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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.85410 | −2.38993 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.00000 | 1.80907 | 0.904534 | − | 0.426401i | \(-0.140219\pi\) | ||||
0.904534 | + | 0.426401i | \(0.140219\pi\) | |||||||
\(12\) | 10.8541 | 3.13331 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −3.23607 | −0.784862 | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392431 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(18\) | −5.23607 | −1.23415 | ||||||||
\(19\) | −0.472136 | −0.108315 | −0.0541577 | − | 0.998532i | \(-0.517247\pi\) | ||||
−0.0541577 | + | 0.998532i | \(0.517247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23607 | 0.487950 | ||||||||
\(22\) | −15.7082 | −3.34900 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −16.7082 | −3.41055 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.85410 | 1.54032 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 4.85410 | 0.917339 | ||||||||
\(29\) | −1.47214 | −0.273369 | −0.136684 | − | 0.990615i | \(-0.543645\pi\) | ||||
−0.136684 | + | 0.990615i | \(0.543645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.47214 | 0.623614 | 0.311807 | − | 0.950145i | \(-0.399066\pi\) | ||||
0.311807 | + | 0.950145i | \(0.399066\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 13.4164 | 2.33550 | ||||||||
\(34\) | 8.47214 | 1.45296 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.70820 | 1.61803 | ||||||||
\(37\) | 2.76393 | 0.454388 | 0.227194 | − | 0.973850i | \(-0.427045\pi\) | ||||
0.227194 | + | 0.973850i | \(0.427045\pi\) | |||||||
\(38\) | 1.23607 | 0.200517 | ||||||||
\(39\) | −6.70820 | −1.07417 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.70820 | −1.04765 | −0.523823 | − | 0.851827i | \(-0.675495\pi\) | ||||
−0.523823 | + | 0.851827i | \(0.675495\pi\) | |||||||
\(42\) | −5.85410 | −0.903308 | ||||||||
\(43\) | 9.70820 | 1.48049 | 0.740244 | − | 0.672339i | \(-0.234710\pi\) | ||||
0.740244 | + | 0.672339i | \(0.234710\pi\) | |||||||
\(44\) | 29.1246 | 4.39070 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.61803 | 0.386008 | ||||||||
\(47\) | −0.236068 | −0.0344341 | −0.0172170 | − | 0.999852i | \(-0.505481\pi\) | ||||
−0.0172170 | + | 0.999852i | \(0.505481\pi\) | |||||||
\(48\) | 22.0344 | 3.18040 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.23607 | −1.01325 | ||||||||
\(52\) | −14.5623 | −2.01943 | ||||||||
\(53\) | 13.2361 | 1.81811 | 0.909057 | − | 0.416672i | \(-0.136804\pi\) | ||||
0.909057 | + | 0.416672i | \(0.136804\pi\) | |||||||
\(54\) | 5.85410 | 0.796642 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.47214 | −0.998506 | ||||||||
\(57\) | −1.05573 | −0.139835 | ||||||||
\(58\) | 3.85410 | 0.506068 | ||||||||
\(59\) | 2.47214 | 0.321845 | 0.160922 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160922 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7082 | 1.49908 | 0.749541 | − | 0.661958i | \(-0.230274\pi\) | ||||
0.749541 | + | 0.661958i | \(0.230274\pi\) | |||||||
\(62\) | −9.09017 | −1.15445 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −35.1246 | −4.32354 | ||||||||
\(67\) | 1.23607 | 0.151010 | 0.0755049 | − | 0.997145i | \(-0.475943\pi\) | ||||
0.0755049 | + | 0.997145i | \(0.475943\pi\) | |||||||
\(68\) | −15.7082 | −1.90490 | ||||||||
\(69\) | −2.23607 | −0.269191 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.236068 | 0.0280161 | 0.0140081 | − | 0.999902i | \(-0.495541\pi\) | ||||
0.0140081 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(72\) | −14.9443 | −1.76120 | ||||||||
\(73\) | −9.00000 | −1.05337 | −0.526685 | − | 0.850060i | \(-0.676565\pi\) | ||||
−0.526685 | + | 0.850060i | \(0.676565\pi\) | |||||||
\(74\) | −7.23607 | −0.841176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.29180 | −0.262887 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 17.5623 | 1.98854 | ||||||||
\(79\) | 13.4164 | 1.50946 | 0.754732 | − | 0.656033i | \(-0.227767\pi\) | ||||
0.754732 | + | 0.656033i | \(0.227767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 17.5623 | 1.93943 | ||||||||
\(83\) | 9.70820 | 1.06561 | 0.532807 | − | 0.846237i | \(-0.321137\pi\) | ||||
0.532807 | + | 0.846237i | \(0.321137\pi\) | |||||||
\(84\) | 10.8541 | 1.18428 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25.4164 | −2.74072 | ||||||||
\(87\) | −3.29180 | −0.352918 | ||||||||
\(88\) | −44.8328 | −4.77919 | ||||||||
\(89\) | −4.76393 | −0.504976 | −0.252488 | − | 0.967600i | \(-0.581249\pi\) | ||||
−0.252488 | + | 0.967600i | \(0.581249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | −0.314485 | ||||||||
\(92\) | −4.85410 | −0.506075 | ||||||||
\(93\) | 7.76393 | 0.805082 | ||||||||
\(94\) | 0.618034 | 0.0637453 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −24.2705 | −2.47710 | ||||||||
\(97\) | 13.7082 | 1.39186 | 0.695929 | − | 0.718111i | \(-0.254993\pi\) | ||||
0.695929 | + | 0.718111i | \(0.254993\pi\) | |||||||
\(98\) | −2.61803 | −0.264461 | ||||||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9443 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(102\) | 18.9443 | 1.87576 | ||||||||
\(103\) | 16.9443 | 1.66957 | 0.834784 | − | 0.550577i | \(-0.185592\pi\) | ||||
0.834784 | + | 0.550577i | \(0.185592\pi\) | |||||||
\(104\) | 22.4164 | 2.19811 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −34.6525 | −3.36575 | ||||||||
\(107\) | −19.8885 | −1.92270 | −0.961349 | − | 0.275333i | \(-0.911212\pi\) | ||||
−0.961349 | + | 0.275333i | \(0.911212\pi\) | |||||||
\(108\) | −10.8541 | −1.04444 | ||||||||
\(109\) | −1.70820 | −0.163616 | −0.0818081 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818081 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.18034 | 0.586612 | ||||||||
\(112\) | 9.85410 | 0.931125 | ||||||||
\(113\) | 19.4164 | 1.82654 | 0.913271 | − | 0.407353i | \(-0.133548\pi\) | ||||
0.913271 | + | 0.407353i | \(0.133548\pi\) | |||||||
\(114\) | 2.76393 | 0.258866 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.14590 | −0.663480 | ||||||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | −6.47214 | −0.595808 | ||||||||
\(119\) | −3.23607 | −0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | −30.6525 | −2.77514 | ||||||||
\(123\) | −15.0000 | −1.35250 | ||||||||
\(124\) | 16.8541 | 1.51354 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.23607 | −0.466466 | ||||||||
\(127\) | −3.00000 | −0.266207 | −0.133103 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133103 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | 21.7082 | 1.91130 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.4721 | 1.70129 | 0.850644 | − | 0.525742i | \(-0.176212\pi\) | ||||
0.850644 | + | 0.525742i | \(0.176212\pi\) | |||||||
\(132\) | 65.1246 | 5.66837 | ||||||||
\(133\) | −0.472136 | −0.0409394 | ||||||||
\(134\) | −3.23607 | −0.279554 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.1803 | 2.07345 | ||||||||
\(137\) | 3.23607 | 0.276476 | 0.138238 | − | 0.990399i | \(-0.455856\pi\) | ||||
0.138238 | + | 0.990399i | \(0.455856\pi\) | |||||||
\(138\) | 5.85410 | 0.498334 | ||||||||
\(139\) | −2.52786 | −0.214411 | −0.107205 | − | 0.994237i | \(-0.534190\pi\) | ||||
−0.107205 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.527864 | −0.0444542 | ||||||||
\(142\) | −0.618034 | −0.0518643 | ||||||||
\(143\) | −18.0000 | −1.50524 | ||||||||
\(144\) | 19.7082 | 1.64235 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.5623 | 1.95003 | ||||||||
\(147\) | 2.23607 | 0.184428 | ||||||||
\(148\) | 13.4164 | 1.10282 | ||||||||
\(149\) | 9.23607 | 0.756648 | 0.378324 | − | 0.925673i | \(-0.376500\pi\) | ||||
0.378324 | + | 0.925673i | \(0.376500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7639 | 1.44561 | 0.722804 | − | 0.691053i | \(-0.242853\pi\) | ||||
0.722804 | + | 0.691053i | \(0.242853\pi\) | |||||||
\(152\) | 3.52786 | 0.286148 | ||||||||
\(153\) | −6.47214 | −0.523241 | ||||||||
\(154\) | −15.7082 | −1.26580 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −32.5623 | −2.60707 | ||||||||
\(157\) | 19.2361 | 1.53521 | 0.767603 | − | 0.640926i | \(-0.221449\pi\) | ||||
0.767603 | + | 0.640926i | \(0.221449\pi\) | |||||||
\(158\) | −35.1246 | −2.79436 | ||||||||
\(159\) | 29.5967 | 2.34717 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 28.7984 | 2.26261 | ||||||||
\(163\) | 17.0000 | 1.33154 | 0.665771 | − | 0.746156i | \(-0.268103\pi\) | ||||
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | −32.5623 | −2.54269 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.4164 | −1.97270 | ||||||||
\(167\) | 0.944272 | 0.0730700 | 0.0365350 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365350 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(168\) | −16.7082 | −1.28907 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.944272 | −0.0722103 | ||||||||
\(172\) | 47.1246 | 3.59322 | ||||||||
\(173\) | −14.9443 | −1.13619 | −0.568096 | − | 0.822962i | \(-0.692320\pi\) | ||||
−0.568096 | + | 0.822962i | \(0.692320\pi\) | |||||||
\(174\) | 8.61803 | 0.653331 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 59.1246 | 4.45669 | ||||||||
\(177\) | 5.52786 | 0.415500 | ||||||||
\(178\) | 12.4721 | 0.934826 | ||||||||
\(179\) | 5.29180 | 0.395527 | 0.197764 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197764 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 7.85410 | 0.582185 | ||||||||
\(183\) | 26.1803 | 1.93531 | ||||||||
\(184\) | 7.47214 | 0.550853 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.3262 | −1.49039 | ||||||||
\(187\) | −19.4164 | −1.41987 | ||||||||
\(188\) | −1.14590 | −0.0835732 | ||||||||
\(189\) | −2.23607 | −0.162650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.47214 | −0.613022 | −0.306511 | − | 0.951867i | \(-0.599162\pi\) | ||||
−0.306511 | + | 0.951867i | \(0.599162\pi\) | |||||||
\(192\) | 19.4721 | 1.40528 | ||||||||
\(193\) | 6.23607 | 0.448882 | 0.224441 | − | 0.974488i | \(-0.427944\pi\) | ||||
0.224441 | + | 0.974488i | \(0.427944\pi\) | |||||||
\(194\) | −35.8885 | −2.57665 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | −18.7082 | −1.33290 | −0.666452 | − | 0.745548i | \(-0.732188\pi\) | ||||
−0.666452 | + | 0.745548i | \(0.732188\pi\) | |||||||
\(198\) | −31.4164 | −2.23267 | ||||||||
\(199\) | −25.4164 | −1.80172 | −0.900861 | − | 0.434108i | \(-0.857064\pi\) | ||||
−0.900861 | + | 0.434108i | \(0.857064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.76393 | 0.194953 | ||||||||
\(202\) | 28.6525 | 2.01598 | ||||||||
\(203\) | −1.47214 | −0.103324 | ||||||||
\(204\) | −35.1246 | −2.45921 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −44.3607 | −3.09076 | ||||||||
\(207\) | −2.00000 | −0.139010 | ||||||||
\(208\) | −29.5623 | −2.04978 | ||||||||
\(209\) | −2.83282 | −0.195950 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.944272 | 0.0650064 | 0.0325032 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325032 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(212\) | 64.2492 | 4.41265 | ||||||||
\(213\) | 0.527864 | 0.0361686 | ||||||||
\(214\) | 52.0689 | 3.55936 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | 3.47214 | 0.235704 | ||||||||
\(218\) | 4.47214 | 0.302891 | ||||||||
\(219\) | −20.1246 | −1.35990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70820 | 0.653044 | ||||||||
\(222\) | −16.1803 | −1.08595 | ||||||||
\(223\) | −4.94427 | −0.331093 | −0.165546 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165546 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(224\) | −10.8541 | −0.725220 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.8328 | −3.38135 | ||||||||
\(227\) | −7.41641 | −0.492244 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(228\) | −5.12461 | −0.339386 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.4164 | 0.882735 | ||||||||
\(232\) | 11.0000 | 0.722185 | ||||||||
\(233\) | 6.70820 | 0.439469 | 0.219735 | − | 0.975560i | \(-0.429481\pi\) | ||||
0.219735 | + | 0.975560i | \(0.429481\pi\) | |||||||
\(234\) | 15.7082 | 1.02688 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 30.0000 | 1.94871 | ||||||||
\(238\) | 8.47214 | 0.549167 | ||||||||
\(239\) | −13.6525 | −0.883105 | −0.441553 | − | 0.897235i | \(-0.645572\pi\) | ||||
−0.441553 | + | 0.897235i | \(0.645572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1246 | 0.716599 | 0.358300 | − | 0.933607i | \(-0.383357\pi\) | ||||
0.358300 | + | 0.933607i | \(0.383357\pi\) | |||||||
\(242\) | −65.4508 | −4.20734 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | 56.8328 | 3.63835 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 39.2705 | 2.50380 | ||||||||
\(247\) | 1.41641 | 0.0901239 | ||||||||
\(248\) | −25.9443 | −1.64746 | ||||||||
\(249\) | 21.7082 | 1.37570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.94427 | 0.564557 | 0.282279 | − | 0.959332i | \(-0.408910\pi\) | ||||
0.282279 | + | 0.959332i | \(0.408910\pi\) | |||||||
\(252\) | 9.70820 | 0.611559 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 7.85410 | 0.492810 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −27.3607 | −1.70671 | −0.853356 | − | 0.521328i | \(-0.825437\pi\) | ||||
−0.853356 | + | 0.521328i | \(0.825437\pi\) | |||||||
\(258\) | −56.8328 | −3.53826 | ||||||||
\(259\) | 2.76393 | 0.171742 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.94427 | −0.182246 | ||||||||
\(262\) | −50.9787 | −3.14948 | ||||||||
\(263\) | −25.5967 | −1.57836 | −0.789182 | − | 0.614160i | \(-0.789495\pi\) | ||||
−0.789182 | + | 0.614160i | \(0.789495\pi\) | |||||||
\(264\) | −100.249 | −6.16991 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.23607 | 0.0757882 | ||||||||
\(267\) | −10.6525 | −0.651921 | ||||||||
\(268\) | 6.00000 | 0.366508 | ||||||||
\(269\) | 6.70820 | 0.409006 | 0.204503 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204503 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.4721 | −1.60807 | −0.804034 | − | 0.594583i | \(-0.797317\pi\) | ||||
−0.804034 | + | 0.594583i | \(0.797317\pi\) | |||||||
\(272\) | −31.8885 | −1.93353 | ||||||||
\(273\) | −6.70820 | −0.405999 | ||||||||
\(274\) | −8.47214 | −0.511820 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.8541 | −0.653340 | ||||||||
\(277\) | 33.0689 | 1.98692 | 0.993458 | − | 0.114195i | \(-0.0364289\pi\) | ||||
0.993458 | + | 0.114195i | \(0.0364289\pi\) | |||||||
\(278\) | 6.61803 | 0.396923 | ||||||||
\(279\) | 6.94427 | 0.415743 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18034 | −0.487998 | −0.243999 | − | 0.969775i | \(-0.578459\pi\) | ||||
−0.243999 | + | 0.969775i | \(0.578459\pi\) | |||||||
\(282\) | 1.38197 | 0.0822949 | ||||||||
\(283\) | −11.1246 | −0.661290 | −0.330645 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330645 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(284\) | 1.14590 | 0.0679965 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 47.1246 | 2.78654 | ||||||||
\(287\) | −6.70820 | −0.395973 | ||||||||
\(288\) | −21.7082 | −1.27917 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.6525 | 1.79688 | ||||||||
\(292\) | −43.6869 | −2.55658 | ||||||||
\(293\) | 32.1803 | 1.88000 | 0.939998 | − | 0.341181i | \(-0.110827\pi\) | ||||
0.939998 | + | 0.341181i | \(0.110827\pi\) | |||||||
\(294\) | −5.85410 | −0.341418 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.6525 | −1.20040 | ||||||||
\(297\) | −13.4164 | −0.778499 | ||||||||
\(298\) | −24.1803 | −1.40073 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.70820 | 0.559572 | ||||||||
\(302\) | −46.5066 | −2.67615 | ||||||||
\(303\) | −24.4721 | −1.40589 | ||||||||
\(304\) | −4.65248 | −0.266838 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.9443 | 0.968640 | ||||||||
\(307\) | −19.4164 | −1.10815 | −0.554076 | − | 0.832466i | \(-0.686928\pi\) | ||||
−0.554076 | + | 0.832466i | \(0.686928\pi\) | |||||||
\(308\) | 29.1246 | 1.65953 | ||||||||
\(309\) | 37.8885 | 2.15540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4164 | −0.590660 | −0.295330 | − | 0.955395i | \(-0.595430\pi\) | ||||
−0.295330 | + | 0.955395i | \(0.595430\pi\) | |||||||
\(312\) | 50.1246 | 2.83775 | ||||||||
\(313\) | 6.29180 | 0.355633 | 0.177817 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177817 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(314\) | −50.3607 | −2.84202 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 65.1246 | 3.66355 | ||||||||
\(317\) | 3.52786 | 0.198145 | 0.0990723 | − | 0.995080i | \(-0.468412\pi\) | ||||
0.0990723 | + | 0.995080i | \(0.468412\pi\) | |||||||
\(318\) | −77.4853 | −4.34516 | ||||||||
\(319\) | −8.83282 | −0.494543 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −44.4721 | −2.48219 | ||||||||
\(322\) | 2.61803 | 0.145897 | ||||||||
\(323\) | 1.52786 | 0.0850126 | ||||||||
\(324\) | −53.3951 | −2.96640 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −44.5066 | −2.46499 | ||||||||
\(327\) | −3.81966 | −0.211228 | ||||||||
\(328\) | 50.1246 | 2.76767 | ||||||||
\(329\) | −0.236068 | −0.0130148 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1246 | 1.10615 | 0.553074 | − | 0.833132i | \(-0.313455\pi\) | ||||
0.553074 | + | 0.833132i | \(0.313455\pi\) | |||||||
\(332\) | 47.1246 | 2.58630 | ||||||||
\(333\) | 5.52786 | 0.302925 | ||||||||
\(334\) | −2.47214 | −0.135269 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.0344 | 1.20208 | ||||||||
\(337\) | 7.41641 | 0.403997 | 0.201999 | − | 0.979386i | \(-0.435256\pi\) | ||||
0.201999 | + | 0.979386i | \(0.435256\pi\) | |||||||
\(338\) | 10.4721 | 0.569609 | ||||||||
\(339\) | 43.4164 | 2.35806 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.8328 | 1.12816 | ||||||||
\(342\) | 2.47214 | 0.133678 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −72.5410 | −3.91115 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 39.1246 | 2.10335 | ||||||||
\(347\) | −30.4721 | −1.63583 | −0.817915 | − | 0.575339i | \(-0.804870\pi\) | ||||
−0.817915 | + | 0.575339i | \(0.804870\pi\) | |||||||
\(348\) | −15.9787 | −0.856549 | ||||||||
\(349\) | −11.7639 | −0.629709 | −0.314854 | − | 0.949140i | \(-0.601956\pi\) | ||||
−0.314854 | + | 0.949140i | \(0.601956\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.70820 | 0.358057 | ||||||||
\(352\) | −65.1246 | −3.47115 | ||||||||
\(353\) | −12.0557 | −0.641662 | −0.320831 | − | 0.947137i | \(-0.603962\pi\) | ||||
−0.320831 | + | 0.947137i | \(0.603962\pi\) | |||||||
\(354\) | −14.4721 | −0.769185 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −23.1246 | −1.22560 | ||||||||
\(357\) | −7.23607 | −0.382973 | ||||||||
\(358\) | −13.8541 | −0.732212 | ||||||||
\(359\) | 2.94427 | 0.155393 | 0.0776964 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776964 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7771 | −0.988268 | ||||||||
\(362\) | 26.1803 | 1.37601 | ||||||||
\(363\) | 55.9017 | 2.93408 | ||||||||
\(364\) | −14.5623 | −0.763272 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −68.5410 | −3.58270 | ||||||||
\(367\) | 4.76393 | 0.248675 | 0.124338 | − | 0.992240i | \(-0.460319\pi\) | ||||
0.124338 | + | 0.992240i | \(0.460319\pi\) | |||||||
\(368\) | −9.85410 | −0.513681 | ||||||||
\(369\) | −13.4164 | −0.698430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2361 | 0.687182 | ||||||||
\(372\) | 37.6869 | 1.95398 | ||||||||
\(373\) | 13.2361 | 0.685338 | 0.342669 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342669 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(374\) | 50.8328 | 2.62850 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.76393 | 0.0909678 | ||||||||
\(377\) | 4.41641 | 0.227457 | ||||||||
\(378\) | 5.85410 | 0.301103 | ||||||||
\(379\) | 31.5967 | 1.62302 | 0.811508 | − | 0.584341i | \(-0.198647\pi\) | ||||
0.811508 | + | 0.584341i | \(0.198647\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.70820 | −0.343672 | ||||||||
\(382\) | 22.1803 | 1.13484 | ||||||||
\(383\) | −2.47214 | −0.126320 | −0.0631601 | − | 0.998003i | \(-0.520118\pi\) | ||||
−0.0631601 | + | 0.998003i | \(0.520118\pi\) | |||||||
\(384\) | −2.43769 | −0.124398 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.3262 | −0.830984 | ||||||||
\(387\) | 19.4164 | 0.986991 | ||||||||
\(388\) | 66.5410 | 3.37811 | ||||||||
\(389\) | 25.8885 | 1.31260 | 0.656301 | − | 0.754499i | \(-0.272120\pi\) | ||||
0.656301 | + | 0.754499i | \(0.272120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.23607 | 0.163655 | ||||||||
\(392\) | −7.47214 | −0.377400 | ||||||||
\(393\) | 43.5410 | 2.19635 | ||||||||
\(394\) | 48.9787 | 2.46751 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 58.2492 | 2.92713 | ||||||||
\(397\) | 0.416408 | 0.0208989 | 0.0104495 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104495 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(398\) | 66.5410 | 3.33540 | ||||||||
\(399\) | −1.05573 | −0.0528525 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5967 | −0.678989 | −0.339495 | − | 0.940608i | \(-0.610256\pi\) | ||||
−0.339495 | + | 0.940608i | \(0.610256\pi\) | |||||||
\(402\) | −7.23607 | −0.360902 | ||||||||
\(403\) | −10.4164 | −0.518878 | ||||||||
\(404\) | −53.1246 | −2.64305 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.85410 | 0.191276 | ||||||||
\(407\) | 16.5836 | 0.822018 | ||||||||
\(408\) | 54.0689 | 2.67681 | ||||||||
\(409\) | 37.1803 | 1.83845 | 0.919225 | − | 0.393733i | \(-0.128817\pi\) | ||||
0.919225 | + | 0.393733i | \(0.128817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.23607 | 0.356929 | ||||||||
\(412\) | 82.2492 | 4.05213 | ||||||||
\(413\) | 2.47214 | 0.121646 | ||||||||
\(414\) | 5.23607 | 0.257339 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.5623 | 1.59650 | ||||||||
\(417\) | −5.65248 | −0.276803 | ||||||||
\(418\) | 7.41641 | 0.362748 | ||||||||
\(419\) | −14.6525 | −0.715820 | −0.357910 | − | 0.933756i | \(-0.616511\pi\) | ||||
−0.357910 | + | 0.933756i | \(0.616511\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | −2.47214 | −0.120342 | ||||||||
\(423\) | −0.472136 | −0.0229560 | ||||||||
\(424\) | −98.9017 | −4.80309 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.38197 | −0.0669565 | ||||||||
\(427\) | 11.7082 | 0.566600 | ||||||||
\(428\) | −96.5410 | −4.66649 | ||||||||
\(429\) | −40.2492 | −1.94325 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.05573 | 0.147189 | 0.0735946 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735946 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(432\) | −22.0344 | −1.06013 | ||||||||
\(433\) | −4.29180 | −0.206251 | −0.103125 | − | 0.994668i | \(-0.532884\pi\) | ||||
−0.103125 | + | 0.994668i | \(0.532884\pi\) | |||||||
\(434\) | −9.09017 | −0.436342 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.29180 | −0.397105 | ||||||||
\(437\) | 0.472136 | 0.0225853 | ||||||||
\(438\) | 52.6869 | 2.51748 | ||||||||
\(439\) | −9.00000 | −0.429547 | −0.214773 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214773 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | −25.4164 | −1.20894 | ||||||||
\(443\) | 7.36068 | 0.349716 | 0.174858 | − | 0.984594i | \(-0.444053\pi\) | ||||
0.174858 | + | 0.984594i | \(0.444053\pi\) | |||||||
\(444\) | 30.0000 | 1.42374 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.9443 | 0.612929 | ||||||||
\(447\) | 20.6525 | 0.976829 | ||||||||
\(448\) | 8.70820 | 0.411424 | ||||||||
\(449\) | −25.4164 | −1.19947 | −0.599737 | − | 0.800197i | \(-0.704728\pi\) | ||||
−0.599737 | + | 0.800197i | \(0.704728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.2492 | −1.89526 | ||||||||
\(452\) | 94.2492 | 4.43311 | ||||||||
\(453\) | 39.7214 | 1.86627 | ||||||||
\(454\) | 19.4164 | 0.911257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.88854 | 0.369415 | ||||||||
\(457\) | 28.7639 | 1.34552 | 0.672760 | − | 0.739861i | \(-0.265109\pi\) | ||||
0.672760 | + | 0.739861i | \(0.265109\pi\) | |||||||
\(458\) | 31.4164 | 1.46799 | ||||||||
\(459\) | 7.23607 | 0.337751 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.65248 | 0.170113 | 0.0850564 | − | 0.996376i | \(-0.472893\pi\) | ||||
0.0850564 | + | 0.996376i | \(0.472893\pi\) | |||||||
\(462\) | −35.1246 | −1.63414 | ||||||||
\(463\) | −34.8328 | −1.61882 | −0.809409 | − | 0.587245i | \(-0.800212\pi\) | ||||
−0.809409 | + | 0.587245i | \(0.800212\pi\) | |||||||
\(464\) | −14.5066 | −0.673451 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5623 | −0.813558 | ||||||||
\(467\) | −9.05573 | −0.419049 | −0.209525 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209525 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(468\) | −29.1246 | −1.34629 | ||||||||
\(469\) | 1.23607 | 0.0570763 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 43.0132 | 1.98194 | ||||||||
\(472\) | −18.4721 | −0.850249 | ||||||||
\(473\) | 58.2492 | 2.67830 | ||||||||
\(474\) | −78.5410 | −3.60751 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.7082 | −0.719984 | ||||||||
\(477\) | 26.4721 | 1.21208 | ||||||||
\(478\) | 35.7426 | 1.63483 | ||||||||
\(479\) | −26.8328 | −1.22602 | −0.613011 | − | 0.790074i | \(-0.710042\pi\) | ||||
−0.613011 | + | 0.790074i | \(0.710042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.29180 | −0.378073 | ||||||||
\(482\) | −29.1246 | −1.32659 | ||||||||
\(483\) | −2.23607 | −0.101745 | ||||||||
\(484\) | 121.353 | 5.51602 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 46.8328 | 2.12438 | ||||||||
\(487\) | 40.4164 | 1.83144 | 0.915721 | − | 0.401814i | \(-0.131620\pi\) | ||||
0.915721 | + | 0.401814i | \(0.131620\pi\) | |||||||
\(488\) | −87.4853 | −3.96027 | ||||||||
\(489\) | 38.0132 | 1.71901 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.18034 | −0.414303 | −0.207151 | − | 0.978309i | \(-0.566419\pi\) | ||||
−0.207151 | + | 0.978309i | \(0.566419\pi\) | |||||||
\(492\) | −72.8115 | −3.28260 | ||||||||
\(493\) | 4.76393 | 0.214557 | ||||||||
\(494\) | −3.70820 | −0.166840 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.2148 | 1.53629 | ||||||||
\(497\) | 0.236068 | 0.0105891 | ||||||||
\(498\) | −56.8328 | −2.54674 | ||||||||
\(499\) | −8.70820 | −0.389833 | −0.194916 | − | 0.980820i | \(-0.562444\pi\) | ||||
−0.194916 | + | 0.980820i | \(0.562444\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.11146 | 0.0943329 | ||||||||
\(502\) | −23.4164 | −1.04513 | ||||||||
\(503\) | −26.7639 | −1.19334 | −0.596672 | − | 0.802485i | \(-0.703511\pi\) | ||||
−0.596672 | + | 0.802485i | \(0.703511\pi\) | |||||||
\(504\) | −14.9443 | −0.665671 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.7082 | 0.698315 | ||||||||
\(507\) | −8.94427 | −0.397229 | ||||||||
\(508\) | −14.5623 | −0.646098 | ||||||||
\(509\) | 40.0132 | 1.77355 | 0.886776 | − | 0.462200i | \(-0.152940\pi\) | ||||
0.886776 | + | 0.462200i | \(0.152940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | −0.398137 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | 1.05573 | 0.0466115 | ||||||||
\(514\) | 71.6312 | 3.15952 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 105.374 | 4.63882 | ||||||||
\(517\) | −1.41641 | −0.0622935 | ||||||||
\(518\) | −7.23607 | −0.317935 | ||||||||
\(519\) | −33.4164 | −1.46682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.88854 | 0.257982 | 0.128991 | − | 0.991646i | \(-0.458826\pi\) | ||||
0.128991 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(522\) | 7.70820 | 0.337379 | ||||||||
\(523\) | −32.5410 | −1.42292 | −0.711460 | − | 0.702727i | \(-0.751966\pi\) | ||||
−0.711460 | + | 0.702727i | \(0.751966\pi\) | |||||||
\(524\) | 94.5197 | 4.12911 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 67.0132 | 2.92191 | ||||||||
\(527\) | −11.2361 | −0.489451 | ||||||||
\(528\) | 132.207 | 5.75356 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.94427 | 0.214563 | ||||||||
\(532\) | −2.29180 | −0.0993620 | ||||||||
\(533\) | 20.1246 | 0.871694 | ||||||||
\(534\) | 27.8885 | 1.20686 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.23607 | −0.398937 | ||||||||
\(537\) | 11.8328 | 0.510624 | ||||||||
\(538\) | −17.5623 | −0.757165 | ||||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0000 | 0.558914 | 0.279457 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279457 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(542\) | 69.3050 | 2.97690 | ||||||||
\(543\) | −22.3607 | −0.959589 | ||||||||
\(544\) | 35.1246 | 1.50596 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 17.5623 | 0.751597 | ||||||||
\(547\) | −33.4721 | −1.43117 | −0.715583 | − | 0.698528i | \(-0.753839\pi\) | ||||
−0.715583 | + | 0.698528i | \(0.753839\pi\) | |||||||
\(548\) | 15.7082 | 0.671021 | ||||||||
\(549\) | 23.4164 | 0.999388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.695048 | 0.0296101 | ||||||||
\(552\) | 16.7082 | 0.711148 | ||||||||
\(553\) | 13.4164 | 0.570524 | ||||||||
\(554\) | −86.5755 | −3.67824 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.2705 | −0.520386 | ||||||||
\(557\) | 12.0000 | 0.508456 | 0.254228 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | −18.1803 | −0.769635 | ||||||||
\(559\) | −29.1246 | −1.23184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43.4164 | −1.83304 | ||||||||
\(562\) | 21.4164 | 0.903397 | ||||||||
\(563\) | −32.1803 | −1.35624 | −0.678120 | − | 0.734951i | \(-0.737205\pi\) | ||||
−0.678120 | + | 0.734951i | \(0.737205\pi\) | |||||||
\(564\) | −2.56231 | −0.107893 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.1246 | 1.22420 | ||||||||
\(567\) | −11.0000 | −0.461957 | ||||||||
\(568\) | −1.76393 | −0.0740129 | ||||||||
\(569\) | −27.5279 | −1.15403 | −0.577014 | − | 0.816734i | \(-0.695782\pi\) | ||||
−0.577014 | + | 0.816734i | \(0.695782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −87.3738 | −3.65328 | ||||||||
\(573\) | −18.9443 | −0.791408 | ||||||||
\(574\) | 17.5623 | 0.733036 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.4164 | 0.725684 | ||||||||
\(577\) | 5.11146 | 0.212793 | 0.106396 | − | 0.994324i | \(-0.466069\pi\) | ||||
0.106396 | + | 0.994324i | \(0.466069\pi\) | |||||||
\(578\) | 17.0902 | 0.710857 | ||||||||
\(579\) | 13.9443 | 0.579504 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.70820 | 0.402764 | ||||||||
\(582\) | −80.2492 | −3.32644 | ||||||||
\(583\) | 79.4164 | 3.28909 | ||||||||
\(584\) | 67.2492 | 2.78279 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −84.2492 | −3.48030 | ||||||||
\(587\) | 37.0689 | 1.53000 | 0.764998 | − | 0.644032i | \(-0.222740\pi\) | ||||
0.764998 | + | 0.644032i | \(0.222740\pi\) | |||||||
\(588\) | 10.8541 | 0.447616 | ||||||||
\(589\) | −1.63932 | −0.0675470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.8328 | −1.72077 | ||||||||
\(592\) | 27.2361 | 1.11940 | ||||||||
\(593\) | −41.7771 | −1.71558 | −0.857790 | − | 0.514001i | \(-0.828163\pi\) | ||||
−0.857790 | + | 0.514001i | \(0.828163\pi\) | |||||||
\(594\) | 35.1246 | 1.44118 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.8328 | 1.83642 | ||||||||
\(597\) | −56.8328 | −2.32601 | ||||||||
\(598\) | −7.85410 | −0.321178 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.5967 | −1.41123 | −0.705615 | − | 0.708595i | \(-0.749329\pi\) | ||||
−0.705615 | + | 0.708595i | \(0.749329\pi\) | |||||||
\(602\) | −25.4164 | −1.03590 | ||||||||
\(603\) | 2.47214 | 0.100673 | ||||||||
\(604\) | 86.2279 | 3.50857 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 64.0689 | 2.60262 | ||||||||
\(607\) | 23.4164 | 0.950443 | 0.475221 | − | 0.879866i | \(-0.342368\pi\) | ||||
0.475221 | + | 0.879866i | \(0.342368\pi\) | |||||||
\(608\) | 5.12461 | 0.207830 | ||||||||
\(609\) | −3.29180 | −0.133390 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.708204 | 0.0286509 | ||||||||
\(612\) | −31.4164 | −1.26993 | ||||||||
\(613\) | 33.5279 | 1.35418 | 0.677089 | − | 0.735901i | \(-0.263241\pi\) | ||||
0.677089 | + | 0.735901i | \(0.263241\pi\) | |||||||
\(614\) | 50.8328 | 2.05145 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −44.8328 | −1.80637 | ||||||||
\(617\) | −16.4721 | −0.663143 | −0.331572 | − | 0.943430i | \(-0.607579\pi\) | ||||
−0.331572 | + | 0.943430i | \(0.607579\pi\) | |||||||
\(618\) | −99.1935 | −3.99015 | ||||||||
\(619\) | −22.6525 | −0.910480 | −0.455240 | − | 0.890369i | \(-0.650447\pi\) | ||||
−0.455240 | + | 0.890369i | \(0.650447\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.23607 | 0.0897303 | ||||||||
\(622\) | 27.2705 | 1.09345 | ||||||||
\(623\) | −4.76393 | −0.190863 | ||||||||
\(624\) | −66.1033 | −2.64625 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.4721 | −0.658359 | ||||||||
\(627\) | −6.33437 | −0.252970 | ||||||||
\(628\) | 93.3738 | 3.72602 | ||||||||
\(629\) | −8.94427 | −0.356631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7639 | −0.826599 | −0.413300 | − | 0.910595i | \(-0.635624\pi\) | ||||
−0.413300 | + | 0.910595i | \(0.635624\pi\) | |||||||
\(632\) | −100.249 | −3.98770 | ||||||||
\(633\) | 2.11146 | 0.0839228 | ||||||||
\(634\) | −9.23607 | −0.366811 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 143.666 | 5.69671 | ||||||||
\(637\) | −3.00000 | −0.118864 | ||||||||
\(638\) | 23.1246 | 0.915512 | ||||||||
\(639\) | 0.472136 | 0.0186774 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.1246 | 1.62432 | 0.812162 | − | 0.583432i | \(-0.198290\pi\) | ||||
0.812162 | + | 0.583432i | \(0.198290\pi\) | |||||||
\(642\) | 116.430 | 4.59511 | ||||||||
\(643\) | 43.8885 | 1.73080 | 0.865398 | − | 0.501086i | \(-0.167066\pi\) | ||||
0.865398 | + | 0.501086i | \(0.167066\pi\) | |||||||
\(644\) | −4.85410 | −0.191278 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | 27.1803 | 1.06857 | 0.534285 | − | 0.845305i | \(-0.320581\pi\) | ||||
0.534285 | + | 0.845305i | \(0.320581\pi\) | |||||||
\(648\) | 82.1935 | 3.22887 | ||||||||
\(649\) | 14.8328 | 0.582239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.76393 | 0.304292 | ||||||||
\(652\) | 82.5197 | 3.23172 | ||||||||
\(653\) | −6.59675 | −0.258151 | −0.129075 | − | 0.991635i | \(-0.541201\pi\) | ||||
−0.129075 | + | 0.991635i | \(0.541201\pi\) | |||||||
\(654\) | 10.0000 | 0.391031 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −66.1033 | −2.58090 | ||||||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | 0.618034 | 0.0240935 | ||||||||
\(659\) | 15.0557 | 0.586488 | 0.293244 | − | 0.956038i | \(-0.405265\pi\) | ||||
0.293244 | + | 0.956038i | \(0.405265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2918 | −0.478095 | −0.239048 | − | 0.971008i | \(-0.576835\pi\) | ||||
−0.239048 | + | 0.971008i | \(0.576835\pi\) | |||||||
\(662\) | −52.6869 | −2.04774 | ||||||||
\(663\) | 21.7082 | 0.843077 | ||||||||
\(664\) | −72.5410 | −2.81514 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.4721 | −0.560784 | ||||||||
\(667\) | 1.47214 | 0.0570013 | ||||||||
\(668\) | 4.58359 | 0.177345 | ||||||||
\(669\) | −11.0557 | −0.427439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.2492 | 2.71194 | ||||||||
\(672\) | −24.2705 | −0.936255 | ||||||||
\(673\) | −40.7082 | −1.56919 | −0.784593 | − | 0.620011i | \(-0.787128\pi\) | ||||
−0.784593 | + | 0.620011i | \(0.787128\pi\) | |||||||
\(674\) | −19.4164 | −0.747892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.4164 | −0.746785 | ||||||||
\(677\) | 13.8197 | 0.531133 | 0.265566 | − | 0.964093i | \(-0.414441\pi\) | ||||
0.265566 | + | 0.964093i | \(0.414441\pi\) | |||||||
\(678\) | −113.666 | −4.36530 | ||||||||
\(679\) | 13.7082 | 0.526073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.5836 | −0.635485 | ||||||||
\(682\) | −54.5410 | −2.08848 | ||||||||
\(683\) | 1.36068 | 0.0520650 | 0.0260325 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260325 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(684\) | −4.58359 | −0.175258 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.61803 | −0.0999570 | ||||||||
\(687\) | −26.8328 | −1.02374 | ||||||||
\(688\) | 95.6656 | 3.64722 | ||||||||
\(689\) | −39.7082 | −1.51276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.83282 | −0.259933 | −0.129966 | − | 0.991518i | \(-0.541487\pi\) | ||||
−0.129966 | + | 0.991518i | \(0.541487\pi\) | |||||||
\(692\) | −72.5410 | −2.75760 | ||||||||
\(693\) | 12.0000 | 0.455842 | ||||||||
\(694\) | 79.7771 | 3.02830 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 24.5967 | 0.932337 | ||||||||
\(697\) | 21.7082 | 0.822257 | ||||||||
\(698\) | 30.7984 | 1.16574 | ||||||||
\(699\) | 15.0000 | 0.567352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.70820 | 0.366674 | 0.183337 | − | 0.983050i | \(-0.441310\pi\) | ||||
0.183337 | + | 0.983050i | \(0.441310\pi\) | |||||||
\(702\) | −17.5623 | −0.662847 | ||||||||
\(703\) | −1.30495 | −0.0492172 | ||||||||
\(704\) | 52.2492 | 1.96922 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.5623 | 1.18786 | ||||||||
\(707\) | −10.9443 | −0.411602 | ||||||||
\(708\) | 26.8328 | 1.00844 | ||||||||
\(709\) | −16.9443 | −0.636355 | −0.318178 | − | 0.948031i | \(-0.603071\pi\) | ||||
−0.318178 | + | 0.948031i | \(0.603071\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.8328 | 1.00631 | ||||||||
\(712\) | 35.5967 | 1.33404 | ||||||||
\(713\) | −3.47214 | −0.130033 | ||||||||
\(714\) | 18.9443 | 0.708972 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.6869 | 0.959965 | ||||||||
\(717\) | −30.5279 | −1.14008 | ||||||||
\(718\) | −7.70820 | −0.287668 | ||||||||
\(719\) | 28.9443 | 1.07944 | 0.539720 | − | 0.841845i | \(-0.318530\pi\) | ||||
0.539720 | + | 0.841845i | \(0.318530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9443 | 0.631038 | ||||||||
\(722\) | 49.1591 | 1.82951 | ||||||||
\(723\) | 24.8754 | 0.925126 | ||||||||
\(724\) | −48.5410 | −1.80401 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −146.353 | −5.43165 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 22.4164 | 0.830807 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.4164 | −1.16198 | ||||||||
\(732\) | 127.082 | 4.69709 | ||||||||
\(733\) | 9.70820 | 0.358581 | 0.179290 | − | 0.983796i | \(-0.442620\pi\) | ||||
0.179290 | + | 0.983796i | \(0.442620\pi\) | |||||||
\(734\) | −12.4721 | −0.460355 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.8541 | 0.400088 | ||||||||
\(737\) | 7.41641 | 0.273187 | ||||||||
\(738\) | 35.1246 | 1.29295 | ||||||||
\(739\) | 20.1246 | 0.740296 | 0.370148 | − | 0.928973i | \(-0.379307\pi\) | ||||
0.370148 | + | 0.928973i | \(0.379307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.16718 | 0.116349 | ||||||||
\(742\) | −34.6525 | −1.27213 | ||||||||
\(743\) | 38.0689 | 1.39661 | 0.698306 | − | 0.715799i | \(-0.253938\pi\) | ||||
0.698306 | + | 0.715799i | \(0.253938\pi\) | |||||||
\(744\) | −58.0132 | −2.12687 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.6525 | −1.26872 | ||||||||
\(747\) | 19.4164 | 0.710409 | ||||||||
\(748\) | −94.2492 | −3.44609 | ||||||||
\(749\) | −19.8885 | −0.726712 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.87539 | 0.250886 | 0.125443 | − | 0.992101i | \(-0.459965\pi\) | ||||
0.125443 | + | 0.992101i | \(0.459965\pi\) | |||||||
\(752\) | −2.32624 | −0.0848292 | ||||||||
\(753\) | 20.0000 | 0.728841 | ||||||||
\(754\) | −11.5623 | −0.421074 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.8541 | −0.394760 | ||||||||
\(757\) | 27.3050 | 0.992415 | 0.496208 | − | 0.868204i | \(-0.334725\pi\) | ||||
0.496208 | + | 0.868204i | \(0.334725\pi\) | |||||||
\(758\) | −82.7214 | −3.00458 | ||||||||
\(759\) | −13.4164 | −0.486985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.23607 | −0.0810574 | −0.0405287 | − | 0.999178i | \(-0.512904\pi\) | ||||
−0.0405287 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(762\) | 17.5623 | 0.636215 | ||||||||
\(763\) | −1.70820 | −0.0618411 | ||||||||
\(764\) | −41.1246 | −1.48784 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.47214 | 0.233848 | ||||||||
\(767\) | −7.41641 | −0.267791 | ||||||||
\(768\) | −32.5623 | −1.17499 | ||||||||
\(769\) | 16.8328 | 0.607007 | 0.303503 | − | 0.952830i | \(-0.401844\pi\) | ||||
0.303503 | + | 0.952830i | \(0.401844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −61.1803 | −2.20336 | ||||||||
\(772\) | 30.2705 | 1.08946 | ||||||||
\(773\) | 2.83282 | 0.101889 | 0.0509446 | − | 0.998701i | \(-0.483777\pi\) | ||||
0.0509446 | + | 0.998701i | \(0.483777\pi\) | |||||||
\(774\) | −50.8328 | −1.82715 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −102.430 | −3.67701 | ||||||||
\(777\) | 6.18034 | 0.221718 | ||||||||
\(778\) | −67.7771 | −2.42993 | ||||||||
\(779\) | 3.16718 | 0.113476 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41641 | 0.0506831 | ||||||||
\(782\) | −8.47214 | −0.302963 | ||||||||
\(783\) | 3.29180 | 0.117639 | ||||||||
\(784\) | 9.85410 | 0.351932 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −113.992 | −4.06596 | ||||||||
\(787\) | −3.63932 | −0.129728 | −0.0648639 | − | 0.997894i | \(-0.520661\pi\) | ||||
−0.0648639 | + | 0.997894i | \(0.520661\pi\) | |||||||
\(788\) | −90.8115 | −3.23503 | ||||||||
\(789\) | −57.2361 | −2.03766 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.4164 | 0.690368 | ||||||||
\(792\) | −89.6656 | −3.18613 | ||||||||
\(793\) | −35.1246 | −1.24731 | ||||||||
\(794\) | −1.09017 | −0.0386887 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −123.374 | −4.37287 | ||||||||
\(797\) | −10.9443 | −0.387666 | −0.193833 | − | 0.981035i | \(-0.562092\pi\) | ||||
−0.193833 | + | 0.981035i | \(0.562092\pi\) | |||||||
\(798\) | 2.76393 | 0.0978421 | ||||||||
\(799\) | 0.763932 | 0.0270260 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.52786 | −0.336651 | ||||||||
\(802\) | 35.5967 | 1.25696 | ||||||||
\(803\) | −54.0000 | −1.90562 | ||||||||
\(804\) | 13.4164 | 0.473160 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.2705 | 0.960563 | ||||||||
\(807\) | 15.0000 | 0.528025 | ||||||||
\(808\) | 81.7771 | 2.87691 | ||||||||
\(809\) | −0.111456 | −0.00391859 | −0.00195930 | − | 0.999998i | \(-0.500624\pi\) | ||||
−0.00195930 | + | 0.999998i | \(0.500624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | −7.14590 | −0.250772 | ||||||||
\(813\) | −59.1935 | −2.07601 | ||||||||
\(814\) | −43.4164 | −1.52174 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −71.3050 | −2.49617 | ||||||||
\(817\) | −4.58359 | −0.160360 | ||||||||
\(818\) | −97.3394 | −3.40339 | ||||||||
\(819\) | −6.00000 | −0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3607 | −0.361590 | −0.180795 | − | 0.983521i | \(-0.557867\pi\) | ||||
−0.180795 | + | 0.983521i | \(0.557867\pi\) | |||||||
\(822\) | −18.9443 | −0.660757 | ||||||||
\(823\) | −19.8328 | −0.691328 | −0.345664 | − | 0.938358i | \(-0.612346\pi\) | ||||
−0.345664 | + | 0.938358i | \(0.612346\pi\) | |||||||
\(824\) | −126.610 | −4.41066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.47214 | −0.225194 | ||||||||
\(827\) | −29.3050 | −1.01903 | −0.509517 | − | 0.860461i | \(-0.670176\pi\) | ||||
−0.509517 | + | 0.860461i | \(0.670176\pi\) | |||||||
\(828\) | −9.70820 | −0.337383 | ||||||||
\(829\) | −30.0000 | −1.04194 | −0.520972 | − | 0.853574i | \(-0.674430\pi\) | ||||
−0.520972 | + | 0.853574i | \(0.674430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 73.9443 | 2.56510 | ||||||||
\(832\) | −26.1246 | −0.905708 | ||||||||
\(833\) | −3.23607 | −0.112123 | ||||||||
\(834\) | 14.7984 | 0.512426 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13.7508 | −0.475581 | ||||||||
\(837\) | −7.76393 | −0.268361 | ||||||||
\(838\) | 38.3607 | 1.32515 | ||||||||
\(839\) | 6.87539 | 0.237365 | 0.118682 | − | 0.992932i | \(-0.462133\pi\) | ||||
0.118682 | + | 0.992932i | \(0.462133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8328 | −0.925270 | ||||||||
\(842\) | −83.7771 | −2.88715 | ||||||||
\(843\) | −18.2918 | −0.630003 | ||||||||
\(844\) | 4.58359 | 0.157774 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.23607 | 0.0424969 | ||||||||
\(847\) | 25.0000 | 0.859010 | ||||||||
\(848\) | 130.430 | 4.47897 | ||||||||
\(849\) | −24.8754 | −0.853721 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.76393 | −0.0947464 | ||||||||
\(852\) | 2.56231 | 0.0877832 | ||||||||
\(853\) | −23.3050 | −0.797946 | −0.398973 | − | 0.916963i | \(-0.630633\pi\) | ||||
−0.398973 | + | 0.916963i | \(0.630633\pi\) | |||||||
\(854\) | −30.6525 | −1.04891 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 148.610 | 5.07938 | ||||||||
\(857\) | 17.9443 | 0.612965 | 0.306482 | − | 0.951876i | \(-0.400848\pi\) | ||||
0.306482 | + | 0.951876i | \(0.400848\pi\) | |||||||
\(858\) | 105.374 | 3.59740 | ||||||||
\(859\) | −29.4721 | −1.00558 | −0.502788 | − | 0.864410i | \(-0.667692\pi\) | ||||
−0.502788 | + | 0.864410i | \(0.667692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | −0.511199 | ||||||||
\(862\) | −8.00000 | −0.272481 | ||||||||
\(863\) | 17.3607 | 0.590964 | 0.295482 | − | 0.955348i | \(-0.404520\pi\) | ||||
0.295482 | + | 0.955348i | \(0.404520\pi\) | |||||||
\(864\) | 24.2705 | 0.825700 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.2361 | 0.381817 | ||||||||
\(867\) | −14.5967 | −0.495732 | ||||||||
\(868\) | 16.8541 | 0.572065 | ||||||||
\(869\) | 80.4984 | 2.73072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.70820 | −0.125648 | ||||||||
\(872\) | 12.7639 | 0.432241 | ||||||||
\(873\) | 27.4164 | 0.927905 | ||||||||
\(874\) | −1.23607 | −0.0418106 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −97.6869 | −3.30054 | ||||||||
\(877\) | −33.4164 | −1.12839 | −0.564196 | − | 0.825641i | \(-0.690814\pi\) | ||||
−0.564196 | + | 0.825641i | \(0.690814\pi\) | |||||||
\(878\) | 23.5623 | 0.795189 | ||||||||
\(879\) | 71.9574 | 2.42706 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8328 | −1.30831 | −0.654155 | − | 0.756360i | \(-0.726976\pi\) | ||||
−0.654155 | + | 0.756360i | \(0.726976\pi\) | |||||||
\(882\) | −5.23607 | −0.176308 | ||||||||
\(883\) | −2.11146 | −0.0710562 | −0.0355281 | − | 0.999369i | \(-0.511311\pi\) | ||||
−0.0355281 | + | 0.999369i | \(0.511311\pi\) | |||||||
\(884\) | 47.1246 | 1.58497 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.2705 | −0.647405 | ||||||||
\(887\) | 34.0132 | 1.14205 | 0.571025 | − | 0.820933i | \(-0.306546\pi\) | ||||
0.571025 | + | 0.820933i | \(0.306546\pi\) | |||||||
\(888\) | −46.1803 | −1.54971 | ||||||||
\(889\) | −3.00000 | −0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.0000 | −2.21108 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | 0.111456 | 0.00372974 | ||||||||
\(894\) | −54.0689 | −1.80833 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.09017 | −0.0364200 | ||||||||
\(897\) | 6.70820 | 0.223980 | ||||||||
\(898\) | 66.5410 | 2.22050 | ||||||||
\(899\) | −5.11146 | −0.170477 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.8328 | −1.42697 | ||||||||
\(902\) | 105.374 | 3.50856 | ||||||||
\(903\) | 21.7082 | 0.722404 | ||||||||
\(904\) | −145.082 | −4.82536 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −103.992 | −3.45490 | ||||||||
\(907\) | −36.2492 | −1.20364 | −0.601818 | − | 0.798633i | \(-0.705557\pi\) | ||||
−0.601818 | + | 0.798633i | \(0.705557\pi\) | |||||||
\(908\) | −36.0000 | −1.19470 | ||||||||
\(909\) | −21.8885 | −0.725997 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7082 | 0.520436 | 0.260218 | − | 0.965550i | \(-0.416206\pi\) | ||||
0.260218 | + | 0.965550i | \(0.416206\pi\) | |||||||
\(912\) | −10.4033 | −0.344486 | ||||||||
\(913\) | 58.2492 | 1.92777 | ||||||||
\(914\) | −75.3050 | −2.49087 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −58.2492 | −1.92461 | ||||||||
\(917\) | 19.4721 | 0.643027 | ||||||||
\(918\) | −18.9443 | −0.625254 | ||||||||
\(919\) | −5.12461 | −0.169045 | −0.0845227 | − | 0.996422i | \(-0.526937\pi\) | ||||
−0.0845227 | + | 0.996422i | \(0.526937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.4164 | −1.43062 | ||||||||
\(922\) | −9.56231 | −0.314918 | ||||||||
\(923\) | −0.708204 | −0.0233108 | ||||||||
\(924\) | 65.1246 | 2.14244 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 91.1935 | 2.99680 | ||||||||
\(927\) | 33.8885 | 1.11305 | ||||||||
\(928\) | 15.9787 | 0.524527 | ||||||||
\(929\) | 46.9574 | 1.54062 | 0.770312 | − | 0.637668i | \(-0.220101\pi\) | ||||
0.770312 | + | 0.637668i | \(0.220101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.472136 | −0.0154736 | ||||||||
\(932\) | 32.5623 | 1.06661 | ||||||||
\(933\) | −23.2918 | −0.762539 | ||||||||
\(934\) | 23.7082 | 0.775756 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 44.8328 | 1.46541 | ||||||||
\(937\) | −28.6525 | −0.936036 | −0.468018 | − | 0.883719i | \(-0.655032\pi\) | ||||
−0.468018 | + | 0.883719i | \(0.655032\pi\) | |||||||
\(938\) | −3.23607 | −0.105661 | ||||||||
\(939\) | 14.0689 | 0.459121 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.3050 | 1.34650 | 0.673251 | − | 0.739414i | \(-0.264897\pi\) | ||||
0.673251 | + | 0.739414i | \(0.264897\pi\) | |||||||
\(942\) | −112.610 | −3.66903 | ||||||||
\(943\) | 6.70820 | 0.218449 | ||||||||
\(944\) | 24.3607 | 0.792873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −152.498 | −4.95815 | ||||||||
\(947\) | −4.41641 | −0.143514 | −0.0717570 | − | 0.997422i | \(-0.522861\pi\) | ||||
−0.0717570 | + | 0.997422i | \(0.522861\pi\) | |||||||
\(948\) | 145.623 | 4.72962 | ||||||||
\(949\) | 27.0000 | 0.876457 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.88854 | 0.255804 | ||||||||
\(952\) | 24.1803 | 0.783689 | ||||||||
\(953\) | 14.9443 | 0.484092 | 0.242046 | − | 0.970265i | \(-0.422181\pi\) | ||||
0.242046 | + | 0.970265i | \(0.422181\pi\) | |||||||
\(954\) | −69.3050 | −2.24383 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −66.2705 | −2.14334 | ||||||||
\(957\) | −19.7508 | −0.638452 | ||||||||
\(958\) | 70.2492 | 2.26965 | ||||||||
\(959\) | 3.23607 | 0.104498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.9443 | −0.611106 | ||||||||
\(962\) | 21.7082 | 0.699901 | ||||||||
\(963\) | −39.7771 | −1.28180 | ||||||||
\(964\) | 54.0000 | 1.73922 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.85410 | 0.188353 | ||||||||
\(967\) | −17.1115 | −0.550267 | −0.275134 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275134 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(968\) | −186.803 | −6.00409 | ||||||||
\(969\) | 3.41641 | 0.109751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.18034 | 0.0699704 | 0.0349852 | − | 0.999388i | \(-0.488862\pi\) | ||||
0.0349852 | + | 0.999388i | \(0.488862\pi\) | |||||||
\(972\) | −86.8328 | −2.78516 | ||||||||
\(973\) | −2.52786 | −0.0810396 | ||||||||
\(974\) | −105.812 | −3.39042 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 115.374 | 3.69303 | ||||||||
\(977\) | −45.2361 | −1.44723 | −0.723615 | − | 0.690204i | \(-0.757521\pi\) | ||||
−0.723615 | + | 0.690204i | \(0.757521\pi\) | |||||||
\(978\) | −99.5197 | −3.18229 | ||||||||
\(979\) | −28.5836 | −0.913536 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.41641 | −0.109078 | ||||||||
\(982\) | 24.0344 | 0.766970 | ||||||||
\(983\) | −25.0132 | −0.797796 | −0.398898 | − | 0.916995i | \(-0.630607\pi\) | ||||
−0.398898 | + | 0.916995i | \(0.630607\pi\) | |||||||
\(984\) | 112.082 | 3.57304 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.4721 | −0.397194 | ||||||||
\(987\) | −0.527864 | −0.0168021 | ||||||||
\(988\) | 6.87539 | 0.218735 | ||||||||
\(989\) | −9.70820 | −0.308703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | −37.6869 | −1.19656 | ||||||||
\(993\) | 45.0000 | 1.42803 | ||||||||
\(994\) | −0.618034 | −0.0196028 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 105.374 | 3.33890 | ||||||||
\(997\) | −48.8328 | −1.54655 | −0.773275 | − | 0.634070i | \(-0.781383\pi\) | ||||
−0.773275 | + | 0.634070i | \(0.781383\pi\) | |||||||
\(998\) | 22.7984 | 0.721670 | ||||||||
\(999\) | −6.18034 | −0.195537 |
(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.h.1.1 | 2 | ||
5.4 | even | 2 | 805.2.a.e.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 7245.2.a.v.1.1 | 2 | |||
35.34 | odd | 2 | 5635.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.e.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
4025.2.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5635.2.a.q.1.2 | 2 | 35.34 | odd | 2 | |||
7245.2.a.v.1.1 | 2 | 15.14 | odd | 2 |