Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(3149,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.3149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3149.5 | ||
Root | \(-0.916813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.3149 |
Dual form | 3150.2.d.f.3149.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.648285 | − | 2.56510i | 0.245029 | − | 0.969516i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.29657i | − | 0.390930i | −0.980711 | − | 0.195465i | \(-0.937378\pi\) | ||
0.980711 | − | 0.195465i | \(-0.0626217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.13020 | −0.868160 | −0.434080 | − | 0.900874i | \(-0.642926\pi\) | ||||
−0.434080 | + | 0.900874i | \(0.642926\pi\) | |||||||
\(14\) | 0.648285 | − | 2.56510i | 0.173261 | − | 0.685551i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.53921i | − | 1.34346i | −0.740798 | − | 0.671728i | \(-0.765552\pi\) | ||
0.740798 | − | 0.671728i | \(-0.234448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.37284i | 1.69144i | 0.533623 | + | 0.845722i | \(0.320830\pi\) | ||||
−0.533623 | + | 0.845722i | \(0.679170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.29657i | − | 0.276430i | ||||||
\(23\) | 1.83363 | 0.382337 | 0.191169 | − | 0.981557i | \(-0.438772\pi\) | ||||
0.191169 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.13020 | −0.613882 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.648285 | − | 2.56510i | 0.122514 | − | 0.484758i | ||||
\(29\) | − | 1.83363i | − | 0.340496i | −0.985401 | − | 0.170248i | \(-0.945543\pi\) | ||
0.985401 | − | 0.170248i | \(-0.0544569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.4268i | − | 1.87270i | −0.351065 | − | 0.936351i | \(-0.614180\pi\) | ||
0.351065 | − | 0.936351i | \(-0.385820\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.53921i | − | 0.949967i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.6694i | − | 1.75404i | −0.480454 | − | 0.877020i | \(-0.659528\pi\) | ||
0.480454 | − | 0.877020i | \(-0.340472\pi\) | |||||||
\(38\) | 7.37284i | 1.19603i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.13020 | −0.488854 | −0.244427 | − | 0.969668i | \(-0.578600\pi\) | ||||
−0.244427 | + | 0.969668i | \(0.578600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.53921i | − | 0.539724i | −0.962899 | − | 0.269862i | \(-0.913022\pi\) | ||
0.962899 | − | 0.269862i | \(-0.0869782\pi\) | |||||||
\(44\) | − | 1.29657i | − | 0.195465i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.83363 | 0.270353 | ||||||||
\(47\) | 10.7797i | 1.57238i | 0.617985 | + | 0.786190i | \(0.287949\pi\) | ||||
−0.617985 | + | 0.786190i | \(0.712051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.15945 | − | 3.32583i | −0.879922 | − | 0.475118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.13020 | −0.434080 | ||||||||
\(53\) | 4.42677 | 0.608063 | 0.304031 | − | 0.952662i | \(-0.401667\pi\) | ||||
0.304031 | + | 0.952662i | \(0.401667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.648285 | − | 2.56510i | 0.0866307 | − | 0.342776i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.83363i | − | 0.240767i | ||||||
\(59\) | 7.18871 | 0.935891 | 0.467945 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467945 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.88755i | 0.625787i | 0.949788 | + | 0.312894i | \(0.101298\pi\) | ||||
−0.949788 | + | 0.312894i | \(0.898702\pi\) | |||||||
\(62\) | − | 10.4268i | − | 1.32420i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.79960i | − | 1.19721i | −0.801044 | − | 0.598606i | \(-0.795722\pi\) | ||
0.801044 | − | 0.598606i | \(-0.204278\pi\) | |||||||
\(68\) | − | 5.53921i | − | 0.671728i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.37284i | − | 0.874995i | −0.899220 | − | 0.437497i | \(-0.855865\pi\) | ||
0.899220 | − | 0.437497i | \(-0.144135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.40686 | −0.398743 | −0.199371 | − | 0.979924i | \(-0.563890\pi\) | ||||
−0.199371 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(74\) | − | 10.6694i | − | 1.24029i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.37284i | 0.845722i | ||||||||
\(77\) | −3.32583 | − | 0.840546i | −0.379013 | − | 0.0957891i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.01990 | −1.01482 | −0.507409 | − | 0.861705i | \(-0.669397\pi\) | ||||
−0.507409 | + | 0.861705i | \(0.669397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.13020 | −0.345672 | ||||||||
\(83\) | − | 6.26039i | − | 0.687167i | −0.939122 | − | 0.343584i | \(-0.888359\pi\) | ||
0.939122 | − | 0.343584i | \(-0.111641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 3.53921i | − | 0.381643i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.29657i | − | 0.138215i | ||||||
\(89\) | −7.94822 | −0.842510 | −0.421255 | − | 0.906942i | \(-0.638410\pi\) | ||||
−0.421255 | + | 0.906942i | \(0.638410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02926 | + | 8.02926i | −0.212724 | + | 0.841695i | ||||
\(92\) | 1.83363 | 0.191169 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.7797i | 1.11184i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.09402 | −0.821823 | −0.410911 | − | 0.911675i | \(-0.634789\pi\) | ||||
−0.410911 | + | 0.911675i | \(0.634789\pi\) | |||||||
\(98\) | −6.15945 | − | 3.32583i | −0.622199 | − | 0.335959i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.05852 | −0.403837 | −0.201919 | − | 0.979402i | \(-0.564718\pi\) | ||||
−0.201919 | + | 0.979402i | \(0.564718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.61548 | −0.553309 | −0.276655 | − | 0.960969i | \(-0.589226\pi\) | ||||
−0.276655 | + | 0.960969i | \(0.589226\pi\) | |||||||
\(104\) | −3.13020 | −0.306941 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.42677 | 0.429965 | ||||||||
\(107\) | −0.651655 | −0.0629979 | −0.0314989 | − | 0.999504i | \(-0.510028\pi\) | ||||
−0.0314989 | + | 0.999504i | \(0.510028\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.3388 | −1.46919 | −0.734596 | − | 0.678505i | \(-0.762628\pi\) | ||||
−0.734596 | + | 0.678505i | \(0.762628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.648285 | − | 2.56510i | 0.0612572 | − | 0.242379i | ||||
\(113\) | 17.0784 | 1.60660 | 0.803301 | − | 0.595573i | \(-0.203075\pi\) | ||||
0.803301 | + | 0.595573i | \(0.203075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.83363i | − | 0.170248i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.18871 | 0.661775 | ||||||||
\(119\) | −14.2086 | − | 3.59099i | −1.30250 | − | 0.329185i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.31891 | 0.847173 | ||||||||
\(122\) | 4.88755i | 0.442498i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.4268i | − | 0.936351i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.39059i | − | 0.655809i | −0.944711 | − | 0.327904i | \(-0.893658\pi\) | ||
0.944711 | − | 0.327904i | \(-0.106342\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2086 | 1.76563 | 0.882817 | − | 0.469716i | \(-0.155644\pi\) | ||||
0.882817 | + | 0.469716i | \(0.155644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.9120 | + | 4.77970i | 1.63988 | + | 0.414452i | ||||
\(134\) | − | 9.79960i | − | 0.846557i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.53921i | − | 0.474983i | ||||||
\(137\) | 20.7457 | 1.77242 | 0.886211 | − | 0.463281i | \(-0.153328\pi\) | ||||
0.886211 | + | 0.463281i | \(0.153328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.20646i | 0.780882i | 0.920628 | + | 0.390441i | \(0.127677\pi\) | ||||
−0.920628 | + | 0.390441i | \(0.872323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 7.37284i | − | 0.618715i | ||||||
\(143\) | 4.05852i | 0.339390i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.40686 | −0.281954 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 10.6694i | − | 0.877020i | ||||||
\(149\) | 10.3189i | 0.845358i | 0.906279 | + | 0.422679i | \(0.138910\pi\) | ||||
−0.906279 | + | 0.422679i | \(0.861090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24049 | −0.100949 | −0.0504747 | − | 0.998725i | \(-0.516073\pi\) | ||||
−0.0504747 | + | 0.998725i | \(0.516073\pi\) | |||||||
\(152\) | 7.37284i | 0.598016i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.32583 | − | 0.840546i | −0.268003 | − | 0.0677331i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4629 | 0.914842 | 0.457421 | − | 0.889250i | \(-0.348773\pi\) | ||||
0.457421 | + | 0.889250i | \(0.348773\pi\) | |||||||
\(158\) | −9.01990 | −0.717585 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.18871 | − | 4.70343i | 0.0936836 | − | 0.370682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.27882i | − | 0.100165i | −0.998745 | − | 0.0500824i | \(-0.984052\pi\) | ||
0.998745 | − | 0.0500824i | \(-0.0159484\pi\) | |||||||
\(164\) | −3.13020 | −0.244427 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 6.26039i | − | 0.485901i | ||||||
\(167\) | 6.72118i | 0.520101i | 0.965595 | + | 0.260050i | \(0.0837392\pi\) | ||||
−0.965595 | + | 0.260050i | \(0.916261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.20188 | −0.246298 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 3.53921i | − | 0.269862i | ||||||
\(173\) | − | 16.3189i | − | 1.24070i | −0.784324 | − | 0.620352i | \(-0.786990\pi\) | ||
0.784324 | − | 0.620352i | \(-0.213010\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.29657i | − | 0.0977326i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.94822 | −0.595745 | ||||||||
\(179\) | − | 19.1887i | − | 1.43423i | −0.696954 | − | 0.717116i | \(-0.745462\pi\) | ||
0.696954 | − | 0.717116i | \(-0.254538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.7797i | − | 0.801249i | −0.916242 | − | 0.400624i | \(-0.868793\pi\) | ||
0.916242 | − | 0.400624i | \(-0.131207\pi\) | |||||||
\(182\) | −2.02926 | + | 8.02926i | −0.150419 | + | 0.595168i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.83363 | 0.135177 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.18197 | −0.525198 | ||||||||
\(188\) | 10.7797i | 0.786190i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3728i | 1.40177i | 0.713275 | + | 0.700885i | \(0.247211\pi\) | ||||
−0.713275 | + | 0.700885i | \(0.752789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81803i | 0.490772i | 0.969425 | + | 0.245386i | \(0.0789148\pi\) | ||||
−0.969425 | + | 0.245386i | \(0.921085\pi\) | |||||||
\(194\) | −8.09402 | −0.581117 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.15945 | − | 3.32583i | −0.439961 | − | 0.237559i | ||||
\(197\) | 14.7457 | 1.05059 | 0.525293 | − | 0.850922i | \(-0.323956\pi\) | ||||
0.525293 | + | 0.850922i | \(0.323956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94148i | 0.137628i | 0.997630 | + | 0.0688141i | \(0.0219215\pi\) | ||||
−0.997630 | + | 0.0688141i | \(0.978078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.05852 | −0.285556 | ||||||||
\(203\) | −4.70343 | − | 1.18871i | −0.330116 | − | 0.0834312i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.61548 | −0.391249 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.13020 | −0.217040 | ||||||||
\(209\) | 9.55939 | 0.661237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 4.42677 | 0.304031 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.651655 | −0.0445462 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.7457 | − | 6.75951i | −1.81561 | − | 0.458866i | ||||
\(218\) | −15.3388 | −1.03888 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3388i | 1.16633i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.76195 | −0.586743 | −0.293372 | − | 0.955998i | \(-0.594777\pi\) | ||||
−0.293372 | + | 0.955998i | \(0.594777\pi\) | |||||||
\(224\) | 0.648285 | − | 2.56510i | 0.0433153 | − | 0.171388i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0784 | 1.13604 | ||||||||
\(227\) | − | 23.0784i | − | 1.53177i | −0.642978 | − | 0.765884i | \(-0.722302\pi\) | ||
0.642978 | − | 0.765884i | \(-0.277698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.70558i | − | 0.641363i | −0.947187 | − | 0.320682i | \(-0.896088\pi\) | ||
0.947187 | − | 0.320682i | \(-0.103912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.83363i | − | 0.120383i | ||||||
\(233\) | 6.36825 | 0.417198 | 0.208599 | − | 0.978001i | \(-0.433110\pi\) | ||||
0.208599 | + | 0.978001i | \(0.433110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.18871 | 0.467945 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.2086 | − | 3.59099i | −0.921008 | − | 0.232769i | ||||
\(239\) | 19.3728i | 1.25312i | 0.779371 | + | 0.626562i | \(0.215539\pi\) | ||||
−0.779371 | + | 0.626562i | \(0.784461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.3587i | 1.56908i | 0.620076 | + | 0.784541i | \(0.287102\pi\) | ||||
−0.620076 | + | 0.784541i | \(0.712898\pi\) | |||||||
\(242\) | 9.31891 | 0.599042 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.88755i | 0.312894i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 23.0784i | − | 1.46844i | ||||||
\(248\) | − | 10.4268i | − | 0.662100i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.94822 | −0.122971 | −0.0614854 | − | 0.998108i | \(-0.519584\pi\) | ||||
−0.0614854 | + | 0.998108i | \(0.519584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.37742i | − | 0.149467i | ||||||
\(254\) | − | 7.39059i | − | 0.463727i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 25.2420i | − | 1.57455i | −0.616602 | − | 0.787275i | \(-0.711491\pi\) | ||
0.616602 | − | 0.787275i | \(-0.288509\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.3681 | − | 6.91681i | −1.70057 | − | 0.429790i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.2086 | 1.24849 | ||||||||
\(263\) | 0.912047 | 0.0562392 | 0.0281196 | − | 0.999605i | \(-0.491048\pi\) | ||||
0.0281196 | + | 0.999605i | \(0.491048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 18.9120 | + | 4.77970i | 1.15957 | + | 0.293062i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 9.79960i | − | 0.598606i | ||||||
\(269\) | 16.5793 | 1.01086 | 0.505429 | − | 0.862868i | \(-0.331334\pi\) | ||||
0.505429 | + | 0.862868i | \(0.331334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.83363i | − | 0.475859i | −0.971282 | − | 0.237929i | \(-0.923531\pi\) | ||
0.971282 | − | 0.237929i | \(-0.0764687\pi\) | |||||||
\(272\) | − | 5.53921i | − | 0.335864i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.7457 | 1.25329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5910i | 0.696435i | 0.937414 | + | 0.348217i | \(0.113213\pi\) | ||||
−0.937414 | + | 0.348217i | \(0.886787\pi\) | |||||||
\(278\) | 9.20646i | 0.552167i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3566i | 1.15472i | 0.816491 | + | 0.577358i | \(0.195916\pi\) | ||||
−0.816491 | + | 0.577358i | \(0.804084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.28983 | −0.0766724 | −0.0383362 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383362 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(284\) | − | 7.37284i | − | 0.437497i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.05852i | 0.239985i | ||||||||
\(287\) | −2.02926 | + | 8.02926i | −0.119783 | + | 0.473952i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6828 | −0.804873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.40686 | −0.199371 | ||||||||
\(293\) | 17.5992i | 1.02816i | 0.857743 | + | 0.514078i | \(0.171866\pi\) | ||||
−0.857743 | + | 0.514078i | \(0.828134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 10.6694i | − | 0.620147i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.3189i | 0.597758i | ||||||||
\(299\) | −5.73961 | −0.331930 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.07842 | − | 2.29442i | −0.523271 | − | 0.132248i | ||||
\(302\) | −1.24049 | −0.0713820 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.37284i | 0.422861i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.7457 | 1.52646 | 0.763228 | − | 0.646129i | \(-0.223613\pi\) | ||||
0.763228 | + | 0.646129i | \(0.223613\pi\) | |||||||
\(308\) | −3.32583 | − | 0.840546i | −0.189507 | − | 0.0478946i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3388 | −1.66365 | −0.831826 | − | 0.555037i | \(-0.812704\pi\) | ||||
−0.831826 | + | 0.555037i | \(0.812704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.4172 | 1.94538 | 0.972688 | − | 0.232114i | \(-0.0745644\pi\) | ||||
0.972688 | + | 0.232114i | \(0.0745644\pi\) | |||||||
\(314\) | 11.4629 | 0.646891 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.01990 | −0.507409 | ||||||||
\(317\) | 4.53462 | 0.254690 | 0.127345 | − | 0.991858i | \(-0.459354\pi\) | ||||
0.127345 | + | 0.991858i | \(0.459354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.37742 | −0.133110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.18871 | − | 4.70343i | 0.0662443 | − | 0.262112i | ||||
\(323\) | 40.8397 | 2.27238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.27882i | − | 0.0708272i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.13020 | −0.172836 | ||||||||
\(329\) | 27.6510 | + | 6.98831i | 1.52445 | + | 0.385278i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.94148 | −0.216644 | −0.108322 | − | 0.994116i | \(-0.534548\pi\) | ||||
−0.108322 | + | 0.994116i | \(0.534548\pi\) | |||||||
\(332\) | − | 6.26039i | − | 0.343584i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.72118i | 0.367767i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8198i | 1.40649i | 0.710946 | + | 0.703247i | \(0.248267\pi\) | ||||
−0.710946 | + | 0.703247i | \(0.751733\pi\) | |||||||
\(338\) | −3.20188 | −0.174159 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5190 | −0.732096 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5242 | + | 13.6435i | −0.676241 | + | 0.736681i | ||||
\(344\) | − | 3.53921i | − | 0.190821i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 16.3189i | − | 0.877310i | ||||||
\(347\) | 10.7102 | 0.574952 | 0.287476 | − | 0.957788i | \(-0.407184\pi\) | ||||
0.287476 | + | 0.957788i | \(0.407184\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5236i | 0.777431i | 0.921358 | + | 0.388716i | \(0.127081\pi\) | ||||
−0.921358 | + | 0.388716i | \(0.872919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 1.29657i | − | 0.0691074i | ||||||
\(353\) | 28.6176i | 1.52316i | 0.648069 | + | 0.761581i | \(0.275577\pi\) | ||||
−0.648069 | + | 0.761581i | \(0.724423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.94822 | −0.421255 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 19.1887i | − | 1.01415i | ||||||
\(359\) | 29.3771i | 1.55047i | 0.631675 | + | 0.775233i | \(0.282368\pi\) | ||||
−0.631675 | + | 0.775233i | \(0.717632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.3587 | −1.86099 | ||||||||
\(362\) | − | 10.7797i | − | 0.566568i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.02926 | + | 8.02926i | −0.106362 | + | 0.420847i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.2671 | −0.953537 | −0.476768 | − | 0.879029i | \(-0.658192\pi\) | ||||
−0.476768 | + | 0.879029i | \(0.658192\pi\) | |||||||
\(368\) | 1.83363 | 0.0955844 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.86980 | − | 11.3551i | 0.148993 | − | 0.589527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.6694i | − | 1.17378i | −0.809668 | − | 0.586889i | \(-0.800353\pi\) | ||
0.809668 | − | 0.586889i | \(-0.199647\pi\) | |||||||
\(374\) | −7.18197 | −0.371371 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.7797i | 0.555920i | ||||||||
\(377\) | 5.73961i | 0.295605i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1955 | 0.780538 | 0.390269 | − | 0.920701i | \(-0.372382\pi\) | ||||
0.390269 | + | 0.920701i | \(0.372382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.3728i | 0.991201i | ||||||||
\(383\) | 1.22030i | 0.0623546i | 0.999514 | + | 0.0311773i | \(0.00992564\pi\) | ||||
−0.999514 | + | 0.0311773i | \(0.990074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.81803i | 0.347029i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.09402 | −0.410911 | ||||||||
\(389\) | − | 13.4654i | − | 0.682722i | −0.939932 | − | 0.341361i | \(-0.889112\pi\) | ||
0.939932 | − | 0.341361i | \(-0.110888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.1568i | − | 0.513654i | ||||||
\(392\) | −6.15945 | − | 3.32583i | −0.311099 | − | 0.167980i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.7457 | 0.742876 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9053 | 0.647699 | 0.323849 | − | 0.946109i | \(-0.395023\pi\) | ||||
0.323849 | + | 0.946109i | \(0.395023\pi\) | |||||||
\(398\) | 1.94148i | 0.0973178i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.7677i | 1.33672i | 0.743839 | + | 0.668358i | \(0.233003\pi\) | ||||
−0.743839 | + | 0.668358i | \(0.766997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.6378i | 1.62581i | ||||||||
\(404\) | −4.05852 | −0.201919 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.70343 | − | 1.18871i | −0.233427 | − | 0.0589948i | ||||
\(407\) | −13.8336 | −0.685707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.61548 | −0.276655 | ||||||||
\(413\) | 4.66033 | − | 18.4397i | 0.229320 | − | 0.907361i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.13020 | −0.153470 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.55939 | 0.467565 | ||||||||
\(419\) | −12.9283 | −0.631590 | −0.315795 | − | 0.948827i | \(-0.602271\pi\) | ||||
−0.315795 | + | 0.948827i | \(0.602271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4424 | −0.557667 | −0.278833 | − | 0.960340i | \(-0.589948\pi\) | ||||
−0.278833 | + | 0.960340i | \(0.589948\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.42677 | 0.214983 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5371 | + | 3.16853i | 0.606711 | + | 0.153336i | ||||
\(428\) | −0.651655 | −0.0314989 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.7411i | − | 0.950895i | −0.879744 | − | 0.475447i | \(-0.842286\pi\) | ||
0.879744 | − | 0.475447i | \(-0.157714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.95066 | −0.478198 | −0.239099 | − | 0.970995i | \(-0.576852\pi\) | ||||
−0.239099 | + | 0.970995i | \(0.576852\pi\) | |||||||
\(434\) | −26.7457 | − | 6.75951i | −1.28383 | − | 0.324467i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.3388 | −0.734596 | ||||||||
\(437\) | 13.5190i | 0.646703i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.64735i | − | 0.126351i | −0.998002 | − | 0.0631755i | \(-0.979877\pi\) | ||
0.998002 | − | 0.0631755i | \(-0.0201228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.3388i | 0.824723i | ||||||||
\(443\) | −26.8982 | −1.27797 | −0.638986 | − | 0.769218i | \(-0.720646\pi\) | ||||
−0.638986 | + | 0.769218i | \(0.720646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.76195 | −0.414890 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.648285 | − | 2.56510i | 0.0306286 | − | 0.121189i | ||||
\(449\) | 41.1317i | 1.94112i | 0.240852 | + | 0.970562i | \(0.422573\pi\) | ||||
−0.240852 | + | 0.970562i | \(0.577427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.05852i | 0.191108i | ||||||||
\(452\) | 17.0784 | 0.803301 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.0784i | − | 1.08312i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0398i | 0.563198i | 0.959532 | + | 0.281599i | \(0.0908649\pi\) | ||||
−0.959532 | + | 0.281599i | \(0.909135\pi\) | |||||||
\(458\) | − | 9.70558i | − | 0.453512i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.8397 | 1.62265 | 0.811323 | − | 0.584598i | \(-0.198748\pi\) | ||||
0.811323 | + | 0.584598i | \(0.198748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.3256i | − | 1.13051i | −0.824917 | − | 0.565254i | \(-0.808778\pi\) | ||
0.824917 | − | 0.565254i | \(-0.191222\pi\) | |||||||
\(464\) | − | 1.83363i | − | 0.0851240i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.36825 | 0.295003 | ||||||||
\(467\) | 18.7812i | 0.869089i | 0.900650 | + | 0.434545i | \(0.143091\pi\) | ||||
−0.900650 | + | 0.434545i | \(0.856909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.1369 | − | 6.35293i | −1.16072 | − | 0.293351i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.18871 | 0.330887 | ||||||||
\(473\) | −4.58883 | −0.210995 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.2086 | − | 3.59099i | −0.651251 | − | 0.164593i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.3728i | 0.886093i | ||||||||
\(479\) | 6.66119 | 0.304357 | 0.152179 | − | 0.988353i | \(-0.451371\pi\) | ||||
0.152179 | + | 0.988353i | \(0.451371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.3973i | 1.52279i | ||||||||
\(482\) | 24.3587i | 1.10951i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.31891 | 0.423587 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9096i | 0.947505i | 0.880658 | + | 0.473752i | \(0.157101\pi\) | ||||
−0.880658 | + | 0.473752i | \(0.842899\pi\) | |||||||
\(488\) | 4.88755i | 0.221249i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.374990i | − | 0.0169231i | −0.999964 | − | 0.00846153i | \(-0.997307\pi\) | ||
0.999964 | − | 0.00846153i | \(-0.00269342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1568 | −0.457441 | ||||||||
\(494\) | − | 23.0784i | − | 1.03835i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10.4268i | − | 0.468176i | ||||||
\(497\) | −18.9120 | − | 4.77970i | −0.848321 | − | 0.214399i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1785 | 1.61957 | 0.809786 | − | 0.586725i | \(-0.199583\pi\) | ||||
0.809786 | + | 0.586725i | \(0.199583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.94822 | −0.0869535 | ||||||||
\(503\) | − | 36.8195i | − | 1.64170i | −0.571143 | − | 0.820850i | \(-0.693500\pi\) | ||
0.571143 | − | 0.820850i | \(-0.306500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.37742i | − | 0.105689i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 7.39059i | − | 0.327904i | ||||||
\(509\) | 11.7396 | 0.520349 | 0.260175 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260175 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.20862 | + | 8.73893i | −0.0977034 | + | 0.386588i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 25.2420i | − | 1.11338i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9766 | 0.614691 | ||||||||
\(518\) | −27.3681 | − | 6.91681i | −1.20248 | − | 0.303907i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.9500 | 1.35594 | 0.677972 | − | 0.735088i | \(-0.262859\pi\) | ||||
0.677972 | + | 0.735088i | \(0.262859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.4853 | −0.895759 | −0.447879 | − | 0.894094i | \(-0.647821\pi\) | ||||
−0.447879 | + | 0.894094i | \(0.647821\pi\) | |||||||
\(524\) | 20.2086 | 0.882817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.912047 | 0.0397671 | ||||||||
\(527\) | −57.7560 | −2.51589 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6378 | −0.853818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.9120 | + | 4.77970i | 0.819941 | + | 0.207226i | ||||
\(533\) | 9.79812 | 0.424404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 9.79960i | − | 0.423278i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5793 | 0.714784 | ||||||||
\(539\) | −4.31217 | + | 7.98616i | −0.185738 | + | 0.343988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.7414 | −0.633781 | −0.316890 | − | 0.948462i | \(-0.602639\pi\) | ||||
−0.316890 | + | 0.948462i | \(0.602639\pi\) | |||||||
\(542\) | − | 7.83363i | − | 0.336483i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.53921i | − | 0.237492i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.61763i | 0.282949i | 0.989942 | + | 0.141475i | \(0.0451844\pi\) | ||||
−0.989942 | + | 0.141475i | \(0.954816\pi\) | |||||||
\(548\) | 20.7457 | 0.886211 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5190 | 0.575930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.84747 | + | 23.1369i | −0.248660 | + | 0.983883i | ||||
\(554\) | 11.5910i | 0.492454i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.20646i | 0.390441i | ||||||||
\(557\) | 16.1568 | 0.684587 | 0.342294 | − | 0.939593i | \(-0.388796\pi\) | ||||
0.342294 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0784i | 0.468567i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.3566i | 0.816507i | ||||||||
\(563\) | − | 9.55939i | − | 0.402880i | −0.979501 | − | 0.201440i | \(-0.935438\pi\) | ||
0.979501 | − | 0.201440i | \(-0.0645622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.28983 | −0.0542155 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 7.37284i | − | 0.309357i | ||||||
\(569\) | 30.9883i | 1.29910i | 0.760320 | + | 0.649549i | \(0.225042\pi\) | ||||
−0.760320 | + | 0.649549i | \(0.774958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4623 | 0.688924 | 0.344462 | − | 0.938800i | \(-0.388061\pi\) | ||||
0.344462 | + | 0.938800i | \(0.388061\pi\) | |||||||
\(572\) | 4.05852i | 0.169695i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.02926 | + | 8.02926i | −0.0846996 | + | 0.335135i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.1863 | −0.965257 | −0.482629 | − | 0.875825i | \(-0.660318\pi\) | ||||
−0.482629 | + | 0.875825i | \(0.660318\pi\) | |||||||
\(578\) | −13.6828 | −0.569132 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0585 | − | 4.05852i | −0.666220 | − | 0.168376i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.73961i | − | 0.237710i | ||||||
\(584\) | −3.40686 | −0.140977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.5992i | 0.727016i | ||||||||
\(587\) | − | 7.18197i | − | 0.296432i | −0.988955 | − | 0.148216i | \(-0.952647\pi\) | ||
0.988955 | − | 0.148216i | \(-0.0473530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 76.8748 | 3.16757 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 10.6694i | − | 0.438510i | ||||||
\(593\) | 9.75979i | 0.400787i | 0.979716 | + | 0.200393i | \(0.0642220\pi\) | ||||
−0.979716 | + | 0.200393i | \(0.935778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3189i | 0.422679i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.73961 | −0.234710 | ||||||||
\(599\) | − | 14.4158i | − | 0.589012i | −0.955650 | − | 0.294506i | \(-0.904845\pi\) | ||
0.955650 | − | 0.294506i | \(-0.0951551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.1326i | − | 0.698855i | −0.936963 | − | 0.349427i | \(-0.886376\pi\) | ||
0.936963 | − | 0.349427i | \(-0.113624\pi\) | |||||||
\(602\) | −9.07842 | − | 2.29442i | −0.370009 | − | 0.0935134i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.24049 | −0.0504747 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1345 | −0.776646 | −0.388323 | − | 0.921523i | \(-0.626945\pi\) | ||||
−0.388323 | + | 0.921523i | \(0.626945\pi\) | |||||||
\(608\) | 7.37284i | 0.299008i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 33.7426i | − | 1.36508i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.5676i | 1.35578i | 0.735162 | + | 0.677892i | \(0.237106\pi\) | ||||
−0.735162 | + | 0.677892i | \(0.762894\pi\) | |||||||
\(614\) | 26.7457 | 1.07937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.32583 | − | 0.840546i | −0.134001 | − | 0.0338666i | ||||
\(617\) | −0.476107 | −0.0191673 | −0.00958366 | − | 0.999954i | \(-0.503051\pi\) | ||||
−0.00958366 | + | 0.999954i | \(0.503051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.9521i | − | 1.44504i | −0.691351 | − | 0.722519i | \(-0.742984\pi\) | ||
0.691351 | − | 0.722519i | \(-0.257016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.3388 | −1.17638 | ||||||||
\(623\) | −5.15271 | + | 20.3880i | −0.206439 | + | 0.816827i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.4172 | 1.37559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.4629 | 0.457421 | ||||||||
\(629\) | −59.1001 | −2.35647 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.8982 | 1.86699 | 0.933494 | − | 0.358593i | \(-0.116743\pi\) | ||||
0.933494 | + | 0.358593i | \(0.116743\pi\) | |||||||
\(632\) | −9.01990 | −0.358793 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.53462 | 0.180093 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2803 | + | 10.4105i | 0.763913 | + | 0.412479i | ||||
\(638\) | −2.37742 | −0.0941231 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6893i | 0.619690i | 0.950787 | + | 0.309845i | \(0.100277\pi\) | ||||
−0.950787 | + | 0.309845i | \(0.899723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.8198 | 1.57034 | 0.785170 | − | 0.619281i | \(-0.212576\pi\) | ||||
0.785170 | + | 0.619281i | \(0.212576\pi\) | |||||||
\(644\) | 1.18871 | − | 4.70343i | 0.0468418 | − | 0.185341i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40.8397 | 1.60682 | ||||||||
\(647\) | 11.3005i | 0.444268i | 0.975016 | + | 0.222134i | \(0.0713022\pi\) | ||||
−0.975016 | + | 0.222134i | \(0.928698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.32066i | − | 0.365868i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 1.27882i | − | 0.0500824i | ||||||
\(653\) | −42.1430 | −1.64918 | −0.824592 | − | 0.565729i | \(-0.808595\pi\) | ||||
−0.824592 | + | 0.565729i | \(0.808595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.13020 | −0.122214 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.6510 | + | 6.98831i | 1.07795 | + | 0.272433i | ||||
\(659\) | 17.5172i | 0.682371i | 0.939996 | + | 0.341186i | \(0.110828\pi\) | ||||
−0.939996 | + | 0.341186i | \(0.889172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.2307i | − | 1.25363i | −0.779169 | − | 0.626814i | \(-0.784359\pi\) | ||
0.779169 | − | 0.626814i | \(-0.215641\pi\) | |||||||
\(662\) | −3.94148 | −0.153190 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.26039i | − | 0.242950i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.36218i | − | 0.130184i | ||||||
\(668\) | 6.72118i | 0.260050i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.33705 | 0.244639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.9351i | − | 0.421516i | −0.977538 | − | 0.210758i | \(-0.932407\pi\) | ||
0.977538 | − | 0.210758i | \(-0.0675931\pi\) | |||||||
\(674\) | 25.8198i | 0.994541i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.20188 | −0.123149 | ||||||||
\(677\) | 44.5606i | 1.71260i | 0.516477 | + | 0.856301i | \(0.327243\pi\) | ||||
−0.516477 | + | 0.856301i | \(0.672757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.24723 | + | 20.7619i | −0.201370 | + | 0.796770i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.5190 | −0.517670 | ||||||||
\(683\) | 7.98616 | 0.305582 | 0.152791 | − | 0.988259i | \(-0.451174\pi\) | ||||
0.152791 | + | 0.988259i | \(0.451174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.5242 | + | 13.6435i | −0.478174 | + | 0.520912i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 3.53921i | − | 0.134931i | ||||||
\(689\) | −13.8566 | −0.527896 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 45.1969i | − | 1.71937i | −0.510823 | − | 0.859686i | \(-0.670659\pi\) | ||
0.510823 | − | 0.859686i | \(-0.329341\pi\) | |||||||
\(692\) | − | 16.3189i | − | 0.620352i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.7102 | 0.406553 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3388i | 0.656754i | ||||||||
\(698\) | 14.5236i | 0.549727i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31284i | 0.0495854i | 0.999693 | + | 0.0247927i | \(0.00789257\pi\) | ||||
−0.999693 | + | 0.0247927i | \(0.992107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 78.6638 | 2.96686 | ||||||||
\(704\) | − | 1.29657i | − | 0.0488663i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.6176i | 1.07704i | ||||||||
\(707\) | −2.63107 | + | 10.4105i | −0.0989517 | + | 0.391527i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0784 | 0.491170 | 0.245585 | − | 0.969375i | \(-0.421020\pi\) | ||||
0.245585 | + | 0.969375i | \(0.421020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.94822 | −0.297872 | ||||||||
\(713\) | − | 19.1188i | − | 0.716004i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 19.1887i | − | 0.717116i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.3771i | 1.09635i | ||||||||
\(719\) | 34.1568 | 1.27384 | 0.636918 | − | 0.770932i | \(-0.280209\pi\) | ||||
0.636918 | + | 0.770932i | \(0.280209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.64043 | + | 14.4042i | −0.135577 | + | 0.536442i | ||||
\(722\) | −35.3587 | −1.31592 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.7797i | − | 0.400624i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0965 | 0.596984 | 0.298492 | − | 0.954412i | \(-0.403516\pi\) | ||||
0.298492 | + | 0.954412i | \(0.403516\pi\) | |||||||
\(728\) | −2.02926 | + | 8.02926i | −0.0752093 | + | 0.297584i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.6044 | −0.725096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.2484 | −1.48661 | −0.743305 | − | 0.668953i | \(-0.766743\pi\) | ||||
−0.743305 | + | 0.668953i | \(0.766743\pi\) | |||||||
\(734\) | −18.2671 | −0.674252 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.83363 | 0.0675884 | ||||||||
\(737\) | −12.7059 | −0.468027 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.3838 | 0.492333 | 0.246166 | − | 0.969228i | \(-0.420829\pi\) | ||||
0.246166 | + | 0.969228i | \(0.420829\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.86980 | − | 11.3551i | 0.105354 | − | 0.416858i | ||||
\(743\) | −4.18803 | −0.153644 | −0.0768221 | − | 0.997045i | \(-0.524477\pi\) | ||||
−0.0768221 | + | 0.997045i | \(0.524477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 22.6694i | − | 0.829986i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.18197 | −0.262599 | ||||||||
\(749\) | −0.422458 | + | 1.67156i | −0.0154363 | + | 0.0610774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7812 | 0.831297 | 0.415648 | − | 0.909525i | \(-0.363555\pi\) | ||||
0.415648 | + | 0.909525i | \(0.363555\pi\) | |||||||
\(752\) | 10.7797i | 0.393095i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.73961i | 0.209024i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.7092i | 1.62498i | 0.582972 | + | 0.812492i | \(0.301890\pi\) | ||||
−0.582972 | + | 0.812492i | \(0.698110\pi\) | |||||||
\(758\) | 15.1955 | 0.551924 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.5474 | −1.57859 | −0.789297 | − | 0.614012i | \(-0.789555\pi\) | ||||
−0.789297 | + | 0.614012i | \(0.789555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.94392 | + | 39.3456i | −0.359994 | + | 1.42440i | ||||
\(764\) | 19.3728i | 0.700885i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.22030i | 0.0440913i | ||||||||
\(767\) | −22.5021 | −0.812503 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.2803i | − | 1.34436i | −0.740387 | − | 0.672181i | \(-0.765358\pi\) | ||
0.740387 | − | 0.672181i | \(-0.234642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.81803i | 0.245386i | ||||||||
\(773\) | − | 39.2353i | − | 1.41119i | −0.708613 | − | 0.705597i | \(-0.750679\pi\) | ||
0.708613 | − | 0.705597i | \(-0.249321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.09402 | −0.290558 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 13.4654i | − | 0.482757i | ||||||
\(779\) | − | 23.0784i | − | 0.826870i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.55939 | −0.342062 | ||||||||
\(782\) | − | 10.1568i | − | 0.363208i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.15945 | − | 3.32583i | −0.219980 | − | 0.118780i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.15078 | −0.0410208 | −0.0205104 | − | 0.999790i | \(-0.506529\pi\) | ||||
−0.0205104 | + | 0.999790i | \(0.506529\pi\) | |||||||
\(788\) | 14.7457 | 0.525293 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0717 | − | 43.8078i | 0.393664 | − | 1.55763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.2990i | − | 0.543284i | ||||||
\(794\) | 12.9053 | 0.457992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.94148i | 0.0688141i | ||||||||
\(797\) | − | 16.3189i | − | 0.578045i | −0.957322 | − | 0.289023i | \(-0.906670\pi\) | ||
0.957322 | − | 0.289023i | \(-0.0933303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.7110 | 2.11242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.7677i | 0.945201i | ||||||||
\(803\) | 4.41723i | 0.155881i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.6378i | 1.14962i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.05852 | −0.142778 | ||||||||
\(809\) | − | 13.4970i | − | 0.474528i | −0.971445 | − | 0.237264i | \(-0.923749\pi\) | ||
0.971445 | − | 0.237264i | \(-0.0762507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.2866i | 1.09862i | 0.835618 | + | 0.549311i | \(0.185110\pi\) | ||||
−0.835618 | + | 0.549311i | \(0.814890\pi\) | |||||||
\(812\) | −4.70343 | − | 1.18871i | −0.165058 | − | 0.0417156i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.8336 | −0.484868 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0940 | 0.912914 | ||||||||
\(818\) | 12.0000i | 0.419570i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.8059i | 1.87784i | 0.344135 | + | 0.938920i | \(0.388172\pi\) | ||||
−0.344135 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5860i | 0.926731i | 0.886167 | + | 0.463366i | \(0.153358\pi\) | ||||
−0.886167 | + | 0.463366i | \(0.846642\pi\) | |||||||
\(824\) | −5.61548 | −0.195624 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.66033 | − | 18.4397i | 0.162154 | − | 0.641601i | ||||
\(827\) | −23.7517 | −0.825929 | −0.412964 | − | 0.910747i | \(-0.635507\pi\) | ||||
−0.412964 | + | 0.910747i | \(0.635507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3109i | 1.05274i | 0.850256 | + | 0.526370i | \(0.176447\pi\) | ||||
−0.850256 | + | 0.526370i | \(0.823553\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.13020 | −0.108520 | ||||||||
\(833\) | −18.4225 | + | 34.1185i | −0.638300 | + | 1.18214i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.55939 | 0.330619 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.9283 | −0.446601 | ||||||||
\(839\) | 37.1182 | 1.28146 | 0.640732 | − | 0.767765i | \(-0.278631\pi\) | ||||
0.640732 | + | 0.767765i | \(0.278631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6378 | 0.884063 | ||||||||
\(842\) | −11.4424 | −0.394330 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.04131 | − | 23.9039i | 0.207582 | − | 0.821348i | ||||
\(848\) | 4.42677 | 0.152016 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 19.5637i | − | 0.670635i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.7692 | −1.80678 | −0.903392 | − | 0.428816i | \(-0.858931\pi\) | ||||
−0.903392 | + | 0.428816i | \(0.858931\pi\) | |||||||
\(854\) | 12.5371 | + | 3.16853i | 0.429009 | + | 0.108425i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.651655 | −0.0222731 | ||||||||
\(857\) | 27.6961i | 0.946079i | 0.881041 | + | 0.473040i | \(0.156843\pi\) | ||||
−0.881041 | + | 0.473040i | \(0.843157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.46996i | 0.288991i | 0.989505 | + | 0.144496i | \(0.0461560\pi\) | ||||
−0.989505 | + | 0.144496i | \(0.953844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.7411i | − | 0.672384i | ||||||
\(863\) | 30.2374 | 1.02929 | 0.514646 | − | 0.857403i | \(-0.327923\pi\) | ||||
0.514646 | + | 0.857403i | \(0.327923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.95066 | −0.338137 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.7457 | − | 6.75951i | −0.907807 | − | 0.229433i | ||||
\(869\) | 11.6949i | 0.396723i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6747i | 1.03937i | ||||||||
\(872\) | −15.3388 | −0.519438 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.5190i | 0.457288i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.30546i | 0.280456i | 0.990119 | + | 0.140228i | \(0.0447835\pi\) | ||||
−0.990119 | + | 0.140228i | \(0.955217\pi\) | |||||||
\(878\) | − | 2.64735i | − | 0.0893437i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.98803 | −0.336505 | −0.168253 | − | 0.985744i | \(-0.553812\pi\) | ||||
−0.168253 | + | 0.985744i | \(0.553812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.08337i | 0.204722i | 0.994747 | + | 0.102361i | \(0.0326396\pi\) | ||||
−0.994747 | + | 0.102361i | \(0.967360\pi\) | |||||||
\(884\) | 17.3388i | 0.583167i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.8982 | −0.903663 | ||||||||
\(887\) | − | 37.5158i | − | 1.25966i | −0.776734 | − | 0.629829i | \(-0.783125\pi\) | ||
0.776734 | − | 0.629829i | \(-0.216875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9576 | − | 4.79120i | −0.635817 | − | 0.160692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.76195 | −0.293372 | ||||||||
\(893\) | −79.4769 | −2.65959 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.648285 | − | 2.56510i | 0.0216577 | − | 0.0856939i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.1317i | 1.37258i | ||||||||
\(899\) | −19.1188 | −0.637647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 24.5208i | − | 0.816906i | ||||||
\(902\) | 4.05852i | 0.135134i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.0784 | 0.568020 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.5796i | 1.18140i | 0.806891 | + | 0.590700i | \(0.201148\pi\) | ||||
−0.806891 | + | 0.590700i | \(0.798852\pi\) | |||||||
\(908\) | − | 23.0784i | − | 0.765884i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.3495i | − | 1.50249i | −0.660021 | − | 0.751247i | \(-0.729453\pi\) | ||
0.660021 | − | 0.751247i | \(-0.270547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.11703 | −0.268635 | ||||||||
\(914\) | 12.0398i | 0.398241i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 9.70558i | − | 0.320682i | ||||||
\(917\) | 13.1009 | − | 51.8371i | 0.432631 | − | 1.71181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.741366 | 0.0244554 | 0.0122277 | − | 0.999925i | \(-0.496108\pi\) | ||||
0.0122277 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.8397 | 1.14738 | ||||||||
\(923\) | 23.0784i | 0.759635i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 24.3256i | − | 0.799390i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 1.83363i | − | 0.0601917i | ||||||
\(929\) | −6.49238 | −0.213008 | −0.106504 | − | 0.994312i | \(-0.533966\pi\) | ||||
−0.106504 | + | 0.994312i | \(0.533966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.5208 | − | 45.4126i | 0.803636 | − | 1.48834i | ||||
\(932\) | 6.36825 | 0.208599 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.7812i | 0.614539i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.4562 | 0.374258 | 0.187129 | − | 0.982335i | \(-0.440082\pi\) | ||||
0.187129 | + | 0.982335i | \(0.440082\pi\) | |||||||
\(938\) | −25.1369 | − | 6.35293i | −0.820750 | − | 0.207431i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.3189 | 1.50995 | 0.754977 | − | 0.655752i | \(-0.227648\pi\) | ||||
0.754977 | + | 0.655752i | \(0.227648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.73961 | −0.186907 | ||||||||
\(944\) | 7.18871 | 0.233973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.58883 | −0.149196 | ||||||||
\(947\) | −45.2569 | −1.47065 | −0.735326 | − | 0.677713i | \(-0.762971\pi\) | ||||
−0.735326 | + | 0.677713i | \(0.762971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6641 | 0.346173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.2086 | − | 3.59099i | −0.460504 | − | 0.116385i | ||||
\(953\) | 57.9723 | 1.87791 | 0.938954 | − | 0.344043i | \(-0.111797\pi\) | ||||
0.938954 | + | 0.344043i | \(0.111797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19.3728i | 0.626562i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.66119 | 0.215213 | ||||||||
\(959\) | 13.4491 | − | 53.2147i | 0.434294 | − | 1.71839i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.7174 | −2.50701 | ||||||||
\(962\) | 33.3973i | 1.07677i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.3587i | 0.784541i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.8716i | − | 0.574711i | −0.957824 | − | 0.287355i | \(-0.907224\pi\) | ||
0.957824 | − | 0.287355i | \(-0.0927761\pi\) | |||||||
\(968\) | 9.31891 | 0.299521 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.9898 | −0.866144 | −0.433072 | − | 0.901359i | \(-0.642570\pi\) | ||||
−0.433072 | + | 0.901359i | \(0.642570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.6155 | + | 5.96841i | 0.757077 | + | 0.191338i | ||||
\(974\) | 20.9096i | 0.669987i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.88755i | 0.156447i | ||||||||
\(977\) | −14.4853 | −0.463425 | −0.231713 | − | 0.972784i | \(-0.574433\pi\) | ||||
−0.231713 | + | 0.972784i | \(0.574433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3054i | 0.329363i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 0.374990i | − | 0.0119664i | ||||||
\(983\) | 17.6241i | 0.562120i | 0.959690 | + | 0.281060i | \(0.0906860\pi\) | ||||
−0.959690 | + | 0.281060i | \(0.909314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.1568 | −0.323460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 23.0784i | − | 0.734222i | ||||||
\(989\) | − | 6.48959i | − | 0.206357i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1551 | −0.608481 | −0.304241 | − | 0.952595i | \(-0.598403\pi\) | ||||
−0.304241 | + | 0.952595i | \(0.598403\pi\) | |||||||
\(992\) | − | 10.4268i | − | 0.331050i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.9120 | − | 4.77970i | −0.599854 | − | 0.151603i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.8862 | 1.16820 | 0.584099 | − | 0.811682i | \(-0.301448\pi\) | ||||
0.584099 | + | 0.811682i | \(0.301448\pi\) | |||||||
\(998\) | 36.1785 | 1.14521 | ||||||||
\(999\) | 0 | 0 |
(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 | 3150.2.d.f.3149.5 | 8 | ||
3.2 | odd | 2 | 3150.2.d.c.3149.5 | 8 | |||
5.2 | odd | 4 | 3150.2.b.f.251.8 | 8 | |||
5.3 | odd | 4 | 630.2.b.b.251.1 | yes | 8 | ||
5.4 | even | 2 | 3150.2.d.a.3149.4 | 8 | |||
7.6 | odd | 2 | 3150.2.d.d.3149.3 | 8 | |||
15.2 | even | 4 | 3150.2.b.e.251.4 | 8 | |||
15.8 | even | 4 | 630.2.b.a.251.5 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.d.d.3149.4 | 8 | |||
20.3 | even | 4 | 5040.2.f.i.881.8 | 8 | |||
21.20 | even | 2 | 3150.2.d.a.3149.3 | 8 | |||
35.13 | even | 4 | 630.2.b.a.251.1 | ✓ | 8 | ||
35.27 | even | 4 | 3150.2.b.e.251.8 | 8 | |||
35.34 | odd | 2 | 3150.2.d.c.3149.6 | 8 | |||
60.23 | odd | 4 | 5040.2.f.f.881.8 | 8 | |||
105.62 | odd | 4 | 3150.2.b.f.251.4 | 8 | |||
105.83 | odd | 4 | 630.2.b.b.251.5 | yes | 8 | ||
105.104 | even | 2 | inner | 3150.2.d.f.3149.6 | 8 | ||
140.83 | odd | 4 | 5040.2.f.f.881.7 | 8 | |||
420.83 | even | 4 | 5040.2.f.i.881.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.1 | ✓ | 8 | 35.13 | even | 4 | ||
630.2.b.a.251.5 | yes | 8 | 15.8 | even | 4 | ||
630.2.b.b.251.1 | yes | 8 | 5.3 | odd | 4 | ||
630.2.b.b.251.5 | yes | 8 | 105.83 | odd | 4 | ||
3150.2.b.e.251.4 | 8 | 15.2 | even | 4 | |||
3150.2.b.e.251.8 | 8 | 35.27 | even | 4 | |||
3150.2.b.f.251.4 | 8 | 105.62 | odd | 4 | |||
3150.2.b.f.251.8 | 8 | 5.2 | odd | 4 | |||
3150.2.d.a.3149.3 | 8 | 21.20 | even | 2 | |||
3150.2.d.a.3149.4 | 8 | 5.4 | even | 2 | |||
3150.2.d.c.3149.5 | 8 | 3.2 | odd | 2 | |||
3150.2.d.c.3149.6 | 8 | 35.34 | odd | 2 | |||
3150.2.d.d.3149.3 | 8 | 7.6 | odd | 2 | |||
3150.2.d.d.3149.4 | 8 | 15.14 | odd | 2 | |||
3150.2.d.f.3149.5 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.d.f.3149.6 | 8 | 105.104 | even | 2 | inner | ||
5040.2.f.f.881.7 | 8 | 140.83 | odd | 4 | |||
5040.2.f.f.881.8 | 8 | 60.23 | odd | 4 | |||
5040.2.f.i.881.7 | 8 | 420.83 | even | 4 | |||
5040.2.f.i.881.8 | 8 | 20.3 | even | 4 |