Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87703 | −1.32726 | −0.663630 | − | 0.748061i | \(-0.730985\pi\) | ||||
−0.663630 | + | 0.748061i | \(0.730985\pi\) | |||||||
\(3\) | −2.63781 | −1.52294 | −0.761471 | − | 0.648199i | \(-0.775523\pi\) | ||||
−0.761471 | + | 0.648199i | \(0.775523\pi\) | |||||||
\(4\) | 1.52324 | 0.761618 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 4.95125 | 2.02134 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.894900 | 0.316395 | ||||||||
\(9\) | 3.95806 | 1.31935 | ||||||||
\(10\) | 1.87703 | 0.593569 | ||||||||
\(11\) | −0.835767 | −0.251993 | −0.125997 | − | 0.992031i | \(-0.540213\pi\) | ||||
−0.125997 | + | 0.992031i | \(0.540213\pi\) | |||||||
\(12\) | −4.01801 | −1.15990 | ||||||||
\(13\) | −2.57449 | −0.714034 | −0.357017 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357017 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(14\) | 1.87703 | 0.501657 | ||||||||
\(15\) | 2.63781 | 0.681080 | ||||||||
\(16\) | −4.72622 | −1.18156 | ||||||||
\(17\) | 5.00673 | 1.21431 | 0.607155 | − | 0.794583i | \(-0.292311\pi\) | ||||
0.607155 | + | 0.794583i | \(0.292311\pi\) | |||||||
\(18\) | −7.42939 | −1.75112 | ||||||||
\(19\) | 1.69114 | 0.387975 | 0.193987 | − | 0.981004i | \(-0.437858\pi\) | ||||
0.193987 | + | 0.981004i | \(0.437858\pi\) | |||||||
\(20\) | −1.52324 | −0.340606 | ||||||||
\(21\) | 2.63781 | 0.575618 | ||||||||
\(22\) | 1.56876 | 0.334460 | ||||||||
\(23\) | 7.52045 | 1.56812 | 0.784061 | − | 0.620683i | \(-0.213145\pi\) | ||||
0.784061 | + | 0.620683i | \(0.213145\pi\) | |||||||
\(24\) | −2.36058 | −0.481851 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.83238 | 0.947708 | ||||||||
\(27\) | −2.52718 | −0.486355 | ||||||||
\(28\) | −1.52324 | −0.287865 | ||||||||
\(29\) | −0.896200 | −0.166420 | −0.0832101 | − | 0.996532i | \(-0.526517\pi\) | ||||
−0.0832101 | + | 0.996532i | \(0.526517\pi\) | |||||||
\(30\) | −4.95125 | −0.903970 | ||||||||
\(31\) | 0.661756 | 0.118855 | 0.0594274 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594274 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(32\) | 7.08146 | 1.25184 | ||||||||
\(33\) | 2.20460 | 0.383771 | ||||||||
\(34\) | −9.39777 | −1.61170 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 6.02906 | 1.00484 | ||||||||
\(37\) | −6.42100 | −1.05561 | −0.527803 | − | 0.849367i | \(-0.676984\pi\) | ||||
−0.527803 | + | 0.849367i | \(0.676984\pi\) | |||||||
\(38\) | −3.17432 | −0.514943 | ||||||||
\(39\) | 6.79101 | 1.08743 | ||||||||
\(40\) | −0.894900 | −0.141496 | ||||||||
\(41\) | 6.40349 | 1.00006 | 0.500029 | − | 0.866009i | \(-0.333323\pi\) | ||||
0.500029 | + | 0.866009i | \(0.333323\pi\) | |||||||
\(42\) | −4.95125 | −0.763994 | ||||||||
\(43\) | 4.66509 | 0.711419 | 0.355710 | − | 0.934597i | \(-0.384239\pi\) | ||||
0.355710 | + | 0.934597i | \(0.384239\pi\) | |||||||
\(44\) | −1.27307 | −0.191923 | ||||||||
\(45\) | −3.95806 | −0.590032 | ||||||||
\(46\) | −14.1161 | −2.08131 | ||||||||
\(47\) | 9.46667 | 1.38086 | 0.690428 | − | 0.723401i | \(-0.257422\pi\) | ||||
0.690428 | + | 0.723401i | \(0.257422\pi\) | |||||||
\(48\) | 12.4669 | 1.79944 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.87703 | −0.265452 | ||||||||
\(51\) | −13.2068 | −1.84932 | ||||||||
\(52\) | −3.92155 | −0.543821 | ||||||||
\(53\) | 7.01772 | 0.963958 | 0.481979 | − | 0.876183i | \(-0.339918\pi\) | ||||
0.481979 | + | 0.876183i | \(0.339918\pi\) | |||||||
\(54\) | 4.74358 | 0.645520 | ||||||||
\(55\) | 0.835767 | 0.112695 | ||||||||
\(56\) | −0.894900 | −0.119586 | ||||||||
\(57\) | −4.46092 | −0.590863 | ||||||||
\(58\) | 1.68219 | 0.220883 | ||||||||
\(59\) | −5.07702 | −0.660972 | −0.330486 | − | 0.943811i | \(-0.607213\pi\) | ||||
−0.330486 | + | 0.943811i | \(0.607213\pi\) | |||||||
\(60\) | 4.01801 | 0.518723 | ||||||||
\(61\) | 4.74747 | 0.607851 | 0.303925 | − | 0.952696i | \(-0.401703\pi\) | ||||
0.303925 | + | 0.952696i | \(0.401703\pi\) | |||||||
\(62\) | −1.24213 | −0.157751 | ||||||||
\(63\) | −3.95806 | −0.498668 | ||||||||
\(64\) | −3.83965 | −0.479956 | ||||||||
\(65\) | 2.57449 | 0.319326 | ||||||||
\(66\) | −4.13809 | −0.509364 | ||||||||
\(67\) | 10.3551 | 1.26508 | 0.632539 | − | 0.774528i | \(-0.282013\pi\) | ||||
0.632539 | + | 0.774528i | \(0.282013\pi\) | |||||||
\(68\) | 7.62643 | 0.924840 | ||||||||
\(69\) | −19.8376 | −2.38816 | ||||||||
\(70\) | −1.87703 | −0.224348 | ||||||||
\(71\) | −5.55683 | −0.659474 | −0.329737 | − | 0.944073i | \(-0.606960\pi\) | ||||
−0.329737 | + | 0.944073i | \(0.606960\pi\) | |||||||
\(72\) | 3.54206 | 0.417436 | ||||||||
\(73\) | 15.0713 | 1.76396 | 0.881980 | − | 0.471287i | \(-0.156210\pi\) | ||||
0.881980 | + | 0.471287i | \(0.156210\pi\) | |||||||
\(74\) | 12.0524 | 1.40106 | ||||||||
\(75\) | −2.63781 | −0.304588 | ||||||||
\(76\) | 2.57601 | 0.295488 | ||||||||
\(77\) | 0.835767 | 0.0952445 | ||||||||
\(78\) | −12.7469 | −1.44330 | ||||||||
\(79\) | 3.09837 | 0.348594 | 0.174297 | − | 0.984693i | \(-0.444235\pi\) | ||||
0.174297 | + | 0.984693i | \(0.444235\pi\) | |||||||
\(80\) | 4.72622 | 0.528408 | ||||||||
\(81\) | −5.20795 | −0.578661 | ||||||||
\(82\) | −12.0195 | −1.32734 | ||||||||
\(83\) | 3.78224 | 0.415155 | 0.207577 | − | 0.978219i | \(-0.433442\pi\) | ||||
0.207577 | + | 0.978219i | \(0.433442\pi\) | |||||||
\(84\) | 4.01801 | 0.438401 | ||||||||
\(85\) | −5.00673 | −0.543056 | ||||||||
\(86\) | −8.75650 | −0.944238 | ||||||||
\(87\) | 2.36401 | 0.253448 | ||||||||
\(88\) | −0.747928 | −0.0797294 | ||||||||
\(89\) | 4.77527 | 0.506177 | 0.253089 | − | 0.967443i | \(-0.418554\pi\) | ||||
0.253089 | + | 0.967443i | \(0.418554\pi\) | |||||||
\(90\) | 7.42939 | 0.783126 | ||||||||
\(91\) | 2.57449 | 0.269879 | ||||||||
\(92\) | 11.4554 | 1.19431 | ||||||||
\(93\) | −1.74559 | −0.181009 | ||||||||
\(94\) | −17.7692 | −1.83275 | ||||||||
\(95\) | −1.69114 | −0.173508 | ||||||||
\(96\) | −18.6796 | −1.90647 | ||||||||
\(97\) | 4.44039 | 0.450853 | 0.225427 | − | 0.974260i | \(-0.427622\pi\) | ||||
0.225427 | + | 0.974260i | \(0.427622\pi\) | |||||||
\(98\) | −1.87703 | −0.189609 | ||||||||
\(99\) | −3.30801 | −0.332468 | ||||||||
\(100\) | 1.52324 | 0.152324 | ||||||||
\(101\) | 11.6798 | 1.16218 | 0.581091 | − | 0.813839i | \(-0.302626\pi\) | ||||
0.581091 | + | 0.813839i | \(0.302626\pi\) | |||||||
\(102\) | 24.7896 | 2.45453 | ||||||||
\(103\) | −15.0595 | −1.48386 | −0.741929 | − | 0.670479i | \(-0.766089\pi\) | ||||
−0.741929 | + | 0.670479i | \(0.766089\pi\) | |||||||
\(104\) | −2.30391 | −0.225917 | ||||||||
\(105\) | −2.63781 | −0.257424 | ||||||||
\(106\) | −13.1725 | −1.27942 | ||||||||
\(107\) | 0.413285 | 0.0399538 | 0.0199769 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199769 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(108\) | −3.84949 | −0.370417 | ||||||||
\(109\) | −4.50672 | −0.431666 | −0.215833 | − | 0.976430i | \(-0.569247\pi\) | ||||
−0.215833 | + | 0.976430i | \(0.569247\pi\) | |||||||
\(110\) | −1.56876 | −0.149575 | ||||||||
\(111\) | 16.9374 | 1.60763 | ||||||||
\(112\) | 4.72622 | 0.446586 | ||||||||
\(113\) | 19.1810 | 1.80439 | 0.902197 | − | 0.431324i | \(-0.141953\pi\) | ||||
0.902197 | + | 0.431324i | \(0.141953\pi\) | |||||||
\(114\) | 8.37327 | 0.784229 | ||||||||
\(115\) | −7.52045 | −0.701286 | ||||||||
\(116\) | −1.36512 | −0.126749 | ||||||||
\(117\) | −10.1900 | −0.942062 | ||||||||
\(118\) | 9.52971 | 0.877281 | ||||||||
\(119\) | −5.00673 | −0.458966 | ||||||||
\(120\) | 2.36058 | 0.215490 | ||||||||
\(121\) | −10.3015 | −0.936499 | ||||||||
\(122\) | −8.91113 | −0.806776 | ||||||||
\(123\) | −16.8912 | −1.52303 | ||||||||
\(124\) | 1.00801 | 0.0905220 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.42939 | 0.661862 | ||||||||
\(127\) | 17.4795 | 1.55105 | 0.775526 | − | 0.631316i | \(-0.217485\pi\) | ||||
0.775526 | + | 0.631316i | \(0.217485\pi\) | |||||||
\(128\) | −6.95578 | −0.614810 | ||||||||
\(129\) | −12.3056 | −1.08345 | ||||||||
\(130\) | −4.83238 | −0.423828 | ||||||||
\(131\) | −17.1515 | −1.49853 | −0.749267 | − | 0.662268i | \(-0.769594\pi\) | ||||
−0.749267 | + | 0.662268i | \(0.769594\pi\) | |||||||
\(132\) | 3.35812 | 0.292287 | ||||||||
\(133\) | −1.69114 | −0.146641 | ||||||||
\(134\) | −19.4369 | −1.67909 | ||||||||
\(135\) | 2.52718 | 0.217505 | ||||||||
\(136\) | 4.48052 | 0.384201 | ||||||||
\(137\) | 14.2336 | 1.21606 | 0.608029 | − | 0.793915i | \(-0.291960\pi\) | ||||
0.608029 | + | 0.793915i | \(0.291960\pi\) | |||||||
\(138\) | 37.2356 | 3.16971 | ||||||||
\(139\) | 17.6851 | 1.50003 | 0.750014 | − | 0.661422i | \(-0.230047\pi\) | ||||
0.750014 | + | 0.661422i | \(0.230047\pi\) | |||||||
\(140\) | 1.52324 | 0.128737 | ||||||||
\(141\) | −24.9713 | −2.10296 | ||||||||
\(142\) | 10.4303 | 0.875293 | ||||||||
\(143\) | 2.15167 | 0.179932 | ||||||||
\(144\) | −18.7067 | −1.55889 | ||||||||
\(145\) | 0.896200 | 0.0744254 | ||||||||
\(146\) | −28.2892 | −2.34123 | ||||||||
\(147\) | −2.63781 | −0.217563 | ||||||||
\(148\) | −9.78070 | −0.803969 | ||||||||
\(149\) | 8.37621 | 0.686206 | 0.343103 | − | 0.939298i | \(-0.388522\pi\) | ||||
0.343103 | + | 0.939298i | \(0.388522\pi\) | |||||||
\(150\) | 4.95125 | 0.404268 | ||||||||
\(151\) | 23.9202 | 1.94660 | 0.973298 | − | 0.229546i | \(-0.0737240\pi\) | ||||
0.973298 | + | 0.229546i | \(0.0737240\pi\) | |||||||
\(152\) | 1.51340 | 0.122753 | ||||||||
\(153\) | 19.8169 | 1.60210 | ||||||||
\(154\) | −1.56876 | −0.126414 | ||||||||
\(155\) | −0.661756 | −0.0531535 | ||||||||
\(156\) | 10.3443 | 0.828208 | ||||||||
\(157\) | −20.8928 | −1.66743 | −0.833715 | − | 0.552194i | \(-0.813791\pi\) | ||||
−0.833715 | + | 0.552194i | \(0.813791\pi\) | |||||||
\(158\) | −5.81573 | −0.462675 | ||||||||
\(159\) | −18.5114 | −1.46805 | ||||||||
\(160\) | −7.08146 | −0.559838 | ||||||||
\(161\) | −7.52045 | −0.592695 | ||||||||
\(162\) | 9.77548 | 0.768034 | ||||||||
\(163\) | −15.8991 | −1.24531 | −0.622655 | − | 0.782496i | \(-0.713946\pi\) | ||||
−0.622655 | + | 0.782496i | \(0.713946\pi\) | |||||||
\(164\) | 9.75403 | 0.761662 | ||||||||
\(165\) | −2.20460 | −0.171628 | ||||||||
\(166\) | −7.09937 | −0.551018 | ||||||||
\(167\) | 9.50740 | 0.735704 | 0.367852 | − | 0.929884i | \(-0.380093\pi\) | ||||
0.367852 | + | 0.929884i | \(0.380093\pi\) | |||||||
\(168\) | 2.36058 | 0.182123 | ||||||||
\(169\) | −6.37202 | −0.490156 | ||||||||
\(170\) | 9.39777 | 0.720776 | ||||||||
\(171\) | 6.69364 | 0.511875 | ||||||||
\(172\) | 7.10603 | 0.541830 | ||||||||
\(173\) | 3.57021 | 0.271438 | 0.135719 | − | 0.990747i | \(-0.456666\pi\) | ||||
0.135719 | + | 0.990747i | \(0.456666\pi\) | |||||||
\(174\) | −4.43731 | −0.336392 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.95002 | 0.297744 | ||||||||
\(177\) | 13.3922 | 1.00662 | ||||||||
\(178\) | −8.96332 | −0.671829 | ||||||||
\(179\) | −25.4025 | −1.89867 | −0.949336 | − | 0.314262i | \(-0.898243\pi\) | ||||
−0.949336 | + | 0.314262i | \(0.898243\pi\) | |||||||
\(180\) | −6.02906 | −0.449379 | ||||||||
\(181\) | 4.20561 | 0.312601 | 0.156300 | − | 0.987710i | \(-0.450043\pi\) | ||||
0.156300 | + | 0.987710i | \(0.450043\pi\) | |||||||
\(182\) | −4.83238 | −0.358200 | ||||||||
\(183\) | −12.5229 | −0.925721 | ||||||||
\(184\) | 6.73005 | 0.496146 | ||||||||
\(185\) | 6.42100 | 0.472081 | ||||||||
\(186\) | 3.27652 | 0.240246 | ||||||||
\(187\) | −4.18446 | −0.305998 | ||||||||
\(188\) | 14.4200 | 1.05168 | ||||||||
\(189\) | 2.52718 | 0.183825 | ||||||||
\(190\) | 3.17432 | 0.230290 | ||||||||
\(191\) | −17.8923 | −1.29464 | −0.647322 | − | 0.762217i | \(-0.724111\pi\) | ||||
−0.647322 | + | 0.762217i | \(0.724111\pi\) | |||||||
\(192\) | 10.1283 | 0.730945 | ||||||||
\(193\) | −25.4087 | −1.82896 | −0.914481 | − | 0.404629i | \(-0.867401\pi\) | ||||
−0.914481 | + | 0.404629i | \(0.867401\pi\) | |||||||
\(194\) | −8.33474 | −0.598399 | ||||||||
\(195\) | −6.79101 | −0.486314 | ||||||||
\(196\) | 1.52324 | 0.108803 | ||||||||
\(197\) | 8.66587 | 0.617417 | 0.308709 | − | 0.951157i | \(-0.400103\pi\) | ||||
0.308709 | + | 0.951157i | \(0.400103\pi\) | |||||||
\(198\) | 6.20924 | 0.441271 | ||||||||
\(199\) | 13.2680 | 0.940541 | 0.470271 | − | 0.882522i | \(-0.344156\pi\) | ||||
0.470271 | + | 0.882522i | \(0.344156\pi\) | |||||||
\(200\) | 0.894900 | 0.0632790 | ||||||||
\(201\) | −27.3149 | −1.92664 | ||||||||
\(202\) | −21.9233 | −1.54252 | ||||||||
\(203\) | 0.896200 | 0.0629009 | ||||||||
\(204\) | −20.1171 | −1.40848 | ||||||||
\(205\) | −6.40349 | −0.447239 | ||||||||
\(206\) | 28.2671 | 1.96946 | ||||||||
\(207\) | 29.7664 | 2.06891 | ||||||||
\(208\) | 12.1676 | 0.843671 | ||||||||
\(209\) | −1.41340 | −0.0977670 | ||||||||
\(210\) | 4.95125 | 0.341669 | ||||||||
\(211\) | 20.9869 | 1.44480 | 0.722398 | − | 0.691478i | \(-0.243040\pi\) | ||||
0.722398 | + | 0.691478i | \(0.243040\pi\) | |||||||
\(212\) | 10.6896 | 0.734168 | ||||||||
\(213\) | 14.6579 | 1.00434 | ||||||||
\(214\) | −0.775748 | −0.0530291 | ||||||||
\(215\) | −4.66509 | −0.318156 | ||||||||
\(216\) | −2.26157 | −0.153880 | ||||||||
\(217\) | −0.661756 | −0.0449229 | ||||||||
\(218\) | 8.45924 | 0.572932 | ||||||||
\(219\) | −39.7552 | −2.68641 | ||||||||
\(220\) | 1.27307 | 0.0858304 | ||||||||
\(221\) | −12.8897 | −0.867058 | ||||||||
\(222\) | −31.7920 | −2.13374 | ||||||||
\(223\) | −23.2213 | −1.55501 | −0.777505 | − | 0.628876i | \(-0.783515\pi\) | ||||
−0.777505 | + | 0.628876i | \(0.783515\pi\) | |||||||
\(224\) | −7.08146 | −0.473150 | ||||||||
\(225\) | 3.95806 | 0.263871 | ||||||||
\(226\) | −36.0032 | −2.39490 | ||||||||
\(227\) | 5.61757 | 0.372852 | 0.186426 | − | 0.982469i | \(-0.440310\pi\) | ||||
0.186426 | + | 0.982469i | \(0.440310\pi\) | |||||||
\(228\) | −6.79503 | −0.450012 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 14.1161 | 0.930788 | ||||||||
\(231\) | −2.20460 | −0.145052 | ||||||||
\(232\) | −0.802010 | −0.0526545 | ||||||||
\(233\) | −3.64771 | −0.238970 | −0.119485 | − | 0.992836i | \(-0.538124\pi\) | ||||
−0.119485 | + | 0.992836i | \(0.538124\pi\) | |||||||
\(234\) | 19.1268 | 1.25036 | ||||||||
\(235\) | −9.46667 | −0.617538 | ||||||||
\(236\) | −7.73350 | −0.503408 | ||||||||
\(237\) | −8.17292 | −0.530888 | ||||||||
\(238\) | 9.39777 | 0.609167 | ||||||||
\(239\) | −11.7715 | −0.761435 | −0.380717 | − | 0.924691i | \(-0.624323\pi\) | ||||
−0.380717 | + | 0.924691i | \(0.624323\pi\) | |||||||
\(240\) | −12.4669 | −0.804735 | ||||||||
\(241\) | 4.85143 | 0.312508 | 0.156254 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156254 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(242\) | 19.3362 | 1.24298 | ||||||||
\(243\) | 21.3191 | 1.36762 | ||||||||
\(244\) | 7.23151 | 0.462950 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 31.7053 | 2.02146 | ||||||||
\(247\) | −4.35382 | −0.277027 | ||||||||
\(248\) | 0.592205 | 0.0376051 | ||||||||
\(249\) | −9.97684 | −0.632256 | ||||||||
\(250\) | 1.87703 | 0.118714 | ||||||||
\(251\) | −23.7678 | −1.50021 | −0.750107 | − | 0.661317i | \(-0.769998\pi\) | ||||
−0.750107 | + | 0.661317i | \(0.769998\pi\) | |||||||
\(252\) | −6.02906 | −0.379795 | ||||||||
\(253\) | −6.28535 | −0.395156 | ||||||||
\(254\) | −32.8095 | −2.05865 | ||||||||
\(255\) | 13.2068 | 0.827043 | ||||||||
\(256\) | 20.7355 | 1.29597 | ||||||||
\(257\) | 1.50627 | 0.0939583 | 0.0469791 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469791 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(258\) | 23.0980 | 1.43802 | ||||||||
\(259\) | 6.42100 | 0.398982 | ||||||||
\(260\) | 3.92155 | 0.243204 | ||||||||
\(261\) | −3.54721 | −0.219567 | ||||||||
\(262\) | 32.1939 | 1.98894 | ||||||||
\(263\) | −7.88263 | −0.486064 | −0.243032 | − | 0.970018i | \(-0.578142\pi\) | ||||
−0.243032 | + | 0.970018i | \(0.578142\pi\) | |||||||
\(264\) | 1.97289 | 0.121423 | ||||||||
\(265\) | −7.01772 | −0.431095 | ||||||||
\(266\) | 3.17432 | 0.194630 | ||||||||
\(267\) | −12.5963 | −0.770879 | ||||||||
\(268\) | 15.7733 | 0.963507 | ||||||||
\(269\) | −1.23044 | −0.0750215 | −0.0375108 | − | 0.999296i | \(-0.511943\pi\) | ||||
−0.0375108 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(270\) | −4.74358 | −0.288685 | ||||||||
\(271\) | −21.3318 | −1.29581 | −0.647906 | − | 0.761720i | \(-0.724355\pi\) | ||||
−0.647906 | + | 0.761720i | \(0.724355\pi\) | |||||||
\(272\) | −23.6629 | −1.43478 | ||||||||
\(273\) | −6.79101 | −0.411011 | ||||||||
\(274\) | −26.7169 | −1.61402 | ||||||||
\(275\) | −0.835767 | −0.0503986 | ||||||||
\(276\) | −30.2173 | −1.81887 | ||||||||
\(277\) | −26.5974 | −1.59808 | −0.799042 | − | 0.601275i | \(-0.794660\pi\) | ||||
−0.799042 | + | 0.601275i | \(0.794660\pi\) | |||||||
\(278\) | −33.1954 | −1.99093 | ||||||||
\(279\) | 2.61927 | 0.156811 | ||||||||
\(280\) | 0.894900 | 0.0534805 | ||||||||
\(281\) | −1.56037 | −0.0930838 | −0.0465419 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465419 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(282\) | 46.8719 | 2.79118 | ||||||||
\(283\) | 13.7741 | 0.818784 | 0.409392 | − | 0.912359i | \(-0.365741\pi\) | ||||
0.409392 | + | 0.912359i | \(0.365741\pi\) | |||||||
\(284\) | −8.46436 | −0.502267 | ||||||||
\(285\) | 4.46092 | 0.264242 | ||||||||
\(286\) | −4.03875 | −0.238816 | ||||||||
\(287\) | −6.40349 | −0.377986 | ||||||||
\(288\) | 28.0288 | 1.65161 | ||||||||
\(289\) | 8.06732 | 0.474548 | ||||||||
\(290\) | −1.68219 | −0.0987818 | ||||||||
\(291\) | −11.7129 | −0.686623 | ||||||||
\(292\) | 22.9571 | 1.34346 | ||||||||
\(293\) | 0.651516 | 0.0380619 | 0.0190310 | − | 0.999819i | \(-0.493942\pi\) | ||||
0.0190310 | + | 0.999819i | \(0.493942\pi\) | |||||||
\(294\) | 4.95125 | 0.288763 | ||||||||
\(295\) | 5.07702 | 0.295596 | ||||||||
\(296\) | −5.74615 | −0.333988 | ||||||||
\(297\) | 2.11213 | 0.122558 | ||||||||
\(298\) | −15.7224 | −0.910774 | ||||||||
\(299\) | −19.3613 | −1.11969 | ||||||||
\(300\) | −4.01801 | −0.231980 | ||||||||
\(301\) | −4.66509 | −0.268891 | ||||||||
\(302\) | −44.8988 | −2.58364 | ||||||||
\(303\) | −30.8091 | −1.76994 | ||||||||
\(304\) | −7.99272 | −0.458414 | ||||||||
\(305\) | −4.74747 | −0.271839 | ||||||||
\(306\) | −37.1969 | −2.12641 | ||||||||
\(307\) | 12.8516 | 0.733480 | 0.366740 | − | 0.930324i | \(-0.380474\pi\) | ||||
0.366740 | + | 0.930324i | \(0.380474\pi\) | |||||||
\(308\) | 1.27307 | 0.0725399 | ||||||||
\(309\) | 39.7242 | 2.25983 | ||||||||
\(310\) | 1.24213 | 0.0705485 | ||||||||
\(311\) | −4.36812 | −0.247694 | −0.123847 | − | 0.992301i | \(-0.539523\pi\) | ||||
−0.123847 | + | 0.992301i | \(0.539523\pi\) | |||||||
\(312\) | 6.07728 | 0.344058 | ||||||||
\(313\) | 29.3585 | 1.65944 | 0.829721 | − | 0.558178i | \(-0.188499\pi\) | ||||
0.829721 | + | 0.558178i | \(0.188499\pi\) | |||||||
\(314\) | 39.2165 | 2.21311 | ||||||||
\(315\) | 3.95806 | 0.223011 | ||||||||
\(316\) | 4.71955 | 0.265495 | ||||||||
\(317\) | −9.39855 | −0.527875 | −0.263938 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263938 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(318\) | 34.7465 | 1.94849 | ||||||||
\(319\) | 0.749015 | 0.0419368 | ||||||||
\(320\) | 3.83965 | 0.214643 | ||||||||
\(321\) | −1.09017 | −0.0608473 | ||||||||
\(322\) | 14.1161 | 0.786660 | ||||||||
\(323\) | 8.46709 | 0.471121 | ||||||||
\(324\) | −7.93294 | −0.440719 | ||||||||
\(325\) | −2.57449 | −0.142807 | ||||||||
\(326\) | 29.8430 | 1.65285 | ||||||||
\(327\) | 11.8879 | 0.657402 | ||||||||
\(328\) | 5.73048 | 0.316413 | ||||||||
\(329\) | −9.46667 | −0.521915 | ||||||||
\(330\) | 4.13809 | 0.227794 | ||||||||
\(331\) | −4.70679 | −0.258709 | −0.129354 | − | 0.991598i | \(-0.541290\pi\) | ||||
−0.129354 | + | 0.991598i | \(0.541290\pi\) | |||||||
\(332\) | 5.76124 | 0.316189 | ||||||||
\(333\) | −25.4147 | −1.39272 | ||||||||
\(334\) | −17.8457 | −0.976471 | ||||||||
\(335\) | −10.3551 | −0.565760 | ||||||||
\(336\) | −12.4669 | −0.680125 | ||||||||
\(337\) | −10.8898 | −0.593207 | −0.296604 | − | 0.955001i | \(-0.595854\pi\) | ||||
−0.296604 | + | 0.955001i | \(0.595854\pi\) | |||||||
\(338\) | 11.9605 | 0.650564 | ||||||||
\(339\) | −50.5958 | −2.74799 | ||||||||
\(340\) | −7.62643 | −0.413601 | ||||||||
\(341\) | −0.553074 | −0.0299506 | ||||||||
\(342\) | −12.5642 | −0.679391 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.17479 | 0.225089 | ||||||||
\(345\) | 19.8376 | 1.06802 | ||||||||
\(346\) | −6.70139 | −0.360269 | ||||||||
\(347\) | −8.97483 | −0.481794 | −0.240897 | − | 0.970551i | \(-0.577442\pi\) | ||||
−0.240897 | + | 0.970551i | \(0.577442\pi\) | |||||||
\(348\) | 3.60094 | 0.193031 | ||||||||
\(349\) | 20.8846 | 1.11793 | 0.558963 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558963 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(350\) | 1.87703 | 0.100331 | ||||||||
\(351\) | 6.50618 | 0.347274 | ||||||||
\(352\) | −5.91845 | −0.315454 | ||||||||
\(353\) | −21.6208 | −1.15076 | −0.575380 | − | 0.817886i | \(-0.695146\pi\) | ||||
−0.575380 | + | 0.817886i | \(0.695146\pi\) | |||||||
\(354\) | −25.1376 | −1.33605 | ||||||||
\(355\) | 5.55683 | 0.294926 | ||||||||
\(356\) | 7.27386 | 0.385514 | ||||||||
\(357\) | 13.2068 | 0.698979 | ||||||||
\(358\) | 47.6812 | 2.52003 | ||||||||
\(359\) | −15.0577 | −0.794714 | −0.397357 | − | 0.917664i | \(-0.630073\pi\) | ||||
−0.397357 | + | 0.917664i | \(0.630073\pi\) | |||||||
\(360\) | −3.54206 | −0.186683 | ||||||||
\(361\) | −16.1400 | −0.849476 | ||||||||
\(362\) | −7.89405 | −0.414902 | ||||||||
\(363\) | 27.1734 | 1.42623 | ||||||||
\(364\) | 3.92155 | 0.205545 | ||||||||
\(365\) | −15.0713 | −0.788867 | ||||||||
\(366\) | 23.5059 | 1.22867 | ||||||||
\(367\) | −14.0132 | −0.731482 | −0.365741 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365741 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(368\) | −35.5433 | −1.85283 | ||||||||
\(369\) | 25.3454 | 1.31943 | ||||||||
\(370\) | −12.0524 | −0.626575 | ||||||||
\(371\) | −7.01772 | −0.364342 | ||||||||
\(372\) | −2.65894 | −0.137860 | ||||||||
\(373\) | 19.3993 | 1.00446 | 0.502229 | − | 0.864735i | \(-0.332514\pi\) | ||||
0.502229 | + | 0.864735i | \(0.332514\pi\) | |||||||
\(374\) | 7.85435 | 0.406139 | ||||||||
\(375\) | 2.63781 | 0.136216 | ||||||||
\(376\) | 8.47172 | 0.436896 | ||||||||
\(377\) | 2.30726 | 0.118830 | ||||||||
\(378\) | −4.74358 | −0.243984 | ||||||||
\(379\) | −0.956797 | −0.0491474 | −0.0245737 | − | 0.999698i | \(-0.507823\pi\) | ||||
−0.0245737 | + | 0.999698i | \(0.507823\pi\) | |||||||
\(380\) | −2.57601 | −0.132146 | ||||||||
\(381\) | −46.1076 | −2.36216 | ||||||||
\(382\) | 33.5844 | 1.71833 | ||||||||
\(383\) | −6.00556 | −0.306870 | −0.153435 | − | 0.988159i | \(-0.549034\pi\) | ||||
−0.153435 | + | 0.988159i | \(0.549034\pi\) | |||||||
\(384\) | 18.3481 | 0.936320 | ||||||||
\(385\) | −0.835767 | −0.0425946 | ||||||||
\(386\) | 47.6929 | 2.42751 | ||||||||
\(387\) | 18.4647 | 0.938613 | ||||||||
\(388\) | 6.76376 | 0.343378 | ||||||||
\(389\) | 0.329573 | 0.0167100 | 0.00835501 | − | 0.999965i | \(-0.497340\pi\) | ||||
0.00835501 | + | 0.999965i | \(0.497340\pi\) | |||||||
\(390\) | 12.7469 | 0.645466 | ||||||||
\(391\) | 37.6529 | 1.90419 | ||||||||
\(392\) | 0.894900 | 0.0451993 | ||||||||
\(393\) | 45.2425 | 2.28218 | ||||||||
\(394\) | −16.2661 | −0.819473 | ||||||||
\(395\) | −3.09837 | −0.155896 | ||||||||
\(396\) | −5.03889 | −0.253214 | ||||||||
\(397\) | −25.1035 | −1.25991 | −0.629954 | − | 0.776632i | \(-0.716926\pi\) | ||||
−0.629954 | + | 0.776632i | \(0.716926\pi\) | |||||||
\(398\) | −24.9043 | −1.24834 | ||||||||
\(399\) | 4.46092 | 0.223325 | ||||||||
\(400\) | −4.72622 | −0.236311 | ||||||||
\(401\) | −28.0654 | −1.40152 | −0.700759 | − | 0.713398i | \(-0.747155\pi\) | ||||
−0.700759 | + | 0.713398i | \(0.747155\pi\) | |||||||
\(402\) | 51.2708 | 2.55715 | ||||||||
\(403\) | −1.70368 | −0.0848664 | ||||||||
\(404\) | 17.7911 | 0.885138 | ||||||||
\(405\) | 5.20795 | 0.258785 | ||||||||
\(406\) | −1.68219 | −0.0834859 | ||||||||
\(407\) | 5.36646 | 0.266006 | ||||||||
\(408\) | −11.8188 | −0.585116 | ||||||||
\(409\) | 8.41613 | 0.416151 | 0.208075 | − | 0.978113i | \(-0.433280\pi\) | ||||
0.208075 | + | 0.978113i | \(0.433280\pi\) | |||||||
\(410\) | 12.0195 | 0.593603 | ||||||||
\(411\) | −37.5456 | −1.85199 | ||||||||
\(412\) | −22.9392 | −1.13013 | ||||||||
\(413\) | 5.07702 | 0.249824 | ||||||||
\(414\) | −55.8724 | −2.74598 | ||||||||
\(415\) | −3.78224 | −0.185663 | ||||||||
\(416\) | −18.2311 | −0.893854 | ||||||||
\(417\) | −46.6499 | −2.28446 | ||||||||
\(418\) | 2.65299 | 0.129762 | ||||||||
\(419\) | 18.8440 | 0.920590 | 0.460295 | − | 0.887766i | \(-0.347744\pi\) | ||||
0.460295 | + | 0.887766i | \(0.347744\pi\) | |||||||
\(420\) | −4.01801 | −0.196059 | ||||||||
\(421\) | 2.72399 | 0.132759 | 0.0663796 | − | 0.997794i | \(-0.478855\pi\) | ||||
0.0663796 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(422\) | −39.3929 | −1.91762 | ||||||||
\(423\) | 37.4696 | 1.82184 | ||||||||
\(424\) | 6.28016 | 0.304991 | ||||||||
\(425\) | 5.00673 | 0.242862 | ||||||||
\(426\) | −27.5132 | −1.33302 | ||||||||
\(427\) | −4.74747 | −0.229746 | ||||||||
\(428\) | 0.629531 | 0.0304295 | ||||||||
\(429\) | −5.67570 | −0.274026 | ||||||||
\(430\) | 8.75650 | 0.422276 | ||||||||
\(431\) | −0.502546 | −0.0242068 | −0.0121034 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121034 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(432\) | 11.9440 | 0.574656 | ||||||||
\(433\) | 38.5521 | 1.85269 | 0.926347 | − | 0.376671i | \(-0.122931\pi\) | ||||
0.926347 | + | 0.376671i | \(0.122931\pi\) | |||||||
\(434\) | 1.24213 | 0.0596244 | ||||||||
\(435\) | −2.36401 | −0.113346 | ||||||||
\(436\) | −6.86480 | −0.328764 | ||||||||
\(437\) | 12.7182 | 0.608392 | ||||||||
\(438\) | 74.6217 | 3.56556 | ||||||||
\(439\) | 35.5405 | 1.69625 | 0.848127 | − | 0.529793i | \(-0.177730\pi\) | ||||
0.848127 | + | 0.529793i | \(0.177730\pi\) | |||||||
\(440\) | 0.747928 | 0.0356561 | ||||||||
\(441\) | 3.95806 | 0.188479 | ||||||||
\(442\) | 24.1944 | 1.15081 | ||||||||
\(443\) | −9.88780 | −0.469783 | −0.234892 | − | 0.972022i | \(-0.575474\pi\) | ||||
−0.234892 | + | 0.972022i | \(0.575474\pi\) | |||||||
\(444\) | 25.7997 | 1.22440 | ||||||||
\(445\) | −4.77527 | −0.226369 | ||||||||
\(446\) | 43.5870 | 2.06390 | ||||||||
\(447\) | −22.0949 | −1.04505 | ||||||||
\(448\) | 3.83965 | 0.181406 | ||||||||
\(449\) | 40.5318 | 1.91281 | 0.956406 | − | 0.292040i | \(-0.0943341\pi\) | ||||
0.956406 | + | 0.292040i | \(0.0943341\pi\) | |||||||
\(450\) | −7.42939 | −0.350225 | ||||||||
\(451\) | −5.35183 | −0.252008 | ||||||||
\(452\) | 29.2172 | 1.37426 | ||||||||
\(453\) | −63.0969 | −2.96455 | ||||||||
\(454\) | −10.5443 | −0.494871 | ||||||||
\(455\) | −2.57449 | −0.120694 | ||||||||
\(456\) | −3.99207 | −0.186946 | ||||||||
\(457\) | 10.7056 | 0.500786 | 0.250393 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250393 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(458\) | −1.87703 | −0.0877078 | ||||||||
\(459\) | −12.6529 | −0.590586 | ||||||||
\(460\) | −11.4554 | −0.534112 | ||||||||
\(461\) | 11.4693 | 0.534180 | 0.267090 | − | 0.963672i | \(-0.413938\pi\) | ||||
0.267090 | + | 0.963672i | \(0.413938\pi\) | |||||||
\(462\) | 4.13809 | 0.192521 | ||||||||
\(463\) | 23.9804 | 1.11447 | 0.557233 | − | 0.830356i | \(-0.311863\pi\) | ||||
0.557233 | + | 0.830356i | \(0.311863\pi\) | |||||||
\(464\) | 4.23564 | 0.196635 | ||||||||
\(465\) | 1.74559 | 0.0809497 | ||||||||
\(466\) | 6.84686 | 0.317175 | ||||||||
\(467\) | −35.3534 | −1.63596 | −0.817981 | − | 0.575246i | \(-0.804906\pi\) | ||||
−0.817981 | + | 0.575246i | \(0.804906\pi\) | |||||||
\(468\) | −15.5217 | −0.717492 | ||||||||
\(469\) | −10.3551 | −0.478155 | ||||||||
\(470\) | 17.7692 | 0.819633 | ||||||||
\(471\) | 55.1114 | 2.53940 | ||||||||
\(472\) | −4.54343 | −0.209128 | ||||||||
\(473\) | −3.89893 | −0.179273 | ||||||||
\(474\) | 15.3408 | 0.704627 | ||||||||
\(475\) | 1.69114 | 0.0775949 | ||||||||
\(476\) | −7.62643 | −0.349557 | ||||||||
\(477\) | 27.7766 | 1.27180 | ||||||||
\(478\) | 22.0954 | 1.01062 | ||||||||
\(479\) | 1.30632 | 0.0596872 | 0.0298436 | − | 0.999555i | \(-0.490499\pi\) | ||||
0.0298436 | + | 0.999555i | \(0.490499\pi\) | |||||||
\(480\) | 18.6796 | 0.852601 | ||||||||
\(481\) | 16.5308 | 0.753739 | ||||||||
\(482\) | −9.10627 | −0.414779 | ||||||||
\(483\) | 19.8376 | 0.902640 | ||||||||
\(484\) | −15.6916 | −0.713255 | ||||||||
\(485\) | −4.44039 | −0.201628 | ||||||||
\(486\) | −40.0166 | −1.81519 | ||||||||
\(487\) | 23.2701 | 1.05447 | 0.527234 | − | 0.849720i | \(-0.323229\pi\) | ||||
0.527234 | + | 0.849720i | \(0.323229\pi\) | |||||||
\(488\) | 4.24851 | 0.192321 | ||||||||
\(489\) | 41.9387 | 1.89653 | ||||||||
\(490\) | 1.87703 | 0.0847955 | ||||||||
\(491\) | −41.2192 | −1.86020 | −0.930099 | − | 0.367310i | \(-0.880279\pi\) | ||||
−0.930099 | + | 0.367310i | \(0.880279\pi\) | |||||||
\(492\) | −25.7293 | −1.15997 | ||||||||
\(493\) | −4.48703 | −0.202086 | ||||||||
\(494\) | 8.17225 | 0.367687 | ||||||||
\(495\) | 3.30801 | 0.148684 | ||||||||
\(496\) | −3.12761 | −0.140434 | ||||||||
\(497\) | 5.55683 | 0.249258 | ||||||||
\(498\) | 18.7268 | 0.839168 | ||||||||
\(499\) | −21.3853 | −0.957336 | −0.478668 | − | 0.877996i | \(-0.658880\pi\) | ||||
−0.478668 | + | 0.877996i | \(0.658880\pi\) | |||||||
\(500\) | −1.52324 | −0.0681212 | ||||||||
\(501\) | −25.0787 | −1.12044 | ||||||||
\(502\) | 44.6129 | 1.99117 | ||||||||
\(503\) | −3.84614 | −0.171491 | −0.0857455 | − | 0.996317i | \(-0.527327\pi\) | ||||
−0.0857455 | + | 0.996317i | \(0.527327\pi\) | |||||||
\(504\) | −3.54206 | −0.157776 | ||||||||
\(505\) | −11.6798 | −0.519743 | ||||||||
\(506\) | 11.7978 | 0.524475 | ||||||||
\(507\) | 16.8082 | 0.746479 | ||||||||
\(508\) | 26.6254 | 1.18131 | ||||||||
\(509\) | −1.96040 | −0.0868931 | −0.0434466 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434466 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(510\) | −24.7896 | −1.09770 | ||||||||
\(511\) | −15.0713 | −0.666714 | ||||||||
\(512\) | −25.0096 | −1.10528 | ||||||||
\(513\) | −4.27382 | −0.188694 | ||||||||
\(514\) | −2.82730 | −0.124707 | ||||||||
\(515\) | 15.0595 | 0.663601 | ||||||||
\(516\) | −18.7444 | −0.825175 | ||||||||
\(517\) | −7.91193 | −0.347966 | ||||||||
\(518\) | −12.0524 | −0.529552 | ||||||||
\(519\) | −9.41755 | −0.413385 | ||||||||
\(520\) | 2.30391 | 0.101033 | ||||||||
\(521\) | 44.9547 | 1.96950 | 0.984751 | − | 0.173972i | \(-0.0556604\pi\) | ||||
0.984751 | + | 0.173972i | \(0.0556604\pi\) | |||||||
\(522\) | 6.65822 | 0.291422 | ||||||||
\(523\) | 40.1380 | 1.75511 | 0.877557 | − | 0.479473i | \(-0.159172\pi\) | ||||
0.877557 | + | 0.479473i | \(0.159172\pi\) | |||||||
\(524\) | −26.1258 | −1.14131 | ||||||||
\(525\) | 2.63781 | 0.115124 | ||||||||
\(526\) | 14.7959 | 0.645133 | ||||||||
\(527\) | 3.31323 | 0.144327 | ||||||||
\(528\) | −10.4194 | −0.453447 | ||||||||
\(529\) | 33.5572 | 1.45901 | ||||||||
\(530\) | 13.1725 | 0.572175 | ||||||||
\(531\) | −20.0951 | −0.872055 | ||||||||
\(532\) | −2.57601 | −0.111684 | ||||||||
\(533\) | −16.4857 | −0.714075 | ||||||||
\(534\) | 23.6436 | 1.02316 | ||||||||
\(535\) | −0.413285 | −0.0178679 | ||||||||
\(536\) | 9.26679 | 0.400264 | ||||||||
\(537\) | 67.0071 | 2.89157 | ||||||||
\(538\) | 2.30958 | 0.0995730 | ||||||||
\(539\) | −0.835767 | −0.0359990 | ||||||||
\(540\) | 3.84949 | 0.165656 | ||||||||
\(541\) | −44.6724 | −1.92062 | −0.960309 | − | 0.278938i | \(-0.910018\pi\) | ||||
−0.960309 | + | 0.278938i | \(0.910018\pi\) | |||||||
\(542\) | 40.0403 | 1.71988 | ||||||||
\(543\) | −11.0936 | −0.476073 | ||||||||
\(544\) | 35.4549 | 1.52012 | ||||||||
\(545\) | 4.50672 | 0.193047 | ||||||||
\(546\) | 12.7469 | 0.545518 | ||||||||
\(547\) | 24.6582 | 1.05431 | 0.527153 | − | 0.849770i | \(-0.323259\pi\) | ||||
0.527153 | + | 0.849770i | \(0.323259\pi\) | |||||||
\(548\) | 21.6811 | 0.926171 | ||||||||
\(549\) | 18.7907 | 0.801969 | ||||||||
\(550\) | 1.56876 | 0.0668921 | ||||||||
\(551\) | −1.51560 | −0.0645668 | ||||||||
\(552\) | −17.7526 | −0.755602 | ||||||||
\(553\) | −3.09837 | −0.131756 | ||||||||
\(554\) | 49.9241 | 2.12107 | ||||||||
\(555\) | −16.9374 | −0.718953 | ||||||||
\(556\) | 26.9385 | 1.14245 | ||||||||
\(557\) | 38.6938 | 1.63951 | 0.819755 | − | 0.572714i | \(-0.194110\pi\) | ||||
0.819755 | + | 0.572714i | \(0.194110\pi\) | |||||||
\(558\) | −4.91644 | −0.208129 | ||||||||
\(559\) | −12.0102 | −0.507977 | ||||||||
\(560\) | −4.72622 | −0.199719 | ||||||||
\(561\) | 11.0378 | 0.466017 | ||||||||
\(562\) | 2.92886 | 0.123546 | ||||||||
\(563\) | 26.6125 | 1.12158 | 0.560792 | − | 0.827957i | \(-0.310497\pi\) | ||||
0.560792 | + | 0.827957i | \(0.310497\pi\) | |||||||
\(564\) | −38.0372 | −1.60165 | ||||||||
\(565\) | −19.1810 | −0.806950 | ||||||||
\(566\) | −25.8543 | −1.08674 | ||||||||
\(567\) | 5.20795 | 0.218713 | ||||||||
\(568\) | −4.97280 | −0.208654 | ||||||||
\(569\) | 20.5636 | 0.862072 | 0.431036 | − | 0.902335i | \(-0.358148\pi\) | ||||
0.431036 | + | 0.902335i | \(0.358148\pi\) | |||||||
\(570\) | −8.37327 | −0.350718 | ||||||||
\(571\) | 7.16049 | 0.299657 | 0.149829 | − | 0.988712i | \(-0.452128\pi\) | ||||
0.149829 | + | 0.988712i | \(0.452128\pi\) | |||||||
\(572\) | 3.27750 | 0.137039 | ||||||||
\(573\) | 47.1966 | 1.97167 | ||||||||
\(574\) | 12.0195 | 0.501686 | ||||||||
\(575\) | 7.52045 | 0.313625 | ||||||||
\(576\) | −15.1976 | −0.633231 | ||||||||
\(577\) | 43.7448 | 1.82112 | 0.910560 | − | 0.413377i | \(-0.135651\pi\) | ||||
0.910560 | + | 0.413377i | \(0.135651\pi\) | |||||||
\(578\) | −15.1426 | −0.629849 | ||||||||
\(579\) | 67.0235 | 2.78540 | ||||||||
\(580\) | 1.36512 | 0.0566837 | ||||||||
\(581\) | −3.78224 | −0.156914 | ||||||||
\(582\) | 21.9855 | 0.911327 | ||||||||
\(583\) | −5.86518 | −0.242911 | ||||||||
\(584\) | 13.4873 | 0.558108 | ||||||||
\(585\) | 10.1900 | 0.421303 | ||||||||
\(586\) | −1.22291 | −0.0505181 | ||||||||
\(587\) | −43.7484 | −1.80569 | −0.902846 | − | 0.429965i | \(-0.858526\pi\) | ||||
−0.902846 | + | 0.429965i | \(0.858526\pi\) | |||||||
\(588\) | −4.01801 | −0.165700 | ||||||||
\(589\) | 1.11912 | 0.0461127 | ||||||||
\(590\) | −9.52971 | −0.392332 | ||||||||
\(591\) | −22.8589 | −0.940291 | ||||||||
\(592\) | 30.3471 | 1.24726 | ||||||||
\(593\) | 25.7238 | 1.05635 | 0.528175 | − | 0.849135i | \(-0.322876\pi\) | ||||
0.528175 | + | 0.849135i | \(0.322876\pi\) | |||||||
\(594\) | −3.96453 | −0.162667 | ||||||||
\(595\) | 5.00673 | 0.205256 | ||||||||
\(596\) | 12.7589 | 0.522627 | ||||||||
\(597\) | −34.9984 | −1.43239 | ||||||||
\(598\) | 36.3417 | 1.48612 | ||||||||
\(599\) | −0.342812 | −0.0140069 | −0.00700345 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700345 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(600\) | −2.36058 | −0.0963702 | ||||||||
\(601\) | 3.49654 | 0.142627 | 0.0713134 | − | 0.997454i | \(-0.477281\pi\) | ||||
0.0713134 | + | 0.997454i | \(0.477281\pi\) | |||||||
\(602\) | 8.75650 | 0.356888 | ||||||||
\(603\) | 40.9862 | 1.66909 | ||||||||
\(604\) | 36.4361 | 1.48256 | ||||||||
\(605\) | 10.3015 | 0.418815 | ||||||||
\(606\) | 57.8295 | 2.34916 | ||||||||
\(607\) | −2.89038 | −0.117317 | −0.0586586 | − | 0.998278i | \(-0.518682\pi\) | ||||
−0.0586586 | + | 0.998278i | \(0.518682\pi\) | |||||||
\(608\) | 11.9758 | 0.485681 | ||||||||
\(609\) | −2.36401 | −0.0957945 | ||||||||
\(610\) | 8.91113 | 0.360801 | ||||||||
\(611\) | −24.3718 | −0.985978 | ||||||||
\(612\) | 30.1858 | 1.22019 | ||||||||
\(613\) | 30.7954 | 1.24381 | 0.621907 | − | 0.783091i | \(-0.286358\pi\) | ||||
0.621907 | + | 0.783091i | \(0.286358\pi\) | |||||||
\(614\) | −24.1228 | −0.973518 | ||||||||
\(615\) | 16.8912 | 0.681120 | ||||||||
\(616\) | 0.747928 | 0.0301349 | ||||||||
\(617\) | 42.6220 | 1.71590 | 0.857949 | − | 0.513734i | \(-0.171738\pi\) | ||||
0.857949 | + | 0.513734i | \(0.171738\pi\) | |||||||
\(618\) | −74.5634 | −2.99938 | ||||||||
\(619\) | −37.2296 | −1.49638 | −0.748191 | − | 0.663483i | \(-0.769078\pi\) | ||||
−0.748191 | + | 0.663483i | \(0.769078\pi\) | |||||||
\(620\) | −1.00801 | −0.0404827 | ||||||||
\(621\) | −19.0055 | −0.762665 | ||||||||
\(622\) | 8.19909 | 0.328754 | ||||||||
\(623\) | −4.77527 | −0.191317 | ||||||||
\(624\) | −32.0958 | −1.28486 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −55.1068 | −2.20251 | ||||||||
\(627\) | 3.72829 | 0.148893 | ||||||||
\(628\) | −31.8247 | −1.26995 | ||||||||
\(629\) | −32.1482 | −1.28183 | ||||||||
\(630\) | −7.42939 | −0.295994 | ||||||||
\(631\) | 17.9955 | 0.716390 | 0.358195 | − | 0.933647i | \(-0.383392\pi\) | ||||
0.358195 | + | 0.933647i | \(0.383392\pi\) | |||||||
\(632\) | 2.77273 | 0.110293 | ||||||||
\(633\) | −55.3594 | −2.20034 | ||||||||
\(634\) | 17.6413 | 0.700627 | ||||||||
\(635\) | −17.4795 | −0.693652 | ||||||||
\(636\) | −28.1973 | −1.11810 | ||||||||
\(637\) | −2.57449 | −0.102005 | ||||||||
\(638\) | −1.40592 | −0.0556610 | ||||||||
\(639\) | −21.9942 | −0.870079 | ||||||||
\(640\) | 6.95578 | 0.274952 | ||||||||
\(641\) | −10.7140 | −0.423177 | −0.211588 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211588 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(642\) | 2.04628 | 0.0807602 | ||||||||
\(643\) | −32.5029 | −1.28179 | −0.640894 | − | 0.767629i | \(-0.721436\pi\) | ||||
−0.640894 | + | 0.767629i | \(0.721436\pi\) | |||||||
\(644\) | −11.4554 | −0.451407 | ||||||||
\(645\) | 12.3056 | 0.484534 | ||||||||
\(646\) | −15.8930 | −0.625300 | ||||||||
\(647\) | 31.2258 | 1.22761 | 0.613806 | − | 0.789457i | \(-0.289638\pi\) | ||||
0.613806 | + | 0.789457i | \(0.289638\pi\) | |||||||
\(648\) | −4.66060 | −0.183086 | ||||||||
\(649\) | 4.24321 | 0.166560 | ||||||||
\(650\) | 4.83238 | 0.189542 | ||||||||
\(651\) | 1.74559 | 0.0684150 | ||||||||
\(652\) | −24.2180 | −0.948450 | ||||||||
\(653\) | −50.7514 | −1.98606 | −0.993028 | − | 0.117883i | \(-0.962389\pi\) | ||||
−0.993028 | + | 0.117883i | \(0.962389\pi\) | |||||||
\(654\) | −22.3139 | −0.872543 | ||||||||
\(655\) | 17.1515 | 0.670165 | ||||||||
\(656\) | −30.2643 | −1.18162 | ||||||||
\(657\) | 59.6530 | 2.32728 | ||||||||
\(658\) | 17.7692 | 0.692716 | ||||||||
\(659\) | −10.9571 | −0.426827 | −0.213413 | − | 0.976962i | \(-0.568458\pi\) | ||||
−0.213413 | + | 0.976962i | \(0.568458\pi\) | |||||||
\(660\) | −3.35812 | −0.130715 | ||||||||
\(661\) | −9.25264 | −0.359886 | −0.179943 | − | 0.983677i | \(-0.557591\pi\) | ||||
−0.179943 | + | 0.983677i | \(0.557591\pi\) | |||||||
\(662\) | 8.83478 | 0.343374 | ||||||||
\(663\) | 34.0007 | 1.32048 | ||||||||
\(664\) | 3.38472 | 0.131353 | ||||||||
\(665\) | 1.69114 | 0.0655797 | ||||||||
\(666\) | 47.7041 | 1.84850 | ||||||||
\(667\) | −6.73983 | −0.260967 | ||||||||
\(668\) | 14.4820 | 0.560326 | ||||||||
\(669\) | 61.2533 | 2.36819 | ||||||||
\(670\) | 19.4369 | 0.750911 | ||||||||
\(671\) | −3.96778 | −0.153174 | ||||||||
\(672\) | 18.6796 | 0.720580 | ||||||||
\(673\) | 19.5396 | 0.753197 | 0.376599 | − | 0.926377i | \(-0.377094\pi\) | ||||
0.376599 | + | 0.926377i | \(0.377094\pi\) | |||||||
\(674\) | 20.4405 | 0.787340 | ||||||||
\(675\) | −2.52718 | −0.0972711 | ||||||||
\(676\) | −9.70609 | −0.373311 | ||||||||
\(677\) | 23.7477 | 0.912700 | 0.456350 | − | 0.889800i | \(-0.349156\pi\) | ||||
0.456350 | + | 0.889800i | \(0.349156\pi\) | |||||||
\(678\) | 94.9698 | 3.64729 | ||||||||
\(679\) | −4.44039 | −0.170407 | ||||||||
\(680\) | −4.48052 | −0.171820 | ||||||||
\(681\) | −14.8181 | −0.567831 | ||||||||
\(682\) | 1.03813 | 0.0397522 | ||||||||
\(683\) | 4.43123 | 0.169556 | 0.0847782 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847782 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(684\) | 10.1960 | 0.389853 | ||||||||
\(685\) | −14.2336 | −0.543838 | ||||||||
\(686\) | 1.87703 | 0.0716653 | ||||||||
\(687\) | −2.63781 | −0.100639 | ||||||||
\(688\) | −22.0483 | −0.840582 | ||||||||
\(689\) | −18.0670 | −0.688299 | ||||||||
\(690\) | −37.2356 | −1.41754 | ||||||||
\(691\) | 23.8436 | 0.907053 | 0.453526 | − | 0.891243i | \(-0.350166\pi\) | ||||
0.453526 | + | 0.891243i | \(0.350166\pi\) | |||||||
\(692\) | 5.43827 | 0.206732 | ||||||||
\(693\) | 3.30801 | 0.125661 | ||||||||
\(694\) | 16.8460 | 0.639466 | ||||||||
\(695\) | −17.6851 | −0.670833 | ||||||||
\(696\) | 2.11555 | 0.0801898 | ||||||||
\(697\) | 32.0605 | 1.21438 | ||||||||
\(698\) | −39.2010 | −1.48378 | ||||||||
\(699\) | 9.62198 | 0.363937 | ||||||||
\(700\) | −1.52324 | −0.0575729 | ||||||||
\(701\) | −32.1321 | −1.21361 | −0.606806 | − | 0.794850i | \(-0.707549\pi\) | ||||
−0.606806 | + | 0.794850i | \(0.707549\pi\) | |||||||
\(702\) | −12.2123 | −0.460923 | ||||||||
\(703\) | −10.8588 | −0.409549 | ||||||||
\(704\) | 3.20905 | 0.120946 | ||||||||
\(705\) | 24.9713 | 0.940474 | ||||||||
\(706\) | 40.5829 | 1.52736 | ||||||||
\(707\) | −11.6798 | −0.439263 | ||||||||
\(708\) | 20.3995 | 0.766661 | ||||||||
\(709\) | 18.0898 | 0.679378 | 0.339689 | − | 0.940538i | \(-0.389678\pi\) | ||||
0.339689 | + | 0.940538i | \(0.389678\pi\) | |||||||
\(710\) | −10.4303 | −0.391443 | ||||||||
\(711\) | 12.2635 | 0.459918 | ||||||||
\(712\) | 4.27339 | 0.160152 | ||||||||
\(713\) | 4.97670 | 0.186379 | ||||||||
\(714\) | −24.7896 | −0.927726 | ||||||||
\(715\) | −2.15167 | −0.0804679 | ||||||||
\(716\) | −38.6940 | −1.44606 | ||||||||
\(717\) | 31.0510 | 1.15962 | ||||||||
\(718\) | 28.2637 | 1.05479 | ||||||||
\(719\) | 6.27395 | 0.233979 | 0.116989 | − | 0.993133i | \(-0.462676\pi\) | ||||
0.116989 | + | 0.993133i | \(0.462676\pi\) | |||||||
\(720\) | 18.7067 | 0.697156 | ||||||||
\(721\) | 15.0595 | 0.560845 | ||||||||
\(722\) | 30.2953 | 1.12747 | ||||||||
\(723\) | −12.7972 | −0.475932 | ||||||||
\(724\) | 6.40614 | 0.238082 | ||||||||
\(725\) | −0.896200 | −0.0332840 | ||||||||
\(726\) | −51.0053 | −1.89298 | ||||||||
\(727\) | −50.2441 | −1.86345 | −0.931725 | − | 0.363165i | \(-0.881696\pi\) | ||||
−0.931725 | + | 0.363165i | \(0.881696\pi\) | |||||||
\(728\) | 2.30391 | 0.0853885 | ||||||||
\(729\) | −40.6120 | −1.50415 | ||||||||
\(730\) | 28.2892 | 1.04703 | ||||||||
\(731\) | 23.3568 | 0.863883 | ||||||||
\(732\) | −19.0754 | −0.705046 | ||||||||
\(733\) | 43.4030 | 1.60313 | 0.801564 | − | 0.597909i | \(-0.204002\pi\) | ||||
0.801564 | + | 0.597909i | \(0.204002\pi\) | |||||||
\(734\) | 26.3031 | 0.970867 | ||||||||
\(735\) | 2.63781 | 0.0972972 | ||||||||
\(736\) | 53.2558 | 1.96303 | ||||||||
\(737\) | −8.65447 | −0.318791 | ||||||||
\(738\) | −47.5740 | −1.75122 | ||||||||
\(739\) | 39.2057 | 1.44221 | 0.721103 | − | 0.692828i | \(-0.243635\pi\) | ||||
0.721103 | + | 0.692828i | \(0.243635\pi\) | |||||||
\(740\) | 9.78070 | 0.359546 | ||||||||
\(741\) | 11.4846 | 0.421896 | ||||||||
\(742\) | 13.1725 | 0.483576 | ||||||||
\(743\) | −44.6657 | −1.63863 | −0.819313 | − | 0.573347i | \(-0.805645\pi\) | ||||
−0.819313 | + | 0.573347i | \(0.805645\pi\) | |||||||
\(744\) | −1.56213 | −0.0572703 | ||||||||
\(745\) | −8.37621 | −0.306881 | ||||||||
\(746\) | −36.4130 | −1.33318 | ||||||||
\(747\) | 14.9703 | 0.547735 | ||||||||
\(748\) | −6.37392 | −0.233053 | ||||||||
\(749\) | −0.413285 | −0.0151011 | ||||||||
\(750\) | −4.95125 | −0.180794 | ||||||||
\(751\) | −52.1124 | −1.90161 | −0.950804 | − | 0.309793i | \(-0.899740\pi\) | ||||
−0.950804 | + | 0.309793i | \(0.899740\pi\) | |||||||
\(752\) | −44.7416 | −1.63156 | ||||||||
\(753\) | 62.6951 | 2.28474 | ||||||||
\(754\) | −4.33078 | −0.157718 | ||||||||
\(755\) | −23.9202 | −0.870544 | ||||||||
\(756\) | 3.84949 | 0.140004 | ||||||||
\(757\) | 40.5574 | 1.47409 | 0.737043 | − | 0.675846i | \(-0.236222\pi\) | ||||
0.737043 | + | 0.675846i | \(0.236222\pi\) | |||||||
\(758\) | 1.79593 | 0.0652313 | ||||||||
\(759\) | 16.5796 | 0.601800 | ||||||||
\(760\) | −1.51340 | −0.0548969 | ||||||||
\(761\) | −11.6861 | −0.423621 | −0.211811 | − | 0.977311i | \(-0.567936\pi\) | ||||
−0.211811 | + | 0.977311i | \(0.567936\pi\) | |||||||
\(762\) | 86.5452 | 3.13520 | ||||||||
\(763\) | 4.50672 | 0.163154 | ||||||||
\(764\) | −27.2542 | −0.986024 | ||||||||
\(765\) | −19.8169 | −0.716482 | ||||||||
\(766\) | 11.2726 | 0.407296 | ||||||||
\(767\) | 13.0707 | 0.471956 | ||||||||
\(768\) | −54.6964 | −1.97369 | ||||||||
\(769\) | −11.9369 | −0.430456 | −0.215228 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215228 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(770\) | 1.56876 | 0.0565341 | ||||||||
\(771\) | −3.97325 | −0.143093 | ||||||||
\(772\) | −38.7035 | −1.39297 | ||||||||
\(773\) | −6.52893 | −0.234829 | −0.117415 | − | 0.993083i | \(-0.537461\pi\) | ||||
−0.117415 | + | 0.993083i | \(0.537461\pi\) | |||||||
\(774\) | −34.6587 | −1.24578 | ||||||||
\(775\) | 0.661756 | 0.0237710 | ||||||||
\(776\) | 3.97370 | 0.142648 | ||||||||
\(777\) | −16.9374 | −0.607626 | ||||||||
\(778\) | −0.618618 | −0.0221785 | ||||||||
\(779\) | 10.8292 | 0.387997 | ||||||||
\(780\) | −10.3443 | −0.370386 | ||||||||
\(781\) | 4.64421 | 0.166183 | ||||||||
\(782\) | −70.6755 | −2.52735 | ||||||||
\(783\) | 2.26486 | 0.0809394 | ||||||||
\(784\) | −4.72622 | −0.168794 | ||||||||
\(785\) | 20.8928 | 0.745698 | ||||||||
\(786\) | −84.9214 | −3.02905 | ||||||||
\(787\) | −42.1405 | −1.50215 | −0.751073 | − | 0.660219i | \(-0.770463\pi\) | ||||
−0.751073 | + | 0.660219i | \(0.770463\pi\) | |||||||
\(788\) | 13.2002 | 0.470236 | ||||||||
\(789\) | 20.7929 | 0.740247 | ||||||||
\(790\) | 5.81573 | 0.206914 | ||||||||
\(791\) | −19.1810 | −0.681997 | ||||||||
\(792\) | −2.96034 | −0.105191 | ||||||||
\(793\) | −12.2223 | −0.434026 | ||||||||
\(794\) | 47.1200 | 1.67223 | ||||||||
\(795\) | 18.5114 | 0.656533 | ||||||||
\(796\) | 20.2102 | 0.716333 | ||||||||
\(797\) | 25.5112 | 0.903651 | 0.451826 | − | 0.892106i | \(-0.350773\pi\) | ||||
0.451826 | + | 0.892106i | \(0.350773\pi\) | |||||||
\(798\) | −8.37327 | −0.296411 | ||||||||
\(799\) | 47.3970 | 1.67679 | ||||||||
\(800\) | 7.08146 | 0.250367 | ||||||||
\(801\) | 18.9008 | 0.667827 | ||||||||
\(802\) | 52.6795 | 1.86018 | ||||||||
\(803\) | −12.5961 | −0.444506 | ||||||||
\(804\) | −41.6070 | −1.46737 | ||||||||
\(805\) | 7.52045 | 0.265061 | ||||||||
\(806\) | 3.19786 | 0.112640 | ||||||||
\(807\) | 3.24568 | 0.114253 | ||||||||
\(808\) | 10.4522 | 0.367708 | ||||||||
\(809\) | −41.7146 | −1.46661 | −0.733304 | − | 0.679901i | \(-0.762023\pi\) | ||||
−0.733304 | + | 0.679901i | \(0.762023\pi\) | |||||||
\(810\) | −9.77548 | −0.343475 | ||||||||
\(811\) | 41.0939 | 1.44300 | 0.721501 | − | 0.692413i | \(-0.243452\pi\) | ||||
0.721501 | + | 0.692413i | \(0.243452\pi\) | |||||||
\(812\) | 1.36512 | 0.0479065 | ||||||||
\(813\) | 56.2692 | 1.97345 | ||||||||
\(814\) | −10.0730 | −0.353059 | ||||||||
\(815\) | 15.8991 | 0.556920 | ||||||||
\(816\) | 62.4184 | 2.18508 | ||||||||
\(817\) | 7.88933 | 0.276013 | ||||||||
\(818\) | −15.7973 | −0.552340 | ||||||||
\(819\) | 10.1900 | 0.356066 | ||||||||
\(820\) | −9.75403 | −0.340626 | ||||||||
\(821\) | −44.2387 | −1.54394 | −0.771970 | − | 0.635658i | \(-0.780729\pi\) | ||||
−0.771970 | + | 0.635658i | \(0.780729\pi\) | |||||||
\(822\) | 70.4741 | 2.45807 | ||||||||
\(823\) | −45.6664 | −1.59183 | −0.795915 | − | 0.605408i | \(-0.793010\pi\) | ||||
−0.795915 | + | 0.605408i | \(0.793010\pi\) | |||||||
\(824\) | −13.4768 | −0.469485 | ||||||||
\(825\) | 2.20460 | 0.0767542 | ||||||||
\(826\) | −9.52971 | −0.331581 | ||||||||
\(827\) | −36.4509 | −1.26752 | −0.633760 | − | 0.773530i | \(-0.718489\pi\) | ||||
−0.633760 | + | 0.773530i | \(0.718489\pi\) | |||||||
\(828\) | 45.3412 | 1.57572 | ||||||||
\(829\) | 47.4883 | 1.64934 | 0.824668 | − | 0.565616i | \(-0.191362\pi\) | ||||
0.824668 | + | 0.565616i | \(0.191362\pi\) | |||||||
\(830\) | 7.09937 | 0.246423 | ||||||||
\(831\) | 70.1590 | 2.43379 | ||||||||
\(832\) | 9.88512 | 0.342705 | ||||||||
\(833\) | 5.00673 | 0.173473 | ||||||||
\(834\) | 87.5632 | 3.03206 | ||||||||
\(835\) | −9.50740 | −0.329017 | ||||||||
\(836\) | −2.15294 | −0.0744611 | ||||||||
\(837\) | −1.67237 | −0.0578057 | ||||||||
\(838\) | −35.3707 | −1.22186 | ||||||||
\(839\) | 22.3479 | 0.771536 | 0.385768 | − | 0.922596i | \(-0.373936\pi\) | ||||
0.385768 | + | 0.922596i | \(0.373936\pi\) | |||||||
\(840\) | −2.36058 | −0.0814477 | ||||||||
\(841\) | −28.1968 | −0.972304 | ||||||||
\(842\) | −5.11301 | −0.176206 | ||||||||
\(843\) | 4.11596 | 0.141761 | ||||||||
\(844\) | 31.9680 | 1.10038 | ||||||||
\(845\) | 6.37202 | 0.219204 | ||||||||
\(846\) | −70.3316 | −2.41805 | ||||||||
\(847\) | 10.3015 | 0.353964 | ||||||||
\(848\) | −33.1673 | −1.13897 | ||||||||
\(849\) | −36.3335 | −1.24696 | ||||||||
\(850\) | −9.39777 | −0.322341 | ||||||||
\(851\) | −48.2889 | −1.65532 | ||||||||
\(852\) | 22.3274 | 0.764924 | ||||||||
\(853\) | 8.02611 | 0.274809 | 0.137404 | − | 0.990515i | \(-0.456124\pi\) | ||||
0.137404 | + | 0.990515i | \(0.456124\pi\) | |||||||
\(854\) | 8.91113 | 0.304933 | ||||||||
\(855\) | −6.69364 | −0.228918 | ||||||||
\(856\) | 0.369849 | 0.0126412 | ||||||||
\(857\) | 14.3073 | 0.488728 | 0.244364 | − | 0.969684i | \(-0.421421\pi\) | ||||
0.244364 | + | 0.969684i | \(0.421421\pi\) | |||||||
\(858\) | 10.6535 | 0.363703 | ||||||||
\(859\) | 19.7835 | 0.675003 | 0.337501 | − | 0.941325i | \(-0.390418\pi\) | ||||
0.337501 | + | 0.941325i | \(0.390418\pi\) | |||||||
\(860\) | −7.10603 | −0.242314 | ||||||||
\(861\) | 16.8912 | 0.575651 | ||||||||
\(862\) | 0.943293 | 0.0321287 | ||||||||
\(863\) | 31.2974 | 1.06538 | 0.532688 | − | 0.846311i | \(-0.321182\pi\) | ||||
0.532688 | + | 0.846311i | \(0.321182\pi\) | |||||||
\(864\) | −17.8961 | −0.608837 | ||||||||
\(865\) | −3.57021 | −0.121391 | ||||||||
\(866\) | −72.3633 | −2.45901 | ||||||||
\(867\) | −21.2801 | −0.722710 | ||||||||
\(868\) | −1.00801 | −0.0342141 | ||||||||
\(869\) | −2.58952 | −0.0878433 | ||||||||
\(870\) | 4.43731 | 0.150439 | ||||||||
\(871\) | −26.6591 | −0.903309 | ||||||||
\(872\) | −4.03306 | −0.136577 | ||||||||
\(873\) | 17.5753 | 0.594834 | ||||||||
\(874\) | −23.8723 | −0.807494 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −60.5566 | −2.04602 | ||||||||
\(877\) | −20.3738 | −0.687975 | −0.343987 | − | 0.938974i | \(-0.611778\pi\) | ||||
−0.343987 | + | 0.938974i | \(0.611778\pi\) | |||||||
\(878\) | −66.7105 | −2.25137 | ||||||||
\(879\) | −1.71858 | −0.0579661 | ||||||||
\(880\) | −3.95002 | −0.133155 | ||||||||
\(881\) | −3.08834 | −0.104049 | −0.0520243 | − | 0.998646i | \(-0.516567\pi\) | ||||
−0.0520243 | + | 0.998646i | \(0.516567\pi\) | |||||||
\(882\) | −7.42939 | −0.250160 | ||||||||
\(883\) | −39.3746 | −1.32506 | −0.662530 | − | 0.749035i | \(-0.730517\pi\) | ||||
−0.662530 | + | 0.749035i | \(0.730517\pi\) | |||||||
\(884\) | −19.6341 | −0.660367 | ||||||||
\(885\) | −13.3922 | −0.450175 | ||||||||
\(886\) | 18.5597 | 0.623525 | ||||||||
\(887\) | −16.1720 | −0.543004 | −0.271502 | − | 0.962438i | \(-0.587520\pi\) | ||||
−0.271502 | + | 0.962438i | \(0.587520\pi\) | |||||||
\(888\) | 15.1573 | 0.508645 | ||||||||
\(889\) | −17.4795 | −0.586243 | ||||||||
\(890\) | 8.96332 | 0.300451 | ||||||||
\(891\) | 4.35264 | 0.145819 | ||||||||
\(892\) | −35.3715 | −1.18432 | ||||||||
\(893\) | 16.0095 | 0.535737 | ||||||||
\(894\) | 41.4727 | 1.38706 | ||||||||
\(895\) | 25.4025 | 0.849112 | ||||||||
\(896\) | 6.95578 | 0.232376 | ||||||||
\(897\) | 51.0715 | 1.70523 | ||||||||
\(898\) | −76.0793 | −2.53880 | ||||||||
\(899\) | −0.593066 | −0.0197799 | ||||||||
\(900\) | 6.02906 | 0.200969 | ||||||||
\(901\) | 35.1358 | 1.17054 | ||||||||
\(902\) | 10.0455 | 0.334480 | ||||||||
\(903\) | 12.3056 | 0.409506 | ||||||||
\(904\) | 17.1651 | 0.570901 | ||||||||
\(905\) | −4.20561 | −0.139799 | ||||||||
\(906\) | 118.435 | 3.93473 | ||||||||
\(907\) | −15.9244 | −0.528762 | −0.264381 | − | 0.964418i | \(-0.585168\pi\) | ||||
−0.264381 | + | 0.964418i | \(0.585168\pi\) | |||||||
\(908\) | 8.55689 | 0.283970 | ||||||||
\(909\) | 46.2292 | 1.53333 | ||||||||
\(910\) | 4.83238 | 0.160192 | ||||||||
\(911\) | 44.8109 | 1.48465 | 0.742326 | − | 0.670038i | \(-0.233722\pi\) | ||||
0.742326 | + | 0.670038i | \(0.233722\pi\) | |||||||
\(912\) | 21.0833 | 0.698138 | ||||||||
\(913\) | −3.16107 | −0.104616 | ||||||||
\(914\) | −20.0947 | −0.664673 | ||||||||
\(915\) | 12.5229 | 0.413995 | ||||||||
\(916\) | 1.52324 | 0.0503291 | ||||||||
\(917\) | 17.1515 | 0.566393 | ||||||||
\(918\) | 23.7498 | 0.783861 | ||||||||
\(919\) | −4.48235 | −0.147859 | −0.0739296 | − | 0.997263i | \(-0.523554\pi\) | ||||
−0.0739296 | + | 0.997263i | \(0.523554\pi\) | |||||||
\(920\) | −6.73005 | −0.221883 | ||||||||
\(921\) | −33.9001 | −1.11705 | ||||||||
\(922\) | −21.5283 | −0.708996 | ||||||||
\(923\) | 14.3060 | 0.470887 | ||||||||
\(924\) | −3.35812 | −0.110474 | ||||||||
\(925\) | −6.42100 | −0.211121 | ||||||||
\(926\) | −45.0120 | −1.47918 | ||||||||
\(927\) | −59.6064 | −1.95773 | ||||||||
\(928\) | −6.34641 | −0.208331 | ||||||||
\(929\) | 33.5100 | 1.09943 | 0.549714 | − | 0.835353i | \(-0.314737\pi\) | ||||
0.549714 | + | 0.835353i | \(0.314737\pi\) | |||||||
\(930\) | −3.27652 | −0.107441 | ||||||||
\(931\) | 1.69114 | 0.0554250 | ||||||||
\(932\) | −5.55632 | −0.182003 | ||||||||
\(933\) | 11.5223 | 0.377223 | ||||||||
\(934\) | 66.3594 | 2.17135 | ||||||||
\(935\) | 4.18446 | 0.136846 | ||||||||
\(936\) | −9.11900 | −0.298064 | ||||||||
\(937\) | −8.38107 | −0.273798 | −0.136899 | − | 0.990585i | \(-0.543714\pi\) | ||||
−0.136899 | + | 0.990585i | \(0.543714\pi\) | |||||||
\(938\) | 19.4369 | 0.634636 | ||||||||
\(939\) | −77.4423 | −2.52723 | ||||||||
\(940\) | −14.4200 | −0.470328 | ||||||||
\(941\) | 13.8655 | 0.452003 | 0.226002 | − | 0.974127i | \(-0.427435\pi\) | ||||
0.226002 | + | 0.974127i | \(0.427435\pi\) | |||||||
\(942\) | −103.446 | −3.37044 | ||||||||
\(943\) | 48.1572 | 1.56821 | ||||||||
\(944\) | 23.9951 | 0.780975 | ||||||||
\(945\) | −2.52718 | −0.0822091 | ||||||||
\(946\) | 7.31840 | 0.237942 | ||||||||
\(947\) | 30.2186 | 0.981973 | 0.490986 | − | 0.871167i | \(-0.336636\pi\) | ||||
0.490986 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(948\) | −12.4493 | −0.404334 | ||||||||
\(949\) | −38.8008 | −1.25953 | ||||||||
\(950\) | −3.17432 | −0.102989 | ||||||||
\(951\) | 24.7916 | 0.803923 | ||||||||
\(952\) | −4.48052 | −0.145214 | ||||||||
\(953\) | 28.2354 | 0.914633 | 0.457316 | − | 0.889304i | \(-0.348811\pi\) | ||||
0.457316 | + | 0.889304i | \(0.348811\pi\) | |||||||
\(954\) | −52.1374 | −1.68801 | ||||||||
\(955\) | 17.8923 | 0.578982 | ||||||||
\(956\) | −17.9308 | −0.579922 | ||||||||
\(957\) | −1.97576 | −0.0638673 | ||||||||
\(958\) | −2.45200 | −0.0792205 | ||||||||
\(959\) | −14.2336 | −0.459627 | ||||||||
\(960\) | −10.1283 | −0.326889 | ||||||||
\(961\) | −30.5621 | −0.985874 | ||||||||
\(962\) | −31.0287 | −1.00041 | ||||||||
\(963\) | 1.63581 | 0.0527131 | ||||||||
\(964\) | 7.38987 | 0.238012 | ||||||||
\(965\) | 25.4087 | 0.817937 | ||||||||
\(966\) | −37.2356 | −1.19804 | ||||||||
\(967\) | 11.5248 | 0.370612 | 0.185306 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185306 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(968\) | −9.21880 | −0.296304 | ||||||||
\(969\) | −22.3346 | −0.717491 | ||||||||
\(970\) | 8.33474 | 0.267612 | ||||||||
\(971\) | 22.7562 | 0.730282 | 0.365141 | − | 0.930952i | \(-0.381021\pi\) | ||||
0.365141 | + | 0.930952i | \(0.381021\pi\) | |||||||
\(972\) | 32.4741 | 1.04161 | ||||||||
\(973\) | −17.6851 | −0.566957 | ||||||||
\(974\) | −43.6786 | −1.39955 | ||||||||
\(975\) | 6.79101 | 0.217486 | ||||||||
\(976\) | −22.4376 | −0.718210 | ||||||||
\(977\) | −53.5666 | −1.71375 | −0.856874 | − | 0.515525i | \(-0.827597\pi\) | ||||
−0.856874 | + | 0.515525i | \(0.827597\pi\) | |||||||
\(978\) | −78.7202 | −2.51719 | ||||||||
\(979\) | −3.99101 | −0.127553 | ||||||||
\(980\) | −1.52324 | −0.0486580 | ||||||||
\(981\) | −17.8379 | −0.569519 | ||||||||
\(982\) | 77.3696 | 2.46896 | ||||||||
\(983\) | 25.2092 | 0.804050 | 0.402025 | − | 0.915629i | \(-0.368306\pi\) | ||||
0.402025 | + | 0.915629i | \(0.368306\pi\) | |||||||
\(984\) | −15.1159 | −0.481879 | ||||||||
\(985\) | −8.66587 | −0.276117 | ||||||||
\(986\) | 8.42229 | 0.268220 | ||||||||
\(987\) | 24.9713 | 0.794846 | ||||||||
\(988\) | −6.63190 | −0.210989 | ||||||||
\(989\) | 35.0836 | 1.11559 | ||||||||
\(990\) | −6.20924 | −0.197342 | ||||||||
\(991\) | 10.9941 | 0.349241 | 0.174620 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174620 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(992\) | 4.68620 | 0.148787 | ||||||||
\(993\) | 12.4156 | 0.393998 | ||||||||
\(994\) | −10.4303 | −0.330830 | ||||||||
\(995\) | −13.2680 | −0.420623 | ||||||||
\(996\) | −15.1971 | −0.481538 | ||||||||
\(997\) | −12.2800 | −0.388912 | −0.194456 | − | 0.980911i | \(-0.562294\pi\) | ||||
−0.194456 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(998\) | 40.1408 | 1.27063 | ||||||||
\(999\) | 16.2270 | 0.513400 |
(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 | 8015.2.a.l.1.13 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.13 | ✓ | 62 | 1.1 | even | 1 | trivial |