Properties

Label 6041.2.a.f.1.8
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

Related objects

Downloads

Learn more about

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 1.8
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60157 q^{2}\) \(+0.915852 q^{3}\) \(+4.76817 q^{4}\) \(-4.25711 q^{5}\) \(-2.38265 q^{6}\) \(+1.00000 q^{7}\) \(-7.20159 q^{8}\) \(-2.16122 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60157 q^{2}\) \(+0.915852 q^{3}\) \(+4.76817 q^{4}\) \(-4.25711 q^{5}\) \(-2.38265 q^{6}\) \(+1.00000 q^{7}\) \(-7.20159 q^{8}\) \(-2.16122 q^{9}\) \(+11.0752 q^{10}\) \(+0.535628 q^{11}\) \(+4.36694 q^{12}\) \(+3.11863 q^{13}\) \(-2.60157 q^{14}\) \(-3.89888 q^{15}\) \(+9.19910 q^{16}\) \(+2.52035 q^{17}\) \(+5.62256 q^{18}\) \(+1.79226 q^{19}\) \(-20.2986 q^{20}\) \(+0.915852 q^{21}\) \(-1.39347 q^{22}\) \(+1.05441 q^{23}\) \(-6.59559 q^{24}\) \(+13.1230 q^{25}\) \(-8.11333 q^{26}\) \(-4.72691 q^{27}\) \(+4.76817 q^{28}\) \(+8.42416 q^{29}\) \(+10.1432 q^{30}\) \(-7.53448 q^{31}\) \(-9.52894 q^{32}\) \(+0.490556 q^{33}\) \(-6.55686 q^{34}\) \(-4.25711 q^{35}\) \(-10.3050 q^{36}\) \(+7.37919 q^{37}\) \(-4.66270 q^{38}\) \(+2.85620 q^{39}\) \(+30.6580 q^{40}\) \(-11.4021 q^{41}\) \(-2.38265 q^{42}\) \(+7.82399 q^{43}\) \(+2.55396 q^{44}\) \(+9.20054 q^{45}\) \(-2.74313 q^{46}\) \(-9.30525 q^{47}\) \(+8.42501 q^{48}\) \(+1.00000 q^{49}\) \(-34.1404 q^{50}\) \(+2.30826 q^{51}\) \(+14.8701 q^{52}\) \(+5.88495 q^{53}\) \(+12.2974 q^{54}\) \(-2.28023 q^{55}\) \(-7.20159 q^{56}\) \(+1.64145 q^{57}\) \(-21.9161 q^{58}\) \(+9.36524 q^{59}\) \(-18.5905 q^{60}\) \(-4.82680 q^{61}\) \(+19.6015 q^{62}\) \(-2.16122 q^{63}\) \(+6.39200 q^{64}\) \(-13.2763 q^{65}\) \(-1.27621 q^{66}\) \(+5.73380 q^{67}\) \(+12.0174 q^{68}\) \(+0.965687 q^{69}\) \(+11.0752 q^{70}\) \(-14.7838 q^{71}\) \(+15.5642 q^{72}\) \(-3.90120 q^{73}\) \(-19.1975 q^{74}\) \(+12.0187 q^{75}\) \(+8.54581 q^{76}\) \(+0.535628 q^{77}\) \(-7.43060 q^{78}\) \(+8.77085 q^{79}\) \(-39.1616 q^{80}\) \(+2.15450 q^{81}\) \(+29.6634 q^{82}\) \(-1.52254 q^{83}\) \(+4.36694 q^{84}\) \(-10.7294 q^{85}\) \(-20.3547 q^{86}\) \(+7.71528 q^{87}\) \(-3.85737 q^{88}\) \(-2.42793 q^{89}\) \(-23.9359 q^{90}\) \(+3.11863 q^{91}\) \(+5.02762 q^{92}\) \(-6.90046 q^{93}\) \(+24.2083 q^{94}\) \(-7.62986 q^{95}\) \(-8.72709 q^{96}\) \(-16.3991 q^{97}\) \(-2.60157 q^{98}\) \(-1.15761 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60157 −1.83959 −0.919794 0.392401i \(-0.871644\pi\)
−0.919794 + 0.392401i \(0.871644\pi\)
\(3\) 0.915852 0.528767 0.264384 0.964418i \(-0.414832\pi\)
0.264384 + 0.964418i \(0.414832\pi\)
\(4\) 4.76817 2.38408
\(5\) −4.25711 −1.90384 −0.951919 0.306349i \(-0.900892\pi\)
−0.951919 + 0.306349i \(0.900892\pi\)
\(6\) −2.38265 −0.972714
\(7\) 1.00000 0.377964
\(8\) −7.20159 −2.54615
\(9\) −2.16122 −0.720405
\(10\) 11.0752 3.50228
\(11\) 0.535628 0.161498 0.0807489 0.996734i \(-0.474269\pi\)
0.0807489 + 0.996734i \(0.474269\pi\)
\(12\) 4.36694 1.26063
\(13\) 3.11863 0.864951 0.432476 0.901646i \(-0.357640\pi\)
0.432476 + 0.901646i \(0.357640\pi\)
\(14\) −2.60157 −0.695299
\(15\) −3.89888 −1.00669
\(16\) 9.19910 2.29978
\(17\) 2.52035 0.611274 0.305637 0.952148i \(-0.401131\pi\)
0.305637 + 0.952148i \(0.401131\pi\)
\(18\) 5.62256 1.32525
\(19\) 1.79226 0.411173 0.205587 0.978639i \(-0.434090\pi\)
0.205587 + 0.978639i \(0.434090\pi\)
\(20\) −20.2986 −4.53891
\(21\) 0.915852 0.199855
\(22\) −1.39347 −0.297090
\(23\) 1.05441 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(24\) −6.59559 −1.34632
\(25\) 13.1230 2.62460
\(26\) −8.11333 −1.59115
\(27\) −4.72691 −0.909694
\(28\) 4.76817 0.901099
\(29\) 8.42416 1.56433 0.782164 0.623073i \(-0.214116\pi\)
0.782164 + 0.623073i \(0.214116\pi\)
\(30\) 10.1432 1.85189
\(31\) −7.53448 −1.35323 −0.676616 0.736336i \(-0.736554\pi\)
−0.676616 + 0.736336i \(0.736554\pi\)
\(32\) −9.52894 −1.68449
\(33\) 0.490556 0.0853948
\(34\) −6.55686 −1.12449
\(35\) −4.25711 −0.719583
\(36\) −10.3050 −1.71751
\(37\) 7.37919 1.21313 0.606566 0.795033i \(-0.292547\pi\)
0.606566 + 0.795033i \(0.292547\pi\)
\(38\) −4.66270 −0.756389
\(39\) 2.85620 0.457358
\(40\) 30.6580 4.84745
\(41\) −11.4021 −1.78071 −0.890355 0.455266i \(-0.849544\pi\)
−0.890355 + 0.455266i \(0.849544\pi\)
\(42\) −2.38265 −0.367651
\(43\) 7.82399 1.19315 0.596574 0.802558i \(-0.296528\pi\)
0.596574 + 0.802558i \(0.296528\pi\)
\(44\) 2.55396 0.385025
\(45\) 9.20054 1.37154
\(46\) −2.74313 −0.404453
\(47\) −9.30525 −1.35731 −0.678655 0.734457i \(-0.737437\pi\)
−0.678655 + 0.734457i \(0.737437\pi\)
\(48\) 8.42501 1.21605
\(49\) 1.00000 0.142857
\(50\) −34.1404 −4.82818
\(51\) 2.30826 0.323221
\(52\) 14.8701 2.06212
\(53\) 5.88495 0.808359 0.404180 0.914680i \(-0.367557\pi\)
0.404180 + 0.914680i \(0.367557\pi\)
\(54\) 12.2974 1.67346
\(55\) −2.28023 −0.307466
\(56\) −7.20159 −0.962353
\(57\) 1.64145 0.217415
\(58\) −21.9161 −2.87772
\(59\) 9.36524 1.21925 0.609625 0.792690i \(-0.291320\pi\)
0.609625 + 0.792690i \(0.291320\pi\)
\(60\) −18.5905 −2.40003
\(61\) −4.82680 −0.618009 −0.309005 0.951061i \(-0.599996\pi\)
−0.309005 + 0.951061i \(0.599996\pi\)
\(62\) 19.6015 2.48939
\(63\) −2.16122 −0.272288
\(64\) 6.39200 0.799000
\(65\) −13.2763 −1.64673
\(66\) −1.27621 −0.157091
\(67\) 5.73380 0.700495 0.350247 0.936657i \(-0.386098\pi\)
0.350247 + 0.936657i \(0.386098\pi\)
\(68\) 12.0174 1.45733
\(69\) 0.965687 0.116255
\(70\) 11.0752 1.32374
\(71\) −14.7838 −1.75452 −0.877258 0.480020i \(-0.840630\pi\)
−0.877258 + 0.480020i \(0.840630\pi\)
\(72\) 15.5642 1.83426
\(73\) −3.90120 −0.456601 −0.228300 0.973591i \(-0.573317\pi\)
−0.228300 + 0.973591i \(0.573317\pi\)
\(74\) −19.1975 −2.23166
\(75\) 12.0187 1.38780
\(76\) 8.54581 0.980272
\(77\) 0.535628 0.0610404
\(78\) −7.43060 −0.841350
\(79\) 8.77085 0.986797 0.493399 0.869803i \(-0.335754\pi\)
0.493399 + 0.869803i \(0.335754\pi\)
\(80\) −39.1616 −4.37840
\(81\) 2.15450 0.239389
\(82\) 29.6634 3.27577
\(83\) −1.52254 −0.167120 −0.0835601 0.996503i \(-0.526629\pi\)
−0.0835601 + 0.996503i \(0.526629\pi\)
\(84\) 4.36694 0.476472
\(85\) −10.7294 −1.16377
\(86\) −20.3547 −2.19490
\(87\) 7.71528 0.827165
\(88\) −3.85737 −0.411197
\(89\) −2.42793 −0.257360 −0.128680 0.991686i \(-0.541074\pi\)
−0.128680 + 0.991686i \(0.541074\pi\)
\(90\) −23.9359 −2.52306
\(91\) 3.11863 0.326921
\(92\) 5.02762 0.524166
\(93\) −6.90046 −0.715544
\(94\) 24.2083 2.49689
\(95\) −7.62986 −0.782807
\(96\) −8.72709 −0.890705
\(97\) −16.3991 −1.66508 −0.832538 0.553967i \(-0.813113\pi\)
−0.832538 + 0.553967i \(0.813113\pi\)
\(98\) −2.60157 −0.262798
\(99\) −1.15761 −0.116344
\(100\) 62.5727 6.25727
\(101\) −9.15391 −0.910848 −0.455424 0.890275i \(-0.650512\pi\)
−0.455424 + 0.890275i \(0.650512\pi\)
\(102\) −6.00511 −0.594594
\(103\) −7.63561 −0.752359 −0.376180 0.926547i \(-0.622762\pi\)
−0.376180 + 0.926547i \(0.622762\pi\)
\(104\) −22.4591 −2.20229
\(105\) −3.89888 −0.380492
\(106\) −15.3101 −1.48705
\(107\) 5.02839 0.486113 0.243057 0.970012i \(-0.421850\pi\)
0.243057 + 0.970012i \(0.421850\pi\)
\(108\) −22.5387 −2.16879
\(109\) 12.8559 1.23137 0.615686 0.787991i \(-0.288879\pi\)
0.615686 + 0.787991i \(0.288879\pi\)
\(110\) 5.93217 0.565610
\(111\) 6.75824 0.641464
\(112\) 9.19910 0.869234
\(113\) −2.04921 −0.192774 −0.0963868 0.995344i \(-0.530729\pi\)
−0.0963868 + 0.995344i \(0.530729\pi\)
\(114\) −4.27034 −0.399954
\(115\) −4.48876 −0.418579
\(116\) 40.1678 3.72949
\(117\) −6.74002 −0.623115
\(118\) −24.3643 −2.24292
\(119\) 2.52035 0.231040
\(120\) 28.0782 2.56317
\(121\) −10.7131 −0.973918
\(122\) 12.5573 1.13688
\(123\) −10.4426 −0.941581
\(124\) −35.9257 −3.22622
\(125\) −34.5805 −3.09298
\(126\) 5.62256 0.500897
\(127\) −8.55230 −0.758894 −0.379447 0.925213i \(-0.623886\pi\)
−0.379447 + 0.925213i \(0.623886\pi\)
\(128\) 2.42863 0.214663
\(129\) 7.16562 0.630897
\(130\) 34.5393 3.02930
\(131\) 9.40716 0.821907 0.410954 0.911656i \(-0.365196\pi\)
0.410954 + 0.911656i \(0.365196\pi\)
\(132\) 2.33905 0.203588
\(133\) 1.79226 0.155409
\(134\) −14.9169 −1.28862
\(135\) 20.1230 1.73191
\(136\) −18.1505 −1.55639
\(137\) −5.29343 −0.452249 −0.226124 0.974098i \(-0.572606\pi\)
−0.226124 + 0.974098i \(0.572606\pi\)
\(138\) −2.51230 −0.213861
\(139\) 1.42688 0.121026 0.0605130 0.998167i \(-0.480726\pi\)
0.0605130 + 0.998167i \(0.480726\pi\)
\(140\) −20.2986 −1.71555
\(141\) −8.52223 −0.717701
\(142\) 38.4611 3.22759
\(143\) 1.67042 0.139688
\(144\) −19.8813 −1.65677
\(145\) −35.8626 −2.97823
\(146\) 10.1492 0.839958
\(147\) 0.915852 0.0755382
\(148\) 35.1852 2.89221
\(149\) 8.13443 0.666398 0.333199 0.942856i \(-0.391872\pi\)
0.333199 + 0.942856i \(0.391872\pi\)
\(150\) −31.2676 −2.55299
\(151\) −7.31121 −0.594978 −0.297489 0.954725i \(-0.596149\pi\)
−0.297489 + 0.954725i \(0.596149\pi\)
\(152\) −12.9071 −1.04691
\(153\) −5.44701 −0.440365
\(154\) −1.39347 −0.112289
\(155\) 32.0751 2.57633
\(156\) 13.6188 1.09038
\(157\) 11.5153 0.919024 0.459512 0.888172i \(-0.348024\pi\)
0.459512 + 0.888172i \(0.348024\pi\)
\(158\) −22.8180 −1.81530
\(159\) 5.38974 0.427434
\(160\) 40.5658 3.20701
\(161\) 1.05441 0.0830994
\(162\) −5.60509 −0.440377
\(163\) −4.62404 −0.362183 −0.181091 0.983466i \(-0.557963\pi\)
−0.181091 + 0.983466i \(0.557963\pi\)
\(164\) −54.3672 −4.24537
\(165\) −2.08835 −0.162578
\(166\) 3.96099 0.307432
\(167\) 19.1535 1.48214 0.741071 0.671427i \(-0.234318\pi\)
0.741071 + 0.671427i \(0.234318\pi\)
\(168\) −6.59559 −0.508861
\(169\) −3.27417 −0.251859
\(170\) 27.9133 2.14085
\(171\) −3.87347 −0.296211
\(172\) 37.3061 2.84457
\(173\) −0.781574 −0.0594220 −0.0297110 0.999559i \(-0.509459\pi\)
−0.0297110 + 0.999559i \(0.509459\pi\)
\(174\) −20.0719 −1.52164
\(175\) 13.1230 0.992006
\(176\) 4.92730 0.371409
\(177\) 8.57717 0.644700
\(178\) 6.31643 0.473437
\(179\) −6.23843 −0.466282 −0.233141 0.972443i \(-0.574900\pi\)
−0.233141 + 0.972443i \(0.574900\pi\)
\(180\) 43.8697 3.26986
\(181\) −2.92533 −0.217438 −0.108719 0.994073i \(-0.534675\pi\)
−0.108719 + 0.994073i \(0.534675\pi\)
\(182\) −8.11333 −0.601400
\(183\) −4.42064 −0.326783
\(184\) −7.59346 −0.559797
\(185\) −31.4140 −2.30961
\(186\) 17.9520 1.31631
\(187\) 1.34997 0.0987194
\(188\) −44.3690 −3.23594
\(189\) −4.72691 −0.343832
\(190\) 19.8496 1.44004
\(191\) 9.41099 0.680956 0.340478 0.940253i \(-0.389411\pi\)
0.340478 + 0.940253i \(0.389411\pi\)
\(192\) 5.85413 0.422485
\(193\) 7.46634 0.537439 0.268719 0.963219i \(-0.413400\pi\)
0.268719 + 0.963219i \(0.413400\pi\)
\(194\) 42.6634 3.06306
\(195\) −12.1592 −0.870735
\(196\) 4.76817 0.340584
\(197\) 0.0198307 0.00141288 0.000706438 1.00000i \(-0.499775\pi\)
0.000706438 1.00000i \(0.499775\pi\)
\(198\) 3.01160 0.214025
\(199\) −10.7600 −0.762756 −0.381378 0.924419i \(-0.624550\pi\)
−0.381378 + 0.924419i \(0.624550\pi\)
\(200\) −94.5065 −6.68262
\(201\) 5.25131 0.370399
\(202\) 23.8145 1.67558
\(203\) 8.42416 0.591260
\(204\) 11.0062 0.770587
\(205\) 48.5401 3.39019
\(206\) 19.8646 1.38403
\(207\) −2.27882 −0.158389
\(208\) 28.6886 1.98919
\(209\) 0.959985 0.0664036
\(210\) 10.1432 0.699949
\(211\) 20.6271 1.42003 0.710014 0.704188i \(-0.248689\pi\)
0.710014 + 0.704188i \(0.248689\pi\)
\(212\) 28.0604 1.92720
\(213\) −13.5398 −0.927730
\(214\) −13.0817 −0.894248
\(215\) −33.3076 −2.27156
\(216\) 34.0412 2.31621
\(217\) −7.53448 −0.511474
\(218\) −33.4456 −2.26522
\(219\) −3.57292 −0.241436
\(220\) −10.8725 −0.733025
\(221\) 7.86002 0.528722
\(222\) −17.5820 −1.18003
\(223\) 11.4562 0.767162 0.383581 0.923507i \(-0.374691\pi\)
0.383581 + 0.923507i \(0.374691\pi\)
\(224\) −9.52894 −0.636679
\(225\) −28.3616 −1.89078
\(226\) 5.33117 0.354624
\(227\) −27.6085 −1.83244 −0.916221 0.400672i \(-0.868777\pi\)
−0.916221 + 0.400672i \(0.868777\pi\)
\(228\) 7.82669 0.518336
\(229\) 14.0866 0.930867 0.465434 0.885083i \(-0.345898\pi\)
0.465434 + 0.885083i \(0.345898\pi\)
\(230\) 11.6778 0.770013
\(231\) 0.490556 0.0322762
\(232\) −60.6674 −3.98301
\(233\) 16.4597 1.07831 0.539157 0.842205i \(-0.318743\pi\)
0.539157 + 0.842205i \(0.318743\pi\)
\(234\) 17.5346 1.14628
\(235\) 39.6135 2.58410
\(236\) 44.6551 2.90680
\(237\) 8.03279 0.521786
\(238\) −6.55686 −0.425018
\(239\) 29.5579 1.91194 0.955972 0.293458i \(-0.0948060\pi\)
0.955972 + 0.293458i \(0.0948060\pi\)
\(240\) −35.8662 −2.31515
\(241\) 10.1956 0.656756 0.328378 0.944546i \(-0.393498\pi\)
0.328378 + 0.944546i \(0.393498\pi\)
\(242\) 27.8709 1.79161
\(243\) 16.1539 1.03627
\(244\) −23.0150 −1.47339
\(245\) −4.25711 −0.271977
\(246\) 27.1673 1.73212
\(247\) 5.58940 0.355645
\(248\) 54.2602 3.44553
\(249\) −1.39442 −0.0883677
\(250\) 89.9637 5.68980
\(251\) 1.67840 0.105940 0.0529700 0.998596i \(-0.483131\pi\)
0.0529700 + 0.998596i \(0.483131\pi\)
\(252\) −10.3050 −0.649157
\(253\) 0.564773 0.0355070
\(254\) 22.2494 1.39605
\(255\) −9.82653 −0.615361
\(256\) −19.1023 −1.19389
\(257\) 14.4746 0.902902 0.451451 0.892296i \(-0.350907\pi\)
0.451451 + 0.892296i \(0.350907\pi\)
\(258\) −18.6419 −1.16059
\(259\) 7.37919 0.458521
\(260\) −63.3038 −3.92594
\(261\) −18.2064 −1.12695
\(262\) −24.4734 −1.51197
\(263\) 12.7104 0.783754 0.391877 0.920018i \(-0.371826\pi\)
0.391877 + 0.920018i \(0.371826\pi\)
\(264\) −3.53278 −0.217428
\(265\) −25.0529 −1.53899
\(266\) −4.66270 −0.285888
\(267\) −2.22362 −0.136084
\(268\) 27.3397 1.67004
\(269\) 3.12545 0.190562 0.0952809 0.995450i \(-0.469625\pi\)
0.0952809 + 0.995450i \(0.469625\pi\)
\(270\) −52.3513 −3.18600
\(271\) 20.0376 1.21720 0.608599 0.793478i \(-0.291732\pi\)
0.608599 + 0.793478i \(0.291732\pi\)
\(272\) 23.1849 1.40579
\(273\) 2.85620 0.172865
\(274\) 13.7712 0.831951
\(275\) 7.02904 0.423867
\(276\) 4.60456 0.277162
\(277\) −5.42397 −0.325895 −0.162947 0.986635i \(-0.552100\pi\)
−0.162947 + 0.986635i \(0.552100\pi\)
\(278\) −3.71212 −0.222638
\(279\) 16.2836 0.974875
\(280\) 30.6580 1.83216
\(281\) 15.4820 0.923578 0.461789 0.886990i \(-0.347208\pi\)
0.461789 + 0.886990i \(0.347208\pi\)
\(282\) 22.1712 1.32027
\(283\) 18.8417 1.12003 0.560013 0.828484i \(-0.310796\pi\)
0.560013 + 0.828484i \(0.310796\pi\)
\(284\) −70.4917 −4.18291
\(285\) −6.98782 −0.413923
\(286\) −4.34572 −0.256968
\(287\) −11.4021 −0.673045
\(288\) 20.5941 1.21352
\(289\) −10.6479 −0.626344
\(290\) 93.2991 5.47871
\(291\) −15.0191 −0.880438
\(292\) −18.6016 −1.08858
\(293\) 12.6956 0.741684 0.370842 0.928696i \(-0.379069\pi\)
0.370842 + 0.928696i \(0.379069\pi\)
\(294\) −2.38265 −0.138959
\(295\) −39.8689 −2.32126
\(296\) −53.1419 −3.08881
\(297\) −2.53186 −0.146914
\(298\) −21.1623 −1.22590
\(299\) 3.28832 0.190169
\(300\) 57.3073 3.30864
\(301\) 7.82399 0.450968
\(302\) 19.0206 1.09451
\(303\) −8.38362 −0.481626
\(304\) 16.4872 0.945606
\(305\) 20.5482 1.17659
\(306\) 14.1708 0.810090
\(307\) −8.49388 −0.484771 −0.242386 0.970180i \(-0.577930\pi\)
−0.242386 + 0.970180i \(0.577930\pi\)
\(308\) 2.55396 0.145526
\(309\) −6.99309 −0.397823
\(310\) −83.4457 −4.73939
\(311\) −12.7982 −0.725718 −0.362859 0.931844i \(-0.618199\pi\)
−0.362859 + 0.931844i \(0.618199\pi\)
\(312\) −20.5692 −1.16450
\(313\) −17.4383 −0.985670 −0.492835 0.870123i \(-0.664039\pi\)
−0.492835 + 0.870123i \(0.664039\pi\)
\(314\) −29.9580 −1.69063
\(315\) 9.20054 0.518392
\(316\) 41.8209 2.35261
\(317\) −10.3135 −0.579262 −0.289631 0.957138i \(-0.593533\pi\)
−0.289631 + 0.957138i \(0.593533\pi\)
\(318\) −14.0218 −0.786302
\(319\) 4.51222 0.252636
\(320\) −27.2115 −1.52117
\(321\) 4.60526 0.257041
\(322\) −2.74313 −0.152869
\(323\) 4.51712 0.251339
\(324\) 10.2730 0.570724
\(325\) 40.9257 2.27015
\(326\) 12.0298 0.666267
\(327\) 11.7741 0.651109
\(328\) 82.1133 4.53395
\(329\) −9.30525 −0.513015
\(330\) 5.43299 0.299076
\(331\) −34.2160 −1.88068 −0.940340 0.340238i \(-0.889493\pi\)
−0.940340 + 0.340238i \(0.889493\pi\)
\(332\) −7.25972 −0.398429
\(333\) −15.9480 −0.873946
\(334\) −49.8291 −2.72653
\(335\) −24.4094 −1.33363
\(336\) 8.42501 0.459622
\(337\) −12.8029 −0.697418 −0.348709 0.937231i \(-0.613380\pi\)
−0.348709 + 0.937231i \(0.613380\pi\)
\(338\) 8.51799 0.463318
\(339\) −1.87677 −0.101932
\(340\) −51.1596 −2.77452
\(341\) −4.03567 −0.218544
\(342\) 10.0771 0.544907
\(343\) 1.00000 0.0539949
\(344\) −56.3452 −3.03793
\(345\) −4.11104 −0.221331
\(346\) 2.03332 0.109312
\(347\) 15.1292 0.812176 0.406088 0.913834i \(-0.366893\pi\)
0.406088 + 0.913834i \(0.366893\pi\)
\(348\) 36.7878 1.97203
\(349\) −10.2788 −0.550211 −0.275105 0.961414i \(-0.588713\pi\)
−0.275105 + 0.961414i \(0.588713\pi\)
\(350\) −34.1404 −1.82488
\(351\) −14.7415 −0.786841
\(352\) −5.10396 −0.272042
\(353\) −7.99564 −0.425565 −0.212782 0.977100i \(-0.568253\pi\)
−0.212782 + 0.977100i \(0.568253\pi\)
\(354\) −22.3141 −1.18598
\(355\) 62.9363 3.34031
\(356\) −11.5768 −0.613568
\(357\) 2.30826 0.122166
\(358\) 16.2297 0.857767
\(359\) −9.55303 −0.504190 −0.252095 0.967703i \(-0.581119\pi\)
−0.252095 + 0.967703i \(0.581119\pi\)
\(360\) −66.2585 −3.49213
\(361\) −15.7878 −0.830937
\(362\) 7.61046 0.399997
\(363\) −9.81161 −0.514976
\(364\) 14.8701 0.779407
\(365\) 16.6078 0.869294
\(366\) 11.5006 0.601146
\(367\) 30.5161 1.59293 0.796463 0.604687i \(-0.206702\pi\)
0.796463 + 0.604687i \(0.206702\pi\)
\(368\) 9.69966 0.505630
\(369\) 24.6424 1.28283
\(370\) 81.7259 4.24872
\(371\) 5.88495 0.305531
\(372\) −32.9026 −1.70592
\(373\) 16.3614 0.847162 0.423581 0.905858i \(-0.360773\pi\)
0.423581 + 0.905858i \(0.360773\pi\)
\(374\) −3.51204 −0.181603
\(375\) −31.6706 −1.63546
\(376\) 67.0126 3.45591
\(377\) 26.2718 1.35307
\(378\) 12.2974 0.632509
\(379\) 30.9380 1.58918 0.794588 0.607149i \(-0.207687\pi\)
0.794588 + 0.607149i \(0.207687\pi\)
\(380\) −36.3805 −1.86628
\(381\) −7.83264 −0.401278
\(382\) −24.4834 −1.25268
\(383\) −16.6554 −0.851054 −0.425527 0.904946i \(-0.639911\pi\)
−0.425527 + 0.904946i \(0.639911\pi\)
\(384\) 2.22427 0.113507
\(385\) −2.28023 −0.116211
\(386\) −19.4242 −0.988666
\(387\) −16.9093 −0.859550
\(388\) −78.1937 −3.96968
\(389\) 10.0382 0.508954 0.254477 0.967079i \(-0.418097\pi\)
0.254477 + 0.967079i \(0.418097\pi\)
\(390\) 31.6329 1.60179
\(391\) 2.65749 0.134395
\(392\) −7.20159 −0.363735
\(393\) 8.61556 0.434597
\(394\) −0.0515909 −0.00259911
\(395\) −37.3385 −1.87870
\(396\) −5.51967 −0.277374
\(397\) −14.7559 −0.740577 −0.370288 0.928917i \(-0.620741\pi\)
−0.370288 + 0.928917i \(0.620741\pi\)
\(398\) 27.9929 1.40316
\(399\) 1.64145 0.0821751
\(400\) 120.720 6.03599
\(401\) −26.0936 −1.30305 −0.651526 0.758626i \(-0.725871\pi\)
−0.651526 + 0.758626i \(0.725871\pi\)
\(402\) −13.6616 −0.681381
\(403\) −23.4972 −1.17048
\(404\) −43.6474 −2.17154
\(405\) −9.17196 −0.455758
\(406\) −21.9161 −1.08768
\(407\) 3.95250 0.195918
\(408\) −16.6232 −0.822969
\(409\) 32.2198 1.59317 0.796584 0.604528i \(-0.206638\pi\)
0.796584 + 0.604528i \(0.206638\pi\)
\(410\) −126.280 −6.23655
\(411\) −4.84800 −0.239134
\(412\) −36.4079 −1.79369
\(413\) 9.36524 0.460833
\(414\) 5.92850 0.291370
\(415\) 6.48161 0.318170
\(416\) −29.7172 −1.45701
\(417\) 1.30681 0.0639946
\(418\) −2.49747 −0.122155
\(419\) 4.72985 0.231068 0.115534 0.993304i \(-0.463142\pi\)
0.115534 + 0.993304i \(0.463142\pi\)
\(420\) −18.5905 −0.907125
\(421\) 34.0463 1.65931 0.829657 0.558274i \(-0.188536\pi\)
0.829657 + 0.558274i \(0.188536\pi\)
\(422\) −53.6628 −2.61227
\(423\) 20.1107 0.977814
\(424\) −42.3810 −2.05820
\(425\) 33.0745 1.60435
\(426\) 35.2247 1.70664
\(427\) −4.82680 −0.233585
\(428\) 23.9762 1.15894
\(429\) 1.52986 0.0738623
\(430\) 86.6521 4.17874
\(431\) 19.6125 0.944700 0.472350 0.881411i \(-0.343406\pi\)
0.472350 + 0.881411i \(0.343406\pi\)
\(432\) −43.4833 −2.09209
\(433\) −19.9898 −0.960648 −0.480324 0.877091i \(-0.659481\pi\)
−0.480324 + 0.877091i \(0.659481\pi\)
\(434\) 19.6015 0.940901
\(435\) −32.8448 −1.57479
\(436\) 61.2992 2.93570
\(437\) 1.88979 0.0904007
\(438\) 9.29521 0.444142
\(439\) 23.0437 1.09982 0.549908 0.835225i \(-0.314663\pi\)
0.549908 + 0.835225i \(0.314663\pi\)
\(440\) 16.4213 0.782853
\(441\) −2.16122 −0.102915
\(442\) −20.4484 −0.972631
\(443\) −17.7733 −0.844434 −0.422217 0.906495i \(-0.638748\pi\)
−0.422217 + 0.906495i \(0.638748\pi\)
\(444\) 32.2245 1.52930
\(445\) 10.3360 0.489972
\(446\) −29.8040 −1.41126
\(447\) 7.44993 0.352370
\(448\) 6.39200 0.301994
\(449\) −9.13707 −0.431205 −0.215602 0.976481i \(-0.569172\pi\)
−0.215602 + 0.976481i \(0.569172\pi\)
\(450\) 73.7848 3.47825
\(451\) −6.10729 −0.287581
\(452\) −9.77099 −0.459588
\(453\) −6.69598 −0.314605
\(454\) 71.8256 3.37094
\(455\) −13.2763 −0.622404
\(456\) −11.8210 −0.553570
\(457\) 24.2242 1.13316 0.566580 0.824007i \(-0.308266\pi\)
0.566580 + 0.824007i \(0.308266\pi\)
\(458\) −36.6472 −1.71241
\(459\) −11.9134 −0.556072
\(460\) −21.4032 −0.997927
\(461\) 16.8887 0.786587 0.393294 0.919413i \(-0.371336\pi\)
0.393294 + 0.919413i \(0.371336\pi\)
\(462\) −1.27621 −0.0593749
\(463\) −9.83912 −0.457263 −0.228631 0.973513i \(-0.573425\pi\)
−0.228631 + 0.973513i \(0.573425\pi\)
\(464\) 77.4948 3.59760
\(465\) 29.3760 1.36228
\(466\) −42.8212 −1.98365
\(467\) −31.0103 −1.43498 −0.717492 0.696567i \(-0.754710\pi\)
−0.717492 + 0.696567i \(0.754710\pi\)
\(468\) −32.1376 −1.48556
\(469\) 5.73380 0.264762
\(470\) −103.057 −4.75368
\(471\) 10.5463 0.485950
\(472\) −67.4446 −3.10439
\(473\) 4.19075 0.192691
\(474\) −20.8979 −0.959872
\(475\) 23.5199 1.07917
\(476\) 12.0174 0.550818
\(477\) −12.7186 −0.582346
\(478\) −76.8971 −3.51719
\(479\) 9.36654 0.427968 0.213984 0.976837i \(-0.431356\pi\)
0.213984 + 0.976837i \(0.431356\pi\)
\(480\) 37.1522 1.69576
\(481\) 23.0129 1.04930
\(482\) −26.5246 −1.20816
\(483\) 0.965687 0.0439403
\(484\) −51.0819 −2.32190
\(485\) 69.8128 3.17004
\(486\) −42.0256 −1.90632
\(487\) −40.0607 −1.81532 −0.907661 0.419703i \(-0.862134\pi\)
−0.907661 + 0.419703i \(0.862134\pi\)
\(488\) 34.7607 1.57354
\(489\) −4.23493 −0.191510
\(490\) 11.0752 0.500326
\(491\) −37.2770 −1.68229 −0.841144 0.540811i \(-0.818117\pi\)
−0.841144 + 0.540811i \(0.818117\pi\)
\(492\) −49.7923 −2.24481
\(493\) 21.2318 0.956233
\(494\) −14.5412 −0.654240
\(495\) 4.92806 0.221500
\(496\) −69.3104 −3.11213
\(497\) −14.7838 −0.663145
\(498\) 3.62768 0.162560
\(499\) −5.57734 −0.249676 −0.124838 0.992177i \(-0.539841\pi\)
−0.124838 + 0.992177i \(0.539841\pi\)
\(500\) −164.886 −7.37392
\(501\) 17.5418 0.783708
\(502\) −4.36649 −0.194886
\(503\) −21.6403 −0.964892 −0.482446 0.875926i \(-0.660251\pi\)
−0.482446 + 0.875926i \(0.660251\pi\)
\(504\) 15.5642 0.693284
\(505\) 38.9692 1.73411
\(506\) −1.46930 −0.0653182
\(507\) −2.99866 −0.133175
\(508\) −40.7788 −1.80927
\(509\) 38.7004 1.71537 0.857683 0.514180i \(-0.171904\pi\)
0.857683 + 0.514180i \(0.171904\pi\)
\(510\) 25.5644 1.13201
\(511\) −3.90120 −0.172579
\(512\) 44.8386 1.98161
\(513\) −8.47186 −0.374042
\(514\) −37.6568 −1.66097
\(515\) 32.5057 1.43237
\(516\) 34.1669 1.50411
\(517\) −4.98415 −0.219203
\(518\) −19.1975 −0.843489
\(519\) −0.715806 −0.0314204
\(520\) 95.6107 4.19281
\(521\) 42.8103 1.87555 0.937776 0.347241i \(-0.112882\pi\)
0.937776 + 0.347241i \(0.112882\pi\)
\(522\) 47.3653 2.07312
\(523\) 26.7535 1.16985 0.584924 0.811088i \(-0.301124\pi\)
0.584924 + 0.811088i \(0.301124\pi\)
\(524\) 44.8549 1.95950
\(525\) 12.0187 0.524540
\(526\) −33.0669 −1.44178
\(527\) −18.9895 −0.827195
\(528\) 4.51267 0.196389
\(529\) −21.8882 −0.951661
\(530\) 65.1768 2.83110
\(531\) −20.2403 −0.878355
\(532\) 8.54581 0.370508
\(533\) −35.5589 −1.54023
\(534\) 5.78492 0.250338
\(535\) −21.4064 −0.925481
\(536\) −41.2924 −1.78356
\(537\) −5.71348 −0.246555
\(538\) −8.13107 −0.350555
\(539\) 0.535628 0.0230711
\(540\) 95.9498 4.12902
\(541\) 3.25954 0.140139 0.0700694 0.997542i \(-0.477678\pi\)
0.0700694 + 0.997542i \(0.477678\pi\)
\(542\) −52.1292 −2.23914
\(543\) −2.67917 −0.114974
\(544\) −24.0162 −1.02969
\(545\) −54.7290 −2.34433
\(546\) −7.43060 −0.318000
\(547\) 16.8610 0.720926 0.360463 0.932774i \(-0.382619\pi\)
0.360463 + 0.932774i \(0.382619\pi\)
\(548\) −25.2400 −1.07820
\(549\) 10.4318 0.445217
\(550\) −18.2866 −0.779741
\(551\) 15.0983 0.643210
\(552\) −6.95448 −0.296002
\(553\) 8.77085 0.372974
\(554\) 14.1109 0.599513
\(555\) −28.7706 −1.22124
\(556\) 6.80359 0.288536
\(557\) 26.3701 1.11734 0.558668 0.829391i \(-0.311313\pi\)
0.558668 + 0.829391i \(0.311313\pi\)
\(558\) −42.3630 −1.79337
\(559\) 24.4001 1.03201
\(560\) −39.1616 −1.65488
\(561\) 1.23637 0.0521996
\(562\) −40.2775 −1.69900
\(563\) −13.9222 −0.586752 −0.293376 0.955997i \(-0.594779\pi\)
−0.293376 + 0.955997i \(0.594779\pi\)
\(564\) −40.6354 −1.71106
\(565\) 8.72372 0.367010
\(566\) −49.0181 −2.06039
\(567\) 2.15450 0.0904806
\(568\) 106.467 4.46725
\(569\) −6.44127 −0.270032 −0.135016 0.990843i \(-0.543109\pi\)
−0.135016 + 0.990843i \(0.543109\pi\)
\(570\) 18.1793 0.761447
\(571\) 30.4970 1.27626 0.638130 0.769929i \(-0.279708\pi\)
0.638130 + 0.769929i \(0.279708\pi\)
\(572\) 7.96486 0.333027
\(573\) 8.61907 0.360067
\(574\) 29.6634 1.23813
\(575\) 13.8371 0.577046
\(576\) −13.8145 −0.575604
\(577\) −47.2121 −1.96546 −0.982732 0.185036i \(-0.940760\pi\)
−0.982732 + 0.185036i \(0.940760\pi\)
\(578\) 27.7011 1.15222
\(579\) 6.83806 0.284180
\(580\) −170.999 −7.10035
\(581\) −1.52254 −0.0631655
\(582\) 39.0734 1.61964
\(583\) 3.15214 0.130548
\(584\) 28.0948 1.16257
\(585\) 28.6930 1.18631
\(586\) −33.0285 −1.36439
\(587\) 5.61724 0.231848 0.115924 0.993258i \(-0.463017\pi\)
0.115924 + 0.993258i \(0.463017\pi\)
\(588\) 4.36694 0.180089
\(589\) −13.5038 −0.556413
\(590\) 103.722 4.27016
\(591\) 0.0181620 0.000747083 0
\(592\) 67.8819 2.78993
\(593\) 14.4608 0.593834 0.296917 0.954903i \(-0.404042\pi\)
0.296917 + 0.954903i \(0.404042\pi\)
\(594\) 6.58682 0.270261
\(595\) −10.7294 −0.439862
\(596\) 38.7863 1.58875
\(597\) −9.85457 −0.403321
\(598\) −8.55480 −0.349832
\(599\) −8.52795 −0.348442 −0.174221 0.984707i \(-0.555741\pi\)
−0.174221 + 0.984707i \(0.555741\pi\)
\(600\) −86.5539 −3.53355
\(601\) −28.1144 −1.14681 −0.573405 0.819272i \(-0.694378\pi\)
−0.573405 + 0.819272i \(0.694378\pi\)
\(602\) −20.3547 −0.829595
\(603\) −12.3920 −0.504640
\(604\) −34.8611 −1.41848
\(605\) 45.6069 1.85418
\(606\) 21.8106 0.885994
\(607\) −17.8727 −0.725430 −0.362715 0.931900i \(-0.618150\pi\)
−0.362715 + 0.931900i \(0.618150\pi\)
\(608\) −17.0784 −0.692619
\(609\) 7.71528 0.312639
\(610\) −53.4577 −2.16444
\(611\) −29.0196 −1.17401
\(612\) −25.9723 −1.04987
\(613\) −35.8608 −1.44840 −0.724201 0.689589i \(-0.757791\pi\)
−0.724201 + 0.689589i \(0.757791\pi\)
\(614\) 22.0974 0.891779
\(615\) 44.4555 1.79262
\(616\) −3.85737 −0.155418
\(617\) 15.0620 0.606374 0.303187 0.952931i \(-0.401949\pi\)
0.303187 + 0.952931i \(0.401949\pi\)
\(618\) 18.1930 0.731830
\(619\) 11.4661 0.460861 0.230431 0.973089i \(-0.425987\pi\)
0.230431 + 0.973089i \(0.425987\pi\)
\(620\) 152.940 6.14220
\(621\) −4.98412 −0.200006
\(622\) 33.2954 1.33502
\(623\) −2.42793 −0.0972730
\(624\) 26.2745 1.05182
\(625\) 81.5982 3.26393
\(626\) 45.3669 1.81323
\(627\) 0.879204 0.0351120
\(628\) 54.9071 2.19103
\(629\) 18.5981 0.741555
\(630\) −23.9359 −0.953627
\(631\) 20.2172 0.804836 0.402418 0.915456i \(-0.368170\pi\)
0.402418 + 0.915456i \(0.368170\pi\)
\(632\) −63.1640 −2.51253
\(633\) 18.8914 0.750864
\(634\) 26.8312 1.06560
\(635\) 36.4081 1.44481
\(636\) 25.6992 1.01904
\(637\) 3.11863 0.123564
\(638\) −11.7388 −0.464745
\(639\) 31.9510 1.26396
\(640\) −10.3390 −0.408683
\(641\) 17.8100 0.703453 0.351727 0.936103i \(-0.385595\pi\)
0.351727 + 0.936103i \(0.385595\pi\)
\(642\) −11.9809 −0.472849
\(643\) 43.3475 1.70946 0.854729 0.519075i \(-0.173723\pi\)
0.854729 + 0.519075i \(0.173723\pi\)
\(644\) 5.02762 0.198116
\(645\) −30.5048 −1.20113
\(646\) −11.7516 −0.462361
\(647\) 32.7663 1.28818 0.644088 0.764951i \(-0.277237\pi\)
0.644088 + 0.764951i \(0.277237\pi\)
\(648\) −15.5158 −0.609520
\(649\) 5.01628 0.196906
\(650\) −106.471 −4.17614
\(651\) −6.90046 −0.270450
\(652\) −22.0482 −0.863475
\(653\) 3.57824 0.140027 0.0700136 0.997546i \(-0.477696\pi\)
0.0700136 + 0.997546i \(0.477696\pi\)
\(654\) −30.6312 −1.19777
\(655\) −40.0473 −1.56478
\(656\) −104.889 −4.09524
\(657\) 8.43134 0.328938
\(658\) 24.2083 0.943737
\(659\) −9.47166 −0.368963 −0.184482 0.982836i \(-0.559061\pi\)
−0.184482 + 0.982836i \(0.559061\pi\)
\(660\) −9.95761 −0.387599
\(661\) 42.9108 1.66904 0.834519 0.550979i \(-0.185746\pi\)
0.834519 + 0.550979i \(0.185746\pi\)
\(662\) 89.0152 3.45968
\(663\) 7.19861 0.279571
\(664\) 10.9647 0.425512
\(665\) −7.62986 −0.295873
\(666\) 41.4899 1.60770
\(667\) 8.88255 0.343934
\(668\) 91.3271 3.53355
\(669\) 10.4921 0.405650
\(670\) 63.5028 2.45333
\(671\) −2.58537 −0.0998071
\(672\) −8.72709 −0.336655
\(673\) 44.0276 1.69714 0.848570 0.529083i \(-0.177464\pi\)
0.848570 + 0.529083i \(0.177464\pi\)
\(674\) 33.3076 1.28296
\(675\) −62.0312 −2.38758
\(676\) −15.6118 −0.600454
\(677\) 24.2095 0.930446 0.465223 0.885194i \(-0.345974\pi\)
0.465223 + 0.885194i \(0.345974\pi\)
\(678\) 4.88256 0.187513
\(679\) −16.3991 −0.629340
\(680\) 77.2687 2.96312
\(681\) −25.2853 −0.968935
\(682\) 10.4991 0.402031
\(683\) 4.85029 0.185591 0.0927957 0.995685i \(-0.470420\pi\)
0.0927957 + 0.995685i \(0.470420\pi\)
\(684\) −18.4693 −0.706193
\(685\) 22.5347 0.861008
\(686\) −2.60157 −0.0993284
\(687\) 12.9012 0.492212
\(688\) 71.9737 2.74397
\(689\) 18.3529 0.699191
\(690\) 10.6951 0.407157
\(691\) 20.0829 0.763991 0.381995 0.924164i \(-0.375237\pi\)
0.381995 + 0.924164i \(0.375237\pi\)
\(692\) −3.72668 −0.141667
\(693\) −1.15761 −0.0439739
\(694\) −39.3596 −1.49407
\(695\) −6.07437 −0.230414
\(696\) −55.5623 −2.10608
\(697\) −28.7373 −1.08850
\(698\) 26.7410 1.01216
\(699\) 15.0747 0.570177
\(700\) 62.5727 2.36503
\(701\) 32.5584 1.22971 0.614856 0.788639i \(-0.289214\pi\)
0.614856 + 0.788639i \(0.289214\pi\)
\(702\) 38.3509 1.44746
\(703\) 13.2254 0.498807
\(704\) 3.42373 0.129037
\(705\) 36.2801 1.36639
\(706\) 20.8012 0.782864
\(707\) −9.15391 −0.344268
\(708\) 40.8974 1.53702
\(709\) 7.40470 0.278089 0.139045 0.990286i \(-0.455597\pi\)
0.139045 + 0.990286i \(0.455597\pi\)
\(710\) −163.733 −6.14480
\(711\) −18.9557 −0.710894
\(712\) 17.4850 0.655277
\(713\) −7.94446 −0.297522
\(714\) −6.00511 −0.224736
\(715\) −7.11118 −0.265943
\(716\) −29.7459 −1.11166
\(717\) 27.0707 1.01097
\(718\) 24.8529 0.927501
\(719\) 34.7350 1.29540 0.647698 0.761897i \(-0.275732\pi\)
0.647698 + 0.761897i \(0.275732\pi\)
\(720\) 84.6367 3.15422
\(721\) −7.63561 −0.284365
\(722\) 41.0731 1.52858
\(723\) 9.33765 0.347271
\(724\) −13.9485 −0.518391
\(725\) 110.550 4.10574
\(726\) 25.5256 0.947344
\(727\) −13.1261 −0.486819 −0.243409 0.969924i \(-0.578266\pi\)
−0.243409 + 0.969924i \(0.578266\pi\)
\(728\) −22.4591 −0.832388
\(729\) 8.33109 0.308559
\(730\) −43.2065 −1.59914
\(731\) 19.7192 0.729340
\(732\) −21.0783 −0.779078
\(733\) 18.4536 0.681598 0.340799 0.940136i \(-0.389302\pi\)
0.340799 + 0.940136i \(0.389302\pi\)
\(734\) −79.3897 −2.93033
\(735\) −3.89888 −0.143812
\(736\) −10.0474 −0.370354
\(737\) 3.07118 0.113128
\(738\) −64.1090 −2.35989
\(739\) 39.6017 1.45677 0.728386 0.685167i \(-0.240271\pi\)
0.728386 + 0.685167i \(0.240271\pi\)
\(740\) −149.787 −5.50630
\(741\) 5.11906 0.188053
\(742\) −15.3101 −0.562052
\(743\) 43.3290 1.58959 0.794794 0.606880i \(-0.207579\pi\)
0.794794 + 0.606880i \(0.207579\pi\)
\(744\) 49.6943 1.82188
\(745\) −34.6292 −1.26871
\(746\) −42.5654 −1.55843
\(747\) 3.29053 0.120394
\(748\) 6.43687 0.235355
\(749\) 5.02839 0.183734
\(750\) 82.3934 3.00858
\(751\) 4.15232 0.151520 0.0757601 0.997126i \(-0.475862\pi\)
0.0757601 + 0.997126i \(0.475862\pi\)
\(752\) −85.6000 −3.12151
\(753\) 1.53717 0.0560176
\(754\) −68.3480 −2.48909
\(755\) 31.1246 1.13274
\(756\) −22.5387 −0.819725
\(757\) 12.0037 0.436281 0.218141 0.975917i \(-0.430001\pi\)
0.218141 + 0.975917i \(0.430001\pi\)
\(758\) −80.4873 −2.92343
\(759\) 0.517249 0.0187749
\(760\) 54.9471 1.99314
\(761\) 47.9326 1.73755 0.868777 0.495204i \(-0.164907\pi\)
0.868777 + 0.495204i \(0.164907\pi\)
\(762\) 20.3772 0.738187
\(763\) 12.8559 0.465415
\(764\) 44.8732 1.62346
\(765\) 23.1885 0.838383
\(766\) 43.3303 1.56559
\(767\) 29.2067 1.05459
\(768\) −17.4948 −0.631291
\(769\) −25.2413 −0.910225 −0.455113 0.890434i \(-0.650401\pi\)
−0.455113 + 0.890434i \(0.650401\pi\)
\(770\) 5.93217 0.213781
\(771\) 13.2566 0.477425
\(772\) 35.6008 1.28130
\(773\) −8.42881 −0.303163 −0.151582 0.988445i \(-0.548437\pi\)
−0.151582 + 0.988445i \(0.548437\pi\)
\(774\) 43.9908 1.58122
\(775\) −98.8749 −3.55169
\(776\) 118.100 4.23953
\(777\) 6.75824 0.242451
\(778\) −26.1150 −0.936267
\(779\) −20.4356 −0.732181
\(780\) −57.9769 −2.07591
\(781\) −7.91862 −0.283350
\(782\) −6.91364 −0.247231
\(783\) −39.8202 −1.42306
\(784\) 9.19910 0.328539
\(785\) −49.0221 −1.74967
\(786\) −22.4140 −0.799480
\(787\) 34.3142 1.22317 0.611585 0.791179i \(-0.290532\pi\)
0.611585 + 0.791179i \(0.290532\pi\)
\(788\) 0.0945560 0.00336842
\(789\) 11.6408 0.414423
\(790\) 97.1387 3.45604
\(791\) −2.04921 −0.0728615
\(792\) 8.33661 0.296229
\(793\) −15.0530 −0.534548
\(794\) 38.3885 1.36236
\(795\) −22.9447 −0.813765
\(796\) −51.3055 −1.81848
\(797\) −44.5599 −1.57839 −0.789196 0.614141i \(-0.789503\pi\)
−0.789196 + 0.614141i \(0.789503\pi\)
\(798\) −4.27034 −0.151168
\(799\) −23.4525 −0.829688
\(800\) −125.048 −4.42113
\(801\) 5.24728 0.185404
\(802\) 67.8844 2.39708
\(803\) −2.08959 −0.0737401
\(804\) 25.0391 0.883062
\(805\) −4.48876 −0.158208
\(806\) 61.1297 2.15320
\(807\) 2.86244 0.100763
\(808\) 65.9227 2.31915
\(809\) 26.5735 0.934276 0.467138 0.884184i \(-0.345285\pi\)
0.467138 + 0.884184i \(0.345285\pi\)
\(810\) 23.8615 0.838407
\(811\) −17.9232 −0.629367 −0.314684 0.949197i \(-0.601898\pi\)
−0.314684 + 0.949197i \(0.601898\pi\)
\(812\) 40.1678 1.40962
\(813\) 18.3515 0.643614
\(814\) −10.2827 −0.360409
\(815\) 19.6851 0.689538
\(816\) 21.2339 0.743337
\(817\) 14.0227 0.490590
\(818\) −83.8221 −2.93077
\(819\) −6.74002 −0.235516
\(820\) 231.447 8.08249
\(821\) −26.4949 −0.924680 −0.462340 0.886703i \(-0.652990\pi\)
−0.462340 + 0.886703i \(0.652990\pi\)
\(822\) 12.6124 0.439908
\(823\) −11.9771 −0.417495 −0.208747 0.977970i \(-0.566939\pi\)
−0.208747 + 0.977970i \(0.566939\pi\)
\(824\) 54.9885 1.91562
\(825\) 6.43756 0.224127
\(826\) −24.3643 −0.847744
\(827\) 44.5208 1.54814 0.774069 0.633101i \(-0.218218\pi\)
0.774069 + 0.633101i \(0.218218\pi\)
\(828\) −10.8658 −0.377612
\(829\) 37.9894 1.31943 0.659713 0.751518i \(-0.270678\pi\)
0.659713 + 0.751518i \(0.270678\pi\)
\(830\) −16.8624 −0.585301
\(831\) −4.96755 −0.172323
\(832\) 19.9343 0.691096
\(833\) 2.52035 0.0873248
\(834\) −3.39975 −0.117724
\(835\) −81.5385 −2.82176
\(836\) 4.57737 0.158312
\(837\) 35.6148 1.23103
\(838\) −12.3050 −0.425071
\(839\) −15.4558 −0.533594 −0.266797 0.963753i \(-0.585965\pi\)
−0.266797 + 0.963753i \(0.585965\pi\)
\(840\) 28.0782 0.968788
\(841\) 41.9665 1.44712
\(842\) −88.5737 −3.05245
\(843\) 14.1792 0.488358
\(844\) 98.3535 3.38547
\(845\) 13.9385 0.479500
\(846\) −52.3193 −1.79877
\(847\) −10.7131 −0.368107
\(848\) 54.1362 1.85905
\(849\) 17.2562 0.592233
\(850\) −86.0457 −2.95134
\(851\) 7.78072 0.266720
\(852\) −64.5600 −2.21179
\(853\) −10.1258 −0.346699 −0.173350 0.984860i \(-0.555459\pi\)
−0.173350 + 0.984860i \(0.555459\pi\)
\(854\) 12.5573 0.429701
\(855\) 16.4898 0.563939
\(856\) −36.2124 −1.23772
\(857\) 5.83237 0.199230 0.0996149 0.995026i \(-0.468239\pi\)
0.0996149 + 0.995026i \(0.468239\pi\)
\(858\) −3.98004 −0.135876
\(859\) −39.4030 −1.34441 −0.672206 0.740364i \(-0.734653\pi\)
−0.672206 + 0.740364i \(0.734653\pi\)
\(860\) −158.816 −5.41559
\(861\) −10.4426 −0.355884
\(862\) −51.0233 −1.73786
\(863\) −1.00000 −0.0340404
\(864\) 45.0424 1.53237
\(865\) 3.32725 0.113130
\(866\) 52.0048 1.76720
\(867\) −9.75185 −0.331190
\(868\) −35.9257 −1.21940
\(869\) 4.69791 0.159366
\(870\) 85.4481 2.89696
\(871\) 17.8816 0.605894
\(872\) −92.5830 −3.13526
\(873\) 35.4420 1.19953
\(874\) −4.91641 −0.166300
\(875\) −34.5805 −1.16904
\(876\) −17.0363 −0.575603
\(877\) −53.8729 −1.81916 −0.909579 0.415530i \(-0.863596\pi\)
−0.909579 + 0.415530i \(0.863596\pi\)
\(878\) −59.9499 −2.02321
\(879\) 11.6273 0.392178
\(880\) −20.9760 −0.707102
\(881\) 47.1895 1.58985 0.794927 0.606705i \(-0.207509\pi\)
0.794927 + 0.606705i \(0.207509\pi\)
\(882\) 5.62256 0.189321
\(883\) −2.02456 −0.0681317 −0.0340659 0.999420i \(-0.510846\pi\)
−0.0340659 + 0.999420i \(0.510846\pi\)
\(884\) 37.4779 1.26052
\(885\) −36.5140 −1.22740
\(886\) 46.2384 1.55341
\(887\) 52.3010 1.75610 0.878048 0.478572i \(-0.158846\pi\)
0.878048 + 0.478572i \(0.158846\pi\)
\(888\) −48.6701 −1.63326
\(889\) −8.55230 −0.286835
\(890\) −26.8898 −0.901347
\(891\) 1.15401 0.0386608
\(892\) 54.6249 1.82898
\(893\) −16.6775 −0.558090
\(894\) −19.3815 −0.648215
\(895\) 26.5577 0.887726
\(896\) 2.42863 0.0811349
\(897\) 3.01161 0.100555
\(898\) 23.7707 0.793239
\(899\) −63.4717 −2.11690
\(900\) −135.233 −4.50777
\(901\) 14.8321 0.494129
\(902\) 15.8885 0.529031
\(903\) 7.16562 0.238457
\(904\) 14.7576 0.490830
\(905\) 12.4535 0.413967
\(906\) 17.4201 0.578743
\(907\) 8.93423 0.296656 0.148328 0.988938i \(-0.452611\pi\)
0.148328 + 0.988938i \(0.452611\pi\)
\(908\) −131.642 −4.36870
\(909\) 19.7836 0.656180
\(910\) 34.5393 1.14497
\(911\) −30.2835 −1.00334 −0.501669 0.865060i \(-0.667280\pi\)
−0.501669 + 0.865060i \(0.667280\pi\)
\(912\) 15.0998 0.500005
\(913\) −0.815513 −0.0269895
\(914\) −63.0209 −2.08455
\(915\) 18.8191 0.622142
\(916\) 67.1672 2.21927
\(917\) 9.40716 0.310652
\(918\) 30.9937 1.02294
\(919\) −53.1601 −1.75359 −0.876795 0.480864i \(-0.840323\pi\)
−0.876795 + 0.480864i \(0.840323\pi\)
\(920\) 32.3262 1.06576
\(921\) −7.77913 −0.256331
\(922\) −43.9373 −1.44700
\(923\) −46.1052 −1.51757
\(924\) 2.33905 0.0769492
\(925\) 96.8371 3.18399
\(926\) 25.5972 0.841175
\(927\) 16.5022 0.542004
\(928\) −80.2734 −2.63510
\(929\) 40.2169 1.31947 0.659737 0.751497i \(-0.270668\pi\)
0.659737 + 0.751497i \(0.270668\pi\)
\(930\) −76.4238 −2.50604
\(931\) 1.79226 0.0587390
\(932\) 78.4829 2.57079
\(933\) −11.7212 −0.383736
\(934\) 80.6754 2.63978
\(935\) −5.74696 −0.187946
\(936\) 48.5389 1.58654
\(937\) −25.2472 −0.824789 −0.412394 0.911005i \(-0.635307\pi\)
−0.412394 + 0.911005i \(0.635307\pi\)
\(938\) −14.9169 −0.487053
\(939\) −15.9709 −0.521190
\(940\) 188.884 6.16071
\(941\) −26.2736 −0.856494 −0.428247 0.903662i \(-0.640869\pi\)
−0.428247 + 0.903662i \(0.640869\pi\)
\(942\) −27.4371 −0.893947
\(943\) −12.0225 −0.391508
\(944\) 86.1518 2.80400
\(945\) 20.1230 0.654600
\(946\) −10.9025 −0.354472
\(947\) −26.0790 −0.847453 −0.423726 0.905790i \(-0.639278\pi\)
−0.423726 + 0.905790i \(0.639278\pi\)
\(948\) 38.3017 1.24398
\(949\) −12.1664 −0.394938
\(950\) −61.1886 −1.98522
\(951\) −9.44560 −0.306294
\(952\) −18.1505 −0.588261
\(953\) −38.4418 −1.24525 −0.622626 0.782520i \(-0.713934\pi\)
−0.622626 + 0.782520i \(0.713934\pi\)
\(954\) 33.0884 1.07128
\(955\) −40.0637 −1.29643
\(956\) 140.937 4.55824
\(957\) 4.13252 0.133585
\(958\) −24.3677 −0.787286
\(959\) −5.29343 −0.170934
\(960\) −24.9217 −0.804343
\(961\) 25.7683 0.831236
\(962\) −59.8698 −1.93028
\(963\) −10.8674 −0.350199
\(964\) 48.6143 1.56576
\(965\) −31.7850 −1.02320
\(966\) −2.51230 −0.0808320
\(967\) 23.8010 0.765389 0.382695 0.923875i \(-0.374996\pi\)
0.382695 + 0.923875i \(0.374996\pi\)
\(968\) 77.1514 2.47974
\(969\) 4.13701 0.132900
\(970\) −181.623 −5.83156
\(971\) 28.1205 0.902430 0.451215 0.892415i \(-0.350991\pi\)
0.451215 + 0.892415i \(0.350991\pi\)
\(972\) 77.0247 2.47057
\(973\) 1.42688 0.0457435
\(974\) 104.221 3.33945
\(975\) 37.4819 1.20038
\(976\) −44.4023 −1.42128
\(977\) −43.9649 −1.40656 −0.703281 0.710912i \(-0.748282\pi\)
−0.703281 + 0.710912i \(0.748282\pi\)
\(978\) 11.0175 0.352300
\(979\) −1.30047 −0.0415631
\(980\) −20.2986 −0.648416
\(981\) −27.7844 −0.887087
\(982\) 96.9788 3.09472
\(983\) −13.2073 −0.421249 −0.210624 0.977567i \(-0.567550\pi\)
−0.210624 + 0.977567i \(0.567550\pi\)
\(984\) 75.2036 2.39740
\(985\) −0.0844214 −0.00268989
\(986\) −55.2361 −1.75907
\(987\) −8.52223 −0.271266
\(988\) 26.6512 0.847887
\(989\) 8.24973 0.262326
\(990\) −12.8207 −0.407469
\(991\) −3.49676 −0.111078 −0.0555391 0.998457i \(-0.517688\pi\)
−0.0555391 + 0.998457i \(0.517688\pi\)
\(992\) 71.7956 2.27951
\(993\) −31.3367 −0.994441
\(994\) 38.4611 1.21991
\(995\) 45.8065 1.45217
\(996\) −6.64882 −0.210676
\(997\) −22.3740 −0.708592 −0.354296 0.935133i \(-0.615279\pi\)
−0.354296 + 0.935133i \(0.615279\pi\)
\(998\) 14.5099 0.459301
\(999\) −34.8808 −1.10358
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 \(a_p\))