Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(401,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.l (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-35}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(0.500000 - 2.95804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.401 |
Dual form | 1200.3.l.k.401.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | + | 2.95804i | −0.166667 | + | 0.986013i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | −1.14286 | −0.571429 | − | 0.820652i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820652i | \(0.693611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.50000 | − | 2.95804i | −0.944444 | − | 0.328671i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.7482i | 1.61348i | 0.590909 | + | 0.806738i | \(0.298769\pi\) | ||||
−0.590909 | + | 0.806738i | \(0.701231\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.153846 | 0.0769231 | − | 0.997037i | \(-0.475490\pi\) | ||||
0.0769231 | + | 0.997037i | \(0.475490\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.7482i | 1.04401i | 0.852941 | + | 0.522007i | \(0.174817\pi\) | ||||
−0.852941 | + | 0.522007i | \(0.825183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.0000 | −0.578947 | −0.289474 | − | 0.957186i | \(-0.593480\pi\) | ||||
−0.289474 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 23.6643i | 0.190476 | − | 1.12687i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.4965i | 1.54333i | 0.636032 | + | 0.771663i | \(0.280575\pi\) | ||||
−0.636032 | + | 0.771663i | \(0.719425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.0000 | − | 23.6643i | 0.481481 | − | 0.876456i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 35.4965i | − | 1.22402i | −0.790851 | − | 0.612008i | \(-0.790362\pi\) | ||
0.790851 | − | 0.612008i | \(-0.209638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.0000 | 1.48387 | 0.741935 | − | 0.670471i | \(-0.233908\pi\) | ||||
0.741935 | + | 0.670471i | \(0.233908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −52.5000 | − | 8.87412i | −1.59091 | − | 0.268913i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.0000 | −0.432432 | −0.216216 | − | 0.976346i | \(-0.569372\pi\) | ||||
−0.216216 | + | 0.976346i | \(0.569372\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | + | 5.91608i | −0.0256410 | + | 0.151694i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 53.2447i | − | 1.29865i | −0.760510 | − | 0.649326i | \(-0.775051\pi\) | ||
0.760510 | − | 0.649326i | \(-0.224949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −62.0000 | −1.44186 | −0.720930 | − | 0.693008i | \(-0.756285\pi\) | ||||
−0.720930 | + | 0.693008i | \(0.756285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 35.4965i | − | 0.755244i | −0.925960 | − | 0.377622i | \(-0.876742\pi\) | ||
0.925960 | − | 0.377622i | \(-0.123258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.5000 | − | 8.87412i | −1.02941 | − | 0.174002i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.4965i | 0.669745i | 0.942263 | + | 0.334872i | \(0.108693\pi\) | ||||
−0.942263 | + | 0.334872i | \(0.891307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.50000 | − | 32.5384i | 0.0964912 | − | 0.570850i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 70.9930i | − | 1.20327i | −0.798771 | − | 0.601635i | \(-0.794516\pi\) | ||
0.798771 | − | 0.601635i | \(-0.205484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16.0000 | −0.262295 | −0.131148 | − | 0.991363i | \(-0.541866\pi\) | ||||
−0.131148 | + | 0.991363i | \(0.541866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 68.0000 | + | 23.6643i | 1.07937 | + | 0.375624i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −113.000 | −1.68657 | −0.843284 | − | 0.537469i | \(-0.819381\pi\) | ||||
−0.843284 | + | 0.537469i | \(0.819381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −105.000 | − | 17.7482i | −1.52174 | − | 0.257221i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 106.489i | − | 1.49985i | −0.661522 | − | 0.749926i | \(-0.730089\pi\) | ||
0.661522 | − | 0.749926i | \(-0.269911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 101.000 | 1.38356 | 0.691781 | − | 0.722108i | \(-0.256826\pi\) | ||||
0.691781 | + | 0.722108i | \(0.256826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 141.986i | − | 1.84397i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −68.0000 | −0.860759 | −0.430380 | − | 0.902648i | \(-0.641620\pi\) | ||||
−0.430380 | + | 0.902648i | \(0.641620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 63.5000 | + | 50.2867i | 0.783951 | + | 0.620823i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.7482i | − | 0.213834i | −0.994268 | − | 0.106917i | \(-0.965902\pi\) | ||
0.994268 | − | 0.106917i | \(-0.0340979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 105.000 | + | 17.7482i | 1.20690 | + | 0.204003i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 53.2447i | − | 0.598255i | −0.954213 | − | 0.299128i | \(-0.903304\pi\) | ||
0.954213 | − | 0.299128i | \(-0.0966956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.0000 | −0.175824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.0000 | + | 136.070i | −0.247312 | + | 1.46312i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −22.0000 | −0.226804 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 52.5000 | − | 150.860i | 0.530303 | − | 1.52384i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141.986i | 1.40580i | 0.711288 | + | 0.702901i | \(0.248112\pi\) | ||||
−0.711288 | + | 0.702901i | \(0.751888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26.0000 | −0.252427 | −0.126214 | − | 0.992003i | \(-0.540282\pi\) | ||||
−0.126214 | + | 0.992003i | \(0.540282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17.7482i | − | 0.165871i | −0.996555 | − | 0.0829357i | \(-0.973570\pi\) | ||
0.996555 | − | 0.0829357i | \(-0.0264296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 176.000 | 1.61468 | 0.807339 | − | 0.590087i | \(-0.200907\pi\) | ||||
0.807339 | + | 0.590087i | \(0.200907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | − | 47.3286i | 0.0720721 | − | 0.426384i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 124.238i | 1.09945i | 0.835346 | + | 0.549724i | \(0.185267\pi\) | ||||
−0.835346 | + | 0.549724i | \(0.814733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.0000 | − | 5.91608i | −0.145299 | − | 0.0505648i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 141.986i | − | 1.19316i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −194.000 | −1.60331 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 157.500 | + | 26.6224i | 1.28049 | + | 0.216442i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000 | 0.834646 | 0.417323 | − | 0.908758i | \(-0.362968\pi\) | ||||
0.417323 | + | 0.908758i | \(0.362968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.0000 | − | 183.398i | 0.240310 | − | 1.42169i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 70.9930i | − | 0.541931i | −0.962589 | − | 0.270965i | \(-0.912657\pi\) | ||
0.962589 | − | 0.270965i | \(-0.0873429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 88.0000 | 0.661654 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 53.2447i | − | 0.388648i | −0.980937 | − | 0.194324i | \(-0.937749\pi\) | ||
0.980937 | − | 0.194324i | \(-0.0622512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 127.000 | 0.913669 | 0.456835 | − | 0.889552i | \(-0.348983\pi\) | ||||
0.456835 | + | 0.889552i | \(0.348983\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 105.000 | + | 17.7482i | 0.744681 | + | 0.125874i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.4965i | 0.248227i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.50000 | + | 44.3706i | −0.0510204 | + | 0.301841i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 106.489i | − | 0.714694i | −0.933972 | − | 0.357347i | \(-0.883681\pi\) | ||
0.933972 | − | 0.357347i | \(-0.116319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −164.000 | −1.08609 | −0.543046 | − | 0.839703i | \(-0.682729\pi\) | ||||
−0.543046 | + | 0.839703i | \(0.682729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 52.5000 | − | 150.860i | 0.343137 | − | 0.986013i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 38.0000 | 0.242038 | 0.121019 | − | 0.992650i | \(-0.461384\pi\) | ||||
0.121019 | + | 0.992650i | \(0.461384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −105.000 | − | 17.7482i | −0.660377 | − | 0.111624i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 283.972i | − | 1.76380i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −47.0000 | −0.288344 | −0.144172 | − | 0.989553i | \(-0.546052\pi\) | ||||
−0.144172 | + | 0.989553i | \(0.546052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 177.482i | − | 1.06277i | −0.847131 | − | 0.531384i | \(-0.821672\pi\) | ||
0.847131 | − | 0.531384i | \(-0.178328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −165.000 | −0.976331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 93.5000 | + | 32.5384i | 0.546784 | + | 0.190283i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 70.9930i | − | 0.410364i | −0.978724 | − | 0.205182i | \(-0.934221\pi\) | ||
0.978724 | − | 0.205182i | \(-0.0657786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 210.000 | + | 35.4965i | 1.18644 | + | 0.200545i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.7482i | − | 0.0991522i | −0.998770 | − | 0.0495761i | \(-0.984213\pi\) | ||
0.998770 | − | 0.0495761i | \(-0.0157870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −106.000 | −0.585635 | −0.292818 | − | 0.956168i | \(-0.594593\pi\) | ||||
−0.292818 | + | 0.956168i | \(0.594593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | − | 47.3286i | 0.0437158 | − | 0.258626i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −315.000 | −1.68449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −104.000 | + | 189.315i | −0.550265 | + | 1.00166i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 248.475i | 1.30092i | 0.759541 | + | 0.650459i | \(0.225423\pi\) | ||||
−0.759541 | + | 0.650459i | \(0.774577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −193.000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 35.4965i | 0.180185i | 0.995933 | + | 0.0900926i | \(0.0287163\pi\) | ||||
−0.995933 | + | 0.0900926i | \(0.971284\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.0201005 | 0.0100503 | − | 0.999949i | \(-0.496801\pi\) | ||||
0.0100503 | + | 0.999949i | \(0.496801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 56.5000 | − | 334.259i | 0.281095 | − | 1.66298i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 283.972i | 1.39888i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 105.000 | − | 301.720i | 0.507246 | − | 1.45758i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 195.231i | − | 0.934118i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −209.000 | −0.990521 | −0.495261 | − | 0.868744i | \(-0.664927\pi\) | ||||
−0.495261 | + | 0.868744i | \(0.664927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 315.000 | + | 53.2447i | 1.47887 | + | 0.249975i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −368.000 | −1.69585 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −50.5000 | + | 298.762i | −0.230594 | + | 1.36421i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.4965i | 0.160618i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 148.000 | 0.663677 | 0.331839 | − | 0.943336i | \(-0.392331\pi\) | ||||
0.331839 | + | 0.943336i | \(0.392331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 116.000 | 0.506550 | 0.253275 | − | 0.967394i | \(-0.418492\pi\) | ||||
0.253275 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 420.000 | + | 70.9930i | 1.81818 | + | 0.307329i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 212.979i | − | 0.914072i | −0.889448 | − | 0.457036i | \(-0.848911\pi\) | ||
0.889448 | − | 0.457036i | \(-0.151089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.0000 | − | 201.147i | 0.143460 | − | 0.848720i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 177.482i | 0.742604i | 0.928512 | + | 0.371302i | \(0.121089\pi\) | ||||
−0.928512 | + | 0.371302i | \(0.878911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 59.0000 | 0.244813 | 0.122407 | − | 0.992480i | \(-0.460939\pi\) | ||||
0.122407 | + | 0.992480i | \(0.460939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −180.500 | + | 162.692i | −0.742798 | + | 0.669515i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.0000 | −0.0890688 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 52.5000 | + | 8.87412i | 0.210843 | + | 0.0356390i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 124.238i | 0.494971i | 0.968892 | + | 0.247485i | \(0.0796042\pi\) | ||||
−0.968892 | + | 0.247485i | \(0.920396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −630.000 | −2.49012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 496.951i | 1.93366i | 0.255420 | + | 0.966830i | \(0.417786\pi\) | ||||
−0.255420 | + | 0.966830i | \(0.582214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 128.000 | 0.494208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −105.000 | + | 301.720i | −0.402299 | + | 1.15602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 248.475i | − | 0.944773i | −0.881391 | − | 0.472387i | \(-0.843393\pi\) | ||
0.881391 | − | 0.472387i | \(-0.156607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 157.500 | + | 26.6224i | 0.589888 | + | 0.0997092i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 354.965i | 1.31957i | 0.751454 | + | 0.659786i | \(0.229353\pi\) | ||||
−0.751454 | + | 0.659786i | \(0.770647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 178.000 | 0.656827 | 0.328413 | − | 0.944534i | \(-0.393486\pi\) | ||||
0.328413 | + | 0.944534i | \(0.393486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | − | 47.3286i | 0.0293040 | − | 0.173365i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −202.000 | −0.729242 | −0.364621 | − | 0.931156i | \(-0.618801\pi\) | ||||
−0.364621 | + | 0.931156i | \(0.618801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −391.000 | − | 136.070i | −1.40143 | − | 0.487706i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 70.9930i | − | 0.252644i | −0.991989 | − | 0.126322i | \(-0.959683\pi\) | ||
0.991989 | − | 0.126322i | \(-0.0403173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −197.000 | −0.696113 | −0.348057 | − | 0.937474i | \(-0.613158\pi\) | ||||
−0.348057 | + | 0.937474i | \(0.613158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 425.958i | 1.48417i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.0000 | −0.0899654 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0000 | − | 65.0769i | 0.0378007 | − | 0.223632i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 425.958i | 1.45378i | 0.686754 | + | 0.726890i | \(0.259035\pi\) | ||||
−0.686754 | + | 0.726890i | \(0.740965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 420.000 | + | 230.727i | 1.41414 | + | 0.776859i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 70.9930i | 0.237435i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 496.000 | 1.64784 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −420.000 | − | 70.9930i | −1.38614 | − | 0.234300i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 127.000 | 0.413681 | 0.206840 | − | 0.978375i | \(-0.433682\pi\) | ||||
0.206840 | + | 0.978375i | \(0.433682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0000 | − | 76.9090i | 0.0420712 | − | 0.248897i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 283.972i | − | 0.913093i | −0.889700 | − | 0.456546i | \(-0.849086\pi\) | ||
0.889700 | − | 0.456546i | \(-0.150914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −58.0000 | −0.185304 | −0.0926518 | − | 0.995699i | \(-0.529534\pi\) | ||||
−0.0926518 | + | 0.995699i | \(0.529534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 283.972i | − | 0.895810i | −0.894081 | − | 0.447905i | \(-0.852170\pi\) | ||
0.894081 | − | 0.447905i | \(-0.147830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 630.000 | 1.97492 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52.5000 | + | 8.87412i | 0.163551 | + | 0.0276452i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 195.231i | − | 0.604429i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −88.0000 | + | 520.615i | −0.269113 | + | 1.59209i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 283.972i | 0.863136i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −257.000 | −0.776435 | −0.388218 | − | 0.921568i | \(-0.626909\pi\) | ||||
−0.388218 | + | 0.921568i | \(0.626909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 136.000 | + | 47.3286i | 0.408408 | + | 0.142128i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −127.000 | −0.376855 | −0.188427 | − | 0.982087i | \(-0.560339\pi\) | ||||
−0.188427 | + | 0.982087i | \(0.560339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −367.500 | − | 62.1188i | −1.08407 | − | 0.183241i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 816.419i | 2.39419i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 272.000 | 0.793003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 372.713i | 1.07410i | 0.843550 | + | 0.537050i | \(0.180462\pi\) | ||||
−0.843550 | + | 0.537050i | \(0.819538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −292.000 | −0.836676 | −0.418338 | − | 0.908291i | \(-0.637387\pi\) | ||||
−0.418338 | + | 0.908291i | \(0.637387\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.0000 | − | 47.3286i | 0.0740741 | − | 0.134839i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 638.937i | − | 1.81002i | −0.425392 | − | 0.905009i | \(-0.639864\pi\) | ||
0.425392 | − | 0.905009i | \(-0.360136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 420.000 | + | 70.9930i | 1.17647 | + | 0.198860i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 283.972i | 0.791008i | 0.918464 | + | 0.395504i | \(0.129430\pi\) | ||||
−0.918464 | + | 0.395504i | \(0.870570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.000 | −0.664820 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 97.0000 | − | 573.860i | 0.267218 | − | 1.58088i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −668.000 | −1.82016 | −0.910082 | − | 0.414429i | \(-0.863981\pi\) | ||||
−0.910082 | + | 0.414429i | \(0.863981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −157.500 | + | 452.580i | −0.426829 | + | 1.22650i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 283.972i | − | 0.765423i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 242.000 | 0.648794 | 0.324397 | − | 0.945921i | \(-0.394839\pi\) | ||||
0.324397 | + | 0.945921i | \(0.394839\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 70.9930i | − | 0.188310i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −191.000 | −0.503958 | −0.251979 | − | 0.967733i | \(-0.581081\pi\) | ||||
−0.251979 | + | 0.967733i | \(0.581081\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −53.0000 | + | 313.552i | −0.139108 | + | 0.822972i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 283.972i | − | 0.741441i | −0.928745 | − | 0.370720i | \(-0.879111\pi\) | ||
0.928745 | − | 0.370720i | \(-0.120889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 527.000 | + | 183.398i | 1.36176 | + | 0.473898i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 603.440i | 1.55126i | 0.631188 | + | 0.775630i | \(0.282568\pi\) | ||||
−0.631188 | + | 0.775630i | \(0.717432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −630.000 | −1.61125 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 210.000 | + | 35.4965i | 0.534351 | + | 0.0903218i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −772.000 | −1.94458 | −0.972292 | − | 0.233769i | \(-0.924894\pi\) | ||||
−0.972292 | + | 0.233769i | \(0.924894\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44.0000 | + | 260.308i | −0.110276 | + | 0.652400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 266.224i | − | 0.663899i | −0.943297 | − | 0.331950i | \(-0.892294\pi\) | ||
0.943297 | − | 0.331950i | \(-0.107706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 92.0000 | 0.228288 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 283.972i | − | 0.697719i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 701.000 | 1.71394 | 0.856968 | − | 0.515369i | \(-0.172345\pi\) | ||||
0.856968 | + | 0.515369i | \(0.172345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 157.500 | + | 26.6224i | 0.383212 | + | 0.0647746i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 567.944i | 1.37517i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −63.5000 | + | 375.671i | −0.152278 | + | 0.900890i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 301.720i | 0.720096i | 0.932934 | + | 0.360048i | \(0.117240\pi\) | ||||
−0.932934 | + | 0.360048i | \(0.882760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −148.000 | −0.351544 | −0.175772 | − | 0.984431i | \(-0.556242\pi\) | ||||
−0.175772 | + | 0.984431i | \(0.556242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −105.000 | + | 301.720i | −0.248227 | + | 0.713286i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 128.000 | 0.299766 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −105.000 | − | 17.7482i | −0.244755 | − | 0.0413712i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 212.979i | 0.494151i | 0.968996 | + | 0.247075i | \(0.0794695\pi\) | ||||
−0.968996 | + | 0.247075i | \(0.920531\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −463.000 | −1.06928 | −0.534642 | − | 0.845079i | \(-0.679554\pi\) | ||||
−0.534642 | + | 0.845079i | \(0.679554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 390.461i | − | 0.893504i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 394.000 | 0.897494 | 0.448747 | − | 0.893659i | \(-0.351870\pi\) | ||||
0.448747 | + | 0.893659i | \(0.351870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −127.500 | − | 44.3706i | −0.289116 | − | 0.100614i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 656.685i | − | 1.48236i | −0.671307 | − | 0.741179i | \(-0.734267\pi\) | ||
0.671307 | − | 0.741179i | \(-0.265733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 315.000 | + | 53.2447i | 0.704698 | + | 0.119116i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 124.238i | − | 0.276699i | −0.990383 | − | 0.138349i | \(-0.955820\pi\) | ||
0.990383 | − | 0.138349i | \(-0.0441797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 945.000 | 2.09534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 82.0000 | − | 485.119i | 0.181015 | − | 1.07090i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 509.000 | 1.11379 | 0.556893 | − | 0.830584i | \(-0.311993\pi\) | ||||
0.556893 | + | 0.830584i | \(0.311993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 420.000 | + | 230.727i | 0.915033 | + | 0.502673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 212.979i | 0.461993i | 0.972955 | + | 0.230997i | \(0.0741986\pi\) | ||||
−0.972955 | + | 0.230997i | \(0.925801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 64.0000 | 0.138229 | 0.0691145 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691145 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 638.937i | − | 1.36817i | −0.729401 | − | 0.684086i | \(-0.760201\pi\) | ||
0.729401 | − | 0.684086i | \(-0.239799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 904.000 | 1.92751 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.0000 | + | 112.406i | −0.0403397 | + | 0.238653i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1100.39i | − | 2.32641i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 105.000 | − | 301.720i | 0.220126 | − | 0.632537i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 248.475i | 0.518738i | 0.965778 | + | 0.259369i | \(0.0835145\pi\) | ||||
−0.965778 | + | 0.259369i | \(0.916485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0000 | −0.0665281 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 840.000 | + | 141.986i | 1.73913 | + | 0.293967i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 382.000 | 0.784394 | 0.392197 | − | 0.919881i | \(-0.371715\pi\) | ||||
0.392197 | + | 0.919881i | \(0.371715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.5000 | − | 139.028i | 0.0480573 | − | 0.284311i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 709.930i | 1.44589i | 0.690908 | + | 0.722943i | \(0.257211\pi\) | ||||
−0.690908 | + | 0.722943i | \(0.742789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 630.000 | 1.27789 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 851.915i | 1.71412i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 94.0000 | 0.188377 | 0.0941884 | − | 0.995554i | \(-0.469974\pi\) | ||||
0.0941884 | + | 0.995554i | \(0.469974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 525.000 | + | 88.7412i | 1.04790 | + | 0.177128i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 780.923i | 1.55253i | 0.630407 | + | 0.776265i | \(0.282888\pi\) | ||||
−0.630407 | + | 0.776265i | \(0.717112\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 82.5000 | − | 488.077i | 0.162722 | − | 0.962676i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 319.468i | 0.627639i | 0.949483 | + | 0.313820i | \(0.101609\pi\) | ||||
−0.949483 | + | 0.313820i | \(0.898391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −808.000 | −1.58121 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −143.000 | + | 260.308i | −0.278752 | + | 0.507422i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 630.000 | 1.21857 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 210.000 | + | 35.4965i | 0.404624 | + | 0.0683940i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 798.671i | − | 1.53296i | −0.642270 | − | 0.766479i | \(-0.722007\pi\) | ||
0.642270 | − | 0.766479i | \(-0.277993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −467.000 | −0.892925 | −0.446463 | − | 0.894802i | \(-0.647316\pi\) | ||||
−0.446463 | + | 0.894802i | \(0.647316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 816.419i | 1.54918i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −731.000 | −1.38185 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −210.000 | + | 603.440i | −0.395480 | + | 1.13642i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 106.489i | − | 0.199793i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 52.5000 | + | 8.87412i | 0.0977654 | + | 0.0165254i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 266.224i | 0.493921i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −976.000 | −1.80407 | −0.902033 | − | 0.431667i | \(-0.857926\pi\) | ||||
−0.902033 | + | 0.431667i | \(0.857926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 53.0000 | − | 313.552i | 0.0976059 | − | 0.577444i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −779.000 | −1.42413 | −0.712066 | − | 0.702113i | \(-0.752240\pi\) | ||||
−0.712066 | + | 0.702113i | \(0.752240\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 136.000 | + | 47.3286i | 0.247723 | + | 0.0862088i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 390.461i | 0.708641i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 544.000 | 0.983725 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 745.426i | 1.33829i | 0.743133 | + | 0.669144i | \(0.233339\pi\) | ||||
−0.743133 | + | 0.669144i | \(0.766661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −124.000 | −0.221825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 157.500 | − | 931.783i | 0.280749 | − | 1.66093i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 70.9930i | 0.126098i | 0.998010 | + | 0.0630488i | \(0.0200824\pi\) | ||||
−0.998010 | + | 0.0630488i | \(0.979918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −508.000 | − | 402.293i | −0.895944 | − | 0.709512i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 976.153i | − | 1.71556i | −0.514018 | − | 0.857780i | \(-0.671843\pi\) | ||
0.514018 | − | 0.857780i | \(-0.328157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 286.000 | 0.500876 | 0.250438 | − | 0.968133i | \(-0.419425\pi\) | ||||
0.250438 | + | 0.968133i | \(0.419425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −735.000 | − | 124.238i | −1.28272 | − | 0.216820i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −487.000 | −0.844021 | −0.422010 | − | 0.906591i | \(-0.638675\pi\) | ||||
−0.422010 | + | 0.906591i | \(0.638675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 96.5000 | − | 570.902i | 0.166667 | − | 0.986013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 141.986i | 0.244382i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −630.000 | −1.08062 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 585.692i | 0.997772i | 0.866668 | + | 0.498886i | \(0.166257\pi\) | ||||
−0.866668 | + | 0.498886i | \(0.833743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −506.000 | −0.859083 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −105.000 | − | 17.7482i | −0.177665 | − | 0.0300309i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 88.7412i | 0.149648i | 0.997197 | + | 0.0748239i | \(0.0238395\pi\) | ||||
−0.997197 | + | 0.0748239i | \(0.976161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.00000 | + | 11.8322i | −0.00335008 | + | 0.0198194i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 638.937i | − | 1.06667i | −0.845903 | − | 0.533336i | \(-0.820938\pi\) | ||
0.845903 | − | 0.533336i | \(-0.179062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −271.000 | −0.450915 | −0.225458 | − | 0.974253i | \(-0.572388\pi\) | ||||
−0.225458 | + | 0.974253i | \(0.572388\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 960.500 | + | 334.259i | 1.59287 | + | 0.554326i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −404.000 | −0.665568 | −0.332784 | − | 0.943003i | \(-0.607988\pi\) | ||||
−0.332784 | + | 0.943003i | \(0.607988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −840.000 | − | 141.986i | −1.37931 | − | 0.233146i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 70.9930i | − | 0.116191i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.0000 | −0.0554649 | −0.0277325 | − | 0.999615i | \(-0.508829\pi\) | ||||
−0.0277325 | + | 0.999615i | \(0.508829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 425.958i | 0.690369i | 0.938535 | + | 0.345185i | \(0.112184\pi\) | ||||
−0.938535 | + | 0.345185i | \(0.887816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1046.00 | −1.68982 | −0.844911 | − | 0.534907i | \(-0.820347\pi\) | ||||
−0.844911 | + | 0.534907i | \(0.820347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 840.000 | + | 461.454i | 1.35266 | + | 0.743082i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 425.958i | 0.683720i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 577.500 | + | 97.6153i | 0.921053 | + | 0.155686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 283.972i | − | 0.451466i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 106.000 | 0.167987 | 0.0839937 | − | 0.996466i | \(-0.473232\pi\) | ||||
0.0839937 | + | 0.996466i | \(0.473232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 104.500 | − | 618.230i | 0.165087 | − | 0.976667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.0000 | 0.0470958 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −315.000 | + | 905.160i | −0.492958 | + | 1.41653i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 212.979i | − | 0.332260i | −0.986104 | − | 0.166130i | \(-0.946873\pi\) | ||
0.986104 | − | 0.166130i | \(-0.0531272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −566.000 | −0.880249 | −0.440124 | − | 0.897937i | \(-0.645066\pi\) | ||||
−0.440124 | + | 0.897937i | \(0.645066\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 496.951i | − | 0.768085i | −0.923316 | − | 0.384042i | \(-0.874532\pi\) | ||
0.923316 | − | 0.384042i | \(-0.125468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1260.00 | 1.94145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 184.000 | − | 1088.56i | 0.282642 | − | 1.67213i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 496.951i | 0.761027i | 0.924775 | + | 0.380514i | \(0.124253\pi\) | ||||
−0.924775 | + | 0.380514i | \(0.875747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −858.500 | − | 298.762i | −1.30670 | − | 0.454737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 550.195i | − | 0.834894i | −0.908701 | − | 0.417447i | \(-0.862925\pi\) | ||
0.908701 | − | 0.417447i | \(-0.137075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −298.000 | −0.450832 | −0.225416 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225416 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −105.000 | − | 17.7482i | −0.158371 | − | 0.0267696i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1260.00 | 1.88906 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −74.0000 | + | 437.790i | −0.110613 | + | 0.654394i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 283.972i | − | 0.423207i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −274.000 | −0.407132 | −0.203566 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203566 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 993.901i | − | 1.46810i | −0.679097 | − | 0.734048i | \(-0.737629\pi\) | ||
0.679097 | − | 0.734048i | \(-0.262371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 176.000 | 0.259205 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 124.238i | − | 0.181900i | −0.995855 | − | 0.0909500i | \(-0.971010\pi\) | ||
0.995855 | − | 0.0909500i | \(-0.0289903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.0000 | + | 343.133i | −0.0844250 | + | 0.499465i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 70.9930i | 0.103038i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 373.000 | 0.539797 | 0.269899 | − | 0.962889i | \(-0.413010\pi\) | ||||
0.269899 | + | 0.962889i | \(0.413010\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −420.000 | + | 1206.88i | −0.606061 | + | 1.74153i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 945.000 | 1.35581 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 630.000 | + | 106.489i | 0.901288 | + | 0.152345i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 674.433i | 0.962101i | 0.876693 | + | 0.481051i | \(0.159745\pi\) | ||||
−0.876693 | + | 0.481051i | \(0.840255\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 176.000 | 0.250356 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1135.89i | − | 1.60663i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −184.000 | −0.259520 | −0.129760 | − | 0.991545i | \(-0.541421\pi\) | ||||
−0.129760 | + | 0.991545i | \(0.541421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 578.000 | + | 201.147i | 0.812940 | + | 0.282907i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1632.84i | 2.29010i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −525.000 | − | 88.7412i | −0.732218 | − | 0.123767i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 638.937i | − | 0.888646i | −0.895867 | − | 0.444323i | \(-0.853444\pi\) | ||
0.895867 | − | 0.444323i | \(-0.146556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 208.000 | 0.288488 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.5000 | + | 174.524i | −0.0408022 | + | 0.241389i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −758.000 | −1.04264 | −0.521320 | − | 0.853361i | \(-0.674560\pi\) | ||||
−0.521320 | + | 0.853361i | \(0.674560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −391.000 | − | 615.272i | −0.536351 | − | 0.843995i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1100.39i | − | 1.50532i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.0354707 | 0.0177353 | − | 0.999843i | \(-0.494354\pi\) | ||||
0.0177353 | + | 0.999843i | \(0.494354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2005.55i | − | 2.72124i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1298.00 | −1.75643 | −0.878214 | − | 0.478268i | \(-0.841265\pi\) | ||||
−0.878214 | + | 0.478268i | \(0.841265\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.0000 | − | 65.0769i | 0.0148448 | − | 0.0878230i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 532.447i | − | 0.716618i | −0.933603 | − | 0.358309i | \(-0.883353\pi\) | ||
0.933603 | − | 0.358309i | \(-0.116647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.5000 | + | 150.860i | −0.0702811 | + | 0.201955i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 141.986i | 0.189567i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 478.000 | 0.636485 | 0.318242 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318242 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −367.500 | − | 62.1188i | −0.488048 | − | 0.0824951i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1072.00 | −1.41612 | −0.708058 | − | 0.706154i | \(-0.750429\pi\) | ||||
−0.708058 | + | 0.706154i | \(0.750429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 315.000 | − | 1863.57i | 0.415020 | − | 2.45529i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 550.195i | 0.722990i | 0.932374 | + | 0.361495i | \(0.117734\pi\) | ||||
−0.932374 | + | 0.361495i | \(0.882266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1408.00 | −1.84535 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 141.986i | − | 0.185119i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −169.000 | −0.219766 | −0.109883 | − | 0.993945i | \(-0.535048\pi\) | ||||
−0.109883 | + | 0.993945i | \(0.535048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1470.00 | − | 248.475i | −1.90661 | − | 0.322277i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 461.454i | − | 0.596965i | −0.954415 | − | 0.298483i | \(-0.903519\pi\) | ||
0.954415 | − | 0.298483i | \(-0.0964805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −64.0000 | + | 378.629i | −0.0823681 | + | 0.487296i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 585.692i | 0.751851i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1890.00 | 2.41997 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −840.000 | − | 461.454i | −1.07280 | − | 0.589341i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −878.000 | −1.11563 | −0.557814 | − | 0.829966i | \(-0.688360\pi\) | ||||
−0.557814 | + | 0.829966i | \(0.688360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 735.000 | + | 124.238i | 0.931559 | + | 0.157462i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 993.901i | − | 1.25651i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −0.0403531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 816.419i | − | 1.02437i | −0.858877 | − | 0.512183i | \(-0.828837\pi\) | ||
0.858877 | − | 0.512183i | \(-0.171163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 630.000 | 0.788486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −157.500 | + | 452.580i | −0.196629 | + | 0.565019i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1792.57i | 2.23234i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1050.00 | − | 177.482i | −1.30112 | − | 0.219929i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 212.979i | 0.263262i | 0.991299 | + | 0.131631i | \(0.0420214\pi\) | ||||
−0.991299 | + | 0.131631i | \(0.957979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 106.000 | 0.130703 | 0.0653514 | − | 0.997862i | \(-0.479183\pi\) | ||||
0.0653514 | + | 0.997862i | \(0.479183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −89.0000 | + | 526.531i | −0.109471 | + | 0.647640i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 682.000 | 0.834761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 136.000 | + | 47.3286i | 0.166056 | + | 0.0577883i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 603.440i | − | 0.735006i | −0.930022 | − | 0.367503i | \(-0.880213\pi\) | ||
0.930022 | − | 0.367503i | \(-0.119787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1348.00 | 1.63791 | 0.818955 | − | 0.573858i | \(-0.194554\pi\) | ||||
0.818955 | + | 0.573858i | \(0.194554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1082.64i | 1.30912i | 0.756010 | + | 0.654560i | \(0.227146\pi\) | ||||
−0.756010 | + | 0.654560i | \(0.772854\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1222.00 | −1.47407 | −0.737033 | − | 0.675857i | \(-0.763774\pi\) | ||||
−0.737033 | + | 0.675857i | \(0.763774\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 101.000 | − | 597.524i | 0.121540 | − | 0.719042i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 266.224i | 0.319596i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 598.000 | − | 1088.56i | 0.714456 | − | 1.30055i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 425.958i | − | 0.507697i | −0.967244 | − | 0.253848i | \(-0.918304\pi\) | ||
0.967244 | − | 0.253848i | \(-0.0816965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −419.000 | −0.498216 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 210.000 | + | 35.4965i | 0.249110 | + | 0.0421073i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1552.00 | 1.83235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 98.5000 | − | 582.734i | 0.116019 | − | 0.686377i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 567.944i | − | 0.667384i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 902.000 | 1.05744 | 0.528722 | − | 0.848795i | \(-0.322671\pi\) | ||||
0.528722 | + | 0.848795i | \(0.322671\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 834.167i | 0.973357i | 0.873581 | + | 0.486679i | \(0.161792\pi\) | ||||
−0.873581 | + | 0.486679i | \(0.838208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 577.000 | 0.671711 | 0.335856 | − | 0.941913i | \(-0.390975\pi\) | ||||
0.335856 | + | 0.941913i | \(0.390975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1260.00 | − | 212.979i | −1.46341 | − | 0.247362i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1455.36i | − | 1.68639i | −0.537607 | − | 0.843196i | \(-0.680672\pi\) | ||
0.537607 | − | 0.843196i | \(-0.319328\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | − | 76.9090i | 0.0149942 | − | 0.0887071i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1206.88i | − | 1.38882i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −226.000 | −0.259472 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 187.000 | + | 65.0769i | 0.214204 | + | 0.0745440i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 488.000 | 0.556442 | 0.278221 | − | 0.960517i | \(-0.410255\pi\) | ||||
0.278221 | + | 0.960517i | \(0.410255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1260.00 | − | 212.979i | −1.43345 | − | 0.242297i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1064.89i | − | 1.20873i | −0.796706 | − | 0.604367i | \(-0.793426\pi\) | ||
0.796706 | − | 0.604367i | \(-0.206574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 313.000 | 0.354473 | 0.177237 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177237 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1135.89i | − | 1.28059i | −0.768127 | − | 0.640297i | \(-0.778811\pi\) | ||
0.768127 | − | 0.640297i | \(-0.221189\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −848.000 | −0.953881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −892.500 | + | 1127.01i | −1.00168 | + | 1.26489i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 390.461i | 0.437247i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −210.000 | − | 35.4965i | −0.234114 | − | 0.0395724i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1632.84i | − | 1.81628i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −630.000 | −0.699223 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −248.000 | + | 1467.19i | −0.274640 | + | 1.62479i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −374.000 | −0.412348 | −0.206174 | − | 0.978515i | \(-0.566101\pi\) | ||||
−0.206174 | + | 0.978515i | \(0.566101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 420.000 | − | 1206.88i | 0.462046 | − | 1.32770i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 638.937i | 0.701357i | 0.936496 | + | 0.350679i | \(0.114049\pi\) | ||||
−0.936496 | + | 0.350679i | \(0.885951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 315.000 | 0.345016 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 567.944i | 0.619350i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1286.00 | −1.39935 | −0.699674 | − | 0.714463i | \(-0.746671\pi\) | ||||
−0.699674 | + | 0.714463i | \(0.746671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63.5000 | + | 375.671i | −0.0689468 | + | 0.407895i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 212.979i | − | 0.230746i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 221.000 | + | 76.9090i | 0.238403 | + | 0.0829655i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 496.951i | 0.534931i | 0.963567 | + | 0.267465i | \(0.0861861\pi\) | ||||
−0.963567 | + | 0.267465i | \(0.913814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −165.000 | −0.177229 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 840.000 | + | 141.986i | 0.900322 | + | 0.152182i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1597.00 | −1.70438 | −0.852188 | − | 0.523236i | \(-0.824725\pi\) | ||||
−0.852188 | + | 0.523236i | \(0.824725\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.0000 | − | 171.566i | 0.0308839 | − | 0.182712i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 248.475i | − | 0.264055i | −0.991246 | − | 0.132027i | \(-0.957851\pi\) | ||
0.991246 | − | 0.132027i | \(-0.0421487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1890.00 | 2.00424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 354.965i | − | 0.374831i | −0.982281 | − | 0.187415i | \(-0.939989\pi\) | ||
0.982281 | − | 0.187415i | \(-0.0600110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 202.000 | 0.212856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 840.000 | + | 141.986i | 0.883281 | + | 0.149302i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 621.188i | − | 0.651824i | −0.945400 | − | 0.325912i | \(-0.894329\pi\) | ||
0.945400 | − | 0.325912i | \(-0.105671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −315.000 | + | 1863.57i | −0.329154 | + | 1.94730i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 425.958i | 0.444169i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1155.00 | 1.20187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −52.5000 | + | 150.860i | −0.0545171 | + | 0.156656i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1576.00 | 1.62978 | 0.814891 | − | 0.579614i | \(-0.196797\pi\) | ||||
0.814891 | + | 0.579614i | \(0.196797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 577.500 | + | 97.6153i | 0.595975 | + | 0.100738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1153.64i | 1.18809i | 0.804432 | + | 0.594045i | \(0.202470\pi\) | ||||
−0.804432 | + | 0.594045i | \(0.797530\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1016.00 | −1.04419 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 479.202i | 0.490484i | 0.969462 | + | 0.245242i | \(0.0788674\pi\) | ||||
−0.969462 | + | 0.245242i | \(0.921133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 945.000 | 0.965271 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1496.00 | − | 520.615i | −1.52497 | − | 0.530698i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1419.86i | 1.44441i | 0.691677 | + | 0.722207i | \(0.256872\pi\) | ||||
−0.691677 | + | 0.722207i | \(0.743128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −840.000 | − | 141.986i | −0.851064 | − | 0.143856i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2200.78i | − | 2.22526i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 676.000 | 0.682139 | 0.341070 | − | 0.940038i | \(-0.389211\pi\) | ||||
0.341070 | + | 0.940038i | \(0.389211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 128.500 | − | 760.216i | 0.129406 | − | 0.765575i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1004.00 | 1.00702 | 0.503511 | − | 0.863989i | \(-0.332042\pi\) | ||||
0.503511 | + | 0.863989i | \(0.332042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −208.000 | + | 378.629i | −0.208208 | + | 0.379008i |
(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 | 1200.3.l.k.401.2 | 2 | ||
3.2 | odd | 2 | inner | 1200.3.l.k.401.1 | 2 | ||
4.3 | odd | 2 | 300.3.g.g.101.1 | yes | 2 | ||
5.2 | odd | 4 | 1200.3.c.j.449.4 | 4 | |||
5.3 | odd | 4 | 1200.3.c.j.449.1 | 4 | |||
5.4 | even | 2 | 1200.3.l.m.401.1 | 2 | |||
12.11 | even | 2 | 300.3.g.g.101.2 | yes | 2 | ||
15.2 | even | 4 | 1200.3.c.j.449.2 | 4 | |||
15.8 | even | 4 | 1200.3.c.j.449.3 | 4 | |||
15.14 | odd | 2 | 1200.3.l.m.401.2 | 2 | |||
20.3 | even | 4 | 300.3.b.d.149.4 | 4 | |||
20.7 | even | 4 | 300.3.b.d.149.1 | 4 | |||
20.19 | odd | 2 | 300.3.g.f.101.2 | yes | 2 | ||
60.23 | odd | 4 | 300.3.b.d.149.2 | 4 | |||
60.47 | odd | 4 | 300.3.b.d.149.3 | 4 | |||
60.59 | even | 2 | 300.3.g.f.101.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.b.d.149.1 | 4 | 20.7 | even | 4 | |||
300.3.b.d.149.2 | 4 | 60.23 | odd | 4 | |||
300.3.b.d.149.3 | 4 | 60.47 | odd | 4 | |||
300.3.b.d.149.4 | 4 | 20.3 | even | 4 | |||
300.3.g.f.101.1 | ✓ | 2 | 60.59 | even | 2 | ||
300.3.g.f.101.2 | yes | 2 | 20.19 | odd | 2 | ||
300.3.g.g.101.1 | yes | 2 | 4.3 | odd | 2 | ||
300.3.g.g.101.2 | yes | 2 | 12.11 | even | 2 | ||
1200.3.c.j.449.1 | 4 | 5.3 | odd | 4 | |||
1200.3.c.j.449.2 | 4 | 15.2 | even | 4 | |||
1200.3.c.j.449.3 | 4 | 15.8 | even | 4 | |||
1200.3.c.j.449.4 | 4 | 5.2 | odd | 4 | |||
1200.3.l.k.401.1 | 2 | 3.2 | odd | 2 | inner | ||
1200.3.l.k.401.2 | 2 | 1.1 | even | 1 | trivial | ||
1200.3.l.m.401.1 | 2 | 5.4 | even | 2 | |||
1200.3.l.m.401.2 | 2 | 15.14 | odd | 2 |