Properties

Label 6026.2.a.h.1.2
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.03806 q^{3}\) \(+1.00000 q^{4}\) \(+2.76911 q^{5}\) \(+3.03806 q^{6}\) \(-0.589865 q^{7}\) \(-1.00000 q^{8}\) \(+6.22984 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.03806 q^{3}\) \(+1.00000 q^{4}\) \(+2.76911 q^{5}\) \(+3.03806 q^{6}\) \(-0.589865 q^{7}\) \(-1.00000 q^{8}\) \(+6.22984 q^{9}\) \(-2.76911 q^{10}\) \(-4.13029 q^{11}\) \(-3.03806 q^{12}\) \(+2.56341 q^{13}\) \(+0.589865 q^{14}\) \(-8.41273 q^{15}\) \(+1.00000 q^{16}\) \(+1.30388 q^{17}\) \(-6.22984 q^{18}\) \(-5.13670 q^{19}\) \(+2.76911 q^{20}\) \(+1.79205 q^{21}\) \(+4.13029 q^{22}\) \(-1.00000 q^{23}\) \(+3.03806 q^{24}\) \(+2.66796 q^{25}\) \(-2.56341 q^{26}\) \(-9.81246 q^{27}\) \(-0.589865 q^{28}\) \(+3.77899 q^{29}\) \(+8.41273 q^{30}\) \(+6.58712 q^{31}\) \(-1.00000 q^{32}\) \(+12.5481 q^{33}\) \(-1.30388 q^{34}\) \(-1.63340 q^{35}\) \(+6.22984 q^{36}\) \(+6.66887 q^{37}\) \(+5.13670 q^{38}\) \(-7.78782 q^{39}\) \(-2.76911 q^{40}\) \(-0.317115 q^{41}\) \(-1.79205 q^{42}\) \(-4.28351 q^{43}\) \(-4.13029 q^{44}\) \(+17.2511 q^{45}\) \(+1.00000 q^{46}\) \(+6.67301 q^{47}\) \(-3.03806 q^{48}\) \(-6.65206 q^{49}\) \(-2.66796 q^{50}\) \(-3.96126 q^{51}\) \(+2.56341 q^{52}\) \(-13.8012 q^{53}\) \(+9.81246 q^{54}\) \(-11.4372 q^{55}\) \(+0.589865 q^{56}\) \(+15.6056 q^{57}\) \(-3.77899 q^{58}\) \(-6.57837 q^{59}\) \(-8.41273 q^{60}\) \(-4.26115 q^{61}\) \(-6.58712 q^{62}\) \(-3.67476 q^{63}\) \(+1.00000 q^{64}\) \(+7.09837 q^{65}\) \(-12.5481 q^{66}\) \(-6.71973 q^{67}\) \(+1.30388 q^{68}\) \(+3.03806 q^{69}\) \(+1.63340 q^{70}\) \(+11.4583 q^{71}\) \(-6.22984 q^{72}\) \(+5.20789 q^{73}\) \(-6.66887 q^{74}\) \(-8.10545 q^{75}\) \(-5.13670 q^{76}\) \(+2.43631 q^{77}\) \(+7.78782 q^{78}\) \(-4.85884 q^{79}\) \(+2.76911 q^{80}\) \(+11.1214 q^{81}\) \(+0.317115 q^{82}\) \(+5.44110 q^{83}\) \(+1.79205 q^{84}\) \(+3.61057 q^{85}\) \(+4.28351 q^{86}\) \(-11.4808 q^{87}\) \(+4.13029 q^{88}\) \(-4.24789 q^{89}\) \(-17.2511 q^{90}\) \(-1.51207 q^{91}\) \(-1.00000 q^{92}\) \(-20.0121 q^{93}\) \(-6.67301 q^{94}\) \(-14.2241 q^{95}\) \(+3.03806 q^{96}\) \(-9.63313 q^{97}\) \(+6.65206 q^{98}\) \(-25.7310 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.03806 −1.75403 −0.877014 0.480465i \(-0.840468\pi\)
−0.877014 + 0.480465i \(0.840468\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.76911 1.23838 0.619192 0.785240i \(-0.287460\pi\)
0.619192 + 0.785240i \(0.287460\pi\)
\(6\) 3.03806 1.24028
\(7\) −0.589865 −0.222948 −0.111474 0.993767i \(-0.535557\pi\)
−0.111474 + 0.993767i \(0.535557\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.22984 2.07661
\(10\) −2.76911 −0.875669
\(11\) −4.13029 −1.24533 −0.622665 0.782489i \(-0.713950\pi\)
−0.622665 + 0.782489i \(0.713950\pi\)
\(12\) −3.03806 −0.877014
\(13\) 2.56341 0.710963 0.355482 0.934683i \(-0.384317\pi\)
0.355482 + 0.934683i \(0.384317\pi\)
\(14\) 0.589865 0.157648
\(15\) −8.41273 −2.17216
\(16\) 1.00000 0.250000
\(17\) 1.30388 0.316236 0.158118 0.987420i \(-0.449457\pi\)
0.158118 + 0.987420i \(0.449457\pi\)
\(18\) −6.22984 −1.46839
\(19\) −5.13670 −1.17844 −0.589220 0.807972i \(-0.700565\pi\)
−0.589220 + 0.807972i \(0.700565\pi\)
\(20\) 2.76911 0.619192
\(21\) 1.79205 0.391057
\(22\) 4.13029 0.880581
\(23\) −1.00000 −0.208514
\(24\) 3.03806 0.620142
\(25\) 2.66796 0.533593
\(26\) −2.56341 −0.502727
\(27\) −9.81246 −1.88841
\(28\) −0.589865 −0.111474
\(29\) 3.77899 0.701740 0.350870 0.936424i \(-0.385886\pi\)
0.350870 + 0.936424i \(0.385886\pi\)
\(30\) 8.41273 1.53595
\(31\) 6.58712 1.18308 0.591540 0.806275i \(-0.298520\pi\)
0.591540 + 0.806275i \(0.298520\pi\)
\(32\) −1.00000 −0.176777
\(33\) 12.5481 2.18434
\(34\) −1.30388 −0.223613
\(35\) −1.63340 −0.276095
\(36\) 6.22984 1.03831
\(37\) 6.66887 1.09636 0.548178 0.836362i \(-0.315322\pi\)
0.548178 + 0.836362i \(0.315322\pi\)
\(38\) 5.13670 0.833283
\(39\) −7.78782 −1.24705
\(40\) −2.76911 −0.437835
\(41\) −0.317115 −0.0495250 −0.0247625 0.999693i \(-0.507883\pi\)
−0.0247625 + 0.999693i \(0.507883\pi\)
\(42\) −1.79205 −0.276519
\(43\) −4.28351 −0.653229 −0.326614 0.945158i \(-0.605908\pi\)
−0.326614 + 0.945158i \(0.605908\pi\)
\(44\) −4.13029 −0.622665
\(45\) 17.2511 2.57164
\(46\) 1.00000 0.147442
\(47\) 6.67301 0.973359 0.486680 0.873581i \(-0.338208\pi\)
0.486680 + 0.873581i \(0.338208\pi\)
\(48\) −3.03806 −0.438507
\(49\) −6.65206 −0.950294
\(50\) −2.66796 −0.377307
\(51\) −3.96126 −0.554687
\(52\) 2.56341 0.355482
\(53\) −13.8012 −1.89575 −0.947873 0.318648i \(-0.896771\pi\)
−0.947873 + 0.318648i \(0.896771\pi\)
\(54\) 9.81246 1.33531
\(55\) −11.4372 −1.54219
\(56\) 0.589865 0.0788240
\(57\) 15.6056 2.06702
\(58\) −3.77899 −0.496205
\(59\) −6.57837 −0.856431 −0.428216 0.903677i \(-0.640858\pi\)
−0.428216 + 0.903677i \(0.640858\pi\)
\(60\) −8.41273 −1.08608
\(61\) −4.26115 −0.545584 −0.272792 0.962073i \(-0.587947\pi\)
−0.272792 + 0.962073i \(0.587947\pi\)
\(62\) −6.58712 −0.836565
\(63\) −3.67476 −0.462977
\(64\) 1.00000 0.125000
\(65\) 7.09837 0.880445
\(66\) −12.5481 −1.54456
\(67\) −6.71973 −0.820946 −0.410473 0.911873i \(-0.634636\pi\)
−0.410473 + 0.911873i \(0.634636\pi\)
\(68\) 1.30388 0.158118
\(69\) 3.03806 0.365740
\(70\) 1.63340 0.195229
\(71\) 11.4583 1.35985 0.679924 0.733283i \(-0.262013\pi\)
0.679924 + 0.733283i \(0.262013\pi\)
\(72\) −6.22984 −0.734193
\(73\) 5.20789 0.609537 0.304769 0.952426i \(-0.401421\pi\)
0.304769 + 0.952426i \(0.401421\pi\)
\(74\) −6.66887 −0.775241
\(75\) −8.10545 −0.935936
\(76\) −5.13670 −0.589220
\(77\) 2.43631 0.277644
\(78\) 7.78782 0.881797
\(79\) −4.85884 −0.546662 −0.273331 0.961920i \(-0.588125\pi\)
−0.273331 + 0.961920i \(0.588125\pi\)
\(80\) 2.76911 0.309596
\(81\) 11.1214 1.23571
\(82\) 0.317115 0.0350195
\(83\) 5.44110 0.597238 0.298619 0.954372i \(-0.403474\pi\)
0.298619 + 0.954372i \(0.403474\pi\)
\(84\) 1.79205 0.195528
\(85\) 3.61057 0.391622
\(86\) 4.28351 0.461902
\(87\) −11.4808 −1.23087
\(88\) 4.13029 0.440290
\(89\) −4.24789 −0.450275 −0.225138 0.974327i \(-0.572283\pi\)
−0.225138 + 0.974327i \(0.572283\pi\)
\(90\) −17.2511 −1.81843
\(91\) −1.51207 −0.158508
\(92\) −1.00000 −0.104257
\(93\) −20.0121 −2.07516
\(94\) −6.67301 −0.688269
\(95\) −14.2241 −1.45936
\(96\) 3.03806 0.310071
\(97\) −9.63313 −0.978096 −0.489048 0.872257i \(-0.662656\pi\)
−0.489048 + 0.872257i \(0.662656\pi\)
\(98\) 6.65206 0.671959
\(99\) −25.7310 −2.58607
\(100\) 2.66796 0.266796
\(101\) 10.8490 1.07952 0.539759 0.841820i \(-0.318516\pi\)
0.539759 + 0.841820i \(0.318516\pi\)
\(102\) 3.96126 0.392223
\(103\) −3.18569 −0.313895 −0.156948 0.987607i \(-0.550165\pi\)
−0.156948 + 0.987607i \(0.550165\pi\)
\(104\) −2.56341 −0.251363
\(105\) 4.96238 0.484278
\(106\) 13.8012 1.34050
\(107\) −2.77969 −0.268723 −0.134361 0.990932i \(-0.542898\pi\)
−0.134361 + 0.990932i \(0.542898\pi\)
\(108\) −9.81246 −0.944204
\(109\) 4.62957 0.443432 0.221716 0.975111i \(-0.428834\pi\)
0.221716 + 0.975111i \(0.428834\pi\)
\(110\) 11.4372 1.09050
\(111\) −20.2605 −1.92304
\(112\) −0.589865 −0.0557370
\(113\) −10.6533 −1.00218 −0.501091 0.865395i \(-0.667068\pi\)
−0.501091 + 0.865395i \(0.667068\pi\)
\(114\) −15.6056 −1.46160
\(115\) −2.76911 −0.258221
\(116\) 3.77899 0.350870
\(117\) 15.9697 1.47639
\(118\) 6.57837 0.605588
\(119\) −0.769111 −0.0705043
\(120\) 8.41273 0.767974
\(121\) 6.05929 0.550845
\(122\) 4.26115 0.385786
\(123\) 0.963416 0.0868683
\(124\) 6.58712 0.591540
\(125\) −6.45766 −0.577591
\(126\) 3.67476 0.327374
\(127\) 20.6296 1.83058 0.915289 0.402797i \(-0.131962\pi\)
0.915289 + 0.402797i \(0.131962\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 13.0136 1.14578
\(130\) −7.09837 −0.622568
\(131\) −1.00000 −0.0873704
\(132\) 12.5481 1.09217
\(133\) 3.02996 0.262731
\(134\) 6.71973 0.580496
\(135\) −27.1718 −2.33857
\(136\) −1.30388 −0.111806
\(137\) 19.6959 1.68273 0.841366 0.540466i \(-0.181752\pi\)
0.841366 + 0.540466i \(0.181752\pi\)
\(138\) −3.03806 −0.258617
\(139\) −19.7377 −1.67413 −0.837065 0.547104i \(-0.815730\pi\)
−0.837065 + 0.547104i \(0.815730\pi\)
\(140\) −1.63340 −0.138048
\(141\) −20.2730 −1.70730
\(142\) −11.4583 −0.961557
\(143\) −10.5876 −0.885383
\(144\) 6.22984 0.519153
\(145\) 10.4644 0.869024
\(146\) −5.20789 −0.431008
\(147\) 20.2094 1.66684
\(148\) 6.66887 0.548178
\(149\) −3.89948 −0.319458 −0.159729 0.987161i \(-0.551062\pi\)
−0.159729 + 0.987161i \(0.551062\pi\)
\(150\) 8.10545 0.661807
\(151\) −1.69204 −0.137697 −0.0688483 0.997627i \(-0.521932\pi\)
−0.0688483 + 0.997627i \(0.521932\pi\)
\(152\) 5.13670 0.416642
\(153\) 8.12294 0.656700
\(154\) −2.43631 −0.196324
\(155\) 18.2404 1.46511
\(156\) −7.78782 −0.623524
\(157\) −5.66849 −0.452394 −0.226197 0.974082i \(-0.572629\pi\)
−0.226197 + 0.974082i \(0.572629\pi\)
\(158\) 4.85884 0.386548
\(159\) 41.9291 3.32519
\(160\) −2.76911 −0.218917
\(161\) 0.589865 0.0464879
\(162\) −11.1214 −0.873777
\(163\) 16.3791 1.28291 0.641455 0.767161i \(-0.278331\pi\)
0.641455 + 0.767161i \(0.278331\pi\)
\(164\) −0.317115 −0.0247625
\(165\) 34.7470 2.70505
\(166\) −5.44110 −0.422311
\(167\) −12.7211 −0.984387 −0.492194 0.870486i \(-0.663805\pi\)
−0.492194 + 0.870486i \(0.663805\pi\)
\(168\) −1.79205 −0.138260
\(169\) −6.42891 −0.494531
\(170\) −3.61057 −0.276918
\(171\) −32.0008 −2.44716
\(172\) −4.28351 −0.326614
\(173\) 4.48202 0.340762 0.170381 0.985378i \(-0.445500\pi\)
0.170381 + 0.985378i \(0.445500\pi\)
\(174\) 11.4808 0.870358
\(175\) −1.57374 −0.118963
\(176\) −4.13029 −0.311332
\(177\) 19.9855 1.50220
\(178\) 4.24789 0.318393
\(179\) 8.90521 0.665607 0.332803 0.942996i \(-0.392005\pi\)
0.332803 + 0.942996i \(0.392005\pi\)
\(180\) 17.2511 1.28582
\(181\) 12.3782 0.920067 0.460033 0.887902i \(-0.347837\pi\)
0.460033 + 0.887902i \(0.347837\pi\)
\(182\) 1.51207 0.112082
\(183\) 12.9456 0.956969
\(184\) 1.00000 0.0737210
\(185\) 18.4668 1.35771
\(186\) 20.0121 1.46736
\(187\) −5.38539 −0.393818
\(188\) 6.67301 0.486680
\(189\) 5.78802 0.421017
\(190\) 14.2241 1.03192
\(191\) 17.1516 1.24105 0.620524 0.784187i \(-0.286920\pi\)
0.620524 + 0.784187i \(0.286920\pi\)
\(192\) −3.03806 −0.219253
\(193\) −9.65340 −0.694867 −0.347433 0.937705i \(-0.612947\pi\)
−0.347433 + 0.937705i \(0.612947\pi\)
\(194\) 9.63313 0.691618
\(195\) −21.5653 −1.54432
\(196\) −6.65206 −0.475147
\(197\) 9.13171 0.650607 0.325304 0.945610i \(-0.394534\pi\)
0.325304 + 0.945610i \(0.394534\pi\)
\(198\) 25.7310 1.82862
\(199\) −2.74921 −0.194886 −0.0974432 0.995241i \(-0.531066\pi\)
−0.0974432 + 0.995241i \(0.531066\pi\)
\(200\) −2.66796 −0.188654
\(201\) 20.4150 1.43996
\(202\) −10.8490 −0.763334
\(203\) −2.22909 −0.156452
\(204\) −3.96126 −0.277344
\(205\) −0.878126 −0.0613310
\(206\) 3.18569 0.221957
\(207\) −6.22984 −0.433004
\(208\) 2.56341 0.177741
\(209\) 21.2161 1.46755
\(210\) −4.96238 −0.342437
\(211\) −15.6704 −1.07880 −0.539399 0.842050i \(-0.681349\pi\)
−0.539399 + 0.842050i \(0.681349\pi\)
\(212\) −13.8012 −0.947873
\(213\) −34.8110 −2.38521
\(214\) 2.77969 0.190016
\(215\) −11.8615 −0.808947
\(216\) 9.81246 0.667653
\(217\) −3.88551 −0.263766
\(218\) −4.62957 −0.313554
\(219\) −15.8219 −1.06914
\(220\) −11.4372 −0.771097
\(221\) 3.34237 0.224832
\(222\) 20.2605 1.35979
\(223\) 24.2771 1.62572 0.812859 0.582461i \(-0.197910\pi\)
0.812859 + 0.582461i \(0.197910\pi\)
\(224\) 0.589865 0.0394120
\(225\) 16.6210 1.10807
\(226\) 10.6533 0.708649
\(227\) −16.8590 −1.11897 −0.559487 0.828839i \(-0.689002\pi\)
−0.559487 + 0.828839i \(0.689002\pi\)
\(228\) 15.6056 1.03351
\(229\) 10.8728 0.718497 0.359249 0.933242i \(-0.383033\pi\)
0.359249 + 0.933242i \(0.383033\pi\)
\(230\) 2.76911 0.182590
\(231\) −7.40168 −0.486995
\(232\) −3.77899 −0.248103
\(233\) 4.89569 0.320728 0.160364 0.987058i \(-0.448733\pi\)
0.160364 + 0.987058i \(0.448733\pi\)
\(234\) −15.9697 −1.04397
\(235\) 18.4783 1.20539
\(236\) −6.57837 −0.428216
\(237\) 14.7615 0.958860
\(238\) 0.769111 0.0498541
\(239\) −18.8560 −1.21970 −0.609848 0.792518i \(-0.708770\pi\)
−0.609848 + 0.792518i \(0.708770\pi\)
\(240\) −8.41273 −0.543040
\(241\) −0.473098 −0.0304749 −0.0152375 0.999884i \(-0.504850\pi\)
−0.0152375 + 0.999884i \(0.504850\pi\)
\(242\) −6.05929 −0.389506
\(243\) −4.35006 −0.279056
\(244\) −4.26115 −0.272792
\(245\) −18.4203 −1.17683
\(246\) −0.963416 −0.0614252
\(247\) −13.1675 −0.837828
\(248\) −6.58712 −0.418282
\(249\) −16.5304 −1.04757
\(250\) 6.45766 0.408418
\(251\) −14.9105 −0.941140 −0.470570 0.882363i \(-0.655952\pi\)
−0.470570 + 0.882363i \(0.655952\pi\)
\(252\) −3.67476 −0.231488
\(253\) 4.13029 0.259669
\(254\) −20.6296 −1.29441
\(255\) −10.9692 −0.686915
\(256\) 1.00000 0.0625000
\(257\) 7.23043 0.451022 0.225511 0.974241i \(-0.427595\pi\)
0.225511 + 0.974241i \(0.427595\pi\)
\(258\) −13.0136 −0.810189
\(259\) −3.93374 −0.244430
\(260\) 7.09837 0.440222
\(261\) 23.5425 1.45724
\(262\) 1.00000 0.0617802
\(263\) 18.2639 1.12620 0.563100 0.826389i \(-0.309609\pi\)
0.563100 + 0.826389i \(0.309609\pi\)
\(264\) −12.5481 −0.772281
\(265\) −38.2171 −2.34766
\(266\) −3.02996 −0.185779
\(267\) 12.9054 0.789795
\(268\) −6.71973 −0.410473
\(269\) −28.2283 −1.72111 −0.860555 0.509357i \(-0.829883\pi\)
−0.860555 + 0.509357i \(0.829883\pi\)
\(270\) 27.1718 1.65362
\(271\) −9.53661 −0.579308 −0.289654 0.957131i \(-0.593540\pi\)
−0.289654 + 0.957131i \(0.593540\pi\)
\(272\) 1.30388 0.0790591
\(273\) 4.59376 0.278027
\(274\) −19.6959 −1.18987
\(275\) −11.0195 −0.664499
\(276\) 3.03806 0.182870
\(277\) −29.1023 −1.74859 −0.874294 0.485396i \(-0.838675\pi\)
−0.874294 + 0.485396i \(0.838675\pi\)
\(278\) 19.7377 1.18379
\(279\) 41.0367 2.45680
\(280\) 1.63340 0.0976143
\(281\) 0.807882 0.0481942 0.0240971 0.999710i \(-0.492329\pi\)
0.0240971 + 0.999710i \(0.492329\pi\)
\(282\) 20.2730 1.20724
\(283\) 16.3162 0.969898 0.484949 0.874543i \(-0.338838\pi\)
0.484949 + 0.874543i \(0.338838\pi\)
\(284\) 11.4583 0.679924
\(285\) 43.2137 2.55976
\(286\) 10.5876 0.626060
\(287\) 0.187055 0.0110415
\(288\) −6.22984 −0.367097
\(289\) −15.2999 −0.899995
\(290\) −10.4644 −0.614492
\(291\) 29.2661 1.71561
\(292\) 5.20789 0.304769
\(293\) 6.07234 0.354750 0.177375 0.984143i \(-0.443239\pi\)
0.177375 + 0.984143i \(0.443239\pi\)
\(294\) −20.2094 −1.17864
\(295\) −18.2162 −1.06059
\(296\) −6.66887 −0.387620
\(297\) 40.5283 2.35169
\(298\) 3.89948 0.225891
\(299\) −2.56341 −0.148246
\(300\) −8.10545 −0.467968
\(301\) 2.52669 0.145636
\(302\) 1.69204 0.0973661
\(303\) −32.9600 −1.89350
\(304\) −5.13670 −0.294610
\(305\) −11.7996 −0.675642
\(306\) −8.12294 −0.464357
\(307\) 8.54528 0.487705 0.243852 0.969812i \(-0.421589\pi\)
0.243852 + 0.969812i \(0.421589\pi\)
\(308\) 2.43631 0.138822
\(309\) 9.67833 0.550581
\(310\) −18.2404 −1.03599
\(311\) 1.55722 0.0883020 0.0441510 0.999025i \(-0.485942\pi\)
0.0441510 + 0.999025i \(0.485942\pi\)
\(312\) 7.78782 0.440898
\(313\) 1.63197 0.0922446 0.0461223 0.998936i \(-0.485314\pi\)
0.0461223 + 0.998936i \(0.485314\pi\)
\(314\) 5.66849 0.319891
\(315\) −10.1758 −0.573342
\(316\) −4.85884 −0.273331
\(317\) 17.3202 0.972800 0.486400 0.873736i \(-0.338310\pi\)
0.486400 + 0.873736i \(0.338310\pi\)
\(318\) −41.9291 −2.35127
\(319\) −15.6083 −0.873898
\(320\) 2.76911 0.154798
\(321\) 8.44488 0.471348
\(322\) −0.589865 −0.0328719
\(323\) −6.69762 −0.372666
\(324\) 11.1214 0.617854
\(325\) 6.83910 0.379365
\(326\) −16.3791 −0.907154
\(327\) −14.0649 −0.777792
\(328\) 0.317115 0.0175097
\(329\) −3.93618 −0.217008
\(330\) −34.7470 −1.91276
\(331\) −2.99303 −0.164512 −0.0822559 0.996611i \(-0.526212\pi\)
−0.0822559 + 0.996611i \(0.526212\pi\)
\(332\) 5.44110 0.298619
\(333\) 41.5460 2.27671
\(334\) 12.7211 0.696067
\(335\) −18.6077 −1.01665
\(336\) 1.79205 0.0977642
\(337\) 10.7880 0.587660 0.293830 0.955858i \(-0.405070\pi\)
0.293830 + 0.955858i \(0.405070\pi\)
\(338\) 6.42891 0.349687
\(339\) 32.3655 1.75785
\(340\) 3.61057 0.195811
\(341\) −27.2067 −1.47333
\(342\) 32.0008 1.73041
\(343\) 8.05287 0.434814
\(344\) 4.28351 0.230951
\(345\) 8.41273 0.452926
\(346\) −4.48202 −0.240955
\(347\) 8.97975 0.482058 0.241029 0.970518i \(-0.422515\pi\)
0.241029 + 0.970518i \(0.422515\pi\)
\(348\) −11.4808 −0.615436
\(349\) −28.1230 −1.50539 −0.752696 0.658368i \(-0.771247\pi\)
−0.752696 + 0.658368i \(0.771247\pi\)
\(350\) 1.57374 0.0841199
\(351\) −25.1534 −1.34259
\(352\) 4.13029 0.220145
\(353\) −0.475681 −0.0253179 −0.0126590 0.999920i \(-0.504030\pi\)
−0.0126590 + 0.999920i \(0.504030\pi\)
\(354\) −19.9855 −1.06222
\(355\) 31.7292 1.68401
\(356\) −4.24789 −0.225138
\(357\) 2.33661 0.123666
\(358\) −8.90521 −0.470655
\(359\) 6.69582 0.353392 0.176696 0.984265i \(-0.443459\pi\)
0.176696 + 0.984265i \(0.443459\pi\)
\(360\) −17.2511 −0.909213
\(361\) 7.38572 0.388722
\(362\) −12.3782 −0.650585
\(363\) −18.4085 −0.966197
\(364\) −1.51207 −0.0792539
\(365\) 14.4212 0.754840
\(366\) −12.9456 −0.676679
\(367\) −35.7248 −1.86482 −0.932410 0.361402i \(-0.882298\pi\)
−0.932410 + 0.361402i \(0.882298\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −1.97557 −0.102844
\(370\) −18.4668 −0.960045
\(371\) 8.14087 0.422653
\(372\) −20.0121 −1.03758
\(373\) −14.9145 −0.772243 −0.386121 0.922448i \(-0.626185\pi\)
−0.386121 + 0.922448i \(0.626185\pi\)
\(374\) 5.38539 0.278472
\(375\) 19.6188 1.01311
\(376\) −6.67301 −0.344134
\(377\) 9.68711 0.498912
\(378\) −5.78802 −0.297704
\(379\) −30.8996 −1.58720 −0.793602 0.608437i \(-0.791797\pi\)
−0.793602 + 0.608437i \(0.791797\pi\)
\(380\) −14.2241 −0.729680
\(381\) −62.6740 −3.21088
\(382\) −17.1516 −0.877554
\(383\) −24.6470 −1.25940 −0.629701 0.776837i \(-0.716823\pi\)
−0.629701 + 0.776837i \(0.716823\pi\)
\(384\) 3.03806 0.155036
\(385\) 6.74642 0.343829
\(386\) 9.65340 0.491345
\(387\) −26.6855 −1.35650
\(388\) −9.63313 −0.489048
\(389\) −16.0040 −0.811433 −0.405717 0.913999i \(-0.632978\pi\)
−0.405717 + 0.913999i \(0.632978\pi\)
\(390\) 21.5653 1.09200
\(391\) −1.30388 −0.0659398
\(392\) 6.65206 0.335980
\(393\) 3.03806 0.153250
\(394\) −9.13171 −0.460049
\(395\) −13.4547 −0.676977
\(396\) −25.7310 −1.29303
\(397\) −10.6544 −0.534727 −0.267363 0.963596i \(-0.586152\pi\)
−0.267363 + 0.963596i \(0.586152\pi\)
\(398\) 2.74921 0.137805
\(399\) −9.20522 −0.460837
\(400\) 2.66796 0.133398
\(401\) −29.6320 −1.47975 −0.739876 0.672743i \(-0.765116\pi\)
−0.739876 + 0.672743i \(0.765116\pi\)
\(402\) −20.4150 −1.01821
\(403\) 16.8855 0.841127
\(404\) 10.8490 0.539759
\(405\) 30.7963 1.53028
\(406\) 2.22909 0.110628
\(407\) −27.5444 −1.36532
\(408\) 3.96126 0.196112
\(409\) 19.2010 0.949430 0.474715 0.880140i \(-0.342551\pi\)
0.474715 + 0.880140i \(0.342551\pi\)
\(410\) 0.878126 0.0433675
\(411\) −59.8373 −2.95156
\(412\) −3.18569 −0.156948
\(413\) 3.88035 0.190940
\(414\) 6.22984 0.306180
\(415\) 15.0670 0.739609
\(416\) −2.56341 −0.125682
\(417\) 59.9644 2.93647
\(418\) −21.2161 −1.03771
\(419\) −2.67260 −0.130565 −0.0652826 0.997867i \(-0.520795\pi\)
−0.0652826 + 0.997867i \(0.520795\pi\)
\(420\) 4.96238 0.242139
\(421\) −12.3364 −0.601239 −0.300619 0.953744i \(-0.597193\pi\)
−0.300619 + 0.953744i \(0.597193\pi\)
\(422\) 15.6704 0.762826
\(423\) 41.5718 2.02129
\(424\) 13.8012 0.670248
\(425\) 3.47869 0.168741
\(426\) 34.8110 1.68660
\(427\) 2.51350 0.121637
\(428\) −2.77969 −0.134361
\(429\) 32.1659 1.55299
\(430\) 11.8615 0.572012
\(431\) −13.4337 −0.647081 −0.323540 0.946214i \(-0.604873\pi\)
−0.323540 + 0.946214i \(0.604873\pi\)
\(432\) −9.81246 −0.472102
\(433\) −11.5891 −0.556938 −0.278469 0.960445i \(-0.589827\pi\)
−0.278469 + 0.960445i \(0.589827\pi\)
\(434\) 3.88551 0.186510
\(435\) −31.7916 −1.52429
\(436\) 4.62957 0.221716
\(437\) 5.13670 0.245722
\(438\) 15.8219 0.756000
\(439\) 31.6119 1.50875 0.754376 0.656442i \(-0.227939\pi\)
0.754376 + 0.656442i \(0.227939\pi\)
\(440\) 11.4372 0.545248
\(441\) −41.4412 −1.97339
\(442\) −3.34237 −0.158981
\(443\) 0.241028 0.0114516 0.00572578 0.999984i \(-0.498177\pi\)
0.00572578 + 0.999984i \(0.498177\pi\)
\(444\) −20.2605 −0.961519
\(445\) −11.7629 −0.557613
\(446\) −24.2771 −1.14956
\(447\) 11.8469 0.560338
\(448\) −0.589865 −0.0278685
\(449\) −7.92471 −0.373990 −0.186995 0.982361i \(-0.559875\pi\)
−0.186995 + 0.982361i \(0.559875\pi\)
\(450\) −16.6210 −0.783521
\(451\) 1.30978 0.0616750
\(452\) −10.6533 −0.501091
\(453\) 5.14054 0.241523
\(454\) 16.8590 0.791234
\(455\) −4.18708 −0.196293
\(456\) −15.6056 −0.730801
\(457\) −13.5867 −0.635561 −0.317780 0.948164i \(-0.602937\pi\)
−0.317780 + 0.948164i \(0.602937\pi\)
\(458\) −10.8728 −0.508054
\(459\) −12.7942 −0.597183
\(460\) −2.76911 −0.129110
\(461\) −19.8797 −0.925888 −0.462944 0.886388i \(-0.653207\pi\)
−0.462944 + 0.886388i \(0.653207\pi\)
\(462\) 7.40168 0.344357
\(463\) 29.5355 1.37263 0.686315 0.727304i \(-0.259227\pi\)
0.686315 + 0.727304i \(0.259227\pi\)
\(464\) 3.77899 0.175435
\(465\) −55.4156 −2.56984
\(466\) −4.89569 −0.226789
\(467\) 7.06845 0.327089 0.163544 0.986536i \(-0.447707\pi\)
0.163544 + 0.986536i \(0.447707\pi\)
\(468\) 15.9697 0.738197
\(469\) 3.96373 0.183028
\(470\) −18.4783 −0.852340
\(471\) 17.2212 0.793512
\(472\) 6.57837 0.302794
\(473\) 17.6921 0.813485
\(474\) −14.7615 −0.678017
\(475\) −13.7045 −0.628807
\(476\) −0.769111 −0.0352521
\(477\) −85.9795 −3.93673
\(478\) 18.8560 0.862456
\(479\) −29.8821 −1.36535 −0.682674 0.730723i \(-0.739183\pi\)
−0.682674 + 0.730723i \(0.739183\pi\)
\(480\) 8.41273 0.383987
\(481\) 17.0951 0.779469
\(482\) 0.473098 0.0215490
\(483\) −1.79205 −0.0815410
\(484\) 6.05929 0.275422
\(485\) −26.6752 −1.21126
\(486\) 4.35006 0.197323
\(487\) −28.4167 −1.28768 −0.643841 0.765159i \(-0.722660\pi\)
−0.643841 + 0.765159i \(0.722660\pi\)
\(488\) 4.26115 0.192893
\(489\) −49.7608 −2.25026
\(490\) 18.4203 0.832143
\(491\) 13.0876 0.590633 0.295317 0.955399i \(-0.404575\pi\)
0.295317 + 0.955399i \(0.404575\pi\)
\(492\) 0.963416 0.0434341
\(493\) 4.92733 0.221916
\(494\) 13.1675 0.592434
\(495\) −71.2520 −3.20254
\(496\) 6.58712 0.295770
\(497\) −6.75884 −0.303175
\(498\) 16.5304 0.740745
\(499\) 30.4548 1.36334 0.681671 0.731659i \(-0.261253\pi\)
0.681671 + 0.731659i \(0.261253\pi\)
\(500\) −6.45766 −0.288795
\(501\) 38.6475 1.72664
\(502\) 14.9105 0.665486
\(503\) −0.0897794 −0.00400306 −0.00200153 0.999998i \(-0.500637\pi\)
−0.00200153 + 0.999998i \(0.500637\pi\)
\(504\) 3.67476 0.163687
\(505\) 30.0421 1.33686
\(506\) −4.13029 −0.183614
\(507\) 19.5314 0.867422
\(508\) 20.6296 0.915289
\(509\) −16.0198 −0.710066 −0.355033 0.934854i \(-0.615530\pi\)
−0.355033 + 0.934854i \(0.615530\pi\)
\(510\) 10.9692 0.485723
\(511\) −3.07195 −0.135895
\(512\) −1.00000 −0.0441942
\(513\) 50.4037 2.22538
\(514\) −7.23043 −0.318921
\(515\) −8.82152 −0.388723
\(516\) 13.0136 0.572890
\(517\) −27.5615 −1.21215
\(518\) 3.93374 0.172838
\(519\) −13.6167 −0.597705
\(520\) −7.09837 −0.311284
\(521\) −13.5039 −0.591618 −0.295809 0.955247i \(-0.595589\pi\)
−0.295809 + 0.955247i \(0.595589\pi\)
\(522\) −23.5425 −1.03043
\(523\) −29.9911 −1.31142 −0.655711 0.755012i \(-0.727631\pi\)
−0.655711 + 0.755012i \(0.727631\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 4.78112 0.208665
\(526\) −18.2639 −0.796344
\(527\) 8.58878 0.374133
\(528\) 12.5481 0.546085
\(529\) 1.00000 0.0434783
\(530\) 38.2171 1.66005
\(531\) −40.9822 −1.77848
\(532\) 3.02996 0.131365
\(533\) −0.812897 −0.0352105
\(534\) −12.9054 −0.558469
\(535\) −7.69727 −0.332782
\(536\) 6.71973 0.290248
\(537\) −27.0546 −1.16749
\(538\) 28.2283 1.21701
\(539\) 27.4749 1.18343
\(540\) −27.1718 −1.16929
\(541\) −33.2494 −1.42950 −0.714752 0.699378i \(-0.753461\pi\)
−0.714752 + 0.699378i \(0.753461\pi\)
\(542\) 9.53661 0.409632
\(543\) −37.6059 −1.61382
\(544\) −1.30388 −0.0559032
\(545\) 12.8198 0.549139
\(546\) −4.59376 −0.196595
\(547\) −1.39779 −0.0597653 −0.0298826 0.999553i \(-0.509513\pi\)
−0.0298826 + 0.999553i \(0.509513\pi\)
\(548\) 19.6959 0.841366
\(549\) −26.5463 −1.13297
\(550\) 11.0195 0.469871
\(551\) −19.4115 −0.826959
\(552\) −3.03806 −0.129309
\(553\) 2.86606 0.121877
\(554\) 29.1023 1.23644
\(555\) −56.1034 −2.38146
\(556\) −19.7377 −0.837065
\(557\) 6.23559 0.264210 0.132105 0.991236i \(-0.457826\pi\)
0.132105 + 0.991236i \(0.457826\pi\)
\(558\) −41.0367 −1.73722
\(559\) −10.9804 −0.464421
\(560\) −1.63340 −0.0690238
\(561\) 16.3611 0.690768
\(562\) −0.807882 −0.0340784
\(563\) 6.19742 0.261190 0.130595 0.991436i \(-0.458311\pi\)
0.130595 + 0.991436i \(0.458311\pi\)
\(564\) −20.2730 −0.853649
\(565\) −29.5003 −1.24108
\(566\) −16.3162 −0.685821
\(567\) −6.56010 −0.275498
\(568\) −11.4583 −0.480779
\(569\) −36.3951 −1.52576 −0.762882 0.646538i \(-0.776216\pi\)
−0.762882 + 0.646538i \(0.776216\pi\)
\(570\) −43.2137 −1.81002
\(571\) −30.6498 −1.28265 −0.641326 0.767268i \(-0.721616\pi\)
−0.641326 + 0.767268i \(0.721616\pi\)
\(572\) −10.5876 −0.442692
\(573\) −52.1078 −2.17683
\(574\) −0.187055 −0.00780753
\(575\) −2.66796 −0.111262
\(576\) 6.22984 0.259577
\(577\) 10.7902 0.449201 0.224600 0.974451i \(-0.427892\pi\)
0.224600 + 0.974451i \(0.427892\pi\)
\(578\) 15.2999 0.636392
\(579\) 29.3277 1.21882
\(580\) 10.4644 0.434512
\(581\) −3.20951 −0.133153
\(582\) −29.2661 −1.21312
\(583\) 57.0031 2.36083
\(584\) −5.20789 −0.215504
\(585\) 44.2217 1.82834
\(586\) −6.07234 −0.250846
\(587\) −12.9731 −0.535456 −0.267728 0.963495i \(-0.586273\pi\)
−0.267728 + 0.963495i \(0.586273\pi\)
\(588\) 20.2094 0.833421
\(589\) −33.8361 −1.39419
\(590\) 18.2162 0.749950
\(591\) −27.7427 −1.14118
\(592\) 6.66887 0.274089
\(593\) 32.6182 1.33947 0.669735 0.742600i \(-0.266408\pi\)
0.669735 + 0.742600i \(0.266408\pi\)
\(594\) −40.5283 −1.66290
\(595\) −2.12975 −0.0873113
\(596\) −3.89948 −0.159729
\(597\) 8.35228 0.341836
\(598\) 2.56341 0.104826
\(599\) 38.8390 1.58692 0.793459 0.608624i \(-0.208278\pi\)
0.793459 + 0.608624i \(0.208278\pi\)
\(600\) 8.10545 0.330903
\(601\) −20.7255 −0.845411 −0.422705 0.906267i \(-0.638920\pi\)
−0.422705 + 0.906267i \(0.638920\pi\)
\(602\) −2.52669 −0.102980
\(603\) −41.8628 −1.70479
\(604\) −1.69204 −0.0688483
\(605\) 16.7788 0.682157
\(606\) 32.9600 1.33891
\(607\) 9.22426 0.374401 0.187201 0.982322i \(-0.440059\pi\)
0.187201 + 0.982322i \(0.440059\pi\)
\(608\) 5.13670 0.208321
\(609\) 6.77213 0.274420
\(610\) 11.7996 0.477751
\(611\) 17.1057 0.692022
\(612\) 8.12294 0.328350
\(613\) −17.7051 −0.715101 −0.357550 0.933894i \(-0.616388\pi\)
−0.357550 + 0.933894i \(0.616388\pi\)
\(614\) −8.54528 −0.344859
\(615\) 2.66780 0.107576
\(616\) −2.43631 −0.0981619
\(617\) −16.3562 −0.658477 −0.329238 0.944247i \(-0.606792\pi\)
−0.329238 + 0.944247i \(0.606792\pi\)
\(618\) −9.67833 −0.389320
\(619\) −21.1415 −0.849749 −0.424875 0.905252i \(-0.639682\pi\)
−0.424875 + 0.905252i \(0.639682\pi\)
\(620\) 18.2404 0.732554
\(621\) 9.81246 0.393760
\(622\) −1.55722 −0.0624390
\(623\) 2.50568 0.100388
\(624\) −7.78782 −0.311762
\(625\) −31.2218 −1.24887
\(626\) −1.63197 −0.0652268
\(627\) −64.4558 −2.57412
\(628\) −5.66849 −0.226197
\(629\) 8.69538 0.346708
\(630\) 10.1758 0.405414
\(631\) 26.8050 1.06709 0.533546 0.845771i \(-0.320859\pi\)
0.533546 + 0.845771i \(0.320859\pi\)
\(632\) 4.85884 0.193274
\(633\) 47.6078 1.89224
\(634\) −17.3202 −0.687873
\(635\) 57.1255 2.26696
\(636\) 41.9291 1.66260
\(637\) −17.0520 −0.675624
\(638\) 15.6083 0.617939
\(639\) 71.3832 2.82388
\(640\) −2.76911 −0.109459
\(641\) −19.8044 −0.782227 −0.391114 0.920342i \(-0.627910\pi\)
−0.391114 + 0.920342i \(0.627910\pi\)
\(642\) −8.44488 −0.333293
\(643\) −4.95085 −0.195242 −0.0976211 0.995224i \(-0.531123\pi\)
−0.0976211 + 0.995224i \(0.531123\pi\)
\(644\) 0.589865 0.0232439
\(645\) 36.0360 1.41892
\(646\) 6.69762 0.263514
\(647\) −48.6906 −1.91423 −0.957113 0.289713i \(-0.906440\pi\)
−0.957113 + 0.289713i \(0.906440\pi\)
\(648\) −11.1214 −0.436888
\(649\) 27.1706 1.06654
\(650\) −6.83910 −0.268251
\(651\) 11.8044 0.462652
\(652\) 16.3791 0.641455
\(653\) 36.4873 1.42786 0.713929 0.700218i \(-0.246914\pi\)
0.713929 + 0.700218i \(0.246914\pi\)
\(654\) 14.0649 0.549982
\(655\) −2.76911 −0.108198
\(656\) −0.317115 −0.0123813
\(657\) 32.4443 1.26577
\(658\) 3.93618 0.153448
\(659\) −13.2663 −0.516782 −0.258391 0.966040i \(-0.583192\pi\)
−0.258391 + 0.966040i \(0.583192\pi\)
\(660\) 34.7470 1.35253
\(661\) 34.1640 1.32882 0.664412 0.747367i \(-0.268682\pi\)
0.664412 + 0.747367i \(0.268682\pi\)
\(662\) 2.99303 0.116327
\(663\) −10.1543 −0.394362
\(664\) −5.44110 −0.211156
\(665\) 8.39029 0.325362
\(666\) −41.5460 −1.60987
\(667\) −3.77899 −0.146323
\(668\) −12.7211 −0.492194
\(669\) −73.7555 −2.85155
\(670\) 18.6077 0.718877
\(671\) 17.5998 0.679432
\(672\) −1.79205 −0.0691298
\(673\) −35.0194 −1.34990 −0.674950 0.737863i \(-0.735835\pi\)
−0.674950 + 0.737863i \(0.735835\pi\)
\(674\) −10.7880 −0.415538
\(675\) −26.1793 −1.00764
\(676\) −6.42891 −0.247266
\(677\) 41.6392 1.60033 0.800163 0.599783i \(-0.204746\pi\)
0.800163 + 0.599783i \(0.204746\pi\)
\(678\) −32.3655 −1.24299
\(679\) 5.68224 0.218065
\(680\) −3.61057 −0.138459
\(681\) 51.2189 1.96271
\(682\) 27.2067 1.04180
\(683\) 43.2998 1.65682 0.828411 0.560121i \(-0.189245\pi\)
0.828411 + 0.560121i \(0.189245\pi\)
\(684\) −32.0008 −1.22358
\(685\) 54.5400 2.08387
\(686\) −8.05287 −0.307460
\(687\) −33.0324 −1.26026
\(688\) −4.28351 −0.163307
\(689\) −35.3783 −1.34781
\(690\) −8.41273 −0.320267
\(691\) −12.5483 −0.477361 −0.238680 0.971098i \(-0.576715\pi\)
−0.238680 + 0.971098i \(0.576715\pi\)
\(692\) 4.48202 0.170381
\(693\) 15.1778 0.576558
\(694\) −8.97975 −0.340867
\(695\) −54.6558 −2.07321
\(696\) 11.4808 0.435179
\(697\) −0.413479 −0.0156616
\(698\) 28.1230 1.06447
\(699\) −14.8734 −0.562565
\(700\) −1.57374 −0.0594817
\(701\) −8.19024 −0.309341 −0.154671 0.987966i \(-0.549432\pi\)
−0.154671 + 0.987966i \(0.549432\pi\)
\(702\) 25.1534 0.949353
\(703\) −34.2560 −1.29199
\(704\) −4.13029 −0.155666
\(705\) −56.1383 −2.11429
\(706\) 0.475681 0.0179025
\(707\) −6.39945 −0.240676
\(708\) 19.9855 0.751102
\(709\) −4.00330 −0.150347 −0.0751736 0.997170i \(-0.523951\pi\)
−0.0751736 + 0.997170i \(0.523951\pi\)
\(710\) −31.7292 −1.19078
\(711\) −30.2698 −1.13521
\(712\) 4.24789 0.159196
\(713\) −6.58712 −0.246689
\(714\) −2.33661 −0.0874454
\(715\) −29.3183 −1.09644
\(716\) 8.90521 0.332803
\(717\) 57.2859 2.13938
\(718\) −6.69582 −0.249886
\(719\) −27.0042 −1.00709 −0.503543 0.863970i \(-0.667970\pi\)
−0.503543 + 0.863970i \(0.667970\pi\)
\(720\) 17.2511 0.642910
\(721\) 1.87913 0.0699823
\(722\) −7.38572 −0.274868
\(723\) 1.43730 0.0534538
\(724\) 12.3782 0.460033
\(725\) 10.0822 0.374444
\(726\) 18.4085 0.683204
\(727\) −47.6680 −1.76791 −0.883955 0.467572i \(-0.845129\pi\)
−0.883955 + 0.467572i \(0.845129\pi\)
\(728\) 1.51207 0.0560410
\(729\) −20.1483 −0.746235
\(730\) −14.4212 −0.533753
\(731\) −5.58516 −0.206575
\(732\) 12.9456 0.478485
\(733\) 24.9077 0.919988 0.459994 0.887922i \(-0.347852\pi\)
0.459994 + 0.887922i \(0.347852\pi\)
\(734\) 35.7248 1.31863
\(735\) 55.9620 2.06419
\(736\) 1.00000 0.0368605
\(737\) 27.7544 1.02235
\(738\) 1.97557 0.0727219
\(739\) −41.7076 −1.53424 −0.767120 0.641503i \(-0.778311\pi\)
−0.767120 + 0.641503i \(0.778311\pi\)
\(740\) 18.4668 0.678854
\(741\) 40.0037 1.46957
\(742\) −8.14087 −0.298861
\(743\) 15.4330 0.566184 0.283092 0.959093i \(-0.408640\pi\)
0.283092 + 0.959093i \(0.408640\pi\)
\(744\) 20.0121 0.733679
\(745\) −10.7981 −0.395611
\(746\) 14.9145 0.546058
\(747\) 33.8972 1.24023
\(748\) −5.38539 −0.196909
\(749\) 1.63964 0.0599113
\(750\) −19.6188 −0.716377
\(751\) 14.5140 0.529624 0.264812 0.964300i \(-0.414690\pi\)
0.264812 + 0.964300i \(0.414690\pi\)
\(752\) 6.67301 0.243340
\(753\) 45.2989 1.65079
\(754\) −9.68711 −0.352784
\(755\) −4.68545 −0.170521
\(756\) 5.78802 0.210508
\(757\) −42.5985 −1.54827 −0.774135 0.633021i \(-0.781815\pi\)
−0.774135 + 0.633021i \(0.781815\pi\)
\(758\) 30.8996 1.12232
\(759\) −12.5481 −0.455467
\(760\) 14.2241 0.515962
\(761\) −29.8419 −1.08177 −0.540884 0.841097i \(-0.681910\pi\)
−0.540884 + 0.841097i \(0.681910\pi\)
\(762\) 62.6740 2.27044
\(763\) −2.73082 −0.0988624
\(764\) 17.1516 0.620524
\(765\) 22.4933 0.813247
\(766\) 24.6470 0.890532
\(767\) −16.8631 −0.608891
\(768\) −3.03806 −0.109627
\(769\) −24.5136 −0.883983 −0.441991 0.897019i \(-0.645728\pi\)
−0.441991 + 0.897019i \(0.645728\pi\)
\(770\) −6.74642 −0.243124
\(771\) −21.9665 −0.791105
\(772\) −9.65340 −0.347433
\(773\) 0.495664 0.0178278 0.00891390 0.999960i \(-0.497163\pi\)
0.00891390 + 0.999960i \(0.497163\pi\)
\(774\) 26.6855 0.959192
\(775\) 17.5742 0.631283
\(776\) 9.63313 0.345809
\(777\) 11.9509 0.428738
\(778\) 16.0040 0.573770
\(779\) 1.62893 0.0583623
\(780\) −21.5653 −0.772162
\(781\) −47.3260 −1.69346
\(782\) 1.30388 0.0466265
\(783\) −37.0812 −1.32517
\(784\) −6.65206 −0.237574
\(785\) −15.6967 −0.560238
\(786\) −3.03806 −0.108364
\(787\) −8.46695 −0.301814 −0.150907 0.988548i \(-0.548219\pi\)
−0.150907 + 0.988548i \(0.548219\pi\)
\(788\) 9.13171 0.325304
\(789\) −55.4869 −1.97539
\(790\) 13.4547 0.478695
\(791\) 6.28403 0.223434
\(792\) 25.7310 0.914312
\(793\) −10.9231 −0.387890
\(794\) 10.6544 0.378109
\(795\) 116.106 4.11786
\(796\) −2.74921 −0.0974432
\(797\) −51.4113 −1.82108 −0.910540 0.413420i \(-0.864334\pi\)
−0.910540 + 0.413420i \(0.864334\pi\)
\(798\) 9.20522 0.325861
\(799\) 8.70078 0.307812
\(800\) −2.66796 −0.0943268
\(801\) −26.4637 −0.935047
\(802\) 29.6320 1.04634
\(803\) −21.5101 −0.759074
\(804\) 20.4150 0.719981
\(805\) 1.63340 0.0575698
\(806\) −16.8855 −0.594767
\(807\) 85.7594 3.01887
\(808\) −10.8490 −0.381667
\(809\) −2.24294 −0.0788574 −0.0394287 0.999222i \(-0.512554\pi\)
−0.0394287 + 0.999222i \(0.512554\pi\)
\(810\) −30.7963 −1.08207
\(811\) −23.1867 −0.814194 −0.407097 0.913385i \(-0.633459\pi\)
−0.407097 + 0.913385i \(0.633459\pi\)
\(812\) −2.22909 −0.0782258
\(813\) 28.9728 1.01612
\(814\) 27.5444 0.965430
\(815\) 45.3555 1.58873
\(816\) −3.96126 −0.138672
\(817\) 22.0031 0.769791
\(818\) −19.2010 −0.671348
\(819\) −9.41994 −0.329159
\(820\) −0.878126 −0.0306655
\(821\) 7.94110 0.277146 0.138573 0.990352i \(-0.455748\pi\)
0.138573 + 0.990352i \(0.455748\pi\)
\(822\) 59.8373 2.08707
\(823\) −37.1219 −1.29399 −0.646993 0.762496i \(-0.723974\pi\)
−0.646993 + 0.762496i \(0.723974\pi\)
\(824\) 3.18569 0.110979
\(825\) 33.4778 1.16555
\(826\) −3.88035 −0.135015
\(827\) −17.6195 −0.612689 −0.306345 0.951921i \(-0.599106\pi\)
−0.306345 + 0.951921i \(0.599106\pi\)
\(828\) −6.22984 −0.216502
\(829\) 14.1377 0.491021 0.245511 0.969394i \(-0.421044\pi\)
0.245511 + 0.969394i \(0.421044\pi\)
\(830\) −15.0670 −0.522983
\(831\) 88.4147 3.06707
\(832\) 2.56341 0.0888704
\(833\) −8.67346 −0.300518
\(834\) −59.9644 −2.07640
\(835\) −35.2261 −1.21905
\(836\) 21.2161 0.733773
\(837\) −64.6358 −2.23414
\(838\) 2.67260 0.0923236
\(839\) −56.8226 −1.96173 −0.980867 0.194680i \(-0.937633\pi\)
−0.980867 + 0.194680i \(0.937633\pi\)
\(840\) −4.96238 −0.171218
\(841\) −14.7193 −0.507560
\(842\) 12.3364 0.425140
\(843\) −2.45440 −0.0845339
\(844\) −15.6704 −0.539399
\(845\) −17.8023 −0.612419
\(846\) −41.5718 −1.42927
\(847\) −3.57416 −0.122810
\(848\) −13.8012 −0.473937
\(849\) −49.5697 −1.70123
\(850\) −3.47869 −0.119318
\(851\) −6.66887 −0.228606
\(852\) −34.8110 −1.19260
\(853\) 24.3191 0.832669 0.416334 0.909212i \(-0.363315\pi\)
0.416334 + 0.909212i \(0.363315\pi\)
\(854\) −2.51350 −0.0860103
\(855\) −88.6138 −3.03053
\(856\) 2.77969 0.0950079
\(857\) 41.4078 1.41446 0.707231 0.706982i \(-0.249944\pi\)
0.707231 + 0.706982i \(0.249944\pi\)
\(858\) −32.1659 −1.09813
\(859\) −4.90502 −0.167357 −0.0836786 0.996493i \(-0.526667\pi\)
−0.0836786 + 0.996493i \(0.526667\pi\)
\(860\) −11.8615 −0.404474
\(861\) −0.568285 −0.0193671
\(862\) 13.4337 0.457555
\(863\) 11.6332 0.395999 0.197999 0.980202i \(-0.436556\pi\)
0.197999 + 0.980202i \(0.436556\pi\)
\(864\) 9.81246 0.333827
\(865\) 12.4112 0.421994
\(866\) 11.5891 0.393815
\(867\) 46.4821 1.57862
\(868\) −3.88551 −0.131883
\(869\) 20.0684 0.680774
\(870\) 31.7916 1.07784
\(871\) −17.2255 −0.583662
\(872\) −4.62957 −0.156777
\(873\) −60.0128 −2.03113
\(874\) −5.13670 −0.173752
\(875\) 3.80915 0.128773
\(876\) −15.8219 −0.534572
\(877\) −28.2073 −0.952492 −0.476246 0.879312i \(-0.658003\pi\)
−0.476246 + 0.879312i \(0.658003\pi\)
\(878\) −31.6119 −1.06685
\(879\) −18.4482 −0.622241
\(880\) −11.4372 −0.385549
\(881\) 20.1941 0.680358 0.340179 0.940361i \(-0.389512\pi\)
0.340179 + 0.940361i \(0.389512\pi\)
\(882\) 41.4412 1.39540
\(883\) 5.53717 0.186341 0.0931703 0.995650i \(-0.470300\pi\)
0.0931703 + 0.995650i \(0.470300\pi\)
\(884\) 3.34237 0.112416
\(885\) 55.3421 1.86030
\(886\) −0.241028 −0.00809748
\(887\) 27.1557 0.911799 0.455900 0.890031i \(-0.349318\pi\)
0.455900 + 0.890031i \(0.349318\pi\)
\(888\) 20.2605 0.679897
\(889\) −12.1687 −0.408124
\(890\) 11.7629 0.394292
\(891\) −45.9345 −1.53886
\(892\) 24.2771 0.812859
\(893\) −34.2773 −1.14705
\(894\) −11.8469 −0.396219
\(895\) 24.6595 0.824276
\(896\) 0.589865 0.0197060
\(897\) 7.78782 0.260028
\(898\) 7.92471 0.264451
\(899\) 24.8926 0.830216
\(900\) 16.6210 0.554033
\(901\) −17.9951 −0.599504
\(902\) −1.30978 −0.0436108
\(903\) −7.67625 −0.255450
\(904\) 10.6533 0.354325
\(905\) 34.2767 1.13939
\(906\) −5.14054 −0.170783
\(907\) −5.61529 −0.186453 −0.0932264 0.995645i \(-0.529718\pi\)
−0.0932264 + 0.995645i \(0.529718\pi\)
\(908\) −16.8590 −0.559487
\(909\) 67.5876 2.24174
\(910\) 4.18708 0.138800
\(911\) 51.9923 1.72258 0.861291 0.508111i \(-0.169656\pi\)
0.861291 + 0.508111i \(0.169656\pi\)
\(912\) 15.6056 0.516754
\(913\) −22.4733 −0.743758
\(914\) 13.5867 0.449409
\(915\) 35.8479 1.18509
\(916\) 10.8728 0.359249
\(917\) 0.589865 0.0194791
\(918\) 12.7942 0.422272
\(919\) −44.7524 −1.47624 −0.738122 0.674667i \(-0.764287\pi\)
−0.738122 + 0.674667i \(0.764287\pi\)
\(920\) 2.76911 0.0912948
\(921\) −25.9611 −0.855448
\(922\) 19.8797 0.654702
\(923\) 29.3723 0.966801
\(924\) −7.40168 −0.243497
\(925\) 17.7923 0.585008
\(926\) −29.5355 −0.970597
\(927\) −19.8463 −0.651839
\(928\) −3.77899 −0.124051
\(929\) −10.8104 −0.354679 −0.177340 0.984150i \(-0.556749\pi\)
−0.177340 + 0.984150i \(0.556749\pi\)
\(930\) 55.4156 1.81715
\(931\) 34.1697 1.11987
\(932\) 4.89569 0.160364
\(933\) −4.73095 −0.154884
\(934\) −7.06845 −0.231287
\(935\) −14.9127 −0.487698
\(936\) −15.9697 −0.521984
\(937\) −43.4874 −1.42067 −0.710336 0.703863i \(-0.751457\pi\)
−0.710336 + 0.703863i \(0.751457\pi\)
\(938\) −3.96373 −0.129421
\(939\) −4.95804 −0.161800
\(940\) 18.4783 0.602696
\(941\) 8.68636 0.283167 0.141584 0.989926i \(-0.454781\pi\)
0.141584 + 0.989926i \(0.454781\pi\)
\(942\) −17.2212 −0.561098
\(943\) 0.317115 0.0103267
\(944\) −6.57837 −0.214108
\(945\) 16.0277 0.521380
\(946\) −17.6921 −0.575220
\(947\) 56.3932 1.83253 0.916267 0.400569i \(-0.131187\pi\)
0.916267 + 0.400569i \(0.131187\pi\)
\(948\) 14.7615 0.479430
\(949\) 13.3500 0.433358
\(950\) 13.7045 0.444634
\(951\) −52.6199 −1.70632
\(952\) 0.769111 0.0249270
\(953\) 8.97819 0.290832 0.145416 0.989371i \(-0.453548\pi\)
0.145416 + 0.989371i \(0.453548\pi\)
\(954\) 85.9795 2.78369
\(955\) 47.4947 1.53689
\(956\) −18.8560 −0.609848
\(957\) 47.4191 1.53284
\(958\) 29.8821 0.965447
\(959\) −11.6179 −0.375162
\(960\) −8.41273 −0.271520
\(961\) 12.3901 0.399680
\(962\) −17.0951 −0.551168
\(963\) −17.3170 −0.558034
\(964\) −0.473098 −0.0152375
\(965\) −26.7313 −0.860511
\(966\) 1.79205 0.0576582
\(967\) 39.7055 1.27684 0.638422 0.769686i \(-0.279587\pi\)
0.638422 + 0.769686i \(0.279587\pi\)
\(968\) −6.05929 −0.194753
\(969\) 20.3478 0.653666
\(970\) 26.6752 0.856488
\(971\) 20.6915 0.664021 0.332011 0.943276i \(-0.392273\pi\)
0.332011 + 0.943276i \(0.392273\pi\)
\(972\) −4.35006 −0.139528
\(973\) 11.6426 0.373244
\(974\) 28.4167 0.910529
\(975\) −20.7776 −0.665416
\(976\) −4.26115 −0.136396
\(977\) 10.6967 0.342219 0.171109 0.985252i \(-0.445265\pi\)
0.171109 + 0.985252i \(0.445265\pi\)
\(978\) 49.7608 1.59117
\(979\) 17.5450 0.560741
\(980\) −18.4203 −0.588414
\(981\) 28.8415 0.920837
\(982\) −13.0876 −0.417641
\(983\) −0.589921 −0.0188155 −0.00940777 0.999956i \(-0.502995\pi\)
−0.00940777 + 0.999956i \(0.502995\pi\)
\(984\) −0.963416 −0.0307126
\(985\) 25.2867 0.805701
\(986\) −4.92733 −0.156918
\(987\) 11.9584 0.380639
\(988\) −13.1675 −0.418914
\(989\) 4.28351 0.136208
\(990\) 71.2520 2.26454
\(991\) 43.9059 1.39472 0.697359 0.716722i \(-0.254359\pi\)
0.697359 + 0.716722i \(0.254359\pi\)
\(992\) −6.58712 −0.209141
\(993\) 9.09301 0.288558
\(994\) 6.75884 0.214377
\(995\) −7.61286 −0.241344
\(996\) −16.5304 −0.523786
\(997\) −44.6498 −1.41407 −0.707036 0.707178i \(-0.749968\pi\)
−0.707036 + 0.707178i \(0.749968\pi\)
\(998\) −30.4548 −0.964029
\(999\) −65.4380 −2.07037
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 \(a_p\))