Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.17518 | −0.678492 | −0.339246 | − | 0.940698i | \(-0.610172\pi\) | ||||
−0.339246 | + | 0.940698i | \(0.610172\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.11669 | −1.39383 | −0.696914 | − | 0.717155i | \(-0.745444\pi\) | ||||
−0.696914 | + | 0.717155i | \(0.745444\pi\) | |||||||
\(6\) | −1.17518 | −0.479766 | ||||||||
\(7\) | −1.35191 | −0.510974 | −0.255487 | − | 0.966812i | \(-0.582236\pi\) | ||||
−0.255487 | + | 0.966812i | \(0.582236\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.61895 | −0.539649 | ||||||||
\(10\) | −3.11669 | −0.985585 | ||||||||
\(11\) | −0.503259 | −0.151738 | −0.0758692 | − | 0.997118i | \(-0.524173\pi\) | ||||
−0.0758692 | + | 0.997118i | \(0.524173\pi\) | |||||||
\(12\) | −1.17518 | −0.339246 | ||||||||
\(13\) | −3.71888 | −1.03143 | −0.515715 | − | 0.856760i | \(-0.672474\pi\) | ||||
−0.515715 | + | 0.856760i | \(0.672474\pi\) | |||||||
\(14\) | −1.35191 | −0.361313 | ||||||||
\(15\) | 3.66268 | 0.945701 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.16970 | −1.49637 | −0.748186 | − | 0.663489i | \(-0.769075\pi\) | ||||
−0.748186 | + | 0.663489i | \(0.769075\pi\) | |||||||
\(18\) | −1.61895 | −0.381589 | ||||||||
\(19\) | −1.88511 | −0.432473 | −0.216237 | − | 0.976341i | \(-0.569378\pi\) | ||||
−0.216237 | + | 0.976341i | \(0.569378\pi\) | |||||||
\(20\) | −3.11669 | −0.696914 | ||||||||
\(21\) | 1.58874 | 0.346692 | ||||||||
\(22\) | −0.503259 | −0.107295 | ||||||||
\(23\) | −6.86881 | −1.43225 | −0.716123 | − | 0.697974i | \(-0.754085\pi\) | ||||
−0.716123 | + | 0.697974i | \(0.754085\pi\) | |||||||
\(24\) | −1.17518 | −0.239883 | ||||||||
\(25\) | 4.71378 | 0.942755 | ||||||||
\(26\) | −3.71888 | −0.729332 | ||||||||
\(27\) | 5.42810 | 1.04464 | ||||||||
\(28\) | −1.35191 | −0.255487 | ||||||||
\(29\) | −2.46209 | −0.457199 | −0.228599 | − | 0.973521i | \(-0.573415\pi\) | ||||
−0.228599 | + | 0.973521i | \(0.573415\pi\) | |||||||
\(30\) | 3.66268 | 0.668711 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.591422 | 0.102953 | ||||||||
\(34\) | −6.16970 | −1.05809 | ||||||||
\(35\) | 4.21349 | 0.712210 | ||||||||
\(36\) | −1.61895 | −0.269824 | ||||||||
\(37\) | −2.09342 | −0.344156 | −0.172078 | − | 0.985083i | \(-0.555048\pi\) | ||||
−0.172078 | + | 0.985083i | \(0.555048\pi\) | |||||||
\(38\) | −1.88511 | −0.305805 | ||||||||
\(39\) | 4.37036 | 0.699817 | ||||||||
\(40\) | −3.11669 | −0.492792 | ||||||||
\(41\) | 7.07625 | 1.10512 | 0.552562 | − | 0.833472i | \(-0.313650\pi\) | ||||
0.552562 | + | 0.833472i | \(0.313650\pi\) | |||||||
\(42\) | 1.58874 | 0.245148 | ||||||||
\(43\) | 5.02319 | 0.766029 | 0.383015 | − | 0.923742i | \(-0.374886\pi\) | ||||
0.383015 | + | 0.923742i | \(0.374886\pi\) | |||||||
\(44\) | −0.503259 | −0.0758692 | ||||||||
\(45\) | 5.04576 | 0.752177 | ||||||||
\(46\) | −6.86881 | −1.01275 | ||||||||
\(47\) | −5.22293 | −0.761842 | −0.380921 | − | 0.924608i | \(-0.624393\pi\) | ||||
−0.380921 | + | 0.924608i | \(0.624393\pi\) | |||||||
\(48\) | −1.17518 | −0.169623 | ||||||||
\(49\) | −5.17234 | −0.738906 | ||||||||
\(50\) | 4.71378 | 0.666629 | ||||||||
\(51\) | 7.25052 | 1.01528 | ||||||||
\(52\) | −3.71888 | −0.515715 | ||||||||
\(53\) | −13.9970 | −1.92263 | −0.961316 | − | 0.275447i | \(-0.911174\pi\) | ||||
−0.961316 | + | 0.275447i | \(0.911174\pi\) | |||||||
\(54\) | 5.42810 | 0.738671 | ||||||||
\(55\) | 1.56851 | 0.211497 | ||||||||
\(56\) | −1.35191 | −0.180657 | ||||||||
\(57\) | 2.21534 | 0.293429 | ||||||||
\(58\) | −2.46209 | −0.323289 | ||||||||
\(59\) | −6.02325 | −0.784161 | −0.392080 | − | 0.919931i | \(-0.628244\pi\) | ||||
−0.392080 | + | 0.919931i | \(0.628244\pi\) | |||||||
\(60\) | 3.66268 | 0.472850 | ||||||||
\(61\) | 12.0367 | 1.54114 | 0.770572 | − | 0.637352i | \(-0.219970\pi\) | ||||
0.770572 | + | 0.637352i | \(0.219970\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 2.18867 | 0.275746 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.5906 | 1.43764 | ||||||||
\(66\) | 0.591422 | 0.0727990 | ||||||||
\(67\) | −11.0860 | −1.35437 | −0.677183 | − | 0.735815i | \(-0.736799\pi\) | ||||
−0.677183 | + | 0.735815i | \(0.736799\pi\) | |||||||
\(68\) | −6.16970 | −0.748186 | ||||||||
\(69\) | 8.07210 | 0.971767 | ||||||||
\(70\) | 4.21349 | 0.503608 | ||||||||
\(71\) | −3.72033 | −0.441522 | −0.220761 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220761 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(72\) | −1.61895 | −0.190795 | ||||||||
\(73\) | 4.40766 | 0.515878 | 0.257939 | − | 0.966161i | \(-0.416957\pi\) | ||||
0.257939 | + | 0.966161i | \(0.416957\pi\) | |||||||
\(74\) | −2.09342 | −0.243355 | ||||||||
\(75\) | −5.53955 | −0.639652 | ||||||||
\(76\) | −1.88511 | −0.216237 | ||||||||
\(77\) | 0.680362 | 0.0775344 | ||||||||
\(78\) | 4.37036 | 0.494846 | ||||||||
\(79\) | 3.43746 | 0.386745 | 0.193372 | − | 0.981125i | \(-0.438057\pi\) | ||||
0.193372 | + | 0.981125i | \(0.438057\pi\) | |||||||
\(80\) | −3.11669 | −0.348457 | ||||||||
\(81\) | −1.52217 | −0.169130 | ||||||||
\(82\) | 7.07625 | 0.781441 | ||||||||
\(83\) | −7.01960 | −0.770502 | −0.385251 | − | 0.922812i | \(-0.625885\pi\) | ||||
−0.385251 | + | 0.922812i | \(0.625885\pi\) | |||||||
\(84\) | 1.58874 | 0.173346 | ||||||||
\(85\) | 19.2291 | 2.08568 | ||||||||
\(86\) | 5.02319 | 0.541665 | ||||||||
\(87\) | 2.89341 | 0.310206 | ||||||||
\(88\) | −0.503259 | −0.0536476 | ||||||||
\(89\) | 9.40623 | 0.997058 | 0.498529 | − | 0.866873i | \(-0.333874\pi\) | ||||
0.498529 | + | 0.866873i | \(0.333874\pi\) | |||||||
\(90\) | 5.04576 | 0.531870 | ||||||||
\(91\) | 5.02759 | 0.527034 | ||||||||
\(92\) | −6.86881 | −0.716123 | ||||||||
\(93\) | 1.17518 | 0.121861 | ||||||||
\(94\) | −5.22293 | −0.538704 | ||||||||
\(95\) | 5.87530 | 0.602793 | ||||||||
\(96\) | −1.17518 | −0.119942 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | −5.17234 | −0.522485 | ||||||||
\(99\) | 0.814750 | 0.0818855 | ||||||||
\(100\) | 4.71378 | 0.471378 | ||||||||
\(101\) | 12.3081 | 1.22470 | 0.612349 | − | 0.790587i | \(-0.290225\pi\) | ||||
0.612349 | + | 0.790587i | \(0.290225\pi\) | |||||||
\(102\) | 7.25052 | 0.717909 | ||||||||
\(103\) | 9.57290 | 0.943246 | 0.471623 | − | 0.881800i | \(-0.343668\pi\) | ||||
0.471623 | + | 0.881800i | \(0.343668\pi\) | |||||||
\(104\) | −3.71888 | −0.364666 | ||||||||
\(105\) | −4.95162 | −0.483228 | ||||||||
\(106\) | −13.9970 | −1.35951 | ||||||||
\(107\) | −0.201888 | −0.0195172 | −0.00975861 | − | 0.999952i | \(-0.503106\pi\) | ||||
−0.00975861 | + | 0.999952i | \(0.503106\pi\) | |||||||
\(108\) | 5.42810 | 0.522320 | ||||||||
\(109\) | 2.29119 | 0.219456 | 0.109728 | − | 0.993962i | \(-0.465002\pi\) | ||||
0.109728 | + | 0.993962i | \(0.465002\pi\) | |||||||
\(110\) | 1.56851 | 0.149551 | ||||||||
\(111\) | 2.46015 | 0.233507 | ||||||||
\(112\) | −1.35191 | −0.127743 | ||||||||
\(113\) | 3.47032 | 0.326460 | 0.163230 | − | 0.986588i | \(-0.447809\pi\) | ||||
0.163230 | + | 0.986588i | \(0.447809\pi\) | |||||||
\(114\) | 2.21534 | 0.207486 | ||||||||
\(115\) | 21.4080 | 1.99630 | ||||||||
\(116\) | −2.46209 | −0.228599 | ||||||||
\(117\) | 6.02066 | 0.556610 | ||||||||
\(118\) | −6.02325 | −0.554485 | ||||||||
\(119\) | 8.34088 | 0.764607 | ||||||||
\(120\) | 3.66268 | 0.334356 | ||||||||
\(121\) | −10.7467 | −0.976975 | ||||||||
\(122\) | 12.0367 | 1.08975 | ||||||||
\(123\) | −8.31588 | −0.749818 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0.892069 | 0.0797891 | ||||||||
\(126\) | 2.18867 | 0.194982 | ||||||||
\(127\) | 8.77250 | 0.778434 | 0.389217 | − | 0.921146i | \(-0.372746\pi\) | ||||
0.389217 | + | 0.921146i | \(0.372746\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.90317 | −0.519745 | ||||||||
\(130\) | 11.5906 | 1.01656 | ||||||||
\(131\) | 2.04069 | 0.178296 | 0.0891479 | − | 0.996018i | \(-0.471586\pi\) | ||||
0.0891479 | + | 0.996018i | \(0.471586\pi\) | |||||||
\(132\) | 0.591422 | 0.0514767 | ||||||||
\(133\) | 2.54849 | 0.220982 | ||||||||
\(134\) | −11.0860 | −0.957681 | ||||||||
\(135\) | −16.9177 | −1.45605 | ||||||||
\(136\) | −6.16970 | −0.529047 | ||||||||
\(137\) | −7.09997 | −0.606592 | −0.303296 | − | 0.952896i | \(-0.598087\pi\) | ||||
−0.303296 | + | 0.952896i | \(0.598087\pi\) | |||||||
\(138\) | 8.07210 | 0.687143 | ||||||||
\(139\) | −21.8990 | −1.85745 | −0.928726 | − | 0.370768i | \(-0.879095\pi\) | ||||
−0.928726 | + | 0.370768i | \(0.879095\pi\) | |||||||
\(140\) | 4.21349 | 0.356105 | ||||||||
\(141\) | 6.13789 | 0.516904 | ||||||||
\(142\) | −3.72033 | −0.312203 | ||||||||
\(143\) | 1.87156 | 0.156508 | ||||||||
\(144\) | −1.61895 | −0.134912 | ||||||||
\(145\) | 7.67359 | 0.637257 | ||||||||
\(146\) | 4.40766 | 0.364781 | ||||||||
\(147\) | 6.07844 | 0.501341 | ||||||||
\(148\) | −2.09342 | −0.172078 | ||||||||
\(149\) | −14.9355 | −1.22356 | −0.611781 | − | 0.791027i | \(-0.709547\pi\) | ||||
−0.611781 | + | 0.791027i | \(0.709547\pi\) | |||||||
\(150\) | −5.53955 | −0.452302 | ||||||||
\(151\) | −2.99086 | −0.243392 | −0.121696 | − | 0.992567i | \(-0.538833\pi\) | ||||
−0.121696 | + | 0.992567i | \(0.538833\pi\) | |||||||
\(152\) | −1.88511 | −0.152902 | ||||||||
\(153\) | 9.98841 | 0.807515 | ||||||||
\(154\) | 0.680362 | 0.0548251 | ||||||||
\(155\) | 3.11669 | 0.250339 | ||||||||
\(156\) | 4.37036 | 0.349909 | ||||||||
\(157\) | −3.56243 | −0.284313 | −0.142157 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142157 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(158\) | 3.43746 | 0.273470 | ||||||||
\(159\) | 16.4490 | 1.30449 | ||||||||
\(160\) | −3.11669 | −0.246396 | ||||||||
\(161\) | 9.28601 | 0.731840 | ||||||||
\(162\) | −1.52217 | −0.119593 | ||||||||
\(163\) | 6.54744 | 0.512835 | 0.256418 | − | 0.966566i | \(-0.417458\pi\) | ||||
0.256418 | + | 0.966566i | \(0.417458\pi\) | |||||||
\(164\) | 7.07625 | 0.552562 | ||||||||
\(165\) | −1.84328 | −0.143499 | ||||||||
\(166\) | −7.01960 | −0.544827 | ||||||||
\(167\) | −1.56658 | −0.121225 | −0.0606127 | − | 0.998161i | \(-0.519305\pi\) | ||||
−0.0606127 | + | 0.998161i | \(0.519305\pi\) | |||||||
\(168\) | 1.58874 | 0.122574 | ||||||||
\(169\) | 0.830043 | 0.0638494 | ||||||||
\(170\) | 19.2291 | 1.47480 | ||||||||
\(171\) | 3.05189 | 0.233384 | ||||||||
\(172\) | 5.02319 | 0.383015 | ||||||||
\(173\) | −0.618297 | −0.0470083 | −0.0235041 | − | 0.999724i | \(-0.507482\pi\) | ||||
−0.0235041 | + | 0.999724i | \(0.507482\pi\) | |||||||
\(174\) | 2.89341 | 0.219349 | ||||||||
\(175\) | −6.37260 | −0.481723 | ||||||||
\(176\) | −0.503259 | −0.0379346 | ||||||||
\(177\) | 7.07842 | 0.532047 | ||||||||
\(178\) | 9.40623 | 0.705027 | ||||||||
\(179\) | 2.28458 | 0.170757 | 0.0853787 | − | 0.996349i | \(-0.472790\pi\) | ||||
0.0853787 | + | 0.996349i | \(0.472790\pi\) | |||||||
\(180\) | 5.04576 | 0.376089 | ||||||||
\(181\) | 24.8791 | 1.84925 | 0.924625 | − | 0.380878i | \(-0.124378\pi\) | ||||
0.924625 | + | 0.380878i | \(0.124378\pi\) | |||||||
\(182\) | 5.02759 | 0.372669 | ||||||||
\(183\) | −14.1453 | −1.04565 | ||||||||
\(184\) | −6.86881 | −0.506375 | ||||||||
\(185\) | 6.52454 | 0.479693 | ||||||||
\(186\) | 1.17518 | 0.0861686 | ||||||||
\(187\) | 3.10496 | 0.227057 | ||||||||
\(188\) | −5.22293 | −0.380921 | ||||||||
\(189\) | −7.33831 | −0.533783 | ||||||||
\(190\) | 5.87530 | 0.426239 | ||||||||
\(191\) | −17.2209 | −1.24606 | −0.623031 | − | 0.782197i | \(-0.714099\pi\) | ||||
−0.623031 | + | 0.782197i | \(0.714099\pi\) | |||||||
\(192\) | −1.17518 | −0.0848115 | ||||||||
\(193\) | 11.7501 | 0.845787 | 0.422894 | − | 0.906179i | \(-0.361014\pi\) | ||||
0.422894 | + | 0.906179i | \(0.361014\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −13.6211 | −0.975425 | ||||||||
\(196\) | −5.17234 | −0.369453 | ||||||||
\(197\) | 4.25474 | 0.303138 | 0.151569 | − | 0.988447i | \(-0.451567\pi\) | ||||
0.151569 | + | 0.988447i | \(0.451567\pi\) | |||||||
\(198\) | 0.814750 | 0.0579018 | ||||||||
\(199\) | −18.4646 | −1.30892 | −0.654460 | − | 0.756097i | \(-0.727104\pi\) | ||||
−0.654460 | + | 0.756097i | \(0.727104\pi\) | |||||||
\(200\) | 4.71378 | 0.333314 | ||||||||
\(201\) | 13.0280 | 0.918926 | ||||||||
\(202\) | 12.3081 | 0.865993 | ||||||||
\(203\) | 3.32853 | 0.233617 | ||||||||
\(204\) | 7.25052 | 0.507638 | ||||||||
\(205\) | −22.0545 | −1.54035 | ||||||||
\(206\) | 9.57290 | 0.666976 | ||||||||
\(207\) | 11.1202 | 0.772910 | ||||||||
\(208\) | −3.71888 | −0.257858 | ||||||||
\(209\) | 0.948698 | 0.0656228 | ||||||||
\(210\) | −4.95162 | −0.341694 | ||||||||
\(211\) | 6.35725 | 0.437651 | 0.218826 | − | 0.975764i | \(-0.429777\pi\) | ||||
0.218826 | + | 0.975764i | \(0.429777\pi\) | |||||||
\(212\) | −13.9970 | −0.961316 | ||||||||
\(213\) | 4.37207 | 0.299569 | ||||||||
\(214\) | −0.201888 | −0.0138008 | ||||||||
\(215\) | −15.6557 | −1.06771 | ||||||||
\(216\) | 5.42810 | 0.369336 | ||||||||
\(217\) | 1.35191 | 0.0917736 | ||||||||
\(218\) | 2.29119 | 0.155179 | ||||||||
\(219\) | −5.17981 | −0.350019 | ||||||||
\(220\) | 1.56851 | 0.105749 | ||||||||
\(221\) | 22.9444 | 1.54340 | ||||||||
\(222\) | 2.46015 | 0.165114 | ||||||||
\(223\) | −4.77373 | −0.319672 | −0.159836 | − | 0.987144i | \(-0.551097\pi\) | ||||
−0.159836 | + | 0.987144i | \(0.551097\pi\) | |||||||
\(224\) | −1.35191 | −0.0903283 | ||||||||
\(225\) | −7.63135 | −0.508757 | ||||||||
\(226\) | 3.47032 | 0.230842 | ||||||||
\(227\) | −19.1074 | −1.26820 | −0.634102 | − | 0.773250i | \(-0.718630\pi\) | ||||
−0.634102 | + | 0.773250i | \(0.718630\pi\) | |||||||
\(228\) | 2.21534 | 0.146715 | ||||||||
\(229\) | 18.8803 | 1.24765 | 0.623823 | − | 0.781566i | \(-0.285579\pi\) | ||||
0.623823 | + | 0.781566i | \(0.285579\pi\) | |||||||
\(230\) | 21.4080 | 1.41160 | ||||||||
\(231\) | −0.799549 | −0.0526065 | ||||||||
\(232\) | −2.46209 | −0.161644 | ||||||||
\(233\) | −25.1234 | −1.64589 | −0.822944 | − | 0.568123i | \(-0.807670\pi\) | ||||
−0.822944 | + | 0.568123i | \(0.807670\pi\) | |||||||
\(234\) | 6.02066 | 0.393583 | ||||||||
\(235\) | 16.2783 | 1.06188 | ||||||||
\(236\) | −6.02325 | −0.392080 | ||||||||
\(237\) | −4.03965 | −0.262403 | ||||||||
\(238\) | 8.34088 | 0.540659 | ||||||||
\(239\) | 22.4591 | 1.45276 | 0.726379 | − | 0.687294i | \(-0.241202\pi\) | ||||
0.726379 | + | 0.687294i | \(0.241202\pi\) | |||||||
\(240\) | 3.66268 | 0.236425 | ||||||||
\(241\) | −7.88547 | −0.507948 | −0.253974 | − | 0.967211i | \(-0.581738\pi\) | ||||
−0.253974 | + | 0.967211i | \(0.581738\pi\) | |||||||
\(242\) | −10.7467 | −0.690826 | ||||||||
\(243\) | −14.4955 | −0.929886 | ||||||||
\(244\) | 12.0367 | 0.770572 | ||||||||
\(245\) | 16.1206 | 1.02991 | ||||||||
\(246\) | −8.31588 | −0.530201 | ||||||||
\(247\) | 7.01048 | 0.446066 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 8.24931 | 0.522779 | ||||||||
\(250\) | 0.892069 | 0.0564194 | ||||||||
\(251\) | 25.0265 | 1.57966 | 0.789829 | − | 0.613328i | \(-0.210170\pi\) | ||||
0.789829 | + | 0.613328i | \(0.210170\pi\) | |||||||
\(252\) | 2.18867 | 0.137873 | ||||||||
\(253\) | 3.45679 | 0.217327 | ||||||||
\(254\) | 8.77250 | 0.550436 | ||||||||
\(255\) | −22.5977 | −1.41512 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.7567 | −1.35714 | −0.678572 | − | 0.734534i | \(-0.737401\pi\) | ||||
−0.678572 | + | 0.734534i | \(0.737401\pi\) | |||||||
\(258\) | −5.90317 | −0.367515 | ||||||||
\(259\) | 2.83011 | 0.175854 | ||||||||
\(260\) | 11.5906 | 0.718818 | ||||||||
\(261\) | 3.98599 | 0.246727 | ||||||||
\(262\) | 2.04069 | 0.126074 | ||||||||
\(263\) | 29.1935 | 1.80015 | 0.900073 | − | 0.435739i | \(-0.143513\pi\) | ||||
0.900073 | + | 0.435739i | \(0.143513\pi\) | |||||||
\(264\) | 0.591422 | 0.0363995 | ||||||||
\(265\) | 43.6243 | 2.67982 | ||||||||
\(266\) | 2.54849 | 0.156258 | ||||||||
\(267\) | −11.0540 | −0.676496 | ||||||||
\(268\) | −11.0860 | −0.677183 | ||||||||
\(269\) | 29.3467 | 1.78930 | 0.894651 | − | 0.446765i | \(-0.147424\pi\) | ||||
0.894651 | + | 0.446765i | \(0.147424\pi\) | |||||||
\(270\) | −16.9177 | −1.02958 | ||||||||
\(271\) | 27.8230 | 1.69013 | 0.845065 | − | 0.534664i | \(-0.179562\pi\) | ||||
0.845065 | + | 0.534664i | \(0.179562\pi\) | |||||||
\(272\) | −6.16970 | −0.374093 | ||||||||
\(273\) | −5.90833 | −0.357588 | ||||||||
\(274\) | −7.09997 | −0.428925 | ||||||||
\(275\) | −2.37225 | −0.143052 | ||||||||
\(276\) | 8.07210 | 0.485883 | ||||||||
\(277\) | −18.4852 | −1.11067 | −0.555333 | − | 0.831628i | \(-0.687409\pi\) | ||||
−0.555333 | + | 0.831628i | \(0.687409\pi\) | |||||||
\(278\) | −21.8990 | −1.31342 | ||||||||
\(279\) | 1.61895 | 0.0969238 | ||||||||
\(280\) | 4.21349 | 0.251804 | ||||||||
\(281\) | 18.8333 | 1.12350 | 0.561751 | − | 0.827307i | \(-0.310128\pi\) | ||||
0.561751 | + | 0.827307i | \(0.310128\pi\) | |||||||
\(282\) | 6.13789 | 0.365506 | ||||||||
\(283\) | 2.73265 | 0.162439 | 0.0812195 | − | 0.996696i | \(-0.474119\pi\) | ||||
0.0812195 | + | 0.996696i | \(0.474119\pi\) | |||||||
\(284\) | −3.72033 | −0.220761 | ||||||||
\(285\) | −6.90455 | −0.408990 | ||||||||
\(286\) | 1.87156 | 0.110668 | ||||||||
\(287\) | −9.56645 | −0.564690 | ||||||||
\(288\) | −1.61895 | −0.0953973 | ||||||||
\(289\) | 21.0652 | 1.23913 | ||||||||
\(290\) | 7.67359 | 0.450608 | ||||||||
\(291\) | 1.17518 | 0.0688904 | ||||||||
\(292\) | 4.40766 | 0.257939 | ||||||||
\(293\) | −17.7076 | −1.03449 | −0.517245 | − | 0.855837i | \(-0.673042\pi\) | ||||
−0.517245 | + | 0.855837i | \(0.673042\pi\) | |||||||
\(294\) | 6.07844 | 0.354502 | ||||||||
\(295\) | 18.7726 | 1.09298 | ||||||||
\(296\) | −2.09342 | −0.121677 | ||||||||
\(297\) | −2.73175 | −0.158512 | ||||||||
\(298\) | −14.9355 | −0.865189 | ||||||||
\(299\) | 25.5442 | 1.47726 | ||||||||
\(300\) | −5.53955 | −0.319826 | ||||||||
\(301\) | −6.79090 | −0.391421 | ||||||||
\(302\) | −2.99086 | −0.172104 | ||||||||
\(303\) | −14.4642 | −0.830948 | ||||||||
\(304\) | −1.88511 | −0.108118 | ||||||||
\(305\) | −37.5148 | −2.14809 | ||||||||
\(306\) | 9.98841 | 0.571000 | ||||||||
\(307\) | 21.1166 | 1.20519 | 0.602593 | − | 0.798049i | \(-0.294134\pi\) | ||||
0.602593 | + | 0.798049i | \(0.294134\pi\) | |||||||
\(308\) | 0.680362 | 0.0387672 | ||||||||
\(309\) | −11.2499 | −0.639985 | ||||||||
\(310\) | 3.11669 | 0.177016 | ||||||||
\(311\) | −6.85979 | −0.388983 | −0.194491 | − | 0.980904i | \(-0.562306\pi\) | ||||
−0.194491 | + | 0.980904i | \(0.562306\pi\) | |||||||
\(312\) | 4.37036 | 0.247423 | ||||||||
\(313\) | −9.04124 | −0.511041 | −0.255521 | − | 0.966804i | \(-0.582247\pi\) | ||||
−0.255521 | + | 0.966804i | \(0.582247\pi\) | |||||||
\(314\) | −3.56243 | −0.201040 | ||||||||
\(315\) | −6.82141 | −0.384343 | ||||||||
\(316\) | 3.43746 | 0.193372 | ||||||||
\(317\) | −1.57113 | −0.0882434 | −0.0441217 | − | 0.999026i | \(-0.514049\pi\) | ||||
−0.0441217 | + | 0.999026i | \(0.514049\pi\) | |||||||
\(318\) | 16.4490 | 0.922414 | ||||||||
\(319\) | 1.23907 | 0.0693747 | ||||||||
\(320\) | −3.11669 | −0.174228 | ||||||||
\(321\) | 0.237255 | 0.0132423 | ||||||||
\(322\) | 9.28601 | 0.517489 | ||||||||
\(323\) | 11.6305 | 0.647141 | ||||||||
\(324\) | −1.52217 | −0.0845652 | ||||||||
\(325\) | −17.5300 | −0.972387 | ||||||||
\(326\) | 6.54744 | 0.362629 | ||||||||
\(327\) | −2.69256 | −0.148899 | ||||||||
\(328\) | 7.07625 | 0.390721 | ||||||||
\(329\) | 7.06093 | 0.389281 | ||||||||
\(330\) | −1.84328 | −0.101469 | ||||||||
\(331\) | −4.25054 | −0.233631 | −0.116815 | − | 0.993154i | \(-0.537269\pi\) | ||||
−0.116815 | + | 0.993154i | \(0.537269\pi\) | |||||||
\(332\) | −7.01960 | −0.385251 | ||||||||
\(333\) | 3.38913 | 0.185723 | ||||||||
\(334\) | −1.56658 | −0.0857193 | ||||||||
\(335\) | 34.5515 | 1.88775 | ||||||||
\(336\) | 1.58874 | 0.0866729 | ||||||||
\(337\) | −21.1690 | −1.15315 | −0.576576 | − | 0.817044i | \(-0.695611\pi\) | ||||
−0.576576 | + | 0.817044i | \(0.695611\pi\) | |||||||
\(338\) | 0.830043 | 0.0451484 | ||||||||
\(339\) | −4.07826 | −0.221501 | ||||||||
\(340\) | 19.2291 | 1.04284 | ||||||||
\(341\) | 0.503259 | 0.0272530 | ||||||||
\(342\) | 3.05189 | 0.165027 | ||||||||
\(343\) | 16.4559 | 0.888535 | ||||||||
\(344\) | 5.02319 | 0.270832 | ||||||||
\(345\) | −25.1583 | −1.35448 | ||||||||
\(346\) | −0.618297 | −0.0332399 | ||||||||
\(347\) | −19.8435 | −1.06525 | −0.532627 | − | 0.846350i | \(-0.678795\pi\) | ||||
−0.532627 | + | 0.846350i | \(0.678795\pi\) | |||||||
\(348\) | 2.89341 | 0.155103 | ||||||||
\(349\) | 13.9060 | 0.744373 | 0.372186 | − | 0.928158i | \(-0.378608\pi\) | ||||
0.372186 | + | 0.928158i | \(0.378608\pi\) | |||||||
\(350\) | −6.37260 | −0.340630 | ||||||||
\(351\) | −20.1865 | −1.07747 | ||||||||
\(352\) | −0.503259 | −0.0268238 | ||||||||
\(353\) | −4.85218 | −0.258256 | −0.129128 | − | 0.991628i | \(-0.541218\pi\) | ||||
−0.129128 | + | 0.991628i | \(0.541218\pi\) | |||||||
\(354\) | 7.07842 | 0.376214 | ||||||||
\(355\) | 11.5951 | 0.615406 | ||||||||
\(356\) | 9.40623 | 0.498529 | ||||||||
\(357\) | −9.80205 | −0.518780 | ||||||||
\(358\) | 2.28458 | 0.120744 | ||||||||
\(359\) | −11.6213 | −0.613348 | −0.306674 | − | 0.951815i | \(-0.599216\pi\) | ||||
−0.306674 | + | 0.951815i | \(0.599216\pi\) | |||||||
\(360\) | 5.04576 | 0.265935 | ||||||||
\(361\) | −15.4464 | −0.812967 | ||||||||
\(362\) | 24.8791 | 1.30762 | ||||||||
\(363\) | 12.6294 | 0.662870 | ||||||||
\(364\) | 5.02759 | 0.263517 | ||||||||
\(365\) | −13.7373 | −0.719045 | ||||||||
\(366\) | −14.1453 | −0.739389 | ||||||||
\(367\) | 18.1152 | 0.945608 | 0.472804 | − | 0.881168i | \(-0.343242\pi\) | ||||
0.472804 | + | 0.881168i | \(0.343242\pi\) | |||||||
\(368\) | −6.86881 | −0.358061 | ||||||||
\(369\) | −11.4561 | −0.596379 | ||||||||
\(370\) | 6.52454 | 0.339194 | ||||||||
\(371\) | 18.9227 | 0.982415 | ||||||||
\(372\) | 1.17518 | 0.0609304 | ||||||||
\(373\) | 21.6742 | 1.12225 | 0.561124 | − | 0.827732i | \(-0.310369\pi\) | ||||
0.561124 | + | 0.827732i | \(0.310369\pi\) | |||||||
\(374\) | 3.10496 | 0.160554 | ||||||||
\(375\) | −1.04834 | −0.0541363 | ||||||||
\(376\) | −5.22293 | −0.269352 | ||||||||
\(377\) | 9.15622 | 0.471569 | ||||||||
\(378\) | −7.33831 | −0.377442 | ||||||||
\(379\) | −18.8301 | −0.967237 | −0.483618 | − | 0.875279i | \(-0.660678\pi\) | ||||
−0.483618 | + | 0.875279i | \(0.660678\pi\) | |||||||
\(380\) | 5.87530 | 0.301396 | ||||||||
\(381\) | −10.3093 | −0.528161 | ||||||||
\(382\) | −17.2209 | −0.881099 | ||||||||
\(383\) | −2.79420 | −0.142777 | −0.0713884 | − | 0.997449i | \(-0.522743\pi\) | ||||
−0.0713884 | + | 0.997449i | \(0.522743\pi\) | |||||||
\(384\) | −1.17518 | −0.0599708 | ||||||||
\(385\) | −2.12048 | −0.108070 | ||||||||
\(386\) | 11.7501 | 0.598062 | ||||||||
\(387\) | −8.13228 | −0.413387 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 24.8123 | 1.25803 | 0.629017 | − | 0.777392i | \(-0.283458\pi\) | ||||
0.629017 | + | 0.777392i | \(0.283458\pi\) | |||||||
\(390\) | −13.6211 | −0.689729 | ||||||||
\(391\) | 42.3785 | 2.14317 | ||||||||
\(392\) | −5.17234 | −0.261243 | ||||||||
\(393\) | −2.39818 | −0.120972 | ||||||||
\(394\) | 4.25474 | 0.214351 | ||||||||
\(395\) | −10.7135 | −0.539056 | ||||||||
\(396\) | 0.814750 | 0.0409427 | ||||||||
\(397\) | 6.84583 | 0.343582 | 0.171791 | − | 0.985133i | \(-0.445045\pi\) | ||||
0.171791 | + | 0.985133i | \(0.445045\pi\) | |||||||
\(398\) | −18.4646 | −0.925546 | ||||||||
\(399\) | −2.99495 | −0.149935 | ||||||||
\(400\) | 4.71378 | 0.235689 | ||||||||
\(401\) | −30.7281 | −1.53449 | −0.767245 | − | 0.641354i | \(-0.778373\pi\) | ||||
−0.767245 | + | 0.641354i | \(0.778373\pi\) | |||||||
\(402\) | 13.0280 | 0.649779 | ||||||||
\(403\) | 3.71888 | 0.185250 | ||||||||
\(404\) | 12.3081 | 0.612349 | ||||||||
\(405\) | 4.74415 | 0.235739 | ||||||||
\(406\) | 3.32853 | 0.165192 | ||||||||
\(407\) | 1.05353 | 0.0522216 | ||||||||
\(408\) | 7.25052 | 0.358954 | ||||||||
\(409\) | −29.2232 | −1.44500 | −0.722498 | − | 0.691373i | \(-0.757006\pi\) | ||||
−0.722498 | + | 0.691373i | \(0.757006\pi\) | |||||||
\(410\) | −22.0545 | −1.08919 | ||||||||
\(411\) | 8.34376 | 0.411567 | ||||||||
\(412\) | 9.57290 | 0.471623 | ||||||||
\(413\) | 8.14290 | 0.400686 | ||||||||
\(414\) | 11.1202 | 0.546530 | ||||||||
\(415\) | 21.8779 | 1.07395 | ||||||||
\(416\) | −3.71888 | −0.182333 | ||||||||
\(417\) | 25.7354 | 1.26027 | ||||||||
\(418\) | 0.948698 | 0.0464023 | ||||||||
\(419\) | −29.4577 | −1.43910 | −0.719552 | − | 0.694439i | \(-0.755653\pi\) | ||||
−0.719552 | + | 0.694439i | \(0.755653\pi\) | |||||||
\(420\) | −4.95162 | −0.241614 | ||||||||
\(421\) | 6.32190 | 0.308111 | 0.154055 | − | 0.988062i | \(-0.450767\pi\) | ||||
0.154055 | + | 0.988062i | \(0.450767\pi\) | |||||||
\(422\) | 6.35725 | 0.309466 | ||||||||
\(423\) | 8.45564 | 0.411127 | ||||||||
\(424\) | −13.9970 | −0.679753 | ||||||||
\(425\) | −29.0826 | −1.41071 | ||||||||
\(426\) | 4.37207 | 0.211827 | ||||||||
\(427\) | −16.2726 | −0.787485 | ||||||||
\(428\) | −0.201888 | −0.00975861 | ||||||||
\(429\) | −2.19942 | −0.106189 | ||||||||
\(430\) | −15.6557 | −0.754987 | ||||||||
\(431\) | 7.99353 | 0.385035 | 0.192517 | − | 0.981294i | \(-0.438335\pi\) | ||||
0.192517 | + | 0.981294i | \(0.438335\pi\) | |||||||
\(432\) | 5.42810 | 0.261160 | ||||||||
\(433\) | −28.0270 | −1.34689 | −0.673447 | − | 0.739236i | \(-0.735187\pi\) | ||||
−0.673447 | + | 0.739236i | \(0.735187\pi\) | |||||||
\(434\) | 1.35191 | 0.0648938 | ||||||||
\(435\) | −9.01786 | −0.432373 | ||||||||
\(436\) | 2.29119 | 0.109728 | ||||||||
\(437\) | 12.9484 | 0.619408 | ||||||||
\(438\) | −5.17981 | −0.247501 | ||||||||
\(439\) | −17.5860 | −0.839333 | −0.419667 | − | 0.907678i | \(-0.637853\pi\) | ||||
−0.419667 | + | 0.907678i | \(0.637853\pi\) | |||||||
\(440\) | 1.56851 | 0.0747756 | ||||||||
\(441\) | 8.37374 | 0.398750 | ||||||||
\(442\) | 22.9444 | 1.09135 | ||||||||
\(443\) | −30.5104 | −1.44959 | −0.724796 | − | 0.688963i | \(-0.758066\pi\) | ||||
−0.724796 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(444\) | 2.46015 | 0.116753 | ||||||||
\(445\) | −29.3163 | −1.38973 | ||||||||
\(446\) | −4.77373 | −0.226043 | ||||||||
\(447\) | 17.5519 | 0.830177 | ||||||||
\(448\) | −1.35191 | −0.0638717 | ||||||||
\(449\) | 3.94993 | 0.186409 | 0.0932045 | − | 0.995647i | \(-0.470289\pi\) | ||||
0.0932045 | + | 0.995647i | \(0.470289\pi\) | |||||||
\(450\) | −7.63135 | −0.359745 | ||||||||
\(451\) | −3.56119 | −0.167690 | ||||||||
\(452\) | 3.47032 | 0.163230 | ||||||||
\(453\) | 3.51480 | 0.165140 | ||||||||
\(454\) | −19.1074 | −0.896755 | ||||||||
\(455\) | −15.6694 | −0.734595 | ||||||||
\(456\) | 2.21534 | 0.103743 | ||||||||
\(457\) | 36.3410 | 1.69996 | 0.849981 | − | 0.526813i | \(-0.176613\pi\) | ||||
0.849981 | + | 0.526813i | \(0.176613\pi\) | |||||||
\(458\) | 18.8803 | 0.882219 | ||||||||
\(459\) | −33.4898 | −1.56317 | ||||||||
\(460\) | 21.4080 | 0.998152 | ||||||||
\(461\) | −35.1792 | −1.63846 | −0.819228 | − | 0.573468i | \(-0.805598\pi\) | ||||
−0.819228 | + | 0.573468i | \(0.805598\pi\) | |||||||
\(462\) | −0.799549 | −0.0371984 | ||||||||
\(463\) | −10.3995 | −0.483305 | −0.241653 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241653 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(464\) | −2.46209 | −0.114300 | ||||||||
\(465\) | −3.66268 | −0.169853 | ||||||||
\(466\) | −25.1234 | −1.16382 | ||||||||
\(467\) | 30.6763 | 1.41953 | 0.709765 | − | 0.704438i | \(-0.248801\pi\) | ||||
0.709765 | + | 0.704438i | \(0.248801\pi\) | |||||||
\(468\) | 6.02066 | 0.278305 | ||||||||
\(469\) | 14.9872 | 0.692045 | ||||||||
\(470\) | 16.2783 | 0.750860 | ||||||||
\(471\) | 4.18651 | 0.192904 | ||||||||
\(472\) | −6.02325 | −0.277243 | ||||||||
\(473\) | −2.52797 | −0.116236 | ||||||||
\(474\) | −4.03965 | −0.185547 | ||||||||
\(475\) | −8.88597 | −0.407716 | ||||||||
\(476\) | 8.34088 | 0.382304 | ||||||||
\(477\) | 22.6604 | 1.03755 | ||||||||
\(478\) | 22.4591 | 1.02725 | ||||||||
\(479\) | 14.3833 | 0.657190 | 0.328595 | − | 0.944471i | \(-0.393425\pi\) | ||||
0.328595 | + | 0.944471i | \(0.393425\pi\) | |||||||
\(480\) | 3.66268 | 0.167178 | ||||||||
\(481\) | 7.78516 | 0.354973 | ||||||||
\(482\) | −7.88547 | −0.359173 | ||||||||
\(483\) | −10.9128 | −0.496548 | ||||||||
\(484\) | −10.7467 | −0.488488 | ||||||||
\(485\) | 3.11669 | 0.141522 | ||||||||
\(486\) | −14.4955 | −0.657528 | ||||||||
\(487\) | −20.1700 | −0.913988 | −0.456994 | − | 0.889470i | \(-0.651074\pi\) | ||||
−0.456994 | + | 0.889470i | \(0.651074\pi\) | |||||||
\(488\) | 12.0367 | 0.544877 | ||||||||
\(489\) | −7.69444 | −0.347955 | ||||||||
\(490\) | 16.1206 | 0.728254 | ||||||||
\(491\) | 26.0934 | 1.17758 | 0.588788 | − | 0.808287i | \(-0.299605\pi\) | ||||
0.588788 | + | 0.808287i | \(0.299605\pi\) | |||||||
\(492\) | −8.31588 | −0.374909 | ||||||||
\(493\) | 15.1904 | 0.684140 | ||||||||
\(494\) | 7.01048 | 0.315416 | ||||||||
\(495\) | −2.53933 | −0.114134 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 5.02955 | 0.225606 | ||||||||
\(498\) | 8.24931 | 0.369661 | ||||||||
\(499\) | −24.8179 | −1.11100 | −0.555501 | − | 0.831516i | \(-0.687474\pi\) | ||||
−0.555501 | + | 0.831516i | \(0.687474\pi\) | |||||||
\(500\) | 0.892069 | 0.0398946 | ||||||||
\(501\) | 1.84101 | 0.0822504 | ||||||||
\(502\) | 25.0265 | 1.11699 | ||||||||
\(503\) | 40.7878 | 1.81864 | 0.909318 | − | 0.416102i | \(-0.136604\pi\) | ||||
0.909318 | + | 0.416102i | \(0.136604\pi\) | |||||||
\(504\) | 2.18867 | 0.0974911 | ||||||||
\(505\) | −38.3605 | −1.70702 | ||||||||
\(506\) | 3.45679 | 0.153673 | ||||||||
\(507\) | −0.975452 | −0.0433213 | ||||||||
\(508\) | 8.77250 | 0.389217 | ||||||||
\(509\) | −5.84313 | −0.258992 | −0.129496 | − | 0.991580i | \(-0.541336\pi\) | ||||
−0.129496 | + | 0.991580i | \(0.541336\pi\) | |||||||
\(510\) | −22.5977 | −1.00064 | ||||||||
\(511\) | −5.95876 | −0.263600 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.2326 | −0.451778 | ||||||||
\(514\) | −21.7567 | −0.959646 | ||||||||
\(515\) | −29.8358 | −1.31472 | ||||||||
\(516\) | −5.90317 | −0.259872 | ||||||||
\(517\) | 2.62849 | 0.115601 | ||||||||
\(518\) | 2.83011 | 0.124348 | ||||||||
\(519\) | 0.726612 | 0.0318947 | ||||||||
\(520\) | 11.5906 | 0.508281 | ||||||||
\(521\) | 9.92640 | 0.434883 | 0.217442 | − | 0.976073i | \(-0.430229\pi\) | ||||
0.217442 | + | 0.976073i | \(0.430229\pi\) | |||||||
\(522\) | 3.98599 | 0.174462 | ||||||||
\(523\) | 2.55478 | 0.111713 | 0.0558565 | − | 0.998439i | \(-0.482211\pi\) | ||||
0.0558565 | + | 0.998439i | \(0.482211\pi\) | |||||||
\(524\) | 2.04069 | 0.0891479 | ||||||||
\(525\) | 7.48897 | 0.326845 | ||||||||
\(526\) | 29.1935 | 1.27290 | ||||||||
\(527\) | 6.16970 | 0.268756 | ||||||||
\(528\) | 0.591422 | 0.0257383 | ||||||||
\(529\) | 24.1805 | 1.05133 | ||||||||
\(530\) | 43.6243 | 1.89492 | ||||||||
\(531\) | 9.75132 | 0.423171 | ||||||||
\(532\) | 2.54849 | 0.110491 | ||||||||
\(533\) | −26.3157 | −1.13986 | ||||||||
\(534\) | −11.0540 | −0.478355 | ||||||||
\(535\) | 0.629222 | 0.0272036 | ||||||||
\(536\) | −11.0860 | −0.478840 | ||||||||
\(537\) | −2.68480 | −0.115858 | ||||||||
\(538\) | 29.3467 | 1.26523 | ||||||||
\(539\) | 2.60303 | 0.112120 | ||||||||
\(540\) | −16.9177 | −0.728023 | ||||||||
\(541\) | 26.1151 | 1.12278 | 0.561389 | − | 0.827552i | \(-0.310267\pi\) | ||||
0.561389 | + | 0.827552i | \(0.310267\pi\) | |||||||
\(542\) | 27.8230 | 1.19510 | ||||||||
\(543\) | −29.2375 | −1.25470 | ||||||||
\(544\) | −6.16970 | −0.264524 | ||||||||
\(545\) | −7.14093 | −0.305884 | ||||||||
\(546\) | −5.90833 | −0.252853 | ||||||||
\(547\) | −29.1031 | −1.24436 | −0.622178 | − | 0.782876i | \(-0.713752\pi\) | ||||
−0.622178 | + | 0.782876i | \(0.713752\pi\) | |||||||
\(548\) | −7.09997 | −0.303296 | ||||||||
\(549\) | −19.4868 | −0.831677 | ||||||||
\(550\) | −2.37225 | −0.101153 | ||||||||
\(551\) | 4.64131 | 0.197726 | ||||||||
\(552\) | 8.07210 | 0.343571 | ||||||||
\(553\) | −4.64714 | −0.197617 | ||||||||
\(554\) | −18.4852 | −0.785359 | ||||||||
\(555\) | −7.66752 | −0.325468 | ||||||||
\(556\) | −21.8990 | −0.928726 | ||||||||
\(557\) | −37.3233 | −1.58144 | −0.790719 | − | 0.612180i | \(-0.790293\pi\) | ||||
−0.790719 | + | 0.612180i | \(0.790293\pi\) | |||||||
\(558\) | 1.61895 | 0.0685355 | ||||||||
\(559\) | −18.6806 | −0.790106 | ||||||||
\(560\) | 4.21349 | 0.178052 | ||||||||
\(561\) | −3.64889 | −0.154056 | ||||||||
\(562\) | 18.8333 | 0.794435 | ||||||||
\(563\) | 2.88637 | 0.121646 | 0.0608231 | − | 0.998149i | \(-0.480627\pi\) | ||||
0.0608231 | + | 0.998149i | \(0.480627\pi\) | |||||||
\(564\) | 6.13789 | 0.258452 | ||||||||
\(565\) | −10.8159 | −0.455030 | ||||||||
\(566\) | 2.73265 | 0.114862 | ||||||||
\(567\) | 2.05784 | 0.0864212 | ||||||||
\(568\) | −3.72033 | −0.156102 | ||||||||
\(569\) | 5.37156 | 0.225187 | 0.112594 | − | 0.993641i | \(-0.464084\pi\) | ||||
0.112594 | + | 0.993641i | \(0.464084\pi\) | |||||||
\(570\) | −6.90455 | −0.289200 | ||||||||
\(571\) | −35.1682 | −1.47174 | −0.735872 | − | 0.677121i | \(-0.763227\pi\) | ||||
−0.735872 | + | 0.677121i | \(0.763227\pi\) | |||||||
\(572\) | 1.87156 | 0.0782539 | ||||||||
\(573\) | 20.2377 | 0.845443 | ||||||||
\(574\) | −9.56645 | −0.399296 | ||||||||
\(575\) | −32.3780 | −1.35026 | ||||||||
\(576\) | −1.61895 | −0.0674561 | ||||||||
\(577\) | −22.3177 | −0.929098 | −0.464549 | − | 0.885547i | \(-0.653784\pi\) | ||||
−0.464549 | + | 0.885547i | \(0.653784\pi\) | |||||||
\(578\) | 21.0652 | 0.876197 | ||||||||
\(579\) | −13.8085 | −0.573860 | ||||||||
\(580\) | 7.67359 | 0.318628 | ||||||||
\(581\) | 9.48987 | 0.393706 | ||||||||
\(582\) | 1.17518 | 0.0487129 | ||||||||
\(583\) | 7.04411 | 0.291737 | ||||||||
\(584\) | 4.40766 | 0.182390 | ||||||||
\(585\) | −18.7646 | −0.775819 | ||||||||
\(586\) | −17.7076 | −0.731495 | ||||||||
\(587\) | 19.2495 | 0.794511 | 0.397255 | − | 0.917708i | \(-0.369963\pi\) | ||||
0.397255 | + | 0.917708i | \(0.369963\pi\) | |||||||
\(588\) | 6.07844 | 0.250671 | ||||||||
\(589\) | 1.88511 | 0.0776745 | ||||||||
\(590\) | 18.7726 | 0.772857 | ||||||||
\(591\) | −5.00010 | −0.205677 | ||||||||
\(592\) | −2.09342 | −0.0860389 | ||||||||
\(593\) | 13.1342 | 0.539359 | 0.269679 | − | 0.962950i | \(-0.413082\pi\) | ||||
0.269679 | + | 0.962950i | \(0.413082\pi\) | |||||||
\(594\) | −2.73175 | −0.112085 | ||||||||
\(595\) | −25.9960 | −1.06573 | ||||||||
\(596\) | −14.9355 | −0.611781 | ||||||||
\(597\) | 21.6992 | 0.888091 | ||||||||
\(598\) | 25.5442 | 1.04458 | ||||||||
\(599\) | −34.8319 | −1.42319 | −0.711597 | − | 0.702588i | \(-0.752028\pi\) | ||||
−0.711597 | + | 0.702588i | \(0.752028\pi\) | |||||||
\(600\) | −5.53955 | −0.226151 | ||||||||
\(601\) | 21.1898 | 0.864348 | 0.432174 | − | 0.901790i | \(-0.357747\pi\) | ||||
0.432174 | + | 0.901790i | \(0.357747\pi\) | |||||||
\(602\) | −6.79090 | −0.276777 | ||||||||
\(603\) | 17.9476 | 0.730881 | ||||||||
\(604\) | −2.99086 | −0.121696 | ||||||||
\(605\) | 33.4943 | 1.36174 | ||||||||
\(606\) | −14.4642 | −0.587569 | ||||||||
\(607\) | 4.36638 | 0.177226 | 0.0886129 | − | 0.996066i | \(-0.471757\pi\) | ||||
0.0886129 | + | 0.996066i | \(0.471757\pi\) | |||||||
\(608\) | −1.88511 | −0.0764512 | ||||||||
\(609\) | −3.91163 | −0.158507 | ||||||||
\(610\) | −37.5148 | −1.51893 | ||||||||
\(611\) | 19.4234 | 0.785787 | ||||||||
\(612\) | 9.98841 | 0.403758 | ||||||||
\(613\) | −33.1134 | −1.33744 | −0.668718 | − | 0.743516i | \(-0.733157\pi\) | ||||
−0.668718 | + | 0.743516i | \(0.733157\pi\) | |||||||
\(614\) | 21.1166 | 0.852195 | ||||||||
\(615\) | 25.9181 | 1.04512 | ||||||||
\(616\) | 0.680362 | 0.0274125 | ||||||||
\(617\) | −29.7359 | −1.19712 | −0.598562 | − | 0.801077i | \(-0.704261\pi\) | ||||
−0.598562 | + | 0.801077i | \(0.704261\pi\) | |||||||
\(618\) | −11.2499 | −0.452537 | ||||||||
\(619\) | 12.4441 | 0.500169 | 0.250084 | − | 0.968224i | \(-0.419542\pi\) | ||||
0.250084 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(620\) | 3.11669 | 0.125169 | ||||||||
\(621\) | −37.2846 | −1.49618 | ||||||||
\(622\) | −6.85979 | −0.275052 | ||||||||
\(623\) | −12.7164 | −0.509471 | ||||||||
\(624\) | 4.37036 | 0.174954 | ||||||||
\(625\) | −26.3492 | −1.05397 | ||||||||
\(626\) | −9.04124 | −0.361361 | ||||||||
\(627\) | −1.11489 | −0.0445245 | ||||||||
\(628\) | −3.56243 | −0.142157 | ||||||||
\(629\) | 12.9158 | 0.514985 | ||||||||
\(630\) | −6.82141 | −0.271772 | ||||||||
\(631\) | −18.6825 | −0.743740 | −0.371870 | − | 0.928285i | \(-0.621283\pi\) | ||||
−0.371870 | + | 0.928285i | \(0.621283\pi\) | |||||||
\(632\) | 3.43746 | 0.136735 | ||||||||
\(633\) | −7.47093 | −0.296943 | ||||||||
\(634\) | −1.57113 | −0.0623975 | ||||||||
\(635\) | −27.3412 | −1.08500 | ||||||||
\(636\) | 16.4490 | 0.652245 | ||||||||
\(637\) | 19.2353 | 0.762130 | ||||||||
\(638\) | 1.23907 | 0.0490553 | ||||||||
\(639\) | 6.02302 | 0.238267 | ||||||||
\(640\) | −3.11669 | −0.123198 | ||||||||
\(641\) | −15.4341 | −0.609611 | −0.304806 | − | 0.952415i | \(-0.598592\pi\) | ||||
−0.304806 | + | 0.952415i | \(0.598592\pi\) | |||||||
\(642\) | 0.237255 | 0.00936370 | ||||||||
\(643\) | 22.4723 | 0.886222 | 0.443111 | − | 0.896467i | \(-0.353875\pi\) | ||||
0.443111 | + | 0.896467i | \(0.353875\pi\) | |||||||
\(644\) | 9.28601 | 0.365920 | ||||||||
\(645\) | 18.3984 | 0.724435 | ||||||||
\(646\) | 11.6305 | 0.457598 | ||||||||
\(647\) | −24.1890 | −0.950966 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(648\) | −1.52217 | −0.0597966 | ||||||||
\(649\) | 3.03126 | 0.118987 | ||||||||
\(650\) | −17.5300 | −0.687581 | ||||||||
\(651\) | −1.58874 | −0.0622677 | ||||||||
\(652\) | 6.54744 | 0.256418 | ||||||||
\(653\) | 14.3611 | 0.561995 | 0.280998 | − | 0.959708i | \(-0.409335\pi\) | ||||
0.280998 | + | 0.959708i | \(0.409335\pi\) | |||||||
\(654\) | −2.69256 | −0.105288 | ||||||||
\(655\) | −6.36020 | −0.248513 | ||||||||
\(656\) | 7.07625 | 0.276281 | ||||||||
\(657\) | −7.13577 | −0.278393 | ||||||||
\(658\) | 7.06093 | 0.275264 | ||||||||
\(659\) | 6.06296 | 0.236179 | 0.118090 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118090 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(660\) | −1.84328 | −0.0717496 | ||||||||
\(661\) | −14.5759 | −0.566936 | −0.283468 | − | 0.958982i | \(-0.591485\pi\) | ||||
−0.283468 | + | 0.958982i | \(0.591485\pi\) | |||||||
\(662\) | −4.25054 | −0.165202 | ||||||||
\(663\) | −26.9638 | −1.04719 | ||||||||
\(664\) | −7.01960 | −0.272413 | ||||||||
\(665\) | −7.94288 | −0.308011 | ||||||||
\(666\) | 3.38913 | 0.131326 | ||||||||
\(667\) | 16.9116 | 0.654821 | ||||||||
\(668\) | −1.56658 | −0.0606127 | ||||||||
\(669\) | 5.61000 | 0.216895 | ||||||||
\(670\) | 34.5515 | 1.33484 | ||||||||
\(671\) | −6.05760 | −0.233851 | ||||||||
\(672\) | 1.58874 | 0.0612870 | ||||||||
\(673\) | 16.6456 | 0.641641 | 0.320820 | − | 0.947140i | \(-0.396041\pi\) | ||||
0.320820 | + | 0.947140i | \(0.396041\pi\) | |||||||
\(674\) | −21.1690 | −0.815401 | ||||||||
\(675\) | 25.5869 | 0.984839 | ||||||||
\(676\) | 0.830043 | 0.0319247 | ||||||||
\(677\) | 17.7935 | 0.683861 | 0.341931 | − | 0.939725i | \(-0.388919\pi\) | ||||
0.341931 | + | 0.939725i | \(0.388919\pi\) | |||||||
\(678\) | −4.07826 | −0.156625 | ||||||||
\(679\) | 1.35191 | 0.0518815 | ||||||||
\(680\) | 19.2291 | 0.737401 | ||||||||
\(681\) | 22.4547 | 0.860466 | ||||||||
\(682\) | 0.503259 | 0.0192708 | ||||||||
\(683\) | 10.4423 | 0.399563 | 0.199781 | − | 0.979840i | \(-0.435977\pi\) | ||||
0.199781 | + | 0.979840i | \(0.435977\pi\) | |||||||
\(684\) | 3.05189 | 0.116692 | ||||||||
\(685\) | 22.1284 | 0.845484 | ||||||||
\(686\) | 16.4559 | 0.628289 | ||||||||
\(687\) | −22.1878 | −0.846517 | ||||||||
\(688\) | 5.02319 | 0.191507 | ||||||||
\(689\) | 52.0530 | 1.98306 | ||||||||
\(690\) | −25.1583 | −0.957759 | ||||||||
\(691\) | 1.49700 | 0.0569486 | 0.0284743 | − | 0.999595i | \(-0.490935\pi\) | ||||
0.0284743 | + | 0.999595i | \(0.490935\pi\) | |||||||
\(692\) | −0.618297 | −0.0235041 | ||||||||
\(693\) | −1.10147 | −0.0418413 | ||||||||
\(694\) | −19.8435 | −0.753248 | ||||||||
\(695\) | 68.2526 | 2.58897 | ||||||||
\(696\) | 2.89341 | 0.109674 | ||||||||
\(697\) | −43.6583 | −1.65368 | ||||||||
\(698\) | 13.9060 | 0.526351 | ||||||||
\(699\) | 29.5246 | 1.11672 | ||||||||
\(700\) | −6.37260 | −0.240862 | ||||||||
\(701\) | −31.8451 | −1.20277 | −0.601387 | − | 0.798958i | \(-0.705385\pi\) | ||||
−0.601387 | + | 0.798958i | \(0.705385\pi\) | |||||||
\(702\) | −20.1865 | −0.761888 | ||||||||
\(703\) | 3.94631 | 0.148838 | ||||||||
\(704\) | −0.503259 | −0.0189673 | ||||||||
\(705\) | −19.1299 | −0.720475 | ||||||||
\(706\) | −4.85218 | −0.182614 | ||||||||
\(707\) | −16.6394 | −0.625789 | ||||||||
\(708\) | 7.07842 | 0.266023 | ||||||||
\(709\) | 5.77003 | 0.216698 | 0.108349 | − | 0.994113i | \(-0.465444\pi\) | ||||
0.108349 | + | 0.994113i | \(0.465444\pi\) | |||||||
\(710\) | 11.5951 | 0.435158 | ||||||||
\(711\) | −5.56507 | −0.208706 | ||||||||
\(712\) | 9.40623 | 0.352513 | ||||||||
\(713\) | 6.86881 | 0.257239 | ||||||||
\(714\) | −9.80205 | −0.366833 | ||||||||
\(715\) | −5.83308 | −0.218145 | ||||||||
\(716\) | 2.28458 | 0.0853787 | ||||||||
\(717\) | −26.3935 | −0.985684 | ||||||||
\(718\) | −11.6213 | −0.433703 | ||||||||
\(719\) | 2.02507 | 0.0755223 | 0.0377612 | − | 0.999287i | \(-0.487977\pi\) | ||||
0.0377612 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(720\) | 5.04576 | 0.188044 | ||||||||
\(721\) | −12.9417 | −0.481974 | ||||||||
\(722\) | −15.4464 | −0.574854 | ||||||||
\(723\) | 9.26687 | 0.344639 | ||||||||
\(724\) | 24.8791 | 0.924625 | ||||||||
\(725\) | −11.6058 | −0.431027 | ||||||||
\(726\) | 12.6294 | 0.468720 | ||||||||
\(727\) | −35.9955 | −1.33500 | −0.667499 | − | 0.744610i | \(-0.732635\pi\) | ||||
−0.667499 | + | 0.744610i | \(0.732635\pi\) | |||||||
\(728\) | 5.02759 | 0.186335 | ||||||||
\(729\) | 21.6014 | 0.800050 | ||||||||
\(730\) | −13.7373 | −0.508442 | ||||||||
\(731\) | −30.9916 | −1.14627 | ||||||||
\(732\) | −14.1453 | −0.522827 | ||||||||
\(733\) | 3.77883 | 0.139574 | 0.0697871 | − | 0.997562i | \(-0.477768\pi\) | ||||
0.0697871 | + | 0.997562i | \(0.477768\pi\) | |||||||
\(734\) | 18.1152 | 0.668646 | ||||||||
\(735\) | −18.9446 | −0.698784 | ||||||||
\(736\) | −6.86881 | −0.253188 | ||||||||
\(737\) | 5.57911 | 0.205509 | ||||||||
\(738\) | −11.4561 | −0.421704 | ||||||||
\(739\) | 41.2705 | 1.51816 | 0.759081 | − | 0.650996i | \(-0.225649\pi\) | ||||
0.759081 | + | 0.650996i | \(0.225649\pi\) | |||||||
\(740\) | 6.52454 | 0.239847 | ||||||||
\(741\) | −8.23859 | −0.302652 | ||||||||
\(742\) | 18.9227 | 0.694672 | ||||||||
\(743\) | 6.11467 | 0.224325 | 0.112163 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112163 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(744\) | 1.17518 | 0.0430843 | ||||||||
\(745\) | 46.5493 | 1.70543 | ||||||||
\(746\) | 21.6742 | 0.793549 | ||||||||
\(747\) | 11.3644 | 0.415800 | ||||||||
\(748\) | 3.10496 | 0.113529 | ||||||||
\(749\) | 0.272934 | 0.00997279 | ||||||||
\(750\) | −1.04834 | −0.0382801 | ||||||||
\(751\) | 8.44230 | 0.308064 | 0.154032 | − | 0.988066i | \(-0.450774\pi\) | ||||
0.154032 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(752\) | −5.22293 | −0.190461 | ||||||||
\(753\) | −29.4107 | −1.07178 | ||||||||
\(754\) | 9.15622 | 0.333450 | ||||||||
\(755\) | 9.32158 | 0.339247 | ||||||||
\(756\) | −7.33831 | −0.266892 | ||||||||
\(757\) | 20.5927 | 0.748453 | 0.374227 | − | 0.927337i | \(-0.377908\pi\) | ||||
0.374227 | + | 0.927337i | \(0.377908\pi\) | |||||||
\(758\) | −18.8301 | −0.683940 | ||||||||
\(759\) | −4.06236 | −0.147454 | ||||||||
\(760\) | 5.87530 | 0.213119 | ||||||||
\(761\) | 24.6776 | 0.894561 | 0.447280 | − | 0.894394i | \(-0.352393\pi\) | ||||
0.447280 | + | 0.894394i | \(0.352393\pi\) | |||||||
\(762\) | −10.3093 | −0.373466 | ||||||||
\(763\) | −3.09748 | −0.112136 | ||||||||
\(764\) | −17.2209 | −0.623031 | ||||||||
\(765\) | −31.1308 | −1.12554 | ||||||||
\(766\) | −2.79420 | −0.100958 | ||||||||
\(767\) | 22.3997 | 0.808807 | ||||||||
\(768\) | −1.17518 | −0.0424057 | ||||||||
\(769\) | −35.6125 | −1.28422 | −0.642110 | − | 0.766613i | \(-0.721941\pi\) | ||||
−0.642110 | + | 0.766613i | \(0.721941\pi\) | |||||||
\(770\) | −2.12048 | −0.0764167 | ||||||||
\(771\) | 25.5681 | 0.920811 | ||||||||
\(772\) | 11.7501 | 0.422894 | ||||||||
\(773\) | −4.35126 | −0.156504 | −0.0782520 | − | 0.996934i | \(-0.524934\pi\) | ||||
−0.0782520 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(774\) | −8.13228 | −0.292309 | ||||||||
\(775\) | −4.71378 | −0.169324 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | −3.32590 | −0.119316 | ||||||||
\(778\) | 24.8123 | 0.889564 | ||||||||
\(779\) | −13.3395 | −0.477937 | ||||||||
\(780\) | −13.6211 | −0.487712 | ||||||||
\(781\) | 1.87229 | 0.0669959 | ||||||||
\(782\) | 42.3785 | 1.51545 | ||||||||
\(783\) | −13.3645 | −0.477608 | ||||||||
\(784\) | −5.17234 | −0.184726 | ||||||||
\(785\) | 11.1030 | 0.396283 | ||||||||
\(786\) | −2.39818 | −0.0855403 | ||||||||
\(787\) | 9.86072 | 0.351497 | 0.175748 | − | 0.984435i | \(-0.443765\pi\) | ||||
0.175748 | + | 0.984435i | \(0.443765\pi\) | |||||||
\(788\) | 4.25474 | 0.151569 | ||||||||
\(789\) | −34.3076 | −1.22138 | ||||||||
\(790\) | −10.7135 | −0.381170 | ||||||||
\(791\) | −4.69156 | −0.166813 | ||||||||
\(792\) | 0.814750 | 0.0289509 | ||||||||
\(793\) | −44.7631 | −1.58958 | ||||||||
\(794\) | 6.84583 | 0.242949 | ||||||||
\(795\) | −51.2665 | −1.81824 | ||||||||
\(796\) | −18.4646 | −0.654460 | ||||||||
\(797\) | −36.8714 | −1.30605 | −0.653026 | − | 0.757336i | \(-0.726501\pi\) | ||||
−0.653026 | + | 0.757336i | \(0.726501\pi\) | |||||||
\(798\) | −2.99495 | −0.106020 | ||||||||
\(799\) | 32.2239 | 1.14000 | ||||||||
\(800\) | 4.71378 | 0.166657 | ||||||||
\(801\) | −15.2282 | −0.538061 | ||||||||
\(802\) | −30.7281 | −1.08505 | ||||||||
\(803\) | −2.21820 | −0.0782785 | ||||||||
\(804\) | 13.0280 | 0.459463 | ||||||||
\(805\) | −28.9416 | −1.02006 | ||||||||
\(806\) | 3.71888 | 0.130992 | ||||||||
\(807\) | −34.4878 | −1.21403 | ||||||||
\(808\) | 12.3081 | 0.432996 | ||||||||
\(809\) | −27.4342 | −0.964536 | −0.482268 | − | 0.876024i | \(-0.660187\pi\) | ||||
−0.482268 | + | 0.876024i | \(0.660187\pi\) | |||||||
\(810\) | 4.74415 | 0.166692 | ||||||||
\(811\) | 34.0822 | 1.19679 | 0.598394 | − | 0.801202i | \(-0.295806\pi\) | ||||
0.598394 | + | 0.801202i | \(0.295806\pi\) | |||||||
\(812\) | 3.32853 | 0.116808 | ||||||||
\(813\) | −32.6971 | −1.14674 | ||||||||
\(814\) | 1.05353 | 0.0369263 | ||||||||
\(815\) | −20.4064 | −0.714804 | ||||||||
\(816\) | 7.25052 | 0.253819 | ||||||||
\(817\) | −9.46925 | −0.331287 | ||||||||
\(818\) | −29.2232 | −1.02177 | ||||||||
\(819\) | −8.13939 | −0.284413 | ||||||||
\(820\) | −22.0545 | −0.770177 | ||||||||
\(821\) | −52.3870 | −1.82832 | −0.914160 | − | 0.405355i | \(-0.867148\pi\) | ||||
−0.914160 | + | 0.405355i | \(0.867148\pi\) | |||||||
\(822\) | 8.34376 | 0.291022 | ||||||||
\(823\) | −9.83421 | −0.342799 | −0.171400 | − | 0.985202i | \(-0.554829\pi\) | ||||
−0.171400 | + | 0.985202i | \(0.554829\pi\) | |||||||
\(824\) | 9.57290 | 0.333488 | ||||||||
\(825\) | 2.78783 | 0.0970598 | ||||||||
\(826\) | 8.14290 | 0.283328 | ||||||||
\(827\) | −3.79922 | −0.132112 | −0.0660560 | − | 0.997816i | \(-0.521042\pi\) | ||||
−0.0660560 | + | 0.997816i | \(0.521042\pi\) | |||||||
\(828\) | 11.1202 | 0.386455 | ||||||||
\(829\) | 29.4857 | 1.02408 | 0.512040 | − | 0.858961i | \(-0.328890\pi\) | ||||
0.512040 | + | 0.858961i | \(0.328890\pi\) | |||||||
\(830\) | 21.8779 | 0.759395 | ||||||||
\(831\) | 21.7234 | 0.753578 | ||||||||
\(832\) | −3.71888 | −0.128929 | ||||||||
\(833\) | 31.9118 | 1.10568 | ||||||||
\(834\) | 25.7354 | 0.891142 | ||||||||
\(835\) | 4.88254 | 0.168967 | ||||||||
\(836\) | 0.948698 | 0.0328114 | ||||||||
\(837\) | −5.42810 | −0.187623 | ||||||||
\(838\) | −29.4577 | −1.01760 | ||||||||
\(839\) | −26.4924 | −0.914620 | −0.457310 | − | 0.889307i | \(-0.651187\pi\) | ||||
−0.457310 | + | 0.889307i | \(0.651187\pi\) | |||||||
\(840\) | −4.95162 | −0.170847 | ||||||||
\(841\) | −22.9381 | −0.790969 | ||||||||
\(842\) | 6.32190 | 0.217867 | ||||||||
\(843\) | −22.1326 | −0.762286 | ||||||||
\(844\) | 6.35725 | 0.218826 | ||||||||
\(845\) | −2.58699 | −0.0889951 | ||||||||
\(846\) | 8.45564 | 0.290711 | ||||||||
\(847\) | 14.5286 | 0.499209 | ||||||||
\(848\) | −13.9970 | −0.480658 | ||||||||
\(849\) | −3.21136 | −0.110213 | ||||||||
\(850\) | −29.0826 | −0.997525 | ||||||||
\(851\) | 14.3793 | 0.492915 | ||||||||
\(852\) | 4.37207 | 0.149785 | ||||||||
\(853\) | −23.7846 | −0.814368 | −0.407184 | − | 0.913346i | \(-0.633489\pi\) | ||||
−0.407184 | + | 0.913346i | \(0.633489\pi\) | |||||||
\(854\) | −16.2726 | −0.556836 | ||||||||
\(855\) | −9.51179 | −0.325296 | ||||||||
\(856\) | −0.201888 | −0.00690038 | ||||||||
\(857\) | −5.38016 | −0.183783 | −0.0918914 | − | 0.995769i | \(-0.529291\pi\) | ||||
−0.0918914 | + | 0.995769i | \(0.529291\pi\) | |||||||
\(858\) | −2.19942 | −0.0750871 | ||||||||
\(859\) | −31.9547 | −1.09028 | −0.545140 | − | 0.838345i | \(-0.683524\pi\) | ||||
−0.545140 | + | 0.838345i | \(0.683524\pi\) | |||||||
\(860\) | −15.6557 | −0.533856 | ||||||||
\(861\) | 11.2423 | 0.383137 | ||||||||
\(862\) | 7.99353 | 0.272261 | ||||||||
\(863\) | 41.5495 | 1.41436 | 0.707181 | − | 0.707033i | \(-0.249967\pi\) | ||||
0.707181 | + | 0.707033i | \(0.249967\pi\) | |||||||
\(864\) | 5.42810 | 0.184668 | ||||||||
\(865\) | 1.92704 | 0.0655214 | ||||||||
\(866\) | −28.0270 | −0.952397 | ||||||||
\(867\) | −24.7555 | −0.840739 | ||||||||
\(868\) | 1.35191 | 0.0458868 | ||||||||
\(869\) | −1.72994 | −0.0586841 | ||||||||
\(870\) | −9.01786 | −0.305734 | ||||||||
\(871\) | 41.2273 | 1.39693 | ||||||||
\(872\) | 2.29119 | 0.0775894 | ||||||||
\(873\) | 1.61895 | 0.0547930 | ||||||||
\(874\) | 12.9484 | 0.437987 | ||||||||
\(875\) | −1.20600 | −0.0407702 | ||||||||
\(876\) | −5.17981 | −0.175010 | ||||||||
\(877\) | −49.2393 | −1.66269 | −0.831347 | − | 0.555754i | \(-0.812430\pi\) | ||||
−0.831347 | + | 0.555754i | \(0.812430\pi\) | |||||||
\(878\) | −17.5860 | −0.593498 | ||||||||
\(879\) | 20.8097 | 0.701893 | ||||||||
\(880\) | 1.56851 | 0.0528743 | ||||||||
\(881\) | −42.9786 | −1.44799 | −0.723993 | − | 0.689807i | \(-0.757695\pi\) | ||||
−0.723993 | + | 0.689807i | \(0.757695\pi\) | |||||||
\(882\) | 8.37374 | 0.281958 | ||||||||
\(883\) | 5.20784 | 0.175258 | 0.0876289 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876289 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(884\) | 22.9444 | 0.771702 | ||||||||
\(885\) | −22.0613 | −0.741581 | ||||||||
\(886\) | −30.5104 | −1.02502 | ||||||||
\(887\) | 2.86037 | 0.0960419 | 0.0480210 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480210 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(888\) | 2.46015 | 0.0825571 | ||||||||
\(889\) | −11.8596 | −0.397759 | ||||||||
\(890\) | −29.3163 | −0.982686 | ||||||||
\(891\) | 0.766048 | 0.0256636 | ||||||||
\(892\) | −4.77373 | −0.159836 | ||||||||
\(893\) | 9.84577 | 0.329476 | ||||||||
\(894\) | 17.5519 | 0.587024 | ||||||||
\(895\) | −7.12033 | −0.238006 | ||||||||
\(896\) | −1.35191 | −0.0451641 | ||||||||
\(897\) | −30.0192 | −1.00231 | ||||||||
\(898\) | 3.94993 | 0.131811 | ||||||||
\(899\) | 2.46209 | 0.0821154 | ||||||||
\(900\) | −7.63135 | −0.254378 | ||||||||
\(901\) | 86.3572 | 2.87697 | ||||||||
\(902\) | −3.56119 | −0.118575 | ||||||||
\(903\) | 7.98055 | 0.265576 | ||||||||
\(904\) | 3.47032 | 0.115421 | ||||||||
\(905\) | −77.5406 | −2.57754 | ||||||||
\(906\) | 3.51480 | 0.116771 | ||||||||
\(907\) | −6.90658 | −0.229329 | −0.114665 | − | 0.993404i | \(-0.536579\pi\) | ||||
−0.114665 | + | 0.993404i | \(0.536579\pi\) | |||||||
\(908\) | −19.1074 | −0.634102 | ||||||||
\(909\) | −19.9261 | −0.660907 | ||||||||
\(910\) | −15.6694 | −0.519437 | ||||||||
\(911\) | −16.3588 | −0.541993 | −0.270996 | − | 0.962580i | \(-0.587353\pi\) | ||||
−0.270996 | + | 0.962580i | \(0.587353\pi\) | |||||||
\(912\) | 2.21534 | 0.0733574 | ||||||||
\(913\) | 3.53268 | 0.116915 | ||||||||
\(914\) | 36.3410 | 1.20205 | ||||||||
\(915\) | 44.0867 | 1.45746 | ||||||||
\(916\) | 18.8803 | 0.623823 | ||||||||
\(917\) | −2.75883 | −0.0911045 | ||||||||
\(918\) | −33.4898 | −1.10533 | ||||||||
\(919\) | 25.0870 | 0.827544 | 0.413772 | − | 0.910381i | \(-0.364211\pi\) | ||||
0.413772 | + | 0.910381i | \(0.364211\pi\) | |||||||
\(920\) | 21.4080 | 0.705800 | ||||||||
\(921\) | −24.8158 | −0.817709 | ||||||||
\(922\) | −35.1792 | −1.15856 | ||||||||
\(923\) | 13.8355 | 0.455399 | ||||||||
\(924\) | −0.799549 | −0.0263032 | ||||||||
\(925\) | −9.86790 | −0.324454 | ||||||||
\(926\) | −10.3995 | −0.341748 | ||||||||
\(927\) | −15.4980 | −0.509021 | ||||||||
\(928\) | −2.46209 | −0.0808221 | ||||||||
\(929\) | 13.8904 | 0.455729 | 0.227864 | − | 0.973693i | \(-0.426826\pi\) | ||||
0.227864 | + | 0.973693i | \(0.426826\pi\) | |||||||
\(930\) | −3.66268 | −0.120104 | ||||||||
\(931\) | 9.75041 | 0.319557 | ||||||||
\(932\) | −25.1234 | −0.822944 | ||||||||
\(933\) | 8.06150 | 0.263922 | ||||||||
\(934\) | 30.6763 | 1.00376 | ||||||||
\(935\) | −9.67721 | −0.316479 | ||||||||
\(936\) | 6.02066 | 0.196791 | ||||||||
\(937\) | 22.5384 | 0.736297 | 0.368149 | − | 0.929767i | \(-0.379992\pi\) | ||||
0.368149 | + | 0.929767i | \(0.379992\pi\) | |||||||
\(938\) | 14.9872 | 0.489350 | ||||||||
\(939\) | 10.6251 | 0.346737 | ||||||||
\(940\) | 16.2783 | 0.530938 | ||||||||
\(941\) | −11.7815 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(942\) | 4.18651 | 0.136404 | ||||||||
\(943\) | −48.6054 | −1.58281 | ||||||||
\(944\) | −6.02325 | −0.196040 | ||||||||
\(945\) | 22.8713 | 0.744002 | ||||||||
\(946\) | −2.52797 | −0.0821913 | ||||||||
\(947\) | −17.4825 | −0.568105 | −0.284053 | − | 0.958809i | \(-0.591679\pi\) | ||||
−0.284053 | + | 0.958809i | \(0.591679\pi\) | |||||||
\(948\) | −4.03965 | −0.131202 | ||||||||
\(949\) | −16.3916 | −0.532092 | ||||||||
\(950\) | −8.88597 | −0.288299 | ||||||||
\(951\) | 1.84636 | 0.0598724 | ||||||||
\(952\) | 8.34088 | 0.270329 | ||||||||
\(953\) | 4.56052 | 0.147730 | 0.0738649 | − | 0.997268i | \(-0.476467\pi\) | ||||
0.0738649 | + | 0.997268i | \(0.476467\pi\) | |||||||
\(954\) | 22.6604 | 0.733656 | ||||||||
\(955\) | 53.6723 | 1.73680 | ||||||||
\(956\) | 22.4591 | 0.726379 | ||||||||
\(957\) | −1.45613 | −0.0470701 | ||||||||
\(958\) | 14.3833 | 0.464704 | ||||||||
\(959\) | 9.59852 | 0.309953 | ||||||||
\(960\) | 3.66268 | 0.118213 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 7.78516 | 0.251004 | ||||||||
\(963\) | 0.326845 | 0.0105324 | ||||||||
\(964\) | −7.88547 | −0.253974 | ||||||||
\(965\) | −36.6213 | −1.17888 | ||||||||
\(966\) | −10.9128 | −0.351112 | ||||||||
\(967\) | −26.7408 | −0.859925 | −0.429963 | − | 0.902847i | \(-0.641473\pi\) | ||||
−0.429963 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(968\) | −10.7467 | −0.345413 | ||||||||
\(969\) | −13.6680 | −0.439080 | ||||||||
\(970\) | 3.11669 | 0.100071 | ||||||||
\(971\) | 27.0302 | 0.867441 | 0.433721 | − | 0.901047i | \(-0.357200\pi\) | ||||
0.433721 | + | 0.901047i | \(0.357200\pi\) | |||||||
\(972\) | −14.4955 | −0.464943 | ||||||||
\(973\) | 29.6055 | 0.949109 | ||||||||
\(974\) | −20.1700 | −0.646287 | ||||||||
\(975\) | 20.6009 | 0.659757 | ||||||||
\(976\) | 12.0367 | 0.385286 | ||||||||
\(977\) | −4.95700 | −0.158588 | −0.0792942 | − | 0.996851i | \(-0.525267\pi\) | ||||
−0.0792942 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(978\) | −7.69444 | −0.246041 | ||||||||
\(979\) | −4.73377 | −0.151292 | ||||||||
\(980\) | 16.1206 | 0.514954 | ||||||||
\(981\) | −3.70931 | −0.118429 | ||||||||
\(982\) | 26.0934 | 0.832672 | ||||||||
\(983\) | 19.3673 | 0.617721 | 0.308860 | − | 0.951107i | \(-0.400052\pi\) | ||||
0.308860 | + | 0.951107i | \(0.400052\pi\) | |||||||
\(984\) | −8.31588 | −0.265101 | ||||||||
\(985\) | −13.2607 | −0.422522 | ||||||||
\(986\) | 15.1904 | 0.483760 | ||||||||
\(987\) | −8.29788 | −0.264124 | ||||||||
\(988\) | 7.01048 | 0.223033 | ||||||||
\(989\) | −34.5033 | −1.09714 | ||||||||
\(990\) | −2.53933 | −0.0807051 | ||||||||
\(991\) | 6.66340 | 0.211670 | 0.105835 | − | 0.994384i | \(-0.466248\pi\) | ||||
0.105835 | + | 0.994384i | \(0.466248\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 4.99516 | 0.158517 | ||||||||
\(994\) | 5.02955 | 0.159528 | ||||||||
\(995\) | 57.5484 | 1.82441 | ||||||||
\(996\) | 8.24931 | 0.261390 | ||||||||
\(997\) | −16.4146 | −0.519856 | −0.259928 | − | 0.965628i | \(-0.583699\pi\) | ||||
−0.259928 | + | 0.965628i | \(0.583699\pi\) | |||||||
\(998\) | −24.8179 | −0.785597 | ||||||||
\(999\) | −11.3633 | −0.359518 |
(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 | 6014.2.a.i.1.8 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.i.1.8 | ✓ | 28 | 1.1 | even | 1 | trivial |