Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3600,3,Mod(449,3600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, 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("3600.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.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: | \(98.0928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3600.449 |
Dual form | 3600.3.c.i.449.4 |
$q$-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 \(\left(\mathbb{Z}/3600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(2801\) | \(3151\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.837722i | 0.119675i | 0.998208 | + | 0.0598373i | \(0.0190582\pi\) | ||||
−0.998208 | + | 0.0598373i | \(0.980942\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 14.3716i | − 1.30651i | −0.757137 | − | 0.653256i | \(-0.773403\pi\) | ||||
0.757137 | − | 0.653256i | \(-0.226597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 21.8114i | − 1.67780i | −0.544286 | − | 0.838900i | \(-0.683199\pi\) | ||||
0.544286 | − | 0.838900i | \(-0.316801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.5454 | 1.38502 | 0.692512 | − | 0.721407i | \(-0.256504\pi\) | ||||
0.692512 | + | 0.721407i | \(0.256504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.32456 | −0.332871 | −0.166436 | − | 0.986052i | \(-0.553226\pi\) | ||||
−0.166436 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −38.8723 | −1.69010 | −0.845049 | − | 0.534689i | \(-0.820429\pi\) | ||||
−0.845049 | + | 0.534689i | \(0.820429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.266737i | 0.00919784i | 0.999989 | + | 0.00459892i | \(0.00146389\pi\) | ||||
−0.999989 | + | 0.00459892i | \(0.998536\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.2719 | −0.976512 | −0.488256 | − | 0.872700i | \(-0.662367\pi\) | ||||
−0.488256 | + | 0.872700i | \(0.662367\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.53950i | − 0.257824i | −0.991656 | − | 0.128912i | \(-0.958851\pi\) | ||||
0.991656 | − | 0.128912i | \(-0.0411485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 19.3028i | − 0.470799i | −0.971899 | − | 0.235399i | \(-0.924360\pi\) | ||||
0.971899 | − | 0.235399i | \(-0.0756398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 19.6228i | − 0.456344i | −0.973621 | − | 0.228172i | \(-0.926725\pi\) | ||||
0.973621 | − | 0.228172i | \(-0.0732748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22.1684 | −0.471669 | −0.235834 | − | 0.971793i | \(-0.575782\pi\) | ||||
−0.235834 | + | 0.971793i | \(0.575782\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.2982 | 0.985678 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −49.0012 | −0.924552 | −0.462276 | − | 0.886736i | \(-0.652967\pi\) | ||||
−0.462276 | + | 0.886736i | \(0.652967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 73.2351i | − 1.24127i | −0.784098 | − | 0.620637i | \(-0.786874\pi\) | ||||
0.784098 | − | 0.620637i | \(-0.213126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.3246 | −0.792206 | −0.396103 | − | 0.918206i | \(-0.629638\pi\) | ||||
−0.396103 | + | 0.918206i | \(0.629638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.2982i | 1.15370i | 0.816848 | + | 0.576852i | \(0.195719\pi\) | ||||
−0.816848 | + | 0.576852i | \(0.804281\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 104.044i | 1.46541i | 0.680548 | + | 0.732703i | \(0.261742\pi\) | ||||
−0.680548 | + | 0.732703i | \(0.738258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.6754i | 0.653088i | 0.945182 | + | 0.326544i | \(0.105884\pi\) | ||||
−0.945182 | + | 0.326544i | \(0.894116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0394 | 0.156356 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.2192 | 0.863534 | 0.431767 | − | 0.901985i | \(-0.357890\pi\) | ||||
0.431767 | + | 0.901985i | \(0.357890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.2098 | 0.339877 | 0.169938 | − | 0.985455i | \(-0.445643\pi\) | ||||
0.169938 | + | 0.985455i | \(0.445643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 53.7774i | 0.604240i | 0.953270 | + | 0.302120i | \(0.0976943\pi\) | ||||
−0.953270 | + | 0.302120i | \(0.902306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.2719 | 0.200790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 114.921i | 1.18475i | 0.805661 | + | 0.592376i | \(0.201810\pi\) | ||||
−0.805661 | + | 0.592376i | \(0.798190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5473i | 0.173736i | 0.996220 | + | 0.0868679i | \(0.0276858\pi\) | ||||
−0.996220 | + | 0.0868679i | \(0.972314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 71.5395i | 0.694558i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −76.3675 | −0.713715 | −0.356858 | − | 0.934159i | \(-0.616152\pi\) | ||||
−0.356858 | + | 0.934159i | \(0.616152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 126.921 | 1.16441 | 0.582206 | − | 0.813041i | \(-0.302190\pi\) | ||||
0.582206 | + | 0.813041i | \(0.302190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0601 | −0.133275 | −0.0666377 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666377 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.7245i | 0.165752i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.5438 | −0.706973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 158.031i | 1.24434i | 0.782884 | + | 0.622168i | \(0.213748\pi\) | ||||
−0.782884 | + | 0.622168i | \(0.786252\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 211.220i | − 1.61237i | −0.591665 | − | 0.806184i | \(-0.701529\pi\) | ||||
0.591665 | − | 0.806184i | \(-0.298471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.29822i | − 0.0398363i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 69.2592 | 0.505542 | 0.252771 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252771 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −159.842 | −1.14994 | −0.574971 | − | 0.818174i | \(-0.694987\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −313.465 | −2.19206 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 9.81897i | − 0.0658991i | −0.999457 | − | 0.0329496i | \(-0.989510\pi\) | ||||
0.999457 | − | 0.0329496i | \(-0.0104901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −210.649 | −1.39503 | −0.697514 | − | 0.716572i | \(-0.745710\pi\) | ||||
−0.697514 | + | 0.716572i | \(0.745710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 211.276i | − 1.34571i | −0.739775 | − | 0.672854i | \(-0.765068\pi\) | ||||
0.739775 | − | 0.672854i | \(-0.234932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 32.5642i | − 0.202262i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.763i | 1.36664i | 0.730117 | + | 0.683322i | \(0.239465\pi\) | ||||
−0.730117 | + | 0.683322i | \(0.760535\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −33.3644 | −0.199787 | −0.0998933 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998933 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −306.737 | −1.81501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −29.8102 | −0.172313 | −0.0861567 | − | 0.996282i | \(-0.527459\pi\) | ||||
−0.0861567 | + | 0.996282i | \(0.527459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 111.841i | 0.624808i | 0.949949 | + | 0.312404i | \(0.101134\pi\) | ||||
−0.949949 | + | 0.312404i | \(0.898866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −49.0790 | −0.271155 | −0.135577 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135577 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 338.386i | − 1.80955i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 278.947i | − 1.46046i | −0.683203 | − | 0.730229i | \(-0.739414\pi\) | ||||
0.683203 | − | 0.730229i | \(-0.260586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89.8947i | 0.465775i | 0.972504 | + | 0.232888i | \(0.0748175\pi\) | ||||
−0.972504 | + | 0.232888i | \(0.925183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −212.709 | −1.07974 | −0.539870 | − | 0.841748i | \(-0.681527\pi\) | ||||
−0.539870 | + | 0.841748i | \(0.681527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 96.4911 | 0.484880 | 0.242440 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242440 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.223452 | −0.00110075 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 90.8942i | 0.434900i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 65.7893 | 0.311798 | 0.155899 | − | 0.987773i | \(-0.450173\pi\) | ||||
0.155899 | + | 0.987773i | \(0.450173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 25.3594i | − 0.116864i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 513.558i | − 2.32379i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 102.302i | − 0.458756i | −0.973337 | − | 0.229378i | \(-0.926331\pi\) | ||||
0.973337 | − | 0.229378i | \(-0.0736691\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5296 | 0.0551966 | 0.0275983 | − | 0.999619i | \(-0.491214\pi\) | ||||
0.0275983 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2982 | −0.101739 | −0.0508695 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508695 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −356.382 | −1.52954 | −0.764768 | − | 0.644306i | \(-0.777146\pi\) | ||||
−0.764768 | + | 0.644306i | \(0.777146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 175.524i | − 0.734408i | −0.930140 | − | 0.367204i | \(-0.880315\pi\) | ||||
0.930140 | − | 0.367204i | \(-0.119685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.438 | 0.433355 | 0.216677 | − | 0.976243i | \(-0.430478\pi\) | ||||
0.216677 | + | 0.976243i | \(0.430478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 137.947i | 0.558491i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 130.945i | − 0.521694i | −0.965380 | − | 0.260847i | \(-0.915998\pi\) | ||||
0.965380 | − | 0.260847i | \(-0.0840018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 558.658i | 2.20813i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −425.641 | −1.65619 | −0.828095 | − | 0.560587i | \(-0.810575\pi\) | ||||
−0.828095 | + | 0.560587i | \(0.810575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.99145 | 0.0308550 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 74.5004 | 0.283271 | 0.141636 | − | 0.989919i | \(-0.454764\pi\) | ||||
0.141636 | + | 0.989919i | \(0.454764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 205.067i | − 0.762331i | −0.924507 | − | 0.381165i | \(-0.875523\pi\) | ||||
0.924507 | − | 0.381165i | \(-0.124477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 233.351 | 0.861073 | 0.430537 | − | 0.902573i | \(-0.358324\pi\) | ||||
0.430537 | + | 0.902573i | \(0.358324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 423.715i | 1.52966i | 0.644235 | + | 0.764828i | \(0.277176\pi\) | ||||
−0.644235 | + | 0.764828i | \(0.722824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 402.604i | − 1.43275i | −0.697713 | − | 0.716377i | \(-0.745799\pi\) | ||||
0.697713 | − | 0.716377i | \(-0.254201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 272.333i | 0.962308i | 0.876636 | + | 0.481154i | \(0.159782\pi\) | ||||
−0.876636 | + | 0.481154i | \(0.840218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.1704 | 0.0563427 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 265.386 | 0.918290 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −443.188 | −1.51259 | −0.756294 | − | 0.654232i | \(-0.772992\pi\) | ||||
−0.756294 | + | 0.654232i | \(0.772992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 847.858i | 2.83564i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4384 | 0.0546128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 390.824i | − 1.27304i | −0.771259 | − | 0.636522i | \(-0.780373\pi\) | ||||
0.771259 | − | 0.636522i | \(-0.219627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.97739i | − 0.00957362i | −0.999989 | − | 0.00478681i | \(-0.998476\pi\) | ||||
0.999989 | − | 0.00478681i | \(-0.00152369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 130.105i | 0.415672i | 0.978164 | + | 0.207836i | \(0.0666420\pi\) | ||||
−0.978164 | + | 0.207836i | \(0.933358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −131.677 | −0.415384 | −0.207692 | − | 0.978194i | \(-0.566595\pi\) | ||||
−0.207692 | + | 0.978194i | \(0.566595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.83345 | 0.0120171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −148.914 | −0.461035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 18.5710i | − 0.0564468i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160.483 | −0.484842 | −0.242421 | − | 0.970171i | \(-0.577941\pi\) | ||||
−0.242421 | + | 0.970171i | \(0.577941\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 128.114i | 0.380160i | 0.981769 | + | 0.190080i | \(0.0608747\pi\) | ||||
−0.981769 | + | 0.190080i | \(0.939125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 435.056i | 1.27583i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 81.5089i | 0.237635i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −219.637 | −0.632959 | −0.316480 | − | 0.948599i | \(-0.602501\pi\) | ||||
−0.316480 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −403.465 | −1.15606 | −0.578030 | − | 0.816016i | \(-0.696178\pi\) | ||||
−0.578030 | + | 0.816016i | \(0.696178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 54.8192 | 0.155295 | 0.0776475 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776475 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 480.460i | − 1.33833i | −0.743114 | − | 0.669165i | \(-0.766652\pi\) | ||||
0.743114 | − | 0.669165i | \(-0.233348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −321.000 | −0.889197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 522.364i | 1.42333i | 0.702517 | + | 0.711667i | \(0.252060\pi\) | ||||
−0.702517 | + | 0.711667i | \(0.747940\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 41.0494i | − 0.110645i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 233.285i | − 0.625428i | −0.949847 | − | 0.312714i | \(-0.898762\pi\) | ||||
0.949847 | − | 0.312714i | \(-0.101238\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.81791 | 0.0154321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 248.596 | 0.655927 | 0.327964 | − | 0.944690i | \(-0.393638\pi\) | ||||
0.327964 | + | 0.944690i | \(0.393638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −468.291 | −1.22269 | −0.611346 | − | 0.791364i | \(-0.709372\pi\) | ||||
−0.611346 | + | 0.791364i | \(0.709372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 484.238i | 1.24483i | 0.782688 | + | 0.622414i | \(0.213848\pi\) | ||||
−0.782688 | + | 0.622414i | \(0.786152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −915.263 | −2.34083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 298.943i | 0.753005i | 0.926416 | + | 0.376503i | \(0.122873\pi\) | ||||
−0.926416 | + | 0.376503i | \(0.877127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 467.509i | 1.16586i | 0.812523 | + | 0.582929i | \(0.198093\pi\) | ||||
−0.812523 | + | 0.582929i | \(0.801907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 660.272i | 1.63839i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −137.098 | −0.336851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 184.158 | 0.450264 | 0.225132 | − | 0.974328i | \(-0.427719\pi\) | ||||
0.225132 | + | 0.974328i | \(0.427719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 61.3507 | 0.148549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 429.840i | 1.02587i | 0.858427 | + | 0.512936i | \(0.171442\pi\) | ||||
−0.858427 | + | 0.512936i | \(0.828558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −305.035 | −0.724548 | −0.362274 | − | 0.932072i | \(-0.618000\pi\) | ||||
−0.362274 | + | 0.932072i | \(0.618000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 40.4826i | − 0.0948069i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 128.880i | − 0.299025i | −0.988760 | − | 0.149512i | \(-0.952230\pi\) | ||||
0.988760 | − | 0.149512i | \(-0.0477704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 243.886i | 0.563247i | 0.959525 | + | 0.281624i | \(0.0908730\pi\) | ||||
−0.959525 | + | 0.281624i | \(0.909127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 245.850 | 0.562585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −259.614 | −0.591376 | −0.295688 | − | 0.955285i | \(-0.595549\pi\) | ||||
−0.295688 | + | 0.955285i | \(0.595549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −541.011 | −1.22124 | −0.610622 | − | 0.791923i | \(-0.709080\pi\) | ||||
−0.610622 | + | 0.791923i | \(0.709080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 791.947i | − 1.76380i | −0.471436 | − | 0.881900i | \(-0.656264\pi\) | ||||
0.471436 | − | 0.881900i | \(-0.343736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −277.412 | −0.615104 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 611.359i | − 1.33777i | −0.743367 | − | 0.668883i | \(-0.766773\pi\) | ||||
0.743367 | − | 0.668883i | \(-0.233227\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 586.991i | − 1.27330i | −0.771153 | − | 0.636650i | \(-0.780320\pi\) | ||||
0.771153 | − | 0.636650i | \(-0.219680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 195.285i | − 0.421781i | −0.977510 | − | 0.210891i | \(-0.932364\pi\) | ||||
0.977510 | − | 0.210891i | \(-0.0676364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 753.763 | 1.61405 | 0.807027 | − | 0.590515i | \(-0.201075\pi\) | ||||
0.807027 | + | 0.590515i | \(0.201075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.7544 | −0.138069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −282.011 | −0.596218 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 614.848i | − 1.28361i | −0.766869 | − | 0.641803i | \(-0.778186\pi\) | ||||
0.766869 | − | 0.641803i | \(-0.221814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −208.070 | −0.432577 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 478.197i | 0.981924i | 0.871181 | + | 0.490962i | \(0.163355\pi\) | ||||
−0.871181 | + | 0.490962i | \(0.836645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 617.223i | − 1.25707i | −0.777780 | − | 0.628537i | \(-0.783654\pi\) | ||||
0.777780 | − | 0.628537i | \(-0.216346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.28043i | 0.0127392i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −87.1599 | −0.175372 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 783.096 | 1.56933 | 0.784665 | − | 0.619919i | \(-0.212835\pi\) | ||||
0.784665 | + | 0.619919i | \(0.212835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −369.395 | −0.734383 | −0.367191 | − | 0.930145i | \(-0.619681\pi\) | ||||
−0.367191 | + | 0.930145i | \(0.619681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 225.635i | 0.443291i | 0.975127 | + | 0.221645i | \(0.0711427\pi\) | ||||
−0.975127 | + | 0.221645i | \(0.928857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.9388 | −0.0781581 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 318.596i | 0.616241i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1007.73i | − 1.93422i | −0.254367 | − | 0.967108i | \(-0.581867\pi\) | ||||
0.254367 | − | 0.967108i | \(-0.418133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 935.517i | − 1.78875i | −0.447316 | − | 0.894376i | \(-0.647620\pi\) | ||||
0.447316 | − | 0.894376i | \(-0.352380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −712.764 | −1.35249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 982.052 | 1.85643 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −421.020 | −0.789906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 694.124i | − 1.28780i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −399.149 | −0.737798 | −0.368899 | − | 0.929469i | \(-0.620265\pi\) | ||||
−0.368899 | + | 0.929469i | \(0.620265\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 480.833i | 0.879036i | 0.898234 | + | 0.439518i | \(0.144851\pi\) | ||||
−0.898234 | + | 0.439518i | \(0.855149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.68699i | − 0.00306170i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 57.1488i | 0.103343i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 751.542 | 1.34927 | 0.674634 | − | 0.738152i | \(-0.264301\pi\) | ||||
0.674634 | + | 0.738152i | \(0.264301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −428.000 | −0.765653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 670.820 | 1.19151 | 0.595755 | − | 0.803166i | \(-0.296853\pi\) | ||||
0.595755 | + | 0.803166i | \(0.296853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 275.325i | 0.483875i | 0.970292 | + | 0.241937i | \(0.0777829\pi\) | ||||
−0.970292 | + | 0.241937i | \(0.922217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 900.289 | 1.57669 | 0.788344 | − | 0.615235i | \(-0.210939\pi\) | ||||
0.788344 | + | 0.615235i | \(0.210939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 596.236i | 1.03334i | 0.856185 | + | 0.516669i | \(0.172828\pi\) | ||||
−0.856185 | + | 0.516669i | \(0.827172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.6320i | 0.0406746i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 704.228i | 1.20794i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 497.431 | 0.847412 | 0.423706 | − | 0.905800i | \(-0.360729\pi\) | ||||
0.423706 | + | 0.905800i | \(0.360729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 191.456 | 0.325053 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −898.856 | −1.51578 | −0.757889 | − | 0.652384i | \(-0.773769\pi\) | ||||
−0.757889 | + | 0.652384i | \(0.773769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 28.5701i | − 0.0476964i | −0.999716 | − | 0.0238482i | \(-0.992408\pi\) | ||||
0.999716 | − | 0.0238482i | \(-0.00759183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2107 | −0.0336284 | −0.0168142 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168142 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 713.626i | − 1.17566i | −0.808984 | − | 0.587831i | \(-0.799982\pi\) | ||||
0.808984 | − | 0.587831i | \(-0.200018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 483.524i | 0.791365i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 76.1530i | − 0.124230i | −0.998069 | − | 0.0621150i | \(-0.980215\pi\) | ||||
0.998069 | − | 0.0621150i | \(-0.0197846\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −201.599 | −0.326741 | −0.163371 | − | 0.986565i | \(-0.552237\pi\) | ||||
−0.163371 | + | 0.986565i | \(0.552237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −204.263 | −0.329989 | −0.164995 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164995 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.0505 | −0.0723122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 224.611i | − 0.357093i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 639.903 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1053.45i | − 1.65377i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 570.709i | 0.890342i | 0.895446 | + | 0.445171i | \(0.146857\pi\) | ||||
−0.895446 | + | 0.445171i | \(0.853143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 453.693i | − 0.705587i | −0.935701 | − | 0.352794i | \(-0.885232\pi\) | ||||
0.935701 | − | 0.352794i | \(-0.114768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −983.536 | −1.52015 | −0.760074 | − | 0.649837i | \(-0.774837\pi\) | ||||
−0.760074 | + | 0.649837i | \(0.774837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1052.51 | −1.62174 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 544.478 | 0.833811 | 0.416905 | − | 0.908950i | \(-0.363115\pi\) | ||||
0.416905 | + | 0.908950i | \(0.363115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 107.933i | 0.163783i | 0.996641 | + | 0.0818916i | \(0.0260961\pi\) | ||||
−0.996641 | + | 0.0818916i | \(0.973904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 345.728 | 0.523038 | 0.261519 | − | 0.965198i | \(-0.415777\pi\) | ||||
0.261519 | + | 0.965198i | \(0.415777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 10.3687i | − 0.0155452i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 694.503i | 1.03503i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1204.78i | − 1.79016i | −0.445902 | − | 0.895082i | \(-0.647117\pi\) | ||||
0.445902 | − | 0.895082i | \(-0.352883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −574.598 | −0.848742 | −0.424371 | − | 0.905488i | \(-0.639505\pi\) | ||||
−0.424371 | + | 0.905488i | \(0.639505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −96.2719 | −0.141785 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −334.387 | −0.489585 | −0.244792 | − | 0.969575i | \(-0.578720\pi\) | ||||
−0.244792 | + | 0.969575i | \(0.578720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1068.79i | 1.55121i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −901.149 | −1.30412 | −0.652061 | − | 0.758166i | \(-0.726096\pi\) | ||||
−0.652061 | + | 0.758166i | \(0.726096\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 454.491i | − 0.652068i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 887.934i | 1.26667i | 0.773879 | + | 0.633334i | \(0.218314\pi\) | ||||
−0.773879 | + | 0.633334i | \(0.781686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.3331i | 0.0858223i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.6998 | −0.0207918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1026.35 | 1.44760 | 0.723801 | − | 0.690008i | \(-0.242393\pi\) | ||||
0.723801 | + | 0.690008i | \(0.242393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1176.74 | 1.65040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 740.080i | 1.02932i | 0.857395 | + | 0.514659i | \(0.172081\pi\) | ||||
−0.857395 | + | 0.514659i | \(0.827919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.9302 | −0.0831210 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1063.75i | 1.46321i | 0.681731 | + | 0.731603i | \(0.261227\pi\) | ||||
−0.681731 | + | 0.731603i | \(0.738773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 462.026i | − 0.632047i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 134.749i | 0.183833i | 0.995767 | + | 0.0919164i | \(0.0292993\pi\) | ||||
−0.995767 | + | 0.0919164i | \(0.970701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1110.90 | 1.50733 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −711.429 | −0.962692 | −0.481346 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481346 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −466.330 | −0.627631 | −0.313816 | − | 0.949484i | \(-0.601607\pi\) | ||||
−0.313816 | + | 0.949484i | \(0.601607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 63.9748i | − 0.0854136i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −227.359 | −0.302742 | −0.151371 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151371 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 552.258i | 0.729535i | 0.931099 | + | 0.364768i | \(0.118852\pi\) | ||||
−0.931099 | + | 0.364768i | \(0.881148\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 303.051i | 0.398228i | 0.979976 | + | 0.199114i | \(0.0638064\pi\) | ||||
−0.979976 | + | 0.199114i | \(0.936194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 106.325i | 0.139351i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1597.36 | −2.08261 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −739.684 | −0.961878 | −0.480939 | − | 0.876754i | \(-0.659704\pi\) | ||||
−0.480939 | + | 0.876754i | \(0.659704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 603.479 | 0.780697 | 0.390348 | − | 0.920667i | \(-0.372355\pi\) | ||||
0.390348 | + | 0.920667i | \(0.372355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 122.081i | 0.156715i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1495.28 | 1.91457 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 660.483i | − 0.839241i | −0.907700 | − | 0.419620i | \(-0.862163\pi\) | ||||
0.907700 | − | 0.419620i | \(-0.137837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 12.6162i | − 0.0159497i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1054.03i | 1.32916i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −634.969 | −0.796699 | −0.398349 | − | 0.917234i | \(-0.630417\pi\) | ||||
−0.398349 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −521.964 | −0.653272 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 685.174 | 0.853268 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 405.048i | 0.500677i | 0.968158 | + | 0.250339i | \(0.0805419\pi\) | ||||
−0.968158 | + | 0.250339i | \(0.919458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −406.034 | −0.500659 | −0.250329 | − | 0.968161i | \(-0.580539\pi\) | ||||
−0.250329 | + | 0.968161i | \(0.580539\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 124.105i | 0.151904i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 550.073i | − 0.670003i | −0.942218 | − | 0.335002i | \(-0.891263\pi\) | ||||
0.942218 | − | 0.335002i | \(-0.108737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1472.51i | 1.78920i | 0.446868 | + | 0.894600i | \(0.352540\pi\) | ||||
−0.446868 | + | 0.894600i | \(0.647460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1510.47 | 1.82644 | 0.913220 | − | 0.407466i | \(-0.133587\pi\) | ||||
0.913220 | + | 0.407466i | \(0.133587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −712.692 | −0.859701 | −0.429850 | − | 0.902900i | \(-0.641434\pi\) | ||||
−0.429850 | + | 0.902900i | \(0.641434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1137.20 | 1.36519 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 530.579i | − 0.632394i | −0.948694 | − | 0.316197i | \(-0.897594\pi\) | ||||
0.948694 | − | 0.316197i | \(-0.102406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.929 | 0.999915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 71.6619i | − 0.0846068i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 370.822i | 0.435748i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 215.232i | 0.252324i | 0.992010 | + | 0.126162i | \(0.0402659\pi\) | ||||
−0.992010 | + | 0.126162i | \(0.959734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.97441 | 0.00580445 | 0.00290222 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290222 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1652.28 | 1.92349 | 0.961746 | − | 0.273941i | \(-0.0883273\pi\) | ||||
0.961746 | + | 0.273941i | \(0.0883273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 379.077 | 0.439255 | 0.219627 | − | 0.975584i | \(-0.429516\pi\) | ||||
0.219627 | + | 0.975584i | \(0.429516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 980.421i | − 1.12822i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1685.98 | 1.93568 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1101.60i | − 1.25610i | −0.778173 | − | 0.628051i | \(-0.783853\pi\) | ||||
0.778173 | − | 0.628051i | \(-0.216147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 184.877i | 0.209850i | 0.994480 | + | 0.104925i | \(0.0334602\pi\) | ||||
−0.994480 | + | 0.104925i | \(0.966540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 978.236i | − 1.10786i | −0.832565 | − | 0.553928i | \(-0.813128\pi\) | ||||
0.832565 | − | 0.553928i | \(-0.186872\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 667.937 | 0.753029 | 0.376514 | − | 0.926411i | \(-0.377123\pi\) | ||||
0.376514 | + | 0.926411i | \(0.377123\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −132.386 | −0.148915 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 140.205 | 0.157005 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 8.07464i | − 0.00898180i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1153.75 | −1.28053 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 832.622i | − 0.917996i | −0.888437 | − | 0.458998i | \(-0.848209\pi\) | ||||
0.888437 | − | 0.458998i | \(-0.151791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 565.263i | − 0.620486i | −0.950657 | − | 0.310243i | \(-0.899590\pi\) | ||||
0.950657 | − | 0.310243i | \(-0.100410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 405.421i | − 0.444053i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 176.944 | 0.192959 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1185.75 | −1.29026 | −0.645128 | − | 0.764075i | \(-0.723196\pi\) | ||||
−0.645128 | + | 0.764075i | \(0.723196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2269.34 | 2.45866 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 942.995i | − 1.01506i | −0.861633 | − | 0.507532i | \(-0.830558\pi\) | ||||
0.861633 | − | 0.507532i | \(-0.169442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −305.465 | −0.328104 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 531.281i | 0.567002i | 0.958972 | + | 0.283501i | \(0.0914960\pi\) | ||||
−0.958972 | + | 0.283501i | \(0.908504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 595.650i | − 0.632996i | −0.948593 | − | 0.316498i | \(-0.897493\pi\) | ||||
0.948593 | − | 0.316498i | \(-0.102507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 750.342i | 0.795696i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 782.246 | 0.826026 | 0.413013 | − | 0.910725i | \(-0.364476\pi\) | ||||
0.413013 | + | 0.910725i | \(0.364476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1039.87 | 1.09575 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −426.708 | −0.447752 | −0.223876 | − | 0.974618i | \(-0.571871\pi\) | ||||
−0.223876 | + | 0.974618i | \(0.571871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.0200i | 0.0605005i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.6128 | −0.0464234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1210.91i | − 1.25223i | −0.779730 | − | 0.626116i | \(-0.784644\pi\) | ||||
0.779730 | − | 0.626116i | \(-0.215356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1193.69i | 1.22934i | 0.788784 | + | 0.614670i | \(0.210711\pi\) | ||||
−0.788784 | + | 0.614670i | \(0.789289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 133.903i | − 0.137619i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 909.475 | 0.930886 | 0.465443 | − | 0.885078i | \(-0.345895\pi\) | ||||
0.465443 | + | 0.885078i | \(0.345895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 772.868 | 0.789447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1560.88 | 1.58788 | 0.793938 | − | 0.607999i | \(-0.208028\pi\) | ||||
0.793938 | + | 0.607999i | \(0.208028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 762.782i | 0.771265i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1692.63 | 1.70800 | 0.854001 | − | 0.520271i | \(-0.174169\pi\) | ||||
0.854001 | + | 0.520271i | \(0.174169\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 16.5744i | − 0.0166243i | −0.999965 | − | 0.00831213i | \(-0.997354\pi\) | ||||
0.999965 | − | 0.00831213i | \(-0.00264586\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3600.3.c.i.449.5 | 8 | ||
3.2 | odd | 2 | inner | 3600.3.c.i.449.6 | 8 | ||
4.3 | odd | 2 | 225.3.d.b.224.3 | 8 | |||
5.2 | odd | 4 | 720.3.l.a.161.2 | 4 | |||
5.3 | odd | 4 | 3600.3.l.v.1601.1 | 4 | |||
5.4 | even | 2 | inner | 3600.3.c.i.449.3 | 8 | ||
12.11 | even | 2 | 225.3.d.b.224.5 | 8 | |||
15.2 | even | 4 | 720.3.l.a.161.4 | 4 | |||
15.8 | even | 4 | 3600.3.l.v.1601.2 | 4 | |||
15.14 | odd | 2 | inner | 3600.3.c.i.449.4 | 8 | ||
20.3 | even | 4 | 225.3.c.c.26.3 | 4 | |||
20.7 | even | 4 | 45.3.c.a.26.2 | ✓ | 4 | ||
20.19 | odd | 2 | 225.3.d.b.224.6 | 8 | |||
40.27 | even | 4 | 2880.3.l.g.1601.3 | 4 | |||
40.37 | odd | 4 | 2880.3.l.c.1601.4 | 4 | |||
60.23 | odd | 4 | 225.3.c.c.26.2 | 4 | |||
60.47 | odd | 4 | 45.3.c.a.26.3 | yes | 4 | ||
60.59 | even | 2 | 225.3.d.b.224.4 | 8 | |||
120.77 | even | 4 | 2880.3.l.c.1601.2 | 4 | |||
120.107 | odd | 4 | 2880.3.l.g.1601.1 | 4 | |||
180.7 | even | 12 | 405.3.i.d.296.2 | 8 | |||
180.47 | odd | 12 | 405.3.i.d.296.3 | 8 | |||
180.67 | even | 12 | 405.3.i.d.26.3 | 8 | |||
180.167 | odd | 12 | 405.3.i.d.26.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.c.a.26.2 | ✓ | 4 | 20.7 | even | 4 | ||
45.3.c.a.26.3 | yes | 4 | 60.47 | odd | 4 | ||
225.3.c.c.26.2 | 4 | 60.23 | odd | 4 | |||
225.3.c.c.26.3 | 4 | 20.3 | even | 4 | |||
225.3.d.b.224.3 | 8 | 4.3 | odd | 2 | |||
225.3.d.b.224.4 | 8 | 60.59 | even | 2 | |||
225.3.d.b.224.5 | 8 | 12.11 | even | 2 | |||
225.3.d.b.224.6 | 8 | 20.19 | odd | 2 | |||
405.3.i.d.26.2 | 8 | 180.167 | odd | 12 | |||
405.3.i.d.26.3 | 8 | 180.67 | even | 12 | |||
405.3.i.d.296.2 | 8 | 180.7 | even | 12 | |||
405.3.i.d.296.3 | 8 | 180.47 | odd | 12 | |||
720.3.l.a.161.2 | 4 | 5.2 | odd | 4 | |||
720.3.l.a.161.4 | 4 | 15.2 | even | 4 | |||
2880.3.l.c.1601.2 | 4 | 120.77 | even | 4 | |||
2880.3.l.c.1601.4 | 4 | 40.37 | odd | 4 | |||
2880.3.l.g.1601.1 | 4 | 120.107 | odd | 4 | |||
2880.3.l.g.1601.3 | 4 | 40.27 | even | 4 | |||
3600.3.c.i.449.3 | 8 | 5.4 | even | 2 | inner | ||
3600.3.c.i.449.4 | 8 | 15.14 | odd | 2 | inner | ||
3600.3.c.i.449.5 | 8 | 1.1 | even | 1 | trivial | ||
3600.3.c.i.449.6 | 8 | 3.2 | odd | 2 | inner | ||
3600.3.l.v.1601.1 | 4 | 5.3 | odd | 4 | |||
3600.3.l.v.1601.2 | 4 | 15.8 | even | 4 |