Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.88727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88727 | −1.33450 | −0.667250 | − | 0.744834i | \(-0.732529\pi\) | ||||
−0.667250 | + | 0.744834i | \(0.732529\pi\) | |||||||
\(3\) | 0.805985 | 0.465336 | 0.232668 | − | 0.972556i | \(-0.425255\pi\) | ||||
0.232668 | + | 0.972556i | \(0.425255\pi\) | |||||||
\(4\) | 1.56178 | 0.780888 | ||||||||
\(5\) | 0.126968 | 0.0567818 | 0.0283909 | − | 0.999597i | \(-0.490962\pi\) | ||||
0.0283909 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(6\) | −1.52111 | −0.620990 | ||||||||
\(7\) | 1.51778 | 0.573666 | 0.286833 | − | 0.957981i | \(-0.407397\pi\) | ||||
0.286833 | + | 0.957981i | \(0.407397\pi\) | |||||||
\(8\) | 0.827047 | 0.292405 | ||||||||
\(9\) | −2.35039 | −0.783463 | ||||||||
\(10\) | −0.239623 | −0.0757753 | ||||||||
\(11\) | 4.20742 | 1.26858 | 0.634292 | − | 0.773093i | \(-0.281292\pi\) | ||||
0.634292 | + | 0.773093i | \(0.281292\pi\) | |||||||
\(12\) | 1.25877 | 0.363375 | ||||||||
\(13\) | 2.33450 | 0.647474 | 0.323737 | − | 0.946147i | \(-0.395061\pi\) | ||||
0.323737 | + | 0.946147i | \(0.395061\pi\) | |||||||
\(14\) | −2.86445 | −0.765557 | ||||||||
\(15\) | 0.102334 | 0.0264226 | ||||||||
\(16\) | −4.68441 | −1.17110 | ||||||||
\(17\) | −5.59036 | −1.35586 | −0.677931 | − | 0.735126i | \(-0.737123\pi\) | ||||
−0.677931 | + | 0.735126i | \(0.737123\pi\) | |||||||
\(18\) | 4.43581 | 1.04553 | ||||||||
\(19\) | −4.97337 | −1.14097 | −0.570485 | − | 0.821308i | \(-0.693245\pi\) | ||||
−0.570485 | + | 0.821308i | \(0.693245\pi\) | |||||||
\(20\) | 0.198296 | 0.0443402 | ||||||||
\(21\) | 1.22331 | 0.266947 | ||||||||
\(22\) | −7.94052 | −1.69292 | ||||||||
\(23\) | −8.06526 | −1.68172 | −0.840861 | − | 0.541251i | \(-0.817951\pi\) | ||||
−0.840861 | + | 0.541251i | \(0.817951\pi\) | |||||||
\(24\) | 0.666587 | 0.136067 | ||||||||
\(25\) | −4.98388 | −0.996776 | ||||||||
\(26\) | −4.40583 | −0.864054 | ||||||||
\(27\) | −4.31233 | −0.829909 | ||||||||
\(28\) | 2.37043 | 0.447969 | ||||||||
\(29\) | 2.64659 | 0.491460 | 0.245730 | − | 0.969338i | \(-0.420972\pi\) | ||||
0.245730 | + | 0.969338i | \(0.420972\pi\) | |||||||
\(30\) | −0.193132 | −0.0352610 | ||||||||
\(31\) | −1.48706 | −0.267083 | −0.133542 | − | 0.991043i | \(-0.542635\pi\) | ||||
−0.133542 | + | 0.991043i | \(0.542635\pi\) | |||||||
\(32\) | 7.18663 | 1.27043 | ||||||||
\(33\) | 3.39112 | 0.590318 | ||||||||
\(34\) | 10.5505 | 1.80940 | ||||||||
\(35\) | 0.192709 | 0.0325738 | ||||||||
\(36\) | −3.67078 | −0.611796 | ||||||||
\(37\) | 5.37156 | 0.883078 | 0.441539 | − | 0.897242i | \(-0.354433\pi\) | ||||
0.441539 | + | 0.897242i | \(0.354433\pi\) | |||||||
\(38\) | 9.38608 | 1.52262 | ||||||||
\(39\) | 1.88157 | 0.301293 | ||||||||
\(40\) | 0.105009 | 0.0166033 | ||||||||
\(41\) | −4.56519 | −0.712962 | −0.356481 | − | 0.934303i | \(-0.616024\pi\) | ||||
−0.356481 | + | 0.934303i | \(0.616024\pi\) | |||||||
\(42\) | −2.30871 | −0.356241 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 6.57104 | 0.990622 | ||||||||
\(45\) | −0.298424 | −0.0444865 | ||||||||
\(46\) | 15.2213 | 2.24426 | ||||||||
\(47\) | 5.99224 | 0.874057 | 0.437029 | − | 0.899448i | \(-0.356031\pi\) | ||||
0.437029 | + | 0.899448i | \(0.356031\pi\) | |||||||
\(48\) | −3.77556 | −0.544956 | ||||||||
\(49\) | −4.69635 | −0.670907 | ||||||||
\(50\) | 9.40591 | 1.33020 | ||||||||
\(51\) | −4.50575 | −0.630931 | ||||||||
\(52\) | 3.64597 | 0.505605 | ||||||||
\(53\) | −4.41545 | −0.606509 | −0.303254 | − | 0.952910i | \(-0.598073\pi\) | ||||
−0.303254 | + | 0.952910i | \(0.598073\pi\) | |||||||
\(54\) | 8.13852 | 1.10751 | ||||||||
\(55\) | 0.534208 | 0.0720326 | ||||||||
\(56\) | 1.25527 | 0.167743 | ||||||||
\(57\) | −4.00846 | −0.530934 | ||||||||
\(58\) | −4.99483 | −0.655853 | ||||||||
\(59\) | −13.8133 | −1.79834 | −0.899171 | − | 0.437598i | \(-0.855829\pi\) | ||||
−0.899171 | + | 0.437598i | \(0.855829\pi\) | |||||||
\(60\) | 0.159823 | 0.0206331 | ||||||||
\(61\) | 9.98483 | 1.27843 | 0.639213 | − | 0.769030i | \(-0.279260\pi\) | ||||
0.639213 | + | 0.769030i | \(0.279260\pi\) | |||||||
\(62\) | 2.80647 | 0.356422 | ||||||||
\(63\) | −3.56737 | −0.449446 | ||||||||
\(64\) | −4.19428 | −0.524285 | ||||||||
\(65\) | 0.296407 | 0.0367648 | ||||||||
\(66\) | −6.39994 | −0.787778 | ||||||||
\(67\) | −2.10668 | −0.257371 | −0.128686 | − | 0.991685i | \(-0.541076\pi\) | ||||
−0.128686 | + | 0.991685i | \(0.541076\pi\) | |||||||
\(68\) | −8.73088 | −1.05878 | ||||||||
\(69\) | −6.50048 | −0.782565 | ||||||||
\(70\) | −0.363694 | −0.0434698 | ||||||||
\(71\) | 4.55021 | 0.540010 | 0.270005 | − | 0.962859i | \(-0.412975\pi\) | ||||
0.270005 | + | 0.962859i | \(0.412975\pi\) | |||||||
\(72\) | −1.94388 | −0.229089 | ||||||||
\(73\) | −15.1051 | −1.76791 | −0.883957 | − | 0.467568i | \(-0.845130\pi\) | ||||
−0.883957 | + | 0.467568i | \(0.845130\pi\) | |||||||
\(74\) | −10.1376 | −1.17847 | ||||||||
\(75\) | −4.01693 | −0.463835 | ||||||||
\(76\) | −7.76729 | −0.890969 | ||||||||
\(77\) | 6.38593 | 0.727744 | ||||||||
\(78\) | −3.55103 | −0.402075 | ||||||||
\(79\) | 14.9751 | 1.68483 | 0.842414 | − | 0.538831i | \(-0.181134\pi\) | ||||
0.842414 | + | 0.538831i | \(0.181134\pi\) | |||||||
\(80\) | −0.594770 | −0.0664973 | ||||||||
\(81\) | 3.57549 | 0.397277 | ||||||||
\(82\) | 8.61572 | 0.951447 | ||||||||
\(83\) | −2.09355 | −0.229797 | −0.114898 | − | 0.993377i | \(-0.536654\pi\) | ||||
−0.114898 | + | 0.993377i | \(0.536654\pi\) | |||||||
\(84\) | 1.91053 | 0.208456 | ||||||||
\(85\) | −0.709797 | −0.0769883 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.13312 | 0.228694 | ||||||||
\(88\) | 3.47973 | 0.370941 | ||||||||
\(89\) | −14.1765 | −1.50270 | −0.751351 | − | 0.659903i | \(-0.770598\pi\) | ||||
−0.751351 | + | 0.659903i | \(0.770598\pi\) | |||||||
\(90\) | 0.563206 | 0.0593671 | ||||||||
\(91\) | 3.54326 | 0.371434 | ||||||||
\(92\) | −12.5961 | −1.31324 | ||||||||
\(93\) | −1.19855 | −0.124283 | ||||||||
\(94\) | −11.3089 | −1.16643 | ||||||||
\(95\) | −0.631459 | −0.0647864 | ||||||||
\(96\) | 5.79232 | 0.591176 | ||||||||
\(97\) | 5.55966 | 0.564498 | 0.282249 | − | 0.959341i | \(-0.408920\pi\) | ||||
0.282249 | + | 0.959341i | \(0.408920\pi\) | |||||||
\(98\) | 8.86326 | 0.895325 | ||||||||
\(99\) | −9.88907 | −0.993889 | ||||||||
\(100\) | −7.78370 | −0.778370 | ||||||||
\(101\) | −11.2689 | −1.12130 | −0.560650 | − | 0.828053i | \(-0.689449\pi\) | ||||
−0.560650 | + | 0.828053i | \(0.689449\pi\) | |||||||
\(102\) | 8.50354 | 0.841976 | ||||||||
\(103\) | −2.13212 | −0.210084 | −0.105042 | − | 0.994468i | \(-0.533498\pi\) | ||||
−0.105042 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(104\) | 1.93074 | 0.189325 | ||||||||
\(105\) | 0.155321 | 0.0151578 | ||||||||
\(106\) | 8.33313 | 0.809385 | ||||||||
\(107\) | −1.42861 | −0.138109 | −0.0690543 | − | 0.997613i | \(-0.521998\pi\) | ||||
−0.0690543 | + | 0.997613i | \(0.521998\pi\) | |||||||
\(108\) | −6.73489 | −0.648066 | ||||||||
\(109\) | 5.67601 | 0.543663 | 0.271832 | − | 0.962345i | \(-0.412371\pi\) | ||||
0.271832 | + | 0.962345i | \(0.412371\pi\) | |||||||
\(110\) | −1.00819 | −0.0961274 | ||||||||
\(111\) | 4.32939 | 0.410928 | ||||||||
\(112\) | −7.10990 | −0.671822 | ||||||||
\(113\) | 13.0542 | 1.22803 | 0.614016 | − | 0.789293i | \(-0.289553\pi\) | ||||
0.614016 | + | 0.789293i | \(0.289553\pi\) | |||||||
\(114\) | 7.56504 | 0.708531 | ||||||||
\(115\) | −1.02403 | −0.0954913 | ||||||||
\(116\) | 4.13339 | 0.383775 | ||||||||
\(117\) | −5.48699 | −0.507272 | ||||||||
\(118\) | 26.0694 | 2.39989 | ||||||||
\(119\) | −8.48493 | −0.777812 | ||||||||
\(120\) | 0.0846353 | 0.00772611 | ||||||||
\(121\) | 6.70238 | 0.609307 | ||||||||
\(122\) | −18.8440 | −1.70606 | ||||||||
\(123\) | −3.67947 | −0.331767 | ||||||||
\(124\) | −2.32245 | −0.208562 | ||||||||
\(125\) | −1.26763 | −0.113381 | ||||||||
\(126\) | 6.73258 | 0.599786 | ||||||||
\(127\) | 10.5480 | 0.935981 | 0.467991 | − | 0.883733i | \(-0.344978\pi\) | ||||
0.467991 | + | 0.883733i | \(0.344978\pi\) | |||||||
\(128\) | −6.45755 | −0.570772 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.559399 | −0.0490626 | ||||||||
\(131\) | −3.32904 | −0.290860 | −0.145430 | − | 0.989369i | \(-0.546457\pi\) | ||||
−0.145430 | + | 0.989369i | \(0.546457\pi\) | |||||||
\(132\) | 5.29616 | 0.460972 | ||||||||
\(133\) | −7.54848 | −0.654536 | ||||||||
\(134\) | 3.97586 | 0.343462 | ||||||||
\(135\) | −0.547529 | −0.0471238 | ||||||||
\(136\) | −4.62349 | −0.396461 | ||||||||
\(137\) | −11.8040 | −1.00848 | −0.504242 | − | 0.863562i | \(-0.668228\pi\) | ||||
−0.504242 | + | 0.863562i | \(0.668228\pi\) | |||||||
\(138\) | 12.2681 | 1.04433 | ||||||||
\(139\) | −3.72683 | −0.316106 | −0.158053 | − | 0.987431i | \(-0.550522\pi\) | ||||
−0.158053 | + | 0.987431i | \(0.550522\pi\) | |||||||
\(140\) | 0.300969 | 0.0254365 | ||||||||
\(141\) | 4.82965 | 0.406730 | ||||||||
\(142\) | −8.58745 | −0.720643 | ||||||||
\(143\) | 9.82223 | 0.821376 | ||||||||
\(144\) | 11.0102 | 0.917515 | ||||||||
\(145\) | 0.336033 | 0.0279060 | ||||||||
\(146\) | 28.5073 | 2.35928 | ||||||||
\(147\) | −3.78519 | −0.312197 | ||||||||
\(148\) | 8.38916 | 0.689585 | ||||||||
\(149\) | −9.25643 | −0.758316 | −0.379158 | − | 0.925332i | \(-0.623786\pi\) | ||||
−0.379158 | + | 0.925332i | \(0.623786\pi\) | |||||||
\(150\) | 7.58102 | 0.618988 | ||||||||
\(151\) | 16.4755 | 1.34076 | 0.670378 | − | 0.742020i | \(-0.266132\pi\) | ||||
0.670378 | + | 0.742020i | \(0.266132\pi\) | |||||||
\(152\) | −4.11321 | −0.333626 | ||||||||
\(153\) | 13.1395 | 1.06227 | ||||||||
\(154\) | −12.0520 | −0.971174 | ||||||||
\(155\) | −0.188809 | −0.0151655 | ||||||||
\(156\) | 2.93859 | 0.235276 | ||||||||
\(157\) | −23.3387 | −1.86263 | −0.931315 | − | 0.364216i | \(-0.881337\pi\) | ||||
−0.931315 | + | 0.364216i | \(0.881337\pi\) | |||||||
\(158\) | −28.2620 | −2.24840 | ||||||||
\(159\) | −3.55879 | −0.282230 | ||||||||
\(160\) | 0.912473 | 0.0721373 | ||||||||
\(161\) | −12.2413 | −0.964748 | ||||||||
\(162\) | −6.74790 | −0.530165 | ||||||||
\(163\) | −17.7009 | −1.38644 | −0.693220 | − | 0.720726i | \(-0.743808\pi\) | ||||
−0.693220 | + | 0.720726i | \(0.743808\pi\) | |||||||
\(164\) | −7.12979 | −0.556743 | ||||||||
\(165\) | 0.430564 | 0.0335193 | ||||||||
\(166\) | 3.95108 | 0.306664 | ||||||||
\(167\) | −7.17863 | −0.555499 | −0.277749 | − | 0.960654i | \(-0.589589\pi\) | ||||
−0.277749 | + | 0.960654i | \(0.589589\pi\) | |||||||
\(168\) | 1.01173 | 0.0780568 | ||||||||
\(169\) | −7.55010 | −0.580777 | ||||||||
\(170\) | 1.33958 | 0.102741 | ||||||||
\(171\) | 11.6894 | 0.893907 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.63680 | −0.352529 | −0.176265 | − | 0.984343i | \(-0.556401\pi\) | ||||
−0.176265 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(174\) | −4.02576 | −0.305192 | ||||||||
\(175\) | −7.56443 | −0.571817 | ||||||||
\(176\) | −19.7093 | −1.48564 | ||||||||
\(177\) | −11.1333 | −0.836833 | ||||||||
\(178\) | 26.7548 | 2.00535 | ||||||||
\(179\) | −5.73214 | −0.428440 | −0.214220 | − | 0.976785i | \(-0.568721\pi\) | ||||
−0.214220 | + | 0.976785i | \(0.568721\pi\) | |||||||
\(180\) | −0.466072 | −0.0347389 | ||||||||
\(181\) | 0.971446 | 0.0722070 | 0.0361035 | − | 0.999348i | \(-0.488505\pi\) | ||||
0.0361035 | + | 0.999348i | \(0.488505\pi\) | |||||||
\(182\) | −6.68707 | −0.495679 | ||||||||
\(183\) | 8.04762 | 0.594897 | ||||||||
\(184\) | −6.67035 | −0.491744 | ||||||||
\(185\) | 0.682016 | 0.0501428 | ||||||||
\(186\) | 2.26197 | 0.165856 | ||||||||
\(187\) | −23.5210 | −1.72002 | ||||||||
\(188\) | 9.35853 | 0.682541 | ||||||||
\(189\) | −6.54517 | −0.476091 | ||||||||
\(190\) | 1.19173 | 0.0864573 | ||||||||
\(191\) | −1.17671 | −0.0851436 | −0.0425718 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425718 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(192\) | −3.38052 | −0.243968 | ||||||||
\(193\) | 3.87170 | 0.278691 | 0.139345 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139345 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(194\) | −10.4926 | −0.753321 | ||||||||
\(195\) | 0.238900 | 0.0171080 | ||||||||
\(196\) | −7.33464 | −0.523903 | ||||||||
\(197\) | 18.1072 | 1.29008 | 0.645042 | − | 0.764147i | \(-0.276840\pi\) | ||||
0.645042 | + | 0.764147i | \(0.276840\pi\) | |||||||
\(198\) | 18.6633 | 1.32634 | ||||||||
\(199\) | 17.8987 | 1.26881 | 0.634403 | − | 0.773003i | \(-0.281246\pi\) | ||||
0.634403 | + | 0.773003i | \(0.281246\pi\) | |||||||
\(200\) | −4.12190 | −0.291462 | ||||||||
\(201\) | −1.69795 | −0.119764 | ||||||||
\(202\) | 21.2675 | 1.49637 | ||||||||
\(203\) | 4.01695 | 0.281934 | ||||||||
\(204\) | −7.03696 | −0.492686 | ||||||||
\(205\) | −0.579633 | −0.0404833 | ||||||||
\(206\) | 4.02388 | 0.280357 | ||||||||
\(207\) | 18.9565 | 1.31757 | ||||||||
\(208\) | −10.9358 | −0.758258 | ||||||||
\(209\) | −20.9251 | −1.44742 | ||||||||
\(210\) | −0.293132 | −0.0202280 | ||||||||
\(211\) | 23.1719 | 1.59522 | 0.797609 | − | 0.603175i | \(-0.206098\pi\) | ||||
0.797609 | + | 0.603175i | \(0.206098\pi\) | |||||||
\(212\) | −6.89594 | −0.473615 | ||||||||
\(213\) | 3.66740 | 0.251286 | ||||||||
\(214\) | 2.69616 | 0.184306 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.56650 | −0.242670 | ||||||||
\(217\) | −2.25702 | −0.153217 | ||||||||
\(218\) | −10.7121 | −0.725518 | ||||||||
\(219\) | −12.1745 | −0.822674 | ||||||||
\(220\) | 0.834313 | 0.0562494 | ||||||||
\(221\) | −13.0507 | −0.877885 | ||||||||
\(222\) | −8.17072 | −0.548383 | ||||||||
\(223\) | 5.07688 | 0.339973 | 0.169986 | − | 0.985446i | \(-0.445628\pi\) | ||||
0.169986 | + | 0.985446i | \(0.445628\pi\) | |||||||
\(224\) | 10.9077 | 0.728803 | ||||||||
\(225\) | 11.7141 | 0.780937 | ||||||||
\(226\) | −24.6367 | −1.63881 | ||||||||
\(227\) | −8.59401 | −0.570404 | −0.285202 | − | 0.958467i | \(-0.592061\pi\) | ||||
−0.285202 | + | 0.958467i | \(0.592061\pi\) | |||||||
\(228\) | −6.26032 | −0.414600 | ||||||||
\(229\) | −19.1845 | −1.26775 | −0.633873 | − | 0.773437i | \(-0.718536\pi\) | ||||
−0.633873 | + | 0.773437i | \(0.718536\pi\) | |||||||
\(230\) | 1.93262 | 0.127433 | ||||||||
\(231\) | 5.14696 | 0.338645 | ||||||||
\(232\) | 2.18886 | 0.143706 | ||||||||
\(233\) | −22.8579 | −1.49747 | −0.748736 | − | 0.662869i | \(-0.769339\pi\) | ||||
−0.748736 | + | 0.662869i | \(0.769339\pi\) | |||||||
\(234\) | 10.3554 | 0.676954 | ||||||||
\(235\) | 0.760823 | 0.0496306 | ||||||||
\(236\) | −21.5733 | −1.40430 | ||||||||
\(237\) | 12.0697 | 0.784011 | ||||||||
\(238\) | 16.0133 | 1.03799 | ||||||||
\(239\) | −11.0421 | −0.714253 | −0.357127 | − | 0.934056i | \(-0.616244\pi\) | ||||
−0.357127 | + | 0.934056i | \(0.616244\pi\) | |||||||
\(240\) | −0.479376 | −0.0309436 | ||||||||
\(241\) | 12.6547 | 0.815158 | 0.407579 | − | 0.913170i | \(-0.366373\pi\) | ||||
0.407579 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(242\) | −12.6492 | −0.813119 | ||||||||
\(243\) | 15.8188 | 1.01478 | ||||||||
\(244\) | 15.5941 | 0.998307 | ||||||||
\(245\) | −0.596286 | −0.0380953 | ||||||||
\(246\) | 6.94414 | 0.442742 | ||||||||
\(247\) | −11.6103 | −0.738749 | ||||||||
\(248\) | −1.22987 | −0.0780965 | ||||||||
\(249\) | −1.68737 | −0.106933 | ||||||||
\(250\) | 2.39236 | 0.151306 | ||||||||
\(251\) | −11.4052 | −0.719888 | −0.359944 | − | 0.932974i | \(-0.617204\pi\) | ||||
−0.359944 | + | 0.932974i | \(0.617204\pi\) | |||||||
\(252\) | −5.57143 | −0.350967 | ||||||||
\(253\) | −33.9339 | −2.13341 | ||||||||
\(254\) | −19.9068 | −1.24907 | ||||||||
\(255\) | −0.572086 | −0.0358254 | ||||||||
\(256\) | 20.5757 | 1.28598 | ||||||||
\(257\) | 17.0581 | 1.06406 | 0.532028 | − | 0.846726i | \(-0.321430\pi\) | ||||
0.532028 | + | 0.846726i | \(0.321430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.15283 | 0.506592 | ||||||||
\(260\) | 0.462921 | 0.0287092 | ||||||||
\(261\) | −6.22053 | −0.385041 | ||||||||
\(262\) | 6.28279 | 0.388152 | ||||||||
\(263\) | 6.77841 | 0.417974 | 0.208987 | − | 0.977918i | \(-0.432983\pi\) | ||||
0.208987 | + | 0.977918i | \(0.432983\pi\) | |||||||
\(264\) | 2.80461 | 0.172612 | ||||||||
\(265\) | −0.560621 | −0.0344387 | ||||||||
\(266\) | 14.2460 | 0.873478 | ||||||||
\(267\) | −11.4260 | −0.699261 | ||||||||
\(268\) | −3.29015 | −0.200978 | ||||||||
\(269\) | −19.1767 | −1.16922 | −0.584611 | − | 0.811314i | \(-0.698753\pi\) | ||||
−0.584611 | + | 0.811314i | \(0.698753\pi\) | |||||||
\(270\) | 1.03333 | 0.0628866 | ||||||||
\(271\) | −6.35388 | −0.385971 | −0.192985 | − | 0.981202i | \(-0.561817\pi\) | ||||
−0.192985 | + | 0.981202i | \(0.561817\pi\) | |||||||
\(272\) | 26.1875 | 1.58785 | ||||||||
\(273\) | 2.85581 | 0.172842 | ||||||||
\(274\) | 22.2773 | 1.34582 | ||||||||
\(275\) | −20.9693 | −1.26449 | ||||||||
\(276\) | −10.1523 | −0.611096 | ||||||||
\(277\) | −18.6255 | −1.11910 | −0.559548 | − | 0.828798i | \(-0.689025\pi\) | ||||
−0.559548 | + | 0.828798i | \(0.689025\pi\) | |||||||
\(278\) | 7.03353 | 0.421843 | ||||||||
\(279\) | 3.49516 | 0.209250 | ||||||||
\(280\) | 0.159380 | 0.00952476 | ||||||||
\(281\) | −6.78540 | −0.404783 | −0.202391 | − | 0.979305i | \(-0.564871\pi\) | ||||
−0.202391 | + | 0.979305i | \(0.564871\pi\) | |||||||
\(282\) | −9.11484 | −0.542781 | ||||||||
\(283\) | −7.23759 | −0.430230 | −0.215115 | − | 0.976589i | \(-0.569013\pi\) | ||||
−0.215115 | + | 0.976589i | \(0.569013\pi\) | |||||||
\(284\) | 7.10640 | 0.421687 | ||||||||
\(285\) | −0.508947 | −0.0301474 | ||||||||
\(286\) | −18.5372 | −1.09613 | ||||||||
\(287\) | −6.92894 | −0.409002 | ||||||||
\(288\) | −16.8914 | −0.995334 | ||||||||
\(289\) | 14.2521 | 0.838360 | ||||||||
\(290\) | −0.634184 | −0.0372406 | ||||||||
\(291\) | 4.48100 | 0.262681 | ||||||||
\(292\) | −23.5907 | −1.38054 | ||||||||
\(293\) | 8.89839 | 0.519850 | 0.259925 | − | 0.965629i | \(-0.416302\pi\) | ||||
0.259925 | + | 0.965629i | \(0.416302\pi\) | |||||||
\(294\) | 7.14365 | 0.416626 | ||||||||
\(295\) | −1.75385 | −0.102113 | ||||||||
\(296\) | 4.44253 | 0.258217 | ||||||||
\(297\) | −18.1438 | −1.05281 | ||||||||
\(298\) | 17.4694 | 1.01197 | ||||||||
\(299\) | −18.8284 | −1.08887 | ||||||||
\(300\) | −6.27354 | −0.362203 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −31.0936 | −1.78924 | ||||||||
\(303\) | −9.08259 | −0.521781 | ||||||||
\(304\) | 23.2973 | 1.33619 | ||||||||
\(305\) | 1.26775 | 0.0725914 | ||||||||
\(306\) | −24.7978 | −1.41759 | ||||||||
\(307\) | 15.0380 | 0.858263 | 0.429131 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429131 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(308\) | 9.97339 | 0.568287 | ||||||||
\(309\) | −1.71846 | −0.0977595 | ||||||||
\(310\) | 0.356332 | 0.0202383 | ||||||||
\(311\) | −20.3119 | −1.15178 | −0.575891 | − | 0.817526i | \(-0.695345\pi\) | ||||
−0.575891 | + | 0.817526i | \(0.695345\pi\) | |||||||
\(312\) | 1.55615 | 0.0880996 | ||||||||
\(313\) | −2.25316 | −0.127356 | −0.0636781 | − | 0.997970i | \(-0.520283\pi\) | ||||
−0.0636781 | + | 0.997970i | \(0.520283\pi\) | |||||||
\(314\) | 44.0463 | 2.48568 | ||||||||
\(315\) | −0.452942 | −0.0255204 | ||||||||
\(316\) | 23.3877 | 1.31566 | ||||||||
\(317\) | −8.07220 | −0.453380 | −0.226690 | − | 0.973967i | \(-0.572790\pi\) | ||||
−0.226690 | + | 0.973967i | \(0.572790\pi\) | |||||||
\(318\) | 6.71638 | 0.376636 | ||||||||
\(319\) | 11.1353 | 0.623459 | ||||||||
\(320\) | −0.532539 | −0.0297699 | ||||||||
\(321\) | −1.15143 | −0.0642668 | ||||||||
\(322\) | 23.1026 | 1.28745 | ||||||||
\(323\) | 27.8029 | 1.54700 | ||||||||
\(324\) | 5.58411 | 0.310228 | ||||||||
\(325\) | −11.6349 | −0.645387 | ||||||||
\(326\) | 33.4063 | 1.85020 | ||||||||
\(327\) | 4.57478 | 0.252986 | ||||||||
\(328\) | −3.77562 | −0.208474 | ||||||||
\(329\) | 9.09489 | 0.501417 | ||||||||
\(330\) | −0.812588 | −0.0447315 | ||||||||
\(331\) | −3.99703 | −0.219697 | −0.109848 | − | 0.993948i | \(-0.535036\pi\) | ||||
−0.109848 | + | 0.993948i | \(0.535036\pi\) | |||||||
\(332\) | −3.26965 | −0.179445 | ||||||||
\(333\) | −12.6252 | −0.691859 | ||||||||
\(334\) | 13.5480 | 0.741313 | ||||||||
\(335\) | −0.267481 | −0.0146140 | ||||||||
\(336\) | −5.73047 | −0.312623 | ||||||||
\(337\) | 30.5333 | 1.66325 | 0.831627 | − | 0.555334i | \(-0.187410\pi\) | ||||
0.831627 | + | 0.555334i | \(0.187410\pi\) | |||||||
\(338\) | 14.2491 | 0.775046 | ||||||||
\(339\) | 10.5215 | 0.571447 | ||||||||
\(340\) | −1.10854 | −0.0601192 | ||||||||
\(341\) | −6.25667 | −0.338818 | ||||||||
\(342\) | −22.0609 | −1.19292 | ||||||||
\(343\) | −17.7525 | −0.958543 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.825353 | −0.0444355 | ||||||||
\(346\) | 8.75087 | 0.470450 | ||||||||
\(347\) | −13.3094 | −0.714484 | −0.357242 | − | 0.934012i | \(-0.616283\pi\) | ||||
−0.357242 | + | 0.934012i | \(0.616283\pi\) | |||||||
\(348\) | 3.33145 | 0.178584 | ||||||||
\(349\) | 26.7370 | 1.43120 | 0.715598 | − | 0.698512i | \(-0.246154\pi\) | ||||
0.715598 | + | 0.698512i | \(0.246154\pi\) | |||||||
\(350\) | 14.2761 | 0.763089 | ||||||||
\(351\) | −10.0671 | −0.537345 | ||||||||
\(352\) | 30.2372 | 1.61165 | ||||||||
\(353\) | −0.146688 | −0.00780744 | −0.00390372 | − | 0.999992i | \(-0.501243\pi\) | ||||
−0.00390372 | + | 0.999992i | \(0.501243\pi\) | |||||||
\(354\) | 21.0116 | 1.11675 | ||||||||
\(355\) | 0.577731 | 0.0306628 | ||||||||
\(356\) | −22.1405 | −1.17344 | ||||||||
\(357\) | −6.83872 | −0.361944 | ||||||||
\(358\) | 10.8181 | 0.571753 | ||||||||
\(359\) | 25.9280 | 1.36843 | 0.684214 | − | 0.729281i | \(-0.260145\pi\) | ||||
0.684214 | + | 0.729281i | \(0.260145\pi\) | |||||||
\(360\) | −0.246811 | −0.0130081 | ||||||||
\(361\) | 5.73443 | 0.301812 | ||||||||
\(362\) | −1.83338 | −0.0963602 | ||||||||
\(363\) | 5.40201 | 0.283532 | ||||||||
\(364\) | 5.53377 | 0.290048 | ||||||||
\(365\) | −1.91786 | −0.100385 | ||||||||
\(366\) | −15.1880 | −0.793890 | ||||||||
\(367\) | 20.4684 | 1.06844 | 0.534221 | − | 0.845345i | \(-0.320605\pi\) | ||||
0.534221 | + | 0.845345i | \(0.320605\pi\) | |||||||
\(368\) | 37.7810 | 1.96947 | ||||||||
\(369\) | 10.7300 | 0.558579 | ||||||||
\(370\) | −1.28715 | −0.0669155 | ||||||||
\(371\) | −6.70167 | −0.347934 | ||||||||
\(372\) | −1.87186 | −0.0970513 | ||||||||
\(373\) | 34.1590 | 1.76869 | 0.884344 | − | 0.466835i | \(-0.154606\pi\) | ||||
0.884344 | + | 0.466835i | \(0.154606\pi\) | |||||||
\(374\) | 44.3904 | 2.29537 | ||||||||
\(375\) | −1.02169 | −0.0527600 | ||||||||
\(376\) | 4.95586 | 0.255579 | ||||||||
\(377\) | 6.17848 | 0.318208 | ||||||||
\(378\) | 12.3525 | 0.635343 | ||||||||
\(379\) | −21.8917 | −1.12450 | −0.562250 | − | 0.826968i | \(-0.690064\pi\) | ||||
−0.562250 | + | 0.826968i | \(0.690064\pi\) | |||||||
\(380\) | −0.986198 | −0.0505909 | ||||||||
\(381\) | 8.50151 | 0.435545 | ||||||||
\(382\) | 2.22076 | 0.113624 | ||||||||
\(383\) | −18.3858 | −0.939471 | −0.469735 | − | 0.882807i | \(-0.655651\pi\) | ||||
−0.469735 | + | 0.882807i | \(0.655651\pi\) | |||||||
\(384\) | −5.20469 | −0.265601 | ||||||||
\(385\) | 0.810809 | 0.0413227 | ||||||||
\(386\) | −7.30693 | −0.371913 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.68293 | 0.440809 | ||||||||
\(389\) | 8.37856 | 0.424810 | 0.212405 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212405 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(390\) | −0.450868 | −0.0228306 | ||||||||
\(391\) | 45.0877 | 2.28018 | ||||||||
\(392\) | −3.88410 | −0.196177 | ||||||||
\(393\) | −2.68316 | −0.135347 | ||||||||
\(394\) | −34.1731 | −1.72162 | ||||||||
\(395\) | 1.90136 | 0.0956677 | ||||||||
\(396\) | −15.4445 | −0.776115 | ||||||||
\(397\) | 16.8086 | 0.843598 | 0.421799 | − | 0.906689i | \(-0.361399\pi\) | ||||
0.421799 | + | 0.906689i | \(0.361399\pi\) | |||||||
\(398\) | −33.7796 | −1.69322 | ||||||||
\(399\) | −6.08396 | −0.304579 | ||||||||
\(400\) | 23.3465 | 1.16733 | ||||||||
\(401\) | 5.69004 | 0.284147 | 0.142074 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142074 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(402\) | 3.20448 | 0.159825 | ||||||||
\(403\) | −3.47154 | −0.172929 | ||||||||
\(404\) | −17.5995 | −0.875610 | ||||||||
\(405\) | 0.453973 | 0.0225581 | ||||||||
\(406\) | −7.58105 | −0.376241 | ||||||||
\(407\) | 22.6004 | 1.12026 | ||||||||
\(408\) | −3.72646 | −0.184487 | ||||||||
\(409\) | −35.6595 | −1.76325 | −0.881624 | − | 0.471952i | \(-0.843549\pi\) | ||||
−0.881624 | + | 0.471952i | \(0.843549\pi\) | |||||||
\(410\) | 1.09392 | 0.0540249 | ||||||||
\(411\) | −9.51386 | −0.469284 | ||||||||
\(412\) | −3.32989 | −0.164052 | ||||||||
\(413\) | −20.9656 | −1.03165 | ||||||||
\(414\) | −35.7759 | −1.75829 | ||||||||
\(415\) | −0.265814 | −0.0130483 | ||||||||
\(416\) | 16.7772 | 0.822570 | ||||||||
\(417\) | −3.00377 | −0.147095 | ||||||||
\(418\) | 39.4912 | 1.93158 | ||||||||
\(419\) | −16.1497 | −0.788965 | −0.394482 | − | 0.918903i | \(-0.629076\pi\) | ||||
−0.394482 | + | 0.918903i | \(0.629076\pi\) | |||||||
\(420\) | 0.242576 | 0.0118365 | ||||||||
\(421\) | −13.5145 | −0.658658 | −0.329329 | − | 0.944215i | \(-0.606823\pi\) | ||||
−0.329329 | + | 0.944215i | \(0.606823\pi\) | |||||||
\(422\) | −43.7315 | −2.12882 | ||||||||
\(423\) | −14.0841 | −0.684791 | ||||||||
\(424\) | −3.65178 | −0.177346 | ||||||||
\(425\) | 27.8617 | 1.35149 | ||||||||
\(426\) | −6.92136 | −0.335341 | ||||||||
\(427\) | 15.1548 | 0.733390 | ||||||||
\(428\) | −2.23116 | −0.107847 | ||||||||
\(429\) | 7.91657 | 0.382215 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6669 | 0.850987 | 0.425493 | − | 0.904962i | \(-0.360101\pi\) | ||||
0.425493 | + | 0.904962i | \(0.360101\pi\) | |||||||
\(432\) | 20.2007 | 0.971908 | ||||||||
\(433\) | 8.76277 | 0.421112 | 0.210556 | − | 0.977582i | \(-0.432473\pi\) | ||||
0.210556 | + | 0.977582i | \(0.432473\pi\) | |||||||
\(434\) | 4.25960 | 0.204467 | ||||||||
\(435\) | 0.270838 | 0.0129857 | ||||||||
\(436\) | 8.86465 | 0.424540 | ||||||||
\(437\) | 40.1115 | 1.91879 | ||||||||
\(438\) | 22.9764 | 1.09786 | ||||||||
\(439\) | −31.0062 | −1.47984 | −0.739921 | − | 0.672693i | \(-0.765137\pi\) | ||||
−0.739921 | + | 0.672693i | \(0.765137\pi\) | |||||||
\(440\) | 0.441815 | 0.0210627 | ||||||||
\(441\) | 11.0382 | 0.525631 | ||||||||
\(442\) | 24.6302 | 1.17154 | ||||||||
\(443\) | −13.5160 | −0.642164 | −0.321082 | − | 0.947051i | \(-0.604046\pi\) | ||||
−0.321082 | + | 0.947051i | \(0.604046\pi\) | |||||||
\(444\) | 6.76154 | 0.320888 | ||||||||
\(445\) | −1.79996 | −0.0853262 | ||||||||
\(446\) | −9.58142 | −0.453693 | ||||||||
\(447\) | −7.46054 | −0.352872 | ||||||||
\(448\) | −6.36599 | −0.300765 | ||||||||
\(449\) | 9.20057 | 0.434202 | 0.217101 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217101 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(450\) | −22.1075 | −1.04216 | ||||||||
\(451\) | −19.2076 | −0.904453 | ||||||||
\(452\) | 20.3877 | 0.958955 | ||||||||
\(453\) | 13.2790 | 0.623902 | ||||||||
\(454\) | 16.2192 | 0.761204 | ||||||||
\(455\) | 0.449880 | 0.0210907 | ||||||||
\(456\) | −3.31519 | −0.155248 | ||||||||
\(457\) | −1.72720 | −0.0807950 | −0.0403975 | − | 0.999184i | \(-0.512862\pi\) | ||||
−0.0403975 | + | 0.999184i | \(0.512862\pi\) | |||||||
\(458\) | 36.2062 | 1.69181 | ||||||||
\(459\) | 24.1075 | 1.12524 | ||||||||
\(460\) | −1.59931 | −0.0745680 | ||||||||
\(461\) | −15.9037 | −0.740709 | −0.370354 | − | 0.928891i | \(-0.620764\pi\) | ||||
−0.370354 | + | 0.928891i | \(0.620764\pi\) | |||||||
\(462\) | −9.71369 | −0.451922 | ||||||||
\(463\) | 37.0012 | 1.71959 | 0.859795 | − | 0.510639i | \(-0.170591\pi\) | ||||
0.859795 | + | 0.510639i | \(0.170591\pi\) | |||||||
\(464\) | −12.3977 | −0.575550 | ||||||||
\(465\) | −0.152177 | −0.00705704 | ||||||||
\(466\) | 43.1390 | 1.99837 | ||||||||
\(467\) | 24.9002 | 1.15225 | 0.576123 | − | 0.817363i | \(-0.304565\pi\) | ||||
0.576123 | + | 0.817363i | \(0.304565\pi\) | |||||||
\(468\) | −8.56944 | −0.396122 | ||||||||
\(469\) | −3.19747 | −0.147645 | ||||||||
\(470\) | −1.43588 | −0.0662320 | ||||||||
\(471\) | −18.8106 | −0.866748 | ||||||||
\(472\) | −11.4243 | −0.525845 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −22.7787 | −1.04626 | ||||||||
\(475\) | 24.7867 | 1.13729 | ||||||||
\(476\) | −13.2516 | −0.607384 | ||||||||
\(477\) | 10.3780 | 0.475177 | ||||||||
\(478\) | 20.8394 | 0.953170 | ||||||||
\(479\) | −24.2938 | −1.11001 | −0.555007 | − | 0.831846i | \(-0.687284\pi\) | ||||
−0.555007 | + | 0.831846i | \(0.687284\pi\) | |||||||
\(480\) | 0.735440 | 0.0335681 | ||||||||
\(481\) | 12.5399 | 0.571771 | ||||||||
\(482\) | −23.8827 | −1.08783 | ||||||||
\(483\) | −9.86628 | −0.448931 | ||||||||
\(484\) | 10.4676 | 0.475800 | ||||||||
\(485\) | 0.705899 | 0.0320532 | ||||||||
\(486\) | −29.8543 | −1.35422 | ||||||||
\(487\) | −2.21295 | −0.100278 | −0.0501392 | − | 0.998742i | \(-0.515966\pi\) | ||||
−0.0501392 | + | 0.998742i | \(0.515966\pi\) | |||||||
\(488\) | 8.25792 | 0.373818 | ||||||||
\(489\) | −14.2666 | −0.645160 | ||||||||
\(490\) | 1.12535 | 0.0508382 | ||||||||
\(491\) | −17.2974 | −0.780621 | −0.390311 | − | 0.920683i | \(-0.627632\pi\) | ||||
−0.390311 | + | 0.920683i | \(0.627632\pi\) | |||||||
\(492\) | −5.74651 | −0.259073 | ||||||||
\(493\) | −14.7954 | −0.666352 | ||||||||
\(494\) | 21.9118 | 0.985859 | ||||||||
\(495\) | −1.25560 | −0.0564348 | ||||||||
\(496\) | 6.96598 | 0.312782 | ||||||||
\(497\) | 6.90621 | 0.309786 | ||||||||
\(498\) | 3.18451 | 0.142701 | ||||||||
\(499\) | 0.427045 | 0.0191171 | 0.00955857 | − | 0.999954i | \(-0.496957\pi\) | ||||
0.00955857 | + | 0.999954i | \(0.496957\pi\) | |||||||
\(500\) | −1.97976 | −0.0885375 | ||||||||
\(501\) | −5.78587 | −0.258493 | ||||||||
\(502\) | 21.5246 | 0.960690 | ||||||||
\(503\) | −9.00341 | −0.401442 | −0.200721 | − | 0.979648i | \(-0.564328\pi\) | ||||
−0.200721 | + | 0.979648i | \(0.564328\pi\) | |||||||
\(504\) | −2.95038 | −0.131420 | ||||||||
\(505\) | −1.43079 | −0.0636695 | ||||||||
\(506\) | 64.0424 | 2.84703 | ||||||||
\(507\) | −6.08527 | −0.270256 | ||||||||
\(508\) | 16.4736 | 0.730896 | ||||||||
\(509\) | 25.3091 | 1.12180 | 0.560902 | − | 0.827882i | \(-0.310454\pi\) | ||||
0.560902 | + | 0.827882i | \(0.310454\pi\) | |||||||
\(510\) | 1.07968 | 0.0478090 | ||||||||
\(511\) | −22.9262 | −1.01419 | ||||||||
\(512\) | −25.9167 | −1.14537 | ||||||||
\(513\) | 21.4468 | 0.946901 | ||||||||
\(514\) | −32.1932 | −1.41998 | ||||||||
\(515\) | −0.270711 | −0.0119290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.2118 | 1.10882 | ||||||||
\(518\) | −15.3866 | −0.676047 | ||||||||
\(519\) | −3.73719 | −0.164044 | ||||||||
\(520\) | 0.245143 | 0.0107502 | ||||||||
\(521\) | 11.2777 | 0.494086 | 0.247043 | − | 0.969004i | \(-0.420541\pi\) | ||||
0.247043 | + | 0.969004i | \(0.420541\pi\) | |||||||
\(522\) | 11.7398 | 0.513837 | ||||||||
\(523\) | 10.7109 | 0.468354 | 0.234177 | − | 0.972194i | \(-0.424761\pi\) | ||||
0.234177 | + | 0.972194i | \(0.424761\pi\) | |||||||
\(524\) | −5.19922 | −0.227129 | ||||||||
\(525\) | −6.09681 | −0.266087 | ||||||||
\(526\) | −12.7927 | −0.557787 | ||||||||
\(527\) | 8.31318 | 0.362128 | ||||||||
\(528\) | −15.8854 | −0.691322 | ||||||||
\(529\) | 42.0484 | 1.82819 | ||||||||
\(530\) | 1.05804 | 0.0459584 | ||||||||
\(531\) | 32.4667 | 1.40893 | ||||||||
\(532\) | −11.7890 | −0.511119 | ||||||||
\(533\) | −10.6574 | −0.461625 | ||||||||
\(534\) | 21.5639 | 0.933163 | ||||||||
\(535\) | −0.181387 | −0.00784206 | ||||||||
\(536\) | −1.74232 | −0.0752567 | ||||||||
\(537\) | −4.62002 | −0.199369 | ||||||||
\(538\) | 36.1915 | 1.56032 | ||||||||
\(539\) | −19.7595 | −0.851102 | ||||||||
\(540\) | −0.855117 | −0.0367984 | ||||||||
\(541\) | −3.71797 | −0.159848 | −0.0799240 | − | 0.996801i | \(-0.525468\pi\) | ||||
−0.0799240 | + | 0.996801i | \(0.525468\pi\) | |||||||
\(542\) | 11.9915 | 0.515077 | ||||||||
\(543\) | 0.782971 | 0.0336005 | ||||||||
\(544\) | −40.1759 | −1.72253 | ||||||||
\(545\) | 0.720672 | 0.0308702 | ||||||||
\(546\) | −5.38968 | −0.230657 | ||||||||
\(547\) | 4.46329 | 0.190837 | 0.0954183 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954183 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(548\) | −18.4352 | −0.787513 | ||||||||
\(549\) | −23.4682 | −1.00160 | ||||||||
\(550\) | 39.5746 | 1.68747 | ||||||||
\(551\) | −13.1625 | −0.560741 | ||||||||
\(552\) | −5.37620 | −0.228826 | ||||||||
\(553\) | 22.7289 | 0.966529 | ||||||||
\(554\) | 35.1512 | 1.49343 | ||||||||
\(555\) | 0.549695 | 0.0233332 | ||||||||
\(556\) | −5.82048 | −0.246843 | ||||||||
\(557\) | 20.6313 | 0.874174 | 0.437087 | − | 0.899419i | \(-0.356010\pi\) | ||||
0.437087 | + | 0.899419i | \(0.356010\pi\) | |||||||
\(558\) | −6.59630 | −0.279244 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.902730 | −0.0381473 | ||||||||
\(561\) | −18.9576 | −0.800389 | ||||||||
\(562\) | 12.8059 | 0.540182 | ||||||||
\(563\) | 18.4481 | 0.777493 | 0.388747 | − | 0.921345i | \(-0.372908\pi\) | ||||
0.388747 | + | 0.921345i | \(0.372908\pi\) | |||||||
\(564\) | 7.54283 | 0.317610 | ||||||||
\(565\) | 1.65746 | 0.0697300 | ||||||||
\(566\) | 13.6593 | 0.574142 | ||||||||
\(567\) | 5.42680 | 0.227904 | ||||||||
\(568\) | 3.76323 | 0.157902 | ||||||||
\(569\) | 28.0115 | 1.17430 | 0.587151 | − | 0.809477i | \(-0.300249\pi\) | ||||
0.587151 | + | 0.809477i | \(0.300249\pi\) | |||||||
\(570\) | 0.960518 | 0.0402317 | ||||||||
\(571\) | 10.8537 | 0.454214 | 0.227107 | − | 0.973870i | \(-0.427073\pi\) | ||||
0.227107 | + | 0.973870i | \(0.427073\pi\) | |||||||
\(572\) | 15.3401 | 0.641402 | ||||||||
\(573\) | −0.948409 | −0.0396204 | ||||||||
\(574\) | 13.0768 | 0.545813 | ||||||||
\(575\) | 40.1963 | 1.67630 | ||||||||
\(576\) | 9.85818 | 0.410758 | ||||||||
\(577\) | −9.95115 | −0.414272 | −0.207136 | − | 0.978312i | \(-0.566414\pi\) | ||||
−0.207136 | + | 0.978312i | \(0.566414\pi\) | |||||||
\(578\) | −26.8975 | −1.11879 | ||||||||
\(579\) | 3.12053 | 0.129685 | ||||||||
\(580\) | 0.524808 | 0.0217915 | ||||||||
\(581\) | −3.17754 | −0.131827 | ||||||||
\(582\) | −8.45684 | −0.350547 | ||||||||
\(583\) | −18.5776 | −0.769407 | ||||||||
\(584\) | −12.4926 | −0.516947 | ||||||||
\(585\) | −0.696672 | −0.0288038 | ||||||||
\(586\) | −16.7936 | −0.693739 | ||||||||
\(587\) | 21.0785 | 0.870002 | 0.435001 | − | 0.900430i | \(-0.356748\pi\) | ||||
0.435001 | + | 0.900430i | \(0.356748\pi\) | |||||||
\(588\) | −5.91161 | −0.243791 | ||||||||
\(589\) | 7.39568 | 0.304734 | ||||||||
\(590\) | 3.30999 | 0.136270 | ||||||||
\(591\) | 14.5941 | 0.600322 | ||||||||
\(592\) | −25.1626 | −1.03417 | ||||||||
\(593\) | 20.2135 | 0.830071 | 0.415035 | − | 0.909805i | \(-0.363769\pi\) | ||||
0.415035 | + | 0.909805i | \(0.363769\pi\) | |||||||
\(594\) | 34.2422 | 1.40497 | ||||||||
\(595\) | −1.07731 | −0.0441656 | ||||||||
\(596\) | −14.4565 | −0.592160 | ||||||||
\(597\) | 14.4261 | 0.590420 | ||||||||
\(598\) | 35.5341 | 1.45310 | ||||||||
\(599\) | −38.6386 | −1.57873 | −0.789366 | − | 0.613923i | \(-0.789590\pi\) | ||||
−0.789366 | + | 0.613923i | \(0.789590\pi\) | |||||||
\(600\) | −3.32219 | −0.135628 | ||||||||
\(601\) | 33.5518 | 1.36861 | 0.684304 | − | 0.729197i | \(-0.260106\pi\) | ||||
0.684304 | + | 0.729197i | \(0.260106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.95151 | 0.201641 | ||||||||
\(604\) | 25.7310 | 1.04698 | ||||||||
\(605\) | 0.850988 | 0.0345976 | ||||||||
\(606\) | 17.1413 | 0.696316 | ||||||||
\(607\) | −20.5281 | −0.833208 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(608\) | −35.7418 | −1.44952 | ||||||||
\(609\) | 3.23760 | 0.131194 | ||||||||
\(610\) | −2.39259 | −0.0968731 | ||||||||
\(611\) | 13.9889 | 0.565930 | ||||||||
\(612\) | 20.5210 | 0.829511 | ||||||||
\(613\) | −8.09532 | −0.326967 | −0.163484 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163484 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(614\) | −28.3807 | −1.14535 | ||||||||
\(615\) | −0.467175 | −0.0188383 | ||||||||
\(616\) | 5.28146 | 0.212796 | ||||||||
\(617\) | −3.35191 | −0.134943 | −0.0674715 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674715 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(618\) | 3.24318 | 0.130460 | ||||||||
\(619\) | 8.03530 | 0.322966 | 0.161483 | − | 0.986876i | \(-0.448372\pi\) | ||||
0.161483 | + | 0.986876i | \(0.448372\pi\) | |||||||
\(620\) | −0.294877 | −0.0118425 | ||||||||
\(621\) | 34.7801 | 1.39568 | ||||||||
\(622\) | 38.3340 | 1.53705 | ||||||||
\(623\) | −21.5167 | −0.862050 | ||||||||
\(624\) | −8.81406 | −0.352845 | ||||||||
\(625\) | 24.7584 | 0.990338 | ||||||||
\(626\) | 4.25231 | 0.169957 | ||||||||
\(627\) | −16.8653 | −0.673535 | ||||||||
\(628\) | −36.4498 | −1.45450 | ||||||||
\(629\) | −30.0289 | −1.19733 | ||||||||
\(630\) | 0.854822 | 0.0340569 | ||||||||
\(631\) | 3.99405 | 0.159001 | 0.0795004 | − | 0.996835i | \(-0.474668\pi\) | ||||
0.0795004 | + | 0.996835i | \(0.474668\pi\) | |||||||
\(632\) | 12.3851 | 0.492653 | ||||||||
\(633\) | 18.6762 | 0.742312 | ||||||||
\(634\) | 15.2344 | 0.605035 | ||||||||
\(635\) | 1.33926 | 0.0531467 | ||||||||
\(636\) | −5.55802 | −0.220390 | ||||||||
\(637\) | −10.9636 | −0.434395 | ||||||||
\(638\) | −21.0153 | −0.832005 | ||||||||
\(639\) | −10.6947 | −0.423078 | ||||||||
\(640\) | −0.819902 | −0.0324095 | ||||||||
\(641\) | −6.96404 | −0.275063 | −0.137531 | − | 0.990497i | \(-0.543917\pi\) | ||||
−0.137531 | + | 0.990497i | \(0.543917\pi\) | |||||||
\(642\) | 2.17306 | 0.0857640 | ||||||||
\(643\) | 2.90942 | 0.114736 | 0.0573681 | − | 0.998353i | \(-0.481729\pi\) | ||||
0.0573681 | + | 0.998353i | \(0.481729\pi\) | |||||||
\(644\) | −19.1181 | −0.753360 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −52.4715 | −2.06447 | ||||||||
\(647\) | −5.91505 | −0.232545 | −0.116272 | − | 0.993217i | \(-0.537095\pi\) | ||||
−0.116272 | + | 0.993217i | \(0.537095\pi\) | |||||||
\(648\) | 2.95710 | 0.116166 | ||||||||
\(649\) | −58.1185 | −2.28135 | ||||||||
\(650\) | 21.9581 | 0.861268 | ||||||||
\(651\) | −1.81913 | −0.0712972 | ||||||||
\(652\) | −27.6448 | −1.08265 | ||||||||
\(653\) | 40.6003 | 1.58881 | 0.794406 | − | 0.607386i | \(-0.207782\pi\) | ||||
0.794406 | + | 0.607386i | \(0.207782\pi\) | |||||||
\(654\) | −8.63383 | −0.337609 | ||||||||
\(655\) | −0.422682 | −0.0165156 | ||||||||
\(656\) | 21.3852 | 0.834952 | ||||||||
\(657\) | 35.5028 | 1.38510 | ||||||||
\(658\) | −17.1645 | −0.669141 | ||||||||
\(659\) | −37.7627 | −1.47102 | −0.735512 | − | 0.677511i | \(-0.763058\pi\) | ||||
−0.735512 | + | 0.677511i | \(0.763058\pi\) | |||||||
\(660\) | 0.672444 | 0.0261748 | ||||||||
\(661\) | −16.6857 | −0.648998 | −0.324499 | − | 0.945886i | \(-0.605196\pi\) | ||||
−0.324499 | + | 0.945886i | \(0.605196\pi\) | |||||||
\(662\) | 7.54346 | 0.293185 | ||||||||
\(663\) | −10.5187 | −0.408511 | ||||||||
\(664\) | −1.73146 | −0.0671938 | ||||||||
\(665\) | −0.958416 | −0.0371658 | ||||||||
\(666\) | 23.8272 | 0.923285 | ||||||||
\(667\) | −21.3455 | −0.826500 | ||||||||
\(668\) | −11.2114 | −0.433782 | ||||||||
\(669\) | 4.09189 | 0.158201 | ||||||||
\(670\) | 0.504807 | 0.0195024 | ||||||||
\(671\) | 42.0103 | 1.62179 | ||||||||
\(672\) | 8.79146 | 0.339138 | ||||||||
\(673\) | 18.0195 | 0.694599 | 0.347300 | − | 0.937754i | \(-0.387099\pi\) | ||||
0.347300 | + | 0.937754i | \(0.387099\pi\) | |||||||
\(674\) | −57.6245 | −2.21961 | ||||||||
\(675\) | 21.4921 | 0.827233 | ||||||||
\(676\) | −11.7916 | −0.453522 | ||||||||
\(677\) | 11.6551 | 0.447940 | 0.223970 | − | 0.974596i | \(-0.428098\pi\) | ||||
0.223970 | + | 0.974596i | \(0.428098\pi\) | |||||||
\(678\) | −19.8568 | −0.762596 | ||||||||
\(679\) | 8.43833 | 0.323833 | ||||||||
\(680\) | −0.587035 | −0.0225118 | ||||||||
\(681\) | −6.92664 | −0.265429 | ||||||||
\(682\) | 11.8080 | 0.452152 | ||||||||
\(683\) | −40.1996 | −1.53820 | −0.769098 | − | 0.639131i | \(-0.779294\pi\) | ||||
−0.769098 | + | 0.639131i | \(0.779294\pi\) | |||||||
\(684\) | 18.2561 | 0.698041 | ||||||||
\(685\) | −1.49873 | −0.0572636 | ||||||||
\(686\) | 33.5036 | 1.27917 | ||||||||
\(687\) | −15.4624 | −0.589928 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3079 | −0.392699 | ||||||||
\(690\) | 1.55766 | 0.0592991 | ||||||||
\(691\) | 32.2000 | 1.22495 | 0.612474 | − | 0.790491i | \(-0.290175\pi\) | ||||
0.612474 | + | 0.790491i | \(0.290175\pi\) | |||||||
\(692\) | −7.24163 | −0.275286 | ||||||||
\(693\) | −15.0094 | −0.570161 | ||||||||
\(694\) | 25.1183 | 0.953478 | ||||||||
\(695\) | −0.473189 | −0.0179491 | ||||||||
\(696\) | 1.76419 | 0.0668713 | ||||||||
\(697\) | 25.5210 | 0.966678 | ||||||||
\(698\) | −50.4598 | −1.90993 | ||||||||
\(699\) | −18.4231 | −0.696827 | ||||||||
\(700\) | −11.8139 | −0.446525 | ||||||||
\(701\) | 4.57474 | 0.172786 | 0.0863928 | − | 0.996261i | \(-0.472466\pi\) | ||||
0.0863928 | + | 0.996261i | \(0.472466\pi\) | |||||||
\(702\) | 18.9994 | 0.717086 | ||||||||
\(703\) | −26.7147 | −1.00757 | ||||||||
\(704\) | −17.6471 | −0.665099 | ||||||||
\(705\) | 0.613212 | 0.0230949 | ||||||||
\(706\) | 0.276840 | 0.0104190 | ||||||||
\(707\) | −17.1037 | −0.643252 | ||||||||
\(708\) | −17.3878 | −0.653472 | ||||||||
\(709\) | 24.4283 | 0.917425 | 0.458713 | − | 0.888585i | \(-0.348311\pi\) | ||||
0.458713 | + | 0.888585i | \(0.348311\pi\) | |||||||
\(710\) | −1.09033 | −0.0409194 | ||||||||
\(711\) | −35.1973 | −1.32000 | ||||||||
\(712\) | −11.7246 | −0.439398 | ||||||||
\(713\) | 11.9935 | 0.449160 | ||||||||
\(714\) | 12.9065 | 0.483013 | ||||||||
\(715\) | 1.24711 | 0.0466392 | ||||||||
\(716\) | −8.95232 | −0.334564 | ||||||||
\(717\) | −8.89975 | −0.332367 | ||||||||
\(718\) | −48.9331 | −1.82617 | ||||||||
\(719\) | −38.7132 | −1.44376 | −0.721879 | − | 0.692019i | \(-0.756721\pi\) | ||||
−0.721879 | + | 0.692019i | \(0.756721\pi\) | |||||||
\(720\) | 1.39794 | 0.0520982 | ||||||||
\(721\) | −3.23608 | −0.120518 | ||||||||
\(722\) | −10.8224 | −0.402768 | ||||||||
\(723\) | 10.1995 | 0.379322 | ||||||||
\(724\) | 1.51718 | 0.0563856 | ||||||||
\(725\) | −13.1903 | −0.489876 | ||||||||
\(726\) | −10.1950 | −0.378373 | ||||||||
\(727\) | 24.9476 | 0.925256 | 0.462628 | − | 0.886553i | \(-0.346907\pi\) | ||||
0.462628 | + | 0.886553i | \(0.346907\pi\) | |||||||
\(728\) | 2.93044 | 0.108609 | ||||||||
\(729\) | 2.02324 | 0.0749347 | ||||||||
\(730\) | 3.61952 | 0.133964 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 12.5686 | 0.464548 | ||||||||
\(733\) | −42.6308 | −1.57460 | −0.787302 | − | 0.616568i | \(-0.788523\pi\) | ||||
−0.787302 | + | 0.616568i | \(0.788523\pi\) | |||||||
\(734\) | −38.6293 | −1.42583 | ||||||||
\(735\) | −0.480598 | −0.0177271 | ||||||||
\(736\) | −57.9621 | −2.13651 | ||||||||
\(737\) | −8.86367 | −0.326497 | ||||||||
\(738\) | −20.2503 | −0.745424 | ||||||||
\(739\) | −35.3259 | −1.29948 | −0.649741 | − | 0.760155i | \(-0.725123\pi\) | ||||
−0.649741 | + | 0.760155i | \(0.725123\pi\) | |||||||
\(740\) | 1.06516 | 0.0391559 | ||||||||
\(741\) | −9.35776 | −0.343766 | ||||||||
\(742\) | 12.6478 | 0.464317 | ||||||||
\(743\) | −1.09759 | −0.0402668 | −0.0201334 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201334 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(744\) | −0.991253 | −0.0363411 | ||||||||
\(745\) | −1.17527 | −0.0430586 | ||||||||
\(746\) | −64.4672 | −2.36031 | ||||||||
\(747\) | 4.92065 | 0.180037 | ||||||||
\(748\) | −36.7345 | −1.34315 | ||||||||
\(749\) | −2.16831 | −0.0792282 | ||||||||
\(750\) | 1.92821 | 0.0704082 | ||||||||
\(751\) | −0.238664 | −0.00870899 | −0.00435449 | − | 0.999991i | \(-0.501386\pi\) | ||||
−0.00435449 | + | 0.999991i | \(0.501386\pi\) | |||||||
\(752\) | −28.0701 | −1.02361 | ||||||||
\(753\) | −9.19240 | −0.334990 | ||||||||
\(754\) | −11.6604 | −0.424648 | ||||||||
\(755\) | 2.09186 | 0.0761306 | ||||||||
\(756\) | −10.2221 | −0.371773 | ||||||||
\(757\) | 11.4593 | 0.416494 | 0.208247 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208247 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(758\) | 41.3154 | 1.50064 | ||||||||
\(759\) | −27.3502 | −0.992750 | ||||||||
\(760\) | −0.522247 | −0.0189439 | ||||||||
\(761\) | −2.43813 | −0.0883821 | −0.0441910 | − | 0.999023i | \(-0.514071\pi\) | ||||
−0.0441910 | + | 0.999023i | \(0.514071\pi\) | |||||||
\(762\) | −16.0446 | −0.581235 | ||||||||
\(763\) | 8.61493 | 0.311881 | ||||||||
\(764\) | −1.83775 | −0.0664876 | ||||||||
\(765\) | 1.66830 | 0.0603175 | ||||||||
\(766\) | 34.6989 | 1.25372 | ||||||||
\(767\) | −32.2472 | −1.16438 | ||||||||
\(768\) | 16.5837 | 0.598412 | ||||||||
\(769\) | −20.4390 | −0.737048 | −0.368524 | − | 0.929618i | \(-0.620137\pi\) | ||||
−0.368524 | + | 0.929618i | \(0.620137\pi\) | |||||||
\(770\) | −1.53021 | −0.0551451 | ||||||||
\(771\) | 13.7486 | 0.495144 | ||||||||
\(772\) | 6.04672 | 0.217626 | ||||||||
\(773\) | 37.8123 | 1.36002 | 0.680008 | − | 0.733205i | \(-0.261976\pi\) | ||||
0.680008 | + | 0.733205i | \(0.261976\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.41131 | 0.266222 | ||||||||
\(776\) | 4.59810 | 0.165062 | ||||||||
\(777\) | 6.57106 | 0.235736 | ||||||||
\(778\) | −15.8126 | −0.566908 | ||||||||
\(779\) | 22.7044 | 0.813468 | ||||||||
\(780\) | 0.373108 | 0.0133594 | ||||||||
\(781\) | 19.1446 | 0.685048 | ||||||||
\(782\) | −85.0925 | −3.04290 | ||||||||
\(783\) | −11.4130 | −0.407867 | ||||||||
\(784\) | 21.9996 | 0.785700 | ||||||||
\(785\) | −2.96327 | −0.105764 | ||||||||
\(786\) | 5.06384 | 0.180621 | ||||||||
\(787\) | −44.4684 | −1.58513 | −0.792564 | − | 0.609789i | \(-0.791254\pi\) | ||||
−0.792564 | + | 0.609789i | \(0.791254\pi\) | |||||||
\(788\) | 28.2794 | 1.00741 | ||||||||
\(789\) | 5.46329 | 0.194498 | ||||||||
\(790\) | −3.58837 | −0.127668 | ||||||||
\(791\) | 19.8133 | 0.704481 | ||||||||
\(792\) | −8.17872 | −0.290618 | ||||||||
\(793\) | 23.3096 | 0.827748 | ||||||||
\(794\) | −31.7223 | −1.12578 | ||||||||
\(795\) | −0.451852 | −0.0160255 | ||||||||
\(796\) | 27.9538 | 0.990794 | ||||||||
\(797\) | 49.3365 | 1.74759 | 0.873794 | − | 0.486296i | \(-0.161652\pi\) | ||||
0.873794 | + | 0.486296i | \(0.161652\pi\) | |||||||
\(798\) | 11.4821 | 0.406460 | ||||||||
\(799\) | −33.4987 | −1.18510 | ||||||||
\(800\) | −35.8173 | −1.26633 | ||||||||
\(801\) | 33.3202 | 1.17731 | ||||||||
\(802\) | −10.7386 | −0.379194 | ||||||||
\(803\) | −63.5534 | −2.24275 | ||||||||
\(804\) | −2.65181 | −0.0935223 | ||||||||
\(805\) | −1.55425 | −0.0547802 | ||||||||
\(806\) | 6.55171 | 0.230774 | ||||||||
\(807\) | −15.4561 | −0.544080 | ||||||||
\(808\) | −9.31993 | −0.327874 | ||||||||
\(809\) | −8.20188 | −0.288363 | −0.144181 | − | 0.989551i | \(-0.546055\pi\) | ||||
−0.144181 | + | 0.989551i | \(0.546055\pi\) | |||||||
\(810\) | −0.856768 | −0.0301038 | ||||||||
\(811\) | −41.7992 | −1.46777 | −0.733884 | − | 0.679275i | \(-0.762295\pi\) | ||||
−0.733884 | + | 0.679275i | \(0.762295\pi\) | |||||||
\(812\) | 6.27357 | 0.220159 | ||||||||
\(813\) | −5.12113 | −0.179606 | ||||||||
\(814\) | −42.6530 | −1.49499 | ||||||||
\(815\) | −2.24745 | −0.0787246 | ||||||||
\(816\) | 21.1068 | 0.738884 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 67.2990 | 2.35305 | ||||||||
\(819\) | −8.32803 | −0.291005 | ||||||||
\(820\) | −0.905256 | −0.0316129 | ||||||||
\(821\) | −21.6404 | −0.755255 | −0.377627 | − | 0.925958i | \(-0.623260\pi\) | ||||
−0.377627 | + | 0.925958i | \(0.623260\pi\) | |||||||
\(822\) | 17.9552 | 0.626259 | ||||||||
\(823\) | 7.82315 | 0.272698 | 0.136349 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136349 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(824\) | −1.76336 | −0.0614296 | ||||||||
\(825\) | −16.9009 | −0.588414 | ||||||||
\(826\) | 39.5676 | 1.37673 | ||||||||
\(827\) | 2.98386 | 0.103759 | 0.0518794 | − | 0.998653i | \(-0.483479\pi\) | ||||
0.0518794 | + | 0.998653i | \(0.483479\pi\) | |||||||
\(828\) | 29.6058 | 1.02887 | ||||||||
\(829\) | 2.03260 | 0.0705950 | 0.0352975 | − | 0.999377i | \(-0.488762\pi\) | ||||
0.0352975 | + | 0.999377i | \(0.488762\pi\) | |||||||
\(830\) | 0.501661 | 0.0174129 | ||||||||
\(831\) | −15.0118 | −0.520755 | ||||||||
\(832\) | −9.79155 | −0.339461 | ||||||||
\(833\) | 26.2543 | 0.909657 | ||||||||
\(834\) | 5.66892 | 0.196299 | ||||||||
\(835\) | −0.911457 | −0.0315423 | ||||||||
\(836\) | −32.6802 | −1.13027 | ||||||||
\(837\) | 6.41268 | 0.221655 | ||||||||
\(838\) | 30.4788 | 1.05287 | ||||||||
\(839\) | −3.18181 | −0.109848 | −0.0549242 | − | 0.998491i | \(-0.517492\pi\) | ||||
−0.0549242 | + | 0.998491i | \(0.517492\pi\) | |||||||
\(840\) | 0.128458 | 0.00443221 | ||||||||
\(841\) | −21.9955 | −0.758467 | ||||||||
\(842\) | 25.5055 | 0.878979 | ||||||||
\(843\) | −5.46893 | −0.188360 | ||||||||
\(844\) | 36.1893 | 1.24569 | ||||||||
\(845\) | −0.958622 | −0.0329776 | ||||||||
\(846\) | 26.5804 | 0.913853 | ||||||||
\(847\) | 10.1727 | 0.349539 | ||||||||
\(848\) | 20.6838 | 0.710284 | ||||||||
\(849\) | −5.83339 | −0.200201 | ||||||||
\(850\) | −52.5824 | −1.80356 | ||||||||
\(851\) | −43.3230 | −1.48509 | ||||||||
\(852\) | 5.72765 | 0.196226 | ||||||||
\(853\) | −56.3145 | −1.92817 | −0.964085 | − | 0.265592i | \(-0.914433\pi\) | ||||
−0.964085 | + | 0.265592i | \(0.914433\pi\) | |||||||
\(854\) | −28.6011 | −0.978708 | ||||||||
\(855\) | 1.48417 | 0.0507577 | ||||||||
\(856\) | −1.18152 | −0.0403836 | ||||||||
\(857\) | −0.562224 | −0.0192052 | −0.00960260 | − | 0.999954i | \(-0.503057\pi\) | ||||
−0.00960260 | + | 0.999954i | \(0.503057\pi\) | |||||||
\(858\) | −14.9407 | −0.510066 | ||||||||
\(859\) | −44.0608 | −1.50334 | −0.751668 | − | 0.659542i | \(-0.770750\pi\) | ||||
−0.751668 | + | 0.659542i | \(0.770750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.58462 | −0.190323 | ||||||||
\(862\) | −33.3422 | −1.13564 | ||||||||
\(863\) | 18.2385 | 0.620845 | 0.310422 | − | 0.950599i | \(-0.399529\pi\) | ||||
0.310422 | + | 0.950599i | \(0.399529\pi\) | |||||||
\(864\) | −30.9912 | −1.05434 | ||||||||
\(865\) | −0.588725 | −0.0200173 | ||||||||
\(866\) | −16.5377 | −0.561973 | ||||||||
\(867\) | 11.4870 | 0.390119 | ||||||||
\(868\) | −3.52496 | −0.119645 | ||||||||
\(869\) | 63.0064 | 2.13735 | ||||||||
\(870\) | −0.511143 | −0.0173294 | ||||||||
\(871\) | −4.91804 | −0.166641 | ||||||||
\(872\) | 4.69433 | 0.158970 | ||||||||
\(873\) | −13.0674 | −0.442263 | ||||||||
\(874\) | −75.7011 | −2.56063 | ||||||||
\(875\) | −1.92399 | −0.0650427 | ||||||||
\(876\) | −19.0138 | −0.642416 | ||||||||
\(877\) | 39.1775 | 1.32293 | 0.661465 | − | 0.749976i | \(-0.269935\pi\) | ||||
0.661465 | + | 0.749976i | \(0.269935\pi\) | |||||||
\(878\) | 58.5169 | 1.97485 | ||||||||
\(879\) | 7.17197 | 0.241905 | ||||||||
\(880\) | −2.50245 | −0.0843575 | ||||||||
\(881\) | −55.5131 | −1.87028 | −0.935142 | − | 0.354273i | \(-0.884729\pi\) | ||||
−0.935142 | + | 0.354273i | \(0.884729\pi\) | |||||||
\(882\) | −20.8321 | −0.701453 | ||||||||
\(883\) | −10.7984 | −0.363395 | −0.181698 | − | 0.983354i | \(-0.558159\pi\) | ||||
−0.181698 | + | 0.983354i | \(0.558159\pi\) | |||||||
\(884\) | −20.3823 | −0.685530 | ||||||||
\(885\) | −1.41358 | −0.0475169 | ||||||||
\(886\) | 25.5083 | 0.856967 | ||||||||
\(887\) | 44.6297 | 1.49852 | 0.749259 | − | 0.662277i | \(-0.230410\pi\) | ||||
0.749259 | + | 0.662277i | \(0.230410\pi\) | |||||||
\(888\) | 3.58061 | 0.120157 | ||||||||
\(889\) | 16.0095 | 0.536941 | ||||||||
\(890\) | 3.39700 | 0.113868 | ||||||||
\(891\) | 15.0436 | 0.503979 | ||||||||
\(892\) | 7.92894 | 0.265481 | ||||||||
\(893\) | −29.8016 | −0.997273 | ||||||||
\(894\) | 14.0800 | 0.470907 | ||||||||
\(895\) | −0.727799 | −0.0243276 | ||||||||
\(896\) | −9.80113 | −0.327433 | ||||||||
\(897\) | −15.1754 | −0.506691 | ||||||||
\(898\) | −17.3639 | −0.579442 | ||||||||
\(899\) | −3.93564 | −0.131261 | ||||||||
\(900\) | 18.2947 | 0.609824 | ||||||||
\(901\) | 24.6839 | 0.822341 | ||||||||
\(902\) | 36.2500 | 1.20699 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.7964 | 0.359083 | ||||||||
\(905\) | 0.123343 | 0.00410005 | ||||||||
\(906\) | −25.0610 | −0.832596 | ||||||||
\(907\) | 34.9966 | 1.16204 | 0.581021 | − | 0.813888i | \(-0.302653\pi\) | ||||
0.581021 | + | 0.813888i | \(0.302653\pi\) | |||||||
\(908\) | −13.4219 | −0.445422 | ||||||||
\(909\) | 26.4864 | 0.878497 | ||||||||
\(910\) | −0.849044 | −0.0281455 | ||||||||
\(911\) | −27.3418 | −0.905873 | −0.452936 | − | 0.891543i | \(-0.649624\pi\) | ||||
−0.452936 | + | 0.891543i | \(0.649624\pi\) | |||||||
\(912\) | 18.7773 | 0.621778 | ||||||||
\(913\) | −8.80843 | −0.291517 | ||||||||
\(914\) | 3.25969 | 0.107821 | ||||||||
\(915\) | 1.02179 | 0.0337794 | ||||||||
\(916\) | −29.9619 | −0.989967 | ||||||||
\(917\) | −5.05275 | −0.166857 | ||||||||
\(918\) | −45.4973 | −1.50163 | ||||||||
\(919\) | 42.0714 | 1.38781 | 0.693904 | − | 0.720068i | \(-0.255889\pi\) | ||||
0.693904 | + | 0.720068i | \(0.255889\pi\) | |||||||
\(920\) | −0.846921 | −0.0279222 | ||||||||
\(921\) | 12.1204 | 0.399380 | ||||||||
\(922\) | 30.0145 | 0.988475 | ||||||||
\(923\) | 10.6225 | 0.349643 | ||||||||
\(924\) | 8.03840 | 0.264444 | ||||||||
\(925\) | −26.7712 | −0.880231 | ||||||||
\(926\) | −69.8311 | −2.29479 | ||||||||
\(927\) | 5.01131 | 0.164593 | ||||||||
\(928\) | 19.0201 | 0.624366 | ||||||||
\(929\) | −37.2406 | −1.22183 | −0.610913 | − | 0.791698i | \(-0.709197\pi\) | ||||
−0.610913 | + | 0.791698i | \(0.709197\pi\) | |||||||
\(930\) | 0.287198 | 0.00941761 | ||||||||
\(931\) | 23.3567 | 0.765484 | ||||||||
\(932\) | −35.6989 | −1.16936 | ||||||||
\(933\) | −16.3711 | −0.535966 | ||||||||
\(934\) | −46.9934 | −1.53767 | ||||||||
\(935\) | −2.98641 | −0.0976662 | ||||||||
\(936\) | −4.53799 | −0.148329 | ||||||||
\(937\) | 1.17331 | 0.0383302 | 0.0191651 | − | 0.999816i | \(-0.493899\pi\) | ||||
0.0191651 | + | 0.999816i | \(0.493899\pi\) | |||||||
\(938\) | 6.03447 | 0.197033 | ||||||||
\(939\) | −1.81601 | −0.0592633 | ||||||||
\(940\) | 1.18823 | 0.0387559 | ||||||||
\(941\) | 44.7514 | 1.45886 | 0.729428 | − | 0.684058i | \(-0.239786\pi\) | ||||
0.729428 | + | 0.684058i | \(0.239786\pi\) | |||||||
\(942\) | 35.5007 | 1.15667 | ||||||||
\(943\) | 36.8194 | 1.19900 | ||||||||
\(944\) | 64.7073 | 2.10604 | ||||||||
\(945\) | −0.831027 | −0.0270333 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.6885 | −1.02974 | −0.514868 | − | 0.857269i | \(-0.672159\pi\) | ||||
−0.514868 | + | 0.857269i | \(0.672159\pi\) | |||||||
\(948\) | 18.8501 | 0.612224 | ||||||||
\(949\) | −35.2628 | −1.14468 | ||||||||
\(950\) | −46.7791 | −1.51771 | ||||||||
\(951\) | −6.50607 | −0.210974 | ||||||||
\(952\) | −7.01743 | −0.227436 | ||||||||
\(953\) | −22.2967 | −0.722261 | −0.361131 | − | 0.932515i | \(-0.617609\pi\) | ||||
−0.361131 | + | 0.932515i | \(0.617609\pi\) | |||||||
\(954\) | −19.5861 | −0.634123 | ||||||||
\(955\) | −0.149404 | −0.00483461 | ||||||||
\(956\) | −17.2453 | −0.557751 | ||||||||
\(957\) | 8.97491 | 0.290118 | ||||||||
\(958\) | 45.8489 | 1.48131 | ||||||||
\(959\) | −17.9159 | −0.578534 | ||||||||
\(960\) | −0.429219 | −0.0138530 | ||||||||
\(961\) | −28.7887 | −0.928667 | ||||||||
\(962\) | −23.6661 | −0.763027 | ||||||||
\(963\) | 3.35778 | 0.108203 | ||||||||
\(964\) | 19.7637 | 0.636547 | ||||||||
\(965\) | 0.491582 | 0.0158246 | ||||||||
\(966\) | 18.6203 | 0.599099 | ||||||||
\(967\) | −6.29057 | −0.202291 | −0.101146 | − | 0.994872i | \(-0.532251\pi\) | ||||
−0.101146 | + | 0.994872i | \(0.532251\pi\) | |||||||
\(968\) | 5.54318 | 0.178165 | ||||||||
\(969\) | 22.4087 | 0.719873 | ||||||||
\(970\) | −1.33222 | −0.0427750 | ||||||||
\(971\) | −25.9204 | −0.831825 | −0.415913 | − | 0.909405i | \(-0.636538\pi\) | ||||
−0.415913 | + | 0.909405i | \(0.636538\pi\) | |||||||
\(972\) | 24.7054 | 0.792426 | ||||||||
\(973\) | −5.65651 | −0.181339 | ||||||||
\(974\) | 4.17643 | 0.133821 | ||||||||
\(975\) | −9.37753 | −0.300321 | ||||||||
\(976\) | −46.7730 | −1.49717 | ||||||||
\(977\) | −17.6307 | −0.564056 | −0.282028 | − | 0.959406i | \(-0.591007\pi\) | ||||
−0.282028 | + | 0.959406i | \(0.591007\pi\) | |||||||
\(978\) | 26.9250 | 0.860965 | ||||||||
\(979\) | −59.6463 | −1.90630 | ||||||||
\(980\) | −0.931265 | −0.0297482 | ||||||||
\(981\) | −13.3408 | −0.425940 | ||||||||
\(982\) | 32.6448 | 1.04174 | ||||||||
\(983\) | 45.8216 | 1.46148 | 0.730741 | − | 0.682655i | \(-0.239175\pi\) | ||||
0.730741 | + | 0.682655i | \(0.239175\pi\) | |||||||
\(984\) | −3.04309 | −0.0970103 | ||||||||
\(985\) | 2.29904 | 0.0732534 | ||||||||
\(986\) | 27.9229 | 0.889246 | ||||||||
\(987\) | 7.33034 | 0.233327 | ||||||||
\(988\) | −18.1327 | −0.576880 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.36964 | 0.0753122 | ||||||||
\(991\) | 39.0259 | 1.23970 | 0.619850 | − | 0.784721i | \(-0.287194\pi\) | ||||
0.619850 | + | 0.784721i | \(0.287194\pi\) | |||||||
\(992\) | −10.6869 | −0.339310 | ||||||||
\(993\) | −3.22154 | −0.102233 | ||||||||
\(994\) | −13.0339 | −0.413409 | ||||||||
\(995\) | 2.27256 | 0.0720451 | ||||||||
\(996\) | −2.63529 | −0.0835024 | ||||||||
\(997\) | −6.51911 | −0.206462 | −0.103231 | − | 0.994657i | \(-0.532918\pi\) | ||||
−0.103231 | + | 0.994657i | \(0.532918\pi\) | |||||||
\(998\) | −0.805947 | −0.0255118 | ||||||||
\(999\) | −23.1639 | −0.732875 |
(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 | 1849.2.a.q.1.4 | ✓ | 20 | |
43.42 | odd | 2 | inner | 1849.2.a.q.1.17 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.q.1.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1849.2.a.q.1.17 | yes | 20 | 43.42 | odd | 2 | inner |