Properties

Label 6019.2.a.c.1.19
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 1.19
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.14163 q^{2}\) \(-1.26927 q^{3}\) \(+2.58656 q^{4}\) \(+2.68002 q^{5}\) \(+2.71830 q^{6}\) \(-0.999709 q^{7}\) \(-1.25619 q^{8}\) \(-1.38895 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.14163 q^{2}\) \(-1.26927 q^{3}\) \(+2.58656 q^{4}\) \(+2.68002 q^{5}\) \(+2.71830 q^{6}\) \(-0.999709 q^{7}\) \(-1.25619 q^{8}\) \(-1.38895 q^{9}\) \(-5.73960 q^{10}\) \(+4.98528 q^{11}\) \(-3.28304 q^{12}\) \(-1.00000 q^{13}\) \(+2.14100 q^{14}\) \(-3.40167 q^{15}\) \(-2.48283 q^{16}\) \(-4.20263 q^{17}\) \(+2.97462 q^{18}\) \(-2.34524 q^{19}\) \(+6.93203 q^{20}\) \(+1.26890 q^{21}\) \(-10.6766 q^{22}\) \(+1.15596 q^{23}\) \(+1.59444 q^{24}\) \(+2.18250 q^{25}\) \(+2.14163 q^{26}\) \(+5.57077 q^{27}\) \(-2.58580 q^{28}\) \(+3.60732 q^{29}\) \(+7.28510 q^{30}\) \(-3.80668 q^{31}\) \(+7.82967 q^{32}\) \(-6.32767 q^{33}\) \(+9.00045 q^{34}\) \(-2.67924 q^{35}\) \(-3.59261 q^{36}\) \(+1.07597 q^{37}\) \(+5.02263 q^{38}\) \(+1.26927 q^{39}\) \(-3.36660 q^{40}\) \(+3.96277 q^{41}\) \(-2.71751 q^{42}\) \(+1.58411 q^{43}\) \(+12.8947 q^{44}\) \(-3.72242 q^{45}\) \(-2.47562 q^{46}\) \(+1.95607 q^{47}\) \(+3.15139 q^{48}\) \(-6.00058 q^{49}\) \(-4.67411 q^{50}\) \(+5.33427 q^{51}\) \(-2.58656 q^{52}\) \(+4.00730 q^{53}\) \(-11.9305 q^{54}\) \(+13.3607 q^{55}\) \(+1.25582 q^{56}\) \(+2.97674 q^{57}\) \(-7.72552 q^{58}\) \(-8.29874 q^{59}\) \(-8.79861 q^{60}\) \(-7.91055 q^{61}\) \(+8.15249 q^{62}\) \(+1.38855 q^{63}\) \(-11.8026 q^{64}\) \(-2.68002 q^{65}\) \(+13.5515 q^{66}\) \(-9.70831 q^{67}\) \(-10.8703 q^{68}\) \(-1.46722 q^{69}\) \(+5.73792 q^{70}\) \(+12.3016 q^{71}\) \(+1.74479 q^{72}\) \(+10.9163 q^{73}\) \(-2.30433 q^{74}\) \(-2.77019 q^{75}\) \(-6.06610 q^{76}\) \(-4.98383 q^{77}\) \(-2.71830 q^{78}\) \(-17.5605 q^{79}\) \(-6.65405 q^{80}\) \(-2.90395 q^{81}\) \(-8.48678 q^{82}\) \(+8.28510 q^{83}\) \(+3.28208 q^{84}\) \(-11.2631 q^{85}\) \(-3.39257 q^{86}\) \(-4.57866 q^{87}\) \(-6.26245 q^{88}\) \(+0.581140 q^{89}\) \(+7.97204 q^{90}\) \(+0.999709 q^{91}\) \(+2.98995 q^{92}\) \(+4.83171 q^{93}\) \(-4.18918 q^{94}\) \(-6.28529 q^{95}\) \(-9.93797 q^{96}\) \(+5.40300 q^{97}\) \(+12.8510 q^{98}\) \(-6.92433 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14163 −1.51436 −0.757179 0.653208i \(-0.773423\pi\)
−0.757179 + 0.653208i \(0.773423\pi\)
\(3\) −1.26927 −0.732813 −0.366407 0.930455i \(-0.619412\pi\)
−0.366407 + 0.930455i \(0.619412\pi\)
\(4\) 2.58656 1.29328
\(5\) 2.68002 1.19854 0.599271 0.800547i \(-0.295457\pi\)
0.599271 + 0.800547i \(0.295457\pi\)
\(6\) 2.71830 1.10974
\(7\) −0.999709 −0.377854 −0.188927 0.981991i \(-0.560501\pi\)
−0.188927 + 0.981991i \(0.560501\pi\)
\(8\) −1.25619 −0.444129
\(9\) −1.38895 −0.462985
\(10\) −5.73960 −1.81502
\(11\) 4.98528 1.50312 0.751560 0.659665i \(-0.229302\pi\)
0.751560 + 0.659665i \(0.229302\pi\)
\(12\) −3.28304 −0.947732
\(13\) −1.00000 −0.277350
\(14\) 2.14100 0.572207
\(15\) −3.40167 −0.878307
\(16\) −2.48283 −0.620709
\(17\) −4.20263 −1.01929 −0.509643 0.860386i \(-0.670223\pi\)
−0.509643 + 0.860386i \(0.670223\pi\)
\(18\) 2.97462 0.701124
\(19\) −2.34524 −0.538035 −0.269018 0.963135i \(-0.586699\pi\)
−0.269018 + 0.963135i \(0.586699\pi\)
\(20\) 6.93203 1.55005
\(21\) 1.26890 0.276897
\(22\) −10.6766 −2.27626
\(23\) 1.15596 0.241034 0.120517 0.992711i \(-0.461545\pi\)
0.120517 + 0.992711i \(0.461545\pi\)
\(24\) 1.59444 0.325464
\(25\) 2.18250 0.436501
\(26\) 2.14163 0.420007
\(27\) 5.57077 1.07209
\(28\) −2.58580 −0.488671
\(29\) 3.60732 0.669862 0.334931 0.942243i \(-0.391287\pi\)
0.334931 + 0.942243i \(0.391287\pi\)
\(30\) 7.28510 1.33007
\(31\) −3.80668 −0.683701 −0.341850 0.939754i \(-0.611054\pi\)
−0.341850 + 0.939754i \(0.611054\pi\)
\(32\) 7.82967 1.38410
\(33\) −6.32767 −1.10151
\(34\) 9.00045 1.54356
\(35\) −2.67924 −0.452874
\(36\) −3.59261 −0.598768
\(37\) 1.07597 0.176889 0.0884444 0.996081i \(-0.471810\pi\)
0.0884444 + 0.996081i \(0.471810\pi\)
\(38\) 5.02263 0.814778
\(39\) 1.26927 0.203246
\(40\) −3.36660 −0.532307
\(41\) 3.96277 0.618881 0.309441 0.950919i \(-0.399858\pi\)
0.309441 + 0.950919i \(0.399858\pi\)
\(42\) −2.71751 −0.419321
\(43\) 1.58411 0.241574 0.120787 0.992678i \(-0.461458\pi\)
0.120787 + 0.992678i \(0.461458\pi\)
\(44\) 12.8947 1.94395
\(45\) −3.72242 −0.554906
\(46\) −2.47562 −0.365011
\(47\) 1.95607 0.285323 0.142661 0.989772i \(-0.454434\pi\)
0.142661 + 0.989772i \(0.454434\pi\)
\(48\) 3.15139 0.454864
\(49\) −6.00058 −0.857226
\(50\) −4.67411 −0.661018
\(51\) 5.33427 0.746947
\(52\) −2.58656 −0.358691
\(53\) 4.00730 0.550445 0.275222 0.961381i \(-0.411249\pi\)
0.275222 + 0.961381i \(0.411249\pi\)
\(54\) −11.9305 −1.62353
\(55\) 13.3607 1.80155
\(56\) 1.25582 0.167816
\(57\) 2.97674 0.394279
\(58\) −7.72552 −1.01441
\(59\) −8.29874 −1.08040 −0.540202 0.841535i \(-0.681652\pi\)
−0.540202 + 0.841535i \(0.681652\pi\)
\(60\) −8.79861 −1.13590
\(61\) −7.91055 −1.01284 −0.506421 0.862286i \(-0.669032\pi\)
−0.506421 + 0.862286i \(0.669032\pi\)
\(62\) 8.15249 1.03537
\(63\) 1.38855 0.174941
\(64\) −11.8026 −1.47532
\(65\) −2.68002 −0.332416
\(66\) 13.5515 1.66807
\(67\) −9.70831 −1.18606 −0.593029 0.805181i \(-0.702068\pi\)
−0.593029 + 0.805181i \(0.702068\pi\)
\(68\) −10.8703 −1.31822
\(69\) −1.46722 −0.176633
\(70\) 5.73792 0.685813
\(71\) 12.3016 1.45993 0.729965 0.683485i \(-0.239537\pi\)
0.729965 + 0.683485i \(0.239537\pi\)
\(72\) 1.74479 0.205625
\(73\) 10.9163 1.27765 0.638826 0.769352i \(-0.279421\pi\)
0.638826 + 0.769352i \(0.279421\pi\)
\(74\) −2.30433 −0.267873
\(75\) −2.77019 −0.319874
\(76\) −6.06610 −0.695830
\(77\) −4.98383 −0.567960
\(78\) −2.71830 −0.307787
\(79\) −17.5605 −1.97571 −0.987856 0.155372i \(-0.950342\pi\)
−0.987856 + 0.155372i \(0.950342\pi\)
\(80\) −6.65405 −0.743945
\(81\) −2.90395 −0.322661
\(82\) −8.48678 −0.937208
\(83\) 8.28510 0.909407 0.454704 0.890643i \(-0.349745\pi\)
0.454704 + 0.890643i \(0.349745\pi\)
\(84\) 3.28208 0.358105
\(85\) −11.2631 −1.22166
\(86\) −3.39257 −0.365830
\(87\) −4.57866 −0.490884
\(88\) −6.26245 −0.667579
\(89\) 0.581140 0.0616007 0.0308004 0.999526i \(-0.490194\pi\)
0.0308004 + 0.999526i \(0.490194\pi\)
\(90\) 7.97204 0.840326
\(91\) 0.999709 0.104798
\(92\) 2.98995 0.311724
\(93\) 4.83171 0.501025
\(94\) −4.18918 −0.432081
\(95\) −6.28529 −0.644858
\(96\) −9.93797 −1.01429
\(97\) 5.40300 0.548591 0.274296 0.961645i \(-0.411555\pi\)
0.274296 + 0.961645i \(0.411555\pi\)
\(98\) 12.8510 1.29815
\(99\) −6.92433 −0.695921
\(100\) 5.64517 0.564517
\(101\) −1.66496 −0.165670 −0.0828348 0.996563i \(-0.526397\pi\)
−0.0828348 + 0.996563i \(0.526397\pi\)
\(102\) −11.4240 −1.13114
\(103\) −4.97468 −0.490170 −0.245085 0.969502i \(-0.578816\pi\)
−0.245085 + 0.969502i \(0.578816\pi\)
\(104\) 1.25619 0.123179
\(105\) 3.40068 0.331872
\(106\) −8.58213 −0.833570
\(107\) −3.44355 −0.332901 −0.166450 0.986050i \(-0.553231\pi\)
−0.166450 + 0.986050i \(0.553231\pi\)
\(108\) 14.4091 1.38652
\(109\) 1.01732 0.0974418 0.0487209 0.998812i \(-0.484486\pi\)
0.0487209 + 0.998812i \(0.484486\pi\)
\(110\) −28.6135 −2.72819
\(111\) −1.36570 −0.129627
\(112\) 2.48211 0.234537
\(113\) −11.0147 −1.03617 −0.518086 0.855328i \(-0.673355\pi\)
−0.518086 + 0.855328i \(0.673355\pi\)
\(114\) −6.37507 −0.597080
\(115\) 3.09798 0.288889
\(116\) 9.33053 0.866318
\(117\) 1.38895 0.128409
\(118\) 17.7728 1.63612
\(119\) 4.20140 0.385142
\(120\) 4.27313 0.390082
\(121\) 13.8531 1.25937
\(122\) 16.9414 1.53381
\(123\) −5.02983 −0.453525
\(124\) −9.84621 −0.884216
\(125\) −7.55094 −0.675377
\(126\) −2.97375 −0.264923
\(127\) −19.5738 −1.73690 −0.868449 0.495778i \(-0.834883\pi\)
−0.868449 + 0.495778i \(0.834883\pi\)
\(128\) 9.61730 0.850057
\(129\) −2.01066 −0.177029
\(130\) 5.73960 0.503396
\(131\) −2.15006 −0.187851 −0.0939257 0.995579i \(-0.529942\pi\)
−0.0939257 + 0.995579i \(0.529942\pi\)
\(132\) −16.3669 −1.42455
\(133\) 2.34456 0.203299
\(134\) 20.7916 1.79612
\(135\) 14.9298 1.28495
\(136\) 5.27928 0.452695
\(137\) 16.5736 1.41598 0.707991 0.706221i \(-0.249602\pi\)
0.707991 + 0.706221i \(0.249602\pi\)
\(138\) 3.14224 0.267485
\(139\) −13.2765 −1.12609 −0.563047 0.826425i \(-0.690371\pi\)
−0.563047 + 0.826425i \(0.690371\pi\)
\(140\) −6.93000 −0.585692
\(141\) −2.48279 −0.209088
\(142\) −26.3454 −2.21085
\(143\) −4.98528 −0.416890
\(144\) 3.44854 0.287379
\(145\) 9.66768 0.802857
\(146\) −23.3785 −1.93482
\(147\) 7.61636 0.628187
\(148\) 2.78307 0.228767
\(149\) −19.7151 −1.61512 −0.807562 0.589783i \(-0.799213\pi\)
−0.807562 + 0.589783i \(0.799213\pi\)
\(150\) 5.93270 0.484403
\(151\) 6.87972 0.559864 0.279932 0.960020i \(-0.409688\pi\)
0.279932 + 0.960020i \(0.409688\pi\)
\(152\) 2.94606 0.238957
\(153\) 5.83725 0.471914
\(154\) 10.6735 0.860095
\(155\) −10.2020 −0.819443
\(156\) 3.28304 0.262854
\(157\) −12.6695 −1.01114 −0.505569 0.862786i \(-0.668717\pi\)
−0.505569 + 0.862786i \(0.668717\pi\)
\(158\) 37.6080 2.99193
\(159\) −5.08634 −0.403373
\(160\) 20.9837 1.65891
\(161\) −1.15562 −0.0910756
\(162\) 6.21916 0.488623
\(163\) −14.5646 −1.14079 −0.570393 0.821372i \(-0.693209\pi\)
−0.570393 + 0.821372i \(0.693209\pi\)
\(164\) 10.2499 0.800386
\(165\) −16.9583 −1.32020
\(166\) −17.7436 −1.37717
\(167\) 20.0392 1.55068 0.775340 0.631545i \(-0.217579\pi\)
0.775340 + 0.631545i \(0.217579\pi\)
\(168\) −1.59398 −0.122978
\(169\) 1.00000 0.0769231
\(170\) 24.1214 1.85003
\(171\) 3.25743 0.249102
\(172\) 4.09739 0.312423
\(173\) −11.6673 −0.887050 −0.443525 0.896262i \(-0.646272\pi\)
−0.443525 + 0.896262i \(0.646272\pi\)
\(174\) 9.80577 0.743374
\(175\) −2.18187 −0.164934
\(176\) −12.3776 −0.932999
\(177\) 10.5333 0.791734
\(178\) −1.24458 −0.0932855
\(179\) 14.0555 1.05056 0.525279 0.850930i \(-0.323961\pi\)
0.525279 + 0.850930i \(0.323961\pi\)
\(180\) −9.62826 −0.717648
\(181\) 8.12199 0.603703 0.301851 0.953355i \(-0.402395\pi\)
0.301851 + 0.953355i \(0.402395\pi\)
\(182\) −2.14100 −0.158702
\(183\) 10.0406 0.742224
\(184\) −1.45210 −0.107050
\(185\) 2.88363 0.212009
\(186\) −10.3477 −0.758731
\(187\) −20.9513 −1.53211
\(188\) 5.05950 0.369002
\(189\) −5.56914 −0.405096
\(190\) 13.4607 0.976545
\(191\) −2.92464 −0.211620 −0.105810 0.994386i \(-0.533743\pi\)
−0.105810 + 0.994386i \(0.533743\pi\)
\(192\) 14.9806 1.08113
\(193\) 23.8904 1.71967 0.859835 0.510572i \(-0.170566\pi\)
0.859835 + 0.510572i \(0.170566\pi\)
\(194\) −11.5712 −0.830764
\(195\) 3.40167 0.243599
\(196\) −15.5209 −1.10863
\(197\) 18.6836 1.33115 0.665574 0.746332i \(-0.268187\pi\)
0.665574 + 0.746332i \(0.268187\pi\)
\(198\) 14.8293 1.05387
\(199\) −18.0215 −1.27751 −0.638754 0.769411i \(-0.720550\pi\)
−0.638754 + 0.769411i \(0.720550\pi\)
\(200\) −2.74163 −0.193863
\(201\) 12.3225 0.869159
\(202\) 3.56572 0.250883
\(203\) −3.60627 −0.253110
\(204\) 13.7974 0.966010
\(205\) 10.6203 0.741755
\(206\) 10.6539 0.742293
\(207\) −1.60557 −0.111595
\(208\) 2.48283 0.172154
\(209\) −11.6917 −0.808732
\(210\) −7.28297 −0.502573
\(211\) −18.1423 −1.24897 −0.624483 0.781039i \(-0.714690\pi\)
−0.624483 + 0.781039i \(0.714690\pi\)
\(212\) 10.3651 0.711879
\(213\) −15.6140 −1.06986
\(214\) 7.37480 0.504131
\(215\) 4.24544 0.289537
\(216\) −6.99792 −0.476148
\(217\) 3.80557 0.258339
\(218\) −2.17872 −0.147562
\(219\) −13.8557 −0.936280
\(220\) 34.5581 2.32991
\(221\) 4.20263 0.282699
\(222\) 2.92482 0.196301
\(223\) 0.177211 0.0118669 0.00593346 0.999982i \(-0.498111\pi\)
0.00593346 + 0.999982i \(0.498111\pi\)
\(224\) −7.82739 −0.522990
\(225\) −3.03140 −0.202093
\(226\) 23.5893 1.56914
\(227\) 29.1108 1.93215 0.966076 0.258257i \(-0.0831483\pi\)
0.966076 + 0.258257i \(0.0831483\pi\)
\(228\) 7.69952 0.509913
\(229\) 12.8940 0.852061 0.426031 0.904709i \(-0.359912\pi\)
0.426031 + 0.904709i \(0.359912\pi\)
\(230\) −6.63472 −0.437481
\(231\) 6.32583 0.416209
\(232\) −4.53146 −0.297505
\(233\) −9.52911 −0.624273 −0.312136 0.950037i \(-0.601045\pi\)
−0.312136 + 0.950037i \(0.601045\pi\)
\(234\) −2.97462 −0.194457
\(235\) 5.24232 0.341971
\(236\) −21.4652 −1.39726
\(237\) 22.2890 1.44783
\(238\) −8.99783 −0.583242
\(239\) −10.9179 −0.706222 −0.353111 0.935581i \(-0.614876\pi\)
−0.353111 + 0.935581i \(0.614876\pi\)
\(240\) 8.44578 0.545173
\(241\) −11.9107 −0.767237 −0.383619 0.923492i \(-0.625322\pi\)
−0.383619 + 0.923492i \(0.625322\pi\)
\(242\) −29.6681 −1.90714
\(243\) −13.0264 −0.835645
\(244\) −20.4611 −1.30989
\(245\) −16.0817 −1.02742
\(246\) 10.7720 0.686798
\(247\) 2.34524 0.149224
\(248\) 4.78191 0.303651
\(249\) −10.5160 −0.666426
\(250\) 16.1713 1.02276
\(251\) 25.1095 1.58490 0.792448 0.609939i \(-0.208806\pi\)
0.792448 + 0.609939i \(0.208806\pi\)
\(252\) 3.59156 0.226247
\(253\) 5.76277 0.362302
\(254\) 41.9198 2.63028
\(255\) 14.2959 0.895246
\(256\) 3.00846 0.188029
\(257\) −18.8644 −1.17673 −0.588364 0.808596i \(-0.700228\pi\)
−0.588364 + 0.808596i \(0.700228\pi\)
\(258\) 4.30608 0.268085
\(259\) −1.07566 −0.0668382
\(260\) −6.93203 −0.429906
\(261\) −5.01040 −0.310136
\(262\) 4.60462 0.284474
\(263\) 7.41681 0.457340 0.228670 0.973504i \(-0.426562\pi\)
0.228670 + 0.973504i \(0.426562\pi\)
\(264\) 7.94874 0.489211
\(265\) 10.7396 0.659731
\(266\) −5.02116 −0.307867
\(267\) −0.737623 −0.0451418
\(268\) −25.1111 −1.53390
\(269\) −20.5498 −1.25294 −0.626470 0.779445i \(-0.715501\pi\)
−0.626470 + 0.779445i \(0.715501\pi\)
\(270\) −31.9740 −1.94587
\(271\) 6.58675 0.400116 0.200058 0.979784i \(-0.435887\pi\)
0.200058 + 0.979784i \(0.435887\pi\)
\(272\) 10.4344 0.632680
\(273\) −1.26890 −0.0767973
\(274\) −35.4945 −2.14430
\(275\) 10.8804 0.656113
\(276\) −3.79505 −0.228435
\(277\) 13.3562 0.802497 0.401248 0.915969i \(-0.368576\pi\)
0.401248 + 0.915969i \(0.368576\pi\)
\(278\) 28.4332 1.70531
\(279\) 5.28731 0.316543
\(280\) 3.36562 0.201134
\(281\) −25.0117 −1.49207 −0.746037 0.665904i \(-0.768046\pi\)
−0.746037 + 0.665904i \(0.768046\pi\)
\(282\) 5.31720 0.316634
\(283\) 27.3269 1.62441 0.812207 0.583369i \(-0.198266\pi\)
0.812207 + 0.583369i \(0.198266\pi\)
\(284\) 31.8188 1.88810
\(285\) 7.97773 0.472560
\(286\) 10.6766 0.631321
\(287\) −3.96162 −0.233847
\(288\) −10.8751 −0.640819
\(289\) 0.662067 0.0389451
\(290\) −20.7045 −1.21581
\(291\) −6.85786 −0.402015
\(292\) 28.2355 1.65236
\(293\) −26.2963 −1.53625 −0.768125 0.640300i \(-0.778810\pi\)
−0.768125 + 0.640300i \(0.778810\pi\)
\(294\) −16.3114 −0.951299
\(295\) −22.2408 −1.29491
\(296\) −1.35162 −0.0785615
\(297\) 27.7719 1.61149
\(298\) 42.2224 2.44588
\(299\) −1.15596 −0.0668507
\(300\) −7.16525 −0.413686
\(301\) −1.58365 −0.0912799
\(302\) −14.7338 −0.847834
\(303\) 2.11328 0.121405
\(304\) 5.82285 0.333963
\(305\) −21.2004 −1.21393
\(306\) −12.5012 −0.714647
\(307\) −2.75894 −0.157461 −0.0787306 0.996896i \(-0.525087\pi\)
−0.0787306 + 0.996896i \(0.525087\pi\)
\(308\) −12.8910 −0.734531
\(309\) 6.31421 0.359203
\(310\) 21.8488 1.24093
\(311\) −2.04105 −0.115738 −0.0578688 0.998324i \(-0.518431\pi\)
−0.0578688 + 0.998324i \(0.518431\pi\)
\(312\) −1.59444 −0.0902674
\(313\) 3.31670 0.187471 0.0937356 0.995597i \(-0.470119\pi\)
0.0937356 + 0.995597i \(0.470119\pi\)
\(314\) 27.1334 1.53122
\(315\) 3.72134 0.209674
\(316\) −45.4213 −2.55515
\(317\) 27.1691 1.52597 0.762983 0.646418i \(-0.223734\pi\)
0.762983 + 0.646418i \(0.223734\pi\)
\(318\) 10.8930 0.610851
\(319\) 17.9835 1.00688
\(320\) −31.6311 −1.76823
\(321\) 4.37080 0.243954
\(322\) 2.47490 0.137921
\(323\) 9.85617 0.548412
\(324\) −7.51122 −0.417290
\(325\) −2.18250 −0.121064
\(326\) 31.1919 1.72756
\(327\) −1.29126 −0.0714066
\(328\) −4.97798 −0.274863
\(329\) −1.95550 −0.107810
\(330\) 36.3183 1.99926
\(331\) −4.21982 −0.231942 −0.115971 0.993253i \(-0.536998\pi\)
−0.115971 + 0.993253i \(0.536998\pi\)
\(332\) 21.4299 1.17612
\(333\) −1.49448 −0.0818968
\(334\) −42.9164 −2.34828
\(335\) −26.0185 −1.42154
\(336\) −3.15047 −0.171872
\(337\) −4.64781 −0.253182 −0.126591 0.991955i \(-0.540404\pi\)
−0.126591 + 0.991955i \(0.540404\pi\)
\(338\) −2.14163 −0.116489
\(339\) 13.9806 0.759321
\(340\) −29.1327 −1.57994
\(341\) −18.9774 −1.02768
\(342\) −6.97620 −0.377230
\(343\) 12.9968 0.701761
\(344\) −1.98994 −0.107290
\(345\) −3.93218 −0.211701
\(346\) 24.9870 1.34331
\(347\) 13.0431 0.700191 0.350095 0.936714i \(-0.386149\pi\)
0.350095 + 0.936714i \(0.386149\pi\)
\(348\) −11.8430 −0.634850
\(349\) 19.4208 1.03957 0.519787 0.854296i \(-0.326011\pi\)
0.519787 + 0.854296i \(0.326011\pi\)
\(350\) 4.67274 0.249769
\(351\) −5.57077 −0.297346
\(352\) 39.0332 2.08047
\(353\) −33.5958 −1.78812 −0.894061 0.447945i \(-0.852156\pi\)
−0.894061 + 0.447945i \(0.852156\pi\)
\(354\) −22.5585 −1.19897
\(355\) 32.9685 1.74979
\(356\) 1.50315 0.0796669
\(357\) −5.33271 −0.282237
\(358\) −30.1016 −1.59092
\(359\) 0.295661 0.0156044 0.00780219 0.999970i \(-0.497516\pi\)
0.00780219 + 0.999970i \(0.497516\pi\)
\(360\) 4.67606 0.246450
\(361\) −13.4998 −0.710518
\(362\) −17.3943 −0.914222
\(363\) −17.5833 −0.922883
\(364\) 2.58580 0.135533
\(365\) 29.2558 1.53132
\(366\) −21.5033 −1.12399
\(367\) −4.54975 −0.237495 −0.118747 0.992924i \(-0.537888\pi\)
−0.118747 + 0.992924i \(0.537888\pi\)
\(368\) −2.87005 −0.149612
\(369\) −5.50411 −0.286533
\(370\) −6.17565 −0.321057
\(371\) −4.00613 −0.207988
\(372\) 12.4975 0.647965
\(373\) −4.79406 −0.248227 −0.124113 0.992268i \(-0.539609\pi\)
−0.124113 + 0.992268i \(0.539609\pi\)
\(374\) 44.8698 2.32016
\(375\) 9.58418 0.494925
\(376\) −2.45719 −0.126720
\(377\) −3.60732 −0.185786
\(378\) 11.9270 0.613460
\(379\) 27.5185 1.41353 0.706765 0.707449i \(-0.250154\pi\)
0.706765 + 0.707449i \(0.250154\pi\)
\(380\) −16.2573 −0.833981
\(381\) 24.8445 1.27282
\(382\) 6.26349 0.320468
\(383\) −6.54855 −0.334615 −0.167308 0.985905i \(-0.553507\pi\)
−0.167308 + 0.985905i \(0.553507\pi\)
\(384\) −12.2070 −0.622933
\(385\) −13.3568 −0.680724
\(386\) −51.1643 −2.60419
\(387\) −2.20025 −0.111845
\(388\) 13.9752 0.709482
\(389\) −34.1179 −1.72985 −0.864924 0.501903i \(-0.832633\pi\)
−0.864924 + 0.501903i \(0.832633\pi\)
\(390\) −7.28510 −0.368895
\(391\) −4.85805 −0.245682
\(392\) 7.53785 0.380719
\(393\) 2.72900 0.137660
\(394\) −40.0132 −2.01583
\(395\) −47.0625 −2.36797
\(396\) −17.9102 −0.900020
\(397\) 13.7482 0.690003 0.345001 0.938602i \(-0.387878\pi\)
0.345001 + 0.938602i \(0.387878\pi\)
\(398\) 38.5953 1.93461
\(399\) −2.97588 −0.148980
\(400\) −5.41880 −0.270940
\(401\) 18.4953 0.923612 0.461806 0.886981i \(-0.347202\pi\)
0.461806 + 0.886981i \(0.347202\pi\)
\(402\) −26.3901 −1.31622
\(403\) 3.80668 0.189624
\(404\) −4.30651 −0.214257
\(405\) −7.78263 −0.386722
\(406\) 7.72327 0.383299
\(407\) 5.36403 0.265885
\(408\) −6.70083 −0.331741
\(409\) −7.68862 −0.380178 −0.190089 0.981767i \(-0.560878\pi\)
−0.190089 + 0.981767i \(0.560878\pi\)
\(410\) −22.7447 −1.12328
\(411\) −21.0364 −1.03765
\(412\) −12.8673 −0.633926
\(413\) 8.29632 0.408235
\(414\) 3.43853 0.168994
\(415\) 22.2042 1.08996
\(416\) −7.82967 −0.383881
\(417\) 16.8514 0.825217
\(418\) 25.0392 1.22471
\(419\) 0.773742 0.0377998 0.0188999 0.999821i \(-0.493984\pi\)
0.0188999 + 0.999821i \(0.493984\pi\)
\(420\) 8.79605 0.429203
\(421\) 11.4552 0.558294 0.279147 0.960248i \(-0.409948\pi\)
0.279147 + 0.960248i \(0.409948\pi\)
\(422\) 38.8539 1.89138
\(423\) −2.71690 −0.132100
\(424\) −5.03392 −0.244469
\(425\) −9.17225 −0.444919
\(426\) 33.4394 1.62014
\(427\) 7.90825 0.382707
\(428\) −8.90694 −0.430533
\(429\) 6.32767 0.305503
\(430\) −9.09215 −0.438462
\(431\) 20.4471 0.984902 0.492451 0.870340i \(-0.336101\pi\)
0.492451 + 0.870340i \(0.336101\pi\)
\(432\) −13.8313 −0.665458
\(433\) −18.9558 −0.910956 −0.455478 0.890247i \(-0.650532\pi\)
−0.455478 + 0.890247i \(0.650532\pi\)
\(434\) −8.15011 −0.391218
\(435\) −12.2709 −0.588344
\(436\) 2.63136 0.126019
\(437\) −2.71100 −0.129685
\(438\) 29.6737 1.41786
\(439\) −12.5710 −0.599983 −0.299991 0.953942i \(-0.596984\pi\)
−0.299991 + 0.953942i \(0.596984\pi\)
\(440\) −16.7835 −0.800121
\(441\) 8.33453 0.396883
\(442\) −9.00045 −0.428108
\(443\) 22.6978 1.07841 0.539203 0.842176i \(-0.318726\pi\)
0.539203 + 0.842176i \(0.318726\pi\)
\(444\) −3.53246 −0.167643
\(445\) 1.55747 0.0738310
\(446\) −0.379519 −0.0179708
\(447\) 25.0238 1.18358
\(448\) 11.7991 0.557456
\(449\) −38.8029 −1.83122 −0.915611 0.402064i \(-0.868293\pi\)
−0.915611 + 0.402064i \(0.868293\pi\)
\(450\) 6.49212 0.306041
\(451\) 19.7556 0.930253
\(452\) −28.4901 −1.34006
\(453\) −8.73222 −0.410276
\(454\) −62.3444 −2.92597
\(455\) 2.67924 0.125605
\(456\) −3.73935 −0.175111
\(457\) −31.5600 −1.47631 −0.738157 0.674629i \(-0.764304\pi\)
−0.738157 + 0.674629i \(0.764304\pi\)
\(458\) −27.6142 −1.29033
\(459\) −23.4119 −1.09277
\(460\) 8.01312 0.373613
\(461\) −23.7704 −1.10710 −0.553550 0.832816i \(-0.686727\pi\)
−0.553550 + 0.832816i \(0.686727\pi\)
\(462\) −13.5476 −0.630289
\(463\) −1.00000 −0.0464739
\(464\) −8.95637 −0.415789
\(465\) 12.9491 0.600499
\(466\) 20.4078 0.945372
\(467\) 18.1742 0.841002 0.420501 0.907292i \(-0.361854\pi\)
0.420501 + 0.907292i \(0.361854\pi\)
\(468\) 3.59261 0.166068
\(469\) 9.70548 0.448157
\(470\) −11.2271 −0.517866
\(471\) 16.0810 0.740975
\(472\) 10.4248 0.479839
\(473\) 7.89723 0.363115
\(474\) −47.7347 −2.19253
\(475\) −5.11850 −0.234853
\(476\) 10.8672 0.498096
\(477\) −5.56595 −0.254848
\(478\) 23.3821 1.06947
\(479\) −20.2342 −0.924526 −0.462263 0.886743i \(-0.652962\pi\)
−0.462263 + 0.886743i \(0.652962\pi\)
\(480\) −26.6340 −1.21567
\(481\) −1.07597 −0.0490602
\(482\) 25.5083 1.16187
\(483\) 1.46679 0.0667414
\(484\) 35.8317 1.62872
\(485\) 14.4801 0.657509
\(486\) 27.8977 1.26546
\(487\) −37.6508 −1.70612 −0.853061 0.521811i \(-0.825257\pi\)
−0.853061 + 0.521811i \(0.825257\pi\)
\(488\) 9.93713 0.449833
\(489\) 18.4864 0.835984
\(490\) 34.4409 1.55588
\(491\) 22.5907 1.01950 0.509752 0.860322i \(-0.329737\pi\)
0.509752 + 0.860322i \(0.329737\pi\)
\(492\) −13.0099 −0.586534
\(493\) −15.1602 −0.682781
\(494\) −5.02263 −0.225979
\(495\) −18.5573 −0.834090
\(496\) 9.45137 0.424379
\(497\) −12.2980 −0.551641
\(498\) 22.5214 1.00921
\(499\) −24.6952 −1.10551 −0.552755 0.833344i \(-0.686423\pi\)
−0.552755 + 0.833344i \(0.686423\pi\)
\(500\) −19.5309 −0.873451
\(501\) −25.4351 −1.13636
\(502\) −53.7751 −2.40010
\(503\) 4.30220 0.191826 0.0959128 0.995390i \(-0.469423\pi\)
0.0959128 + 0.995390i \(0.469423\pi\)
\(504\) −1.74428 −0.0776963
\(505\) −4.46212 −0.198562
\(506\) −12.3417 −0.548655
\(507\) −1.26927 −0.0563703
\(508\) −50.6289 −2.24629
\(509\) −7.67043 −0.339986 −0.169993 0.985445i \(-0.554374\pi\)
−0.169993 + 0.985445i \(0.554374\pi\)
\(510\) −30.6165 −1.35572
\(511\) −10.9131 −0.482766
\(512\) −25.6776 −1.13480
\(513\) −13.0648 −0.576825
\(514\) 40.4004 1.78199
\(515\) −13.3322 −0.587489
\(516\) −5.20069 −0.228948
\(517\) 9.75158 0.428874
\(518\) 2.30366 0.101217
\(519\) 14.8090 0.650042
\(520\) 3.36660 0.147635
\(521\) 5.24240 0.229674 0.114837 0.993384i \(-0.463365\pi\)
0.114837 + 0.993384i \(0.463365\pi\)
\(522\) 10.7304 0.469657
\(523\) 39.5954 1.73139 0.865693 0.500574i \(-0.166878\pi\)
0.865693 + 0.500574i \(0.166878\pi\)
\(524\) −5.56125 −0.242944
\(525\) 2.76938 0.120866
\(526\) −15.8840 −0.692577
\(527\) 15.9981 0.696887
\(528\) 15.7106 0.683714
\(529\) −21.6638 −0.941903
\(530\) −23.0003 −0.999068
\(531\) 11.5266 0.500210
\(532\) 6.06434 0.262922
\(533\) −3.96277 −0.171647
\(534\) 1.57971 0.0683608
\(535\) −9.22879 −0.398995
\(536\) 12.1954 0.526763
\(537\) −17.8402 −0.769862
\(538\) 44.0099 1.89740
\(539\) −29.9146 −1.28851
\(540\) 38.6167 1.66180
\(541\) −20.9979 −0.902769 −0.451385 0.892330i \(-0.649070\pi\)
−0.451385 + 0.892330i \(0.649070\pi\)
\(542\) −14.1063 −0.605919
\(543\) −10.3090 −0.442401
\(544\) −32.9052 −1.41080
\(545\) 2.72644 0.116788
\(546\) 2.71751 0.116299
\(547\) −7.75944 −0.331770 −0.165885 0.986145i \(-0.553048\pi\)
−0.165885 + 0.986145i \(0.553048\pi\)
\(548\) 42.8687 1.83126
\(549\) 10.9874 0.468930
\(550\) −23.3017 −0.993590
\(551\) −8.46003 −0.360409
\(552\) 1.84310 0.0784477
\(553\) 17.5554 0.746531
\(554\) −28.6040 −1.21527
\(555\) −3.66010 −0.155363
\(556\) −34.3403 −1.45635
\(557\) −7.90723 −0.335040 −0.167520 0.985869i \(-0.553576\pi\)
−0.167520 + 0.985869i \(0.553576\pi\)
\(558\) −11.3234 −0.479359
\(559\) −1.58411 −0.0670007
\(560\) 6.65211 0.281103
\(561\) 26.5928 1.12275
\(562\) 53.5657 2.25953
\(563\) −10.7445 −0.452826 −0.226413 0.974031i \(-0.572700\pi\)
−0.226413 + 0.974031i \(0.572700\pi\)
\(564\) −6.42187 −0.270409
\(565\) −29.5195 −1.24190
\(566\) −58.5239 −2.45994
\(567\) 2.90310 0.121919
\(568\) −15.4531 −0.648397
\(569\) 10.2061 0.427860 0.213930 0.976849i \(-0.431374\pi\)
0.213930 + 0.976849i \(0.431374\pi\)
\(570\) −17.0853 −0.715625
\(571\) −17.3170 −0.724693 −0.362346 0.932044i \(-0.618024\pi\)
−0.362346 + 0.932044i \(0.618024\pi\)
\(572\) −12.8947 −0.539156
\(573\) 3.71216 0.155078
\(574\) 8.48430 0.354128
\(575\) 2.52288 0.105211
\(576\) 16.3932 0.683050
\(577\) −14.0713 −0.585796 −0.292898 0.956144i \(-0.594620\pi\)
−0.292898 + 0.956144i \(0.594620\pi\)
\(578\) −1.41790 −0.0589768
\(579\) −30.3234 −1.26020
\(580\) 25.0060 1.03832
\(581\) −8.28268 −0.343624
\(582\) 14.6870 0.608795
\(583\) 19.9775 0.827385
\(584\) −13.7129 −0.567442
\(585\) 3.72242 0.153903
\(586\) 56.3169 2.32643
\(587\) 3.58274 0.147876 0.0739378 0.997263i \(-0.476443\pi\)
0.0739378 + 0.997263i \(0.476443\pi\)
\(588\) 19.7002 0.812421
\(589\) 8.92759 0.367855
\(590\) 47.6314 1.96095
\(591\) −23.7145 −0.975483
\(592\) −2.67146 −0.109796
\(593\) −39.9394 −1.64011 −0.820057 0.572282i \(-0.806058\pi\)
−0.820057 + 0.572282i \(0.806058\pi\)
\(594\) −59.4769 −2.44037
\(595\) 11.2598 0.461608
\(596\) −50.9942 −2.08881
\(597\) 22.8741 0.936176
\(598\) 2.47562 0.101236
\(599\) −45.3703 −1.85378 −0.926891 0.375331i \(-0.877529\pi\)
−0.926891 + 0.375331i \(0.877529\pi\)
\(600\) 3.47987 0.142065
\(601\) −36.6776 −1.49611 −0.748055 0.663637i \(-0.769012\pi\)
−0.748055 + 0.663637i \(0.769012\pi\)
\(602\) 3.39158 0.138230
\(603\) 13.4844 0.549127
\(604\) 17.7948 0.724060
\(605\) 37.1265 1.50941
\(606\) −4.52586 −0.183850
\(607\) −4.12365 −0.167374 −0.0836869 0.996492i \(-0.526670\pi\)
−0.0836869 + 0.996492i \(0.526670\pi\)
\(608\) −18.3625 −0.744697
\(609\) 4.57732 0.185483
\(610\) 45.4034 1.83833
\(611\) −1.95607 −0.0791343
\(612\) 15.0984 0.610316
\(613\) −37.1717 −1.50135 −0.750676 0.660671i \(-0.770272\pi\)
−0.750676 + 0.660671i \(0.770272\pi\)
\(614\) 5.90862 0.238453
\(615\) −13.4800 −0.543568
\(616\) 6.26062 0.252248
\(617\) −42.8425 −1.72477 −0.862387 0.506249i \(-0.831032\pi\)
−0.862387 + 0.506249i \(0.831032\pi\)
\(618\) −13.5227 −0.543962
\(619\) 19.3446 0.777526 0.388763 0.921338i \(-0.372903\pi\)
0.388763 + 0.921338i \(0.372903\pi\)
\(620\) −26.3880 −1.05977
\(621\) 6.43956 0.258411
\(622\) 4.37117 0.175268
\(623\) −0.580970 −0.0232761
\(624\) −3.15139 −0.126156
\(625\) −31.1492 −1.24597
\(626\) −7.10313 −0.283898
\(627\) 14.8399 0.592649
\(628\) −32.7704 −1.30768
\(629\) −4.52191 −0.180300
\(630\) −7.96971 −0.317521
\(631\) 10.4181 0.414740 0.207370 0.978263i \(-0.433510\pi\)
0.207370 + 0.978263i \(0.433510\pi\)
\(632\) 22.0593 0.877471
\(633\) 23.0274 0.915259
\(634\) −58.1860 −2.31086
\(635\) −52.4583 −2.08174
\(636\) −13.1561 −0.521674
\(637\) 6.00058 0.237752
\(638\) −38.5139 −1.52478
\(639\) −17.0863 −0.675925
\(640\) 25.7746 1.01883
\(641\) −45.9029 −1.81306 −0.906528 0.422145i \(-0.861277\pi\)
−0.906528 + 0.422145i \(0.861277\pi\)
\(642\) −9.36061 −0.369434
\(643\) 15.6251 0.616193 0.308097 0.951355i \(-0.400308\pi\)
0.308097 + 0.951355i \(0.400308\pi\)
\(644\) −2.98908 −0.117786
\(645\) −5.38861 −0.212176
\(646\) −21.1082 −0.830492
\(647\) −25.3089 −0.994994 −0.497497 0.867466i \(-0.665747\pi\)
−0.497497 + 0.867466i \(0.665747\pi\)
\(648\) 3.64790 0.143303
\(649\) −41.3716 −1.62398
\(650\) 4.67411 0.183334
\(651\) −4.83030 −0.189314
\(652\) −37.6722 −1.47536
\(653\) −16.5402 −0.647267 −0.323633 0.946183i \(-0.604904\pi\)
−0.323633 + 0.946183i \(0.604904\pi\)
\(654\) 2.76539 0.108135
\(655\) −5.76220 −0.225148
\(656\) −9.83891 −0.384145
\(657\) −15.1622 −0.591533
\(658\) 4.18796 0.163264
\(659\) 26.9563 1.05007 0.525034 0.851081i \(-0.324053\pi\)
0.525034 + 0.851081i \(0.324053\pi\)
\(660\) −43.8636 −1.70739
\(661\) −11.6477 −0.453042 −0.226521 0.974006i \(-0.572735\pi\)
−0.226521 + 0.974006i \(0.572735\pi\)
\(662\) 9.03728 0.351244
\(663\) −5.33427 −0.207166
\(664\) −10.4076 −0.403894
\(665\) 6.28346 0.243662
\(666\) 3.20061 0.124021
\(667\) 4.16990 0.161459
\(668\) 51.8325 2.00546
\(669\) −0.224928 −0.00869623
\(670\) 55.7218 2.15272
\(671\) −39.4363 −1.52242
\(672\) 9.93507 0.383254
\(673\) −18.3980 −0.709190 −0.354595 0.935020i \(-0.615381\pi\)
−0.354595 + 0.935020i \(0.615381\pi\)
\(674\) 9.95387 0.383409
\(675\) 12.1582 0.467970
\(676\) 2.58656 0.0994830
\(677\) 6.59599 0.253504 0.126752 0.991934i \(-0.459545\pi\)
0.126752 + 0.991934i \(0.459545\pi\)
\(678\) −29.9412 −1.14988
\(679\) −5.40142 −0.207288
\(680\) 14.1486 0.542573
\(681\) −36.9495 −1.41591
\(682\) 40.6425 1.55628
\(683\) −20.7130 −0.792561 −0.396281 0.918129i \(-0.629699\pi\)
−0.396281 + 0.918129i \(0.629699\pi\)
\(684\) 8.42554 0.322159
\(685\) 44.4177 1.69711
\(686\) −27.8343 −1.06272
\(687\) −16.3660 −0.624402
\(688\) −3.93308 −0.149947
\(689\) −4.00730 −0.152666
\(690\) 8.42125 0.320592
\(691\) 14.3143 0.544541 0.272271 0.962221i \(-0.412225\pi\)
0.272271 + 0.962221i \(0.412225\pi\)
\(692\) −30.1782 −1.14720
\(693\) 6.92231 0.262957
\(694\) −27.9334 −1.06034
\(695\) −35.5812 −1.34967
\(696\) 5.75165 0.218016
\(697\) −16.6541 −0.630818
\(698\) −41.5922 −1.57429
\(699\) 12.0950 0.457475
\(700\) −5.64353 −0.213305
\(701\) −46.8481 −1.76943 −0.884715 0.466133i \(-0.845647\pi\)
−0.884715 + 0.466133i \(0.845647\pi\)
\(702\) 11.9305 0.450287
\(703\) −2.52342 −0.0951725
\(704\) −58.8391 −2.21758
\(705\) −6.65391 −0.250601
\(706\) 71.9495 2.70786
\(707\) 1.66447 0.0625990
\(708\) 27.2451 1.02393
\(709\) 24.0278 0.902382 0.451191 0.892427i \(-0.350999\pi\)
0.451191 + 0.892427i \(0.350999\pi\)
\(710\) −70.6061 −2.64980
\(711\) 24.3907 0.914724
\(712\) −0.730020 −0.0273587
\(713\) −4.40036 −0.164795
\(714\) 11.4207 0.427408
\(715\) −13.3607 −0.499660
\(716\) 36.3554 1.35866
\(717\) 13.8578 0.517529
\(718\) −0.633195 −0.0236306
\(719\) −10.7621 −0.401357 −0.200678 0.979657i \(-0.564315\pi\)
−0.200678 + 0.979657i \(0.564315\pi\)
\(720\) 9.24216 0.344435
\(721\) 4.97323 0.185213
\(722\) 28.9116 1.07598
\(723\) 15.1179 0.562242
\(724\) 21.0080 0.780756
\(725\) 7.87299 0.292395
\(726\) 37.6568 1.39757
\(727\) 19.1990 0.712052 0.356026 0.934476i \(-0.384131\pi\)
0.356026 + 0.934476i \(0.384131\pi\)
\(728\) −1.25582 −0.0465438
\(729\) 25.2459 0.935032
\(730\) −62.6549 −2.31896
\(731\) −6.65742 −0.246233
\(732\) 25.9707 0.959903
\(733\) 30.3036 1.11929 0.559645 0.828733i \(-0.310938\pi\)
0.559645 + 0.828733i \(0.310938\pi\)
\(734\) 9.74385 0.359652
\(735\) 20.4120 0.752908
\(736\) 9.05076 0.333615
\(737\) −48.3987 −1.78279
\(738\) 11.7877 0.433913
\(739\) −23.5109 −0.864862 −0.432431 0.901667i \(-0.642344\pi\)
−0.432431 + 0.901667i \(0.642344\pi\)
\(740\) 7.45867 0.274186
\(741\) −2.97674 −0.109353
\(742\) 8.57963 0.314968
\(743\) 28.7470 1.05462 0.527312 0.849672i \(-0.323200\pi\)
0.527312 + 0.849672i \(0.323200\pi\)
\(744\) −6.06953 −0.222520
\(745\) −52.8369 −1.93579
\(746\) 10.2671 0.375904
\(747\) −11.5076 −0.421042
\(748\) −54.1917 −1.98145
\(749\) 3.44255 0.125788
\(750\) −20.5257 −0.749494
\(751\) −8.01252 −0.292381 −0.146190 0.989256i \(-0.546701\pi\)
−0.146190 + 0.989256i \(0.546701\pi\)
\(752\) −4.85661 −0.177102
\(753\) −31.8707 −1.16143
\(754\) 7.72552 0.281347
\(755\) 18.4378 0.671020
\(756\) −14.4049 −0.523902
\(757\) −3.73847 −0.135877 −0.0679385 0.997690i \(-0.521642\pi\)
−0.0679385 + 0.997690i \(0.521642\pi\)
\(758\) −58.9343 −2.14059
\(759\) −7.31451 −0.265500
\(760\) 7.89550 0.286400
\(761\) 30.7600 1.11505 0.557524 0.830161i \(-0.311751\pi\)
0.557524 + 0.830161i \(0.311751\pi\)
\(762\) −53.2076 −1.92751
\(763\) −1.01703 −0.0368188
\(764\) −7.56476 −0.273683
\(765\) 15.6440 0.565608
\(766\) 14.0245 0.506727
\(767\) 8.29874 0.299650
\(768\) −3.81854 −0.137790
\(769\) −38.0363 −1.37162 −0.685811 0.727779i \(-0.740553\pi\)
−0.685811 + 0.727779i \(0.740553\pi\)
\(770\) 28.6052 1.03086
\(771\) 23.9440 0.862322
\(772\) 61.7939 2.22401
\(773\) 20.1392 0.724357 0.362179 0.932109i \(-0.382033\pi\)
0.362179 + 0.932109i \(0.382033\pi\)
\(774\) 4.71212 0.169374
\(775\) −8.30810 −0.298436
\(776\) −6.78717 −0.243645
\(777\) 1.36530 0.0489799
\(778\) 73.0678 2.61961
\(779\) −9.29367 −0.332980
\(780\) 8.79861 0.315041
\(781\) 61.3269 2.19445
\(782\) 10.4041 0.372051
\(783\) 20.0955 0.718155
\(784\) 14.8985 0.532088
\(785\) −33.9546 −1.21189
\(786\) −5.84450 −0.208467
\(787\) 27.1517 0.967853 0.483927 0.875109i \(-0.339210\pi\)
0.483927 + 0.875109i \(0.339210\pi\)
\(788\) 48.3261 1.72155
\(789\) −9.41394 −0.335145
\(790\) 100.790 3.58596
\(791\) 11.0115 0.391522
\(792\) 8.69825 0.309079
\(793\) 7.91055 0.280912
\(794\) −29.4435 −1.04491
\(795\) −13.6315 −0.483459
\(796\) −46.6136 −1.65218
\(797\) −25.7658 −0.912673 −0.456336 0.889807i \(-0.650839\pi\)
−0.456336 + 0.889807i \(0.650839\pi\)
\(798\) 6.37321 0.225609
\(799\) −8.22065 −0.290826
\(800\) 17.0883 0.604163
\(801\) −0.807176 −0.0285202
\(802\) −39.6100 −1.39868
\(803\) 54.4206 1.92046
\(804\) 31.8728 1.12407
\(805\) −3.09708 −0.109158
\(806\) −8.15249 −0.287159
\(807\) 26.0832 0.918171
\(808\) 2.09150 0.0735787
\(809\) 7.24088 0.254576 0.127288 0.991866i \(-0.459373\pi\)
0.127288 + 0.991866i \(0.459373\pi\)
\(810\) 16.6675 0.585635
\(811\) −43.9551 −1.54347 −0.771736 0.635943i \(-0.780611\pi\)
−0.771736 + 0.635943i \(0.780611\pi\)
\(812\) −9.32782 −0.327342
\(813\) −8.36036 −0.293211
\(814\) −11.4877 −0.402645
\(815\) −39.0334 −1.36728
\(816\) −13.2441 −0.463636
\(817\) −3.71512 −0.129976
\(818\) 16.4661 0.575725
\(819\) −1.38855 −0.0485198
\(820\) 27.4701 0.959296
\(821\) 30.2176 1.05460 0.527301 0.849679i \(-0.323204\pi\)
0.527301 + 0.849679i \(0.323204\pi\)
\(822\) 45.0521 1.57137
\(823\) −2.32273 −0.0809654 −0.0404827 0.999180i \(-0.512890\pi\)
−0.0404827 + 0.999180i \(0.512890\pi\)
\(824\) 6.24913 0.217699
\(825\) −13.8102 −0.480808
\(826\) −17.7676 −0.618214
\(827\) −36.3428 −1.26376 −0.631881 0.775065i \(-0.717717\pi\)
−0.631881 + 0.775065i \(0.717717\pi\)
\(828\) −4.15290 −0.144323
\(829\) 49.7278 1.72712 0.863559 0.504248i \(-0.168230\pi\)
0.863559 + 0.504248i \(0.168230\pi\)
\(830\) −47.5531 −1.65059
\(831\) −16.9526 −0.588080
\(832\) 11.8026 0.409180
\(833\) 25.2182 0.873759
\(834\) −36.0894 −1.24967
\(835\) 53.7054 1.85855
\(836\) −30.2413 −1.04592
\(837\) −21.2061 −0.732992
\(838\) −1.65706 −0.0572424
\(839\) −9.22564 −0.318505 −0.159252 0.987238i \(-0.550908\pi\)
−0.159252 + 0.987238i \(0.550908\pi\)
\(840\) −4.27188 −0.147394
\(841\) −15.9873 −0.551285
\(842\) −24.5328 −0.845456
\(843\) 31.7466 1.09341
\(844\) −46.9260 −1.61526
\(845\) 2.68002 0.0921955
\(846\) 5.81857 0.200047
\(847\) −13.8490 −0.475858
\(848\) −9.94946 −0.341666
\(849\) −34.6852 −1.19039
\(850\) 19.6435 0.673767
\(851\) 1.24378 0.0426362
\(852\) −40.3866 −1.38362
\(853\) −7.90291 −0.270590 −0.135295 0.990805i \(-0.543198\pi\)
−0.135295 + 0.990805i \(0.543198\pi\)
\(854\) −16.9365 −0.579555
\(855\) 8.72998 0.298559
\(856\) 4.32574 0.147851
\(857\) 17.9659 0.613704 0.306852 0.951757i \(-0.400724\pi\)
0.306852 + 0.951757i \(0.400724\pi\)
\(858\) −13.5515 −0.462641
\(859\) 19.5492 0.667012 0.333506 0.942748i \(-0.391768\pi\)
0.333506 + 0.942748i \(0.391768\pi\)
\(860\) 10.9811 0.374452
\(861\) 5.02836 0.171366
\(862\) −43.7900 −1.49149
\(863\) −46.5262 −1.58377 −0.791885 0.610670i \(-0.790900\pi\)
−0.791885 + 0.610670i \(0.790900\pi\)
\(864\) 43.6173 1.48389
\(865\) −31.2687 −1.06317
\(866\) 40.5961 1.37951
\(867\) −0.840341 −0.0285395
\(868\) 9.84334 0.334105
\(869\) −87.5442 −2.96973
\(870\) 26.2797 0.890964
\(871\) 9.70831 0.328953
\(872\) −1.27795 −0.0432767
\(873\) −7.50452 −0.253989
\(874\) 5.80594 0.196389
\(875\) 7.54874 0.255194
\(876\) −35.8385 −1.21087
\(877\) −19.4183 −0.655711 −0.327855 0.944728i \(-0.606326\pi\)
−0.327855 + 0.944728i \(0.606326\pi\)
\(878\) 26.9224 0.908588
\(879\) 33.3772 1.12578
\(880\) −33.1723 −1.11824
\(881\) 14.9427 0.503432 0.251716 0.967801i \(-0.419005\pi\)
0.251716 + 0.967801i \(0.419005\pi\)
\(882\) −17.8494 −0.601022
\(883\) 4.85666 0.163440 0.0817199 0.996655i \(-0.473959\pi\)
0.0817199 + 0.996655i \(0.473959\pi\)
\(884\) 10.8703 0.365609
\(885\) 28.2296 0.948926
\(886\) −48.6102 −1.63309
\(887\) 13.8584 0.465321 0.232660 0.972558i \(-0.425257\pi\)
0.232660 + 0.972558i \(0.425257\pi\)
\(888\) 1.71557 0.0575709
\(889\) 19.5681 0.656294
\(890\) −3.33551 −0.111806
\(891\) −14.4770 −0.484998
\(892\) 0.458366 0.0153472
\(893\) −4.58747 −0.153514
\(894\) −53.5916 −1.79237
\(895\) 37.6690 1.25914
\(896\) −9.61450 −0.321198
\(897\) 1.46722 0.0489891
\(898\) 83.1013 2.77313
\(899\) −13.7319 −0.457985
\(900\) −7.84089 −0.261363
\(901\) −16.8412 −0.561061
\(902\) −42.3090 −1.40874
\(903\) 2.01008 0.0668911
\(904\) 13.8365 0.460194
\(905\) 21.7671 0.723563
\(906\) 18.7011 0.621304
\(907\) 1.34919 0.0447992 0.0223996 0.999749i \(-0.492869\pi\)
0.0223996 + 0.999749i \(0.492869\pi\)
\(908\) 75.2968 2.49881
\(909\) 2.31255 0.0767025
\(910\) −5.73792 −0.190210
\(911\) 4.69373 0.155510 0.0777551 0.996972i \(-0.475225\pi\)
0.0777551 + 0.996972i \(0.475225\pi\)
\(912\) −7.39077 −0.244733
\(913\) 41.3036 1.36695
\(914\) 67.5897 2.23567
\(915\) 26.9091 0.889586
\(916\) 33.3511 1.10195
\(917\) 2.14943 0.0709805
\(918\) 50.1394 1.65485
\(919\) −42.8558 −1.41368 −0.706841 0.707372i \(-0.749881\pi\)
−0.706841 + 0.707372i \(0.749881\pi\)
\(920\) −3.89165 −0.128304
\(921\) 3.50184 0.115390
\(922\) 50.9074 1.67654
\(923\) −12.3016 −0.404912
\(924\) 16.3621 0.538274
\(925\) 2.34832 0.0772122
\(926\) 2.14163 0.0703782
\(927\) 6.90960 0.226941
\(928\) 28.2441 0.927159
\(929\) −3.71897 −0.122015 −0.0610077 0.998137i \(-0.519431\pi\)
−0.0610077 + 0.998137i \(0.519431\pi\)
\(930\) −27.7321 −0.909370
\(931\) 14.0728 0.461218
\(932\) −24.6476 −0.807359
\(933\) 2.59065 0.0848141
\(934\) −38.9223 −1.27358
\(935\) −56.1499 −1.83630
\(936\) −1.74479 −0.0570301
\(937\) −18.2530 −0.596300 −0.298150 0.954519i \(-0.596370\pi\)
−0.298150 + 0.954519i \(0.596370\pi\)
\(938\) −20.7855 −0.678670
\(939\) −4.20979 −0.137381
\(940\) 13.5596 0.442264
\(941\) 6.55980 0.213843 0.106922 0.994267i \(-0.465901\pi\)
0.106922 + 0.994267i \(0.465901\pi\)
\(942\) −34.4396 −1.12210
\(943\) 4.58079 0.149171
\(944\) 20.6044 0.670616
\(945\) −14.9254 −0.485524
\(946\) −16.9129 −0.549886
\(947\) −47.2682 −1.53601 −0.768006 0.640443i \(-0.778751\pi\)
−0.768006 + 0.640443i \(0.778751\pi\)
\(948\) 57.6519 1.87245
\(949\) −10.9163 −0.354357
\(950\) 10.9619 0.355651
\(951\) −34.4849 −1.11825
\(952\) −5.27774 −0.171053
\(953\) 32.0332 1.03766 0.518829 0.854878i \(-0.326368\pi\)
0.518829 + 0.854878i \(0.326368\pi\)
\(954\) 11.9202 0.385930
\(955\) −7.83810 −0.253635
\(956\) −28.2398 −0.913342
\(957\) −22.8259 −0.737857
\(958\) 43.3342 1.40006
\(959\) −16.5688 −0.535035
\(960\) 40.1484 1.29578
\(961\) −16.5092 −0.532554
\(962\) 2.30433 0.0742946
\(963\) 4.78293 0.154128
\(964\) −30.8078 −0.992252
\(965\) 64.0268 2.06109
\(966\) −3.14132 −0.101070
\(967\) 31.1878 1.00293 0.501466 0.865177i \(-0.332794\pi\)
0.501466 + 0.865177i \(0.332794\pi\)
\(968\) −17.4020 −0.559322
\(969\) −12.5101 −0.401884
\(970\) −31.0110 −0.995704
\(971\) −17.4453 −0.559847 −0.279924 0.960022i \(-0.590309\pi\)
−0.279924 + 0.960022i \(0.590309\pi\)
\(972\) −33.6936 −1.08072
\(973\) 13.2726 0.425500
\(974\) 80.6340 2.58368
\(975\) 2.77019 0.0887170
\(976\) 19.6406 0.628680
\(977\) 19.5591 0.625750 0.312875 0.949794i \(-0.398708\pi\)
0.312875 + 0.949794i \(0.398708\pi\)
\(978\) −39.5909 −1.26598
\(979\) 2.89715 0.0925932
\(980\) −41.5962 −1.32874
\(981\) −1.41301 −0.0451140
\(982\) −48.3808 −1.54389
\(983\) 34.0565 1.08623 0.543116 0.839658i \(-0.317244\pi\)
0.543116 + 0.839658i \(0.317244\pi\)
\(984\) 6.31841 0.201423
\(985\) 50.0723 1.59544
\(986\) 32.4675 1.03398
\(987\) 2.48206 0.0790049
\(988\) 6.06610 0.192988
\(989\) 1.83116 0.0582275
\(990\) 39.7429 1.26311
\(991\) 16.6178 0.527881 0.263941 0.964539i \(-0.414978\pi\)
0.263941 + 0.964539i \(0.414978\pi\)
\(992\) −29.8051 −0.946313
\(993\) 5.35609 0.169970
\(994\) 26.3377 0.835381
\(995\) −48.2979 −1.53115
\(996\) −27.2003 −0.861874
\(997\) 9.54068 0.302156 0.151078 0.988522i \(-0.451725\pi\)
0.151078 + 0.988522i \(0.451725\pi\)
\(998\) 52.8879 1.67414
\(999\) 5.99400 0.189642
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 \(a_p\))