Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 19x^{5} + 12x^{4} - 34x^{3} - 12x^{2} + 17x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.86556\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86556 | −1.31915 | −0.659575 | − | 0.751639i | \(-0.729264\pi\) | ||||
−0.659575 | + | 0.751639i | \(0.729264\pi\) | |||||||
\(3\) | 1.47264 | 0.850229 | 0.425115 | − | 0.905140i | \(-0.360234\pi\) | ||||
0.425115 | + | 0.905140i | \(0.360234\pi\) | |||||||
\(4\) | 1.48032 | 0.740158 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.74730 | −1.12158 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.969501 | 0.342770 | ||||||||
\(9\) | −0.831331 | −0.277110 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.38861 | 0.720193 | 0.360096 | − | 0.932915i | \(-0.382744\pi\) | ||||
0.360096 | + | 0.932915i | \(0.382744\pi\) | |||||||
\(12\) | 2.17997 | 0.629304 | ||||||||
\(13\) | −5.15152 | −1.42878 | −0.714388 | − | 0.699750i | \(-0.753295\pi\) | ||||
−0.714388 | + | 0.699750i | \(0.753295\pi\) | |||||||
\(14\) | 1.86556 | 0.498592 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.76930 | −1.19232 | ||||||||
\(17\) | 3.94710 | 0.957313 | 0.478657 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478657 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(18\) | 1.55090 | 0.365550 | ||||||||
\(19\) | −8.03699 | −1.84381 | −0.921907 | − | 0.387412i | \(-0.873369\pi\) | ||||
−0.921907 | + | 0.387412i | \(0.873369\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47264 | −0.321356 | ||||||||
\(22\) | −4.45610 | −0.950043 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.42773 | 0.291433 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.61048 | 1.88477 | ||||||||
\(27\) | −5.64217 | −1.08584 | ||||||||
\(28\) | −1.48032 | −0.279754 | ||||||||
\(29\) | −3.71096 | −0.689107 | −0.344554 | − | 0.938767i | \(-0.611970\pi\) | ||||
−0.344554 | + | 0.938767i | \(0.611970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20350 | 0.754971 | 0.377485 | − | 0.926016i | \(-0.376789\pi\) | ||||
0.377485 | + | 0.926016i | \(0.376789\pi\) | |||||||
\(32\) | 6.95841 | 1.23008 | ||||||||
\(33\) | 3.51756 | 0.612329 | ||||||||
\(34\) | −7.36356 | −1.26284 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.23063 | −0.205105 | ||||||||
\(37\) | −2.12680 | −0.349644 | −0.174822 | − | 0.984600i | \(-0.555935\pi\) | ||||
−0.174822 | + | 0.984600i | \(0.555935\pi\) | |||||||
\(38\) | 14.9935 | 2.43227 | ||||||||
\(39\) | −7.58634 | −1.21479 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.12162 | 0.331341 | 0.165671 | − | 0.986181i | \(-0.447021\pi\) | ||||
0.165671 | + | 0.986181i | \(0.447021\pi\) | |||||||
\(42\) | 2.74730 | 0.423918 | ||||||||
\(43\) | 5.36459 | 0.818092 | 0.409046 | − | 0.912514i | \(-0.365862\pi\) | ||||
0.409046 | + | 0.912514i | \(0.365862\pi\) | |||||||
\(44\) | 3.53590 | 0.533057 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86556 | 0.275062 | ||||||||
\(47\) | 6.57020 | 0.958362 | 0.479181 | − | 0.877716i | \(-0.340934\pi\) | ||||
0.479181 | + | 0.877716i | \(0.340934\pi\) | |||||||
\(48\) | −7.02346 | −1.01375 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.81267 | 0.813936 | ||||||||
\(52\) | −7.62589 | −1.05752 | ||||||||
\(53\) | 12.6510 | 1.73775 | 0.868875 | − | 0.495032i | \(-0.164844\pi\) | ||||
0.868875 | + | 0.495032i | \(0.164844\pi\) | |||||||
\(54\) | 10.5258 | 1.43238 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.969501 | −0.129555 | ||||||||
\(57\) | −11.8356 | −1.56766 | ||||||||
\(58\) | 6.92302 | 0.909036 | ||||||||
\(59\) | 2.07665 | 0.270357 | 0.135178 | − | 0.990821i | \(-0.456839\pi\) | ||||
0.135178 | + | 0.990821i | \(0.456839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.74616 | −0.351610 | −0.175805 | − | 0.984425i | \(-0.556253\pi\) | ||||
−0.175805 | + | 0.984425i | \(0.556253\pi\) | |||||||
\(62\) | −7.84188 | −0.995920 | ||||||||
\(63\) | 0.831331 | 0.104738 | ||||||||
\(64\) | −3.44274 | −0.430343 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.56223 | −0.807754 | ||||||||
\(67\) | 5.56259 | 0.679579 | 0.339789 | − | 0.940502i | \(-0.389644\pi\) | ||||
0.339789 | + | 0.940502i | \(0.389644\pi\) | |||||||
\(68\) | 5.84296 | 0.708563 | ||||||||
\(69\) | −1.47264 | −0.177285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.20033 | 0.735843 | 0.367922 | − | 0.929857i | \(-0.380069\pi\) | ||||
0.367922 | + | 0.929857i | \(0.380069\pi\) | |||||||
\(72\) | −0.805976 | −0.0949852 | ||||||||
\(73\) | 5.19586 | 0.608130 | 0.304065 | − | 0.952651i | \(-0.401656\pi\) | ||||
0.304065 | + | 0.952651i | \(0.401656\pi\) | |||||||
\(74\) | 3.96767 | 0.461233 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.8973 | −1.36471 | ||||||||
\(77\) | −2.38861 | −0.272207 | ||||||||
\(78\) | 14.1528 | 1.60249 | ||||||||
\(79\) | −6.41433 | −0.721668 | −0.360834 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360834 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.81490 | −0.646100 | ||||||||
\(82\) | −3.95801 | −0.437089 | ||||||||
\(83\) | −6.39627 | −0.702082 | −0.351041 | − | 0.936360i | \(-0.614172\pi\) | ||||
−0.351041 | + | 0.936360i | \(0.614172\pi\) | |||||||
\(84\) | −2.17997 | −0.237855 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.0080 | −1.07919 | ||||||||
\(87\) | −5.46491 | −0.585899 | ||||||||
\(88\) | 2.31576 | 0.246861 | ||||||||
\(89\) | −1.93591 | −0.205206 | −0.102603 | − | 0.994722i | \(-0.532717\pi\) | ||||
−0.102603 | + | 0.994722i | \(0.532717\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.15152 | 0.540026 | ||||||||
\(92\) | −1.48032 | −0.154334 | ||||||||
\(93\) | 6.19024 | 0.641898 | ||||||||
\(94\) | −12.2571 | −1.26422 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.2472 | 1.04585 | ||||||||
\(97\) | 5.62379 | 0.571009 | 0.285505 | − | 0.958377i | \(-0.407839\pi\) | ||||
0.285505 | + | 0.958377i | \(0.407839\pi\) | |||||||
\(98\) | −1.86556 | −0.188450 | ||||||||
\(99\) | −1.98572 | −0.199573 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0961 | 1.40262 | 0.701308 | − | 0.712858i | \(-0.252600\pi\) | ||||
0.701308 | + | 0.712858i | \(0.252600\pi\) | |||||||
\(102\) | −10.8439 | −1.07370 | ||||||||
\(103\) | 13.6737 | 1.34731 | 0.673653 | − | 0.739048i | \(-0.264724\pi\) | ||||
0.673653 | + | 0.739048i | \(0.264724\pi\) | |||||||
\(104\) | −4.99441 | −0.489742 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.6012 | −2.29235 | ||||||||
\(107\) | 14.0571 | 1.35895 | 0.679477 | − | 0.733697i | \(-0.262207\pi\) | ||||
0.679477 | + | 0.733697i | \(0.262207\pi\) | |||||||
\(108\) | −8.35220 | −0.803691 | ||||||||
\(109\) | −9.50172 | −0.910100 | −0.455050 | − | 0.890466i | \(-0.650379\pi\) | ||||
−0.455050 | + | 0.890466i | \(0.650379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.13201 | −0.297277 | ||||||||
\(112\) | 4.76930 | 0.450656 | ||||||||
\(113\) | 17.4801 | 1.64439 | 0.822196 | − | 0.569204i | \(-0.192749\pi\) | ||||
0.822196 | + | 0.569204i | \(0.192749\pi\) | |||||||
\(114\) | 22.0800 | 2.06798 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.49339 | −0.510049 | ||||||||
\(117\) | 4.28262 | 0.395928 | ||||||||
\(118\) | −3.87412 | −0.356641 | ||||||||
\(119\) | −3.94710 | −0.361830 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.29454 | −0.481322 | ||||||||
\(122\) | 5.12313 | 0.463826 | ||||||||
\(123\) | 3.12438 | 0.281716 | ||||||||
\(124\) | 6.22251 | 0.558798 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.55090 | −0.138165 | ||||||||
\(127\) | 1.58046 | 0.140243 | 0.0701216 | − | 0.997538i | \(-0.477661\pi\) | ||||
0.0701216 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(128\) | −7.49418 | −0.662398 | ||||||||
\(129\) | 7.90011 | 0.695566 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.80847 | −0.332748 | −0.166374 | − | 0.986063i | \(-0.553206\pi\) | ||||
−0.166374 | + | 0.986063i | \(0.553206\pi\) | |||||||
\(132\) | 5.20711 | 0.453220 | ||||||||
\(133\) | 8.03699 | 0.696896 | ||||||||
\(134\) | −10.3774 | −0.896467 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.82672 | 0.328139 | ||||||||
\(137\) | −4.78795 | −0.409062 | −0.204531 | − | 0.978860i | \(-0.565567\pi\) | ||||
−0.204531 | + | 0.978860i | \(0.565567\pi\) | |||||||
\(138\) | 2.74730 | 0.233866 | ||||||||
\(139\) | −2.18731 | −0.185525 | −0.0927625 | − | 0.995688i | \(-0.529570\pi\) | ||||
−0.0927625 | + | 0.995688i | \(0.529570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.67554 | 0.814827 | ||||||||
\(142\) | −11.5671 | −0.970688 | ||||||||
\(143\) | −12.3050 | −1.02899 | ||||||||
\(144\) | 3.96486 | 0.330405 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.69320 | −0.802215 | ||||||||
\(147\) | 1.47264 | 0.121461 | ||||||||
\(148\) | −3.14834 | −0.258792 | ||||||||
\(149\) | 9.84123 | 0.806225 | 0.403112 | − | 0.915150i | \(-0.367928\pi\) | ||||
0.403112 | + | 0.915150i | \(0.367928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.29915 | −0.675375 | −0.337687 | − | 0.941258i | \(-0.609645\pi\) | ||||
−0.337687 | + | 0.941258i | \(0.609645\pi\) | |||||||
\(152\) | −7.79188 | −0.632005 | ||||||||
\(153\) | −3.28135 | −0.265281 | ||||||||
\(154\) | 4.45610 | 0.359082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.2302 | −0.899135 | ||||||||
\(157\) | −4.29360 | −0.342667 | −0.171333 | − | 0.985213i | \(-0.554808\pi\) | ||||
−0.171333 | + | 0.985213i | \(0.554808\pi\) | |||||||
\(158\) | 11.9663 | 0.951989 | ||||||||
\(159\) | 18.6304 | 1.47749 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 10.8480 | 0.852303 | ||||||||
\(163\) | −7.31735 | −0.573139 | −0.286570 | − | 0.958059i | \(-0.592515\pi\) | ||||
−0.286570 | + | 0.958059i | \(0.592515\pi\) | |||||||
\(164\) | 3.14067 | 0.245245 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9326 | 0.926152 | ||||||||
\(167\) | 17.4368 | 1.34930 | 0.674648 | − | 0.738139i | \(-0.264295\pi\) | ||||
0.674648 | + | 0.738139i | \(0.264295\pi\) | |||||||
\(168\) | −1.42773 | −0.110151 | ||||||||
\(169\) | 13.5382 | 1.04140 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.68140 | 0.510939 | ||||||||
\(172\) | 7.94129 | 0.605517 | ||||||||
\(173\) | 1.62465 | 0.123520 | 0.0617598 | − | 0.998091i | \(-0.480329\pi\) | ||||
0.0617598 | + | 0.998091i | \(0.480329\pi\) | |||||||
\(174\) | 10.1951 | 0.772889 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.3920 | −0.858703 | ||||||||
\(177\) | 3.05816 | 0.229865 | ||||||||
\(178\) | 3.61155 | 0.270697 | ||||||||
\(179\) | −9.29389 | −0.694658 | −0.347329 | − | 0.937743i | \(-0.612911\pi\) | ||||
−0.347329 | + | 0.937743i | \(0.612911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.59757 | 0.193076 | 0.0965379 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965379 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(182\) | −9.61048 | −0.712376 | ||||||||
\(183\) | −4.04411 | −0.298949 | ||||||||
\(184\) | −0.969501 | −0.0714726 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.5483 | −0.846760 | ||||||||
\(187\) | 9.42809 | 0.689450 | ||||||||
\(188\) | 9.72597 | 0.709339 | ||||||||
\(189\) | 5.64217 | 0.410408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8844 | −0.932281 | −0.466141 | − | 0.884711i | \(-0.654356\pi\) | ||||
−0.466141 | + | 0.884711i | \(0.654356\pi\) | |||||||
\(192\) | −5.06992 | −0.365890 | ||||||||
\(193\) | 8.49047 | 0.611157 | 0.305579 | − | 0.952167i | \(-0.401150\pi\) | ||||
0.305579 | + | 0.952167i | \(0.401150\pi\) | |||||||
\(194\) | −10.4915 | −0.753247 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48032 | 0.105737 | ||||||||
\(197\) | 10.0052 | 0.712842 | 0.356421 | − | 0.934325i | \(-0.383997\pi\) | ||||
0.356421 | + | 0.934325i | \(0.383997\pi\) | |||||||
\(198\) | 3.70449 | 0.263267 | ||||||||
\(199\) | 25.1848 | 1.78530 | 0.892652 | − | 0.450746i | \(-0.148842\pi\) | ||||
0.892652 | + | 0.450746i | \(0.148842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.19170 | 0.577798 | ||||||||
\(202\) | −26.2972 | −1.85026 | ||||||||
\(203\) | 3.71096 | 0.260458 | ||||||||
\(204\) | 8.60458 | 0.602441 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −25.5090 | −1.77730 | ||||||||
\(207\) | 0.831331 | 0.0577815 | ||||||||
\(208\) | 24.5691 | 1.70356 | ||||||||
\(209\) | −19.1972 | −1.32790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2507 | −1.53180 | −0.765900 | − | 0.642960i | \(-0.777706\pi\) | ||||
−0.765900 | + | 0.642960i | \(0.777706\pi\) | |||||||
\(212\) | 18.7275 | 1.28621 | ||||||||
\(213\) | 9.13085 | 0.625635 | ||||||||
\(214\) | −26.2244 | −1.79266 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.47009 | −0.372193 | ||||||||
\(217\) | −4.20350 | −0.285352 | ||||||||
\(218\) | 17.7260 | 1.20056 | ||||||||
\(219\) | 7.65164 | 0.517050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.3336 | −1.36779 | ||||||||
\(222\) | 5.84295 | 0.392153 | ||||||||
\(223\) | 24.7280 | 1.65591 | 0.827955 | − | 0.560795i | \(-0.189504\pi\) | ||||
0.827955 | + | 0.560795i | \(0.189504\pi\) | |||||||
\(224\) | −6.95841 | −0.464928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.6102 | −2.16920 | ||||||||
\(227\) | 17.6036 | 1.16840 | 0.584198 | − | 0.811611i | \(-0.301409\pi\) | ||||
0.584198 | + | 0.811611i | \(0.301409\pi\) | |||||||
\(228\) | −17.5204 | −1.16032 | ||||||||
\(229\) | 8.24072 | 0.544562 | 0.272281 | − | 0.962218i | \(-0.412222\pi\) | ||||
0.272281 | + | 0.962218i | \(0.412222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.51756 | −0.231439 | ||||||||
\(232\) | −3.59778 | −0.236206 | ||||||||
\(233\) | −7.67428 | −0.502759 | −0.251380 | − | 0.967889i | \(-0.580884\pi\) | ||||
−0.251380 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(234\) | −7.98949 | −0.522289 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.07410 | 0.200107 | ||||||||
\(237\) | −9.44600 | −0.613584 | ||||||||
\(238\) | 7.36356 | 0.477309 | ||||||||
\(239\) | 25.7901 | 1.66822 | 0.834112 | − | 0.551595i | \(-0.185981\pi\) | ||||
0.834112 | + | 0.551595i | \(0.185981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2500 | 1.17559 | 0.587793 | − | 0.809012i | \(-0.299997\pi\) | ||||
0.587793 | + | 0.809012i | \(0.299997\pi\) | |||||||
\(242\) | 9.87729 | 0.634937 | ||||||||
\(243\) | 8.36326 | 0.536504 | ||||||||
\(244\) | −4.06519 | −0.260247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.82872 | −0.371626 | ||||||||
\(247\) | 41.4028 | 2.63440 | ||||||||
\(248\) | 4.07530 | 0.258782 | ||||||||
\(249\) | −9.41941 | −0.596931 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4199 | 0.657696 | 0.328848 | − | 0.944383i | \(-0.393340\pi\) | ||||
0.328848 | + | 0.944383i | \(0.393340\pi\) | |||||||
\(252\) | 1.23063 | 0.0775225 | ||||||||
\(253\) | −2.38861 | −0.150171 | ||||||||
\(254\) | −2.94844 | −0.185002 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.8663 | 1.30415 | ||||||||
\(257\) | −29.6739 | −1.85101 | −0.925505 | − | 0.378737i | \(-0.876359\pi\) | ||||
−0.925505 | + | 0.378737i | \(0.876359\pi\) | |||||||
\(258\) | −14.7381 | −0.917556 | ||||||||
\(259\) | 2.12680 | 0.132153 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.08503 | 0.190959 | ||||||||
\(262\) | 7.10494 | 0.438945 | ||||||||
\(263\) | −25.3969 | −1.56604 | −0.783020 | − | 0.621996i | \(-0.786322\pi\) | ||||
−0.783020 | + | 0.621996i | \(0.786322\pi\) | |||||||
\(264\) | 3.41028 | 0.209888 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.9935 | −0.919311 | ||||||||
\(267\) | −2.85090 | −0.174472 | ||||||||
\(268\) | 8.23440 | 0.502996 | ||||||||
\(269\) | −9.01494 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.89439 | 0.540296 | 0.270148 | − | 0.962819i | \(-0.412927\pi\) | ||||
0.270148 | + | 0.962819i | \(0.412927\pi\) | |||||||
\(272\) | −18.8249 | −1.14143 | ||||||||
\(273\) | 7.58634 | 0.459146 | ||||||||
\(274\) | 8.93221 | 0.539614 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.17997 | −0.131219 | ||||||||
\(277\) | 1.59622 | 0.0959075 | 0.0479538 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479538 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(278\) | 4.08056 | 0.244735 | ||||||||
\(279\) | −3.49450 | −0.209210 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0273 | −1.67197 | −0.835986 | − | 0.548751i | \(-0.815103\pi\) | ||||
−0.835986 | + | 0.548751i | \(0.815103\pi\) | |||||||
\(282\) | −18.0503 | −1.07488 | ||||||||
\(283\) | −9.37346 | −0.557194 | −0.278597 | − | 0.960408i | \(-0.589869\pi\) | ||||
−0.278597 | + | 0.960408i | \(0.589869\pi\) | |||||||
\(284\) | 9.17844 | 0.544640 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22.9557 | 1.35740 | ||||||||
\(287\) | −2.12162 | −0.125235 | ||||||||
\(288\) | −5.78474 | −0.340869 | ||||||||
\(289\) | −1.42037 | −0.0835510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.28182 | 0.485489 | ||||||||
\(292\) | 7.69152 | 0.450112 | ||||||||
\(293\) | −8.11404 | −0.474027 | −0.237014 | − | 0.971506i | \(-0.576169\pi\) | ||||
−0.237014 | + | 0.971506i | \(0.576169\pi\) | |||||||
\(294\) | −2.74730 | −0.160226 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.06193 | −0.119847 | ||||||||
\(297\) | −13.4769 | −0.782012 | ||||||||
\(298\) | −18.3594 | −1.06353 | ||||||||
\(299\) | 5.15152 | 0.297920 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.36459 | −0.309210 | ||||||||
\(302\) | 15.4826 | 0.890921 | ||||||||
\(303\) | 20.7585 | 1.19255 | ||||||||
\(304\) | 38.3308 | 2.19842 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.12155 | 0.349946 | ||||||||
\(307\) | −31.8495 | −1.81775 | −0.908873 | − | 0.417073i | \(-0.863056\pi\) | ||||
−0.908873 | + | 0.417073i | \(0.863056\pi\) | |||||||
\(308\) | −3.53590 | −0.201476 | ||||||||
\(309\) | 20.1364 | 1.14552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.13562 | 0.177805 | 0.0889024 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889024 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(312\) | −7.35497 | −0.416393 | ||||||||
\(313\) | 23.2352 | 1.31333 | 0.656666 | − | 0.754181i | \(-0.271966\pi\) | ||||
0.656666 | + | 0.754181i | \(0.271966\pi\) | |||||||
\(314\) | 8.00998 | 0.452029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.49524 | −0.534149 | ||||||||
\(317\) | −15.6598 | −0.879540 | −0.439770 | − | 0.898110i | \(-0.644940\pi\) | ||||
−0.439770 | + | 0.898110i | \(0.644940\pi\) | |||||||
\(318\) | −34.7561 | −1.94903 | ||||||||
\(319\) | −8.86403 | −0.496290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.7011 | 1.15542 | ||||||||
\(322\) | −1.86556 | −0.103964 | ||||||||
\(323\) | −31.7229 | −1.76511 | ||||||||
\(324\) | −8.60789 | −0.478216 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.6510 | 0.756057 | ||||||||
\(327\) | −13.9926 | −0.773794 | ||||||||
\(328\) | 2.05691 | 0.113574 | ||||||||
\(329\) | −6.57020 | −0.362227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.8143 | −1.19902 | −0.599512 | − | 0.800365i | \(-0.704639\pi\) | ||||
−0.599512 | + | 0.800365i | \(0.704639\pi\) | |||||||
\(332\) | −9.46851 | −0.519652 | ||||||||
\(333\) | 1.76807 | 0.0968898 | ||||||||
\(334\) | −32.5293 | −1.77993 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.02346 | 0.383161 | ||||||||
\(337\) | 5.42470 | 0.295502 | 0.147751 | − | 0.989025i | \(-0.452797\pi\) | ||||
0.147751 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(338\) | −25.2563 | −1.37376 | ||||||||
\(339\) | 25.7419 | 1.39811 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0405 | 0.543724 | ||||||||
\(342\) | −12.4646 | −0.674006 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.20097 | 0.280418 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.03088 | −0.162941 | ||||||||
\(347\) | 11.4060 | 0.612309 | 0.306154 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306154 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(348\) | −8.08979 | −0.433658 | ||||||||
\(349\) | 13.3270 | 0.713379 | 0.356690 | − | 0.934223i | \(-0.383905\pi\) | ||||
0.356690 | + | 0.934223i | \(0.383905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.0658 | 1.55142 | ||||||||
\(352\) | 16.6209 | 0.885898 | ||||||||
\(353\) | −27.3740 | −1.45697 | −0.728485 | − | 0.685062i | \(-0.759775\pi\) | ||||
−0.728485 | + | 0.685062i | \(0.759775\pi\) | |||||||
\(354\) | −5.70518 | −0.303227 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.86576 | −0.151885 | ||||||||
\(357\) | −5.81267 | −0.307639 | ||||||||
\(358\) | 17.3383 | 0.916359 | ||||||||
\(359\) | −14.0136 | −0.739612 | −0.369806 | − | 0.929109i | \(-0.620576\pi\) | ||||
−0.369806 | + | 0.929109i | \(0.620576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.5933 | 2.39965 | ||||||||
\(362\) | −4.84592 | −0.254696 | ||||||||
\(363\) | −7.79696 | −0.409234 | ||||||||
\(364\) | 7.62589 | 0.399705 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.54453 | 0.394359 | ||||||||
\(367\) | 6.01486 | 0.313973 | 0.156986 | − | 0.987601i | \(-0.449822\pi\) | ||||
0.156986 | + | 0.987601i | \(0.449822\pi\) | |||||||
\(368\) | 4.76930 | 0.248617 | ||||||||
\(369\) | −1.76377 | −0.0918180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.6510 | −0.656807 | ||||||||
\(372\) | 9.16352 | 0.475106 | ||||||||
\(373\) | 8.76458 | 0.453813 | 0.226906 | − | 0.973917i | \(-0.427139\pi\) | ||||
0.226906 | + | 0.973917i | \(0.427139\pi\) | |||||||
\(374\) | −17.5887 | −0.909489 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.36982 | 0.328498 | ||||||||
\(377\) | 19.1171 | 0.984580 | ||||||||
\(378\) | −10.5258 | −0.541389 | ||||||||
\(379\) | −15.7948 | −0.811325 | −0.405662 | − | 0.914023i | \(-0.632959\pi\) | ||||
−0.405662 | + | 0.914023i | \(0.632959\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.32745 | 0.119239 | ||||||||
\(382\) | 24.0366 | 1.22982 | ||||||||
\(383\) | −31.6206 | −1.61574 | −0.807869 | − | 0.589362i | \(-0.799379\pi\) | ||||
−0.807869 | + | 0.589362i | \(0.799379\pi\) | |||||||
\(384\) | −11.0362 | −0.563190 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.8395 | −0.806208 | ||||||||
\(387\) | −4.45974 | −0.226702 | ||||||||
\(388\) | 8.32498 | 0.422637 | ||||||||
\(389\) | 17.1433 | 0.869198 | 0.434599 | − | 0.900624i | \(-0.356890\pi\) | ||||
0.434599 | + | 0.900624i | \(0.356890\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.94710 | −0.199614 | ||||||||
\(392\) | 0.969501 | 0.0489672 | ||||||||
\(393\) | −5.60851 | −0.282912 | ||||||||
\(394\) | −18.6653 | −0.940346 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.93950 | −0.147715 | ||||||||
\(397\) | 32.4863 | 1.63044 | 0.815221 | − | 0.579150i | \(-0.196615\pi\) | ||||
0.815221 | + | 0.579150i | \(0.196615\pi\) | |||||||
\(398\) | −46.9838 | −2.35509 | ||||||||
\(399\) | 11.8356 | 0.592521 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5317 | 0.725679 | 0.362840 | − | 0.931852i | \(-0.381807\pi\) | ||||
0.362840 | + | 0.931852i | \(0.381807\pi\) | |||||||
\(402\) | −15.2821 | −0.762202 | ||||||||
\(403\) | −21.6544 | −1.07868 | ||||||||
\(404\) | 20.8667 | 1.03816 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.92302 | −0.343584 | ||||||||
\(407\) | −5.08009 | −0.251811 | ||||||||
\(408\) | 5.63539 | 0.278993 | ||||||||
\(409\) | 19.6266 | 0.970474 | 0.485237 | − | 0.874383i | \(-0.338733\pi\) | ||||
0.485237 | + | 0.874383i | \(0.338733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.05092 | −0.347796 | ||||||||
\(412\) | 20.2413 | 0.997219 | ||||||||
\(413\) | −2.07665 | −0.102185 | ||||||||
\(414\) | −1.55090 | −0.0762225 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −35.8464 | −1.75751 | ||||||||
\(417\) | −3.22112 | −0.157739 | ||||||||
\(418\) | 35.8136 | 1.75170 | ||||||||
\(419\) | 27.1779 | 1.32773 | 0.663863 | − | 0.747854i | \(-0.268916\pi\) | ||||
0.663863 | + | 0.747854i | \(0.268916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.6505 | 1.59129 | 0.795645 | − | 0.605764i | \(-0.207132\pi\) | ||||
0.795645 | + | 0.605764i | \(0.207132\pi\) | |||||||
\(422\) | 41.5100 | 2.02067 | ||||||||
\(423\) | −5.46201 | −0.265572 | ||||||||
\(424\) | 12.2652 | 0.595649 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −17.0342 | −0.825307 | ||||||||
\(427\) | 2.74616 | 0.132896 | ||||||||
\(428\) | 20.8090 | 1.00584 | ||||||||
\(429\) | −18.1208 | −0.874881 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5655 | 1.08694 | 0.543471 | − | 0.839428i | \(-0.317110\pi\) | ||||
0.543471 | + | 0.839428i | \(0.317110\pi\) | |||||||
\(432\) | 26.9092 | 1.29467 | ||||||||
\(433\) | −5.41260 | −0.260113 | −0.130056 | − | 0.991507i | \(-0.541516\pi\) | ||||
−0.130056 | + | 0.991507i | \(0.541516\pi\) | |||||||
\(434\) | 7.84188 | 0.376422 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0656 | −0.673618 | ||||||||
\(437\) | 8.03699 | 0.384462 | ||||||||
\(438\) | −14.2746 | −0.682067 | ||||||||
\(439\) | 19.5191 | 0.931598 | 0.465799 | − | 0.884891i | \(-0.345767\pi\) | ||||
0.465799 | + | 0.884891i | \(0.345767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.831331 | −0.0395872 | ||||||||
\(442\) | 37.9336 | 1.80432 | ||||||||
\(443\) | 22.2864 | 1.05886 | 0.529430 | − | 0.848354i | \(-0.322406\pi\) | ||||
0.529430 | + | 0.848354i | \(0.322406\pi\) | |||||||
\(444\) | −4.63637 | −0.220032 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −46.1316 | −2.18439 | ||||||||
\(447\) | 14.4926 | 0.685476 | ||||||||
\(448\) | 3.44274 | 0.162654 | ||||||||
\(449\) | 18.3447 | 0.865740 | 0.432870 | − | 0.901456i | \(-0.357501\pi\) | ||||
0.432870 | + | 0.901456i | \(0.357501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.06772 | 0.238629 | ||||||||
\(452\) | 25.8761 | 1.21711 | ||||||||
\(453\) | −12.2217 | −0.574224 | ||||||||
\(454\) | −32.8407 | −1.54129 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4746 | −0.537349 | ||||||||
\(457\) | 30.4321 | 1.42355 | 0.711776 | − | 0.702406i | \(-0.247891\pi\) | ||||
0.711776 | + | 0.702406i | \(0.247891\pi\) | |||||||
\(458\) | −15.3736 | −0.718360 | ||||||||
\(459\) | −22.2702 | −1.03949 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.5427 | 1.56224 | 0.781119 | − | 0.624383i | \(-0.214649\pi\) | ||||
0.781119 | + | 0.624383i | \(0.214649\pi\) | |||||||
\(462\) | 6.56223 | 0.305302 | ||||||||
\(463\) | 20.3855 | 0.947394 | 0.473697 | − | 0.880688i | \(-0.342919\pi\) | ||||
0.473697 | + | 0.880688i | \(0.342919\pi\) | |||||||
\(464\) | 17.6987 | 0.821639 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.3168 | 0.663215 | ||||||||
\(467\) | 15.3079 | 0.708363 | 0.354182 | − | 0.935177i | \(-0.384759\pi\) | ||||
0.354182 | + | 0.935177i | \(0.384759\pi\) | |||||||
\(468\) | 6.33963 | 0.293050 | ||||||||
\(469\) | −5.56259 | −0.256857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.32293 | −0.291345 | ||||||||
\(472\) | 2.01331 | 0.0926703 | ||||||||
\(473\) | 12.8139 | 0.589184 | ||||||||
\(474\) | 17.6221 | 0.809409 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.84296 | −0.267812 | ||||||||
\(477\) | −10.5172 | −0.481548 | ||||||||
\(478\) | −48.1130 | −2.20064 | ||||||||
\(479\) | −18.3531 | −0.838575 | −0.419288 | − | 0.907853i | \(-0.637720\pi\) | ||||
−0.419288 | + | 0.907853i | \(0.637720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9563 | 0.499562 | ||||||||
\(482\) | −34.0465 | −1.55077 | ||||||||
\(483\) | 1.47264 | 0.0670075 | ||||||||
\(484\) | −7.83760 | −0.356255 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.6022 | −0.707729 | ||||||||
\(487\) | −8.20282 | −0.371705 | −0.185853 | − | 0.982578i | \(-0.559505\pi\) | ||||
−0.185853 | + | 0.982578i | \(0.559505\pi\) | |||||||
\(488\) | −2.66241 | −0.120521 | ||||||||
\(489\) | −10.7758 | −0.487300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0280 | 0.497686 | 0.248843 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248843 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(492\) | 4.62507 | 0.208514 | ||||||||
\(493\) | −14.6475 | −0.659692 | ||||||||
\(494\) | −77.2394 | −3.47516 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0477 | −0.900170 | ||||||||
\(497\) | −6.20033 | −0.278123 | ||||||||
\(498\) | 17.5725 | 0.787442 | ||||||||
\(499\) | 10.6322 | 0.475965 | 0.237982 | − | 0.971269i | \(-0.423514\pi\) | ||||
0.237982 | + | 0.971269i | \(0.423514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.6781 | 1.14721 | ||||||||
\(502\) | −19.4389 | −0.867600 | ||||||||
\(503\) | −17.0269 | −0.759191 | −0.379595 | − | 0.925153i | \(-0.623937\pi\) | ||||
−0.379595 | + | 0.925153i | \(0.623937\pi\) | |||||||
\(504\) | 0.805976 | 0.0359010 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.45610 | 0.198098 | ||||||||
\(507\) | 19.9369 | 0.885429 | ||||||||
\(508\) | 2.33958 | 0.103802 | ||||||||
\(509\) | −7.96156 | −0.352890 | −0.176445 | − | 0.984311i | \(-0.556460\pi\) | ||||
−0.176445 | + | 0.984311i | \(0.556460\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.19586 | −0.229852 | ||||||||
\(512\) | −23.9390 | −1.05797 | ||||||||
\(513\) | 45.3461 | 2.00208 | ||||||||
\(514\) | 55.3585 | 2.44176 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.6947 | 0.514829 | ||||||||
\(517\) | 15.6936 | 0.690205 | ||||||||
\(518\) | −3.96767 | −0.174330 | ||||||||
\(519\) | 2.39252 | 0.105020 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.19516 | 0.315226 | 0.157613 | − | 0.987501i | \(-0.449620\pi\) | ||||
0.157613 | + | 0.987501i | \(0.449620\pi\) | |||||||
\(522\) | −5.75531 | −0.251903 | ||||||||
\(523\) | 45.4879 | 1.98905 | 0.994523 | − | 0.104516i | \(-0.0333294\pi\) | ||||
0.994523 | + | 0.104516i | \(0.0333294\pi\) | |||||||
\(524\) | −5.63775 | −0.246286 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.3795 | 2.06584 | ||||||||
\(527\) | 16.5916 | 0.722744 | ||||||||
\(528\) | −16.7763 | −0.730095 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.72638 | −0.0749186 | ||||||||
\(532\) | 11.8973 | 0.515813 | ||||||||
\(533\) | −10.9296 | −0.473412 | ||||||||
\(534\) | 5.31852 | 0.230155 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.39294 | 0.232940 | ||||||||
\(537\) | −13.6866 | −0.590619 | ||||||||
\(538\) | 16.8179 | 0.725072 | ||||||||
\(539\) | 2.38861 | 0.102885 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9932 | −1.67645 | −0.838225 | − | 0.545325i | \(-0.816406\pi\) | ||||
−0.838225 | + | 0.545325i | \(0.816406\pi\) | |||||||
\(542\) | −16.5930 | −0.712731 | ||||||||
\(543\) | 3.82529 | 0.164159 | ||||||||
\(544\) | 27.4656 | 1.17758 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.1528 | −0.605683 | ||||||||
\(547\) | −42.0336 | −1.79723 | −0.898613 | − | 0.438742i | \(-0.855424\pi\) | ||||
−0.898613 | + | 0.438742i | \(0.855424\pi\) | |||||||
\(548\) | −7.08768 | −0.302771 | ||||||||
\(549\) | 2.28297 | 0.0974347 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.8249 | 1.27059 | ||||||||
\(552\) | −1.42773 | −0.0607681 | ||||||||
\(553\) | 6.41433 | 0.272765 | ||||||||
\(554\) | −2.97784 | −0.126516 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.23791 | −0.137318 | ||||||||
\(557\) | 1.72572 | 0.0731213 | 0.0365606 | − | 0.999331i | \(-0.488360\pi\) | ||||
0.0365606 | + | 0.999331i | \(0.488360\pi\) | |||||||
\(558\) | 6.51920 | 0.275980 | ||||||||
\(559\) | −27.6358 | −1.16887 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8842 | 0.586191 | ||||||||
\(562\) | 52.2867 | 2.20558 | ||||||||
\(563\) | 6.91648 | 0.291495 | 0.145747 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145747 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(564\) | 14.3229 | 0.603101 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.4868 | 0.735023 | ||||||||
\(567\) | 5.81490 | 0.244203 | ||||||||
\(568\) | 6.01122 | 0.252225 | ||||||||
\(569\) | 33.4704 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7343 | −0.742158 | −0.371079 | − | 0.928601i | \(-0.621012\pi\) | ||||
−0.371079 | + | 0.928601i | \(0.621012\pi\) | |||||||
\(572\) | −18.2153 | −0.761618 | ||||||||
\(573\) | −18.9741 | −0.792653 | ||||||||
\(574\) | 3.95801 | 0.165204 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.86206 | 0.119252 | ||||||||
\(577\) | −14.3568 | −0.597682 | −0.298841 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298841 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(578\) | 2.64978 | 0.110216 | ||||||||
\(579\) | 12.5034 | 0.519624 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.39627 | 0.265362 | ||||||||
\(582\) | −15.4502 | −0.640433 | ||||||||
\(583\) | 30.2183 | 1.25151 | ||||||||
\(584\) | 5.03740 | 0.208449 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.1372 | 0.625313 | ||||||||
\(587\) | −37.6419 | −1.55365 | −0.776823 | − | 0.629718i | \(-0.783170\pi\) | ||||
−0.776823 | + | 0.629718i | \(0.783170\pi\) | |||||||
\(588\) | 2.17997 | 0.0899006 | ||||||||
\(589\) | −33.7835 | −1.39202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.7341 | 0.606079 | ||||||||
\(592\) | 10.1433 | 0.416888 | ||||||||
\(593\) | 44.3928 | 1.82299 | 0.911497 | − | 0.411307i | \(-0.134927\pi\) | ||||
0.911497 | + | 0.411307i | \(0.134927\pi\) | |||||||
\(594\) | 25.1421 | 1.03159 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.5681 | 0.596734 | ||||||||
\(597\) | 37.0882 | 1.51792 | ||||||||
\(598\) | −9.61048 | −0.393002 | ||||||||
\(599\) | 7.74272 | 0.316359 | 0.158180 | − | 0.987410i | \(-0.449438\pi\) | ||||
0.158180 | + | 0.987410i | \(0.449438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9476 | 1.30317 | 0.651584 | − | 0.758576i | \(-0.274105\pi\) | ||||
0.651584 | + | 0.758576i | \(0.274105\pi\) | |||||||
\(602\) | 10.0080 | 0.407894 | ||||||||
\(603\) | −4.62435 | −0.188318 | ||||||||
\(604\) | −12.2854 | −0.499884 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −38.7263 | −1.57315 | ||||||||
\(607\) | 21.1266 | 0.857501 | 0.428750 | − | 0.903423i | \(-0.358954\pi\) | ||||
0.428750 | + | 0.903423i | \(0.358954\pi\) | |||||||
\(608\) | −55.9247 | −2.26805 | ||||||||
\(609\) | 5.46491 | 0.221449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.8465 | −1.36928 | ||||||||
\(612\) | −4.85743 | −0.196350 | ||||||||
\(613\) | −39.7435 | −1.60523 | −0.802613 | − | 0.596500i | \(-0.796558\pi\) | ||||
−0.802613 | + | 0.596500i | \(0.796558\pi\) | |||||||
\(614\) | 59.4171 | 2.39788 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.31576 | −0.0933046 | ||||||||
\(617\) | −7.62182 | −0.306843 | −0.153421 | − | 0.988161i | \(-0.549029\pi\) | ||||
−0.153421 | + | 0.988161i | \(0.549029\pi\) | |||||||
\(618\) | −37.5656 | −1.51111 | ||||||||
\(619\) | −7.69341 | −0.309224 | −0.154612 | − | 0.987975i | \(-0.549413\pi\) | ||||
−0.154612 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.64217 | 0.226413 | ||||||||
\(622\) | −5.84969 | −0.234551 | ||||||||
\(623\) | 1.93591 | 0.0775605 | ||||||||
\(624\) | 36.1815 | 1.44842 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −43.3467 | −1.73248 | ||||||||
\(627\) | −28.2706 | −1.12902 | ||||||||
\(628\) | −6.35589 | −0.253628 | ||||||||
\(629\) | −8.39470 | −0.334719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2726 | 1.28475 | 0.642377 | − | 0.766389i | \(-0.277949\pi\) | ||||
0.642377 | + | 0.766389i | \(0.277949\pi\) | |||||||
\(632\) | −6.21870 | −0.247367 | ||||||||
\(633\) | −32.7672 | −1.30238 | ||||||||
\(634\) | 29.2142 | 1.16025 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 27.5789 | 1.09357 | ||||||||
\(637\) | −5.15152 | −0.204111 | ||||||||
\(638\) | 16.5364 | 0.654682 | ||||||||
\(639\) | −5.15452 | −0.203910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4456 | −1.71600 | −0.857999 | − | 0.513651i | \(-0.828293\pi\) | ||||
−0.857999 | + | 0.513651i | \(0.828293\pi\) | |||||||
\(642\) | −38.6191 | −1.52418 | ||||||||
\(643\) | 38.9653 | 1.53664 | 0.768321 | − | 0.640065i | \(-0.221093\pi\) | ||||
0.768321 | + | 0.640065i | \(0.221093\pi\) | |||||||
\(644\) | 1.48032 | 0.0583326 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 59.1809 | 2.32844 | ||||||||
\(647\) | 37.1483 | 1.46045 | 0.730226 | − | 0.683206i | \(-0.239415\pi\) | ||||
0.730226 | + | 0.683206i | \(0.239415\pi\) | |||||||
\(648\) | −5.63755 | −0.221464 | ||||||||
\(649\) | 4.96031 | 0.194709 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.19024 | −0.242615 | ||||||||
\(652\) | −10.8320 | −0.424214 | ||||||||
\(653\) | −12.1524 | −0.475560 | −0.237780 | − | 0.971319i | \(-0.576420\pi\) | ||||
−0.237780 | + | 0.971319i | \(0.576420\pi\) | |||||||
\(654\) | 26.1041 | 1.02075 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.1186 | −0.395066 | ||||||||
\(657\) | −4.31948 | −0.168519 | ||||||||
\(658\) | 12.2571 | 0.477832 | ||||||||
\(659\) | −31.5160 | −1.22769 | −0.613845 | − | 0.789427i | \(-0.710378\pi\) | ||||
−0.613845 | + | 0.789427i | \(0.710378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.13154 | 0.0440117 | 0.0220058 | − | 0.999758i | \(-0.492995\pi\) | ||||
0.0220058 | + | 0.999758i | \(0.492995\pi\) | |||||||
\(662\) | 40.6960 | 1.58169 | ||||||||
\(663\) | −29.9441 | −1.16293 | ||||||||
\(664\) | −6.20119 | −0.240653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.29845 | −0.127812 | ||||||||
\(667\) | 3.71096 | 0.143689 | ||||||||
\(668\) | 25.8119 | 0.998693 | ||||||||
\(669\) | 36.4155 | 1.40790 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.55951 | −0.253227 | ||||||||
\(672\) | −10.2472 | −0.395296 | ||||||||
\(673\) | 38.2300 | 1.47366 | 0.736829 | − | 0.676080i | \(-0.236323\pi\) | ||||
0.736829 | + | 0.676080i | \(0.236323\pi\) | |||||||
\(674\) | −10.1201 | −0.389812 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.0408 | 0.770801 | ||||||||
\(677\) | −29.5706 | −1.13649 | −0.568245 | − | 0.822859i | \(-0.692378\pi\) | ||||
−0.568245 | + | 0.822859i | \(0.692378\pi\) | |||||||
\(678\) | −48.0232 | −1.84432 | ||||||||
\(679\) | −5.62379 | −0.215821 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9238 | 0.993404 | ||||||||
\(682\) | −18.7312 | −0.717254 | ||||||||
\(683\) | −25.5066 | −0.975982 | −0.487991 | − | 0.872849i | \(-0.662270\pi\) | ||||
−0.487991 | + | 0.872849i | \(0.662270\pi\) | |||||||
\(684\) | 9.89058 | 0.378176 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.86556 | 0.0712274 | ||||||||
\(687\) | 12.1356 | 0.463003 | ||||||||
\(688\) | −25.5853 | −0.975431 | ||||||||
\(689\) | −65.1720 | −2.48285 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.00938603 | 0.000357061 0 | 0.000178531 | − | 1.00000i | \(-0.499943\pi\) | ||||
0.000178531 | 1.00000i | \(0.499943\pi\) | ||||||||
\(692\) | 2.40499 | 0.0914241 | ||||||||
\(693\) | 1.98572 | 0.0754314 | ||||||||
\(694\) | −21.2787 | −0.807727 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.29823 | −0.200829 | ||||||||
\(697\) | 8.37425 | 0.317197 | ||||||||
\(698\) | −24.8624 | −0.941055 | ||||||||
\(699\) | −11.3015 | −0.427460 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.19980 | −0.0830852 | −0.0415426 | − | 0.999137i | \(-0.513227\pi\) | ||||
−0.0415426 | + | 0.999137i | \(0.513227\pi\) | |||||||
\(702\) | −54.2240 | −2.04655 | ||||||||
\(703\) | 17.0931 | 0.644677 | ||||||||
\(704\) | −8.22336 | −0.309930 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 51.0678 | 1.92196 | ||||||||
\(707\) | −14.0961 | −0.530139 | ||||||||
\(708\) | 4.52704 | 0.170137 | ||||||||
\(709\) | 38.2506 | 1.43653 | 0.718266 | − | 0.695768i | \(-0.244936\pi\) | ||||
0.718266 | + | 0.695768i | \(0.244936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.33243 | 0.199982 | ||||||||
\(712\) | −1.87686 | −0.0703385 | ||||||||
\(713\) | −4.20350 | −0.157422 | ||||||||
\(714\) | 10.8439 | 0.405822 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.7579 | −0.514157 | ||||||||
\(717\) | 37.9796 | 1.41837 | ||||||||
\(718\) | 26.1433 | 0.975659 | ||||||||
\(719\) | −16.5752 | −0.618149 | −0.309074 | − | 0.951038i | \(-0.600019\pi\) | ||||
−0.309074 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.6737 | −0.509234 | ||||||||
\(722\) | −85.0570 | −3.16549 | ||||||||
\(723\) | 26.8757 | 0.999517 | ||||||||
\(724\) | 3.84523 | 0.142907 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.5457 | 0.539842 | ||||||||
\(727\) | −51.1494 | −1.89703 | −0.948513 | − | 0.316739i | \(-0.897412\pi\) | ||||
−0.948513 | + | 0.316739i | \(0.897412\pi\) | |||||||
\(728\) | 4.99441 | 0.185105 | ||||||||
\(729\) | 29.7608 | 1.10225 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.1746 | 0.783170 | ||||||||
\(732\) | −5.98656 | −0.221270 | ||||||||
\(733\) | −22.7843 | −0.841557 | −0.420778 | − | 0.907163i | \(-0.638243\pi\) | ||||
−0.420778 | + | 0.907163i | \(0.638243\pi\) | |||||||
\(734\) | −11.2211 | −0.414178 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.95841 | −0.256490 | ||||||||
\(737\) | 13.2869 | 0.489428 | ||||||||
\(738\) | 3.29041 | 0.121122 | ||||||||
\(739\) | −28.0978 | −1.03360 | −0.516798 | − | 0.856107i | \(-0.672876\pi\) | ||||
−0.516798 | + | 0.856107i | \(0.672876\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 60.9714 | 2.23984 | ||||||||
\(742\) | 23.6012 | 0.866428 | ||||||||
\(743\) | 40.5765 | 1.48861 | 0.744303 | − | 0.667842i | \(-0.232782\pi\) | ||||
0.744303 | + | 0.667842i | \(0.232782\pi\) | |||||||
\(744\) | 6.00145 | 0.220024 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.3508 | −0.598647 | ||||||||
\(747\) | 5.31742 | 0.194554 | ||||||||
\(748\) | 13.9566 | 0.510302 | ||||||||
\(749\) | −14.0571 | −0.513636 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1626 | −0.480309 | −0.240154 | − | 0.970735i | \(-0.577198\pi\) | ||||
−0.240154 | + | 0.970735i | \(0.577198\pi\) | |||||||
\(752\) | −31.3352 | −1.14268 | ||||||||
\(753\) | 15.3447 | 0.559192 | ||||||||
\(754\) | −35.6641 | −1.29881 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.35220 | 0.303767 | ||||||||
\(757\) | 7.26122 | 0.263914 | 0.131957 | − | 0.991255i | \(-0.457874\pi\) | ||||
0.131957 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(758\) | 29.4662 | 1.07026 | ||||||||
\(759\) | −3.51756 | −0.127679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.4997 | −0.380614 | −0.190307 | − | 0.981725i | \(-0.560948\pi\) | ||||
−0.190307 | + | 0.981725i | \(0.560948\pi\) | |||||||
\(762\) | −4.34200 | −0.157294 | ||||||||
\(763\) | 9.50172 | 0.343986 | ||||||||
\(764\) | −19.0730 | −0.690036 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 58.9902 | 2.13140 | ||||||||
\(767\) | −10.6979 | −0.386279 | ||||||||
\(768\) | 30.7286 | 1.10882 | ||||||||
\(769\) | 7.08830 | 0.255610 | 0.127805 | − | 0.991799i | \(-0.459207\pi\) | ||||
0.127805 | + | 0.991799i | \(0.459207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.6990 | −1.57378 | ||||||||
\(772\) | 12.5686 | 0.452353 | ||||||||
\(773\) | −1.64999 | −0.0593460 | −0.0296730 | − | 0.999560i | \(-0.509447\pi\) | ||||
−0.0296730 | + | 0.999560i | \(0.509447\pi\) | |||||||
\(774\) | 8.31992 | 0.299054 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.45227 | 0.195725 | ||||||||
\(777\) | 3.13201 | 0.112360 | ||||||||
\(778\) | −31.9818 | −1.14660 | ||||||||
\(779\) | −17.0514 | −0.610931 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.8102 | 0.529949 | ||||||||
\(782\) | 7.36356 | 0.263320 | ||||||||
\(783\) | 20.9379 | 0.748258 | ||||||||
\(784\) | −4.76930 | −0.170332 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.4630 | 0.373204 | ||||||||
\(787\) | 2.18169 | 0.0777690 | 0.0388845 | − | 0.999244i | \(-0.487620\pi\) | ||||
0.0388845 | + | 0.999244i | \(0.487620\pi\) | |||||||
\(788\) | 14.8109 | 0.527616 | ||||||||
\(789\) | −37.4005 | −1.33149 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4801 | −0.621522 | ||||||||
\(792\) | −1.92516 | −0.0684076 | ||||||||
\(793\) | 14.1469 | 0.502372 | ||||||||
\(794\) | −60.6052 | −2.15080 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.2815 | 1.32141 | ||||||||
\(797\) | 36.9437 | 1.30861 | 0.654306 | − | 0.756230i | \(-0.272961\pi\) | ||||
0.654306 | + | 0.756230i | \(0.272961\pi\) | |||||||
\(798\) | −22.0800 | −0.781625 | ||||||||
\(799\) | 25.9333 | 0.917453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.60938 | 0.0568646 | ||||||||
\(802\) | −27.1098 | −0.957280 | ||||||||
\(803\) | 12.4109 | 0.437971 | ||||||||
\(804\) | 12.1263 | 0.427662 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.3976 | 1.42295 | ||||||||
\(807\) | −13.2758 | −0.467329 | ||||||||
\(808\) | 13.6662 | 0.480775 | ||||||||
\(809\) | −21.5021 | −0.755974 | −0.377987 | − | 0.925811i | \(-0.623384\pi\) | ||||
−0.377987 | + | 0.925811i | \(0.623384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5149 | −1.28221 | −0.641106 | − | 0.767452i | \(-0.721524\pi\) | ||||
−0.641106 | + | 0.767452i | \(0.721524\pi\) | |||||||
\(812\) | 5.49339 | 0.192780 | ||||||||
\(813\) | 13.0982 | 0.459375 | ||||||||
\(814\) | 9.47722 | 0.332176 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −27.7223 | −0.970475 | ||||||||
\(817\) | −43.1152 | −1.50841 | ||||||||
\(818\) | −36.6147 | −1.28020 | ||||||||
\(819\) | −4.28262 | −0.149647 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8174 | 1.56414 | 0.782068 | − | 0.623193i | \(-0.214165\pi\) | ||||
0.782068 | + | 0.623193i | \(0.214165\pi\) | |||||||
\(822\) | 13.1539 | 0.458796 | ||||||||
\(823\) | −23.5737 | −0.821727 | −0.410863 | − | 0.911697i | \(-0.634773\pi\) | ||||
−0.410863 | + | 0.911697i | \(0.634773\pi\) | |||||||
\(824\) | 13.2566 | 0.461817 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.87412 | 0.134798 | ||||||||
\(827\) | 15.2355 | 0.529791 | 0.264895 | − | 0.964277i | \(-0.414663\pi\) | ||||
0.264895 | + | 0.964277i | \(0.414663\pi\) | |||||||
\(828\) | 1.23063 | 0.0427674 | ||||||||
\(829\) | −45.0464 | −1.56453 | −0.782263 | − | 0.622949i | \(-0.785934\pi\) | ||||
−0.782263 | + | 0.622949i | \(0.785934\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.35066 | 0.0815434 | ||||||||
\(832\) | 17.7354 | 0.614863 | ||||||||
\(833\) | 3.94710 | 0.136759 | ||||||||
\(834\) | 6.00919 | 0.208081 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.4180 | −0.982857 | ||||||||
\(837\) | −23.7169 | −0.819775 | ||||||||
\(838\) | −50.7020 | −1.75147 | ||||||||
\(839\) | 41.1443 | 1.42046 | 0.710230 | − | 0.703970i | \(-0.248591\pi\) | ||||
0.710230 | + | 0.703970i | \(0.248591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2288 | −0.525131 | ||||||||
\(842\) | −60.9115 | −2.09915 | ||||||||
\(843\) | −41.2742 | −1.42156 | ||||||||
\(844\) | −32.9380 | −1.13377 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.1897 | 0.350329 | ||||||||
\(847\) | 5.29454 | 0.181923 | ||||||||
\(848\) | −60.3364 | −2.07196 | ||||||||
\(849\) | −13.8037 | −0.473743 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.12680 | 0.0729057 | ||||||||
\(852\) | 13.5165 | 0.463069 | ||||||||
\(853\) | −44.1920 | −1.51311 | −0.756553 | − | 0.653933i | \(-0.773118\pi\) | ||||
−0.756553 | + | 0.653933i | \(0.773118\pi\) | |||||||
\(854\) | −5.12313 | −0.175310 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.6284 | 0.465809 | ||||||||
\(857\) | 5.66995 | 0.193682 | 0.0968410 | − | 0.995300i | \(-0.469126\pi\) | ||||
0.0968410 | + | 0.995300i | \(0.469126\pi\) | |||||||
\(858\) | 33.8055 | 1.15410 | ||||||||
\(859\) | −24.7661 | −0.845008 | −0.422504 | − | 0.906361i | \(-0.638849\pi\) | ||||
−0.422504 | + | 0.906361i | \(0.638849\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.12438 | −0.106479 | ||||||||
\(862\) | −42.0973 | −1.43384 | ||||||||
\(863\) | 51.6782 | 1.75915 | 0.879574 | − | 0.475763i | \(-0.157828\pi\) | ||||
0.879574 | + | 0.475763i | \(0.157828\pi\) | |||||||
\(864\) | −39.2605 | −1.33567 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.0975 | 0.343128 | ||||||||
\(867\) | −2.09169 | −0.0710375 | ||||||||
\(868\) | −6.22251 | −0.211206 | ||||||||
\(869\) | −15.3213 | −0.519740 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.6558 | −0.970966 | ||||||||
\(872\) | −9.21193 | −0.311955 | ||||||||
\(873\) | −4.67523 | −0.158232 | ||||||||
\(874\) | −14.9935 | −0.507163 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.3268 | 0.382699 | ||||||||
\(877\) | −22.5801 | −0.762477 | −0.381238 | − | 0.924477i | \(-0.624502\pi\) | ||||
−0.381238 | + | 0.924477i | \(0.624502\pi\) | |||||||
\(878\) | −36.4141 | −1.22892 | ||||||||
\(879\) | −11.9491 | −0.403032 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.2804 | −0.784337 | −0.392169 | − | 0.919893i | \(-0.628275\pi\) | ||||
−0.392169 | + | 0.919893i | \(0.628275\pi\) | |||||||
\(882\) | 1.55090 | 0.0522214 | ||||||||
\(883\) | 18.3267 | 0.616741 | 0.308371 | − | 0.951266i | \(-0.400216\pi\) | ||||
0.308371 | + | 0.951266i | \(0.400216\pi\) | |||||||
\(884\) | −30.1002 | −1.01238 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.5767 | −1.39680 | ||||||||
\(887\) | 24.7614 | 0.831406 | 0.415703 | − | 0.909500i | \(-0.363536\pi\) | ||||
0.415703 | + | 0.909500i | \(0.363536\pi\) | |||||||
\(888\) | −3.03649 | −0.101898 | ||||||||
\(889\) | −1.58046 | −0.0530069 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.8895 | −0.465316 | ||||||||
\(892\) | 36.6053 | 1.22564 | ||||||||
\(893\) | −52.8046 | −1.76704 | ||||||||
\(894\) | −27.0368 | −0.904246 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.49418 | 0.250363 | ||||||||
\(897\) | 7.58634 | 0.253301 | ||||||||
\(898\) | −34.2232 | −1.14204 | ||||||||
\(899\) | −15.5990 | −0.520256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.9348 | 1.66357 | ||||||||
\(902\) | −9.45413 | −0.314788 | ||||||||
\(903\) | −7.90011 | −0.262899 | ||||||||
\(904\) | 16.9470 | 0.563649 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.8002 | 0.757487 | ||||||||
\(907\) | 45.5765 | 1.51334 | 0.756672 | − | 0.653795i | \(-0.226824\pi\) | ||||
0.756672 | + | 0.653795i | \(0.226824\pi\) | |||||||
\(908\) | 26.0590 | 0.864797 | ||||||||
\(909\) | −11.7185 | −0.388679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7278 | −0.653611 | −0.326805 | − | 0.945092i | \(-0.605972\pi\) | ||||
−0.326805 | + | 0.945092i | \(0.605972\pi\) | |||||||
\(912\) | 56.4475 | 1.86916 | ||||||||
\(913\) | −15.2782 | −0.505635 | ||||||||
\(914\) | −56.7729 | −1.87788 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.1989 | 0.403062 | ||||||||
\(917\) | 3.80847 | 0.125767 | ||||||||
\(918\) | 41.5465 | 1.37124 | ||||||||
\(919\) | 31.0813 | 1.02528 | 0.512639 | − | 0.858604i | \(-0.328668\pi\) | ||||
0.512639 | + | 0.858604i | \(0.328668\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.9028 | −1.54550 | ||||||||
\(922\) | −62.5759 | −2.06083 | ||||||||
\(923\) | −31.9411 | −1.05135 | ||||||||
\(924\) | −5.20711 | −0.171301 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −38.0304 | −1.24976 | ||||||||
\(927\) | −11.3673 | −0.373352 | ||||||||
\(928\) | −25.8224 | −0.847660 | ||||||||
\(929\) | 25.4983 | 0.836571 | 0.418286 | − | 0.908316i | \(-0.362631\pi\) | ||||
0.418286 | + | 0.908316i | \(0.362631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.03699 | −0.263402 | ||||||||
\(932\) | −11.3604 | −0.372121 | ||||||||
\(933\) | 4.61764 | 0.151175 | ||||||||
\(934\) | −28.5577 | −0.934438 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.15200 | 0.135713 | ||||||||
\(937\) | −16.3831 | −0.535213 | −0.267607 | − | 0.963528i | \(-0.586233\pi\) | ||||
−0.267607 | + | 0.963528i | \(0.586233\pi\) | |||||||
\(938\) | 10.3774 | 0.338833 | ||||||||
\(939\) | 34.2171 | 1.11663 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4129 | −0.795839 | −0.397920 | − | 0.917420i | \(-0.630268\pi\) | ||||
−0.397920 | + | 0.917420i | \(0.630268\pi\) | |||||||
\(942\) | 11.7958 | 0.384328 | ||||||||
\(943\) | −2.12162 | −0.0690894 | ||||||||
\(944\) | −9.90416 | −0.322353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.9051 | −0.777222 | ||||||||
\(947\) | −38.2048 | −1.24149 | −0.620745 | − | 0.784012i | \(-0.713170\pi\) | ||||
−0.620745 | + | 0.784012i | \(0.713170\pi\) | |||||||
\(948\) | −13.9831 | −0.454149 | ||||||||
\(949\) | −26.7666 | −0.868881 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0612 | −0.747811 | ||||||||
\(952\) | −3.82672 | −0.124025 | ||||||||
\(953\) | −12.1510 | −0.393610 | −0.196805 | − | 0.980443i | \(-0.563057\pi\) | ||||
−0.196805 | + | 0.980443i | \(0.563057\pi\) | |||||||
\(954\) | 19.6204 | 0.635234 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 38.1775 | 1.23475 | ||||||||
\(957\) | −13.0535 | −0.421961 | ||||||||
\(958\) | 34.2389 | 1.10621 | ||||||||
\(959\) | 4.78795 | 0.154611 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3306 | −0.430019 | ||||||||
\(962\) | −20.4396 | −0.658998 | ||||||||
\(963\) | −11.6861 | −0.376580 | ||||||||
\(964\) | 27.0158 | 0.870119 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.74730 | −0.0883929 | ||||||||
\(967\) | 54.2381 | 1.74418 | 0.872089 | − | 0.489347i | \(-0.162765\pi\) | ||||
0.872089 | + | 0.489347i | \(0.162765\pi\) | |||||||
\(968\) | −5.13307 | −0.164983 | ||||||||
\(969\) | −46.7164 | −1.50075 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.88823 | 0.0605962 | 0.0302981 | − | 0.999541i | \(-0.490354\pi\) | ||||
0.0302981 | + | 0.999541i | \(0.490354\pi\) | |||||||
\(972\) | 12.3803 | 0.397097 | ||||||||
\(973\) | 2.18731 | 0.0701219 | ||||||||
\(974\) | 15.3029 | 0.490335 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.0973 | 0.419233 | ||||||||
\(977\) | 22.4378 | 0.717850 | 0.358925 | − | 0.933366i | \(-0.383143\pi\) | ||||
0.358925 | + | 0.933366i | \(0.383143\pi\) | |||||||
\(978\) | 20.1030 | 0.642822 | ||||||||
\(979\) | −4.62413 | −0.147788 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.89907 | 0.252198 | ||||||||
\(982\) | −20.5734 | −0.656523 | ||||||||
\(983\) | −60.1504 | −1.91850 | −0.959250 | − | 0.282558i | \(-0.908817\pi\) | ||||
−0.959250 | + | 0.282558i | \(0.908817\pi\) | |||||||
\(984\) | 3.02909 | 0.0965639 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.3259 | 0.870233 | ||||||||
\(987\) | −9.67554 | −0.307976 | ||||||||
\(988\) | 61.2892 | 1.94987 | ||||||||
\(989\) | −5.36459 | −0.170584 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0838 | 1.52743 | 0.763717 | − | 0.645551i | \(-0.223372\pi\) | ||||
0.763717 | + | 0.645551i | \(0.223372\pi\) | |||||||
\(992\) | 29.2497 | 0.928678 | ||||||||
\(993\) | −32.1247 | −1.01945 | ||||||||
\(994\) | 11.5671 | 0.366886 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.9437 | −0.441823 | ||||||||
\(997\) | −37.0280 | −1.17269 | −0.586344 | − | 0.810062i | \(-0.699433\pi\) | ||||
−0.586344 | + | 0.810062i | \(0.699433\pi\) | |||||||
\(998\) | −19.8351 | −0.627869 | ||||||||
\(999\) | 11.9998 | 0.379656 |
(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 | 4025.2.a.w.1.1 | yes | 8 | |
5.4 | even | 2 | 4025.2.a.s.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.s.1.8 | ✓ | 8 | 5.4 | even | 2 | ||
4025.2.a.w.1.1 | yes | 8 | 1.1 | even | 1 | trivial |