Properties

Label 6019.2.a.c.1.20
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.12654 q^{2}\) \(-0.167601 q^{3}\) \(+2.52216 q^{4}\) \(-1.92531 q^{5}\) \(+0.356410 q^{6}\) \(+0.0410631 q^{7}\) \(-1.11038 q^{8}\) \(-2.97191 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.12654 q^{2}\) \(-0.167601 q^{3}\) \(+2.52216 q^{4}\) \(-1.92531 q^{5}\) \(+0.356410 q^{6}\) \(+0.0410631 q^{7}\) \(-1.11038 q^{8}\) \(-2.97191 q^{9}\) \(+4.09424 q^{10}\) \(+3.07732 q^{11}\) \(-0.422716 q^{12}\) \(-1.00000 q^{13}\) \(-0.0873222 q^{14}\) \(+0.322684 q^{15}\) \(-2.68304 q^{16}\) \(-4.74077 q^{17}\) \(+6.31987 q^{18}\) \(-1.80299 q^{19}\) \(-4.85593 q^{20}\) \(-0.00688222 q^{21}\) \(-6.54404 q^{22}\) \(-4.58005 q^{23}\) \(+0.186102 q^{24}\) \(-1.29318 q^{25}\) \(+2.12654 q^{26}\) \(+1.00090 q^{27}\) \(+0.103568 q^{28}\) \(+2.69979 q^{29}\) \(-0.686199 q^{30}\) \(+8.90052 q^{31}\) \(+7.92635 q^{32}\) \(-0.515762 q^{33}\) \(+10.0814 q^{34}\) \(-0.0790592 q^{35}\) \(-7.49562 q^{36}\) \(+7.81755 q^{37}\) \(+3.83412 q^{38}\) \(+0.167601 q^{39}\) \(+2.13783 q^{40}\) \(+9.02010 q^{41}\) \(+0.0146353 q^{42}\) \(+5.06430 q^{43}\) \(+7.76149 q^{44}\) \(+5.72185 q^{45}\) \(+9.73965 q^{46}\) \(+12.4793 q^{47}\) \(+0.449680 q^{48}\) \(-6.99831 q^{49}\) \(+2.75000 q^{50}\) \(+0.794558 q^{51}\) \(-2.52216 q^{52}\) \(-1.95071 q^{53}\) \(-2.12845 q^{54}\) \(-5.92480 q^{55}\) \(-0.0455959 q^{56}\) \(+0.302183 q^{57}\) \(-5.74121 q^{58}\) \(-14.0622 q^{59}\) \(+0.813859 q^{60}\) \(-0.519818 q^{61}\) \(-18.9273 q^{62}\) \(-0.122036 q^{63}\) \(-11.4896 q^{64}\) \(+1.92531 q^{65}\) \(+1.09679 q^{66}\) \(-14.4946 q^{67}\) \(-11.9570 q^{68}\) \(+0.767621 q^{69}\) \(+0.168122 q^{70}\) \(-2.74485 q^{71}\) \(+3.29996 q^{72}\) \(-3.91130 q^{73}\) \(-16.6243 q^{74}\) \(+0.216739 q^{75}\) \(-4.54742 q^{76}\) \(+0.126364 q^{77}\) \(-0.356410 q^{78}\) \(+12.3492 q^{79}\) \(+5.16568 q^{80}\) \(+8.74798 q^{81}\) \(-19.1816 q^{82}\) \(-2.28778 q^{83}\) \(-0.0173580 q^{84}\) \(+9.12745 q^{85}\) \(-10.7694 q^{86}\) \(-0.452488 q^{87}\) \(-3.41701 q^{88}\) \(-6.45962 q^{89}\) \(-12.1677 q^{90}\) \(-0.0410631 q^{91}\) \(-11.5516 q^{92}\) \(-1.49174 q^{93}\) \(-26.5376 q^{94}\) \(+3.47131 q^{95}\) \(-1.32846 q^{96}\) \(+5.74742 q^{97}\) \(+14.8822 q^{98}\) \(-9.14552 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12654 −1.50369 −0.751844 0.659341i \(-0.770835\pi\)
−0.751844 + 0.659341i \(0.770835\pi\)
\(3\) −0.167601 −0.0967645 −0.0483822 0.998829i \(-0.515407\pi\)
−0.0483822 + 0.998829i \(0.515407\pi\)
\(4\) 2.52216 1.26108
\(5\) −1.92531 −0.861024 −0.430512 0.902585i \(-0.641667\pi\)
−0.430512 + 0.902585i \(0.641667\pi\)
\(6\) 0.356410 0.145504
\(7\) 0.0410631 0.0155204 0.00776020 0.999970i \(-0.497530\pi\)
0.00776020 + 0.999970i \(0.497530\pi\)
\(8\) −1.11038 −0.392580
\(9\) −2.97191 −0.990637
\(10\) 4.09424 1.29471
\(11\) 3.07732 0.927847 0.463924 0.885875i \(-0.346441\pi\)
0.463924 + 0.885875i \(0.346441\pi\)
\(12\) −0.422716 −0.122028
\(13\) −1.00000 −0.277350
\(14\) −0.0873222 −0.0233379
\(15\) 0.322684 0.0833166
\(16\) −2.68304 −0.670760
\(17\) −4.74077 −1.14981 −0.574903 0.818222i \(-0.694960\pi\)
−0.574903 + 0.818222i \(0.694960\pi\)
\(18\) 6.31987 1.48961
\(19\) −1.80299 −0.413634 −0.206817 0.978380i \(-0.566310\pi\)
−0.206817 + 0.978380i \(0.566310\pi\)
\(20\) −4.85593 −1.08582
\(21\) −0.00688222 −0.00150182
\(22\) −6.54404 −1.39519
\(23\) −4.58005 −0.955007 −0.477503 0.878630i \(-0.658458\pi\)
−0.477503 + 0.878630i \(0.658458\pi\)
\(24\) 0.186102 0.0379878
\(25\) −1.29318 −0.258637
\(26\) 2.12654 0.417048
\(27\) 1.00090 0.192623
\(28\) 0.103568 0.0195724
\(29\) 2.69979 0.501339 0.250669 0.968073i \(-0.419349\pi\)
0.250669 + 0.968073i \(0.419349\pi\)
\(30\) −0.686199 −0.125282
\(31\) 8.90052 1.59858 0.799290 0.600945i \(-0.205209\pi\)
0.799290 + 0.600945i \(0.205209\pi\)
\(32\) 7.92635 1.40119
\(33\) −0.515762 −0.0897827
\(34\) 10.0814 1.72895
\(35\) −0.0790592 −0.0133634
\(36\) −7.49562 −1.24927
\(37\) 7.81755 1.28520 0.642598 0.766203i \(-0.277856\pi\)
0.642598 + 0.766203i \(0.277856\pi\)
\(38\) 3.83412 0.621976
\(39\) 0.167601 0.0268376
\(40\) 2.13783 0.338021
\(41\) 9.02010 1.40870 0.704351 0.709852i \(-0.251238\pi\)
0.704351 + 0.709852i \(0.251238\pi\)
\(42\) 0.0146353 0.00225828
\(43\) 5.06430 0.772299 0.386149 0.922436i \(-0.373805\pi\)
0.386149 + 0.922436i \(0.373805\pi\)
\(44\) 7.76149 1.17009
\(45\) 5.72185 0.852962
\(46\) 9.73965 1.43603
\(47\) 12.4793 1.82029 0.910145 0.414290i \(-0.135970\pi\)
0.910145 + 0.414290i \(0.135970\pi\)
\(48\) 0.449680 0.0649057
\(49\) −6.99831 −0.999759
\(50\) 2.75000 0.388909
\(51\) 0.794558 0.111260
\(52\) −2.52216 −0.349760
\(53\) −1.95071 −0.267951 −0.133976 0.990985i \(-0.542774\pi\)
−0.133976 + 0.990985i \(0.542774\pi\)
\(54\) −2.12845 −0.289645
\(55\) −5.92480 −0.798899
\(56\) −0.0455959 −0.00609301
\(57\) 0.302183 0.0400251
\(58\) −5.74121 −0.753857
\(59\) −14.0622 −1.83074 −0.915370 0.402613i \(-0.868102\pi\)
−0.915370 + 0.402613i \(0.868102\pi\)
\(60\) 0.813859 0.105069
\(61\) −0.519818 −0.0665558 −0.0332779 0.999446i \(-0.510595\pi\)
−0.0332779 + 0.999446i \(0.510595\pi\)
\(62\) −18.9273 −2.40377
\(63\) −0.122036 −0.0153751
\(64\) −11.4896 −1.43620
\(65\) 1.92531 0.238805
\(66\) 1.09679 0.135005
\(67\) −14.4946 −1.77080 −0.885401 0.464828i \(-0.846116\pi\)
−0.885401 + 0.464828i \(0.846116\pi\)
\(68\) −11.9570 −1.45000
\(69\) 0.767621 0.0924107
\(70\) 0.168122 0.0200945
\(71\) −2.74485 −0.325753 −0.162877 0.986646i \(-0.552077\pi\)
−0.162877 + 0.986646i \(0.552077\pi\)
\(72\) 3.29996 0.388904
\(73\) −3.91130 −0.457783 −0.228891 0.973452i \(-0.573510\pi\)
−0.228891 + 0.973452i \(0.573510\pi\)
\(74\) −16.6243 −1.93253
\(75\) 0.216739 0.0250269
\(76\) −4.54742 −0.521624
\(77\) 0.126364 0.0144006
\(78\) −0.356410 −0.0403554
\(79\) 12.3492 1.38939 0.694697 0.719303i \(-0.255539\pi\)
0.694697 + 0.719303i \(0.255539\pi\)
\(80\) 5.16568 0.577541
\(81\) 8.74798 0.971998
\(82\) −19.1816 −2.11825
\(83\) −2.28778 −0.251116 −0.125558 0.992086i \(-0.540072\pi\)
−0.125558 + 0.992086i \(0.540072\pi\)
\(84\) −0.0173580 −0.00189392
\(85\) 9.12745 0.990011
\(86\) −10.7694 −1.16130
\(87\) −0.452488 −0.0485118
\(88\) −3.41701 −0.364255
\(89\) −6.45962 −0.684718 −0.342359 0.939569i \(-0.611226\pi\)
−0.342359 + 0.939569i \(0.611226\pi\)
\(90\) −12.1677 −1.28259
\(91\) −0.0410631 −0.00430459
\(92\) −11.5516 −1.20434
\(93\) −1.49174 −0.154686
\(94\) −26.5376 −2.73715
\(95\) 3.47131 0.356149
\(96\) −1.32846 −0.135586
\(97\) 5.74742 0.583562 0.291781 0.956485i \(-0.405752\pi\)
0.291781 + 0.956485i \(0.405752\pi\)
\(98\) 14.8822 1.50333
\(99\) −9.14552 −0.919160
\(100\) −3.26161 −0.326161
\(101\) −13.4576 −1.33908 −0.669539 0.742777i \(-0.733508\pi\)
−0.669539 + 0.742777i \(0.733508\pi\)
\(102\) −1.68966 −0.167301
\(103\) 15.2889 1.50646 0.753230 0.657757i \(-0.228494\pi\)
0.753230 + 0.657757i \(0.228494\pi\)
\(104\) 1.11038 0.108882
\(105\) 0.0132504 0.00129311
\(106\) 4.14826 0.402915
\(107\) 13.1298 1.26931 0.634655 0.772796i \(-0.281142\pi\)
0.634655 + 0.772796i \(0.281142\pi\)
\(108\) 2.52442 0.242913
\(109\) 4.07881 0.390679 0.195339 0.980736i \(-0.437419\pi\)
0.195339 + 0.980736i \(0.437419\pi\)
\(110\) 12.5993 1.20130
\(111\) −1.31023 −0.124361
\(112\) −0.110174 −0.0104105
\(113\) 5.48600 0.516079 0.258040 0.966134i \(-0.416923\pi\)
0.258040 + 0.966134i \(0.416923\pi\)
\(114\) −0.642602 −0.0601852
\(115\) 8.81801 0.822284
\(116\) 6.80930 0.632228
\(117\) 2.97191 0.274753
\(118\) 29.9038 2.75286
\(119\) −0.194671 −0.0178455
\(120\) −0.358303 −0.0327085
\(121\) −1.53009 −0.139099
\(122\) 1.10541 0.100079
\(123\) −1.51178 −0.136312
\(124\) 22.4485 2.01594
\(125\) 12.1163 1.08372
\(126\) 0.259514 0.0231193
\(127\) 15.4543 1.37135 0.685674 0.727909i \(-0.259508\pi\)
0.685674 + 0.727909i \(0.259508\pi\)
\(128\) 8.58034 0.758402
\(129\) −0.848782 −0.0747311
\(130\) −4.09424 −0.359089
\(131\) −12.8990 −1.12699 −0.563495 0.826119i \(-0.690544\pi\)
−0.563495 + 0.826119i \(0.690544\pi\)
\(132\) −1.30083 −0.113223
\(133\) −0.0740363 −0.00641976
\(134\) 30.8234 2.66273
\(135\) −1.92704 −0.165853
\(136\) 5.26408 0.451391
\(137\) −17.4507 −1.49092 −0.745458 0.666553i \(-0.767769\pi\)
−0.745458 + 0.666553i \(0.767769\pi\)
\(138\) −1.63237 −0.138957
\(139\) −18.0474 −1.53076 −0.765378 0.643580i \(-0.777448\pi\)
−0.765378 + 0.643580i \(0.777448\pi\)
\(140\) −0.199400 −0.0168524
\(141\) −2.09154 −0.176139
\(142\) 5.83701 0.489831
\(143\) −3.07732 −0.257339
\(144\) 7.97375 0.664479
\(145\) −5.19794 −0.431665
\(146\) 8.31751 0.688362
\(147\) 1.17292 0.0967412
\(148\) 19.7171 1.62073
\(149\) 20.8768 1.71030 0.855148 0.518385i \(-0.173466\pi\)
0.855148 + 0.518385i \(0.173466\pi\)
\(150\) −0.460904 −0.0376326
\(151\) −4.34170 −0.353323 −0.176661 0.984272i \(-0.556530\pi\)
−0.176661 + 0.984272i \(0.556530\pi\)
\(152\) 2.00201 0.162384
\(153\) 14.0891 1.13904
\(154\) −0.268719 −0.0216540
\(155\) −17.1363 −1.37642
\(156\) 0.422716 0.0338444
\(157\) 14.5110 1.15810 0.579052 0.815291i \(-0.303423\pi\)
0.579052 + 0.815291i \(0.303423\pi\)
\(158\) −26.2610 −2.08921
\(159\) 0.326942 0.0259282
\(160\) −15.2607 −1.20646
\(161\) −0.188071 −0.0148221
\(162\) −18.6029 −1.46158
\(163\) 23.9646 1.87705 0.938527 0.345206i \(-0.112191\pi\)
0.938527 + 0.345206i \(0.112191\pi\)
\(164\) 22.7501 1.77648
\(165\) 0.993002 0.0773051
\(166\) 4.86504 0.377601
\(167\) −20.5263 −1.58837 −0.794185 0.607676i \(-0.792102\pi\)
−0.794185 + 0.607676i \(0.792102\pi\)
\(168\) 0.00764192 0.000589587 0
\(169\) 1.00000 0.0769231
\(170\) −19.4099 −1.48867
\(171\) 5.35832 0.409761
\(172\) 12.7730 0.973929
\(173\) 1.79921 0.136791 0.0683956 0.997658i \(-0.478212\pi\)
0.0683956 + 0.997658i \(0.478212\pi\)
\(174\) 0.962232 0.0729466
\(175\) −0.0531022 −0.00401415
\(176\) −8.25658 −0.622363
\(177\) 2.35684 0.177151
\(178\) 13.7366 1.02960
\(179\) −7.36235 −0.550288 −0.275144 0.961403i \(-0.588725\pi\)
−0.275144 + 0.961403i \(0.588725\pi\)
\(180\) 14.4314 1.07565
\(181\) 6.61714 0.491848 0.245924 0.969289i \(-0.420909\pi\)
0.245924 + 0.969289i \(0.420909\pi\)
\(182\) 0.0873222 0.00647276
\(183\) 0.0871220 0.00644024
\(184\) 5.08562 0.374917
\(185\) −15.0512 −1.10659
\(186\) 3.17223 0.232599
\(187\) −14.5889 −1.06684
\(188\) 31.4747 2.29553
\(189\) 0.0411000 0.00298959
\(190\) −7.38186 −0.535537
\(191\) −13.6371 −0.986743 −0.493372 0.869819i \(-0.664236\pi\)
−0.493372 + 0.869819i \(0.664236\pi\)
\(192\) 1.92567 0.138973
\(193\) 1.01066 0.0727488 0.0363744 0.999338i \(-0.488419\pi\)
0.0363744 + 0.999338i \(0.488419\pi\)
\(194\) −12.2221 −0.877496
\(195\) −0.322684 −0.0231079
\(196\) −17.6508 −1.26077
\(197\) −0.540203 −0.0384878 −0.0192439 0.999815i \(-0.506126\pi\)
−0.0192439 + 0.999815i \(0.506126\pi\)
\(198\) 19.4483 1.38213
\(199\) 22.3714 1.58587 0.792933 0.609309i \(-0.208553\pi\)
0.792933 + 0.609309i \(0.208553\pi\)
\(200\) 1.43593 0.101536
\(201\) 2.42932 0.171351
\(202\) 28.6180 2.01355
\(203\) 0.110862 0.00778098
\(204\) 2.00400 0.140308
\(205\) −17.3665 −1.21293
\(206\) −32.5124 −2.26525
\(207\) 13.6115 0.946065
\(208\) 2.68304 0.186035
\(209\) −5.54837 −0.383789
\(210\) −0.0281775 −0.00194443
\(211\) 2.76956 0.190664 0.0953321 0.995446i \(-0.469609\pi\)
0.0953321 + 0.995446i \(0.469609\pi\)
\(212\) −4.92001 −0.337907
\(213\) 0.460039 0.0315214
\(214\) −27.9211 −1.90865
\(215\) −9.75035 −0.664968
\(216\) −1.11138 −0.0756200
\(217\) 0.365483 0.0248106
\(218\) −8.67373 −0.587459
\(219\) 0.655537 0.0442971
\(220\) −14.9433 −1.00747
\(221\) 4.74077 0.318899
\(222\) 2.78625 0.187001
\(223\) −5.90104 −0.395163 −0.197581 0.980286i \(-0.563309\pi\)
−0.197581 + 0.980286i \(0.563309\pi\)
\(224\) 0.325481 0.0217471
\(225\) 3.84323 0.256215
\(226\) −11.6662 −0.776022
\(227\) −18.6060 −1.23492 −0.617461 0.786601i \(-0.711839\pi\)
−0.617461 + 0.786601i \(0.711839\pi\)
\(228\) 0.762152 0.0504747
\(229\) 12.8389 0.848420 0.424210 0.905564i \(-0.360552\pi\)
0.424210 + 0.905564i \(0.360552\pi\)
\(230\) −18.7518 −1.23646
\(231\) −0.0211788 −0.00139346
\(232\) −2.99781 −0.196816
\(233\) −8.40261 −0.550473 −0.275237 0.961377i \(-0.588756\pi\)
−0.275237 + 0.961377i \(0.588756\pi\)
\(234\) −6.31987 −0.413143
\(235\) −24.0265 −1.56731
\(236\) −35.4670 −2.30871
\(237\) −2.06974 −0.134444
\(238\) 0.413975 0.0268340
\(239\) −20.7790 −1.34408 −0.672041 0.740514i \(-0.734582\pi\)
−0.672041 + 0.740514i \(0.734582\pi\)
\(240\) −0.865773 −0.0558854
\(241\) −3.84725 −0.247823 −0.123912 0.992293i \(-0.539544\pi\)
−0.123912 + 0.992293i \(0.539544\pi\)
\(242\) 3.25379 0.209162
\(243\) −4.46886 −0.286678
\(244\) −1.31106 −0.0839321
\(245\) 13.4739 0.860817
\(246\) 3.21485 0.204971
\(247\) 1.80299 0.114721
\(248\) −9.88300 −0.627571
\(249\) 0.383434 0.0242991
\(250\) −25.7658 −1.62957
\(251\) 24.5615 1.55031 0.775155 0.631771i \(-0.217672\pi\)
0.775155 + 0.631771i \(0.217672\pi\)
\(252\) −0.307794 −0.0193892
\(253\) −14.0943 −0.886101
\(254\) −32.8641 −2.06208
\(255\) −1.52977 −0.0957979
\(256\) 4.73279 0.295799
\(257\) 2.71235 0.169192 0.0845959 0.996415i \(-0.473040\pi\)
0.0845959 + 0.996415i \(0.473040\pi\)
\(258\) 1.80497 0.112372
\(259\) 0.321013 0.0199468
\(260\) 4.85593 0.301152
\(261\) −8.02354 −0.496645
\(262\) 27.4302 1.69464
\(263\) 1.75020 0.107922 0.0539611 0.998543i \(-0.482815\pi\)
0.0539611 + 0.998543i \(0.482815\pi\)
\(264\) 0.572695 0.0352469
\(265\) 3.75573 0.230712
\(266\) 0.157441 0.00965332
\(267\) 1.08264 0.0662564
\(268\) −36.5577 −2.23312
\(269\) 4.66312 0.284315 0.142158 0.989844i \(-0.454596\pi\)
0.142158 + 0.989844i \(0.454596\pi\)
\(270\) 4.09792 0.249391
\(271\) −1.11372 −0.0676538 −0.0338269 0.999428i \(-0.510769\pi\)
−0.0338269 + 0.999428i \(0.510769\pi\)
\(272\) 12.7197 0.771244
\(273\) 0.00688222 0.000416531 0
\(274\) 37.1096 2.24187
\(275\) −3.97955 −0.239976
\(276\) 1.93606 0.116537
\(277\) −3.57329 −0.214698 −0.107349 0.994221i \(-0.534236\pi\)
−0.107349 + 0.994221i \(0.534236\pi\)
\(278\) 38.3784 2.30178
\(279\) −26.4515 −1.58361
\(280\) 0.0877862 0.00524623
\(281\) −13.2494 −0.790393 −0.395196 0.918597i \(-0.629323\pi\)
−0.395196 + 0.918597i \(0.629323\pi\)
\(282\) 4.44774 0.264859
\(283\) 13.8599 0.823884 0.411942 0.911210i \(-0.364851\pi\)
0.411942 + 0.911210i \(0.364851\pi\)
\(284\) −6.92293 −0.410800
\(285\) −0.581795 −0.0344625
\(286\) 6.54404 0.386957
\(287\) 0.370393 0.0218636
\(288\) −23.5564 −1.38807
\(289\) 5.47491 0.322054
\(290\) 11.0536 0.649090
\(291\) −0.963274 −0.0564681
\(292\) −9.86490 −0.577300
\(293\) 31.8458 1.86045 0.930226 0.366987i \(-0.119611\pi\)
0.930226 + 0.366987i \(0.119611\pi\)
\(294\) −2.49427 −0.145469
\(295\) 27.0741 1.57631
\(296\) −8.68048 −0.504543
\(297\) 3.08009 0.178725
\(298\) −44.3953 −2.57175
\(299\) 4.58005 0.264871
\(300\) 0.546650 0.0315608
\(301\) 0.207956 0.0119864
\(302\) 9.23279 0.531287
\(303\) 2.25550 0.129575
\(304\) 4.83749 0.277449
\(305\) 1.00081 0.0573062
\(306\) −29.9611 −1.71276
\(307\) −0.113410 −0.00647268 −0.00323634 0.999995i \(-0.501030\pi\)
−0.00323634 + 0.999995i \(0.501030\pi\)
\(308\) 0.318711 0.0181602
\(309\) −2.56244 −0.145772
\(310\) 36.4409 2.06970
\(311\) 18.4376 1.04550 0.522750 0.852486i \(-0.324906\pi\)
0.522750 + 0.852486i \(0.324906\pi\)
\(312\) −0.186102 −0.0105359
\(313\) −9.47042 −0.535300 −0.267650 0.963516i \(-0.586247\pi\)
−0.267650 + 0.963516i \(0.586247\pi\)
\(314\) −30.8581 −1.74143
\(315\) 0.234957 0.0132383
\(316\) 31.1466 1.75213
\(317\) −0.327446 −0.0183912 −0.00919560 0.999958i \(-0.502927\pi\)
−0.00919560 + 0.999958i \(0.502927\pi\)
\(318\) −0.695253 −0.0389879
\(319\) 8.30813 0.465166
\(320\) 22.1210 1.23660
\(321\) −2.20057 −0.122824
\(322\) 0.399940 0.0222878
\(323\) 8.54755 0.475598
\(324\) 22.0638 1.22577
\(325\) 1.29318 0.0717330
\(326\) −50.9616 −2.82250
\(327\) −0.683612 −0.0378039
\(328\) −10.0158 −0.553029
\(329\) 0.512438 0.0282516
\(330\) −2.11165 −0.116243
\(331\) −31.2009 −1.71496 −0.857479 0.514519i \(-0.827971\pi\)
−0.857479 + 0.514519i \(0.827971\pi\)
\(332\) −5.77014 −0.316677
\(333\) −23.2330 −1.27316
\(334\) 43.6499 2.38841
\(335\) 27.9067 1.52470
\(336\) 0.0184653 0.00100736
\(337\) 2.42583 0.132143 0.0660717 0.997815i \(-0.478953\pi\)
0.0660717 + 0.997815i \(0.478953\pi\)
\(338\) −2.12654 −0.115668
\(339\) −0.919459 −0.0499381
\(340\) 23.0209 1.24848
\(341\) 27.3898 1.48324
\(342\) −11.3947 −0.616152
\(343\) −0.574815 −0.0310371
\(344\) −5.62332 −0.303189
\(345\) −1.47791 −0.0795679
\(346\) −3.82608 −0.205691
\(347\) −26.7225 −1.43454 −0.717269 0.696796i \(-0.754608\pi\)
−0.717269 + 0.696796i \(0.754608\pi\)
\(348\) −1.14125 −0.0611772
\(349\) 13.9159 0.744903 0.372451 0.928052i \(-0.378517\pi\)
0.372451 + 0.928052i \(0.378517\pi\)
\(350\) 0.112924 0.00603603
\(351\) −1.00090 −0.0534240
\(352\) 24.3919 1.30009
\(353\) −0.453367 −0.0241303 −0.0120651 0.999927i \(-0.503841\pi\)
−0.0120651 + 0.999927i \(0.503841\pi\)
\(354\) −5.01190 −0.266379
\(355\) 5.28468 0.280482
\(356\) −16.2922 −0.863484
\(357\) 0.0326270 0.00172681
\(358\) 15.6563 0.827461
\(359\) −29.9920 −1.58292 −0.791460 0.611221i \(-0.790678\pi\)
−0.791460 + 0.611221i \(0.790678\pi\)
\(360\) −6.35345 −0.334856
\(361\) −15.7492 −0.828907
\(362\) −14.0716 −0.739586
\(363\) 0.256445 0.0134599
\(364\) −0.103568 −0.00542842
\(365\) 7.53045 0.394162
\(366\) −0.185268 −0.00968411
\(367\) −23.8742 −1.24622 −0.623110 0.782134i \(-0.714131\pi\)
−0.623110 + 0.782134i \(0.714131\pi\)
\(368\) 12.2885 0.640580
\(369\) −26.8069 −1.39551
\(370\) 32.0069 1.66396
\(371\) −0.0801024 −0.00415871
\(372\) −3.76239 −0.195071
\(373\) −20.1275 −1.04216 −0.521081 0.853507i \(-0.674471\pi\)
−0.521081 + 0.853507i \(0.674471\pi\)
\(374\) 31.0238 1.60420
\(375\) −2.03071 −0.104865
\(376\) −13.8568 −0.714610
\(377\) −2.69979 −0.139046
\(378\) −0.0874007 −0.00449541
\(379\) −30.0630 −1.54423 −0.772116 0.635481i \(-0.780802\pi\)
−0.772116 + 0.635481i \(0.780802\pi\)
\(380\) 8.75518 0.449131
\(381\) −2.59016 −0.132698
\(382\) 28.9997 1.48375
\(383\) −23.4974 −1.20066 −0.600332 0.799751i \(-0.704965\pi\)
−0.600332 + 0.799751i \(0.704965\pi\)
\(384\) −1.43807 −0.0733863
\(385\) −0.243291 −0.0123992
\(386\) −2.14920 −0.109391
\(387\) −15.0506 −0.765067
\(388\) 14.4959 0.735918
\(389\) −20.9710 −1.06327 −0.531637 0.846973i \(-0.678423\pi\)
−0.531637 + 0.846973i \(0.678423\pi\)
\(390\) 0.686199 0.0347470
\(391\) 21.7130 1.09807
\(392\) 7.77082 0.392486
\(393\) 2.16189 0.109053
\(394\) 1.14876 0.0578737
\(395\) −23.7760 −1.19630
\(396\) −23.0664 −1.15913
\(397\) −30.4229 −1.52688 −0.763442 0.645876i \(-0.776492\pi\)
−0.763442 + 0.645876i \(0.776492\pi\)
\(398\) −47.5736 −2.38465
\(399\) 0.0124086 0.000621205 0
\(400\) 3.46967 0.173483
\(401\) 24.0363 1.20032 0.600159 0.799881i \(-0.295104\pi\)
0.600159 + 0.799881i \(0.295104\pi\)
\(402\) −5.16603 −0.257658
\(403\) −8.90052 −0.443367
\(404\) −33.9421 −1.68868
\(405\) −16.8426 −0.836914
\(406\) −0.235752 −0.0117002
\(407\) 24.0571 1.19247
\(408\) −0.882265 −0.0436786
\(409\) −14.1843 −0.701366 −0.350683 0.936494i \(-0.614051\pi\)
−0.350683 + 0.936494i \(0.614051\pi\)
\(410\) 36.9304 1.82386
\(411\) 2.92476 0.144268
\(412\) 38.5610 1.89977
\(413\) −0.577437 −0.0284138
\(414\) −28.9453 −1.42259
\(415\) 4.40468 0.216217
\(416\) −7.92635 −0.388621
\(417\) 3.02476 0.148123
\(418\) 11.7988 0.577099
\(419\) −19.3169 −0.943693 −0.471846 0.881681i \(-0.656412\pi\)
−0.471846 + 0.881681i \(0.656412\pi\)
\(420\) 0.0334196 0.00163071
\(421\) 9.36974 0.456653 0.228327 0.973585i \(-0.426675\pi\)
0.228327 + 0.973585i \(0.426675\pi\)
\(422\) −5.88957 −0.286700
\(423\) −37.0873 −1.80325
\(424\) 2.16604 0.105192
\(425\) 6.13069 0.297382
\(426\) −0.978290 −0.0473983
\(427\) −0.0213453 −0.00103297
\(428\) 33.1155 1.60070
\(429\) 0.515762 0.0249012
\(430\) 20.7345 0.999905
\(431\) −11.3595 −0.547166 −0.273583 0.961848i \(-0.588209\pi\)
−0.273583 + 0.961848i \(0.588209\pi\)
\(432\) −2.68545 −0.129204
\(433\) 34.1724 1.64222 0.821110 0.570769i \(-0.193355\pi\)
0.821110 + 0.570769i \(0.193355\pi\)
\(434\) −0.777213 −0.0373074
\(435\) 0.871179 0.0417698
\(436\) 10.2874 0.492677
\(437\) 8.25778 0.395023
\(438\) −1.39402 −0.0666090
\(439\) −22.6638 −1.08168 −0.540841 0.841125i \(-0.681894\pi\)
−0.540841 + 0.841125i \(0.681894\pi\)
\(440\) 6.57880 0.313632
\(441\) 20.7984 0.990398
\(442\) −10.0814 −0.479524
\(443\) −18.2731 −0.868179 −0.434090 0.900870i \(-0.642930\pi\)
−0.434090 + 0.900870i \(0.642930\pi\)
\(444\) −3.30460 −0.156829
\(445\) 12.4368 0.589559
\(446\) 12.5488 0.594202
\(447\) −3.49897 −0.165496
\(448\) −0.471799 −0.0222904
\(449\) −5.98117 −0.282269 −0.141134 0.989990i \(-0.545075\pi\)
−0.141134 + 0.989990i \(0.545075\pi\)
\(450\) −8.17277 −0.385268
\(451\) 27.7577 1.30706
\(452\) 13.8365 0.650816
\(453\) 0.727674 0.0341891
\(454\) 39.5663 1.85694
\(455\) 0.0790592 0.00370635
\(456\) −0.335539 −0.0157130
\(457\) 29.1975 1.36580 0.682901 0.730511i \(-0.260718\pi\)
0.682901 + 0.730511i \(0.260718\pi\)
\(458\) −27.3024 −1.27576
\(459\) −4.74503 −0.221479
\(460\) 22.2404 1.03696
\(461\) −18.4840 −0.860885 −0.430442 0.902618i \(-0.641642\pi\)
−0.430442 + 0.902618i \(0.641642\pi\)
\(462\) 0.0450375 0.00209533
\(463\) −1.00000 −0.0464739
\(464\) −7.24365 −0.336278
\(465\) 2.87205 0.133188
\(466\) 17.8685 0.827740
\(467\) −24.2985 −1.12440 −0.562201 0.827001i \(-0.690045\pi\)
−0.562201 + 0.827001i \(0.690045\pi\)
\(468\) 7.49562 0.346485
\(469\) −0.595195 −0.0274836
\(470\) 51.0932 2.35675
\(471\) −2.43206 −0.112063
\(472\) 15.6144 0.718713
\(473\) 15.5845 0.716575
\(474\) 4.40137 0.202162
\(475\) 2.33160 0.106981
\(476\) −0.490991 −0.0225045
\(477\) 5.79735 0.265442
\(478\) 44.1873 2.02108
\(479\) 19.5729 0.894309 0.447155 0.894457i \(-0.352437\pi\)
0.447155 + 0.894457i \(0.352437\pi\)
\(480\) 2.55770 0.116743
\(481\) −7.81755 −0.356449
\(482\) 8.18132 0.372649
\(483\) 0.0315209 0.00143425
\(484\) −3.85913 −0.175415
\(485\) −11.0656 −0.502461
\(486\) 9.50320 0.431074
\(487\) −23.1114 −1.04728 −0.523639 0.851941i \(-0.675426\pi\)
−0.523639 + 0.851941i \(0.675426\pi\)
\(488\) 0.577198 0.0261285
\(489\) −4.01649 −0.181632
\(490\) −28.6528 −1.29440
\(491\) 27.6965 1.24992 0.624962 0.780655i \(-0.285114\pi\)
0.624962 + 0.780655i \(0.285114\pi\)
\(492\) −3.81294 −0.171901
\(493\) −12.7991 −0.576442
\(494\) −3.83412 −0.172505
\(495\) 17.6080 0.791419
\(496\) −23.8804 −1.07226
\(497\) −0.112712 −0.00505582
\(498\) −0.815386 −0.0365383
\(499\) 0.616476 0.0275973 0.0137986 0.999905i \(-0.495608\pi\)
0.0137986 + 0.999905i \(0.495608\pi\)
\(500\) 30.5593 1.36665
\(501\) 3.44022 0.153698
\(502\) −52.2310 −2.33118
\(503\) 15.1551 0.675731 0.337866 0.941194i \(-0.390295\pi\)
0.337866 + 0.941194i \(0.390295\pi\)
\(504\) 0.135507 0.00603595
\(505\) 25.9100 1.15298
\(506\) 29.9720 1.33242
\(507\) −0.167601 −0.00744342
\(508\) 38.9782 1.72938
\(509\) −36.2041 −1.60472 −0.802360 0.596840i \(-0.796423\pi\)
−0.802360 + 0.596840i \(0.796423\pi\)
\(510\) 3.25311 0.144050
\(511\) −0.160610 −0.00710497
\(512\) −27.2251 −1.20319
\(513\) −1.80461 −0.0796753
\(514\) −5.76791 −0.254412
\(515\) −29.4359 −1.29710
\(516\) −2.14076 −0.0942418
\(517\) 38.4028 1.68895
\(518\) −0.682646 −0.0299937
\(519\) −0.301549 −0.0132365
\(520\) −2.13783 −0.0937502
\(521\) −7.94924 −0.348263 −0.174131 0.984722i \(-0.555712\pi\)
−0.174131 + 0.984722i \(0.555712\pi\)
\(522\) 17.0624 0.746799
\(523\) 19.5301 0.853992 0.426996 0.904254i \(-0.359572\pi\)
0.426996 + 0.904254i \(0.359572\pi\)
\(524\) −32.5333 −1.42122
\(525\) 0.00889999 0.000388427 0
\(526\) −3.72187 −0.162281
\(527\) −42.1953 −1.83806
\(528\) 1.38381 0.0602226
\(529\) −2.02313 −0.0879621
\(530\) −7.98669 −0.346920
\(531\) 41.7916 1.81360
\(532\) −0.186731 −0.00809582
\(533\) −9.02010 −0.390704
\(534\) −2.30227 −0.0996290
\(535\) −25.2790 −1.09291
\(536\) 16.0946 0.695182
\(537\) 1.23394 0.0532483
\(538\) −9.91629 −0.427521
\(539\) −21.5361 −0.927624
\(540\) −4.86029 −0.209154
\(541\) 32.1231 1.38108 0.690541 0.723294i \(-0.257373\pi\)
0.690541 + 0.723294i \(0.257373\pi\)
\(542\) 2.36837 0.101730
\(543\) −1.10904 −0.0475934
\(544\) −37.5770 −1.61110
\(545\) −7.85297 −0.336384
\(546\) −0.0146353 −0.000626333 0
\(547\) −42.0649 −1.79856 −0.899282 0.437370i \(-0.855910\pi\)
−0.899282 + 0.437370i \(0.855910\pi\)
\(548\) −44.0134 −1.88016
\(549\) 1.54485 0.0659326
\(550\) 8.46265 0.360849
\(551\) −4.86769 −0.207371
\(552\) −0.852355 −0.0362786
\(553\) 0.507097 0.0215640
\(554\) 7.59874 0.322840
\(555\) 2.52259 0.107078
\(556\) −45.5183 −1.93040
\(557\) −19.7273 −0.835873 −0.417936 0.908476i \(-0.637246\pi\)
−0.417936 + 0.908476i \(0.637246\pi\)
\(558\) 56.2502 2.38126
\(559\) −5.06430 −0.214197
\(560\) 0.212119 0.00896366
\(561\) 2.44511 0.103233
\(562\) 28.1753 1.18850
\(563\) −23.6207 −0.995496 −0.497748 0.867322i \(-0.665839\pi\)
−0.497748 + 0.867322i \(0.665839\pi\)
\(564\) −5.27519 −0.222126
\(565\) −10.5622 −0.444357
\(566\) −29.4735 −1.23887
\(567\) 0.359219 0.0150858
\(568\) 3.04784 0.127884
\(569\) −12.4247 −0.520871 −0.260435 0.965491i \(-0.583866\pi\)
−0.260435 + 0.965491i \(0.583866\pi\)
\(570\) 1.23721 0.0518209
\(571\) −4.18465 −0.175122 −0.0875612 0.996159i \(-0.527907\pi\)
−0.0875612 + 0.996159i \(0.527907\pi\)
\(572\) −7.76149 −0.324524
\(573\) 2.28559 0.0954817
\(574\) −0.787655 −0.0328761
\(575\) 5.92285 0.247000
\(576\) 34.1460 1.42275
\(577\) 13.7380 0.571922 0.285961 0.958241i \(-0.407687\pi\)
0.285961 + 0.958241i \(0.407687\pi\)
\(578\) −11.6426 −0.484268
\(579\) −0.169387 −0.00703950
\(580\) −13.1100 −0.544363
\(581\) −0.0939434 −0.00389743
\(582\) 2.04844 0.0849104
\(583\) −6.00297 −0.248618
\(584\) 4.34304 0.179716
\(585\) −5.72185 −0.236569
\(586\) −67.7213 −2.79754
\(587\) 20.0531 0.827678 0.413839 0.910350i \(-0.364188\pi\)
0.413839 + 0.910350i \(0.364188\pi\)
\(588\) 2.95830 0.121998
\(589\) −16.0475 −0.661227
\(590\) −57.5740 −2.37028
\(591\) 0.0905385 0.00372426
\(592\) −20.9748 −0.862058
\(593\) −19.4705 −0.799557 −0.399779 0.916612i \(-0.630913\pi\)
−0.399779 + 0.916612i \(0.630913\pi\)
\(594\) −6.54991 −0.268746
\(595\) 0.374802 0.0153654
\(596\) 52.6546 2.15682
\(597\) −3.74947 −0.153456
\(598\) −9.73965 −0.398284
\(599\) −28.6342 −1.16996 −0.584980 0.811048i \(-0.698898\pi\)
−0.584980 + 0.811048i \(0.698898\pi\)
\(600\) −0.240664 −0.00982506
\(601\) −13.7836 −0.562244 −0.281122 0.959672i \(-0.590706\pi\)
−0.281122 + 0.959672i \(0.590706\pi\)
\(602\) −0.442226 −0.0180238
\(603\) 43.0768 1.75422
\(604\) −10.9505 −0.445568
\(605\) 2.94590 0.119768
\(606\) −4.79640 −0.194841
\(607\) −37.5822 −1.52542 −0.762708 0.646743i \(-0.776130\pi\)
−0.762708 + 0.646743i \(0.776130\pi\)
\(608\) −14.2911 −0.579581
\(609\) −0.0185806 −0.000752923 0
\(610\) −2.12826 −0.0861706
\(611\) −12.4793 −0.504858
\(612\) 35.5350 1.43642
\(613\) 0.394258 0.0159239 0.00796196 0.999968i \(-0.497466\pi\)
0.00796196 + 0.999968i \(0.497466\pi\)
\(614\) 0.241171 0.00973289
\(615\) 2.91064 0.117368
\(616\) −0.140313 −0.00565338
\(617\) 48.2584 1.94281 0.971404 0.237431i \(-0.0763055\pi\)
0.971404 + 0.237431i \(0.0763055\pi\)
\(618\) 5.44911 0.219196
\(619\) 35.7294 1.43608 0.718042 0.696000i \(-0.245039\pi\)
0.718042 + 0.696000i \(0.245039\pi\)
\(620\) −43.2203 −1.73577
\(621\) −4.58416 −0.183956
\(622\) −39.2082 −1.57211
\(623\) −0.265252 −0.0106271
\(624\) −0.449680 −0.0180016
\(625\) −16.8617 −0.674470
\(626\) 20.1392 0.804924
\(627\) 0.929913 0.0371371
\(628\) 36.5990 1.46046
\(629\) −37.0612 −1.47773
\(630\) −0.499644 −0.0199063
\(631\) −6.56552 −0.261369 −0.130685 0.991424i \(-0.541718\pi\)
−0.130685 + 0.991424i \(0.541718\pi\)
\(632\) −13.7124 −0.545449
\(633\) −0.464181 −0.0184495
\(634\) 0.696326 0.0276546
\(635\) −29.7543 −1.18076
\(636\) 0.824598 0.0326974
\(637\) 6.99831 0.277283
\(638\) −17.6675 −0.699465
\(639\) 8.15744 0.322703
\(640\) −16.5198 −0.653002
\(641\) 9.86437 0.389619 0.194810 0.980841i \(-0.437591\pi\)
0.194810 + 0.980841i \(0.437591\pi\)
\(642\) 4.67960 0.184689
\(643\) −32.7342 −1.29091 −0.645455 0.763798i \(-0.723332\pi\)
−0.645455 + 0.763798i \(0.723332\pi\)
\(644\) −0.474345 −0.0186918
\(645\) 1.63417 0.0643453
\(646\) −18.1767 −0.715152
\(647\) 26.3856 1.03732 0.518662 0.854979i \(-0.326430\pi\)
0.518662 + 0.854979i \(0.326430\pi\)
\(648\) −9.71362 −0.381587
\(649\) −43.2739 −1.69865
\(650\) −2.75000 −0.107864
\(651\) −0.0612554 −0.00240079
\(652\) 60.4425 2.36711
\(653\) −47.1434 −1.84486 −0.922432 0.386159i \(-0.873802\pi\)
−0.922432 + 0.386159i \(0.873802\pi\)
\(654\) 1.45373 0.0568452
\(655\) 24.8346 0.970366
\(656\) −24.2013 −0.944901
\(657\) 11.6240 0.453496
\(658\) −1.08972 −0.0424817
\(659\) 7.54754 0.294010 0.147005 0.989136i \(-0.453037\pi\)
0.147005 + 0.989136i \(0.453037\pi\)
\(660\) 2.50451 0.0974878
\(661\) 39.1731 1.52366 0.761829 0.647778i \(-0.224302\pi\)
0.761829 + 0.647778i \(0.224302\pi\)
\(662\) 66.3499 2.57876
\(663\) −0.794558 −0.0308581
\(664\) 2.54031 0.0985833
\(665\) 0.142543 0.00552757
\(666\) 49.4059 1.91444
\(667\) −12.3652 −0.478782
\(668\) −51.7705 −2.00306
\(669\) 0.989020 0.0382377
\(670\) −59.3445 −2.29268
\(671\) −1.59965 −0.0617536
\(672\) −0.0545509 −0.00210435
\(673\) 23.9209 0.922083 0.461041 0.887379i \(-0.347476\pi\)
0.461041 + 0.887379i \(0.347476\pi\)
\(674\) −5.15862 −0.198702
\(675\) −1.29435 −0.0498194
\(676\) 2.52216 0.0970060
\(677\) 29.2001 1.12225 0.561125 0.827731i \(-0.310369\pi\)
0.561125 + 0.827731i \(0.310369\pi\)
\(678\) 1.95526 0.0750914
\(679\) 0.236007 0.00905712
\(680\) −10.1350 −0.388659
\(681\) 3.11838 0.119497
\(682\) −58.2453 −2.23033
\(683\) −33.8080 −1.29363 −0.646813 0.762649i \(-0.723898\pi\)
−0.646813 + 0.762649i \(0.723898\pi\)
\(684\) 13.5145 0.516740
\(685\) 33.5980 1.28371
\(686\) 1.22236 0.0466701
\(687\) −2.15182 −0.0820969
\(688\) −13.5877 −0.518027
\(689\) 1.95071 0.0743163
\(690\) 3.14283 0.119645
\(691\) −6.36915 −0.242294 −0.121147 0.992635i \(-0.538657\pi\)
−0.121147 + 0.992635i \(0.538657\pi\)
\(692\) 4.53788 0.172504
\(693\) −0.375544 −0.0142657
\(694\) 56.8263 2.15710
\(695\) 34.7467 1.31802
\(696\) 0.502436 0.0190448
\(697\) −42.7622 −1.61973
\(698\) −29.5927 −1.12010
\(699\) 1.40829 0.0532663
\(700\) −0.133932 −0.00506216
\(701\) 9.74768 0.368165 0.184082 0.982911i \(-0.441069\pi\)
0.184082 + 0.982911i \(0.441069\pi\)
\(702\) 2.12845 0.0803330
\(703\) −14.0949 −0.531601
\(704\) −35.3572 −1.33257
\(705\) 4.02686 0.151660
\(706\) 0.964102 0.0362844
\(707\) −0.552610 −0.0207830
\(708\) 5.94431 0.223401
\(709\) −12.1235 −0.455306 −0.227653 0.973742i \(-0.573105\pi\)
−0.227653 + 0.973742i \(0.573105\pi\)
\(710\) −11.2381 −0.421757
\(711\) −36.7007 −1.37638
\(712\) 7.17267 0.268807
\(713\) −40.7648 −1.52666
\(714\) −0.0693826 −0.00259658
\(715\) 5.92480 0.221575
\(716\) −18.5690 −0.693956
\(717\) 3.48258 0.130059
\(718\) 63.7792 2.38022
\(719\) 17.1380 0.639140 0.319570 0.947563i \(-0.396461\pi\)
0.319570 + 0.947563i \(0.396461\pi\)
\(720\) −15.3519 −0.572133
\(721\) 0.627810 0.0233809
\(722\) 33.4913 1.24642
\(723\) 0.644804 0.0239805
\(724\) 16.6895 0.620259
\(725\) −3.49133 −0.129665
\(726\) −0.545339 −0.0202394
\(727\) 13.1194 0.486572 0.243286 0.969955i \(-0.421775\pi\)
0.243286 + 0.969955i \(0.421775\pi\)
\(728\) 0.0455959 0.00168990
\(729\) −25.4949 −0.944257
\(730\) −16.0138 −0.592697
\(731\) −24.0087 −0.887994
\(732\) 0.219735 0.00812165
\(733\) 45.3647 1.67558 0.837792 0.545989i \(-0.183846\pi\)
0.837792 + 0.545989i \(0.183846\pi\)
\(734\) 50.7692 1.87393
\(735\) −2.25824 −0.0832965
\(736\) −36.3031 −1.33815
\(737\) −44.6047 −1.64303
\(738\) 57.0059 2.09842
\(739\) −10.7344 −0.394871 −0.197435 0.980316i \(-0.563261\pi\)
−0.197435 + 0.980316i \(0.563261\pi\)
\(740\) −37.9615 −1.39549
\(741\) −0.302183 −0.0111010
\(742\) 0.170341 0.00625340
\(743\) −4.77880 −0.175317 −0.0876585 0.996151i \(-0.527938\pi\)
−0.0876585 + 0.996151i \(0.527938\pi\)
\(744\) 1.65640 0.0607266
\(745\) −40.1943 −1.47261
\(746\) 42.8019 1.56709
\(747\) 6.79907 0.248765
\(748\) −36.7954 −1.34537
\(749\) 0.539152 0.0197002
\(750\) 4.31838 0.157685
\(751\) −9.45753 −0.345110 −0.172555 0.985000i \(-0.555202\pi\)
−0.172555 + 0.985000i \(0.555202\pi\)
\(752\) −33.4824 −1.22098
\(753\) −4.11654 −0.150015
\(754\) 5.74121 0.209082
\(755\) 8.35912 0.304219
\(756\) 0.103661 0.00377010
\(757\) 21.9693 0.798487 0.399243 0.916845i \(-0.369273\pi\)
0.399243 + 0.916845i \(0.369273\pi\)
\(758\) 63.9300 2.32204
\(759\) 2.36222 0.0857431
\(760\) −3.85449 −0.139817
\(761\) −53.0060 −1.92147 −0.960733 0.277476i \(-0.910502\pi\)
−0.960733 + 0.277476i \(0.910502\pi\)
\(762\) 5.50806 0.199536
\(763\) 0.167489 0.00606350
\(764\) −34.3948 −1.24436
\(765\) −27.1260 −0.980741
\(766\) 49.9682 1.80542
\(767\) 14.0622 0.507756
\(768\) −0.793221 −0.0286229
\(769\) −29.9712 −1.08079 −0.540395 0.841412i \(-0.681725\pi\)
−0.540395 + 0.841412i \(0.681725\pi\)
\(770\) 0.517366 0.0186446
\(771\) −0.454593 −0.0163718
\(772\) 2.54904 0.0917419
\(773\) −42.8860 −1.54250 −0.771252 0.636530i \(-0.780369\pi\)
−0.771252 + 0.636530i \(0.780369\pi\)
\(774\) 32.0057 1.15042
\(775\) −11.5100 −0.413452
\(776\) −6.38185 −0.229095
\(777\) −0.0538021 −0.00193014
\(778\) 44.5956 1.59883
\(779\) −16.2631 −0.582687
\(780\) −0.813859 −0.0291408
\(781\) −8.44677 −0.302249
\(782\) −46.1734 −1.65116
\(783\) 2.70222 0.0965694
\(784\) 18.7768 0.670598
\(785\) −27.9381 −0.997155
\(786\) −4.59733 −0.163981
\(787\) 41.1824 1.46799 0.733996 0.679153i \(-0.237653\pi\)
0.733996 + 0.679153i \(0.237653\pi\)
\(788\) −1.36248 −0.0485362
\(789\) −0.293336 −0.0104430
\(790\) 50.5606 1.79886
\(791\) 0.225272 0.00800976
\(792\) 10.1551 0.360844
\(793\) 0.519818 0.0184593
\(794\) 64.6955 2.29596
\(795\) −0.629464 −0.0223248
\(796\) 56.4242 1.99990
\(797\) 26.5727 0.941255 0.470627 0.882332i \(-0.344028\pi\)
0.470627 + 0.882332i \(0.344028\pi\)
\(798\) −0.0263873 −0.000934099 0
\(799\) −59.1614 −2.09298
\(800\) −10.2502 −0.362401
\(801\) 19.1974 0.678307
\(802\) −51.1142 −1.80490
\(803\) −12.0363 −0.424752
\(804\) 6.12711 0.216087
\(805\) 0.362095 0.0127622
\(806\) 18.9273 0.666685
\(807\) −0.781543 −0.0275116
\(808\) 14.9431 0.525695
\(809\) −23.9655 −0.842582 −0.421291 0.906926i \(-0.638423\pi\)
−0.421291 + 0.906926i \(0.638423\pi\)
\(810\) 35.8163 1.25846
\(811\) 11.3020 0.396868 0.198434 0.980114i \(-0.436414\pi\)
0.198434 + 0.980114i \(0.436414\pi\)
\(812\) 0.279611 0.00981243
\(813\) 0.186661 0.00654649
\(814\) −51.1583 −1.79310
\(815\) −46.1393 −1.61619
\(816\) −2.13183 −0.0746290
\(817\) −9.13087 −0.319449
\(818\) 30.1633 1.05464
\(819\) 0.122036 0.00426428
\(820\) −43.8010 −1.52960
\(821\) −22.8285 −0.796720 −0.398360 0.917229i \(-0.630420\pi\)
−0.398360 + 0.917229i \(0.630420\pi\)
\(822\) −6.21960 −0.216934
\(823\) −7.37589 −0.257107 −0.128554 0.991703i \(-0.541033\pi\)
−0.128554 + 0.991703i \(0.541033\pi\)
\(824\) −16.9766 −0.591407
\(825\) 0.666976 0.0232211
\(826\) 1.22794 0.0427256
\(827\) 27.5616 0.958412 0.479206 0.877702i \(-0.340925\pi\)
0.479206 + 0.877702i \(0.340925\pi\)
\(828\) 34.3303 1.19306
\(829\) −21.5148 −0.747240 −0.373620 0.927582i \(-0.621884\pi\)
−0.373620 + 0.927582i \(0.621884\pi\)
\(830\) −9.36671 −0.325123
\(831\) 0.598888 0.0207752
\(832\) 11.4896 0.398330
\(833\) 33.1774 1.14953
\(834\) −6.43225 −0.222731
\(835\) 39.5194 1.36763
\(836\) −13.9939 −0.483988
\(837\) 8.90851 0.307923
\(838\) 41.0781 1.41902
\(839\) 3.95055 0.136388 0.0681941 0.997672i \(-0.478276\pi\)
0.0681941 + 0.997672i \(0.478276\pi\)
\(840\) −0.0147130 −0.000507648 0
\(841\) −21.7111 −0.748659
\(842\) −19.9251 −0.686664
\(843\) 2.22061 0.0764819
\(844\) 6.98526 0.240443
\(845\) −1.92531 −0.0662326
\(846\) 78.8675 2.71152
\(847\) −0.0628303 −0.00215887
\(848\) 5.23384 0.179731
\(849\) −2.32293 −0.0797227
\(850\) −13.0371 −0.447170
\(851\) −35.8048 −1.22737
\(852\) 1.16029 0.0397509
\(853\) 33.9708 1.16314 0.581569 0.813497i \(-0.302439\pi\)
0.581569 + 0.813497i \(0.302439\pi\)
\(854\) 0.0453916 0.00155327
\(855\) −10.3164 −0.352814
\(856\) −14.5792 −0.498306
\(857\) −34.4912 −1.17820 −0.589099 0.808061i \(-0.700517\pi\)
−0.589099 + 0.808061i \(0.700517\pi\)
\(858\) −1.09679 −0.0374437
\(859\) −45.2599 −1.54425 −0.772124 0.635471i \(-0.780806\pi\)
−0.772124 + 0.635471i \(0.780806\pi\)
\(860\) −24.5919 −0.838577
\(861\) −0.0620783 −0.00211562
\(862\) 24.1563 0.822767
\(863\) 30.5418 1.03966 0.519828 0.854271i \(-0.325996\pi\)
0.519828 + 0.854271i \(0.325996\pi\)
\(864\) 7.93347 0.269902
\(865\) −3.46403 −0.117780
\(866\) −72.6689 −2.46939
\(867\) −0.917601 −0.0311634
\(868\) 0.921806 0.0312881
\(869\) 38.0025 1.28915
\(870\) −1.85259 −0.0628088
\(871\) 14.4946 0.491132
\(872\) −4.52905 −0.153373
\(873\) −17.0808 −0.578098
\(874\) −17.5605 −0.593991
\(875\) 0.497534 0.0168197
\(876\) 1.65337 0.0558621
\(877\) −37.6125 −1.27008 −0.635042 0.772477i \(-0.719017\pi\)
−0.635042 + 0.772477i \(0.719017\pi\)
\(878\) 48.1953 1.62651
\(879\) −5.33739 −0.180026
\(880\) 15.8965 0.535870
\(881\) 14.0753 0.474208 0.237104 0.971484i \(-0.423802\pi\)
0.237104 + 0.971484i \(0.423802\pi\)
\(882\) −44.2285 −1.48925
\(883\) 37.1421 1.24993 0.624966 0.780652i \(-0.285113\pi\)
0.624966 + 0.780652i \(0.285113\pi\)
\(884\) 11.9570 0.402156
\(885\) −4.53764 −0.152531
\(886\) 38.8583 1.30547
\(887\) −47.6824 −1.60102 −0.800510 0.599320i \(-0.795438\pi\)
−0.800510 + 0.599320i \(0.795438\pi\)
\(888\) 1.45486 0.0488218
\(889\) 0.634602 0.0212839
\(890\) −26.4472 −0.886513
\(891\) 26.9203 0.901865
\(892\) −14.8833 −0.498331
\(893\) −22.5000 −0.752933
\(894\) 7.44070 0.248854
\(895\) 14.1748 0.473811
\(896\) 0.352335 0.0117707
\(897\) −0.767621 −0.0256301
\(898\) 12.7192 0.424444
\(899\) 24.0296 0.801431
\(900\) 9.69322 0.323107
\(901\) 9.24789 0.308092
\(902\) −59.0278 −1.96541
\(903\) −0.0348536 −0.00115986
\(904\) −6.09157 −0.202603
\(905\) −12.7400 −0.423493
\(906\) −1.54742 −0.0514097
\(907\) 21.0593 0.699263 0.349631 0.936887i \(-0.386307\pi\)
0.349631 + 0.936887i \(0.386307\pi\)
\(908\) −46.9272 −1.55733
\(909\) 39.9947 1.32654
\(910\) −0.168122 −0.00557320
\(911\) 9.82605 0.325552 0.162776 0.986663i \(-0.447955\pi\)
0.162776 + 0.986663i \(0.447955\pi\)
\(912\) −0.810768 −0.0268472
\(913\) −7.04023 −0.232998
\(914\) −62.0896 −2.05374
\(915\) −0.167737 −0.00554520
\(916\) 32.3818 1.06992
\(917\) −0.529673 −0.0174914
\(918\) 10.0905 0.333035
\(919\) −20.2081 −0.666603 −0.333301 0.942820i \(-0.608163\pi\)
−0.333301 + 0.942820i \(0.608163\pi\)
\(920\) −9.79139 −0.322813
\(921\) 0.0190077 0.000626325 0
\(922\) 39.3069 1.29450
\(923\) 2.74485 0.0903477
\(924\) −0.0534163 −0.00175727
\(925\) −10.1095 −0.332399
\(926\) 2.12654 0.0698823
\(927\) −45.4373 −1.49236
\(928\) 21.3995 0.702473
\(929\) 33.4399 1.09713 0.548565 0.836108i \(-0.315174\pi\)
0.548565 + 0.836108i \(0.315174\pi\)
\(930\) −6.10753 −0.200274
\(931\) 12.6179 0.413534
\(932\) −21.1927 −0.694190
\(933\) −3.09016 −0.101167
\(934\) 51.6717 1.69075
\(935\) 28.0881 0.918579
\(936\) −3.29996 −0.107863
\(937\) 11.2836 0.368618 0.184309 0.982868i \(-0.440995\pi\)
0.184309 + 0.982868i \(0.440995\pi\)
\(938\) 1.26570 0.0413267
\(939\) 1.58725 0.0517980
\(940\) −60.5985 −1.97651
\(941\) −20.3569 −0.663616 −0.331808 0.943347i \(-0.607659\pi\)
−0.331808 + 0.943347i \(0.607659\pi\)
\(942\) 5.17186 0.168508
\(943\) −41.3125 −1.34532
\(944\) 37.7294 1.22799
\(945\) −0.0791302 −0.00257411
\(946\) −33.1410 −1.07751
\(947\) 18.2561 0.593243 0.296621 0.954995i \(-0.404140\pi\)
0.296621 + 0.954995i \(0.404140\pi\)
\(948\) −5.22020 −0.169544
\(949\) 3.91130 0.126966
\(950\) −4.95822 −0.160866
\(951\) 0.0548803 0.00177961
\(952\) 0.216160 0.00700577
\(953\) 0.106277 0.00344265 0.00172132 0.999999i \(-0.499452\pi\)
0.00172132 + 0.999999i \(0.499452\pi\)
\(954\) −12.3283 −0.399142
\(955\) 26.2556 0.849610
\(956\) −52.4079 −1.69499
\(957\) −1.39245 −0.0450116
\(958\) −41.6225 −1.34476
\(959\) −0.716581 −0.0231396
\(960\) −3.70750 −0.119659
\(961\) 48.2193 1.55546
\(962\) 16.6243 0.535989
\(963\) −39.0207 −1.25742
\(964\) −9.70338 −0.312525
\(965\) −1.94583 −0.0626385
\(966\) −0.0670304 −0.00215667
\(967\) −37.9888 −1.22164 −0.610819 0.791770i \(-0.709160\pi\)
−0.610819 + 0.791770i \(0.709160\pi\)
\(968\) 1.69899 0.0546076
\(969\) −1.43258 −0.0460210
\(970\) 23.5313 0.755545
\(971\) −22.5744 −0.724448 −0.362224 0.932091i \(-0.617983\pi\)
−0.362224 + 0.932091i \(0.617983\pi\)
\(972\) −11.2712 −0.361523
\(973\) −0.741081 −0.0237580
\(974\) 49.1472 1.57478
\(975\) −0.216739 −0.00694121
\(976\) 1.39469 0.0446430
\(977\) 3.94105 0.126085 0.0630427 0.998011i \(-0.479920\pi\)
0.0630427 + 0.998011i \(0.479920\pi\)
\(978\) 8.54122 0.273118
\(979\) −19.8783 −0.635314
\(980\) 33.9833 1.08556
\(981\) −12.1219 −0.387021
\(982\) −58.8975 −1.87950
\(983\) 7.53961 0.240476 0.120238 0.992745i \(-0.461634\pi\)
0.120238 + 0.992745i \(0.461634\pi\)
\(984\) 1.67865 0.0535136
\(985\) 1.04006 0.0331390
\(986\) 27.2178 0.866790
\(987\) −0.0858852 −0.00273376
\(988\) 4.54742 0.144673
\(989\) −23.1948 −0.737550
\(990\) −37.4440 −1.19005
\(991\) 22.6447 0.719332 0.359666 0.933081i \(-0.382891\pi\)
0.359666 + 0.933081i \(0.382891\pi\)
\(992\) 70.5486 2.23992
\(993\) 5.22931 0.165947
\(994\) 0.239686 0.00760238
\(995\) −43.0718 −1.36547
\(996\) 0.967081 0.0306431
\(997\) 1.86014 0.0589113 0.0294556 0.999566i \(-0.490623\pi\)
0.0294556 + 0.999566i \(0.490623\pi\)
\(998\) −1.31096 −0.0414977
\(999\) 7.82457 0.247558
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 \(a_p\))