Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, 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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.670430\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | 0.670430 | 0.387073 | 0.193536 | − | 0.981093i | \(-0.438004\pi\) | ||||
0.193536 | + | 0.981093i | \(0.438004\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.45227 | 0.649474 | 0.324737 | − | 0.945804i | \(-0.394724\pi\) | ||||
0.324737 | + | 0.945804i | \(0.394724\pi\) | |||||||
\(6\) | −0.670430 | −0.273702 | ||||||||
\(7\) | 0.581735 | 0.219875 | 0.109938 | − | 0.993938i | \(-0.464935\pi\) | ||||
0.109938 | + | 0.993938i | \(0.464935\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.55052 | −0.850175 | ||||||||
\(10\) | −1.45227 | −0.459247 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.670430 | 0.193536 | ||||||||
\(13\) | −1.74957 | −0.485244 | −0.242622 | − | 0.970121i | \(-0.578007\pi\) | ||||
−0.242622 | + | 0.970121i | \(0.578007\pi\) | |||||||
\(14\) | −0.581735 | −0.155475 | ||||||||
\(15\) | 0.973643 | 0.251394 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.878022 | 0.212952 | 0.106476 | − | 0.994315i | \(-0.466043\pi\) | ||||
0.106476 | + | 0.994315i | \(0.466043\pi\) | |||||||
\(18\) | 2.55052 | 0.601164 | ||||||||
\(19\) | −1.44313 | −0.331077 | −0.165538 | − | 0.986203i | \(-0.552936\pi\) | ||||
−0.165538 | + | 0.986203i | \(0.552936\pi\) | |||||||
\(20\) | 1.45227 | 0.324737 | ||||||||
\(21\) | 0.390013 | 0.0851077 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.79749 | 0.374803 | 0.187402 | − | 0.982283i | \(-0.439993\pi\) | ||||
0.187402 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(24\) | −0.670430 | −0.136851 | ||||||||
\(25\) | −2.89092 | −0.578184 | ||||||||
\(26\) | 1.74957 | 0.343119 | ||||||||
\(27\) | −3.72124 | −0.716152 | ||||||||
\(28\) | 0.581735 | 0.109938 | ||||||||
\(29\) | −4.72877 | −0.878111 | −0.439055 | − | 0.898460i | \(-0.644687\pi\) | ||||
−0.439055 | + | 0.898460i | \(0.644687\pi\) | |||||||
\(30\) | −0.973643 | −0.177762 | ||||||||
\(31\) | −7.21035 | −1.29502 | −0.647509 | − | 0.762058i | \(-0.724189\pi\) | ||||
−0.647509 | + | 0.762058i | \(0.724189\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.670430 | 0.116707 | ||||||||
\(34\) | −0.878022 | −0.150580 | ||||||||
\(35\) | 0.844835 | 0.142803 | ||||||||
\(36\) | −2.55052 | −0.425087 | ||||||||
\(37\) | 9.47907 | 1.55835 | 0.779175 | − | 0.626806i | \(-0.215638\pi\) | ||||
0.779175 | + | 0.626806i | \(0.215638\pi\) | |||||||
\(38\) | 1.44313 | 0.234107 | ||||||||
\(39\) | −1.17297 | −0.187825 | ||||||||
\(40\) | −1.45227 | −0.229624 | ||||||||
\(41\) | 2.09545 | 0.327254 | 0.163627 | − | 0.986522i | \(-0.447681\pi\) | ||||
0.163627 | + | 0.986522i | \(0.447681\pi\) | |||||||
\(42\) | −0.390013 | −0.0601803 | ||||||||
\(43\) | 3.72420 | 0.567935 | 0.283968 | − | 0.958834i | \(-0.408349\pi\) | ||||
0.283968 | + | 0.958834i | \(0.408349\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −3.70404 | −0.552166 | ||||||||
\(46\) | −1.79749 | −0.265026 | ||||||||
\(47\) | −7.30278 | −1.06522 | −0.532610 | − | 0.846361i | \(-0.678789\pi\) | ||||
−0.532610 | + | 0.846361i | \(0.678789\pi\) | |||||||
\(48\) | 0.670430 | 0.0967682 | ||||||||
\(49\) | −6.66158 | −0.951655 | ||||||||
\(50\) | 2.89092 | 0.408838 | ||||||||
\(51\) | 0.588652 | 0.0824278 | ||||||||
\(52\) | −1.74957 | −0.242622 | ||||||||
\(53\) | −5.86818 | −0.806056 | −0.403028 | − | 0.915188i | \(-0.632042\pi\) | ||||
−0.403028 | + | 0.915188i | \(0.632042\pi\) | |||||||
\(54\) | 3.72124 | 0.506396 | ||||||||
\(55\) | 1.45227 | 0.195824 | ||||||||
\(56\) | −0.581735 | −0.0777376 | ||||||||
\(57\) | −0.967517 | −0.128151 | ||||||||
\(58\) | 4.72877 | 0.620918 | ||||||||
\(59\) | −2.37342 | −0.308993 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(60\) | 0.973643 | 0.125697 | ||||||||
\(61\) | 3.41206 | 0.436869 | 0.218435 | − | 0.975852i | \(-0.429905\pi\) | ||||
0.218435 | + | 0.975852i | \(0.429905\pi\) | |||||||
\(62\) | 7.21035 | 0.915716 | ||||||||
\(63\) | −1.48373 | −0.186932 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.54085 | −0.315153 | ||||||||
\(66\) | −0.670430 | −0.0825242 | ||||||||
\(67\) | 2.44924 | 0.299222 | 0.149611 | − | 0.988745i | \(-0.452198\pi\) | ||||
0.149611 | + | 0.988745i | \(0.452198\pi\) | |||||||
\(68\) | 0.878022 | 0.106476 | ||||||||
\(69\) | 1.20509 | 0.145076 | ||||||||
\(70\) | −0.844835 | −0.100977 | ||||||||
\(71\) | −4.12441 | −0.489477 | −0.244739 | − | 0.969589i | \(-0.578702\pi\) | ||||
−0.244739 | + | 0.969589i | \(0.578702\pi\) | |||||||
\(72\) | 2.55052 | 0.300582 | ||||||||
\(73\) | −8.26236 | −0.967036 | −0.483518 | − | 0.875334i | \(-0.660641\pi\) | ||||
−0.483518 | + | 0.875334i | \(0.660641\pi\) | |||||||
\(74\) | −9.47907 | −1.10192 | ||||||||
\(75\) | −1.93816 | −0.223799 | ||||||||
\(76\) | −1.44313 | −0.165538 | ||||||||
\(77\) | 0.581735 | 0.0662949 | ||||||||
\(78\) | 1.17297 | 0.132812 | ||||||||
\(79\) | 11.2789 | 1.26898 | 0.634489 | − | 0.772932i | \(-0.281211\pi\) | ||||
0.634489 | + | 0.772932i | \(0.281211\pi\) | |||||||
\(80\) | 1.45227 | 0.162368 | ||||||||
\(81\) | 5.15674 | 0.572971 | ||||||||
\(82\) | −2.09545 | −0.231404 | ||||||||
\(83\) | −13.1640 | −1.44494 | −0.722469 | − | 0.691403i | \(-0.756993\pi\) | ||||
−0.722469 | + | 0.691403i | \(0.756993\pi\) | |||||||
\(84\) | 0.390013 | 0.0425539 | ||||||||
\(85\) | 1.27512 | 0.138306 | ||||||||
\(86\) | −3.72420 | −0.401591 | ||||||||
\(87\) | −3.17031 | −0.339893 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 10.9176 | 1.15726 | 0.578631 | − | 0.815589i | \(-0.303587\pi\) | ||||
0.578631 | + | 0.815589i | \(0.303587\pi\) | |||||||
\(90\) | 3.70404 | 0.390440 | ||||||||
\(91\) | −1.01779 | −0.106693 | ||||||||
\(92\) | 1.79749 | 0.187402 | ||||||||
\(93\) | −4.83404 | −0.501266 | ||||||||
\(94\) | 7.30278 | 0.753224 | ||||||||
\(95\) | −2.09581 | −0.215025 | ||||||||
\(96\) | −0.670430 | −0.0684255 | ||||||||
\(97\) | −17.5033 | −1.77719 | −0.888596 | − | 0.458690i | \(-0.848319\pi\) | ||||
−0.888596 | + | 0.458690i | \(0.848319\pi\) | |||||||
\(98\) | 6.66158 | 0.672922 | ||||||||
\(99\) | −2.55052 | −0.256337 | ||||||||
\(100\) | −2.89092 | −0.289092 | ||||||||
\(101\) | −15.8836 | −1.58048 | −0.790238 | − | 0.612801i | \(-0.790043\pi\) | ||||
−0.790238 | + | 0.612801i | \(0.790043\pi\) | |||||||
\(102\) | −0.588652 | −0.0582853 | ||||||||
\(103\) | −5.48887 | −0.540835 | −0.270417 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270417 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(104\) | 1.74957 | 0.171560 | ||||||||
\(105\) | 0.566403 | 0.0552752 | ||||||||
\(106\) | 5.86818 | 0.569968 | ||||||||
\(107\) | −9.85634 | −0.952848 | −0.476424 | − | 0.879216i | \(-0.658067\pi\) | ||||
−0.476424 | + | 0.879216i | \(0.658067\pi\) | |||||||
\(108\) | −3.72124 | −0.358076 | ||||||||
\(109\) | 1.41601 | 0.135629 | 0.0678146 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678146 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(110\) | −1.45227 | −0.138468 | ||||||||
\(111\) | 6.35506 | 0.603195 | ||||||||
\(112\) | 0.581735 | 0.0549688 | ||||||||
\(113\) | 4.18759 | 0.393936 | 0.196968 | − | 0.980410i | \(-0.436891\pi\) | ||||
0.196968 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(114\) | 0.967517 | 0.0906163 | ||||||||
\(115\) | 2.61044 | 0.243425 | ||||||||
\(116\) | −4.72877 | −0.439055 | ||||||||
\(117\) | 4.46233 | 0.412542 | ||||||||
\(118\) | 2.37342 | 0.218491 | ||||||||
\(119\) | 0.510776 | 0.0468228 | ||||||||
\(120\) | −0.973643 | −0.0888811 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.41206 | −0.308913 | ||||||||
\(123\) | 1.40485 | 0.126671 | ||||||||
\(124\) | −7.21035 | −0.647509 | ||||||||
\(125\) | −11.4597 | −1.02499 | ||||||||
\(126\) | 1.48373 | 0.132181 | ||||||||
\(127\) | −11.2158 | −0.995246 | −0.497623 | − | 0.867394i | \(-0.665794\pi\) | ||||
−0.497623 | + | 0.867394i | \(0.665794\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.49681 | 0.219832 | ||||||||
\(130\) | 2.54085 | 0.222847 | ||||||||
\(131\) | −4.42703 | −0.386791 | −0.193396 | − | 0.981121i | \(-0.561950\pi\) | ||||
−0.193396 | + | 0.981121i | \(0.561950\pi\) | |||||||
\(132\) | 0.670430 | 0.0583534 | ||||||||
\(133\) | −0.839519 | −0.0727955 | ||||||||
\(134\) | −2.44924 | −0.211582 | ||||||||
\(135\) | −5.40423 | −0.465122 | ||||||||
\(136\) | −0.878022 | −0.0752898 | ||||||||
\(137\) | 7.62121 | 0.651124 | 0.325562 | − | 0.945521i | \(-0.394447\pi\) | ||||
0.325562 | + | 0.945521i | \(0.394447\pi\) | |||||||
\(138\) | −1.20509 | −0.102584 | ||||||||
\(139\) | 2.70108 | 0.229102 | 0.114551 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114551 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(140\) | 0.844835 | 0.0714016 | ||||||||
\(141\) | −4.89600 | −0.412318 | ||||||||
\(142\) | 4.12441 | 0.346113 | ||||||||
\(143\) | −1.74957 | −0.146307 | ||||||||
\(144\) | −2.55052 | −0.212544 | ||||||||
\(145\) | −6.86744 | −0.570310 | ||||||||
\(146\) | 8.26236 | 0.683798 | ||||||||
\(147\) | −4.46613 | −0.368360 | ||||||||
\(148\) | 9.47907 | 0.779175 | ||||||||
\(149\) | 8.17643 | 0.669839 | 0.334920 | − | 0.942247i | \(-0.391291\pi\) | ||||
0.334920 | + | 0.942247i | \(0.391291\pi\) | |||||||
\(150\) | 1.93816 | 0.158250 | ||||||||
\(151\) | 20.6190 | 1.67795 | 0.838977 | − | 0.544168i | \(-0.183154\pi\) | ||||
0.838977 | + | 0.544168i | \(0.183154\pi\) | |||||||
\(152\) | 1.44313 | 0.117053 | ||||||||
\(153\) | −2.23942 | −0.181046 | ||||||||
\(154\) | −0.581735 | −0.0468776 | ||||||||
\(155\) | −10.4714 | −0.841080 | ||||||||
\(156\) | −1.17297 | −0.0939124 | ||||||||
\(157\) | −13.8852 | −1.10816 | −0.554079 | − | 0.832464i | \(-0.686929\pi\) | ||||
−0.554079 | + | 0.832464i | \(0.686929\pi\) | |||||||
\(158\) | −11.2789 | −0.897303 | ||||||||
\(159\) | −3.93420 | −0.312002 | ||||||||
\(160\) | −1.45227 | −0.114812 | ||||||||
\(161\) | 1.04567 | 0.0824100 | ||||||||
\(162\) | −5.15674 | −0.405152 | ||||||||
\(163\) | −8.11776 | −0.635832 | −0.317916 | − | 0.948119i | \(-0.602983\pi\) | ||||
−0.317916 | + | 0.948119i | \(0.602983\pi\) | |||||||
\(164\) | 2.09545 | 0.163627 | ||||||||
\(165\) | 0.973643 | 0.0757980 | ||||||||
\(166\) | 13.1640 | 1.02173 | ||||||||
\(167\) | −18.7088 | −1.44773 | −0.723863 | − | 0.689943i | \(-0.757635\pi\) | ||||
−0.723863 | + | 0.689943i | \(0.757635\pi\) | |||||||
\(168\) | −0.390013 | −0.0300901 | ||||||||
\(169\) | −9.93900 | −0.764538 | ||||||||
\(170\) | −1.27512 | −0.0977974 | ||||||||
\(171\) | 3.68074 | 0.281473 | ||||||||
\(172\) | 3.72420 | 0.283968 | ||||||||
\(173\) | 13.1071 | 0.996515 | 0.498257 | − | 0.867029i | \(-0.333973\pi\) | ||||
0.498257 | + | 0.867029i | \(0.333973\pi\) | |||||||
\(174\) | 3.17031 | 0.240341 | ||||||||
\(175\) | −1.68175 | −0.127128 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −1.59121 | −0.119603 | ||||||||
\(178\) | −10.9176 | −0.818308 | ||||||||
\(179\) | 6.14776 | 0.459505 | 0.229753 | − | 0.973249i | \(-0.426208\pi\) | ||||
0.229753 | + | 0.973249i | \(0.426208\pi\) | |||||||
\(180\) | −3.70404 | −0.276083 | ||||||||
\(181\) | −20.2627 | −1.50611 | −0.753056 | − | 0.657956i | \(-0.771421\pi\) | ||||
−0.753056 | + | 0.657956i | \(0.771421\pi\) | |||||||
\(182\) | 1.01779 | 0.0754434 | ||||||||
\(183\) | 2.28754 | 0.169100 | ||||||||
\(184\) | −1.79749 | −0.132513 | ||||||||
\(185\) | 13.7661 | 1.01211 | ||||||||
\(186\) | 4.83404 | 0.354449 | ||||||||
\(187\) | 0.878022 | 0.0642073 | ||||||||
\(188\) | −7.30278 | −0.532610 | ||||||||
\(189\) | −2.16477 | −0.157464 | ||||||||
\(190\) | 2.09581 | 0.152046 | ||||||||
\(191\) | 16.7647 | 1.21305 | 0.606527 | − | 0.795063i | \(-0.292562\pi\) | ||||
0.606527 | + | 0.795063i | \(0.292562\pi\) | |||||||
\(192\) | 0.670430 | 0.0483841 | ||||||||
\(193\) | 24.3605 | 1.75351 | 0.876755 | − | 0.480938i | \(-0.159704\pi\) | ||||
0.876755 | + | 0.480938i | \(0.159704\pi\) | |||||||
\(194\) | 17.5033 | 1.25667 | ||||||||
\(195\) | −1.70346 | −0.121987 | ||||||||
\(196\) | −6.66158 | −0.475827 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 2.55052 | 0.181258 | ||||||||
\(199\) | −9.12252 | −0.646678 | −0.323339 | − | 0.946283i | \(-0.604805\pi\) | ||||
−0.323339 | + | 0.946283i | \(0.604805\pi\) | |||||||
\(200\) | 2.89092 | 0.204419 | ||||||||
\(201\) | 1.64204 | 0.115821 | ||||||||
\(202\) | 15.8836 | 1.11756 | ||||||||
\(203\) | −2.75089 | −0.193075 | ||||||||
\(204\) | 0.588652 | 0.0412139 | ||||||||
\(205\) | 3.04315 | 0.212543 | ||||||||
\(206\) | 5.48887 | 0.382428 | ||||||||
\(207\) | −4.58455 | −0.318648 | ||||||||
\(208\) | −1.74957 | −0.121311 | ||||||||
\(209\) | −1.44313 | −0.0998234 | ||||||||
\(210\) | −0.566403 | −0.0390855 | ||||||||
\(211\) | 2.65293 | 0.182635 | 0.0913177 | − | 0.995822i | \(-0.470892\pi\) | ||||
0.0913177 | + | 0.995822i | \(0.470892\pi\) | |||||||
\(212\) | −5.86818 | −0.403028 | ||||||||
\(213\) | −2.76513 | −0.189463 | ||||||||
\(214\) | 9.85634 | 0.673765 | ||||||||
\(215\) | 5.40853 | 0.368859 | ||||||||
\(216\) | 3.72124 | 0.253198 | ||||||||
\(217\) | −4.19452 | −0.284742 | ||||||||
\(218\) | −1.41601 | −0.0959044 | ||||||||
\(219\) | −5.53933 | −0.374313 | ||||||||
\(220\) | 1.45227 | 0.0979118 | ||||||||
\(221\) | −1.53616 | −0.103333 | ||||||||
\(222\) | −6.35506 | −0.426523 | ||||||||
\(223\) | −20.2664 | −1.35714 | −0.678568 | − | 0.734537i | \(-0.737399\pi\) | ||||
−0.678568 | + | 0.734537i | \(0.737399\pi\) | |||||||
\(224\) | −0.581735 | −0.0388688 | ||||||||
\(225\) | 7.37336 | 0.491557 | ||||||||
\(226\) | −4.18759 | −0.278555 | ||||||||
\(227\) | 12.0399 | 0.799113 | 0.399557 | − | 0.916708i | \(-0.369164\pi\) | ||||
0.399557 | + | 0.916708i | \(0.369164\pi\) | |||||||
\(228\) | −0.967517 | −0.0640754 | ||||||||
\(229\) | 6.05609 | 0.400198 | 0.200099 | − | 0.979776i | \(-0.435874\pi\) | ||||
0.200099 | + | 0.979776i | \(0.435874\pi\) | |||||||
\(230\) | −2.61044 | −0.172127 | ||||||||
\(231\) | 0.390013 | 0.0256609 | ||||||||
\(232\) | 4.72877 | 0.310459 | ||||||||
\(233\) | 21.5358 | 1.41086 | 0.705429 | − | 0.708781i | \(-0.250754\pi\) | ||||
0.705429 | + | 0.708781i | \(0.250754\pi\) | |||||||
\(234\) | −4.46233 | −0.291711 | ||||||||
\(235\) | −10.6056 | −0.691832 | ||||||||
\(236\) | −2.37342 | −0.154497 | ||||||||
\(237\) | 7.56172 | 0.491187 | ||||||||
\(238\) | −0.510776 | −0.0331087 | ||||||||
\(239\) | −0.970463 | −0.0627741 | −0.0313870 | − | 0.999507i | \(-0.509992\pi\) | ||||
−0.0313870 | + | 0.999507i | \(0.509992\pi\) | |||||||
\(240\) | 0.973643 | 0.0628484 | ||||||||
\(241\) | 5.52821 | 0.356103 | 0.178052 | − | 0.984021i | \(-0.443021\pi\) | ||||
0.178052 | + | 0.984021i | \(0.443021\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 14.6209 | 0.937934 | ||||||||
\(244\) | 3.41206 | 0.218435 | ||||||||
\(245\) | −9.67440 | −0.618075 | ||||||||
\(246\) | −1.40485 | −0.0895701 | ||||||||
\(247\) | 2.52486 | 0.160653 | ||||||||
\(248\) | 7.21035 | 0.457858 | ||||||||
\(249\) | −8.82555 | −0.559296 | ||||||||
\(250\) | 11.4597 | 0.724777 | ||||||||
\(251\) | −5.81521 | −0.367053 | −0.183526 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183526 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(252\) | −1.48373 | −0.0934662 | ||||||||
\(253\) | 1.79749 | 0.113007 | ||||||||
\(254\) | 11.2158 | 0.703745 | ||||||||
\(255\) | 0.854880 | 0.0535347 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.8393 | −0.800894 | −0.400447 | − | 0.916320i | \(-0.631145\pi\) | ||||
−0.400447 | + | 0.916320i | \(0.631145\pi\) | |||||||
\(258\) | −2.49681 | −0.155445 | ||||||||
\(259\) | 5.51431 | 0.342643 | ||||||||
\(260\) | −2.54085 | −0.157577 | ||||||||
\(261\) | 12.0608 | 0.746547 | ||||||||
\(262\) | 4.42703 | 0.273503 | ||||||||
\(263\) | 24.7083 | 1.52358 | 0.761788 | − | 0.647826i | \(-0.224322\pi\) | ||||
0.761788 | + | 0.647826i | \(0.224322\pi\) | |||||||
\(264\) | −0.670430 | −0.0412621 | ||||||||
\(265\) | −8.52216 | −0.523512 | ||||||||
\(266\) | 0.839519 | 0.0514742 | ||||||||
\(267\) | 7.31948 | 0.447945 | ||||||||
\(268\) | 2.44924 | 0.149611 | ||||||||
\(269\) | 14.2598 | 0.869436 | 0.434718 | − | 0.900567i | \(-0.356848\pi\) | ||||
0.434718 | + | 0.900567i | \(0.356848\pi\) | |||||||
\(270\) | 5.40423 | 0.328891 | ||||||||
\(271\) | −1.52473 | −0.0926208 | −0.0463104 | − | 0.998927i | \(-0.514746\pi\) | ||||
−0.0463104 | + | 0.998927i | \(0.514746\pi\) | |||||||
\(272\) | 0.878022 | 0.0532379 | ||||||||
\(273\) | −0.682355 | −0.0412980 | ||||||||
\(274\) | −7.62121 | −0.460414 | ||||||||
\(275\) | −2.89092 | −0.174329 | ||||||||
\(276\) | 1.20509 | 0.0725381 | ||||||||
\(277\) | −12.3034 | −0.739242 | −0.369621 | − | 0.929183i | \(-0.620513\pi\) | ||||
−0.369621 | + | 0.929183i | \(0.620513\pi\) | |||||||
\(278\) | −2.70108 | −0.162000 | ||||||||
\(279\) | 18.3902 | 1.10099 | ||||||||
\(280\) | −0.844835 | −0.0504885 | ||||||||
\(281\) | 2.57833 | 0.153810 | 0.0769052 | − | 0.997038i | \(-0.475496\pi\) | ||||
0.0769052 | + | 0.997038i | \(0.475496\pi\) | |||||||
\(282\) | 4.89600 | 0.291553 | ||||||||
\(283\) | 18.5999 | 1.10565 | 0.552825 | − | 0.833297i | \(-0.313550\pi\) | ||||
0.552825 | + | 0.833297i | \(0.313550\pi\) | |||||||
\(284\) | −4.12441 | −0.244739 | ||||||||
\(285\) | −1.40509 | −0.0832305 | ||||||||
\(286\) | 1.74957 | 0.103454 | ||||||||
\(287\) | 1.21900 | 0.0719551 | ||||||||
\(288\) | 2.55052 | 0.150291 | ||||||||
\(289\) | −16.2291 | −0.954652 | ||||||||
\(290\) | 6.86744 | 0.403270 | ||||||||
\(291\) | −11.7348 | −0.687903 | ||||||||
\(292\) | −8.26236 | −0.483518 | ||||||||
\(293\) | −10.5237 | −0.614799 | −0.307399 | − | 0.951581i | \(-0.599459\pi\) | ||||
−0.307399 | + | 0.951581i | \(0.599459\pi\) | |||||||
\(294\) | 4.46613 | 0.260470 | ||||||||
\(295\) | −3.44684 | −0.200683 | ||||||||
\(296\) | −9.47907 | −0.550960 | ||||||||
\(297\) | −3.72124 | −0.215928 | ||||||||
\(298\) | −8.17643 | −0.473648 | ||||||||
\(299\) | −3.14484 | −0.181871 | ||||||||
\(300\) | −1.93816 | −0.111900 | ||||||||
\(301\) | 2.16650 | 0.124875 | ||||||||
\(302\) | −20.6190 | −1.18649 | ||||||||
\(303\) | −10.6488 | −0.611759 | ||||||||
\(304\) | −1.44313 | −0.0827692 | ||||||||
\(305\) | 4.95522 | 0.283735 | ||||||||
\(306\) | 2.23942 | 0.128019 | ||||||||
\(307\) | −24.9200 | −1.42226 | −0.711129 | − | 0.703061i | \(-0.751816\pi\) | ||||
−0.711129 | + | 0.703061i | \(0.751816\pi\) | |||||||
\(308\) | 0.581735 | 0.0331474 | ||||||||
\(309\) | −3.67990 | −0.209342 | ||||||||
\(310\) | 10.4714 | 0.594733 | ||||||||
\(311\) | −4.58415 | −0.259943 | −0.129972 | − | 0.991518i | \(-0.541489\pi\) | ||||
−0.129972 | + | 0.991518i | \(0.541489\pi\) | |||||||
\(312\) | 1.17297 | 0.0664061 | ||||||||
\(313\) | −9.44214 | −0.533701 | −0.266851 | − | 0.963738i | \(-0.585983\pi\) | ||||
−0.266851 | + | 0.963738i | \(0.585983\pi\) | |||||||
\(314\) | 13.8852 | 0.783586 | ||||||||
\(315\) | −2.15477 | −0.121408 | ||||||||
\(316\) | 11.2789 | 0.634489 | ||||||||
\(317\) | −6.26478 | −0.351865 | −0.175933 | − | 0.984402i | \(-0.556294\pi\) | ||||
−0.175933 | + | 0.984402i | \(0.556294\pi\) | |||||||
\(318\) | 3.93420 | 0.220619 | ||||||||
\(319\) | −4.72877 | −0.264760 | ||||||||
\(320\) | 1.45227 | 0.0811842 | ||||||||
\(321\) | −6.60798 | −0.368822 | ||||||||
\(322\) | −1.04567 | −0.0582726 | ||||||||
\(323\) | −1.26710 | −0.0705033 | ||||||||
\(324\) | 5.15674 | 0.286486 | ||||||||
\(325\) | 5.05787 | 0.280560 | ||||||||
\(326\) | 8.11776 | 0.449601 | ||||||||
\(327\) | 0.949336 | 0.0524984 | ||||||||
\(328\) | −2.09545 | −0.115702 | ||||||||
\(329\) | −4.24828 | −0.234215 | ||||||||
\(330\) | −0.973643 | −0.0535973 | ||||||||
\(331\) | −36.3314 | −1.99695 | −0.998477 | − | 0.0551670i | \(-0.982431\pi\) | ||||
−0.998477 | + | 0.0551670i | \(0.982431\pi\) | |||||||
\(332\) | −13.1640 | −0.722469 | ||||||||
\(333\) | −24.1766 | −1.32487 | ||||||||
\(334\) | 18.7088 | 1.02370 | ||||||||
\(335\) | 3.55695 | 0.194337 | ||||||||
\(336\) | 0.390013 | 0.0212769 | ||||||||
\(337\) | −1.20970 | −0.0658963 | −0.0329481 | − | 0.999457i | \(-0.510490\pi\) | ||||
−0.0329481 | + | 0.999457i | \(0.510490\pi\) | |||||||
\(338\) | 9.93900 | 0.540610 | ||||||||
\(339\) | 2.80749 | 0.152482 | ||||||||
\(340\) | 1.27512 | 0.0691532 | ||||||||
\(341\) | −7.21035 | −0.390463 | ||||||||
\(342\) | −3.68074 | −0.199031 | ||||||||
\(343\) | −7.94742 | −0.429121 | ||||||||
\(344\) | −3.72420 | −0.200795 | ||||||||
\(345\) | 1.75012 | 0.0942232 | ||||||||
\(346\) | −13.1071 | −0.704642 | ||||||||
\(347\) | −27.4242 | −1.47221 | −0.736104 | − | 0.676869i | \(-0.763336\pi\) | ||||
−0.736104 | + | 0.676869i | \(0.763336\pi\) | |||||||
\(348\) | −3.17031 | −0.169946 | ||||||||
\(349\) | −3.73862 | −0.200124 | −0.100062 | − | 0.994981i | \(-0.531904\pi\) | ||||
−0.100062 | + | 0.994981i | \(0.531904\pi\) | |||||||
\(350\) | 1.68175 | 0.0898933 | ||||||||
\(351\) | 6.51057 | 0.347509 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 13.7047 | 0.729428 | 0.364714 | − | 0.931120i | \(-0.381167\pi\) | ||||
0.364714 | + | 0.931120i | \(0.381167\pi\) | |||||||
\(354\) | 1.59121 | 0.0845721 | ||||||||
\(355\) | −5.98974 | −0.317902 | ||||||||
\(356\) | 10.9176 | 0.578631 | ||||||||
\(357\) | 0.342440 | 0.0181238 | ||||||||
\(358\) | −6.14776 | −0.324919 | ||||||||
\(359\) | 2.09314 | 0.110472 | 0.0552359 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552359 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(360\) | 3.70404 | 0.195220 | ||||||||
\(361\) | −16.9174 | −0.890388 | ||||||||
\(362\) | 20.2627 | 1.06498 | ||||||||
\(363\) | 0.670430 | 0.0351884 | ||||||||
\(364\) | −1.01779 | −0.0533466 | ||||||||
\(365\) | −11.9992 | −0.628064 | ||||||||
\(366\) | −2.28754 | −0.119572 | ||||||||
\(367\) | −20.2990 | −1.05960 | −0.529799 | − | 0.848123i | \(-0.677733\pi\) | ||||
−0.529799 | + | 0.848123i | \(0.677733\pi\) | |||||||
\(368\) | 1.79749 | 0.0937008 | ||||||||
\(369\) | −5.34449 | −0.278223 | ||||||||
\(370\) | −13.7661 | −0.715668 | ||||||||
\(371\) | −3.41372 | −0.177232 | ||||||||
\(372\) | −4.83404 | −0.250633 | ||||||||
\(373\) | 23.8442 | 1.23460 | 0.617302 | − | 0.786726i | \(-0.288226\pi\) | ||||
0.617302 | + | 0.786726i | \(0.288226\pi\) | |||||||
\(374\) | −0.878022 | −0.0454014 | ||||||||
\(375\) | −7.68294 | −0.396745 | ||||||||
\(376\) | 7.30278 | 0.376612 | ||||||||
\(377\) | 8.27333 | 0.426098 | ||||||||
\(378\) | 2.16477 | 0.111344 | ||||||||
\(379\) | 2.46301 | 0.126516 | 0.0632582 | − | 0.997997i | \(-0.479851\pi\) | ||||
0.0632582 | + | 0.997997i | \(0.479851\pi\) | |||||||
\(380\) | −2.09581 | −0.107513 | ||||||||
\(381\) | −7.51944 | −0.385233 | ||||||||
\(382\) | −16.7647 | −0.857759 | ||||||||
\(383\) | −7.71307 | −0.394120 | −0.197060 | − | 0.980391i | \(-0.563139\pi\) | ||||
−0.197060 | + | 0.980391i | \(0.563139\pi\) | |||||||
\(384\) | −0.670430 | −0.0342127 | ||||||||
\(385\) | 0.844835 | 0.0430568 | ||||||||
\(386\) | −24.3605 | −1.23992 | ||||||||
\(387\) | −9.49866 | −0.482844 | ||||||||
\(388\) | −17.5033 | −0.888596 | ||||||||
\(389\) | −25.4912 | −1.29245 | −0.646227 | − | 0.763145i | \(-0.723654\pi\) | ||||
−0.646227 | + | 0.763145i | \(0.723654\pi\) | |||||||
\(390\) | 1.70346 | 0.0862580 | ||||||||
\(391\) | 1.57824 | 0.0798150 | ||||||||
\(392\) | 6.66158 | 0.336461 | ||||||||
\(393\) | −2.96801 | −0.149716 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 16.3800 | 0.824167 | ||||||||
\(396\) | −2.55052 | −0.128169 | ||||||||
\(397\) | −5.90761 | −0.296495 | −0.148247 | − | 0.988950i | \(-0.547363\pi\) | ||||
−0.148247 | + | 0.988950i | \(0.547363\pi\) | |||||||
\(398\) | 9.12252 | 0.457270 | ||||||||
\(399\) | −0.562839 | −0.0281772 | ||||||||
\(400\) | −2.89092 | −0.144546 | ||||||||
\(401\) | 11.8176 | 0.590143 | 0.295071 | − | 0.955475i | \(-0.404657\pi\) | ||||
0.295071 | + | 0.955475i | \(0.404657\pi\) | |||||||
\(402\) | −1.64204 | −0.0818977 | ||||||||
\(403\) | 12.6150 | 0.628400 | ||||||||
\(404\) | −15.8836 | −0.790238 | ||||||||
\(405\) | 7.48897 | 0.372130 | ||||||||
\(406\) | 2.75089 | 0.136524 | ||||||||
\(407\) | 9.47907 | 0.469860 | ||||||||
\(408\) | −0.588652 | −0.0291426 | ||||||||
\(409\) | −31.3317 | −1.54925 | −0.774626 | − | 0.632420i | \(-0.782062\pi\) | ||||
−0.774626 | + | 0.632420i | \(0.782062\pi\) | |||||||
\(410\) | −3.04315 | −0.150291 | ||||||||
\(411\) | 5.10949 | 0.252032 | ||||||||
\(412\) | −5.48887 | −0.270417 | ||||||||
\(413\) | −1.38070 | −0.0679400 | ||||||||
\(414\) | 4.58455 | 0.225318 | ||||||||
\(415\) | −19.1177 | −0.938449 | ||||||||
\(416\) | 1.74957 | 0.0857798 | ||||||||
\(417\) | 1.81088 | 0.0886793 | ||||||||
\(418\) | 1.44313 | 0.0705858 | ||||||||
\(419\) | 21.8166 | 1.06581 | 0.532905 | − | 0.846175i | \(-0.321100\pi\) | ||||
0.532905 | + | 0.846175i | \(0.321100\pi\) | |||||||
\(420\) | 0.566403 | 0.0276376 | ||||||||
\(421\) | 11.9342 | 0.581635 | 0.290818 | − | 0.956779i | \(-0.406073\pi\) | ||||
0.290818 | + | 0.956779i | \(0.406073\pi\) | |||||||
\(422\) | −2.65293 | −0.129143 | ||||||||
\(423\) | 18.6259 | 0.905623 | ||||||||
\(424\) | 5.86818 | 0.284984 | ||||||||
\(425\) | −2.53829 | −0.123125 | ||||||||
\(426\) | 2.76513 | 0.133971 | ||||||||
\(427\) | 1.98491 | 0.0960567 | ||||||||
\(428\) | −9.85634 | −0.476424 | ||||||||
\(429\) | −1.17297 | −0.0566313 | ||||||||
\(430\) | −5.40853 | −0.260823 | ||||||||
\(431\) | 20.4229 | 0.983739 | 0.491869 | − | 0.870669i | \(-0.336314\pi\) | ||||
0.491869 | + | 0.870669i | \(0.336314\pi\) | |||||||
\(432\) | −3.72124 | −0.179038 | ||||||||
\(433\) | −21.6487 | −1.04037 | −0.520186 | − | 0.854053i | \(-0.674137\pi\) | ||||
−0.520186 | + | 0.854053i | \(0.674137\pi\) | |||||||
\(434\) | 4.19452 | 0.201343 | ||||||||
\(435\) | −4.60414 | −0.220751 | ||||||||
\(436\) | 1.41601 | 0.0678146 | ||||||||
\(437\) | −2.59402 | −0.124089 | ||||||||
\(438\) | 5.53933 | 0.264680 | ||||||||
\(439\) | −28.0791 | −1.34014 | −0.670071 | − | 0.742297i | \(-0.733736\pi\) | ||||
−0.670071 | + | 0.742297i | \(0.733736\pi\) | |||||||
\(440\) | −1.45227 | −0.0692341 | ||||||||
\(441\) | 16.9905 | 0.809073 | ||||||||
\(442\) | 1.53616 | 0.0730678 | ||||||||
\(443\) | 33.1630 | 1.57562 | 0.787810 | − | 0.615918i | \(-0.211215\pi\) | ||||
0.787810 | + | 0.615918i | \(0.211215\pi\) | |||||||
\(444\) | 6.35506 | 0.301598 | ||||||||
\(445\) | 15.8553 | 0.751611 | ||||||||
\(446\) | 20.2664 | 0.959640 | ||||||||
\(447\) | 5.48172 | 0.259277 | ||||||||
\(448\) | 0.581735 | 0.0274844 | ||||||||
\(449\) | −9.86370 | −0.465497 | −0.232748 | − | 0.972537i | \(-0.574772\pi\) | ||||
−0.232748 | + | 0.972537i | \(0.574772\pi\) | |||||||
\(450\) | −7.37336 | −0.347584 | ||||||||
\(451\) | 2.09545 | 0.0986708 | ||||||||
\(452\) | 4.18759 | 0.196968 | ||||||||
\(453\) | 13.8236 | 0.649490 | ||||||||
\(454\) | −12.0399 | −0.565058 | ||||||||
\(455\) | −1.47810 | −0.0692944 | ||||||||
\(456\) | 0.967517 | 0.0453081 | ||||||||
\(457\) | 27.8772 | 1.30404 | 0.652020 | − | 0.758202i | \(-0.273922\pi\) | ||||
0.652020 | + | 0.758202i | \(0.273922\pi\) | |||||||
\(458\) | −6.05609 | −0.282983 | ||||||||
\(459\) | −3.26733 | −0.152506 | ||||||||
\(460\) | 2.61044 | 0.121712 | ||||||||
\(461\) | 6.85531 | 0.319283 | 0.159642 | − | 0.987175i | \(-0.448966\pi\) | ||||
0.159642 | + | 0.987175i | \(0.448966\pi\) | |||||||
\(462\) | −0.390013 | −0.0181450 | ||||||||
\(463\) | 24.8941 | 1.15693 | 0.578463 | − | 0.815709i | \(-0.303653\pi\) | ||||
0.578463 | + | 0.815709i | \(0.303653\pi\) | |||||||
\(464\) | −4.72877 | −0.219528 | ||||||||
\(465\) | −7.02031 | −0.325559 | ||||||||
\(466\) | −21.5358 | −0.997627 | ||||||||
\(467\) | 24.4652 | 1.13211 | 0.566056 | − | 0.824367i | \(-0.308469\pi\) | ||||
0.566056 | + | 0.824367i | \(0.308469\pi\) | |||||||
\(468\) | 4.46233 | 0.206271 | ||||||||
\(469\) | 1.42481 | 0.0657916 | ||||||||
\(470\) | 10.6056 | 0.489199 | ||||||||
\(471\) | −9.30904 | −0.428938 | ||||||||
\(472\) | 2.37342 | 0.109246 | ||||||||
\(473\) | 3.72420 | 0.171239 | ||||||||
\(474\) | −7.56172 | −0.347321 | ||||||||
\(475\) | 4.17197 | 0.191423 | ||||||||
\(476\) | 0.510776 | 0.0234114 | ||||||||
\(477\) | 14.9669 | 0.685288 | ||||||||
\(478\) | 0.970463 | 0.0443880 | ||||||||
\(479\) | 6.97325 | 0.318616 | 0.159308 | − | 0.987229i | \(-0.449074\pi\) | ||||
0.159308 | + | 0.987229i | \(0.449074\pi\) | |||||||
\(480\) | −0.973643 | −0.0444405 | ||||||||
\(481\) | −16.5843 | −0.756180 | ||||||||
\(482\) | −5.52821 | −0.251803 | ||||||||
\(483\) | 0.701045 | 0.0318987 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −25.4195 | −1.15424 | ||||||||
\(486\) | −14.6209 | −0.663220 | ||||||||
\(487\) | 20.1608 | 0.913574 | 0.456787 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456787 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(488\) | −3.41206 | −0.154457 | ||||||||
\(489\) | −5.44239 | −0.246113 | ||||||||
\(490\) | 9.67440 | 0.437045 | ||||||||
\(491\) | −10.0159 | −0.452012 | −0.226006 | − | 0.974126i | \(-0.572567\pi\) | ||||
−0.226006 | + | 0.974126i | \(0.572567\pi\) | |||||||
\(492\) | 1.40485 | 0.0633356 | ||||||||
\(493\) | −4.15196 | −0.186995 | ||||||||
\(494\) | −2.52486 | −0.113599 | ||||||||
\(495\) | −3.70404 | −0.166484 | ||||||||
\(496\) | −7.21035 | −0.323754 | ||||||||
\(497\) | −2.39931 | −0.107624 | ||||||||
\(498\) | 8.82555 | 0.395482 | ||||||||
\(499\) | −14.6515 | −0.655891 | −0.327946 | − | 0.944697i | \(-0.606356\pi\) | ||||
−0.327946 | + | 0.944697i | \(0.606356\pi\) | |||||||
\(500\) | −11.4597 | −0.512494 | ||||||||
\(501\) | −12.5429 | −0.560376 | ||||||||
\(502\) | 5.81521 | 0.259546 | ||||||||
\(503\) | 30.5437 | 1.36188 | 0.680939 | − | 0.732340i | \(-0.261572\pi\) | ||||
0.680939 | + | 0.732340i | \(0.261572\pi\) | |||||||
\(504\) | 1.48373 | 0.0660906 | ||||||||
\(505\) | −23.0672 | −1.02648 | ||||||||
\(506\) | −1.79749 | −0.0799083 | ||||||||
\(507\) | −6.66340 | −0.295932 | ||||||||
\(508\) | −11.2158 | −0.497623 | ||||||||
\(509\) | −27.1028 | −1.20131 | −0.600655 | − | 0.799509i | \(-0.705093\pi\) | ||||
−0.600655 | + | 0.799509i | \(0.705093\pi\) | |||||||
\(510\) | −0.854880 | −0.0378547 | ||||||||
\(511\) | −4.80650 | −0.212627 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.37023 | 0.237101 | ||||||||
\(514\) | 12.8393 | 0.566317 | ||||||||
\(515\) | −7.97131 | −0.351258 | ||||||||
\(516\) | 2.49681 | 0.109916 | ||||||||
\(517\) | −7.30278 | −0.321176 | ||||||||
\(518\) | −5.51431 | −0.242285 | ||||||||
\(519\) | 8.78740 | 0.385724 | ||||||||
\(520\) | 2.54085 | 0.111423 | ||||||||
\(521\) | −30.2126 | −1.32364 | −0.661819 | − | 0.749664i | \(-0.730215\pi\) | ||||
−0.661819 | + | 0.749664i | \(0.730215\pi\) | |||||||
\(522\) | −12.0608 | −0.527889 | ||||||||
\(523\) | −25.5303 | −1.11636 | −0.558180 | − | 0.829720i | \(-0.688500\pi\) | ||||
−0.558180 | + | 0.829720i | \(0.688500\pi\) | |||||||
\(524\) | −4.42703 | −0.193396 | ||||||||
\(525\) | −1.12750 | −0.0492079 | ||||||||
\(526\) | −24.7083 | −1.07733 | ||||||||
\(527\) | −6.33085 | −0.275776 | ||||||||
\(528\) | 0.670430 | 0.0291767 | ||||||||
\(529\) | −19.7690 | −0.859522 | ||||||||
\(530\) | 8.52216 | 0.370179 | ||||||||
\(531\) | 6.05347 | 0.262698 | ||||||||
\(532\) | −0.839519 | −0.0363978 | ||||||||
\(533\) | −3.66614 | −0.158798 | ||||||||
\(534\) | −7.31948 | −0.316745 | ||||||||
\(535\) | −14.3140 | −0.618850 | ||||||||
\(536\) | −2.44924 | −0.105791 | ||||||||
\(537\) | 4.12164 | 0.177862 | ||||||||
\(538\) | −14.2598 | −0.614784 | ||||||||
\(539\) | −6.66158 | −0.286935 | ||||||||
\(540\) | −5.40423 | −0.232561 | ||||||||
\(541\) | −40.3397 | −1.73434 | −0.867170 | − | 0.498012i | \(-0.834063\pi\) | ||||
−0.867170 | + | 0.498012i | \(0.834063\pi\) | |||||||
\(542\) | 1.52473 | 0.0654928 | ||||||||
\(543\) | −13.5847 | −0.582975 | ||||||||
\(544\) | −0.878022 | −0.0376449 | ||||||||
\(545\) | 2.05643 | 0.0880876 | ||||||||
\(546\) | 0.682355 | 0.0292021 | ||||||||
\(547\) | 25.3920 | 1.08568 | 0.542842 | − | 0.839835i | \(-0.317348\pi\) | ||||
0.542842 | + | 0.839835i | \(0.317348\pi\) | |||||||
\(548\) | 7.62121 | 0.325562 | ||||||||
\(549\) | −8.70253 | −0.371415 | ||||||||
\(550\) | 2.89092 | 0.123269 | ||||||||
\(551\) | 6.82423 | 0.290722 | ||||||||
\(552\) | −1.20509 | −0.0512922 | ||||||||
\(553\) | 6.56134 | 0.279017 | ||||||||
\(554\) | 12.3034 | 0.522723 | ||||||||
\(555\) | 9.22924 | 0.391759 | ||||||||
\(556\) | 2.70108 | 0.114551 | ||||||||
\(557\) | 31.1387 | 1.31939 | 0.659695 | − | 0.751533i | \(-0.270685\pi\) | ||||
0.659695 | + | 0.751533i | \(0.270685\pi\) | |||||||
\(558\) | −18.3902 | −0.778518 | ||||||||
\(559\) | −6.51576 | −0.275587 | ||||||||
\(560\) | 0.844835 | 0.0357008 | ||||||||
\(561\) | 0.588652 | 0.0248529 | ||||||||
\(562\) | −2.57833 | −0.108760 | ||||||||
\(563\) | −9.46949 | −0.399091 | −0.199546 | − | 0.979889i | \(-0.563947\pi\) | ||||
−0.199546 | + | 0.979889i | \(0.563947\pi\) | |||||||
\(564\) | −4.89600 | −0.206159 | ||||||||
\(565\) | 6.08150 | 0.255851 | ||||||||
\(566\) | −18.5999 | −0.781813 | ||||||||
\(567\) | 2.99986 | 0.125982 | ||||||||
\(568\) | 4.12441 | 0.173056 | ||||||||
\(569\) | −20.9254 | −0.877239 | −0.438620 | − | 0.898673i | \(-0.644532\pi\) | ||||
−0.438620 | + | 0.898673i | \(0.644532\pi\) | |||||||
\(570\) | 1.40509 | 0.0588529 | ||||||||
\(571\) | 9.73681 | 0.407473 | 0.203736 | − | 0.979026i | \(-0.434691\pi\) | ||||
0.203736 | + | 0.979026i | \(0.434691\pi\) | |||||||
\(572\) | −1.74957 | −0.0731533 | ||||||||
\(573\) | 11.2396 | 0.469540 | ||||||||
\(574\) | −1.21900 | −0.0508799 | ||||||||
\(575\) | −5.19641 | −0.216705 | ||||||||
\(576\) | −2.55052 | −0.106272 | ||||||||
\(577\) | −23.0279 | −0.958665 | −0.479333 | − | 0.877633i | \(-0.659121\pi\) | ||||
−0.479333 | + | 0.877633i | \(0.659121\pi\) | |||||||
\(578\) | 16.2291 | 0.675041 | ||||||||
\(579\) | 16.3320 | 0.678736 | ||||||||
\(580\) | −6.86744 | −0.285155 | ||||||||
\(581\) | −7.65797 | −0.317706 | ||||||||
\(582\) | 11.7348 | 0.486421 | ||||||||
\(583\) | −5.86818 | −0.243035 | ||||||||
\(584\) | 8.26236 | 0.341899 | ||||||||
\(585\) | 6.48049 | 0.267935 | ||||||||
\(586\) | 10.5237 | 0.434728 | ||||||||
\(587\) | 38.8693 | 1.60431 | 0.802153 | − | 0.597118i | \(-0.203688\pi\) | ||||
0.802153 | + | 0.597118i | \(0.203688\pi\) | |||||||
\(588\) | −4.46613 | −0.184180 | ||||||||
\(589\) | 10.4055 | 0.428750 | ||||||||
\(590\) | 3.44684 | 0.141904 | ||||||||
\(591\) | 0.670430 | 0.0275778 | ||||||||
\(592\) | 9.47907 | 0.389588 | ||||||||
\(593\) | −39.6982 | −1.63021 | −0.815105 | − | 0.579313i | \(-0.803321\pi\) | ||||
−0.815105 | + | 0.579313i | \(0.803321\pi\) | |||||||
\(594\) | 3.72124 | 0.152684 | ||||||||
\(595\) | 0.741783 | 0.0304102 | ||||||||
\(596\) | 8.17643 | 0.334920 | ||||||||
\(597\) | −6.11601 | −0.250312 | ||||||||
\(598\) | 3.14484 | 0.128602 | ||||||||
\(599\) | −12.4375 | −0.508183 | −0.254092 | − | 0.967180i | \(-0.581776\pi\) | ||||
−0.254092 | + | 0.967180i | \(0.581776\pi\) | |||||||
\(600\) | 1.93816 | 0.0791250 | ||||||||
\(601\) | 28.5369 | 1.16405 | 0.582023 | − | 0.813172i | \(-0.302261\pi\) | ||||
0.582023 | + | 0.813172i | \(0.302261\pi\) | |||||||
\(602\) | −2.16650 | −0.0882999 | ||||||||
\(603\) | −6.24685 | −0.254391 | ||||||||
\(604\) | 20.6190 | 0.838977 | ||||||||
\(605\) | 1.45227 | 0.0590430 | ||||||||
\(606\) | 10.6488 | 0.432579 | ||||||||
\(607\) | −14.0992 | −0.572269 | −0.286134 | − | 0.958190i | \(-0.592370\pi\) | ||||
−0.286134 | + | 0.958190i | \(0.592370\pi\) | |||||||
\(608\) | 1.44313 | 0.0585266 | ||||||||
\(609\) | −1.84428 | −0.0747340 | ||||||||
\(610\) | −4.95522 | −0.200631 | ||||||||
\(611\) | 12.7767 | 0.516892 | ||||||||
\(612\) | −2.23942 | −0.0905230 | ||||||||
\(613\) | 6.23306 | 0.251751 | 0.125875 | − | 0.992046i | \(-0.459826\pi\) | ||||
0.125875 | + | 0.992046i | \(0.459826\pi\) | |||||||
\(614\) | 24.9200 | 1.00569 | ||||||||
\(615\) | 2.04022 | 0.0822696 | ||||||||
\(616\) | −0.581735 | −0.0234388 | ||||||||
\(617\) | −15.3672 | −0.618661 | −0.309330 | − | 0.950955i | \(-0.600105\pi\) | ||||
−0.309330 | + | 0.950955i | \(0.600105\pi\) | |||||||
\(618\) | 3.67990 | 0.148027 | ||||||||
\(619\) | −43.7344 | −1.75783 | −0.878916 | − | 0.476976i | \(-0.841733\pi\) | ||||
−0.878916 | + | 0.476976i | \(0.841733\pi\) | |||||||
\(620\) | −10.4714 | −0.420540 | ||||||||
\(621\) | −6.68890 | −0.268416 | ||||||||
\(622\) | 4.58415 | 0.183807 | ||||||||
\(623\) | 6.35115 | 0.254453 | ||||||||
\(624\) | −1.17297 | −0.0469562 | ||||||||
\(625\) | −2.18798 | −0.0875190 | ||||||||
\(626\) | 9.44214 | 0.377384 | ||||||||
\(627\) | −0.967517 | −0.0386389 | ||||||||
\(628\) | −13.8852 | −0.554079 | ||||||||
\(629\) | 8.32284 | 0.331853 | ||||||||
\(630\) | 2.15477 | 0.0858481 | ||||||||
\(631\) | 20.2652 | 0.806745 | 0.403372 | − | 0.915036i | \(-0.367838\pi\) | ||||
0.403372 | + | 0.915036i | \(0.367838\pi\) | |||||||
\(632\) | −11.2789 | −0.448651 | ||||||||
\(633\) | 1.77860 | 0.0706932 | ||||||||
\(634\) | 6.26478 | 0.248806 | ||||||||
\(635\) | −16.2884 | −0.646386 | ||||||||
\(636\) | −3.93420 | −0.156001 | ||||||||
\(637\) | 11.6549 | 0.461785 | ||||||||
\(638\) | 4.72877 | 0.187214 | ||||||||
\(639\) | 10.5194 | 0.416141 | ||||||||
\(640\) | −1.45227 | −0.0574059 | ||||||||
\(641\) | 40.8509 | 1.61351 | 0.806757 | − | 0.590884i | \(-0.201221\pi\) | ||||
0.806757 | + | 0.590884i | \(0.201221\pi\) | |||||||
\(642\) | 6.60798 | 0.260796 | ||||||||
\(643\) | 42.9460 | 1.69363 | 0.846813 | − | 0.531891i | \(-0.178518\pi\) | ||||
0.846813 | + | 0.531891i | \(0.178518\pi\) | |||||||
\(644\) | 1.04567 | 0.0412050 | ||||||||
\(645\) | 3.62604 | 0.142775 | ||||||||
\(646\) | 1.26710 | 0.0498534 | ||||||||
\(647\) | −18.6608 | −0.733634 | −0.366817 | − | 0.930293i | \(-0.619552\pi\) | ||||
−0.366817 | + | 0.930293i | \(0.619552\pi\) | |||||||
\(648\) | −5.15674 | −0.202576 | ||||||||
\(649\) | −2.37342 | −0.0931650 | ||||||||
\(650\) | −5.05787 | −0.198386 | ||||||||
\(651\) | −2.81213 | −0.110216 | ||||||||
\(652\) | −8.11776 | −0.317916 | ||||||||
\(653\) | −4.60539 | −0.180223 | −0.0901114 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901114 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(654\) | −0.949336 | −0.0371220 | ||||||||
\(655\) | −6.42923 | −0.251211 | ||||||||
\(656\) | 2.09545 | 0.0818135 | ||||||||
\(657\) | 21.0733 | 0.822149 | ||||||||
\(658\) | 4.24828 | 0.165615 | ||||||||
\(659\) | −5.01451 | −0.195338 | −0.0976689 | − | 0.995219i | \(-0.531139\pi\) | ||||
−0.0976689 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(660\) | 0.973643 | 0.0378990 | ||||||||
\(661\) | −11.5506 | −0.449265 | −0.224632 | − | 0.974444i | \(-0.572118\pi\) | ||||
−0.224632 | + | 0.974444i | \(0.572118\pi\) | |||||||
\(662\) | 36.3314 | 1.41206 | ||||||||
\(663\) | −1.02989 | −0.0399976 | ||||||||
\(664\) | 13.1640 | 0.510863 | ||||||||
\(665\) | −1.21921 | −0.0472788 | ||||||||
\(666\) | 24.1766 | 0.936824 | ||||||||
\(667\) | −8.49993 | −0.329119 | ||||||||
\(668\) | −18.7088 | −0.723863 | ||||||||
\(669\) | −13.5872 | −0.525311 | ||||||||
\(670\) | −3.55695 | −0.137417 | ||||||||
\(671\) | 3.41206 | 0.131721 | ||||||||
\(672\) | −0.390013 | −0.0150451 | ||||||||
\(673\) | −34.9431 | −1.34696 | −0.673479 | − | 0.739207i | \(-0.735201\pi\) | ||||
−0.673479 | + | 0.739207i | \(0.735201\pi\) | |||||||
\(674\) | 1.20970 | 0.0465957 | ||||||||
\(675\) | 10.7578 | 0.414068 | ||||||||
\(676\) | −9.93900 | −0.382269 | ||||||||
\(677\) | −6.04807 | −0.232446 | −0.116223 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116223 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(678\) | −2.80749 | −0.107821 | ||||||||
\(679\) | −10.1823 | −0.390761 | ||||||||
\(680\) | −1.27512 | −0.0488987 | ||||||||
\(681\) | 8.07188 | 0.309315 | ||||||||
\(682\) | 7.21035 | 0.276099 | ||||||||
\(683\) | 34.1221 | 1.30565 | 0.652823 | − | 0.757510i | \(-0.273584\pi\) | ||||
0.652823 | + | 0.757510i | \(0.273584\pi\) | |||||||
\(684\) | 3.68074 | 0.140736 | ||||||||
\(685\) | 11.0680 | 0.422888 | ||||||||
\(686\) | 7.94742 | 0.303434 | ||||||||
\(687\) | 4.06019 | 0.154906 | ||||||||
\(688\) | 3.72420 | 0.141984 | ||||||||
\(689\) | 10.2668 | 0.391134 | ||||||||
\(690\) | −1.75012 | −0.0666258 | ||||||||
\(691\) | 16.4399 | 0.625403 | 0.312701 | − | 0.949851i | \(-0.398766\pi\) | ||||
0.312701 | + | 0.949851i | \(0.398766\pi\) | |||||||
\(692\) | 13.1071 | 0.498257 | ||||||||
\(693\) | −1.48373 | −0.0563622 | ||||||||
\(694\) | 27.4242 | 1.04101 | ||||||||
\(695\) | 3.92269 | 0.148796 | ||||||||
\(696\) | 3.17031 | 0.120170 | ||||||||
\(697\) | 1.83985 | 0.0696893 | ||||||||
\(698\) | 3.73862 | 0.141509 | ||||||||
\(699\) | 14.4383 | 0.546105 | ||||||||
\(700\) | −1.68175 | −0.0635642 | ||||||||
\(701\) | −47.5629 | −1.79642 | −0.898212 | − | 0.439562i | \(-0.855134\pi\) | ||||
−0.898212 | + | 0.439562i | \(0.855134\pi\) | |||||||
\(702\) | −6.51057 | −0.245726 | ||||||||
\(703\) | −13.6795 | −0.515933 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −7.11030 | −0.267789 | ||||||||
\(706\) | −13.7047 | −0.515783 | ||||||||
\(707\) | −9.24004 | −0.347507 | ||||||||
\(708\) | −1.59121 | −0.0598015 | ||||||||
\(709\) | 13.5331 | 0.508247 | 0.254123 | − | 0.967172i | \(-0.418213\pi\) | ||||
0.254123 | + | 0.967172i | \(0.418213\pi\) | |||||||
\(710\) | 5.98974 | 0.224791 | ||||||||
\(711\) | −28.7671 | −1.07885 | ||||||||
\(712\) | −10.9176 | −0.409154 | ||||||||
\(713\) | −12.9606 | −0.485377 | ||||||||
\(714\) | −0.342440 | −0.0128155 | ||||||||
\(715\) | −2.54085 | −0.0950223 | ||||||||
\(716\) | 6.14776 | 0.229753 | ||||||||
\(717\) | −0.650628 | −0.0242981 | ||||||||
\(718\) | −2.09314 | −0.0781154 | ||||||||
\(719\) | 1.59784 | 0.0595892 | 0.0297946 | − | 0.999556i | \(-0.490515\pi\) | ||||
0.0297946 | + | 0.999556i | \(0.490515\pi\) | |||||||
\(720\) | −3.70404 | −0.138041 | ||||||||
\(721\) | −3.19307 | −0.118916 | ||||||||
\(722\) | 16.9174 | 0.629600 | ||||||||
\(723\) | 3.70628 | 0.137838 | ||||||||
\(724\) | −20.2627 | −0.753056 | ||||||||
\(725\) | 13.6705 | 0.507710 | ||||||||
\(726\) | −0.670430 | −0.0248820 | ||||||||
\(727\) | −4.16812 | −0.154587 | −0.0772935 | − | 0.997008i | \(-0.524628\pi\) | ||||
−0.0772935 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(728\) | 1.01779 | 0.0377217 | ||||||||
\(729\) | −5.66791 | −0.209922 | ||||||||
\(730\) | 11.9992 | 0.444108 | ||||||||
\(731\) | 3.26993 | 0.120943 | ||||||||
\(732\) | 2.28754 | 0.0845501 | ||||||||
\(733\) | −7.02841 | −0.259600 | −0.129800 | − | 0.991540i | \(-0.541434\pi\) | ||||
−0.129800 | + | 0.991540i | \(0.541434\pi\) | |||||||
\(734\) | 20.2990 | 0.749249 | ||||||||
\(735\) | −6.48601 | −0.239240 | ||||||||
\(736\) | −1.79749 | −0.0662565 | ||||||||
\(737\) | 2.44924 | 0.0902189 | ||||||||
\(738\) | 5.34449 | 0.196733 | ||||||||
\(739\) | 37.5307 | 1.38059 | 0.690295 | − | 0.723528i | \(-0.257481\pi\) | ||||
0.690295 | + | 0.723528i | \(0.257481\pi\) | |||||||
\(740\) | 13.7661 | 0.506054 | ||||||||
\(741\) | 1.69274 | 0.0621844 | ||||||||
\(742\) | 3.41372 | 0.125322 | ||||||||
\(743\) | 40.4714 | 1.48475 | 0.742375 | − | 0.669985i | \(-0.233699\pi\) | ||||
0.742375 | + | 0.669985i | \(0.233699\pi\) | |||||||
\(744\) | 4.83404 | 0.177224 | ||||||||
\(745\) | 11.8744 | 0.435043 | ||||||||
\(746\) | −23.8442 | −0.872997 | ||||||||
\(747\) | 33.5751 | 1.22845 | ||||||||
\(748\) | 0.878022 | 0.0321037 | ||||||||
\(749\) | −5.73378 | −0.209508 | ||||||||
\(750\) | 7.68294 | 0.280541 | ||||||||
\(751\) | −13.6803 | −0.499202 | −0.249601 | − | 0.968349i | \(-0.580300\pi\) | ||||
−0.249601 | + | 0.968349i | \(0.580300\pi\) | |||||||
\(752\) | −7.30278 | −0.266305 | ||||||||
\(753\) | −3.89869 | −0.142076 | ||||||||
\(754\) | −8.27333 | −0.301297 | ||||||||
\(755\) | 29.9443 | 1.08979 | ||||||||
\(756\) | −2.16477 | −0.0787321 | ||||||||
\(757\) | −25.4181 | −0.923838 | −0.461919 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461919 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(758\) | −2.46301 | −0.0894606 | ||||||||
\(759\) | 1.20509 | 0.0437421 | ||||||||
\(760\) | 2.09581 | 0.0760230 | ||||||||
\(761\) | 32.9698 | 1.19515 | 0.597577 | − | 0.801811i | \(-0.296130\pi\) | ||||
0.597577 | + | 0.801811i | \(0.296130\pi\) | |||||||
\(762\) | 7.51944 | 0.272401 | ||||||||
\(763\) | 0.823743 | 0.0298215 | ||||||||
\(764\) | 16.7647 | 0.606527 | ||||||||
\(765\) | −3.25223 | −0.117585 | ||||||||
\(766\) | 7.71307 | 0.278685 | ||||||||
\(767\) | 4.15248 | 0.149937 | ||||||||
\(768\) | 0.670430 | 0.0241921 | ||||||||
\(769\) | 16.4058 | 0.591608 | 0.295804 | − | 0.955249i | \(-0.404413\pi\) | ||||
0.295804 | + | 0.955249i | \(0.404413\pi\) | |||||||
\(770\) | −0.844835 | −0.0304457 | ||||||||
\(771\) | −8.60785 | −0.310004 | ||||||||
\(772\) | 24.3605 | 0.876755 | ||||||||
\(773\) | −10.9550 | −0.394023 | −0.197011 | − | 0.980401i | \(-0.563124\pi\) | ||||
−0.197011 | + | 0.980401i | \(0.563124\pi\) | |||||||
\(774\) | 9.49866 | 0.341422 | ||||||||
\(775\) | 20.8446 | 0.748759 | ||||||||
\(776\) | 17.5033 | 0.628333 | ||||||||
\(777\) | 3.69696 | 0.132628 | ||||||||
\(778\) | 25.4912 | 0.913904 | ||||||||
\(779\) | −3.02400 | −0.108346 | ||||||||
\(780\) | −1.70346 | −0.0609936 | ||||||||
\(781\) | −4.12441 | −0.147583 | ||||||||
\(782\) | −1.57824 | −0.0564377 | ||||||||
\(783\) | 17.5969 | 0.628861 | ||||||||
\(784\) | −6.66158 | −0.237914 | ||||||||
\(785\) | −20.1650 | −0.719719 | ||||||||
\(786\) | 2.96801 | 0.105865 | ||||||||
\(787\) | 22.3992 | 0.798445 | 0.399223 | − | 0.916854i | \(-0.369280\pi\) | ||||
0.399223 | + | 0.916854i | \(0.369280\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 16.5652 | 0.589735 | ||||||||
\(790\) | −16.3800 | −0.582774 | ||||||||
\(791\) | 2.43607 | 0.0866167 | ||||||||
\(792\) | 2.55052 | 0.0906289 | ||||||||
\(793\) | −5.96964 | −0.211988 | ||||||||
\(794\) | 5.90761 | 0.209653 | ||||||||
\(795\) | −5.71351 | −0.202637 | ||||||||
\(796\) | −9.12252 | −0.323339 | ||||||||
\(797\) | −5.81433 | −0.205954 | −0.102977 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102977 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(798\) | 0.562839 | 0.0199243 | ||||||||
\(799\) | −6.41200 | −0.226840 | ||||||||
\(800\) | 2.89092 | 0.102209 | ||||||||
\(801\) | −27.8456 | −0.983875 | ||||||||
\(802\) | −11.8176 | −0.417294 | ||||||||
\(803\) | −8.26236 | −0.291572 | ||||||||
\(804\) | 1.64204 | 0.0579104 | ||||||||
\(805\) | 1.51858 | 0.0535231 | ||||||||
\(806\) | −12.6150 | −0.444346 | ||||||||
\(807\) | 9.56020 | 0.336535 | ||||||||
\(808\) | 15.8836 | 0.558782 | ||||||||
\(809\) | −24.8672 | −0.874286 | −0.437143 | − | 0.899392i | \(-0.644010\pi\) | ||||
−0.437143 | + | 0.899392i | \(0.644010\pi\) | |||||||
\(810\) | −7.48897 | −0.263135 | ||||||||
\(811\) | −33.8516 | −1.18869 | −0.594345 | − | 0.804210i | \(-0.702589\pi\) | ||||
−0.594345 | + | 0.804210i | \(0.702589\pi\) | |||||||
\(812\) | −2.75089 | −0.0965374 | ||||||||
\(813\) | −1.02222 | −0.0358510 | ||||||||
\(814\) | −9.47907 | −0.332241 | ||||||||
\(815\) | −11.7892 | −0.412956 | ||||||||
\(816\) | 0.588652 | 0.0206069 | ||||||||
\(817\) | −5.37450 | −0.188030 | ||||||||
\(818\) | 31.3317 | 1.09549 | ||||||||
\(819\) | 2.59589 | 0.0907078 | ||||||||
\(820\) | 3.04315 | 0.106271 | ||||||||
\(821\) | −11.7921 | −0.411546 | −0.205773 | − | 0.978600i | \(-0.565971\pi\) | ||||
−0.205773 | + | 0.978600i | \(0.565971\pi\) | |||||||
\(822\) | −5.10949 | −0.178214 | ||||||||
\(823\) | 22.2348 | 0.775057 | 0.387528 | − | 0.921858i | \(-0.373329\pi\) | ||||
0.387528 | + | 0.921858i | \(0.373329\pi\) | |||||||
\(824\) | 5.48887 | 0.191214 | ||||||||
\(825\) | −1.93816 | −0.0674781 | ||||||||
\(826\) | 1.38070 | 0.0480408 | ||||||||
\(827\) | 49.6898 | 1.72788 | 0.863942 | − | 0.503592i | \(-0.167988\pi\) | ||||
0.863942 | + | 0.503592i | \(0.167988\pi\) | |||||||
\(828\) | −4.58455 | −0.159324 | ||||||||
\(829\) | −2.30742 | −0.0801401 | −0.0400700 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400700 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(830\) | 19.1177 | 0.663584 | ||||||||
\(831\) | −8.24860 | −0.286141 | ||||||||
\(832\) | −1.74957 | −0.0606555 | ||||||||
\(833\) | −5.84902 | −0.202656 | ||||||||
\(834\) | −1.81088 | −0.0627058 | ||||||||
\(835\) | −27.1701 | −0.940260 | ||||||||
\(836\) | −1.44313 | −0.0499117 | ||||||||
\(837\) | 26.8314 | 0.927430 | ||||||||
\(838\) | −21.8166 | −0.753642 | ||||||||
\(839\) | −23.0998 | −0.797495 | −0.398747 | − | 0.917061i | \(-0.630555\pi\) | ||||
−0.398747 | + | 0.917061i | \(0.630555\pi\) | |||||||
\(840\) | −0.566403 | −0.0195427 | ||||||||
\(841\) | −6.63873 | −0.228922 | ||||||||
\(842\) | −11.9342 | −0.411278 | ||||||||
\(843\) | 1.72859 | 0.0595358 | ||||||||
\(844\) | 2.65293 | 0.0913177 | ||||||||
\(845\) | −14.4341 | −0.496547 | ||||||||
\(846\) | −18.6259 | −0.640372 | ||||||||
\(847\) | 0.581735 | 0.0199887 | ||||||||
\(848\) | −5.86818 | −0.201514 | ||||||||
\(849\) | 12.4699 | 0.427967 | ||||||||
\(850\) | 2.53829 | 0.0870627 | ||||||||
\(851\) | 17.0386 | 0.584075 | ||||||||
\(852\) | −2.76513 | −0.0947317 | ||||||||
\(853\) | 21.8585 | 0.748422 | 0.374211 | − | 0.927344i | \(-0.377914\pi\) | ||||
0.374211 | + | 0.927344i | \(0.377914\pi\) | |||||||
\(854\) | −1.98491 | −0.0679223 | ||||||||
\(855\) | 5.34541 | 0.182809 | ||||||||
\(856\) | 9.85634 | 0.336883 | ||||||||
\(857\) | 23.5931 | 0.805924 | 0.402962 | − | 0.915217i | \(-0.367981\pi\) | ||||
0.402962 | + | 0.915217i | \(0.367981\pi\) | |||||||
\(858\) | 1.17297 | 0.0400444 | ||||||||
\(859\) | −47.5269 | −1.62160 | −0.810799 | − | 0.585325i | \(-0.800967\pi\) | ||||
−0.810799 | + | 0.585325i | \(0.800967\pi\) | |||||||
\(860\) | 5.40853 | 0.184429 | ||||||||
\(861\) | 0.817252 | 0.0278519 | ||||||||
\(862\) | −20.4229 | −0.695608 | ||||||||
\(863\) | −0.543606 | −0.0185046 | −0.00925229 | − | 0.999957i | \(-0.502945\pi\) | ||||
−0.00925229 | + | 0.999957i | \(0.502945\pi\) | |||||||
\(864\) | 3.72124 | 0.126599 | ||||||||
\(865\) | 19.0350 | 0.647210 | ||||||||
\(866\) | 21.6487 | 0.735654 | ||||||||
\(867\) | −10.8805 | −0.369520 | ||||||||
\(868\) | −4.19452 | −0.142371 | ||||||||
\(869\) | 11.2789 | 0.382611 | ||||||||
\(870\) | 4.60414 | 0.156095 | ||||||||
\(871\) | −4.28512 | −0.145196 | ||||||||
\(872\) | −1.41601 | −0.0479522 | ||||||||
\(873\) | 44.6426 | 1.51092 | ||||||||
\(874\) | 2.59402 | 0.0877439 | ||||||||
\(875\) | −6.66652 | −0.225370 | ||||||||
\(876\) | −5.53933 | −0.187157 | ||||||||
\(877\) | 12.3806 | 0.418064 | 0.209032 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209032 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(878\) | 28.0791 | 0.947623 | ||||||||
\(879\) | −7.05538 | −0.237972 | ||||||||
\(880\) | 1.45227 | 0.0489559 | ||||||||
\(881\) | 47.9940 | 1.61696 | 0.808479 | − | 0.588525i | \(-0.200291\pi\) | ||||
0.808479 | + | 0.588525i | \(0.200291\pi\) | |||||||
\(882\) | −16.9905 | −0.572101 | ||||||||
\(883\) | 43.6675 | 1.46953 | 0.734764 | − | 0.678323i | \(-0.237293\pi\) | ||||
0.734764 | + | 0.678323i | \(0.237293\pi\) | |||||||
\(884\) | −1.53616 | −0.0516667 | ||||||||
\(885\) | −2.31087 | −0.0776790 | ||||||||
\(886\) | −33.1630 | −1.11413 | ||||||||
\(887\) | 15.3029 | 0.513822 | 0.256911 | − | 0.966435i | \(-0.417295\pi\) | ||||
0.256911 | + | 0.966435i | \(0.417295\pi\) | |||||||
\(888\) | −6.35506 | −0.213262 | ||||||||
\(889\) | −6.52465 | −0.218830 | ||||||||
\(890\) | −15.8553 | −0.531470 | ||||||||
\(891\) | 5.15674 | 0.172757 | ||||||||
\(892\) | −20.2664 | −0.678568 | ||||||||
\(893\) | 10.5389 | 0.352669 | ||||||||
\(894\) | −5.48172 | −0.183336 | ||||||||
\(895\) | 8.92819 | 0.298436 | ||||||||
\(896\) | −0.581735 | −0.0194344 | ||||||||
\(897\) | −2.10840 | −0.0703974 | ||||||||
\(898\) | 9.86370 | 0.329156 | ||||||||
\(899\) | 34.0961 | 1.13717 | ||||||||
\(900\) | 7.37336 | 0.245779 | ||||||||
\(901\) | −5.15239 | −0.171651 | ||||||||
\(902\) | −2.09545 | −0.0697708 | ||||||||
\(903\) | 1.45248 | 0.0483357 | ||||||||
\(904\) | −4.18759 | −0.139277 | ||||||||
\(905\) | −29.4268 | −0.978180 | ||||||||
\(906\) | −13.8236 | −0.459259 | ||||||||
\(907\) | −13.4133 | −0.445383 | −0.222691 | − | 0.974889i | \(-0.571484\pi\) | ||||
−0.222691 | + | 0.974889i | \(0.571484\pi\) | |||||||
\(908\) | 12.0399 | 0.399557 | ||||||||
\(909\) | 40.5114 | 1.34368 | ||||||||
\(910\) | 1.47810 | 0.0489985 | ||||||||
\(911\) | 21.9989 | 0.728855 | 0.364427 | − | 0.931232i | \(-0.381265\pi\) | ||||
0.364427 | + | 0.931232i | \(0.381265\pi\) | |||||||
\(912\) | −0.967517 | −0.0320377 | ||||||||
\(913\) | −13.1640 | −0.435665 | ||||||||
\(914\) | −27.8772 | −0.922095 | ||||||||
\(915\) | 3.32213 | 0.109826 | ||||||||
\(916\) | 6.05609 | 0.200099 | ||||||||
\(917\) | −2.57536 | −0.0850458 | ||||||||
\(918\) | 3.26733 | 0.107838 | ||||||||
\(919\) | 51.8312 | 1.70975 | 0.854877 | − | 0.518831i | \(-0.173633\pi\) | ||||
0.854877 | + | 0.518831i | \(0.173633\pi\) | |||||||
\(920\) | −2.61044 | −0.0860637 | ||||||||
\(921\) | −16.7071 | −0.550518 | ||||||||
\(922\) | −6.85531 | −0.225768 | ||||||||
\(923\) | 7.21595 | 0.237516 | ||||||||
\(924\) | 0.390013 | 0.0128305 | ||||||||
\(925\) | −27.4033 | −0.901013 | ||||||||
\(926\) | −24.8941 | −0.818070 | ||||||||
\(927\) | 13.9995 | 0.459804 | ||||||||
\(928\) | 4.72877 | 0.155229 | ||||||||
\(929\) | 43.7786 | 1.43633 | 0.718165 | − | 0.695873i | \(-0.244982\pi\) | ||||
0.718165 | + | 0.695873i | \(0.244982\pi\) | |||||||
\(930\) | 7.02031 | 0.230205 | ||||||||
\(931\) | 9.61353 | 0.315071 | ||||||||
\(932\) | 21.5358 | 0.705429 | ||||||||
\(933\) | −3.07335 | −0.100617 | ||||||||
\(934\) | −24.4652 | −0.800524 | ||||||||
\(935\) | 1.27512 | 0.0417010 | ||||||||
\(936\) | −4.46233 | −0.145856 | ||||||||
\(937\) | 58.8654 | 1.92305 | 0.961524 | − | 0.274722i | \(-0.0885857\pi\) | ||||
0.961524 | + | 0.274722i | \(0.0885857\pi\) | |||||||
\(938\) | −1.42481 | −0.0465217 | ||||||||
\(939\) | −6.33029 | −0.206581 | ||||||||
\(940\) | −10.6056 | −0.345916 | ||||||||
\(941\) | 10.2901 | 0.335447 | 0.167724 | − | 0.985834i | \(-0.446358\pi\) | ||||
0.167724 | + | 0.985834i | \(0.446358\pi\) | |||||||
\(942\) | 9.30904 | 0.303305 | ||||||||
\(943\) | 3.76656 | 0.122656 | ||||||||
\(944\) | −2.37342 | −0.0772484 | ||||||||
\(945\) | −3.14383 | −0.102269 | ||||||||
\(946\) | −3.72420 | −0.121084 | ||||||||
\(947\) | −36.8445 | −1.19728 | −0.598642 | − | 0.801016i | \(-0.704293\pi\) | ||||
−0.598642 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(948\) | 7.56172 | 0.245593 | ||||||||
\(949\) | 14.4556 | 0.469248 | ||||||||
\(950\) | −4.17197 | −0.135357 | ||||||||
\(951\) | −4.20010 | −0.136197 | ||||||||
\(952\) | −0.510776 | −0.0165544 | ||||||||
\(953\) | 17.3996 | 0.563629 | 0.281814 | − | 0.959469i | \(-0.409064\pi\) | ||||
0.281814 | + | 0.959469i | \(0.409064\pi\) | |||||||
\(954\) | −14.9669 | −0.484572 | ||||||||
\(955\) | 24.3469 | 0.787847 | ||||||||
\(956\) | −0.970463 | −0.0313870 | ||||||||
\(957\) | −3.17031 | −0.102482 | ||||||||
\(958\) | −6.97325 | −0.225295 | ||||||||
\(959\) | 4.43353 | 0.143166 | ||||||||
\(960\) | 0.973643 | 0.0314242 | ||||||||
\(961\) | 20.9892 | 0.677071 | ||||||||
\(962\) | 16.5843 | 0.534700 | ||||||||
\(963\) | 25.1388 | 0.810087 | ||||||||
\(964\) | 5.52821 | 0.178052 | ||||||||
\(965\) | 35.3780 | 1.13886 | ||||||||
\(966\) | −0.701045 | −0.0225558 | ||||||||
\(967\) | −40.3722 | −1.29828 | −0.649141 | − | 0.760668i | \(-0.724872\pi\) | ||||
−0.649141 | + | 0.760668i | \(0.724872\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −0.849501 | −0.0272899 | ||||||||
\(970\) | 25.4195 | 0.816171 | ||||||||
\(971\) | −10.6896 | −0.343047 | −0.171523 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171523 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(972\) | 14.6209 | 0.468967 | ||||||||
\(973\) | 1.57131 | 0.0503739 | ||||||||
\(974\) | −20.1608 | −0.645995 | ||||||||
\(975\) | 3.39095 | 0.108597 | ||||||||
\(976\) | 3.41206 | 0.109217 | ||||||||
\(977\) | 27.2821 | 0.872831 | 0.436415 | − | 0.899745i | \(-0.356248\pi\) | ||||
0.436415 | + | 0.899745i | \(0.356248\pi\) | |||||||
\(978\) | 5.44239 | 0.174028 | ||||||||
\(979\) | 10.9176 | 0.348928 | ||||||||
\(980\) | −9.67440 | −0.309037 | ||||||||
\(981\) | −3.61157 | −0.115309 | ||||||||
\(982\) | 10.0159 | 0.319621 | ||||||||
\(983\) | −48.8256 | −1.55729 | −0.778647 | − | 0.627463i | \(-0.784093\pi\) | ||||
−0.778647 | + | 0.627463i | \(0.784093\pi\) | |||||||
\(984\) | −1.40485 | −0.0447850 | ||||||||
\(985\) | 1.45227 | 0.0462731 | ||||||||
\(986\) | 4.15196 | 0.132225 | ||||||||
\(987\) | −2.84818 | −0.0906585 | ||||||||
\(988\) | 2.52486 | 0.0803265 | ||||||||
\(989\) | 6.69422 | 0.212864 | ||||||||
\(990\) | 3.70404 | 0.117722 | ||||||||
\(991\) | 44.6020 | 1.41683 | 0.708414 | − | 0.705797i | \(-0.249411\pi\) | ||||
0.708414 | + | 0.705797i | \(0.249411\pi\) | |||||||
\(992\) | 7.21035 | 0.228929 | ||||||||
\(993\) | −24.3577 | −0.772967 | ||||||||
\(994\) | 2.39931 | 0.0761016 | ||||||||
\(995\) | −13.2483 | −0.420000 | ||||||||
\(996\) | −8.82555 | −0.279648 | ||||||||
\(997\) | 21.5525 | 0.682575 | 0.341287 | − | 0.939959i | \(-0.389137\pi\) | ||||
0.341287 | + | 0.939959i | \(0.389137\pi\) | |||||||
\(998\) | 14.6515 | 0.463785 | ||||||||
\(999\) | −35.2739 | −1.11602 |
(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 | 4334.2.a.a.1.10 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.10 | ✓ | 15 | 1.1 | even | 1 | trivial |