47454
\(189\) 1.92838 0.140269
\(190\) −3.40046 −0.246695
\(191\) 13.9763 1.01129 0.505644 0.862742i \(-0.331255\pi\)
0.505644 + 0.862742i \(0.331255\pi\)
\(192\) −78.7807 −5.68551
\(193\) −1.91960 −0.138176 −0.0690878 0.997611i \(-0.522009\pi\)
−0.0690878 + 0.997611i \(0.522009\pi\)
\(194\) 25.4833 1.82959
\(195\) 58.3324 4.17727
\(196\) 5.57639 0.398313
\(197\) −26.2985 −1.87369 −0.936846 0.349742i \(-0.886269\pi\)
−0.936846 + 0.349742i \(0.886269\pi\)
\(198\) −33.1433 −2.35540
\(199\) 7.44641 0.527862 0.263931 0.964542i \(-0.414981\pi\)
0.263931 + 0.964542i \(0.414981\pi\)
\(200\) −111.210 −7.86374
\(201\) −29.3397 −2.06946
\(202\) −17.9898 −1.26576
\(203\) 3.33467 0.234048
\(204\) −46.6418 −3.26558
\(205\) −28.0821 −1.96134
\(206\) 9.39105 0.654305
\(207\) 9.40840 0.653929
\(208\) −101.512 −7.03860
\(209\) 1.71365 0.118535
\(210\) 25.2175 1.74017
\(211\) 22.8447 1.57269 0.786346 0.617786i \(-0.211970\pi\)
0.786346 + 0.617786i \(0.211970\pi\)
\(212\) 68.1411 4.67995
\(213\) 3.39853 0.232863
\(214\) −25.6307 −1.75208
\(215\) −34.1920 −2.33188
\(216\) −18.9831 −1.29164
\(217\) −5.49463 −0.373000
\(218\) −31.3676 −2.12448
\(219\) −13.5206 −0.913635
\(220\) 126.061 8.49900
\(221\) −23.4664 −1.57852
\(222\) 5.45777 0.366302
\(223\) −17.9074 −1.19916 −0.599582 0.800313i \(-0.704667\pi\)
−0.599582 + 0.800313i \(0.704667\pi\)
\(224\) −24.1962 −1.61668
\(225\) 24.2920 1.61947
\(226\) 42.5831 2.83258
\(227\) −6.64621 −0.441124 −0.220562 0.975373i \(-0.570789\pi\)
−0.220562 + 0.975373i \(0.570789\pi\)
\(228\) −3.87274 −0.256479
\(229\) 3.04788 0.201409 0.100705 0.994916i \(-0.467890\pi\)
0.100705 + 0.994916i \(0.467890\pi\)
\(230\) −48.6192 −3.20586
\(231\) −12.7083 −0.836142
\(232\) −32.8268 −2.15519
\(233\) −11.3683 −0.744760 −0.372380 0.928080i \(-0.621458\pi\)
−0.372380 + 0.928080i \(0.621458\pi\)
\(234\) 37.6847 2.46352
\(235\) −54.3412 −3.54483
\(236\) 53.3864 3.47516
\(237\) −13.1191 −0.852177
\(238\) −10.1447 −0.657582
\(239\) −10.8856 −0.704131 −0.352065 0.935975i \(-0.614521\pi\)
−0.352065 + 0.935975i \(0.614521\pi\)
\(240\) −146.066 −9.42854
\(241\) −3.12332 −0.201190 −0.100595 0.994927i \(-0.532075\pi\)
−0.100595 + 0.994927i \(0.532075\pi\)
\(242\) −56.0345 −3.60203
\(243\) 18.7862 1.20514
\(244\) −40.9074 −2.61883
\(245\) 4.03697 0.257913
\(246\) −43.4531 −2.77047
\(247\) −1.94845 −0.123977
\(248\) 54.0896 3.43470
\(249\) −1.21900 −0.0772510
\(250\) −69.9729 −4.42547
\(251\) 21.6662 1.36756 0.683780 0.729688i \(-0.260335\pi\)
0.683780 + 0.729688i \(0.260335\pi\)
\(252\) 11.9908 0.755348
\(253\) 24.5015 1.54039
\(254\) −43.7920 −2.74776
\(255\) −33.7659 −2.11450
\(256\) 60.3774 3.77358
\(257\) 0.981209 0.0612061 0.0306031 0.999532i \(-0.490257\pi\)
0.0306031 + 0.999532i \(0.490257\pi\)
\(258\) −52.9073 −3.29387
\(259\) 0.873713 0.0542899
\(260\) −143.333 −8.88917
\(261\) 7.17047 0.443841
\(262\) 6.23437 0.385161
\(263\) 28.4589 1.75485 0.877427 0.479711i \(-0.159259\pi\)
0.877427 + 0.479711i \(0.159259\pi\)
\(264\) 125.101 7.69945
\(265\) 49.3301 3.03032
\(266\) −0.842329 −0.0516465
\(267\) −8.02631 −0.491202
\(268\) 72.0931 4.40379
\(269\) 14.2842 0.870924 0.435462 0.900207i \(-0.356585\pi\)
0.435462 + 0.900207i \(0.356585\pi\)
\(270\) −21.4279 −1.30406
\(271\) 5.59980 0.340163 0.170082 0.985430i \(-0.445597\pi\)
0.170082 + 0.985430i \(0.445597\pi\)
\(272\) 58.7606 3.56288
\(273\) 14.4496 0.874527
\(274\) 0.925006 0.0558816
\(275\) 63.2614 3.81481
\(276\) −55.3719 −3.33300
\(277\) 14.9843 0.900318 0.450159 0.892948i \(-0.351367\pi\)
0.450159 + 0.892948i \(0.351367\pi\)
\(278\) 0.222368 0.0133367
\(279\) −11.8150 −0.707344
\(280\) −39.7403 −2.37494
\(281\) −10.5310 −0.628229 −0.314115 0.949385i \(-0.601708\pi\)
−0.314115 + 0.949385i \(0.601708\pi\)
\(282\) −84.0854 −5.00721
\(283\) −20.0101 −1.18947 −0.594737 0.803920i \(-0.702744\pi\)
−0.594737 + 0.803920i \(0.702744\pi\)
\(284\) −8.35081 −0.495530
\(285\) −2.80364 −0.166073
\(286\) 98.1388 5.80307
\(287\) −6.95623 −0.410613
\(288\) −52.0286 −3.06581
\(289\) −3.41643 −0.200966
\(290\) −37.0544 −2.17591
\(291\) 21.0106 1.23167
\(292\) 33.2225 1.94420
\(293\) −15.1033 −0.882347 −0.441173 0.897422i \(-0.645438\pi\)
−0.441173 + 0.897422i \(0.645438\pi\)
\(294\) 6.24664 0.364311
\(295\) 38.6486 2.25021
\(296\) −8.60092 −0.499918
\(297\) 10.7985 0.626592
\(298\) −38.1756 −2.21145
\(299\) −27.8587 −1.61111
\(300\) −142.967 −8.25422
\(301\) −8.46973 −0.488187
\(302\) −11.1607 −0.642228
\(303\) −14.8323 −0.852096
\(304\) 4.87899 0.279829
\(305\) −29.6145 −1.69572
\(306\) −21.8139 −1.24702
\(307\) 14.4431 0.824312 0.412156 0.911113i \(-0.364776\pi\)
0.412156 + 0.911113i \(0.364776\pi\)
\(308\) 31.2265 1.77930
\(309\) 7.74280 0.440473
\(310\) 61.0555 3.46772
\(311\) −0.259509 −0.0147154 −0.00735771 0.999973i \(-0.502342\pi\)
−0.00735771 + 0.999973i \(0.502342\pi\)
\(312\) −142.243 −8.05291
\(313\) 21.0940 1.19230 0.596151 0.802872i \(-0.296696\pi\)
0.596151 + 0.802872i \(0.296696\pi\)
\(314\) 38.3884 2.16638
\(315\) 8.68061 0.489097
\(316\) 32.2360 1.81342
\(317\) −19.5633 −1.09878 −0.549392 0.835565i \(-0.685141\pi\)
−0.549392 + 0.835565i \(0.685141\pi\)
\(318\) 76.3313 4.28045
\(319\) 18.6734 1.04551
\(320\) 140.139 7.83403
\(321\) −21.1322 −1.17949
\(322\) −12.0435 −0.671158
\(323\) 1.12787 0.0627561
\(324\) −60.3763 −3.35424
\(325\) −71.9295 −3.98993
\(326\) −18.7758 −1.03989
\(327\) −25.8622 −1.43018
\(328\) 68.4778 3.78105
\(329\) −13.4609 −0.742123
\(330\) 141.212 7.77348
\(331\) −5.71041 −0.313872 −0.156936 0.987609i \(-0.550162\pi\)
−0.156936 + 0.987609i \(0.550162\pi\)
\(332\) 2.99531 0.164389
\(333\) 1.87873 0.102954
\(334\) 29.9491 1.63874
\(335\) 52.1911 2.85150
\(336\) −36.1821 −1.97390
\(337\) 24.0421 1.30965 0.654827 0.755779i \(-0.272741\pi\)
0.654827 + 0.755779i \(0.272741\pi\)
\(338\) −75.8031 −4.12314
\(339\) 35.1092 1.90687
\(340\) 82.9689 4.49962
\(341\) −30.7687 −1.66622
\(342\) −1.81124 −0.0979407
\(343\) 1.00000 0.0539949
\(344\) 83.3768 4.49537
\(345\) −40.0860 −2.15816
\(346\) −35.1305 −1.88862
\(347\) −0.329970 −0.0177137 −0.00885687 0.999961i \(-0.502819\pi\)
−0.00885687 + 0.999961i \(0.502819\pi\)
\(348\) −42.2009 −2.26220
\(349\) 6.67993 0.357569 0.178784 0.983888i \(-0.442784\pi\)
0.178784 + 0.983888i \(0.442784\pi\)
\(350\) −31.0956 −1.66213
\(351\) −12.2781 −0.655357
\(352\) −135.493 −7.22182
\(353\) −12.2971 −0.654510 −0.327255 0.944936i \(-0.606124\pi\)
−0.327255 + 0.944936i \(0.606124\pi\)
\(354\) 59.8032 3.17850
\(355\) −6.04549 −0.320861
\(356\) 19.7221 1.04527
\(357\) −8.36416 −0.442678
\(358\) −22.4977 −1.18904
\(359\) −19.4540 −1.02674 −0.513371 0.858167i \(-0.671604\pi\)
−0.513371 + 0.858167i \(0.671604\pi\)
\(360\) −85.4527 −4.50375
\(361\) −18.9064 −0.995071
\(362\) −40.1376 −2.10959
\(363\) −46.1998 −2.42486
\(364\) −35.5052 −1.86098
\(365\) 24.0511 1.25889
\(366\) −45.8243 −2.39527
\(367\) 15.5108 0.809657 0.404828 0.914393i \(-0.367331\pi\)
0.404828 + 0.914393i \(0.367331\pi\)
\(368\) 69.7590 3.63644
\(369\) −14.9578 −0.778673
\(370\) −9.70858 −0.504725
\(371\) 12.2196 0.634409
\(372\) 69.5355 3.60525
\(373\) −7.78323 −0.403000 −0.201500 0.979488i \(-0.564582\pi\)
−0.201500 + 0.979488i \(0.564582\pi\)
\(374\) −56.8079 −2.93747
\(375\) −57.6918 −2.97919
\(376\) 132.510 6.83370
\(377\) −21.2321 −1.09351
\(378\) −5.30791 −0.273009
\(379\) 29.3733 1.50881 0.754404 0.656411i \(-0.227926\pi\)
0.754404 + 0.656411i \(0.227926\pi\)
\(380\) 6.88905 0.353401
\(381\) −36.1060 −1.84977
\(382\) −38.4700 −1.96830
\(383\) 18.0431 0.921960 0.460980 0.887410i \(-0.347498\pi\)
0.460980 + 0.887410i \(0.347498\pi\)
\(384\) 107.023 5.46149
\(385\) 22.6061 1.15212
\(386\) 5.28374 0.268935
\(387\) −18.2123 −0.925781
\(388\) −51.6270 −2.62097
\(389\) −16.9277 −0.858269 −0.429134 0.903241i \(-0.641181\pi\)
−0.429134 + 0.903241i \(0.641181\pi\)
\(390\) −160.561 −8.13034
\(391\) 16.1261 0.815530
\(392\) −9.84409 −0.497202
\(393\) 5.14016 0.259287
\(394\) 72.3873 3.64682
\(395\) 23.3370 1.17421
\(396\) 67.1457 3.37420
\(397\) −14.7989 −0.742734 −0.371367 0.928486i \(-0.621111\pi\)
−0.371367 + 0.928486i \(0.621111\pi\)
\(398\) −20.4964 −1.02739
\(399\) −0.694490 −0.0347680
\(400\) 180.114 9.00570
\(401\) −11.3183 −0.565210 −0.282605 0.959236i \(-0.591199\pi\)
−0.282605 + 0.959236i \(0.591199\pi\)
\(402\) 80.7583 4.02786
\(403\) 34.9846 1.74271
\(404\) 36.4458 1.81325
\(405\) −43.7088 −2.17191
\(406\) −9.17876 −0.455534
\(407\) 4.89260 0.242517
\(408\) 82.3376 4.07632
\(409\) −30.8220 −1.52405 −0.762026 0.647547i \(-0.775795\pi\)
−0.762026 + 0.647547i \(0.775795\pi\)
\(410\) 77.2966 3.81741
\(411\) 0.762656 0.0376190
\(412\) −19.0255 −0.937319
\(413\) 9.57366 0.471089
\(414\) −25.8969 −1.27276
\(415\) 2.16842 0.106444
\(416\) 154.059 7.55335
\(417\) 0.183340 0.00897818
\(418\) −4.71685 −0.230709
\(419\) 15.6141 0.762799 0.381400 0.924410i \(-0.375442\pi\)
0.381400 + 0.924410i \(0.375442\pi\)
\(420\) −51.0886 −2.49287
\(421\) −38.1872 −1.86113 −0.930564 0.366130i \(-0.880683\pi\)
−0.930564 + 0.366130i \(0.880683\pi\)
\(422\) −62.8805 −3.06098
\(423\) −28.9447 −1.40734
\(424\) −120.291 −5.84183
\(425\) 41.6366 2.01967
\(426\) −9.35453 −0.453229
\(427\) −7.33583 −0.355006
\(428\) 51.9257 2.50993
\(429\) 80.9143 3.90658
\(430\) 94.1144 4.53860
\(431\) −3.59797 −0.173308 −0.0866541 0.996238i \(-0.527617\pi\)
−0.0866541 + 0.996238i \(0.527617\pi\)
\(432\) 30.7448 1.47921
\(433\) 3.57470 0.171789 0.0858945 0.996304i \(-0.472625\pi\)
0.0858945 + 0.996304i \(0.472625\pi\)
\(434\) 15.1241 0.725980
\(435\) −30.5509 −1.46480
\(436\) 63.5481 3.04340
\(437\) 1.33897 0.0640518
\(438\) 37.2157 1.77823
\(439\) −6.60211 −0.315101 −0.157551 0.987511i \(-0.550360\pi\)
−0.157551 + 0.987511i \(0.550360\pi\)
\(440\) −222.537 −10.6090
\(441\) 2.15028 0.102394
\(442\) 64.5918 3.07232
\(443\) 39.2262 1.86369 0.931847 0.362852i \(-0.118197\pi\)
0.931847 + 0.362852i \(0.118197\pi\)
\(444\) −11.0570 −0.524742
\(445\) 14.2776 0.676824
\(446\) 49.2904 2.33397
\(447\) −31.4753 −1.48873
\(448\) 34.7140 1.64008
\(449\) 24.2865 1.14615 0.573076 0.819502i \(-0.305750\pi\)
0.573076 + 0.819502i \(0.305750\pi\)
\(450\) −66.8642 −3.15201
\(451\) −38.9533 −1.83424
\(452\) −86.2698 −4.05779
\(453\) −9.20189 −0.432342
\(454\) 18.2938 0.858573
\(455\) −25.7036 −1.20501
\(456\) 6.83662 0.320154
\(457\) −16.7421 −0.783163 −0.391581 0.920143i \(-0.628072\pi\)
−0.391581 + 0.920143i \(0.628072\pi\)
\(458\) −8.38935 −0.392009
\(459\) 7.10721 0.331736
\(460\) 98.4986 4.59252
\(461\) −18.6385 −0.868083 −0.434042 0.900893i \(-0.642913\pi\)
−0.434042 + 0.900893i \(0.642913\pi\)
\(462\) 34.9798 1.62741
\(463\) 0.884971 0.0411281 0.0205640 0.999789i \(-0.493454\pi\)
0.0205640 + 0.999789i \(0.493454\pi\)
\(464\) 53.1658 2.46816
\(465\) 50.3395 2.33444
\(466\) 31.2914 1.44955
\(467\) 21.5353 0.996534 0.498267 0.867024i \(-0.333970\pi\)
0.498267 + 0.867024i \(0.333970\pi\)
\(468\) −76.3461 −3.52910
\(469\) 12.9283 0.596972
\(470\) 149.576 6.89941
\(471\) 31.6508 1.45839
\(472\) −94.2440 −4.33793
\(473\) −47.4286 −2.18077
\(474\) 36.1106 1.65862
\(475\) 3.45715 0.158625
\(476\) 20.5523 0.942012
\(477\) 26.2755 1.20307
\(478\) 29.9629 1.37047
\(479\) −41.0404 −1.87518 −0.937592 0.347738i \(-0.886950\pi\)
−0.937592 + 0.347738i \(0.886950\pi\)
\(480\) 221.676 10.1181
\(481\) −5.56299 −0.253650
\(482\) 8.59700 0.391583
\(483\) −9.92971 −0.451818
\(484\) 113.521 5.16006
\(485\) −37.3749 −1.69711
\(486\) −51.7095 −2.34559
\(487\) 7.54063 0.341699 0.170849 0.985297i \(-0.445349\pi\)
0.170849 + 0.985297i \(0.445349\pi\)
\(488\) 72.2146 3.26900
\(489\) −15.4804 −0.700047
\(490\) −11.1119 −0.501983
\(491\) −8.90635 −0.401938 −0.200969 0.979598i \(-0.564409\pi\)
−0.200969 + 0.979598i \(0.564409\pi\)
\(492\) 88.0323 3.96880
\(493\) 12.2902 0.553524
\(494\) 5.36316 0.241300
\(495\) 48.6095 2.18483
\(496\) −87.6027 −3.93348
\(497\) −1.49753 −0.0671734
\(498\) 3.35533 0.150356
\(499\) 20.9496 0.937835 0.468917 0.883242i \(-0.344644\pi\)
0.468917 + 0.883242i \(0.344644\pi\)
\(500\) 141.759 6.33967
\(501\) 24.6927 1.10319
\(502\) −59.6368 −2.66172
\(503\) 5.42274 0.241788 0.120894 0.992665i \(-0.461424\pi\)
0.120894 + 0.992665i \(0.461424\pi\)
\(504\) −21.1675 −0.942877
\(505\) 26.3846 1.17410
\(506\) −67.4409 −2.99811
\(507\) −62.4987 −2.77566
\(508\) 88.7191 3.93627
\(509\) −16.5523 −0.733666 −0.366833 0.930287i \(-0.619558\pi\)
−0.366833 + 0.930287i \(0.619558\pi\)
\(510\) 92.9414 4.11551
\(511\) 5.95771 0.263554
\(512\) −71.8728 −3.17636
\(513\) 0.590123 0.0260546
\(514\) −2.70080 −0.119127
\(515\) −13.7733 −0.606925
\(516\) 107.186 4.71860
\(517\) −75.3780 −3.31512
\(518\) −2.40492 −0.105666
\(519\) −28.9646 −1.27141
\(520\) 253.029 11.0961
\(521\) 7.19428 0.315187 0.157594 0.987504i \(-0.449626\pi\)
0.157594 + 0.987504i \(0.449626\pi\)
\(522\) −19.7369 −0.863860
\(523\) 2.17422 0.0950720 0.0475360 0.998870i \(-0.484863\pi\)
0.0475360 + 0.998870i \(0.484863\pi\)
\(524\) −12.6303 −0.551758
\(525\) −25.6380 −1.11893
\(526\) −78.3339 −3.41552
\(527\) −20.2509 −0.882145
\(528\) −202.612 −8.81755
\(529\) −3.85556 −0.167633
\(530\) −135.782 −5.89800
\(531\) 20.5860 0.893358
\(532\) 1.70649 0.0739857
\(533\) 44.2907 1.91844
\(534\) 22.0926 0.956040
\(535\) 37.5911 1.62521
\(536\) −127.267 −5.49710
\(537\) −18.5491 −0.800451
\(538\) −39.3177 −1.69510
\(539\) 5.59978 0.241199
\(540\) 43.4111 1.86812
\(541\) −19.1835 −0.824763 −0.412382 0.911011i \(-0.635303\pi\)
−0.412382 + 0.911011i \(0.635303\pi\)
\(542\) −15.4136 −0.662070
\(543\) −33.0930 −1.42015
\(544\) −89.1773 −3.82344
\(545\) 46.0050 1.97064
\(546\) −39.7727 −1.70212
\(547\) −35.6979 −1.52633 −0.763166 0.646202i \(-0.776356\pi\)
−0.763166 + 0.646202i \(0.776356\pi\)
\(548\) −1.87399 −0.0800527
\(549\) −15.7741 −0.673221
\(550\) −174.129 −7.42487
\(551\) 1.02048 0.0434738
\(552\) 97.7490 4.16047
\(553\) 5.78081 0.245825
\(554\) −41.2446 −1.75231
\(555\) −8.00460 −0.339777
\(556\) −0.450499 −0.0191054
\(557\) −18.8724 −0.799651 −0.399826 0.916591i \(-0.630929\pi\)
−0.399826 + 0.916591i \(0.630929\pi\)
\(558\) 32.5210 1.37672
\(559\) 53.9273 2.28088
\(560\) 64.3628 2.71982
\(561\) −46.8374 −1.97748
\(562\) 28.9870 1.22274
\(563\) −34.9320 −1.47221 −0.736105 0.676867i \(-0.763337\pi\)
−0.736105 + 0.676867i \(0.763337\pi\)
\(564\) 170.350 7.17303
\(565\) −62.4542 −2.62747
\(566\) 55.0782 2.31511
\(567\) −10.8271 −0.454697
\(568\) 14.7418 0.618554
\(569\) −9.90202 −0.415114 −0.207557 0.978223i \(-0.566551\pi\)
−0.207557 + 0.978223i \(0.566551\pi\)
\(570\) 7.71707 0.323233
\(571\) −26.8154 −1.12219 −0.561095 0.827752i \(-0.689620\pi\)
−0.561095 + 0.827752i \(0.689620\pi\)
\(572\) −198.821 −8.31313
\(573\) −31.7181 −1.32504
\(574\) 19.1472 0.799188
\(575\) 49.4299 2.06137
\(576\) 74.6447 3.11020
\(577\) 4.66582 0.194240 0.0971202 0.995273i \(-0.469037\pi\)
0.0971202 + 0.995273i \(0.469037\pi\)
\(578\) 9.40380 0.391147
\(579\) 4.35638 0.181045
\(580\) 75.0692 3.11708
\(581\) 0.537141 0.0222844
\(582\) −57.8323 −2.39723
\(583\) 68.4269 2.83395
\(584\) −58.6483 −2.42688
\(585\) −55.2700 −2.28513
\(586\) 41.5723 1.71734
\(587\) −24.6937 −1.01922 −0.509608 0.860407i \(-0.670210\pi\)
−0.509608 + 0.860407i \(0.670210\pi\)
\(588\) −12.6552 −0.521891
\(589\) −1.68147 −0.0692837
\(590\) −106.381 −4.37964
\(591\) 59.6825 2.45501
\(592\) 13.9299 0.572515
\(593\) 15.4558 0.634696 0.317348 0.948309i \(-0.397208\pi\)
0.317348 + 0.948309i \(0.397208\pi\)
\(594\) −29.7231 −1.21955
\(595\) 14.8786 0.609964
\(596\) 77.3406 3.16799
\(597\) −16.8991 −0.691632
\(598\) 76.6817 3.13575
\(599\) −34.4534 −1.40773 −0.703864 0.710335i \(-0.748543\pi\)
−0.703864 + 0.710335i \(0.748543\pi\)
\(600\) 252.383 10.3035
\(601\) 20.9532 0.854697 0.427348 0.904087i \(-0.359448\pi\)
0.427348 + 0.904087i \(0.359448\pi\)
\(602\) 23.3131 0.950172
\(603\) 27.7994 1.13208
\(604\) 22.6107 0.920017
\(605\) 82.1826 3.34120
\(606\) 40.8264 1.65846
\(607\) 35.1636 1.42725 0.713623 0.700530i \(-0.247053\pi\)
0.713623 + 0.700530i \(0.247053\pi\)
\(608\) −7.40454 −0.300294
\(609\) −7.56778 −0.306662
\(610\) 81.5147 3.30043
\(611\) 85.7063 3.46731
\(612\) 44.1931 1.78640
\(613\) 46.8476 1.89216 0.946079 0.323937i \(-0.105007\pi\)
0.946079 + 0.323937i \(0.105007\pi\)
\(614\) −39.7550 −1.60438
\(615\) 63.7301 2.56985
\(616\) −55.1247 −2.22104
\(617\) −20.3129 −0.817768 −0.408884 0.912586i \(-0.634082\pi\)
−0.408884 + 0.912586i \(0.634082\pi\)
\(618\) −21.3123 −0.857305
\(619\) −0.422058 −0.0169640 −0.00848198 0.999964i \(-0.502700\pi\)
−0.00848198 + 0.999964i \(0.502700\pi\)
\(620\) −123.694 −4.96765
\(621\) 8.43750 0.338585
\(622\) 0.714305 0.0286410
\(623\) 3.53672 0.141696
\(624\) 230.374 9.22234
\(625\) 46.1396 1.84558
\(626\) −58.0617 −2.32061
\(627\) −3.88899 −0.155311
\(628\) −77.7718 −3.10343
\(629\) 3.22015 0.128396
\(630\) −23.8936 −0.951943
\(631\) 19.0673 0.759057 0.379528 0.925180i \(-0.376086\pi\)
0.379528 + 0.925180i \(0.376086\pi\)
\(632\) −56.9068 −2.26363
\(633\) −51.8442 −2.06062
\(634\) 53.8484 2.13859
\(635\) 64.2273 2.54878
\(636\) −154.641 −6.13191
\(637\) −6.36706 −0.252272
\(638\) −51.3990 −2.03491
\(639\) −3.22011 −0.127385
\(640\) −190.378 −7.52536
\(641\) −4.16979 −0.164697 −0.0823484 0.996604i \(-0.526242\pi\)
−0.0823484 + 0.996604i \(0.526242\pi\)
\(642\) 58.1669 2.29567
\(643\) 17.8953 0.705723 0.352861 0.935676i \(-0.385209\pi\)
0.352861 + 0.935676i \(0.385209\pi\)
\(644\) 24.3991 0.961460
\(645\) 77.5962 3.05535
\(646\) −3.10448 −0.122144
\(647\) 30.7522 1.20899 0.604496 0.796608i \(-0.293374\pi\)
0.604496 + 0.796608i \(0.293374\pi\)
\(648\) 106.583 4.18699
\(649\) 53.6104 2.10439
\(650\) 197.988 7.76572
\(651\) 12.4696 0.488723
\(652\) 38.0381 1.48969
\(653\) 13.9743 0.546857 0.273428 0.961892i \(-0.411842\pi\)
0.273428 + 0.961892i \(0.411842\pi\)
\(654\) 71.1863 2.78360
\(655\) −9.14359 −0.357270
\(656\) −110.905 −4.33013
\(657\) 12.8107 0.499794
\(658\) 37.0514 1.44442
\(659\) −13.2136 −0.514729 −0.257365 0.966314i \(-0.582854\pi\)
−0.257365 + 0.966314i \(0.582854\pi\)
\(660\) −286.085 −11.1358
\(661\) 39.8009 1.54807 0.774037 0.633140i \(-0.218234\pi\)
0.774037 + 0.633140i \(0.218234\pi\)
\(662\) 15.7180 0.610899
\(663\) 53.2551 2.06826
\(664\) −5.28767 −0.205201
\(665\) 1.23540 0.0479066
\(666\) −5.17124 −0.200381
\(667\) 14.5906 0.564952
\(668\) −60.6745 −2.34757
\(669\) 40.6393 1.57121
\(670\) −143.657 −5.54996
\(671\) −41.0790 −1.58584
\(672\) 54.9114 2.11825
\(673\) 10.1016 0.389388 0.194694 0.980864i \(-0.437629\pi\)
0.194694 + 0.980864i \(0.437629\pi\)
\(674\) −66.1763 −2.54902
\(675\) 21.7851 0.838511
\(676\) 153.571 5.90657
\(677\) 1.71973 0.0660944 0.0330472 0.999454i \(-0.489479\pi\)
0.0330472 + 0.999454i \(0.489479\pi\)
\(678\) −96.6389 −3.71140
\(679\) −9.25815 −0.355295
\(680\) −146.467 −5.61673
\(681\) 15.0831 0.577984
\(682\) 84.6916 3.24301
\(683\) 7.50469 0.287159 0.143580 0.989639i \(-0.454139\pi\)
0.143580 + 0.989639i \(0.454139\pi\)
\(684\) 3.66943 0.140304
\(685\) −1.35665 −0.0518351
\(686\) −2.75252 −0.105092
\(687\) −6.91692 −0.263897
\(688\) −135.036 −5.14818
\(689\) −77.8028 −2.96405
\(690\) 110.338 4.20048
\(691\) 2.26007 0.0859772 0.0429886 0.999076i \(-0.486312\pi\)
0.0429886 + 0.999076i \(0.486312\pi\)
\(692\) 71.1714 2.70553
\(693\) 12.0411 0.457403
\(694\) 0.908251 0.0344767
\(695\) −0.326135 −0.0123710
\(696\) 74.4979 2.82384
\(697\) −25.6378 −0.971101
\(698\) −18.3867 −0.695946
\(699\) 25.7994 0.975822
\(700\) 62.9972 2.38107
\(701\) −21.7335 −0.820862 −0.410431 0.911892i \(-0.634622\pi\)
−0.410431 + 0.911892i \(0.634622\pi\)
\(702\) 33.7958 1.27554
\(703\) 0.267374 0.0100842
\(704\) 194.391 7.32637
\(705\) 123.323 4.64462
\(706\) 33.8481 1.27389
\(707\) 6.53574 0.245802
\(708\) −121.156 −4.55334
\(709\) 5.55232 0.208522 0.104261 0.994550i \(-0.466752\pi\)
0.104261 + 0.994550i \(0.466752\pi\)
\(710\) 16.6403 0.624501
\(711\) 12.4303 0.466174
\(712\) −34.8158 −1.30478
\(713\) −24.0414 −0.900357
\(714\) 23.0225 0.861597
\(715\) −143.935 −5.38285
\(716\) 45.5784 1.70335
\(717\) 24.7040 0.922588
\(718\) 53.5476 1.99838
\(719\) 38.0539 1.41917 0.709585 0.704620i \(-0.248883\pi\)
0.709585 + 0.704620i \(0.248883\pi\)
\(720\) 138.398 5.15778
\(721\) −3.41180 −0.127062
\(722\) 52.0402 1.93674
\(723\) 7.08812 0.263610
\(724\) 81.3155 3.02207
\(725\) 37.6722 1.39911
\(726\) 127.166 4.71957
\(727\) 43.9899 1.63149 0.815747 0.578409i \(-0.196326\pi\)
0.815747 + 0.578409i \(0.196326\pi\)
\(728\) 62.6780 2.32300
\(729\) −10.1524 −0.376016
\(730\) −66.2013 −2.45022
\(731\) −31.2159 −1.15456
\(732\) 92.8362 3.43132
\(733\) 34.9919 1.29246 0.646228 0.763145i \(-0.276346\pi\)
0.646228 + 0.763145i \(0.276346\pi\)
\(734\) −42.6938 −1.57586
\(735\) −9.16159 −0.337930
\(736\) −105.869 −3.90238
\(737\) 72.3954 2.66672
\(738\) 41.1718 1.51555
\(739\) −11.6467 −0.428432 −0.214216 0.976786i \(-0.568720\pi\)
−0.214216 + 0.976786i \(0.568720\pi\)
\(740\) 19.6688 0.723039
\(741\) 4.42186 0.162441
\(742\) −33.6347 −1.23477
\(743\) 4.80862 0.176411 0.0882056 0.996102i \(-0.471887\pi\)
0.0882056 + 0.996102i \(0.471887\pi\)
\(744\) −122.752 −4.50032
\(745\) 55.9899 2.05131
\(746\) 21.4235 0.784371
\(747\) 1.15500 0.0422593
\(748\) 115.088 4.20804
\(749\) 9.31172 0.340243
\(750\) 158.798 5.79848
\(751\) 43.8853 1.60140 0.800698 0.599068i \(-0.204462\pi\)
0.800698 + 0.599068i \(0.204462\pi\)
\(752\) −214.611 −7.82607
\(753\) −49.1698 −1.79185
\(754\) 58.4418 2.12832
\(755\) 16.3688 0.595722
\(756\) 10.7534 0.391097
\(757\) −42.6501 −1.55014 −0.775072 0.631872i \(-0.782287\pi\)
−0.775072 + 0.631872i \(0.782287\pi\)
\(758\) −80.8508 −2.93663
\(759\) −55.6042 −2.01830
\(760\) −12.1614 −0.441139
\(761\) −1.24666 −0.0451912 −0.0225956 0.999745i \(-0.507193\pi\)
−0.0225956 + 0.999745i \(0.507193\pi\)
\(762\) 99.3826 3.60025
\(763\) 11.3959 0.412560
\(764\) 77.9371 2.81967
\(765\) 31.9932 1.15672
\(766\) −49.6641 −1.79444
\(767\) −60.9561 −2.20100
\(768\) −137.022 −4.94435
\(769\) −25.8256 −0.931294 −0.465647 0.884971i \(-0.654178\pi\)
−0.465647 + 0.884971i \(0.654178\pi\)
\(770\) −62.2239 −2.24239
\(771\) −2.22678 −0.0801954
\(772\) −10.7044 −0.385260
\(773\) 33.0297 1.18799 0.593997 0.804467i \(-0.297549\pi\)
0.593997 + 0.804467i \(0.297549\pi\)
\(774\) 50.1297 1.80187
\(775\) −62.0736 −2.22975
\(776\) 91.1381 3.27167
\(777\) −1.98282 −0.0711334
\(778\) 46.5939 1.67047
\(779\) −2.12875 −0.0762703
\(780\) 325.284 11.6470
\(781\) −8.38584 −0.300069
\(782\) −44.3874 −1.58729
\(783\) 6.43051 0.229808
\(784\) 15.9433 0.569405
\(785\) −56.3021 −2.00951
\(786\) −14.1484 −0.504657
\(787\) 17.3694 0.619152 0.309576 0.950875i \(-0.399813\pi\)
0.309576 + 0.950875i \(0.399813\pi\)
\(788\) −146.651 −5.22422
\(789\) −64.5853 −2.29930
\(790\) −64.2355 −2.28540
\(791\) −15.4706 −0.550069
\(792\) −118.533 −4.21190
\(793\) 46.7077 1.65864
\(794\) 40.7343 1.44561
\(795\) −111.951 −3.97049
\(796\) 41.5241 1.47178
\(797\) 30.5718 1.08291 0.541454 0.840730i \(-0.317874\pi\)
0.541454 + 0.840730i \(0.317874\pi\)
\(798\) 1.91160 0.0676699
\(799\) −49.6113 −1.75512
\(800\) −273.348 −9.66430
\(801\) 7.60493 0.268707
\(802\) 31.1539 1.10008
\(803\) 33.3619 1.17731
\(804\) −163.610 −5.77007
\(805\) 17.6635 0.622557
\(806\) −96.2961 −3.39188
\(807\) −32.4169 −1.14113
\(808\) −64.3384 −2.26342
\(809\) −36.4530 −1.28162 −0.640809 0.767700i \(-0.721401\pi\)
−0.640809 + 0.767700i \(0.721401\pi\)
\(810\) 120.310 4.22725
\(811\) 3.31899 0.116546 0.0582728 0.998301i \(-0.481441\pi\)
0.0582728 + 0.998301i \(0.481441\pi\)
\(812\) 18.5954 0.652571
\(813\) −12.7083 −0.445700
\(814\) −13.4670 −0.472018
\(815\) 27.5373 0.964591
\(816\) −133.353 −4.66827
\(817\) −2.59191 −0.0906795
\(818\) 84.8384 2.96630
\(819\) −13.6910 −0.478401
\(820\) −156.597 −5.46859
\(821\) −29.4861 −1.02907 −0.514536 0.857468i \(-0.672036\pi\)
−0.514536 + 0.857468i \(0.672036\pi\)
\(822\) −2.09923 −0.0732190
\(823\) 25.9180 0.903446 0.451723 0.892158i \(-0.350810\pi\)
0.451723 + 0.892158i \(0.350810\pi\)
\(824\) 33.5860 1.17002
\(825\) −143.567 −4.99836
\(826\) −26.3517 −0.916894
\(827\) 48.0656 1.67140 0.835702 0.549183i \(-0.185061\pi\)
0.835702 + 0.549183i \(0.185061\pi\)
\(828\) 52.4649 1.82328
\(829\) −20.2709 −0.704037 −0.352019 0.935993i \(-0.614505\pi\)
−0.352019 + 0.935993i \(0.614505\pi\)
\(830\) −5.96863 −0.207174
\(831\) −34.0056 −1.17964
\(832\) −221.026 −7.66270
\(833\) 3.68559 0.127698
\(834\) −0.504647 −0.0174745
\(835\) −43.9247 −1.52008
\(836\) 9.55596 0.330500
\(837\) −10.5957 −0.366242
\(838\) −42.9782 −1.48466
\(839\) 15.8256 0.546359 0.273180 0.961963i \(-0.411925\pi\)
0.273180 + 0.961963i \(0.411925\pi\)
\(840\) 90.1876 3.11177
\(841\) −17.8800 −0.616550
\(842\) 105.111 3.62237
\(843\) 23.8994 0.823139
\(844\) 127.391 4.38497
\(845\) 111.176 3.82457
\(846\) 79.6709 2.73914
\(847\) 20.3575 0.699492
\(848\) 194.821 6.69017
\(849\) 45.4113 1.55851
\(850\) −114.606 −3.93094
\(851\) 3.82288 0.131047
\(852\) 18.9515 0.649268
\(853\) 16.3067 0.558330 0.279165 0.960243i \(-0.409942\pi\)
0.279165 + 0.960243i \(0.409942\pi\)
\(854\) 20.1920 0.690957
\(855\) 2.65644 0.0908485
\(856\) −91.6654 −3.13306
\(857\) −7.58254 −0.259015 −0.129507 0.991578i \(-0.541340\pi\)
−0.129507 + 0.991578i \(0.541340\pi\)
\(858\) −222.718 −7.60348
\(859\) −21.6731 −0.739477 −0.369739 0.929136i \(-0.620553\pi\)
−0.369739 + 0.929136i \(0.620553\pi\)
\(860\) −190.668 −6.50173
\(861\) 15.7866 0.538007
\(862\) 9.90350 0.337315
\(863\) −1.00000 −0.0340404
\(864\) −46.6594 −1.58739
\(865\) 51.5238 1.75186
\(866\) −9.83944 −0.334358
\(867\) 7.75332 0.263317
\(868\) −30.6402 −1.04000
\(869\) 32.3712 1.09812
\(870\) 84.0921 2.85099
\(871\) −82.3151 −2.78914
\(872\) −112.183 −3.79898
\(873\) −19.9076 −0.673770
\(874\) −3.68556 −0.124666
\(875\) 25.4213 0.859398
\(876\) −75.3959 −2.54739
\(877\) 40.3619 1.36293 0.681463 0.731853i \(-0.261344\pi\)
0.681463 + 0.731853i \(0.261344\pi\)
\(878\) 18.1725 0.613291
\(879\) 34.2759 1.15610
\(880\) 360.417 12.1497
\(881\) 38.5069 1.29733 0.648666 0.761073i \(-0.275327\pi\)
0.648666 + 0.761073i \(0.275327\pi\)
\(882\) −5.91869 −0.199293
\(883\) −38.9146 −1.30958 −0.654791 0.755810i \(-0.727243\pi\)
−0.654791 + 0.755810i \(0.727243\pi\)
\(884\) −130.858 −4.40122
\(885\) −87.7100 −2.94834
\(886\) −107.971 −3.62736
\(887\) −19.3811 −0.650755 −0.325377 0.945584i \(-0.605491\pi\)
−0.325377 + 0.945584i \(0.605491\pi\)
\(888\) 19.5191 0.655018
\(889\) 15.9098 0.533597
\(890\) −39.2995 −1.31732
\(891\) −60.6296 −2.03117
\(892\) −99.8583 −3.34350
\(893\) −4.11931 −0.137847
\(894\) 86.6365 2.89756
\(895\) 32.9961 1.10294
\(896\) −47.1587 −1.57546
\(897\) 63.2231 2.11096
\(898\) −66.8492 −2.23079
\(899\) −18.3228 −0.611099
\(900\) 135.461 4.51538
\(901\) 45.0364 1.50038
\(902\) 107.220 3.57003
\(903\) 19.2214 0.639648
\(904\) 152.294 5.06521
\(905\) 58.8675 1.95682
\(906\) 25.3284 0.841480
\(907\) −12.1399 −0.403098 −0.201549 0.979478i \(-0.564598\pi\)
−0.201549 + 0.979478i \(0.564598\pi\)
\(908\) −37.0618 −1.22994
\(909\) 14.0537 0.466130
\(910\) 70.7499 2.34534
\(911\) 24.1882 0.801392 0.400696 0.916211i \(-0.368768\pi\)
0.400696 + 0.916211i \(0.368768\pi\)
\(912\) −11.0725 −0.366646
\(913\) 3.00787 0.0995459
\(914\) 46.0831 1.52429
\(915\) 67.2078 2.22182
\(916\) 16.9961 0.561568
\(917\) −2.26496 −0.0747957
\(918\) −19.5628 −0.645668
\(919\) 15.3900 0.507669 0.253835 0.967248i \(-0.418308\pi\)
0.253835 + 0.967248i \(0.418308\pi\)
\(920\) −173.881 −5.73269
\(921\) −32.7775 −1.08006
\(922\) 51.3030 1.68957
\(923\) 9.53487 0.313844
\(924\) −70.8662 −2.33133
\(925\) 9.87046 0.324539
\(926\) −2.43590 −0.0800487
\(927\) −7.33631 −0.240956
\(928\) −80.6864 −2.64866
\(929\) 9.34089 0.306465 0.153232 0.988190i \(-0.451032\pi\)
0.153232 + 0.988190i \(0.451032\pi\)
\(930\) −138.561 −4.54359
\(931\) 0.306021 0.0100294
\(932\) −63.3938 −2.07653
\(933\) 0.588936 0.0192809
\(934\) −59.2764 −1.93958
\(935\) 83.3169 2.72475
\(936\) 134.775 4.40526
\(937\) −57.6677 −1.88392 −0.941961 0.335721i \(-0.891020\pi\)
−0.941961 + 0.335721i \(0.891020\pi\)
\(938\) −35.5854 −1.16190
\(939\) −47.8712 −1.56222
\(940\) −303.028 −9.88368
\(941\) −30.2752 −0.986944 −0.493472 0.869762i \(-0.664272\pi\)
−0.493472 + 0.869762i \(0.664272\pi\)
\(942\) −87.1196 −2.83851
\(943\) −30.4365 −0.991150
\(944\) 152.636 4.96788
\(945\) 7.78481 0.253240
\(946\) 130.548 4.24449
\(947\) −0.954310 −0.0310109 −0.0155055 0.999880i \(-0.504936\pi\)
−0.0155055 + 0.999880i \(0.504936\pi\)
\(948\) −73.1572 −2.37603
\(949\) −37.9331 −1.23136
\(950\) −9.51590 −0.308737
\(951\) 44.3974 1.43968
\(952\) −36.2813 −1.17588
\(953\) 51.7656 1.67685 0.838427 0.545014i \(-0.183476\pi\)
0.838427 + 0.545014i \(0.183476\pi\)
\(954\) −72.3239 −2.34157
\(955\) 56.4218 1.82577
\(956\) −60.7023 −1.96325
\(957\) −42.3779 −1.36988
\(958\) 112.965 3.64972
\(959\) −0.336057 −0.0108519
\(960\) −318.035 −10.2645
\(961\) −0.809057 −0.0260986
\(962\) 15.3123 0.493687
\(963\) 20.0228 0.645225
\(964\) −17.4168 −0.560958
\(965\) −7.74936 −0.249461
\(966\) 27.3318 0.879385
\(967\) −9.01813 −0.290004 −0.145002 0.989431i \(-0.546319\pi\)
−0.145002 + 0.989431i \(0.546319\pi\)
\(968\) −200.401 −6.44113
\(969\) −2.55960 −0.0822263
\(970\) 102.875 3.30312
\(971\) 7.96092 0.255478 0.127739 0.991808i \(-0.459228\pi\)
0.127739 + 0.991808i \(0.459228\pi\)
\(972\) 104.759 3.36015
\(973\) −0.0807869 −0.00258991
\(974\) −20.7558 −0.665058
\(975\) 163.239 5.22782
\(976\) −116.957 −3.74372
\(977\) 11.9982 0.383856 0.191928 0.981409i \(-0.438526\pi\)
0.191928 + 0.981409i \(0.438526\pi\)
\(978\) 42.6101 1.36252
\(979\) 19.8048 0.632965
\(980\) 22.5117 0.719110
\(981\) 24.5044 0.782366
\(982\) 24.5150 0.782304
\(983\) 40.8538 1.30303 0.651517 0.758634i \(-0.274133\pi\)
0.651517 + 0.758634i \(0.274133\pi\)
\(984\) −155.405 −4.95413
\(985\) −106.166 −3.38274
\(986\) −33.8292 −1.07734
\(987\) 30.5485 0.972368
\(988\) −10.8653 −0.345672
\(989\) −37.0587 −1.17840
\(990\) −133.799 −4.25240
\(991\) 50.6979 1.61047 0.805235 0.592955i \(-0.202039\pi\)
0.805235 + 0.592955i \(0.202039\pi\)
\(992\) 132.949 4.22114
\(993\) 12.9593 0.411252
\(994\) 4.12199 0.130742
\(995\) 30.0609 0.952996
\(996\) −6.79761 −0.215391
\(997\) 53.0875 1.68130 0.840650 0.541579i \(-0.182173\pi\)
0.840650 + 0.541579i \(0.182173\pi\)
\(998\) −57.6644 −1.82533
\(999\) 1.68485 0.0533063
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 \(a_p\))