Properties

Label 4019.2.a.b.1.17
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.43453 q^{2}\) \(+2.49356 q^{3}\) \(+3.92696 q^{4}\) \(+3.69129 q^{5}\) \(-6.07065 q^{6}\) \(+0.601351 q^{7}\) \(-4.69125 q^{8}\) \(+3.21782 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.43453 q^{2}\) \(+2.49356 q^{3}\) \(+3.92696 q^{4}\) \(+3.69129 q^{5}\) \(-6.07065 q^{6}\) \(+0.601351 q^{7}\) \(-4.69125 q^{8}\) \(+3.21782 q^{9}\) \(-8.98658 q^{10}\) \(-5.31971 q^{11}\) \(+9.79209 q^{12}\) \(+3.09616 q^{13}\) \(-1.46401 q^{14}\) \(+9.20444 q^{15}\) \(+3.56709 q^{16}\) \(+0.734755 q^{17}\) \(-7.83390 q^{18}\) \(+2.83652 q^{19}\) \(+14.4956 q^{20}\) \(+1.49950 q^{21}\) \(+12.9510 q^{22}\) \(-1.79373 q^{23}\) \(-11.6979 q^{24}\) \(+8.62564 q^{25}\) \(-7.53771 q^{26}\) \(+0.543152 q^{27}\) \(+2.36148 q^{28}\) \(+7.08600 q^{29}\) \(-22.4085 q^{30}\) \(+2.28441 q^{31}\) \(+0.698289 q^{32}\) \(-13.2650 q^{33}\) \(-1.78879 q^{34}\) \(+2.21976 q^{35}\) \(+12.6363 q^{36}\) \(+9.08400 q^{37}\) \(-6.90560 q^{38}\) \(+7.72045 q^{39}\) \(-17.3168 q^{40}\) \(+1.45684 q^{41}\) \(-3.65059 q^{42}\) \(+0.573711 q^{43}\) \(-20.8903 q^{44}\) \(+11.8779 q^{45}\) \(+4.36689 q^{46}\) \(-7.18313 q^{47}\) \(+8.89475 q^{48}\) \(-6.63838 q^{49}\) \(-20.9994 q^{50}\) \(+1.83215 q^{51}\) \(+12.1585 q^{52}\) \(+1.63729 q^{53}\) \(-1.32232 q^{54}\) \(-19.6366 q^{55}\) \(-2.82109 q^{56}\) \(+7.07301 q^{57}\) \(-17.2511 q^{58}\) \(+0.375061 q^{59}\) \(+36.1455 q^{60}\) \(-3.59350 q^{61}\) \(-5.56147 q^{62}\) \(+1.93504 q^{63}\) \(-8.83420 q^{64}\) \(+11.4288 q^{65}\) \(+32.2941 q^{66}\) \(+9.13823 q^{67}\) \(+2.88535 q^{68}\) \(-4.47276 q^{69}\) \(-5.40409 q^{70}\) \(-3.82383 q^{71}\) \(-15.0956 q^{72}\) \(+6.13553 q^{73}\) \(-22.1153 q^{74}\) \(+21.5085 q^{75}\) \(+11.1389 q^{76}\) \(-3.19901 q^{77}\) \(-18.7957 q^{78}\) \(+5.08529 q^{79}\) \(+13.1672 q^{80}\) \(-8.29909 q^{81}\) \(-3.54673 q^{82}\) \(-1.18851 q^{83}\) \(+5.88849 q^{84}\) \(+2.71219 q^{85}\) \(-1.39672 q^{86}\) \(+17.6693 q^{87}\) \(+24.9561 q^{88}\) \(-15.1270 q^{89}\) \(-28.9172 q^{90}\) \(+1.86188 q^{91}\) \(-7.04389 q^{92}\) \(+5.69630 q^{93}\) \(+17.4876 q^{94}\) \(+10.4704 q^{95}\) \(+1.74122 q^{96}\) \(+5.67676 q^{97}\) \(+16.1614 q^{98}\) \(-17.1179 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43453 −1.72148 −0.860738 0.509048i \(-0.829997\pi\)
−0.860738 + 0.509048i \(0.829997\pi\)
\(3\) 2.49356 1.43966 0.719828 0.694153i \(-0.244221\pi\)
0.719828 + 0.694153i \(0.244221\pi\)
\(4\) 3.92696 1.96348
\(5\) 3.69129 1.65080 0.825398 0.564551i \(-0.190951\pi\)
0.825398 + 0.564551i \(0.190951\pi\)
\(6\) −6.07065 −2.47833
\(7\) 0.601351 0.227289 0.113645 0.993521i \(-0.463747\pi\)
0.113645 + 0.993521i \(0.463747\pi\)
\(8\) −4.69125 −1.65861
\(9\) 3.21782 1.07261
\(10\) −8.98658 −2.84181
\(11\) −5.31971 −1.60395 −0.801976 0.597356i \(-0.796218\pi\)
−0.801976 + 0.597356i \(0.796218\pi\)
\(12\) 9.79209 2.82673
\(13\) 3.09616 0.858721 0.429360 0.903133i \(-0.358739\pi\)
0.429360 + 0.903133i \(0.358739\pi\)
\(14\) −1.46401 −0.391273
\(15\) 9.20444 2.37658
\(16\) 3.56709 0.891773
\(17\) 0.734755 0.178204 0.0891021 0.996022i \(-0.471600\pi\)
0.0891021 + 0.996022i \(0.471600\pi\)
\(18\) −7.83390 −1.84647
\(19\) 2.83652 0.650742 0.325371 0.945587i \(-0.394511\pi\)
0.325371 + 0.945587i \(0.394511\pi\)
\(20\) 14.4956 3.24130
\(21\) 1.49950 0.327218
\(22\) 12.9510 2.76117
\(23\) −1.79373 −0.374018 −0.187009 0.982358i \(-0.559879\pi\)
−0.187009 + 0.982358i \(0.559879\pi\)
\(24\) −11.6979 −2.38782
\(25\) 8.62564 1.72513
\(26\) −7.53771 −1.47827
\(27\) 0.543152 0.104530
\(28\) 2.36148 0.446278
\(29\) 7.08600 1.31584 0.657919 0.753089i \(-0.271437\pi\)
0.657919 + 0.753089i \(0.271437\pi\)
\(30\) −22.4085 −4.09122
\(31\) 2.28441 0.410292 0.205146 0.978731i \(-0.434233\pi\)
0.205146 + 0.978731i \(0.434233\pi\)
\(32\) 0.698289 0.123441
\(33\) −13.2650 −2.30914
\(34\) −1.78879 −0.306774
\(35\) 2.21976 0.375208
\(36\) 12.6363 2.10604
\(37\) 9.08400 1.49340 0.746700 0.665161i \(-0.231637\pi\)
0.746700 + 0.665161i \(0.231637\pi\)
\(38\) −6.90560 −1.12024
\(39\) 7.72045 1.23626
\(40\) −17.3168 −2.73802
\(41\) 1.45684 0.227521 0.113760 0.993508i \(-0.463710\pi\)
0.113760 + 0.993508i \(0.463710\pi\)
\(42\) −3.65059 −0.563298
\(43\) 0.573711 0.0874901 0.0437450 0.999043i \(-0.486071\pi\)
0.0437450 + 0.999043i \(0.486071\pi\)
\(44\) −20.8903 −3.14933
\(45\) 11.8779 1.77066
\(46\) 4.36689 0.643862
\(47\) −7.18313 −1.04777 −0.523884 0.851790i \(-0.675517\pi\)
−0.523884 + 0.851790i \(0.675517\pi\)
\(48\) 8.89475 1.28385
\(49\) −6.63838 −0.948340
\(50\) −20.9994 −2.96976
\(51\) 1.83215 0.256553
\(52\) 12.1585 1.68608
\(53\) 1.63729 0.224899 0.112449 0.993657i \(-0.464130\pi\)
0.112449 + 0.993657i \(0.464130\pi\)
\(54\) −1.32232 −0.179945
\(55\) −19.6366 −2.64780
\(56\) −2.82109 −0.376984
\(57\) 7.07301 0.936844
\(58\) −17.2511 −2.26518
\(59\) 0.375061 0.0488288 0.0244144 0.999702i \(-0.492228\pi\)
0.0244144 + 0.999702i \(0.492228\pi\)
\(60\) 36.1455 4.66636
\(61\) −3.59350 −0.460101 −0.230051 0.973179i \(-0.573889\pi\)
−0.230051 + 0.973179i \(0.573889\pi\)
\(62\) −5.56147 −0.706308
\(63\) 1.93504 0.243792
\(64\) −8.83420 −1.10427
\(65\) 11.4288 1.41757
\(66\) 32.2941 3.97513
\(67\) 9.13823 1.11641 0.558206 0.829702i \(-0.311490\pi\)
0.558206 + 0.829702i \(0.311490\pi\)
\(68\) 2.88535 0.349900
\(69\) −4.47276 −0.538457
\(70\) −5.40409 −0.645912
\(71\) −3.82383 −0.453806 −0.226903 0.973917i \(-0.572860\pi\)
−0.226903 + 0.973917i \(0.572860\pi\)
\(72\) −15.0956 −1.77903
\(73\) 6.13553 0.718109 0.359055 0.933317i \(-0.383099\pi\)
0.359055 + 0.933317i \(0.383099\pi\)
\(74\) −22.1153 −2.57085
\(75\) 21.5085 2.48359
\(76\) 11.1389 1.27772
\(77\) −3.19901 −0.364561
\(78\) −18.7957 −2.12820
\(79\) 5.08529 0.572140 0.286070 0.958209i \(-0.407651\pi\)
0.286070 + 0.958209i \(0.407651\pi\)
\(80\) 13.1672 1.47214
\(81\) −8.29909 −0.922121
\(82\) −3.54673 −0.391671
\(83\) −1.18851 −0.130456 −0.0652278 0.997870i \(-0.520777\pi\)
−0.0652278 + 0.997870i \(0.520777\pi\)
\(84\) 5.88849 0.642486
\(85\) 2.71219 0.294179
\(86\) −1.39672 −0.150612
\(87\) 17.6693 1.89435
\(88\) 24.9561 2.66033
\(89\) −15.1270 −1.60346 −0.801731 0.597685i \(-0.796087\pi\)
−0.801731 + 0.597685i \(0.796087\pi\)
\(90\) −28.9172 −3.04814
\(91\) 1.86188 0.195178
\(92\) −7.04389 −0.734376
\(93\) 5.69630 0.590679
\(94\) 17.4876 1.80371
\(95\) 10.4704 1.07424
\(96\) 1.74122 0.177713
\(97\) 5.67676 0.576387 0.288194 0.957572i \(-0.406945\pi\)
0.288194 + 0.957572i \(0.406945\pi\)
\(98\) 16.1614 1.63254
\(99\) −17.1179 −1.72041
\(100\) 33.8725 3.38725
\(101\) 4.69810 0.467478 0.233739 0.972299i \(-0.424904\pi\)
0.233739 + 0.972299i \(0.424904\pi\)
\(102\) −4.46044 −0.441649
\(103\) 0.0154012 0.00151752 0.000758762 1.00000i \(-0.499758\pi\)
0.000758762 1.00000i \(0.499758\pi\)
\(104\) −14.5249 −1.42428
\(105\) 5.53510 0.540171
\(106\) −3.98604 −0.387158
\(107\) 5.38239 0.520335 0.260168 0.965563i \(-0.416222\pi\)
0.260168 + 0.965563i \(0.416222\pi\)
\(108\) 2.13294 0.205242
\(109\) 5.66536 0.542643 0.271322 0.962489i \(-0.412539\pi\)
0.271322 + 0.962489i \(0.412539\pi\)
\(110\) 47.8060 4.55812
\(111\) 22.6515 2.14998
\(112\) 2.14507 0.202691
\(113\) 17.1675 1.61498 0.807491 0.589880i \(-0.200825\pi\)
0.807491 + 0.589880i \(0.200825\pi\)
\(114\) −17.2195 −1.61275
\(115\) −6.62117 −0.617427
\(116\) 27.8264 2.58362
\(117\) 9.96290 0.921070
\(118\) −0.913100 −0.0840577
\(119\) 0.441846 0.0405039
\(120\) −43.1803 −3.94181
\(121\) 17.2993 1.57266
\(122\) 8.74851 0.792053
\(123\) 3.63272 0.327551
\(124\) 8.97078 0.805600
\(125\) 13.3833 1.19704
\(126\) −4.71092 −0.419682
\(127\) −4.41377 −0.391659 −0.195829 0.980638i \(-0.562740\pi\)
−0.195829 + 0.980638i \(0.562740\pi\)
\(128\) 20.1106 1.77754
\(129\) 1.43058 0.125956
\(130\) −27.8239 −2.44032
\(131\) 10.1268 0.884780 0.442390 0.896823i \(-0.354131\pi\)
0.442390 + 0.896823i \(0.354131\pi\)
\(132\) −52.0911 −4.53395
\(133\) 1.70574 0.147907
\(134\) −22.2473 −1.92188
\(135\) 2.00493 0.172557
\(136\) −3.44692 −0.295571
\(137\) −4.27066 −0.364867 −0.182434 0.983218i \(-0.558397\pi\)
−0.182434 + 0.983218i \(0.558397\pi\)
\(138\) 10.8891 0.926940
\(139\) −14.2167 −1.20585 −0.602924 0.797799i \(-0.705998\pi\)
−0.602924 + 0.797799i \(0.705998\pi\)
\(140\) 8.71692 0.736714
\(141\) −17.9115 −1.50842
\(142\) 9.30926 0.781216
\(143\) −16.4707 −1.37735
\(144\) 11.4783 0.956523
\(145\) 26.1565 2.17218
\(146\) −14.9372 −1.23621
\(147\) −16.5532 −1.36528
\(148\) 35.6725 2.93226
\(149\) 14.8062 1.21297 0.606487 0.795093i \(-0.292578\pi\)
0.606487 + 0.795093i \(0.292578\pi\)
\(150\) −52.3632 −4.27544
\(151\) 5.28959 0.430461 0.215230 0.976563i \(-0.430950\pi\)
0.215230 + 0.976563i \(0.430950\pi\)
\(152\) −13.3068 −1.07932
\(153\) 2.36431 0.191143
\(154\) 7.78811 0.627584
\(155\) 8.43242 0.677308
\(156\) 30.3179 2.42738
\(157\) 19.5849 1.56304 0.781522 0.623878i \(-0.214444\pi\)
0.781522 + 0.623878i \(0.214444\pi\)
\(158\) −12.3803 −0.984925
\(159\) 4.08267 0.323777
\(160\) 2.57759 0.203776
\(161\) −1.07866 −0.0850102
\(162\) 20.2044 1.58741
\(163\) −10.1123 −0.792057 −0.396029 0.918238i \(-0.629612\pi\)
−0.396029 + 0.918238i \(0.629612\pi\)
\(164\) 5.72096 0.446732
\(165\) −48.9650 −3.81192
\(166\) 2.89346 0.224576
\(167\) −21.2967 −1.64799 −0.823995 0.566597i \(-0.808260\pi\)
−0.823995 + 0.566597i \(0.808260\pi\)
\(168\) −7.03454 −0.542727
\(169\) −3.41378 −0.262599
\(170\) −6.60293 −0.506422
\(171\) 9.12741 0.697990
\(172\) 2.25294 0.171785
\(173\) −7.48612 −0.569159 −0.284579 0.958652i \(-0.591854\pi\)
−0.284579 + 0.958652i \(0.591854\pi\)
\(174\) −43.0166 −3.26108
\(175\) 5.18703 0.392103
\(176\) −18.9759 −1.43036
\(177\) 0.935237 0.0702967
\(178\) 36.8273 2.76032
\(179\) 10.0049 0.747799 0.373900 0.927469i \(-0.378020\pi\)
0.373900 + 0.927469i \(0.378020\pi\)
\(180\) 46.6441 3.47665
\(181\) 4.19987 0.312174 0.156087 0.987743i \(-0.450112\pi\)
0.156087 + 0.987743i \(0.450112\pi\)
\(182\) −4.53281 −0.335994
\(183\) −8.96060 −0.662387
\(184\) 8.41482 0.620349
\(185\) 33.5317 2.46530
\(186\) −13.8678 −1.01684
\(187\) −3.90868 −0.285831
\(188\) −28.2079 −2.05727
\(189\) 0.326625 0.0237585
\(190\) −25.4906 −1.84928
\(191\) 5.03540 0.364349 0.182174 0.983266i \(-0.441686\pi\)
0.182174 + 0.983266i \(0.441686\pi\)
\(192\) −22.0286 −1.58977
\(193\) 8.26807 0.595149 0.297575 0.954699i \(-0.403822\pi\)
0.297575 + 0.954699i \(0.403822\pi\)
\(194\) −13.8203 −0.992237
\(195\) 28.4984 2.04082
\(196\) −26.0686 −1.86205
\(197\) −10.7100 −0.763059 −0.381530 0.924357i \(-0.624603\pi\)
−0.381530 + 0.924357i \(0.624603\pi\)
\(198\) 41.6741 2.96165
\(199\) −26.4384 −1.87417 −0.937085 0.349101i \(-0.886487\pi\)
−0.937085 + 0.349101i \(0.886487\pi\)
\(200\) −40.4650 −2.86131
\(201\) 22.7867 1.60725
\(202\) −11.4377 −0.804753
\(203\) 4.26117 0.299076
\(204\) 7.19479 0.503736
\(205\) 5.37763 0.375590
\(206\) −0.0374947 −0.00261238
\(207\) −5.77189 −0.401174
\(208\) 11.0443 0.765784
\(209\) −15.0894 −1.04376
\(210\) −13.4754 −0.929891
\(211\) 14.3172 0.985639 0.492820 0.870131i \(-0.335966\pi\)
0.492820 + 0.870131i \(0.335966\pi\)
\(212\) 6.42956 0.441584
\(213\) −9.53495 −0.653324
\(214\) −13.1036 −0.895745
\(215\) 2.11773 0.144428
\(216\) −2.54806 −0.173374
\(217\) 1.37373 0.0932550
\(218\) −13.7925 −0.934148
\(219\) 15.2993 1.03383
\(220\) −77.1121 −5.19890
\(221\) 2.27492 0.153028
\(222\) −55.1458 −3.70114
\(223\) 3.16593 0.212006 0.106003 0.994366i \(-0.466195\pi\)
0.106003 + 0.994366i \(0.466195\pi\)
\(224\) 0.419917 0.0280569
\(225\) 27.7558 1.85038
\(226\) −41.7949 −2.78015
\(227\) −8.05663 −0.534738 −0.267369 0.963594i \(-0.586154\pi\)
−0.267369 + 0.963594i \(0.586154\pi\)
\(228\) 27.7754 1.83947
\(229\) −19.4781 −1.28715 −0.643576 0.765382i \(-0.722550\pi\)
−0.643576 + 0.765382i \(0.722550\pi\)
\(230\) 16.1195 1.06289
\(231\) −7.97692 −0.524843
\(232\) −33.2422 −2.18246
\(233\) 4.21749 0.276297 0.138149 0.990412i \(-0.455885\pi\)
0.138149 + 0.990412i \(0.455885\pi\)
\(234\) −24.2550 −1.58560
\(235\) −26.5150 −1.72965
\(236\) 1.47285 0.0958744
\(237\) 12.6805 0.823684
\(238\) −1.07569 −0.0697265
\(239\) 22.3511 1.44577 0.722887 0.690966i \(-0.242815\pi\)
0.722887 + 0.690966i \(0.242815\pi\)
\(240\) 32.8331 2.11937
\(241\) −14.0275 −0.903588 −0.451794 0.892122i \(-0.649216\pi\)
−0.451794 + 0.892122i \(0.649216\pi\)
\(242\) −42.1158 −2.70730
\(243\) −22.3237 −1.43207
\(244\) −14.1115 −0.903399
\(245\) −24.5042 −1.56552
\(246\) −8.84398 −0.563872
\(247\) 8.78231 0.558805
\(248\) −10.7167 −0.680513
\(249\) −2.96361 −0.187811
\(250\) −32.5821 −2.06067
\(251\) −23.6110 −1.49032 −0.745158 0.666888i \(-0.767626\pi\)
−0.745158 + 0.666888i \(0.767626\pi\)
\(252\) 7.59883 0.478681
\(253\) 9.54210 0.599907
\(254\) 10.7455 0.674231
\(255\) 6.76301 0.423516
\(256\) −31.2915 −1.95572
\(257\) 7.43931 0.464052 0.232026 0.972710i \(-0.425465\pi\)
0.232026 + 0.972710i \(0.425465\pi\)
\(258\) −3.48280 −0.216829
\(259\) 5.46267 0.339434
\(260\) 44.8806 2.78338
\(261\) 22.8015 1.41138
\(262\) −24.6540 −1.52313
\(263\) −10.4682 −0.645498 −0.322749 0.946485i \(-0.604607\pi\)
−0.322749 + 0.946485i \(0.604607\pi\)
\(264\) 62.2294 3.82996
\(265\) 6.04371 0.371262
\(266\) −4.15269 −0.254618
\(267\) −37.7201 −2.30843
\(268\) 35.8854 2.19205
\(269\) −14.3566 −0.875338 −0.437669 0.899136i \(-0.644196\pi\)
−0.437669 + 0.899136i \(0.644196\pi\)
\(270\) −4.88108 −0.297053
\(271\) 22.1562 1.34589 0.672946 0.739692i \(-0.265029\pi\)
0.672946 + 0.739692i \(0.265029\pi\)
\(272\) 2.62094 0.158918
\(273\) 4.64270 0.280989
\(274\) 10.3971 0.628110
\(275\) −45.8859 −2.76702
\(276\) −17.5643 −1.05725
\(277\) −17.3505 −1.04249 −0.521245 0.853407i \(-0.674532\pi\)
−0.521245 + 0.853407i \(0.674532\pi\)
\(278\) 34.6111 2.07584
\(279\) 7.35082 0.440082
\(280\) −10.4135 −0.622323
\(281\) 25.3707 1.51349 0.756746 0.653709i \(-0.226788\pi\)
0.756746 + 0.653709i \(0.226788\pi\)
\(282\) 43.6063 2.59672
\(283\) 20.4560 1.21598 0.607992 0.793943i \(-0.291975\pi\)
0.607992 + 0.793943i \(0.291975\pi\)
\(284\) −15.0160 −0.891038
\(285\) 26.1086 1.54654
\(286\) 40.0984 2.37107
\(287\) 0.876074 0.0517130
\(288\) 2.24697 0.132404
\(289\) −16.4601 −0.968243
\(290\) −63.6789 −3.73935
\(291\) 14.1553 0.829799
\(292\) 24.0940 1.40999
\(293\) −28.3662 −1.65717 −0.828585 0.559863i \(-0.810854\pi\)
−0.828585 + 0.559863i \(0.810854\pi\)
\(294\) 40.2993 2.35030
\(295\) 1.38446 0.0806064
\(296\) −42.6153 −2.47696
\(297\) −2.88941 −0.167661
\(298\) −36.0463 −2.08811
\(299\) −5.55367 −0.321177
\(300\) 84.4630 4.87648
\(301\) 0.345001 0.0198856
\(302\) −12.8777 −0.741028
\(303\) 11.7150 0.673008
\(304\) 10.1181 0.580314
\(305\) −13.2647 −0.759533
\(306\) −5.75600 −0.329048
\(307\) 32.1940 1.83741 0.918705 0.394944i \(-0.129236\pi\)
0.918705 + 0.394944i \(0.129236\pi\)
\(308\) −12.5624 −0.715809
\(309\) 0.0384037 0.00218471
\(310\) −20.5290 −1.16597
\(311\) 2.09951 0.119053 0.0595263 0.998227i \(-0.481041\pi\)
0.0595263 + 0.998227i \(0.481041\pi\)
\(312\) −36.2186 −2.05047
\(313\) 14.2327 0.804478 0.402239 0.915535i \(-0.368232\pi\)
0.402239 + 0.915535i \(0.368232\pi\)
\(314\) −47.6801 −2.69074
\(315\) 7.14280 0.402451
\(316\) 19.9697 1.12338
\(317\) −8.68030 −0.487534 −0.243767 0.969834i \(-0.578383\pi\)
−0.243767 + 0.969834i \(0.578383\pi\)
\(318\) −9.93940 −0.557374
\(319\) −37.6955 −2.11054
\(320\) −32.6096 −1.82293
\(321\) 13.4213 0.749104
\(322\) 2.62603 0.146343
\(323\) 2.08414 0.115965
\(324\) −32.5902 −1.81057
\(325\) 26.7064 1.48140
\(326\) 24.6188 1.36351
\(327\) 14.1269 0.781220
\(328\) −6.83441 −0.377367
\(329\) −4.31958 −0.238146
\(330\) 119.207 6.56212
\(331\) −19.6921 −1.08238 −0.541189 0.840901i \(-0.682026\pi\)
−0.541189 + 0.840901i \(0.682026\pi\)
\(332\) −4.66722 −0.256147
\(333\) 29.2307 1.60183
\(334\) 51.8476 2.83697
\(335\) 33.7319 1.84297
\(336\) 5.34886 0.291804
\(337\) 15.5386 0.846440 0.423220 0.906027i \(-0.360900\pi\)
0.423220 + 0.906027i \(0.360900\pi\)
\(338\) 8.31097 0.452057
\(339\) 42.8081 2.32502
\(340\) 10.6507 0.577614
\(341\) −12.1524 −0.658089
\(342\) −22.2210 −1.20157
\(343\) −8.20145 −0.442837
\(344\) −2.69142 −0.145112
\(345\) −16.5102 −0.888882
\(346\) 18.2252 0.979794
\(347\) −25.0547 −1.34501 −0.672504 0.740093i \(-0.734781\pi\)
−0.672504 + 0.740093i \(0.734781\pi\)
\(348\) 69.3868 3.71952
\(349\) −13.2362 −0.708516 −0.354258 0.935148i \(-0.615267\pi\)
−0.354258 + 0.935148i \(0.615267\pi\)
\(350\) −12.6280 −0.674996
\(351\) 1.68169 0.0897618
\(352\) −3.71470 −0.197994
\(353\) −7.63692 −0.406472 −0.203236 0.979130i \(-0.565146\pi\)
−0.203236 + 0.979130i \(0.565146\pi\)
\(354\) −2.27687 −0.121014
\(355\) −14.1149 −0.749140
\(356\) −59.4032 −3.14837
\(357\) 1.10177 0.0583117
\(358\) −24.3572 −1.28732
\(359\) −24.6093 −1.29883 −0.649414 0.760435i \(-0.724986\pi\)
−0.649414 + 0.760435i \(0.724986\pi\)
\(360\) −55.7223 −2.93682
\(361\) −10.9542 −0.576535
\(362\) −10.2247 −0.537400
\(363\) 43.1368 2.26409
\(364\) 7.31153 0.383228
\(365\) 22.6480 1.18545
\(366\) 21.8149 1.14028
\(367\) −0.284992 −0.0148765 −0.00743824 0.999972i \(-0.502368\pi\)
−0.00743824 + 0.999972i \(0.502368\pi\)
\(368\) −6.39839 −0.333539
\(369\) 4.68786 0.244040
\(370\) −81.6341 −4.24395
\(371\) 0.984585 0.0511171
\(372\) 22.3692 1.15979
\(373\) 23.9465 1.23990 0.619952 0.784639i \(-0.287152\pi\)
0.619952 + 0.784639i \(0.287152\pi\)
\(374\) 9.51582 0.492051
\(375\) 33.3720 1.72332
\(376\) 33.6979 1.73784
\(377\) 21.9394 1.12994
\(378\) −0.795180 −0.0408997
\(379\) 3.26051 0.167481 0.0837405 0.996488i \(-0.473313\pi\)
0.0837405 + 0.996488i \(0.473313\pi\)
\(380\) 41.1169 2.10925
\(381\) −11.0060 −0.563854
\(382\) −12.2589 −0.627218
\(383\) 13.9046 0.710494 0.355247 0.934773i \(-0.384397\pi\)
0.355247 + 0.934773i \(0.384397\pi\)
\(384\) 50.1469 2.55905
\(385\) −11.8085 −0.601816
\(386\) −20.1289 −1.02453
\(387\) 1.84610 0.0938425
\(388\) 22.2924 1.13173
\(389\) −7.94227 −0.402689 −0.201344 0.979521i \(-0.564531\pi\)
−0.201344 + 0.979521i \(0.564531\pi\)
\(390\) −69.3805 −3.51322
\(391\) −1.31795 −0.0666515
\(392\) 31.1423 1.57292
\(393\) 25.2517 1.27378
\(394\) 26.0740 1.31359
\(395\) 18.7713 0.944486
\(396\) −67.2212 −3.37799
\(397\) 11.3180 0.568032 0.284016 0.958820i \(-0.408333\pi\)
0.284016 + 0.958820i \(0.408333\pi\)
\(398\) 64.3653 3.22634
\(399\) 4.25336 0.212935
\(400\) 30.7684 1.53842
\(401\) 16.2927 0.813620 0.406810 0.913513i \(-0.366641\pi\)
0.406810 + 0.913513i \(0.366641\pi\)
\(402\) −55.4750 −2.76684
\(403\) 7.07290 0.352326
\(404\) 18.4493 0.917885
\(405\) −30.6343 −1.52223
\(406\) −10.3740 −0.514852
\(407\) −48.3242 −2.39534
\(408\) −8.59509 −0.425520
\(409\) 25.7301 1.27227 0.636136 0.771577i \(-0.280532\pi\)
0.636136 + 0.771577i \(0.280532\pi\)
\(410\) −13.0920 −0.646569
\(411\) −10.6491 −0.525283
\(412\) 0.0604798 0.00297963
\(413\) 0.225544 0.0110983
\(414\) 14.0519 0.690612
\(415\) −4.38712 −0.215355
\(416\) 2.16202 0.106002
\(417\) −35.4502 −1.73600
\(418\) 36.7358 1.79681
\(419\) −12.2672 −0.599294 −0.299647 0.954050i \(-0.596869\pi\)
−0.299647 + 0.954050i \(0.596869\pi\)
\(420\) 21.7361 1.06061
\(421\) −24.3308 −1.18581 −0.592904 0.805273i \(-0.702019\pi\)
−0.592904 + 0.805273i \(0.702019\pi\)
\(422\) −34.8558 −1.69675
\(423\) −23.1140 −1.12384
\(424\) −7.68093 −0.373019
\(425\) 6.33773 0.307425
\(426\) 23.2132 1.12468
\(427\) −2.16096 −0.104576
\(428\) 21.1364 1.02167
\(429\) −41.0706 −1.98291
\(430\) −5.15570 −0.248630
\(431\) −16.4251 −0.791167 −0.395584 0.918430i \(-0.629458\pi\)
−0.395584 + 0.918430i \(0.629458\pi\)
\(432\) 1.93747 0.0932168
\(433\) −7.36783 −0.354075 −0.177038 0.984204i \(-0.556651\pi\)
−0.177038 + 0.984204i \(0.556651\pi\)
\(434\) −3.34440 −0.160536
\(435\) 65.2227 3.12719
\(436\) 22.2477 1.06547
\(437\) −5.08793 −0.243389
\(438\) −37.2466 −1.77971
\(439\) −33.1716 −1.58319 −0.791596 0.611045i \(-0.790749\pi\)
−0.791596 + 0.611045i \(0.790749\pi\)
\(440\) 92.1202 4.39166
\(441\) −21.3611 −1.01720
\(442\) −5.53837 −0.263433
\(443\) −4.95690 −0.235510 −0.117755 0.993043i \(-0.537570\pi\)
−0.117755 + 0.993043i \(0.537570\pi\)
\(444\) 88.9514 4.22144
\(445\) −55.8383 −2.64699
\(446\) −7.70756 −0.364963
\(447\) 36.9202 1.74627
\(448\) −5.31245 −0.250990
\(449\) 9.78207 0.461644 0.230822 0.972996i \(-0.425858\pi\)
0.230822 + 0.972996i \(0.425858\pi\)
\(450\) −67.5724 −3.18539
\(451\) −7.74998 −0.364932
\(452\) 67.4161 3.17099
\(453\) 13.1899 0.619715
\(454\) 19.6142 0.920538
\(455\) 6.87274 0.322199
\(456\) −33.1813 −1.55386
\(457\) 27.9404 1.30700 0.653499 0.756928i \(-0.273300\pi\)
0.653499 + 0.756928i \(0.273300\pi\)
\(458\) 47.4202 2.21580
\(459\) 0.399084 0.0186276
\(460\) −26.0010 −1.21231
\(461\) 9.97962 0.464797 0.232399 0.972621i \(-0.425343\pi\)
0.232399 + 0.972621i \(0.425343\pi\)
\(462\) 19.4201 0.903504
\(463\) −0.624714 −0.0290329 −0.0145165 0.999895i \(-0.504621\pi\)
−0.0145165 + 0.999895i \(0.504621\pi\)
\(464\) 25.2764 1.17343
\(465\) 21.0267 0.975091
\(466\) −10.2676 −0.475639
\(467\) −32.4701 −1.50254 −0.751268 0.659998i \(-0.770557\pi\)
−0.751268 + 0.659998i \(0.770557\pi\)
\(468\) 39.1239 1.80850
\(469\) 5.49528 0.253749
\(470\) 64.5518 2.97755
\(471\) 48.8360 2.25024
\(472\) −1.75951 −0.0809879
\(473\) −3.05197 −0.140330
\(474\) −30.8710 −1.41795
\(475\) 24.4668 1.12261
\(476\) 1.73511 0.0795286
\(477\) 5.26850 0.241228
\(478\) −54.4146 −2.48886
\(479\) 4.41468 0.201712 0.100856 0.994901i \(-0.467842\pi\)
0.100856 + 0.994901i \(0.467842\pi\)
\(480\) 6.42737 0.293368
\(481\) 28.1255 1.28241
\(482\) 34.1503 1.55551
\(483\) −2.68970 −0.122385
\(484\) 67.9337 3.08789
\(485\) 20.9546 0.951498
\(486\) 54.3478 2.46527
\(487\) 36.9204 1.67303 0.836513 0.547948i \(-0.184591\pi\)
0.836513 + 0.547948i \(0.184591\pi\)
\(488\) 16.8580 0.763127
\(489\) −25.2156 −1.14029
\(490\) 59.6563 2.69500
\(491\) 13.5450 0.611276 0.305638 0.952148i \(-0.401130\pi\)
0.305638 + 0.952148i \(0.401130\pi\)
\(492\) 14.2655 0.643140
\(493\) 5.20647 0.234488
\(494\) −21.3809 −0.961970
\(495\) −63.1871 −2.84005
\(496\) 8.14870 0.365887
\(497\) −2.29947 −0.103145
\(498\) 7.21501 0.323312
\(499\) −1.60533 −0.0718645 −0.0359322 0.999354i \(-0.511440\pi\)
−0.0359322 + 0.999354i \(0.511440\pi\)
\(500\) 52.5556 2.35036
\(501\) −53.1046 −2.37254
\(502\) 57.4819 2.56554
\(503\) −34.7901 −1.55121 −0.775607 0.631217i \(-0.782556\pi\)
−0.775607 + 0.631217i \(0.782556\pi\)
\(504\) −9.07776 −0.404356
\(505\) 17.3421 0.771712
\(506\) −23.2306 −1.03273
\(507\) −8.51246 −0.378051
\(508\) −17.3327 −0.769014
\(509\) −5.63955 −0.249969 −0.124984 0.992159i \(-0.539888\pi\)
−0.124984 + 0.992159i \(0.539888\pi\)
\(510\) −16.4648 −0.729073
\(511\) 3.68961 0.163219
\(512\) 35.9591 1.58918
\(513\) 1.54066 0.0680218
\(514\) −18.1113 −0.798854
\(515\) 0.0568503 0.00250512
\(516\) 5.61783 0.247311
\(517\) 38.2122 1.68057
\(518\) −13.2991 −0.584327
\(519\) −18.6671 −0.819393
\(520\) −53.6155 −2.35120
\(521\) 18.7120 0.819787 0.409893 0.912133i \(-0.365566\pi\)
0.409893 + 0.912133i \(0.365566\pi\)
\(522\) −55.5110 −2.42965
\(523\) −36.5166 −1.59676 −0.798380 0.602153i \(-0.794310\pi\)
−0.798380 + 0.602153i \(0.794310\pi\)
\(524\) 39.7674 1.73725
\(525\) 12.9342 0.564493
\(526\) 25.4853 1.11121
\(527\) 1.67848 0.0731158
\(528\) −47.3175 −2.05923
\(529\) −19.7825 −0.860111
\(530\) −14.7136 −0.639119
\(531\) 1.20688 0.0523742
\(532\) 6.69838 0.290412
\(533\) 4.51062 0.195377
\(534\) 91.8309 3.97391
\(535\) 19.8680 0.858968
\(536\) −42.8697 −1.85169
\(537\) 24.9477 1.07657
\(538\) 34.9517 1.50687
\(539\) 35.3142 1.52109
\(540\) 7.87329 0.338813
\(541\) −15.4034 −0.662246 −0.331123 0.943588i \(-0.607427\pi\)
−0.331123 + 0.943588i \(0.607427\pi\)
\(542\) −53.9400 −2.31692
\(543\) 10.4726 0.449423
\(544\) 0.513072 0.0219978
\(545\) 20.9125 0.895794
\(546\) −11.3028 −0.483716
\(547\) 15.4116 0.658952 0.329476 0.944164i \(-0.393128\pi\)
0.329476 + 0.944164i \(0.393128\pi\)
\(548\) −16.7707 −0.716409
\(549\) −11.5633 −0.493508
\(550\) 111.711 4.76336
\(551\) 20.0996 0.856270
\(552\) 20.9828 0.893088
\(553\) 3.05804 0.130041
\(554\) 42.2404 1.79462
\(555\) 83.6131 3.54918
\(556\) −55.8285 −2.36766
\(557\) −29.1179 −1.23376 −0.616882 0.787056i \(-0.711604\pi\)
−0.616882 + 0.787056i \(0.711604\pi\)
\(558\) −17.8958 −0.757591
\(559\) 1.77630 0.0751295
\(560\) 7.91810 0.334601
\(561\) −9.74652 −0.411498
\(562\) −61.7659 −2.60544
\(563\) 12.8153 0.540098 0.270049 0.962847i \(-0.412960\pi\)
0.270049 + 0.962847i \(0.412960\pi\)
\(564\) −70.3379 −2.96176
\(565\) 63.3702 2.66601
\(566\) −49.8009 −2.09329
\(567\) −4.99066 −0.209588
\(568\) 17.9386 0.752685
\(569\) −16.0969 −0.674819 −0.337409 0.941358i \(-0.609551\pi\)
−0.337409 + 0.941358i \(0.609551\pi\)
\(570\) −63.5622 −2.66233
\(571\) −23.5591 −0.985918 −0.492959 0.870053i \(-0.664085\pi\)
−0.492959 + 0.870053i \(0.664085\pi\)
\(572\) −64.6797 −2.70439
\(573\) 12.5561 0.524537
\(574\) −2.13283 −0.0890227
\(575\) −15.4720 −0.645228
\(576\) −28.4269 −1.18445
\(577\) 8.56909 0.356736 0.178368 0.983964i \(-0.442918\pi\)
0.178368 + 0.983964i \(0.442918\pi\)
\(578\) 40.0728 1.66681
\(579\) 20.6169 0.856809
\(580\) 102.716 4.26503
\(581\) −0.714710 −0.0296511
\(582\) −34.4616 −1.42848
\(583\) −8.70990 −0.360727
\(584\) −28.7833 −1.19106
\(585\) 36.7760 1.52050
\(586\) 69.0585 2.85278
\(587\) −7.07398 −0.291974 −0.145987 0.989286i \(-0.546636\pi\)
−0.145987 + 0.989286i \(0.546636\pi\)
\(588\) −65.0036 −2.68070
\(589\) 6.47977 0.266994
\(590\) −3.37052 −0.138762
\(591\) −26.7061 −1.09854
\(592\) 32.4035 1.33177
\(593\) 1.55758 0.0639621 0.0319810 0.999488i \(-0.489818\pi\)
0.0319810 + 0.999488i \(0.489818\pi\)
\(594\) 7.03437 0.288624
\(595\) 1.63098 0.0668637
\(596\) 58.1435 2.38165
\(597\) −65.9257 −2.69816
\(598\) 13.5206 0.552898
\(599\) −6.57098 −0.268483 −0.134241 0.990949i \(-0.542860\pi\)
−0.134241 + 0.990949i \(0.542860\pi\)
\(600\) −100.902 −4.11930
\(601\) 45.8307 1.86947 0.934736 0.355342i \(-0.115636\pi\)
0.934736 + 0.355342i \(0.115636\pi\)
\(602\) −0.839918 −0.0342325
\(603\) 29.4052 1.19747
\(604\) 20.7720 0.845201
\(605\) 63.8568 2.59615
\(606\) −28.5205 −1.15857
\(607\) 41.8400 1.69823 0.849116 0.528206i \(-0.177135\pi\)
0.849116 + 0.528206i \(0.177135\pi\)
\(608\) 1.98071 0.0803284
\(609\) 10.6255 0.430566
\(610\) 32.2933 1.30752
\(611\) −22.2401 −0.899740
\(612\) 9.28455 0.375306
\(613\) 12.7214 0.513813 0.256906 0.966436i \(-0.417297\pi\)
0.256906 + 0.966436i \(0.417297\pi\)
\(614\) −78.3775 −3.16306
\(615\) 13.4094 0.540720
\(616\) 15.0074 0.604664
\(617\) −46.8984 −1.88806 −0.944029 0.329862i \(-0.892998\pi\)
−0.944029 + 0.329862i \(0.892998\pi\)
\(618\) −0.0934952 −0.00376093
\(619\) 11.5737 0.465187 0.232593 0.972574i \(-0.425279\pi\)
0.232593 + 0.972574i \(0.425279\pi\)
\(620\) 33.1138 1.32988
\(621\) −0.974266 −0.0390960
\(622\) −5.11134 −0.204946
\(623\) −9.09666 −0.364450
\(624\) 27.5396 1.10247
\(625\) 6.27341 0.250936
\(626\) −34.6499 −1.38489
\(627\) −37.6264 −1.50265
\(628\) 76.9090 3.06900
\(629\) 6.67451 0.266130
\(630\) −17.3894 −0.692810
\(631\) 10.0405 0.399705 0.199852 0.979826i \(-0.435954\pi\)
0.199852 + 0.979826i \(0.435954\pi\)
\(632\) −23.8564 −0.948955
\(633\) 35.7008 1.41898
\(634\) 21.1325 0.839279
\(635\) −16.2925 −0.646549
\(636\) 16.0325 0.635729
\(637\) −20.5535 −0.814359
\(638\) 91.7709 3.63325
\(639\) −12.3044 −0.486755
\(640\) 74.2340 2.93436
\(641\) −16.0539 −0.634093 −0.317046 0.948410i \(-0.602691\pi\)
−0.317046 + 0.948410i \(0.602691\pi\)
\(642\) −32.6746 −1.28956
\(643\) 20.4249 0.805481 0.402741 0.915314i \(-0.368058\pi\)
0.402741 + 0.915314i \(0.368058\pi\)
\(644\) −4.23585 −0.166916
\(645\) 5.28069 0.207927
\(646\) −5.07392 −0.199631
\(647\) −22.2969 −0.876581 −0.438290 0.898833i \(-0.644416\pi\)
−0.438290 + 0.898833i \(0.644416\pi\)
\(648\) 38.9331 1.52944
\(649\) −1.99522 −0.0783191
\(650\) −65.0176 −2.55020
\(651\) 3.42548 0.134255
\(652\) −39.7106 −1.55519
\(653\) −1.68848 −0.0660753 −0.0330377 0.999454i \(-0.510518\pi\)
−0.0330377 + 0.999454i \(0.510518\pi\)
\(654\) −34.3924 −1.34485
\(655\) 37.3809 1.46059
\(656\) 5.19669 0.202897
\(657\) 19.7430 0.770249
\(658\) 10.5162 0.409963
\(659\) −33.4864 −1.30445 −0.652223 0.758027i \(-0.726163\pi\)
−0.652223 + 0.758027i \(0.726163\pi\)
\(660\) −192.283 −7.48462
\(661\) 30.4639 1.18491 0.592454 0.805605i \(-0.298159\pi\)
0.592454 + 0.805605i \(0.298159\pi\)
\(662\) 47.9412 1.86329
\(663\) 5.67264 0.220307
\(664\) 5.57558 0.216374
\(665\) 6.29639 0.244164
\(666\) −71.1631 −2.75752
\(667\) −12.7103 −0.492146
\(668\) −83.6314 −3.23579
\(669\) 7.89441 0.305216
\(670\) −82.1214 −3.17263
\(671\) 19.1164 0.737980
\(672\) 1.04709 0.0403923
\(673\) 27.0782 1.04379 0.521895 0.853010i \(-0.325225\pi\)
0.521895 + 0.853010i \(0.325225\pi\)
\(674\) −37.8292 −1.45713
\(675\) 4.68503 0.180327
\(676\) −13.4058 −0.515607
\(677\) 39.1940 1.50635 0.753173 0.657822i \(-0.228522\pi\)
0.753173 + 0.657822i \(0.228522\pi\)
\(678\) −104.218 −4.00246
\(679\) 3.41372 0.131007
\(680\) −12.7236 −0.487927
\(681\) −20.0897 −0.769838
\(682\) 29.5854 1.13288
\(683\) −36.9955 −1.41559 −0.707797 0.706416i \(-0.750311\pi\)
−0.707797 + 0.706416i \(0.750311\pi\)
\(684\) 35.8430 1.37049
\(685\) −15.7643 −0.602321
\(686\) 19.9667 0.762333
\(687\) −48.5698 −1.85306
\(688\) 2.04648 0.0780213
\(689\) 5.06931 0.193125
\(690\) 40.1948 1.53019
\(691\) −26.1845 −0.996106 −0.498053 0.867147i \(-0.665952\pi\)
−0.498053 + 0.867147i \(0.665952\pi\)
\(692\) −29.3977 −1.11753
\(693\) −10.2939 −0.391031
\(694\) 60.9966 2.31540
\(695\) −52.4781 −1.99061
\(696\) −82.8913 −3.14199
\(697\) 1.07042 0.0405451
\(698\) 32.2239 1.21969
\(699\) 10.5166 0.397773
\(700\) 20.3693 0.769886
\(701\) 0.832365 0.0314380 0.0157190 0.999876i \(-0.494996\pi\)
0.0157190 + 0.999876i \(0.494996\pi\)
\(702\) −4.09413 −0.154523
\(703\) 25.7669 0.971817
\(704\) 46.9954 1.77120
\(705\) −66.1167 −2.49010
\(706\) 18.5924 0.699733
\(707\) 2.82521 0.106253
\(708\) 3.67264 0.138026
\(709\) 42.3148 1.58916 0.794582 0.607157i \(-0.207690\pi\)
0.794582 + 0.607157i \(0.207690\pi\)
\(710\) 34.3632 1.28963
\(711\) 16.3636 0.613681
\(712\) 70.9647 2.65951
\(713\) −4.09760 −0.153456
\(714\) −2.68229 −0.100382
\(715\) −60.7981 −2.27372
\(716\) 39.2887 1.46829
\(717\) 55.7338 2.08142
\(718\) 59.9121 2.23590
\(719\) −23.7287 −0.884930 −0.442465 0.896786i \(-0.645896\pi\)
−0.442465 + 0.896786i \(0.645896\pi\)
\(720\) 42.3696 1.57902
\(721\) 0.00926152 0.000344917 0
\(722\) 26.6683 0.992492
\(723\) −34.9783 −1.30086
\(724\) 16.4927 0.612947
\(725\) 61.1213 2.26999
\(726\) −105.018 −3.89758
\(727\) −39.8410 −1.47762 −0.738811 0.673913i \(-0.764612\pi\)
−0.738811 + 0.673913i \(0.764612\pi\)
\(728\) −8.73455 −0.323724
\(729\) −30.7681 −1.13956
\(730\) −55.1374 −2.04073
\(731\) 0.421537 0.0155911
\(732\) −35.1879 −1.30058
\(733\) −37.7531 −1.39444 −0.697222 0.716855i \(-0.745581\pi\)
−0.697222 + 0.716855i \(0.745581\pi\)
\(734\) 0.693824 0.0256095
\(735\) −61.1026 −2.25380
\(736\) −1.25254 −0.0461692
\(737\) −48.6127 −1.79067
\(738\) −11.4128 −0.420110
\(739\) −1.66619 −0.0612918 −0.0306459 0.999530i \(-0.509756\pi\)
−0.0306459 + 0.999530i \(0.509756\pi\)
\(740\) 131.678 4.84056
\(741\) 21.8992 0.804487
\(742\) −2.39701 −0.0879969
\(743\) −10.7136 −0.393043 −0.196521 0.980500i \(-0.562965\pi\)
−0.196521 + 0.980500i \(0.562965\pi\)
\(744\) −26.7228 −0.979705
\(745\) 54.6542 2.00237
\(746\) −58.2987 −2.13447
\(747\) −3.82440 −0.139928
\(748\) −15.3492 −0.561224
\(749\) 3.23671 0.118267
\(750\) −81.2452 −2.96665
\(751\) −20.1714 −0.736064 −0.368032 0.929813i \(-0.619968\pi\)
−0.368032 + 0.929813i \(0.619968\pi\)
\(752\) −25.6229 −0.934371
\(753\) −58.8754 −2.14554
\(754\) −53.4123 −1.94516
\(755\) 19.5254 0.710603
\(756\) 1.28264 0.0466493
\(757\) −34.6586 −1.25969 −0.629844 0.776722i \(-0.716881\pi\)
−0.629844 + 0.776722i \(0.716881\pi\)
\(758\) −7.93782 −0.288315
\(759\) 23.7938 0.863659
\(760\) −49.1193 −1.78174
\(761\) −45.1246 −1.63577 −0.817883 0.575385i \(-0.804852\pi\)
−0.817883 + 0.575385i \(0.804852\pi\)
\(762\) 26.7944 0.970661
\(763\) 3.40687 0.123337
\(764\) 19.7738 0.715392
\(765\) 8.72736 0.315538
\(766\) −33.8513 −1.22310
\(767\) 1.16125 0.0419303
\(768\) −78.0271 −2.81556
\(769\) −4.51050 −0.162653 −0.0813263 0.996688i \(-0.525916\pi\)
−0.0813263 + 0.996688i \(0.525916\pi\)
\(770\) 28.7482 1.03601
\(771\) 18.5503 0.668074
\(772\) 32.4684 1.16856
\(773\) 41.5940 1.49603 0.748016 0.663681i \(-0.231007\pi\)
0.748016 + 0.663681i \(0.231007\pi\)
\(774\) −4.49439 −0.161548
\(775\) 19.7045 0.707806
\(776\) −26.6311 −0.956001
\(777\) 13.6215 0.488668
\(778\) 19.3357 0.693219
\(779\) 4.13236 0.148057
\(780\) 111.912 4.00710
\(781\) 20.3417 0.727883
\(782\) 3.20859 0.114739
\(783\) 3.84878 0.137544
\(784\) −23.6797 −0.845704
\(785\) 72.2935 2.58027
\(786\) −61.4761 −2.19278
\(787\) 24.7458 0.882094 0.441047 0.897484i \(-0.354607\pi\)
0.441047 + 0.897484i \(0.354607\pi\)
\(788\) −42.0579 −1.49825
\(789\) −26.1031 −0.929295
\(790\) −45.6993 −1.62591
\(791\) 10.3237 0.367068
\(792\) 80.3043 2.85349
\(793\) −11.1261 −0.395098
\(794\) −27.5540 −0.977853
\(795\) 15.0703 0.534489
\(796\) −103.823 −3.67990
\(797\) −51.9929 −1.84168 −0.920842 0.389937i \(-0.872497\pi\)
−0.920842 + 0.389937i \(0.872497\pi\)
\(798\) −10.3550 −0.366562
\(799\) −5.27784 −0.186717
\(800\) 6.02319 0.212952
\(801\) −48.6761 −1.71989
\(802\) −39.6652 −1.40063
\(803\) −32.6392 −1.15181
\(804\) 89.4824 3.15580
\(805\) −3.98164 −0.140335
\(806\) −17.2192 −0.606521
\(807\) −35.7990 −1.26019
\(808\) −22.0400 −0.775363
\(809\) 20.2651 0.712484 0.356242 0.934394i \(-0.384058\pi\)
0.356242 + 0.934394i \(0.384058\pi\)
\(810\) 74.5804 2.62049
\(811\) 10.0684 0.353550 0.176775 0.984251i \(-0.443433\pi\)
0.176775 + 0.984251i \(0.443433\pi\)
\(812\) 16.7335 0.587229
\(813\) 55.2477 1.93762
\(814\) 117.647 4.12353
\(815\) −37.3275 −1.30753
\(816\) 6.53546 0.228787
\(817\) 1.62734 0.0569334
\(818\) −62.6408 −2.19019
\(819\) 5.99120 0.209349
\(820\) 21.1177 0.737464
\(821\) 44.1178 1.53972 0.769861 0.638212i \(-0.220326\pi\)
0.769861 + 0.638212i \(0.220326\pi\)
\(822\) 25.9257 0.904262
\(823\) −32.2660 −1.12472 −0.562361 0.826892i \(-0.690107\pi\)
−0.562361 + 0.826892i \(0.690107\pi\)
\(824\) −0.0722508 −0.00251698
\(825\) −114.419 −3.98356
\(826\) −0.549094 −0.0191054
\(827\) 6.98761 0.242983 0.121491 0.992592i \(-0.461232\pi\)
0.121491 + 0.992592i \(0.461232\pi\)
\(828\) −22.6660 −0.787697
\(829\) 6.75511 0.234615 0.117307 0.993096i \(-0.462574\pi\)
0.117307 + 0.993096i \(0.462574\pi\)
\(830\) 10.6806 0.370729
\(831\) −43.2644 −1.50083
\(832\) −27.3521 −0.948263
\(833\) −4.87758 −0.168998
\(834\) 86.3048 2.98849
\(835\) −78.6124 −2.72049
\(836\) −59.2556 −2.04940
\(837\) 1.24078 0.0428877
\(838\) 29.8650 1.03167
\(839\) −24.1545 −0.833905 −0.416952 0.908928i \(-0.636902\pi\)
−0.416952 + 0.908928i \(0.636902\pi\)
\(840\) −25.9665 −0.895931
\(841\) 21.2114 0.731428
\(842\) 59.2341 2.04134
\(843\) 63.2634 2.17891
\(844\) 56.2232 1.93528
\(845\) −12.6013 −0.433497
\(846\) 56.2719 1.93467
\(847\) 10.4030 0.357450
\(848\) 5.84036 0.200559
\(849\) 51.0083 1.75060
\(850\) −15.4294 −0.529225
\(851\) −16.2942 −0.558558
\(852\) −37.4433 −1.28279
\(853\) −33.5108 −1.14739 −0.573694 0.819070i \(-0.694490\pi\)
−0.573694 + 0.819070i \(0.694490\pi\)
\(854\) 5.26093 0.180025
\(855\) 33.6919 1.15224
\(856\) −25.2501 −0.863032
\(857\) −32.8649 −1.12264 −0.561322 0.827598i \(-0.689707\pi\)
−0.561322 + 0.827598i \(0.689707\pi\)
\(858\) 99.9877 3.41352
\(859\) 26.6143 0.908069 0.454035 0.890984i \(-0.349984\pi\)
0.454035 + 0.890984i \(0.349984\pi\)
\(860\) 8.31625 0.283582
\(861\) 2.18454 0.0744489
\(862\) 39.9874 1.36198
\(863\) 33.0835 1.12618 0.563088 0.826397i \(-0.309613\pi\)
0.563088 + 0.826397i \(0.309613\pi\)
\(864\) 0.379278 0.0129033
\(865\) −27.6334 −0.939565
\(866\) 17.9372 0.609532
\(867\) −41.0443 −1.39394
\(868\) 5.39459 0.183104
\(869\) −27.0523 −0.917685
\(870\) −158.787 −5.38338
\(871\) 28.2934 0.958686
\(872\) −26.5776 −0.900032
\(873\) 18.2668 0.618237
\(874\) 12.3867 0.418988
\(875\) 8.04805 0.272074
\(876\) 60.0797 2.02990
\(877\) −36.8752 −1.24519 −0.622594 0.782545i \(-0.713921\pi\)
−0.622594 + 0.782545i \(0.713921\pi\)
\(878\) 80.7573 2.72543
\(879\) −70.7327 −2.38575
\(880\) −70.0456 −2.36124
\(881\) 35.5834 1.19884 0.599418 0.800436i \(-0.295399\pi\)
0.599418 + 0.800436i \(0.295399\pi\)
\(882\) 52.0044 1.75108
\(883\) −22.4567 −0.755728 −0.377864 0.925861i \(-0.623341\pi\)
−0.377864 + 0.925861i \(0.623341\pi\)
\(884\) 8.93352 0.300467
\(885\) 3.45223 0.116045
\(886\) 12.0678 0.405424
\(887\) 18.5758 0.623713 0.311856 0.950129i \(-0.399049\pi\)
0.311856 + 0.950129i \(0.399049\pi\)
\(888\) −106.264 −3.56597
\(889\) −2.65423 −0.0890199
\(890\) 135.940 4.55673
\(891\) 44.1487 1.47904
\(892\) 12.4325 0.416270
\(893\) −20.3751 −0.681826
\(894\) −89.8835 −3.00615
\(895\) 36.9309 1.23446
\(896\) 12.0935 0.404016
\(897\) −13.8484 −0.462384
\(898\) −23.8148 −0.794710
\(899\) 16.1873 0.539878
\(900\) 108.996 3.63319
\(901\) 1.20301 0.0400779
\(902\) 18.8676 0.628222
\(903\) 0.860281 0.0286283
\(904\) −80.5370 −2.67862
\(905\) 15.5029 0.515335
\(906\) −32.1113 −1.06683
\(907\) 37.8416 1.25651 0.628255 0.778008i \(-0.283770\pi\)
0.628255 + 0.778008i \(0.283770\pi\)
\(908\) −31.6381 −1.04995
\(909\) 15.1177 0.501421
\(910\) −16.7319 −0.554658
\(911\) −17.0920 −0.566282 −0.283141 0.959078i \(-0.591376\pi\)
−0.283141 + 0.959078i \(0.591376\pi\)
\(912\) 25.2301 0.835452
\(913\) 6.32251 0.209244
\(914\) −68.0219 −2.24997
\(915\) −33.0762 −1.09347
\(916\) −76.4899 −2.52730
\(917\) 6.08975 0.201101
\(918\) −0.971583 −0.0320670
\(919\) 30.6834 1.01215 0.506076 0.862489i \(-0.331096\pi\)
0.506076 + 0.862489i \(0.331096\pi\)
\(920\) 31.0615 1.02407
\(921\) 80.2776 2.64524
\(922\) −24.2957 −0.800138
\(923\) −11.8392 −0.389692
\(924\) −31.3250 −1.03052
\(925\) 78.3553 2.57630
\(926\) 1.52089 0.0499795
\(927\) 0.0495583 0.00162771
\(928\) 4.94808 0.162429
\(929\) 57.6983 1.89302 0.946510 0.322674i \(-0.104582\pi\)
0.946510 + 0.322674i \(0.104582\pi\)
\(930\) −51.1903 −1.67860
\(931\) −18.8299 −0.617124
\(932\) 16.5619 0.542504
\(933\) 5.23526 0.171395
\(934\) 79.0495 2.58658
\(935\) −14.4281 −0.471849
\(936\) −46.7385 −1.52769
\(937\) −7.60650 −0.248494 −0.124247 0.992251i \(-0.539651\pi\)
−0.124247 + 0.992251i \(0.539651\pi\)
\(938\) −13.3785 −0.436822
\(939\) 35.4899 1.15817
\(940\) −104.123 −3.39613
\(941\) −23.5063 −0.766284 −0.383142 0.923689i \(-0.625158\pi\)
−0.383142 + 0.923689i \(0.625158\pi\)
\(942\) −118.893 −3.87374
\(943\) −2.61318 −0.0850967
\(944\) 1.33788 0.0435442
\(945\) 1.20567 0.0392204
\(946\) 7.43014 0.241575
\(947\) −32.2998 −1.04960 −0.524802 0.851224i \(-0.675861\pi\)
−0.524802 + 0.851224i \(0.675861\pi\)
\(948\) 49.7956 1.61729
\(949\) 18.9966 0.616655
\(950\) −59.5652 −1.93255
\(951\) −21.6448 −0.701881
\(952\) −2.07281 −0.0671801
\(953\) −34.2499 −1.10946 −0.554731 0.832030i \(-0.687179\pi\)
−0.554731 + 0.832030i \(0.687179\pi\)
\(954\) −12.8264 −0.415269
\(955\) 18.5871 0.601466
\(956\) 87.7719 2.83875
\(957\) −93.9958 −3.03845
\(958\) −10.7477 −0.347242
\(959\) −2.56817 −0.0829304
\(960\) −81.3139 −2.62439
\(961\) −25.7815 −0.831660
\(962\) −68.4726 −2.20764
\(963\) 17.3196 0.558116
\(964\) −55.0853 −1.77418
\(965\) 30.5199 0.982470
\(966\) 6.54816 0.210684
\(967\) −9.48334 −0.304964 −0.152482 0.988306i \(-0.548727\pi\)
−0.152482 + 0.988306i \(0.548727\pi\)
\(968\) −81.1554 −2.60843
\(969\) 5.19693 0.166949
\(970\) −51.0146 −1.63798
\(971\) 0.642932 0.0206327 0.0103163 0.999947i \(-0.496716\pi\)
0.0103163 + 0.999947i \(0.496716\pi\)
\(972\) −87.6642 −2.81183
\(973\) −8.54925 −0.274076
\(974\) −89.8841 −2.88007
\(975\) 66.5938 2.13271
\(976\) −12.8184 −0.410306
\(977\) −23.2839 −0.744919 −0.372460 0.928048i \(-0.621485\pi\)
−0.372460 + 0.928048i \(0.621485\pi\)
\(978\) 61.3883 1.96298
\(979\) 80.4714 2.57188
\(980\) −96.2270 −3.07386
\(981\) 18.2301 0.582043
\(982\) −32.9757 −1.05230
\(983\) −20.0409 −0.639204 −0.319602 0.947552i \(-0.603549\pi\)
−0.319602 + 0.947552i \(0.603549\pi\)
\(984\) −17.0420 −0.543279
\(985\) −39.5339 −1.25965
\(986\) −12.6753 −0.403665
\(987\) −10.7711 −0.342849
\(988\) 34.4878 1.09720
\(989\) −1.02908 −0.0327228
\(990\) 153.831 4.88908
\(991\) 19.1982 0.609852 0.304926 0.952376i \(-0.401368\pi\)
0.304926 + 0.952376i \(0.401368\pi\)
\(992\) 1.59518 0.0506470
\(993\) −49.1035 −1.55825
\(994\) 5.59813 0.177562
\(995\) −97.5919 −3.09387
\(996\) −11.6380 −0.368763
\(997\) −47.9412 −1.51831 −0.759157 0.650908i \(-0.774388\pi\)
−0.759157 + 0.650908i \(0.774388\pi\)
\(998\) 3.90823 0.123713
\(999\) 4.93399 0.156105
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 \(a_p\))