Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.a (trivial) |
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: | yes |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56155 | 0.901563 | 0.450781 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.68466 | −1.85399 | −0.926995 | − | 0.375073i | \(-0.877618\pi\) | ||||
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.56155 | 1.83395 | 0.916973 | − | 0.398949i | \(-0.130625\pi\) | ||||
0.916973 | + | 0.398949i | \(0.130625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.12311 | 1.63415 | 0.817076 | − | 0.576530i | \(-0.195593\pi\) | ||||
0.817076 | + | 0.576530i | \(0.195593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.56155 | 0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.12311 | 0.651213 | 0.325606 | − | 0.945505i | \(-0.394432\pi\) | ||||
0.325606 | + | 0.945505i | \(0.394432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.438447 | −0.0814176 | −0.0407088 | − | 0.999171i | \(-0.512962\pi\) | ||||
−0.0407088 | + | 0.999171i | \(0.512962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24621 | 1.12185 | 0.560926 | − | 0.827866i | \(-0.310445\pi\) | ||||
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.43845 | −0.424479 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621 | 1.35567 | 0.677834 | − | 0.735215i | \(-0.262919\pi\) | ||||
0.677834 | + | 0.735215i | \(0.262919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.4384 | −1.67149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12311 | 1.08626 | 0.543132 | − | 0.839648i | \(-0.317238\pi\) | ||||
0.543132 | + | 0.839648i | \(0.317238\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.43845 | 0.355684 | 0.177842 | − | 0.984059i | \(-0.443088\pi\) | ||||
0.177842 | + | 0.984059i | \(0.443088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.8078 | 1.65342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1231 | 1.80260 | 0.901299 | − | 0.433198i | \(-0.142615\pi\) | ||||
0.901299 | + | 0.433198i | \(0.142615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56155 | 0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1231 | 1.47329 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.87689 | 0.880496 | 0.440248 | − | 0.897876i | \(-0.354891\pi\) | ||||
0.440248 | + | 0.897876i | \(0.354891\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.68466 | 0.829130 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.24621 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.87689 | 0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.56155 | −0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.684658 | 0.0770301 | 0.0385150 | − | 0.999258i | \(-0.487737\pi\) | ||||
0.0385150 | + | 0.999258i | \(0.487737\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.56155 | −0.820166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.684658 | −0.0734031 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.12311 | 0.543048 | 0.271524 | − | 0.962432i | \(-0.412472\pi\) | ||||
0.271524 | + | 0.962432i | \(0.412472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.68466 | −0.700743 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.75379 | 1.01142 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.12311 | −0.730815 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31534 | 0.133553 | 0.0667764 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667764 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.876894 | 0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8078 | −1.16345 | −0.581727 | − | 0.813384i | \(-0.697623\pi\) | ||||
−0.581727 | + | 0.813384i | \(0.697623\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.56155 | −0.152392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1231 | −1.46201 | −0.731003 | − | 0.682374i | \(-0.760947\pi\) | ||||
−0.731003 | + | 0.682374i | \(0.760947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.43845 | 0.425126 | 0.212563 | − | 0.977147i | \(-0.431819\pi\) | ||||
0.212563 | + | 0.977147i | \(0.431819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8769 | 1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.24621 | 0.775738 | 0.387869 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387869 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12311 | −0.291231 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.75379 | 0.347038 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.56155 | 0.693166 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75379 | −0.158134 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1231 | 0.979335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1231 | −1.32131 | −0.660656 | − | 0.750689i | \(-0.729722\pi\) | ||||
−0.660656 | + | 0.750689i | \(0.729722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.12311 | 0.617652 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.36932 | −0.629603 | −0.314802 | − | 0.949157i | \(-0.601938\pi\) | ||||
−0.314802 | + | 0.949157i | \(0.601938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3693 | 1.81252 | 0.906261 | − | 0.422719i | \(-0.138924\pi\) | ||||
0.906261 | + | 0.422719i | \(0.138924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.80776 | 0.320672 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4384 | 0.872907 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.438447 | 0.0364111 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.56155 | 0.128795 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.246211 | 0.0201704 | 0.0100852 | − | 0.999949i | \(-0.496790\pi\) | ||||
0.0100852 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.8078 | −1.61193 | −0.805966 | − | 0.591961i | \(-0.798354\pi\) | ||||
−0.805966 | + | 0.591961i | \(0.798354\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24621 | −0.343286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.24621 | −0.501708 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.24621 | −0.338885 | −0.169442 | − | 0.985540i | \(-0.554197\pi\) | ||||
−0.169442 | + | 0.985540i | \(0.554197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.4924 | 1.62515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.12311 | 0.246135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6155 | −1.53641 | −0.768203 | − | 0.640206i | \(-0.778849\pi\) | ||||
−0.768203 | + | 0.640206i | \(0.778849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.43845 | 0.189833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.19224 | 0.324405 | 0.162202 | − | 0.986757i | \(-0.448140\pi\) | ||||
0.162202 | + | 0.986757i | \(0.448140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.6847 | 2.43728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.1771 | 1.76212 | 0.881060 | − | 0.473004i | \(-0.156830\pi\) | ||||
0.881060 | + | 0.473004i | \(0.156830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.24621 | 0.469494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.12311 | 0.380797 | 0.190399 | − | 0.981707i | \(-0.439022\pi\) | ||||
0.190399 | + | 0.981707i | \(0.439022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7386 | 0.793823 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.24621 | −0.606274 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8078 | −0.863469 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.56155 | −0.404543 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.684658 | −0.0495401 | −0.0247701 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247701 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.1231 | 0.944622 | 0.472311 | − | 0.881432i | \(-0.343420\pi\) | ||||
0.472311 | + | 0.881432i | \(0.343420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.4384 | 0.747513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1231 | 0.934983 | 0.467491 | − | 0.883998i | \(-0.345158\pi\) | ||||
0.467491 | + | 0.883998i | \(0.345158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2462 | −1.00989 | −0.504944 | − | 0.863152i | \(-0.668487\pi\) | ||||
−0.504944 | + | 0.863152i | \(0.668487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.50758 | −0.247405 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.438447 | −0.0307730 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.12311 | 0.0784411 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.75379 | −0.121897 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1231 | −0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5616 | 1.20899 | 0.604494 | − | 0.796610i | \(-0.293376\pi\) | ||||
0.604494 | + | 0.796610i | \(0.293376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.12311 | −0.485792 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.24621 | 0.424020 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.63068 | −0.448060 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −50.5464 | −3.40012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.6847 | 1.65301 | 0.826503 | − | 0.562932i | \(-0.190327\pi\) | ||||
0.826503 | + | 0.562932i | \(0.190327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3153 | 0.751026 | 0.375513 | − | 0.926817i | \(-0.377467\pi\) | ||||
0.375513 | + | 0.926817i | \(0.377467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3693 | 0.751306 | 0.375653 | − | 0.926760i | \(-0.377419\pi\) | ||||
0.375653 | + | 0.926760i | \(0.377419\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8769 | −0.712569 | −0.356285 | − | 0.934378i | \(-0.615957\pi\) | ||||
−0.356285 | + | 0.934378i | \(0.615957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.43845 | −0.159067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.06913 | 0.0694475 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0540 | −1.16781 | −0.583907 | − | 0.811820i | \(-0.698477\pi\) | ||||
−0.583907 | + | 0.811820i | \(0.698477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −47.6155 | −3.02970 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.7386 | −1.18751 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3693 | −0.843864 | −0.421932 | − | 0.906628i | \(-0.638648\pi\) | ||||
−0.421932 | + | 0.906628i | \(0.638648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.87689 | −0.306608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.8078 | −0.739431 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.4924 | −1.15353 | −0.576763 | − | 0.816912i | \(-0.695684\pi\) | ||||
−0.576763 | + | 0.816912i | \(0.695684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24621 | 0.512395 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.246211 | 0.0152401 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.36932 | 0.577737 | 0.288868 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288868 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.1231 | −0.806146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.00000 | 0.489592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.24621 | −0.258896 | −0.129448 | − | 0.991586i | \(-0.541321\pi\) | ||||
−0.129448 | + | 0.991586i | \(0.541321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.24621 | −0.379430 | −0.189715 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189715 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.4384 | −0.631764 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.56155 | −0.0941652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.24621 | 0.495467 | 0.247733 | − | 0.968828i | \(-0.420314\pi\) | ||||
0.247733 | + | 0.968828i | \(0.420314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.50758 | −0.209993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5616 | −1.16694 | −0.583472 | − | 0.812133i | \(-0.698306\pi\) | ||||
−0.583472 | + | 0.812133i | \(0.698306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.68466 | 0.278474 | 0.139237 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139237 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1231 | −0.658876 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.12311 | −0.0662948 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.1771 | 2.36336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.05398 | 0.120406 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.0540 | −1.87261 | −0.936307 | − | 0.351184i | \(-0.885779\pi\) | ||||
−0.936307 | + | 0.351184i | \(0.885779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.68466 | 0.503935 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.8769 | −1.20734 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.12311 | 0.410569 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.36932 | −0.538253 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.87689 | −0.393770 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.6847 | 1.63712 | 0.818560 | − | 0.574421i | \(-0.194773\pi\) | ||||
0.818560 | + | 0.574421i | \(0.194773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4384 | −1.04893 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8769 | −0.730182 | −0.365091 | − | 0.930972i | \(-0.618962\pi\) | ||||
−0.365091 | + | 0.930972i | \(0.618962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.6847 | 1.50831 | 0.754153 | − | 0.656699i | \(-0.228048\pi\) | ||||
0.754153 | + | 0.656699i | \(0.228048\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.561553 | 0.0316399 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0000 | 0.561656 | 0.280828 | − | 0.959758i | \(-0.409391\pi\) | ||||
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.684658 | 0.0383335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.6155 | −1.31809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53.8617 | 2.99695 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.68466 | −0.370798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.93087 | 0.383278 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.43845 | 0.134436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.63068 | −0.253760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.24621 | 0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.8769 | 0.699377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.75379 | −0.528197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.87689 | −0.262563 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1231 | −0.811851 | −0.405925 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405925 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7538 | 0.629166 | 0.314583 | − | 0.949230i | \(-0.398135\pi\) | ||||
0.314583 | + | 0.949230i | \(0.398135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.1771 | 1.98437 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.19224 | −0.116681 | −0.0583405 | − | 0.998297i | \(-0.518581\pi\) | ||||
−0.0583405 | + | 0.998297i | \(0.518581\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.8078 | 0.624933 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0000 | 1.68890 | 0.844448 | − | 0.535638i | \(-0.179929\pi\) | ||||
0.844448 | + | 0.535638i | \(0.179929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.3693 | −0.701707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.24621 | 0.222257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9309 | 0.779385 | 0.389693 | − | 0.920945i | \(-0.372581\pi\) | ||||
0.389693 | + | 0.920945i | \(0.372581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.630683 | 0.0328321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.1231 | 0.681318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3693 | −0.795793 | −0.397897 | − | 0.917430i | \(-0.630260\pi\) | ||||
−0.397897 | + | 0.917430i | \(0.630260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.93087 | 0.150947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4924 | −1.66902 | −0.834512 | − | 0.550990i | \(-0.814250\pi\) | ||||
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.75379 | −0.499702 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.75379 | −0.498395 | −0.249198 | − | 0.968453i | \(-0.580167\pi\) | ||||
−0.249198 | + | 0.968453i | \(0.580167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56155 | 0.0795841 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.3002 | −1.13066 | −0.565332 | − | 0.824863i | \(-0.691252\pi\) | ||||
−0.565332 | + | 0.824863i | \(0.691252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6155 | 1.19429 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.6155 | −1.19125 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.684658 | −0.0344489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1771 | 1.16322 | 0.581612 | − | 0.813466i | \(-0.302422\pi\) | ||||
0.581612 | + | 0.813466i | \(0.302422\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.1231 | 0.556852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.9309 | −0.645737 | −0.322868 | − | 0.946444i | \(-0.604647\pi\) | ||||
−0.322868 | + | 0.946444i | \(0.604647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.7538 | −2.07990 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8769 | −0.638284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.4924 | −0.914391 | −0.457196 | − | 0.889366i | \(-0.651146\pi\) | ||||
−0.457196 | + | 0.889366i | \(0.651146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5076 | −0.567627 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.3693 | 1.63410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.2462 | 0.891386 | 0.445693 | − | 0.895186i | \(-0.352957\pi\) | ||||
0.445693 | + | 0.895186i | \(0.352957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.56155 | −0.173579 | −0.0867897 | − | 0.996227i | \(-0.527661\pi\) | ||||
−0.0867897 | + | 0.996227i | \(0.527661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.36932 | −0.0665785 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.56155 | 0.366789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.87689 | 0.332796 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.3002 | 0.786980 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9309 | −1.10454 | −0.552271 | − | 0.833665i | \(-0.686238\pi\) | ||||
−0.552271 | + | 0.833665i | \(0.686238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7538 | 0.949307 | 0.474653 | − | 0.880173i | \(-0.342573\pi\) | ||||
0.474653 | + | 0.880173i | \(0.342573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.684658 | 0.0328269 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.2462 | 1.06418 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.1231 | 0.912696 | 0.456348 | − | 0.889801i | \(-0.349157\pi\) | ||||
0.456348 | + | 0.889801i | \(0.349157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.561553 | −0.0267406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6155 | 0.931962 | 0.465981 | − | 0.884795i | \(-0.345702\pi\) | ||||
0.465981 | + | 0.884795i | \(0.345702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.12311 | −0.242858 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.384472 | 0.0181849 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3153 | −1.00593 | −0.502967 | − | 0.864306i | \(-0.667758\pi\) | ||||
−0.502967 | + | 0.864306i | \(0.667758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75379 | 0.0825827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.9309 | −1.45326 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.68466 | 0.313382 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.63068 | 0.403726 | 0.201863 | − | 0.979414i | \(-0.435300\pi\) | ||||
0.201863 | + | 0.979414i | \(0.435300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.0540 | −1.96291 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8769 | −0.879185 | −0.439592 | − | 0.898197i | \(-0.644877\pi\) | ||||
−0.439592 | + | 0.898197i | \(0.644877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24621 | −0.290286 | −0.145143 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145143 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.75379 | −0.452321 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5616 | −1.18285 | −0.591424 | − | 0.806361i | \(-0.701434\pi\) | ||||
−0.591424 | + | 0.806361i | \(0.701434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.24621 | −0.103720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.63068 | −0.305526 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.1231 | −0.511441 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.12311 | 0.326831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.36932 | −0.337418 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.3693 | 0.793624 | 0.396812 | − | 0.917900i | \(-0.370116\pi\) | ||||
0.396812 | + | 0.917900i | \(0.370116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −55.1231 | −2.51340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.87689 | 0.221906 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.31534 | −0.0597266 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.12311 | 0.141521 | 0.0707607 | − | 0.997493i | \(-0.477457\pi\) | ||||
0.0707607 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.6307 | −1.38517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.31534 | 0.149619 | 0.0748096 | − | 0.997198i | \(-0.476165\pi\) | ||||
0.0748096 | + | 0.997198i | \(0.476165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.31534 | −0.149315 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.876894 | −0.0394135 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.192236 | 0.00860566 | 0.00430283 | − | 0.999991i | \(-0.498630\pi\) | ||||
0.00430283 | + | 0.999991i | \(0.498630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.54640 | 0.292471 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1771 | −1.30094 | −0.650471 | − | 0.759531i | \(-0.725428\pi\) | ||||
−0.650471 | + | 0.759531i | \(0.725428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.4773 | 2.19736 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.7386 | −1.45111 | −0.725557 | − | 0.688162i | \(-0.758418\pi\) | ||||
−0.725557 | + | 0.688162i | \(0.758418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.24621 | −0.187841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.6155 | −1.74907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.8078 | 0.520312 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.80776 | −0.167465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.1922 | 1.58866 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2462 | −0.536516 | −0.268258 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268258 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000 | 0.524723 | 0.262362 | − | 0.964970i | \(-0.415499\pi\) | ||||
0.262362 | + | 0.964970i | \(0.415499\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.56155 | 0.0681518 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.2311 | 2.05742 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2462 | −0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24621 | −0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50758 | 0.325189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.1231 | 0.653829 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.24621 | 0.269544 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.56155 | −0.0672608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.4233 | −1.78093 | −0.890463 | − | 0.455055i | \(-0.849620\pi\) | ||||
−0.890463 | + | 0.455055i | \(0.849620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.43845 | −0.190122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.86174 | −0.164815 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12311 | −0.133049 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.684658 | 0.0291146 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.8769 | −0.546594 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.6155 | 0.746394 | 0.373197 | − | 0.927752i | \(-0.378262\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.6155 | −2.01392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.4384 | −0.778472 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.50758 | 0.316407 | 0.158203 | − | 0.987407i | \(-0.449430\pi\) | ||||
0.158203 | + | 0.987407i | \(0.449430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.24621 | −0.346921 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | −0.293972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9848 | 0.795886 | 0.397943 | − | 0.917410i | \(-0.369724\pi\) | ||||
0.397943 | + | 0.917410i | \(0.369724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.06913 | −0.0446636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12311 | 0.130243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.56155 | −0.148269 | −0.0741347 | − | 0.997248i | \(-0.523619\pi\) | ||||
−0.0741347 | + | 0.997248i | \(0.523619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4924 | 0.851636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.4924 | −0.848709 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.75379 | −0.155200 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2462 | −0.422906 | −0.211453 | − | 0.977388i | \(-0.567820\pi\) | ||||
−0.211453 | + | 0.977388i | \(0.567820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.4924 | 1.83328 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.4924 | 0.842946 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4233 | 1.53679 | 0.768395 | − | 0.639976i | \(-0.221056\pi\) | ||||
0.768395 | + | 0.639976i | \(0.221056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.56155 | −0.309993 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.2462 | −0.910477 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.9309 | −1.91754 | −0.958772 | − | 0.284178i | \(-0.908279\pi\) | ||||
−0.958772 | + | 0.284178i | \(0.908279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.26137 | 0.0513668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.56155 | 0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.68466 | −0.352499 | −0.176250 | − | 0.984345i | \(-0.556397\pi\) | ||||
−0.176250 | + | 0.984345i | \(0.556397\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.684658 | −0.0277438 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.3002 | −0.659435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.7386 | −0.676067 | −0.338034 | − | 0.941134i | \(-0.609762\pi\) | ||||
−0.338034 | + | 0.941134i | \(0.609762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.75379 | 0.0707196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7538 | −0.634224 | −0.317112 | − | 0.948388i | \(-0.602713\pi\) | ||||
−0.317112 | + | 0.948388i | \(0.602713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6307 | −0.427283 | −0.213642 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213642 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.3693 | −0.697007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.12311 | 0.205253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.3693 | −0.693664 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.3542 | 2.48622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4233 | −1.09170 | −0.545852 | − | 0.837882i | \(-0.683794\pi\) | ||||
−0.545852 | + | 0.837882i | \(0.683794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.4233 | 1.08998 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.24621 | 0.247873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.68466 | −0.264856 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9848 | −0.907847 | −0.453923 | − | 0.891041i | \(-0.649976\pi\) | ||||
−0.453923 | + | 0.891041i | \(0.649976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.0540 | 1.18521 | 0.592607 | − | 0.805492i | \(-0.298099\pi\) | ||||
0.592607 | + | 0.805492i | \(0.298099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.1231 | −0.437972 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000 | 0.314512 | 0.157256 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157256 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.24621 | −0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.75379 | 0.382281 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.4924 | 1.50632 | 0.753162 | − | 0.657835i | \(-0.228527\pi\) | ||||
0.753162 | + | 0.657835i | \(0.228527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.1231 | 0.590909 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.38447 | 0.0930271 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.192236 | 0.00748845 | 0.00374422 | − | 0.999993i | \(-0.498808\pi\) | ||||
0.00374422 | + | 0.999993i | \(0.498808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6155 | 0.685165 | 0.342582 | − | 0.939488i | \(-0.388698\pi\) | ||||
0.342582 | + | 0.939488i | \(0.388698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −78.9309 | −3.06542 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.12311 | −0.276222 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.36932 | −0.0530202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.5464 | 1.49029 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7386 | −0.414560 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.6155 | 1.60416 | 0.802080 | − | 0.597216i | \(-0.203727\pi\) | ||||
0.802080 | + | 0.597216i | \(0.203727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.56155 | −0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.31534 | 0.0505527 | 0.0252763 | − | 0.999681i | \(-0.491953\pi\) | ||||
0.0252763 | + | 0.999681i | \(0.491953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.31534 | 0.0504782 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6695 | 0.677097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.9848 | −1.72130 | −0.860649 | − | 0.509199i | \(-0.829942\pi\) | ||||
−0.860649 | + | 0.509199i | \(0.829942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.36932 | 0.281567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7538 | 0.677349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −87.7235 | −3.34200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4924 | −0.627401 | −0.313701 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313701 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.876894 | 0.0333105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.3693 | −0.810584 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.49242 | −0.321673 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.9848 | −0.642426 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.31534 | 0.351836 | 0.175918 | − | 0.984405i | \(-0.443711\pi\) | ||||
0.175918 | + | 0.984405i | \(0.443711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.7386 | 2.21537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.80776 | −0.143409 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.05398 | 0.152250 | 0.0761251 | − | 0.997098i | \(-0.475745\pi\) | ||||
0.0761251 | + | 0.997098i | \(0.475745\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.384472 | −0.0144188 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5076 | 0.730565 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.4384 | −0.390376 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.1922 | −1.05286 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6155 | −0.880711 | −0.440355 | − | 0.897824i | \(-0.645148\pi\) | ||||
−0.440355 | + | 0.897824i | \(0.645148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.8078 | −0.439744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.12311 | 0.116150 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.438447 | −0.0162835 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9848 | 1.81675 | 0.908374 | − | 0.418159i | \(-0.137325\pi\) | ||||
0.908374 | + | 0.418159i | \(0.137325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53.8617 | 1.99215 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.4384 | −0.607168 | −0.303584 | − | 0.952805i | \(-0.598183\pi\) | ||||
−0.303584 | + | 0.952805i | \(0.598183\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.56155 | −0.0575987 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.50758 | 0.129203 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.43845 | 0.236842 | 0.118421 | − | 0.992963i | \(-0.462217\pi\) | ||||
0.118421 | + | 0.992963i | \(0.462217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −74.3542 | −2.73147 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.246211 | −0.00902048 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.73863 | 0.246554 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1231 | −0.552586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.3153 | −1.14271 | −0.571357 | − | 0.820702i | \(-0.693583\pi\) | ||||
−0.571357 | + | 0.820702i | \(0.693583\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.8769 | −0.760796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.8078 | 0.720878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3693 | −0.558607 | −0.279304 | − | 0.960203i | \(-0.590104\pi\) | ||||
−0.279304 | + | 0.960203i | \(0.590104\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.61553 | −0.276426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0000 | 0.942499 | 0.471250 | − | 0.882000i | \(-0.343803\pi\) | ||||
0.471250 | + | 0.882000i | \(0.343803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.43845 | 0.160683 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.24621 | 0.153522 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.7386 | −0.965476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9848 | 1.55007 | 0.775037 | − | 0.631916i | \(-0.217731\pi\) | ||||
0.775037 | + | 0.631916i | \(0.217731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.8769 | −1.03998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.8078 | 1.07211 | 0.536055 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536055 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.24621 | 0.224371 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.8769 | 0.461956 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.43845 | 0.0871430 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.24621 | 0.151554 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.1771 | −1.18264 | −0.591318 | − | 0.806439i | \(-0.701392\pi\) | ||||
−0.591318 | + | 0.806439i | \(0.701392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.6307 | 0.520866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.24621 | 0.293202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.9697 | −1.63243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.4924 | −0.726791 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.8078 | −0.630783 | −0.315392 | − | 0.948962i | \(-0.602136\pi\) | ||||
−0.315392 | + | 0.948962i | \(0.602136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.4384 | 0.652305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.87689 | −0.101650 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.63068 | 0.233992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.12311 | −0.110075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.63068 | −0.233411 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.05398 | 0.142530 | 0.0712651 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712651 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.6155 | 0.969712 | 0.484856 | − | 0.874594i | \(-0.338872\pi\) | ||||
0.484856 | + | 0.874594i | \(0.338872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.75379 | −0.342080 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.6155 | 0.687102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.7386 | 1.77512 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.75379 | 0.131168 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.3002 | −1.89509 | −0.947545 | − | 0.319623i | \(-0.896444\pi\) | ||||
−0.947545 | + | 0.319623i | \(0.896444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.7538 | −0.618858 | −0.309429 | − | 0.950923i | \(-0.600138\pi\) | ||||
−0.309429 | + | 0.950923i | \(0.600138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.43845 | −0.0848958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.8769 | −0.865054 | −0.432527 | − | 0.901621i | \(-0.642378\pi\) | ||||
−0.432527 | + | 0.901621i | \(0.642378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.61553 | −0.195035 | −0.0975177 | − | 0.995234i | \(-0.531090\pi\) | ||||
−0.0975177 | + | 0.995234i | \(0.531090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.8769 | 0.446695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.56155 | 0.261992 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.19224 | −0.145078 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.7386 | −1.20074 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1231 | 0.660203 | 0.330101 | − | 0.943945i | \(-0.392917\pi\) | ||||
0.330101 | + | 0.943945i | \(0.392917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8078 | −0.993371 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.5464 | −1.05207 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.6847 | −1.08999 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.56155 | −0.294178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.31534 | 0.251062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.7538 | 0.882829 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7538 | −0.539399 | −0.269700 | − | 0.962944i | \(-0.586924\pi\) | ||||
−0.269700 | + | 0.962944i | \(0.586924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.7386 | 1.80152 | 0.900759 | − | 0.434320i | \(-0.143011\pi\) | ||||
0.900759 | + | 0.434320i | \(0.143011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.9848 | −1.26191 | −0.630953 | − | 0.775821i | \(-0.717336\pi\) | ||||
−0.630953 | + | 0.775821i | \(0.717336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.75379 | −0.0597690 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.4924 | 0.969893 | 0.484947 | − | 0.874544i | \(-0.338839\pi\) | ||||
0.484947 | + | 0.874544i | \(0.338839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.1771 | −0.788044 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 62.7386 | 2.13072 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.06913 | −0.0362678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.0152 | 0.508769 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.738634 | −0.0249990 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5076 | 0.456118 | 0.228059 | − | 0.973647i | \(-0.426762\pi\) | ||||
0.228059 | + | 0.973647i | \(0.426762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −50.0540 | −1.68828 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.1080 | 1.82294 | 0.911472 | − | 0.411363i | \(-0.134947\pi\) | ||||
0.911472 | + | 0.411363i | \(0.134947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.7538 | −0.732073 | −0.366037 | − | 0.930600i | \(-0.619286\pi\) | ||||
−0.366037 | + | 0.930600i | \(0.619286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.24621 | −0.209964 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.4924 | −1.22530 | −0.612648 | − | 0.790356i | \(-0.709896\pi\) | ||||
−0.612648 | + | 0.790356i | \(0.709896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.24621 | −0.209491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9309 | 0.366198 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.3693 | 0.581242 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.6004 | −1.08849 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.73863 | −0.0913385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 99.2311 | 3.30587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.1231 | 0.370154 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.12311 | −0.170298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1080 | 1.59740 | 0.798699 | − | 0.601731i | \(-0.205522\pi\) | ||||
0.798699 | + | 0.601731i | \(0.205522\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.36932 | 0.111753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.7386 | 0.620158 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.7386 | −0.355008 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.1231 | −0.499409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.43845 | 0.0804370 | 0.0402185 | − | 0.999191i | \(-0.487195\pi\) | ||||
0.0402185 | + | 0.999191i | \(0.487195\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.7926 | 1.47597 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.24621 | 0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.63068 | 0.217780 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.87689 | −0.0943878 | −0.0471939 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471939 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.12311 | 0.233450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.1080 | −0.658305 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.8078 | 0.386155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8078 | 1.23513 | 0.617563 | − | 0.786521i | \(-0.288120\pi\) | ||||
0.617563 | + | 0.786521i | \(0.288120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.6695 | 1.35983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.6307 | −0.933334 | −0.466667 | − | 0.884433i | \(-0.654545\pi\) | ||||
−0.466667 | + | 0.884433i | \(0.654545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.50758 | −0.114222 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.56155 | 0.180917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.2311 | 1.14486 | 0.572428 | − | 0.819955i | \(-0.306002\pi\) | ||||
0.572428 | + | 0.819955i | \(0.306002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3845 | 0.921399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6155 | 0.506368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.8617 | −1.67997 | −0.839983 | − | 0.542612i | \(-0.817435\pi\) | ||||
−0.839983 | + | 0.542612i | \(0.817435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.684658 | 0.0221550 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.06913 | 0.0345601 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.36932 | −0.237968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.01515 | 0.258553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.49242 | 0.273664 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.1231 | −0.422448 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.1080 | 1.41842 | 0.709208 | − | 0.704999i | \(-0.249053\pi\) | ||||
0.709208 | + | 0.704999i | \(0.249053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 84.1080 | 2.70194 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7386 | 0.729717 | 0.364859 | − | 0.931063i | \(-0.381117\pi\) | ||||
0.364859 | + | 0.931063i | \(0.381117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3693 | 0.685069 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.4384 | −0.334298 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9848 | 0.351436 | 0.175718 | − | 0.984441i | \(-0.443775\pi\) | ||||
0.175718 | + | 0.984441i | \(0.443775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.49242 | −0.0795769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.1771 | −0.930604 | −0.465302 | − | 0.885152i | \(-0.654054\pi\) | ||||
−0.465302 | + | 0.885152i | \(0.654054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1231 | −0.418137 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.80776 | 0.121202 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.2462 | 0.707388 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4924 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7386 | 0.594653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2462 | 0.451635 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.9309 | 1.80302 | 0.901509 | − | 0.432760i | \(-0.142460\pi\) | ||||
0.901509 | + | 0.432760i | \(0.142460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.8617 | −1.45100 |
(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 | 2240.2.a.be.1.2 | 2 | ||
4.3 | odd | 2 | 2240.2.a.bi.1.1 | 2 | |||
8.3 | odd | 2 | 560.2.a.g.1.2 | 2 | |||
8.5 | even | 2 | 280.2.a.d.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 2520.2.a.w.1.1 | 2 | |||
24.11 | even | 2 | 5040.2.a.bq.1.2 | 2 | |||
40.3 | even | 4 | 2800.2.g.u.449.3 | 4 | |||
40.13 | odd | 4 | 1400.2.g.k.449.2 | 4 | |||
40.19 | odd | 2 | 2800.2.a.bn.1.1 | 2 | |||
40.27 | even | 4 | 2800.2.g.u.449.2 | 4 | |||
40.29 | even | 2 | 1400.2.a.p.1.2 | 2 | |||
40.37 | odd | 4 | 1400.2.g.k.449.3 | 4 | |||
56.5 | odd | 6 | 1960.2.q.u.361.1 | 4 | |||
56.13 | odd | 2 | 1960.2.a.r.1.2 | 2 | |||
56.27 | even | 2 | 3920.2.a.bu.1.1 | 2 | |||
56.37 | even | 6 | 1960.2.q.s.361.2 | 4 | |||
56.45 | odd | 6 | 1960.2.q.u.961.1 | 4 | |||
56.53 | even | 6 | 1960.2.q.s.961.2 | 4 | |||
280.69 | odd | 2 | 9800.2.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
560.2.a.g.1.2 | 2 | 8.3 | odd | 2 | |||
1400.2.a.p.1.2 | 2 | 40.29 | even | 2 | |||
1400.2.g.k.449.2 | 4 | 40.13 | odd | 4 | |||
1400.2.g.k.449.3 | 4 | 40.37 | odd | 4 | |||
1960.2.a.r.1.2 | 2 | 56.13 | odd | 2 | |||
1960.2.q.s.361.2 | 4 | 56.37 | even | 6 | |||
1960.2.q.s.961.2 | 4 | 56.53 | even | 6 | |||
1960.2.q.u.361.1 | 4 | 56.5 | odd | 6 | |||
1960.2.q.u.961.1 | 4 | 56.45 | odd | 6 | |||
2240.2.a.be.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2240.2.a.bi.1.1 | 2 | 4.3 | odd | 2 | |||
2520.2.a.w.1.1 | 2 | 24.5 | odd | 2 | |||
2800.2.a.bn.1.1 | 2 | 40.19 | odd | 2 | |||
2800.2.g.u.449.2 | 4 | 40.27 | even | 4 | |||
2800.2.g.u.449.3 | 4 | 40.3 | even | 4 | |||
3920.2.a.bu.1.1 | 2 | 56.27 | even | 2 | |||
5040.2.a.bq.1.2 | 2 | 24.11 | even | 2 | |||
9800.2.a.by.1.1 | 2 | 280.69 | odd | 2 |