Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1471,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.i (of order \(2\), degree \(1\), 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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 33x^{12} - 98x^{10} + 272x^{8} - 882x^{6} + 2673x^{4} - 5832x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.12 | ||
Root | \(1.59950 + 0.664536i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1471 |
Dual form | 1840.2.i.b.1471.5 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.32907i | 0.767340i | 0.923470 | + | 0.383670i | \(0.125340\pi\) | ||||
−0.923470 | + | 0.383670i | \(0.874660\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.37473 | 1.27553 | 0.637764 | − | 0.770232i | \(-0.279859\pi\) | ||||
0.637764 | + | 0.770232i | \(0.279859\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.23357 | 0.411189 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.86992 | −0.563803 | −0.281901 | − | 0.959443i | \(-0.590965\pi\) | ||||
−0.281901 | + | 0.959443i | \(0.590965\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.25170 | −1.17921 | −0.589604 | − | 0.807692i | \(-0.700716\pi\) | ||||
−0.589604 | + | 0.807692i | \(0.700716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.32907 | −0.343165 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.38881i | 0.821907i | 0.911656 | + | 0.410953i | \(0.134804\pi\) | ||||
−0.911656 | + | 0.410953i | \(0.865196\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.52807 | −1.03881 | −0.519405 | − | 0.854528i | \(-0.673846\pi\) | ||||
−0.519405 | + | 0.854528i | \(0.673846\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.48526i | 0.978764i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47789 | + | 3.30216i | −0.725191 | + | 0.688548i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.62672i | 1.08286i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.15524 | 0.585914 | 0.292957 | − | 0.956126i | \(-0.405361\pi\) | ||||
0.292957 | + | 0.956126i | \(0.405361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04566i | 0.367411i | 0.982981 | + | 0.183706i | \(0.0588093\pi\) | ||||
−0.982981 | + | 0.183706i | \(0.941191\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.48526i | − | 0.432629i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37473i | 0.570434i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.40694i | 0.888895i | 0.895805 | + | 0.444448i | \(0.146600\pi\) | ||||
−0.895805 | + | 0.444448i | \(0.853400\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.65081i | − | 0.904854i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1258 | 1.58138 | 0.790689 | − | 0.612217i | \(-0.209722\pi\) | ||||
0.790689 | + | 0.612217i | \(0.209722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.07625 | −0.316625 | −0.158313 | − | 0.987389i | \(-0.550605\pi\) | ||||
−0.158313 | + | 0.987389i | \(0.550605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23357i | 0.183889i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.06892i | 0.739377i | 0.929156 | + | 0.369689i | \(0.120536\pi\) | ||||
−0.929156 | + | 0.369689i | \(0.879464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.38881 | 0.626973 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50397 | −0.630682 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.8922i | − | 1.63352i | −0.576978 | − | 0.816760i | \(-0.695768\pi\) | ||
0.576978 | − | 0.816760i | \(-0.304232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.86992i | − | 0.252140i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.01813i | − | 0.797121i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1187i | 1.44754i | 0.690043 | + | 0.723769i | \(0.257592\pi\) | ||||
−0.690043 | + | 0.723769i | \(0.742408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.01813i | 0.514469i | 0.966349 | + | 0.257234i | \(0.0828112\pi\) | ||||
−0.966349 | + | 0.257234i | \(0.917189\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.16295 | 0.524483 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.25170i | − | 0.527358i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.68140 | −0.694094 | −0.347047 | − | 0.937848i | \(-0.612816\pi\) | ||||
−0.347047 | + | 0.937848i | \(0.612816\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.38881 | − | 4.62237i | −0.528350 | − | 0.556468i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.69419i | − | 0.201063i | −0.994934 | − | 0.100531i | \(-0.967946\pi\) | ||
0.994934 | − | 0.100531i | \(-0.0320543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.02931 | 0.822719 | 0.411359 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411359 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.32907i | − | 0.153468i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.31048 | −0.719146 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.52807 | −0.509447 | −0.254724 | − | 0.967014i | \(-0.581985\pi\) | ||||
−0.254724 | + | 0.967014i | \(0.581985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.77762 | −0.419735 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.81148 | −0.418364 | −0.209182 | − | 0.977877i | \(-0.567080\pi\) | ||||
−0.209182 | + | 0.977877i | \(0.567080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.38881 | −0.367568 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.19355i | 0.449595i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.32861i | 0.458832i | 0.973328 | + | 0.229416i | \(0.0736816\pi\) | ||||
−0.973328 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3483 | −1.50411 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.71883 | −0.281929 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.52807i | − | 0.464570i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.95239i | 0.908978i | 0.890752 | + | 0.454489i | \(0.150178\pi\) | ||||
−0.890752 | + | 0.454489i | \(0.849822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.30667 | −0.231829 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8922 | 1.18332 | 0.591659 | − | 0.806188i | \(-0.298473\pi\) | ||||
0.591659 | + | 0.806188i | \(0.298473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.29764 | −0.423459 | −0.211730 | − | 0.977328i | \(-0.567910\pi\) | ||||
−0.211730 | + | 0.977328i | \(0.567910\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.48526 | −0.437717 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.29303 | 0.221676 | 0.110838 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110838 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.79575i | − | 0.650914i | −0.945557 | − | 0.325457i | \(-0.894482\pi\) | ||
0.945557 | − | 0.325457i | \(-0.105518\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.18621 | −0.682085 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.56359i | 0.335234i | 0.985852 | + | 0.167617i | \(0.0536072\pi\) | ||||
−0.985852 | + | 0.167617i | \(0.946393\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.30216 | − | 3.47789i | −0.307928 | − | 0.324315i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.24475 | −0.484877 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4363i | 1.04837i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.50339 | −0.682127 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4579i | 1.21346i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7928i | 1.75633i | 0.478360 | + | 0.878164i | \(0.341232\pi\) | ||||
−0.478360 | + | 0.878164i | \(0.658768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2.75949i | − | 0.242959i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.8946i | − | 1.21398i | −0.794710 | − | 0.606990i | \(-0.792377\pi\) | ||
0.794710 | − | 0.606990i | \(-0.207623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.2810 | −1.32503 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.62672 | −0.484271 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.50339i | − | 0.213879i | −0.994266 | − | 0.106940i | \(-0.965895\pi\) | ||
0.994266 | − | 0.106940i | \(-0.0341051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6058i | 1.32366i | 0.749652 | + | 0.661832i | \(0.230221\pi\) | ||||
−0.749652 | + | 0.661832i | \(0.769779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.73696 | −0.567354 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.95034 | 0.664841 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.15524i | 0.262029i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.83304i | 0.481101i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 21.2810i | − | 1.74341i | −0.490033 | − | 0.871704i | \(-0.663015\pi\) | ||
0.490033 | − | 0.871704i | \(-0.336985\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.395705i | − | 0.0322020i | −0.999870 | − | 0.0161010i | \(-0.994875\pi\) | ||
0.999870 | − | 0.0161010i | \(-0.00512533\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.18032i | 0.337959i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.04566 | −0.164311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8446i | 1.18473i | 0.805671 | + | 0.592364i | \(0.201805\pi\) | ||||
−0.805671 | + | 0.592364i | \(0.798195\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.8056 | 1.25347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7370 | + | 11.1439i | −0.925002 | + | 0.878262i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.44467i | 0.191482i | 0.995406 | + | 0.0957408i | \(0.0305220\pi\) | ||||
−0.995406 | + | 0.0957408i | \(0.969478\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.48526 | 0.193477 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.8690i | − | 1.15060i | −0.817942 | − | 0.575300i | \(-0.804885\pi\) | ||
0.817942 | − | 0.575300i | \(-0.195115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.07692 | 0.390532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.58567 | −0.427147 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.97052 | 0.529959 | 0.264980 | − | 0.964254i | \(-0.414635\pi\) | ||||
0.264980 | + | 0.964254i | \(0.414635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37473 | −0.255106 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.7776 | −1.11075 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.19958i | − | 0.612866i | −0.951892 | − | 0.306433i | \(-0.900865\pi\) | ||
0.951892 | − | 0.306433i | \(-0.0991355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.7663i | − | 1.91519i | −0.288115 | − | 0.957596i | \(-0.593028\pi\) | ||
0.288115 | − | 0.957596i | \(-0.406972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.34039 | −0.394773 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.40694 | −0.397526 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.33681i | − | 0.463393i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.9887i | 1.38122i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.67738 | −0.627873 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.74830 | 0.269809 | 0.134904 | − | 0.990859i | \(-0.456927\pi\) | ||||
0.134904 | + | 0.990859i | \(0.456927\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.65081 | 0.404663 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5984 | 0.755107 | 0.377554 | − | 0.925988i | \(-0.376765\pi\) | ||||
0.377554 | + | 0.925988i | \(0.376765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2520 | 1.36474 | 0.682368 | − | 0.731009i | \(-0.260950\pi\) | ||||
0.682368 | + | 0.731009i | \(0.260950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.55100i | − | 0.532606i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.6481 | 0.747350 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1258i | 0.707214i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.29021 | + | 4.07343i | −0.298190 | + | 0.283123i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.46713 | 0.585684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.74127i | 0.395245i | 0.980278 | + | 0.197623i | \(0.0633221\pi\) | ||||
−0.980278 | + | 0.197623i | \(0.936678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.25170 | 0.154284 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.07625i | − | 0.141599i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.90355i | 0.468643i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.34247i | 0.631305i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.4082i | − | 0.969199i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 27.2042i | − | 1.82173i | −0.412709 | − | 0.910863i | \(-0.635417\pi\) | ||
0.412709 | − | 0.910863i | \(-0.364583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.23357 | −0.0822377 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.6460 | 1.23758 | 0.618788 | − | 0.785558i | \(-0.287624\pi\) | ||||
0.618788 | + | 0.785558i | \(0.287624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.52152i | − | 0.166627i | −0.996523 | − | 0.0833134i | \(-0.973450\pi\) | ||
0.996523 | − | 0.0833134i | \(-0.0265503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.38709i | − | 0.551830i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9998 | 1.57228 | 0.786141 | − | 0.618048i | \(-0.212076\pi\) | ||||
0.786141 | + | 0.618048i | \(0.212076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.06892 | −0.330660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.01813i | − | 0.390920i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.9572i | − | 1.03219i | −0.856532 | − | 0.516094i | \(-0.827386\pi\) | ||
0.856532 | − | 0.516094i | \(-0.172614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.19291i | − | 0.270089i | −0.990840 | − | 0.135044i | \(-0.956882\pi\) | ||
0.990840 | − | 0.135044i | \(-0.0431177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.8594i | 0.760782i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.38881i | 0.280391i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.2520 | 1.22497 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.06574i | − | 0.321028i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1571 | −1.01983 | −0.509913 | − | 0.860226i | \(-0.670322\pi\) | ||||
−0.509913 | + | 0.860226i | \(0.670322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.50339 | − | 6.17478i | 0.408865 | − | 0.388205i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 4.50397i | − | 0.282050i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0656 | −1.18928 | −0.594639 | − | 0.803993i | \(-0.702705\pi\) | ||||
−0.594639 | + | 0.803993i | \(0.702705\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.2470i | 1.13381i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.89220 | 0.240921 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3584 | 0.947039 | 0.473519 | − | 0.880783i | \(-0.342983\pi\) | ||||
0.473519 | + | 0.880783i | \(0.342983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.8922 | 0.730532 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.75304 | −0.352080 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.39999 | 0.512156 | 0.256078 | − | 0.966656i | \(-0.417570\pi\) | ||||
0.256078 | + | 0.966656i | \(0.417570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.3127i | − | 1.84137i | −0.390311 | − | 0.920683i | \(-0.627633\pi\) | ||
0.390311 | − | 0.920683i | \(-0.372367\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 19.0700i | − | 1.15417i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.86992 | 0.112761 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1565 | 1.33125 | 0.665627 | − | 0.746285i | \(-0.268164\pi\) | ||||
0.665627 | + | 0.746285i | \(0.268164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.52345i | 0.151075i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4490i | 0.742645i | 0.928504 | + | 0.371323i | \(0.121096\pi\) | ||||
−0.928504 | + | 0.371323i | \(0.878904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.7901 | −1.47362 | −0.736809 | − | 0.676101i | \(-0.763668\pi\) | ||||
−0.736809 | + | 0.676101i | \(0.763668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.01813 | 0.356483 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.1717 | 2.01709 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.51598 | 0.324469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.8984 | −0.697495 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6698i | 0.857020i | 0.903537 | + | 0.428510i | \(0.140961\pi\) | ||||
−0.903537 | + | 0.428510i | \(0.859039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1187 | −0.647358 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.5215i | − | 0.610521i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.7869 | − | 14.0398i | 0.855151 | − | 0.811941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00678 | −0.403864 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.8056i | 0.908008i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.01813 | −0.230077 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.2411i | 1.72595i | 0.505247 | + | 0.862975i | \(0.331401\pi\) | ||||
−0.505247 | + | 0.862975i | \(0.668599\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.71188i | − | 0.324938i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.9654i | − | 0.962021i | −0.876715 | − | 0.481011i | \(-0.840270\pi\) | ||
0.876715 | − | 0.481011i | \(-0.159730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6403i | 1.56232i | 0.624328 | + | 0.781162i | \(0.285373\pi\) | ||||
−0.624328 | + | 0.781162i | \(0.714627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.16295i | 0.234556i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.19291 | −0.235497 | −0.117749 | − | 0.993043i | \(-0.537568\pi\) | ||||
−0.117749 | + | 0.993043i | \(0.537568\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.90006 | −0.330340 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.04761i | 0.170101i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 15.3447i | − | 0.853805i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.25170 | 0.235842 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.03204 | 0.499473 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.1062i | 0.943097i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.551304i | 0.0303024i | 0.999885 | + | 0.0151512i | \(0.00482296\pi\) | ||||
−0.999885 | + | 0.0151512i | \(0.995177\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.66982i | 0.365504i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.68140i | − | 0.310408i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.55100i | 0.411329i | 0.978623 | + | 0.205665i | \(0.0659356\pi\) | ||||
−0.978623 | + | 0.205665i | \(0.934064\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.73626 | −0.257239 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.82522i | − | 0.207147i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.81207 | −0.475807 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.62237 | − | 4.38881i | 0.248860 | − | 0.236285i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5897i | 0.675848i | 0.941173 | + | 0.337924i | \(0.109725\pi\) | ||||
−0.941173 | + | 0.337924i | \(0.890275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.8153 | −0.739515 | −0.369758 | − | 0.929128i | \(-0.620559\pi\) | ||||
−0.369758 | + | 0.929128i | \(0.620559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 23.9231i | − | 1.27692i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.68935 | −0.302814 | −0.151407 | − | 0.988472i | \(-0.548380\pi\) | ||||
−0.151407 | + | 0.988472i | \(0.548380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.69419 | 0.0899180 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.1997 | −0.804453 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.5473 | −0.556665 | −0.278333 | − | 0.960485i | \(-0.589782\pi\) | ||||
−0.278333 | + | 0.960485i | \(0.589782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50339 | 0.0791259 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 9.97255i | − | 0.523423i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.02931i | 0.367931i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8865 | 1.03806 | 0.519032 | − | 0.854755i | \(-0.326292\pi\) | ||||
0.519032 | + | 0.854755i | \(0.326292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.4908 | 0.650245 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 40.1330i | − | 2.08360i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.96374i | 0.515903i | 0.966158 | + | 0.257951i | \(0.0830475\pi\) | ||||
−0.966158 | + | 0.257951i | \(0.916953\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.32907 | 0.0686330 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.4151 | −0.690914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.6803 | 1.37047 | 0.685237 | − | 0.728320i | \(-0.259699\pi\) | ||||
0.685237 | + | 0.728320i | \(0.259699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.3061 | −1.34770 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.6043 | 1.56381 | 0.781904 | − | 0.623399i | \(-0.214249\pi\) | ||||
0.781904 | + | 0.623399i | \(0.214249\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.31048i | − | 0.321612i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.56119 | −0.130193 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.28101i | 0.267758i | 0.990998 | + | 0.133879i | \(0.0427433\pi\) | ||||
−0.990998 | + | 0.133879i | \(0.957257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1904 | − | 11.7859i | −0.565922 | − | 0.596039i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.4670 | 0.931535 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4.52807i | − | 0.227832i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6599 | 1.53878 | 0.769388 | − | 0.638782i | \(-0.220562\pi\) | ||||
0.769388 | + | 0.638782i | \(0.220562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 20.3096i | − | 1.01675i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.4082i | 1.31876i | 0.751809 | + | 0.659381i | \(0.229181\pi\) | ||||
−0.751809 | + | 0.659381i | \(0.770819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.69752i | − | 0.433254i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.77762i | − | 0.187711i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.1106i | − | 0.501161i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.1915 | −0.652278 | −0.326139 | − | 0.945322i | \(-0.605748\pi\) | ||||
−0.326139 | + | 0.945322i | \(0.605748\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.32719 | 0.164118 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.5228i | 1.84637i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.81148i | − | 0.187098i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.7412 | −1.01570 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.1187 | 1.71566 | 0.857831 | − | 0.513931i | \(-0.171811\pi\) | ||||
0.857831 | + | 0.513931i | \(0.171811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6782i | 0.520422i | 0.965552 | + | 0.260211i | \(0.0837922\pi\) | ||||
−0.965552 | + | 0.260211i | \(0.916208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.25284i | 0.304024i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.38881i | − | 0.164381i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.5601i | 0.656220i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5666i | 0.510159i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9470 | 1.20166 | 0.600828 | − | 0.799379i | \(-0.294838\pi\) | ||||
0.600828 | + | 0.799379i | \(0.294838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 33.3299i | − | 1.60173i | −0.598844 | − | 0.800865i | \(-0.704373\pi\) | ||
0.598844 | − | 0.800865i | \(-0.295627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.19355 | −0.201065 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7481 | − | 14.9524i | 0.753336 | − | 0.715270i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17.2557i | − | 0.823570i | −0.911281 | − | 0.411785i | \(-0.864905\pi\) | ||
0.911281 | − | 0.411785i | \(-0.135095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.41389 | 0.257804 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.75135i | − | 0.225743i | −0.993610 | − | 0.112872i | \(-0.963995\pi\) | ||
0.993610 | − | 0.112872i | \(-0.0360049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.32861 | −0.205196 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.2840 | 1.33779 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.1732 | −1.18800 | −0.593999 | − | 0.804466i | \(-0.702452\pi\) | ||||
−0.593999 | + | 0.804466i | \(0.702452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.9344 | −0.891586 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.525920 | 0.0247099 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 14.3483i | − | 0.672660i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.5455i | − | 1.00785i | −0.863746 | − | 0.503927i | \(-0.831888\pi\) | ||
0.863746 | − | 0.503927i | \(-0.168112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.0679 | −0.890012 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0112 | 0.605991 | 0.302996 | − | 0.952992i | \(-0.402013\pi\) | ||||
0.302996 | + | 0.952992i | \(0.402013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.21595i | − | 0.149458i | −0.997204 | − | 0.0747288i | \(-0.976191\pi\) | ||
0.997204 | − | 0.0747288i | \(-0.0238091\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 2.71883i | − | 0.126083i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.7453 | 1.23762 | 0.618812 | − | 0.785539i | \(-0.287614\pi\) | ||||
0.618812 | + | 0.785539i | \(0.287614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.1732 | −0.885336 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.7295 | −0.909089 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.88242 | 0.178514 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.52807 | 0.207762 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 14.6698i | − | 0.671685i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.0799 | −1.23731 | −0.618657 | − | 0.785661i | \(-0.712323\pi\) | ||||
−0.618657 | + | 0.785661i | \(0.712323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22.9887i | − | 1.04819i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.8110 | − | 15.5993i | −0.673926 | − | 0.709791i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.95239 | −0.406507 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.57289i | 0.433789i | 0.976195 | + | 0.216894i | \(0.0695928\pi\) | ||||
−0.976195 | + | 0.216894i | \(0.930407\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.24915 | −0.146932 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.12775i | 0.0960240i | 0.998847 | + | 0.0480120i | \(0.0152886\pi\) | ||||
−0.998847 | + | 0.0480120i | \(0.984711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.6925i | 0.481566i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 2.30667i | − | 0.103677i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.71742i | − | 0.256461i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1001i | 0.765506i | 0.923851 | + | 0.382753i | \(0.125024\pi\) | ||||
−0.923851 | + | 0.382753i | \(0.874976\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.7620 | 0.882903 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.2060 | 1.88187 | 0.940937 | − | 0.338582i | \(-0.109947\pi\) | ||||
0.940937 | + | 0.338582i | \(0.109947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8922i | 0.529196i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.74759i | 0.299671i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.92308 | 0.173888 | 0.0869438 | − | 0.996213i | \(-0.472290\pi\) | ||||
0.0869438 | + | 0.996213i | \(0.472290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7220 | 1.04940 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 25.4782i | − | 1.12489i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.29764i | − | 0.189377i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.47848i | − | 0.416863i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.26433i | 0.406659i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.22238i | 0.228797i | 0.993435 | + | 0.114398i | \(0.0364940\pi\) | ||||
−0.993435 | + | 0.114398i | \(0.963506\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2337 | 0.753578 | 0.376789 | − | 0.926299i | \(-0.377028\pi\) | ||||
0.376789 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 4.48526i | − | 0.195753i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.93234 | −0.301978 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.19150 | − | 22.9691i | 0.0518044 | − | 0.998657i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.7157i | 0.595211i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.0517 | −1.86478 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.29303i | 0.0991364i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.8978 | 0.470277 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.20673 | −0.353489 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.1423 | 1.85483 | 0.927417 | − | 0.374030i | \(-0.122024\pi\) | ||||
0.927417 | + | 0.374030i | \(0.122024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.2452 | 1.46960 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.79575 | 0.291098 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.807044i | − | 0.0345067i | −0.999851 | − | 0.0172534i | \(-0.994508\pi\) | ||
0.999851 | − | 0.0172534i | \(-0.00549218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.95663i | 0.211544i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.2871 | −0.608653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2810 | −0.649815 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 7.18621i | − | 0.305038i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9398i | 0.887248i | 0.896213 | + | 0.443624i | \(0.146307\pi\) | ||||
−0.896213 | + | 0.443624i | \(0.853693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.82758 | 0.373367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.42208 | 0.355580 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2027 | −0.472138 | −0.236069 | − | 0.971736i | \(-0.575859\pi\) | ||||
−0.236069 | + | 0.971736i | \(0.575859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.56359 | −0.149921 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.7484 | −0.535384 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 10.0000i | − | 0.419222i | −0.977785 | − | 0.209611i | \(-0.932780\pi\) | ||
0.977785 | − | 0.209611i | \(-0.0672197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0398 | −0.880488 | −0.440244 | − | 0.897878i | \(-0.645108\pi\) | ||||
−0.440244 | + | 0.897878i | \(0.645108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.5329i | − | 0.481792i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.47789 | − | 3.30216i | 0.145038 | − | 0.137710i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.6933 | 1.86061 | 0.930304 | − | 0.366790i | \(-0.119543\pi\) | ||||
0.930304 | + | 0.366790i | \(0.119543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.98177i | 0.207035i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8627 | −0.533636 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.2375i | 0.920983i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.24475i | − | 0.216844i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.43001i | − | 0.347944i | −0.984751 | − | 0.173972i | \(-0.944340\pi\) | ||
0.984751 | − | 0.173972i | \(-0.0556602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.26288i | − | 0.381670i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0861i | 0.579424i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.91190 | −0.365968 | −0.182984 | − | 0.983116i | \(-0.558576\pi\) | ||||
−0.182984 | + | 0.983116i | \(0.558576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4363 | −0.468843 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.5873i | 1.04722i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.30667i | − | 0.0942481i | −0.998889 | − | 0.0471240i | \(-0.984994\pi\) | ||
0.998889 | − | 0.0471240i | \(-0.0150056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4657 | −0.630860 | −0.315430 | − | 0.948949i | \(-0.602149\pi\) | ||||
−0.315430 | + | 0.948949i | \(0.602149\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.00839 | −0.285404 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.50339i | − | 0.305056i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.8678i | − | 0.806408i | −0.915110 | − | 0.403204i | \(-0.867897\pi\) | ||
0.915110 | − | 0.403204i | \(-0.132103\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.1521i | 0.573471i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 21.5515i | − | 0.871880i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.6640i | − | 0.955780i | −0.878420 | − | 0.477890i | \(-0.841402\pi\) | ||
0.878420 | − | 0.477890i | \(-0.158598\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.4579 | −0.542674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 45.6222i | − | 1.83668i | −0.395791 | − | 0.918341i | \(-0.629530\pi\) | ||
0.395791 | − | 0.918341i | \(-0.370470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.3426 | 1.70189 | 0.850946 | − | 0.525253i | \(-0.176029\pi\) | ||||
0.850946 | + | 0.525253i | \(0.176029\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.5803 | − | 19.5691i | −0.745602 | − | 0.785282i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6079i | 0.585253i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.2534i | 0.449419i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.3231 | −0.730589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.4459 | −1.53051 | −0.765254 | − | 0.643728i | \(-0.777387\pi\) | ||||
−0.765254 | + | 0.643728i | \(0.777387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.63056 | −0.303288 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.7928 | −0.785454 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6599 | −0.739331 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2.08989i | − | 0.0826748i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.9456i | − | 0.471823i | −0.971775 | − | 0.235912i | \(-0.924192\pi\) | ||
0.971775 | − | 0.235912i | \(-0.0758076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.2111 | −1.30972 | −0.654859 | − | 0.755751i | \(-0.727272\pi\) | ||||
−0.654859 | + | 0.755751i | \(0.727272\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.75949 | 0.108655 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.7672i | 1.09164i | 0.837901 | + | 0.545822i | \(0.183782\pi\) | ||||
−0.837901 | + | 0.545822i | \(0.816218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.7912i | − | 0.816125i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.17531 | −0.359609 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.33980 | −0.208962 | −0.104481 | − | 0.994527i | \(-0.533318\pi\) | ||||
−0.104481 | + | 0.994527i | \(0.533318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8946 | 0.542908 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.67112 | 0.338293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.7574 | 1.93827 | 0.969136 | − | 0.246528i | \(-0.0792896\pi\) | ||||
0.969136 | + | 0.246528i | \(0.0792896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1674i | 1.56233i | 0.624324 | + | 0.781165i | \(0.285374\pi\) | ||||
−0.624324 | + | 0.781165i | \(0.714626\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.1495 | 0.743706 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 15.2810i | − | 0.592572i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9736 | + | 10.4191i | −0.424899 | + | 0.403429i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.1563 | 1.39788 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.51359i | − | 0.290059i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6531 | −0.988854 | −0.494427 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494427 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 5.62672i | − | 0.216572i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.3370i | 0.551014i | 0.961299 | + | 0.275507i | \(0.0888458\pi\) | ||||
−0.961299 | + | 0.275507i | \(0.911154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.2119i | 1.15943i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.7819i | 0.949643i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3898i | 0.856721i | 0.903608 | + | 0.428360i | \(0.140909\pi\) | ||||
−0.903608 | + | 0.428360i | \(0.859091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.50339 | 0.0956497 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.35128 | 0.127859 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50.5620i | 1.92626i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 34.2966i | − | 1.30470i | −0.757916 | − | 0.652352i | \(-0.773782\pi\) | ||
0.757916 | − | 0.652352i | \(-0.226218\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.78440 | −0.295705 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.6058 | −0.591960 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.3143i | 1.29975i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.8975i | 1.20648i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.2266i | − | 1.17941i | −0.807618 | − | 0.589707i | \(-0.799243\pi\) | ||
0.807618 | − | 0.589707i | \(-0.200757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.4830i | − | 0.923393i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6.73696i | − | 0.253729i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.1330 | 1.50936 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6391i | 0.399560i | 0.979841 | + | 0.199780i | \(0.0640227\pi\) | ||||
−0.979841 | + | 0.199780i | \(0.935977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.58567 | −0.209479 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.75509 | − | 7.11458i | −0.252980 | − | 0.266443i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.95034i | 0.297326i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.2083 | 0.792039 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 46.1183i | − | 1.71992i | −0.510359 | − | 0.859961i | \(-0.670488\pi\) | ||
0.510359 | − | 0.859961i | \(-0.329512\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5034 | −0.540135 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.57268 | 0.207250 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.15524 | −0.117183 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.44534 | −0.350308 | −0.175154 | − | 0.984541i | \(-0.556042\pi\) | ||||
−0.175154 | + | 0.984541i | \(0.556042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0949 | −1.00351 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.03601i | − | 0.260236i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.4545i | − | 0.533891i | −0.963712 | − | 0.266945i | \(-0.913986\pi\) | ||
0.963712 | − | 0.266945i | \(-0.0860143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.83304 | −0.215155 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.6238 | 0.391332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.3972i | 0.603180i | 0.953438 | + | 0.301590i | \(0.0975173\pi\) | ||||
−0.953438 | + | 0.301590i | \(0.902483\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.5873i | 0.939971i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.8494 | −1.60868 | −0.804339 | − | 0.594171i | \(-0.797480\pi\) | ||||
−0.804339 | + | 0.594171i | \(0.797480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.2810 | 0.779676 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.70171 | −0.172027 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.73837 | 0.282754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.10540 | −0.0768272 | −0.0384136 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384136 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.4739i | − | 0.782553i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.395705 | 0.0144012 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.0826i | − | 1.05702i | −0.848926 | − | 0.528512i | \(-0.822750\pi\) | ||
0.848926 | − | 0.528512i | \(-0.177250\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.20673 | + | 8.64348i | 0.297885 | + | 0.313738i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.162025 | −0.00587340 | −0.00293670 | − | 0.999996i | \(-0.500935\pi\) | ||||
−0.00293670 | + | 0.999996i | \(0.500935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 22.9338i | − | 0.830260i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.18032 | −0.151140 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 47.2735i | − | 1.70695i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.6306i | 1.57336i | 0.617362 | + | 0.786679i | \(0.288201\pi\) | ||||
−0.617362 | + | 0.786679i | \(0.711799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.3395i | − | 0.912581i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0042i | 0.935307i | 0.883912 | + | 0.467654i | \(0.154901\pi\) | ||||
−0.883912 | + | 0.467654i | \(0.845099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.04566i | − | 0.0734822i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.2515 | −0.870019 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45.8501 | −1.64275 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.16800i | 0.113360i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.7537i | 0.634464i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8446 | −0.529826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.43273 | 0.122364 | 0.0611818 | − | 0.998127i | \(-0.480513\pi\) | ||||
0.0611818 | + | 0.998127i | \(0.480513\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.4124i | 0.726701i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0261i | 0.427600i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.0839i | − | 0.606666i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.8056i | 0.560567i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.81942i | − | 0.0998688i | −0.998752 | − | 0.0499344i | \(-0.984099\pi\) | ||
0.998752 | − | 0.0499344i | \(-0.0159012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.1776 | −0.607699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.33963i | 0.188667i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1443 | −0.463851 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1439 | − | 11.7370i | −0.392771 | − | 0.413673i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.1642i | 0.392998i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.18032 | 0.146972 | 0.0734861 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734861 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.5060i | 1.84373i | 0.387507 | + | 0.921867i | \(0.373336\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.2878 | 1.41295 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.44467 | −0.0856331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.40140 | 0.328913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.6996 | −0.618475 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7481 | 0.549614 | 0.274807 | − | 0.961499i | \(-0.411386\pi\) | ||||
0.274807 | + | 0.961499i | \(0.411386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.7555i | 1.80408i | 0.431650 | + | 0.902041i | \(0.357932\pi\) | ||||
−0.431650 | + | 0.902041i | \(0.642068\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.48526i | 0.0865257i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5915 | −0.959451 | −0.479725 | − | 0.877419i | \(-0.659264\pi\) | ||||
−0.479725 | + | 0.877419i | \(0.659264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5160 | −0.434698 | −0.217349 | − | 0.976094i | \(-0.569741\pi\) | ||||
−0.217349 | + | 0.976094i | \(0.569741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4476i | 1.02153i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8728i | 0.515313i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.8690 | 0.514564 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.5103 | −0.397856 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1296 | 0.660427 | 0.330214 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330214 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0444 | −0.656705 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.5456 | −0.569862 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.07692i | 0.174651i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3219 | −0.870072 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 32.9478i | − | 1.13077i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.8546 | − | 18.8048i | −0.612047 | − | 0.644619i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.5620 | −1.66273 | −0.831366 | − | 0.555725i | \(-0.812441\pi\) | ||||
−0.831366 | + | 0.555725i | \(0.812441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.58567i | − | 0.191026i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.8978 | 1.12377 | 0.561884 | − | 0.827216i | \(-0.310077\pi\) | ||||
0.561884 | + | 0.827216i | \(0.310077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.5140i | 1.58704i | 0.608546 | + | 0.793519i | \(0.291753\pi\) | ||||
−0.608546 | + | 0.793519i | \(0.708247\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45.4167i | 1.54780i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.90384i | 0.303090i | 0.988450 | + | 0.151545i | \(0.0484249\pi\) | ||||
−0.988450 | + | 0.151545i | \(0.951575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.97052i | 0.237005i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.33114i | 0.248979i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.46713 | 0.287228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.1556 | 0.818481 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0434i | 0.373761i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.37473i | − | 0.114087i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6640 | 0.799077 | 0.399538 | − | 0.916716i | \(-0.369170\pi\) | ||||
0.399538 | + | 0.916716i | \(0.369170\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.4972 | −0.657626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.00000i | − | 0.0673817i | −0.999432 | − | 0.0336909i | \(-0.989274\pi\) | ||
0.999432 | − | 0.0336909i | \(-0.0107262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.70407i | − | 0.124652i | −0.998056 | − | 0.0623260i | \(-0.980148\pi\) | ||
0.998056 | − | 0.0623260i | \(-0.0198518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 14.7776i | − | 0.496744i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.8489i | 0.968653i | 0.874887 | + | 0.484326i | \(0.160935\pi\) | ||||
−0.874887 | + | 0.484326i | \(0.839065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 66.7954i | 2.24025i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.06385 | 0.236648 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 22.9524i | − | 0.768073i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.19958 | 0.274082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.6599 | + | 19.6529i | 0.623035 | + | 0.656192i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.45455i | 0.215271i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.3004 | 1.34260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 9.31252i | − | 0.309901i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.7663 | 0.856500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.129634 | 0.00430442 | 0.00215221 | − | 0.999998i | \(-0.499315\pi\) | ||||
0.00215221 | + | 0.999998i | \(0.499315\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.6698 | 0.486567 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4040 | 0.344701 | 0.172350 | − | 0.985036i | \(-0.444864\pi\) | ||||
0.172350 | + | 0.985036i | \(0.444864\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.12717 | 0.235875 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 5.34039i | − | 0.176548i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 46.8906i | − | 1.54846i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.2214 | −0.535096 | −0.267548 | − | 0.963545i | \(-0.586213\pi\) | ||||
−0.267548 | + | 0.963545i | \(0.586213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.1926 | −1.32439 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.20316i | 0.237095i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.40694i | − | 0.177779i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.30143 | −0.174122 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.903382 | 0.0296390 | 0.0148195 | − | 0.999890i | \(-0.495283\pi\) | ||||
0.0148195 | + | 0.999890i | \(0.495283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8728 | −0.651305 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.5483 | 0.738198 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.33681 | 0.207236 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.60962i | 0.183258i | 0.995793 | + | 0.0916292i | \(0.0292074\pi\) | ||||
−0.995793 | + | 0.0916292i | \(0.970793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.7360 | −1.19883 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 58.1926i | − | 1.89702i | −0.316741 | − | 0.948512i | \(-0.602589\pi\) | ||
0.316741 | − | 0.948512i | \(-0.397411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.2163 | + | 33.4369i | −1.14680 | + | 1.08885i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.9887 | −0.617701 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 11.0400i | − | 0.358751i | −0.983781 | − | 0.179375i | \(-0.942592\pi\) | ||
0.983781 | − | 0.179375i | \(-0.0574076\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.8865 | −0.970157 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 5.57268i | − | 0.180707i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.9634i | 1.35933i | 0.733523 | + | 0.679664i | \(0.237874\pi\) | ||||
−0.733523 | + | 0.679664i | \(0.762126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.67738i | − | 0.280793i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.84160i | − | 0.253483i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 8.44827i | − | 0.272809i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.8153 | 0.865009 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.82861 | 0.0911506 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.74830i | 0.120662i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.4731i | 1.49447i | 0.664558 | + | 0.747237i | \(0.268620\pi\) | ||||
−0.664558 | + | 0.747237i | \(0.731380\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.3943 | 0.655159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8169 | −0.411314 | −0.205657 | − | 0.978624i | \(-0.565933\pi\) | ||||
−0.205657 | + | 0.978624i | \(0.565933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.6653i | 1.68837i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.65081i | 0.180971i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.44320i | 0.0461720i | 0.999733 | + | 0.0230860i | \(0.00734915\pi\) | ||||
−0.999733 | + | 0.0230860i | \(0.992651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.09417i | − | 0.258691i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 8.38300i | − | 0.267649i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.9492 | 0.923336 | 0.461668 | − | 0.887053i | \(-0.347251\pi\) | ||||
0.461668 | + | 0.887053i | \(0.347251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5984i | 0.337694i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.7354 | −0.723676 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.22098 | − | 6.85610i | 0.229614 | − | 0.218011i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.0299i | − | 0.382142i | −0.981576 | − | 0.191071i | \(-0.938804\pi\) | ||
0.981576 | − | 0.191071i | \(-0.0611961\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.732723 | −0.0232523 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2520i | 0.610328i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.22917 | −0.260620 | −0.130310 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130310 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4233 | −0.962551 |
(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 | 1840.2.i.b.1471.12 | yes | 16 | |
4.3 | odd | 2 | inner | 1840.2.i.b.1471.6 | yes | 16 | |
23.22 | odd | 2 | inner | 1840.2.i.b.1471.11 | yes | 16 | |
92.91 | even | 2 | inner | 1840.2.i.b.1471.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.i.b.1471.5 | ✓ | 16 | 92.91 | even | 2 | inner | |
1840.2.i.b.1471.6 | yes | 16 | 4.3 | odd | 2 | inner | |
1840.2.i.b.1471.11 | yes | 16 | 23.22 | odd | 2 | inner | |
1840.2.i.b.1471.12 | yes | 16 | 1.1 | even | 1 | trivial |