Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(4591,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("5040.4591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.d (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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 328 x^{8} - 658 x^{7} + 1045 x^{6} - 1270 x^{5} + 1183 x^{4} + \cdots + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1680) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4591.3 | ||
Root | \(0.500000 - 1.18724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.4591 |
Dual form | 5040.2.d.g.4591.9 |
$q$-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 \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.321212 | + | 2.62618i | −0.121407 | + | 0.992603i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.68712i | 0.508686i | 0.967114 | + | 0.254343i | \(0.0818592\pi\) | ||||
−0.967114 | + | 0.254343i | \(0.918141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.64242i | − | 0.732876i | −0.930442 | − | 0.366438i | \(-0.880577\pi\) | ||
0.930442 | − | 0.366438i | \(-0.119423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.53212i | 1.34174i | 0.741577 | + | 0.670868i | \(0.234078\pi\) | ||||
−0.741577 | + | 0.670868i | \(0.765922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.06801 | 0.933266 | 0.466633 | − | 0.884451i | \(-0.345467\pi\) | ||||
0.466633 | + | 0.884451i | \(0.345467\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.17454i | − | 1.70451i | −0.523127 | − | 0.852255i | \(-0.675235\pi\) | ||
0.523127 | − | 0.852255i | \(-0.324765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.02934 | −1.30532 | −0.652658 | − | 0.757653i | \(-0.726346\pi\) | ||||
−0.652658 | + | 0.757653i | \(0.726346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.21924 | 0.937402 | 0.468701 | − | 0.883357i | \(-0.344722\pi\) | ||||
0.468701 | + | 0.883357i | \(0.344722\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.62618 | + | 0.321212i | 0.443905 | + | 0.0542947i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93948 | 0.812046 | 0.406023 | − | 0.913863i | \(-0.366915\pi\) | ||||
0.406023 | + | 0.913863i | \(0.366915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.96688i | − | 0.307174i | −0.988135 | − | 0.153587i | \(-0.950917\pi\) | ||
0.988135 | − | 0.153587i | \(-0.0490826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.922816i | 0.140728i | 0.997521 | + | 0.0703641i | \(0.0224161\pi\) | ||||
−0.997521 | + | 0.0703641i | \(0.977584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.67177 | 1.41077 | 0.705386 | − | 0.708823i | \(-0.250774\pi\) | ||||
0.705386 | + | 0.708823i | \(0.250774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79365 | − | 1.68712i | −0.970521 | − | 0.241017i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.279755 | 0.0384273 | 0.0192136 | − | 0.999815i | \(-0.493884\pi\) | ||||
0.0192136 | + | 0.999815i | \(0.493884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.68712 | 0.227491 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.49659 | 0.455217 | 0.227609 | − | 0.973753i | \(-0.426909\pi\) | ||||
0.227609 | + | 0.973753i | \(0.426909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1421i | 1.81070i | 0.424662 | + | 0.905352i | \(0.360393\pi\) | ||||
−0.424662 | + | 0.905352i | \(0.639607\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.64242 | −0.327752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.3613i | 1.87668i | 0.345714 | + | 0.938340i | \(0.387637\pi\) | ||||
−0.345714 | + | 0.938340i | \(0.612363\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.6112i | − | 1.25932i | −0.776870 | − | 0.629662i | \(-0.783194\pi\) | ||
0.776870 | − | 0.629662i | \(-0.216806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.380893i | 0.0445802i | 0.999752 | + | 0.0222901i | \(0.00709574\pi\) | ||||
−0.999752 | + | 0.0222901i | \(0.992904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.43068 | − | 0.541923i | −0.504923 | − | 0.0617579i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0898605i | 0.0101101i | 0.999987 | + | 0.00505505i | \(0.00160908\pi\) | ||||
−0.999987 | + | 0.00505505i | \(0.998391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.4385 | −1.58483 | −0.792414 | − | 0.609984i | \(-0.791176\pi\) | ||||
−0.792414 | + | 0.609984i | \(0.791176\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.53212 | 0.600042 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.54339i | 0.587599i | 0.955867 | + | 0.293799i | \(0.0949197\pi\) | ||||
−0.955867 | + | 0.293799i | \(0.905080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.93948 | + | 0.848778i | 0.727455 | + | 0.0889761i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.06801i | − | 0.417369i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8856i | 1.10527i | 0.833424 | + | 0.552633i | \(0.186377\pi\) | ||||
−0.833424 | + | 0.552633i | \(0.813623\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.21305i | 0.618222i | 0.951026 | + | 0.309111i | \(0.100031\pi\) | ||||
−0.951026 | + | 0.309111i | \(0.899969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.06591 | −0.105027 | −0.0525134 | − | 0.998620i | \(-0.516723\pi\) | ||||
−0.0525134 | + | 0.998620i | \(0.516723\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.03851i | 0.390418i | 0.980762 | + | 0.195209i | \(0.0625385\pi\) | ||||
−0.980762 | + | 0.195209i | \(0.937462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0150 | 1.91709 | 0.958544 | − | 0.284944i | \(-0.0919750\pi\) | ||||
0.958544 | + | 0.284944i | \(0.0919750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5822 | −0.995490 | −0.497745 | − | 0.867324i | \(-0.665838\pi\) | ||||
−0.497745 | + | 0.867324i | \(0.665838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.17454 | −0.762280 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.5283 | − | 1.77698i | −1.33181 | − | 0.162896i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.15362 | 0.741239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.40118i | − | 0.568013i | −0.958822 | − | 0.284006i | \(-0.908336\pi\) | ||
0.958822 | − | 0.284006i | \(-0.0916637\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.78826 | −0.156241 | −0.0781205 | − | 0.996944i | \(-0.524892\pi\) | ||||
−0.0781205 | + | 0.996944i | \(0.524892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.30669 | + | 10.6833i | −0.113305 | + | 0.926363i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0227 | 0.856296 | 0.428148 | − | 0.903709i | \(-0.359166\pi\) | ||||
0.428148 | + | 0.903709i | \(0.359166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.84185 | 0.749956 | 0.374978 | − | 0.927034i | \(-0.377650\pi\) | ||||
0.374978 | + | 0.927034i | \(0.377650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.45809 | 0.372804 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.02934i | 0.583755i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.74449 | −0.142915 | −0.0714573 | − | 0.997444i | \(-0.522765\pi\) | ||||
−0.0714573 | + | 0.997444i | \(0.522765\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1793i | 0.828376i | 0.910191 | + | 0.414188i | \(0.135934\pi\) | ||||
−0.910191 | + | 0.414188i | \(0.864066\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.21924i | − | 0.419219i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9265i | 1.51050i | 0.655436 | + | 0.755251i | \(0.272485\pi\) | ||||
−0.655436 | + | 0.755251i | \(0.727515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.4678 | + | 2.62576i | 1.69190 | + | 0.206939i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.07164i | 0.162263i | 0.996703 | + | 0.0811315i | \(0.0258534\pi\) | ||||
−0.996703 | + | 0.0811315i | \(0.974147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8078 | 1.06848 | 0.534240 | − | 0.845333i | \(-0.320598\pi\) | ||||
0.534240 | + | 0.845333i | \(0.320598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.01760 | 0.462892 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.7178i | 1.27103i | 0.772089 | + | 0.635514i | \(0.219212\pi\) | ||||
−0.772089 | + | 0.635514i | \(0.780788\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.321212 | − | 2.62618i | 0.0242813 | − | 0.198521i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.538301i | 0.0402345i | 0.999798 | + | 0.0201172i | \(0.00640395\pi\) | ||||
−0.999798 | + | 0.0201172i | \(0.993596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.0833689i | − | 0.00619676i | −0.999995 | − | 0.00309838i | \(-0.999014\pi\) | ||
0.999995 | − | 0.00309838i | \(-0.000986246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.93948i | − | 0.363158i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.33335 | −0.682522 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6660i | 0.916482i | 0.888828 | + | 0.458241i | \(0.151520\pi\) | ||||
−0.888828 | + | 0.458241i | \(0.848480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.3611 | −1.89752 | −0.948758 | − | 0.316004i | \(-0.897659\pi\) | ||||
−0.948758 | + | 0.316004i | \(0.897659\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4873 | −1.10342 | −0.551711 | − | 0.834036i | \(-0.686025\pi\) | ||||
−0.551711 | + | 0.834036i | \(0.686025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7184 | 1.61047 | 0.805233 | − | 0.592959i | \(-0.202040\pi\) | ||||
0.805233 | + | 0.592959i | \(0.202040\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.25791 | − | 18.4603i | 0.158474 | − | 1.29566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.96688 | −0.137373 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.86323i | 0.474740i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.3815i | − | 0.714694i | −0.933972 | − | 0.357347i | \(-0.883681\pi\) | ||
0.933972 | − | 0.357347i | \(-0.116319\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.922816 | 0.0629356 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.67648 | + | 13.7067i | −0.113807 | + | 0.930468i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6182 | 0.983326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7011 | 1.25232 | 0.626159 | − | 0.779695i | \(-0.284626\pi\) | ||||
0.626159 | + | 0.779695i | \(0.284626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.1947 | 1.20763 | 0.603813 | − | 0.797126i | \(-0.293647\pi\) | ||||
0.603813 | + | 0.797126i | \(0.293647\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4761i | 0.824447i | 0.911083 | + | 0.412223i | \(0.135248\pi\) | ||||
−0.911083 | + | 0.412223i | \(0.864752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0099 | 0.852307 | 0.426153 | − | 0.904651i | \(-0.359868\pi\) | ||||
0.426153 | + | 0.904651i | \(0.359868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.67177i | − | 0.630916i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5518i | 1.26470i | 0.774682 | + | 0.632351i | \(0.217910\pi\) | ||||
−0.774682 | + | 0.632351i | \(0.782090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.0894i | − | 0.649915i | −0.945729 | − | 0.324957i | \(-0.894650\pi\) | ||
0.945729 | − | 0.324957i | \(-0.105350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.68712 | + | 6.79365i | −0.107786 | + | 0.434030i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.7494i | − | 0.683969i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.78826 | 0.112874 | 0.0564370 | − | 0.998406i | \(-0.482026\pi\) | ||||
0.0564370 | + | 0.998406i | \(0.482026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7914 | 0.867060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 29.9808i | − | 1.87015i | −0.354451 | − | 0.935075i | \(-0.615332\pi\) | ||
0.354451 | − | 0.935075i | \(-0.384668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58662 | + | 12.9720i | −0.0985878 | + | 0.806039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.18211i | − | 0.134554i | −0.997734 | − | 0.0672772i | \(-0.978569\pi\) | ||
0.997734 | − | 0.0672772i | \(-0.0214312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.279755i | − | 0.0171852i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5514i | 0.643327i | 0.946854 | + | 0.321664i | \(0.104242\pi\) | ||||
−0.946854 | + | 0.321664i | \(0.895758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8065 | −1.50689 | −0.753445 | − | 0.657511i | \(-0.771609\pi\) | ||||
−0.753445 | + | 0.657511i | \(0.771609\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.68712i | − | 0.101737i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.4216 | −1.16693 | −0.583467 | − | 0.812137i | \(-0.698304\pi\) | ||||
−0.583467 | + | 0.812137i | \(0.698304\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.71255 | 0.102162 | 0.0510809 | − | 0.998695i | \(-0.483733\pi\) | ||||
0.0510809 | + | 0.998695i | \(0.483733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2055 | 1.55775 | 0.778877 | − | 0.627176i | \(-0.215790\pi\) | ||||
0.778877 | + | 0.627176i | \(0.215790\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.16537 | + | 0.631784i | 0.304902 | + | 0.0372930i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6043 | −0.800253 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.57652i | 0.559466i | 0.960078 | + | 0.279733i | \(0.0902460\pi\) | ||||
−0.960078 | + | 0.279733i | \(0.909754\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.49659i | − | 0.203579i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.6006 | −1.24919 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.42348 | − | 0.296420i | −0.139687 | − | 0.0170853i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.1421 | 0.809772 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.4864 | −1.16922 | −0.584610 | − | 0.811315i | \(-0.698752\pi\) | ||||
−0.584610 | + | 0.811315i | \(0.698752\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8688 | 0.899836 | 0.449918 | − | 0.893070i | \(-0.351453\pi\) | ||||
0.449918 | + | 0.893070i | \(0.351453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6165i | 0.713127i | 0.934271 | + | 0.356563i | \(0.116052\pi\) | ||||
−0.934271 | + | 0.356563i | \(0.883948\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.3466 | −1.53594 | −0.767969 | − | 0.640487i | \(-0.778733\pi\) | ||||
−0.767969 | + | 0.640487i | \(0.778733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.8593i | − | 0.663996i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.5047i | 1.25220i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.64242i | 0.146575i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.10669 | + | 25.3998i | −0.171277 | + | 1.40034i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.2537i | − | 1.05828i | −0.848535 | − | 0.529139i | \(-0.822515\pi\) | ||
0.848535 | − | 0.529139i | \(-0.177485\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.3613 | 0.839277 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85513 | 0.427896 | 0.213948 | − | 0.976845i | \(-0.431368\pi\) | ||||
0.213948 | + | 0.976845i | \(0.431368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.80548i | 0.476843i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.61288 | − | 17.2994i | 0.357062 | − | 0.934081i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0796i | 0.702150i | 0.936347 | + | 0.351075i | \(0.114184\pi\) | ||||
−0.936347 | + | 0.351075i | \(0.885816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.4397i | − | 0.879997i | −0.897999 | − | 0.439998i | \(-0.854979\pi\) | ||
0.897999 | − | 0.439998i | \(-0.145021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.4705i | − | 0.557289i | −0.960394 | − | 0.278644i | \(-0.910115\pi\) | ||
0.960394 | − | 0.278644i | \(-0.0898851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.6112 | −0.563186 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1058i | 1.21948i | 0.792603 | + | 0.609738i | \(0.208725\pi\) | ||||
−0.792603 | + | 0.609738i | \(0.791275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.45126 | −0.129014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.380893 | 0.0199369 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8088 | 0.564217 | 0.282108 | − | 0.959383i | \(-0.408966\pi\) | ||||
0.282108 | + | 0.959383i | \(0.408966\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0898605 | + | 0.734686i | −0.00466533 | + | 0.0381430i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.4990 | 1.11318 | 0.556588 | − | 0.830789i | \(-0.312110\pi\) | ||||
0.556588 | + | 0.830789i | \(0.312110\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.5745i | 0.956635i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.7362i | − | 1.21924i | −0.792692 | − | 0.609622i | \(-0.791321\pi\) | ||
0.792692 | − | 0.609622i | \(-0.208679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7491 | 0.600351 | 0.300176 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300176 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.541923 | + | 4.43068i | −0.0276190 | + | 0.225808i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9191 | 1.06064 | 0.530320 | − | 0.847798i | \(-0.322072\pi\) | ||||
0.530320 | + | 0.847798i | \(0.322072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.2225 | 2.28700 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0898605 | 0.00452137 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.71550i | 0.186475i | 0.995644 | + | 0.0932377i | \(0.0297217\pi\) | ||||
−0.995644 | + | 0.0932377i | \(0.970278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.0561 | 1.65074 | 0.825371 | − | 0.564591i | \(-0.190966\pi\) | ||||
0.825371 | + | 0.564591i | \(0.190966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.7914i | − | 0.687000i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.33350i | 0.413076i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6515i | 0.724471i | 0.932087 | + | 0.362236i | \(0.117986\pi\) | ||||
−0.932087 | + | 0.362236i | \(0.882014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.12315 | + | 9.18267i | −0.0552664 | + | 0.451850i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4385i | 0.708757i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0218345 | 0.00106669 | 0.000533343 | − | 1.00000i | \(-0.499830\pi\) | ||||
0.000533343 | 1.00000i | \(0.499830\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.9206 | 1.11708 | 0.558542 | − | 0.829476i | \(-0.311361\pi\) | ||||
0.558542 | + | 0.829476i | \(0.311361\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.53212i | − | 0.268347i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.1396 | − | 4.54259i | −1.79731 | − | 0.219832i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 38.1985i | − | 1.83996i | −0.391967 | − | 0.919979i | \(-0.628205\pi\) | ||
0.391967 | − | 0.919979i | \(-0.371795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.8712i | 1.72386i | 0.507026 | + | 0.861931i | \(0.330745\pi\) | ||||
−0.507026 | + | 0.861931i | \(0.669255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 33.2541i | − | 1.59076i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 41.5602 | 1.98356 | 0.991779 | − | 0.127962i | \(-0.0408435\pi\) | ||||
0.991779 | + | 0.127962i | \(0.0408435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.5304i | 0.832896i | 0.909159 | + | 0.416448i | \(0.136725\pi\) | ||||
−0.909159 | + | 0.416448i | \(0.863275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.54339 | 0.262782 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9056 | −0.609055 | −0.304528 | − | 0.952504i | \(-0.598499\pi\) | ||||
−0.304528 | + | 0.952504i | \(0.598499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.31836 | 0.156255 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.848778 | − | 6.93948i | 0.0397913 | − | 0.325328i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.3239 | −1.27816 | −0.639079 | − | 0.769141i | \(-0.720684\pi\) | ||||
−0.639079 | + | 0.769141i | \(0.720684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 11.7144i | − | 0.545594i | −0.962072 | − | 0.272797i | \(-0.912051\pi\) | ||
0.962072 | − | 0.272797i | \(-0.0879488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.43763i | − | 0.113286i | −0.998394 | − | 0.0566431i | \(-0.981960\pi\) | ||
0.998394 | − | 0.0566431i | \(-0.0180397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.9974 | 0.601448 | 0.300724 | − | 0.953711i | \(-0.402772\pi\) | ||||
0.300724 | + | 0.953711i | \(0.402772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.3415 | − | 4.93423i | −1.86280 | − | 0.227841i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.55690 | −0.0715864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.06801 | −0.186653 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6250 | −0.896690 | −0.448345 | − | 0.893861i | \(-0.647986\pi\) | ||||
−0.448345 | + | 0.893861i | \(0.647986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13.0522i | − | 0.595129i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.8856 | 0.494290 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8370i | 0.762959i | 0.924377 | + | 0.381479i | \(0.124585\pi\) | ||||
−0.924377 | + | 0.381479i | \(0.875415\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.4104i | 0.966240i | 0.875554 | + | 0.483120i | \(0.160496\pi\) | ||||
−0.875554 | + | 0.483120i | \(0.839504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 38.8871i | − | 1.75139i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.8670 | + | 3.40846i | 1.25001 | + | 0.152890i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.6596i | 0.477187i | 0.971120 | + | 0.238594i | \(0.0766864\pi\) | ||||
−0.971120 | + | 0.238594i | \(0.923314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.35914 | −0.0606009 | −0.0303004 | − | 0.999541i | \(-0.509646\pi\) | ||||
−0.0303004 | + | 0.999541i | \(0.509646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.21305 | 0.276477 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 11.4104i | − | 0.505756i | −0.967498 | − | 0.252878i | \(-0.918623\pi\) | ||
0.967498 | − | 0.252878i | \(-0.0813771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00029 | − | 0.122347i | −0.0442504 | − | 0.00541233i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.06591i | 0.0469694i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3174i | 0.717640i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.83474i | 0.430868i | 0.976518 | + | 0.215434i | \(0.0691166\pi\) | ||||
−0.976518 | + | 0.215434i | \(0.930883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0176 | −0.569220 | −0.284610 | − | 0.958643i | \(-0.591864\pi\) | ||||
−0.284610 | + | 0.958643i | \(0.591864\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.8734i | 1.25775i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −43.8231 | −1.90535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.19732 | −0.225121 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.03851 | 0.174600 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.84638 | − | 11.4617i | 0.122602 | − | 0.493690i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7644 | 1.15069 | 0.575346 | − | 0.817910i | \(-0.304867\pi\) | ||||
0.575346 | + | 0.817910i | \(0.304867\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 20.0150i | − | 0.857348i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.6210i | − | 0.710661i | −0.934741 | − | 0.355330i | \(-0.884368\pi\) | ||
0.934741 | − | 0.355330i | \(-0.115632\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.5955 | −1.21821 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.235990 | − | 0.0288643i | −0.0100353 | − | 0.00122743i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.6485 | −1.51047 | −0.755237 | − | 0.655452i | \(-0.772478\pi\) | ||||
−0.755237 | + | 0.655452i | \(0.772478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.43847 | 0.103136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.1530 | −0.807204 | −0.403602 | − | 0.914935i | \(-0.632242\pi\) | ||||
−0.403602 | + | 0.914935i | \(0.632242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5822i | 0.445196i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7579 | −0.912140 | −0.456070 | − | 0.889944i | \(-0.650743\pi\) | ||||
−0.456070 | + | 0.889944i | \(0.650743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5160i | 0.523777i | 0.965098 | + | 0.261888i | \(0.0843452\pi\) | ||||
−0.965098 | + | 0.261888i | \(0.915655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.17454i | 0.340902i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.9404i | − | 1.03828i | −0.854688 | − | 0.519141i | \(-0.826252\pi\) | ||
0.854688 | − | 0.519141i | \(-0.173748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.63781 | − | 37.9180i | 0.192409 | − | 1.57310i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.471980i | 0.0195474i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.76701 | 0.155481 | 0.0777406 | − | 0.996974i | \(-0.475229\pi\) | ||||
0.0777406 | + | 0.996974i | \(0.475229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2319 | 0.874846 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.7552i | 1.67362i | 0.547497 | + | 0.836808i | \(0.315581\pi\) | ||||
−0.547497 | + | 0.836808i | \(0.684419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.77698 | + | 14.5283i | −0.0728491 | + | 0.595604i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26.3094i | − | 1.07497i | −0.843272 | − | 0.537486i | \(-0.819374\pi\) | ||
0.843272 | − | 0.537486i | \(-0.180626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9465i | 0.528101i | 0.964509 | + | 0.264050i | \(0.0850585\pi\) | ||||
−0.964509 | + | 0.264050i | \(0.914942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 8.15362i | − | 0.331492i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.09681 | −0.328639 | −0.164320 | − | 0.986407i | \(-0.552543\pi\) | ||||
−0.164320 | + | 0.986407i | \(0.552543\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 25.5569i | − | 1.03392i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.9476 | −1.69425 | −0.847125 | − | 0.531394i | \(-0.821668\pi\) | ||||
−0.847125 | + | 0.531394i | \(0.821668\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.8424 | −1.92606 | −0.963032 | − | 0.269389i | \(-0.913178\pi\) | ||||
−0.963032 | + | 0.269389i | \(0.913178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2585 | 0.492711 | 0.246356 | − | 0.969180i | \(-0.420767\pi\) | ||||
0.246356 | + | 0.969180i | \(0.420767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5580 | − | 1.78060i | −0.583252 | − | 0.0713384i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3258i | 1.08955i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.2870i | − | 1.24552i | −0.782415 | − | 0.622758i | \(-0.786012\pi\) | ||
0.782415 | − | 0.622758i | \(-0.213988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.40118 | −0.254023 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.45809 | + | 17.9517i | −0.176636 | + | 0.711272i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4022 | 0.608351 | 0.304175 | − | 0.952616i | \(-0.401619\pi\) | ||||
0.304175 | + | 0.952616i | \(0.401619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.3761 | −1.35566 | −0.677831 | − | 0.735218i | \(-0.737080\pi\) | ||||
−0.677831 | + | 0.735218i | \(0.737080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.0411 | 1.84937 | 0.924687 | − | 0.380727i | \(-0.124326\pi\) | ||||
0.924687 | + | 0.380727i | \(0.124326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.89917i | 0.231563i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.7906 | −1.04840 | −0.524198 | − | 0.851597i | \(-0.675635\pi\) | ||||
−0.524198 | + | 0.851597i | \(0.675635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.78826i | 0.0698731i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.888654i | − | 0.0346171i | −0.999850 | − | 0.0173085i | \(-0.994490\pi\) | ||
0.999850 | − | 0.0173085i | \(-0.00550975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.2341i | 1.09818i | 0.835764 | + | 0.549089i | \(0.185025\pi\) | ||||
−0.835764 | + | 0.549089i | \(0.814975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.6833 | + | 1.30669i | 0.414282 | + | 0.0506714i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.4616i | 2.22492i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.8593 | −0.921080 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0519 | 0.734395 | 0.367198 | − | 0.930143i | \(-0.380317\pi\) | ||||
0.367198 | + | 0.930143i | \(0.380317\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.1925i | 1.39099i | 0.718531 | + | 0.695495i | \(0.244815\pi\) | ||||
−0.718531 | + | 0.695495i | \(0.755185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.5876 | − | 3.49659i | −1.09709 | − | 0.134187i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.4770i | 1.16617i | 0.812411 | + | 0.583085i | \(0.198154\pi\) | ||||
−0.812411 | + | 0.583085i | \(0.801846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.0227i | − | 0.382947i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.739231i | − | 0.0281624i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.7242 | −1.66335 | −0.831673 | − | 0.555266i | \(-0.812617\pi\) | ||||
−0.831673 | + | 0.555266i | \(0.812617\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.84185i | − | 0.335390i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8810 | 0.412147 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.87319 | −0.146288 | −0.0731441 | − | 0.997321i | \(-0.523303\pi\) | ||||
−0.0731441 | + | 0.997321i | \(0.523303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0939 | 0.757855 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.3166 | − | 1.99571i | −0.613649 | − | 0.0750562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8066 | 0.593631 | 0.296815 | − | 0.954935i | \(-0.404075\pi\) | ||||
0.296815 | + | 0.954935i | \(0.404075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 42.6648i | − | 1.59781i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.45809i | − | 0.166723i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5671 | 0.431380 | 0.215690 | − | 0.976462i | \(-0.430800\pi\) | ||||
0.215690 | + | 0.976462i | \(0.430800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.342382 | − | 2.79926i | 0.0127510 | − | 0.104250i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.02934 | 0.261063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.6356 | −0.431541 | −0.215770 | − | 0.976444i | \(-0.569226\pi\) | ||||
−0.215770 | + | 0.976444i | \(0.569226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.10513 | −0.188820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.5670i | − | 1.46144i | −0.682678 | − | 0.730719i | \(-0.739185\pi\) | ||
0.682678 | − | 0.730719i | \(-0.260815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9163 | −0.954641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.14668i | 0.152538i | 0.997087 | + | 0.0762690i | \(0.0243008\pi\) | ||||
−0.997087 | + | 0.0762690i | \(0.975699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.8410i | 0.874643i | 0.899305 | + | 0.437321i | \(0.144073\pi\) | ||||
−0.899305 | + | 0.437321i | \(0.855927\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.74449i | 0.0639133i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6059 | − | 1.29722i | −0.387530 | − | 0.0473993i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.4817i | − | 0.747388i | −0.927552 | − | 0.373694i | \(-0.878091\pi\) | ||
0.927552 | − | 0.373694i | \(-0.121909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.1793 | 0.370461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3561 | 0.449092 | 0.224546 | − | 0.974464i | \(-0.427910\pi\) | ||||
0.224546 | + | 0.974464i | \(0.427910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.1367i | 0.911203i | 0.890184 | + | 0.455602i | \(0.150576\pi\) | ||||
−0.890184 | + | 0.455602i | \(0.849424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.42905 | + | 52.5630i | −0.232747 | + | 1.90291i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.23947i | − | 0.333618i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 46.7026i | − | 1.68414i | −0.539368 | − | 0.842070i | \(-0.681337\pi\) | ||
0.539368 | − | 0.842070i | \(-0.318663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.30873i | − | 0.0830394i | −0.999138 | − | 0.0415197i | \(-0.986780\pi\) | ||
0.999138 | − | 0.0415197i | \(-0.0132199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.21924 | −0.187480 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 8.00128i | − | 0.286675i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9025 | 0.640600 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9265 | 0.675517 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.434256 | 0.0154795 | 0.00773977 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00773977 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.39913 | − | 27.7908i | 0.120859 | − | 0.988126i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.3693 | 1.32702 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31.9145i | − | 1.13047i | −0.824930 | − | 0.565235i | \(-0.808786\pi\) | ||
0.824930 | − | 0.565235i | \(-0.191214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.5053i | 1.89288i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.642613 | −0.0226773 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.62576 | − | 21.4678i | 0.0925458 | − | 0.756641i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.49917 | −0.263657 | −0.131828 | − | 0.991273i | \(-0.542085\pi\) | ||||
−0.131828 | + | 0.991273i | \(0.542085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.97307 | −0.315087 | −0.157544 | − | 0.987512i | \(-0.550357\pi\) | ||||
−0.157544 | + | 0.987512i | \(0.550357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.07164 | 0.0725663 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.75403i | 0.131337i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.6347 | 1.27856 | 0.639281 | − | 0.768973i | \(-0.279232\pi\) | ||||
0.639281 | + | 0.768973i | \(0.279232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4269i | 0.502889i | 0.967872 | + | 0.251444i | \(0.0809055\pi\) | ||||
−0.967872 | + | 0.251444i | \(0.919094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 31.4626i | − | 1.09406i | −0.837112 | − | 0.547031i | \(-0.815758\pi\) | ||
0.837112 | − | 0.547031i | \(-0.184242\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.2807i | − | 1.60740i | −0.595038 | − | 0.803698i | \(-0.702863\pi\) | ||
0.595038 | − | 0.803698i | \(-0.297137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.33335 | − | 37.5832i | 0.323381 | − | 1.30218i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13.8078i | − | 0.477838i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.1922 | 1.24949 | 0.624746 | − | 0.780828i | \(-0.285202\pi\) | ||||
0.624746 | + | 0.780828i | \(0.285202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.4116 | 0.703850 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.01760i | − | 0.207012i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.61904 | + | 21.4129i | −0.0899913 | + | 0.735756i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 40.3780i | − | 1.38414i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.1493i | − | 1.58012i | −0.613027 | − | 0.790062i | \(-0.710048\pi\) | ||
0.613027 | − | 0.790062i | \(-0.289952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.67833i | 0.262287i | 0.991363 | + | 0.131143i | \(0.0418648\pi\) | ||||
−0.991363 | + | 0.131143i | \(0.958135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3146 | −0.522527 | −0.261263 | − | 0.965268i | \(-0.584139\pi\) | ||||
−0.261263 | + | 0.965268i | \(0.584139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19.0404i | − | 0.648142i | −0.946033 | − | 0.324071i | \(-0.894948\pi\) | ||
0.946033 | − | 0.324071i | \(-0.105052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7178 | 0.568421 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.151606 | −0.00514287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.5910 | 1.37537 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.62618 | − | 0.321212i | −0.0887811 | − | 0.0108589i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.5743 | −1.16749 | −0.583746 | − | 0.811936i | \(-0.698414\pi\) | ||||
−0.583746 | + | 0.811936i | \(0.698414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.2873i | 0.649804i | 0.945748 | + | 0.324902i | \(0.105331\pi\) | ||||
−0.945748 | + | 0.324902i | \(0.894669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.02686i | 0.0345565i | 0.999851 | + | 0.0172783i | \(0.00550011\pi\) | ||||
−0.999851 | + | 0.0172783i | \(0.994500\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1001 | −0.876354 | −0.438177 | − | 0.898889i | \(-0.644376\pi\) | ||||
−0.438177 | + | 0.898889i | \(0.644376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8107 | + | 2.05614i | 0.563811 | + | 0.0689606i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.3449 | 1.31663 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.538301 | 0.0179934 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.6878 | −1.22361 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.54764i | 0.0515592i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0833689 | −0.00277127 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.9339i | − | 0.628690i | −0.949309 | − | 0.314345i | \(-0.898215\pi\) | ||
0.949309 | − | 0.314345i | \(-0.101785\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 55.6242i | − | 1.84291i | −0.388482 | − | 0.921456i | \(-0.627000\pi\) | ||
0.388482 | − | 0.921456i | \(-0.373000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.3594i | − | 0.806180i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.574410 | − | 4.69629i | 0.0189687 | − | 0.155085i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.3140i | − | 0.604123i | −0.953288 | − | 0.302062i | \(-0.902325\pi\) | ||
0.953288 | − | 0.302062i | \(-0.0976749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.0394 | −0.922928 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.93948 | −0.162409 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 50.5518i | − | 1.65855i | −0.558840 | − | 0.829276i | \(-0.688753\pi\) | ||
0.558840 | − | 0.829276i | \(-0.311247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6366 | − | 6.86323i | −0.905754 | − | 0.224933i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.33335i | 0.305233i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.8586i | − | 0.387404i | −0.981060 | − | 0.193702i | \(-0.937951\pi\) | ||
0.981060 | − | 0.193702i | \(-0.0620495\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 22.8012i | − | 0.743298i | −0.928373 | − | 0.371649i | \(-0.878793\pi\) | ||
0.928373 | − | 0.371649i | \(-0.121207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0783 | −0.523581 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.0946i | − | 0.458012i | −0.973425 | − | 0.229006i | \(-0.926452\pi\) | ||
0.973425 | − | 0.229006i | \(-0.0735476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00648 | 0.0326718 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.3897 | −0.692881 | −0.346440 | − | 0.938072i | \(-0.612610\pi\) | ||||
−0.346440 | + | 0.938072i | \(0.612610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6660 | 0.409863 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.21941 | + | 26.3214i | −0.103960 | + | 0.849962i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.75958 | −0.121277 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.3611i | 0.848595i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.12889i | 0.197092i | 0.995132 | + | 0.0985460i | \(0.0314192\pi\) | ||||
−0.995132 | + | 0.0985460i | \(0.968581\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.1735 | −0.647397 | −0.323699 | − | 0.946160i | \(-0.604926\pi\) | ||||
−0.323699 | + | 0.946160i | \(0.604926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.84011 | + | 23.2203i | −0.0910497 | + | 0.744408i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.7224 | −0.662970 | −0.331485 | − | 0.943461i | \(-0.607550\pi\) | ||||
−0.331485 | + | 0.943461i | \(0.607550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.35237 | −0.298903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.7908 | 1.10965 | 0.554827 | − | 0.831966i | \(-0.312785\pi\) | ||||
0.554827 | + | 0.831966i | \(0.312785\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.4873i | 0.493465i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.54360 | 0.239872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5467i | 0.652687i | 0.945251 | + | 0.326343i | \(0.105817\pi\) | ||||
−0.945251 | + | 0.326343i | \(0.894183\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 22.7184i | − | 0.720222i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 37.4749i | − | 1.18684i | −0.804892 | − | 0.593422i | \(-0.797777\pi\) | ||
0.804892 | − | 0.593422i | \(-0.202223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5040.2.d.g.4591.3 | 12 | ||
3.2 | odd | 2 | 1680.2.d.c.1231.9 | yes | 12 | ||
4.3 | odd | 2 | 5040.2.d.f.4591.4 | 12 | |||
7.6 | odd | 2 | 5040.2.d.f.4591.10 | 12 | |||
12.11 | even | 2 | 1680.2.d.d.1231.10 | yes | 12 | ||
21.20 | even | 2 | 1680.2.d.d.1231.4 | yes | 12 | ||
28.27 | even | 2 | inner | 5040.2.d.g.4591.9 | 12 | ||
84.83 | odd | 2 | 1680.2.d.c.1231.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1680.2.d.c.1231.3 | ✓ | 12 | 84.83 | odd | 2 | ||
1680.2.d.c.1231.9 | yes | 12 | 3.2 | odd | 2 | ||
1680.2.d.d.1231.4 | yes | 12 | 21.20 | even | 2 | ||
1680.2.d.d.1231.10 | yes | 12 | 12.11 | even | 2 | ||
5040.2.d.f.4591.4 | 12 | 4.3 | odd | 2 | |||
5040.2.d.f.4591.10 | 12 | 7.6 | odd | 2 | |||
5040.2.d.g.4591.3 | 12 | 1.1 | even | 1 | trivial | ||
5040.2.d.g.4591.9 | 12 | 28.27 | even | 2 | inner |