Properties

Label 6019.2.a.c.1.2
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 1.2
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.73685 q^{2}\) \(-2.13610 q^{3}\) \(+5.49032 q^{4}\) \(-3.88543 q^{5}\) \(+5.84618 q^{6}\) \(-1.04170 q^{7}\) \(-9.55248 q^{8}\) \(+1.56292 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.73685 q^{2}\) \(-2.13610 q^{3}\) \(+5.49032 q^{4}\) \(-3.88543 q^{5}\) \(+5.84618 q^{6}\) \(-1.04170 q^{7}\) \(-9.55248 q^{8}\) \(+1.56292 q^{9}\) \(+10.6338 q^{10}\) \(-4.81178 q^{11}\) \(-11.7279 q^{12}\) \(-1.00000 q^{13}\) \(+2.85096 q^{14}\) \(+8.29967 q^{15}\) \(+15.1630 q^{16}\) \(-2.43895 q^{17}\) \(-4.27748 q^{18}\) \(-8.54378 q^{19}\) \(-21.3323 q^{20}\) \(+2.22517 q^{21}\) \(+13.1691 q^{22}\) \(-5.04586 q^{23}\) \(+20.4051 q^{24}\) \(+10.0966 q^{25}\) \(+2.73685 q^{26}\) \(+3.06974 q^{27}\) \(-5.71924 q^{28}\) \(-7.12604 q^{29}\) \(-22.7149 q^{30}\) \(-2.50853 q^{31}\) \(-22.3939 q^{32}\) \(+10.2784 q^{33}\) \(+6.67504 q^{34}\) \(+4.04744 q^{35}\) \(+8.58096 q^{36}\) \(+6.71960 q^{37}\) \(+23.3830 q^{38}\) \(+2.13610 q^{39}\) \(+37.1155 q^{40}\) \(-0.0878123 q^{41}\) \(-6.08993 q^{42}\) \(+5.33517 q^{43}\) \(-26.4182 q^{44}\) \(-6.07264 q^{45}\) \(+13.8097 q^{46}\) \(-2.03063 q^{47}\) \(-32.3897 q^{48}\) \(-5.91487 q^{49}\) \(-27.6328 q^{50}\) \(+5.20985 q^{51}\) \(-5.49032 q^{52}\) \(-5.73324 q^{53}\) \(-8.40140 q^{54}\) \(+18.6958 q^{55}\) \(+9.95077 q^{56}\) \(+18.2504 q^{57}\) \(+19.5029 q^{58}\) \(-1.84161 q^{59}\) \(+45.5679 q^{60}\) \(-2.15880 q^{61}\) \(+6.86546 q^{62}\) \(-1.62809 q^{63}\) \(+30.9625 q^{64}\) \(+3.88543 q^{65}\) \(-28.1305 q^{66}\) \(-3.26451 q^{67}\) \(-13.3906 q^{68}\) \(+10.7785 q^{69}\) \(-11.0772 q^{70}\) \(+0.628292 q^{71}\) \(-14.9298 q^{72}\) \(-5.01715 q^{73}\) \(-18.3905 q^{74}\) \(-21.5673 q^{75}\) \(-46.9081 q^{76}\) \(+5.01241 q^{77}\) \(-5.84618 q^{78}\) \(-5.04220 q^{79}\) \(-58.9149 q^{80}\) \(-11.2460 q^{81}\) \(+0.240329 q^{82}\) \(+13.1361 q^{83}\) \(+12.2169 q^{84}\) \(+9.47639 q^{85}\) \(-14.6015 q^{86}\) \(+15.2219 q^{87}\) \(+45.9644 q^{88}\) \(+11.0135 q^{89}\) \(+16.6199 q^{90}\) \(+1.04170 q^{91}\) \(-27.7034 q^{92}\) \(+5.35847 q^{93}\) \(+5.55753 q^{94}\) \(+33.1963 q^{95}\) \(+47.8356 q^{96}\) \(+7.21743 q^{97}\) \(+16.1881 q^{98}\) \(-7.52045 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73685 −1.93524 −0.967621 0.252407i \(-0.918778\pi\)
−0.967621 + 0.252407i \(0.918778\pi\)
\(3\) −2.13610 −1.23328 −0.616639 0.787246i \(-0.711506\pi\)
−0.616639 + 0.787246i \(0.711506\pi\)
\(4\) 5.49032 2.74516
\(5\) −3.88543 −1.73762 −0.868809 0.495147i \(-0.835114\pi\)
−0.868809 + 0.495147i \(0.835114\pi\)
\(6\) 5.84618 2.38669
\(7\) −1.04170 −0.393724 −0.196862 0.980431i \(-0.563075\pi\)
−0.196862 + 0.980431i \(0.563075\pi\)
\(8\) −9.55248 −3.37731
\(9\) 1.56292 0.520975
\(10\) 10.6338 3.36271
\(11\) −4.81178 −1.45081 −0.725403 0.688325i \(-0.758347\pi\)
−0.725403 + 0.688325i \(0.758347\pi\)
\(12\) −11.7279 −3.38555
\(13\) −1.00000 −0.277350
\(14\) 2.85096 0.761951
\(15\) 8.29967 2.14297
\(16\) 15.1630 3.79075
\(17\) −2.43895 −0.591533 −0.295766 0.955260i \(-0.595575\pi\)
−0.295766 + 0.955260i \(0.595575\pi\)
\(18\) −4.27748 −1.00821
\(19\) −8.54378 −1.96008 −0.980038 0.198809i \(-0.936293\pi\)
−0.980038 + 0.198809i \(0.936293\pi\)
\(20\) −21.3323 −4.77004
\(21\) 2.22517 0.485571
\(22\) 13.1691 2.80766
\(23\) −5.04586 −1.05213 −0.526067 0.850443i \(-0.676334\pi\)
−0.526067 + 0.850443i \(0.676334\pi\)
\(24\) 20.4051 4.16516
\(25\) 10.0966 2.01932
\(26\) 2.73685 0.536740
\(27\) 3.06974 0.590771
\(28\) −5.71924 −1.08084
\(29\) −7.12604 −1.32327 −0.661636 0.749825i \(-0.730138\pi\)
−0.661636 + 0.749825i \(0.730138\pi\)
\(30\) −22.7149 −4.14716
\(31\) −2.50853 −0.450545 −0.225273 0.974296i \(-0.572327\pi\)
−0.225273 + 0.974296i \(0.572327\pi\)
\(32\) −22.3939 −3.95871
\(33\) 10.2784 1.78925
\(34\) 6.67504 1.14476
\(35\) 4.04744 0.684142
\(36\) 8.58096 1.43016
\(37\) 6.71960 1.10470 0.552348 0.833614i \(-0.313732\pi\)
0.552348 + 0.833614i \(0.313732\pi\)
\(38\) 23.3830 3.79322
\(39\) 2.13610 0.342050
\(40\) 37.1155 5.86848
\(41\) −0.0878123 −0.0137140 −0.00685699 0.999976i \(-0.502183\pi\)
−0.00685699 + 0.999976i \(0.502183\pi\)
\(42\) −6.08993 −0.939697
\(43\) 5.33517 0.813605 0.406803 0.913516i \(-0.366644\pi\)
0.406803 + 0.913516i \(0.366644\pi\)
\(44\) −26.4182 −3.98270
\(45\) −6.07264 −0.905256
\(46\) 13.8097 2.03613
\(47\) −2.03063 −0.296198 −0.148099 0.988973i \(-0.547315\pi\)
−0.148099 + 0.988973i \(0.547315\pi\)
\(48\) −32.3897 −4.67505
\(49\) −5.91487 −0.844982
\(50\) −27.6328 −3.90787
\(51\) 5.20985 0.729525
\(52\) −5.49032 −0.761371
\(53\) −5.73324 −0.787521 −0.393761 0.919213i \(-0.628826\pi\)
−0.393761 + 0.919213i \(0.628826\pi\)
\(54\) −8.40140 −1.14329
\(55\) 18.6958 2.52095
\(56\) 9.95077 1.32973
\(57\) 18.2504 2.41732
\(58\) 19.5029 2.56085
\(59\) −1.84161 −0.239757 −0.119879 0.992789i \(-0.538251\pi\)
−0.119879 + 0.992789i \(0.538251\pi\)
\(60\) 45.5679 5.88279
\(61\) −2.15880 −0.276406 −0.138203 0.990404i \(-0.544133\pi\)
−0.138203 + 0.990404i \(0.544133\pi\)
\(62\) 6.86546 0.871914
\(63\) −1.62809 −0.205120
\(64\) 30.9625 3.87032
\(65\) 3.88543 0.481929
\(66\) −28.1305 −3.46263
\(67\) −3.26451 −0.398824 −0.199412 0.979916i \(-0.563903\pi\)
−0.199412 + 0.979916i \(0.563903\pi\)
\(68\) −13.3906 −1.62385
\(69\) 10.7785 1.29757
\(70\) −11.0772 −1.32398
\(71\) 0.628292 0.0745646 0.0372823 0.999305i \(-0.488130\pi\)
0.0372823 + 0.999305i \(0.488130\pi\)
\(72\) −14.9298 −1.75949
\(73\) −5.01715 −0.587213 −0.293607 0.955926i \(-0.594856\pi\)
−0.293607 + 0.955926i \(0.594856\pi\)
\(74\) −18.3905 −2.13785
\(75\) −21.5673 −2.49038
\(76\) −46.9081 −5.38073
\(77\) 5.01241 0.571217
\(78\) −5.84618 −0.661949
\(79\) −5.04220 −0.567292 −0.283646 0.958929i \(-0.591544\pi\)
−0.283646 + 0.958929i \(0.591544\pi\)
\(80\) −58.9149 −6.58688
\(81\) −11.2460 −1.24956
\(82\) 0.240329 0.0265399
\(83\) 13.1361 1.44187 0.720936 0.693002i \(-0.243712\pi\)
0.720936 + 0.693002i \(0.243712\pi\)
\(84\) 12.2169 1.33297
\(85\) 9.47639 1.02786
\(86\) −14.6015 −1.57452
\(87\) 15.2219 1.63196
\(88\) 45.9644 4.89982
\(89\) 11.0135 1.16742 0.583712 0.811961i \(-0.301600\pi\)
0.583712 + 0.811961i \(0.301600\pi\)
\(90\) 16.6199 1.75189
\(91\) 1.04170 0.109199
\(92\) −27.7034 −2.88828
\(93\) 5.35847 0.555648
\(94\) 5.55753 0.573215
\(95\) 33.1963 3.40586
\(96\) 47.8356 4.88220
\(97\) 7.21743 0.732819 0.366410 0.930454i \(-0.380587\pi\)
0.366410 + 0.930454i \(0.380587\pi\)
\(98\) 16.1881 1.63524
\(99\) −7.52045 −0.755833
\(100\) 55.4335 5.54335
\(101\) −2.30728 −0.229583 −0.114791 0.993390i \(-0.536620\pi\)
−0.114791 + 0.993390i \(0.536620\pi\)
\(102\) −14.2585 −1.41181
\(103\) 2.09318 0.206247 0.103123 0.994669i \(-0.467116\pi\)
0.103123 + 0.994669i \(0.467116\pi\)
\(104\) 9.55248 0.936698
\(105\) −8.64573 −0.843737
\(106\) 15.6910 1.52404
\(107\) 14.7454 1.42549 0.712744 0.701425i \(-0.247452\pi\)
0.712744 + 0.701425i \(0.247452\pi\)
\(108\) 16.8539 1.62176
\(109\) −16.1087 −1.54294 −0.771468 0.636268i \(-0.780477\pi\)
−0.771468 + 0.636268i \(0.780477\pi\)
\(110\) −51.1676 −4.87864
\(111\) −14.3537 −1.36240
\(112\) −15.7952 −1.49251
\(113\) 6.01998 0.566312 0.283156 0.959074i \(-0.408619\pi\)
0.283156 + 0.959074i \(0.408619\pi\)
\(114\) −49.9484 −4.67810
\(115\) 19.6053 1.82821
\(116\) −39.1243 −3.63260
\(117\) −1.56292 −0.144492
\(118\) 5.04021 0.463989
\(119\) 2.54065 0.232901
\(120\) −79.2825 −7.23747
\(121\) 12.1532 1.10484
\(122\) 5.90830 0.534912
\(123\) 0.187576 0.0169131
\(124\) −13.7726 −1.23682
\(125\) −19.8024 −1.77118
\(126\) 4.45583 0.396957
\(127\) 0.243216 0.0215820 0.0107910 0.999942i \(-0.496565\pi\)
0.0107910 + 0.999942i \(0.496565\pi\)
\(128\) −39.9520 −3.53129
\(129\) −11.3965 −1.00340
\(130\) −10.6338 −0.932649
\(131\) 19.3749 1.69279 0.846397 0.532552i \(-0.178767\pi\)
0.846397 + 0.532552i \(0.178767\pi\)
\(132\) 56.4320 4.91177
\(133\) 8.90001 0.771729
\(134\) 8.93447 0.771821
\(135\) −11.9273 −1.02653
\(136\) 23.2980 1.99779
\(137\) −6.89862 −0.589389 −0.294695 0.955591i \(-0.595218\pi\)
−0.294695 + 0.955591i \(0.595218\pi\)
\(138\) −29.4990 −2.51112
\(139\) −1.50039 −0.127261 −0.0636305 0.997974i \(-0.520268\pi\)
−0.0636305 + 0.997974i \(0.520268\pi\)
\(140\) 22.2217 1.87808
\(141\) 4.33764 0.365295
\(142\) −1.71954 −0.144301
\(143\) 4.81178 0.402381
\(144\) 23.6987 1.97489
\(145\) 27.6877 2.29934
\(146\) 13.7312 1.13640
\(147\) 12.6348 1.04210
\(148\) 36.8928 3.03257
\(149\) −17.0457 −1.39643 −0.698217 0.715886i \(-0.746023\pi\)
−0.698217 + 0.715886i \(0.746023\pi\)
\(150\) 59.0264 4.81949
\(151\) −20.8041 −1.69301 −0.846507 0.532377i \(-0.821299\pi\)
−0.846507 + 0.532377i \(0.821299\pi\)
\(152\) 81.6142 6.61979
\(153\) −3.81190 −0.308174
\(154\) −13.7182 −1.10544
\(155\) 9.74672 0.782876
\(156\) 11.7279 0.938982
\(157\) −14.5062 −1.15772 −0.578861 0.815426i \(-0.696503\pi\)
−0.578861 + 0.815426i \(0.696503\pi\)
\(158\) 13.7997 1.09785
\(159\) 12.2468 0.971233
\(160\) 87.0099 6.87873
\(161\) 5.25625 0.414250
\(162\) 30.7787 2.41820
\(163\) 2.54841 0.199607 0.0998034 0.995007i \(-0.468179\pi\)
0.0998034 + 0.995007i \(0.468179\pi\)
\(164\) −0.482118 −0.0376471
\(165\) −39.9362 −3.10903
\(166\) −35.9514 −2.79037
\(167\) −14.1168 −1.09239 −0.546194 0.837659i \(-0.683924\pi\)
−0.546194 + 0.837659i \(0.683924\pi\)
\(168\) −21.2558 −1.63992
\(169\) 1.00000 0.0769231
\(170\) −25.9354 −1.98915
\(171\) −13.3533 −1.02115
\(172\) 29.2918 2.23348
\(173\) −3.31480 −0.252020 −0.126010 0.992029i \(-0.540217\pi\)
−0.126010 + 0.992029i \(0.540217\pi\)
\(174\) −41.6601 −3.15824
\(175\) −10.5176 −0.795053
\(176\) −72.9611 −5.49965
\(177\) 3.93387 0.295688
\(178\) −30.1421 −2.25925
\(179\) −7.34557 −0.549034 −0.274517 0.961582i \(-0.588518\pi\)
−0.274517 + 0.961582i \(0.588518\pi\)
\(180\) −33.3408 −2.48507
\(181\) −6.80415 −0.505749 −0.252874 0.967499i \(-0.581376\pi\)
−0.252874 + 0.967499i \(0.581376\pi\)
\(182\) −2.85096 −0.211327
\(183\) 4.61141 0.340885
\(184\) 48.2004 3.55338
\(185\) −26.1086 −1.91954
\(186\) −14.6653 −1.07531
\(187\) 11.7357 0.858199
\(188\) −11.1488 −0.813112
\(189\) −3.19773 −0.232601
\(190\) −90.8531 −6.59117
\(191\) 25.3409 1.83361 0.916803 0.399340i \(-0.130761\pi\)
0.916803 + 0.399340i \(0.130761\pi\)
\(192\) −66.1391 −4.77318
\(193\) 20.8841 1.50327 0.751634 0.659581i \(-0.229266\pi\)
0.751634 + 0.659581i \(0.229266\pi\)
\(194\) −19.7530 −1.41818
\(195\) −8.29967 −0.594352
\(196\) −32.4746 −2.31961
\(197\) −10.4203 −0.742414 −0.371207 0.928550i \(-0.621056\pi\)
−0.371207 + 0.928550i \(0.621056\pi\)
\(198\) 20.5823 1.46272
\(199\) 24.7080 1.75150 0.875751 0.482762i \(-0.160367\pi\)
0.875751 + 0.482762i \(0.160367\pi\)
\(200\) −96.4474 −6.81986
\(201\) 6.97333 0.491861
\(202\) 6.31466 0.444298
\(203\) 7.42316 0.521004
\(204\) 28.6038 2.00266
\(205\) 0.341189 0.0238297
\(206\) −5.72870 −0.399138
\(207\) −7.88630 −0.548135
\(208\) −15.1630 −1.05137
\(209\) 41.1108 2.84369
\(210\) 23.6620 1.63284
\(211\) 12.3077 0.847299 0.423649 0.905826i \(-0.360749\pi\)
0.423649 + 0.905826i \(0.360749\pi\)
\(212\) −31.4774 −2.16187
\(213\) −1.34210 −0.0919589
\(214\) −40.3558 −2.75866
\(215\) −20.7294 −1.41374
\(216\) −29.3236 −1.99522
\(217\) 2.61312 0.177390
\(218\) 44.0871 2.98596
\(219\) 10.7171 0.724197
\(220\) 102.646 6.92041
\(221\) 2.43895 0.164062
\(222\) 39.2840 2.63657
\(223\) −2.10609 −0.141034 −0.0705170 0.997511i \(-0.522465\pi\)
−0.0705170 + 0.997511i \(0.522465\pi\)
\(224\) 23.3276 1.55864
\(225\) 15.7802 1.05201
\(226\) −16.4758 −1.09595
\(227\) 19.0185 1.26230 0.631150 0.775661i \(-0.282583\pi\)
0.631150 + 0.775661i \(0.282583\pi\)
\(228\) 100.200 6.63593
\(229\) −19.0552 −1.25920 −0.629600 0.776919i \(-0.716781\pi\)
−0.629600 + 0.776919i \(0.716781\pi\)
\(230\) −53.6568 −3.53802
\(231\) −10.7070 −0.704469
\(232\) 68.0713 4.46910
\(233\) 20.6972 1.35592 0.677960 0.735099i \(-0.262864\pi\)
0.677960 + 0.735099i \(0.262864\pi\)
\(234\) 4.27748 0.279628
\(235\) 7.88989 0.514679
\(236\) −10.1110 −0.658173
\(237\) 10.7707 0.699629
\(238\) −6.95335 −0.450719
\(239\) 29.0535 1.87931 0.939657 0.342118i \(-0.111144\pi\)
0.939657 + 0.342118i \(0.111144\pi\)
\(240\) 125.848 8.12346
\(241\) −10.1928 −0.656574 −0.328287 0.944578i \(-0.606471\pi\)
−0.328287 + 0.944578i \(0.606471\pi\)
\(242\) −33.2615 −2.13813
\(243\) 14.8135 0.950284
\(244\) −11.8525 −0.758779
\(245\) 22.9818 1.46826
\(246\) −0.513366 −0.0327310
\(247\) 8.54378 0.543627
\(248\) 23.9627 1.52163
\(249\) −28.0600 −1.77823
\(250\) 54.1962 3.42767
\(251\) 1.24427 0.0785375 0.0392687 0.999229i \(-0.487497\pi\)
0.0392687 + 0.999229i \(0.487497\pi\)
\(252\) −8.93875 −0.563088
\(253\) 24.2795 1.52644
\(254\) −0.665646 −0.0417663
\(255\) −20.2425 −1.26764
\(256\) 47.4173 2.96358
\(257\) 9.81600 0.612306 0.306153 0.951982i \(-0.400958\pi\)
0.306153 + 0.951982i \(0.400958\pi\)
\(258\) 31.1903 1.94183
\(259\) −6.99978 −0.434945
\(260\) 21.3323 1.32297
\(261\) −11.1375 −0.689392
\(262\) −53.0262 −3.27597
\(263\) 19.2664 1.18802 0.594010 0.804458i \(-0.297544\pi\)
0.594010 + 0.804458i \(0.297544\pi\)
\(264\) −98.1846 −6.04284
\(265\) 22.2761 1.36841
\(266\) −24.3580 −1.49348
\(267\) −23.5259 −1.43976
\(268\) −17.9232 −1.09484
\(269\) 17.9430 1.09401 0.547003 0.837130i \(-0.315768\pi\)
0.547003 + 0.837130i \(0.315768\pi\)
\(270\) 32.6431 1.98659
\(271\) 15.2724 0.927733 0.463867 0.885905i \(-0.346462\pi\)
0.463867 + 0.885905i \(0.346462\pi\)
\(272\) −36.9819 −2.24236
\(273\) −2.22517 −0.134673
\(274\) 18.8805 1.14061
\(275\) −48.5825 −2.92964
\(276\) 59.1772 3.56205
\(277\) −15.9268 −0.956947 −0.478473 0.878102i \(-0.658810\pi\)
−0.478473 + 0.878102i \(0.658810\pi\)
\(278\) 4.10632 0.246281
\(279\) −3.92064 −0.234723
\(280\) −38.6631 −2.31056
\(281\) 31.8854 1.90212 0.951061 0.309004i \(-0.0999958\pi\)
0.951061 + 0.309004i \(0.0999958\pi\)
\(282\) −11.8714 −0.706934
\(283\) 31.9100 1.89685 0.948427 0.316995i \(-0.102674\pi\)
0.948427 + 0.316995i \(0.102674\pi\)
\(284\) 3.44953 0.204692
\(285\) −70.9106 −4.20038
\(286\) −13.1691 −0.778705
\(287\) 0.0914736 0.00539952
\(288\) −34.9999 −2.06239
\(289\) −11.0515 −0.650089
\(290\) −75.7771 −4.44978
\(291\) −15.4172 −0.903770
\(292\) −27.5458 −1.61200
\(293\) 31.8826 1.86260 0.931302 0.364249i \(-0.118674\pi\)
0.931302 + 0.364249i \(0.118674\pi\)
\(294\) −34.5794 −2.01671
\(295\) 7.15546 0.416607
\(296\) −64.1889 −3.73090
\(297\) −14.7709 −0.857094
\(298\) 46.6513 2.70244
\(299\) 5.04586 0.291809
\(300\) −118.412 −6.83650
\(301\) −5.55762 −0.320336
\(302\) 56.9376 3.27639
\(303\) 4.92858 0.283139
\(304\) −129.549 −7.43017
\(305\) 8.38787 0.480288
\(306\) 10.4326 0.596391
\(307\) −25.3407 −1.44627 −0.723135 0.690707i \(-0.757299\pi\)
−0.723135 + 0.690707i \(0.757299\pi\)
\(308\) 27.5197 1.56808
\(309\) −4.47124 −0.254360
\(310\) −26.6753 −1.51505
\(311\) −26.9588 −1.52870 −0.764348 0.644804i \(-0.776939\pi\)
−0.764348 + 0.644804i \(0.776939\pi\)
\(312\) −20.4051 −1.15521
\(313\) 5.22590 0.295385 0.147693 0.989033i \(-0.452815\pi\)
0.147693 + 0.989033i \(0.452815\pi\)
\(314\) 39.7013 2.24047
\(315\) 6.32584 0.356421
\(316\) −27.6833 −1.55731
\(317\) −33.4451 −1.87846 −0.939232 0.343284i \(-0.888461\pi\)
−0.939232 + 0.343284i \(0.888461\pi\)
\(318\) −33.5175 −1.87957
\(319\) 34.2889 1.91981
\(320\) −120.303 −6.72513
\(321\) −31.4976 −1.75802
\(322\) −14.3855 −0.801674
\(323\) 20.8379 1.15945
\(324\) −61.7444 −3.43025
\(325\) −10.0966 −0.560058
\(326\) −6.97460 −0.386287
\(327\) 34.4099 1.90287
\(328\) 0.838825 0.0463164
\(329\) 2.11530 0.116620
\(330\) 109.299 6.01672
\(331\) −16.7547 −0.920923 −0.460462 0.887680i \(-0.652316\pi\)
−0.460462 + 0.887680i \(0.652316\pi\)
\(332\) 72.1213 3.95817
\(333\) 10.5022 0.575519
\(334\) 38.6354 2.11404
\(335\) 12.6840 0.693004
\(336\) 33.7402 1.84068
\(337\) −3.19255 −0.173909 −0.0869546 0.996212i \(-0.527713\pi\)
−0.0869546 + 0.996212i \(0.527713\pi\)
\(338\) −2.73685 −0.148865
\(339\) −12.8593 −0.698420
\(340\) 52.0284 2.82164
\(341\) 12.0705 0.653654
\(342\) 36.5459 1.97617
\(343\) 13.4534 0.726413
\(344\) −50.9641 −2.74780
\(345\) −41.8790 −2.25469
\(346\) 9.07210 0.487719
\(347\) 5.06081 0.271678 0.135839 0.990731i \(-0.456627\pi\)
0.135839 + 0.990731i \(0.456627\pi\)
\(348\) 83.5734 4.48000
\(349\) 35.2229 1.88544 0.942720 0.333584i \(-0.108258\pi\)
0.942720 + 0.333584i \(0.108258\pi\)
\(350\) 28.7850 1.53862
\(351\) −3.06974 −0.163850
\(352\) 107.754 5.74333
\(353\) −6.28219 −0.334367 −0.167184 0.985926i \(-0.553467\pi\)
−0.167184 + 0.985926i \(0.553467\pi\)
\(354\) −10.7664 −0.572227
\(355\) −2.44119 −0.129565
\(356\) 60.4675 3.20477
\(357\) −5.42707 −0.287231
\(358\) 20.1037 1.06251
\(359\) −30.4132 −1.60515 −0.802575 0.596551i \(-0.796537\pi\)
−0.802575 + 0.596551i \(0.796537\pi\)
\(360\) 58.0088 3.05733
\(361\) 53.9961 2.84190
\(362\) 18.6219 0.978746
\(363\) −25.9605 −1.36257
\(364\) 5.71924 0.299770
\(365\) 19.4938 1.02035
\(366\) −12.6207 −0.659696
\(367\) 7.29088 0.380581 0.190290 0.981728i \(-0.439057\pi\)
0.190290 + 0.981728i \(0.439057\pi\)
\(368\) −76.5104 −3.98838
\(369\) −0.137244 −0.00714464
\(370\) 71.4551 3.71477
\(371\) 5.97229 0.310066
\(372\) 29.4197 1.52534
\(373\) −12.4891 −0.646661 −0.323331 0.946286i \(-0.604803\pi\)
−0.323331 + 0.946286i \(0.604803\pi\)
\(374\) −32.1188 −1.66082
\(375\) 42.3000 2.18436
\(376\) 19.3976 1.00035
\(377\) 7.12604 0.367010
\(378\) 8.75169 0.450139
\(379\) −12.4662 −0.640344 −0.320172 0.947359i \(-0.603741\pi\)
−0.320172 + 0.947359i \(0.603741\pi\)
\(380\) 182.258 9.34965
\(381\) −0.519535 −0.0266166
\(382\) −69.3542 −3.54847
\(383\) −1.93620 −0.0989354 −0.0494677 0.998776i \(-0.515752\pi\)
−0.0494677 + 0.998776i \(0.515752\pi\)
\(384\) 85.3414 4.35506
\(385\) −19.4754 −0.992557
\(386\) −57.1564 −2.90919
\(387\) 8.33846 0.423868
\(388\) 39.6261 2.01171
\(389\) −34.5307 −1.75078 −0.875388 0.483421i \(-0.839394\pi\)
−0.875388 + 0.483421i \(0.839394\pi\)
\(390\) 22.7149 1.15022
\(391\) 12.3066 0.622372
\(392\) 56.5017 2.85377
\(393\) −41.3868 −2.08769
\(394\) 28.5187 1.43675
\(395\) 19.5911 0.985738
\(396\) −41.2897 −2.07489
\(397\) 27.6361 1.38702 0.693508 0.720449i \(-0.256064\pi\)
0.693508 + 0.720449i \(0.256064\pi\)
\(398\) −67.6219 −3.38958
\(399\) −19.0113 −0.951756
\(400\) 153.095 7.65473
\(401\) 2.15291 0.107511 0.0537557 0.998554i \(-0.482881\pi\)
0.0537557 + 0.998554i \(0.482881\pi\)
\(402\) −19.0849 −0.951869
\(403\) 2.50853 0.124959
\(404\) −12.6677 −0.630242
\(405\) 43.6957 2.17126
\(406\) −20.3160 −1.00827
\(407\) −32.3332 −1.60270
\(408\) −49.7670 −2.46383
\(409\) 8.39495 0.415103 0.207552 0.978224i \(-0.433450\pi\)
0.207552 + 0.978224i \(0.433450\pi\)
\(410\) −0.933781 −0.0461162
\(411\) 14.7362 0.726881
\(412\) 11.4922 0.566181
\(413\) 1.91840 0.0943982
\(414\) 21.5836 1.06077
\(415\) −51.0393 −2.50542
\(416\) 22.3939 1.09795
\(417\) 3.20497 0.156948
\(418\) −112.514 −5.50323
\(419\) −10.3148 −0.503913 −0.251957 0.967739i \(-0.581074\pi\)
−0.251957 + 0.967739i \(0.581074\pi\)
\(420\) −47.4679 −2.31619
\(421\) 17.6791 0.861628 0.430814 0.902441i \(-0.358226\pi\)
0.430814 + 0.902441i \(0.358226\pi\)
\(422\) −33.6843 −1.63973
\(423\) −3.17373 −0.154312
\(424\) 54.7667 2.65970
\(425\) −24.6251 −1.19449
\(426\) 3.67311 0.177963
\(427\) 2.24881 0.108828
\(428\) 80.9568 3.91319
\(429\) −10.2784 −0.496248
\(430\) 56.7333 2.73592
\(431\) 30.3188 1.46040 0.730202 0.683232i \(-0.239426\pi\)
0.730202 + 0.683232i \(0.239426\pi\)
\(432\) 46.5465 2.23947
\(433\) 4.82589 0.231917 0.115959 0.993254i \(-0.463006\pi\)
0.115959 + 0.993254i \(0.463006\pi\)
\(434\) −7.15172 −0.343293
\(435\) −59.1438 −2.83573
\(436\) −88.4422 −4.23561
\(437\) 43.1107 2.06226
\(438\) −29.3312 −1.40150
\(439\) −10.7155 −0.511422 −0.255711 0.966753i \(-0.582310\pi\)
−0.255711 + 0.966753i \(0.582310\pi\)
\(440\) −178.592 −8.51402
\(441\) −9.24450 −0.440214
\(442\) −6.67504 −0.317499
\(443\) −36.8263 −1.74967 −0.874836 0.484419i \(-0.839031\pi\)
−0.874836 + 0.484419i \(0.839031\pi\)
\(444\) −78.8067 −3.74000
\(445\) −42.7921 −2.02854
\(446\) 5.76403 0.272935
\(447\) 36.4112 1.72219
\(448\) −32.2535 −1.52384
\(449\) −15.6406 −0.738124 −0.369062 0.929405i \(-0.620321\pi\)
−0.369062 + 0.929405i \(0.620321\pi\)
\(450\) −43.1880 −2.03590
\(451\) 0.422533 0.0198963
\(452\) 33.0516 1.55462
\(453\) 44.4397 2.08796
\(454\) −52.0506 −2.44286
\(455\) −4.04744 −0.189747
\(456\) −174.336 −8.16404
\(457\) 1.26029 0.0589541 0.0294771 0.999565i \(-0.490616\pi\)
0.0294771 + 0.999565i \(0.490616\pi\)
\(458\) 52.1511 2.43686
\(459\) −7.48694 −0.349461
\(460\) 107.640 5.01873
\(461\) −14.3915 −0.670280 −0.335140 0.942168i \(-0.608784\pi\)
−0.335140 + 0.942168i \(0.608784\pi\)
\(462\) 29.3034 1.36332
\(463\) −1.00000 −0.0464739
\(464\) −108.052 −5.01620
\(465\) −20.8200 −0.965503
\(466\) −56.6451 −2.62403
\(467\) −0.539807 −0.0249793 −0.0124896 0.999922i \(-0.503976\pi\)
−0.0124896 + 0.999922i \(0.503976\pi\)
\(468\) −8.58096 −0.396655
\(469\) 3.40063 0.157026
\(470\) −21.5934 −0.996029
\(471\) 30.9867 1.42779
\(472\) 17.5920 0.809736
\(473\) −25.6716 −1.18038
\(474\) −29.4776 −1.35395
\(475\) −86.2630 −3.95802
\(476\) 13.9490 0.639350
\(477\) −8.96062 −0.410279
\(478\) −79.5149 −3.63693
\(479\) 12.7481 0.582476 0.291238 0.956651i \(-0.405933\pi\)
0.291238 + 0.956651i \(0.405933\pi\)
\(480\) −185.862 −8.48339
\(481\) −6.71960 −0.306388
\(482\) 27.8961 1.27063
\(483\) −11.2279 −0.510886
\(484\) 66.7251 3.03296
\(485\) −28.0429 −1.27336
\(486\) −40.5422 −1.83903
\(487\) −41.6084 −1.88546 −0.942728 0.333562i \(-0.891749\pi\)
−0.942728 + 0.333562i \(0.891749\pi\)
\(488\) 20.6219 0.933509
\(489\) −5.44366 −0.246171
\(490\) −62.8977 −2.84143
\(491\) −18.0035 −0.812489 −0.406244 0.913764i \(-0.633162\pi\)
−0.406244 + 0.913764i \(0.633162\pi\)
\(492\) 1.02985 0.0464293
\(493\) 17.3801 0.782759
\(494\) −23.3830 −1.05205
\(495\) 29.2202 1.31335
\(496\) −38.0369 −1.70791
\(497\) −0.654489 −0.0293578
\(498\) 76.7958 3.44130
\(499\) 3.67993 0.164736 0.0823681 0.996602i \(-0.473752\pi\)
0.0823681 + 0.996602i \(0.473752\pi\)
\(500\) −108.722 −4.86219
\(501\) 30.1548 1.34722
\(502\) −3.40537 −0.151989
\(503\) 8.84749 0.394490 0.197245 0.980354i \(-0.436801\pi\)
0.197245 + 0.980354i \(0.436801\pi\)
\(504\) 15.5523 0.692755
\(505\) 8.96477 0.398927
\(506\) −66.4494 −2.95403
\(507\) −2.13610 −0.0948675
\(508\) 1.33534 0.0592460
\(509\) −7.25431 −0.321541 −0.160771 0.986992i \(-0.551398\pi\)
−0.160771 + 0.986992i \(0.551398\pi\)
\(510\) 55.4006 2.45318
\(511\) 5.22634 0.231200
\(512\) −49.8698 −2.20395
\(513\) −26.2271 −1.15796
\(514\) −26.8649 −1.18496
\(515\) −8.13290 −0.358378
\(516\) −62.5702 −2.75450
\(517\) 9.77096 0.429726
\(518\) 19.1573 0.841724
\(519\) 7.08075 0.310810
\(520\) −37.1155 −1.62762
\(521\) −38.6762 −1.69443 −0.847217 0.531247i \(-0.821723\pi\)
−0.847217 + 0.531247i \(0.821723\pi\)
\(522\) 30.4815 1.33414
\(523\) 15.3399 0.670768 0.335384 0.942082i \(-0.391134\pi\)
0.335384 + 0.942082i \(0.391134\pi\)
\(524\) 106.375 4.64700
\(525\) 22.4666 0.980522
\(526\) −52.7293 −2.29911
\(527\) 6.11819 0.266512
\(528\) 155.852 6.78259
\(529\) 2.46068 0.106986
\(530\) −60.9663 −2.64821
\(531\) −2.87830 −0.124908
\(532\) 48.8639 2.11852
\(533\) 0.0878123 0.00380357
\(534\) 64.3866 2.78628
\(535\) −57.2921 −2.47695
\(536\) 31.1842 1.34695
\(537\) 15.6909 0.677111
\(538\) −49.1073 −2.11717
\(539\) 28.4610 1.22590
\(540\) −65.4845 −2.81800
\(541\) 5.15144 0.221478 0.110739 0.993850i \(-0.464678\pi\)
0.110739 + 0.993850i \(0.464678\pi\)
\(542\) −41.7983 −1.79539
\(543\) 14.5344 0.623729
\(544\) 54.6176 2.34171
\(545\) 62.5894 2.68104
\(546\) 6.08993 0.260625
\(547\) 24.4581 1.04575 0.522876 0.852409i \(-0.324859\pi\)
0.522876 + 0.852409i \(0.324859\pi\)
\(548\) −37.8757 −1.61797
\(549\) −3.37404 −0.144001
\(550\) 132.963 5.66956
\(551\) 60.8833 2.59372
\(552\) −102.961 −4.38231
\(553\) 5.25244 0.223356
\(554\) 43.5891 1.85192
\(555\) 55.7705 2.36733
\(556\) −8.23760 −0.349352
\(557\) −10.7088 −0.453747 −0.226874 0.973924i \(-0.572850\pi\)
−0.226874 + 0.973924i \(0.572850\pi\)
\(558\) 10.7302 0.454245
\(559\) −5.33517 −0.225654
\(560\) 61.3713 2.59341
\(561\) −25.0686 −1.05840
\(562\) −87.2653 −3.68107
\(563\) −31.4244 −1.32438 −0.662189 0.749337i \(-0.730373\pi\)
−0.662189 + 0.749337i \(0.730373\pi\)
\(564\) 23.8150 1.00279
\(565\) −23.3902 −0.984034
\(566\) −87.3328 −3.67087
\(567\) 11.7149 0.491982
\(568\) −6.00175 −0.251828
\(569\) −28.2959 −1.18623 −0.593114 0.805119i \(-0.702102\pi\)
−0.593114 + 0.805119i \(0.702102\pi\)
\(570\) 194.071 8.12875
\(571\) −13.4088 −0.561139 −0.280569 0.959834i \(-0.590523\pi\)
−0.280569 + 0.959834i \(0.590523\pi\)
\(572\) 26.4182 1.10460
\(573\) −54.1308 −2.26135
\(574\) −0.250349 −0.0104494
\(575\) −50.9459 −2.12459
\(576\) 48.3921 2.01634
\(577\) −0.176938 −0.00736601 −0.00368301 0.999993i \(-0.501172\pi\)
−0.00368301 + 0.999993i \(0.501172\pi\)
\(578\) 30.2463 1.25808
\(579\) −44.6104 −1.85395
\(580\) 152.015 6.31207
\(581\) −13.6838 −0.567699
\(582\) 42.1944 1.74901
\(583\) 27.5871 1.14254
\(584\) 47.9263 1.98320
\(585\) 6.07264 0.251073
\(586\) −87.2578 −3.60459
\(587\) −16.6182 −0.685905 −0.342952 0.939353i \(-0.611427\pi\)
−0.342952 + 0.939353i \(0.611427\pi\)
\(588\) 69.3689 2.86073
\(589\) 21.4323 0.883103
\(590\) −19.5834 −0.806235
\(591\) 22.2588 0.915603
\(592\) 101.889 4.18763
\(593\) −4.24910 −0.174490 −0.0872449 0.996187i \(-0.527806\pi\)
−0.0872449 + 0.996187i \(0.527806\pi\)
\(594\) 40.4257 1.65868
\(595\) −9.87151 −0.404692
\(596\) −93.5862 −3.83344
\(597\) −52.7787 −2.16009
\(598\) −13.8097 −0.564722
\(599\) 10.8399 0.442905 0.221452 0.975171i \(-0.428920\pi\)
0.221452 + 0.975171i \(0.428920\pi\)
\(600\) 206.021 8.41079
\(601\) 29.5201 1.20415 0.602075 0.798440i \(-0.294341\pi\)
0.602075 + 0.798440i \(0.294341\pi\)
\(602\) 15.2103 0.619927
\(603\) −5.10219 −0.207777
\(604\) −114.221 −4.64760
\(605\) −47.2205 −1.91979
\(606\) −13.4888 −0.547943
\(607\) 38.4945 1.56244 0.781221 0.624254i \(-0.214597\pi\)
0.781221 + 0.624254i \(0.214597\pi\)
\(608\) 191.328 7.75938
\(609\) −15.8566 −0.642543
\(610\) −22.9563 −0.929474
\(611\) 2.03063 0.0821506
\(612\) −20.9286 −0.845987
\(613\) −36.7654 −1.48494 −0.742471 0.669878i \(-0.766346\pi\)
−0.742471 + 0.669878i \(0.766346\pi\)
\(614\) 69.3535 2.79888
\(615\) −0.728813 −0.0293886
\(616\) −47.8809 −1.92918
\(617\) −17.1088 −0.688773 −0.344386 0.938828i \(-0.611913\pi\)
−0.344386 + 0.938828i \(0.611913\pi\)
\(618\) 12.2371 0.492248
\(619\) −42.9464 −1.72616 −0.863080 0.505067i \(-0.831468\pi\)
−0.863080 + 0.505067i \(0.831468\pi\)
\(620\) 53.5127 2.14912
\(621\) −15.4895 −0.621570
\(622\) 73.7822 2.95840
\(623\) −11.4727 −0.459643
\(624\) 32.3897 1.29663
\(625\) 26.4581 1.05832
\(626\) −14.3025 −0.571642
\(627\) −87.8167 −3.50706
\(628\) −79.6438 −3.17813
\(629\) −16.3888 −0.653464
\(630\) −17.3128 −0.689760
\(631\) 22.5845 0.899077 0.449538 0.893261i \(-0.351589\pi\)
0.449538 + 0.893261i \(0.351589\pi\)
\(632\) 48.1656 1.91592
\(633\) −26.2905 −1.04495
\(634\) 91.5340 3.63528
\(635\) −0.945001 −0.0375012
\(636\) 67.2388 2.66619
\(637\) 5.91487 0.234356
\(638\) −93.8435 −3.71530
\(639\) 0.981974 0.0388463
\(640\) 155.231 6.13603
\(641\) −37.6168 −1.48578 −0.742888 0.669416i \(-0.766544\pi\)
−0.742888 + 0.669416i \(0.766544\pi\)
\(642\) 86.2040 3.40220
\(643\) 29.2487 1.15346 0.576728 0.816936i \(-0.304329\pi\)
0.576728 + 0.816936i \(0.304329\pi\)
\(644\) 28.8585 1.13718
\(645\) 44.2801 1.74353
\(646\) −57.0300 −2.24382
\(647\) −4.90081 −0.192671 −0.0963353 0.995349i \(-0.530712\pi\)
−0.0963353 + 0.995349i \(0.530712\pi\)
\(648\) 107.428 4.22015
\(649\) 8.86143 0.347841
\(650\) 27.6328 1.08385
\(651\) −5.58189 −0.218772
\(652\) 13.9916 0.547953
\(653\) −3.49216 −0.136659 −0.0683293 0.997663i \(-0.521767\pi\)
−0.0683293 + 0.997663i \(0.521767\pi\)
\(654\) −94.1745 −3.68251
\(655\) −75.2799 −2.94143
\(656\) −1.33150 −0.0519863
\(657\) −7.84143 −0.305923
\(658\) −5.78925 −0.225689
\(659\) 8.49550 0.330938 0.165469 0.986215i \(-0.447086\pi\)
0.165469 + 0.986215i \(0.447086\pi\)
\(660\) −219.263 −8.53479
\(661\) −22.6587 −0.881321 −0.440661 0.897674i \(-0.645256\pi\)
−0.440661 + 0.897674i \(0.645256\pi\)
\(662\) 45.8551 1.78221
\(663\) −5.20985 −0.202334
\(664\) −125.482 −4.86965
\(665\) −34.5804 −1.34097
\(666\) −28.7430 −1.11377
\(667\) 35.9570 1.39226
\(668\) −77.5056 −2.99878
\(669\) 4.49881 0.173934
\(670\) −34.7143 −1.34113
\(671\) 10.3877 0.401011
\(672\) −49.8301 −1.92224
\(673\) −0.317076 −0.0122224 −0.00611119 0.999981i \(-0.501945\pi\)
−0.00611119 + 0.999981i \(0.501945\pi\)
\(674\) 8.73751 0.336556
\(675\) 30.9939 1.19295
\(676\) 5.49032 0.211166
\(677\) −11.9933 −0.460941 −0.230471 0.973079i \(-0.574027\pi\)
−0.230471 + 0.973079i \(0.574027\pi\)
\(678\) 35.1939 1.35161
\(679\) −7.51837 −0.288528
\(680\) −90.5230 −3.47140
\(681\) −40.6253 −1.55677
\(682\) −33.0351 −1.26498
\(683\) −26.6880 −1.02119 −0.510594 0.859822i \(-0.670575\pi\)
−0.510594 + 0.859822i \(0.670575\pi\)
\(684\) −73.3138 −2.80322
\(685\) 26.8041 1.02413
\(686\) −36.8198 −1.40579
\(687\) 40.7038 1.55294
\(688\) 80.8972 3.08418
\(689\) 5.73324 0.218419
\(690\) 114.616 4.36337
\(691\) −38.3242 −1.45792 −0.728960 0.684556i \(-0.759996\pi\)
−0.728960 + 0.684556i \(0.759996\pi\)
\(692\) −18.1993 −0.691835
\(693\) 7.83401 0.297590
\(694\) −13.8507 −0.525764
\(695\) 5.82965 0.221131
\(696\) −145.407 −5.51165
\(697\) 0.214170 0.00811227
\(698\) −96.3997 −3.64878
\(699\) −44.2114 −1.67223
\(700\) −57.7448 −2.18255
\(701\) −41.1072 −1.55260 −0.776298 0.630366i \(-0.782905\pi\)
−0.776298 + 0.630366i \(0.782905\pi\)
\(702\) 8.40140 0.317090
\(703\) −57.4108 −2.16529
\(704\) −148.985 −5.61508
\(705\) −16.8536 −0.634743
\(706\) 17.1934 0.647082
\(707\) 2.40348 0.0903922
\(708\) 21.5982 0.811711
\(709\) 44.6891 1.67833 0.839167 0.543874i \(-0.183043\pi\)
0.839167 + 0.543874i \(0.183043\pi\)
\(710\) 6.68115 0.250739
\(711\) −7.88059 −0.295545
\(712\) −105.206 −3.94276
\(713\) 12.6577 0.474034
\(714\) 14.8531 0.555862
\(715\) −18.6958 −0.699185
\(716\) −40.3296 −1.50719
\(717\) −62.0612 −2.31772
\(718\) 83.2364 3.10635
\(719\) 41.6442 1.55307 0.776533 0.630076i \(-0.216976\pi\)
0.776533 + 0.630076i \(0.216976\pi\)
\(720\) −92.0795 −3.43160
\(721\) −2.18045 −0.0812043
\(722\) −147.779 −5.49977
\(723\) 21.7728 0.809739
\(724\) −37.3570 −1.38836
\(725\) −71.9487 −2.67211
\(726\) 71.0498 2.63691
\(727\) 44.5943 1.65391 0.826955 0.562268i \(-0.190071\pi\)
0.826955 + 0.562268i \(0.190071\pi\)
\(728\) −9.95077 −0.368800
\(729\) 2.09508 0.0775956
\(730\) −53.3516 −1.97463
\(731\) −13.0122 −0.481274
\(732\) 25.3181 0.935786
\(733\) −17.6837 −0.653161 −0.326580 0.945169i \(-0.605896\pi\)
−0.326580 + 0.945169i \(0.605896\pi\)
\(734\) −19.9540 −0.736516
\(735\) −49.0915 −1.81077
\(736\) 112.996 4.16510
\(737\) 15.7081 0.578616
\(738\) 0.375616 0.0138266
\(739\) 35.7787 1.31614 0.658071 0.752956i \(-0.271373\pi\)
0.658071 + 0.752956i \(0.271373\pi\)
\(740\) −143.344 −5.26945
\(741\) −18.2504 −0.670444
\(742\) −16.3452 −0.600052
\(743\) −20.1591 −0.739566 −0.369783 0.929118i \(-0.620568\pi\)
−0.369783 + 0.929118i \(0.620568\pi\)
\(744\) −51.1867 −1.87660
\(745\) 66.2297 2.42647
\(746\) 34.1808 1.25145
\(747\) 20.5307 0.751179
\(748\) 64.4328 2.35590
\(749\) −15.3602 −0.561248
\(750\) −115.769 −4.22727
\(751\) 22.0890 0.806039 0.403019 0.915191i \(-0.367961\pi\)
0.403019 + 0.915191i \(0.367961\pi\)
\(752\) −30.7905 −1.12281
\(753\) −2.65788 −0.0968586
\(754\) −19.5029 −0.710253
\(755\) 80.8330 2.94181
\(756\) −17.5566 −0.638526
\(757\) −3.88367 −0.141154 −0.0705772 0.997506i \(-0.522484\pi\)
−0.0705772 + 0.997506i \(0.522484\pi\)
\(758\) 34.1180 1.23922
\(759\) −51.8635 −1.88253
\(760\) −317.107 −11.5027
\(761\) 0.756438 0.0274209 0.0137104 0.999906i \(-0.495636\pi\)
0.0137104 + 0.999906i \(0.495636\pi\)
\(762\) 1.42189 0.0515095
\(763\) 16.7804 0.607491
\(764\) 139.130 5.03355
\(765\) 14.8109 0.535488
\(766\) 5.29909 0.191464
\(767\) 1.84161 0.0664968
\(768\) −101.288 −3.65492
\(769\) 31.5753 1.13864 0.569318 0.822118i \(-0.307208\pi\)
0.569318 + 0.822118i \(0.307208\pi\)
\(770\) 53.3011 1.92084
\(771\) −20.9680 −0.755143
\(772\) 114.660 4.12671
\(773\) −6.87968 −0.247445 −0.123722 0.992317i \(-0.539483\pi\)
−0.123722 + 0.992317i \(0.539483\pi\)
\(774\) −22.8211 −0.820287
\(775\) −25.3276 −0.909794
\(776\) −68.9444 −2.47496
\(777\) 14.9522 0.536408
\(778\) 94.5052 3.38818
\(779\) 0.750249 0.0268804
\(780\) −45.5679 −1.63159
\(781\) −3.02320 −0.108179
\(782\) −33.6813 −1.20444
\(783\) −21.8751 −0.781751
\(784\) −89.6873 −3.20312
\(785\) 56.3629 2.01168
\(786\) 113.269 4.04018
\(787\) −19.5276 −0.696083 −0.348042 0.937479i \(-0.613153\pi\)
−0.348042 + 0.937479i \(0.613153\pi\)
\(788\) −57.2107 −2.03805
\(789\) −41.1551 −1.46516
\(790\) −53.6179 −1.90764
\(791\) −6.27098 −0.222971
\(792\) 71.8389 2.55268
\(793\) 2.15880 0.0766612
\(794\) −75.6357 −2.68421
\(795\) −47.5840 −1.68763
\(796\) 135.655 4.80816
\(797\) −19.2931 −0.683395 −0.341698 0.939810i \(-0.611002\pi\)
−0.341698 + 0.939810i \(0.611002\pi\)
\(798\) 52.0310 1.84188
\(799\) 4.95262 0.175211
\(800\) −226.102 −7.99390
\(801\) 17.2132 0.608199
\(802\) −5.89219 −0.208061
\(803\) 24.1414 0.851932
\(804\) 38.2858 1.35024
\(805\) −20.4228 −0.719809
\(806\) −6.86546 −0.241825
\(807\) −38.3281 −1.34921
\(808\) 22.0402 0.775372
\(809\) 24.6762 0.867569 0.433784 0.901017i \(-0.357178\pi\)
0.433784 + 0.901017i \(0.357178\pi\)
\(810\) −119.588 −4.20191
\(811\) −7.72451 −0.271244 −0.135622 0.990761i \(-0.543303\pi\)
−0.135622 + 0.990761i \(0.543303\pi\)
\(812\) 40.7556 1.43024
\(813\) −32.6234 −1.14415
\(814\) 88.4911 3.10161
\(815\) −9.90167 −0.346840
\(816\) 78.9970 2.76545
\(817\) −45.5825 −1.59473
\(818\) −22.9757 −0.803326
\(819\) 1.62809 0.0568901
\(820\) 1.87324 0.0654163
\(821\) 27.6647 0.965504 0.482752 0.875757i \(-0.339637\pi\)
0.482752 + 0.875757i \(0.339637\pi\)
\(822\) −40.3306 −1.40669
\(823\) −11.9498 −0.416544 −0.208272 0.978071i \(-0.566784\pi\)
−0.208272 + 0.978071i \(0.566784\pi\)
\(824\) −19.9950 −0.696560
\(825\) 103.777 3.61306
\(826\) −5.25036 −0.182683
\(827\) −30.1918 −1.04987 −0.524936 0.851142i \(-0.675911\pi\)
−0.524936 + 0.851142i \(0.675911\pi\)
\(828\) −43.2983 −1.50472
\(829\) −46.8562 −1.62738 −0.813692 0.581297i \(-0.802546\pi\)
−0.813692 + 0.581297i \(0.802546\pi\)
\(830\) 139.687 4.84860
\(831\) 34.0212 1.18018
\(832\) −30.9625 −1.07343
\(833\) 14.4261 0.499834
\(834\) −8.77152 −0.303733
\(835\) 54.8498 1.89815
\(836\) 225.711 7.80639
\(837\) −7.70053 −0.266169
\(838\) 28.2301 0.975194
\(839\) 40.2013 1.38790 0.693952 0.720021i \(-0.255868\pi\)
0.693952 + 0.720021i \(0.255868\pi\)
\(840\) 82.5882 2.84956
\(841\) 21.7804 0.751050
\(842\) −48.3851 −1.66746
\(843\) −68.1103 −2.34584
\(844\) 67.5734 2.32597
\(845\) −3.88543 −0.133663
\(846\) 8.68600 0.298631
\(847\) −12.6599 −0.435001
\(848\) −86.9332 −2.98530
\(849\) −68.1630 −2.33935
\(850\) 67.3951 2.31163
\(851\) −33.9062 −1.16229
\(852\) −7.36854 −0.252442
\(853\) 41.9603 1.43669 0.718347 0.695685i \(-0.244899\pi\)
0.718347 + 0.695685i \(0.244899\pi\)
\(854\) −6.15465 −0.210608
\(855\) 51.8833 1.77437
\(856\) −140.855 −4.81431
\(857\) −29.4403 −1.00566 −0.502830 0.864385i \(-0.667708\pi\)
−0.502830 + 0.864385i \(0.667708\pi\)
\(858\) 28.1305 0.960360
\(859\) −49.8410 −1.70055 −0.850277 0.526336i \(-0.823565\pi\)
−0.850277 + 0.526336i \(0.823565\pi\)
\(860\) −113.811 −3.88093
\(861\) −0.195397 −0.00665911
\(862\) −82.9778 −2.82623
\(863\) −12.5205 −0.426203 −0.213101 0.977030i \(-0.568356\pi\)
−0.213101 + 0.977030i \(0.568356\pi\)
\(864\) −68.7433 −2.33869
\(865\) 12.8794 0.437914
\(866\) −13.2077 −0.448816
\(867\) 23.6071 0.801740
\(868\) 14.3469 0.486965
\(869\) 24.2620 0.823031
\(870\) 161.867 5.48782
\(871\) 3.26451 0.110614
\(872\) 153.878 5.21098
\(873\) 11.2803 0.381781
\(874\) −117.987 −3.99098
\(875\) 20.6281 0.697357
\(876\) 58.8406 1.98804
\(877\) −12.6586 −0.427450 −0.213725 0.976894i \(-0.568560\pi\)
−0.213725 + 0.976894i \(0.568560\pi\)
\(878\) 29.3266 0.989726
\(879\) −68.1045 −2.29711
\(880\) 283.485 9.55629
\(881\) −35.2375 −1.18718 −0.593591 0.804767i \(-0.702290\pi\)
−0.593591 + 0.804767i \(0.702290\pi\)
\(882\) 25.3008 0.851921
\(883\) −45.9961 −1.54789 −0.773946 0.633252i \(-0.781720\pi\)
−0.773946 + 0.633252i \(0.781720\pi\)
\(884\) 13.3906 0.450376
\(885\) −15.2848 −0.513792
\(886\) 100.788 3.38604
\(887\) 20.9057 0.701946 0.350973 0.936386i \(-0.385851\pi\)
0.350973 + 0.936386i \(0.385851\pi\)
\(888\) 137.114 4.60124
\(889\) −0.253357 −0.00849733
\(890\) 117.115 3.92571
\(891\) 54.1135 1.81287
\(892\) −11.5631 −0.387161
\(893\) 17.3493 0.580571
\(894\) −99.6519 −3.33286
\(895\) 28.5407 0.954011
\(896\) 41.6178 1.39035
\(897\) −10.7785 −0.359882
\(898\) 42.8058 1.42845
\(899\) 17.8759 0.596194
\(900\) 86.6384 2.88795
\(901\) 13.9831 0.465845
\(902\) −1.15641 −0.0385042
\(903\) 11.8716 0.395063
\(904\) −57.5057 −1.91261
\(905\) 26.4371 0.878798
\(906\) −121.625 −4.04070
\(907\) −11.6071 −0.385406 −0.192703 0.981257i \(-0.561725\pi\)
−0.192703 + 0.981257i \(0.561725\pi\)
\(908\) 104.418 3.46522
\(909\) −3.60610 −0.119607
\(910\) 11.0772 0.367206
\(911\) −20.8849 −0.691948 −0.345974 0.938244i \(-0.612451\pi\)
−0.345974 + 0.938244i \(0.612451\pi\)
\(912\) 276.731 9.16346
\(913\) −63.2079 −2.09187
\(914\) −3.44923 −0.114090
\(915\) −17.9173 −0.592329
\(916\) −104.619 −3.45671
\(917\) −20.1828 −0.666493
\(918\) 20.4906 0.676291
\(919\) −22.5935 −0.745291 −0.372646 0.927974i \(-0.621549\pi\)
−0.372646 + 0.927974i \(0.621549\pi\)
\(920\) −187.280 −6.17443
\(921\) 54.1302 1.78365
\(922\) 39.3874 1.29715
\(923\) −0.628292 −0.0206805
\(924\) −58.7849 −1.93388
\(925\) 67.8451 2.23073
\(926\) 2.73685 0.0899383
\(927\) 3.27148 0.107449
\(928\) 159.580 5.23846
\(929\) 52.7057 1.72922 0.864610 0.502444i \(-0.167566\pi\)
0.864610 + 0.502444i \(0.167566\pi\)
\(930\) 56.9811 1.86848
\(931\) 50.5353 1.65623
\(932\) 113.635 3.72222
\(933\) 57.5868 1.88531
\(934\) 1.47737 0.0483409
\(935\) −45.5983 −1.49122
\(936\) 14.9298 0.487996
\(937\) −30.0882 −0.982940 −0.491470 0.870895i \(-0.663540\pi\)
−0.491470 + 0.870895i \(0.663540\pi\)
\(938\) −9.30699 −0.303884
\(939\) −11.1630 −0.364292
\(940\) 43.3180 1.41288
\(941\) 8.54893 0.278687 0.139344 0.990244i \(-0.455501\pi\)
0.139344 + 0.990244i \(0.455501\pi\)
\(942\) −84.8059 −2.76313
\(943\) 0.443088 0.0144289
\(944\) −27.9244 −0.908861
\(945\) 12.4246 0.404171
\(946\) 70.2593 2.28433
\(947\) −37.9812 −1.23422 −0.617111 0.786876i \(-0.711697\pi\)
−0.617111 + 0.786876i \(0.711697\pi\)
\(948\) 59.1344 1.92060
\(949\) 5.01715 0.162864
\(950\) 236.088 7.65972
\(951\) 71.4421 2.31667
\(952\) −24.2695 −0.786578
\(953\) 40.4039 1.30881 0.654405 0.756144i \(-0.272919\pi\)
0.654405 + 0.756144i \(0.272919\pi\)
\(954\) 24.5238 0.793989
\(955\) −98.4605 −3.18611
\(956\) 159.513 5.15902
\(957\) −73.2446 −2.36766
\(958\) −34.8896 −1.12723
\(959\) 7.18626 0.232057
\(960\) 256.979 8.29396
\(961\) −24.7073 −0.797009
\(962\) 18.3905 0.592934
\(963\) 23.0459 0.742643
\(964\) −55.9616 −1.80240
\(965\) −81.1436 −2.61210
\(966\) 30.7289 0.988687
\(967\) 20.1013 0.646413 0.323206 0.946328i \(-0.395239\pi\)
0.323206 + 0.946328i \(0.395239\pi\)
\(968\) −116.093 −3.73138
\(969\) −44.5118 −1.42992
\(970\) 76.7490 2.46426
\(971\) 42.9791 1.37927 0.689633 0.724159i \(-0.257772\pi\)
0.689633 + 0.724159i \(0.257772\pi\)
\(972\) 81.3307 2.60868
\(973\) 1.56294 0.0501057
\(974\) 113.876 3.64881
\(975\) 21.5673 0.690707
\(976\) −32.7339 −1.04779
\(977\) 36.1430 1.15632 0.578159 0.815924i \(-0.303771\pi\)
0.578159 + 0.815924i \(0.303771\pi\)
\(978\) 14.8984 0.476400
\(979\) −52.9943 −1.69371
\(980\) 126.178 4.03060
\(981\) −25.1767 −0.803831
\(982\) 49.2729 1.57236
\(983\) −11.6382 −0.371201 −0.185600 0.982625i \(-0.559423\pi\)
−0.185600 + 0.982625i \(0.559423\pi\)
\(984\) −1.79181 −0.0571210
\(985\) 40.4873 1.29003
\(986\) −47.5666 −1.51483
\(987\) −4.51849 −0.143825
\(988\) 46.9081 1.49235
\(989\) −26.9205 −0.856022
\(990\) −79.9712 −2.54165
\(991\) −49.3534 −1.56776 −0.783880 0.620912i \(-0.786763\pi\)
−0.783880 + 0.620912i \(0.786763\pi\)
\(992\) 56.1757 1.78358
\(993\) 35.7898 1.13575
\(994\) 1.79124 0.0568145
\(995\) −96.0012 −3.04344
\(996\) −154.058 −4.88152
\(997\) 28.2173 0.893651 0.446825 0.894621i \(-0.352554\pi\)
0.446825 + 0.894621i \(0.352554\pi\)
\(998\) −10.0714 −0.318805
\(999\) 20.6274 0.652622
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 \(a_p\))