Properties

Label 4019.2.a.b.1.7
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 1.7
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69011 q^{2}\) \(+0.353602 q^{3}\) \(+5.23670 q^{4}\) \(-0.999886 q^{5}\) \(-0.951229 q^{6}\) \(+3.25121 q^{7}\) \(-8.70707 q^{8}\) \(-2.87497 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69011 q^{2}\) \(+0.353602 q^{3}\) \(+5.23670 q^{4}\) \(-0.999886 q^{5}\) \(-0.951229 q^{6}\) \(+3.25121 q^{7}\) \(-8.70707 q^{8}\) \(-2.87497 q^{9}\) \(+2.68981 q^{10}\) \(-3.92179 q^{11}\) \(+1.85171 q^{12}\) \(+2.55128 q^{13}\) \(-8.74612 q^{14}\) \(-0.353562 q^{15}\) \(+12.9496 q^{16}\) \(-3.24551 q^{17}\) \(+7.73398 q^{18}\) \(-6.18143 q^{19}\) \(-5.23610 q^{20}\) \(+1.14964 q^{21}\) \(+10.5500 q^{22}\) \(-6.21887 q^{23}\) \(-3.07884 q^{24}\) \(-4.00023 q^{25}\) \(-6.86322 q^{26}\) \(-2.07740 q^{27}\) \(+17.0256 q^{28}\) \(+2.78073 q^{29}\) \(+0.951121 q^{30}\) \(-2.88281 q^{31}\) \(-17.4217 q^{32}\) \(-1.38675 q^{33}\) \(+8.73079 q^{34}\) \(-3.25084 q^{35}\) \(-15.0553 q^{36}\) \(+7.41193 q^{37}\) \(+16.6287 q^{38}\) \(+0.902137 q^{39}\) \(+8.70609 q^{40}\) \(-2.56356 q^{41}\) \(-3.09265 q^{42}\) \(-7.30959 q^{43}\) \(-20.5372 q^{44}\) \(+2.87464 q^{45}\) \(+16.7295 q^{46}\) \(-0.0357877 q^{47}\) \(+4.57901 q^{48}\) \(+3.57036 q^{49}\) \(+10.7611 q^{50}\) \(-1.14762 q^{51}\) \(+13.3603 q^{52}\) \(+12.9978 q^{53}\) \(+5.58844 q^{54}\) \(+3.92134 q^{55}\) \(-28.3085 q^{56}\) \(-2.18577 q^{57}\) \(-7.48046 q^{58}\) \(-7.42610 q^{59}\) \(-1.85150 q^{60}\) \(+1.59266 q^{61}\) \(+7.75507 q^{62}\) \(-9.34712 q^{63}\) \(+20.9671 q^{64}\) \(-2.55099 q^{65}\) \(+3.73052 q^{66}\) \(-5.79715 q^{67}\) \(-16.9958 q^{68}\) \(-2.19901 q^{69}\) \(+8.74512 q^{70}\) \(-0.814408 q^{71}\) \(+25.0325 q^{72}\) \(+13.1201 q^{73}\) \(-19.9389 q^{74}\) \(-1.41449 q^{75}\) \(-32.3703 q^{76}\) \(-12.7506 q^{77}\) \(-2.42685 q^{78}\) \(+9.45733 q^{79}\) \(-12.9481 q^{80}\) \(+7.89032 q^{81}\) \(+6.89627 q^{82}\) \(-1.90763 q^{83}\) \(+6.02029 q^{84}\) \(+3.24514 q^{85}\) \(+19.6636 q^{86}\) \(+0.983271 q^{87}\) \(+34.1473 q^{88}\) \(+18.3507 q^{89}\) \(-7.73310 q^{90}\) \(+8.29473 q^{91}\) \(-32.5663 q^{92}\) \(-1.01937 q^{93}\) \(+0.0962729 q^{94}\) \(+6.18073 q^{95}\) \(-6.16036 q^{96}\) \(+3.98815 q^{97}\) \(-9.60468 q^{98}\) \(+11.2750 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69011 −1.90220 −0.951098 0.308890i \(-0.900043\pi\)
−0.951098 + 0.308890i \(0.900043\pi\)
\(3\) 0.353602 0.204152 0.102076 0.994777i \(-0.467451\pi\)
0.102076 + 0.994777i \(0.467451\pi\)
\(4\) 5.23670 2.61835
\(5\) −0.999886 −0.447163 −0.223581 0.974685i \(-0.571775\pi\)
−0.223581 + 0.974685i \(0.571775\pi\)
\(6\) −0.951229 −0.388338
\(7\) 3.25121 1.22884 0.614421 0.788978i \(-0.289390\pi\)
0.614421 + 0.788978i \(0.289390\pi\)
\(8\) −8.70707 −3.07842
\(9\) −2.87497 −0.958322
\(10\) 2.68981 0.850591
\(11\) −3.92179 −1.18246 −0.591232 0.806502i \(-0.701358\pi\)
−0.591232 + 0.806502i \(0.701358\pi\)
\(12\) 1.85171 0.534542
\(13\) 2.55128 0.707597 0.353798 0.935322i \(-0.384890\pi\)
0.353798 + 0.935322i \(0.384890\pi\)
\(14\) −8.74612 −2.33750
\(15\) −0.353562 −0.0912894
\(16\) 12.9496 3.23740
\(17\) −3.24551 −0.787153 −0.393576 0.919292i \(-0.628762\pi\)
−0.393576 + 0.919292i \(0.628762\pi\)
\(18\) 7.73398 1.82292
\(19\) −6.18143 −1.41812 −0.709059 0.705149i \(-0.750880\pi\)
−0.709059 + 0.705149i \(0.750880\pi\)
\(20\) −5.23610 −1.17083
\(21\) 1.14964 0.250871
\(22\) 10.5500 2.24928
\(23\) −6.21887 −1.29672 −0.648362 0.761332i \(-0.724546\pi\)
−0.648362 + 0.761332i \(0.724546\pi\)
\(24\) −3.07884 −0.628466
\(25\) −4.00023 −0.800045
\(26\) −6.86322 −1.34599
\(27\) −2.07740 −0.399796
\(28\) 17.0256 3.21754
\(29\) 2.78073 0.516368 0.258184 0.966096i \(-0.416876\pi\)
0.258184 + 0.966096i \(0.416876\pi\)
\(30\) 0.951121 0.173650
\(31\) −2.88281 −0.517767 −0.258884 0.965909i \(-0.583355\pi\)
−0.258884 + 0.965909i \(0.583355\pi\)
\(32\) −17.4217 −3.07975
\(33\) −1.38675 −0.241403
\(34\) 8.73079 1.49732
\(35\) −3.25084 −0.549492
\(36\) −15.0553 −2.50922
\(37\) 7.41193 1.21851 0.609257 0.792973i \(-0.291468\pi\)
0.609257 + 0.792973i \(0.291468\pi\)
\(38\) 16.6287 2.69754
\(39\) 0.902137 0.144458
\(40\) 8.70609 1.37655
\(41\) −2.56356 −0.400361 −0.200181 0.979759i \(-0.564153\pi\)
−0.200181 + 0.979759i \(0.564153\pi\)
\(42\) −3.09265 −0.477206
\(43\) −7.30959 −1.11470 −0.557351 0.830277i \(-0.688182\pi\)
−0.557351 + 0.830277i \(0.688182\pi\)
\(44\) −20.5372 −3.09610
\(45\) 2.87464 0.428526
\(46\) 16.7295 2.46662
\(47\) −0.0357877 −0.00522017 −0.00261009 0.999997i \(-0.500831\pi\)
−0.00261009 + 0.999997i \(0.500831\pi\)
\(48\) 4.57901 0.660923
\(49\) 3.57036 0.510052
\(50\) 10.7611 1.52184
\(51\) −1.14762 −0.160699
\(52\) 13.3603 1.85273
\(53\) 12.9978 1.78539 0.892695 0.450662i \(-0.148812\pi\)
0.892695 + 0.450662i \(0.148812\pi\)
\(54\) 5.58844 0.760490
\(55\) 3.92134 0.528754
\(56\) −28.3085 −3.78289
\(57\) −2.18577 −0.289512
\(58\) −7.48046 −0.982233
\(59\) −7.42610 −0.966796 −0.483398 0.875401i \(-0.660598\pi\)
−0.483398 + 0.875401i \(0.660598\pi\)
\(60\) −1.85150 −0.239027
\(61\) 1.59266 0.203920 0.101960 0.994789i \(-0.467489\pi\)
0.101960 + 0.994789i \(0.467489\pi\)
\(62\) 7.75507 0.984895
\(63\) −9.34712 −1.17763
\(64\) 20.9671 2.62089
\(65\) −2.55099 −0.316411
\(66\) 3.73052 0.459195
\(67\) −5.79715 −0.708234 −0.354117 0.935201i \(-0.615219\pi\)
−0.354117 + 0.935201i \(0.615219\pi\)
\(68\) −16.9958 −2.06104
\(69\) −2.19901 −0.264729
\(70\) 8.74512 1.04524
\(71\) −0.814408 −0.0966524 −0.0483262 0.998832i \(-0.515389\pi\)
−0.0483262 + 0.998832i \(0.515389\pi\)
\(72\) 25.0325 2.95011
\(73\) 13.1201 1.53559 0.767794 0.640697i \(-0.221355\pi\)
0.767794 + 0.640697i \(0.221355\pi\)
\(74\) −19.9389 −2.31785
\(75\) −1.41449 −0.163331
\(76\) −32.3703 −3.71313
\(77\) −12.7506 −1.45306
\(78\) −2.42685 −0.274787
\(79\) 9.45733 1.06403 0.532016 0.846734i \(-0.321434\pi\)
0.532016 + 0.846734i \(0.321434\pi\)
\(80\) −12.9481 −1.44765
\(81\) 7.89032 0.876702
\(82\) 6.89627 0.761565
\(83\) −1.90763 −0.209390 −0.104695 0.994504i \(-0.533387\pi\)
−0.104695 + 0.994504i \(0.533387\pi\)
\(84\) 6.02029 0.656868
\(85\) 3.24514 0.351985
\(86\) 19.6636 2.12038
\(87\) 0.983271 0.105418
\(88\) 34.1473 3.64012
\(89\) 18.3507 1.94517 0.972587 0.232541i \(-0.0747039\pi\)
0.972587 + 0.232541i \(0.0747039\pi\)
\(90\) −7.73310 −0.815140
\(91\) 8.29473 0.869524
\(92\) −32.5663 −3.39528
\(93\) −1.01937 −0.105703
\(94\) 0.0962729 0.00992979
\(95\) 6.18073 0.634129
\(96\) −6.16036 −0.628739
\(97\) 3.98815 0.404935 0.202468 0.979289i \(-0.435104\pi\)
0.202468 + 0.979289i \(0.435104\pi\)
\(98\) −9.60468 −0.970219
\(99\) 11.2750 1.13318
\(100\) −20.9480 −2.09480
\(101\) 9.07095 0.902594 0.451297 0.892374i \(-0.350962\pi\)
0.451297 + 0.892374i \(0.350962\pi\)
\(102\) 3.08723 0.305681
\(103\) 9.80257 0.965876 0.482938 0.875655i \(-0.339570\pi\)
0.482938 + 0.875655i \(0.339570\pi\)
\(104\) −22.2142 −2.17828
\(105\) −1.14950 −0.112180
\(106\) −34.9656 −3.39616
\(107\) 14.2465 1.37726 0.688628 0.725115i \(-0.258213\pi\)
0.688628 + 0.725115i \(0.258213\pi\)
\(108\) −10.8787 −1.04681
\(109\) 10.3058 0.987112 0.493556 0.869714i \(-0.335697\pi\)
0.493556 + 0.869714i \(0.335697\pi\)
\(110\) −10.5488 −1.00579
\(111\) 2.62088 0.248762
\(112\) 42.1019 3.97825
\(113\) 12.1223 1.14037 0.570183 0.821518i \(-0.306872\pi\)
0.570183 + 0.821518i \(0.306872\pi\)
\(114\) 5.87996 0.550709
\(115\) 6.21816 0.579847
\(116\) 14.5618 1.35203
\(117\) −7.33483 −0.678105
\(118\) 19.9770 1.83903
\(119\) −10.5518 −0.967286
\(120\) 3.07849 0.281027
\(121\) 4.38043 0.398221
\(122\) −4.28444 −0.387895
\(123\) −0.906482 −0.0817347
\(124\) −15.0964 −1.35570
\(125\) 8.99921 0.804913
\(126\) 25.1448 2.24007
\(127\) −8.05780 −0.715014 −0.357507 0.933910i \(-0.616373\pi\)
−0.357507 + 0.933910i \(0.616373\pi\)
\(128\) −21.5605 −1.90570
\(129\) −2.58469 −0.227569
\(130\) 6.86244 0.601876
\(131\) −8.09546 −0.707304 −0.353652 0.935377i \(-0.615060\pi\)
−0.353652 + 0.935377i \(0.615060\pi\)
\(132\) −7.26201 −0.632077
\(133\) −20.0971 −1.74264
\(134\) 15.5950 1.34720
\(135\) 2.07717 0.178774
\(136\) 28.2589 2.42318
\(137\) 22.1702 1.89413 0.947066 0.321039i \(-0.104032\pi\)
0.947066 + 0.321039i \(0.104032\pi\)
\(138\) 5.91557 0.503567
\(139\) 5.71832 0.485022 0.242511 0.970149i \(-0.422029\pi\)
0.242511 + 0.970149i \(0.422029\pi\)
\(140\) −17.0237 −1.43876
\(141\) −0.0126546 −0.00106571
\(142\) 2.19085 0.183852
\(143\) −10.0056 −0.836708
\(144\) −37.2297 −3.10247
\(145\) −2.78041 −0.230901
\(146\) −35.2944 −2.92099
\(147\) 1.26249 0.104128
\(148\) 38.8140 3.19049
\(149\) −11.6974 −0.958284 −0.479142 0.877737i \(-0.659052\pi\)
−0.479142 + 0.877737i \(0.659052\pi\)
\(150\) 3.80513 0.310688
\(151\) 5.06610 0.412273 0.206137 0.978523i \(-0.433911\pi\)
0.206137 + 0.978523i \(0.433911\pi\)
\(152\) 53.8222 4.36556
\(153\) 9.33074 0.754345
\(154\) 34.3004 2.76401
\(155\) 2.88248 0.231526
\(156\) 4.72422 0.378240
\(157\) 4.41311 0.352205 0.176102 0.984372i \(-0.443651\pi\)
0.176102 + 0.984372i \(0.443651\pi\)
\(158\) −25.4413 −2.02400
\(159\) 4.59606 0.364491
\(160\) 17.4197 1.37715
\(161\) −20.2189 −1.59347
\(162\) −21.2258 −1.66766
\(163\) −6.15144 −0.481818 −0.240909 0.970548i \(-0.577446\pi\)
−0.240909 + 0.970548i \(0.577446\pi\)
\(164\) −13.4246 −1.04829
\(165\) 1.38660 0.107946
\(166\) 5.13174 0.398300
\(167\) −2.18316 −0.168938 −0.0844690 0.996426i \(-0.526919\pi\)
−0.0844690 + 0.996426i \(0.526919\pi\)
\(168\) −10.0100 −0.772285
\(169\) −6.49099 −0.499307
\(170\) −8.72980 −0.669545
\(171\) 17.7714 1.35901
\(172\) −38.2781 −2.91868
\(173\) −7.39065 −0.561901 −0.280950 0.959722i \(-0.590650\pi\)
−0.280950 + 0.959722i \(0.590650\pi\)
\(174\) −2.64511 −0.200525
\(175\) −13.0056 −0.983129
\(176\) −50.7856 −3.82811
\(177\) −2.62589 −0.197374
\(178\) −49.3655 −3.70010
\(179\) −4.52767 −0.338414 −0.169207 0.985581i \(-0.554121\pi\)
−0.169207 + 0.985581i \(0.554121\pi\)
\(180\) 15.0536 1.12203
\(181\) 2.35496 0.175043 0.0875216 0.996163i \(-0.472105\pi\)
0.0875216 + 0.996163i \(0.472105\pi\)
\(182\) −22.3138 −1.65401
\(183\) 0.563169 0.0416307
\(184\) 54.1482 3.99186
\(185\) −7.41109 −0.544874
\(186\) 2.74221 0.201069
\(187\) 12.7282 0.930779
\(188\) −0.187409 −0.0136682
\(189\) −6.75407 −0.491286
\(190\) −16.6268 −1.20624
\(191\) −15.2688 −1.10481 −0.552406 0.833575i \(-0.686290\pi\)
−0.552406 + 0.833575i \(0.686290\pi\)
\(192\) 7.41403 0.535062
\(193\) 6.24930 0.449835 0.224917 0.974378i \(-0.427789\pi\)
0.224917 + 0.974378i \(0.427789\pi\)
\(194\) −10.7286 −0.770266
\(195\) −0.902035 −0.0645961
\(196\) 18.6969 1.33549
\(197\) −7.42210 −0.528803 −0.264401 0.964413i \(-0.585174\pi\)
−0.264401 + 0.964413i \(0.585174\pi\)
\(198\) −30.3310 −2.15553
\(199\) −8.90657 −0.631370 −0.315685 0.948864i \(-0.602234\pi\)
−0.315685 + 0.948864i \(0.602234\pi\)
\(200\) 34.8303 2.46287
\(201\) −2.04988 −0.144588
\(202\) −24.4019 −1.71691
\(203\) 9.04073 0.634535
\(204\) −6.00974 −0.420766
\(205\) 2.56327 0.179027
\(206\) −26.3700 −1.83728
\(207\) 17.8790 1.24268
\(208\) 33.0380 2.29077
\(209\) 24.2423 1.67687
\(210\) 3.09230 0.213389
\(211\) −0.682757 −0.0470029 −0.0235015 0.999724i \(-0.507481\pi\)
−0.0235015 + 0.999724i \(0.507481\pi\)
\(212\) 68.0657 4.67477
\(213\) −0.287976 −0.0197318
\(214\) −38.3245 −2.61981
\(215\) 7.30876 0.498453
\(216\) 18.0881 1.23074
\(217\) −9.37261 −0.636254
\(218\) −27.7236 −1.87768
\(219\) 4.63928 0.313494
\(220\) 20.5349 1.38446
\(221\) −8.28020 −0.556987
\(222\) −7.05044 −0.473195
\(223\) −19.2400 −1.28841 −0.644204 0.764854i \(-0.722811\pi\)
−0.644204 + 0.764854i \(0.722811\pi\)
\(224\) −56.6417 −3.78453
\(225\) 11.5005 0.766701
\(226\) −32.6102 −2.16920
\(227\) 22.9038 1.52018 0.760088 0.649820i \(-0.225156\pi\)
0.760088 + 0.649820i \(0.225156\pi\)
\(228\) −11.4462 −0.758044
\(229\) 1.05414 0.0696598 0.0348299 0.999393i \(-0.488911\pi\)
0.0348299 + 0.999393i \(0.488911\pi\)
\(230\) −16.7276 −1.10298
\(231\) −4.50863 −0.296646
\(232\) −24.2120 −1.58960
\(233\) −15.9142 −1.04258 −0.521288 0.853381i \(-0.674548\pi\)
−0.521288 + 0.853381i \(0.674548\pi\)
\(234\) 19.7315 1.28989
\(235\) 0.0357836 0.00233427
\(236\) −38.8882 −2.53141
\(237\) 3.34413 0.217225
\(238\) 28.3856 1.83997
\(239\) 4.44642 0.287615 0.143808 0.989606i \(-0.454065\pi\)
0.143808 + 0.989606i \(0.454065\pi\)
\(240\) −4.57849 −0.295540
\(241\) 4.66671 0.300609 0.150304 0.988640i \(-0.451975\pi\)
0.150304 + 0.988640i \(0.451975\pi\)
\(242\) −11.7838 −0.757494
\(243\) 9.02224 0.578777
\(244\) 8.34029 0.533933
\(245\) −3.56996 −0.228076
\(246\) 2.43854 0.155475
\(247\) −15.7705 −1.00346
\(248\) 25.1008 1.59390
\(249\) −0.674542 −0.0427474
\(250\) −24.2089 −1.53110
\(251\) 18.6306 1.17595 0.587976 0.808879i \(-0.299925\pi\)
0.587976 + 0.808879i \(0.299925\pi\)
\(252\) −48.9480 −3.08343
\(253\) 24.3891 1.53333
\(254\) 21.6764 1.36010
\(255\) 1.14749 0.0718587
\(256\) 16.0659 1.00412
\(257\) 5.18730 0.323575 0.161787 0.986826i \(-0.448274\pi\)
0.161787 + 0.986826i \(0.448274\pi\)
\(258\) 6.95309 0.432881
\(259\) 24.0977 1.49736
\(260\) −13.3587 −0.828474
\(261\) −7.99449 −0.494847
\(262\) 21.7777 1.34543
\(263\) 0.929089 0.0572901 0.0286450 0.999590i \(-0.490881\pi\)
0.0286450 + 0.999590i \(0.490881\pi\)
\(264\) 12.0746 0.743138
\(265\) −12.9964 −0.798360
\(266\) 54.0635 3.31485
\(267\) 6.48886 0.397112
\(268\) −30.3579 −1.85440
\(269\) 7.96326 0.485528 0.242764 0.970085i \(-0.421946\pi\)
0.242764 + 0.970085i \(0.421946\pi\)
\(270\) −5.58781 −0.340063
\(271\) 1.94501 0.118151 0.0590754 0.998254i \(-0.481185\pi\)
0.0590754 + 0.998254i \(0.481185\pi\)
\(272\) −42.0281 −2.54833
\(273\) 2.93304 0.177515
\(274\) −59.6404 −3.60301
\(275\) 15.6880 0.946025
\(276\) −11.5155 −0.693154
\(277\) 12.0364 0.723195 0.361597 0.932334i \(-0.382232\pi\)
0.361597 + 0.932334i \(0.382232\pi\)
\(278\) −15.3829 −0.922606
\(279\) 8.28797 0.496188
\(280\) 28.3053 1.69157
\(281\) −10.4581 −0.623878 −0.311939 0.950102i \(-0.600979\pi\)
−0.311939 + 0.950102i \(0.600979\pi\)
\(282\) 0.0340423 0.00202719
\(283\) −1.06203 −0.0631310 −0.0315655 0.999502i \(-0.510049\pi\)
−0.0315655 + 0.999502i \(0.510049\pi\)
\(284\) −4.26481 −0.253070
\(285\) 2.18552 0.129459
\(286\) 26.9161 1.59158
\(287\) −8.33468 −0.491981
\(288\) 50.0868 2.95139
\(289\) −6.46664 −0.380391
\(290\) 7.47961 0.439218
\(291\) 1.41022 0.0826685
\(292\) 68.7058 4.02070
\(293\) 8.35925 0.488352 0.244176 0.969731i \(-0.421482\pi\)
0.244176 + 0.969731i \(0.421482\pi\)
\(294\) −3.39624 −0.198073
\(295\) 7.42525 0.432315
\(296\) −64.5362 −3.75109
\(297\) 8.14713 0.472744
\(298\) 31.4672 1.82284
\(299\) −15.8661 −0.917558
\(300\) −7.40725 −0.427658
\(301\) −23.7650 −1.36979
\(302\) −13.6284 −0.784224
\(303\) 3.20751 0.184267
\(304\) −80.0471 −4.59101
\(305\) −1.59248 −0.0911853
\(306\) −25.1007 −1.43491
\(307\) −22.3856 −1.27762 −0.638808 0.769366i \(-0.720572\pi\)
−0.638808 + 0.769366i \(0.720572\pi\)
\(308\) −66.7708 −3.80462
\(309\) 3.46621 0.197186
\(310\) −7.75419 −0.440408
\(311\) −15.4306 −0.874989 −0.437494 0.899221i \(-0.644134\pi\)
−0.437494 + 0.899221i \(0.644134\pi\)
\(312\) −7.85498 −0.444700
\(313\) −12.7769 −0.722195 −0.361097 0.932528i \(-0.617598\pi\)
−0.361097 + 0.932528i \(0.617598\pi\)
\(314\) −11.8718 −0.669962
\(315\) 9.34605 0.526591
\(316\) 49.5252 2.78601
\(317\) −6.96753 −0.391336 −0.195668 0.980670i \(-0.562687\pi\)
−0.195668 + 0.980670i \(0.562687\pi\)
\(318\) −12.3639 −0.693334
\(319\) −10.9054 −0.610586
\(320\) −20.9648 −1.17197
\(321\) 5.03758 0.281170
\(322\) 54.3910 3.03109
\(323\) 20.0619 1.11627
\(324\) 41.3192 2.29551
\(325\) −10.2057 −0.566110
\(326\) 16.5481 0.916513
\(327\) 3.64414 0.201521
\(328\) 22.3211 1.23248
\(329\) −0.116353 −0.00641477
\(330\) −3.73010 −0.205335
\(331\) 35.3489 1.94295 0.971476 0.237139i \(-0.0762098\pi\)
0.971476 + 0.237139i \(0.0762098\pi\)
\(332\) −9.98968 −0.548255
\(333\) −21.3090 −1.16773
\(334\) 5.87294 0.321353
\(335\) 5.79649 0.316696
\(336\) 14.8873 0.812170
\(337\) −3.83616 −0.208969 −0.104484 0.994527i \(-0.533319\pi\)
−0.104484 + 0.994527i \(0.533319\pi\)
\(338\) 17.4615 0.949779
\(339\) 4.28646 0.232808
\(340\) 16.9938 0.921620
\(341\) 11.3058 0.612241
\(342\) −47.8070 −2.58511
\(343\) −11.1505 −0.602068
\(344\) 63.6451 3.43151
\(345\) 2.19876 0.118377
\(346\) 19.8817 1.06884
\(347\) −21.8511 −1.17303 −0.586515 0.809938i \(-0.699500\pi\)
−0.586515 + 0.809938i \(0.699500\pi\)
\(348\) 5.14909 0.276020
\(349\) 6.87369 0.367940 0.183970 0.982932i \(-0.441105\pi\)
0.183970 + 0.982932i \(0.441105\pi\)
\(350\) 34.9864 1.87010
\(351\) −5.30002 −0.282894
\(352\) 68.3243 3.64170
\(353\) −22.6485 −1.20546 −0.602728 0.797946i \(-0.705920\pi\)
−0.602728 + 0.797946i \(0.705920\pi\)
\(354\) 7.06392 0.375443
\(355\) 0.814315 0.0432194
\(356\) 96.0972 5.09314
\(357\) −3.73116 −0.197474
\(358\) 12.1799 0.643729
\(359\) −12.9264 −0.682228 −0.341114 0.940022i \(-0.610804\pi\)
−0.341114 + 0.940022i \(0.610804\pi\)
\(360\) −25.0297 −1.31918
\(361\) 19.2101 1.01106
\(362\) −6.33512 −0.332966
\(363\) 1.54893 0.0812977
\(364\) 43.4370 2.27672
\(365\) −13.1186 −0.686658
\(366\) −1.51499 −0.0791897
\(367\) −2.24222 −0.117043 −0.0585215 0.998286i \(-0.518639\pi\)
−0.0585215 + 0.998286i \(0.518639\pi\)
\(368\) −80.5319 −4.19802
\(369\) 7.37015 0.383675
\(370\) 19.9366 1.03646
\(371\) 42.2587 2.19396
\(372\) −5.33812 −0.276768
\(373\) −35.5116 −1.83872 −0.919361 0.393414i \(-0.871294\pi\)
−0.919361 + 0.393414i \(0.871294\pi\)
\(374\) −34.2403 −1.77052
\(375\) 3.18214 0.164325
\(376\) 0.311606 0.0160699
\(377\) 7.09440 0.365380
\(378\) 18.1692 0.934522
\(379\) −11.5009 −0.590762 −0.295381 0.955380i \(-0.595447\pi\)
−0.295381 + 0.955380i \(0.595447\pi\)
\(380\) 32.3666 1.66037
\(381\) −2.84926 −0.145972
\(382\) 41.0748 2.10157
\(383\) 19.5259 0.997729 0.498864 0.866680i \(-0.333751\pi\)
0.498864 + 0.866680i \(0.333751\pi\)
\(384\) −7.62385 −0.389053
\(385\) 12.7491 0.649755
\(386\) −16.8113 −0.855674
\(387\) 21.0148 1.06824
\(388\) 20.8847 1.06026
\(389\) 13.3406 0.676395 0.338198 0.941075i \(-0.390183\pi\)
0.338198 + 0.941075i \(0.390183\pi\)
\(390\) 2.42657 0.122874
\(391\) 20.1834 1.02072
\(392\) −31.0874 −1.57015
\(393\) −2.86257 −0.144398
\(394\) 19.9663 1.00589
\(395\) −9.45626 −0.475796
\(396\) 59.0438 2.96706
\(397\) −36.1041 −1.81202 −0.906008 0.423262i \(-0.860885\pi\)
−0.906008 + 0.423262i \(0.860885\pi\)
\(398\) 23.9597 1.20099
\(399\) −7.10639 −0.355765
\(400\) −51.8013 −2.59007
\(401\) 20.3990 1.01868 0.509340 0.860566i \(-0.329890\pi\)
0.509340 + 0.860566i \(0.329890\pi\)
\(402\) 5.51442 0.275034
\(403\) −7.35484 −0.366370
\(404\) 47.5018 2.36330
\(405\) −7.88943 −0.392029
\(406\) −24.3206 −1.20701
\(407\) −29.0680 −1.44085
\(408\) 9.99242 0.494699
\(409\) 25.8625 1.27882 0.639409 0.768867i \(-0.279179\pi\)
0.639409 + 0.768867i \(0.279179\pi\)
\(410\) −6.89548 −0.340544
\(411\) 7.83945 0.386692
\(412\) 51.3331 2.52900
\(413\) −24.1438 −1.18804
\(414\) −48.0966 −2.36382
\(415\) 1.90741 0.0936313
\(416\) −44.4476 −2.17922
\(417\) 2.02201 0.0990184
\(418\) −65.2144 −3.18974
\(419\) −2.01758 −0.0985652 −0.0492826 0.998785i \(-0.515693\pi\)
−0.0492826 + 0.998785i \(0.515693\pi\)
\(420\) −6.01961 −0.293727
\(421\) 20.4455 0.996454 0.498227 0.867047i \(-0.333985\pi\)
0.498227 + 0.867047i \(0.333985\pi\)
\(422\) 1.83669 0.0894088
\(423\) 0.102888 0.00500260
\(424\) −113.173 −5.49617
\(425\) 12.9828 0.629758
\(426\) 0.774689 0.0375338
\(427\) 5.17808 0.250585
\(428\) 74.6043 3.60614
\(429\) −3.53799 −0.170816
\(430\) −19.6614 −0.948155
\(431\) 26.3069 1.26716 0.633580 0.773677i \(-0.281585\pi\)
0.633580 + 0.773677i \(0.281585\pi\)
\(432\) −26.9015 −1.29430
\(433\) −4.77867 −0.229648 −0.114824 0.993386i \(-0.536630\pi\)
−0.114824 + 0.993386i \(0.536630\pi\)
\(434\) 25.2134 1.21028
\(435\) −0.983160 −0.0471389
\(436\) 53.9681 2.58460
\(437\) 38.4415 1.83891
\(438\) −12.4802 −0.596327
\(439\) 36.1670 1.72616 0.863078 0.505071i \(-0.168534\pi\)
0.863078 + 0.505071i \(0.168534\pi\)
\(440\) −34.1434 −1.62772
\(441\) −10.2647 −0.488794
\(442\) 22.2747 1.05950
\(443\) −11.3463 −0.539080 −0.269540 0.962989i \(-0.586872\pi\)
−0.269540 + 0.962989i \(0.586872\pi\)
\(444\) 13.7247 0.651347
\(445\) −18.3486 −0.869809
\(446\) 51.7578 2.45080
\(447\) −4.13621 −0.195636
\(448\) 68.1686 3.22066
\(449\) 40.6597 1.91885 0.959425 0.281965i \(-0.0909862\pi\)
0.959425 + 0.281965i \(0.0909862\pi\)
\(450\) −30.9377 −1.45842
\(451\) 10.0538 0.473413
\(452\) 63.4806 2.98587
\(453\) 1.79138 0.0841665
\(454\) −61.6137 −2.89167
\(455\) −8.29379 −0.388819
\(456\) 19.0316 0.891239
\(457\) 36.6821 1.71592 0.857958 0.513720i \(-0.171733\pi\)
0.857958 + 0.513720i \(0.171733\pi\)
\(458\) −2.83576 −0.132507
\(459\) 6.74223 0.314701
\(460\) 32.5626 1.51824
\(461\) 14.3424 0.667990 0.333995 0.942575i \(-0.391603\pi\)
0.333995 + 0.942575i \(0.391603\pi\)
\(462\) 12.1287 0.564278
\(463\) 20.5777 0.956326 0.478163 0.878271i \(-0.341303\pi\)
0.478163 + 0.878271i \(0.341303\pi\)
\(464\) 36.0093 1.67169
\(465\) 1.01925 0.0472666
\(466\) 42.8110 1.98318
\(467\) 10.8678 0.502902 0.251451 0.967870i \(-0.419092\pi\)
0.251451 + 0.967870i \(0.419092\pi\)
\(468\) −38.4103 −1.77552
\(469\) −18.8477 −0.870308
\(470\) −0.0962619 −0.00444023
\(471\) 1.56049 0.0719035
\(472\) 64.6596 2.97620
\(473\) 28.6667 1.31809
\(474\) −8.99609 −0.413204
\(475\) 24.7271 1.13456
\(476\) −55.2568 −2.53269
\(477\) −37.3683 −1.71098
\(478\) −11.9614 −0.547100
\(479\) 14.5044 0.662723 0.331362 0.943504i \(-0.392492\pi\)
0.331362 + 0.943504i \(0.392492\pi\)
\(480\) 6.15966 0.281149
\(481\) 18.9099 0.862216
\(482\) −12.5540 −0.571817
\(483\) −7.14943 −0.325310
\(484\) 22.9390 1.04268
\(485\) −3.98770 −0.181072
\(486\) −24.2708 −1.10095
\(487\) −22.3017 −1.01059 −0.505294 0.862947i \(-0.668616\pi\)
−0.505294 + 0.862947i \(0.668616\pi\)
\(488\) −13.8674 −0.627749
\(489\) −2.17516 −0.0983644
\(490\) 9.60359 0.433846
\(491\) 7.30407 0.329628 0.164814 0.986325i \(-0.447298\pi\)
0.164814 + 0.986325i \(0.447298\pi\)
\(492\) −4.74697 −0.214010
\(493\) −9.02489 −0.406460
\(494\) 42.4245 1.90877
\(495\) −11.2737 −0.506716
\(496\) −37.3312 −1.67622
\(497\) −2.64781 −0.118771
\(498\) 1.81459 0.0813139
\(499\) 28.9663 1.29671 0.648355 0.761338i \(-0.275457\pi\)
0.648355 + 0.761338i \(0.275457\pi\)
\(500\) 47.1261 2.10754
\(501\) −0.771971 −0.0344891
\(502\) −50.1183 −2.23689
\(503\) 17.6833 0.788459 0.394230 0.919012i \(-0.371011\pi\)
0.394230 + 0.919012i \(0.371011\pi\)
\(504\) 81.3860 3.62522
\(505\) −9.06992 −0.403606
\(506\) −65.6094 −2.91669
\(507\) −2.29523 −0.101935
\(508\) −42.1963 −1.87216
\(509\) −22.5151 −0.997966 −0.498983 0.866612i \(-0.666293\pi\)
−0.498983 + 0.866612i \(0.666293\pi\)
\(510\) −3.08688 −0.136689
\(511\) 42.6561 1.88699
\(512\) −0.0980122 −0.00433157
\(513\) 12.8413 0.566958
\(514\) −13.9544 −0.615502
\(515\) −9.80145 −0.431904
\(516\) −13.5352 −0.595855
\(517\) 0.140352 0.00617267
\(518\) −64.8256 −2.84827
\(519\) −2.61335 −0.114713
\(520\) 22.2116 0.974044
\(521\) 29.1819 1.27848 0.639240 0.769007i \(-0.279249\pi\)
0.639240 + 0.769007i \(0.279249\pi\)
\(522\) 21.5061 0.941295
\(523\) −23.3445 −1.02078 −0.510392 0.859942i \(-0.670500\pi\)
−0.510392 + 0.859942i \(0.670500\pi\)
\(524\) −42.3935 −1.85197
\(525\) −4.59880 −0.200708
\(526\) −2.49935 −0.108977
\(527\) 9.35619 0.407562
\(528\) −17.9579 −0.781518
\(529\) 15.6744 0.681494
\(530\) 34.9616 1.51864
\(531\) 21.3498 0.926501
\(532\) −105.243 −4.56284
\(533\) −6.54036 −0.283294
\(534\) −17.4558 −0.755384
\(535\) −14.2448 −0.615858
\(536\) 50.4762 2.18024
\(537\) −1.60099 −0.0690879
\(538\) −21.4220 −0.923570
\(539\) −14.0022 −0.603118
\(540\) 10.8775 0.468092
\(541\) −9.84022 −0.423064 −0.211532 0.977371i \(-0.567845\pi\)
−0.211532 + 0.977371i \(0.567845\pi\)
\(542\) −5.23229 −0.224746
\(543\) 0.832721 0.0357355
\(544\) 56.5424 2.42424
\(545\) −10.3046 −0.441400
\(546\) −7.89020 −0.337669
\(547\) 12.5086 0.534828 0.267414 0.963582i \(-0.413831\pi\)
0.267414 + 0.963582i \(0.413831\pi\)
\(548\) 116.099 4.95950
\(549\) −4.57885 −0.195421
\(550\) −42.2026 −1.79952
\(551\) −17.1889 −0.732271
\(552\) 19.1469 0.814947
\(553\) 30.7478 1.30753
\(554\) −32.3791 −1.37566
\(555\) −2.62058 −0.111237
\(556\) 29.9451 1.26996
\(557\) −13.1604 −0.557625 −0.278813 0.960346i \(-0.589941\pi\)
−0.278813 + 0.960346i \(0.589941\pi\)
\(558\) −22.2956 −0.943846
\(559\) −18.6488 −0.788759
\(560\) −42.0971 −1.77893
\(561\) 4.50073 0.190021
\(562\) 28.1335 1.18674
\(563\) 10.4178 0.439059 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(564\) −0.0662684 −0.00279040
\(565\) −12.1209 −0.509929
\(566\) 2.85697 0.120087
\(567\) 25.6531 1.07733
\(568\) 7.09111 0.297536
\(569\) 33.3673 1.39883 0.699415 0.714716i \(-0.253444\pi\)
0.699415 + 0.714716i \(0.253444\pi\)
\(570\) −5.87929 −0.246256
\(571\) 4.00863 0.167756 0.0838779 0.996476i \(-0.473269\pi\)
0.0838779 + 0.996476i \(0.473269\pi\)
\(572\) −52.3961 −2.19079
\(573\) −5.39909 −0.225550
\(574\) 22.4212 0.935843
\(575\) 24.8769 1.03744
\(576\) −60.2798 −2.51166
\(577\) −12.4877 −0.519868 −0.259934 0.965626i \(-0.583701\pi\)
−0.259934 + 0.965626i \(0.583701\pi\)
\(578\) 17.3960 0.723578
\(579\) 2.20977 0.0918348
\(580\) −14.5602 −0.604578
\(581\) −6.20211 −0.257307
\(582\) −3.79364 −0.157252
\(583\) −50.9747 −2.11116
\(584\) −114.237 −4.72718
\(585\) 7.33400 0.303224
\(586\) −22.4873 −0.928942
\(587\) −36.3147 −1.49887 −0.749434 0.662079i \(-0.769674\pi\)
−0.749434 + 0.662079i \(0.769674\pi\)
\(588\) 6.61127 0.272644
\(589\) 17.8199 0.734255
\(590\) −19.9748 −0.822348
\(591\) −2.62447 −0.107956
\(592\) 95.9815 3.94482
\(593\) −21.4713 −0.881719 −0.440859 0.897576i \(-0.645326\pi\)
−0.440859 + 0.897576i \(0.645326\pi\)
\(594\) −21.9167 −0.899252
\(595\) 10.5506 0.432534
\(596\) −61.2555 −2.50912
\(597\) −3.14938 −0.128896
\(598\) 42.6815 1.74537
\(599\) 41.4723 1.69451 0.847255 0.531186i \(-0.178253\pi\)
0.847255 + 0.531186i \(0.178253\pi\)
\(600\) 12.3161 0.502801
\(601\) −21.7104 −0.885586 −0.442793 0.896624i \(-0.646012\pi\)
−0.442793 + 0.896624i \(0.646012\pi\)
\(602\) 63.9305 2.60561
\(603\) 16.6666 0.678716
\(604\) 26.5296 1.07947
\(605\) −4.37993 −0.178070
\(606\) −8.62856 −0.350511
\(607\) −16.2310 −0.658795 −0.329397 0.944191i \(-0.606846\pi\)
−0.329397 + 0.944191i \(0.606846\pi\)
\(608\) 107.691 4.36745
\(609\) 3.19682 0.129542
\(610\) 4.28395 0.173452
\(611\) −0.0913043 −0.00369378
\(612\) 48.8622 1.97514
\(613\) −9.52547 −0.384730 −0.192365 0.981323i \(-0.561616\pi\)
−0.192365 + 0.981323i \(0.561616\pi\)
\(614\) 60.2199 2.43028
\(615\) 0.906379 0.0365487
\(616\) 111.020 4.47313
\(617\) −22.0116 −0.886154 −0.443077 0.896484i \(-0.646113\pi\)
−0.443077 + 0.896484i \(0.646113\pi\)
\(618\) −9.32449 −0.375086
\(619\) 2.39082 0.0960952 0.0480476 0.998845i \(-0.484700\pi\)
0.0480476 + 0.998845i \(0.484700\pi\)
\(620\) 15.0947 0.606217
\(621\) 12.9191 0.518425
\(622\) 41.5100 1.66440
\(623\) 59.6621 2.39031
\(624\) 11.6823 0.467667
\(625\) 11.0030 0.440118
\(626\) 34.3714 1.37376
\(627\) 8.57212 0.342338
\(628\) 23.1101 0.922195
\(629\) −24.0555 −0.959156
\(630\) −25.1419 −1.00168
\(631\) −7.37154 −0.293456 −0.146728 0.989177i \(-0.546874\pi\)
−0.146728 + 0.989177i \(0.546874\pi\)
\(632\) −82.3457 −3.27554
\(633\) −0.241425 −0.00959576
\(634\) 18.7434 0.744397
\(635\) 8.05689 0.319728
\(636\) 24.0682 0.954366
\(637\) 9.10899 0.360911
\(638\) 29.3368 1.16145
\(639\) 2.34139 0.0926241
\(640\) 21.5581 0.852158
\(641\) 14.4403 0.570358 0.285179 0.958474i \(-0.407947\pi\)
0.285179 + 0.958474i \(0.407947\pi\)
\(642\) −13.5516 −0.534841
\(643\) −33.7128 −1.32950 −0.664751 0.747065i \(-0.731462\pi\)
−0.664751 + 0.747065i \(0.731462\pi\)
\(644\) −105.880 −4.17226
\(645\) 2.58439 0.101760
\(646\) −53.9688 −2.12337
\(647\) 2.48216 0.0975839 0.0487920 0.998809i \(-0.484463\pi\)
0.0487920 + 0.998809i \(0.484463\pi\)
\(648\) −68.7016 −2.69885
\(649\) 29.1236 1.14320
\(650\) 27.4544 1.07685
\(651\) −3.31418 −0.129893
\(652\) −32.2133 −1.26157
\(653\) 16.5022 0.645782 0.322891 0.946436i \(-0.395345\pi\)
0.322891 + 0.946436i \(0.395345\pi\)
\(654\) −9.80314 −0.383333
\(655\) 8.09454 0.316280
\(656\) −33.1971 −1.29613
\(657\) −37.7197 −1.47159
\(658\) 0.313003 0.0122021
\(659\) −46.8300 −1.82424 −0.912119 0.409925i \(-0.865555\pi\)
−0.912119 + 0.409925i \(0.865555\pi\)
\(660\) 7.26118 0.282641
\(661\) 27.1955 1.05778 0.528891 0.848689i \(-0.322608\pi\)
0.528891 + 0.848689i \(0.322608\pi\)
\(662\) −95.0925 −3.69587
\(663\) −2.92790 −0.113710
\(664\) 16.6099 0.644588
\(665\) 20.0948 0.779245
\(666\) 57.3237 2.22125
\(667\) −17.2930 −0.669587
\(668\) −11.4326 −0.442339
\(669\) −6.80332 −0.263031
\(670\) −15.5932 −0.602418
\(671\) −6.24609 −0.241128
\(672\) −20.0286 −0.772621
\(673\) −16.8344 −0.648917 −0.324458 0.945900i \(-0.605182\pi\)
−0.324458 + 0.945900i \(0.605182\pi\)
\(674\) 10.3197 0.397500
\(675\) 8.31008 0.319855
\(676\) −33.9913 −1.30736
\(677\) 41.9534 1.61240 0.806201 0.591642i \(-0.201520\pi\)
0.806201 + 0.591642i \(0.201520\pi\)
\(678\) −11.5310 −0.442847
\(679\) 12.9663 0.497601
\(680\) −28.2557 −1.08356
\(681\) 8.09883 0.310348
\(682\) −30.4137 −1.16460
\(683\) 29.2647 1.11978 0.559892 0.828566i \(-0.310843\pi\)
0.559892 + 0.828566i \(0.310843\pi\)
\(684\) 93.0634 3.55837
\(685\) −22.1677 −0.846985
\(686\) 29.9960 1.14525
\(687\) 0.372748 0.0142212
\(688\) −94.6562 −3.60873
\(689\) 33.1611 1.26334
\(690\) −5.91490 −0.225176
\(691\) 24.0618 0.915354 0.457677 0.889119i \(-0.348682\pi\)
0.457677 + 0.889119i \(0.348682\pi\)
\(692\) −38.7026 −1.47125
\(693\) 36.6574 1.39250
\(694\) 58.7819 2.23133
\(695\) −5.71767 −0.216884
\(696\) −8.56142 −0.324520
\(697\) 8.32008 0.315145
\(698\) −18.4910 −0.699894
\(699\) −5.62731 −0.212844
\(700\) −68.1063 −2.57417
\(701\) −45.2373 −1.70859 −0.854294 0.519790i \(-0.826010\pi\)
−0.854294 + 0.519790i \(0.826010\pi\)
\(702\) 14.2577 0.538121
\(703\) −45.8163 −1.72800
\(704\) −82.2287 −3.09911
\(705\) 0.0126532 0.000476546 0
\(706\) 60.9269 2.29301
\(707\) 29.4916 1.10914
\(708\) −13.7510 −0.516793
\(709\) −34.1604 −1.28292 −0.641461 0.767156i \(-0.721671\pi\)
−0.641461 + 0.767156i \(0.721671\pi\)
\(710\) −2.19060 −0.0822117
\(711\) −27.1895 −1.01969
\(712\) −159.781 −5.98805
\(713\) 17.9278 0.671401
\(714\) 10.0372 0.375634
\(715\) 10.0044 0.374145
\(716\) −23.7100 −0.886085
\(717\) 1.57227 0.0587173
\(718\) 34.7734 1.29773
\(719\) −41.1197 −1.53350 −0.766752 0.641943i \(-0.778129\pi\)
−0.766752 + 0.641943i \(0.778129\pi\)
\(720\) 37.2254 1.38731
\(721\) 31.8702 1.18691
\(722\) −51.6773 −1.92323
\(723\) 1.65016 0.0613700
\(724\) 12.3322 0.458324
\(725\) −11.1235 −0.413118
\(726\) −4.16679 −0.154644
\(727\) 27.0131 1.00186 0.500931 0.865487i \(-0.332991\pi\)
0.500931 + 0.865487i \(0.332991\pi\)
\(728\) −72.2229 −2.67676
\(729\) −20.4807 −0.758544
\(730\) 35.2904 1.30616
\(731\) 23.7234 0.877440
\(732\) 2.94915 0.109004
\(733\) −42.6350 −1.57476 −0.787380 0.616468i \(-0.788563\pi\)
−0.787380 + 0.616468i \(0.788563\pi\)
\(734\) 6.03182 0.222639
\(735\) −1.26235 −0.0465623
\(736\) 108.343 3.99359
\(737\) 22.7352 0.837461
\(738\) −19.8265 −0.729825
\(739\) −2.49327 −0.0917163 −0.0458582 0.998948i \(-0.514602\pi\)
−0.0458582 + 0.998948i \(0.514602\pi\)
\(740\) −38.8096 −1.42667
\(741\) −5.57650 −0.204858
\(742\) −113.681 −4.17334
\(743\) 1.90224 0.0697865 0.0348932 0.999391i \(-0.488891\pi\)
0.0348932 + 0.999391i \(0.488891\pi\)
\(744\) 8.87570 0.325399
\(745\) 11.6960 0.428509
\(746\) 95.5302 3.49761
\(747\) 5.48437 0.200663
\(748\) 66.6538 2.43711
\(749\) 46.3182 1.69243
\(750\) −8.56031 −0.312578
\(751\) −26.0973 −0.952303 −0.476152 0.879363i \(-0.657969\pi\)
−0.476152 + 0.879363i \(0.657969\pi\)
\(752\) −0.463436 −0.0168998
\(753\) 6.58782 0.240073
\(754\) −19.0847 −0.695025
\(755\) −5.06552 −0.184353
\(756\) −35.3690 −1.28636
\(757\) 18.2526 0.663403 0.331701 0.943384i \(-0.392377\pi\)
0.331701 + 0.943384i \(0.392377\pi\)
\(758\) 30.9387 1.12374
\(759\) 8.62404 0.313033
\(760\) −53.8161 −1.95211
\(761\) −33.4256 −1.21168 −0.605838 0.795588i \(-0.707162\pi\)
−0.605838 + 0.795588i \(0.707162\pi\)
\(762\) 7.66482 0.277667
\(763\) 33.5062 1.21300
\(764\) −79.9582 −2.89278
\(765\) −9.32968 −0.337315
\(766\) −52.5269 −1.89788
\(767\) −18.9460 −0.684101
\(768\) 5.68094 0.204993
\(769\) 15.3937 0.555112 0.277556 0.960709i \(-0.410476\pi\)
0.277556 + 0.960709i \(0.410476\pi\)
\(770\) −34.2965 −1.23596
\(771\) 1.83424 0.0660585
\(772\) 32.7257 1.17782
\(773\) 20.3970 0.733631 0.366815 0.930294i \(-0.380448\pi\)
0.366815 + 0.930294i \(0.380448\pi\)
\(774\) −56.5322 −2.03201
\(775\) 11.5319 0.414237
\(776\) −34.7251 −1.24656
\(777\) 8.52101 0.305690
\(778\) −35.8877 −1.28664
\(779\) 15.8465 0.567759
\(780\) −4.72368 −0.169135
\(781\) 3.19394 0.114288
\(782\) −54.2957 −1.94161
\(783\) −5.77669 −0.206442
\(784\) 46.2348 1.65124
\(785\) −4.41261 −0.157493
\(786\) 7.70064 0.274673
\(787\) 9.49213 0.338358 0.169179 0.985585i \(-0.445888\pi\)
0.169179 + 0.985585i \(0.445888\pi\)
\(788\) −38.8673 −1.38459
\(789\) 0.328528 0.0116959
\(790\) 25.4384 0.905057
\(791\) 39.4120 1.40133
\(792\) −98.1723 −3.48840
\(793\) 4.06332 0.144293
\(794\) 97.1242 3.44681
\(795\) −4.59554 −0.162987
\(796\) −46.6410 −1.65315
\(797\) 10.2928 0.364590 0.182295 0.983244i \(-0.441647\pi\)
0.182295 + 0.983244i \(0.441647\pi\)
\(798\) 19.1170 0.676734
\(799\) 0.116149 0.00410907
\(800\) 69.6908 2.46394
\(801\) −52.7577 −1.86410
\(802\) −54.8757 −1.93773
\(803\) −51.4541 −1.81578
\(804\) −10.7346 −0.378581
\(805\) 20.2166 0.712540
\(806\) 19.7853 0.696908
\(807\) 2.81583 0.0991218
\(808\) −78.9815 −2.77856
\(809\) −22.8025 −0.801693 −0.400847 0.916145i \(-0.631284\pi\)
−0.400847 + 0.916145i \(0.631284\pi\)
\(810\) 21.2234 0.745715
\(811\) 50.9046 1.78750 0.893751 0.448564i \(-0.148065\pi\)
0.893751 + 0.448564i \(0.148065\pi\)
\(812\) 47.3435 1.66143
\(813\) 0.687759 0.0241208
\(814\) 78.1962 2.74078
\(815\) 6.15075 0.215451
\(816\) −14.8612 −0.520247
\(817\) 45.1837 1.58078
\(818\) −69.5730 −2.43256
\(819\) −23.8471 −0.833284
\(820\) 13.4231 0.468754
\(821\) 48.5255 1.69355 0.846776 0.531949i \(-0.178540\pi\)
0.846776 + 0.531949i \(0.178540\pi\)
\(822\) −21.0890 −0.735563
\(823\) 37.8842 1.32056 0.660280 0.751020i \(-0.270438\pi\)
0.660280 + 0.751020i \(0.270438\pi\)
\(824\) −85.3517 −2.97337
\(825\) 5.54733 0.193133
\(826\) 64.9495 2.25988
\(827\) −0.662653 −0.0230427 −0.0115214 0.999934i \(-0.503667\pi\)
−0.0115214 + 0.999934i \(0.503667\pi\)
\(828\) 93.6271 3.25377
\(829\) 55.5636 1.92981 0.964903 0.262608i \(-0.0845826\pi\)
0.964903 + 0.262608i \(0.0845826\pi\)
\(830\) −5.13115 −0.178105
\(831\) 4.25608 0.147642
\(832\) 53.4930 1.85454
\(833\) −11.5877 −0.401489
\(834\) −5.43944 −0.188352
\(835\) 2.18291 0.0755428
\(836\) 126.949 4.39064
\(837\) 5.98875 0.207001
\(838\) 5.42751 0.187490
\(839\) 9.46898 0.326906 0.163453 0.986551i \(-0.447737\pi\)
0.163453 + 0.986551i \(0.447737\pi\)
\(840\) 10.0088 0.345337
\(841\) −21.2676 −0.733364
\(842\) −55.0008 −1.89545
\(843\) −3.69801 −0.127366
\(844\) −3.57539 −0.123070
\(845\) 6.49025 0.223271
\(846\) −0.276781 −0.00951593
\(847\) 14.2417 0.489350
\(848\) 168.317 5.78002
\(849\) −0.375535 −0.0128883
\(850\) −34.9251 −1.19792
\(851\) −46.0938 −1.58008
\(852\) −1.50805 −0.0516648
\(853\) 13.3248 0.456231 0.228116 0.973634i \(-0.426744\pi\)
0.228116 + 0.973634i \(0.426744\pi\)
\(854\) −13.9296 −0.476662
\(855\) −17.7694 −0.607700
\(856\) −124.045 −4.23977
\(857\) −23.0047 −0.785826 −0.392913 0.919576i \(-0.628533\pi\)
−0.392913 + 0.919576i \(0.628533\pi\)
\(858\) 9.51759 0.324925
\(859\) 40.7816 1.39145 0.695725 0.718309i \(-0.255083\pi\)
0.695725 + 0.718309i \(0.255083\pi\)
\(860\) 38.2737 1.30512
\(861\) −2.94716 −0.100439
\(862\) −70.7686 −2.41039
\(863\) −14.3339 −0.487933 −0.243966 0.969784i \(-0.578449\pi\)
−0.243966 + 0.969784i \(0.578449\pi\)
\(864\) 36.1919 1.23127
\(865\) 7.38981 0.251261
\(866\) 12.8551 0.436835
\(867\) −2.28662 −0.0776577
\(868\) −49.0815 −1.66594
\(869\) −37.0897 −1.25818
\(870\) 2.64481 0.0896674
\(871\) −14.7901 −0.501144
\(872\) −89.7330 −3.03874
\(873\) −11.4658 −0.388058
\(874\) −103.412 −3.49796
\(875\) 29.2583 0.989111
\(876\) 24.2945 0.820836
\(877\) −12.2334 −0.413094 −0.206547 0.978437i \(-0.566223\pi\)
−0.206547 + 0.978437i \(0.566223\pi\)
\(878\) −97.2932 −3.28349
\(879\) 2.95585 0.0996983
\(880\) 50.7798 1.71179
\(881\) −40.0849 −1.35049 −0.675247 0.737592i \(-0.735963\pi\)
−0.675247 + 0.737592i \(0.735963\pi\)
\(882\) 27.6131 0.929782
\(883\) 30.9326 1.04096 0.520482 0.853873i \(-0.325752\pi\)
0.520482 + 0.853873i \(0.325752\pi\)
\(884\) −43.3609 −1.45839
\(885\) 2.62559 0.0882581
\(886\) 30.5228 1.02543
\(887\) −56.7326 −1.90490 −0.952448 0.304702i \(-0.901443\pi\)
−0.952448 + 0.304702i \(0.901443\pi\)
\(888\) −22.8202 −0.765794
\(889\) −26.1976 −0.878639
\(890\) 49.3599 1.65455
\(891\) −30.9442 −1.03667
\(892\) −100.754 −3.37350
\(893\) 0.221219 0.00740282
\(894\) 11.1269 0.372138
\(895\) 4.52715 0.151326
\(896\) −70.0978 −2.34180
\(897\) −5.61027 −0.187322
\(898\) −109.379 −3.65003
\(899\) −8.01630 −0.267358
\(900\) 60.2247 2.00749
\(901\) −42.1846 −1.40537
\(902\) −27.0457 −0.900524
\(903\) −8.40336 −0.279646
\(904\) −105.549 −3.51052
\(905\) −2.35470 −0.0782728
\(906\) −4.81902 −0.160101
\(907\) −30.8420 −1.02409 −0.512047 0.858958i \(-0.671112\pi\)
−0.512047 + 0.858958i \(0.671112\pi\)
\(908\) 119.940 3.98035
\(909\) −26.0787 −0.864975
\(910\) 22.3112 0.739610
\(911\) −16.2193 −0.537370 −0.268685 0.963228i \(-0.586589\pi\)
−0.268685 + 0.963228i \(0.586589\pi\)
\(912\) −28.3048 −0.937267
\(913\) 7.48132 0.247596
\(914\) −98.6789 −3.26401
\(915\) −0.563105 −0.0186157
\(916\) 5.52023 0.182394
\(917\) −26.3200 −0.869164
\(918\) −18.1374 −0.598622
\(919\) −4.34727 −0.143403 −0.0717015 0.997426i \(-0.522843\pi\)
−0.0717015 + 0.997426i \(0.522843\pi\)
\(920\) −54.1420 −1.78501
\(921\) −7.91561 −0.260828
\(922\) −38.5825 −1.27065
\(923\) −2.07778 −0.0683909
\(924\) −23.6103 −0.776722
\(925\) −29.6494 −0.974866
\(926\) −55.3563 −1.81912
\(927\) −28.1820 −0.925620
\(928\) −48.4450 −1.59029
\(929\) −2.22372 −0.0729580 −0.0364790 0.999334i \(-0.511614\pi\)
−0.0364790 + 0.999334i \(0.511614\pi\)
\(930\) −2.74190 −0.0899104
\(931\) −22.0700 −0.723314
\(932\) −83.3380 −2.72983
\(933\) −5.45629 −0.178631
\(934\) −29.2356 −0.956618
\(935\) −12.7268 −0.416210
\(936\) 63.8649 2.08749
\(937\) −27.6279 −0.902564 −0.451282 0.892381i \(-0.649033\pi\)
−0.451282 + 0.892381i \(0.649033\pi\)
\(938\) 50.7025 1.65550
\(939\) −4.51795 −0.147438
\(940\) 0.187388 0.00611192
\(941\) 26.9990 0.880144 0.440072 0.897963i \(-0.354953\pi\)
0.440072 + 0.897963i \(0.354953\pi\)
\(942\) −4.19788 −0.136774
\(943\) 15.9425 0.519158
\(944\) −96.1650 −3.12990
\(945\) 6.75330 0.219685
\(946\) −77.1165 −2.50727
\(947\) 15.4751 0.502872 0.251436 0.967874i \(-0.419097\pi\)
0.251436 + 0.967874i \(0.419097\pi\)
\(948\) 17.5122 0.568770
\(949\) 33.4729 1.08658
\(950\) −66.5187 −2.15815
\(951\) −2.46374 −0.0798921
\(952\) 91.8757 2.97771
\(953\) 2.03284 0.0658501 0.0329250 0.999458i \(-0.489518\pi\)
0.0329250 + 0.999458i \(0.489518\pi\)
\(954\) 100.525 3.25461
\(955\) 15.2671 0.494031
\(956\) 23.2846 0.753077
\(957\) −3.85618 −0.124653
\(958\) −39.0185 −1.26063
\(959\) 72.0801 2.32759
\(960\) −7.41319 −0.239260
\(961\) −22.6894 −0.731917
\(962\) −50.8697 −1.64010
\(963\) −40.9581 −1.31985
\(964\) 24.4381 0.787099
\(965\) −6.24859 −0.201149
\(966\) 19.2328 0.618804
\(967\) −48.7916 −1.56903 −0.784516 0.620109i \(-0.787088\pi\)
−0.784516 + 0.620109i \(0.787088\pi\)
\(968\) −38.1407 −1.22589
\(969\) 7.09394 0.227890
\(970\) 10.7273 0.344434
\(971\) 39.4950 1.26746 0.633728 0.773556i \(-0.281524\pi\)
0.633728 + 0.773556i \(0.281524\pi\)
\(972\) 47.2467 1.51544
\(973\) 18.5915 0.596015
\(974\) 59.9941 1.92234
\(975\) −3.60875 −0.115573
\(976\) 20.6243 0.660169
\(977\) −22.4125 −0.717039 −0.358519 0.933522i \(-0.616718\pi\)
−0.358519 + 0.933522i \(0.616718\pi\)
\(978\) 5.85144 0.187108
\(979\) −71.9677 −2.30010
\(980\) −18.6948 −0.597183
\(981\) −29.6287 −0.945971
\(982\) −19.6488 −0.627017
\(983\) 37.5986 1.19921 0.599605 0.800296i \(-0.295324\pi\)
0.599605 + 0.800296i \(0.295324\pi\)
\(984\) 7.89280 0.251613
\(985\) 7.42126 0.236461
\(986\) 24.2779 0.773167
\(987\) −0.0411428 −0.00130959
\(988\) −82.5855 −2.62740
\(989\) 45.4574 1.44546
\(990\) 30.3276 0.963874
\(991\) −25.3130 −0.804094 −0.402047 0.915619i \(-0.631701\pi\)
−0.402047 + 0.915619i \(0.631701\pi\)
\(992\) 50.2234 1.59460
\(993\) 12.4995 0.396658
\(994\) 7.12290 0.225925
\(995\) 8.90556 0.282325
\(996\) −3.53237 −0.111928
\(997\) 40.1089 1.27026 0.635130 0.772405i \(-0.280946\pi\)
0.635130 + 0.772405i \(0.280946\pi\)
\(998\) −77.9226 −2.46660
\(999\) −15.3976 −0.487157
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 \(a_p\))