Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, 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("975.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1821184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} + 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.329386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.329386 | −0.232911 | −0.116456 | − | 0.993196i | \(-0.537153\pi\) | ||||
−0.116456 | + | 0.993196i | \(0.537153\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.89150 | −0.945752 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.329386 | −0.134471 | ||||||||
\(7\) | 3.70203 | 1.39924 | 0.699618 | − | 0.714517i | \(-0.253354\pi\) | ||||
0.699618 | + | 0.714517i | \(0.253354\pi\) | |||||||
\(8\) | 1.28181 | 0.453187 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31322 | −0.998974 | −0.499487 | − | 0.866321i | \(-0.666478\pi\) | ||||
−0.499487 | + | 0.866321i | \(0.666478\pi\) | |||||||
\(12\) | −1.89150 | −0.546030 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.21940 | −0.325897 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.36080 | 0.840200 | ||||||||
\(17\) | −4.36080 | −1.05765 | −0.528825 | − | 0.848731i | \(-0.677367\pi\) | ||||
−0.528825 | + | 0.848731i | \(0.677367\pi\) | |||||||
\(18\) | −0.329386 | −0.0776370 | ||||||||
\(19\) | 5.21940 | 1.19741 | 0.598706 | − | 0.800969i | \(-0.295682\pi\) | ||||
0.598706 | + | 0.800969i | \(0.295682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.70203 | 0.807849 | ||||||||
\(22\) | 1.09133 | 0.232672 | ||||||||
\(23\) | 4.92143 | 1.02619 | 0.513094 | − | 0.858332i | \(-0.328499\pi\) | ||||
0.513094 | + | 0.858332i | \(0.328499\pi\) | |||||||
\(24\) | 1.28181 | 0.261648 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.329386 | −0.0645979 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −7.00241 | −1.32333 | ||||||||
\(29\) | 7.78301 | 1.44527 | 0.722634 | − | 0.691231i | \(-0.242931\pi\) | ||||
0.722634 | + | 0.691231i | \(0.242931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0981475 | 0.0176278 | 0.00881390 | − | 0.999961i | \(-0.497194\pi\) | ||||
0.00881390 | + | 0.999961i | \(0.497194\pi\) | |||||||
\(32\) | −3.67061 | −0.648879 | ||||||||
\(33\) | −3.31322 | −0.576758 | ||||||||
\(34\) | 1.43639 | 0.246338 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.89150 | −0.315251 | ||||||||
\(37\) | −2.92143 | −0.480279 | −0.240140 | − | 0.970738i | \(-0.577193\pi\) | ||||
−0.240140 | + | 0.970738i | \(0.577193\pi\) | |||||||
\(38\) | −1.71920 | −0.278890 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.749608 | −0.117069 | −0.0585345 | − | 0.998285i | \(-0.518643\pi\) | ||||
−0.0585345 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(42\) | −1.21940 | −0.188157 | ||||||||
\(43\) | −3.78301 | −0.576904 | −0.288452 | − | 0.957494i | \(-0.593141\pi\) | ||||
−0.288452 | + | 0.957494i | \(0.593141\pi\) | |||||||
\(44\) | 6.26698 | 0.944782 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.62105 | −0.239010 | ||||||||
\(47\) | 5.67402 | 0.827641 | 0.413821 | − | 0.910358i | \(-0.364194\pi\) | ||||
0.413821 | + | 0.910358i | \(0.364194\pi\) | |||||||
\(48\) | 3.36080 | 0.485090 | ||||||||
\(49\) | 6.70502 | 0.957860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.36080 | −0.610634 | ||||||||
\(52\) | −1.89150 | −0.262305 | ||||||||
\(53\) | −2.19982 | −0.302169 | −0.151085 | − | 0.988521i | \(-0.548277\pi\) | ||||
−0.151085 | + | 0.988521i | \(0.548277\pi\) | |||||||
\(54\) | −0.329386 | −0.0448237 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.74529 | 0.634116 | ||||||||
\(57\) | 5.21940 | 0.691326 | ||||||||
\(58\) | −2.56361 | −0.336619 | ||||||||
\(59\) | 0.108987 | 0.0141890 | 0.00709448 | − | 0.999975i | \(-0.497742\pi\) | ||||
0.00709448 | + | 0.999975i | \(0.497742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1438 | 1.55486 | 0.777428 | − | 0.628972i | \(-0.216524\pi\) | ||||
0.777428 | + | 0.628972i | \(0.216524\pi\) | |||||||
\(62\) | −0.0323284 | −0.00410571 | ||||||||
\(63\) | 3.70203 | 0.466412 | ||||||||
\(64\) | −5.51255 | −0.689069 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.09133 | 0.134333 | ||||||||
\(67\) | 12.4418 | 1.52001 | 0.760003 | − | 0.649920i | \(-0.225198\pi\) | ||||
0.760003 | + | 0.649920i | \(0.225198\pi\) | |||||||
\(68\) | 8.24848 | 1.00027 | ||||||||
\(69\) | 4.92143 | 0.592470 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0348 | 1.42827 | 0.714135 | − | 0.700008i | \(-0.246820\pi\) | ||||
0.714135 | + | 0.700008i | \(0.246820\pi\) | |||||||
\(72\) | 1.28181 | 0.151062 | ||||||||
\(73\) | 9.56602 | 1.11962 | 0.559809 | − | 0.828622i | \(-0.310875\pi\) | ||||
0.559809 | + | 0.828622i | \(0.310875\pi\) | |||||||
\(74\) | 0.962276 | 0.111862 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.87251 | −1.13245 | ||||||||
\(77\) | −12.2656 | −1.39780 | ||||||||
\(78\) | −0.329386 | −0.0372956 | ||||||||
\(79\) | 14.6093 | 1.64367 | 0.821836 | − | 0.569724i | \(-0.192950\pi\) | ||||
0.821836 | + | 0.569724i | \(0.192950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.246910 | 0.0272667 | ||||||||
\(83\) | −16.7001 | −1.83308 | −0.916538 | − | 0.399948i | \(-0.869028\pi\) | ||||
−0.916538 | + | 0.399948i | \(0.869028\pi\) | |||||||
\(84\) | −7.00241 | −0.764025 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.24607 | 0.134367 | ||||||||
\(87\) | 7.78301 | 0.834426 | ||||||||
\(88\) | −4.24691 | −0.452722 | ||||||||
\(89\) | −3.59403 | −0.380966 | −0.190483 | − | 0.981690i | \(-0.561005\pi\) | ||||
−0.190483 | + | 0.981690i | \(0.561005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.70203 | 0.388078 | ||||||||
\(92\) | −9.30890 | −0.970520 | ||||||||
\(93\) | 0.0981475 | 0.0101774 | ||||||||
\(94\) | −1.86894 | −0.192767 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.67061 | −0.374630 | ||||||||
\(97\) | −4.10467 | −0.416766 | −0.208383 | − | 0.978047i | \(-0.566820\pi\) | ||||
−0.208383 | + | 0.978047i | \(0.566820\pi\) | |||||||
\(98\) | −2.20854 | −0.223096 | ||||||||
\(99\) | −3.31322 | −0.332991 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.77761 | 0.276383 | 0.138191 | − | 0.990406i | \(-0.455871\pi\) | ||||
0.138191 | + | 0.990406i | \(0.455871\pi\) | |||||||
\(102\) | 1.43639 | 0.142223 | ||||||||
\(103\) | 16.5046 | 1.62625 | 0.813124 | − | 0.582091i | \(-0.197765\pi\) | ||||
0.813124 | + | 0.582091i | \(0.197765\pi\) | |||||||
\(104\) | 1.28181 | 0.125692 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.724591 | 0.0703785 | ||||||||
\(107\) | −1.04326 | −0.100855 | −0.0504277 | − | 0.998728i | \(-0.516058\pi\) | ||||
−0.0504277 | + | 0.998728i | \(0.516058\pi\) | |||||||
\(108\) | −1.89150 | −0.182010 | ||||||||
\(109\) | −11.0652 | −1.05986 | −0.529929 | − | 0.848042i | \(-0.677781\pi\) | ||||
−0.529929 | + | 0.848042i | \(0.677781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.92143 | −0.277289 | ||||||||
\(112\) | 12.4418 | 1.17564 | ||||||||
\(113\) | −15.9647 | −1.50183 | −0.750915 | − | 0.660398i | \(-0.770387\pi\) | ||||
−0.750915 | + | 0.660398i | \(0.770387\pi\) | |||||||
\(114\) | −1.71920 | −0.161017 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.7216 | −1.36687 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −0.0358989 | −0.00330476 | ||||||||
\(119\) | −16.1438 | −1.47990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0225619 | −0.00205108 | ||||||||
\(122\) | −4.00000 | −0.362143 | ||||||||
\(123\) | −0.749608 | −0.0675899 | ||||||||
\(124\) | −0.185646 | −0.0166715 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.21940 | −0.108632 | ||||||||
\(127\) | −18.9701 | −1.68332 | −0.841661 | − | 0.540006i | \(-0.818422\pi\) | ||||
−0.841661 | + | 0.540006i | \(0.818422\pi\) | |||||||
\(128\) | 9.15699 | 0.809371 | ||||||||
\(129\) | −3.78301 | −0.333075 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.539929 | −0.0471738 | −0.0235869 | − | 0.999722i | \(-0.507509\pi\) | ||||
−0.0235869 | + | 0.999722i | \(0.507509\pi\) | |||||||
\(132\) | 6.26698 | 0.545470 | ||||||||
\(133\) | 19.3224 | 1.67546 | ||||||||
\(134\) | −4.09815 | −0.354026 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.58970 | −0.479313 | ||||||||
\(137\) | −12.2376 | −1.04553 | −0.522766 | − | 0.852476i | \(-0.675100\pi\) | ||||
−0.522766 | + | 0.852476i | \(0.675100\pi\) | |||||||
\(138\) | −1.62105 | −0.137993 | ||||||||
\(139\) | −9.70502 | −0.823169 | −0.411584 | − | 0.911372i | \(-0.635024\pi\) | ||||
−0.411584 | + | 0.911372i | \(0.635024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.67402 | 0.477839 | ||||||||
\(142\) | −3.96410 | −0.332660 | ||||||||
\(143\) | −3.31322 | −0.277066 | ||||||||
\(144\) | 3.36080 | 0.280067 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.15091 | −0.260771 | ||||||||
\(147\) | 6.70502 | 0.553021 | ||||||||
\(148\) | 5.52589 | 0.454225 | ||||||||
\(149\) | 5.28954 | 0.433336 | 0.216668 | − | 0.976245i | \(-0.430481\pi\) | ||||
0.216668 | + | 0.976245i | \(0.430481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3858 | −1.33345 | −0.666727 | − | 0.745302i | \(-0.732305\pi\) | ||||
−0.666727 | + | 0.745302i | \(0.732305\pi\) | |||||||
\(152\) | 6.69026 | 0.542652 | ||||||||
\(153\) | −4.36080 | −0.352550 | ||||||||
\(154\) | 4.04013 | 0.325563 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.89150 | −0.151442 | ||||||||
\(157\) | 6.44477 | 0.514349 | 0.257174 | − | 0.966365i | \(-0.417209\pi\) | ||||
0.257174 | + | 0.966365i | \(0.417209\pi\) | |||||||
\(158\) | −4.81209 | −0.382829 | ||||||||
\(159\) | −2.19982 | −0.174457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2193 | 1.43588 | ||||||||
\(162\) | −0.329386 | −0.0258790 | ||||||||
\(163\) | −12.7673 | −1.00001 | −0.500005 | − | 0.866023i | \(-0.666668\pi\) | ||||
−0.500005 | + | 0.866023i | \(0.666668\pi\) | |||||||
\(164\) | 1.41789 | 0.110718 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.50078 | 0.426943 | ||||||||
\(167\) | −3.98716 | −0.308535 | −0.154268 | − | 0.988029i | \(-0.549302\pi\) | ||||
−0.154268 | + | 0.988029i | \(0.549302\pi\) | |||||||
\(168\) | 4.74529 | 0.366107 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.21940 | 0.399137 | ||||||||
\(172\) | 7.15558 | 0.545608 | ||||||||
\(173\) | −14.8836 | −1.13158 | −0.565788 | − | 0.824551i | \(-0.691428\pi\) | ||||
−0.565788 | + | 0.824551i | \(0.691428\pi\) | |||||||
\(174\) | −2.56361 | −0.194347 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.1351 | −0.839338 | ||||||||
\(177\) | 0.108987 | 0.00819199 | ||||||||
\(178\) | 1.18382 | 0.0887312 | ||||||||
\(179\) | 4.72160 | 0.352909 | 0.176455 | − | 0.984309i | \(-0.443537\pi\) | ||||
0.176455 | + | 0.984309i | \(0.443537\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4614 | −0.851916 | −0.425958 | − | 0.904743i | \(-0.640063\pi\) | ||||
−0.425958 | + | 0.904743i | \(0.640063\pi\) | |||||||
\(182\) | −1.21940 | −0.0903877 | ||||||||
\(183\) | 12.1438 | 0.897696 | ||||||||
\(184\) | 6.30832 | 0.465055 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0323284 | −0.00237043 | ||||||||
\(187\) | 14.4483 | 1.05656 | ||||||||
\(188\) | −10.7324 | −0.782744 | ||||||||
\(189\) | 3.70203 | 0.269283 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9994 | −1.23003 | −0.615017 | − | 0.788514i | \(-0.710851\pi\) | ||||
−0.615017 | + | 0.788514i | \(0.710851\pi\) | |||||||
\(192\) | −5.51255 | −0.397834 | ||||||||
\(193\) | 8.64459 | 0.622252 | 0.311126 | − | 0.950369i | \(-0.399294\pi\) | ||||
0.311126 | + | 0.950369i | \(0.399294\pi\) | |||||||
\(194\) | 1.35202 | 0.0970693 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.6826 | −0.905898 | ||||||||
\(197\) | 19.4540 | 1.38604 | 0.693022 | − | 0.720917i | \(-0.256279\pi\) | ||||
0.693022 | + | 0.720917i | \(0.256279\pi\) | |||||||
\(198\) | 1.09133 | 0.0775573 | ||||||||
\(199\) | −18.2218 | −1.29171 | −0.645855 | − | 0.763460i | \(-0.723499\pi\) | ||||
−0.645855 | + | 0.763460i | \(0.723499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4418 | 0.877576 | ||||||||
\(202\) | −0.914907 | −0.0643726 | ||||||||
\(203\) | 28.8129 | 2.02227 | ||||||||
\(204\) | 8.24848 | 0.577509 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.43639 | −0.378771 | ||||||||
\(207\) | 4.92143 | 0.342063 | ||||||||
\(208\) | 3.36080 | 0.233030 | ||||||||
\(209\) | −17.2930 | −1.19618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.41810 | 0.441840 | 0.220920 | − | 0.975292i | \(-0.429094\pi\) | ||||
0.220920 | + | 0.975292i | \(0.429094\pi\) | |||||||
\(212\) | 4.16098 | 0.285777 | ||||||||
\(213\) | 12.0348 | 0.824612 | ||||||||
\(214\) | 0.343634 | 0.0234903 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.28181 | 0.0872159 | ||||||||
\(217\) | 0.363345 | 0.0246654 | ||||||||
\(218\) | 3.64473 | 0.246852 | ||||||||
\(219\) | 9.56602 | 0.646412 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.36080 | −0.293339 | ||||||||
\(222\) | 0.962276 | 0.0645838 | ||||||||
\(223\) | −2.54292 | −0.170286 | −0.0851432 | − | 0.996369i | \(-0.527135\pi\) | ||||
−0.0851432 | + | 0.996369i | \(0.527135\pi\) | |||||||
\(224\) | −13.5887 | −0.907935 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.25854 | 0.349793 | ||||||||
\(227\) | −27.9311 | −1.85386 | −0.926928 | − | 0.375240i | \(-0.877560\pi\) | ||||
−0.926928 | + | 0.375240i | \(0.877560\pi\) | |||||||
\(228\) | −9.87251 | −0.653823 | ||||||||
\(229\) | 2.58730 | 0.170973 | 0.0854867 | − | 0.996339i | \(-0.472755\pi\) | ||||
0.0854867 | + | 0.996339i | \(0.472755\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2656 | −0.807020 | ||||||||
\(232\) | 9.97632 | 0.654977 | ||||||||
\(233\) | −23.2651 | −1.52414 | −0.762072 | − | 0.647492i | \(-0.775818\pi\) | ||||
−0.762072 | + | 0.647492i | \(0.775818\pi\) | |||||||
\(234\) | −0.329386 | −0.0215326 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.206150 | −0.0134192 | ||||||||
\(237\) | 14.6093 | 0.948975 | ||||||||
\(238\) | 5.31754 | 0.344685 | ||||||||
\(239\) | 15.6008 | 1.00913 | 0.504567 | − | 0.863372i | \(-0.331652\pi\) | ||||
0.504567 | + | 0.863372i | \(0.331652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8689 | 1.73078 | 0.865390 | − | 0.501098i | \(-0.167071\pi\) | ||||
0.865390 | + | 0.501098i | \(0.167071\pi\) | |||||||
\(242\) | 0.00743158 | 0.000477720 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −22.9701 | −1.47051 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.246910 | 0.0157424 | ||||||||
\(247\) | 5.21940 | 0.332102 | ||||||||
\(248\) | 0.125806 | 0.00798869 | ||||||||
\(249\) | −16.7001 | −1.05833 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.90426 | −0.183315 | −0.0916576 | − | 0.995791i | \(-0.529217\pi\) | ||||
−0.0916576 | + | 0.995791i | \(0.529217\pi\) | |||||||
\(252\) | −7.00241 | −0.441110 | ||||||||
\(253\) | −16.3058 | −1.02514 | ||||||||
\(254\) | 6.24848 | 0.392064 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.00892 | 0.500558 | ||||||||
\(257\) | −28.0048 | −1.74689 | −0.873446 | − | 0.486921i | \(-0.838120\pi\) | ||||
−0.873446 | + | 0.486921i | \(0.838120\pi\) | |||||||
\(258\) | 1.24607 | 0.0775769 | ||||||||
\(259\) | −10.8152 | −0.672024 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.78301 | 0.481756 | ||||||||
\(262\) | 0.177845 | 0.0109873 | ||||||||
\(263\) | 2.74828 | 0.169466 | 0.0847330 | − | 0.996404i | \(-0.472996\pi\) | ||||
0.0847330 | + | 0.996404i | \(0.472996\pi\) | |||||||
\(264\) | −4.24691 | −0.261379 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.36451 | −0.390233 | ||||||||
\(267\) | −3.59403 | −0.219951 | ||||||||
\(268\) | −23.5337 | −1.43755 | ||||||||
\(269\) | −27.1224 | −1.65368 | −0.826841 | − | 0.562435i | \(-0.809865\pi\) | ||||
−0.826841 | + | 0.562435i | \(0.809865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6555 | 1.19399 | 0.596994 | − | 0.802246i | \(-0.296362\pi\) | ||||
0.596994 | + | 0.802246i | \(0.296362\pi\) | |||||||
\(272\) | −14.6558 | −0.888637 | ||||||||
\(273\) | 3.70203 | 0.224057 | ||||||||
\(274\) | 4.03090 | 0.243516 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.30890 | −0.560330 | ||||||||
\(277\) | −15.1664 | −0.911259 | −0.455630 | − | 0.890170i | \(-0.650586\pi\) | ||||
−0.455630 | + | 0.890170i | \(0.650586\pi\) | |||||||
\(278\) | 3.19670 | 0.191725 | ||||||||
\(279\) | 0.0981475 | 0.00587593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.97552 | 0.237160 | 0.118580 | − | 0.992945i | \(-0.462166\pi\) | ||||
0.118580 | + | 0.992945i | \(0.462166\pi\) | |||||||
\(282\) | −1.86894 | −0.111294 | ||||||||
\(283\) | −0.768971 | −0.0457106 | −0.0228553 | − | 0.999739i | \(-0.507276\pi\) | ||||
−0.0228553 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(284\) | −22.7639 | −1.35079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.09133 | 0.0645316 | ||||||||
\(287\) | −2.77507 | −0.163807 | ||||||||
\(288\) | −3.67061 | −0.216293 | ||||||||
\(289\) | 2.01658 | 0.118623 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.10467 | −0.240620 | ||||||||
\(292\) | −18.0942 | −1.05888 | ||||||||
\(293\) | 7.85369 | 0.458817 | 0.229409 | − | 0.973330i | \(-0.426321\pi\) | ||||
0.229409 | + | 0.973330i | \(0.426321\pi\) | |||||||
\(294\) | −2.20854 | −0.128805 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.74470 | −0.217656 | ||||||||
\(297\) | −3.31322 | −0.192253 | ||||||||
\(298\) | −1.74230 | −0.100929 | ||||||||
\(299\) | 4.92143 | 0.284613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0048 | −0.807224 | ||||||||
\(302\) | 5.39724 | 0.310576 | ||||||||
\(303\) | 2.77761 | 0.159570 | ||||||||
\(304\) | 17.5414 | 1.00607 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.43639 | 0.0821127 | ||||||||
\(307\) | 0.893913 | 0.0510183 | 0.0255092 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255092 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(308\) | 23.2005 | 1.32197 | ||||||||
\(309\) | 16.5046 | 0.938915 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.4340 | 1.95257 | 0.976286 | − | 0.216486i | \(-0.0694594\pi\) | ||||
0.976286 | + | 0.216486i | \(0.0694594\pi\) | |||||||
\(312\) | 1.28181 | 0.0725680 | ||||||||
\(313\) | −20.6008 | −1.16442 | −0.582212 | − | 0.813037i | \(-0.697813\pi\) | ||||
−0.582212 | + | 0.813037i | \(0.697813\pi\) | |||||||
\(314\) | −2.12282 | −0.119797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.6335 | −1.55451 | ||||||||
\(317\) | 13.1772 | 0.740106 | 0.370053 | − | 0.929011i | \(-0.379340\pi\) | ||||
0.370053 | + | 0.929011i | \(0.379340\pi\) | |||||||
\(318\) | 0.724591 | 0.0406330 | ||||||||
\(319\) | −25.7868 | −1.44379 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.04326 | −0.0582289 | ||||||||
\(322\) | −6.00117 | −0.334432 | ||||||||
\(323\) | −22.7607 | −1.26644 | ||||||||
\(324\) | −1.89150 | −0.105084 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.20536 | 0.232913 | ||||||||
\(327\) | −11.0652 | −0.611909 | ||||||||
\(328\) | −0.960853 | −0.0530542 | ||||||||
\(329\) | 21.0054 | 1.15806 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.0536 | −1.04728 | −0.523640 | − | 0.851939i | \(-0.675426\pi\) | ||||
−0.523640 | + | 0.851939i | \(0.675426\pi\) | |||||||
\(332\) | 31.5883 | 1.73364 | ||||||||
\(333\) | −2.92143 | −0.160093 | ||||||||
\(334\) | 1.31331 | 0.0718613 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.4418 | 0.678755 | ||||||||
\(337\) | 11.6525 | 0.634754 | 0.317377 | − | 0.948299i | \(-0.397198\pi\) | ||||
0.317377 | + | 0.948299i | \(0.397198\pi\) | |||||||
\(338\) | −0.329386 | −0.0179162 | ||||||||
\(339\) | −15.9647 | −0.867083 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.325184 | −0.0176097 | ||||||||
\(342\) | −1.71920 | −0.0929634 | ||||||||
\(343\) | −1.09203 | −0.0589641 | ||||||||
\(344\) | −4.84909 | −0.261445 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.90244 | 0.263557 | ||||||||
\(347\) | −18.4680 | −0.991415 | −0.495707 | − | 0.868490i | \(-0.665091\pi\) | ||||
−0.495707 | + | 0.868490i | \(0.665091\pi\) | |||||||
\(348\) | −14.7216 | −0.789161 | ||||||||
\(349\) | 18.9309 | 1.01335 | 0.506675 | − | 0.862137i | \(-0.330874\pi\) | ||||
0.506675 | + | 0.862137i | \(0.330874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 12.1616 | 0.648213 | ||||||||
\(353\) | 21.9048 | 1.16587 | 0.582937 | − | 0.812517i | \(-0.301903\pi\) | ||||
0.582937 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(354\) | −0.0358989 | −0.00190801 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.79812 | 0.360300 | ||||||||
\(357\) | −16.1438 | −0.854421 | ||||||||
\(358\) | −1.55523 | −0.0821964 | ||||||||
\(359\) | 23.5630 | 1.24361 | 0.621803 | − | 0.783173i | \(-0.286400\pi\) | ||||
0.621803 | + | 0.783173i | \(0.286400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.24210 | 0.433795 | ||||||||
\(362\) | 3.77521 | 0.198421 | ||||||||
\(363\) | −0.0225619 | −0.00118419 | ||||||||
\(364\) | −7.00241 | −0.367026 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.00000 | −0.209083 | ||||||||
\(367\) | 19.9450 | 1.04112 | 0.520560 | − | 0.853825i | \(-0.325723\pi\) | ||||
0.520560 | + | 0.853825i | \(0.325723\pi\) | |||||||
\(368\) | 16.5399 | 0.862203 | ||||||||
\(369\) | −0.749608 | −0.0390230 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.14381 | −0.422806 | ||||||||
\(372\) | −0.185646 | −0.00962532 | ||||||||
\(373\) | 4.48616 | 0.232285 | 0.116142 | − | 0.993233i | \(-0.462947\pi\) | ||||
0.116142 | + | 0.993233i | \(0.462947\pi\) | |||||||
\(374\) | −4.75907 | −0.246085 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.27300 | 0.375076 | ||||||||
\(377\) | 7.78301 | 0.400845 | ||||||||
\(378\) | −1.21940 | −0.0627190 | ||||||||
\(379\) | 4.65976 | 0.239356 | 0.119678 | − | 0.992813i | \(-0.461814\pi\) | ||||
0.119678 | + | 0.992813i | \(0.461814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.9701 | −0.971867 | ||||||||
\(382\) | 5.59937 | 0.286489 | ||||||||
\(383\) | 4.70011 | 0.240165 | 0.120082 | − | 0.992764i | \(-0.461684\pi\) | ||||
0.120082 | + | 0.992764i | \(0.461684\pi\) | |||||||
\(384\) | 9.15699 | 0.467290 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.84741 | −0.144929 | ||||||||
\(387\) | −3.78301 | −0.192301 | ||||||||
\(388\) | 7.76400 | 0.394157 | ||||||||
\(389\) | 14.6128 | 0.740899 | 0.370449 | − | 0.928853i | \(-0.379204\pi\) | ||||
0.370449 | + | 0.928853i | \(0.379204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4614 | −1.08535 | ||||||||
\(392\) | 8.59454 | 0.434090 | ||||||||
\(393\) | −0.539929 | −0.0272358 | ||||||||
\(394\) | −6.40789 | −0.322825 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.26698 | 0.314927 | ||||||||
\(397\) | −22.2911 | −1.11876 | −0.559380 | − | 0.828911i | \(-0.688961\pi\) | ||||
−0.559380 | + | 0.828911i | \(0.688961\pi\) | |||||||
\(398\) | 6.00200 | 0.300853 | ||||||||
\(399\) | 19.3224 | 0.967328 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.61021 | 0.180285 | 0.0901426 | − | 0.995929i | \(-0.471268\pi\) | ||||
0.0901426 | + | 0.995929i | \(0.471268\pi\) | |||||||
\(402\) | −4.09815 | −0.204397 | ||||||||
\(403\) | 0.0981475 | 0.00488907 | ||||||||
\(404\) | −5.25387 | −0.261390 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.49057 | −0.471009 | ||||||||
\(407\) | 9.67933 | 0.479787 | ||||||||
\(408\) | −5.58970 | −0.276732 | ||||||||
\(409\) | 12.6911 | 0.627535 | 0.313767 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313767 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.2376 | −0.603638 | ||||||||
\(412\) | −31.2186 | −1.53803 | ||||||||
\(413\) | 0.403475 | 0.0198537 | ||||||||
\(414\) | −1.62105 | −0.0796702 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.67061 | −0.179967 | ||||||||
\(417\) | −9.70502 | −0.475257 | ||||||||
\(418\) | 5.69608 | 0.278604 | ||||||||
\(419\) | 2.66078 | 0.129987 | 0.0649937 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649937 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0305 | −0.976227 | −0.488113 | − | 0.872780i | \(-0.662315\pi\) | ||||
−0.488113 | + | 0.872780i | \(0.662315\pi\) | |||||||
\(422\) | −2.11403 | −0.102909 | ||||||||
\(423\) | 5.67402 | 0.275880 | ||||||||
\(424\) | −2.81975 | −0.136939 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.96410 | −0.192061 | ||||||||
\(427\) | 44.9567 | 2.17561 | ||||||||
\(428\) | 1.97333 | 0.0953843 | ||||||||
\(429\) | −3.31322 | −0.159964 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.79742 | −0.134747 | −0.0673736 | − | 0.997728i | \(-0.521462\pi\) | ||||
−0.0673736 | + | 0.997728i | \(0.521462\pi\) | |||||||
\(432\) | 3.36080 | 0.161697 | ||||||||
\(433\) | 9.56602 | 0.459714 | 0.229857 | − | 0.973224i | \(-0.426174\pi\) | ||||
0.229857 | + | 0.973224i | \(0.426174\pi\) | |||||||
\(434\) | −0.119681 | −0.00574485 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.9299 | 1.00236 | ||||||||
\(437\) | 25.6869 | 1.22877 | ||||||||
\(438\) | −3.15091 | −0.150556 | ||||||||
\(439\) | −7.45654 | −0.355881 | −0.177941 | − | 0.984041i | \(-0.556944\pi\) | ||||
−0.177941 | + | 0.984041i | \(0.556944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.70502 | 0.319287 | ||||||||
\(442\) | 1.43639 | 0.0683219 | ||||||||
\(443\) | −7.92201 | −0.376386 | −0.188193 | − | 0.982132i | \(-0.560263\pi\) | ||||
−0.188193 | + | 0.982132i | \(0.560263\pi\) | |||||||
\(444\) | 5.52589 | 0.262247 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.837602 | 0.0396616 | ||||||||
\(447\) | 5.28954 | 0.250187 | ||||||||
\(448\) | −20.4076 | −0.964170 | ||||||||
\(449\) | 38.7241 | 1.82750 | 0.913752 | − | 0.406273i | \(-0.133172\pi\) | ||||
0.913752 | + | 0.406273i | \(0.133172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.48362 | 0.116949 | ||||||||
\(452\) | 30.1973 | 1.42036 | ||||||||
\(453\) | −16.3858 | −0.769871 | ||||||||
\(454\) | 9.20012 | 0.431783 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.69026 | 0.313300 | ||||||||
\(457\) | 12.8322 | 0.600267 | 0.300134 | − | 0.953897i | \(-0.402969\pi\) | ||||
0.300134 | + | 0.953897i | \(0.402969\pi\) | |||||||
\(458\) | −0.852220 | −0.0398216 | ||||||||
\(459\) | −4.36080 | −0.203545 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1178 | −1.44930 | −0.724649 | − | 0.689118i | \(-0.757998\pi\) | ||||
−0.724649 | + | 0.689118i | \(0.757998\pi\) | |||||||
\(462\) | 4.04013 | 0.187964 | ||||||||
\(463\) | 10.2588 | 0.476768 | 0.238384 | − | 0.971171i | \(-0.423382\pi\) | ||||
0.238384 | + | 0.971171i | \(0.423382\pi\) | |||||||
\(464\) | 26.1571 | 1.21431 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.66318 | 0.354990 | ||||||||
\(467\) | −12.3315 | −0.570632 | −0.285316 | − | 0.958434i | \(-0.592099\pi\) | ||||
−0.285316 | + | 0.958434i | \(0.592099\pi\) | |||||||
\(468\) | −1.89150 | −0.0874348 | ||||||||
\(469\) | 46.0598 | 2.12685 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.44477 | 0.296959 | ||||||||
\(472\) | 0.139701 | 0.00643025 | ||||||||
\(473\) | 12.5340 | 0.576312 | ||||||||
\(474\) | −4.81209 | −0.221027 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 30.5361 | 1.39962 | ||||||||
\(477\) | −2.19982 | −0.100723 | ||||||||
\(478\) | −5.13870 | −0.235039 | ||||||||
\(479\) | −8.21141 | −0.375189 | −0.187594 | − | 0.982247i | \(-0.560069\pi\) | ||||
−0.187594 | + | 0.982247i | \(0.560069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.92143 | −0.133206 | ||||||||
\(482\) | −8.85025 | −0.403118 | ||||||||
\(483\) | 18.2193 | 0.829005 | ||||||||
\(484\) | 0.0426760 | 0.00193982 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.329386 | −0.0149412 | ||||||||
\(487\) | −23.4860 | −1.06425 | −0.532127 | − | 0.846665i | \(-0.678607\pi\) | ||||
−0.532127 | + | 0.846665i | \(0.678607\pi\) | |||||||
\(488\) | 15.5660 | 0.704641 | ||||||||
\(489\) | −12.7673 | −0.577356 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.21739 | 0.0549401 | 0.0274701 | − | 0.999623i | \(-0.491255\pi\) | ||||
0.0274701 | + | 0.999623i | \(0.491255\pi\) | |||||||
\(492\) | 1.41789 | 0.0639233 | ||||||||
\(493\) | −33.9402 | −1.52859 | ||||||||
\(494\) | −1.71920 | −0.0773503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.329854 | 0.0148109 | ||||||||
\(497\) | 44.5533 | 1.99849 | ||||||||
\(498\) | 5.50078 | 0.246496 | ||||||||
\(499\) | −1.60334 | −0.0717755 | −0.0358877 | − | 0.999356i | \(-0.511426\pi\) | ||||
−0.0358877 | + | 0.999356i | \(0.511426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.98716 | −0.178133 | ||||||||
\(502\) | 0.956622 | 0.0426961 | ||||||||
\(503\) | −27.4355 | −1.22329 | −0.611645 | − | 0.791132i | \(-0.709492\pi\) | ||||
−0.611645 | + | 0.791132i | \(0.709492\pi\) | |||||||
\(504\) | 4.74529 | 0.211372 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.37089 | 0.238765 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 35.8820 | 1.59201 | ||||||||
\(509\) | 11.4124 | 0.505844 | 0.252922 | − | 0.967487i | \(-0.418608\pi\) | ||||
0.252922 | + | 0.967487i | \(0.418608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.4137 | 1.56661 | ||||||||
\(512\) | −20.9520 | −0.925956 | ||||||||
\(513\) | 5.21940 | 0.230442 | ||||||||
\(514\) | 9.22439 | 0.406870 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.15558 | 0.315007 | ||||||||
\(517\) | −18.7993 | −0.826792 | ||||||||
\(518\) | 3.56237 | 0.156522 | ||||||||
\(519\) | −14.8836 | −0.653316 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.6274 | 1.34181 | 0.670906 | − | 0.741542i | \(-0.265905\pi\) | ||||
0.670906 | + | 0.741542i | \(0.265905\pi\) | |||||||
\(522\) | −2.56361 | −0.112206 | ||||||||
\(523\) | −24.9956 | −1.09298 | −0.546490 | − | 0.837465i | \(-0.684036\pi\) | ||||
−0.546490 | + | 0.837465i | \(0.684036\pi\) | |||||||
\(524\) | 1.02128 | 0.0446148 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.905243 | −0.0394705 | ||||||||
\(527\) | −0.428002 | −0.0186440 | ||||||||
\(528\) | −11.1351 | −0.484592 | ||||||||
\(529\) | 1.22042 | 0.0530620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.108987 | 0.00472965 | ||||||||
\(532\) | −36.5483 | −1.58457 | ||||||||
\(533\) | −0.749608 | −0.0324691 | ||||||||
\(534\) | 1.18382 | 0.0512290 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.9480 | 0.688847 | ||||||||
\(537\) | 4.72160 | 0.203752 | ||||||||
\(538\) | 8.93374 | 0.385161 | ||||||||
\(539\) | −22.2152 | −0.956877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.131461 | −0.00565193 | −0.00282596 | − | 0.999996i | \(-0.500900\pi\) | ||||
−0.00282596 | + | 0.999996i | \(0.500900\pi\) | |||||||
\(542\) | −6.47425 | −0.278093 | ||||||||
\(543\) | −11.4614 | −0.491854 | ||||||||
\(544\) | 16.0068 | 0.686287 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.21940 | −0.0521853 | ||||||||
\(547\) | −21.5955 | −0.923358 | −0.461679 | − | 0.887047i | \(-0.652753\pi\) | ||||
−0.461679 | + | 0.887047i | \(0.652753\pi\) | |||||||
\(548\) | 23.1475 | 0.988814 | ||||||||
\(549\) | 12.1438 | 0.518285 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.6226 | 1.73058 | ||||||||
\(552\) | 6.30832 | 0.268500 | ||||||||
\(553\) | 54.0840 | 2.29988 | ||||||||
\(554\) | 4.99559 | 0.212242 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.3571 | 0.778514 | ||||||||
\(557\) | 40.1776 | 1.70238 | 0.851190 | − | 0.524858i | \(-0.175881\pi\) | ||||
0.851190 | + | 0.524858i | \(0.175881\pi\) | |||||||
\(558\) | −0.0323284 | −0.00136857 | ||||||||
\(559\) | −3.78301 | −0.160004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4483 | 0.610008 | ||||||||
\(562\) | −1.30948 | −0.0552371 | ||||||||
\(563\) | −3.57240 | −0.150559 | −0.0752793 | − | 0.997162i | \(-0.523985\pi\) | ||||
−0.0752793 | + | 0.997162i | \(0.523985\pi\) | |||||||
\(564\) | −10.7324 | −0.451917 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.253288 | 0.0106465 | ||||||||
\(567\) | 3.70203 | 0.155471 | ||||||||
\(568\) | 15.4263 | 0.647274 | ||||||||
\(569\) | 0.744448 | 0.0312089 | 0.0156044 | − | 0.999878i | \(-0.495033\pi\) | ||||
0.0156044 | + | 0.999878i | \(0.495033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4234 | 0.729145 | 0.364573 | − | 0.931175i | \(-0.381215\pi\) | ||||
0.364573 | + | 0.931175i | \(0.381215\pi\) | |||||||
\(572\) | 6.26698 | 0.262035 | ||||||||
\(573\) | −16.9994 | −0.710161 | ||||||||
\(574\) | 0.914069 | 0.0381525 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.51255 | −0.229690 | ||||||||
\(577\) | −40.6582 | −1.69262 | −0.846312 | − | 0.532687i | \(-0.821182\pi\) | ||||
−0.846312 | + | 0.532687i | \(0.821182\pi\) | |||||||
\(578\) | −0.664234 | −0.0276285 | ||||||||
\(579\) | 8.64459 | 0.359257 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −61.8243 | −2.56490 | ||||||||
\(582\) | 1.35202 | 0.0560430 | ||||||||
\(583\) | 7.28850 | 0.301859 | ||||||||
\(584\) | 12.2618 | 0.507396 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.58689 | −0.106864 | ||||||||
\(587\) | −5.24004 | −0.216280 | −0.108140 | − | 0.994136i | \(-0.534489\pi\) | ||||
−0.108140 | + | 0.994136i | \(0.534489\pi\) | |||||||
\(588\) | −12.6826 | −0.523021 | ||||||||
\(589\) | 0.512270 | 0.0211077 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.4540 | 0.800232 | ||||||||
\(592\) | −9.81833 | −0.403531 | ||||||||
\(593\) | −4.71557 | −0.193645 | −0.0968227 | − | 0.995302i | \(-0.530868\pi\) | ||||
−0.0968227 | + | 0.995302i | \(0.530868\pi\) | |||||||
\(594\) | 1.09133 | 0.0447778 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0052 | −0.409828 | ||||||||
\(597\) | −18.2218 | −0.745769 | ||||||||
\(598\) | −1.62105 | −0.0662896 | ||||||||
\(599\) | −17.6268 | −0.720213 | −0.360107 | − | 0.932911i | \(-0.617260\pi\) | ||||
−0.360107 | + | 0.932911i | \(0.617260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.38747 | −0.178969 | −0.0894844 | − | 0.995988i | \(-0.528522\pi\) | ||||
−0.0894844 | + | 0.995988i | \(0.528522\pi\) | |||||||
\(602\) | 4.61299 | 0.188011 | ||||||||
\(603\) | 12.4418 | 0.506669 | ||||||||
\(604\) | 30.9938 | 1.26112 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.914907 | −0.0371656 | ||||||||
\(607\) | −25.4225 | −1.03187 | −0.515934 | − | 0.856628i | \(-0.672555\pi\) | ||||
−0.515934 | + | 0.856628i | \(0.672555\pi\) | |||||||
\(608\) | −19.1584 | −0.776975 | ||||||||
\(609\) | 28.8129 | 1.16756 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.67402 | 0.229546 | ||||||||
\(612\) | 8.24848 | 0.333425 | ||||||||
\(613\) | 15.8464 | 0.640029 | 0.320015 | − | 0.947413i | \(-0.396312\pi\) | ||||
0.320015 | + | 0.947413i | \(0.396312\pi\) | |||||||
\(614\) | −0.294442 | −0.0118827 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.7222 | −0.633465 | ||||||||
\(617\) | 9.43461 | 0.379823 | 0.189912 | − | 0.981801i | \(-0.439180\pi\) | ||||
0.189912 | + | 0.981801i | \(0.439180\pi\) | |||||||
\(618\) | −5.43639 | −0.218684 | ||||||||
\(619\) | −19.0899 | −0.767288 | −0.383644 | − | 0.923481i | \(-0.625331\pi\) | ||||
−0.383644 | + | 0.923481i | \(0.625331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.92143 | 0.197490 | ||||||||
\(622\) | −11.3421 | −0.454775 | ||||||||
\(623\) | −13.3052 | −0.533061 | ||||||||
\(624\) | 3.36080 | 0.134540 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.78560 | 0.271207 | ||||||||
\(627\) | −17.2930 | −0.690617 | ||||||||
\(628\) | −12.1903 | −0.486447 | ||||||||
\(629\) | 12.7398 | 0.507967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.58431 | −0.262117 | −0.131059 | − | 0.991375i | \(-0.541838\pi\) | ||||
−0.131059 | + | 0.991375i | \(0.541838\pi\) | |||||||
\(632\) | 18.7263 | 0.744891 | ||||||||
\(633\) | 6.41810 | 0.255096 | ||||||||
\(634\) | −4.34039 | −0.172379 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.16098 | 0.164993 | ||||||||
\(637\) | 6.70502 | 0.265662 | ||||||||
\(638\) | 8.49382 | 0.336274 | ||||||||
\(639\) | 12.0348 | 0.476090 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5606 | 0.812096 | 0.406048 | − | 0.913852i | \(-0.366907\pi\) | ||||
0.406048 | + | 0.913852i | \(0.366907\pi\) | |||||||
\(642\) | 0.343634 | 0.0135622 | ||||||||
\(643\) | 14.7084 | 0.580043 | 0.290022 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290022 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(644\) | −34.4618 | −1.35799 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.49707 | 0.294968 | ||||||||
\(647\) | −30.1145 | −1.18392 | −0.591961 | − | 0.805967i | \(-0.701646\pi\) | ||||
−0.591961 | + | 0.805967i | \(0.701646\pi\) | |||||||
\(648\) | 1.28181 | 0.0503541 | ||||||||
\(649\) | −0.361099 | −0.0141744 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.363345 | 0.0142406 | ||||||||
\(652\) | 24.1493 | 0.945761 | ||||||||
\(653\) | −23.8527 | −0.933427 | −0.466713 | − | 0.884409i | \(-0.654562\pi\) | ||||
−0.466713 | + | 0.884409i | \(0.654562\pi\) | |||||||
\(654\) | 3.64473 | 0.142520 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.51928 | −0.0983615 | ||||||||
\(657\) | 9.56602 | 0.373206 | ||||||||
\(658\) | −6.91888 | −0.269726 | ||||||||
\(659\) | −26.4789 | −1.03147 | −0.515736 | − | 0.856747i | \(-0.672482\pi\) | ||||
−0.515736 | + | 0.856747i | \(0.672482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7579 | 0.574016 | 0.287008 | − | 0.957928i | \(-0.407339\pi\) | ||||
0.287008 | + | 0.957928i | \(0.407339\pi\) | |||||||
\(662\) | 6.27599 | 0.243923 | ||||||||
\(663\) | −4.36080 | −0.169359 | ||||||||
\(664\) | −21.4063 | −0.830726 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.962276 | 0.0372874 | ||||||||
\(667\) | 38.3035 | 1.48312 | ||||||||
\(668\) | 7.54172 | 0.291798 | ||||||||
\(669\) | −2.54292 | −0.0983149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.2351 | −1.55326 | ||||||||
\(672\) | −13.5887 | −0.524196 | ||||||||
\(673\) | −11.2784 | −0.434750 | −0.217375 | − | 0.976088i | \(-0.569749\pi\) | ||||
−0.217375 | + | 0.976088i | \(0.569749\pi\) | |||||||
\(674\) | −3.83818 | −0.147841 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.89150 | −0.0727502 | ||||||||
\(677\) | 29.1052 | 1.11861 | 0.559303 | − | 0.828963i | \(-0.311069\pi\) | ||||
0.559303 | + | 0.828963i | \(0.311069\pi\) | |||||||
\(678\) | 5.25854 | 0.201953 | ||||||||
\(679\) | −15.1956 | −0.583153 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.9311 | −1.07032 | ||||||||
\(682\) | 0.107111 | 0.00410150 | ||||||||
\(683\) | 1.84463 | 0.0705827 | 0.0352914 | − | 0.999377i | \(-0.488764\pi\) | ||||
0.0352914 | + | 0.999377i | \(0.488764\pi\) | |||||||
\(684\) | −9.87251 | −0.377485 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.359700 | 0.0137334 | ||||||||
\(687\) | 2.58730 | 0.0987116 | ||||||||
\(688\) | −12.7139 | −0.484715 | ||||||||
\(689\) | −2.19982 | −0.0838066 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.4103 | −1.15686 | −0.578431 | − | 0.815731i | \(-0.696335\pi\) | ||||
−0.578431 | + | 0.815731i | \(0.696335\pi\) | |||||||
\(692\) | 28.1523 | 1.07019 | ||||||||
\(693\) | −12.2656 | −0.465933 | ||||||||
\(694\) | 6.08310 | 0.230911 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.97632 | 0.378151 | ||||||||
\(697\) | 3.26889 | 0.123818 | ||||||||
\(698\) | −6.23558 | −0.236020 | ||||||||
\(699\) | −23.2651 | −0.879965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.8119 | −1.84360 | −0.921801 | − | 0.387664i | \(-0.873282\pi\) | ||||
−0.921801 | + | 0.387664i | \(0.873282\pi\) | |||||||
\(702\) | −0.329386 | −0.0124319 | ||||||||
\(703\) | −15.2481 | −0.575092 | ||||||||
\(704\) | 18.2643 | 0.688362 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.21513 | −0.271545 | ||||||||
\(707\) | 10.2828 | 0.386725 | ||||||||
\(708\) | −0.206150 | −0.00774760 | ||||||||
\(709\) | 6.74926 | 0.253474 | 0.126737 | − | 0.991936i | \(-0.459550\pi\) | ||||
0.126737 | + | 0.991936i | \(0.459550\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6093 | 0.547891 | ||||||||
\(712\) | −4.60685 | −0.172649 | ||||||||
\(713\) | 0.483025 | 0.0180894 | ||||||||
\(714\) | 5.31754 | 0.199004 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.93093 | −0.333765 | ||||||||
\(717\) | 15.6008 | 0.582624 | ||||||||
\(718\) | −7.76131 | −0.289650 | ||||||||
\(719\) | 0.286459 | 0.0106831 | 0.00534156 | − | 0.999986i | \(-0.498300\pi\) | ||||
0.00534156 | + | 0.999986i | \(0.498300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.1005 | 2.27550 | ||||||||
\(722\) | −2.71483 | −0.101036 | ||||||||
\(723\) | 26.8689 | 0.999267 | ||||||||
\(724\) | 21.6792 | 0.805701 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.00743158 | 0.000275812 0 | ||||||||
\(727\) | −15.1967 | −0.563614 | −0.281807 | − | 0.959471i | \(-0.590934\pi\) | ||||
−0.281807 | + | 0.959471i | \(0.590934\pi\) | |||||||
\(728\) | 4.74529 | 0.175872 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4970 | 0.610162 | ||||||||
\(732\) | −22.9701 | −0.848998 | ||||||||
\(733\) | −8.90456 | −0.328897 | −0.164449 | − | 0.986386i | \(-0.552584\pi\) | ||||
−0.164449 | + | 0.986386i | \(0.552584\pi\) | |||||||
\(734\) | −6.56959 | −0.242488 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.0647 | −0.665872 | ||||||||
\(737\) | −41.2224 | −1.51845 | ||||||||
\(738\) | 0.246910 | 0.00908889 | ||||||||
\(739\) | −31.4422 | −1.15662 | −0.578310 | − | 0.815817i | \(-0.696287\pi\) | ||||
−0.578310 | + | 0.815817i | \(0.696287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.21940 | 0.191739 | ||||||||
\(742\) | 2.68246 | 0.0984761 | ||||||||
\(743\) | 41.3314 | 1.51630 | 0.758150 | − | 0.652080i | \(-0.226103\pi\) | ||||
0.758150 | + | 0.652080i | \(0.226103\pi\) | |||||||
\(744\) | 0.125806 | 0.00461228 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.47768 | −0.0541016 | ||||||||
\(747\) | −16.7001 | −0.611025 | ||||||||
\(748\) | −27.3290 | −0.999248 | ||||||||
\(749\) | −3.86217 | −0.141121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.8813 | −1.85668 | −0.928342 | − | 0.371726i | \(-0.878766\pi\) | ||||
−0.928342 | + | 0.371726i | \(0.878766\pi\) | |||||||
\(752\) | 19.0693 | 0.695384 | ||||||||
\(753\) | −2.90426 | −0.105837 | ||||||||
\(754\) | −2.56361 | −0.0933613 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.00241 | −0.254675 | ||||||||
\(757\) | 45.8173 | 1.66526 | 0.832630 | − | 0.553830i | \(-0.186834\pi\) | ||||
0.832630 | + | 0.553830i | \(0.186834\pi\) | |||||||
\(758\) | −1.53486 | −0.0557486 | ||||||||
\(759\) | −16.3058 | −0.591862 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.9129 | −0.395591 | −0.197795 | − | 0.980243i | \(-0.563378\pi\) | ||||
−0.197795 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(762\) | 6.24848 | 0.226358 | ||||||||
\(763\) | −40.9638 | −1.48299 | ||||||||
\(764\) | 32.1545 | 1.16331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.54815 | −0.0559370 | ||||||||
\(767\) | 0.108987 | 0.00393531 | ||||||||
\(768\) | 8.00892 | 0.288997 | ||||||||
\(769\) | 28.9338 | 1.04338 | 0.521689 | − | 0.853136i | \(-0.325302\pi\) | ||||
0.521689 | + | 0.853136i | \(0.325302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.0048 | −1.00857 | ||||||||
\(772\) | −16.3513 | −0.588496 | ||||||||
\(773\) | 6.42314 | 0.231024 | 0.115512 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115512 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(774\) | 1.24607 | 0.0447891 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.26139 | −0.188873 | ||||||||
\(777\) | −10.8152 | −0.387993 | ||||||||
\(778\) | −4.81325 | −0.172563 | ||||||||
\(779\) | −3.91250 | −0.140180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.8740 | −1.42681 | ||||||||
\(782\) | 7.06907 | 0.252789 | ||||||||
\(783\) | 7.78301 | 0.278142 | ||||||||
\(784\) | 22.5342 | 0.804794 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.177845 | 0.00634352 | ||||||||
\(787\) | 34.8040 | 1.24063 | 0.620314 | − | 0.784354i | \(-0.287005\pi\) | ||||
0.620314 | + | 0.784354i | \(0.287005\pi\) | |||||||
\(788\) | −36.7974 | −1.31085 | ||||||||
\(789\) | 2.74828 | 0.0978412 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.1017 | −2.10142 | ||||||||
\(792\) | −4.24691 | −0.150907 | ||||||||
\(793\) | 12.1438 | 0.431239 | ||||||||
\(794\) | 7.34239 | 0.260572 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.4666 | 1.22164 | ||||||||
\(797\) | 1.30902 | 0.0463679 | 0.0231839 | − | 0.999731i | \(-0.492620\pi\) | ||||
0.0231839 | + | 0.999731i | \(0.492620\pi\) | |||||||
\(798\) | −6.36451 | −0.225301 | ||||||||
\(799\) | −24.7433 | −0.875354 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.59403 | −0.126989 | ||||||||
\(802\) | −1.18915 | −0.0419904 | ||||||||
\(803\) | −31.6943 | −1.11847 | ||||||||
\(804\) | −23.5337 | −0.829969 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0323284 | −0.00113872 | ||||||||
\(807\) | −27.1224 | −0.954754 | ||||||||
\(808\) | 3.56037 | 0.125253 | ||||||||
\(809\) | 17.2262 | 0.605641 | 0.302821 | − | 0.953048i | \(-0.402072\pi\) | ||||
0.302821 | + | 0.953048i | \(0.402072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.97289 | −0.244851 | −0.122426 | − | 0.992478i | \(-0.539067\pi\) | ||||
−0.122426 | + | 0.992478i | \(0.539067\pi\) | |||||||
\(812\) | −54.4998 | −1.91257 | ||||||||
\(813\) | 19.6555 | 0.689349 | ||||||||
\(814\) | −3.18823 | −0.111748 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.6558 | −0.513055 | ||||||||
\(817\) | −19.7450 | −0.690791 | ||||||||
\(818\) | −4.18027 | −0.146160 | ||||||||
\(819\) | 3.70203 | 0.129359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4054 | 1.23566 | 0.617828 | − | 0.786313i | \(-0.288013\pi\) | ||||
0.617828 | + | 0.786313i | \(0.288013\pi\) | |||||||
\(822\) | 4.03090 | 0.140594 | ||||||||
\(823\) | 33.3942 | 1.16405 | 0.582024 | − | 0.813172i | \(-0.302261\pi\) | ||||
0.582024 | + | 0.813172i | \(0.302261\pi\) | |||||||
\(824\) | 21.1557 | 0.736995 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.132899 | −0.00462414 | ||||||||
\(827\) | −17.9643 | −0.624680 | −0.312340 | − | 0.949970i | \(-0.601113\pi\) | ||||
−0.312340 | + | 0.949970i | \(0.601113\pi\) | |||||||
\(828\) | −9.30890 | −0.323507 | ||||||||
\(829\) | 33.6052 | 1.16716 | 0.583578 | − | 0.812057i | \(-0.301652\pi\) | ||||
0.583578 | + | 0.812057i | \(0.301652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.1664 | −0.526116 | ||||||||
\(832\) | −5.51255 | −0.191113 | ||||||||
\(833\) | −29.2392 | −1.01308 | ||||||||
\(834\) | 3.19670 | 0.110693 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.7098 | 1.13129 | ||||||||
\(837\) | 0.0981475 | 0.00339247 | ||||||||
\(838\) | −0.876422 | −0.0302755 | ||||||||
\(839\) | −47.1755 | −1.62868 | −0.814340 | − | 0.580389i | \(-0.802901\pi\) | ||||
−0.814340 | + | 0.580389i | \(0.802901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.5752 | 1.08880 | ||||||||
\(842\) | 6.59776 | 0.227374 | ||||||||
\(843\) | 3.97552 | 0.136924 | ||||||||
\(844\) | −12.1399 | −0.417871 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.86894 | −0.0642556 | ||||||||
\(847\) | −0.0835249 | −0.00286995 | ||||||||
\(848\) | −7.39317 | −0.253882 | ||||||||
\(849\) | −0.768971 | −0.0263910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.3776 | −0.492857 | ||||||||
\(852\) | −22.7639 | −0.779879 | ||||||||
\(853\) | −2.89307 | −0.0990569 | −0.0495284 | − | 0.998773i | \(-0.515772\pi\) | ||||
−0.0495284 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(854\) | −14.8081 | −0.506723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.33725 | −0.0457064 | ||||||||
\(857\) | 25.7442 | 0.879404 | 0.439702 | − | 0.898144i | \(-0.355084\pi\) | ||||
0.439702 | + | 0.898144i | \(0.355084\pi\) | |||||||
\(858\) | 1.09133 | 0.0372573 | ||||||||
\(859\) | −30.0417 | −1.02501 | −0.512505 | − | 0.858684i | \(-0.671282\pi\) | ||||
−0.512505 | + | 0.858684i | \(0.671282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.77507 | −0.0945741 | ||||||||
\(862\) | 0.921432 | 0.0313841 | ||||||||
\(863\) | 23.2852 | 0.792636 | 0.396318 | − | 0.918113i | \(-0.370288\pi\) | ||||
0.396318 | + | 0.918113i | \(0.370288\pi\) | |||||||
\(864\) | −3.67061 | −0.124877 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.15091 | −0.107072 | ||||||||
\(867\) | 2.01658 | 0.0684868 | ||||||||
\(868\) | −0.687268 | −0.0233274 | ||||||||
\(869\) | −48.4038 | −1.64199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4418 | 0.421574 | ||||||||
\(872\) | −14.1835 | −0.480314 | ||||||||
\(873\) | −4.10467 | −0.138922 | ||||||||
\(874\) | −8.46089 | −0.286194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.0942 | −0.611345 | ||||||||
\(877\) | −23.5946 | −0.796731 | −0.398366 | − | 0.917227i | \(-0.630423\pi\) | ||||
−0.398366 | + | 0.917227i | \(0.630423\pi\) | |||||||
\(878\) | 2.45608 | 0.0828887 | ||||||||
\(879\) | 7.85369 | 0.264898 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.7266 | 1.84379 | 0.921893 | − | 0.387445i | \(-0.126642\pi\) | ||||
0.921893 | + | 0.387445i | \(0.126642\pi\) | |||||||
\(882\) | −2.20854 | −0.0743654 | ||||||||
\(883\) | 2.10978 | 0.0709998 | 0.0354999 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354999 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(884\) | 8.24848 | 0.277426 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.60940 | 0.0876644 | ||||||||
\(887\) | −9.66363 | −0.324473 | −0.162236 | − | 0.986752i | \(-0.551871\pi\) | ||||
−0.162236 | + | 0.986752i | \(0.551871\pi\) | |||||||
\(888\) | −3.74470 | −0.125664 | ||||||||
\(889\) | −70.2278 | −2.35536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.31322 | −0.110997 | ||||||||
\(892\) | 4.80994 | 0.161049 | ||||||||
\(893\) | 29.6150 | 0.991027 | ||||||||
\(894\) | −1.74230 | −0.0582712 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 33.8994 | 1.13250 | ||||||||
\(897\) | 4.92143 | 0.164322 | ||||||||
\(898\) | −12.7552 | −0.425646 | ||||||||
\(899\) | 0.763883 | 0.0254769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.59299 | 0.319589 | ||||||||
\(902\) | −0.818069 | −0.0272387 | ||||||||
\(903\) | −14.0048 | −0.466051 | ||||||||
\(904\) | −20.4636 | −0.680611 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.39724 | 0.179311 | ||||||||
\(907\) | −12.3350 | −0.409577 | −0.204788 | − | 0.978806i | \(-0.565651\pi\) | ||||
−0.204788 | + | 0.978806i | \(0.565651\pi\) | |||||||
\(908\) | 52.8319 | 1.75329 | ||||||||
\(909\) | 2.77761 | 0.0921277 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.24151 | −0.140528 | −0.0702638 | − | 0.997528i | \(-0.522384\pi\) | ||||
−0.0702638 | + | 0.997528i | \(0.522384\pi\) | |||||||
\(912\) | 17.5414 | 0.580852 | ||||||||
\(913\) | 55.3312 | 1.83119 | ||||||||
\(914\) | −4.22676 | −0.139809 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.89389 | −0.161699 | ||||||||
\(917\) | −1.99883 | −0.0660073 | ||||||||
\(918\) | 1.43639 | 0.0474078 | ||||||||
\(919\) | −9.01009 | −0.297215 | −0.148608 | − | 0.988896i | \(-0.547479\pi\) | ||||
−0.148608 | + | 0.988896i | \(0.547479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.893913 | 0.0294554 | ||||||||
\(922\) | 10.2498 | 0.337558 | ||||||||
\(923\) | 12.0348 | 0.396131 | ||||||||
\(924\) | 23.2005 | 0.763241 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.37911 | −0.111045 | ||||||||
\(927\) | 16.5046 | 0.542083 | ||||||||
\(928\) | −28.5684 | −0.937805 | ||||||||
\(929\) | 17.1130 | 0.561458 | 0.280729 | − | 0.959787i | \(-0.409424\pi\) | ||||
0.280729 | + | 0.959787i | \(0.409424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.9961 | 1.14695 | ||||||||
\(932\) | 44.0060 | 1.44146 | ||||||||
\(933\) | 34.4340 | 1.12732 | ||||||||
\(934\) | 4.06181 | 0.132906 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.28181 | 0.0418972 | ||||||||
\(937\) | 15.6965 | 0.512782 | 0.256391 | − | 0.966573i | \(-0.417467\pi\) | ||||
0.256391 | + | 0.966573i | \(0.417467\pi\) | |||||||
\(938\) | −15.1715 | −0.495366 | ||||||||
\(939\) | −20.6008 | −0.672280 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.53477 | 0.0826311 | 0.0413156 | − | 0.999146i | \(-0.486845\pi\) | ||||
0.0413156 | + | 0.999146i | \(0.486845\pi\) | |||||||
\(942\) | −2.12282 | −0.0691651 | ||||||||
\(943\) | −3.68914 | −0.120135 | ||||||||
\(944\) | 0.366285 | 0.0119216 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.12851 | −0.134229 | ||||||||
\(947\) | −4.66480 | −0.151586 | −0.0757928 | − | 0.997124i | \(-0.524149\pi\) | ||||
−0.0757928 | + | 0.997124i | \(0.524149\pi\) | |||||||
\(948\) | −27.6335 | −0.897495 | ||||||||
\(949\) | 9.56602 | 0.310526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.1772 | 0.427300 | ||||||||
\(952\) | −20.6932 | −0.670672 | ||||||||
\(953\) | 41.4489 | 1.34266 | 0.671330 | − | 0.741158i | \(-0.265723\pi\) | ||||
0.671330 | + | 0.741158i | \(0.265723\pi\) | |||||||
\(954\) | 0.724591 | 0.0234595 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.5091 | −0.954392 | ||||||||
\(957\) | −25.7868 | −0.833570 | ||||||||
\(958\) | 2.70472 | 0.0873856 | ||||||||
\(959\) | −45.3041 | −1.46295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9904 | −0.999689 | ||||||||
\(962\) | 0.962276 | 0.0310250 | ||||||||
\(963\) | −1.04326 | −0.0336185 | ||||||||
\(964\) | −50.8227 | −1.63689 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.00117 | −0.193084 | ||||||||
\(967\) | 40.1592 | 1.29143 | 0.645716 | − | 0.763578i | \(-0.276559\pi\) | ||||
0.645716 | + | 0.763578i | \(0.276559\pi\) | |||||||
\(968\) | −0.0289200 | −0.000929525 0 | ||||||||
\(969\) | −22.7607 | −0.731181 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.79988 | −0.121944 | −0.0609719 | − | 0.998139i | \(-0.519420\pi\) | ||||
−0.0609719 | + | 0.998139i | \(0.519420\pi\) | |||||||
\(972\) | −1.89150 | −0.0606700 | ||||||||
\(973\) | −35.9283 | −1.15181 | ||||||||
\(974\) | 7.73597 | 0.247876 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.8129 | 1.30639 | ||||||||
\(977\) | 53.7828 | 1.72066 | 0.860332 | − | 0.509734i | \(-0.170256\pi\) | ||||
0.860332 | + | 0.509734i | \(0.170256\pi\) | |||||||
\(978\) | 4.20536 | 0.134472 | ||||||||
\(979\) | 11.9078 | 0.380575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0652 | −0.353286 | ||||||||
\(982\) | −0.400992 | −0.0127962 | ||||||||
\(983\) | −25.6007 | −0.816536 | −0.408268 | − | 0.912862i | \(-0.633867\pi\) | ||||
−0.408268 | + | 0.912862i | \(0.633867\pi\) | |||||||
\(984\) | −0.960853 | −0.0306309 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.1794 | 0.356025 | ||||||||
\(987\) | 21.0054 | 0.668609 | ||||||||
\(988\) | −9.87251 | −0.314086 | ||||||||
\(989\) | −18.6178 | −0.592012 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.0382 | −1.62128 | −0.810640 | − | 0.585544i | \(-0.800881\pi\) | ||||
−0.810640 | + | 0.585544i | \(0.800881\pi\) | |||||||
\(992\) | −0.360261 | −0.0114383 | ||||||||
\(993\) | −19.0536 | −0.604648 | ||||||||
\(994\) | −14.6752 | −0.465470 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31.5883 | 1.00092 | ||||||||
\(997\) | 6.08651 | 0.192762 | 0.0963809 | − | 0.995345i | \(-0.469273\pi\) | ||||
0.0963809 | + | 0.995345i | \(0.469273\pi\) | |||||||
\(998\) | 0.528118 | 0.0167173 | ||||||||
\(999\) | −2.92143 | −0.0924298 |
(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 | 975.2.a.s.1.3 | 5 | ||
3.2 | odd | 2 | 2925.2.a.bm.1.3 | 5 | |||
5.2 | odd | 4 | 195.2.c.b.79.5 | ✓ | 10 | ||
5.3 | odd | 4 | 195.2.c.b.79.6 | yes | 10 | ||
5.4 | even | 2 | 975.2.a.r.1.3 | 5 | |||
15.2 | even | 4 | 585.2.c.c.469.6 | 10 | |||
15.8 | even | 4 | 585.2.c.c.469.5 | 10 | |||
15.14 | odd | 2 | 2925.2.a.bl.1.3 | 5 | |||
20.3 | even | 4 | 3120.2.l.p.1249.5 | 10 | |||
20.7 | even | 4 | 3120.2.l.p.1249.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.c.b.79.5 | ✓ | 10 | 5.2 | odd | 4 | ||
195.2.c.b.79.6 | yes | 10 | 5.3 | odd | 4 | ||
585.2.c.c.469.5 | 10 | 15.8 | even | 4 | |||
585.2.c.c.469.6 | 10 | 15.2 | even | 4 | |||
975.2.a.r.1.3 | 5 | 5.4 | even | 2 | |||
975.2.a.s.1.3 | 5 | 1.1 | even | 1 | trivial | ||
2925.2.a.bl.1.3 | 5 | 15.14 | odd | 2 | |||
2925.2.a.bm.1.3 | 5 | 3.2 | odd | 2 | |||
3120.2.l.p.1249.5 | 10 | 20.3 | even | 4 | |||
3120.2.l.p.1249.10 | 10 | 20.7 | even | 4 |