Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13663 | 0.803718 | 0.401859 | − | 0.915702i | \(-0.368364\pi\) | ||||
0.401859 | + | 0.915702i | \(0.368364\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.708075 | −0.354038 | ||||||||
\(5\) | 0.214323 | 0.0958482 | 0.0479241 | − | 0.998851i | \(-0.484739\pi\) | ||||
0.0479241 | + | 0.998851i | \(0.484739\pi\) | |||||||
\(6\) | −1.13663 | −0.464027 | ||||||||
\(7\) | −3.67011 | −1.38717 | −0.693585 | − | 0.720375i | \(-0.743970\pi\) | ||||
−0.693585 | + | 0.720375i | \(0.743970\pi\) | |||||||
\(8\) | −3.07808 | −1.08826 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.243606 | 0.0770349 | ||||||||
\(11\) | 1.55131 | 0.467738 | 0.233869 | − | 0.972268i | \(-0.424861\pi\) | ||||
0.233869 | + | 0.972268i | \(0.424861\pi\) | |||||||
\(12\) | 0.708075 | 0.204404 | ||||||||
\(13\) | 4.74297 | 1.31546 | 0.657731 | − | 0.753253i | \(-0.271516\pi\) | ||||
0.657731 | + | 0.753253i | \(0.271516\pi\) | |||||||
\(14\) | −4.17155 | −1.11489 | ||||||||
\(15\) | −0.214323 | −0.0553380 | ||||||||
\(16\) | −2.08248 | −0.520620 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.13663 | 0.267906 | ||||||||
\(19\) | 2.11286 | 0.484722 | 0.242361 | − | 0.970186i | \(-0.422078\pi\) | ||||
0.242361 | + | 0.970186i | \(0.422078\pi\) | |||||||
\(20\) | −0.151757 | −0.0339339 | ||||||||
\(21\) | 3.67011 | 0.800883 | ||||||||
\(22\) | 1.76326 | 0.375929 | ||||||||
\(23\) | 6.11579 | 1.27523 | 0.637615 | − | 0.770355i | \(-0.279921\pi\) | ||||
0.637615 | + | 0.770355i | \(0.279921\pi\) | |||||||
\(24\) | 3.07808 | 0.628310 | ||||||||
\(25\) | −4.95407 | −0.990813 | ||||||||
\(26\) | 5.39099 | 1.05726 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.59871 | 0.491110 | ||||||||
\(29\) | 2.33087 | 0.432832 | 0.216416 | − | 0.976301i | \(-0.430563\pi\) | ||||
0.216416 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(30\) | −0.243606 | −0.0444761 | ||||||||
\(31\) | 2.34245 | 0.420716 | 0.210358 | − | 0.977624i | \(-0.432537\pi\) | ||||
0.210358 | + | 0.977624i | \(0.432537\pi\) | |||||||
\(32\) | 3.78915 | 0.669833 | ||||||||
\(33\) | −1.55131 | −0.270048 | ||||||||
\(34\) | −1.13663 | −0.194930 | ||||||||
\(35\) | −0.786588 | −0.132958 | ||||||||
\(36\) | −0.708075 | −0.118013 | ||||||||
\(37\) | −1.25736 | −0.206709 | −0.103355 | − | 0.994645i | \(-0.532958\pi\) | ||||
−0.103355 | + | 0.994645i | \(0.532958\pi\) | |||||||
\(38\) | 2.40153 | 0.389580 | ||||||||
\(39\) | −4.74297 | −0.759483 | ||||||||
\(40\) | −0.659702 | −0.104308 | ||||||||
\(41\) | −5.50155 | −0.859199 | −0.429599 | − | 0.903020i | \(-0.641345\pi\) | ||||
−0.429599 | + | 0.903020i | \(0.641345\pi\) | |||||||
\(42\) | 4.17155 | 0.643684 | ||||||||
\(43\) | −1.86178 | −0.283919 | −0.141959 | − | 0.989873i | \(-0.545340\pi\) | ||||
−0.141959 | + | 0.989873i | \(0.545340\pi\) | |||||||
\(44\) | −1.09844 | −0.165597 | ||||||||
\(45\) | 0.214323 | 0.0319494 | ||||||||
\(46\) | 6.95138 | 1.02492 | ||||||||
\(47\) | −11.7711 | −1.71699 | −0.858497 | − | 0.512819i | \(-0.828601\pi\) | ||||
−0.858497 | + | 0.512819i | \(0.828601\pi\) | |||||||
\(48\) | 2.08248 | 0.300580 | ||||||||
\(49\) | 6.46968 | 0.924240 | ||||||||
\(50\) | −5.63093 | −0.796334 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.35838 | −0.465723 | ||||||||
\(53\) | 10.9367 | 1.50227 | 0.751134 | − | 0.660150i | \(-0.229507\pi\) | ||||
0.751134 | + | 0.660150i | \(0.229507\pi\) | |||||||
\(54\) | −1.13663 | −0.154676 | ||||||||
\(55\) | 0.332481 | 0.0448318 | ||||||||
\(56\) | 11.2969 | 1.50961 | ||||||||
\(57\) | −2.11286 | −0.279855 | ||||||||
\(58\) | 2.64933 | 0.347875 | ||||||||
\(59\) | −9.95337 | −1.29582 | −0.647909 | − | 0.761718i | \(-0.724356\pi\) | ||||
−0.647909 | + | 0.761718i | \(0.724356\pi\) | |||||||
\(60\) | 0.151757 | 0.0195917 | ||||||||
\(61\) | 0.941200 | 0.120508 | 0.0602542 | − | 0.998183i | \(-0.480809\pi\) | ||||
0.0602542 | + | 0.998183i | \(0.480809\pi\) | |||||||
\(62\) | 2.66249 | 0.338137 | ||||||||
\(63\) | −3.67011 | −0.462390 | ||||||||
\(64\) | 8.47181 | 1.05898 | ||||||||
\(65\) | 1.01653 | 0.126085 | ||||||||
\(66\) | −1.76326 | −0.217043 | ||||||||
\(67\) | −9.40312 | −1.14877 | −0.574387 | − | 0.818584i | \(-0.694760\pi\) | ||||
−0.574387 | + | 0.818584i | \(0.694760\pi\) | |||||||
\(68\) | 0.708075 | 0.0858668 | ||||||||
\(69\) | −6.11579 | −0.736254 | ||||||||
\(70\) | −0.894059 | −0.106860 | ||||||||
\(71\) | −11.5189 | −1.36704 | −0.683521 | − | 0.729931i | \(-0.739552\pi\) | ||||
−0.683521 | + | 0.729931i | \(0.739552\pi\) | |||||||
\(72\) | −3.07808 | −0.362755 | ||||||||
\(73\) | 8.55533 | 1.00133 | 0.500663 | − | 0.865642i | \(-0.333090\pi\) | ||||
0.500663 | + | 0.865642i | \(0.333090\pi\) | |||||||
\(74\) | −1.42916 | −0.166136 | ||||||||
\(75\) | 4.95407 | 0.572046 | ||||||||
\(76\) | −1.49606 | −0.171610 | ||||||||
\(77\) | −5.69347 | −0.648831 | ||||||||
\(78\) | −5.39099 | −0.610410 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −0.446323 | −0.0499004 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.25322 | −0.690553 | ||||||||
\(83\) | 0.671241 | 0.0736783 | 0.0368391 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368391 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(84\) | −2.59871 | −0.283543 | ||||||||
\(85\) | −0.214323 | −0.0232466 | ||||||||
\(86\) | −2.11615 | −0.228190 | ||||||||
\(87\) | −2.33087 | −0.249896 | ||||||||
\(88\) | −4.77505 | −0.509022 | ||||||||
\(89\) | 9.15637 | 0.970573 | 0.485287 | − | 0.874355i | \(-0.338715\pi\) | ||||
0.485287 | + | 0.874355i | \(0.338715\pi\) | |||||||
\(90\) | 0.243606 | 0.0256783 | ||||||||
\(91\) | −17.4072 | −1.82477 | ||||||||
\(92\) | −4.33044 | −0.451479 | ||||||||
\(93\) | −2.34245 | −0.242900 | ||||||||
\(94\) | −13.3794 | −1.37998 | ||||||||
\(95\) | 0.452834 | 0.0464597 | ||||||||
\(96\) | −3.78915 | −0.386728 | ||||||||
\(97\) | −9.74734 | −0.989692 | −0.494846 | − | 0.868981i | \(-0.664776\pi\) | ||||
−0.494846 | + | 0.868981i | \(0.664776\pi\) | |||||||
\(98\) | 7.35362 | 0.742828 | ||||||||
\(99\) | 1.55131 | 0.155913 | ||||||||
\(100\) | 3.50785 | 0.350785 | ||||||||
\(101\) | −7.11071 | −0.707542 | −0.353771 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353771 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(102\) | 1.13663 | 0.112543 | ||||||||
\(103\) | −16.2637 | −1.60251 | −0.801253 | − | 0.598325i | \(-0.795833\pi\) | ||||
−0.801253 | + | 0.598325i | \(0.795833\pi\) | |||||||
\(104\) | −14.5992 | −1.43157 | ||||||||
\(105\) | 0.786588 | 0.0767631 | ||||||||
\(106\) | 12.4309 | 1.20740 | ||||||||
\(107\) | 1.70968 | 0.165281 | 0.0826406 | − | 0.996579i | \(-0.473665\pi\) | ||||
0.0826406 | + | 0.996579i | \(0.473665\pi\) | |||||||
\(108\) | 0.708075 | 0.0681346 | ||||||||
\(109\) | −12.4469 | −1.19220 | −0.596099 | − | 0.802911i | \(-0.703283\pi\) | ||||
−0.596099 | + | 0.802911i | \(0.703283\pi\) | |||||||
\(110\) | 0.377908 | 0.0360321 | ||||||||
\(111\) | 1.25736 | 0.119344 | ||||||||
\(112\) | 7.64292 | 0.722188 | ||||||||
\(113\) | −17.4918 | −1.64549 | −0.822745 | − | 0.568411i | \(-0.807558\pi\) | ||||
−0.822745 | + | 0.568411i | \(0.807558\pi\) | |||||||
\(114\) | −2.40153 | −0.224924 | ||||||||
\(115\) | 1.31075 | 0.122228 | ||||||||
\(116\) | −1.65043 | −0.153239 | ||||||||
\(117\) | 4.74297 | 0.438487 | ||||||||
\(118\) | −11.3133 | −1.04147 | ||||||||
\(119\) | 3.67011 | 0.336438 | ||||||||
\(120\) | 0.659702 | 0.0602223 | ||||||||
\(121\) | −8.59344 | −0.781222 | ||||||||
\(122\) | 1.06980 | 0.0968547 | ||||||||
\(123\) | 5.50155 | 0.496058 | ||||||||
\(124\) | −1.65863 | −0.148949 | ||||||||
\(125\) | −2.13339 | −0.190816 | ||||||||
\(126\) | −4.17155 | −0.371631 | ||||||||
\(127\) | 6.09114 | 0.540502 | 0.270251 | − | 0.962790i | \(-0.412893\pi\) | ||||
0.270251 | + | 0.962790i | \(0.412893\pi\) | |||||||
\(128\) | 2.05101 | 0.181285 | ||||||||
\(129\) | 1.86178 | 0.163920 | ||||||||
\(130\) | 1.15541 | 0.101336 | ||||||||
\(131\) | −7.73013 | −0.675384 | −0.337692 | − | 0.941257i | \(-0.609646\pi\) | ||||
−0.337692 | + | 0.941257i | \(0.609646\pi\) | |||||||
\(132\) | 1.09844 | 0.0956073 | ||||||||
\(133\) | −7.75441 | −0.672392 | ||||||||
\(134\) | −10.6879 | −0.923290 | ||||||||
\(135\) | −0.214323 | −0.0184460 | ||||||||
\(136\) | 3.07808 | 0.263943 | ||||||||
\(137\) | 16.9300 | 1.44643 | 0.723215 | − | 0.690623i | \(-0.242664\pi\) | ||||
0.723215 | + | 0.690623i | \(0.242664\pi\) | |||||||
\(138\) | −6.95138 | −0.591741 | ||||||||
\(139\) | 12.7928 | 1.08507 | 0.542534 | − | 0.840034i | \(-0.317465\pi\) | ||||
0.542534 | + | 0.840034i | \(0.317465\pi\) | |||||||
\(140\) | 0.556964 | 0.0470720 | ||||||||
\(141\) | 11.7711 | 0.991307 | ||||||||
\(142\) | −13.0927 | −1.09872 | ||||||||
\(143\) | 7.35781 | 0.615291 | ||||||||
\(144\) | −2.08248 | −0.173540 | ||||||||
\(145\) | 0.499559 | 0.0414861 | ||||||||
\(146\) | 9.72423 | 0.804783 | ||||||||
\(147\) | −6.46968 | −0.533610 | ||||||||
\(148\) | 0.890308 | 0.0731829 | ||||||||
\(149\) | −12.0048 | −0.983468 | −0.491734 | − | 0.870745i | \(-0.663637\pi\) | ||||
−0.491734 | + | 0.870745i | \(0.663637\pi\) | |||||||
\(150\) | 5.63093 | 0.459764 | ||||||||
\(151\) | −4.54958 | −0.370240 | −0.185120 | − | 0.982716i | \(-0.559267\pi\) | ||||
−0.185120 | + | 0.982716i | \(0.559267\pi\) | |||||||
\(152\) | −6.50353 | −0.527506 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −6.47136 | −0.521477 | ||||||||
\(155\) | 0.502040 | 0.0403248 | ||||||||
\(156\) | 3.35838 | 0.268885 | ||||||||
\(157\) | −8.32921 | −0.664744 | −0.332372 | − | 0.943148i | \(-0.607849\pi\) | ||||
−0.332372 | + | 0.943148i | \(0.607849\pi\) | |||||||
\(158\) | −1.13663 | −0.0904253 | ||||||||
\(159\) | −10.9367 | −0.867334 | ||||||||
\(160\) | 0.812101 | 0.0642023 | ||||||||
\(161\) | −22.4456 | −1.76896 | ||||||||
\(162\) | 1.13663 | 0.0893020 | ||||||||
\(163\) | 5.47361 | 0.428726 | 0.214363 | − | 0.976754i | \(-0.431232\pi\) | ||||
0.214363 | + | 0.976754i | \(0.431232\pi\) | |||||||
\(164\) | 3.89552 | 0.304189 | ||||||||
\(165\) | −0.332481 | −0.0258836 | ||||||||
\(166\) | 0.762952 | 0.0592166 | ||||||||
\(167\) | −9.15869 | −0.708721 | −0.354360 | − | 0.935109i | \(-0.615301\pi\) | ||||
−0.354360 | + | 0.935109i | \(0.615301\pi\) | |||||||
\(168\) | −11.2969 | −0.871572 | ||||||||
\(169\) | 9.49574 | 0.730441 | ||||||||
\(170\) | −0.243606 | −0.0186837 | ||||||||
\(171\) | 2.11286 | 0.161574 | ||||||||
\(172\) | 1.31828 | 0.100518 | ||||||||
\(173\) | 12.0426 | 0.915578 | 0.457789 | − | 0.889061i | \(-0.348641\pi\) | ||||
0.457789 | + | 0.889061i | \(0.348641\pi\) | |||||||
\(174\) | −2.64933 | −0.200846 | ||||||||
\(175\) | 18.1819 | 1.37443 | ||||||||
\(176\) | −3.23057 | −0.243513 | ||||||||
\(177\) | 9.95337 | 0.748141 | ||||||||
\(178\) | 10.4074 | 0.780067 | ||||||||
\(179\) | −7.94145 | −0.593572 | −0.296786 | − | 0.954944i | \(-0.595915\pi\) | ||||
−0.296786 | + | 0.954944i | \(0.595915\pi\) | |||||||
\(180\) | −0.151757 | −0.0113113 | ||||||||
\(181\) | 25.8212 | 1.91927 | 0.959636 | − | 0.281245i | \(-0.0907472\pi\) | ||||
0.959636 | + | 0.281245i | \(0.0907472\pi\) | |||||||
\(182\) | −19.7855 | −1.46660 | ||||||||
\(183\) | −0.941200 | −0.0695755 | ||||||||
\(184\) | −18.8249 | −1.38779 | ||||||||
\(185\) | −0.269482 | −0.0198127 | ||||||||
\(186\) | −2.66249 | −0.195223 | ||||||||
\(187\) | −1.55131 | −0.113443 | ||||||||
\(188\) | 8.33484 | 0.607881 | ||||||||
\(189\) | 3.67011 | 0.266961 | ||||||||
\(190\) | 0.514704 | 0.0373405 | ||||||||
\(191\) | −16.3757 | −1.18490 | −0.592452 | − | 0.805606i | \(-0.701840\pi\) | ||||
−0.592452 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(192\) | −8.47181 | −0.611400 | ||||||||
\(193\) | −3.74152 | −0.269320 | −0.134660 | − | 0.990892i | \(-0.542994\pi\) | ||||
−0.134660 | + | 0.990892i | \(0.542994\pi\) | |||||||
\(194\) | −11.0791 | −0.795433 | ||||||||
\(195\) | −1.01653 | −0.0727950 | ||||||||
\(196\) | −4.58102 | −0.327216 | ||||||||
\(197\) | −2.82332 | −0.201153 | −0.100577 | − | 0.994929i | \(-0.532069\pi\) | ||||
−0.100577 | + | 0.994929i | \(0.532069\pi\) | |||||||
\(198\) | 1.76326 | 0.125310 | ||||||||
\(199\) | −12.3050 | −0.872275 | −0.436138 | − | 0.899880i | \(-0.643654\pi\) | ||||
−0.436138 | + | 0.899880i | \(0.643654\pi\) | |||||||
\(200\) | 15.2490 | 1.07827 | ||||||||
\(201\) | 9.40312 | 0.663245 | ||||||||
\(202\) | −8.08223 | −0.568664 | ||||||||
\(203\) | −8.55454 | −0.600411 | ||||||||
\(204\) | −0.708075 | −0.0495752 | ||||||||
\(205\) | −1.17911 | −0.0823526 | ||||||||
\(206\) | −18.4857 | −1.28796 | ||||||||
\(207\) | 6.11579 | 0.425077 | ||||||||
\(208\) | −9.87713 | −0.684855 | ||||||||
\(209\) | 3.27770 | 0.226723 | ||||||||
\(210\) | 0.894059 | 0.0616959 | ||||||||
\(211\) | 22.1380 | 1.52405 | 0.762023 | − | 0.647550i | \(-0.224206\pi\) | ||||
0.762023 | + | 0.647550i | \(0.224206\pi\) | |||||||
\(212\) | −7.74399 | −0.531859 | ||||||||
\(213\) | 11.5189 | 0.789262 | ||||||||
\(214\) | 1.94327 | 0.132839 | ||||||||
\(215\) | −0.399022 | −0.0272131 | ||||||||
\(216\) | 3.07808 | 0.209437 | ||||||||
\(217\) | −8.59702 | −0.583604 | ||||||||
\(218\) | −14.1475 | −0.958191 | ||||||||
\(219\) | −8.55533 | −0.578116 | ||||||||
\(220\) | −0.235422 | −0.0158721 | ||||||||
\(221\) | −4.74297 | −0.319047 | ||||||||
\(222\) | 1.42916 | 0.0959186 | ||||||||
\(223\) | 9.31754 | 0.623948 | 0.311974 | − | 0.950091i | \(-0.399010\pi\) | ||||
0.311974 | + | 0.950091i | \(0.399010\pi\) | |||||||
\(224\) | −13.9066 | −0.929172 | ||||||||
\(225\) | −4.95407 | −0.330271 | ||||||||
\(226\) | −19.8817 | −1.32251 | ||||||||
\(227\) | −6.76431 | −0.448963 | −0.224482 | − | 0.974478i | \(-0.572069\pi\) | ||||
−0.224482 | + | 0.974478i | \(0.572069\pi\) | |||||||
\(228\) | 1.49606 | 0.0990791 | ||||||||
\(229\) | −21.6557 | −1.43105 | −0.715523 | − | 0.698589i | \(-0.753812\pi\) | ||||
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(230\) | 1.48984 | 0.0982372 | ||||||||
\(231\) | 5.69347 | 0.374603 | ||||||||
\(232\) | −7.17460 | −0.471035 | ||||||||
\(233\) | −3.67388 | −0.240684 | −0.120342 | − | 0.992732i | \(-0.538399\pi\) | ||||
−0.120342 | + | 0.992732i | \(0.538399\pi\) | |||||||
\(234\) | 5.39099 | 0.352420 | ||||||||
\(235\) | −2.52282 | −0.164571 | ||||||||
\(236\) | 7.04774 | 0.458769 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 4.17155 | 0.270401 | ||||||||
\(239\) | 3.05888 | 0.197862 | 0.0989312 | − | 0.995094i | \(-0.468458\pi\) | ||||
0.0989312 | + | 0.995094i | \(0.468458\pi\) | |||||||
\(240\) | 0.446323 | 0.0288100 | ||||||||
\(241\) | 1.60800 | 0.103580 | 0.0517902 | − | 0.998658i | \(-0.483507\pi\) | ||||
0.0517902 | + | 0.998658i | \(0.483507\pi\) | |||||||
\(242\) | −9.76755 | −0.627882 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.666441 | −0.0426645 | ||||||||
\(245\) | 1.38660 | 0.0885867 | ||||||||
\(246\) | 6.25322 | 0.398691 | ||||||||
\(247\) | 10.0212 | 0.637634 | ||||||||
\(248\) | −7.21022 | −0.457850 | ||||||||
\(249\) | −0.671241 | −0.0425382 | ||||||||
\(250\) | −2.42487 | −0.153362 | ||||||||
\(251\) | 10.9970 | 0.694122 | 0.347061 | − | 0.937843i | \(-0.387180\pi\) | ||||
0.347061 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(252\) | 2.59871 | 0.163703 | ||||||||
\(253\) | 9.48748 | 0.596473 | ||||||||
\(254\) | 6.92337 | 0.434411 | ||||||||
\(255\) | 0.214323 | 0.0134214 | ||||||||
\(256\) | −14.6124 | −0.913274 | ||||||||
\(257\) | −28.0759 | −1.75133 | −0.875663 | − | 0.482923i | \(-0.839575\pi\) | ||||
−0.875663 | + | 0.482923i | \(0.839575\pi\) | |||||||
\(258\) | 2.11615 | 0.131746 | ||||||||
\(259\) | 4.61466 | 0.286741 | ||||||||
\(260\) | −0.719778 | −0.0446387 | ||||||||
\(261\) | 2.33087 | 0.144277 | ||||||||
\(262\) | −8.78628 | −0.542818 | ||||||||
\(263\) | −8.20013 | −0.505642 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(264\) | 4.77505 | 0.293884 | ||||||||
\(265\) | 2.34398 | 0.143990 | ||||||||
\(266\) | −8.81388 | −0.540414 | ||||||||
\(267\) | −9.15637 | −0.560361 | ||||||||
\(268\) | 6.65812 | 0.406710 | ||||||||
\(269\) | −9.93169 | −0.605546 | −0.302773 | − | 0.953063i | \(-0.597912\pi\) | ||||
−0.302773 | + | 0.953063i | \(0.597912\pi\) | |||||||
\(270\) | −0.243606 | −0.0148254 | ||||||||
\(271\) | −15.1264 | −0.918866 | −0.459433 | − | 0.888212i | \(-0.651947\pi\) | ||||
−0.459433 | + | 0.888212i | \(0.651947\pi\) | |||||||
\(272\) | 2.08248 | 0.126269 | ||||||||
\(273\) | 17.4072 | 1.05353 | ||||||||
\(274\) | 19.2431 | 1.16252 | ||||||||
\(275\) | −7.68529 | −0.463441 | ||||||||
\(276\) | 4.33044 | 0.260662 | ||||||||
\(277\) | 15.3924 | 0.924840 | 0.462420 | − | 0.886661i | \(-0.346981\pi\) | ||||
0.462420 | + | 0.886661i | \(0.346981\pi\) | |||||||
\(278\) | 14.5406 | 0.872088 | ||||||||
\(279\) | 2.34245 | 0.140239 | ||||||||
\(280\) | 2.42118 | 0.144693 | ||||||||
\(281\) | 1.50282 | 0.0896505 | 0.0448253 | − | 0.998995i | \(-0.485727\pi\) | ||||
0.0448253 | + | 0.998995i | \(0.485727\pi\) | |||||||
\(282\) | 13.3794 | 0.796731 | ||||||||
\(283\) | 29.0096 | 1.72444 | 0.862220 | − | 0.506534i | \(-0.169074\pi\) | ||||
0.862220 | + | 0.506534i | \(0.169074\pi\) | |||||||
\(284\) | 8.15625 | 0.483984 | ||||||||
\(285\) | −0.452834 | −0.0268235 | ||||||||
\(286\) | 8.36310 | 0.494521 | ||||||||
\(287\) | 20.1913 | 1.19185 | ||||||||
\(288\) | 3.78915 | 0.223278 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.567813 | 0.0333431 | ||||||||
\(291\) | 9.74734 | 0.571399 | ||||||||
\(292\) | −6.05782 | −0.354507 | ||||||||
\(293\) | −16.1990 | −0.946355 | −0.473178 | − | 0.880967i | \(-0.656893\pi\) | ||||
−0.473178 | + | 0.880967i | \(0.656893\pi\) | |||||||
\(294\) | −7.35362 | −0.428872 | ||||||||
\(295\) | −2.13324 | −0.124202 | ||||||||
\(296\) | 3.87026 | 0.224954 | ||||||||
\(297\) | −1.55131 | −0.0900161 | ||||||||
\(298\) | −13.6450 | −0.790431 | ||||||||
\(299\) | 29.0070 | 1.67752 | ||||||||
\(300\) | −3.50785 | −0.202526 | ||||||||
\(301\) | 6.83292 | 0.393843 | ||||||||
\(302\) | −5.17118 | −0.297568 | ||||||||
\(303\) | 7.11071 | 0.408499 | ||||||||
\(304\) | −4.39998 | −0.252356 | ||||||||
\(305\) | 0.201721 | 0.0115505 | ||||||||
\(306\) | −1.13663 | −0.0649767 | ||||||||
\(307\) | −8.81308 | −0.502989 | −0.251495 | − | 0.967859i | \(-0.580922\pi\) | ||||
−0.251495 | + | 0.967859i | \(0.580922\pi\) | |||||||
\(308\) | 4.03141 | 0.229711 | ||||||||
\(309\) | 16.2637 | 0.925208 | ||||||||
\(310\) | 0.570633 | 0.0324098 | ||||||||
\(311\) | −18.4789 | −1.04784 | −0.523921 | − | 0.851767i | \(-0.675531\pi\) | ||||
−0.523921 | + | 0.851767i | \(0.675531\pi\) | |||||||
\(312\) | 14.5992 | 0.826518 | ||||||||
\(313\) | −14.5072 | −0.819996 | −0.409998 | − | 0.912086i | \(-0.634471\pi\) | ||||
−0.409998 | + | 0.912086i | \(0.634471\pi\) | |||||||
\(314\) | −9.46722 | −0.534266 | ||||||||
\(315\) | −0.786588 | −0.0443192 | ||||||||
\(316\) | 0.708075 | 0.0398324 | ||||||||
\(317\) | 16.4750 | 0.925330 | 0.462665 | − | 0.886533i | \(-0.346893\pi\) | ||||
0.462665 | + | 0.886533i | \(0.346893\pi\) | |||||||
\(318\) | −12.4309 | −0.697092 | ||||||||
\(319\) | 3.61590 | 0.202452 | ||||||||
\(320\) | 1.81570 | 0.101501 | ||||||||
\(321\) | −1.70968 | −0.0954252 | ||||||||
\(322\) | −25.5123 | −1.42174 | ||||||||
\(323\) | −2.11286 | −0.117562 | ||||||||
\(324\) | −0.708075 | −0.0393375 | ||||||||
\(325\) | −23.4970 | −1.30338 | ||||||||
\(326\) | 6.22147 | 0.344575 | ||||||||
\(327\) | 12.4469 | 0.688316 | ||||||||
\(328\) | 16.9342 | 0.935035 | ||||||||
\(329\) | 43.2012 | 2.38176 | ||||||||
\(330\) | −0.377908 | −0.0208031 | ||||||||
\(331\) | −19.5599 | −1.07511 | −0.537554 | − | 0.843229i | \(-0.680652\pi\) | ||||
−0.537554 | + | 0.843229i | \(0.680652\pi\) | |||||||
\(332\) | −0.475289 | −0.0260849 | ||||||||
\(333\) | −1.25736 | −0.0689031 | ||||||||
\(334\) | −10.4100 | −0.569612 | ||||||||
\(335\) | −2.01531 | −0.110108 | ||||||||
\(336\) | −7.64292 | −0.416955 | ||||||||
\(337\) | −8.28556 | −0.451343 | −0.225672 | − | 0.974203i | \(-0.572458\pi\) | ||||
−0.225672 | + | 0.974203i | \(0.572458\pi\) | |||||||
\(338\) | 10.7931 | 0.587069 | ||||||||
\(339\) | 17.4918 | 0.950024 | ||||||||
\(340\) | 0.151757 | 0.00823017 | ||||||||
\(341\) | 3.63386 | 0.196784 | ||||||||
\(342\) | 2.40153 | 0.129860 | ||||||||
\(343\) | 1.94633 | 0.105092 | ||||||||
\(344\) | 5.73069 | 0.308978 | ||||||||
\(345\) | −1.31075 | −0.0705686 | ||||||||
\(346\) | 13.6879 | 0.735867 | ||||||||
\(347\) | 29.3419 | 1.57515 | 0.787577 | − | 0.616216i | \(-0.211335\pi\) | ||||
0.787577 | + | 0.616216i | \(0.211335\pi\) | |||||||
\(348\) | 1.65043 | 0.0884725 | ||||||||
\(349\) | 21.7187 | 1.16257 | 0.581287 | − | 0.813699i | \(-0.302549\pi\) | ||||
0.581287 | + | 0.813699i | \(0.302549\pi\) | |||||||
\(350\) | 20.6661 | 1.10465 | ||||||||
\(351\) | −4.74297 | −0.253161 | ||||||||
\(352\) | 5.87814 | 0.313306 | ||||||||
\(353\) | 24.7560 | 1.31763 | 0.658814 | − | 0.752306i | \(-0.271059\pi\) | ||||
0.658814 | + | 0.752306i | \(0.271059\pi\) | |||||||
\(354\) | 11.3133 | 0.601294 | ||||||||
\(355\) | −2.46876 | −0.131028 | ||||||||
\(356\) | −6.48340 | −0.343620 | ||||||||
\(357\) | −3.67011 | −0.194243 | ||||||||
\(358\) | −9.02648 | −0.477064 | ||||||||
\(359\) | −9.57224 | −0.505204 | −0.252602 | − | 0.967570i | \(-0.581286\pi\) | ||||
−0.252602 | + | 0.967570i | \(0.581286\pi\) | |||||||
\(360\) | −0.659702 | −0.0347694 | ||||||||
\(361\) | −14.5358 | −0.765044 | ||||||||
\(362\) | 29.3491 | 1.54255 | ||||||||
\(363\) | 8.59344 | 0.451038 | ||||||||
\(364\) | 12.3256 | 0.646037 | ||||||||
\(365\) | 1.83360 | 0.0959752 | ||||||||
\(366\) | −1.06980 | −0.0559191 | ||||||||
\(367\) | −27.1320 | −1.41628 | −0.708139 | − | 0.706073i | \(-0.750465\pi\) | ||||
−0.708139 | + | 0.706073i | \(0.750465\pi\) | |||||||
\(368\) | −12.7360 | −0.663910 | ||||||||
\(369\) | −5.50155 | −0.286400 | ||||||||
\(370\) | −0.306301 | −0.0159238 | ||||||||
\(371\) | −40.1387 | −2.08390 | ||||||||
\(372\) | 1.65863 | 0.0859958 | ||||||||
\(373\) | −2.78783 | −0.144348 | −0.0721741 | − | 0.997392i | \(-0.522994\pi\) | ||||
−0.0721741 | + | 0.997392i | \(0.522994\pi\) | |||||||
\(374\) | −1.76326 | −0.0911762 | ||||||||
\(375\) | 2.13339 | 0.110168 | ||||||||
\(376\) | 36.2324 | 1.86854 | ||||||||
\(377\) | 11.0552 | 0.569374 | ||||||||
\(378\) | 4.17155 | 0.214561 | ||||||||
\(379\) | 5.41556 | 0.278178 | 0.139089 | − | 0.990280i | \(-0.455583\pi\) | ||||
0.139089 | + | 0.990280i | \(0.455583\pi\) | |||||||
\(380\) | −0.320640 | −0.0164485 | ||||||||
\(381\) | −6.09114 | −0.312059 | ||||||||
\(382\) | −18.6131 | −0.952328 | ||||||||
\(383\) | −18.9645 | −0.969040 | −0.484520 | − | 0.874780i | \(-0.661006\pi\) | ||||
−0.484520 | + | 0.874780i | \(0.661006\pi\) | |||||||
\(384\) | −2.05101 | −0.104665 | ||||||||
\(385\) | −1.22024 | −0.0621893 | ||||||||
\(386\) | −4.25271 | −0.216457 | ||||||||
\(387\) | −1.86178 | −0.0946395 | ||||||||
\(388\) | 6.90185 | 0.350388 | ||||||||
\(389\) | −9.49053 | −0.481189 | −0.240594 | − | 0.970626i | \(-0.577342\pi\) | ||||
−0.240594 | + | 0.970626i | \(0.577342\pi\) | |||||||
\(390\) | −1.15541 | −0.0585066 | ||||||||
\(391\) | −6.11579 | −0.309289 | ||||||||
\(392\) | −19.9142 | −1.00582 | ||||||||
\(393\) | 7.73013 | 0.389933 | ||||||||
\(394\) | −3.20907 | −0.161670 | ||||||||
\(395\) | −0.214323 | −0.0107838 | ||||||||
\(396\) | −1.09844 | −0.0551989 | ||||||||
\(397\) | 16.9087 | 0.848625 | 0.424313 | − | 0.905516i | \(-0.360516\pi\) | ||||
0.424313 | + | 0.905516i | \(0.360516\pi\) | |||||||
\(398\) | −13.9862 | −0.701063 | ||||||||
\(399\) | 7.75441 | 0.388206 | ||||||||
\(400\) | 10.3167 | 0.515837 | ||||||||
\(401\) | −7.42429 | −0.370751 | −0.185376 | − | 0.982668i | \(-0.559350\pi\) | ||||
−0.185376 | + | 0.982668i | \(0.559350\pi\) | |||||||
\(402\) | 10.6879 | 0.533062 | ||||||||
\(403\) | 11.1101 | 0.553436 | ||||||||
\(404\) | 5.03492 | 0.250497 | ||||||||
\(405\) | 0.214323 | 0.0106498 | ||||||||
\(406\) | −9.72334 | −0.482561 | ||||||||
\(407\) | −1.95056 | −0.0966857 | ||||||||
\(408\) | −3.07808 | −0.152387 | ||||||||
\(409\) | 11.8120 | 0.584065 | 0.292032 | − | 0.956408i | \(-0.405668\pi\) | ||||
0.292032 | + | 0.956408i | \(0.405668\pi\) | |||||||
\(410\) | −1.34021 | −0.0661882 | ||||||||
\(411\) | −16.9300 | −0.835096 | ||||||||
\(412\) | 11.5159 | 0.567348 | ||||||||
\(413\) | 36.5299 | 1.79752 | ||||||||
\(414\) | 6.95138 | 0.341642 | ||||||||
\(415\) | 0.143862 | 0.00706193 | ||||||||
\(416\) | 17.9718 | 0.881140 | ||||||||
\(417\) | −12.7928 | −0.626464 | ||||||||
\(418\) | 3.72552 | 0.182221 | ||||||||
\(419\) | 19.1553 | 0.935797 | 0.467899 | − | 0.883782i | \(-0.345011\pi\) | ||||
0.467899 | + | 0.883782i | \(0.345011\pi\) | |||||||
\(420\) | −0.556964 | −0.0271770 | ||||||||
\(421\) | −8.29817 | −0.404428 | −0.202214 | − | 0.979341i | \(-0.564814\pi\) | ||||
−0.202214 | + | 0.979341i | \(0.564814\pi\) | |||||||
\(422\) | 25.1627 | 1.22490 | ||||||||
\(423\) | −11.7711 | −0.572331 | ||||||||
\(424\) | −33.6639 | −1.63486 | ||||||||
\(425\) | 4.95407 | 0.240307 | ||||||||
\(426\) | 13.0927 | 0.634344 | ||||||||
\(427\) | −3.45431 | −0.167166 | ||||||||
\(428\) | −1.21058 | −0.0585158 | ||||||||
\(429\) | −7.35781 | −0.355239 | ||||||||
\(430\) | −0.453540 | −0.0218716 | ||||||||
\(431\) | 9.27257 | 0.446644 | 0.223322 | − | 0.974745i | \(-0.428310\pi\) | ||||
0.223322 | + | 0.974745i | \(0.428310\pi\) | |||||||
\(432\) | 2.08248 | 0.100193 | ||||||||
\(433\) | −19.2380 | −0.924519 | −0.462260 | − | 0.886745i | \(-0.652961\pi\) | ||||
−0.462260 | + | 0.886745i | \(0.652961\pi\) | |||||||
\(434\) | −9.77162 | −0.469053 | ||||||||
\(435\) | −0.499559 | −0.0239520 | ||||||||
\(436\) | 8.81335 | 0.422083 | ||||||||
\(437\) | 12.9218 | 0.618132 | ||||||||
\(438\) | −9.72423 | −0.464642 | ||||||||
\(439\) | −22.9217 | −1.09399 | −0.546996 | − | 0.837135i | \(-0.684229\pi\) | ||||
−0.546996 | + | 0.837135i | \(0.684229\pi\) | |||||||
\(440\) | −1.02340 | −0.0487888 | ||||||||
\(441\) | 6.46968 | 0.308080 | ||||||||
\(442\) | −5.39099 | −0.256423 | ||||||||
\(443\) | 27.1028 | 1.28769 | 0.643847 | − | 0.765155i | \(-0.277337\pi\) | ||||
0.643847 | + | 0.765155i | \(0.277337\pi\) | |||||||
\(444\) | −0.890308 | −0.0422522 | ||||||||
\(445\) | 1.96242 | 0.0930277 | ||||||||
\(446\) | 10.5906 | 0.501478 | ||||||||
\(447\) | 12.0048 | 0.567806 | ||||||||
\(448\) | −31.0924 | −1.46898 | ||||||||
\(449\) | 37.2215 | 1.75659 | 0.878296 | − | 0.478118i | \(-0.158681\pi\) | ||||
0.878296 | + | 0.478118i | \(0.158681\pi\) | |||||||
\(450\) | −5.63093 | −0.265445 | ||||||||
\(451\) | −8.53462 | −0.401879 | ||||||||
\(452\) | 12.3855 | 0.582565 | ||||||||
\(453\) | 4.54958 | 0.213758 | ||||||||
\(454\) | −7.68851 | −0.360840 | ||||||||
\(455\) | −3.73076 | −0.174901 | ||||||||
\(456\) | 6.50353 | 0.304556 | ||||||||
\(457\) | −7.49997 | −0.350834 | −0.175417 | − | 0.984494i | \(-0.556127\pi\) | ||||
−0.175417 | + | 0.984494i | \(0.556127\pi\) | |||||||
\(458\) | −24.6145 | −1.15016 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.928113 | −0.0432735 | ||||||||
\(461\) | 35.7101 | 1.66319 | 0.831593 | − | 0.555386i | \(-0.187429\pi\) | ||||
0.831593 | + | 0.555386i | \(0.187429\pi\) | |||||||
\(462\) | 6.47136 | 0.301075 | ||||||||
\(463\) | −37.5659 | −1.74583 | −0.872917 | − | 0.487869i | \(-0.837774\pi\) | ||||
−0.872917 | + | 0.487869i | \(0.837774\pi\) | |||||||
\(464\) | −4.85399 | −0.225341 | ||||||||
\(465\) | −0.502040 | −0.0232815 | ||||||||
\(466\) | −4.17584 | −0.193442 | ||||||||
\(467\) | −6.87574 | −0.318171 | −0.159086 | − | 0.987265i | \(-0.550855\pi\) | ||||
−0.159086 | + | 0.987265i | \(0.550855\pi\) | |||||||
\(468\) | −3.35838 | −0.155241 | ||||||||
\(469\) | 34.5105 | 1.59355 | ||||||||
\(470\) | −2.86751 | −0.132268 | ||||||||
\(471\) | 8.32921 | 0.383790 | ||||||||
\(472\) | 30.6372 | 1.41019 | ||||||||
\(473\) | −2.88820 | −0.132799 | ||||||||
\(474\) | 1.13663 | 0.0522071 | ||||||||
\(475\) | −10.4672 | −0.480269 | ||||||||
\(476\) | −2.59871 | −0.119112 | ||||||||
\(477\) | 10.9367 | 0.500756 | ||||||||
\(478\) | 3.47681 | 0.159026 | ||||||||
\(479\) | −12.1106 | −0.553347 | −0.276673 | − | 0.960964i | \(-0.589232\pi\) | ||||
−0.276673 | + | 0.960964i | \(0.589232\pi\) | |||||||
\(480\) | −0.812101 | −0.0370672 | ||||||||
\(481\) | −5.96364 | −0.271918 | ||||||||
\(482\) | 1.82770 | 0.0832494 | ||||||||
\(483\) | 22.4456 | 1.02131 | ||||||||
\(484\) | 6.08480 | 0.276582 | ||||||||
\(485\) | −2.08908 | −0.0948602 | ||||||||
\(486\) | −1.13663 | −0.0515585 | ||||||||
\(487\) | −18.9233 | −0.857494 | −0.428747 | − | 0.903424i | \(-0.641045\pi\) | ||||
−0.428747 | + | 0.903424i | \(0.641045\pi\) | |||||||
\(488\) | −2.89709 | −0.131145 | ||||||||
\(489\) | −5.47361 | −0.247525 | ||||||||
\(490\) | 1.57605 | 0.0711987 | ||||||||
\(491\) | −31.8196 | −1.43600 | −0.717998 | − | 0.696045i | \(-0.754941\pi\) | ||||
−0.717998 | + | 0.696045i | \(0.754941\pi\) | |||||||
\(492\) | −3.89552 | −0.175623 | ||||||||
\(493\) | −2.33087 | −0.104977 | ||||||||
\(494\) | 11.3904 | 0.512478 | ||||||||
\(495\) | 0.332481 | 0.0149439 | ||||||||
\(496\) | −4.87809 | −0.219033 | ||||||||
\(497\) | 42.2756 | 1.89632 | ||||||||
\(498\) | −0.762952 | −0.0341887 | ||||||||
\(499\) | −13.7156 | −0.613994 | −0.306997 | − | 0.951710i | \(-0.599324\pi\) | ||||
−0.306997 | + | 0.951710i | \(0.599324\pi\) | |||||||
\(500\) | 1.51060 | 0.0675560 | ||||||||
\(501\) | 9.15869 | 0.409180 | ||||||||
\(502\) | 12.4995 | 0.557878 | ||||||||
\(503\) | −38.5264 | −1.71781 | −0.858904 | − | 0.512137i | \(-0.828854\pi\) | ||||
−0.858904 | + | 0.512137i | \(0.828854\pi\) | |||||||
\(504\) | 11.2969 | 0.503202 | ||||||||
\(505\) | −1.52399 | −0.0678166 | ||||||||
\(506\) | 10.7837 | 0.479396 | ||||||||
\(507\) | −9.49574 | −0.421721 | ||||||||
\(508\) | −4.31299 | −0.191358 | ||||||||
\(509\) | 14.0220 | 0.621516 | 0.310758 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310758 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(510\) | 0.243606 | 0.0107870 | ||||||||
\(511\) | −31.3990 | −1.38901 | ||||||||
\(512\) | −20.7109 | −0.915300 | ||||||||
\(513\) | −2.11286 | −0.0932849 | ||||||||
\(514\) | −31.9119 | −1.40757 | ||||||||
\(515\) | −3.48568 | −0.153597 | ||||||||
\(516\) | −1.31828 | −0.0580340 | ||||||||
\(517\) | −18.2607 | −0.803103 | ||||||||
\(518\) | 5.24515 | 0.230459 | ||||||||
\(519\) | −12.0426 | −0.528609 | ||||||||
\(520\) | −3.12895 | −0.137213 | ||||||||
\(521\) | −5.75596 | −0.252173 | −0.126087 | − | 0.992019i | \(-0.540242\pi\) | ||||
−0.126087 | + | 0.992019i | \(0.540242\pi\) | |||||||
\(522\) | 2.64933 | 0.115958 | ||||||||
\(523\) | −14.8685 | −0.650155 | −0.325077 | − | 0.945687i | \(-0.605390\pi\) | ||||
−0.325077 | + | 0.945687i | \(0.605390\pi\) | |||||||
\(524\) | 5.47351 | 0.239111 | ||||||||
\(525\) | −18.1819 | −0.793525 | ||||||||
\(526\) | −9.32051 | −0.406393 | ||||||||
\(527\) | −2.34245 | −0.102039 | ||||||||
\(528\) | 3.23057 | 0.140592 | ||||||||
\(529\) | 14.4029 | 0.626211 | ||||||||
\(530\) | 2.66423 | 0.115727 | ||||||||
\(531\) | −9.95337 | −0.431939 | ||||||||
\(532\) | 5.49071 | 0.238052 | ||||||||
\(533\) | −26.0937 | −1.13024 | ||||||||
\(534\) | −10.4074 | −0.450372 | ||||||||
\(535\) | 0.366424 | 0.0158419 | ||||||||
\(536\) | 28.9435 | 1.25017 | ||||||||
\(537\) | 7.94145 | 0.342699 | ||||||||
\(538\) | −11.2886 | −0.486688 | ||||||||
\(539\) | 10.0365 | 0.432302 | ||||||||
\(540\) | 0.151757 | 0.00653057 | ||||||||
\(541\) | −21.2889 | −0.915279 | −0.457640 | − | 0.889138i | \(-0.651305\pi\) | ||||
−0.457640 | + | 0.889138i | \(0.651305\pi\) | |||||||
\(542\) | −17.1931 | −0.738509 | ||||||||
\(543\) | −25.8212 | −1.10809 | ||||||||
\(544\) | −3.78915 | −0.162458 | ||||||||
\(545\) | −2.66766 | −0.114270 | ||||||||
\(546\) | 19.7855 | 0.846742 | ||||||||
\(547\) | −42.6972 | −1.82560 | −0.912801 | − | 0.408405i | \(-0.866085\pi\) | ||||
−0.912801 | + | 0.408405i | \(0.866085\pi\) | |||||||
\(548\) | −11.9877 | −0.512090 | ||||||||
\(549\) | 0.941200 | 0.0401694 | ||||||||
\(550\) | −8.73532 | −0.372475 | ||||||||
\(551\) | 4.92480 | 0.209803 | ||||||||
\(552\) | 18.8249 | 0.801239 | ||||||||
\(553\) | 3.67011 | 0.156069 | ||||||||
\(554\) | 17.4955 | 0.743311 | ||||||||
\(555\) | 0.269482 | 0.0114389 | ||||||||
\(556\) | −9.05824 | −0.384155 | ||||||||
\(557\) | 16.9010 | 0.716119 | 0.358059 | − | 0.933699i | \(-0.383439\pi\) | ||||
0.358059 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(558\) | 2.66249 | 0.112712 | ||||||||
\(559\) | −8.83035 | −0.373484 | ||||||||
\(560\) | 1.63805 | 0.0692204 | ||||||||
\(561\) | 1.55131 | 0.0654964 | ||||||||
\(562\) | 1.70814 | 0.0720537 | ||||||||
\(563\) | 8.33678 | 0.351353 | 0.175677 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175677 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(564\) | −8.33484 | −0.350960 | ||||||||
\(565\) | −3.74889 | −0.157717 | ||||||||
\(566\) | 32.9731 | 1.38596 | ||||||||
\(567\) | −3.67011 | −0.154130 | ||||||||
\(568\) | 35.4560 | 1.48770 | ||||||||
\(569\) | 14.8310 | 0.621748 | 0.310874 | − | 0.950451i | \(-0.399378\pi\) | ||||
0.310874 | + | 0.950451i | \(0.399378\pi\) | |||||||
\(570\) | −0.514704 | −0.0215586 | ||||||||
\(571\) | −1.08522 | −0.0454151 | −0.0227075 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227075 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(572\) | −5.20989 | −0.217836 | ||||||||
\(573\) | 16.3757 | 0.684104 | ||||||||
\(574\) | 22.9500 | 0.957914 | ||||||||
\(575\) | −30.2980 | −1.26351 | ||||||||
\(576\) | 8.47181 | 0.352992 | ||||||||
\(577\) | 18.7475 | 0.780467 | 0.390234 | − | 0.920716i | \(-0.372394\pi\) | ||||
0.390234 | + | 0.920716i | \(0.372394\pi\) | |||||||
\(578\) | 1.13663 | 0.0472775 | ||||||||
\(579\) | 3.74152 | 0.155492 | ||||||||
\(580\) | −0.353726 | −0.0146877 | ||||||||
\(581\) | −2.46353 | −0.102204 | ||||||||
\(582\) | 11.0791 | 0.459244 | ||||||||
\(583\) | 16.9662 | 0.702667 | ||||||||
\(584\) | −26.3340 | −1.08971 | ||||||||
\(585\) | 1.01653 | 0.0420282 | ||||||||
\(586\) | −18.4122 | −0.760603 | ||||||||
\(587\) | 13.9597 | 0.576180 | 0.288090 | − | 0.957603i | \(-0.406980\pi\) | ||||
0.288090 | + | 0.957603i | \(0.406980\pi\) | |||||||
\(588\) | 4.58102 | 0.188918 | ||||||||
\(589\) | 4.94925 | 0.203930 | ||||||||
\(590\) | −2.42470 | −0.0998232 | ||||||||
\(591\) | 2.82332 | 0.116136 | ||||||||
\(592\) | 2.61843 | 0.107617 | ||||||||
\(593\) | 18.3434 | 0.753274 | 0.376637 | − | 0.926361i | \(-0.377080\pi\) | ||||
0.376637 | + | 0.926361i | \(0.377080\pi\) | |||||||
\(594\) | −1.76326 | −0.0723476 | ||||||||
\(595\) | 0.786588 | 0.0322470 | ||||||||
\(596\) | 8.50028 | 0.348185 | ||||||||
\(597\) | 12.3050 | 0.503608 | ||||||||
\(598\) | 32.9702 | 1.34825 | ||||||||
\(599\) | −25.9189 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(600\) | −15.2490 | −0.622537 | ||||||||
\(601\) | −27.6931 | −1.12963 | −0.564813 | − | 0.825219i | \(-0.691052\pi\) | ||||
−0.564813 | + | 0.825219i | \(0.691052\pi\) | |||||||
\(602\) | 7.76650 | 0.316539 | ||||||||
\(603\) | −9.40312 | −0.382925 | ||||||||
\(604\) | 3.22145 | 0.131079 | ||||||||
\(605\) | −1.84177 | −0.0748786 | ||||||||
\(606\) | 8.08223 | 0.328318 | ||||||||
\(607\) | −3.27046 | −0.132744 | −0.0663718 | − | 0.997795i | \(-0.521142\pi\) | ||||
−0.0663718 | + | 0.997795i | \(0.521142\pi\) | |||||||
\(608\) | 8.00592 | 0.324683 | ||||||||
\(609\) | 8.55454 | 0.346648 | ||||||||
\(610\) | 0.229282 | 0.00928334 | ||||||||
\(611\) | −55.8300 | −2.25864 | ||||||||
\(612\) | 0.708075 | 0.0286223 | ||||||||
\(613\) | 20.1956 | 0.815691 | 0.407846 | − | 0.913051i | \(-0.366280\pi\) | ||||
0.407846 | + | 0.913051i | \(0.366280\pi\) | |||||||
\(614\) | −10.0172 | −0.404261 | ||||||||
\(615\) | 1.17911 | 0.0475463 | ||||||||
\(616\) | 17.5249 | 0.706100 | ||||||||
\(617\) | −2.40284 | −0.0967346 | −0.0483673 | − | 0.998830i | \(-0.515402\pi\) | ||||
−0.0483673 | + | 0.998830i | \(0.515402\pi\) | |||||||
\(618\) | 18.4857 | 0.743606 | ||||||||
\(619\) | −6.22988 | −0.250400 | −0.125200 | − | 0.992132i | \(-0.539957\pi\) | ||||
−0.125200 | + | 0.992132i | \(0.539957\pi\) | |||||||
\(620\) | −0.355482 | −0.0142765 | ||||||||
\(621\) | −6.11579 | −0.245418 | ||||||||
\(622\) | −21.0037 | −0.842170 | ||||||||
\(623\) | −33.6049 | −1.34635 | ||||||||
\(624\) | 9.87713 | 0.395401 | ||||||||
\(625\) | 24.3131 | 0.972524 | ||||||||
\(626\) | −16.4893 | −0.659045 | ||||||||
\(627\) | −3.27770 | −0.130899 | ||||||||
\(628\) | 5.89771 | 0.235344 | ||||||||
\(629\) | 1.25736 | 0.0501344 | ||||||||
\(630\) | −0.894059 | −0.0356201 | ||||||||
\(631\) | −21.7900 | −0.867447 | −0.433724 | − | 0.901046i | \(-0.642801\pi\) | ||||
−0.433724 | + | 0.901046i | \(0.642801\pi\) | |||||||
\(632\) | 3.07808 | 0.122439 | ||||||||
\(633\) | −22.1380 | −0.879908 | ||||||||
\(634\) | 18.7260 | 0.743704 | ||||||||
\(635\) | 1.30547 | 0.0518061 | ||||||||
\(636\) | 7.74399 | 0.307069 | ||||||||
\(637\) | 30.6855 | 1.21580 | ||||||||
\(638\) | 4.10994 | 0.162714 | ||||||||
\(639\) | −11.5189 | −0.455681 | ||||||||
\(640\) | 0.439578 | 0.0173758 | ||||||||
\(641\) | −18.8533 | −0.744660 | −0.372330 | − | 0.928100i | \(-0.621441\pi\) | ||||
−0.372330 | + | 0.928100i | \(0.621441\pi\) | |||||||
\(642\) | −1.94327 | −0.0766949 | ||||||||
\(643\) | 17.6240 | 0.695023 | 0.347512 | − | 0.937676i | \(-0.387027\pi\) | ||||
0.347512 | + | 0.937676i | \(0.387027\pi\) | |||||||
\(644\) | 15.8932 | 0.626279 | ||||||||
\(645\) | 0.399022 | 0.0157115 | ||||||||
\(646\) | −2.40153 | −0.0944870 | ||||||||
\(647\) | 18.7515 | 0.737199 | 0.368599 | − | 0.929588i | \(-0.379837\pi\) | ||||
0.368599 | + | 0.929588i | \(0.379837\pi\) | |||||||
\(648\) | −3.07808 | −0.120918 | ||||||||
\(649\) | −15.4408 | −0.606103 | ||||||||
\(650\) | −26.7073 | −1.04755 | ||||||||
\(651\) | 8.59702 | 0.336944 | ||||||||
\(652\) | −3.87573 | −0.151785 | ||||||||
\(653\) | −0.452815 | −0.0177200 | −0.00886002 | − | 0.999961i | \(-0.502820\pi\) | ||||
−0.00886002 | + | 0.999961i | \(0.502820\pi\) | |||||||
\(654\) | 14.1475 | 0.553212 | ||||||||
\(655\) | −1.65674 | −0.0647343 | ||||||||
\(656\) | 11.4569 | 0.447316 | ||||||||
\(657\) | 8.55533 | 0.333775 | ||||||||
\(658\) | 49.1038 | 1.91426 | ||||||||
\(659\) | −35.0830 | −1.36664 | −0.683321 | − | 0.730118i | \(-0.739465\pi\) | ||||
−0.683321 | + | 0.730118i | \(0.739465\pi\) | |||||||
\(660\) | 0.235422 | 0.00916379 | ||||||||
\(661\) | −26.3800 | −1.02606 | −0.513031 | − | 0.858370i | \(-0.671478\pi\) | ||||
−0.513031 | + | 0.858370i | \(0.671478\pi\) | |||||||
\(662\) | −22.2323 | −0.864084 | ||||||||
\(663\) | 4.74297 | 0.184202 | ||||||||
\(664\) | −2.06613 | −0.0801815 | ||||||||
\(665\) | −1.66195 | −0.0644476 | ||||||||
\(666\) | −1.42916 | −0.0553787 | ||||||||
\(667\) | 14.2551 | 0.551960 | ||||||||
\(668\) | 6.48505 | 0.250914 | ||||||||
\(669\) | −9.31754 | −0.360237 | ||||||||
\(670\) | −2.29065 | −0.0884957 | ||||||||
\(671\) | 1.46009 | 0.0563663 | ||||||||
\(672\) | 13.9066 | 0.536458 | ||||||||
\(673\) | −11.5724 | −0.446082 | −0.223041 | − | 0.974809i | \(-0.571598\pi\) | ||||
−0.223041 | + | 0.974809i | \(0.571598\pi\) | |||||||
\(674\) | −9.41761 | −0.362753 | ||||||||
\(675\) | 4.95407 | 0.190682 | ||||||||
\(676\) | −6.72370 | −0.258604 | ||||||||
\(677\) | 7.16339 | 0.275311 | 0.137656 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137656 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(678\) | 19.8817 | 0.763551 | ||||||||
\(679\) | 35.7738 | 1.37287 | ||||||||
\(680\) | 0.659702 | 0.0252984 | ||||||||
\(681\) | 6.76431 | 0.259209 | ||||||||
\(682\) | 4.13035 | 0.158159 | ||||||||
\(683\) | 20.0088 | 0.765614 | 0.382807 | − | 0.923828i | \(-0.374957\pi\) | ||||
0.382807 | + | 0.923828i | \(0.374957\pi\) | |||||||
\(684\) | −1.49606 | −0.0572033 | ||||||||
\(685\) | 3.62849 | 0.138638 | ||||||||
\(686\) | 2.21226 | 0.0844643 | ||||||||
\(687\) | 21.6557 | 0.826215 | ||||||||
\(688\) | 3.87711 | 0.147814 | ||||||||
\(689\) | 51.8723 | 1.97618 | ||||||||
\(690\) | −1.48984 | −0.0567172 | ||||||||
\(691\) | 18.2957 | 0.695999 | 0.348000 | − | 0.937495i | \(-0.386861\pi\) | ||||
0.348000 | + | 0.937495i | \(0.386861\pi\) | |||||||
\(692\) | −8.52704 | −0.324149 | ||||||||
\(693\) | −5.69347 | −0.216277 | ||||||||
\(694\) | 33.3508 | 1.26598 | ||||||||
\(695\) | 2.74178 | 0.104002 | ||||||||
\(696\) | 7.17460 | 0.271952 | ||||||||
\(697\) | 5.50155 | 0.208386 | ||||||||
\(698\) | 24.6861 | 0.934381 | ||||||||
\(699\) | 3.67388 | 0.138959 | ||||||||
\(700\) | −12.8742 | −0.486599 | ||||||||
\(701\) | 22.2297 | 0.839604 | 0.419802 | − | 0.907616i | \(-0.362100\pi\) | ||||
0.419802 | + | 0.907616i | \(0.362100\pi\) | |||||||
\(702\) | −5.39099 | −0.203470 | ||||||||
\(703\) | −2.65663 | −0.100197 | ||||||||
\(704\) | 13.1424 | 0.495323 | ||||||||
\(705\) | 2.52282 | 0.0950149 | ||||||||
\(706\) | 28.1383 | 1.05900 | ||||||||
\(707\) | 26.0971 | 0.981481 | ||||||||
\(708\) | −7.04774 | −0.264870 | ||||||||
\(709\) | −22.7261 | −0.853496 | −0.426748 | − | 0.904371i | \(-0.640341\pi\) | ||||
−0.426748 | + | 0.904371i | \(0.640341\pi\) | |||||||
\(710\) | −2.80607 | −0.105310 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | −28.1840 | −1.05624 | ||||||||
\(713\) | 14.3259 | 0.536509 | ||||||||
\(714\) | −4.17155 | −0.156116 | ||||||||
\(715\) | 1.57695 | 0.0589745 | ||||||||
\(716\) | 5.62315 | 0.210147 | ||||||||
\(717\) | −3.05888 | −0.114236 | ||||||||
\(718\) | −10.8801 | −0.406041 | ||||||||
\(719\) | 44.8953 | 1.67431 | 0.837155 | − | 0.546965i | \(-0.184217\pi\) | ||||
0.837155 | + | 0.546965i | \(0.184217\pi\) | |||||||
\(720\) | −0.446323 | −0.0166335 | ||||||||
\(721\) | 59.6894 | 2.22295 | ||||||||
\(722\) | −16.5218 | −0.614880 | ||||||||
\(723\) | −1.60800 | −0.0598021 | ||||||||
\(724\) | −18.2833 | −0.679495 | ||||||||
\(725\) | −11.5473 | −0.428856 | ||||||||
\(726\) | 9.76755 | 0.362508 | ||||||||
\(727\) | −29.3350 | −1.08797 | −0.543987 | − | 0.839093i | \(-0.683086\pi\) | ||||
−0.543987 | + | 0.839093i | \(0.683086\pi\) | |||||||
\(728\) | 53.5807 | 1.98583 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.08413 | 0.0771370 | ||||||||
\(731\) | 1.86178 | 0.0688604 | ||||||||
\(732\) | 0.666441 | 0.0246324 | ||||||||
\(733\) | 4.31493 | 0.159376 | 0.0796878 | − | 0.996820i | \(-0.474608\pi\) | ||||
0.0796878 | + | 0.996820i | \(0.474608\pi\) | |||||||
\(734\) | −30.8390 | −1.13829 | ||||||||
\(735\) | −1.38660 | −0.0511455 | ||||||||
\(736\) | 23.1736 | 0.854191 | ||||||||
\(737\) | −14.5872 | −0.537325 | ||||||||
\(738\) | −6.25322 | −0.230184 | ||||||||
\(739\) | 6.03080 | 0.221847 | 0.110923 | − | 0.993829i | \(-0.464619\pi\) | ||||
0.110923 | + | 0.993829i | \(0.464619\pi\) | |||||||
\(740\) | 0.190814 | 0.00701445 | ||||||||
\(741\) | −10.0212 | −0.368138 | ||||||||
\(742\) | −45.6228 | −1.67487 | ||||||||
\(743\) | −32.2327 | −1.18250 | −0.591252 | − | 0.806487i | \(-0.701366\pi\) | ||||
−0.591252 | + | 0.806487i | \(0.701366\pi\) | |||||||
\(744\) | 7.21022 | 0.264340 | ||||||||
\(745\) | −2.57290 | −0.0942636 | ||||||||
\(746\) | −3.16872 | −0.116015 | ||||||||
\(747\) | 0.671241 | 0.0245594 | ||||||||
\(748\) | 1.09844 | 0.0401631 | ||||||||
\(749\) | −6.27472 | −0.229273 | ||||||||
\(750\) | 2.42487 | 0.0885436 | ||||||||
\(751\) | 12.4853 | 0.455595 | 0.227798 | − | 0.973708i | \(-0.426848\pi\) | ||||
0.227798 | + | 0.973708i | \(0.426848\pi\) | |||||||
\(752\) | 24.5131 | 0.893901 | ||||||||
\(753\) | −10.9970 | −0.400752 | ||||||||
\(754\) | 12.5657 | 0.457616 | ||||||||
\(755\) | −0.975080 | −0.0354868 | ||||||||
\(756\) | −2.59871 | −0.0945142 | ||||||||
\(757\) | 44.0976 | 1.60275 | 0.801377 | − | 0.598159i | \(-0.204101\pi\) | ||||
0.801377 | + | 0.598159i | \(0.204101\pi\) | |||||||
\(758\) | 6.15548 | 0.223577 | ||||||||
\(759\) | −9.48748 | −0.344374 | ||||||||
\(760\) | −1.39386 | −0.0505605 | ||||||||
\(761\) | 17.3048 | 0.627299 | 0.313650 | − | 0.949539i | \(-0.398448\pi\) | ||||
0.313650 | + | 0.949539i | \(0.398448\pi\) | |||||||
\(762\) | −6.92337 | −0.250807 | ||||||||
\(763\) | 45.6815 | 1.65378 | ||||||||
\(764\) | 11.5952 | 0.419501 | ||||||||
\(765\) | −0.214323 | −0.00774886 | ||||||||
\(766\) | −21.5556 | −0.778835 | ||||||||
\(767\) | −47.2085 | −1.70460 | ||||||||
\(768\) | 14.6124 | 0.527279 | ||||||||
\(769\) | −33.8806 | −1.22177 | −0.610883 | − | 0.791721i | \(-0.709185\pi\) | ||||
−0.610883 | + | 0.791721i | \(0.709185\pi\) | |||||||
\(770\) | −1.38696 | −0.0499826 | ||||||||
\(771\) | 28.0759 | 1.01113 | ||||||||
\(772\) | 2.64928 | 0.0953495 | ||||||||
\(773\) | 32.9682 | 1.18578 | 0.592892 | − | 0.805282i | \(-0.297986\pi\) | ||||
0.592892 | + | 0.805282i | \(0.297986\pi\) | |||||||
\(774\) | −2.11615 | −0.0760635 | ||||||||
\(775\) | −11.6046 | −0.416850 | ||||||||
\(776\) | 30.0030 | 1.07705 | ||||||||
\(777\) | −4.61466 | −0.165550 | ||||||||
\(778\) | −10.7872 | −0.386740 | ||||||||
\(779\) | −11.6240 | −0.416473 | ||||||||
\(780\) | 0.719778 | 0.0257722 | ||||||||
\(781\) | −17.8694 | −0.639417 | ||||||||
\(782\) | −6.95138 | −0.248581 | ||||||||
\(783\) | −2.33087 | −0.0832985 | ||||||||
\(784\) | −13.4730 | −0.481177 | ||||||||
\(785\) | −1.78514 | −0.0637144 | ||||||||
\(786\) | 8.78628 | 0.313396 | ||||||||
\(787\) | 45.4079 | 1.61862 | 0.809309 | − | 0.587383i | \(-0.199842\pi\) | ||||
0.809309 | + | 0.587383i | \(0.199842\pi\) | |||||||
\(788\) | 1.99912 | 0.0712158 | ||||||||
\(789\) | 8.20013 | 0.291933 | ||||||||
\(790\) | −0.243606 | −0.00866710 | ||||||||
\(791\) | 64.1967 | 2.28257 | ||||||||
\(792\) | −4.77505 | −0.169674 | ||||||||
\(793\) | 4.46408 | 0.158524 | ||||||||
\(794\) | 19.2190 | 0.682055 | ||||||||
\(795\) | −2.34398 | −0.0831324 | ||||||||
\(796\) | 8.71284 | 0.308818 | ||||||||
\(797\) | 36.4726 | 1.29192 | 0.645962 | − | 0.763369i | \(-0.276456\pi\) | ||||
0.645962 | + | 0.763369i | \(0.276456\pi\) | |||||||
\(798\) | 8.81388 | 0.312008 | ||||||||
\(799\) | 11.7711 | 0.416432 | ||||||||
\(800\) | −18.7717 | −0.663679 | ||||||||
\(801\) | 9.15637 | 0.323524 | ||||||||
\(802\) | −8.43866 | −0.297979 | ||||||||
\(803\) | 13.2720 | 0.468358 | ||||||||
\(804\) | −6.65812 | −0.234814 | ||||||||
\(805\) | −4.81061 | −0.169552 | ||||||||
\(806\) | 12.6281 | 0.444806 | ||||||||
\(807\) | 9.93169 | 0.349612 | ||||||||
\(808\) | 21.8873 | 0.769992 | ||||||||
\(809\) | 1.26737 | 0.0445583 | 0.0222792 | − | 0.999752i | \(-0.492908\pi\) | ||||
0.0222792 | + | 0.999752i | \(0.492908\pi\) | |||||||
\(810\) | 0.243606 | 0.00855943 | ||||||||
\(811\) | 0.375933 | 0.0132008 | 0.00660039 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660039 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(812\) | 6.05726 | 0.212568 | ||||||||
\(813\) | 15.1264 | 0.530508 | ||||||||
\(814\) | −2.21706 | −0.0777080 | ||||||||
\(815\) | 1.17312 | 0.0410926 | ||||||||
\(816\) | −2.08248 | −0.0729013 | ||||||||
\(817\) | −3.93367 | −0.137622 | ||||||||
\(818\) | 13.4258 | 0.469423 | ||||||||
\(819\) | −17.4072 | −0.608257 | ||||||||
\(820\) | 0.834899 | 0.0291559 | ||||||||
\(821\) | 24.5833 | 0.857962 | 0.428981 | − | 0.903313i | \(-0.358873\pi\) | ||||
0.428981 | + | 0.903313i | \(0.358873\pi\) | |||||||
\(822\) | −19.2431 | −0.671182 | ||||||||
\(823\) | −12.1301 | −0.422829 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(824\) | 50.0608 | 1.74395 | ||||||||
\(825\) | 7.68529 | 0.267568 | ||||||||
\(826\) | 41.5210 | 1.44470 | ||||||||
\(827\) | 49.0258 | 1.70480 | 0.852398 | − | 0.522894i | \(-0.175148\pi\) | ||||
0.852398 | + | 0.522894i | \(0.175148\pi\) | |||||||
\(828\) | −4.33044 | −0.150493 | ||||||||
\(829\) | −37.0272 | −1.28601 | −0.643004 | − | 0.765863i | \(-0.722312\pi\) | ||||
−0.643004 | + | 0.765863i | \(0.722312\pi\) | |||||||
\(830\) | 0.163518 | 0.00567580 | ||||||||
\(831\) | −15.3924 | −0.533957 | ||||||||
\(832\) | 40.1815 | 1.39304 | ||||||||
\(833\) | −6.46968 | −0.224161 | ||||||||
\(834\) | −14.5406 | −0.503500 | ||||||||
\(835\) | −1.96292 | −0.0679296 | ||||||||
\(836\) | −2.32086 | −0.0802685 | ||||||||
\(837\) | −2.34245 | −0.0809667 | ||||||||
\(838\) | 21.7725 | 0.752117 | ||||||||
\(839\) | 57.2941 | 1.97801 | 0.989005 | − | 0.147879i | \(-0.0472447\pi\) | ||||
0.989005 | + | 0.147879i | \(0.0472447\pi\) | |||||||
\(840\) | −2.42118 | −0.0835386 | ||||||||
\(841\) | −23.5670 | −0.812657 | ||||||||
\(842\) | −9.43194 | −0.325046 | ||||||||
\(843\) | −1.50282 | −0.0517598 | ||||||||
\(844\) | −15.6754 | −0.539570 | ||||||||
\(845\) | 2.03516 | 0.0700115 | ||||||||
\(846\) | −13.3794 | −0.459993 | ||||||||
\(847\) | 31.5388 | 1.08369 | ||||||||
\(848\) | −22.7754 | −0.782110 | ||||||||
\(849\) | −29.0096 | −0.995606 | ||||||||
\(850\) | 5.63093 | 0.193139 | ||||||||
\(851\) | −7.68977 | −0.263602 | ||||||||
\(852\) | −8.15625 | −0.279429 | ||||||||
\(853\) | 23.9065 | 0.818542 | 0.409271 | − | 0.912413i | \(-0.365783\pi\) | ||||
0.409271 | + | 0.912413i | \(0.365783\pi\) | |||||||
\(854\) | −3.92626 | −0.134354 | ||||||||
\(855\) | 0.452834 | 0.0154866 | ||||||||
\(856\) | −5.26253 | −0.179870 | ||||||||
\(857\) | 22.7745 | 0.777962 | 0.388981 | − | 0.921246i | \(-0.372827\pi\) | ||||
0.388981 | + | 0.921246i | \(0.372827\pi\) | |||||||
\(858\) | −8.36310 | −0.285512 | ||||||||
\(859\) | −32.6260 | −1.11318 | −0.556592 | − | 0.830786i | \(-0.687891\pi\) | ||||
−0.556592 | + | 0.830786i | \(0.687891\pi\) | |||||||
\(860\) | 0.282538 | 0.00963445 | ||||||||
\(861\) | −20.1913 | −0.688117 | ||||||||
\(862\) | 10.5395 | 0.358976 | ||||||||
\(863\) | −23.0547 | −0.784792 | −0.392396 | − | 0.919796i | \(-0.628354\pi\) | ||||
−0.392396 | + | 0.919796i | \(0.628354\pi\) | |||||||
\(864\) | −3.78915 | −0.128909 | ||||||||
\(865\) | 2.58100 | 0.0877565 | ||||||||
\(866\) | −21.8665 | −0.743053 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 6.08734 | 0.206618 | ||||||||
\(869\) | −1.55131 | −0.0526246 | ||||||||
\(870\) | −0.567813 | −0.0192507 | ||||||||
\(871\) | −44.5987 | −1.51117 | ||||||||
\(872\) | 38.3125 | 1.29743 | ||||||||
\(873\) | −9.74734 | −0.329897 | ||||||||
\(874\) | 14.6873 | 0.496804 | ||||||||
\(875\) | 7.82975 | 0.264694 | ||||||||
\(876\) | 6.05782 | 0.204675 | ||||||||
\(877\) | −29.6363 | −1.00075 | −0.500374 | − | 0.865810i | \(-0.666804\pi\) | ||||
−0.500374 | + | 0.865810i | \(0.666804\pi\) | |||||||
\(878\) | −26.0535 | −0.879261 | ||||||||
\(879\) | 16.1990 | 0.546378 | ||||||||
\(880\) | −0.692385 | −0.0233403 | ||||||||
\(881\) | −4.90474 | −0.165245 | −0.0826225 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826225 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(882\) | 7.35362 | 0.247609 | ||||||||
\(883\) | −11.4422 | −0.385062 | −0.192531 | − | 0.981291i | \(-0.561670\pi\) | ||||
−0.192531 | + | 0.981291i | \(0.561670\pi\) | |||||||
\(884\) | 3.35838 | 0.112955 | ||||||||
\(885\) | 2.13324 | 0.0717079 | ||||||||
\(886\) | 30.8058 | 1.03494 | ||||||||
\(887\) | −33.8172 | −1.13547 | −0.567735 | − | 0.823211i | \(-0.692180\pi\) | ||||
−0.567735 | + | 0.823211i | \(0.692180\pi\) | |||||||
\(888\) | −3.87026 | −0.129877 | ||||||||
\(889\) | −22.3551 | −0.749767 | ||||||||
\(890\) | 2.23054 | 0.0747680 | ||||||||
\(891\) | 1.55131 | 0.0519708 | ||||||||
\(892\) | −6.59752 | −0.220901 | ||||||||
\(893\) | −24.8707 | −0.832265 | ||||||||
\(894\) | 13.6450 | 0.456356 | ||||||||
\(895\) | −1.70204 | −0.0568928 | ||||||||
\(896\) | −7.52741 | −0.251473 | ||||||||
\(897\) | −29.0070 | −0.968515 | ||||||||
\(898\) | 42.3070 | 1.41180 | ||||||||
\(899\) | 5.45994 | 0.182099 | ||||||||
\(900\) | 3.50785 | 0.116928 | ||||||||
\(901\) | −10.9367 | −0.364353 | ||||||||
\(902\) | −9.70069 | −0.322998 | ||||||||
\(903\) | −6.83292 | −0.227385 | ||||||||
\(904\) | 53.8411 | 1.79073 | ||||||||
\(905\) | 5.53407 | 0.183959 | ||||||||
\(906\) | 5.17118 | 0.171801 | ||||||||
\(907\) | 5.05307 | 0.167785 | 0.0838923 | − | 0.996475i | \(-0.473265\pi\) | ||||
0.0838923 | + | 0.996475i | \(0.473265\pi\) | |||||||
\(908\) | 4.78964 | 0.158950 | ||||||||
\(909\) | −7.11071 | −0.235847 | ||||||||
\(910\) | −4.24049 | −0.140571 | ||||||||
\(911\) | 12.0225 | 0.398324 | 0.199162 | − | 0.979967i | \(-0.436178\pi\) | ||||
0.199162 | + | 0.979967i | \(0.436178\pi\) | |||||||
\(912\) | 4.39998 | 0.145698 | ||||||||
\(913\) | 1.04130 | 0.0344621 | ||||||||
\(914\) | −8.52468 | −0.281971 | ||||||||
\(915\) | −0.201721 | −0.00666869 | ||||||||
\(916\) | 15.3338 | 0.506645 | ||||||||
\(917\) | 28.3704 | 0.936873 | ||||||||
\(918\) | 1.13663 | 0.0375143 | ||||||||
\(919\) | −21.5359 | −0.710404 | −0.355202 | − | 0.934790i | \(-0.615588\pi\) | ||||
−0.355202 | + | 0.934790i | \(0.615588\pi\) | |||||||
\(920\) | −4.03460 | −0.133017 | ||||||||
\(921\) | 8.81308 | 0.290401 | ||||||||
\(922\) | 40.5891 | 1.33673 | ||||||||
\(923\) | −54.6338 | −1.79829 | ||||||||
\(924\) | −4.03141 | −0.132624 | ||||||||
\(925\) | 6.22906 | 0.204810 | ||||||||
\(926\) | −42.6984 | −1.40316 | ||||||||
\(927\) | −16.2637 | −0.534169 | ||||||||
\(928\) | 8.83202 | 0.289925 | ||||||||
\(929\) | −24.6960 | −0.810248 | −0.405124 | − | 0.914262i | \(-0.632772\pi\) | ||||
−0.405124 | + | 0.914262i | \(0.632772\pi\) | |||||||
\(930\) | −0.570633 | −0.0187118 | ||||||||
\(931\) | 13.6695 | 0.448000 | ||||||||
\(932\) | 2.60139 | 0.0852112 | ||||||||
\(933\) | 18.4789 | 0.604972 | ||||||||
\(934\) | −7.81517 | −0.255720 | ||||||||
\(935\) | −0.332481 | −0.0108733 | ||||||||
\(936\) | −14.5992 | −0.477190 | ||||||||
\(937\) | −42.7377 | −1.39618 | −0.698090 | − | 0.716010i | \(-0.745967\pi\) | ||||
−0.698090 | + | 0.716010i | \(0.745967\pi\) | |||||||
\(938\) | 39.2256 | 1.28076 | ||||||||
\(939\) | 14.5072 | 0.473425 | ||||||||
\(940\) | 1.78635 | 0.0582642 | ||||||||
\(941\) | 11.2561 | 0.366937 | 0.183469 | − | 0.983026i | \(-0.441267\pi\) | ||||
0.183469 | + | 0.983026i | \(0.441267\pi\) | |||||||
\(942\) | 9.46722 | 0.308459 | ||||||||
\(943\) | −33.6463 | −1.09568 | ||||||||
\(944\) | 20.7277 | 0.674628 | ||||||||
\(945\) | 0.786588 | 0.0255877 | ||||||||
\(946\) | −3.28281 | −0.106733 | ||||||||
\(947\) | 13.1347 | 0.426820 | 0.213410 | − | 0.976963i | \(-0.431543\pi\) | ||||
0.213410 | + | 0.976963i | \(0.431543\pi\) | |||||||
\(948\) | −0.708075 | −0.0229972 | ||||||||
\(949\) | 40.5777 | 1.31721 | ||||||||
\(950\) | −11.8974 | −0.386001 | ||||||||
\(951\) | −16.4750 | −0.534239 | ||||||||
\(952\) | −11.2969 | −0.366134 | ||||||||
\(953\) | 37.0193 | 1.19917 | 0.599586 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599586 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(954\) | 12.4309 | 0.402466 | ||||||||
\(955\) | −3.50969 | −0.113571 | ||||||||
\(956\) | −2.16592 | −0.0700507 | ||||||||
\(957\) | −3.61590 | −0.116886 | ||||||||
\(958\) | −13.7652 | −0.444735 | ||||||||
\(959\) | −62.1350 | −2.00644 | ||||||||
\(960\) | −1.81570 | −0.0586016 | ||||||||
\(961\) | −25.5130 | −0.822998 | ||||||||
\(962\) | −6.77844 | −0.218546 | ||||||||
\(963\) | 1.70968 | 0.0550937 | ||||||||
\(964\) | −1.13858 | −0.0366714 | ||||||||
\(965\) | −0.801893 | −0.0258138 | ||||||||
\(966\) | 25.5123 | 0.820845 | ||||||||
\(967\) | 4.49043 | 0.144402 | 0.0722012 | − | 0.997390i | \(-0.476998\pi\) | ||||
0.0722012 | + | 0.997390i | \(0.476998\pi\) | |||||||
\(968\) | 26.4513 | 0.850175 | ||||||||
\(969\) | 2.11286 | 0.0678747 | ||||||||
\(970\) | −2.37451 | −0.0762408 | ||||||||
\(971\) | −44.7509 | −1.43612 | −0.718062 | − | 0.695979i | \(-0.754971\pi\) | ||||
−0.718062 | + | 0.695979i | \(0.754971\pi\) | |||||||
\(972\) | 0.708075 | 0.0227115 | ||||||||
\(973\) | −46.9508 | −1.50517 | ||||||||
\(974\) | −21.5087 | −0.689184 | ||||||||
\(975\) | 23.4970 | 0.752505 | ||||||||
\(976\) | −1.96003 | −0.0627390 | ||||||||
\(977\) | 50.2998 | 1.60923 | 0.804616 | − | 0.593796i | \(-0.202371\pi\) | ||||
0.804616 | + | 0.593796i | \(0.202371\pi\) | |||||||
\(978\) | −6.22147 | −0.198941 | ||||||||
\(979\) | 14.2044 | 0.453974 | ||||||||
\(980\) | −0.981818 | −0.0313630 | ||||||||
\(981\) | −12.4469 | −0.397399 | ||||||||
\(982\) | −36.1670 | −1.15414 | ||||||||
\(983\) | −12.9761 | −0.413873 | −0.206936 | − | 0.978354i | \(-0.566349\pi\) | ||||
−0.206936 | + | 0.978354i | \(0.566349\pi\) | |||||||
\(984\) | −16.9342 | −0.539843 | ||||||||
\(985\) | −0.605102 | −0.0192802 | ||||||||
\(986\) | −2.64933 | −0.0843720 | ||||||||
\(987\) | −43.2012 | −1.37511 | ||||||||
\(988\) | −7.09577 | −0.225747 | ||||||||
\(989\) | −11.3862 | −0.362061 | ||||||||
\(990\) | 0.377908 | 0.0120107 | ||||||||
\(991\) | 21.3996 | 0.679779 | 0.339890 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339890 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(992\) | 8.87587 | 0.281809 | ||||||||
\(993\) | 19.5599 | 0.620714 | ||||||||
\(994\) | 48.0516 | 1.52411 | ||||||||
\(995\) | −2.63723 | −0.0836060 | ||||||||
\(996\) | 0.475289 | 0.0150601 | ||||||||
\(997\) | −24.3735 | −0.771918 | −0.385959 | − | 0.922516i | \(-0.626129\pi\) | ||||
−0.385959 | + | 0.922516i | \(0.626129\pi\) | |||||||
\(998\) | −15.5895 | −0.493478 | ||||||||
\(999\) | 1.25736 | 0.0397812 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4029.2.a.g.1.15 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.g.1.15 | ✓ | 22 | 1.1 | even | 1 | trivial |