Properties

Label 6026.2.a.i.1.3
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.94225 q^{3}\) \(+1.00000 q^{4}\) \(+2.28313 q^{5}\) \(+2.94225 q^{6}\) \(-4.71427 q^{7}\) \(-1.00000 q^{8}\) \(+5.65684 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.94225 q^{3}\) \(+1.00000 q^{4}\) \(+2.28313 q^{5}\) \(+2.94225 q^{6}\) \(-4.71427 q^{7}\) \(-1.00000 q^{8}\) \(+5.65684 q^{9}\) \(-2.28313 q^{10}\) \(+1.43615 q^{11}\) \(-2.94225 q^{12}\) \(+1.73070 q^{13}\) \(+4.71427 q^{14}\) \(-6.71755 q^{15}\) \(+1.00000 q^{16}\) \(+7.47107 q^{17}\) \(-5.65684 q^{18}\) \(-7.14393 q^{19}\) \(+2.28313 q^{20}\) \(+13.8706 q^{21}\) \(-1.43615 q^{22}\) \(+1.00000 q^{23}\) \(+2.94225 q^{24}\) \(+0.212702 q^{25}\) \(-1.73070 q^{26}\) \(-7.81709 q^{27}\) \(-4.71427 q^{28}\) \(-5.24580 q^{29}\) \(+6.71755 q^{30}\) \(+3.25473 q^{31}\) \(-1.00000 q^{32}\) \(-4.22552 q^{33}\) \(-7.47107 q^{34}\) \(-10.7633 q^{35}\) \(+5.65684 q^{36}\) \(-6.14760 q^{37}\) \(+7.14393 q^{38}\) \(-5.09215 q^{39}\) \(-2.28313 q^{40}\) \(-9.37564 q^{41}\) \(-13.8706 q^{42}\) \(+7.90519 q^{43}\) \(+1.43615 q^{44}\) \(+12.9153 q^{45}\) \(-1.00000 q^{46}\) \(-0.303773 q^{47}\) \(-2.94225 q^{48}\) \(+15.2244 q^{49}\) \(-0.212702 q^{50}\) \(-21.9818 q^{51}\) \(+1.73070 q^{52}\) \(+9.05835 q^{53}\) \(+7.81709 q^{54}\) \(+3.27893 q^{55}\) \(+4.71427 q^{56}\) \(+21.0192 q^{57}\) \(+5.24580 q^{58}\) \(-1.29960 q^{59}\) \(-6.71755 q^{60}\) \(-5.05350 q^{61}\) \(-3.25473 q^{62}\) \(-26.6679 q^{63}\) \(+1.00000 q^{64}\) \(+3.95141 q^{65}\) \(+4.22552 q^{66}\) \(-5.76921 q^{67}\) \(+7.47107 q^{68}\) \(-2.94225 q^{69}\) \(+10.7633 q^{70}\) \(-5.45129 q^{71}\) \(-5.65684 q^{72}\) \(+5.77775 q^{73}\) \(+6.14760 q^{74}\) \(-0.625821 q^{75}\) \(-7.14393 q^{76}\) \(-6.77042 q^{77}\) \(+5.09215 q^{78}\) \(+10.7178 q^{79}\) \(+2.28313 q^{80}\) \(+6.02932 q^{81}\) \(+9.37564 q^{82}\) \(-10.2866 q^{83}\) \(+13.8706 q^{84}\) \(+17.0575 q^{85}\) \(-7.90519 q^{86}\) \(+15.4344 q^{87}\) \(-1.43615 q^{88}\) \(+2.27214 q^{89}\) \(-12.9153 q^{90}\) \(-8.15898 q^{91}\) \(+1.00000 q^{92}\) \(-9.57622 q^{93}\) \(+0.303773 q^{94}\) \(-16.3105 q^{95}\) \(+2.94225 q^{96}\) \(+18.1969 q^{97}\) \(-15.2244 q^{98}\) \(+8.12409 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.94225 −1.69871 −0.849355 0.527823i \(-0.823009\pi\)
−0.849355 + 0.527823i \(0.823009\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.28313 1.02105 0.510524 0.859863i \(-0.329451\pi\)
0.510524 + 0.859863i \(0.329451\pi\)
\(6\) 2.94225 1.20117
\(7\) −4.71427 −1.78183 −0.890914 0.454172i \(-0.849935\pi\)
−0.890914 + 0.454172i \(0.849935\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.65684 1.88561
\(10\) −2.28313 −0.721990
\(11\) 1.43615 0.433017 0.216508 0.976281i \(-0.430533\pi\)
0.216508 + 0.976281i \(0.430533\pi\)
\(12\) −2.94225 −0.849355
\(13\) 1.73070 0.480009 0.240005 0.970772i \(-0.422851\pi\)
0.240005 + 0.970772i \(0.422851\pi\)
\(14\) 4.71427 1.25994
\(15\) −6.71755 −1.73446
\(16\) 1.00000 0.250000
\(17\) 7.47107 1.81200 0.906001 0.423276i \(-0.139120\pi\)
0.906001 + 0.423276i \(0.139120\pi\)
\(18\) −5.65684 −1.33333
\(19\) −7.14393 −1.63893 −0.819465 0.573129i \(-0.805729\pi\)
−0.819465 + 0.573129i \(0.805729\pi\)
\(20\) 2.28313 0.510524
\(21\) 13.8706 3.02681
\(22\) −1.43615 −0.306189
\(23\) 1.00000 0.208514
\(24\) 2.94225 0.600584
\(25\) 0.212702 0.0425403
\(26\) −1.73070 −0.339418
\(27\) −7.81709 −1.50440
\(28\) −4.71427 −0.890914
\(29\) −5.24580 −0.974120 −0.487060 0.873369i \(-0.661931\pi\)
−0.487060 + 0.873369i \(0.661931\pi\)
\(30\) 6.71755 1.22645
\(31\) 3.25473 0.584566 0.292283 0.956332i \(-0.405585\pi\)
0.292283 + 0.956332i \(0.405585\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.22552 −0.735569
\(34\) −7.47107 −1.28128
\(35\) −10.7633 −1.81933
\(36\) 5.65684 0.942807
\(37\) −6.14760 −1.01066 −0.505330 0.862926i \(-0.668629\pi\)
−0.505330 + 0.862926i \(0.668629\pi\)
\(38\) 7.14393 1.15890
\(39\) −5.09215 −0.815396
\(40\) −2.28313 −0.360995
\(41\) −9.37564 −1.46423 −0.732114 0.681182i \(-0.761466\pi\)
−0.732114 + 0.681182i \(0.761466\pi\)
\(42\) −13.8706 −2.14028
\(43\) 7.90519 1.20553 0.602765 0.797919i \(-0.294066\pi\)
0.602765 + 0.797919i \(0.294066\pi\)
\(44\) 1.43615 0.216508
\(45\) 12.9153 1.92530
\(46\) −1.00000 −0.147442
\(47\) −0.303773 −0.0443099 −0.0221550 0.999755i \(-0.507053\pi\)
−0.0221550 + 0.999755i \(0.507053\pi\)
\(48\) −2.94225 −0.424677
\(49\) 15.2244 2.17491
\(50\) −0.212702 −0.0300805
\(51\) −21.9818 −3.07806
\(52\) 1.73070 0.240005
\(53\) 9.05835 1.24426 0.622130 0.782914i \(-0.286268\pi\)
0.622130 + 0.782914i \(0.286268\pi\)
\(54\) 7.81709 1.06377
\(55\) 3.27893 0.442131
\(56\) 4.71427 0.629971
\(57\) 21.0192 2.78407
\(58\) 5.24580 0.688807
\(59\) −1.29960 −0.169194 −0.0845968 0.996415i \(-0.526960\pi\)
−0.0845968 + 0.996415i \(0.526960\pi\)
\(60\) −6.71755 −0.867232
\(61\) −5.05350 −0.647035 −0.323517 0.946222i \(-0.604865\pi\)
−0.323517 + 0.946222i \(0.604865\pi\)
\(62\) −3.25473 −0.413351
\(63\) −26.6679 −3.35984
\(64\) 1.00000 0.125000
\(65\) 3.95141 0.490113
\(66\) 4.22552 0.520126
\(67\) −5.76921 −0.704821 −0.352411 0.935846i \(-0.614638\pi\)
−0.352411 + 0.935846i \(0.614638\pi\)
\(68\) 7.47107 0.906001
\(69\) −2.94225 −0.354205
\(70\) 10.7633 1.28646
\(71\) −5.45129 −0.646950 −0.323475 0.946237i \(-0.604851\pi\)
−0.323475 + 0.946237i \(0.604851\pi\)
\(72\) −5.65684 −0.666665
\(73\) 5.77775 0.676235 0.338118 0.941104i \(-0.390210\pi\)
0.338118 + 0.941104i \(0.390210\pi\)
\(74\) 6.14760 0.714644
\(75\) −0.625821 −0.0722636
\(76\) −7.14393 −0.819465
\(77\) −6.77042 −0.771561
\(78\) 5.09215 0.576572
\(79\) 10.7178 1.20584 0.602921 0.797801i \(-0.294003\pi\)
0.602921 + 0.797801i \(0.294003\pi\)
\(80\) 2.28313 0.255262
\(81\) 6.02932 0.669924
\(82\) 9.37564 1.03537
\(83\) −10.2866 −1.12910 −0.564549 0.825399i \(-0.690950\pi\)
−0.564549 + 0.825399i \(0.690950\pi\)
\(84\) 13.8706 1.51340
\(85\) 17.0575 1.85014
\(86\) −7.90519 −0.852439
\(87\) 15.4344 1.65475
\(88\) −1.43615 −0.153095
\(89\) 2.27214 0.240847 0.120423 0.992723i \(-0.461575\pi\)
0.120423 + 0.992723i \(0.461575\pi\)
\(90\) −12.9153 −1.36139
\(91\) −8.15898 −0.855294
\(92\) 1.00000 0.104257
\(93\) −9.57622 −0.993008
\(94\) 0.303773 0.0313318
\(95\) −16.3105 −1.67343
\(96\) 2.94225 0.300292
\(97\) 18.1969 1.84761 0.923807 0.382858i \(-0.125060\pi\)
0.923807 + 0.382858i \(0.125060\pi\)
\(98\) −15.2244 −1.53789
\(99\) 8.12409 0.816502
\(100\) 0.212702 0.0212702
\(101\) −6.53995 −0.650749 −0.325375 0.945585i \(-0.605490\pi\)
−0.325375 + 0.945585i \(0.605490\pi\)
\(102\) 21.9818 2.17652
\(103\) 6.89029 0.678921 0.339460 0.940620i \(-0.389756\pi\)
0.339460 + 0.940620i \(0.389756\pi\)
\(104\) −1.73070 −0.169709
\(105\) 31.6684 3.09052
\(106\) −9.05835 −0.879825
\(107\) −2.55452 −0.246954 −0.123477 0.992347i \(-0.539405\pi\)
−0.123477 + 0.992347i \(0.539405\pi\)
\(108\) −7.81709 −0.752200
\(109\) −5.12564 −0.490947 −0.245473 0.969403i \(-0.578943\pi\)
−0.245473 + 0.969403i \(0.578943\pi\)
\(110\) −3.27893 −0.312634
\(111\) 18.0878 1.71682
\(112\) −4.71427 −0.445457
\(113\) 8.61364 0.810303 0.405151 0.914250i \(-0.367219\pi\)
0.405151 + 0.914250i \(0.367219\pi\)
\(114\) −21.0192 −1.96863
\(115\) 2.28313 0.212903
\(116\) −5.24580 −0.487060
\(117\) 9.79028 0.905112
\(118\) 1.29960 0.119638
\(119\) −35.2207 −3.22868
\(120\) 6.71755 0.613226
\(121\) −8.93746 −0.812497
\(122\) 5.05350 0.457523
\(123\) 27.5855 2.48730
\(124\) 3.25473 0.292283
\(125\) −10.9300 −0.977613
\(126\) 26.6679 2.37576
\(127\) 19.3539 1.71738 0.858692 0.512491i \(-0.171277\pi\)
0.858692 + 0.512491i \(0.171277\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −23.2591 −2.04785
\(130\) −3.95141 −0.346562
\(131\) 1.00000 0.0873704
\(132\) −4.22552 −0.367785
\(133\) 33.6784 2.92029
\(134\) 5.76921 0.498384
\(135\) −17.8475 −1.53607
\(136\) −7.47107 −0.640639
\(137\) −11.4988 −0.982411 −0.491205 0.871044i \(-0.663444\pi\)
−0.491205 + 0.871044i \(0.663444\pi\)
\(138\) 2.94225 0.250461
\(139\) −3.08554 −0.261712 −0.130856 0.991401i \(-0.541773\pi\)
−0.130856 + 0.991401i \(0.541773\pi\)
\(140\) −10.7633 −0.909667
\(141\) 0.893778 0.0752697
\(142\) 5.45129 0.457462
\(143\) 2.48555 0.207852
\(144\) 5.65684 0.471403
\(145\) −11.9769 −0.994624
\(146\) −5.77775 −0.478170
\(147\) −44.7940 −3.69454
\(148\) −6.14760 −0.505330
\(149\) 1.21139 0.0992412 0.0496206 0.998768i \(-0.484199\pi\)
0.0496206 + 0.998768i \(0.484199\pi\)
\(150\) 0.625821 0.0510981
\(151\) 9.36316 0.761963 0.380982 0.924583i \(-0.375586\pi\)
0.380982 + 0.924583i \(0.375586\pi\)
\(152\) 7.14393 0.579449
\(153\) 42.2627 3.41673
\(154\) 6.77042 0.545576
\(155\) 7.43098 0.596870
\(156\) −5.09215 −0.407698
\(157\) 10.8119 0.862884 0.431442 0.902141i \(-0.358005\pi\)
0.431442 + 0.902141i \(0.358005\pi\)
\(158\) −10.7178 −0.852659
\(159\) −26.6519 −2.11364
\(160\) −2.28313 −0.180498
\(161\) −4.71427 −0.371537
\(162\) −6.02932 −0.473708
\(163\) −6.25972 −0.490299 −0.245150 0.969485i \(-0.578837\pi\)
−0.245150 + 0.969485i \(0.578837\pi\)
\(164\) −9.37564 −0.732114
\(165\) −9.64744 −0.751052
\(166\) 10.2866 0.798393
\(167\) 4.64774 0.359653 0.179827 0.983698i \(-0.442446\pi\)
0.179827 + 0.983698i \(0.442446\pi\)
\(168\) −13.8706 −1.07014
\(169\) −10.0047 −0.769591
\(170\) −17.0575 −1.30825
\(171\) −40.4121 −3.09039
\(172\) 7.90519 0.602765
\(173\) −10.1928 −0.774942 −0.387471 0.921882i \(-0.626651\pi\)
−0.387471 + 0.921882i \(0.626651\pi\)
\(174\) −15.4344 −1.17008
\(175\) −1.00273 −0.0757995
\(176\) 1.43615 0.108254
\(177\) 3.82375 0.287411
\(178\) −2.27214 −0.170304
\(179\) 8.23191 0.615282 0.307641 0.951502i \(-0.400460\pi\)
0.307641 + 0.951502i \(0.400460\pi\)
\(180\) 12.9153 0.962651
\(181\) 26.6264 1.97913 0.989564 0.144095i \(-0.0460269\pi\)
0.989564 + 0.144095i \(0.0460269\pi\)
\(182\) 8.15898 0.604784
\(183\) 14.8687 1.09912
\(184\) −1.00000 −0.0737210
\(185\) −14.0358 −1.03193
\(186\) 9.57622 0.702163
\(187\) 10.7296 0.784627
\(188\) −0.303773 −0.0221550
\(189\) 36.8519 2.68058
\(190\) 16.3105 1.18329
\(191\) −12.0127 −0.869211 −0.434606 0.900621i \(-0.643112\pi\)
−0.434606 + 0.900621i \(0.643112\pi\)
\(192\) −2.94225 −0.212339
\(193\) −3.64531 −0.262395 −0.131198 0.991356i \(-0.541882\pi\)
−0.131198 + 0.991356i \(0.541882\pi\)
\(194\) −18.1969 −1.30646
\(195\) −11.6261 −0.832559
\(196\) 15.2244 1.08746
\(197\) 5.05009 0.359804 0.179902 0.983685i \(-0.442422\pi\)
0.179902 + 0.983685i \(0.442422\pi\)
\(198\) −8.12409 −0.577354
\(199\) −7.59628 −0.538486 −0.269243 0.963072i \(-0.586773\pi\)
−0.269243 + 0.963072i \(0.586773\pi\)
\(200\) −0.212702 −0.0150403
\(201\) 16.9745 1.19729
\(202\) 6.53995 0.460149
\(203\) 24.7301 1.73571
\(204\) −21.9818 −1.53903
\(205\) −21.4058 −1.49505
\(206\) −6.89029 −0.480070
\(207\) 5.65684 0.393178
\(208\) 1.73070 0.120002
\(209\) −10.2598 −0.709684
\(210\) −31.6684 −2.18533
\(211\) −20.3582 −1.40152 −0.700760 0.713397i \(-0.747156\pi\)
−0.700760 + 0.713397i \(0.747156\pi\)
\(212\) 9.05835 0.622130
\(213\) 16.0391 1.09898
\(214\) 2.55452 0.174623
\(215\) 18.0486 1.23091
\(216\) 7.81709 0.531886
\(217\) −15.3437 −1.04160
\(218\) 5.12564 0.347152
\(219\) −16.9996 −1.14873
\(220\) 3.27893 0.221066
\(221\) 12.9302 0.869777
\(222\) −18.0878 −1.21397
\(223\) −23.8002 −1.59378 −0.796890 0.604125i \(-0.793523\pi\)
−0.796890 + 0.604125i \(0.793523\pi\)
\(224\) 4.71427 0.314986
\(225\) 1.20322 0.0802146
\(226\) −8.61364 −0.572971
\(227\) 24.2069 1.60667 0.803334 0.595529i \(-0.203057\pi\)
0.803334 + 0.595529i \(0.203057\pi\)
\(228\) 21.0192 1.39203
\(229\) −18.0713 −1.19418 −0.597091 0.802174i \(-0.703677\pi\)
−0.597091 + 0.802174i \(0.703677\pi\)
\(230\) −2.28313 −0.150545
\(231\) 19.9203 1.31066
\(232\) 5.24580 0.344403
\(233\) 22.3843 1.46645 0.733224 0.679987i \(-0.238015\pi\)
0.733224 + 0.679987i \(0.238015\pi\)
\(234\) −9.79028 −0.640011
\(235\) −0.693556 −0.0452426
\(236\) −1.29960 −0.0845968
\(237\) −31.5343 −2.04837
\(238\) 35.2207 2.28302
\(239\) 21.1116 1.36560 0.682799 0.730606i \(-0.260762\pi\)
0.682799 + 0.730606i \(0.260762\pi\)
\(240\) −6.71755 −0.433616
\(241\) −19.4969 −1.25591 −0.627954 0.778251i \(-0.716107\pi\)
−0.627954 + 0.778251i \(0.716107\pi\)
\(242\) 8.93746 0.574522
\(243\) 5.71150 0.366393
\(244\) −5.05350 −0.323517
\(245\) 34.7593 2.22069
\(246\) −27.5855 −1.75879
\(247\) −12.3640 −0.786701
\(248\) −3.25473 −0.206675
\(249\) 30.2657 1.91801
\(250\) 10.9300 0.691277
\(251\) 7.90434 0.498917 0.249459 0.968385i \(-0.419747\pi\)
0.249459 + 0.968385i \(0.419747\pi\)
\(252\) −26.6679 −1.67992
\(253\) 1.43615 0.0902902
\(254\) −19.3539 −1.21437
\(255\) −50.1873 −3.14285
\(256\) 1.00000 0.0625000
\(257\) 31.1940 1.94583 0.972913 0.231172i \(-0.0742559\pi\)
0.972913 + 0.231172i \(0.0742559\pi\)
\(258\) 23.2591 1.44805
\(259\) 28.9815 1.80082
\(260\) 3.95141 0.245056
\(261\) −29.6746 −1.83681
\(262\) −1.00000 −0.0617802
\(263\) −14.9055 −0.919114 −0.459557 0.888148i \(-0.651992\pi\)
−0.459557 + 0.888148i \(0.651992\pi\)
\(264\) 4.22552 0.260063
\(265\) 20.6814 1.27045
\(266\) −33.6784 −2.06496
\(267\) −6.68522 −0.409129
\(268\) −5.76921 −0.352411
\(269\) 19.5124 1.18969 0.594847 0.803839i \(-0.297212\pi\)
0.594847 + 0.803839i \(0.297212\pi\)
\(270\) 17.8475 1.08616
\(271\) 6.79759 0.412924 0.206462 0.978455i \(-0.433805\pi\)
0.206462 + 0.978455i \(0.433805\pi\)
\(272\) 7.47107 0.453000
\(273\) 24.0058 1.45290
\(274\) 11.4988 0.694669
\(275\) 0.305472 0.0184207
\(276\) −2.94225 −0.177103
\(277\) 7.31058 0.439250 0.219625 0.975584i \(-0.429517\pi\)
0.219625 + 0.975584i \(0.429517\pi\)
\(278\) 3.08554 0.185058
\(279\) 18.4115 1.10227
\(280\) 10.7633 0.643231
\(281\) −6.80311 −0.405839 −0.202920 0.979195i \(-0.565043\pi\)
−0.202920 + 0.979195i \(0.565043\pi\)
\(282\) −0.893778 −0.0532237
\(283\) 3.07532 0.182809 0.0914044 0.995814i \(-0.470864\pi\)
0.0914044 + 0.995814i \(0.470864\pi\)
\(284\) −5.45129 −0.323475
\(285\) 47.9897 2.84267
\(286\) −2.48555 −0.146974
\(287\) 44.1993 2.60900
\(288\) −5.65684 −0.333332
\(289\) 38.8170 2.28335
\(290\) 11.9769 0.703305
\(291\) −53.5398 −3.13856
\(292\) 5.77775 0.338118
\(293\) −27.0749 −1.58173 −0.790867 0.611988i \(-0.790370\pi\)
−0.790867 + 0.611988i \(0.790370\pi\)
\(294\) 44.7940 2.61244
\(295\) −2.96716 −0.172755
\(296\) 6.14760 0.357322
\(297\) −11.2265 −0.651430
\(298\) −1.21139 −0.0701741
\(299\) 1.73070 0.100089
\(300\) −0.625821 −0.0361318
\(301\) −37.2672 −2.14805
\(302\) −9.36316 −0.538789
\(303\) 19.2422 1.10543
\(304\) −7.14393 −0.409732
\(305\) −11.5378 −0.660654
\(306\) −42.2627 −2.41600
\(307\) 19.7213 1.12555 0.562776 0.826609i \(-0.309733\pi\)
0.562776 + 0.826609i \(0.309733\pi\)
\(308\) −6.77042 −0.385781
\(309\) −20.2730 −1.15329
\(310\) −7.43098 −0.422051
\(311\) −14.3327 −0.812733 −0.406367 0.913710i \(-0.633204\pi\)
−0.406367 + 0.913710i \(0.633204\pi\)
\(312\) 5.09215 0.288286
\(313\) −21.3038 −1.20416 −0.602082 0.798434i \(-0.705662\pi\)
−0.602082 + 0.798434i \(0.705662\pi\)
\(314\) −10.8119 −0.610151
\(315\) −60.8864 −3.43056
\(316\) 10.7178 0.602921
\(317\) −8.14817 −0.457647 −0.228823 0.973468i \(-0.573488\pi\)
−0.228823 + 0.973468i \(0.573488\pi\)
\(318\) 26.6519 1.49457
\(319\) −7.53377 −0.421810
\(320\) 2.28313 0.127631
\(321\) 7.51603 0.419504
\(322\) 4.71427 0.262716
\(323\) −53.3728 −2.96974
\(324\) 6.02932 0.334962
\(325\) 0.368122 0.0204197
\(326\) 6.25972 0.346694
\(327\) 15.0809 0.833976
\(328\) 9.37564 0.517683
\(329\) 1.43207 0.0789526
\(330\) 9.64744 0.531074
\(331\) −13.9827 −0.768557 −0.384278 0.923217i \(-0.625550\pi\)
−0.384278 + 0.923217i \(0.625550\pi\)
\(332\) −10.2866 −0.564549
\(333\) −34.7760 −1.90571
\(334\) −4.64774 −0.254313
\(335\) −13.1719 −0.719657
\(336\) 13.8706 0.756702
\(337\) 22.2988 1.21469 0.607347 0.794437i \(-0.292234\pi\)
0.607347 + 0.794437i \(0.292234\pi\)
\(338\) 10.0047 0.544183
\(339\) −25.3435 −1.37647
\(340\) 17.0575 0.925071
\(341\) 4.67429 0.253127
\(342\) 40.4121 2.18523
\(343\) −38.7720 −2.09349
\(344\) −7.90519 −0.426219
\(345\) −6.71755 −0.361661
\(346\) 10.1928 0.547967
\(347\) −29.8703 −1.60352 −0.801761 0.597645i \(-0.796103\pi\)
−0.801761 + 0.597645i \(0.796103\pi\)
\(348\) 15.4344 0.827373
\(349\) −21.8531 −1.16977 −0.584884 0.811117i \(-0.698860\pi\)
−0.584884 + 0.811117i \(0.698860\pi\)
\(350\) 1.00273 0.0535984
\(351\) −13.5290 −0.722125
\(352\) −1.43615 −0.0765473
\(353\) −9.64790 −0.513506 −0.256753 0.966477i \(-0.582653\pi\)
−0.256753 + 0.966477i \(0.582653\pi\)
\(354\) −3.82375 −0.203230
\(355\) −12.4460 −0.660567
\(356\) 2.27214 0.120423
\(357\) 103.628 5.48458
\(358\) −8.23191 −0.435070
\(359\) 1.63180 0.0861233 0.0430617 0.999072i \(-0.486289\pi\)
0.0430617 + 0.999072i \(0.486289\pi\)
\(360\) −12.9153 −0.680697
\(361\) 32.0357 1.68609
\(362\) −26.6264 −1.39945
\(363\) 26.2963 1.38020
\(364\) −8.15898 −0.427647
\(365\) 13.1914 0.690469
\(366\) −14.8687 −0.777198
\(367\) −32.5145 −1.69725 −0.848623 0.528998i \(-0.822568\pi\)
−0.848623 + 0.528998i \(0.822568\pi\)
\(368\) 1.00000 0.0521286
\(369\) −53.0365 −2.76097
\(370\) 14.0358 0.729686
\(371\) −42.7035 −2.21706
\(372\) −9.57622 −0.496504
\(373\) −21.2621 −1.10091 −0.550455 0.834865i \(-0.685546\pi\)
−0.550455 + 0.834865i \(0.685546\pi\)
\(374\) −10.7296 −0.554815
\(375\) 32.1589 1.66068
\(376\) 0.303773 0.0156659
\(377\) −9.07888 −0.467586
\(378\) −36.8519 −1.89546
\(379\) −24.8326 −1.27556 −0.637781 0.770218i \(-0.720148\pi\)
−0.637781 + 0.770218i \(0.720148\pi\)
\(380\) −16.3105 −0.836713
\(381\) −56.9442 −2.91734
\(382\) 12.0127 0.614625
\(383\) −8.38736 −0.428574 −0.214287 0.976771i \(-0.568743\pi\)
−0.214287 + 0.976771i \(0.568743\pi\)
\(384\) 2.94225 0.150146
\(385\) −15.4578 −0.787802
\(386\) 3.64531 0.185542
\(387\) 44.7184 2.27316
\(388\) 18.1969 0.923807
\(389\) −33.0039 −1.67336 −0.836682 0.547688i \(-0.815508\pi\)
−0.836682 + 0.547688i \(0.815508\pi\)
\(390\) 11.6261 0.588708
\(391\) 7.47107 0.377828
\(392\) −15.2244 −0.768947
\(393\) −2.94225 −0.148417
\(394\) −5.05009 −0.254420
\(395\) 24.4701 1.23122
\(396\) 8.12409 0.408251
\(397\) 31.0067 1.55618 0.778092 0.628151i \(-0.216188\pi\)
0.778092 + 0.628151i \(0.216188\pi\)
\(398\) 7.59628 0.380767
\(399\) −99.0904 −4.96073
\(400\) 0.212702 0.0106351
\(401\) −9.59094 −0.478949 −0.239474 0.970903i \(-0.576975\pi\)
−0.239474 + 0.970903i \(0.576975\pi\)
\(402\) −16.9745 −0.846609
\(403\) 5.63295 0.280597
\(404\) −6.53995 −0.325375
\(405\) 13.7657 0.684025
\(406\) −24.7301 −1.22734
\(407\) −8.82890 −0.437632
\(408\) 21.9818 1.08826
\(409\) −9.47826 −0.468670 −0.234335 0.972156i \(-0.575291\pi\)
−0.234335 + 0.972156i \(0.575291\pi\)
\(410\) 21.4058 1.05716
\(411\) 33.8324 1.66883
\(412\) 6.89029 0.339460
\(413\) 6.12667 0.301474
\(414\) −5.65684 −0.278019
\(415\) −23.4856 −1.15286
\(416\) −1.73070 −0.0848544
\(417\) 9.07842 0.444572
\(418\) 10.2598 0.501822
\(419\) 6.38892 0.312119 0.156060 0.987748i \(-0.450121\pi\)
0.156060 + 0.987748i \(0.450121\pi\)
\(420\) 31.6684 1.54526
\(421\) 1.58840 0.0774139 0.0387069 0.999251i \(-0.487676\pi\)
0.0387069 + 0.999251i \(0.487676\pi\)
\(422\) 20.3582 0.991024
\(423\) −1.71840 −0.0835514
\(424\) −9.05835 −0.439912
\(425\) 1.58911 0.0770831
\(426\) −16.0391 −0.777096
\(427\) 23.8236 1.15290
\(428\) −2.55452 −0.123477
\(429\) −7.31311 −0.353080
\(430\) −18.0486 −0.870381
\(431\) −1.09420 −0.0527057 −0.0263528 0.999653i \(-0.508389\pi\)
−0.0263528 + 0.999653i \(0.508389\pi\)
\(432\) −7.81709 −0.376100
\(433\) −14.6104 −0.702132 −0.351066 0.936351i \(-0.614181\pi\)
−0.351066 + 0.936351i \(0.614181\pi\)
\(434\) 15.3437 0.736520
\(435\) 35.2389 1.68958
\(436\) −5.12564 −0.245473
\(437\) −7.14393 −0.341740
\(438\) 16.9996 0.812272
\(439\) −15.3855 −0.734311 −0.367155 0.930160i \(-0.619668\pi\)
−0.367155 + 0.930160i \(0.619668\pi\)
\(440\) −3.27893 −0.156317
\(441\) 86.1219 4.10104
\(442\) −12.9302 −0.615026
\(443\) −26.9669 −1.28124 −0.640618 0.767860i \(-0.721322\pi\)
−0.640618 + 0.767860i \(0.721322\pi\)
\(444\) 18.0878 0.858408
\(445\) 5.18761 0.245916
\(446\) 23.8002 1.12697
\(447\) −3.56422 −0.168582
\(448\) −4.71427 −0.222729
\(449\) 9.18812 0.433614 0.216807 0.976214i \(-0.430436\pi\)
0.216807 + 0.976214i \(0.430436\pi\)
\(450\) −1.20322 −0.0567203
\(451\) −13.4649 −0.634035
\(452\) 8.61364 0.405151
\(453\) −27.5488 −1.29435
\(454\) −24.2069 −1.13609
\(455\) −18.6281 −0.873297
\(456\) −21.0192 −0.984316
\(457\) 7.14228 0.334102 0.167051 0.985948i \(-0.446576\pi\)
0.167051 + 0.985948i \(0.446576\pi\)
\(458\) 18.0713 0.844414
\(459\) −58.4021 −2.72597
\(460\) 2.28313 0.106452
\(461\) −17.9737 −0.837118 −0.418559 0.908190i \(-0.637465\pi\)
−0.418559 + 0.908190i \(0.637465\pi\)
\(462\) −19.9203 −0.926775
\(463\) −24.6083 −1.14365 −0.571823 0.820377i \(-0.693764\pi\)
−0.571823 + 0.820377i \(0.693764\pi\)
\(464\) −5.24580 −0.243530
\(465\) −21.8638 −1.01391
\(466\) −22.3843 −1.03693
\(467\) −37.8524 −1.75160 −0.875801 0.482673i \(-0.839666\pi\)
−0.875801 + 0.482673i \(0.839666\pi\)
\(468\) 9.79028 0.452556
\(469\) 27.1976 1.25587
\(470\) 0.693556 0.0319913
\(471\) −31.8113 −1.46579
\(472\) 1.29960 0.0598190
\(473\) 11.3531 0.522015
\(474\) 31.5343 1.44842
\(475\) −1.51952 −0.0697206
\(476\) −35.2207 −1.61434
\(477\) 51.2416 2.34619
\(478\) −21.1116 −0.965624
\(479\) −19.1001 −0.872707 −0.436354 0.899775i \(-0.643730\pi\)
−0.436354 + 0.899775i \(0.643730\pi\)
\(480\) 6.71755 0.306613
\(481\) −10.6396 −0.485126
\(482\) 19.4969 0.888061
\(483\) 13.8706 0.631133
\(484\) −8.93746 −0.406248
\(485\) 41.5460 1.88650
\(486\) −5.71150 −0.259079
\(487\) −0.962350 −0.0436082 −0.0218041 0.999762i \(-0.506941\pi\)
−0.0218041 + 0.999762i \(0.506941\pi\)
\(488\) 5.05350 0.228761
\(489\) 18.4177 0.832876
\(490\) −34.7593 −1.57027
\(491\) 17.2832 0.779979 0.389990 0.920819i \(-0.372479\pi\)
0.389990 + 0.920819i \(0.372479\pi\)
\(492\) 27.5855 1.24365
\(493\) −39.1917 −1.76511
\(494\) 12.3640 0.556282
\(495\) 18.5484 0.833688
\(496\) 3.25473 0.146142
\(497\) 25.6989 1.15275
\(498\) −30.2657 −1.35624
\(499\) −11.8894 −0.532242 −0.266121 0.963940i \(-0.585742\pi\)
−0.266121 + 0.963940i \(0.585742\pi\)
\(500\) −10.9300 −0.488806
\(501\) −13.6748 −0.610946
\(502\) −7.90434 −0.352788
\(503\) −1.02453 −0.0456816 −0.0228408 0.999739i \(-0.507271\pi\)
−0.0228408 + 0.999739i \(0.507271\pi\)
\(504\) 26.6679 1.18788
\(505\) −14.9316 −0.664447
\(506\) −1.43615 −0.0638448
\(507\) 29.4363 1.30731
\(508\) 19.3539 0.858692
\(509\) 37.5337 1.66365 0.831827 0.555036i \(-0.187295\pi\)
0.831827 + 0.555036i \(0.187295\pi\)
\(510\) 50.1873 2.22233
\(511\) −27.2379 −1.20493
\(512\) −1.00000 −0.0441942
\(513\) 55.8447 2.46560
\(514\) −31.1940 −1.37591
\(515\) 15.7315 0.693211
\(516\) −23.2591 −1.02392
\(517\) −0.436265 −0.0191869
\(518\) −28.9815 −1.27337
\(519\) 29.9897 1.31640
\(520\) −3.95141 −0.173281
\(521\) −5.49704 −0.240830 −0.120415 0.992724i \(-0.538423\pi\)
−0.120415 + 0.992724i \(0.538423\pi\)
\(522\) 29.6746 1.29882
\(523\) 7.64410 0.334253 0.167126 0.985935i \(-0.446551\pi\)
0.167126 + 0.985935i \(0.446551\pi\)
\(524\) 1.00000 0.0436852
\(525\) 2.95029 0.128761
\(526\) 14.9055 0.649912
\(527\) 24.3163 1.05923
\(528\) −4.22552 −0.183892
\(529\) 1.00000 0.0434783
\(530\) −20.6814 −0.898344
\(531\) −7.35163 −0.319034
\(532\) 33.6784 1.46015
\(533\) −16.2264 −0.702843
\(534\) 6.68522 0.289298
\(535\) −5.83230 −0.252152
\(536\) 5.76921 0.249192
\(537\) −24.2204 −1.04519
\(538\) −19.5124 −0.841241
\(539\) 21.8646 0.941773
\(540\) −17.8475 −0.768033
\(541\) 3.03620 0.130536 0.0652682 0.997868i \(-0.479210\pi\)
0.0652682 + 0.997868i \(0.479210\pi\)
\(542\) −6.79759 −0.291981
\(543\) −78.3417 −3.36196
\(544\) −7.47107 −0.320320
\(545\) −11.7025 −0.501281
\(546\) −24.0058 −1.02735
\(547\) −3.59299 −0.153625 −0.0768126 0.997046i \(-0.524474\pi\)
−0.0768126 + 0.997046i \(0.524474\pi\)
\(548\) −11.4988 −0.491205
\(549\) −28.5869 −1.22006
\(550\) −0.305472 −0.0130254
\(551\) 37.4756 1.59651
\(552\) 2.94225 0.125231
\(553\) −50.5264 −2.14860
\(554\) −7.31058 −0.310597
\(555\) 41.2968 1.75295
\(556\) −3.08554 −0.130856
\(557\) −39.0331 −1.65389 −0.826943 0.562286i \(-0.809922\pi\)
−0.826943 + 0.562286i \(0.809922\pi\)
\(558\) −18.4115 −0.779419
\(559\) 13.6815 0.578666
\(560\) −10.7633 −0.454833
\(561\) −31.5692 −1.33285
\(562\) 6.80311 0.286972
\(563\) −43.6217 −1.83844 −0.919218 0.393750i \(-0.871178\pi\)
−0.919218 + 0.393750i \(0.871178\pi\)
\(564\) 0.893778 0.0376348
\(565\) 19.6661 0.827359
\(566\) −3.07532 −0.129265
\(567\) −28.4239 −1.19369
\(568\) 5.45129 0.228731
\(569\) −41.4391 −1.73722 −0.868609 0.495498i \(-0.834986\pi\)
−0.868609 + 0.495498i \(0.834986\pi\)
\(570\) −47.9897 −2.01007
\(571\) 24.1265 1.00966 0.504832 0.863218i \(-0.331554\pi\)
0.504832 + 0.863218i \(0.331554\pi\)
\(572\) 2.48555 0.103926
\(573\) 35.3445 1.47654
\(574\) −44.1993 −1.84484
\(575\) 0.212702 0.00887027
\(576\) 5.65684 0.235702
\(577\) −47.2119 −1.96546 −0.982729 0.185049i \(-0.940756\pi\)
−0.982729 + 0.185049i \(0.940756\pi\)
\(578\) −38.8170 −1.61457
\(579\) 10.7254 0.445734
\(580\) −11.9769 −0.497312
\(581\) 48.4938 2.01186
\(582\) 53.5398 2.21930
\(583\) 13.0092 0.538785
\(584\) −5.77775 −0.239085
\(585\) 22.3525 0.924163
\(586\) 27.0749 1.11846
\(587\) −3.10269 −0.128062 −0.0640308 0.997948i \(-0.520396\pi\)
−0.0640308 + 0.997948i \(0.520396\pi\)
\(588\) −44.7940 −1.84727
\(589\) −23.2515 −0.958063
\(590\) 2.96716 0.122156
\(591\) −14.8586 −0.611202
\(592\) −6.14760 −0.252665
\(593\) −40.1515 −1.64883 −0.824413 0.565988i \(-0.808495\pi\)
−0.824413 + 0.565988i \(0.808495\pi\)
\(594\) 11.2265 0.460631
\(595\) −80.4136 −3.29664
\(596\) 1.21139 0.0496206
\(597\) 22.3501 0.914731
\(598\) −1.73070 −0.0707735
\(599\) 46.8814 1.91552 0.957760 0.287568i \(-0.0928468\pi\)
0.957760 + 0.287568i \(0.0928468\pi\)
\(600\) 0.625821 0.0255490
\(601\) 35.0919 1.43143 0.715714 0.698394i \(-0.246102\pi\)
0.715714 + 0.698394i \(0.246102\pi\)
\(602\) 37.2672 1.51890
\(603\) −32.6355 −1.32902
\(604\) 9.36316 0.380982
\(605\) −20.4054 −0.829599
\(606\) −19.2422 −0.781660
\(607\) −24.8390 −1.00818 −0.504092 0.863650i \(-0.668173\pi\)
−0.504092 + 0.863650i \(0.668173\pi\)
\(608\) 7.14393 0.289725
\(609\) −72.7622 −2.94847
\(610\) 11.5378 0.467153
\(611\) −0.525740 −0.0212692
\(612\) 42.2627 1.70837
\(613\) −39.3082 −1.58764 −0.793822 0.608150i \(-0.791912\pi\)
−0.793822 + 0.608150i \(0.791912\pi\)
\(614\) −19.7213 −0.795886
\(615\) 62.9813 2.53965
\(616\) 6.77042 0.272788
\(617\) −14.9204 −0.600673 −0.300337 0.953833i \(-0.597099\pi\)
−0.300337 + 0.953833i \(0.597099\pi\)
\(618\) 20.2730 0.815499
\(619\) 17.1311 0.688557 0.344278 0.938868i \(-0.388124\pi\)
0.344278 + 0.938868i \(0.388124\pi\)
\(620\) 7.43098 0.298435
\(621\) −7.81709 −0.313689
\(622\) 14.3327 0.574689
\(623\) −10.7115 −0.429148
\(624\) −5.09215 −0.203849
\(625\) −26.0183 −1.04073
\(626\) 21.3038 0.851472
\(627\) 30.1868 1.20555
\(628\) 10.8119 0.431442
\(629\) −45.9292 −1.83132
\(630\) 60.8864 2.42577
\(631\) −4.52986 −0.180331 −0.0901655 0.995927i \(-0.528740\pi\)
−0.0901655 + 0.995927i \(0.528740\pi\)
\(632\) −10.7178 −0.426329
\(633\) 59.8991 2.38077
\(634\) 8.14817 0.323605
\(635\) 44.1877 1.75353
\(636\) −26.6519 −1.05682
\(637\) 26.3488 1.04398
\(638\) 7.53377 0.298265
\(639\) −30.8371 −1.21990
\(640\) −2.28313 −0.0902488
\(641\) 0.237243 0.00937052 0.00468526 0.999989i \(-0.498509\pi\)
0.00468526 + 0.999989i \(0.498509\pi\)
\(642\) −7.51603 −0.296634
\(643\) 45.6389 1.79982 0.899912 0.436072i \(-0.143631\pi\)
0.899912 + 0.436072i \(0.143631\pi\)
\(644\) −4.71427 −0.185768
\(645\) −53.1035 −2.09095
\(646\) 53.3728 2.09993
\(647\) 13.8304 0.543729 0.271864 0.962336i \(-0.412360\pi\)
0.271864 + 0.962336i \(0.412360\pi\)
\(648\) −6.02932 −0.236854
\(649\) −1.86643 −0.0732636
\(650\) −0.368122 −0.0144389
\(651\) 45.1449 1.76937
\(652\) −6.25972 −0.245150
\(653\) −22.4062 −0.876824 −0.438412 0.898774i \(-0.644459\pi\)
−0.438412 + 0.898774i \(0.644459\pi\)
\(654\) −15.0809 −0.589710
\(655\) 2.28313 0.0892094
\(656\) −9.37564 −0.366057
\(657\) 32.6838 1.27512
\(658\) −1.43207 −0.0558280
\(659\) −5.32384 −0.207387 −0.103694 0.994609i \(-0.533066\pi\)
−0.103694 + 0.994609i \(0.533066\pi\)
\(660\) −9.64744 −0.375526
\(661\) −7.92351 −0.308189 −0.154094 0.988056i \(-0.549246\pi\)
−0.154094 + 0.988056i \(0.549246\pi\)
\(662\) 13.9827 0.543452
\(663\) −38.0438 −1.47750
\(664\) 10.2866 0.399197
\(665\) 76.8924 2.98176
\(666\) 34.7760 1.34754
\(667\) −5.24580 −0.203118
\(668\) 4.64774 0.179827
\(669\) 70.0262 2.70737
\(670\) 13.1719 0.508874
\(671\) −7.25761 −0.280177
\(672\) −13.8706 −0.535069
\(673\) −3.73612 −0.144017 −0.0720084 0.997404i \(-0.522941\pi\)
−0.0720084 + 0.997404i \(0.522941\pi\)
\(674\) −22.2988 −0.858918
\(675\) −1.66271 −0.0639976
\(676\) −10.0047 −0.384796
\(677\) −4.77921 −0.183680 −0.0918401 0.995774i \(-0.529275\pi\)
−0.0918401 + 0.995774i \(0.529275\pi\)
\(678\) 25.3435 0.973311
\(679\) −85.7852 −3.29213
\(680\) −17.0575 −0.654124
\(681\) −71.2228 −2.72926
\(682\) −4.67429 −0.178988
\(683\) 11.4538 0.438267 0.219133 0.975695i \(-0.429677\pi\)
0.219133 + 0.975695i \(0.429677\pi\)
\(684\) −40.4121 −1.54519
\(685\) −26.2533 −1.00309
\(686\) 38.7720 1.48032
\(687\) 53.1702 2.02857
\(688\) 7.90519 0.301383
\(689\) 15.6773 0.597256
\(690\) 6.71755 0.255733
\(691\) −11.0261 −0.419454 −0.209727 0.977760i \(-0.567257\pi\)
−0.209727 + 0.977760i \(0.567257\pi\)
\(692\) −10.1928 −0.387471
\(693\) −38.2992 −1.45487
\(694\) 29.8703 1.13386
\(695\) −7.04469 −0.267220
\(696\) −15.4344 −0.585041
\(697\) −70.0461 −2.65318
\(698\) 21.8531 0.827151
\(699\) −65.8604 −2.49107
\(700\) −1.00273 −0.0378998
\(701\) −0.324924 −0.0122722 −0.00613610 0.999981i \(-0.501953\pi\)
−0.00613610 + 0.999981i \(0.501953\pi\)
\(702\) 13.5290 0.510620
\(703\) 43.9180 1.65640
\(704\) 1.43615 0.0541271
\(705\) 2.04061 0.0768540
\(706\) 9.64790 0.363103
\(707\) 30.8311 1.15952
\(708\) 3.82375 0.143705
\(709\) 4.73783 0.177933 0.0889664 0.996035i \(-0.471644\pi\)
0.0889664 + 0.996035i \(0.471644\pi\)
\(710\) 12.4460 0.467091
\(711\) 60.6286 2.27375
\(712\) −2.27214 −0.0851522
\(713\) 3.25473 0.121890
\(714\) −103.628 −3.87819
\(715\) 5.67484 0.212227
\(716\) 8.23191 0.307641
\(717\) −62.1158 −2.31976
\(718\) −1.63180 −0.0608984
\(719\) −29.0124 −1.08198 −0.540990 0.841029i \(-0.681951\pi\)
−0.540990 + 0.841029i \(0.681951\pi\)
\(720\) 12.9153 0.481326
\(721\) −32.4827 −1.20972
\(722\) −32.0357 −1.19225
\(723\) 57.3648 2.13342
\(724\) 26.6264 0.989564
\(725\) −1.11579 −0.0414394
\(726\) −26.2963 −0.975946
\(727\) −5.24302 −0.194453 −0.0972263 0.995262i \(-0.530997\pi\)
−0.0972263 + 0.995262i \(0.530997\pi\)
\(728\) 8.15898 0.302392
\(729\) −34.8926 −1.29232
\(730\) −13.1914 −0.488235
\(731\) 59.0603 2.18442
\(732\) 14.8687 0.549562
\(733\) −17.9141 −0.661672 −0.330836 0.943688i \(-0.607331\pi\)
−0.330836 + 0.943688i \(0.607331\pi\)
\(734\) 32.5145 1.20013
\(735\) −102.271 −3.77231
\(736\) −1.00000 −0.0368605
\(737\) −8.28547 −0.305199
\(738\) 53.0365 1.95230
\(739\) −34.1168 −1.25501 −0.627504 0.778614i \(-0.715923\pi\)
−0.627504 + 0.778614i \(0.715923\pi\)
\(740\) −14.0358 −0.515966
\(741\) 36.3779 1.33638
\(742\) 42.7035 1.56770
\(743\) −4.69768 −0.172341 −0.0861706 0.996280i \(-0.527463\pi\)
−0.0861706 + 0.996280i \(0.527463\pi\)
\(744\) 9.57622 0.351081
\(745\) 2.76577 0.101330
\(746\) 21.2621 0.778461
\(747\) −58.1895 −2.12904
\(748\) 10.7296 0.392313
\(749\) 12.0427 0.440030
\(750\) −32.1589 −1.17428
\(751\) 10.4145 0.380029 0.190014 0.981781i \(-0.439147\pi\)
0.190014 + 0.981781i \(0.439147\pi\)
\(752\) −0.303773 −0.0110775
\(753\) −23.2565 −0.847515
\(754\) 9.07888 0.330633
\(755\) 21.3774 0.778001
\(756\) 36.8519 1.34029
\(757\) 20.0173 0.727541 0.363770 0.931489i \(-0.381489\pi\)
0.363770 + 0.931489i \(0.381489\pi\)
\(758\) 24.8326 0.901959
\(759\) −4.22552 −0.153377
\(760\) 16.3105 0.591646
\(761\) −28.4692 −1.03201 −0.516004 0.856586i \(-0.672581\pi\)
−0.516004 + 0.856586i \(0.672581\pi\)
\(762\) 56.9442 2.06287
\(763\) 24.1637 0.874783
\(764\) −12.0127 −0.434606
\(765\) 96.4914 3.48865
\(766\) 8.38736 0.303048
\(767\) −2.24922 −0.0812144
\(768\) −2.94225 −0.106169
\(769\) −29.7125 −1.07146 −0.535731 0.844389i \(-0.679964\pi\)
−0.535731 + 0.844389i \(0.679964\pi\)
\(770\) 15.4578 0.557060
\(771\) −91.7805 −3.30539
\(772\) −3.64531 −0.131198
\(773\) 9.17020 0.329829 0.164915 0.986308i \(-0.447265\pi\)
0.164915 + 0.986308i \(0.447265\pi\)
\(774\) −44.7184 −1.60737
\(775\) 0.692285 0.0248676
\(776\) −18.1969 −0.653230
\(777\) −85.2708 −3.05907
\(778\) 33.0039 1.18325
\(779\) 66.9789 2.39977
\(780\) −11.6261 −0.416279
\(781\) −7.82890 −0.280140
\(782\) −7.47107 −0.267165
\(783\) 41.0068 1.46547
\(784\) 15.2244 0.543728
\(785\) 24.6850 0.881046
\(786\) 2.94225 0.104947
\(787\) 2.60447 0.0928393 0.0464197 0.998922i \(-0.485219\pi\)
0.0464197 + 0.998922i \(0.485219\pi\)
\(788\) 5.05009 0.179902
\(789\) 43.8558 1.56131
\(790\) −24.4701 −0.870606
\(791\) −40.6071 −1.44382
\(792\) −8.12409 −0.288677
\(793\) −8.74608 −0.310583
\(794\) −31.0067 −1.10039
\(795\) −60.8499 −2.15813
\(796\) −7.59628 −0.269243
\(797\) −3.91991 −0.138850 −0.0694251 0.997587i \(-0.522116\pi\)
−0.0694251 + 0.997587i \(0.522116\pi\)
\(798\) 99.0904 3.50776
\(799\) −2.26951 −0.0802896
\(800\) −0.212702 −0.00752014
\(801\) 12.8532 0.454144
\(802\) 9.59094 0.338668
\(803\) 8.29774 0.292821
\(804\) 16.9745 0.598643
\(805\) −10.7633 −0.379357
\(806\) −5.63295 −0.198412
\(807\) −57.4105 −2.02095
\(808\) 6.53995 0.230075
\(809\) −27.7065 −0.974110 −0.487055 0.873371i \(-0.661929\pi\)
−0.487055 + 0.873371i \(0.661929\pi\)
\(810\) −13.7657 −0.483679
\(811\) 7.00465 0.245967 0.122983 0.992409i \(-0.460754\pi\)
0.122983 + 0.992409i \(0.460754\pi\)
\(812\) 24.7301 0.867857
\(813\) −20.0002 −0.701438
\(814\) 8.82890 0.309453
\(815\) −14.2918 −0.500619
\(816\) −21.9818 −0.769516
\(817\) −56.4741 −1.97578
\(818\) 9.47826 0.331400
\(819\) −46.1541 −1.61275
\(820\) −21.4058 −0.747524
\(821\) −34.7576 −1.21305 −0.606524 0.795065i \(-0.707437\pi\)
−0.606524 + 0.795065i \(0.707437\pi\)
\(822\) −33.8324 −1.18004
\(823\) −20.7040 −0.721695 −0.360847 0.932625i \(-0.617512\pi\)
−0.360847 + 0.932625i \(0.617512\pi\)
\(824\) −6.89029 −0.240035
\(825\) −0.898776 −0.0312914
\(826\) −6.12667 −0.213174
\(827\) 10.7536 0.373939 0.186969 0.982366i \(-0.440134\pi\)
0.186969 + 0.982366i \(0.440134\pi\)
\(828\) 5.65684 0.196589
\(829\) 19.0991 0.663338 0.331669 0.943396i \(-0.392388\pi\)
0.331669 + 0.943396i \(0.392388\pi\)
\(830\) 23.4856 0.815199
\(831\) −21.5096 −0.746158
\(832\) 1.73070 0.0600011
\(833\) 113.743 3.94094
\(834\) −9.07842 −0.314360
\(835\) 10.6114 0.367223
\(836\) −10.2598 −0.354842
\(837\) −25.4425 −0.879421
\(838\) −6.38892 −0.220702
\(839\) 37.9412 1.30987 0.654937 0.755683i \(-0.272695\pi\)
0.654937 + 0.755683i \(0.272695\pi\)
\(840\) −31.6684 −1.09266
\(841\) −1.48163 −0.0510907
\(842\) −1.58840 −0.0547399
\(843\) 20.0165 0.689403
\(844\) −20.3582 −0.700760
\(845\) −22.8420 −0.785790
\(846\) 1.71840 0.0590797
\(847\) 42.1336 1.44773
\(848\) 9.05835 0.311065
\(849\) −9.04836 −0.310539
\(850\) −1.58911 −0.0545060
\(851\) −6.14760 −0.210737
\(852\) 16.0391 0.549490
\(853\) −6.26064 −0.214360 −0.107180 0.994240i \(-0.534182\pi\)
−0.107180 + 0.994240i \(0.534182\pi\)
\(854\) −23.8236 −0.815227
\(855\) −92.2662 −3.15544
\(856\) 2.55452 0.0873115
\(857\) 25.7589 0.879908 0.439954 0.898020i \(-0.354995\pi\)
0.439954 + 0.898020i \(0.354995\pi\)
\(858\) 7.31311 0.249665
\(859\) 11.6471 0.397394 0.198697 0.980061i \(-0.436329\pi\)
0.198697 + 0.980061i \(0.436329\pi\)
\(860\) 18.0486 0.615453
\(861\) −130.045 −4.43194
\(862\) 1.09420 0.0372685
\(863\) 32.1383 1.09400 0.547000 0.837133i \(-0.315770\pi\)
0.547000 + 0.837133i \(0.315770\pi\)
\(864\) 7.81709 0.265943
\(865\) −23.2715 −0.791253
\(866\) 14.6104 0.496482
\(867\) −114.209 −3.87875
\(868\) −15.3437 −0.520798
\(869\) 15.3923 0.522150
\(870\) −35.2389 −1.19471
\(871\) −9.98476 −0.338321
\(872\) 5.12564 0.173576
\(873\) 102.937 3.48389
\(874\) 7.14393 0.241647
\(875\) 51.5272 1.74194
\(876\) −16.9996 −0.574363
\(877\) 26.6486 0.899860 0.449930 0.893064i \(-0.351449\pi\)
0.449930 + 0.893064i \(0.351449\pi\)
\(878\) 15.3855 0.519236
\(879\) 79.6612 2.68691
\(880\) 3.27893 0.110533
\(881\) −12.8234 −0.432031 −0.216016 0.976390i \(-0.569306\pi\)
−0.216016 + 0.976390i \(0.569306\pi\)
\(882\) −86.1219 −2.89988
\(883\) 26.2115 0.882087 0.441043 0.897486i \(-0.354609\pi\)
0.441043 + 0.897486i \(0.354609\pi\)
\(884\) 12.9302 0.434889
\(885\) 8.73013 0.293460
\(886\) 26.9669 0.905970
\(887\) −16.2097 −0.544268 −0.272134 0.962259i \(-0.587729\pi\)
−0.272134 + 0.962259i \(0.587729\pi\)
\(888\) −18.0878 −0.606986
\(889\) −91.2398 −3.06008
\(890\) −5.18761 −0.173889
\(891\) 8.65903 0.290088
\(892\) −23.8002 −0.796890
\(893\) 2.17014 0.0726208
\(894\) 3.56422 0.119205
\(895\) 18.7946 0.628233
\(896\) 4.71427 0.157493
\(897\) −5.09215 −0.170022
\(898\) −9.18812 −0.306611
\(899\) −17.0736 −0.569437
\(900\) 1.20322 0.0401073
\(901\) 67.6756 2.25460
\(902\) 13.4649 0.448331
\(903\) 109.650 3.64891
\(904\) −8.61364 −0.286485
\(905\) 60.7917 2.02079
\(906\) 27.5488 0.915246
\(907\) −33.3600 −1.10770 −0.553851 0.832616i \(-0.686842\pi\)
−0.553851 + 0.832616i \(0.686842\pi\)
\(908\) 24.2069 0.803334
\(909\) −36.9955 −1.22706
\(910\) 18.6281 0.617514
\(911\) −8.18479 −0.271174 −0.135587 0.990765i \(-0.543292\pi\)
−0.135587 + 0.990765i \(0.543292\pi\)
\(912\) 21.0192 0.696016
\(913\) −14.7731 −0.488919
\(914\) −7.14228 −0.236245
\(915\) 33.9472 1.12226
\(916\) −18.0713 −0.597091
\(917\) −4.71427 −0.155679
\(918\) 58.4021 1.92756
\(919\) −2.69643 −0.0889470 −0.0444735 0.999011i \(-0.514161\pi\)
−0.0444735 + 0.999011i \(0.514161\pi\)
\(920\) −2.28313 −0.0752727
\(921\) −58.0249 −1.91199
\(922\) 17.9737 0.591932
\(923\) −9.43454 −0.310542
\(924\) 19.9203 0.655329
\(925\) −1.30760 −0.0429938
\(926\) 24.6083 0.808680
\(927\) 38.9773 1.28018
\(928\) 5.24580 0.172202
\(929\) −22.2282 −0.729282 −0.364641 0.931148i \(-0.618808\pi\)
−0.364641 + 0.931148i \(0.618808\pi\)
\(930\) 21.8638 0.716942
\(931\) −108.762 −3.56453
\(932\) 22.3843 0.733224
\(933\) 42.1704 1.38060
\(934\) 37.8524 1.23857
\(935\) 24.4971 0.801142
\(936\) −9.79028 −0.320005
\(937\) −44.4880 −1.45336 −0.726681 0.686976i \(-0.758938\pi\)
−0.726681 + 0.686976i \(0.758938\pi\)
\(938\) −27.1976 −0.888034
\(939\) 62.6812 2.04552
\(940\) −0.693556 −0.0226213
\(941\) 24.8054 0.808634 0.404317 0.914619i \(-0.367509\pi\)
0.404317 + 0.914619i \(0.367509\pi\)
\(942\) 31.8113 1.03647
\(943\) −9.37564 −0.305313
\(944\) −1.29960 −0.0422984
\(945\) 84.1378 2.73700
\(946\) −11.3531 −0.369120
\(947\) 40.9263 1.32993 0.664963 0.746877i \(-0.268447\pi\)
0.664963 + 0.746877i \(0.268447\pi\)
\(948\) −31.5343 −1.02419
\(949\) 9.99955 0.324599
\(950\) 1.51952 0.0492999
\(951\) 23.9740 0.777409
\(952\) 35.2207 1.14151
\(953\) 0.541449 0.0175393 0.00876963 0.999962i \(-0.497209\pi\)
0.00876963 + 0.999962i \(0.497209\pi\)
\(954\) −51.2416 −1.65901
\(955\) −27.4267 −0.887507
\(956\) 21.1116 0.682799
\(957\) 22.1662 0.716533
\(958\) 19.1001 0.617097
\(959\) 54.2086 1.75049
\(960\) −6.71755 −0.216808
\(961\) −20.4068 −0.658282
\(962\) 10.6396 0.343036
\(963\) −14.4505 −0.465660
\(964\) −19.4969 −0.627954
\(965\) −8.32274 −0.267918
\(966\) −13.8706 −0.446279
\(967\) −6.52760 −0.209913 −0.104957 0.994477i \(-0.533470\pi\)
−0.104957 + 0.994477i \(0.533470\pi\)
\(968\) 8.93746 0.287261
\(969\) 157.036 5.04473
\(970\) −41.5460 −1.33396
\(971\) 46.8342 1.50298 0.751491 0.659743i \(-0.229335\pi\)
0.751491 + 0.659743i \(0.229335\pi\)
\(972\) 5.71150 0.183197
\(973\) 14.5461 0.466325
\(974\) 0.962350 0.0308357
\(975\) −1.08311 −0.0346872
\(976\) −5.05350 −0.161759
\(977\) 15.5997 0.499079 0.249540 0.968365i \(-0.419721\pi\)
0.249540 + 0.968365i \(0.419721\pi\)
\(978\) −18.4177 −0.588932
\(979\) 3.26315 0.104291
\(980\) 34.7593 1.11035
\(981\) −28.9949 −0.925736
\(982\) −17.2832 −0.551529
\(983\) 40.5147 1.29222 0.646109 0.763245i \(-0.276395\pi\)
0.646109 + 0.763245i \(0.276395\pi\)
\(984\) −27.5855 −0.879393
\(985\) 11.5300 0.367377
\(986\) 39.1917 1.24812
\(987\) −4.21351 −0.134118
\(988\) −12.3640 −0.393351
\(989\) 7.90519 0.251370
\(990\) −18.5484 −0.589507
\(991\) 51.3373 1.63078 0.815392 0.578910i \(-0.196522\pi\)
0.815392 + 0.578910i \(0.196522\pi\)
\(992\) −3.25473 −0.103338
\(993\) 41.1405 1.30555
\(994\) −25.6989 −0.815119
\(995\) −17.3433 −0.549820
\(996\) 30.2657 0.959005
\(997\) −5.30366 −0.167969 −0.0839844 0.996467i \(-0.526765\pi\)
−0.0839844 + 0.996467i \(0.526765\pi\)
\(998\) 11.8894 0.376352
\(999\) 48.0563 1.52044
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 \(a_p\))