Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(449,1200)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.c (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: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 17x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(-2.95804 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.449 |
Dual form | 1200.3.c.j.449.1 |
$q$-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 | ||||||||
\(3\) | −2.95804 | + | 0.500000i | −0.986013 | + | 0.166667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8.00000i | − | 1.14286i | −0.820652 | − | 0.571429i | \(-0.806389\pi\) | ||
0.820652 | − | 0.571429i | \(-0.193611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.50000 | − | 2.95804i | 0.944444 | − | 0.328671i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 17.7482i | − | 1.61348i | −0.590909 | − | 0.806738i | \(-0.701231\pi\) | ||
0.590909 | − | 0.806738i | \(-0.298769\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.153846i | −0.997037 | − | 0.0769231i | \(-0.975490\pi\) | ||
0.997037 | − | 0.0769231i | \(-0.0245096\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.7482 | 1.04401 | 0.522007 | − | 0.852941i | \(-0.325183\pi\) | ||||
0.522007 | + | 0.852941i | \(0.325183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.0000 | 0.578947 | 0.289474 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289474 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | + | 23.6643i | 0.190476 | + | 1.12687i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −35.4965 | −1.54333 | −0.771663 | − | 0.636032i | \(-0.780575\pi\) | ||||
−0.771663 | + | 0.636032i | \(0.780575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −23.6643 | + | 13.0000i | −0.876456 | + | 0.481481i | ||||
\(28\) | 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 | ||||||||
\(33\) | 8.87412 | + | 52.5000i | 0.268913 | + | 1.59091i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 16.0000i | − | 0.432432i | −0.976346 | − | 0.216216i | \(-0.930628\pi\) | ||
0.976346 | − | 0.216216i | \(-0.0693716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 5.91608i | 0.0256410 | + | 0.151694i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.2447i | 1.29865i | 0.760510 | + | 0.649326i | \(0.224949\pi\) | ||||
−0.760510 | + | 0.649326i | \(0.775051\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.0000i | 1.44186i | 0.693008 | + | 0.720930i | \(0.256285\pi\) | ||||
−0.693008 | + | 0.720930i | \(0.743715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −35.4965 | −0.755244 | −0.377622 | − | 0.925960i | \(-0.623258\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.0000 | −0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.5000 | + | 8.87412i | −1.02941 | + | 0.174002i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.4965 | −0.669745 | −0.334872 | − | 0.942263i | \(-0.608693\pi\) | ||||
−0.334872 | + | 0.942263i | \(0.608693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −32.5384 | + | 5.50000i | −0.570850 | + | 0.0964912i | ||||
\(58\) | 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 | ||||||||
\(63\) | −23.6643 | − | 68.0000i | −0.375624 | − | 1.07937i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 113.000i | − | 1.68657i | −0.537469 | − | 0.843284i | \(-0.680619\pi\) | ||
0.537469 | − | 0.843284i | \(-0.319381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 105.000 | − | 17.7482i | 1.52174 | − | 0.257221i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 106.489i | 1.49985i | 0.661522 | + | 0.749926i | \(0.269911\pi\) | ||||
−0.661522 | + | 0.749926i | \(0.730089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 101.000i | − | 1.38356i | −0.722108 | − | 0.691781i | \(-0.756826\pi\) | ||
0.722108 | − | 0.691781i | \(-0.243174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −141.986 | −1.84397 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.0000 | 0.860759 | 0.430380 | − | 0.902648i | \(-0.358380\pi\) | ||||
0.430380 | + | 0.902648i | \(0.358380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 63.5000 | − | 50.2867i | 0.783951 | − | 0.620823i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.7482 | 0.213834 | 0.106917 | − | 0.994268i | \(-0.465902\pi\) | ||||
0.106917 | + | 0.994268i | \(0.465902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.7482 | + | 105.000i | 0.204003 | + | 1.20690i | ||||
\(88\) | 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 | ||||||||
\(93\) | −136.070 | + | 23.0000i | −1.46312 | + | 0.247312i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 22.0000i | − | 0.226804i | −0.993549 | − | 0.113402i | \(-0.963825\pi\) | ||
0.993549 | − | 0.113402i | \(-0.0361748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −52.5000 | − | 150.860i | −0.530303 | − | 1.52384i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 141.986i | − | 1.40580i | −0.711288 | − | 0.702901i | \(-0.751888\pi\) | ||
0.711288 | − | 0.702901i | \(-0.248112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26.0000i | 0.252427i | 0.992003 | + | 0.126214i | \(0.0402825\pi\) | ||||
−0.992003 | + | 0.126214i | \(0.959718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.7482 | −0.165871 | −0.0829357 | − | 0.996555i | \(-0.526430\pi\) | ||||
−0.0829357 | + | 0.996555i | \(0.526430\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176.000 | −1.61468 | −0.807339 | − | 0.590087i | \(-0.799093\pi\) | ||||
−0.807339 | + | 0.590087i | \(0.799093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | + | 47.3286i | 0.0720721 | + | 0.426384i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −124.238 | −1.09945 | −0.549724 | − | 0.835346i | \(-0.685267\pi\) | ||||
−0.549724 | + | 0.835346i | \(0.685267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.91608 | − | 17.0000i | −0.0505648 | − | 0.145299i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 141.986i | − | 1.19316i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −194.000 | −1.60331 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.6224 | − | 157.500i | −0.216442 | − | 1.28049i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000i | 0.834646i | 0.908758 | + | 0.417323i | \(0.137032\pi\) | ||||
−0.908758 | + | 0.417323i | \(0.862968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31.0000 | − | 183.398i | −0.240310 | − | 1.42169i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.9930i | 0.541931i | 0.962589 | + | 0.270965i | \(0.0873429\pi\) | ||||
−0.962589 | + | 0.270965i | \(0.912657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 88.0000i | − | 0.661654i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −53.2447 | −0.388648 | −0.194324 | − | 0.980937i | \(-0.562251\pi\) | ||||
−0.194324 | + | 0.980937i | \(0.562251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −127.000 | −0.913669 | −0.456835 | − | 0.889552i | \(-0.651017\pi\) | ||||
−0.456835 | + | 0.889552i | \(0.651017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 105.000 | − | 17.7482i | 0.744681 | − | 0.125874i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35.4965 | −0.248227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 44.3706 | − | 7.50000i | 0.301841 | − | 0.0510204i | ||||
\(148\) | 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 | ||||||||
\(153\) | 150.860 | − | 52.5000i | 0.986013 | − | 0.343137i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 38.0000i | 0.242038i | 0.992650 | + | 0.121019i | \(0.0386162\pi\) | ||||
−0.992650 | + | 0.121019i | \(0.961384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 105.000 | − | 17.7482i | 0.660377 | − | 0.111624i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 283.972i | 1.76380i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 47.0000i | 0.288344i | 0.989553 | + | 0.144172i | \(0.0460518\pi\) | ||||
−0.989553 | + | 0.144172i | \(0.953948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −177.482 | −1.06277 | −0.531384 | − | 0.847131i | \(-0.678328\pi\) | ||||
−0.531384 | + | 0.847131i | \(0.678328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 165.000 | 0.976331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 93.5000 | − | 32.5384i | 0.546784 | − | 0.190283i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 70.9930 | 0.410364 | 0.205182 | − | 0.978724i | \(-0.434221\pi\) | ||||
0.205182 | + | 0.978724i | \(0.434221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35.4965 | + | 210.000i | 0.200545 | + | 1.18644i | ||||
\(178\) | 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 | ||||||||
\(183\) | 47.3286 | − | 8.00000i | 0.258626 | − | 0.0437158i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 315.000i | − | 1.68449i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 104.000 | + | 189.315i | 0.550265 | + | 1.00166i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 248.475i | − | 1.30092i | −0.759541 | − | 0.650459i | \(-0.774577\pi\) | ||
0.759541 | − | 0.650459i | \(-0.225423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 193.000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 35.4965 | 0.180185 | 0.0900926 | − | 0.995933i | \(-0.471284\pi\) | ||||
0.0900926 | + | 0.995933i | \(0.471284\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.0201005 | −0.0100503 | − | 0.999949i | \(-0.503199\pi\) | ||||
−0.0100503 | + | 0.999949i | \(0.503199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 56.5000 | + | 334.259i | 0.281095 | + | 1.66298i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −283.972 | −1.39888 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −301.720 | + | 105.000i | −1.45758 | + | 0.507246i | ||||
\(208\) | 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 | ||||||||
\(213\) | −53.2447 | − | 315.000i | −0.249975 | − | 1.47887i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 368.000i | − | 1.69585i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 50.5000 | + | 298.762i | 0.230594 | + | 1.36421i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 35.4965i | − | 0.160618i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 148.000i | − | 0.663677i | −0.943336 | − | 0.331839i | \(-0.892331\pi\) | ||
0.943336 | − | 0.331839i | \(-0.107669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −116.000 | −0.506550 | −0.253275 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253275 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 420.000 | − | 70.9930i | 1.81818 | − | 0.307329i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 212.979 | 0.914072 | 0.457036 | − | 0.889448i | \(-0.348911\pi\) | ||||
0.457036 | + | 0.889448i | \(0.348911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −201.147 | + | 34.0000i | −0.848720 | + | 0.143460i | ||||
\(238\) | 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 | ||||||||
\(243\) | −162.692 | + | 180.500i | −0.669515 | + | 0.742798i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 22.0000i | − | 0.0890688i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −52.5000 | + | 8.87412i | −0.210843 | + | 0.0356390i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 124.238i | − | 0.494971i | −0.968892 | − | 0.247485i | \(-0.920396\pi\) | ||
0.968892 | − | 0.247485i | \(-0.0796042\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 630.000i | 2.49012i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 496.951 | 1.93366 | 0.966830 | − | 0.255420i | \(-0.0822138\pi\) | ||||
0.966830 | + | 0.255420i | \(0.0822138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −128.000 | −0.494208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −105.000 | − | 301.720i | −0.402299 | − | 1.15602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 248.475 | 0.944773 | 0.472387 | − | 0.881391i | \(-0.343393\pi\) | ||||
0.472387 | + | 0.881391i | \(0.343393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.6224 | + | 157.500i | 0.0997092 | + | 0.589888i | ||||
\(268\) | 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 | ||||||||
\(273\) | 47.3286 | − | 8.00000i | 0.173365 | − | 0.0293040i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 202.000i | − | 0.729242i | −0.931156 | − | 0.364621i | \(-0.881199\pi\) | ||
0.931156 | − | 0.364621i | \(-0.118801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 391.000 | − | 136.070i | 1.40143 | − | 0.487706i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 70.9930i | 0.252644i | 0.991989 | + | 0.126322i | \(0.0403173\pi\) | ||||
−0.991989 | + | 0.126322i | \(0.959683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 197.000i | 0.696113i | 0.937474 | + | 0.348057i | \(0.113158\pi\) | ||||
−0.937474 | + | 0.348057i | \(0.886842\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 425.958 | 1.48417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.0000 | 0.0899654 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0000 | + | 65.0769i | 0.0378007 | + | 0.223632i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −425.958 | −1.45378 | −0.726890 | − | 0.686754i | \(-0.759035\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 230.727 | + | 420.000i | 0.776859 | + | 1.41414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 70.9930i | 0.237435i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 496.000 | 1.64784 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 70.9930 | + | 420.000i | 0.234300 | + | 1.38614i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 127.000i | 0.413681i | 0.978375 | + | 0.206840i | \(0.0663181\pi\) | ||||
−0.978375 | + | 0.206840i | \(0.933682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0000 | − | 76.9090i | −0.0420712 | − | 0.248897i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 283.972i | 0.913093i | 0.889700 | + | 0.456546i | \(0.150914\pi\) | ||||
−0.889700 | + | 0.456546i | \(0.849086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 58.0000i | 0.185304i | 0.995699 | + | 0.0926518i | \(0.0295343\pi\) | ||||
−0.995699 | + | 0.0926518i | \(0.970466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −283.972 | −0.895810 | −0.447905 | − | 0.894081i | \(-0.647830\pi\) | ||||
−0.447905 | + | 0.894081i | \(0.647830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −630.000 | −1.97492 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52.5000 | − | 8.87412i | 0.163551 | − | 0.0276452i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 195.231 | 0.604429 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 520.615 | − | 88.0000i | 1.59209 | − | 0.269113i | ||||
\(328\) | 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 | ||||||||
\(333\) | −47.3286 | − | 136.000i | −0.142128 | − | 0.408408i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 127.000i | − | 0.376855i | −0.982087 | − | 0.188427i | \(-0.939661\pi\) | ||
0.982087 | − | 0.188427i | \(-0.0603390\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 367.500 | − | 62.1188i | 1.08407 | − | 0.183241i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 816.419i | − | 2.39419i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 272.000i | − | 0.793003i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 372.713 | 1.07410 | 0.537050 | − | 0.843550i | \(-0.319538\pi\) | ||||
0.537050 | + | 0.843550i | \(0.319538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 292.000 | 0.836676 | 0.418338 | − | 0.908291i | \(-0.362613\pi\) | ||||
0.418338 | + | 0.908291i | \(0.362613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.0000 | + | 47.3286i | 0.0740741 | + | 0.134839i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 638.937 | 1.81002 | 0.905009 | − | 0.425392i | \(-0.139864\pi\) | ||||
0.905009 | + | 0.425392i | \(0.139864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 70.9930 | + | 420.000i | 0.198860 | + | 1.17647i | ||||
\(358\) | 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 | ||||||||
\(363\) | 573.860 | − | 97.0000i | 1.58088 | − | 0.267218i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 668.000i | − | 1.82016i | −0.414429 | − | 0.910082i | \(-0.636019\pi\) | ||
0.414429 | − | 0.910082i | \(-0.363981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 157.500 | + | 452.580i | 0.426829 | + | 1.22650i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 283.972i | 0.765423i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 242.000i | − | 0.648794i | −0.945921 | − | 0.324397i | \(-0.894839\pi\) | ||
0.945921 | − | 0.324397i | \(-0.105161\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −70.9930 | −0.188310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 191.000 | 0.503958 | 0.251979 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251979 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −53.0000 | − | 313.552i | −0.139108 | − | 0.822972i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 283.972 | 0.741441 | 0.370720 | − | 0.928745i | \(-0.379111\pi\) | ||||
0.370720 | + | 0.928745i | \(0.379111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 183.398 | + | 527.000i | 0.473898 | + | 1.36176i | ||||
\(388\) | 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 | ||||||||
\(393\) | −35.4965 | − | 210.000i | −0.0903218 | − | 0.534351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 772.000i | − | 1.94458i | −0.233769 | − | 0.972292i | \(-0.575106\pi\) | ||
0.233769 | − | 0.972292i | \(-0.424894\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.0000 | + | 260.308i | 0.110276 | + | 0.652400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 266.224i | 0.663899i | 0.943297 | + | 0.331950i | \(0.107706\pi\) | ||||
−0.943297 | + | 0.331950i | \(0.892294\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 92.0000i | − | 0.228288i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −283.972 | −0.697719 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −701.000 | −1.71394 | −0.856968 | − | 0.515369i | \(-0.827655\pi\) | ||||
−0.856968 | + | 0.515369i | \(0.827655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 157.500 | − | 26.6224i | 0.383212 | − | 0.0647746i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −567.944 | −1.37517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 375.671 | − | 63.5000i | 0.900890 | − | 0.152278i | ||||
\(418\) | 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 | ||||||||
\(423\) | −301.720 | + | 105.000i | −0.713286 | + | 0.248227i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 128.000i | 0.299766i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 105.000 | − | 17.7482i | 0.244755 | − | 0.0413712i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 212.979i | − | 0.494151i | −0.968996 | − | 0.247075i | \(-0.920531\pi\) | ||
0.968996 | − | 0.247075i | \(-0.0794695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 463.000i | 1.06928i | 0.845079 | + | 0.534642i | \(0.179554\pi\) | ||||
−0.845079 | + | 0.534642i | \(0.820446\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −390.461 | −0.893504 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −394.000 | −0.897494 | −0.448747 | − | 0.893659i | \(-0.648130\pi\) | ||||
−0.448747 | + | 0.893659i | \(0.648130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −127.500 | + | 44.3706i | −0.289116 | + | 0.100614i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 656.685 | 1.48236 | 0.741179 | − | 0.671307i | \(-0.234267\pi\) | ||||
0.741179 | + | 0.671307i | \(0.234267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 53.2447 | + | 315.000i | 0.119116 | + | 0.704698i | ||||
\(448\) | 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 | ||||||||
\(453\) | 485.119 | − | 82.0000i | 1.07090 | − | 0.181015i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 509.000i | 1.11379i | 0.830584 | + | 0.556893i | \(0.188007\pi\) | ||||
−0.830584 | + | 0.556893i | \(0.811993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −420.000 | + | 230.727i | −0.915033 | + | 0.502673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 212.979i | − | 0.461993i | −0.972955 | − | 0.230997i | \(-0.925801\pi\) | ||
0.972955 | − | 0.230997i | \(-0.0741986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 64.0000i | − | 0.138229i | −0.997609 | − | 0.0691145i | \(-0.977983\pi\) | ||
0.997609 | − | 0.0691145i | \(-0.0220174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −638.937 | −1.36817 | −0.684086 | − | 0.729401i | \(-0.739799\pi\) | ||||
−0.684086 | + | 0.729401i | \(0.739799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −904.000 | −1.92751 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.0000 | − | 112.406i | −0.0403397 | − | 0.238653i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1100.39 | 2.32641 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −301.720 | + | 105.000i | −0.632537 | + | 0.220126i | ||||
\(478\) | 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 | ||||||||
\(483\) | −141.986 | − | 840.000i | −0.293967 | − | 1.73913i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 382.000i | 0.784394i | 0.919881 | + | 0.392197i | \(0.128285\pi\) | ||||
−0.919881 | + | 0.392197i | \(0.871715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.5000 | − | 139.028i | −0.0480573 | − | 0.284311i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 709.930i | − | 1.44589i | −0.690908 | − | 0.722943i | \(-0.742789\pi\) | ||
0.690908 | − | 0.722943i | \(-0.257211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 630.000i | − | 1.27789i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 851.915 | 1.71412 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −94.0000 | −0.188377 | −0.0941884 | − | 0.995554i | \(-0.530026\pi\) | ||||
−0.0941884 | + | 0.995554i | \(0.530026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 525.000 | − | 88.7412i | 1.04790 | − | 0.177128i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −780.923 | −1.55253 | −0.776265 | − | 0.630407i | \(-0.782888\pi\) | ||||
−0.776265 | + | 0.630407i | \(0.782888\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −488.077 | + | 82.5000i | −0.962676 | + | 0.162722i | ||||
\(508\) | 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 | ||||||||
\(513\) | −260.308 | + | 143.000i | −0.507422 | + | 0.278752i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 630.000i | 1.21857i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −210.000 | + | 35.4965i | −0.404624 | + | 0.0683940i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 798.671i | 1.53296i | 0.642270 | + | 0.766479i | \(0.277993\pi\) | ||||
−0.642270 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 467.000i | 0.892925i | 0.894802 | + | 0.446463i | \(0.147316\pi\) | ||||
−0.894802 | + | 0.446463i | \(0.852684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 816.419 | 1.54918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 731.000 | 1.38185 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −210.000 | − | 603.440i | −0.395480 | − | 1.13642i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 106.489 | 0.199793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.87412 | + | 52.5000i | 0.0165254 | + | 0.0977654i | ||||
\(538\) | 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 | ||||||||
\(543\) | 313.552 | − | 53.0000i | 0.577444 | − | 0.0976059i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 779.000i | − | 1.42413i | −0.702113 | − | 0.712066i | \(-0.747760\pi\) | ||
0.702113 | − | 0.712066i | \(-0.252240\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −136.000 | + | 47.3286i | −0.247723 | + | 0.0862088i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 390.461i | − | 0.708641i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 544.000i | − | 0.983725i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 745.426 | 1.33829 | 0.669144 | − | 0.743133i | \(-0.266661\pi\) | ||||
0.669144 | + | 0.743133i | \(0.266661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 124.000 | 0.221825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 157.500 | + | 931.783i | 0.280749 | + | 1.66093i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −70.9930 | −0.126098 | −0.0630488 | − | 0.998010i | \(-0.520082\pi\) | ||||
−0.0630488 | + | 0.998010i | \(0.520082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −402.293 | − | 508.000i | −0.709512 | − | 0.895944i | ||||
\(568\) | 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 | ||||||||
\(573\) | 124.238 | + | 735.000i | 0.216820 | + | 1.28272i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 487.000i | − | 0.844021i | −0.906591 | − | 0.422010i | \(-0.861325\pi\) | ||
0.906591 | − | 0.422010i | \(-0.138675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −96.5000 | − | 570.902i | −0.166667 | − | 0.986013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 141.986i | − | 0.244382i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 630.000i | 1.08062i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 585.692 | 0.997772 | 0.498886 | − | 0.866668i | \(-0.333743\pi\) | ||||
0.498886 | + | 0.866668i | \(0.333743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 506.000 | 0.859083 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −105.000 | + | 17.7482i | −0.177665 | + | 0.0300309i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −88.7412 | −0.149648 | −0.0748239 | − | 0.997197i | \(-0.523839\pi\) | ||||
−0.0748239 | + | 0.997197i | \(0.523839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.8322 | − | 2.00000i | 0.0198194 | − | 0.00335008i | ||||
\(598\) | 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 | ||||||||
\(603\) | −334.259 | − | 960.500i | −0.554326 | − | 1.59287i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 404.000i | − | 0.665568i | −0.943003 | − | 0.332784i | \(-0.892012\pi\) | ||
0.943003 | − | 0.332784i | \(-0.107988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 840.000 | − | 141.986i | 1.37931 | − | 0.233146i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 70.9930i | 0.116191i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.0000i | 0.0554649i | 0.999615 | + | 0.0277325i | \(0.00882865\pi\) | ||||
−0.999615 | + | 0.0277325i | \(0.991171\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 425.958 | 0.690369 | 0.345185 | − | 0.938535i | \(-0.387816\pi\) | ||||
0.345185 | + | 0.938535i | \(0.387816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1046.00 | 1.68982 | 0.844911 | − | 0.534907i | \(-0.179653\pi\) | ||||
0.844911 | + | 0.534907i | \(0.179653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 840.000 | − | 461.454i | 1.35266 | − | 0.743082i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −425.958 | −0.683720 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 97.6153 | + | 577.500i | 0.155686 | + | 0.921053i | ||||
\(628\) | 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 | ||||||||
\(633\) | 618.230 | − | 104.500i | 0.976667 | − | 0.165087i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.0000i | 0.0470958i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 315.000 | + | 905.160i | 0.492958 | + | 1.41653i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 212.979i | 0.332260i | 0.986104 | + | 0.166130i | \(0.0531272\pi\) | ||||
−0.986104 | + | 0.166130i | \(0.946873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 566.000i | 0.880249i | 0.897937 | + | 0.440124i | \(0.145066\pi\) | ||||
−0.897937 | + | 0.440124i | \(0.854934\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −496.951 | −0.768085 | −0.384042 | − | 0.923316i | \(-0.625468\pi\) | ||||
−0.384042 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1260.00 | −1.94145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 184.000 | + | 1088.56i | 0.282642 | + | 1.67213i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −496.951 | −0.761027 | −0.380514 | − | 0.924775i | \(-0.624253\pi\) | ||||
−0.380514 | + | 0.924775i | \(0.624253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −298.762 | − | 858.500i | −0.454737 | − | 1.30670i | ||||
\(658\) | 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 | ||||||||
\(663\) | 17.7482 | + | 105.000i | 0.0267696 | + | 0.158371i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1260.00i | 1.88906i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 74.0000 | + | 437.790i | 0.110613 | + | 0.654394i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 283.972i | 0.423207i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 274.000i | 0.407132i | 0.979061 | + | 0.203566i | \(0.0652532\pi\) | ||||
−0.979061 | + | 0.203566i | \(0.934747\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −993.901 | −1.46810 | −0.734048 | − | 0.679097i | \(-0.762371\pi\) | ||||
−0.734048 | + | 0.679097i | \(0.762371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −176.000 | −0.259205 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 124.238 | 0.181900 | 0.0909500 | − | 0.995855i | \(-0.471010\pi\) | ||||
0.0909500 | + | 0.995855i | \(0.471010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 343.133 | − | 58.0000i | 0.499465 | − | 0.0844250i | ||||
\(688\) | 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 | ||||||||
\(693\) | −1206.88 | + | 420.000i | −1.74153 | + | 0.606061i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 945.000i | 1.35581i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −630.000 | + | 106.489i | −0.901288 | + | 0.152345i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 674.433i | − | 0.962101i | −0.876693 | − | 0.481051i | \(-0.840255\pi\) | ||
0.876693 | − | 0.481051i | \(-0.159745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 176.000i | − | 0.250356i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1135.89 | −1.60663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 184.000 | 0.259520 | 0.129760 | − | 0.991545i | \(-0.458579\pi\) | ||||
0.129760 | + | 0.991545i | \(0.458579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 578.000 | − | 201.147i | 0.812940 | − | 0.282907i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1632.84 | −2.29010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −88.7412 | − | 525.000i | −0.123767 | − | 0.732218i | ||||
\(718\) | 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 | ||||||||
\(723\) | −174.524 | + | 29.5000i | −0.241389 | + | 0.0408022i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 758.000i | − | 1.04264i | −0.853361 | − | 0.521320i | \(-0.825440\pi\) | ||
0.853361 | − | 0.521320i | \(-0.174560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 391.000 | − | 615.272i | 0.536351 | − | 0.843995i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1100.39i | 1.50532i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.0000i | − | 0.0354707i | −0.999843 | − | 0.0177353i | \(-0.994354\pi\) | ||
0.999843 | − | 0.0177353i | \(-0.00564563\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2005.55 | −2.72124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1298.00 | 1.75643 | 0.878214 | − | 0.478268i | \(-0.158735\pi\) | ||||
0.878214 | + | 0.478268i | \(0.158735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.0000 | + | 65.0769i | 0.0148448 | + | 0.0878230i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 532.447 | 0.716618 | 0.358309 | − | 0.933603i | \(-0.383353\pi\) | ||||
0.358309 | + | 0.933603i | \(0.383353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 150.860 | − | 52.5000i | 0.201955 | − | 0.0702811i | ||||
\(748\) | 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 | ||||||||
\(753\) | 62.1188 | + | 367.500i | 0.0824951 | + | 0.488048i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1072.00i | − | 1.41612i | −0.706154 | − | 0.708058i | \(-0.749571\pi\) | ||
0.706154 | − | 0.708058i | \(-0.250429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −315.000 | − | 1863.57i | −0.415020 | − | 2.45529i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 550.195i | − | 0.722990i | −0.932374 | − | 0.361495i | \(-0.882266\pi\) | ||
0.932374 | − | 0.361495i | \(-0.117734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1408.00i | 1.84535i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −141.986 | −0.185119 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 169.000 | 0.219766 | 0.109883 | − | 0.993945i | \(-0.464952\pi\) | ||||
0.109883 | + | 0.993945i | \(0.464952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1470.00 | + | 248.475i | −1.90661 | + | 0.322277i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 461.454 | 0.596965 | 0.298483 | − | 0.954415i | \(-0.403519\pi\) | ||||
0.298483 | + | 0.954415i | \(0.403519\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 378.629 | − | 64.0000i | 0.487296 | − | 0.0823681i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 585.692i | 0.751851i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1890.00 | 2.41997 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 461.454 | + | 840.000i | 0.589341 | + | 1.07280i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 878.000i | − | 1.11563i | −0.829966 | − | 0.557814i | \(-0.811640\pi\) | ||
0.829966 | − | 0.557814i | \(-0.188360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −735.000 | + | 124.238i | −0.931559 | + | 0.157462i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 993.901i | 1.25651i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0000i | 0.0403531i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −816.419 | −1.02437 | −0.512183 | − | 0.858877i | \(-0.671163\pi\) | ||||
−0.512183 | + | 0.858877i | \(0.671163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −630.000 | −0.788486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −157.500 | − | 452.580i | −0.196629 | − | 0.565019i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1792.57 | −2.23234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −177.482 | − | 1050.00i | −0.219929 | − | 1.30112i | ||||
\(808\) | 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 | ||||||||
\(813\) | −526.531 | + | 89.0000i | −0.647640 | + | 0.109471i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 682.000i | 0.834761i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −136.000 | + | 47.3286i | −0.166056 | + | 0.0577883i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 603.440i | 0.735006i | 0.930022 | + | 0.367503i | \(0.119787\pi\) | ||||
−0.930022 | + | 0.367503i | \(0.880213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1348.00i | − | 1.63791i | −0.573858 | − | 0.818955i | \(-0.694554\pi\) | ||
0.573858 | − | 0.818955i | \(-0.305446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1082.64 | 1.30912 | 0.654560 | − | 0.756010i | \(-0.272854\pi\) | ||||
0.654560 | + | 0.756010i | \(0.272854\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1222.00 | 1.47407 | 0.737033 | − | 0.675857i | \(-0.236226\pi\) | ||||
0.737033 | + | 0.675857i | \(0.236226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 101.000 | + | 597.524i | 0.121540 | + | 0.719042i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −266.224 | −0.319596 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1088.56 | + | 598.000i | −1.30055 | + | 0.714456i | ||||
\(838\) | 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 | ||||||||
\(843\) | −35.4965 | − | 210.000i | −0.0421073 | − | 0.249110i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1552.00i | 1.83235i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −98.5000 | − | 582.734i | −0.116019 | − | 0.686377i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 567.944i | 0.667384i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 902.000i | − | 1.05744i | −0.848795 | − | 0.528722i | \(-0.822671\pi\) | ||
0.848795 | − | 0.528722i | \(-0.177329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 834.167 | 0.973357 | 0.486679 | − | 0.873581i | \(-0.338208\pi\) | ||||
0.486679 | + | 0.873581i | \(0.338208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −577.000 | −0.671711 | −0.335856 | − | 0.941913i | \(-0.609025\pi\) | ||||
−0.335856 | + | 0.941913i | \(0.609025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1260.00 | + | 212.979i | −1.46341 | + | 0.247362i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1455.36 | 1.68639 | 0.843196 | − | 0.537607i | \(-0.180672\pi\) | ||||
0.843196 | + | 0.537607i | \(0.180672\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −76.9090 | + | 13.0000i | −0.0887071 | + | 0.0149942i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1206.88i | − | 1.38882i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −226.000 | −0.259472 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −65.0769 | − | 187.000i | −0.0745440 | − | 0.214204i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 488.000i | 0.556442i | 0.960517 | + | 0.278221i | \(0.0897448\pi\) | ||||
−0.960517 | + | 0.278221i | \(0.910255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1260.00 | − | 212.979i | 1.43345 | − | 0.242297i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1064.89i | 1.20873i | 0.796706 | + | 0.604367i | \(0.206574\pi\) | ||||
−0.796706 | + | 0.604367i | \(0.793426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 313.000i | − | 0.354473i | −0.984168 | − | 0.177237i | \(-0.943284\pi\) | ||
0.984168 | − | 0.177237i | \(-0.0567158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1135.89 | −1.28059 | −0.640297 | − | 0.768127i | \(-0.721189\pi\) | ||||
−0.640297 | + | 0.768127i | \(0.721189\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 848.000 | 0.953881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −892.500 | − | 1127.01i | −1.00168 | − | 1.26489i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −390.461 | −0.437247 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.4965 | − | 210.000i | −0.0395724 | − | 0.234114i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1632.84i | − | 1.81628i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −630.000 | −0.699223 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1467.19 | + | 248.000i | −1.62479 | + | 0.274640i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 374.000i | − | 0.412348i | −0.978515 | − | 0.206174i | \(-0.933899\pi\) | ||
0.978515 | − | 0.206174i | \(-0.0661014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −420.000 | − | 1206.88i | −0.462046 | − | 1.32770i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 638.937i | − | 0.701357i | −0.936496 | − | 0.350679i | \(-0.885951\pi\) | ||
0.936496 | − | 0.350679i | \(-0.114049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 315.000i | − | 0.345016i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 567.944 | 0.619350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1286.00 | 1.39935 | 0.699674 | − | 0.714463i | \(-0.253329\pi\) | ||||
0.699674 | + | 0.714463i | \(0.253329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63.5000 | − | 375.671i | −0.0689468 | − | 0.407895i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 212.979 | 0.230746 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 76.9090 | + | 221.000i | 0.0829655 | + | 0.238403i | ||||
\(928\) | 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 | ||||||||
\(933\) | −141.986 | − | 840.000i | −0.152182 | − | 0.900322i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1597.00i | − | 1.70438i | −0.523236 | − | 0.852188i | \(-0.675275\pi\) | ||
0.523236 | − | 0.852188i | \(-0.324725\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.0000 | − | 171.566i | −0.0308839 | − | 0.182712i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 248.475i | 0.264055i | 0.991246 | + | 0.132027i | \(0.0421487\pi\) | ||||
−0.991246 | + | 0.132027i | \(0.957851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1890.00i | − | 2.00424i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −354.965 | −0.374831 | −0.187415 | − | 0.982281i | \(-0.560011\pi\) | ||||
−0.187415 | + | 0.982281i | \(0.560011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −202.000 | −0.212856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 840.000 | − | 141.986i | 0.883281 | − | 0.149302i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 621.188 | 0.651824 | 0.325912 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325912 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1863.57 | − | 315.000i | 1.94730 | − | 0.329154i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 425.958i | 0.444169i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1155.00 | 1.20187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −150.860 | + | 52.5000i | −0.156656 | + | 0.0545171i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1576.00i | 1.62978i | 0.579614 | + | 0.814891i | \(0.303203\pi\) | ||||
−0.579614 | + | 0.814891i | \(0.696797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −577.500 | + | 97.6153i | −0.595975 | + | 0.100738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1153.64i | − | 1.18809i | −0.804432 | − | 0.594045i | \(-0.797530\pi\) | ||
0.804432 | − | 0.594045i | \(-0.202470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1016.00i | 1.04419i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 479.202 | 0.490484 | 0.245242 | − | 0.969462i | \(-0.421133\pi\) | ||||
0.245242 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −945.000 | −0.965271 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1496.00 | + | 520.615i | −1.52497 | + | 0.530698i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1419.86 | −1.44441 | −0.722207 | − | 0.691677i | \(-0.756872\pi\) | ||||
−0.722207 | + | 0.691677i | \(0.756872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −141.986 | − | 840.000i | −0.143856 | − | 0.851064i | ||||
\(988\) | 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 | ||||||||
\(993\) | 760.216 | − | 128.500i | 0.765575 | − | 0.129406i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1004.00i | 1.00702i | 0.863989 | + | 0.503511i | \(0.167958\pi\) | ||||
−0.863989 | + | 0.503511i | \(0.832042\pi\) | |||||||
\(998\) | 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.c.j.449.2 | 4 | ||
3.2 | odd | 2 | inner | 1200.3.c.j.449.4 | 4 | ||
4.3 | odd | 2 | 300.3.b.d.149.3 | 4 | |||
5.2 | odd | 4 | 1200.3.l.m.401.2 | 2 | |||
5.3 | odd | 4 | 1200.3.l.k.401.1 | 2 | |||
5.4 | even | 2 | inner | 1200.3.c.j.449.3 | 4 | ||
12.11 | even | 2 | 300.3.b.d.149.1 | 4 | |||
15.2 | even | 4 | 1200.3.l.m.401.1 | 2 | |||
15.8 | even | 4 | 1200.3.l.k.401.2 | 2 | |||
15.14 | odd | 2 | inner | 1200.3.c.j.449.1 | 4 | ||
20.3 | even | 4 | 300.3.g.g.101.2 | yes | 2 | ||
20.7 | even | 4 | 300.3.g.f.101.1 | ✓ | 2 | ||
20.19 | odd | 2 | 300.3.b.d.149.2 | 4 | |||
60.23 | odd | 4 | 300.3.g.g.101.1 | yes | 2 | ||
60.47 | odd | 4 | 300.3.g.f.101.2 | yes | 2 | ||
60.59 | even | 2 | 300.3.b.d.149.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.b.d.149.1 | 4 | 12.11 | even | 2 | |||
300.3.b.d.149.2 | 4 | 20.19 | odd | 2 | |||
300.3.b.d.149.3 | 4 | 4.3 | odd | 2 | |||
300.3.b.d.149.4 | 4 | 60.59 | even | 2 | |||
300.3.g.f.101.1 | ✓ | 2 | 20.7 | even | 4 | ||
300.3.g.f.101.2 | yes | 2 | 60.47 | odd | 4 | ||
300.3.g.g.101.1 | yes | 2 | 60.23 | odd | 4 | ||
300.3.g.g.101.2 | yes | 2 | 20.3 | even | 4 | ||
1200.3.c.j.449.1 | 4 | 15.14 | odd | 2 | inner | ||
1200.3.c.j.449.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.c.j.449.3 | 4 | 5.4 | even | 2 | inner | ||
1200.3.c.j.449.4 | 4 | 3.2 | odd | 2 | inner | ||
1200.3.l.k.401.1 | 2 | 5.3 | odd | 4 | |||
1200.3.l.k.401.2 | 2 | 15.8 | even | 4 | |||
1200.3.l.m.401.1 | 2 | 15.2 | even | 4 | |||
1200.3.l.m.401.2 | 2 | 5.2 | odd | 4 |