Properties

Label 8011.2.a.b.1.7
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69935 q^{2}\) \(+1.61559 q^{3}\) \(+5.28646 q^{4}\) \(+2.80670 q^{5}\) \(-4.36103 q^{6}\) \(+2.73763 q^{7}\) \(-8.87130 q^{8}\) \(-0.389878 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69935 q^{2}\) \(+1.61559 q^{3}\) \(+5.28646 q^{4}\) \(+2.80670 q^{5}\) \(-4.36103 q^{6}\) \(+2.73763 q^{7}\) \(-8.87130 q^{8}\) \(-0.389878 q^{9}\) \(-7.57626 q^{10}\) \(+3.22381 q^{11}\) \(+8.54074 q^{12}\) \(+4.46543 q^{13}\) \(-7.38981 q^{14}\) \(+4.53447 q^{15}\) \(+13.3738 q^{16}\) \(+5.42508 q^{17}\) \(+1.05242 q^{18}\) \(-2.28573 q^{19}\) \(+14.8375 q^{20}\) \(+4.42288 q^{21}\) \(-8.70217 q^{22}\) \(-6.19782 q^{23}\) \(-14.3324 q^{24}\) \(+2.87757 q^{25}\) \(-12.0537 q^{26}\) \(-5.47664 q^{27}\) \(+14.4724 q^{28}\) \(+0.0185387 q^{29}\) \(-12.2401 q^{30}\) \(+5.36769 q^{31}\) \(-18.3578 q^{32}\) \(+5.20834 q^{33}\) \(-14.6442 q^{34}\) \(+7.68372 q^{35}\) \(-2.06108 q^{36}\) \(-7.87298 q^{37}\) \(+6.16997 q^{38}\) \(+7.21429 q^{39}\) \(-24.8991 q^{40}\) \(+2.29163 q^{41}\) \(-11.9389 q^{42}\) \(-0.973599 q^{43}\) \(+17.0425 q^{44}\) \(-1.09427 q^{45}\) \(+16.7301 q^{46}\) \(+9.69254 q^{47}\) \(+21.6065 q^{48}\) \(+0.494627 q^{49}\) \(-7.76757 q^{50}\) \(+8.76469 q^{51}\) \(+23.6063 q^{52}\) \(-7.73306 q^{53}\) \(+14.7834 q^{54}\) \(+9.04826 q^{55}\) \(-24.2864 q^{56}\) \(-3.69279 q^{57}\) \(-0.0500423 q^{58}\) \(+12.1987 q^{59}\) \(+23.9713 q^{60}\) \(-10.2477 q^{61}\) \(-14.4893 q^{62}\) \(-1.06734 q^{63}\) \(+22.8066 q^{64}\) \(+12.5331 q^{65}\) \(-14.0591 q^{66}\) \(+6.76491 q^{67}\) \(+28.6795 q^{68}\) \(-10.0131 q^{69}\) \(-20.7410 q^{70}\) \(+15.3486 q^{71}\) \(+3.45873 q^{72}\) \(-5.09820 q^{73}\) \(+21.2519 q^{74}\) \(+4.64897 q^{75}\) \(-12.0834 q^{76}\) \(+8.82559 q^{77}\) \(-19.4739 q^{78}\) \(-5.64660 q^{79}\) \(+37.5362 q^{80}\) \(-7.67836 q^{81}\) \(-6.18591 q^{82}\) \(-5.87421 q^{83}\) \(+23.3814 q^{84}\) \(+15.2266 q^{85}\) \(+2.62808 q^{86}\) \(+0.0299509 q^{87}\) \(-28.5994 q^{88}\) \(+0.696095 q^{89}\) \(+2.95382 q^{90}\) \(+12.2247 q^{91}\) \(-32.7646 q^{92}\) \(+8.67198 q^{93}\) \(-26.1635 q^{94}\) \(-6.41536 q^{95}\) \(-29.6587 q^{96}\) \(+8.33689 q^{97}\) \(-1.33517 q^{98}\) \(-1.25689 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69935 −1.90873 −0.954363 0.298650i \(-0.903464\pi\)
−0.954363 + 0.298650i \(0.903464\pi\)
\(3\) 1.61559 0.932760 0.466380 0.884585i \(-0.345558\pi\)
0.466380 + 0.884585i \(0.345558\pi\)
\(4\) 5.28646 2.64323
\(5\) 2.80670 1.25520 0.627598 0.778538i \(-0.284038\pi\)
0.627598 + 0.778538i \(0.284038\pi\)
\(6\) −4.36103 −1.78038
\(7\) 2.73763 1.03473 0.517364 0.855766i \(-0.326913\pi\)
0.517364 + 0.855766i \(0.326913\pi\)
\(8\) −8.87130 −3.13648
\(9\) −0.389878 −0.129959
\(10\) −7.57626 −2.39582
\(11\) 3.22381 0.972014 0.486007 0.873955i \(-0.338453\pi\)
0.486007 + 0.873955i \(0.338453\pi\)
\(12\) 8.54074 2.46550
\(13\) 4.46543 1.23849 0.619244 0.785199i \(-0.287439\pi\)
0.619244 + 0.785199i \(0.287439\pi\)
\(14\) −7.38981 −1.97501
\(15\) 4.53447 1.17080
\(16\) 13.3738 3.34344
\(17\) 5.42508 1.31578 0.657888 0.753116i \(-0.271450\pi\)
0.657888 + 0.753116i \(0.271450\pi\)
\(18\) 1.05242 0.248057
\(19\) −2.28573 −0.524382 −0.262191 0.965016i \(-0.584445\pi\)
−0.262191 + 0.965016i \(0.584445\pi\)
\(20\) 14.8375 3.31777
\(21\) 4.42288 0.965152
\(22\) −8.70217 −1.85531
\(23\) −6.19782 −1.29234 −0.646168 0.763195i \(-0.723629\pi\)
−0.646168 + 0.763195i \(0.723629\pi\)
\(24\) −14.3324 −2.92558
\(25\) 2.87757 0.575515
\(26\) −12.0537 −2.36393
\(27\) −5.47664 −1.05398
\(28\) 14.4724 2.73503
\(29\) 0.0185387 0.00344255 0.00172127 0.999999i \(-0.499452\pi\)
0.00172127 + 0.999999i \(0.499452\pi\)
\(30\) −12.2401 −2.23473
\(31\) 5.36769 0.964066 0.482033 0.876153i \(-0.339899\pi\)
0.482033 + 0.876153i \(0.339899\pi\)
\(32\) −18.3578 −3.24524
\(33\) 5.20834 0.906656
\(34\) −14.6442 −2.51145
\(35\) 7.68372 1.29878
\(36\) −2.06108 −0.343513
\(37\) −7.87298 −1.29431 −0.647155 0.762359i \(-0.724041\pi\)
−0.647155 + 0.762359i \(0.724041\pi\)
\(38\) 6.16997 1.00090
\(39\) 7.21429 1.15521
\(40\) −24.8991 −3.93689
\(41\) 2.29163 0.357893 0.178946 0.983859i \(-0.442731\pi\)
0.178946 + 0.983859i \(0.442731\pi\)
\(42\) −11.9389 −1.84221
\(43\) −0.973599 −0.148472 −0.0742362 0.997241i \(-0.523652\pi\)
−0.0742362 + 0.997241i \(0.523652\pi\)
\(44\) 17.0425 2.56926
\(45\) −1.09427 −0.163124
\(46\) 16.7301 2.46671
\(47\) 9.69254 1.41380 0.706901 0.707312i \(-0.250093\pi\)
0.706901 + 0.707312i \(0.250093\pi\)
\(48\) 21.6065 3.11863
\(49\) 0.494627 0.0706610
\(50\) −7.76757 −1.09850
\(51\) 8.76469 1.22730
\(52\) 23.6063 3.27361
\(53\) −7.73306 −1.06222 −0.531108 0.847304i \(-0.678224\pi\)
−0.531108 + 0.847304i \(0.678224\pi\)
\(54\) 14.7834 2.01176
\(55\) 9.04826 1.22007
\(56\) −24.2864 −3.24540
\(57\) −3.69279 −0.489122
\(58\) −0.0500423 −0.00657088
\(59\) 12.1987 1.58813 0.794065 0.607832i \(-0.207961\pi\)
0.794065 + 0.607832i \(0.207961\pi\)
\(60\) 23.9713 3.09468
\(61\) −10.2477 −1.31208 −0.656042 0.754724i \(-0.727771\pi\)
−0.656042 + 0.754724i \(0.727771\pi\)
\(62\) −14.4893 −1.84014
\(63\) −1.06734 −0.134473
\(64\) 22.8066 2.85082
\(65\) 12.5331 1.55454
\(66\) −14.0591 −1.73056
\(67\) 6.76491 0.826465 0.413233 0.910625i \(-0.364400\pi\)
0.413233 + 0.910625i \(0.364400\pi\)
\(68\) 28.6795 3.47790
\(69\) −10.0131 −1.20544
\(70\) −20.7410 −2.47902
\(71\) 15.3486 1.82155 0.910774 0.412904i \(-0.135486\pi\)
0.910774 + 0.412904i \(0.135486\pi\)
\(72\) 3.45873 0.407615
\(73\) −5.09820 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(74\) 21.2519 2.47048
\(75\) 4.64897 0.536817
\(76\) −12.0834 −1.38606
\(77\) 8.82559 1.00577
\(78\) −19.4739 −2.20498
\(79\) −5.64660 −0.635292 −0.317646 0.948209i \(-0.602892\pi\)
−0.317646 + 0.948209i \(0.602892\pi\)
\(80\) 37.5362 4.19667
\(81\) −7.67836 −0.853151
\(82\) −6.18591 −0.683119
\(83\) −5.87421 −0.644778 −0.322389 0.946607i \(-0.604486\pi\)
−0.322389 + 0.946607i \(0.604486\pi\)
\(84\) 23.3814 2.55112
\(85\) 15.2266 1.65156
\(86\) 2.62808 0.283393
\(87\) 0.0299509 0.00321107
\(88\) −28.5994 −3.04870
\(89\) 0.696095 0.0737860 0.0368930 0.999319i \(-0.488254\pi\)
0.0368930 + 0.999319i \(0.488254\pi\)
\(90\) 2.95382 0.311360
\(91\) 12.2247 1.28150
\(92\) −32.7646 −3.41594
\(93\) 8.67198 0.899242
\(94\) −26.1635 −2.69856
\(95\) −6.41536 −0.658202
\(96\) −29.6587 −3.02703
\(97\) 8.33689 0.846483 0.423241 0.906017i \(-0.360892\pi\)
0.423241 + 0.906017i \(0.360892\pi\)
\(98\) −1.33517 −0.134872
\(99\) −1.25689 −0.126322
\(100\) 15.2122 1.52122
\(101\) 13.6484 1.35807 0.679035 0.734106i \(-0.262398\pi\)
0.679035 + 0.734106i \(0.262398\pi\)
\(102\) −23.6589 −2.34258
\(103\) 9.86724 0.972248 0.486124 0.873890i \(-0.338410\pi\)
0.486124 + 0.873890i \(0.338410\pi\)
\(104\) −39.6142 −3.88449
\(105\) 12.4137 1.21145
\(106\) 20.8742 2.02748
\(107\) 4.82711 0.466655 0.233327 0.972398i \(-0.425039\pi\)
0.233327 + 0.972398i \(0.425039\pi\)
\(108\) −28.9521 −2.78592
\(109\) −2.47040 −0.236622 −0.118311 0.992977i \(-0.537748\pi\)
−0.118311 + 0.992977i \(0.537748\pi\)
\(110\) −24.4244 −2.32877
\(111\) −12.7195 −1.20728
\(112\) 36.6125 3.45955
\(113\) −8.12829 −0.764645 −0.382323 0.924029i \(-0.624876\pi\)
−0.382323 + 0.924029i \(0.624876\pi\)
\(114\) 9.96812 0.933600
\(115\) −17.3954 −1.62213
\(116\) 0.0980042 0.00909946
\(117\) −1.74097 −0.160953
\(118\) −32.9284 −3.03131
\(119\) 14.8519 1.36147
\(120\) −40.2267 −3.67218
\(121\) −0.607074 −0.0551885
\(122\) 27.6621 2.50441
\(123\) 3.70233 0.333828
\(124\) 28.3761 2.54825
\(125\) −5.95701 −0.532812
\(126\) 2.88113 0.256671
\(127\) −16.0014 −1.41990 −0.709949 0.704253i \(-0.751282\pi\)
−0.709949 + 0.704253i \(0.751282\pi\)
\(128\) −24.8472 −2.19620
\(129\) −1.57293 −0.138489
\(130\) −33.8312 −2.96720
\(131\) −5.38695 −0.470660 −0.235330 0.971915i \(-0.575617\pi\)
−0.235330 + 0.971915i \(0.575617\pi\)
\(132\) 27.5337 2.39650
\(133\) −6.25748 −0.542592
\(134\) −18.2608 −1.57750
\(135\) −15.3713 −1.32295
\(136\) −48.1275 −4.12690
\(137\) 10.0662 0.860014 0.430007 0.902826i \(-0.358511\pi\)
0.430007 + 0.902826i \(0.358511\pi\)
\(138\) 27.0289 2.30085
\(139\) −5.65923 −0.480010 −0.240005 0.970772i \(-0.577149\pi\)
−0.240005 + 0.970772i \(0.577149\pi\)
\(140\) 40.6197 3.43299
\(141\) 15.6591 1.31874
\(142\) −41.4313 −3.47684
\(143\) 14.3957 1.20383
\(144\) −5.21414 −0.434512
\(145\) 0.0520326 0.00432107
\(146\) 13.7618 1.13893
\(147\) 0.799113 0.0659098
\(148\) −41.6202 −3.42116
\(149\) 6.90427 0.565620 0.282810 0.959176i \(-0.408733\pi\)
0.282810 + 0.959176i \(0.408733\pi\)
\(150\) −12.5492 −1.02464
\(151\) 10.1032 0.822185 0.411092 0.911594i \(-0.365147\pi\)
0.411092 + 0.911594i \(0.365147\pi\)
\(152\) 20.2774 1.64471
\(153\) −2.11512 −0.170997
\(154\) −23.8233 −1.91974
\(155\) 15.0655 1.21009
\(156\) 38.1381 3.05349
\(157\) 12.8612 1.02644 0.513219 0.858258i \(-0.328453\pi\)
0.513219 + 0.858258i \(0.328453\pi\)
\(158\) 15.2421 1.21260
\(159\) −12.4934 −0.990793
\(160\) −51.5250 −4.07341
\(161\) −16.9674 −1.33722
\(162\) 20.7265 1.62843
\(163\) 16.9697 1.32917 0.664584 0.747214i \(-0.268609\pi\)
0.664584 + 0.747214i \(0.268609\pi\)
\(164\) 12.1146 0.945994
\(165\) 14.6183 1.13803
\(166\) 15.8565 1.23070
\(167\) 7.98754 0.618094 0.309047 0.951047i \(-0.399990\pi\)
0.309047 + 0.951047i \(0.399990\pi\)
\(168\) −39.2367 −3.02718
\(169\) 6.94006 0.533851
\(170\) −41.1018 −3.15237
\(171\) 0.891155 0.0681483
\(172\) −5.14690 −0.392447
\(173\) −3.21956 −0.244779 −0.122389 0.992482i \(-0.539056\pi\)
−0.122389 + 0.992482i \(0.539056\pi\)
\(174\) −0.0808478 −0.00612905
\(175\) 7.87774 0.595501
\(176\) 43.1145 3.24987
\(177\) 19.7080 1.48134
\(178\) −1.87900 −0.140837
\(179\) 11.6585 0.871397 0.435698 0.900093i \(-0.356501\pi\)
0.435698 + 0.900093i \(0.356501\pi\)
\(180\) −5.78483 −0.431176
\(181\) −4.39941 −0.327005 −0.163503 0.986543i \(-0.552279\pi\)
−0.163503 + 0.986543i \(0.552279\pi\)
\(182\) −32.9987 −2.44603
\(183\) −16.5561 −1.22386
\(184\) 54.9828 4.05338
\(185\) −22.0971 −1.62461
\(186\) −23.4087 −1.71641
\(187\) 17.4894 1.27895
\(188\) 51.2393 3.73701
\(189\) −14.9930 −1.09058
\(190\) 17.3173 1.25633
\(191\) 10.5877 0.766098 0.383049 0.923728i \(-0.374874\pi\)
0.383049 + 0.923728i \(0.374874\pi\)
\(192\) 36.8460 2.65913
\(193\) 3.73706 0.268999 0.134500 0.990914i \(-0.457057\pi\)
0.134500 + 0.990914i \(0.457057\pi\)
\(194\) −22.5041 −1.61570
\(195\) 20.2484 1.45002
\(196\) 2.61483 0.186774
\(197\) 16.4679 1.17329 0.586643 0.809845i \(-0.300449\pi\)
0.586643 + 0.809845i \(0.300449\pi\)
\(198\) 3.39278 0.241115
\(199\) −6.85488 −0.485930 −0.242965 0.970035i \(-0.578120\pi\)
−0.242965 + 0.970035i \(0.578120\pi\)
\(200\) −25.5278 −1.80509
\(201\) 10.9293 0.770894
\(202\) −36.8419 −2.59218
\(203\) 0.0507521 0.00356210
\(204\) 46.3342 3.24405
\(205\) 6.43193 0.449225
\(206\) −26.6351 −1.85575
\(207\) 2.41640 0.167951
\(208\) 59.7196 4.14081
\(209\) −7.36874 −0.509707
\(210\) −33.5089 −2.31233
\(211\) −11.4328 −0.787067 −0.393534 0.919310i \(-0.628748\pi\)
−0.393534 + 0.919310i \(0.628748\pi\)
\(212\) −40.8805 −2.80769
\(213\) 24.7971 1.69907
\(214\) −13.0300 −0.890715
\(215\) −2.73260 −0.186362
\(216\) 48.5850 3.30579
\(217\) 14.6948 0.997546
\(218\) 6.66847 0.451646
\(219\) −8.23659 −0.556577
\(220\) 47.8333 3.22492
\(221\) 24.2253 1.62957
\(222\) 34.3343 2.30437
\(223\) 16.5915 1.11105 0.555525 0.831500i \(-0.312517\pi\)
0.555525 + 0.831500i \(0.312517\pi\)
\(224\) −50.2570 −3.35794
\(225\) −1.12190 −0.0747936
\(226\) 21.9411 1.45950
\(227\) −16.2801 −1.08055 −0.540275 0.841489i \(-0.681680\pi\)
−0.540275 + 0.841489i \(0.681680\pi\)
\(228\) −19.5218 −1.29286
\(229\) −27.7587 −1.83435 −0.917173 0.398490i \(-0.869534\pi\)
−0.917173 + 0.398490i \(0.869534\pi\)
\(230\) 46.9563 3.09621
\(231\) 14.2585 0.938141
\(232\) −0.164462 −0.0107975
\(233\) 11.7529 0.769960 0.384980 0.922925i \(-0.374208\pi\)
0.384980 + 0.922925i \(0.374208\pi\)
\(234\) 4.69949 0.307215
\(235\) 27.2041 1.77460
\(236\) 64.4878 4.19780
\(237\) −9.12257 −0.592575
\(238\) −40.0903 −2.59867
\(239\) 20.9303 1.35387 0.676935 0.736043i \(-0.263308\pi\)
0.676935 + 0.736043i \(0.263308\pi\)
\(240\) 60.6430 3.91449
\(241\) 12.8154 0.825514 0.412757 0.910841i \(-0.364566\pi\)
0.412757 + 0.910841i \(0.364566\pi\)
\(242\) 1.63870 0.105340
\(243\) 4.02487 0.258195
\(244\) −54.1741 −3.46814
\(245\) 1.38827 0.0886934
\(246\) −9.99387 −0.637186
\(247\) −10.2068 −0.649440
\(248\) −47.6184 −3.02377
\(249\) −9.49029 −0.601423
\(250\) 16.0800 1.01699
\(251\) −0.636455 −0.0401727 −0.0200863 0.999798i \(-0.506394\pi\)
−0.0200863 + 0.999798i \(0.506394\pi\)
\(252\) −5.64247 −0.355442
\(253\) −19.9806 −1.25617
\(254\) 43.1934 2.71020
\(255\) 24.5999 1.54050
\(256\) 21.4579 1.34112
\(257\) −20.1060 −1.25418 −0.627088 0.778948i \(-0.715753\pi\)
−0.627088 + 0.778948i \(0.715753\pi\)
\(258\) 4.24589 0.264338
\(259\) −21.5533 −1.33926
\(260\) 66.2559 4.10902
\(261\) −0.00722783 −0.000447392 0
\(262\) 14.5412 0.898361
\(263\) 11.1092 0.685025 0.342512 0.939513i \(-0.388722\pi\)
0.342512 + 0.939513i \(0.388722\pi\)
\(264\) −46.2048 −2.84371
\(265\) −21.7044 −1.33329
\(266\) 16.8911 1.03566
\(267\) 1.12460 0.0688246
\(268\) 35.7625 2.18454
\(269\) −4.00083 −0.243935 −0.121968 0.992534i \(-0.538920\pi\)
−0.121968 + 0.992534i \(0.538920\pi\)
\(270\) 41.4925 2.52515
\(271\) 10.1515 0.616659 0.308329 0.951280i \(-0.400230\pi\)
0.308329 + 0.951280i \(0.400230\pi\)
\(272\) 72.5538 4.39922
\(273\) 19.7501 1.19533
\(274\) −27.1722 −1.64153
\(275\) 9.27674 0.559409
\(276\) −52.9340 −3.18625
\(277\) −5.71052 −0.343112 −0.171556 0.985174i \(-0.554879\pi\)
−0.171556 + 0.985174i \(0.554879\pi\)
\(278\) 15.2762 0.916207
\(279\) −2.09275 −0.125289
\(280\) −68.1646 −4.07361
\(281\) 11.8737 0.708326 0.354163 0.935184i \(-0.384766\pi\)
0.354163 + 0.935184i \(0.384766\pi\)
\(282\) −42.2694 −2.51711
\(283\) 15.3477 0.912328 0.456164 0.889896i \(-0.349223\pi\)
0.456164 + 0.889896i \(0.349223\pi\)
\(284\) 81.1400 4.81478
\(285\) −10.3646 −0.613944
\(286\) −38.8589 −2.29778
\(287\) 6.27364 0.370322
\(288\) 7.15732 0.421749
\(289\) 12.4315 0.731266
\(290\) −0.140454 −0.00824774
\(291\) 13.4690 0.789565
\(292\) −26.9514 −1.57721
\(293\) 16.9583 0.990715 0.495357 0.868689i \(-0.335037\pi\)
0.495357 + 0.868689i \(0.335037\pi\)
\(294\) −2.15708 −0.125804
\(295\) 34.2380 1.99341
\(296\) 69.8436 4.05957
\(297\) −17.6556 −1.02448
\(298\) −18.6370 −1.07961
\(299\) −27.6759 −1.60054
\(300\) 24.5766 1.41893
\(301\) −2.66536 −0.153629
\(302\) −27.2720 −1.56932
\(303\) 22.0502 1.26675
\(304\) −30.5688 −1.75324
\(305\) −28.7623 −1.64692
\(306\) 5.70944 0.326387
\(307\) 15.8443 0.904282 0.452141 0.891947i \(-0.350660\pi\)
0.452141 + 0.891947i \(0.350660\pi\)
\(308\) 46.6562 2.65848
\(309\) 15.9414 0.906874
\(310\) −40.6670 −2.30973
\(311\) −30.0204 −1.70230 −0.851150 0.524922i \(-0.824095\pi\)
−0.851150 + 0.524922i \(0.824095\pi\)
\(312\) −64.0001 −3.62329
\(313\) 34.1666 1.93121 0.965606 0.260009i \(-0.0837256\pi\)
0.965606 + 0.260009i \(0.0837256\pi\)
\(314\) −34.7169 −1.95919
\(315\) −2.99571 −0.168789
\(316\) −29.8506 −1.67922
\(317\) −16.3123 −0.916192 −0.458096 0.888903i \(-0.651468\pi\)
−0.458096 + 0.888903i \(0.651468\pi\)
\(318\) 33.7241 1.89115
\(319\) 0.0597652 0.00334621
\(320\) 64.0113 3.57834
\(321\) 7.79862 0.435277
\(322\) 45.8008 2.55238
\(323\) −12.4003 −0.689969
\(324\) −40.5914 −2.25508
\(325\) 12.8496 0.712768
\(326\) −45.8070 −2.53702
\(327\) −3.99115 −0.220711
\(328\) −20.3298 −1.12252
\(329\) 26.5346 1.46290
\(330\) −39.4597 −2.17219
\(331\) −12.4746 −0.685666 −0.342833 0.939396i \(-0.611387\pi\)
−0.342833 + 0.939396i \(0.611387\pi\)
\(332\) −31.0538 −1.70430
\(333\) 3.06950 0.168208
\(334\) −21.5611 −1.17977
\(335\) 18.9871 1.03738
\(336\) 59.1506 3.22693
\(337\) −5.91282 −0.322092 −0.161046 0.986947i \(-0.551487\pi\)
−0.161046 + 0.986947i \(0.551487\pi\)
\(338\) −18.7336 −1.01897
\(339\) −13.1320 −0.713230
\(340\) 80.4948 4.36544
\(341\) 17.3044 0.937086
\(342\) −2.40554 −0.130076
\(343\) −17.8093 −0.961613
\(344\) 8.63709 0.465681
\(345\) −28.1039 −1.51306
\(346\) 8.69071 0.467215
\(347\) −20.0116 −1.07428 −0.537139 0.843494i \(-0.680495\pi\)
−0.537139 + 0.843494i \(0.680495\pi\)
\(348\) 0.158334 0.00848761
\(349\) 32.4820 1.73872 0.869362 0.494176i \(-0.164530\pi\)
0.869362 + 0.494176i \(0.164530\pi\)
\(350\) −21.2647 −1.13665
\(351\) −24.4556 −1.30534
\(352\) −59.1821 −3.15442
\(353\) −28.1593 −1.49877 −0.749384 0.662135i \(-0.769650\pi\)
−0.749384 + 0.662135i \(0.769650\pi\)
\(354\) −53.1987 −2.82748
\(355\) 43.0791 2.28640
\(356\) 3.67988 0.195033
\(357\) 23.9945 1.26992
\(358\) −31.4703 −1.66326
\(359\) −7.12188 −0.375879 −0.187939 0.982181i \(-0.560181\pi\)
−0.187939 + 0.982181i \(0.560181\pi\)
\(360\) 9.70761 0.511636
\(361\) −13.7754 −0.725024
\(362\) 11.8755 0.624164
\(363\) −0.980780 −0.0514776
\(364\) 64.6254 3.38729
\(365\) −14.3091 −0.748974
\(366\) 44.6905 2.33601
\(367\) −29.3222 −1.53061 −0.765303 0.643670i \(-0.777411\pi\)
−0.765303 + 0.643670i \(0.777411\pi\)
\(368\) −82.8883 −4.32085
\(369\) −0.893457 −0.0465115
\(370\) 59.6477 3.10094
\(371\) −21.1703 −1.09911
\(372\) 45.8441 2.37691
\(373\) 4.56753 0.236498 0.118249 0.992984i \(-0.462272\pi\)
0.118249 + 0.992984i \(0.462272\pi\)
\(374\) −47.2100 −2.44117
\(375\) −9.62408 −0.496985
\(376\) −85.9855 −4.43436
\(377\) 0.0827832 0.00426355
\(378\) 40.4714 2.08162
\(379\) −24.3399 −1.25026 −0.625129 0.780522i \(-0.714954\pi\)
−0.625129 + 0.780522i \(0.714954\pi\)
\(380\) −33.9145 −1.73978
\(381\) −25.8517 −1.32442
\(382\) −28.5798 −1.46227
\(383\) −26.1459 −1.33599 −0.667996 0.744165i \(-0.732847\pi\)
−0.667996 + 0.744165i \(0.732847\pi\)
\(384\) −40.1428 −2.04853
\(385\) 24.7708 1.26244
\(386\) −10.0876 −0.513446
\(387\) 0.379585 0.0192954
\(388\) 44.0726 2.23745
\(389\) 24.5896 1.24674 0.623372 0.781925i \(-0.285762\pi\)
0.623372 + 0.781925i \(0.285762\pi\)
\(390\) −54.6573 −2.76768
\(391\) −33.6237 −1.70042
\(392\) −4.38799 −0.221627
\(393\) −8.70309 −0.439013
\(394\) −44.4525 −2.23948
\(395\) −15.8483 −0.797416
\(396\) −6.64451 −0.333899
\(397\) −34.5838 −1.73571 −0.867856 0.496816i \(-0.834503\pi\)
−0.867856 + 0.496816i \(0.834503\pi\)
\(398\) 18.5037 0.927506
\(399\) −10.1095 −0.506108
\(400\) 38.4840 1.92420
\(401\) 16.5443 0.826183 0.413092 0.910689i \(-0.364449\pi\)
0.413092 + 0.910689i \(0.364449\pi\)
\(402\) −29.5020 −1.47142
\(403\) 23.9691 1.19398
\(404\) 72.1520 3.58970
\(405\) −21.5509 −1.07087
\(406\) −0.136997 −0.00679907
\(407\) −25.3810 −1.25809
\(408\) −77.7542 −3.84941
\(409\) −30.7387 −1.51993 −0.759965 0.649964i \(-0.774784\pi\)
−0.759965 + 0.649964i \(0.774784\pi\)
\(410\) −17.3620 −0.857448
\(411\) 16.2628 0.802186
\(412\) 52.1628 2.56988
\(413\) 33.3955 1.64328
\(414\) −6.52269 −0.320573
\(415\) −16.4871 −0.809322
\(416\) −81.9756 −4.01918
\(417\) −9.14298 −0.447734
\(418\) 19.8908 0.972890
\(419\) −12.1334 −0.592757 −0.296378 0.955071i \(-0.595779\pi\)
−0.296378 + 0.955071i \(0.595779\pi\)
\(420\) 65.6246 3.20215
\(421\) −33.6381 −1.63942 −0.819709 0.572780i \(-0.805865\pi\)
−0.819709 + 0.572780i \(0.805865\pi\)
\(422\) 30.8611 1.50230
\(423\) −3.77891 −0.183737
\(424\) 68.6023 3.33162
\(425\) 15.6111 0.757249
\(426\) −66.9359 −3.24305
\(427\) −28.0544 −1.35765
\(428\) 25.5184 1.23348
\(429\) 23.2575 1.12288
\(430\) 7.37624 0.355714
\(431\) 32.2483 1.55335 0.776674 0.629903i \(-0.216905\pi\)
0.776674 + 0.629903i \(0.216905\pi\)
\(432\) −73.2434 −3.52392
\(433\) 14.7476 0.708727 0.354363 0.935108i \(-0.384698\pi\)
0.354363 + 0.935108i \(0.384698\pi\)
\(434\) −39.6662 −1.90404
\(435\) 0.0840632 0.00403052
\(436\) −13.0597 −0.625446
\(437\) 14.1665 0.677677
\(438\) 22.2334 1.06235
\(439\) −10.7878 −0.514875 −0.257437 0.966295i \(-0.582878\pi\)
−0.257437 + 0.966295i \(0.582878\pi\)
\(440\) −80.2699 −3.82672
\(441\) −0.192844 −0.00918306
\(442\) −65.3925 −3.11040
\(443\) −10.8152 −0.513846 −0.256923 0.966432i \(-0.582709\pi\)
−0.256923 + 0.966432i \(0.582709\pi\)
\(444\) −67.2411 −3.19112
\(445\) 1.95373 0.0926158
\(446\) −44.7862 −2.12069
\(447\) 11.1544 0.527587
\(448\) 62.4360 2.94982
\(449\) −18.9551 −0.894548 −0.447274 0.894397i \(-0.647605\pi\)
−0.447274 + 0.894397i \(0.647605\pi\)
\(450\) 3.02840 0.142760
\(451\) 7.38778 0.347877
\(452\) −42.9699 −2.02114
\(453\) 16.3226 0.766901
\(454\) 43.9457 2.06247
\(455\) 34.3111 1.60853
\(456\) 32.7599 1.53412
\(457\) 41.8831 1.95921 0.979605 0.200931i \(-0.0643967\pi\)
0.979605 + 0.200931i \(0.0643967\pi\)
\(458\) 74.9303 3.50126
\(459\) −29.7112 −1.38680
\(460\) −91.9604 −4.28768
\(461\) 18.8518 0.878016 0.439008 0.898483i \(-0.355330\pi\)
0.439008 + 0.898483i \(0.355330\pi\)
\(462\) −38.4887 −1.79065
\(463\) −17.9107 −0.832380 −0.416190 0.909278i \(-0.636635\pi\)
−0.416190 + 0.909278i \(0.636635\pi\)
\(464\) 0.247932 0.0115100
\(465\) 24.3396 1.12872
\(466\) −31.7252 −1.46964
\(467\) −8.62539 −0.399136 −0.199568 0.979884i \(-0.563954\pi\)
−0.199568 + 0.979884i \(0.563954\pi\)
\(468\) −9.20359 −0.425436
\(469\) 18.5198 0.855166
\(470\) −73.4332 −3.38722
\(471\) 20.7784 0.957420
\(472\) −108.218 −4.98114
\(473\) −3.13869 −0.144317
\(474\) 24.6250 1.13106
\(475\) −6.57735 −0.301790
\(476\) 78.5139 3.59868
\(477\) 3.01495 0.138045
\(478\) −56.4982 −2.58417
\(479\) −7.67865 −0.350846 −0.175423 0.984493i \(-0.556129\pi\)
−0.175423 + 0.984493i \(0.556129\pi\)
\(480\) −83.2431 −3.79951
\(481\) −35.1562 −1.60299
\(482\) −34.5932 −1.57568
\(483\) −27.4122 −1.24730
\(484\) −3.20927 −0.145876
\(485\) 23.3992 1.06250
\(486\) −10.8645 −0.492824
\(487\) −38.6373 −1.75082 −0.875411 0.483380i \(-0.839409\pi\)
−0.875411 + 0.483380i \(0.839409\pi\)
\(488\) 90.9105 4.11532
\(489\) 27.4160 1.23979
\(490\) −3.74742 −0.169291
\(491\) 0.300054 0.0135413 0.00677063 0.999977i \(-0.497845\pi\)
0.00677063 + 0.999977i \(0.497845\pi\)
\(492\) 19.5722 0.882385
\(493\) 0.100574 0.00452962
\(494\) 27.5516 1.23960
\(495\) −3.52772 −0.158559
\(496\) 71.7863 3.22330
\(497\) 42.0189 1.88481
\(498\) 25.6176 1.14795
\(499\) 17.7761 0.795766 0.397883 0.917436i \(-0.369745\pi\)
0.397883 + 0.917436i \(0.369745\pi\)
\(500\) −31.4915 −1.40834
\(501\) 12.9046 0.576533
\(502\) 1.71801 0.0766786
\(503\) −12.1693 −0.542603 −0.271301 0.962494i \(-0.587454\pi\)
−0.271301 + 0.962494i \(0.587454\pi\)
\(504\) 9.46872 0.421770
\(505\) 38.3071 1.70464
\(506\) 53.9345 2.39768
\(507\) 11.2123 0.497954
\(508\) −84.5911 −3.75312
\(509\) −19.0334 −0.843638 −0.421819 0.906680i \(-0.638608\pi\)
−0.421819 + 0.906680i \(0.638608\pi\)
\(510\) −66.4036 −2.94040
\(511\) −13.9570 −0.617421
\(512\) −8.22797 −0.363628
\(513\) 12.5181 0.552688
\(514\) 54.2730 2.39388
\(515\) 27.6944 1.22036
\(516\) −8.31526 −0.366059
\(517\) 31.2469 1.37424
\(518\) 58.1798 2.55627
\(519\) −5.20148 −0.228320
\(520\) −111.185 −4.87579
\(521\) 7.78162 0.340919 0.170460 0.985365i \(-0.445475\pi\)
0.170460 + 0.985365i \(0.445475\pi\)
\(522\) 0.0195104 0.000853948 0
\(523\) −12.4006 −0.542241 −0.271120 0.962545i \(-0.587394\pi\)
−0.271120 + 0.962545i \(0.587394\pi\)
\(524\) −28.4779 −1.24406
\(525\) 12.7272 0.555459
\(526\) −29.9876 −1.30752
\(527\) 29.1202 1.26849
\(528\) 69.6552 3.03135
\(529\) 15.4130 0.670132
\(530\) 58.5876 2.54488
\(531\) −4.75599 −0.206392
\(532\) −33.0799 −1.43420
\(533\) 10.2331 0.443246
\(534\) −3.03569 −0.131367
\(535\) 13.5483 0.585743
\(536\) −60.0136 −2.59219
\(537\) 18.8353 0.812804
\(538\) 10.7996 0.465605
\(539\) 1.59458 0.0686835
\(540\) −81.2599 −3.49687
\(541\) 43.8931 1.88711 0.943555 0.331215i \(-0.107459\pi\)
0.943555 + 0.331215i \(0.107459\pi\)
\(542\) −27.4023 −1.17703
\(543\) −7.10763 −0.305018
\(544\) −99.5928 −4.27000
\(545\) −6.93368 −0.297006
\(546\) −53.3123 −2.28155
\(547\) −34.1980 −1.46220 −0.731101 0.682269i \(-0.760993\pi\)
−0.731101 + 0.682269i \(0.760993\pi\)
\(548\) 53.2146 2.27322
\(549\) 3.99536 0.170518
\(550\) −25.0411 −1.06776
\(551\) −0.0423744 −0.00180521
\(552\) 88.8295 3.78083
\(553\) −15.4583 −0.657354
\(554\) 15.4147 0.654906
\(555\) −35.6998 −1.51537
\(556\) −29.9173 −1.26878
\(557\) 29.3786 1.24481 0.622406 0.782694i \(-0.286155\pi\)
0.622406 + 0.782694i \(0.286155\pi\)
\(558\) 5.64904 0.239143
\(559\) −4.34754 −0.183881
\(560\) 102.760 4.34241
\(561\) 28.2557 1.19296
\(562\) −32.0512 −1.35200
\(563\) 46.1162 1.94356 0.971782 0.235880i \(-0.0757973\pi\)
0.971782 + 0.235880i \(0.0757973\pi\)
\(564\) 82.7815 3.48573
\(565\) −22.8137 −0.959779
\(566\) −41.4288 −1.74138
\(567\) −21.0205 −0.882779
\(568\) −136.162 −5.71325
\(569\) −31.4702 −1.31930 −0.659651 0.751572i \(-0.729296\pi\)
−0.659651 + 0.751572i \(0.729296\pi\)
\(570\) 27.9775 1.17185
\(571\) 20.8366 0.871983 0.435991 0.899951i \(-0.356398\pi\)
0.435991 + 0.899951i \(0.356398\pi\)
\(572\) 76.1022 3.18199
\(573\) 17.1053 0.714586
\(574\) −16.9347 −0.706842
\(575\) −17.8347 −0.743759
\(576\) −8.89179 −0.370491
\(577\) −5.56596 −0.231714 −0.115857 0.993266i \(-0.536961\pi\)
−0.115857 + 0.993266i \(0.536961\pi\)
\(578\) −33.5570 −1.39579
\(579\) 6.03754 0.250912
\(580\) 0.275068 0.0114216
\(581\) −16.0814 −0.667170
\(582\) −36.3574 −1.50706
\(583\) −24.9299 −1.03249
\(584\) 45.2277 1.87153
\(585\) −4.88639 −0.202027
\(586\) −45.7763 −1.89100
\(587\) −34.0176 −1.40406 −0.702028 0.712149i \(-0.747722\pi\)
−0.702028 + 0.712149i \(0.747722\pi\)
\(588\) 4.22448 0.174215
\(589\) −12.2691 −0.505539
\(590\) −92.4202 −3.80488
\(591\) 26.6053 1.09439
\(592\) −105.291 −4.32745
\(593\) −15.4788 −0.635638 −0.317819 0.948151i \(-0.602950\pi\)
−0.317819 + 0.948151i \(0.602950\pi\)
\(594\) 47.6587 1.95546
\(595\) 41.6848 1.70891
\(596\) 36.4992 1.49506
\(597\) −11.0747 −0.453256
\(598\) 74.7069 3.05499
\(599\) −2.06024 −0.0841790 −0.0420895 0.999114i \(-0.513401\pi\)
−0.0420895 + 0.999114i \(0.513401\pi\)
\(600\) −41.2424 −1.68372
\(601\) −5.82283 −0.237518 −0.118759 0.992923i \(-0.537892\pi\)
−0.118759 + 0.992923i \(0.537892\pi\)
\(602\) 7.19471 0.293235
\(603\) −2.63749 −0.107407
\(604\) 53.4101 2.17322
\(605\) −1.70387 −0.0692724
\(606\) −59.5212 −2.41788
\(607\) −11.0835 −0.449866 −0.224933 0.974374i \(-0.572216\pi\)
−0.224933 + 0.974374i \(0.572216\pi\)
\(608\) 41.9610 1.70174
\(609\) 0.0819945 0.00332258
\(610\) 77.6393 3.14352
\(611\) 43.2814 1.75098
\(612\) −11.1815 −0.451986
\(613\) −3.81036 −0.153899 −0.0769494 0.997035i \(-0.524518\pi\)
−0.0769494 + 0.997035i \(0.524518\pi\)
\(614\) −42.7692 −1.72603
\(615\) 10.3913 0.419019
\(616\) −78.2945 −3.15458
\(617\) −4.92207 −0.198155 −0.0990776 0.995080i \(-0.531589\pi\)
−0.0990776 + 0.995080i \(0.531589\pi\)
\(618\) −43.0313 −1.73097
\(619\) 4.37056 0.175668 0.0878338 0.996135i \(-0.472006\pi\)
0.0878338 + 0.996135i \(0.472006\pi\)
\(620\) 79.6433 3.19855
\(621\) 33.9433 1.36210
\(622\) 81.0354 3.24922
\(623\) 1.90565 0.0763484
\(624\) 96.4823 3.86238
\(625\) −31.1074 −1.24430
\(626\) −92.2275 −3.68615
\(627\) −11.9048 −0.475434
\(628\) 67.9904 2.71311
\(629\) −42.7115 −1.70302
\(630\) 8.08646 0.322172
\(631\) 7.85577 0.312733 0.156367 0.987699i \(-0.450022\pi\)
0.156367 + 0.987699i \(0.450022\pi\)
\(632\) 50.0927 1.99258
\(633\) −18.4707 −0.734145
\(634\) 44.0326 1.74876
\(635\) −44.9113 −1.78225
\(636\) −66.0461 −2.61890
\(637\) 2.20872 0.0875128
\(638\) −0.161327 −0.00638699
\(639\) −5.98410 −0.236727
\(640\) −69.7386 −2.75666
\(641\) −10.2451 −0.404659 −0.202329 0.979318i \(-0.564851\pi\)
−0.202329 + 0.979318i \(0.564851\pi\)
\(642\) −21.0512 −0.830823
\(643\) −37.7100 −1.48714 −0.743568 0.668661i \(-0.766868\pi\)
−0.743568 + 0.668661i \(0.766868\pi\)
\(644\) −89.6973 −3.53457
\(645\) −4.41476 −0.173831
\(646\) 33.4726 1.31696
\(647\) −5.74231 −0.225753 −0.112877 0.993609i \(-0.536007\pi\)
−0.112877 + 0.993609i \(0.536007\pi\)
\(648\) 68.1171 2.67589
\(649\) 39.3261 1.54369
\(650\) −34.6855 −1.36048
\(651\) 23.7407 0.930470
\(652\) 89.7096 3.51330
\(653\) 38.1894 1.49447 0.747233 0.664562i \(-0.231382\pi\)
0.747233 + 0.664562i \(0.231382\pi\)
\(654\) 10.7735 0.421277
\(655\) −15.1196 −0.590771
\(656\) 30.6478 1.19659
\(657\) 1.98768 0.0775466
\(658\) −71.6261 −2.79227
\(659\) −39.1887 −1.52658 −0.763288 0.646058i \(-0.776416\pi\)
−0.763288 + 0.646058i \(0.776416\pi\)
\(660\) 77.2789 3.00808
\(661\) −36.2542 −1.41012 −0.705062 0.709146i \(-0.749081\pi\)
−0.705062 + 0.709146i \(0.749081\pi\)
\(662\) 33.6733 1.30875
\(663\) 39.1381 1.52000
\(664\) 52.1119 2.02233
\(665\) −17.5629 −0.681059
\(666\) −8.28564 −0.321062
\(667\) −0.114900 −0.00444893
\(668\) 42.2258 1.63377
\(669\) 26.8050 1.03634
\(670\) −51.2527 −1.98006
\(671\) −33.0366 −1.27536
\(672\) −81.1945 −3.13215
\(673\) −36.9331 −1.42367 −0.711833 0.702349i \(-0.752135\pi\)
−0.711833 + 0.702349i \(0.752135\pi\)
\(674\) 15.9608 0.614785
\(675\) −15.7595 −0.606582
\(676\) 36.6884 1.41109
\(677\) −42.4817 −1.63270 −0.816351 0.577556i \(-0.804007\pi\)
−0.816351 + 0.577556i \(0.804007\pi\)
\(678\) 35.4477 1.36136
\(679\) 22.8233 0.875879
\(680\) −135.080 −5.18007
\(681\) −26.3020 −1.00789
\(682\) −46.7106 −1.78864
\(683\) 2.12189 0.0811919 0.0405959 0.999176i \(-0.487074\pi\)
0.0405959 + 0.999176i \(0.487074\pi\)
\(684\) 4.71106 0.180132
\(685\) 28.2528 1.07949
\(686\) 48.0735 1.83545
\(687\) −44.8466 −1.71100
\(688\) −13.0207 −0.496409
\(689\) −34.5314 −1.31554
\(690\) 75.8620 2.88802
\(691\) 5.18365 0.197195 0.0985976 0.995127i \(-0.468564\pi\)
0.0985976 + 0.995127i \(0.468564\pi\)
\(692\) −17.0201 −0.647007
\(693\) −3.44091 −0.130709
\(694\) 54.0182 2.05050
\(695\) −15.8838 −0.602506
\(696\) −0.265703 −0.0100715
\(697\) 12.4323 0.470907
\(698\) −87.6803 −3.31875
\(699\) 18.9879 0.718187
\(700\) 41.6454 1.57405
\(701\) 9.51629 0.359425 0.179713 0.983719i \(-0.442483\pi\)
0.179713 + 0.983719i \(0.442483\pi\)
\(702\) 66.0140 2.49154
\(703\) 17.9955 0.678712
\(704\) 73.5240 2.77104
\(705\) 43.9506 1.65527
\(706\) 76.0117 2.86074
\(707\) 37.3644 1.40523
\(708\) 104.186 3.91554
\(709\) 2.57052 0.0965379 0.0482689 0.998834i \(-0.484630\pi\)
0.0482689 + 0.998834i \(0.484630\pi\)
\(710\) −116.285 −4.36411
\(711\) 2.20149 0.0825622
\(712\) −6.17527 −0.231428
\(713\) −33.2680 −1.24590
\(714\) −64.7694 −2.42394
\(715\) 40.4044 1.51104
\(716\) 61.6322 2.30330
\(717\) 33.8148 1.26284
\(718\) 19.2244 0.717449
\(719\) 14.7960 0.551799 0.275900 0.961186i \(-0.411024\pi\)
0.275900 + 0.961186i \(0.411024\pi\)
\(720\) −14.6345 −0.545397
\(721\) 27.0129 1.00601
\(722\) 37.1847 1.38387
\(723\) 20.7044 0.770006
\(724\) −23.2573 −0.864351
\(725\) 0.0533465 0.00198124
\(726\) 2.64746 0.0982566
\(727\) 8.98077 0.333078 0.166539 0.986035i \(-0.446741\pi\)
0.166539 + 0.986035i \(0.446741\pi\)
\(728\) −108.449 −4.01939
\(729\) 29.5376 1.09399
\(730\) 38.6253 1.42959
\(731\) −5.28186 −0.195356
\(732\) −87.5230 −3.23494
\(733\) −32.0349 −1.18324 −0.591618 0.806218i \(-0.701511\pi\)
−0.591618 + 0.806218i \(0.701511\pi\)
\(734\) 79.1508 2.92151
\(735\) 2.24287 0.0827296
\(736\) 113.779 4.19394
\(737\) 21.8088 0.803336
\(738\) 2.41175 0.0887777
\(739\) 28.8906 1.06276 0.531378 0.847135i \(-0.321674\pi\)
0.531378 + 0.847135i \(0.321674\pi\)
\(740\) −116.816 −4.29422
\(741\) −16.4899 −0.605772
\(742\) 57.1458 2.09789
\(743\) −13.2257 −0.485205 −0.242603 0.970126i \(-0.578001\pi\)
−0.242603 + 0.970126i \(0.578001\pi\)
\(744\) −76.9317 −2.82045
\(745\) 19.3782 0.709963
\(746\) −12.3293 −0.451409
\(747\) 2.29022 0.0837949
\(748\) 92.4572 3.38057
\(749\) 13.2149 0.482860
\(750\) 25.9787 0.948608
\(751\) −37.8946 −1.38279 −0.691397 0.722475i \(-0.743005\pi\)
−0.691397 + 0.722475i \(0.743005\pi\)
\(752\) 129.626 4.72697
\(753\) −1.02825 −0.0374715
\(754\) −0.223461 −0.00813795
\(755\) 28.3566 1.03200
\(756\) −79.2601 −2.88266
\(757\) 9.04277 0.328665 0.164333 0.986405i \(-0.447453\pi\)
0.164333 + 0.986405i \(0.447453\pi\)
\(758\) 65.7018 2.38640
\(759\) −32.2804 −1.17170
\(760\) 56.9126 2.06444
\(761\) 13.1822 0.477853 0.238927 0.971038i \(-0.423204\pi\)
0.238927 + 0.971038i \(0.423204\pi\)
\(762\) 69.7827 2.52796
\(763\) −6.76305 −0.244839
\(764\) 55.9714 2.02498
\(765\) −5.93651 −0.214635
\(766\) 70.5767 2.55004
\(767\) 54.4723 1.96688
\(768\) 34.6671 1.25094
\(769\) 18.1294 0.653764 0.326882 0.945065i \(-0.394002\pi\)
0.326882 + 0.945065i \(0.394002\pi\)
\(770\) −66.8650 −2.40965
\(771\) −32.4830 −1.16984
\(772\) 19.7558 0.711027
\(773\) 50.4186 1.81343 0.906715 0.421745i \(-0.138582\pi\)
0.906715 + 0.421745i \(0.138582\pi\)
\(774\) −1.02463 −0.0368296
\(775\) 15.4459 0.554834
\(776\) −73.9590 −2.65497
\(777\) −34.8213 −1.24921
\(778\) −66.3759 −2.37969
\(779\) −5.23805 −0.187673
\(780\) 107.042 3.83273
\(781\) 49.4810 1.77057
\(782\) 90.7620 3.24564
\(783\) −0.101530 −0.00362838
\(784\) 6.61503 0.236251
\(785\) 36.0976 1.28838
\(786\) 23.4927 0.837955
\(787\) −32.9223 −1.17355 −0.586776 0.809749i \(-0.699603\pi\)
−0.586776 + 0.809749i \(0.699603\pi\)
\(788\) 87.0568 3.10127
\(789\) 17.9479 0.638963
\(790\) 42.7801 1.52205
\(791\) −22.2523 −0.791200
\(792\) 11.1503 0.396207
\(793\) −45.7604 −1.62500
\(794\) 93.3537 3.31300
\(795\) −35.0653 −1.24364
\(796\) −36.2381 −1.28442
\(797\) 7.58142 0.268548 0.134274 0.990944i \(-0.457130\pi\)
0.134274 + 0.990944i \(0.457130\pi\)
\(798\) 27.2890 0.966022
\(799\) 52.5828 1.86025
\(800\) −52.8260 −1.86768
\(801\) −0.271392 −0.00958918
\(802\) −44.6588 −1.57696
\(803\) −16.4356 −0.580000
\(804\) 57.7774 2.03765
\(805\) −47.6223 −1.67847
\(806\) −64.7007 −2.27899
\(807\) −6.46370 −0.227533
\(808\) −121.079 −4.25956
\(809\) −13.4190 −0.471786 −0.235893 0.971779i \(-0.575801\pi\)
−0.235893 + 0.971779i \(0.575801\pi\)
\(810\) 58.1732 2.04400
\(811\) 41.3274 1.45120 0.725600 0.688117i \(-0.241562\pi\)
0.725600 + 0.688117i \(0.241562\pi\)
\(812\) 0.268299 0.00941546
\(813\) 16.4006 0.575194
\(814\) 68.5119 2.40134
\(815\) 47.6288 1.66836
\(816\) 117.217 4.10342
\(817\) 2.22538 0.0778563
\(818\) 82.9744 2.90113
\(819\) −4.76614 −0.166543
\(820\) 34.0022 1.18741
\(821\) −5.55948 −0.194027 −0.0970136 0.995283i \(-0.530929\pi\)
−0.0970136 + 0.995283i \(0.530929\pi\)
\(822\) −43.8990 −1.53115
\(823\) −45.2400 −1.57697 −0.788484 0.615055i \(-0.789134\pi\)
−0.788484 + 0.615055i \(0.789134\pi\)
\(824\) −87.5353 −3.04944
\(825\) 14.9874 0.521794
\(826\) −90.1458 −3.13658
\(827\) −6.93929 −0.241303 −0.120651 0.992695i \(-0.538498\pi\)
−0.120651 + 0.992695i \(0.538498\pi\)
\(828\) 12.7742 0.443934
\(829\) 14.8485 0.515709 0.257855 0.966184i \(-0.416984\pi\)
0.257855 + 0.966184i \(0.416984\pi\)
\(830\) 44.5045 1.54477
\(831\) −9.22584 −0.320041
\(832\) 101.841 3.53071
\(833\) 2.68339 0.0929741
\(834\) 24.6801 0.854601
\(835\) 22.4186 0.775829
\(836\) −38.9546 −1.34727
\(837\) −29.3969 −1.01611
\(838\) 32.7523 1.13141
\(839\) −29.8208 −1.02953 −0.514765 0.857331i \(-0.672121\pi\)
−0.514765 + 0.857331i \(0.672121\pi\)
\(840\) −110.126 −3.79970
\(841\) −28.9997 −0.999988
\(842\) 90.8007 3.12920
\(843\) 19.1830 0.660698
\(844\) −60.4392 −2.08040
\(845\) 19.4787 0.670087
\(846\) 10.2006 0.350703
\(847\) −1.66194 −0.0571051
\(848\) −103.420 −3.55146
\(849\) 24.7956 0.850983
\(850\) −42.1397 −1.44538
\(851\) 48.7953 1.67268
\(852\) 131.089 4.49103
\(853\) 19.1923 0.657132 0.328566 0.944481i \(-0.393435\pi\)
0.328566 + 0.944481i \(0.393435\pi\)
\(854\) 75.7286 2.59138
\(855\) 2.50121 0.0855395
\(856\) −42.8228 −1.46365
\(857\) 0.848419 0.0289814 0.0144907 0.999895i \(-0.495387\pi\)
0.0144907 + 0.999895i \(0.495387\pi\)
\(858\) −62.7799 −2.14327
\(859\) 30.4113 1.03762 0.518810 0.854889i \(-0.326375\pi\)
0.518810 + 0.854889i \(0.326375\pi\)
\(860\) −14.4458 −0.492598
\(861\) 10.1356 0.345421
\(862\) −87.0494 −2.96491
\(863\) −39.6186 −1.34863 −0.674317 0.738442i \(-0.735562\pi\)
−0.674317 + 0.738442i \(0.735562\pi\)
\(864\) 100.539 3.42042
\(865\) −9.03635 −0.307245
\(866\) −39.8090 −1.35276
\(867\) 20.0842 0.682095
\(868\) 77.6834 2.63674
\(869\) −18.2035 −0.617513
\(870\) −0.226916 −0.00769316
\(871\) 30.2082 1.02357
\(872\) 21.9157 0.742159
\(873\) −3.25037 −0.110008
\(874\) −38.2404 −1.29350
\(875\) −16.3081 −0.551315
\(876\) −43.5424 −1.47116
\(877\) −9.66034 −0.326207 −0.163103 0.986609i \(-0.552150\pi\)
−0.163103 + 0.986609i \(0.552150\pi\)
\(878\) 29.1201 0.982755
\(879\) 27.3976 0.924099
\(880\) 121.009 4.07923
\(881\) 6.52132 0.219709 0.109854 0.993948i \(-0.464962\pi\)
0.109854 + 0.993948i \(0.464962\pi\)
\(882\) 0.520553 0.0175279
\(883\) −53.2641 −1.79248 −0.896240 0.443570i \(-0.853712\pi\)
−0.896240 + 0.443570i \(0.853712\pi\)
\(884\) 128.066 4.30734
\(885\) 55.3145 1.85938
\(886\) 29.1940 0.980791
\(887\) 13.9897 0.469727 0.234863 0.972028i \(-0.424536\pi\)
0.234863 + 0.972028i \(0.424536\pi\)
\(888\) 112.838 3.78661
\(889\) −43.8061 −1.46921
\(890\) −5.27380 −0.176778
\(891\) −24.7535 −0.829275
\(892\) 87.7105 2.93676
\(893\) −22.1545 −0.741372
\(894\) −30.1097 −1.00702
\(895\) 32.7219 1.09377
\(896\) −68.0224 −2.27247
\(897\) −44.7129 −1.49292
\(898\) 51.1665 1.70745
\(899\) 0.0995100 0.00331885
\(900\) −5.93090 −0.197697
\(901\) −41.9525 −1.39764
\(902\) −19.9422 −0.664001
\(903\) −4.30611 −0.143299
\(904\) 72.1085 2.39829
\(905\) −12.3478 −0.410456
\(906\) −44.0602 −1.46380
\(907\) 1.50238 0.0498858 0.0249429 0.999689i \(-0.492060\pi\)
0.0249429 + 0.999689i \(0.492060\pi\)
\(908\) −86.0643 −2.85614
\(909\) −5.32123 −0.176494
\(910\) −92.6175 −3.07024
\(911\) −59.1264 −1.95894 −0.979472 0.201581i \(-0.935392\pi\)
−0.979472 + 0.201581i \(0.935392\pi\)
\(912\) −49.3866 −1.63535
\(913\) −18.9373 −0.626733
\(914\) −113.057 −3.73960
\(915\) −46.4679 −1.53618
\(916\) −146.745 −4.84860
\(917\) −14.7475 −0.487005
\(918\) 80.2009 2.64702
\(919\) −36.0789 −1.19013 −0.595066 0.803677i \(-0.702874\pi\)
−0.595066 + 0.803677i \(0.702874\pi\)
\(920\) 154.320 5.08779
\(921\) 25.5978 0.843477
\(922\) −50.8875 −1.67589
\(923\) 68.5383 2.25596
\(924\) 75.3771 2.47973
\(925\) −22.6551 −0.744894
\(926\) 48.3471 1.58878
\(927\) −3.84702 −0.126353
\(928\) −0.340330 −0.0111719
\(929\) −8.87876 −0.291303 −0.145651 0.989336i \(-0.546528\pi\)
−0.145651 + 0.989336i \(0.546528\pi\)
\(930\) −65.7011 −2.15442
\(931\) −1.13058 −0.0370534
\(932\) 62.1314 2.03518
\(933\) −48.5006 −1.58784
\(934\) 23.2829 0.761840
\(935\) 49.0876 1.60534
\(936\) 15.4447 0.504826
\(937\) −6.86339 −0.224217 −0.112109 0.993696i \(-0.535760\pi\)
−0.112109 + 0.993696i \(0.535760\pi\)
\(938\) −49.9914 −1.63228
\(939\) 55.1992 1.80136
\(940\) 143.813 4.69067
\(941\) 25.6964 0.837680 0.418840 0.908060i \(-0.362437\pi\)
0.418840 + 0.908060i \(0.362437\pi\)
\(942\) −56.0882 −1.82745
\(943\) −14.2031 −0.462518
\(944\) 163.142 5.30983
\(945\) −42.0810 −1.36889
\(946\) 8.47242 0.275462
\(947\) 46.0583 1.49669 0.748347 0.663308i \(-0.230848\pi\)
0.748347 + 0.663308i \(0.230848\pi\)
\(948\) −48.2262 −1.56631
\(949\) −22.7656 −0.739004
\(950\) 17.7545 0.576033
\(951\) −26.3540 −0.854587
\(952\) −131.755 −4.27022
\(953\) 5.48758 0.177760 0.0888800 0.996042i \(-0.471671\pi\)
0.0888800 + 0.996042i \(0.471671\pi\)
\(954\) −8.13839 −0.263490
\(955\) 29.7165 0.961603
\(956\) 110.647 3.57859
\(957\) 0.0965558 0.00312121
\(958\) 20.7273 0.669669
\(959\) 27.5576 0.889880
\(960\) 103.416 3.33773
\(961\) −2.18787 −0.0705765
\(962\) 94.8988 3.05966
\(963\) −1.88199 −0.0606461
\(964\) 67.7483 2.18203
\(965\) 10.4888 0.337646
\(966\) 73.9951 2.38075
\(967\) −16.3524 −0.525857 −0.262928 0.964815i \(-0.584688\pi\)
−0.262928 + 0.964815i \(0.584688\pi\)
\(968\) 5.38553 0.173098
\(969\) −20.0337 −0.643575
\(970\) −63.1624 −2.02802
\(971\) −7.74233 −0.248463 −0.124232 0.992253i \(-0.539647\pi\)
−0.124232 + 0.992253i \(0.539647\pi\)
\(972\) 21.2773 0.682471
\(973\) −15.4929 −0.496679
\(974\) 104.295 3.34184
\(975\) 20.7597 0.664841
\(976\) −137.051 −4.38688
\(977\) −3.92299 −0.125507 −0.0627537 0.998029i \(-0.519988\pi\)
−0.0627537 + 0.998029i \(0.519988\pi\)
\(978\) −74.0052 −2.36643
\(979\) 2.24408 0.0717210
\(980\) 7.33905 0.234437
\(981\) 0.963156 0.0307512
\(982\) −0.809950 −0.0258465
\(983\) −38.0284 −1.21292 −0.606458 0.795115i \(-0.707410\pi\)
−0.606458 + 0.795115i \(0.707410\pi\)
\(984\) −32.8445 −1.04704
\(985\) 46.2204 1.47270
\(986\) −0.271484 −0.00864581
\(987\) 42.8690 1.36453
\(988\) −53.9576 −1.71662
\(989\) 6.03420 0.191876
\(990\) 9.52253 0.302646
\(991\) 44.7232 1.42068 0.710339 0.703860i \(-0.248542\pi\)
0.710339 + 0.703860i \(0.248542\pi\)
\(992\) −98.5392 −3.12862
\(993\) −20.1538 −0.639562
\(994\) −113.424 −3.59758
\(995\) −19.2396 −0.609937
\(996\) −50.1701 −1.58970
\(997\) 11.7821 0.373142 0.186571 0.982441i \(-0.440263\pi\)
0.186571 + 0.982441i \(0.440263\pi\)
\(998\) −47.9838 −1.51890
\(999\) 43.1175 1.36418
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 \(a_p\))