Properties

Label 6023.2.a.b.1.15
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.19313 q^{2}\) \(+1.00492 q^{3}\) \(+2.80981 q^{4}\) \(-2.58247 q^{5}\) \(-2.20392 q^{6}\) \(-2.47276 q^{7}\) \(-1.77602 q^{8}\) \(-1.99014 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.19313 q^{2}\) \(+1.00492 q^{3}\) \(+2.80981 q^{4}\) \(-2.58247 q^{5}\) \(-2.20392 q^{6}\) \(-2.47276 q^{7}\) \(-1.77602 q^{8}\) \(-1.99014 q^{9}\) \(+5.66370 q^{10}\) \(-2.59151 q^{11}\) \(+2.82363 q^{12}\) \(+6.65116 q^{13}\) \(+5.42308 q^{14}\) \(-2.59518 q^{15}\) \(-1.72459 q^{16}\) \(-2.10407 q^{17}\) \(+4.36462 q^{18}\) \(-1.00000 q^{19}\) \(-7.25626 q^{20}\) \(-2.48493 q^{21}\) \(+5.68351 q^{22}\) \(+7.81695 q^{23}\) \(-1.78475 q^{24}\) \(+1.66918 q^{25}\) \(-14.5868 q^{26}\) \(-5.01469 q^{27}\) \(-6.94799 q^{28}\) \(+0.305456 q^{29}\) \(+5.69156 q^{30}\) \(+0.378717 q^{31}\) \(+7.33428 q^{32}\) \(-2.60426 q^{33}\) \(+4.61450 q^{34}\) \(+6.38585 q^{35}\) \(-5.59191 q^{36}\) \(-6.35687 q^{37}\) \(+2.19313 q^{38}\) \(+6.68388 q^{39}\) \(+4.58652 q^{40}\) \(+10.4112 q^{41}\) \(+5.44976 q^{42}\) \(-3.77454 q^{43}\) \(-7.28165 q^{44}\) \(+5.13948 q^{45}\) \(-17.1436 q^{46}\) \(-1.95564 q^{47}\) \(-1.73307 q^{48}\) \(-0.885445 q^{49}\) \(-3.66072 q^{50}\) \(-2.11442 q^{51}\) \(+18.6885 q^{52}\) \(+5.54690 q^{53}\) \(+10.9978 q^{54}\) \(+6.69250 q^{55}\) \(+4.39167 q^{56}\) \(-1.00492 q^{57}\) \(-0.669904 q^{58}\) \(-0.917704 q^{59}\) \(-7.29196 q^{60}\) \(-14.4869 q^{61}\) \(-0.830574 q^{62}\) \(+4.92114 q^{63}\) \(-12.6358 q^{64}\) \(-17.1764 q^{65}\) \(+5.71147 q^{66}\) \(+4.25458 q^{67}\) \(-5.91204 q^{68}\) \(+7.85540 q^{69}\) \(-14.0050 q^{70}\) \(+2.92723 q^{71}\) \(+3.53452 q^{72}\) \(+11.6122 q^{73}\) \(+13.9414 q^{74}\) \(+1.67739 q^{75}\) \(-2.80981 q^{76}\) \(+6.40818 q^{77}\) \(-14.6586 q^{78}\) \(+4.71348 q^{79}\) \(+4.45370 q^{80}\) \(+0.931056 q^{81}\) \(-22.8331 q^{82}\) \(+8.89777 q^{83}\) \(-6.98217 q^{84}\) \(+5.43371 q^{85}\) \(+8.27805 q^{86}\) \(+0.306959 q^{87}\) \(+4.60256 q^{88}\) \(-7.43168 q^{89}\) \(-11.2715 q^{90}\) \(-16.4467 q^{91}\) \(+21.9641 q^{92}\) \(+0.380580 q^{93}\) \(+4.28897 q^{94}\) \(+2.58247 q^{95}\) \(+7.37036 q^{96}\) \(+10.0681 q^{97}\) \(+1.94189 q^{98}\) \(+5.15746 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.19313 −1.55078 −0.775388 0.631485i \(-0.782446\pi\)
−0.775388 + 0.631485i \(0.782446\pi\)
\(3\) 1.00492 0.580191 0.290095 0.956998i \(-0.406313\pi\)
0.290095 + 0.956998i \(0.406313\pi\)
\(4\) 2.80981 1.40491
\(5\) −2.58247 −1.15492 −0.577459 0.816420i \(-0.695956\pi\)
−0.577459 + 0.816420i \(0.695956\pi\)
\(6\) −2.20392 −0.899745
\(7\) −2.47276 −0.934616 −0.467308 0.884094i \(-0.654776\pi\)
−0.467308 + 0.884094i \(0.654776\pi\)
\(8\) −1.77602 −0.627917
\(9\) −1.99014 −0.663379
\(10\) 5.66370 1.79102
\(11\) −2.59151 −0.781369 −0.390685 0.920525i \(-0.627762\pi\)
−0.390685 + 0.920525i \(0.627762\pi\)
\(12\) 2.82363 0.815113
\(13\) 6.65116 1.84470 0.922350 0.386356i \(-0.126266\pi\)
0.922350 + 0.386356i \(0.126266\pi\)
\(14\) 5.42308 1.44938
\(15\) −2.59518 −0.670072
\(16\) −1.72459 −0.431147
\(17\) −2.10407 −0.510312 −0.255156 0.966900i \(-0.582127\pi\)
−0.255156 + 0.966900i \(0.582127\pi\)
\(18\) 4.36462 1.02875
\(19\) −1.00000 −0.229416
\(20\) −7.25626 −1.62255
\(21\) −2.48493 −0.542256
\(22\) 5.68351 1.21173
\(23\) 7.81695 1.62995 0.814973 0.579499i \(-0.196752\pi\)
0.814973 + 0.579499i \(0.196752\pi\)
\(24\) −1.78475 −0.364311
\(25\) 1.66918 0.333835
\(26\) −14.5868 −2.86071
\(27\) −5.01469 −0.965077
\(28\) −6.94799 −1.31305
\(29\) 0.305456 0.0567218 0.0283609 0.999598i \(-0.490971\pi\)
0.0283609 + 0.999598i \(0.490971\pi\)
\(30\) 5.69156 1.03913
\(31\) 0.378717 0.0680195 0.0340098 0.999422i \(-0.489172\pi\)
0.0340098 + 0.999422i \(0.489172\pi\)
\(32\) 7.33428 1.29653
\(33\) −2.60426 −0.453343
\(34\) 4.61450 0.791380
\(35\) 6.38585 1.07941
\(36\) −5.59191 −0.931984
\(37\) −6.35687 −1.04506 −0.522532 0.852620i \(-0.675012\pi\)
−0.522532 + 0.852620i \(0.675012\pi\)
\(38\) 2.19313 0.355772
\(39\) 6.68388 1.07028
\(40\) 4.58652 0.725192
\(41\) 10.4112 1.62596 0.812979 0.582293i \(-0.197844\pi\)
0.812979 + 0.582293i \(0.197844\pi\)
\(42\) 5.44976 0.840917
\(43\) −3.77454 −0.575612 −0.287806 0.957689i \(-0.592926\pi\)
−0.287806 + 0.957689i \(0.592926\pi\)
\(44\) −7.28165 −1.09775
\(45\) 5.13948 0.766148
\(46\) −17.1436 −2.52768
\(47\) −1.95564 −0.285260 −0.142630 0.989776i \(-0.545556\pi\)
−0.142630 + 0.989776i \(0.545556\pi\)
\(48\) −1.73307 −0.250147
\(49\) −0.885445 −0.126492
\(50\) −3.66072 −0.517703
\(51\) −2.11442 −0.296078
\(52\) 18.6885 2.59163
\(53\) 5.54690 0.761925 0.380963 0.924590i \(-0.375593\pi\)
0.380963 + 0.924590i \(0.375593\pi\)
\(54\) 10.9978 1.49662
\(55\) 6.69250 0.902417
\(56\) 4.39167 0.586861
\(57\) −1.00492 −0.133105
\(58\) −0.669904 −0.0879628
\(59\) −0.917704 −0.119475 −0.0597375 0.998214i \(-0.519026\pi\)
−0.0597375 + 0.998214i \(0.519026\pi\)
\(60\) −7.29196 −0.941388
\(61\) −14.4869 −1.85486 −0.927431 0.373995i \(-0.877988\pi\)
−0.927431 + 0.373995i \(0.877988\pi\)
\(62\) −0.830574 −0.105483
\(63\) 4.92114 0.620005
\(64\) −12.6358 −1.57948
\(65\) −17.1764 −2.13048
\(66\) 5.71147 0.703033
\(67\) 4.25458 0.519780 0.259890 0.965638i \(-0.416314\pi\)
0.259890 + 0.965638i \(0.416314\pi\)
\(68\) −5.91204 −0.716940
\(69\) 7.85540 0.945679
\(70\) −14.0050 −1.67392
\(71\) 2.92723 0.347398 0.173699 0.984799i \(-0.444428\pi\)
0.173699 + 0.984799i \(0.444428\pi\)
\(72\) 3.53452 0.416547
\(73\) 11.6122 1.35910 0.679551 0.733629i \(-0.262175\pi\)
0.679551 + 0.733629i \(0.262175\pi\)
\(74\) 13.9414 1.62066
\(75\) 1.67739 0.193688
\(76\) −2.80981 −0.322307
\(77\) 6.40818 0.730280
\(78\) −14.6586 −1.65976
\(79\) 4.71348 0.530308 0.265154 0.964206i \(-0.414577\pi\)
0.265154 + 0.964206i \(0.414577\pi\)
\(80\) 4.45370 0.497939
\(81\) 0.931056 0.103451
\(82\) −22.8331 −2.52150
\(83\) 8.89777 0.976657 0.488328 0.872660i \(-0.337607\pi\)
0.488328 + 0.872660i \(0.337607\pi\)
\(84\) −6.98217 −0.761818
\(85\) 5.43371 0.589369
\(86\) 8.27805 0.892645
\(87\) 0.306959 0.0329094
\(88\) 4.60256 0.490635
\(89\) −7.43168 −0.787756 −0.393878 0.919163i \(-0.628867\pi\)
−0.393878 + 0.919163i \(0.628867\pi\)
\(90\) −11.2715 −1.18812
\(91\) −16.4467 −1.72409
\(92\) 21.9641 2.28992
\(93\) 0.380580 0.0394643
\(94\) 4.28897 0.442374
\(95\) 2.58247 0.264956
\(96\) 7.37036 0.752234
\(97\) 10.0681 1.02226 0.511131 0.859503i \(-0.329227\pi\)
0.511131 + 0.859503i \(0.329227\pi\)
\(98\) 1.94189 0.196161
\(99\) 5.15746 0.518344
\(100\) 4.69007 0.469007
\(101\) 12.7136 1.26505 0.632527 0.774539i \(-0.282018\pi\)
0.632527 + 0.774539i \(0.282018\pi\)
\(102\) 4.63720 0.459151
\(103\) 1.27077 0.125213 0.0626064 0.998038i \(-0.480059\pi\)
0.0626064 + 0.998038i \(0.480059\pi\)
\(104\) −11.8126 −1.15832
\(105\) 6.41726 0.626261
\(106\) −12.1651 −1.18158
\(107\) 14.8883 1.43931 0.719655 0.694331i \(-0.244300\pi\)
0.719655 + 0.694331i \(0.244300\pi\)
\(108\) −14.0903 −1.35584
\(109\) −14.6315 −1.40144 −0.700722 0.713434i \(-0.747139\pi\)
−0.700722 + 0.713434i \(0.747139\pi\)
\(110\) −14.6775 −1.39945
\(111\) −6.38814 −0.606336
\(112\) 4.26450 0.402957
\(113\) 13.3067 1.25179 0.625895 0.779907i \(-0.284734\pi\)
0.625895 + 0.779907i \(0.284734\pi\)
\(114\) 2.20392 0.206416
\(115\) −20.1871 −1.88245
\(116\) 0.858274 0.0796887
\(117\) −13.2367 −1.22373
\(118\) 2.01264 0.185279
\(119\) 5.20287 0.476946
\(120\) 4.60908 0.420750
\(121\) −4.28409 −0.389462
\(122\) 31.7717 2.87647
\(123\) 10.4624 0.943365
\(124\) 1.06412 0.0955610
\(125\) 8.60177 0.769366
\(126\) −10.7927 −0.961488
\(127\) −10.3751 −0.920642 −0.460321 0.887753i \(-0.652266\pi\)
−0.460321 + 0.887753i \(0.652266\pi\)
\(128\) 13.0434 1.15289
\(129\) −3.79311 −0.333965
\(130\) 37.6701 3.30389
\(131\) 8.44278 0.737649 0.368825 0.929499i \(-0.379760\pi\)
0.368825 + 0.929499i \(0.379760\pi\)
\(132\) −7.31747 −0.636904
\(133\) 2.47276 0.214416
\(134\) −9.33084 −0.806062
\(135\) 12.9503 1.11458
\(136\) 3.73687 0.320434
\(137\) 6.55626 0.560139 0.280070 0.959980i \(-0.409642\pi\)
0.280070 + 0.959980i \(0.409642\pi\)
\(138\) −17.2279 −1.46654
\(139\) −18.6388 −1.58092 −0.790461 0.612512i \(-0.790159\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(140\) 17.9430 1.51646
\(141\) −1.96526 −0.165505
\(142\) −6.41979 −0.538737
\(143\) −17.2365 −1.44139
\(144\) 3.43217 0.286014
\(145\) −0.788833 −0.0655090
\(146\) −25.4670 −2.10766
\(147\) −0.889801 −0.0733895
\(148\) −17.8616 −1.46821
\(149\) 22.8808 1.87447 0.937234 0.348700i \(-0.113377\pi\)
0.937234 + 0.348700i \(0.113377\pi\)
\(150\) −3.67872 −0.300367
\(151\) 9.25471 0.753137 0.376569 0.926389i \(-0.377104\pi\)
0.376569 + 0.926389i \(0.377104\pi\)
\(152\) 1.77602 0.144054
\(153\) 4.18739 0.338530
\(154\) −14.0540 −1.13250
\(155\) −0.978026 −0.0785569
\(156\) 18.7804 1.50364
\(157\) 17.7783 1.41886 0.709430 0.704776i \(-0.248952\pi\)
0.709430 + 0.704776i \(0.248952\pi\)
\(158\) −10.3373 −0.822389
\(159\) 5.57419 0.442062
\(160\) −18.9406 −1.49738
\(161\) −19.3295 −1.52337
\(162\) −2.04192 −0.160429
\(163\) 13.5079 1.05802 0.529009 0.848616i \(-0.322564\pi\)
0.529009 + 0.848616i \(0.322564\pi\)
\(164\) 29.2535 2.28432
\(165\) 6.72543 0.523574
\(166\) −19.5139 −1.51458
\(167\) −23.4930 −1.81794 −0.908971 0.416859i \(-0.863131\pi\)
−0.908971 + 0.416859i \(0.863131\pi\)
\(168\) 4.41327 0.340491
\(169\) 31.2379 2.40292
\(170\) −11.9168 −0.913979
\(171\) 1.99014 0.152190
\(172\) −10.6057 −0.808681
\(173\) −2.10519 −0.160055 −0.0800274 0.996793i \(-0.525501\pi\)
−0.0800274 + 0.996793i \(0.525501\pi\)
\(174\) −0.673200 −0.0510352
\(175\) −4.12748 −0.312008
\(176\) 4.46928 0.336885
\(177\) −0.922219 −0.0693182
\(178\) 16.2986 1.22163
\(179\) −22.2455 −1.66271 −0.831354 0.555743i \(-0.812434\pi\)
−0.831354 + 0.555743i \(0.812434\pi\)
\(180\) 14.4410 1.07637
\(181\) −21.0550 −1.56500 −0.782501 0.622649i \(-0.786057\pi\)
−0.782501 + 0.622649i \(0.786057\pi\)
\(182\) 36.0698 2.67367
\(183\) −14.5582 −1.07617
\(184\) −13.8830 −1.02347
\(185\) 16.4165 1.20696
\(186\) −0.834660 −0.0612002
\(187\) 5.45272 0.398742
\(188\) −5.49498 −0.400763
\(189\) 12.4001 0.901977
\(190\) −5.66370 −0.410888
\(191\) −13.4362 −0.972212 −0.486106 0.873900i \(-0.661583\pi\)
−0.486106 + 0.873900i \(0.661583\pi\)
\(192\) −12.6980 −0.916398
\(193\) −23.0471 −1.65897 −0.829485 0.558529i \(-0.811366\pi\)
−0.829485 + 0.558529i \(0.811366\pi\)
\(194\) −22.0807 −1.58530
\(195\) −17.2609 −1.23608
\(196\) −2.48793 −0.177709
\(197\) −18.6747 −1.33051 −0.665257 0.746614i \(-0.731678\pi\)
−0.665257 + 0.746614i \(0.731678\pi\)
\(198\) −11.3110 −0.803835
\(199\) 8.29137 0.587760 0.293880 0.955842i \(-0.405053\pi\)
0.293880 + 0.955842i \(0.405053\pi\)
\(200\) −2.96448 −0.209621
\(201\) 4.27551 0.301571
\(202\) −27.8826 −1.96181
\(203\) −0.755321 −0.0530131
\(204\) −5.94113 −0.415962
\(205\) −26.8867 −1.87785
\(206\) −2.78696 −0.194177
\(207\) −15.5568 −1.08127
\(208\) −11.4705 −0.795336
\(209\) 2.59151 0.179258
\(210\) −14.0739 −0.971190
\(211\) −13.8193 −0.951356 −0.475678 0.879619i \(-0.657797\pi\)
−0.475678 + 0.879619i \(0.657797\pi\)
\(212\) 15.5857 1.07043
\(213\) 2.94163 0.201557
\(214\) −32.6520 −2.23205
\(215\) 9.74766 0.664785
\(216\) 8.90617 0.605988
\(217\) −0.936476 −0.0635722
\(218\) 32.0888 2.17333
\(219\) 11.6693 0.788538
\(220\) 18.8047 1.26781
\(221\) −13.9945 −0.941373
\(222\) 14.0100 0.940291
\(223\) 7.55144 0.505682 0.252841 0.967508i \(-0.418635\pi\)
0.252841 + 0.967508i \(0.418635\pi\)
\(224\) −18.1359 −1.21176
\(225\) −3.32189 −0.221459
\(226\) −29.1833 −1.94125
\(227\) 14.8313 0.984390 0.492195 0.870485i \(-0.336195\pi\)
0.492195 + 0.870485i \(0.336195\pi\)
\(228\) −2.82363 −0.187000
\(229\) 5.29415 0.349847 0.174924 0.984582i \(-0.444032\pi\)
0.174924 + 0.984582i \(0.444032\pi\)
\(230\) 44.2728 2.91926
\(231\) 6.43971 0.423702
\(232\) −0.542495 −0.0356166
\(233\) −30.1575 −1.97569 −0.987843 0.155453i \(-0.950316\pi\)
−0.987843 + 0.155453i \(0.950316\pi\)
\(234\) 29.0298 1.89774
\(235\) 5.05039 0.329451
\(236\) −2.57857 −0.167851
\(237\) 4.73667 0.307680
\(238\) −11.4106 −0.739637
\(239\) −9.03587 −0.584482 −0.292241 0.956345i \(-0.594401\pi\)
−0.292241 + 0.956345i \(0.594401\pi\)
\(240\) 4.47561 0.288900
\(241\) −22.3016 −1.43657 −0.718285 0.695749i \(-0.755073\pi\)
−0.718285 + 0.695749i \(0.755073\pi\)
\(242\) 9.39555 0.603969
\(243\) 15.9797 1.02510
\(244\) −40.7055 −2.60590
\(245\) 2.28664 0.146088
\(246\) −22.9454 −1.46295
\(247\) −6.65116 −0.423203
\(248\) −0.672607 −0.0427106
\(249\) 8.94154 0.566647
\(250\) −18.8648 −1.19311
\(251\) 11.6333 0.734285 0.367143 0.930165i \(-0.380336\pi\)
0.367143 + 0.930165i \(0.380336\pi\)
\(252\) 13.8275 0.871048
\(253\) −20.2577 −1.27359
\(254\) 22.7539 1.42771
\(255\) 5.46044 0.341946
\(256\) −3.33427 −0.208392
\(257\) −1.29517 −0.0807906 −0.0403953 0.999184i \(-0.512862\pi\)
−0.0403953 + 0.999184i \(0.512862\pi\)
\(258\) 8.31878 0.517904
\(259\) 15.7190 0.976733
\(260\) −48.2626 −2.99312
\(261\) −0.607900 −0.0376280
\(262\) −18.5161 −1.14393
\(263\) −21.5830 −1.33086 −0.665432 0.746459i \(-0.731752\pi\)
−0.665432 + 0.746459i \(0.731752\pi\)
\(264\) 4.62520 0.284662
\(265\) −14.3247 −0.879961
\(266\) −5.42308 −0.332511
\(267\) −7.46824 −0.457049
\(268\) 11.9546 0.730242
\(269\) −8.16028 −0.497541 −0.248770 0.968562i \(-0.580026\pi\)
−0.248770 + 0.968562i \(0.580026\pi\)
\(270\) −28.4017 −1.72847
\(271\) −27.0940 −1.64585 −0.822923 0.568153i \(-0.807658\pi\)
−0.822923 + 0.568153i \(0.807658\pi\)
\(272\) 3.62866 0.220020
\(273\) −16.5276 −1.00030
\(274\) −14.3787 −0.868650
\(275\) −4.32568 −0.260848
\(276\) 22.0722 1.32859
\(277\) −6.24469 −0.375207 −0.187604 0.982245i \(-0.560072\pi\)
−0.187604 + 0.982245i \(0.560072\pi\)
\(278\) 40.8773 2.45166
\(279\) −0.753698 −0.0451227
\(280\) −11.3414 −0.677777
\(281\) 3.18429 0.189959 0.0949795 0.995479i \(-0.469721\pi\)
0.0949795 + 0.995479i \(0.469721\pi\)
\(282\) 4.31007 0.256661
\(283\) 15.3019 0.909603 0.454802 0.890593i \(-0.349710\pi\)
0.454802 + 0.890593i \(0.349710\pi\)
\(284\) 8.22496 0.488062
\(285\) 2.59518 0.153725
\(286\) 37.8019 2.23527
\(287\) −25.7444 −1.51965
\(288\) −14.5962 −0.860090
\(289\) −12.5729 −0.739581
\(290\) 1.73001 0.101590
\(291\) 10.1177 0.593107
\(292\) 32.6280 1.90941
\(293\) −23.4025 −1.36719 −0.683595 0.729861i \(-0.739585\pi\)
−0.683595 + 0.729861i \(0.739585\pi\)
\(294\) 1.95145 0.113811
\(295\) 2.36995 0.137984
\(296\) 11.2899 0.656213
\(297\) 12.9956 0.754081
\(298\) −50.1805 −2.90688
\(299\) 51.9917 3.00676
\(300\) 4.71314 0.272113
\(301\) 9.33355 0.537977
\(302\) −20.2968 −1.16795
\(303\) 12.7762 0.733972
\(304\) 1.72459 0.0989119
\(305\) 37.4121 2.14221
\(306\) −9.18348 −0.524985
\(307\) 19.7310 1.12611 0.563054 0.826420i \(-0.309626\pi\)
0.563054 + 0.826420i \(0.309626\pi\)
\(308\) 18.0058 1.02597
\(309\) 1.27702 0.0726472
\(310\) 2.14494 0.121824
\(311\) −6.37546 −0.361519 −0.180760 0.983527i \(-0.557856\pi\)
−0.180760 + 0.983527i \(0.557856\pi\)
\(312\) −11.8707 −0.672045
\(313\) −12.6226 −0.713472 −0.356736 0.934205i \(-0.616110\pi\)
−0.356736 + 0.934205i \(0.616110\pi\)
\(314\) −38.9900 −2.20033
\(315\) −12.7087 −0.716055
\(316\) 13.2440 0.745033
\(317\) −1.00000 −0.0561656
\(318\) −12.2249 −0.685539
\(319\) −0.791592 −0.0443206
\(320\) 32.6317 1.82417
\(321\) 14.9616 0.835074
\(322\) 42.3920 2.36241
\(323\) 2.10407 0.117074
\(324\) 2.61609 0.145338
\(325\) 11.1020 0.615825
\(326\) −29.6245 −1.64075
\(327\) −14.7035 −0.813105
\(328\) −18.4905 −1.02097
\(329\) 4.83584 0.266608
\(330\) −14.7497 −0.811945
\(331\) −1.89016 −0.103892 −0.0519462 0.998650i \(-0.516542\pi\)
−0.0519462 + 0.998650i \(0.516542\pi\)
\(332\) 25.0010 1.37211
\(333\) 12.6510 0.693273
\(334\) 51.5231 2.81922
\(335\) −10.9874 −0.600303
\(336\) 4.28547 0.233792
\(337\) −2.98839 −0.162788 −0.0813939 0.996682i \(-0.525937\pi\)
−0.0813939 + 0.996682i \(0.525937\pi\)
\(338\) −68.5087 −3.72638
\(339\) 13.3722 0.726277
\(340\) 15.2677 0.828007
\(341\) −0.981447 −0.0531483
\(342\) −4.36462 −0.236012
\(343\) 19.4988 1.05284
\(344\) 6.70365 0.361437
\(345\) −20.2864 −1.09218
\(346\) 4.61695 0.248209
\(347\) 23.7150 1.27309 0.636544 0.771241i \(-0.280364\pi\)
0.636544 + 0.771241i \(0.280364\pi\)
\(348\) 0.862496 0.0462346
\(349\) −11.9202 −0.638075 −0.319038 0.947742i \(-0.603360\pi\)
−0.319038 + 0.947742i \(0.603360\pi\)
\(350\) 9.05208 0.483854
\(351\) −33.3535 −1.78028
\(352\) −19.0068 −1.01307
\(353\) −28.7321 −1.52926 −0.764628 0.644472i \(-0.777077\pi\)
−0.764628 + 0.644472i \(0.777077\pi\)
\(354\) 2.02254 0.107497
\(355\) −7.55950 −0.401216
\(356\) −20.8816 −1.10672
\(357\) 5.22846 0.276720
\(358\) 48.7873 2.57849
\(359\) 7.87185 0.415460 0.207730 0.978186i \(-0.433392\pi\)
0.207730 + 0.978186i \(0.433392\pi\)
\(360\) −9.12780 −0.481077
\(361\) 1.00000 0.0526316
\(362\) 46.1762 2.42697
\(363\) −4.30516 −0.225962
\(364\) −46.2122 −2.42218
\(365\) −29.9881 −1.56965
\(366\) 31.9280 1.66890
\(367\) −1.30382 −0.0680590 −0.0340295 0.999421i \(-0.510834\pi\)
−0.0340295 + 0.999421i \(0.510834\pi\)
\(368\) −13.4810 −0.702746
\(369\) −20.7197 −1.07863
\(370\) −36.0034 −1.87173
\(371\) −13.7162 −0.712108
\(372\) 1.06936 0.0554436
\(373\) 30.1082 1.55894 0.779471 0.626438i \(-0.215488\pi\)
0.779471 + 0.626438i \(0.215488\pi\)
\(374\) −11.9585 −0.618360
\(375\) 8.64409 0.446379
\(376\) 3.47325 0.179119
\(377\) 2.03164 0.104635
\(378\) −27.1951 −1.39876
\(379\) −2.53929 −0.130435 −0.0652173 0.997871i \(-0.520774\pi\)
−0.0652173 + 0.997871i \(0.520774\pi\)
\(380\) 7.25626 0.372238
\(381\) −10.4261 −0.534148
\(382\) 29.4674 1.50768
\(383\) −24.8155 −1.26801 −0.634006 0.773328i \(-0.718591\pi\)
−0.634006 + 0.773328i \(0.718591\pi\)
\(384\) 13.1076 0.668895
\(385\) −16.5490 −0.843414
\(386\) 50.5453 2.57269
\(387\) 7.51186 0.381849
\(388\) 28.2895 1.43618
\(389\) 16.7815 0.850858 0.425429 0.904992i \(-0.360123\pi\)
0.425429 + 0.904992i \(0.360123\pi\)
\(390\) 37.8555 1.91689
\(391\) −16.4474 −0.831782
\(392\) 1.57257 0.0794265
\(393\) 8.48432 0.427977
\(394\) 40.9559 2.06333
\(395\) −12.1725 −0.612463
\(396\) 14.4915 0.728224
\(397\) −12.9967 −0.652285 −0.326143 0.945321i \(-0.605749\pi\)
−0.326143 + 0.945321i \(0.605749\pi\)
\(398\) −18.1840 −0.911483
\(399\) 2.48493 0.124402
\(400\) −2.87864 −0.143932
\(401\) 12.5005 0.624243 0.312122 0.950042i \(-0.398960\pi\)
0.312122 + 0.950042i \(0.398960\pi\)
\(402\) −9.37675 −0.467670
\(403\) 2.51890 0.125476
\(404\) 35.7229 1.77728
\(405\) −2.40443 −0.119477
\(406\) 1.65651 0.0822114
\(407\) 16.4739 0.816580
\(408\) 3.75525 0.185913
\(409\) −6.78410 −0.335452 −0.167726 0.985834i \(-0.553642\pi\)
−0.167726 + 0.985834i \(0.553642\pi\)
\(410\) 58.9659 2.91212
\(411\) 6.58851 0.324987
\(412\) 3.57062 0.175912
\(413\) 2.26926 0.111663
\(414\) 34.1180 1.67681
\(415\) −22.9783 −1.12796
\(416\) 48.7814 2.39171
\(417\) −18.7305 −0.917236
\(418\) −5.68351 −0.277989
\(419\) 23.5924 1.15256 0.576282 0.817251i \(-0.304503\pi\)
0.576282 + 0.817251i \(0.304503\pi\)
\(420\) 18.0313 0.879837
\(421\) −29.6232 −1.44375 −0.721874 0.692024i \(-0.756719\pi\)
−0.721874 + 0.692024i \(0.756719\pi\)
\(422\) 30.3074 1.47534
\(423\) 3.89199 0.189235
\(424\) −9.85139 −0.478426
\(425\) −3.51206 −0.170360
\(426\) −6.45137 −0.312570
\(427\) 35.8227 1.73358
\(428\) 41.8334 2.02210
\(429\) −17.3213 −0.836281
\(430\) −21.3779 −1.03093
\(431\) 35.5077 1.71035 0.855173 0.518342i \(-0.173451\pi\)
0.855173 + 0.518342i \(0.173451\pi\)
\(432\) 8.64826 0.416090
\(433\) −0.138560 −0.00665877 −0.00332938 0.999994i \(-0.501060\pi\)
−0.00332938 + 0.999994i \(0.501060\pi\)
\(434\) 2.05381 0.0985861
\(435\) −0.792713 −0.0380077
\(436\) −41.1118 −1.96890
\(437\) −7.81695 −0.373935
\(438\) −25.5922 −1.22284
\(439\) −6.28787 −0.300104 −0.150052 0.988678i \(-0.547944\pi\)
−0.150052 + 0.988678i \(0.547944\pi\)
\(440\) −11.8860 −0.566643
\(441\) 1.76216 0.0839122
\(442\) 30.6918 1.45986
\(443\) −23.3950 −1.11153 −0.555765 0.831340i \(-0.687574\pi\)
−0.555765 + 0.831340i \(0.687574\pi\)
\(444\) −17.9495 −0.851844
\(445\) 19.1921 0.909794
\(446\) −16.5613 −0.784199
\(447\) 22.9934 1.08755
\(448\) 31.2454 1.47621
\(449\) 12.3430 0.582500 0.291250 0.956647i \(-0.405929\pi\)
0.291250 + 0.956647i \(0.405929\pi\)
\(450\) 7.28533 0.343434
\(451\) −26.9807 −1.27047
\(452\) 37.3893 1.75865
\(453\) 9.30023 0.436963
\(454\) −32.5270 −1.52657
\(455\) 42.4733 1.99118
\(456\) 1.78475 0.0835788
\(457\) −2.89895 −0.135607 −0.0678036 0.997699i \(-0.521599\pi\)
−0.0678036 + 0.997699i \(0.521599\pi\)
\(458\) −11.6108 −0.542535
\(459\) 10.5513 0.492491
\(460\) −56.7218 −2.64467
\(461\) −33.4032 −1.55574 −0.777870 0.628425i \(-0.783700\pi\)
−0.777870 + 0.628425i \(0.783700\pi\)
\(462\) −14.1231 −0.657066
\(463\) 9.02110 0.419246 0.209623 0.977782i \(-0.432776\pi\)
0.209623 + 0.977782i \(0.432776\pi\)
\(464\) −0.526786 −0.0244554
\(465\) −0.982837 −0.0455780
\(466\) 66.1394 3.06385
\(467\) −29.3905 −1.36003 −0.680014 0.733199i \(-0.738026\pi\)
−0.680014 + 0.733199i \(0.738026\pi\)
\(468\) −37.1927 −1.71923
\(469\) −10.5206 −0.485795
\(470\) −11.0762 −0.510905
\(471\) 17.8657 0.823209
\(472\) 1.62986 0.0750203
\(473\) 9.78176 0.449766
\(474\) −10.3881 −0.477142
\(475\) −1.66918 −0.0765870
\(476\) 14.6191 0.670064
\(477\) −11.0391 −0.505445
\(478\) 19.8168 0.906400
\(479\) 9.47000 0.432695 0.216348 0.976316i \(-0.430586\pi\)
0.216348 + 0.976316i \(0.430586\pi\)
\(480\) −19.0338 −0.868768
\(481\) −42.2805 −1.92783
\(482\) 48.9102 2.22780
\(483\) −19.4245 −0.883847
\(484\) −12.0375 −0.547158
\(485\) −26.0007 −1.18063
\(486\) −35.0455 −1.58970
\(487\) −10.2576 −0.464818 −0.232409 0.972618i \(-0.574661\pi\)
−0.232409 + 0.972618i \(0.574661\pi\)
\(488\) 25.7290 1.16470
\(489\) 13.5743 0.613852
\(490\) −5.01489 −0.226550
\(491\) −4.14188 −0.186920 −0.0934602 0.995623i \(-0.529793\pi\)
−0.0934602 + 0.995623i \(0.529793\pi\)
\(492\) 29.3974 1.32534
\(493\) −0.642702 −0.0289458
\(494\) 14.5868 0.656293
\(495\) −13.3190 −0.598644
\(496\) −0.653130 −0.0293264
\(497\) −7.23834 −0.324684
\(498\) −19.6099 −0.878742
\(499\) −32.1982 −1.44139 −0.720694 0.693253i \(-0.756177\pi\)
−0.720694 + 0.693253i \(0.756177\pi\)
\(500\) 24.1693 1.08089
\(501\) −23.6086 −1.05475
\(502\) −25.5132 −1.13871
\(503\) −19.0907 −0.851211 −0.425605 0.904909i \(-0.639939\pi\)
−0.425605 + 0.904909i \(0.639939\pi\)
\(504\) −8.74002 −0.389312
\(505\) −32.8326 −1.46103
\(506\) 44.4277 1.97505
\(507\) 31.3916 1.39415
\(508\) −29.1521 −1.29341
\(509\) −2.38190 −0.105576 −0.0527880 0.998606i \(-0.516811\pi\)
−0.0527880 + 0.998606i \(0.516811\pi\)
\(510\) −11.9754 −0.530282
\(511\) −28.7141 −1.27024
\(512\) −18.7744 −0.829719
\(513\) 5.01469 0.221404
\(514\) 2.84048 0.125288
\(515\) −3.28173 −0.144610
\(516\) −10.6579 −0.469189
\(517\) 5.06806 0.222893
\(518\) −34.4738 −1.51469
\(519\) −2.11555 −0.0928622
\(520\) 30.5057 1.33776
\(521\) −31.0410 −1.35993 −0.679966 0.733244i \(-0.738005\pi\)
−0.679966 + 0.733244i \(0.738005\pi\)
\(522\) 1.33320 0.0583526
\(523\) 13.4746 0.589204 0.294602 0.955620i \(-0.404813\pi\)
0.294602 + 0.955620i \(0.404813\pi\)
\(524\) 23.7226 1.03633
\(525\) −4.14778 −0.181024
\(526\) 47.3342 2.06387
\(527\) −0.796847 −0.0347112
\(528\) 4.49127 0.195457
\(529\) 38.1047 1.65672
\(530\) 31.4160 1.36462
\(531\) 1.82636 0.0792571
\(532\) 6.94799 0.301234
\(533\) 69.2466 2.99940
\(534\) 16.3788 0.708780
\(535\) −38.4488 −1.66229
\(536\) −7.55621 −0.326379
\(537\) −22.3550 −0.964688
\(538\) 17.8965 0.771574
\(539\) 2.29464 0.0988370
\(540\) 36.3879 1.56589
\(541\) −13.7443 −0.590914 −0.295457 0.955356i \(-0.595472\pi\)
−0.295457 + 0.955356i \(0.595472\pi\)
\(542\) 59.4207 2.55234
\(543\) −21.1585 −0.908000
\(544\) −15.4318 −0.661635
\(545\) 37.7855 1.61855
\(546\) 36.2472 1.55124
\(547\) 9.19955 0.393344 0.196672 0.980469i \(-0.436987\pi\)
0.196672 + 0.980469i \(0.436987\pi\)
\(548\) 18.4218 0.786942
\(549\) 28.8310 1.23048
\(550\) 9.48677 0.404517
\(551\) −0.305456 −0.0130129
\(552\) −13.9513 −0.593808
\(553\) −11.6553 −0.495635
\(554\) 13.6954 0.581862
\(555\) 16.4972 0.700268
\(556\) −52.3715 −2.22105
\(557\) −13.3100 −0.563964 −0.281982 0.959420i \(-0.590992\pi\)
−0.281982 + 0.959420i \(0.590992\pi\)
\(558\) 1.65296 0.0699752
\(559\) −25.1051 −1.06183
\(560\) −11.0130 −0.465382
\(561\) 5.47954 0.231346
\(562\) −6.98356 −0.294584
\(563\) −47.0535 −1.98307 −0.991534 0.129846i \(-0.958552\pi\)
−0.991534 + 0.129846i \(0.958552\pi\)
\(564\) −5.52201 −0.232519
\(565\) −34.3643 −1.44572
\(566\) −33.5590 −1.41059
\(567\) −2.30228 −0.0966867
\(568\) −5.19881 −0.218137
\(569\) −38.9429 −1.63257 −0.816285 0.577649i \(-0.803970\pi\)
−0.816285 + 0.577649i \(0.803970\pi\)
\(570\) −5.69156 −0.238393
\(571\) 0.972507 0.0406982 0.0203491 0.999793i \(-0.493522\pi\)
0.0203491 + 0.999793i \(0.493522\pi\)
\(572\) −48.4314 −2.02502
\(573\) −13.5023 −0.564068
\(574\) 56.4609 2.35663
\(575\) 13.0479 0.544133
\(576\) 25.1470 1.04779
\(577\) 22.9149 0.953958 0.476979 0.878915i \(-0.341732\pi\)
0.476979 + 0.878915i \(0.341732\pi\)
\(578\) 27.5739 1.14692
\(579\) −23.1605 −0.962518
\(580\) −2.21647 −0.0920339
\(581\) −22.0021 −0.912800
\(582\) −22.1893 −0.919776
\(583\) −14.3748 −0.595345
\(584\) −20.6234 −0.853403
\(585\) 34.1835 1.41331
\(586\) 51.3247 2.12021
\(587\) −20.8403 −0.860172 −0.430086 0.902788i \(-0.641517\pi\)
−0.430086 + 0.902788i \(0.641517\pi\)
\(588\) −2.50017 −0.103105
\(589\) −0.378717 −0.0156047
\(590\) −5.19760 −0.213982
\(591\) −18.7665 −0.771952
\(592\) 10.9630 0.450576
\(593\) 24.2440 0.995581 0.497790 0.867297i \(-0.334145\pi\)
0.497790 + 0.867297i \(0.334145\pi\)
\(594\) −28.5010 −1.16941
\(595\) −13.4363 −0.550834
\(596\) 64.2907 2.63345
\(597\) 8.33216 0.341012
\(598\) −114.025 −4.66281
\(599\) 3.00707 0.122866 0.0614328 0.998111i \(-0.480433\pi\)
0.0614328 + 0.998111i \(0.480433\pi\)
\(600\) −2.97907 −0.121620
\(601\) 36.1374 1.47407 0.737037 0.675852i \(-0.236224\pi\)
0.737037 + 0.675852i \(0.236224\pi\)
\(602\) −20.4697 −0.834281
\(603\) −8.46720 −0.344811
\(604\) 26.0040 1.05809
\(605\) 11.0635 0.449797
\(606\) −28.0198 −1.13823
\(607\) −3.75221 −0.152298 −0.0761488 0.997096i \(-0.524262\pi\)
−0.0761488 + 0.997096i \(0.524262\pi\)
\(608\) −7.33428 −0.297444
\(609\) −0.759036 −0.0307577
\(610\) −82.0496 −3.32209
\(611\) −13.0073 −0.526218
\(612\) 11.7658 0.475603
\(613\) 37.4995 1.51459 0.757296 0.653072i \(-0.226520\pi\)
0.757296 + 0.653072i \(0.226520\pi\)
\(614\) −43.2726 −1.74634
\(615\) −27.0190 −1.08951
\(616\) −11.3810 −0.458555
\(617\) 35.1109 1.41351 0.706755 0.707458i \(-0.250158\pi\)
0.706755 + 0.707458i \(0.250158\pi\)
\(618\) −2.80067 −0.112660
\(619\) 24.8105 0.997217 0.498608 0.866827i \(-0.333845\pi\)
0.498608 + 0.866827i \(0.333845\pi\)
\(620\) −2.74807 −0.110365
\(621\) −39.1995 −1.57302
\(622\) 13.9822 0.560635
\(623\) 18.3768 0.736250
\(624\) −11.5269 −0.461447
\(625\) −30.5597 −1.22239
\(626\) 27.6830 1.10644
\(627\) 2.60426 0.104004
\(628\) 49.9536 1.99336
\(629\) 13.3753 0.533309
\(630\) 27.8718 1.11044
\(631\) 38.1927 1.52043 0.760214 0.649673i \(-0.225094\pi\)
0.760214 + 0.649673i \(0.225094\pi\)
\(632\) −8.37123 −0.332990
\(633\) −13.8872 −0.551968
\(634\) 2.19313 0.0871002
\(635\) 26.7934 1.06327
\(636\) 15.6624 0.621055
\(637\) −5.88923 −0.233340
\(638\) 1.73606 0.0687314
\(639\) −5.82559 −0.230457
\(640\) −33.6843 −1.33149
\(641\) −17.0393 −0.673012 −0.336506 0.941681i \(-0.609245\pi\)
−0.336506 + 0.941681i \(0.609245\pi\)
\(642\) −32.8127 −1.29501
\(643\) 12.1561 0.479389 0.239694 0.970848i \(-0.422953\pi\)
0.239694 + 0.970848i \(0.422953\pi\)
\(644\) −54.3121 −2.14020
\(645\) 9.79561 0.385702
\(646\) −4.61450 −0.181555
\(647\) 6.83223 0.268603 0.134301 0.990941i \(-0.457121\pi\)
0.134301 + 0.990941i \(0.457121\pi\)
\(648\) −1.65357 −0.0649584
\(649\) 2.37824 0.0933540
\(650\) −24.3480 −0.955007
\(651\) −0.941083 −0.0368840
\(652\) 37.9546 1.48642
\(653\) 21.9407 0.858607 0.429304 0.903160i \(-0.358759\pi\)
0.429304 + 0.903160i \(0.358759\pi\)
\(654\) 32.2466 1.26094
\(655\) −21.8033 −0.851924
\(656\) −17.9550 −0.701027
\(657\) −23.1098 −0.901599
\(658\) −10.6056 −0.413450
\(659\) −26.7359 −1.04148 −0.520742 0.853714i \(-0.674345\pi\)
−0.520742 + 0.853714i \(0.674345\pi\)
\(660\) 18.8972 0.735571
\(661\) 22.6835 0.882285 0.441142 0.897437i \(-0.354573\pi\)
0.441142 + 0.897437i \(0.354573\pi\)
\(662\) 4.14535 0.161114
\(663\) −14.0634 −0.546176
\(664\) −15.8026 −0.613259
\(665\) −6.38585 −0.247633
\(666\) −27.7454 −1.07511
\(667\) 2.38773 0.0924534
\(668\) −66.0109 −2.55404
\(669\) 7.58859 0.293392
\(670\) 24.0967 0.930936
\(671\) 37.5430 1.44933
\(672\) −18.2251 −0.703050
\(673\) 19.7290 0.760497 0.380249 0.924884i \(-0.375838\pi\)
0.380249 + 0.924884i \(0.375838\pi\)
\(674\) 6.55391 0.252447
\(675\) −8.37039 −0.322176
\(676\) 87.7726 3.37587
\(677\) −30.5871 −1.17556 −0.587779 0.809022i \(-0.699997\pi\)
−0.587779 + 0.809022i \(0.699997\pi\)
\(678\) −29.3269 −1.12629
\(679\) −24.8961 −0.955424
\(680\) −9.65036 −0.370075
\(681\) 14.9043 0.571134
\(682\) 2.15244 0.0824212
\(683\) −47.3340 −1.81119 −0.905593 0.424147i \(-0.860574\pi\)
−0.905593 + 0.424147i \(0.860574\pi\)
\(684\) 5.59191 0.213812
\(685\) −16.9314 −0.646915
\(686\) −42.7634 −1.63272
\(687\) 5.32020 0.202978
\(688\) 6.50953 0.248173
\(689\) 36.8933 1.40552
\(690\) 44.4906 1.69373
\(691\) −46.5311 −1.77012 −0.885062 0.465472i \(-0.845885\pi\)
−0.885062 + 0.465472i \(0.845885\pi\)
\(692\) −5.91519 −0.224862
\(693\) −12.7532 −0.484453
\(694\) −52.0100 −1.97427
\(695\) 48.1342 1.82584
\(696\) −0.545164 −0.0206644
\(697\) −21.9059 −0.829746
\(698\) 26.1426 0.989512
\(699\) −30.3059 −1.14627
\(700\) −11.5974 −0.438341
\(701\) −12.5304 −0.473267 −0.236633 0.971599i \(-0.576044\pi\)
−0.236633 + 0.971599i \(0.576044\pi\)
\(702\) 73.1484 2.76081
\(703\) 6.35687 0.239754
\(704\) 32.7459 1.23416
\(705\) 5.07524 0.191145
\(706\) 63.0132 2.37153
\(707\) −31.4378 −1.18234
\(708\) −2.59126 −0.0973855
\(709\) 29.2110 1.09704 0.548521 0.836137i \(-0.315191\pi\)
0.548521 + 0.836137i \(0.315191\pi\)
\(710\) 16.5789 0.622197
\(711\) −9.38048 −0.351795
\(712\) 13.1988 0.494646
\(713\) 2.96041 0.110868
\(714\) −11.4667 −0.429130
\(715\) 44.5129 1.66469
\(716\) −62.5057 −2.33595
\(717\) −9.08032 −0.339111
\(718\) −17.2640 −0.644286
\(719\) 20.7849 0.775146 0.387573 0.921839i \(-0.373314\pi\)
0.387573 + 0.921839i \(0.373314\pi\)
\(720\) −8.86348 −0.330322
\(721\) −3.14231 −0.117026
\(722\) −2.19313 −0.0816198
\(723\) −22.4113 −0.833485
\(724\) −59.1604 −2.19868
\(725\) 0.509860 0.0189357
\(726\) 9.44177 0.350417
\(727\) −5.39073 −0.199931 −0.0999656 0.994991i \(-0.531873\pi\)
−0.0999656 + 0.994991i \(0.531873\pi\)
\(728\) 29.2097 1.08258
\(729\) 13.2651 0.491301
\(730\) 65.7678 2.43418
\(731\) 7.94191 0.293742
\(732\) −40.9058 −1.51192
\(733\) −32.7613 −1.21007 −0.605033 0.796200i \(-0.706840\pi\)
−0.605033 + 0.796200i \(0.706840\pi\)
\(734\) 2.85945 0.105544
\(735\) 2.29789 0.0847589
\(736\) 57.3316 2.11327
\(737\) −11.0258 −0.406140
\(738\) 45.4410 1.67271
\(739\) 35.3943 1.30200 0.650999 0.759078i \(-0.274350\pi\)
0.650999 + 0.759078i \(0.274350\pi\)
\(740\) 46.1271 1.69567
\(741\) −6.68388 −0.245538
\(742\) 30.0813 1.10432
\(743\) −3.81507 −0.139961 −0.0699807 0.997548i \(-0.522294\pi\)
−0.0699807 + 0.997548i \(0.522294\pi\)
\(744\) −0.675916 −0.0247803
\(745\) −59.0891 −2.16486
\(746\) −66.0311 −2.41757
\(747\) −17.7078 −0.647894
\(748\) 15.3211 0.560195
\(749\) −36.8153 −1.34520
\(750\) −18.9576 −0.692233
\(751\) −36.0127 −1.31412 −0.657060 0.753838i \(-0.728200\pi\)
−0.657060 + 0.753838i \(0.728200\pi\)
\(752\) 3.37267 0.122989
\(753\) 11.6905 0.426025
\(754\) −4.45564 −0.162265
\(755\) −23.9000 −0.869812
\(756\) 34.8420 1.26719
\(757\) −46.4095 −1.68678 −0.843390 0.537302i \(-0.819444\pi\)
−0.843390 + 0.537302i \(0.819444\pi\)
\(758\) 5.56899 0.202275
\(759\) −20.3573 −0.738924
\(760\) −4.58652 −0.166371
\(761\) −6.80037 −0.246513 −0.123257 0.992375i \(-0.539334\pi\)
−0.123257 + 0.992375i \(0.539334\pi\)
\(762\) 22.8659 0.828343
\(763\) 36.1803 1.30981
\(764\) −37.7533 −1.36587
\(765\) −10.8138 −0.390975
\(766\) 54.4236 1.96640
\(767\) −6.10380 −0.220395
\(768\) −3.35067 −0.120907
\(769\) −19.0982 −0.688698 −0.344349 0.938842i \(-0.611900\pi\)
−0.344349 + 0.938842i \(0.611900\pi\)
\(770\) 36.2940 1.30795
\(771\) −1.30154 −0.0468739
\(772\) −64.7581 −2.33069
\(773\) 49.6576 1.78606 0.893029 0.449998i \(-0.148575\pi\)
0.893029 + 0.449998i \(0.148575\pi\)
\(774\) −16.4745 −0.592162
\(775\) 0.632145 0.0227073
\(776\) −17.8812 −0.641896
\(777\) 15.7964 0.566691
\(778\) −36.8041 −1.31949
\(779\) −10.4112 −0.373020
\(780\) −48.5000 −1.73658
\(781\) −7.58594 −0.271446
\(782\) 36.0713 1.28991
\(783\) −1.53177 −0.0547409
\(784\) 1.52703 0.0545367
\(785\) −45.9119 −1.63867
\(786\) −18.6072 −0.663696
\(787\) −0.270469 −0.00964119 −0.00482059 0.999988i \(-0.501534\pi\)
−0.00482059 + 0.999988i \(0.501534\pi\)
\(788\) −52.4722 −1.86925
\(789\) −21.6891 −0.772154
\(790\) 26.6957 0.949792
\(791\) −32.9043 −1.16994
\(792\) −9.15973 −0.325477
\(793\) −96.3549 −3.42166
\(794\) 28.5034 1.01155
\(795\) −14.3952 −0.510545
\(796\) 23.2972 0.825746
\(797\) 51.2552 1.81555 0.907776 0.419456i \(-0.137779\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(798\) −5.44976 −0.192920
\(799\) 4.11481 0.145571
\(800\) 12.2422 0.432827
\(801\) 14.7901 0.522581
\(802\) −27.4151 −0.968061
\(803\) −30.0930 −1.06196
\(804\) 12.0134 0.423679
\(805\) 49.9178 1.75937
\(806\) −5.52428 −0.194584
\(807\) −8.20042 −0.288669
\(808\) −22.5796 −0.794348
\(809\) −21.4069 −0.752628 −0.376314 0.926492i \(-0.622809\pi\)
−0.376314 + 0.926492i \(0.622809\pi\)
\(810\) 5.27322 0.185282
\(811\) −22.5314 −0.791186 −0.395593 0.918426i \(-0.629461\pi\)
−0.395593 + 0.918426i \(0.629461\pi\)
\(812\) −2.12231 −0.0744784
\(813\) −27.2273 −0.954904
\(814\) −36.1293 −1.26633
\(815\) −34.8838 −1.22192
\(816\) 3.64651 0.127653
\(817\) 3.77454 0.132055
\(818\) 14.8784 0.520211
\(819\) 32.7313 1.14372
\(820\) −75.5465 −2.63820
\(821\) 12.4019 0.432828 0.216414 0.976302i \(-0.430564\pi\)
0.216414 + 0.976302i \(0.430564\pi\)
\(822\) −14.4495 −0.503983
\(823\) −21.1065 −0.735726 −0.367863 0.929880i \(-0.619910\pi\)
−0.367863 + 0.929880i \(0.619910\pi\)
\(824\) −2.25691 −0.0786232
\(825\) −4.34696 −0.151342
\(826\) −4.97679 −0.173165
\(827\) −39.7953 −1.38382 −0.691909 0.721985i \(-0.743230\pi\)
−0.691909 + 0.721985i \(0.743230\pi\)
\(828\) −43.7116 −1.51908
\(829\) −24.1089 −0.837337 −0.418668 0.908139i \(-0.637503\pi\)
−0.418668 + 0.908139i \(0.637503\pi\)
\(830\) 50.3943 1.74921
\(831\) −6.27541 −0.217692
\(832\) −84.0429 −2.91366
\(833\) 1.86304 0.0645505
\(834\) 41.0784 1.42243
\(835\) 60.6701 2.09957
\(836\) 7.28165 0.251841
\(837\) −1.89914 −0.0656440
\(838\) −51.7412 −1.78737
\(839\) 21.2399 0.733282 0.366641 0.930362i \(-0.380508\pi\)
0.366641 + 0.930362i \(0.380508\pi\)
\(840\) −11.3972 −0.393240
\(841\) −28.9067 −0.996783
\(842\) 64.9676 2.23893
\(843\) 3.19996 0.110212
\(844\) −38.8295 −1.33657
\(845\) −80.6711 −2.77517
\(846\) −8.53564 −0.293461
\(847\) 10.5935 0.363998
\(848\) −9.56611 −0.328502
\(849\) 15.3772 0.527743
\(850\) 7.70241 0.264190
\(851\) −49.6913 −1.70340
\(852\) 8.26542 0.283169
\(853\) −38.3922 −1.31452 −0.657261 0.753663i \(-0.728285\pi\)
−0.657261 + 0.753663i \(0.728285\pi\)
\(854\) −78.5638 −2.68840
\(855\) −5.13948 −0.175766
\(856\) −26.4420 −0.903768
\(857\) −45.0266 −1.53808 −0.769040 0.639201i \(-0.779265\pi\)
−0.769040 + 0.639201i \(0.779265\pi\)
\(858\) 37.9879 1.29688
\(859\) −20.7032 −0.706384 −0.353192 0.935551i \(-0.614904\pi\)
−0.353192 + 0.935551i \(0.614904\pi\)
\(860\) 27.3891 0.933960
\(861\) −25.8711 −0.881685
\(862\) −77.8730 −2.65236
\(863\) −36.3877 −1.23865 −0.619326 0.785134i \(-0.712594\pi\)
−0.619326 + 0.785134i \(0.712594\pi\)
\(864\) −36.7791 −1.25125
\(865\) 5.43660 0.184850
\(866\) 0.303880 0.0103263
\(867\) −12.6347 −0.429098
\(868\) −2.63132 −0.0893128
\(869\) −12.2150 −0.414367
\(870\) 1.73852 0.0589414
\(871\) 28.2979 0.958838
\(872\) 25.9858 0.879991
\(873\) −20.0369 −0.678148
\(874\) 17.1436 0.579890
\(875\) −21.2701 −0.719062
\(876\) 32.7885 1.10782
\(877\) −35.6706 −1.20451 −0.602256 0.798303i \(-0.705731\pi\)
−0.602256 + 0.798303i \(0.705731\pi\)
\(878\) 13.7901 0.465394
\(879\) −23.5177 −0.793231
\(880\) −11.5418 −0.389074
\(881\) −34.8208 −1.17314 −0.586572 0.809897i \(-0.699523\pi\)
−0.586572 + 0.809897i \(0.699523\pi\)
\(882\) −3.86464 −0.130129
\(883\) −13.6814 −0.460414 −0.230207 0.973142i \(-0.573940\pi\)
−0.230207 + 0.973142i \(0.573940\pi\)
\(884\) −39.3219 −1.32254
\(885\) 2.38161 0.0800568
\(886\) 51.3082 1.72373
\(887\) 1.09074 0.0366234 0.0183117 0.999832i \(-0.494171\pi\)
0.0183117 + 0.999832i \(0.494171\pi\)
\(888\) 11.3455 0.380728
\(889\) 25.6552 0.860447
\(890\) −42.0908 −1.41089
\(891\) −2.41284 −0.0808331
\(892\) 21.2181 0.710435
\(893\) 1.95564 0.0654430
\(894\) −50.4274 −1.68654
\(895\) 57.4485 1.92029
\(896\) −32.2533 −1.07751
\(897\) 52.2475 1.74449
\(898\) −27.0697 −0.903327
\(899\) 0.115681 0.00385819
\(900\) −9.33387 −0.311129
\(901\) −11.6711 −0.388820
\(902\) 59.1722 1.97022
\(903\) 9.37946 0.312129
\(904\) −23.6330 −0.786020
\(905\) 54.3739 1.80745
\(906\) −20.3966 −0.677632
\(907\) −0.767764 −0.0254932 −0.0127466 0.999919i \(-0.504057\pi\)
−0.0127466 + 0.999919i \(0.504057\pi\)
\(908\) 41.6732 1.38297
\(909\) −25.3019 −0.839210
\(910\) −93.1493 −3.08787
\(911\) 2.22474 0.0737088 0.0368544 0.999321i \(-0.488266\pi\)
0.0368544 + 0.999321i \(0.488266\pi\)
\(912\) 1.73307 0.0573877
\(913\) −23.0586 −0.763129
\(914\) 6.35777 0.210296
\(915\) 37.5962 1.24289
\(916\) 14.8756 0.491502
\(917\) −20.8770 −0.689419
\(918\) −23.1403 −0.763742
\(919\) 47.7923 1.57652 0.788261 0.615341i \(-0.210982\pi\)
0.788261 + 0.615341i \(0.210982\pi\)
\(920\) 35.8526 1.18202
\(921\) 19.8281 0.653357
\(922\) 73.2574 2.41260
\(923\) 19.4695 0.640845
\(924\) 18.0944 0.595261
\(925\) −10.6107 −0.348879
\(926\) −19.7844 −0.650157
\(927\) −2.52901 −0.0830635
\(928\) 2.24030 0.0735414
\(929\) −1.13944 −0.0373839 −0.0186920 0.999825i \(-0.505950\pi\)
−0.0186920 + 0.999825i \(0.505950\pi\)
\(930\) 2.15549 0.0706812
\(931\) 0.885445 0.0290193
\(932\) −84.7370 −2.77565
\(933\) −6.40683 −0.209750
\(934\) 64.4571 2.10910
\(935\) −14.0815 −0.460515
\(936\) 23.5086 0.768404
\(937\) −19.2240 −0.628020 −0.314010 0.949420i \(-0.601673\pi\)
−0.314010 + 0.949420i \(0.601673\pi\)
\(938\) 23.0730 0.753359
\(939\) −12.6847 −0.413950
\(940\) 14.1906 0.462848
\(941\) 51.6398 1.68341 0.841705 0.539938i \(-0.181552\pi\)
0.841705 + 0.539938i \(0.181552\pi\)
\(942\) −39.1818 −1.27661
\(943\) 81.3839 2.65022
\(944\) 1.58266 0.0515112
\(945\) −32.0230 −1.04171
\(946\) −21.4526 −0.697486
\(947\) 16.9550 0.550965 0.275482 0.961306i \(-0.411162\pi\)
0.275482 + 0.961306i \(0.411162\pi\)
\(948\) 13.3091 0.432261
\(949\) 77.2343 2.50713
\(950\) 3.66072 0.118769
\(951\) −1.00492 −0.0325867
\(952\) −9.24039 −0.299483
\(953\) −20.9528 −0.678727 −0.339364 0.940655i \(-0.610212\pi\)
−0.339364 + 0.940655i \(0.610212\pi\)
\(954\) 24.2101 0.783832
\(955\) 34.6988 1.12283
\(956\) −25.3891 −0.821142
\(957\) −0.795486 −0.0257144
\(958\) −20.7689 −0.671013
\(959\) −16.2121 −0.523515
\(960\) 32.7922 1.05836
\(961\) −30.8566 −0.995373
\(962\) 92.7267 2.98963
\(963\) −29.6298 −0.954809
\(964\) −62.6632 −2.01825
\(965\) 59.5187 1.91597
\(966\) 42.6005 1.37065
\(967\) 18.9877 0.610604 0.305302 0.952256i \(-0.401243\pi\)
0.305302 + 0.952256i \(0.401243\pi\)
\(968\) 7.60861 0.244550
\(969\) 2.11442 0.0679250
\(970\) 57.0228 1.83089
\(971\) 44.9942 1.44393 0.721967 0.691928i \(-0.243238\pi\)
0.721967 + 0.691928i \(0.243238\pi\)
\(972\) 44.8999 1.44017
\(973\) 46.0893 1.47756
\(974\) 22.4963 0.720829
\(975\) 11.1566 0.357296
\(976\) 24.9840 0.799718
\(977\) 18.4484 0.590216 0.295108 0.955464i \(-0.404644\pi\)
0.295108 + 0.955464i \(0.404644\pi\)
\(978\) −29.7702 −0.951947
\(979\) 19.2593 0.615528
\(980\) 6.42502 0.205240
\(981\) 29.1187 0.929689
\(982\) 9.08367 0.289872
\(983\) 44.2279 1.41065 0.705325 0.708884i \(-0.250801\pi\)
0.705325 + 0.708884i \(0.250801\pi\)
\(984\) −18.5814 −0.592355
\(985\) 48.2268 1.53663
\(986\) 1.40953 0.0448885
\(987\) 4.85963 0.154684
\(988\) −18.6885 −0.594560
\(989\) −29.5054 −0.938217
\(990\) 29.2103 0.928363
\(991\) −28.1177 −0.893188 −0.446594 0.894737i \(-0.647363\pi\)
−0.446594 + 0.894737i \(0.647363\pi\)
\(992\) 2.77761 0.0881893
\(993\) −1.89945 −0.0602774
\(994\) 15.8746 0.503512
\(995\) −21.4122 −0.678814
\(996\) 25.1240 0.796085
\(997\) −10.9603 −0.347117 −0.173558 0.984824i \(-0.555527\pi\)
−0.173558 + 0.984824i \(0.555527\pi\)
\(998\) 70.6147 2.23527
\(999\) 31.8777 1.00857
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 \(a_p\))