Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
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 | 1.4 | ||
Root | \(-0.456850\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18890 | 1.54779 | 0.773893 | − | 0.633316i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.79129 | 1.39564 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.18890 | 0.893615 | ||||||||
\(7\) | 0.913701 | 0.345346 | 0.172673 | − | 0.984979i | \(-0.444760\pi\) | ||||
0.172673 | + | 0.984979i | \(0.444760\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.18890 | −0.692191 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.79129 | 0.805775 | ||||||||
\(13\) | 4.37780 | 1.21418 | 0.607092 | − | 0.794632i | \(-0.292336\pi\) | ||||
0.607092 | + | 0.794632i | \(0.292336\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 2.18890 | 0.515929 | ||||||||
\(19\) | 3.46410 | 0.794719 | 0.397360 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | −2.79129 | −0.624151 | ||||||||
\(21\) | 0.913701 | 0.199386 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.58258 | 1.78959 | 0.894795 | − | 0.446476i | \(-0.147321\pi\) | ||||
0.894795 | + | 0.446476i | \(0.147321\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 9.58258 | 1.87930 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.55040 | 0.481981 | ||||||||
\(29\) | 6.20520 | 1.15228 | 0.576139 | − | 0.817352i | \(-0.304559\pi\) | ||||
0.576139 | + | 0.817352i | \(0.304559\pi\) | |||||||
\(30\) | −2.18890 | −0.399637 | ||||||||
\(31\) | 0.582576 | 0.104634 | 0.0523168 | − | 0.998631i | \(-0.483339\pi\) | ||||
0.0523168 | + | 0.998631i | \(0.483339\pi\) | |||||||
\(32\) | −7.38505 | −1.30551 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.79129 | −0.650201 | ||||||||
\(35\) | −0.913701 | −0.154444 | ||||||||
\(36\) | 2.79129 | 0.465215 | ||||||||
\(37\) | −1.58258 | −0.260174 | −0.130087 | − | 0.991503i | \(-0.541526\pi\) | ||||
−0.130087 | + | 0.991503i | \(0.541526\pi\) | |||||||
\(38\) | 7.58258 | 1.23006 | ||||||||
\(39\) | 4.37780 | 0.701009 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | −6.20520 | −0.946285 | −0.473142 | − | 0.880986i | \(-0.656880\pi\) | ||||
−0.473142 | + | 0.880986i | \(0.656880\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 18.7864 | 2.76990 | ||||||||
\(47\) | 12.5826 | 1.83536 | 0.917679 | − | 0.397323i | \(-0.130061\pi\) | ||||
0.917679 | + | 0.397323i | \(0.130061\pi\) | |||||||
\(48\) | −1.79129 | −0.258550 | ||||||||
\(49\) | −6.16515 | −0.880736 | ||||||||
\(50\) | 2.18890 | 0.309557 | ||||||||
\(51\) | −1.73205 | −0.242536 | ||||||||
\(52\) | 12.2197 | 1.69457 | ||||||||
\(53\) | −6.16515 | −0.846849 | −0.423424 | − | 0.905931i | \(-0.639172\pi\) | ||||
−0.423424 | + | 0.905931i | \(0.639172\pi\) | |||||||
\(54\) | 2.18890 | 0.297872 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.58258 | 0.211481 | ||||||||
\(57\) | 3.46410 | 0.458831 | ||||||||
\(58\) | 13.5826 | 1.78348 | ||||||||
\(59\) | 4.41742 | 0.575100 | 0.287550 | − | 0.957766i | \(-0.407159\pi\) | ||||
0.287550 | + | 0.957766i | \(0.407159\pi\) | |||||||
\(60\) | −2.79129 | −0.360354 | ||||||||
\(61\) | −7.02355 | −0.899274 | −0.449637 | − | 0.893211i | \(-0.648447\pi\) | ||||
−0.449637 | + | 0.893211i | \(0.648447\pi\) | |||||||
\(62\) | 1.27520 | 0.161951 | ||||||||
\(63\) | 0.913701 | 0.115115 | ||||||||
\(64\) | −12.5826 | −1.57282 | ||||||||
\(65\) | −4.37780 | −0.543000 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5826 | −1.65938 | −0.829688 | − | 0.558228i | \(-0.811482\pi\) | ||||
−0.829688 | + | 0.558228i | \(0.811482\pi\) | |||||||
\(68\) | −4.83465 | −0.586288 | ||||||||
\(69\) | 8.58258 | 1.03322 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 1.73205 | 0.204124 | ||||||||
\(73\) | −15.6838 | −1.83565 | −0.917825 | − | 0.396984i | \(-0.870057\pi\) | ||||
−0.917825 | + | 0.396984i | \(0.870057\pi\) | |||||||
\(74\) | −3.46410 | −0.402694 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 9.66930 | 1.10915 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.58258 | 1.08501 | ||||||||
\(79\) | −6.10985 | −0.687412 | −0.343706 | − | 0.939077i | \(-0.611682\pi\) | ||||
−0.343706 | + | 0.939077i | \(0.611682\pi\) | |||||||
\(80\) | 1.79129 | 0.200272 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.58258 | −0.837355 | ||||||||
\(83\) | −15.8745 | −1.74245 | −0.871227 | − | 0.490881i | \(-0.836675\pi\) | ||||
−0.871227 | + | 0.490881i | \(0.836675\pi\) | |||||||
\(84\) | 2.55040 | 0.278272 | ||||||||
\(85\) | 1.73205 | 0.187867 | ||||||||
\(86\) | −13.5826 | −1.46465 | ||||||||
\(87\) | 6.20520 | 0.665268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7477 | −1.35126 | −0.675628 | − | 0.737243i | \(-0.736128\pi\) | ||||
−0.675628 | + | 0.737243i | \(0.736128\pi\) | |||||||
\(90\) | −2.18890 | −0.230730 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 23.9564 | 2.49763 | ||||||||
\(93\) | 0.582576 | 0.0604103 | ||||||||
\(94\) | 27.5420 | 2.84074 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | −7.38505 | −0.753734 | ||||||||
\(97\) | 13.5826 | 1.37910 | 0.689551 | − | 0.724237i | \(-0.257808\pi\) | ||||
0.689551 | + | 0.724237i | \(0.257808\pi\) | |||||||
\(98\) | −13.4949 | −1.36319 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.79129 | 0.279129 | ||||||||
\(101\) | 8.75560 | 0.871215 | 0.435608 | − | 0.900137i | \(-0.356534\pi\) | ||||
0.435608 | + | 0.900137i | \(0.356534\pi\) | |||||||
\(102\) | −3.79129 | −0.375393 | ||||||||
\(103\) | −11.1652 | −1.10014 | −0.550068 | − | 0.835120i | \(-0.685398\pi\) | ||||
−0.550068 | + | 0.835120i | \(0.685398\pi\) | |||||||
\(104\) | 7.58258 | 0.743533 | ||||||||
\(105\) | −0.913701 | −0.0891680 | ||||||||
\(106\) | −13.4949 | −1.31074 | ||||||||
\(107\) | 7.74655 | 0.748888 | 0.374444 | − | 0.927250i | \(-0.377834\pi\) | ||||
0.374444 | + | 0.927250i | \(0.377834\pi\) | |||||||
\(108\) | 2.79129 | 0.268592 | ||||||||
\(109\) | 6.92820 | 0.663602 | 0.331801 | − | 0.943349i | \(-0.392344\pi\) | ||||
0.331801 | + | 0.943349i | \(0.392344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.58258 | −0.150211 | ||||||||
\(112\) | −1.63670 | −0.154654 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 7.58258 | 0.710173 | ||||||||
\(115\) | −8.58258 | −0.800329 | ||||||||
\(116\) | 17.3205 | 1.60817 | ||||||||
\(117\) | 4.37780 | 0.404728 | ||||||||
\(118\) | 9.66930 | 0.890132 | ||||||||
\(119\) | −1.58258 | −0.145074 | ||||||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −15.3739 | −1.39188 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | 1.62614 | 0.146031 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −2.55040 | −0.226312 | −0.113156 | − | 0.993577i | \(-0.536096\pi\) | ||||
−0.113156 | + | 0.993577i | \(0.536096\pi\) | |||||||
\(128\) | −12.7719 | −1.12889 | ||||||||
\(129\) | −6.20520 | −0.546338 | ||||||||
\(130\) | −9.58258 | −0.840447 | ||||||||
\(131\) | 0.190700 | 0.0166616 | 0.00833079 | − | 0.999965i | \(-0.497348\pi\) | ||||
0.00833079 | + | 0.999965i | \(0.497348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.16515 | 0.274453 | ||||||||
\(134\) | −29.7309 | −2.56836 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 17.3303 | 1.48063 | 0.740314 | − | 0.672261i | \(-0.234677\pi\) | ||||
0.740314 | + | 0.672261i | \(0.234677\pi\) | |||||||
\(138\) | 18.7864 | 1.59921 | ||||||||
\(139\) | −13.0381 | −1.10587 | −0.552937 | − | 0.833223i | \(-0.686493\pi\) | ||||
−0.552937 | + | 0.833223i | \(0.686493\pi\) | |||||||
\(140\) | −2.55040 | −0.215548 | ||||||||
\(141\) | 12.5826 | 1.05964 | ||||||||
\(142\) | 17.5112 | 1.46951 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.79129 | −0.149274 | ||||||||
\(145\) | −6.20520 | −0.515314 | ||||||||
\(146\) | −34.3303 | −2.84120 | ||||||||
\(147\) | −6.16515 | −0.508493 | ||||||||
\(148\) | −4.41742 | −0.363110 | ||||||||
\(149\) | −13.1334 | −1.07593 | −0.537965 | − | 0.842967i | \(-0.680807\pi\) | ||||
−0.537965 | + | 0.842967i | \(0.680807\pi\) | |||||||
\(150\) | 2.18890 | 0.178723 | ||||||||
\(151\) | −13.0381 | −1.06102 | −0.530511 | − | 0.847678i | \(-0.678000\pi\) | ||||
−0.530511 | + | 0.847678i | \(0.678000\pi\) | |||||||
\(152\) | 6.00000 | 0.486664 | ||||||||
\(153\) | −1.73205 | −0.140028 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.582576 | −0.0467936 | ||||||||
\(156\) | 12.2197 | 0.978359 | ||||||||
\(157\) | −16.7477 | −1.33661 | −0.668307 | − | 0.743886i | \(-0.732981\pi\) | ||||
−0.668307 | + | 0.743886i | \(0.732981\pi\) | |||||||
\(158\) | −13.3739 | −1.06397 | ||||||||
\(159\) | −6.16515 | −0.488928 | ||||||||
\(160\) | 7.38505 | 0.583840 | ||||||||
\(161\) | 7.84190 | 0.618029 | ||||||||
\(162\) | 2.18890 | 0.171976 | ||||||||
\(163\) | 6.74773 | 0.528523 | 0.264261 | − | 0.964451i | \(-0.414872\pi\) | ||||
0.264261 | + | 0.964451i | \(0.414872\pi\) | |||||||
\(164\) | −9.66930 | −0.755046 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.7477 | −2.69695 | ||||||||
\(167\) | 11.4014 | 0.882263 | 0.441132 | − | 0.897442i | \(-0.354577\pi\) | ||||
0.441132 | + | 0.897442i | \(0.354577\pi\) | |||||||
\(168\) | 1.58258 | 0.122098 | ||||||||
\(169\) | 6.16515 | 0.474242 | ||||||||
\(170\) | 3.79129 | 0.290779 | ||||||||
\(171\) | 3.46410 | 0.264906 | ||||||||
\(172\) | −17.3205 | −1.32068 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 13.5826 | 1.02969 | ||||||||
\(175\) | 0.913701 | 0.0690693 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.41742 | 0.332034 | ||||||||
\(178\) | −27.9035 | −2.09146 | ||||||||
\(179\) | −1.58258 | −0.118287 | −0.0591436 | − | 0.998249i | \(-0.518837\pi\) | ||||
−0.0591436 | + | 0.998249i | \(0.518837\pi\) | |||||||
\(180\) | −2.79129 | −0.208050 | ||||||||
\(181\) | 13.1652 | 0.978558 | 0.489279 | − | 0.872127i | \(-0.337260\pi\) | ||||
0.489279 | + | 0.872127i | \(0.337260\pi\) | |||||||
\(182\) | 8.75560 | 0.649009 | ||||||||
\(183\) | −7.02355 | −0.519196 | ||||||||
\(184\) | 14.8655 | 1.09590 | ||||||||
\(185\) | 1.58258 | 0.116353 | ||||||||
\(186\) | 1.27520 | 0.0935022 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 35.1216 | 2.56151 | ||||||||
\(189\) | 0.913701 | 0.0664619 | ||||||||
\(190\) | −7.58258 | −0.550098 | ||||||||
\(191\) | 4.74773 | 0.343533 | 0.171767 | − | 0.985138i | \(-0.445052\pi\) | ||||
0.171767 | + | 0.985138i | \(0.445052\pi\) | |||||||
\(192\) | −12.5826 | −0.908069 | ||||||||
\(193\) | −21.6983 | −1.56188 | −0.780939 | − | 0.624607i | \(-0.785259\pi\) | ||||
−0.780939 | + | 0.624607i | \(0.785259\pi\) | |||||||
\(194\) | 29.7309 | 2.13456 | ||||||||
\(195\) | −4.37780 | −0.313501 | ||||||||
\(196\) | −17.2087 | −1.22919 | ||||||||
\(197\) | −19.3386 | −1.37782 | −0.688909 | − | 0.724847i | \(-0.741910\pi\) | ||||
−0.688909 | + | 0.724847i | \(0.741910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7477 | 0.832774 | 0.416387 | − | 0.909187i | \(-0.363296\pi\) | ||||
0.416387 | + | 0.909187i | \(0.363296\pi\) | |||||||
\(200\) | 1.73205 | 0.122474 | ||||||||
\(201\) | −13.5826 | −0.958041 | ||||||||
\(202\) | 19.1652 | 1.34846 | ||||||||
\(203\) | 5.66970 | 0.397935 | ||||||||
\(204\) | −4.83465 | −0.338493 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | −24.4394 | −1.70277 | ||||||||
\(207\) | 8.58258 | 0.596530 | ||||||||
\(208\) | −7.84190 | −0.543738 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.00000 | −0.138013 | ||||||||
\(211\) | 18.1389 | 1.24873 | 0.624365 | − | 0.781133i | \(-0.285358\pi\) | ||||
0.624365 | + | 0.781133i | \(0.285358\pi\) | |||||||
\(212\) | −17.2087 | −1.18190 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 16.9564 | 1.15912 | ||||||||
\(215\) | 6.20520 | 0.423191 | ||||||||
\(216\) | 1.73205 | 0.117851 | ||||||||
\(217\) | 0.532300 | 0.0361349 | ||||||||
\(218\) | 15.1652 | 1.02711 | ||||||||
\(219\) | −15.6838 | −1.05981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.58258 | −0.510059 | ||||||||
\(222\) | −3.46410 | −0.232495 | ||||||||
\(223\) | 20.3303 | 1.36142 | 0.680709 | − | 0.732554i | \(-0.261672\pi\) | ||||
0.680709 | + | 0.732554i | \(0.261672\pi\) | |||||||
\(224\) | −6.74773 | −0.450851 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 19.7001 | 1.31043 | ||||||||
\(227\) | −6.30055 | −0.418182 | −0.209091 | − | 0.977896i | \(-0.567051\pi\) | ||||
−0.209091 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(228\) | 9.66930 | 0.640365 | ||||||||
\(229\) | 17.0000 | 1.12339 | 0.561696 | − | 0.827344i | \(-0.310149\pi\) | ||||
0.561696 | + | 0.827344i | \(0.310149\pi\) | |||||||
\(230\) | −18.7864 | −1.23874 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.7477 | 0.705623 | ||||||||
\(233\) | −17.6066 | −1.15344 | −0.576722 | − | 0.816940i | \(-0.695668\pi\) | ||||
−0.576722 | + | 0.816940i | \(0.695668\pi\) | |||||||
\(234\) | 9.58258 | 0.626433 | ||||||||
\(235\) | −12.5826 | −0.820797 | ||||||||
\(236\) | 12.3303 | 0.802634 | ||||||||
\(237\) | −6.10985 | −0.396878 | ||||||||
\(238\) | −3.46410 | −0.224544 | ||||||||
\(239\) | −26.9898 | −1.74583 | −0.872913 | − | 0.487876i | \(-0.837772\pi\) | ||||
−0.872913 | + | 0.487876i | \(0.837772\pi\) | |||||||
\(240\) | 1.79129 | 0.115627 | ||||||||
\(241\) | 5.00545 | 0.322430 | 0.161215 | − | 0.986919i | \(-0.448459\pi\) | ||||
0.161215 | + | 0.986919i | \(0.448459\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −19.6048 | −1.25507 | ||||||||
\(245\) | 6.16515 | 0.393877 | ||||||||
\(246\) | −7.58258 | −0.483447 | ||||||||
\(247\) | 15.1652 | 0.964935 | ||||||||
\(248\) | 1.00905 | 0.0640748 | ||||||||
\(249\) | −15.8745 | −1.00601 | ||||||||
\(250\) | −2.18890 | −0.138438 | ||||||||
\(251\) | 3.58258 | 0.226130 | 0.113065 | − | 0.993588i | \(-0.463933\pi\) | ||||
0.113065 | + | 0.993588i | \(0.463933\pi\) | |||||||
\(252\) | 2.55040 | 0.160660 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.58258 | −0.350282 | ||||||||
\(255\) | 1.73205 | 0.108465 | ||||||||
\(256\) | −2.79129 | −0.174455 | ||||||||
\(257\) | 24.1652 | 1.50738 | 0.753690 | − | 0.657230i | \(-0.228272\pi\) | ||||
0.753690 | + | 0.657230i | \(0.228272\pi\) | |||||||
\(258\) | −13.5826 | −0.845614 | ||||||||
\(259\) | −1.44600 | −0.0898501 | ||||||||
\(260\) | −12.2197 | −0.757834 | ||||||||
\(261\) | 6.20520 | 0.384092 | ||||||||
\(262\) | 0.417424 | 0.0257886 | ||||||||
\(263\) | −4.47315 | −0.275826 | −0.137913 | − | 0.990444i | \(-0.544039\pi\) | ||||
−0.137913 | + | 0.990444i | \(0.544039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.16515 | 0.378722 | ||||||||
\(266\) | 6.92820 | 0.424795 | ||||||||
\(267\) | −12.7477 | −0.780148 | ||||||||
\(268\) | −37.9129 | −2.31590 | ||||||||
\(269\) | −27.1652 | −1.65629 | −0.828144 | − | 0.560515i | \(-0.810603\pi\) | ||||
−0.828144 | + | 0.560515i | \(0.810603\pi\) | |||||||
\(270\) | −2.18890 | −0.133212 | ||||||||
\(271\) | 9.76465 | 0.593161 | 0.296580 | − | 0.955008i | \(-0.404154\pi\) | ||||
0.296580 | + | 0.955008i | \(0.404154\pi\) | |||||||
\(272\) | 3.10260 | 0.188123 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 37.9343 | 2.29170 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 23.9564 | 1.44201 | ||||||||
\(277\) | −8.75560 | −0.526073 | −0.263037 | − | 0.964786i | \(-0.584724\pi\) | ||||
−0.263037 | + | 0.964786i | \(0.584724\pi\) | |||||||
\(278\) | −28.5390 | −1.71166 | ||||||||
\(279\) | 0.582576 | 0.0348779 | ||||||||
\(280\) | −1.58258 | −0.0945770 | ||||||||
\(281\) | −13.3241 | −0.794850 | −0.397425 | − | 0.917635i | \(-0.630096\pi\) | ||||
−0.397425 | + | 0.917635i | \(0.630096\pi\) | |||||||
\(282\) | 27.5420 | 1.64010 | ||||||||
\(283\) | −31.5583 | −1.87595 | −0.937974 | − | 0.346707i | \(-0.887300\pi\) | ||||
−0.937974 | + | 0.346707i | \(0.887300\pi\) | |||||||
\(284\) | 22.3303 | 1.32506 | ||||||||
\(285\) | −3.46410 | −0.205196 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.16515 | −0.186833 | ||||||||
\(288\) | −7.38505 | −0.435168 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | −13.5826 | −0.797596 | ||||||||
\(291\) | 13.5826 | 0.796225 | ||||||||
\(292\) | −43.7780 | −2.56191 | ||||||||
\(293\) | −1.73205 | −0.101187 | −0.0505937 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505937 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(294\) | −13.4949 | −0.787039 | ||||||||
\(295\) | −4.41742 | −0.257192 | ||||||||
\(296\) | −2.74110 | −0.159323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.7477 | −1.66531 | ||||||||
\(299\) | 37.5728 | 2.17289 | ||||||||
\(300\) | 2.79129 | 0.161155 | ||||||||
\(301\) | −5.66970 | −0.326796 | ||||||||
\(302\) | −28.5390 | −1.64224 | ||||||||
\(303\) | 8.75560 | 0.502996 | ||||||||
\(304\) | −6.20520 | −0.355893 | ||||||||
\(305\) | 7.02355 | 0.402167 | ||||||||
\(306\) | −3.79129 | −0.216734 | ||||||||
\(307\) | 26.0761 | 1.48824 | 0.744121 | − | 0.668045i | \(-0.232869\pi\) | ||||
0.744121 | + | 0.668045i | \(0.232869\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.1652 | −0.635163 | ||||||||
\(310\) | −1.27520 | −0.0724265 | ||||||||
\(311\) | −2.41742 | −0.137080 | −0.0685398 | − | 0.997648i | \(-0.521834\pi\) | ||||
−0.0685398 | + | 0.997648i | \(0.521834\pi\) | |||||||
\(312\) | 7.58258 | 0.429279 | ||||||||
\(313\) | −3.58258 | −0.202499 | −0.101250 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101250 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(314\) | −36.6591 | −2.06879 | ||||||||
\(315\) | −0.913701 | −0.0514812 | ||||||||
\(316\) | −17.0544 | −0.959383 | ||||||||
\(317\) | 11.8348 | 0.664711 | 0.332356 | − | 0.943154i | \(-0.392157\pi\) | ||||
0.332356 | + | 0.943154i | \(0.392157\pi\) | |||||||
\(318\) | −13.4949 | −0.756757 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.5826 | 0.703387 | ||||||||
\(321\) | 7.74655 | 0.432370 | ||||||||
\(322\) | 17.1652 | 0.956576 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 2.79129 | 0.155072 | ||||||||
\(325\) | 4.37780 | 0.242837 | ||||||||
\(326\) | 14.7701 | 0.818041 | ||||||||
\(327\) | 6.92820 | 0.383131 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 11.4967 | 0.633834 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.252273 | 0.0138662 | 0.00693309 | − | 0.999976i | \(-0.497793\pi\) | ||||
0.00693309 | + | 0.999976i | \(0.497793\pi\) | |||||||
\(332\) | −44.3103 | −2.43184 | ||||||||
\(333\) | −1.58258 | −0.0867246 | ||||||||
\(334\) | 24.9564 | 1.36556 | ||||||||
\(335\) | 13.5826 | 0.742095 | ||||||||
\(336\) | −1.63670 | −0.0892893 | ||||||||
\(337\) | 20.9753 | 1.14260 | 0.571299 | − | 0.820742i | \(-0.306440\pi\) | ||||
0.571299 | + | 0.820742i | \(0.306440\pi\) | |||||||
\(338\) | 13.4949 | 0.734026 | ||||||||
\(339\) | 9.00000 | 0.488813 | ||||||||
\(340\) | 4.83465 | 0.262196 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.58258 | 0.410019 | ||||||||
\(343\) | −12.0290 | −0.649505 | ||||||||
\(344\) | −10.7477 | −0.579479 | ||||||||
\(345\) | −8.58258 | −0.462070 | ||||||||
\(346\) | 15.1652 | 0.815284 | ||||||||
\(347\) | 15.0562 | 0.808257 | 0.404128 | − | 0.914702i | \(-0.367575\pi\) | ||||
0.404128 | + | 0.914702i | \(0.367575\pi\) | |||||||
\(348\) | 17.3205 | 0.928477 | ||||||||
\(349\) | 25.9808 | 1.39072 | 0.695359 | − | 0.718662i | \(-0.255245\pi\) | ||||
0.695359 | + | 0.718662i | \(0.255245\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 4.37780 | 0.233670 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.1652 | 1.92488 | 0.962438 | − | 0.271500i | \(-0.0875198\pi\) | ||||
0.962438 | + | 0.271500i | \(0.0875198\pi\) | |||||||
\(354\) | 9.66930 | 0.513918 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | −35.5826 | −1.88587 | ||||||||
\(357\) | −1.58258 | −0.0837588 | ||||||||
\(358\) | −3.46410 | −0.183083 | ||||||||
\(359\) | 1.82740 | 0.0964465 | 0.0482233 | − | 0.998837i | \(-0.484644\pi\) | ||||
0.0482233 | + | 0.998837i | \(0.484644\pi\) | |||||||
\(360\) | −1.73205 | −0.0912871 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 28.8172 | 1.51460 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.1652 | 0.585213 | ||||||||
\(365\) | 15.6838 | 0.820928 | ||||||||
\(366\) | −15.3739 | −0.803605 | ||||||||
\(367\) | −28.7477 | −1.50062 | −0.750310 | − | 0.661087i | \(-0.770096\pi\) | ||||
−0.750310 | + | 0.661087i | \(0.770096\pi\) | |||||||
\(368\) | −15.3739 | −0.801418 | ||||||||
\(369\) | −3.46410 | −0.180334 | ||||||||
\(370\) | 3.46410 | 0.180090 | ||||||||
\(371\) | −5.63310 | −0.292456 | ||||||||
\(372\) | 1.62614 | 0.0843112 | ||||||||
\(373\) | 13.8564 | 0.717458 | 0.358729 | − | 0.933442i | \(-0.383210\pi\) | ||||
0.358729 | + | 0.933442i | \(0.383210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 21.7937 | 1.12392 | ||||||||
\(377\) | 27.1652 | 1.39908 | ||||||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | 11.7477 | 0.603440 | 0.301720 | − | 0.953397i | \(-0.402439\pi\) | ||||
0.301720 | + | 0.953397i | \(0.402439\pi\) | |||||||
\(380\) | −9.66930 | −0.496025 | ||||||||
\(381\) | −2.55040 | −0.130661 | ||||||||
\(382\) | 10.3923 | 0.531717 | ||||||||
\(383\) | −30.3303 | −1.54981 | −0.774903 | − | 0.632080i | \(-0.782201\pi\) | ||||
−0.774903 | + | 0.632080i | \(0.782201\pi\) | |||||||
\(384\) | −12.7719 | −0.651764 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −47.4955 | −2.41745 | ||||||||
\(387\) | −6.20520 | −0.315428 | ||||||||
\(388\) | 37.9129 | 1.92473 | ||||||||
\(389\) | −22.7477 | −1.15336 | −0.576678 | − | 0.816972i | \(-0.695651\pi\) | ||||
−0.576678 | + | 0.816972i | \(0.695651\pi\) | |||||||
\(390\) | −9.58258 | −0.485233 | ||||||||
\(391\) | −14.8655 | −0.751778 | ||||||||
\(392\) | −10.6784 | −0.539338 | ||||||||
\(393\) | 0.190700 | 0.00961956 | ||||||||
\(394\) | −42.3303 | −2.13257 | ||||||||
\(395\) | 6.10985 | 0.307420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.33030 | −0.217332 | −0.108666 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108666 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(398\) | 25.7146 | 1.28896 | ||||||||
\(399\) | 3.16515 | 0.158456 | ||||||||
\(400\) | −1.79129 | −0.0895644 | ||||||||
\(401\) | −22.3303 | −1.11512 | −0.557561 | − | 0.830136i | \(-0.688263\pi\) | ||||
−0.557561 | + | 0.830136i | \(0.688263\pi\) | |||||||
\(402\) | −29.7309 | −1.48284 | ||||||||
\(403\) | 2.55040 | 0.127045 | ||||||||
\(404\) | 24.4394 | 1.21591 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 12.4104 | 0.615918 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.00000 | −0.148522 | ||||||||
\(409\) | 22.8981 | 1.13224 | 0.566118 | − | 0.824324i | \(-0.308445\pi\) | ||||
0.566118 | + | 0.824324i | \(0.308445\pi\) | |||||||
\(410\) | 7.58258 | 0.374477 | ||||||||
\(411\) | 17.3303 | 0.854841 | ||||||||
\(412\) | −31.1652 | −1.53540 | ||||||||
\(413\) | 4.03620 | 0.198609 | ||||||||
\(414\) | 18.7864 | 0.923302 | ||||||||
\(415\) | 15.8745 | 0.779249 | ||||||||
\(416\) | −32.3303 | −1.58512 | ||||||||
\(417\) | −13.0381 | −0.638476 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.3303 | 1.57944 | 0.789719 | − | 0.613468i | \(-0.210226\pi\) | ||||
0.789719 | + | 0.613468i | \(0.210226\pi\) | |||||||
\(420\) | −2.55040 | −0.124447 | ||||||||
\(421\) | −2.66970 | −0.130113 | −0.0650565 | − | 0.997882i | \(-0.520723\pi\) | ||||
−0.0650565 | + | 0.997882i | \(0.520723\pi\) | |||||||
\(422\) | 39.7042 | 1.93277 | ||||||||
\(423\) | 12.5826 | 0.611786 | ||||||||
\(424\) | −10.6784 | −0.518587 | ||||||||
\(425\) | −1.73205 | −0.0840168 | ||||||||
\(426\) | 17.5112 | 0.848421 | ||||||||
\(427\) | −6.41742 | −0.310561 | ||||||||
\(428\) | 21.6229 | 1.04518 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.5826 | 0.655010 | ||||||||
\(431\) | 20.0616 | 0.966334 | 0.483167 | − | 0.875528i | \(-0.339486\pi\) | ||||
0.483167 | + | 0.875528i | \(0.339486\pi\) | |||||||
\(432\) | −1.79129 | −0.0861834 | ||||||||
\(433\) | −4.41742 | −0.212288 | −0.106144 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106144 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(434\) | 1.16515 | 0.0559291 | ||||||||
\(435\) | −6.20520 | −0.297517 | ||||||||
\(436\) | 19.3386 | 0.926151 | ||||||||
\(437\) | 29.7309 | 1.42222 | ||||||||
\(438\) | −34.3303 | −1.64037 | ||||||||
\(439\) | 9.57395 | 0.456940 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.16515 | −0.293579 | ||||||||
\(442\) | −16.5975 | −0.789463 | ||||||||
\(443\) | 7.16515 | 0.340427 | 0.170213 | − | 0.985407i | \(-0.445554\pi\) | ||||
0.170213 | + | 0.985407i | \(0.445554\pi\) | |||||||
\(444\) | −4.41742 | −0.209642 | ||||||||
\(445\) | 12.7477 | 0.604300 | ||||||||
\(446\) | 44.5010 | 2.10718 | ||||||||
\(447\) | −13.1334 | −0.621189 | ||||||||
\(448\) | −11.4967 | −0.543168 | ||||||||
\(449\) | 2.83485 | 0.133785 | 0.0668924 | − | 0.997760i | \(-0.478692\pi\) | ||||
0.0668924 | + | 0.997760i | \(0.478692\pi\) | |||||||
\(450\) | 2.18890 | 0.103186 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 25.1216 | 1.18162 | ||||||||
\(453\) | −13.0381 | −0.612581 | ||||||||
\(454\) | −13.7913 | −0.647257 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −22.4213 | −1.04882 | −0.524412 | − | 0.851464i | \(-0.675715\pi\) | ||||
−0.524412 | + | 0.851464i | \(0.675715\pi\) | |||||||
\(458\) | 37.2113 | 1.73877 | ||||||||
\(459\) | −1.73205 | −0.0808452 | ||||||||
\(460\) | −23.9564 | −1.11697 | ||||||||
\(461\) | 8.03260 | 0.374116 | 0.187058 | − | 0.982349i | \(-0.440105\pi\) | ||||
0.187058 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.4955 | −1.64961 | −0.824807 | − | 0.565415i | \(-0.808716\pi\) | ||||
−0.824807 | + | 0.565415i | \(0.808716\pi\) | |||||||
\(464\) | −11.1153 | −0.516015 | ||||||||
\(465\) | −0.582576 | −0.0270163 | ||||||||
\(466\) | −38.5390 | −1.78529 | ||||||||
\(467\) | −3.41742 | −0.158140 | −0.0790698 | − | 0.996869i | \(-0.525195\pi\) | ||||
−0.0790698 | + | 0.996869i | \(0.525195\pi\) | |||||||
\(468\) | 12.2197 | 0.564856 | ||||||||
\(469\) | −12.4104 | −0.573059 | ||||||||
\(470\) | −27.5420 | −1.27042 | ||||||||
\(471\) | −16.7477 | −0.771695 | ||||||||
\(472\) | 7.65120 | 0.352175 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −13.3739 | −0.614282 | ||||||||
\(475\) | 3.46410 | 0.158944 | ||||||||
\(476\) | −4.41742 | −0.202472 | ||||||||
\(477\) | −6.16515 | −0.282283 | ||||||||
\(478\) | −59.0780 | −2.70217 | ||||||||
\(479\) | −27.3712 | −1.25062 | −0.625311 | − | 0.780375i | \(-0.715028\pi\) | ||||
−0.625311 | + | 0.780375i | \(0.715028\pi\) | |||||||
\(480\) | 7.38505 | 0.337080 | ||||||||
\(481\) | −6.92820 | −0.315899 | ||||||||
\(482\) | 10.9564 | 0.499052 | ||||||||
\(483\) | 7.84190 | 0.356819 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5826 | −0.616753 | ||||||||
\(486\) | 2.18890 | 0.0992906 | ||||||||
\(487\) | 3.58258 | 0.162342 | 0.0811710 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811710 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(488\) | −12.1652 | −0.550691 | ||||||||
\(489\) | 6.74773 | 0.305143 | ||||||||
\(490\) | 13.4949 | 0.609638 | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | −9.66930 | −0.435926 | ||||||||
\(493\) | −10.7477 | −0.484053 | ||||||||
\(494\) | 33.1950 | 1.49351 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.04356 | −0.0468573 | ||||||||
\(497\) | 7.30960 | 0.327881 | ||||||||
\(498\) | −34.7477 | −1.55708 | ||||||||
\(499\) | 26.3303 | 1.17871 | 0.589353 | − | 0.807876i | \(-0.299383\pi\) | ||||
0.589353 | + | 0.807876i | \(0.299383\pi\) | |||||||
\(500\) | −2.79129 | −0.124830 | ||||||||
\(501\) | 11.4014 | 0.509375 | ||||||||
\(502\) | 7.84190 | 0.350001 | ||||||||
\(503\) | 0.818350 | 0.0364884 | 0.0182442 | − | 0.999834i | \(-0.494192\pi\) | ||||
0.0182442 | + | 0.999834i | \(0.494192\pi\) | |||||||
\(504\) | 1.58258 | 0.0704935 | ||||||||
\(505\) | −8.75560 | −0.389619 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.16515 | 0.273804 | ||||||||
\(508\) | −7.11890 | −0.315850 | ||||||||
\(509\) | 0.747727 | 0.0331424 | 0.0165712 | − | 0.999863i | \(-0.494725\pi\) | ||||
0.0165712 | + | 0.999863i | \(0.494725\pi\) | |||||||
\(510\) | 3.79129 | 0.167881 | ||||||||
\(511\) | −14.3303 | −0.633935 | ||||||||
\(512\) | 19.4340 | 0.858868 | ||||||||
\(513\) | 3.46410 | 0.152944 | ||||||||
\(514\) | 52.8951 | 2.33310 | ||||||||
\(515\) | 11.1652 | 0.491995 | ||||||||
\(516\) | −17.3205 | −0.762493 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.16515 | −0.139069 | ||||||||
\(519\) | 6.92820 | 0.304114 | ||||||||
\(520\) | −7.58258 | −0.332518 | ||||||||
\(521\) | 9.25227 | 0.405349 | 0.202675 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202675 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(522\) | 13.5826 | 0.594493 | ||||||||
\(523\) | −4.56850 | −0.199767 | −0.0998833 | − | 0.994999i | \(-0.531847\pi\) | ||||
−0.0998833 | + | 0.994999i | \(0.531847\pi\) | |||||||
\(524\) | 0.532300 | 0.0232536 | ||||||||
\(525\) | 0.913701 | 0.0398772 | ||||||||
\(526\) | −9.79129 | −0.426920 | ||||||||
\(527\) | −1.00905 | −0.0439549 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.6606 | 2.20264 | ||||||||
\(530\) | 13.4949 | 0.586181 | ||||||||
\(531\) | 4.41742 | 0.191700 | ||||||||
\(532\) | 8.83485 | 0.383039 | ||||||||
\(533\) | −15.1652 | −0.656876 | ||||||||
\(534\) | −27.9035 | −1.20750 | ||||||||
\(535\) | −7.74655 | −0.334913 | ||||||||
\(536\) | −23.5257 | −1.01616 | ||||||||
\(537\) | −1.58258 | −0.0682932 | ||||||||
\(538\) | −59.4618 | −2.56358 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.79129 | −0.120118 | ||||||||
\(541\) | −29.9216 | −1.28643 | −0.643215 | − | 0.765685i | \(-0.722400\pi\) | ||||
−0.643215 | + | 0.765685i | \(0.722400\pi\) | |||||||
\(542\) | 21.3739 | 0.918086 | ||||||||
\(543\) | 13.1652 | 0.564971 | ||||||||
\(544\) | 12.7913 | 0.548422 | ||||||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 8.75560 | 0.374705 | ||||||||
\(547\) | −3.99640 | −0.170874 | −0.0854369 | − | 0.996344i | \(-0.527229\pi\) | ||||
−0.0854369 | + | 0.996344i | \(0.527229\pi\) | |||||||
\(548\) | 48.3739 | 2.06643 | ||||||||
\(549\) | −7.02355 | −0.299758 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.4955 | 0.915737 | ||||||||
\(552\) | 14.8655 | 0.632716 | ||||||||
\(553\) | −5.58258 | −0.237395 | ||||||||
\(554\) | −19.1652 | −0.814249 | ||||||||
\(555\) | 1.58258 | 0.0671766 | ||||||||
\(556\) | −36.3930 | −1.54341 | ||||||||
\(557\) | 29.6356 | 1.25570 | 0.627850 | − | 0.778335i | \(-0.283935\pi\) | ||||
0.627850 | + | 0.778335i | \(0.283935\pi\) | |||||||
\(558\) | 1.27520 | 0.0539835 | ||||||||
\(559\) | −27.1652 | −1.14896 | ||||||||
\(560\) | 1.63670 | 0.0691632 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.1652 | −1.23026 | ||||||||
\(563\) | 11.8383 | 0.498925 | 0.249463 | − | 0.968384i | \(-0.419746\pi\) | ||||
0.249463 | + | 0.968384i | \(0.419746\pi\) | |||||||
\(564\) | 35.1216 | 1.47889 | ||||||||
\(565\) | −9.00000 | −0.378633 | ||||||||
\(566\) | −69.0780 | −2.90357 | ||||||||
\(567\) | 0.913701 | 0.0383718 | ||||||||
\(568\) | 13.8564 | 0.581402 | ||||||||
\(569\) | 21.5076 | 0.901646 | 0.450823 | − | 0.892613i | \(-0.351131\pi\) | ||||
0.450823 | + | 0.892613i | \(0.351131\pi\) | |||||||
\(570\) | −7.58258 | −0.317599 | ||||||||
\(571\) | −27.0852 | −1.13348 | −0.566739 | − | 0.823897i | \(-0.691795\pi\) | ||||
−0.566739 | + | 0.823897i | \(0.691795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.74773 | 0.198339 | ||||||||
\(574\) | −6.92820 | −0.289178 | ||||||||
\(575\) | 8.58258 | 0.357918 | ||||||||
\(576\) | −12.5826 | −0.524274 | ||||||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | −30.6446 | −1.27465 | ||||||||
\(579\) | −21.6983 | −0.901751 | ||||||||
\(580\) | −17.3205 | −0.719195 | ||||||||
\(581\) | −14.5045 | −0.601750 | ||||||||
\(582\) | 29.7309 | 1.23239 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.1652 | −1.12410 | ||||||||
\(585\) | −4.37780 | −0.181000 | ||||||||
\(586\) | −3.79129 | −0.156617 | ||||||||
\(587\) | −19.7477 | −0.815076 | −0.407538 | − | 0.913188i | \(-0.633613\pi\) | ||||
−0.407538 | + | 0.913188i | \(0.633613\pi\) | |||||||
\(588\) | −17.2087 | −0.709675 | ||||||||
\(589\) | 2.01810 | 0.0831544 | ||||||||
\(590\) | −9.66930 | −0.398079 | ||||||||
\(591\) | −19.3386 | −0.795484 | ||||||||
\(592\) | 2.83485 | 0.116512 | ||||||||
\(593\) | 27.7128 | 1.13803 | 0.569014 | − | 0.822328i | \(-0.307325\pi\) | ||||
0.569014 | + | 0.822328i | \(0.307325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.58258 | 0.0648793 | ||||||||
\(596\) | −36.6591 | −1.50162 | ||||||||
\(597\) | 11.7477 | 0.480802 | ||||||||
\(598\) | 82.2432 | 3.36317 | ||||||||
\(599\) | −20.7477 | −0.847729 | −0.423865 | − | 0.905726i | \(-0.639327\pi\) | ||||
−0.423865 | + | 0.905726i | \(0.639327\pi\) | |||||||
\(600\) | 1.73205 | 0.0707107 | ||||||||
\(601\) | −33.1950 | −1.35405 | −0.677026 | − | 0.735959i | \(-0.736732\pi\) | ||||
−0.677026 | + | 0.735959i | \(0.736732\pi\) | |||||||
\(602\) | −12.4104 | −0.505810 | ||||||||
\(603\) | −13.5826 | −0.553125 | ||||||||
\(604\) | −36.3930 | −1.48081 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19.1652 | 0.778531 | ||||||||
\(607\) | 22.0797 | 0.896188 | 0.448094 | − | 0.893986i | \(-0.352103\pi\) | ||||
0.448094 | + | 0.893986i | \(0.352103\pi\) | |||||||
\(608\) | −25.5826 | −1.03751 | ||||||||
\(609\) | 5.66970 | 0.229748 | ||||||||
\(610\) | 15.3739 | 0.622470 | ||||||||
\(611\) | 55.0840 | 2.22846 | ||||||||
\(612\) | −4.83465 | −0.195429 | ||||||||
\(613\) | 8.75560 | 0.353636 | 0.176818 | − | 0.984244i | \(-0.443420\pi\) | ||||
0.176818 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(614\) | 57.0780 | 2.30348 | ||||||||
\(615\) | 3.46410 | 0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −24.4394 | −0.983097 | ||||||||
\(619\) | −41.4955 | −1.66784 | −0.833922 | − | 0.551883i | \(-0.813910\pi\) | ||||
−0.833922 | + | 0.551883i | \(0.813910\pi\) | |||||||
\(620\) | −1.62614 | −0.0653072 | ||||||||
\(621\) | 8.58258 | 0.344407 | ||||||||
\(622\) | −5.29150 | −0.212170 | ||||||||
\(623\) | −11.6476 | −0.466651 | ||||||||
\(624\) | −7.84190 | −0.313927 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.84190 | −0.313426 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.7477 | −1.86544 | ||||||||
\(629\) | 2.74110 | 0.109295 | ||||||||
\(630\) | −2.00000 | −0.0796819 | ||||||||
\(631\) | −30.5826 | −1.21747 | −0.608737 | − | 0.793372i | \(-0.708323\pi\) | ||||
−0.608737 | + | 0.793372i | \(0.708323\pi\) | |||||||
\(632\) | −10.5826 | −0.420952 | ||||||||
\(633\) | 18.1389 | 0.720955 | ||||||||
\(634\) | 25.9053 | 1.02883 | ||||||||
\(635\) | 2.55040 | 0.101210 | ||||||||
\(636\) | −17.2087 | −0.682370 | ||||||||
\(637\) | −26.9898 | −1.06938 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 12.7719 | 0.504854 | ||||||||
\(641\) | 20.7477 | 0.819486 | 0.409743 | − | 0.912201i | \(-0.365618\pi\) | ||||
0.409743 | + | 0.912201i | \(0.365618\pi\) | |||||||
\(642\) | 16.9564 | 0.669217 | ||||||||
\(643\) | 15.4955 | 0.611081 | 0.305541 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305541 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(644\) | 21.8890 | 0.862548 | ||||||||
\(645\) | 6.20520 | 0.244330 | ||||||||
\(646\) | −13.1334 | −0.516727 | ||||||||
\(647\) | 2.25227 | 0.0885460 | 0.0442730 | − | 0.999019i | \(-0.485903\pi\) | ||||
0.0442730 | + | 0.999019i | \(0.485903\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 9.58258 | 0.375860 | ||||||||
\(651\) | 0.532300 | 0.0208625 | ||||||||
\(652\) | 18.8348 | 0.737630 | ||||||||
\(653\) | −10.0000 | −0.391330 | −0.195665 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195665 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(654\) | 15.1652 | 0.593004 | ||||||||
\(655\) | −0.190700 | −0.00745128 | ||||||||
\(656\) | 6.20520 | 0.242272 | ||||||||
\(657\) | −15.6838 | −0.611884 | ||||||||
\(658\) | 25.1652 | 0.981040 | ||||||||
\(659\) | −12.9427 | −0.504176 | −0.252088 | − | 0.967704i | \(-0.581117\pi\) | ||||
−0.252088 | + | 0.967704i | \(0.581117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0.552200 | 0.0214619 | ||||||||
\(663\) | −7.58258 | −0.294483 | ||||||||
\(664\) | −27.4955 | −1.06703 | ||||||||
\(665\) | −3.16515 | −0.122739 | ||||||||
\(666\) | −3.46410 | −0.134231 | ||||||||
\(667\) | 53.2566 | 2.06210 | ||||||||
\(668\) | 31.8245 | 1.23133 | ||||||||
\(669\) | 20.3303 | 0.786015 | ||||||||
\(670\) | 29.7309 | 1.14861 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −6.74773 | −0.260299 | ||||||||
\(673\) | −6.01450 | −0.231842 | −0.115921 | − | 0.993258i | \(-0.536982\pi\) | ||||
−0.115921 | + | 0.993258i | \(0.536982\pi\) | |||||||
\(674\) | 45.9129 | 1.76850 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 17.2087 | 0.661874 | ||||||||
\(677\) | 22.6120 | 0.869050 | 0.434525 | − | 0.900660i | \(-0.356916\pi\) | ||||
0.434525 | + | 0.900660i | \(0.356916\pi\) | |||||||
\(678\) | 19.7001 | 0.756578 | ||||||||
\(679\) | 12.4104 | 0.476268 | ||||||||
\(680\) | 3.00000 | 0.115045 | ||||||||
\(681\) | −6.30055 | −0.241438 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.66970 | 0.370001 | 0.185000 | − | 0.982738i | \(-0.440771\pi\) | ||||
0.185000 | + | 0.982738i | \(0.440771\pi\) | |||||||
\(684\) | 9.66930 | 0.369715 | ||||||||
\(685\) | −17.3303 | −0.662157 | ||||||||
\(686\) | −26.3303 | −1.00530 | ||||||||
\(687\) | 17.0000 | 0.648590 | ||||||||
\(688\) | 11.1153 | 0.423767 | ||||||||
\(689\) | −26.9898 | −1.02823 | ||||||||
\(690\) | −18.7864 | −0.715186 | ||||||||
\(691\) | 8.58258 | 0.326497 | 0.163248 | − | 0.986585i | \(-0.447803\pi\) | ||||
0.163248 | + | 0.986585i | \(0.447803\pi\) | |||||||
\(692\) | 19.3386 | 0.735144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.9564 | 1.25101 | ||||||||
\(695\) | 13.0381 | 0.494562 | ||||||||
\(696\) | 10.7477 | 0.407392 | ||||||||
\(697\) | 6.00000 | 0.227266 | ||||||||
\(698\) | 56.8693 | 2.15254 | ||||||||
\(699\) | −17.6066 | −0.665941 | ||||||||
\(700\) | 2.55040 | 0.0963961 | ||||||||
\(701\) | −4.56850 | −0.172550 | −0.0862750 | − | 0.996271i | \(-0.527496\pi\) | ||||
−0.0862750 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(702\) | 9.58258 | 0.361671 | ||||||||
\(703\) | −5.48220 | −0.206765 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.5826 | −0.473887 | ||||||||
\(706\) | 79.1619 | 2.97930 | ||||||||
\(707\) | 8.00000 | 0.300871 | ||||||||
\(708\) | 12.3303 | 0.463401 | ||||||||
\(709\) | −45.0000 | −1.69001 | −0.845005 | − | 0.534758i | \(-0.820403\pi\) | ||||
−0.845005 | + | 0.534758i | \(0.820403\pi\) | |||||||
\(710\) | −17.5112 | −0.657184 | ||||||||
\(711\) | −6.10985 | −0.229137 | ||||||||
\(712\) | −22.0797 | −0.827472 | ||||||||
\(713\) | 5.00000 | 0.187251 | ||||||||
\(714\) | −3.46410 | −0.129641 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.41742 | −0.165087 | ||||||||
\(717\) | −26.9898 | −1.00795 | ||||||||
\(718\) | 4.00000 | 0.149279 | ||||||||
\(719\) | 20.3303 | 0.758192 | 0.379096 | − | 0.925357i | \(-0.376235\pi\) | ||||
0.379096 | + | 0.925357i | \(0.376235\pi\) | |||||||
\(720\) | 1.79129 | 0.0667574 | ||||||||
\(721\) | −10.2016 | −0.379928 | ||||||||
\(722\) | −15.3223 | −0.570237 | ||||||||
\(723\) | 5.00545 | 0.186155 | ||||||||
\(724\) | 36.7477 | 1.36572 | ||||||||
\(725\) | 6.20520 | 0.230455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1652 | 0.488268 | 0.244134 | − | 0.969741i | \(-0.421496\pi\) | ||||
0.244134 | + | 0.969741i | \(0.421496\pi\) | |||||||
\(728\) | 6.92820 | 0.256776 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 34.3303 | 1.27062 | ||||||||
\(731\) | 10.7477 | 0.397519 | ||||||||
\(732\) | −19.6048 | −0.724613 | ||||||||
\(733\) | 34.8317 | 1.28654 | 0.643269 | − | 0.765640i | \(-0.277578\pi\) | ||||
0.643269 | + | 0.765640i | \(0.277578\pi\) | |||||||
\(734\) | −62.9259 | −2.32264 | ||||||||
\(735\) | 6.16515 | 0.227405 | ||||||||
\(736\) | −63.3828 | −2.33632 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −7.58258 | −0.279118 | ||||||||
\(739\) | −15.0562 | −0.553850 | −0.276925 | − | 0.960892i | \(-0.589315\pi\) | ||||
−0.276925 | + | 0.960892i | \(0.589315\pi\) | |||||||
\(740\) | 4.41742 | 0.162388 | ||||||||
\(741\) | 15.1652 | 0.557106 | ||||||||
\(742\) | −12.3303 | −0.452660 | ||||||||
\(743\) | 49.6972 | 1.82321 | 0.911606 | − | 0.411065i | \(-0.134843\pi\) | ||||
0.911606 | + | 0.411065i | \(0.134843\pi\) | |||||||
\(744\) | 1.00905 | 0.0369936 | ||||||||
\(745\) | 13.1334 | 0.481171 | ||||||||
\(746\) | 30.3303 | 1.11047 | ||||||||
\(747\) | −15.8745 | −0.580818 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.07803 | 0.258626 | ||||||||
\(750\) | −2.18890 | −0.0799274 | ||||||||
\(751\) | −44.0780 | −1.60843 | −0.804215 | − | 0.594338i | \(-0.797414\pi\) | ||||
−0.804215 | + | 0.594338i | \(0.797414\pi\) | |||||||
\(752\) | −22.5390 | −0.821913 | ||||||||
\(753\) | 3.58258 | 0.130556 | ||||||||
\(754\) | 59.4618 | 2.16547 | ||||||||
\(755\) | 13.0381 | 0.474503 | ||||||||
\(756\) | 2.55040 | 0.0927572 | ||||||||
\(757\) | 25.1652 | 0.914643 | 0.457321 | − | 0.889301i | \(-0.348809\pi\) | ||||
0.457321 | + | 0.889301i | \(0.348809\pi\) | |||||||
\(758\) | 25.7146 | 0.933997 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | −9.47860 | −0.343599 | −0.171800 | − | 0.985132i | \(-0.554958\pi\) | ||||
−0.171800 | + | 0.985132i | \(0.554958\pi\) | |||||||
\(762\) | −5.58258 | −0.202235 | ||||||||
\(763\) | 6.33030 | 0.229172 | ||||||||
\(764\) | 13.2523 | 0.479450 | ||||||||
\(765\) | 1.73205 | 0.0626224 | ||||||||
\(766\) | −66.3900 | −2.39877 | ||||||||
\(767\) | 19.3386 | 0.698277 | ||||||||
\(768\) | −2.79129 | −0.100722 | ||||||||
\(769\) | 7.40495 | 0.267029 | 0.133515 | − | 0.991047i | \(-0.457374\pi\) | ||||
0.133515 | + | 0.991047i | \(0.457374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1652 | 0.870287 | ||||||||
\(772\) | −60.5662 | −2.17983 | ||||||||
\(773\) | −6.49545 | −0.233625 | −0.116813 | − | 0.993154i | \(-0.537268\pi\) | ||||
−0.116813 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(774\) | −13.5826 | −0.488216 | ||||||||
\(775\) | 0.582576 | 0.0209267 | ||||||||
\(776\) | 23.5257 | 0.844524 | ||||||||
\(777\) | −1.44600 | −0.0518750 | ||||||||
\(778\) | −49.7925 | −1.78515 | ||||||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | −12.2197 | −0.437536 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −32.5390 | −1.16359 | ||||||||
\(783\) | 6.20520 | 0.221756 | ||||||||
\(784\) | 11.0436 | 0.394413 | ||||||||
\(785\) | 16.7477 | 0.597752 | ||||||||
\(786\) | 0.417424 | 0.0148890 | ||||||||
\(787\) | 28.0942 | 1.00145 | 0.500725 | − | 0.865606i | \(-0.333067\pi\) | ||||
0.500725 | + | 0.865606i | \(0.333067\pi\) | |||||||
\(788\) | −53.9796 | −1.92294 | ||||||||
\(789\) | −4.47315 | −0.159248 | ||||||||
\(790\) | 13.3739 | 0.475821 | ||||||||
\(791\) | 8.22330 | 0.292387 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7477 | −1.09188 | ||||||||
\(794\) | −9.47860 | −0.336383 | ||||||||
\(795\) | 6.16515 | 0.218655 | ||||||||
\(796\) | 32.7913 | 1.16226 | ||||||||
\(797\) | 32.3303 | 1.14520 | 0.572599 | − | 0.819836i | \(-0.305935\pi\) | ||||
0.572599 | + | 0.819836i | \(0.305935\pi\) | |||||||
\(798\) | 6.92820 | 0.245256 | ||||||||
\(799\) | −21.7937 | −0.771004 | ||||||||
\(800\) | −7.38505 | −0.261101 | ||||||||
\(801\) | −12.7477 | −0.450419 | ||||||||
\(802\) | −48.8788 | −1.72597 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −37.9129 | −1.33708 | ||||||||
\(805\) | −7.84190 | −0.276391 | ||||||||
\(806\) | 5.58258 | 0.196638 | ||||||||
\(807\) | −27.1652 | −0.956259 | ||||||||
\(808\) | 15.1652 | 0.533508 | ||||||||
\(809\) | −1.82740 | −0.0642480 | −0.0321240 | − | 0.999484i | \(-0.510227\pi\) | ||||
−0.0321240 | + | 0.999484i | \(0.510227\pi\) | |||||||
\(810\) | −2.18890 | −0.0769101 | ||||||||
\(811\) | −28.3405 | −0.995168 | −0.497584 | − | 0.867416i | \(-0.665779\pi\) | ||||
−0.497584 | + | 0.867416i | \(0.665779\pi\) | |||||||
\(812\) | 15.8258 | 0.555375 | ||||||||
\(813\) | 9.76465 | 0.342461 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.74773 | −0.236363 | ||||||||
\(816\) | 3.10260 | 0.108613 | ||||||||
\(817\) | −21.4955 | −0.752031 | ||||||||
\(818\) | 50.1216 | 1.75246 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 9.66930 | 0.337667 | ||||||||
\(821\) | −50.5155 | −1.76300 | −0.881502 | − | 0.472180i | \(-0.843467\pi\) | ||||
−0.881502 | + | 0.472180i | \(0.843467\pi\) | |||||||
\(822\) | 37.9343 | 1.32311 | ||||||||
\(823\) | −0.834849 | −0.0291010 | −0.0145505 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145505 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(824\) | −19.3386 | −0.673692 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.83485 | 0.307404 | ||||||||
\(827\) | −47.2421 | −1.64277 | −0.821385 | − | 0.570374i | \(-0.806798\pi\) | ||||
−0.821385 | + | 0.570374i | \(0.806798\pi\) | |||||||
\(828\) | 23.9564 | 0.832544 | ||||||||
\(829\) | 19.0000 | 0.659897 | 0.329949 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329949 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(830\) | 34.7477 | 1.20611 | ||||||||
\(831\) | −8.75560 | −0.303729 | ||||||||
\(832\) | −55.0840 | −1.90970 | ||||||||
\(833\) | 10.6784 | 0.369983 | ||||||||
\(834\) | −28.5390 | −0.988225 | ||||||||
\(835\) | −11.4014 | −0.394560 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.582576 | 0.0201368 | ||||||||
\(838\) | 70.7678 | 2.44463 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | −1.58258 | −0.0546040 | ||||||||
\(841\) | 9.50455 | 0.327743 | ||||||||
\(842\) | −5.84370 | −0.201387 | ||||||||
\(843\) | −13.3241 | −0.458907 | ||||||||
\(844\) | 50.6308 | 1.74278 | ||||||||
\(845\) | −6.16515 | −0.212088 | ||||||||
\(846\) | 27.5420 | 0.946914 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.0436 | 0.379237 | ||||||||
\(849\) | −31.5583 | −1.08308 | ||||||||
\(850\) | −3.79129 | −0.130040 | ||||||||
\(851\) | −13.5826 | −0.465605 | ||||||||
\(852\) | 22.3303 | 0.765024 | ||||||||
\(853\) | −42.1413 | −1.44289 | −0.721446 | − | 0.692471i | \(-0.756522\pi\) | ||||
−0.721446 | + | 0.692471i | \(0.756522\pi\) | |||||||
\(854\) | −14.0471 | −0.480682 | ||||||||
\(855\) | −3.46410 | −0.118470 | ||||||||
\(856\) | 13.4174 | 0.458598 | ||||||||
\(857\) | 17.4159 | 0.594914 | 0.297457 | − | 0.954735i | \(-0.403861\pi\) | ||||
0.297457 | + | 0.954735i | \(0.403861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.6606 | −0.841409 | −0.420705 | − | 0.907198i | \(-0.638217\pi\) | ||||
−0.420705 | + | 0.907198i | \(0.638217\pi\) | |||||||
\(860\) | 17.3205 | 0.590624 | ||||||||
\(861\) | −3.16515 | −0.107868 | ||||||||
\(862\) | 43.9129 | 1.49568 | ||||||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | −7.38505 | −0.251245 | ||||||||
\(865\) | −6.92820 | −0.235566 | ||||||||
\(866\) | −9.66930 | −0.328576 | ||||||||
\(867\) | −14.0000 | −0.475465 | ||||||||
\(868\) | 1.48580 | 0.0504314 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −13.5826 | −0.460492 | ||||||||
\(871\) | −59.4618 | −2.01479 | ||||||||
\(872\) | 12.0000 | 0.406371 | ||||||||
\(873\) | 13.5826 | 0.459701 | ||||||||
\(874\) | 65.0780 | 2.20130 | ||||||||
\(875\) | −0.913701 | −0.0308887 | ||||||||
\(876\) | −43.7780 | −1.47912 | ||||||||
\(877\) | 41.7599 | 1.41013 | 0.705066 | − | 0.709142i | \(-0.250917\pi\) | ||||
0.705066 | + | 0.709142i | \(0.250917\pi\) | |||||||
\(878\) | 20.9564 | 0.707246 | ||||||||
\(879\) | −1.73205 | −0.0584206 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.4955 | 0.858964 | 0.429482 | − | 0.903075i | \(-0.358696\pi\) | ||||
0.429482 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(882\) | −13.4949 | −0.454397 | ||||||||
\(883\) | −48.2432 | −1.62351 | −0.811756 | − | 0.583997i | \(-0.801488\pi\) | ||||
−0.811756 | + | 0.583997i | \(0.801488\pi\) | |||||||
\(884\) | −21.1652 | −0.711861 | ||||||||
\(885\) | −4.41742 | −0.148490 | ||||||||
\(886\) | 15.6838 | 0.526908 | ||||||||
\(887\) | 2.01810 | 0.0677612 | 0.0338806 | − | 0.999426i | \(-0.489213\pi\) | ||||
0.0338806 | + | 0.999426i | \(0.489213\pi\) | |||||||
\(888\) | −2.74110 | −0.0919853 | ||||||||
\(889\) | −2.33030 | −0.0781558 | ||||||||
\(890\) | 27.9035 | 0.935328 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 56.7477 | 1.90005 | ||||||||
\(893\) | 43.5873 | 1.45859 | ||||||||
\(894\) | −28.7477 | −0.961468 | ||||||||
\(895\) | 1.58258 | 0.0528997 | ||||||||
\(896\) | −11.6697 | −0.389857 | ||||||||
\(897\) | 37.5728 | 1.25452 | ||||||||
\(898\) | 6.20520 | 0.207070 | ||||||||
\(899\) | 3.61500 | 0.120567 | ||||||||
\(900\) | 2.79129 | 0.0930429 | ||||||||
\(901\) | 10.6784 | 0.355748 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.66970 | −0.188676 | ||||||||
\(904\) | 15.5885 | 0.518464 | ||||||||
\(905\) | −13.1652 | −0.437624 | ||||||||
\(906\) | −28.5390 | −0.948145 | ||||||||
\(907\) | 29.1652 | 0.968413 | 0.484206 | − | 0.874954i | \(-0.339108\pi\) | ||||
0.484206 | + | 0.874954i | \(0.339108\pi\) | |||||||
\(908\) | −17.5867 | −0.583634 | ||||||||
\(909\) | 8.75560 | 0.290405 | ||||||||
\(910\) | −8.75560 | −0.290245 | ||||||||
\(911\) | −44.7477 | −1.48256 | −0.741279 | − | 0.671197i | \(-0.765781\pi\) | ||||
−0.741279 | + | 0.671197i | \(0.765781\pi\) | |||||||
\(912\) | −6.20520 | −0.205475 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −49.0780 | −1.62336 | ||||||||
\(915\) | 7.02355 | 0.232192 | ||||||||
\(916\) | 47.4519 | 1.56785 | ||||||||
\(917\) | 0.174243 | 0.00575401 | ||||||||
\(918\) | −3.79129 | −0.125131 | ||||||||
\(919\) | 27.9035 | 0.920452 | 0.460226 | − | 0.887802i | \(-0.347768\pi\) | ||||
0.460226 | + | 0.887802i | \(0.347768\pi\) | |||||||
\(920\) | −14.8655 | −0.490100 | ||||||||
\(921\) | 26.0761 | 0.859237 | ||||||||
\(922\) | 17.5826 | 0.579051 | ||||||||
\(923\) | 35.0224 | 1.15278 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58258 | −0.0520348 | ||||||||
\(926\) | −77.6960 | −2.55325 | ||||||||
\(927\) | −11.1652 | −0.366712 | ||||||||
\(928\) | −45.8258 | −1.50430 | ||||||||
\(929\) | −16.3303 | −0.535780 | −0.267890 | − | 0.963450i | \(-0.586326\pi\) | ||||
−0.267890 | + | 0.963450i | \(0.586326\pi\) | |||||||
\(930\) | −1.27520 | −0.0418155 | ||||||||
\(931\) | −21.3567 | −0.699938 | ||||||||
\(932\) | −49.1450 | −1.60980 | ||||||||
\(933\) | −2.41742 | −0.0791429 | ||||||||
\(934\) | −7.48040 | −0.244766 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.58258 | 0.247844 | ||||||||
\(937\) | 27.1805 | 0.887949 | 0.443974 | − | 0.896040i | \(-0.353568\pi\) | ||||
0.443974 | + | 0.896040i | \(0.353568\pi\) | |||||||
\(938\) | −27.1652 | −0.886974 | ||||||||
\(939\) | −3.58258 | −0.116913 | ||||||||
\(940\) | −35.1216 | −1.14554 | ||||||||
\(941\) | 3.99640 | 0.130279 | 0.0651395 | − | 0.997876i | \(-0.479251\pi\) | ||||
0.0651395 | + | 0.997876i | \(0.479251\pi\) | |||||||
\(942\) | −36.6591 | −1.19442 | ||||||||
\(943\) | −29.7309 | −0.968172 | ||||||||
\(944\) | −7.91288 | −0.257542 | ||||||||
\(945\) | −0.913701 | −0.0297227 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.9129 | 0.679577 | 0.339789 | − | 0.940502i | \(-0.389644\pi\) | ||||
0.339789 | + | 0.940502i | \(0.389644\pi\) | |||||||
\(948\) | −17.0544 | −0.553900 | ||||||||
\(949\) | −68.6606 | −2.22882 | ||||||||
\(950\) | 7.58258 | 0.246011 | ||||||||
\(951\) | 11.8348 | 0.383771 | ||||||||
\(952\) | −2.74110 | −0.0888396 | ||||||||
\(953\) | −20.7846 | −0.673280 | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | −13.4949 | −0.436914 | ||||||||
\(955\) | −4.74773 | −0.153633 | ||||||||
\(956\) | −75.3363 | −2.43655 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59.9129 | −1.93570 | ||||||||
\(959\) | 15.8347 | 0.511329 | ||||||||
\(960\) | 12.5826 | 0.406101 | ||||||||
\(961\) | −30.6606 | −0.989052 | ||||||||
\(962\) | −15.1652 | −0.488944 | ||||||||
\(963\) | 7.74655 | 0.249629 | ||||||||
\(964\) | 13.9717 | 0.449997 | ||||||||
\(965\) | 21.6983 | 0.698493 | ||||||||
\(966\) | 17.1652 | 0.552280 | ||||||||
\(967\) | 57.6344 | 1.85340 | 0.926699 | − | 0.375804i | \(-0.122633\pi\) | ||||
0.926699 | + | 0.375804i | \(0.122633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | −0.192748 | ||||||||
\(970\) | −29.7309 | −0.954602 | ||||||||
\(971\) | 16.4174 | 0.526860 | 0.263430 | − | 0.964678i | \(-0.415146\pi\) | ||||
0.263430 | + | 0.964678i | \(0.415146\pi\) | |||||||
\(972\) | 2.79129 | 0.0895306 | ||||||||
\(973\) | −11.9129 | −0.381909 | ||||||||
\(974\) | 7.84190 | 0.251271 | ||||||||
\(975\) | 4.37780 | 0.140202 | ||||||||
\(976\) | 12.5812 | 0.402715 | ||||||||
\(977\) | −6.16515 | −0.197241 | −0.0986203 | − | 0.995125i | \(-0.531443\pi\) | ||||
−0.0986203 | + | 0.995125i | \(0.531443\pi\) | |||||||
\(978\) | 14.7701 | 0.472296 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 17.2087 | 0.549712 | ||||||||
\(981\) | 6.92820 | 0.221201 | ||||||||
\(982\) | 60.6606 | 1.93576 | ||||||||
\(983\) | 30.5826 | 0.975433 | 0.487716 | − | 0.873002i | \(-0.337830\pi\) | ||||
0.487716 | + | 0.873002i | \(0.337830\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 19.3386 | 0.616179 | ||||||||
\(986\) | −23.5257 | −0.749211 | ||||||||
\(987\) | 11.4967 | 0.365944 | ||||||||
\(988\) | 42.3303 | 1.34671 | ||||||||
\(989\) | −53.2566 | −1.69346 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.2432 | 1.43720 | 0.718599 | − | 0.695425i | \(-0.244784\pi\) | ||||
0.718599 | + | 0.695425i | \(0.244784\pi\) | |||||||
\(992\) | −4.30235 | −0.136600 | ||||||||
\(993\) | 0.252273 | 0.00800564 | ||||||||
\(994\) | 16.0000 | 0.507489 | ||||||||
\(995\) | −11.7477 | −0.372428 | ||||||||
\(996\) | −44.3103 | −1.40403 | ||||||||
\(997\) | −37.9542 | −1.20202 | −0.601011 | − | 0.799241i | \(-0.705235\pi\) | ||||
−0.601011 | + | 0.799241i | \(0.705235\pi\) | |||||||
\(998\) | 57.6344 | 1.82439 | ||||||||
\(999\) | −1.58258 | −0.0500705 |
(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 | 1815.2.a.t.1.4 | yes | 4 | |
3.2 | odd | 2 | 5445.2.a.bl.1.1 | 4 | |||
5.4 | even | 2 | 9075.2.a.cu.1.1 | 4 | |||
11.10 | odd | 2 | inner | 1815.2.a.t.1.1 | ✓ | 4 | |
33.32 | even | 2 | 5445.2.a.bl.1.4 | 4 | |||
55.54 | odd | 2 | 9075.2.a.cu.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.t.1.1 | ✓ | 4 | 11.10 | odd | 2 | inner | |
1815.2.a.t.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
5445.2.a.bl.1.1 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bl.1.4 | 4 | 33.32 | even | 2 | |||
9075.2.a.cu.1.1 | 4 | 5.4 | even | 2 | |||
9075.2.a.cu.1.4 | 4 | 55.54 | odd | 2 |