Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.56155 | 0.968176 | 0.484088 | − | 0.875019i | \(-0.339151\pi\) | ||||
0.484088 | + | 0.875019i | \(0.339151\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 2.56155 | 0.684604 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.68466 | −1.76298 | −0.881491 | − | 0.472201i | \(-0.843460\pi\) | ||||
−0.881491 | + | 0.472201i | \(0.843460\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.56155 | −0.558977 | ||||||||
\(22\) | 2.56155 | 0.546125 | ||||||||
\(23\) | 1.43845 | 0.299937 | 0.149968 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149968 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.56155 | 0.484088 | ||||||||
\(29\) | 7.12311 | 1.32273 | 0.661364 | − | 0.750065i | \(-0.269978\pi\) | ||||
0.661364 | + | 0.750065i | \(0.269978\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | 2.56155 | 0.432981 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.12311 | −0.513435 | −0.256718 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256718 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(38\) | −7.68466 | −1.24662 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 7.12311 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(42\) | −2.56155 | −0.395256 | ||||||||
\(43\) | 12.8078 | 1.95317 | 0.976583 | − | 0.215142i | \(-0.0690213\pi\) | ||||
0.976583 | + | 0.215142i | \(0.0690213\pi\) | |||||||
\(44\) | 2.56155 | 0.386169 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.43845 | 0.212087 | ||||||||
\(47\) | 5.12311 | 0.747282 | 0.373641 | − | 0.927573i | \(-0.378109\pi\) | ||||
0.373641 | + | 0.927573i | \(0.378109\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.12311 | 0.437322 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 7.43845 | 1.02175 | 0.510875 | − | 0.859655i | \(-0.329322\pi\) | ||||
0.510875 | + | 0.859655i | \(0.329322\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.56155 | 0.345400 | ||||||||
\(56\) | 2.56155 | 0.342302 | ||||||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | 7.12311 | 0.935310 | ||||||||
\(59\) | −13.1231 | −1.70848 | −0.854241 | − | 0.519877i | \(-0.825978\pi\) | ||||
−0.854241 | + | 0.519877i | \(0.825978\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 2.56155 | 0.322725 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −2.56155 | −0.315305 | ||||||||
\(67\) | −15.3693 | −1.87766 | −0.938830 | − | 0.344380i | \(-0.888089\pi\) | ||||
−0.938830 | + | 0.344380i | \(0.888089\pi\) | |||||||
\(68\) | −3.12311 | −0.378732 | ||||||||
\(69\) | −1.43845 | −0.173169 | ||||||||
\(70\) | 2.56155 | 0.306164 | ||||||||
\(71\) | −7.68466 | −0.912001 | −0.456001 | − | 0.889979i | \(-0.650719\pi\) | ||||
−0.456001 | + | 0.889979i | \(0.650719\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −10.8078 | −1.26495 | −0.632477 | − | 0.774580i | \(-0.717962\pi\) | ||||
−0.632477 | + | 0.774580i | \(0.717962\pi\) | |||||||
\(74\) | −3.12311 | −0.363054 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −7.68466 | −0.881491 | ||||||||
\(77\) | 6.56155 | 0.747758 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −4.31534 | −0.485514 | −0.242757 | − | 0.970087i | \(-0.578052\pi\) | ||||
−0.242757 | + | 0.970087i | \(0.578052\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.12311 | 0.786615 | ||||||||
\(83\) | 14.2462 | 1.56372 | 0.781862 | − | 0.623451i | \(-0.214270\pi\) | ||||
0.781862 | + | 0.623451i | \(0.214270\pi\) | |||||||
\(84\) | −2.56155 | −0.279488 | ||||||||
\(85\) | −3.12311 | −0.338748 | ||||||||
\(86\) | 12.8078 | 1.38110 | ||||||||
\(87\) | −7.12311 | −0.763677 | ||||||||
\(88\) | 2.56155 | 0.273062 | ||||||||
\(89\) | −13.6847 | −1.45057 | −0.725285 | − | 0.688448i | \(-0.758292\pi\) | ||||
−0.725285 | + | 0.688448i | \(0.758292\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 5.12311 | 0.537047 | ||||||||
\(92\) | 1.43845 | 0.149968 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 5.12311 | 0.528408 | ||||||||
\(95\) | −7.68466 | −0.788429 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −0.438447 | −0.0442899 | ||||||||
\(99\) | 2.56155 | 0.257446 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.561553 | −0.0558766 | −0.0279383 | − | 0.999610i | \(-0.508894\pi\) | ||||
−0.0279383 | + | 0.999610i | \(0.508894\pi\) | |||||||
\(102\) | 3.12311 | 0.309234 | ||||||||
\(103\) | −1.75379 | −0.172806 | −0.0864030 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864030 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −2.56155 | −0.249982 | ||||||||
\(106\) | 7.43845 | 0.722486 | ||||||||
\(107\) | −2.56155 | −0.247635 | −0.123817 | − | 0.992305i | \(-0.539514\pi\) | ||||
−0.123817 | + | 0.992305i | \(0.539514\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 5.36932 | 0.514287 | 0.257144 | − | 0.966373i | \(-0.417219\pi\) | ||||
0.257144 | + | 0.966373i | \(0.417219\pi\) | |||||||
\(110\) | 2.56155 | 0.244234 | ||||||||
\(111\) | 3.12311 | 0.296432 | ||||||||
\(112\) | 2.56155 | 0.242044 | ||||||||
\(113\) | −1.68466 | −0.158479 | −0.0792397 | − | 0.996856i | \(-0.525249\pi\) | ||||
−0.0792397 | + | 0.996856i | \(0.525249\pi\) | |||||||
\(114\) | 7.68466 | 0.719734 | ||||||||
\(115\) | 1.43845 | 0.134136 | ||||||||
\(116\) | 7.12311 | 0.661364 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | −13.1231 | −1.20808 | ||||||||
\(119\) | −8.00000 | −0.733359 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −7.12311 | −0.642269 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.56155 | 0.228201 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.8078 | −1.12766 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −15.3693 | −1.34282 | −0.671412 | − | 0.741085i | \(-0.734312\pi\) | ||||
−0.671412 | + | 0.741085i | \(0.734312\pi\) | |||||||
\(132\) | −2.56155 | −0.222955 | ||||||||
\(133\) | −19.6847 | −1.70688 | ||||||||
\(134\) | −15.3693 | −1.32771 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −3.12311 | −0.267804 | ||||||||
\(137\) | 20.2462 | 1.72975 | 0.864875 | − | 0.501987i | \(-0.167397\pi\) | ||||
0.864875 | + | 0.501987i | \(0.167397\pi\) | |||||||
\(138\) | −1.43845 | −0.122449 | ||||||||
\(139\) | −17.1231 | −1.45236 | −0.726181 | − | 0.687503i | \(-0.758707\pi\) | ||||
−0.726181 | + | 0.687503i | \(0.758707\pi\) | |||||||
\(140\) | 2.56155 | 0.216491 | ||||||||
\(141\) | −5.12311 | −0.431443 | ||||||||
\(142\) | −7.68466 | −0.644882 | ||||||||
\(143\) | 5.12311 | 0.428416 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.12311 | 0.591542 | ||||||||
\(146\) | −10.8078 | −0.894457 | ||||||||
\(147\) | 0.438447 | 0.0361625 | ||||||||
\(148\) | −3.12311 | −0.256718 | ||||||||
\(149\) | 17.0540 | 1.39712 | 0.698558 | − | 0.715553i | \(-0.253825\pi\) | ||||
0.698558 | + | 0.715553i | \(0.253825\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | −7.68466 | −0.623308 | ||||||||
\(153\) | −3.12311 | −0.252488 | ||||||||
\(154\) | 6.56155 | 0.528745 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 17.0540 | 1.36106 | 0.680528 | − | 0.732722i | \(-0.261751\pi\) | ||||
0.680528 | + | 0.732722i | \(0.261751\pi\) | |||||||
\(158\) | −4.31534 | −0.343310 | ||||||||
\(159\) | −7.43845 | −0.589907 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.68466 | 0.290392 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.3693 | −1.20382 | −0.601909 | − | 0.798565i | \(-0.705593\pi\) | ||||
−0.601909 | + | 0.798565i | \(0.705593\pi\) | |||||||
\(164\) | 7.12311 | 0.556221 | ||||||||
\(165\) | −2.56155 | −0.199417 | ||||||||
\(166\) | 14.2462 | 1.10572 | ||||||||
\(167\) | −6.56155 | −0.507748 | −0.253874 | − | 0.967237i | \(-0.581705\pi\) | ||||
−0.253874 | + | 0.967237i | \(0.581705\pi\) | |||||||
\(168\) | −2.56155 | −0.197628 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −3.12311 | −0.239531 | ||||||||
\(171\) | −7.68466 | −0.587661 | ||||||||
\(172\) | 12.8078 | 0.976583 | ||||||||
\(173\) | 8.24621 | 0.626948 | 0.313474 | − | 0.949597i | \(-0.398507\pi\) | ||||
0.313474 | + | 0.949597i | \(0.398507\pi\) | |||||||
\(174\) | −7.12311 | −0.540001 | ||||||||
\(175\) | 2.56155 | 0.193635 | ||||||||
\(176\) | 2.56155 | 0.193084 | ||||||||
\(177\) | 13.1231 | 0.986393 | ||||||||
\(178\) | −13.6847 | −1.02571 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −13.0540 | −0.970294 | −0.485147 | − | 0.874433i | \(-0.661234\pi\) | ||||
−0.485147 | + | 0.874433i | \(0.661234\pi\) | |||||||
\(182\) | 5.12311 | 0.379750 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 1.43845 | 0.106044 | ||||||||
\(185\) | −3.12311 | −0.229615 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | −8.00000 | −0.585018 | ||||||||
\(188\) | 5.12311 | 0.373641 | ||||||||
\(189\) | −2.56155 | −0.186326 | ||||||||
\(190\) | −7.68466 | −0.557504 | ||||||||
\(191\) | −14.2462 | −1.03082 | −0.515410 | − | 0.856944i | \(-0.672360\pi\) | ||||
−0.515410 | + | 0.856944i | \(0.672360\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 14.4924 | 1.04319 | 0.521594 | − | 0.853194i | \(-0.325338\pi\) | ||||
0.521594 | + | 0.853194i | \(0.325338\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | −0.438447 | −0.0313177 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 2.56155 | 0.182042 | ||||||||
\(199\) | −16.8078 | −1.19147 | −0.595735 | − | 0.803181i | \(-0.703139\pi\) | ||||
−0.595735 | + | 0.803181i | \(0.703139\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.3693 | 1.08407 | ||||||||
\(202\) | −0.561553 | −0.0395107 | ||||||||
\(203\) | 18.2462 | 1.28063 | ||||||||
\(204\) | 3.12311 | 0.218661 | ||||||||
\(205\) | 7.12311 | 0.497499 | ||||||||
\(206\) | −1.75379 | −0.122192 | ||||||||
\(207\) | 1.43845 | 0.0999790 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −19.6847 | −1.36162 | ||||||||
\(210\) | −2.56155 | −0.176764 | ||||||||
\(211\) | −23.6847 | −1.63052 | −0.815260 | − | 0.579096i | \(-0.803406\pi\) | ||||
−0.815260 | + | 0.579096i | \(0.803406\pi\) | |||||||
\(212\) | 7.43845 | 0.510875 | ||||||||
\(213\) | 7.68466 | 0.526544 | ||||||||
\(214\) | −2.56155 | −0.175104 | ||||||||
\(215\) | 12.8078 | 0.873482 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.56155 | 0.173890 | ||||||||
\(218\) | 5.36932 | 0.363656 | ||||||||
\(219\) | 10.8078 | 0.730321 | ||||||||
\(220\) | 2.56155 | 0.172700 | ||||||||
\(221\) | −6.24621 | −0.420166 | ||||||||
\(222\) | 3.12311 | 0.209609 | ||||||||
\(223\) | −21.1231 | −1.41451 | −0.707254 | − | 0.706960i | \(-0.750066\pi\) | ||||
−0.707254 | + | 0.706960i | \(0.750066\pi\) | |||||||
\(224\) | 2.56155 | 0.171151 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −1.68466 | −0.112062 | ||||||||
\(227\) | 7.68466 | 0.510049 | 0.255024 | − | 0.966935i | \(-0.417917\pi\) | ||||
0.255024 | + | 0.966935i | \(0.417917\pi\) | |||||||
\(228\) | 7.68466 | 0.508929 | ||||||||
\(229\) | −16.5616 | −1.09442 | −0.547209 | − | 0.836996i | \(-0.684310\pi\) | ||||
−0.547209 | + | 0.836996i | \(0.684310\pi\) | |||||||
\(230\) | 1.43845 | 0.0948484 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 7.12311 | 0.467655 | ||||||||
\(233\) | −17.0540 | −1.11724 | −0.558622 | − | 0.829423i | \(-0.688670\pi\) | ||||
−0.558622 | + | 0.829423i | \(0.688670\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | 5.12311 | 0.334195 | ||||||||
\(236\) | −13.1231 | −0.854241 | ||||||||
\(237\) | 4.31534 | 0.280312 | ||||||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | −4.43845 | −0.285314 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −0.438447 | −0.0280114 | ||||||||
\(246\) | −7.12311 | −0.454153 | ||||||||
\(247\) | −15.3693 | −0.977926 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −14.2462 | −0.902817 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 16.4924 | 1.04099 | 0.520496 | − | 0.853864i | \(-0.325747\pi\) | ||||
0.520496 | + | 0.853864i | \(0.325747\pi\) | |||||||
\(252\) | 2.56155 | 0.161363 | ||||||||
\(253\) | 3.68466 | 0.231652 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.12311 | 0.195576 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.68466 | −0.105086 | −0.0525431 | − | 0.998619i | \(-0.516733\pi\) | ||||
−0.0525431 | + | 0.998619i | \(0.516733\pi\) | |||||||
\(258\) | −12.8078 | −0.797377 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 7.12311 | 0.440909 | ||||||||
\(262\) | −15.3693 | −0.949520 | ||||||||
\(263\) | −20.4924 | −1.26362 | −0.631808 | − | 0.775125i | \(-0.717687\pi\) | ||||
−0.631808 | + | 0.775125i | \(0.717687\pi\) | |||||||
\(264\) | −2.56155 | −0.157653 | ||||||||
\(265\) | 7.43845 | 0.456940 | ||||||||
\(266\) | −19.6847 | −1.20694 | ||||||||
\(267\) | 13.6847 | 0.837487 | ||||||||
\(268\) | −15.3693 | −0.938830 | ||||||||
\(269\) | −0.246211 | −0.0150118 | −0.00750588 | − | 0.999972i | \(-0.502389\pi\) | ||||
−0.00750588 | + | 0.999972i | \(0.502389\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 27.0540 | 1.64341 | 0.821706 | − | 0.569912i | \(-0.193023\pi\) | ||||
0.821706 | + | 0.569912i | \(0.193023\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | −5.12311 | −0.310064 | ||||||||
\(274\) | 20.2462 | 1.22312 | ||||||||
\(275\) | 2.56155 | 0.154467 | ||||||||
\(276\) | −1.43845 | −0.0865843 | ||||||||
\(277\) | −5.36932 | −0.322611 | −0.161305 | − | 0.986905i | \(-0.551570\pi\) | ||||
−0.161305 | + | 0.986905i | \(0.551570\pi\) | |||||||
\(278\) | −17.1231 | −1.02698 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 2.56155 | 0.153082 | ||||||||
\(281\) | 4.87689 | 0.290931 | 0.145466 | − | 0.989363i | \(-0.453532\pi\) | ||||
0.145466 | + | 0.989363i | \(0.453532\pi\) | |||||||
\(282\) | −5.12311 | −0.305077 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −7.68466 | −0.456001 | ||||||||
\(285\) | 7.68466 | 0.455200 | ||||||||
\(286\) | 5.12311 | 0.302936 | ||||||||
\(287\) | 18.2462 | 1.07704 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 7.12311 | 0.418283 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | −10.8078 | −0.632477 | ||||||||
\(293\) | 26.4924 | 1.54770 | 0.773852 | − | 0.633367i | \(-0.218327\pi\) | ||||
0.773852 | + | 0.633367i | \(0.218327\pi\) | |||||||
\(294\) | 0.438447 | 0.0255708 | ||||||||
\(295\) | −13.1231 | −0.764057 | ||||||||
\(296\) | −3.12311 | −0.181527 | ||||||||
\(297\) | −2.56155 | −0.148636 | ||||||||
\(298\) | 17.0540 | 0.987910 | ||||||||
\(299\) | 2.87689 | 0.166375 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 32.8078 | 1.89101 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.561553 | 0.0322604 | ||||||||
\(304\) | −7.68466 | −0.440745 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | −3.12311 | −0.178536 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 6.56155 | 0.373879 | ||||||||
\(309\) | 1.75379 | 0.0997696 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −1.75379 | −0.0994482 | −0.0497241 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497241 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 17.0540 | 0.962412 | ||||||||
\(315\) | 2.56155 | 0.144327 | ||||||||
\(316\) | −4.31534 | −0.242757 | ||||||||
\(317\) | 16.8769 | 0.947901 | 0.473950 | − | 0.880552i | \(-0.342828\pi\) | ||||
0.473950 | + | 0.880552i | \(0.342828\pi\) | |||||||
\(318\) | −7.43845 | −0.417127 | ||||||||
\(319\) | 18.2462 | 1.02159 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.56155 | 0.142972 | ||||||||
\(322\) | 3.68466 | 0.205338 | ||||||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −15.3693 | −0.851228 | ||||||||
\(327\) | −5.36932 | −0.296924 | ||||||||
\(328\) | 7.12311 | 0.393308 | ||||||||
\(329\) | 13.1231 | 0.723500 | ||||||||
\(330\) | −2.56155 | −0.141009 | ||||||||
\(331\) | −6.24621 | −0.343323 | −0.171661 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171661 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(332\) | 14.2462 | 0.781862 | ||||||||
\(333\) | −3.12311 | −0.171145 | ||||||||
\(334\) | −6.56155 | −0.359032 | ||||||||
\(335\) | −15.3693 | −0.839715 | ||||||||
\(336\) | −2.56155 | −0.139744 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 1.68466 | 0.0914981 | ||||||||
\(340\) | −3.12311 | −0.169374 | ||||||||
\(341\) | 2.56155 | 0.138716 | ||||||||
\(342\) | −7.68466 | −0.415539 | ||||||||
\(343\) | −19.0540 | −1.02882 | ||||||||
\(344\) | 12.8078 | 0.690548 | ||||||||
\(345\) | −1.43845 | −0.0774434 | ||||||||
\(346\) | 8.24621 | 0.443319 | ||||||||
\(347\) | 14.2462 | 0.764777 | 0.382388 | − | 0.924002i | \(-0.375102\pi\) | ||||
0.382388 | + | 0.924002i | \(0.375102\pi\) | |||||||
\(348\) | −7.12311 | −0.381839 | ||||||||
\(349\) | 5.36932 | 0.287413 | 0.143706 | − | 0.989620i | \(-0.454098\pi\) | ||||
0.143706 | + | 0.989620i | \(0.454098\pi\) | |||||||
\(350\) | 2.56155 | 0.136921 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 2.56155 | 0.136531 | ||||||||
\(353\) | −0.246211 | −0.0131045 | −0.00655225 | − | 0.999979i | \(-0.502086\pi\) | ||||
−0.00655225 | + | 0.999979i | \(0.502086\pi\) | |||||||
\(354\) | 13.1231 | 0.697485 | ||||||||
\(355\) | −7.68466 | −0.407859 | ||||||||
\(356\) | −13.6847 | −0.725285 | ||||||||
\(357\) | 8.00000 | 0.423405 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −31.6847 | −1.67225 | −0.836126 | − | 0.548537i | \(-0.815185\pi\) | ||||
−0.836126 | + | 0.548537i | \(0.815185\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 40.0540 | 2.10810 | ||||||||
\(362\) | −13.0540 | −0.686102 | ||||||||
\(363\) | 4.43845 | 0.232958 | ||||||||
\(364\) | 5.12311 | 0.268524 | ||||||||
\(365\) | −10.8078 | −0.565704 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 15.3693 | 0.802272 | 0.401136 | − | 0.916019i | \(-0.368616\pi\) | ||||
0.401136 | + | 0.916019i | \(0.368616\pi\) | |||||||
\(368\) | 1.43845 | 0.0749842 | ||||||||
\(369\) | 7.12311 | 0.370814 | ||||||||
\(370\) | −3.12311 | −0.162363 | ||||||||
\(371\) | 19.0540 | 0.989233 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | −5.68466 | −0.294340 | −0.147170 | − | 0.989111i | \(-0.547017\pi\) | ||||
−0.147170 | + | 0.989111i | \(0.547017\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 5.12311 | 0.264204 | ||||||||
\(377\) | 14.2462 | 0.733717 | ||||||||
\(378\) | −2.56155 | −0.131752 | ||||||||
\(379\) | −7.05398 | −0.362338 | −0.181169 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181169 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(380\) | −7.68466 | −0.394215 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.2462 | −0.728900 | ||||||||
\(383\) | −10.2462 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 6.56155 | 0.334408 | ||||||||
\(386\) | 14.4924 | 0.737645 | ||||||||
\(387\) | 12.8078 | 0.651055 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | 7.75379 | 0.393133 | 0.196566 | − | 0.980491i | \(-0.437021\pi\) | ||||
0.196566 | + | 0.980491i | \(0.437021\pi\) | |||||||
\(390\) | −2.00000 | −0.101274 | ||||||||
\(391\) | −4.49242 | −0.227192 | ||||||||
\(392\) | −0.438447 | −0.0221449 | ||||||||
\(393\) | 15.3693 | 0.775279 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −4.31534 | −0.217128 | ||||||||
\(396\) | 2.56155 | 0.128723 | ||||||||
\(397\) | 9.05398 | 0.454406 | 0.227203 | − | 0.973847i | \(-0.427042\pi\) | ||||
0.227203 | + | 0.973847i | \(0.427042\pi\) | |||||||
\(398\) | −16.8078 | −0.842497 | ||||||||
\(399\) | 19.6847 | 0.985466 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −13.6847 | −0.683379 | −0.341690 | − | 0.939813i | \(-0.610999\pi\) | ||||
−0.341690 | + | 0.939813i | \(0.610999\pi\) | |||||||
\(402\) | 15.3693 | 0.766552 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | −0.561553 | −0.0279383 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 18.2462 | 0.905544 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 3.12311 | 0.154617 | ||||||||
\(409\) | −37.3693 | −1.84779 | −0.923897 | − | 0.382642i | \(-0.875014\pi\) | ||||
−0.923897 | + | 0.382642i | \(0.875014\pi\) | |||||||
\(410\) | 7.12311 | 0.351785 | ||||||||
\(411\) | −20.2462 | −0.998672 | ||||||||
\(412\) | −1.75379 | −0.0864030 | ||||||||
\(413\) | −33.6155 | −1.65411 | ||||||||
\(414\) | 1.43845 | 0.0706958 | ||||||||
\(415\) | 14.2462 | 0.699319 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 17.1231 | 0.838522 | ||||||||
\(418\) | −19.6847 | −0.962808 | ||||||||
\(419\) | 5.75379 | 0.281091 | 0.140545 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140545 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(420\) | −2.56155 | −0.124991 | ||||||||
\(421\) | −14.4924 | −0.706317 | −0.353159 | − | 0.935563i | \(-0.614892\pi\) | ||||
−0.353159 | + | 0.935563i | \(0.614892\pi\) | |||||||
\(422\) | −23.6847 | −1.15295 | ||||||||
\(423\) | 5.12311 | 0.249094 | ||||||||
\(424\) | 7.43845 | 0.361243 | ||||||||
\(425\) | −3.12311 | −0.151493 | ||||||||
\(426\) | 7.68466 | 0.372323 | ||||||||
\(427\) | 15.3693 | 0.743773 | ||||||||
\(428\) | −2.56155 | −0.123817 | ||||||||
\(429\) | −5.12311 | −0.247346 | ||||||||
\(430\) | 12.8078 | 0.617645 | ||||||||
\(431\) | −30.2462 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 35.3002 | 1.69642 | 0.848209 | − | 0.529661i | \(-0.177681\pi\) | ||||
0.848209 | + | 0.529661i | \(0.177681\pi\) | |||||||
\(434\) | 2.56155 | 0.122958 | ||||||||
\(435\) | −7.12311 | −0.341527 | ||||||||
\(436\) | 5.36932 | 0.257144 | ||||||||
\(437\) | −11.0540 | −0.528783 | ||||||||
\(438\) | 10.8078 | 0.516415 | ||||||||
\(439\) | 9.61553 | 0.458924 | 0.229462 | − | 0.973318i | \(-0.426303\pi\) | ||||
0.229462 | + | 0.973318i | \(0.426303\pi\) | |||||||
\(440\) | 2.56155 | 0.122117 | ||||||||
\(441\) | −0.438447 | −0.0208784 | ||||||||
\(442\) | −6.24621 | −0.297102 | ||||||||
\(443\) | 23.0540 | 1.09533 | 0.547664 | − | 0.836699i | \(-0.315517\pi\) | ||||
0.547664 | + | 0.836699i | \(0.315517\pi\) | |||||||
\(444\) | 3.12311 | 0.148216 | ||||||||
\(445\) | −13.6847 | −0.648715 | ||||||||
\(446\) | −21.1231 | −1.00021 | ||||||||
\(447\) | −17.0540 | −0.806625 | ||||||||
\(448\) | 2.56155 | 0.121022 | ||||||||
\(449\) | 10.4924 | 0.495168 | 0.247584 | − | 0.968866i | \(-0.420363\pi\) | ||||
0.247584 | + | 0.968866i | \(0.420363\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 18.2462 | 0.859181 | ||||||||
\(452\) | −1.68466 | −0.0792397 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.68466 | 0.360659 | ||||||||
\(455\) | 5.12311 | 0.240175 | ||||||||
\(456\) | 7.68466 | 0.359867 | ||||||||
\(457\) | −24.7386 | −1.15722 | −0.578612 | − | 0.815603i | \(-0.696406\pi\) | ||||
−0.578612 | + | 0.815603i | \(0.696406\pi\) | |||||||
\(458\) | −16.5616 | −0.773871 | ||||||||
\(459\) | 3.12311 | 0.145774 | ||||||||
\(460\) | 1.43845 | 0.0670679 | ||||||||
\(461\) | 9.36932 | 0.436373 | 0.218186 | − | 0.975907i | \(-0.429986\pi\) | ||||
0.218186 | + | 0.975907i | \(0.429986\pi\) | |||||||
\(462\) | −6.56155 | −0.305271 | ||||||||
\(463\) | 30.7386 | 1.42855 | 0.714273 | − | 0.699867i | \(-0.246758\pi\) | ||||
0.714273 | + | 0.699867i | \(0.246758\pi\) | |||||||
\(464\) | 7.12311 | 0.330682 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | −17.0540 | −0.790010 | ||||||||
\(467\) | −9.75379 | −0.451352 | −0.225676 | − | 0.974202i | \(-0.572459\pi\) | ||||
−0.225676 | + | 0.974202i | \(0.572459\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −39.3693 | −1.81791 | ||||||||
\(470\) | 5.12311 | 0.236311 | ||||||||
\(471\) | −17.0540 | −0.785806 | ||||||||
\(472\) | −13.1231 | −0.604040 | ||||||||
\(473\) | 32.8078 | 1.50850 | ||||||||
\(474\) | 4.31534 | 0.198210 | ||||||||
\(475\) | −7.68466 | −0.352596 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | 7.43845 | 0.340583 | ||||||||
\(478\) | 24.0000 | 1.09773 | ||||||||
\(479\) | 10.5616 | 0.482570 | 0.241285 | − | 0.970454i | \(-0.422431\pi\) | ||||
0.241285 | + | 0.970454i | \(0.422431\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −6.24621 | −0.284803 | ||||||||
\(482\) | 12.2462 | 0.557800 | ||||||||
\(483\) | −3.68466 | −0.167658 | ||||||||
\(484\) | −4.43845 | −0.201748 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 24.0000 | 1.08754 | 0.543772 | − | 0.839233i | \(-0.316996\pi\) | ||||
0.543772 | + | 0.839233i | \(0.316996\pi\) | |||||||
\(488\) | 6.00000 | 0.271607 | ||||||||
\(489\) | 15.3693 | 0.695025 | ||||||||
\(490\) | −0.438447 | −0.0198070 | ||||||||
\(491\) | −25.9309 | −1.17024 | −0.585122 | − | 0.810945i | \(-0.698953\pi\) | ||||
−0.585122 | + | 0.810945i | \(0.698953\pi\) | |||||||
\(492\) | −7.12311 | −0.321134 | ||||||||
\(493\) | −22.2462 | −1.00192 | ||||||||
\(494\) | −15.3693 | −0.691498 | ||||||||
\(495\) | 2.56155 | 0.115133 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −19.6847 | −0.882978 | ||||||||
\(498\) | −14.2462 | −0.638388 | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 6.56155 | 0.293149 | ||||||||
\(502\) | 16.4924 | 0.736093 | ||||||||
\(503\) | 26.2462 | 1.17026 | 0.585130 | − | 0.810939i | \(-0.301043\pi\) | ||||
0.585130 | + | 0.810939i | \(0.301043\pi\) | |||||||
\(504\) | 2.56155 | 0.114101 | ||||||||
\(505\) | −0.561553 | −0.0249888 | ||||||||
\(506\) | 3.68466 | 0.163803 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6155 | 0.869443 | 0.434721 | − | 0.900565i | \(-0.356847\pi\) | ||||
0.434721 | + | 0.900565i | \(0.356847\pi\) | |||||||
\(510\) | 3.12311 | 0.138293 | ||||||||
\(511\) | −27.6847 | −1.22470 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.68466 | 0.339286 | ||||||||
\(514\) | −1.68466 | −0.0743071 | ||||||||
\(515\) | −1.75379 | −0.0772812 | ||||||||
\(516\) | −12.8078 | −0.563830 | ||||||||
\(517\) | 13.1231 | 0.577154 | ||||||||
\(518\) | −8.00000 | −0.351500 | ||||||||
\(519\) | −8.24621 | −0.361968 | ||||||||
\(520\) | 2.00000 | 0.0877058 | ||||||||
\(521\) | −32.2462 | −1.41273 | −0.706366 | − | 0.707847i | \(-0.749667\pi\) | ||||
−0.706366 | + | 0.707847i | \(0.749667\pi\) | |||||||
\(522\) | 7.12311 | 0.311770 | ||||||||
\(523\) | −22.4233 | −0.980502 | −0.490251 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490251 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(524\) | −15.3693 | −0.671412 | ||||||||
\(525\) | −2.56155 | −0.111795 | ||||||||
\(526\) | −20.4924 | −0.893512 | ||||||||
\(527\) | −3.12311 | −0.136045 | ||||||||
\(528\) | −2.56155 | −0.111477 | ||||||||
\(529\) | −20.9309 | −0.910038 | ||||||||
\(530\) | 7.43845 | 0.323105 | ||||||||
\(531\) | −13.1231 | −0.569494 | ||||||||
\(532\) | −19.6847 | −0.853438 | ||||||||
\(533\) | 14.2462 | 0.617072 | ||||||||
\(534\) | 13.6847 | 0.592193 | ||||||||
\(535\) | −2.56155 | −0.110746 | ||||||||
\(536\) | −15.3693 | −0.663853 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | −0.246211 | −0.0106149 | ||||||||
\(539\) | −1.12311 | −0.0483756 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 19.7538 | 0.849282 | 0.424641 | − | 0.905362i | \(-0.360400\pi\) | ||||
0.424641 | + | 0.905362i | \(0.360400\pi\) | |||||||
\(542\) | 27.0540 | 1.16207 | ||||||||
\(543\) | 13.0540 | 0.560200 | ||||||||
\(544\) | −3.12311 | −0.133902 | ||||||||
\(545\) | 5.36932 | 0.229996 | ||||||||
\(546\) | −5.12311 | −0.219249 | ||||||||
\(547\) | 26.8769 | 1.14917 | 0.574587 | − | 0.818444i | \(-0.305163\pi\) | ||||
0.574587 | + | 0.818444i | \(0.305163\pi\) | |||||||
\(548\) | 20.2462 | 0.864875 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 2.56155 | 0.109225 | ||||||||
\(551\) | −54.7386 | −2.33194 | ||||||||
\(552\) | −1.43845 | −0.0612244 | ||||||||
\(553\) | −11.0540 | −0.470063 | ||||||||
\(554\) | −5.36932 | −0.228120 | ||||||||
\(555\) | 3.12311 | 0.132568 | ||||||||
\(556\) | −17.1231 | −0.726181 | ||||||||
\(557\) | −26.8078 | −1.13588 | −0.567941 | − | 0.823069i | \(-0.692260\pi\) | ||||
−0.567941 | + | 0.823069i | \(0.692260\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | 25.6155 | 1.08342 | ||||||||
\(560\) | 2.56155 | 0.108245 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 4.87689 | 0.205719 | ||||||||
\(563\) | 16.4924 | 0.695073 | 0.347536 | − | 0.937667i | \(-0.387018\pi\) | ||||
0.347536 | + | 0.937667i | \(0.387018\pi\) | |||||||
\(564\) | −5.12311 | −0.215722 | ||||||||
\(565\) | −1.68466 | −0.0708741 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.56155 | 0.107575 | ||||||||
\(568\) | −7.68466 | −0.322441 | ||||||||
\(569\) | 30.8078 | 1.29153 | 0.645764 | − | 0.763537i | \(-0.276539\pi\) | ||||
0.645764 | + | 0.763537i | \(0.276539\pi\) | |||||||
\(570\) | 7.68466 | 0.321875 | ||||||||
\(571\) | 41.1231 | 1.72095 | 0.860474 | − | 0.509494i | \(-0.170167\pi\) | ||||
0.860474 | + | 0.509494i | \(0.170167\pi\) | |||||||
\(572\) | 5.12311 | 0.214208 | ||||||||
\(573\) | 14.2462 | 0.595144 | ||||||||
\(574\) | 18.2462 | 0.761582 | ||||||||
\(575\) | 1.43845 | 0.0599874 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.1231 | 0.629583 | 0.314792 | − | 0.949161i | \(-0.398065\pi\) | ||||
0.314792 | + | 0.949161i | \(0.398065\pi\) | |||||||
\(578\) | −7.24621 | −0.301403 | ||||||||
\(579\) | −14.4924 | −0.602285 | ||||||||
\(580\) | 7.12311 | 0.295771 | ||||||||
\(581\) | 36.4924 | 1.51396 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | 19.0540 | 0.789135 | ||||||||
\(584\) | −10.8078 | −0.447228 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 26.4924 | 1.09439 | ||||||||
\(587\) | −0.492423 | −0.0203245 | −0.0101622 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101622 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(588\) | 0.438447 | 0.0180813 | ||||||||
\(589\) | −7.68466 | −0.316641 | ||||||||
\(590\) | −13.1231 | −0.540270 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −3.12311 | −0.128359 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | −2.56155 | −0.105102 | ||||||||
\(595\) | −8.00000 | −0.327968 | ||||||||
\(596\) | 17.0540 | 0.698558 | ||||||||
\(597\) | 16.8078 | 0.687896 | ||||||||
\(598\) | 2.87689 | 0.117645 | ||||||||
\(599\) | 38.4233 | 1.56993 | 0.784967 | − | 0.619538i | \(-0.212680\pi\) | ||||
0.784967 | + | 0.619538i | \(0.212680\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 32.8078 | 1.33714 | ||||||||
\(603\) | −15.3693 | −0.625887 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.43845 | −0.180449 | ||||||||
\(606\) | 0.561553 | 0.0228115 | ||||||||
\(607\) | 7.05398 | 0.286312 | 0.143156 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143156 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(608\) | −7.68466 | −0.311654 | ||||||||
\(609\) | −18.2462 | −0.739374 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 10.2462 | 0.414517 | ||||||||
\(612\) | −3.12311 | −0.126244 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.12311 | −0.287231 | ||||||||
\(616\) | 6.56155 | 0.264372 | ||||||||
\(617\) | −15.4384 | −0.621528 | −0.310764 | − | 0.950487i | \(-0.600585\pi\) | ||||
−0.310764 | + | 0.950487i | \(0.600585\pi\) | |||||||
\(618\) | 1.75379 | 0.0705477 | ||||||||
\(619\) | 11.3693 | 0.456971 | 0.228486 | − | 0.973547i | \(-0.426623\pi\) | ||||
0.228486 | + | 0.973547i | \(0.426623\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | −1.43845 | −0.0577229 | ||||||||
\(622\) | −1.75379 | −0.0703205 | ||||||||
\(623\) | −35.0540 | −1.40441 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 19.6847 | 0.786130 | ||||||||
\(628\) | 17.0540 | 0.680528 | ||||||||
\(629\) | 9.75379 | 0.388909 | ||||||||
\(630\) | 2.56155 | 0.102055 | ||||||||
\(631\) | 29.3002 | 1.16642 | 0.583211 | − | 0.812321i | \(-0.301796\pi\) | ||||
0.583211 | + | 0.812321i | \(0.301796\pi\) | |||||||
\(632\) | −4.31534 | −0.171655 | ||||||||
\(633\) | 23.6847 | 0.941381 | ||||||||
\(634\) | 16.8769 | 0.670267 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.43845 | −0.294954 | ||||||||
\(637\) | −0.876894 | −0.0347438 | ||||||||
\(638\) | 18.2462 | 0.722374 | ||||||||
\(639\) | −7.68466 | −0.304000 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −5.50758 | −0.217536 | −0.108768 | − | 0.994067i | \(-0.534691\pi\) | ||||
−0.108768 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(642\) | 2.56155 | 0.101096 | ||||||||
\(643\) | −7.05398 | −0.278182 | −0.139091 | − | 0.990280i | \(-0.544418\pi\) | ||||
−0.139091 | + | 0.990280i | \(0.544418\pi\) | |||||||
\(644\) | 3.68466 | 0.145196 | ||||||||
\(645\) | −12.8078 | −0.504305 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | −45.9309 | −1.80573 | −0.902864 | − | 0.429925i | \(-0.858540\pi\) | ||||
−0.902864 | + | 0.429925i | \(0.858540\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −33.6155 | −1.31952 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | −2.56155 | −0.100395 | ||||||||
\(652\) | −15.3693 | −0.601909 | ||||||||
\(653\) | 40.2462 | 1.57496 | 0.787478 | − | 0.616343i | \(-0.211386\pi\) | ||||
0.787478 | + | 0.616343i | \(0.211386\pi\) | |||||||
\(654\) | −5.36932 | −0.209957 | ||||||||
\(655\) | −15.3693 | −0.600529 | ||||||||
\(656\) | 7.12311 | 0.278111 | ||||||||
\(657\) | −10.8078 | −0.421651 | ||||||||
\(658\) | 13.1231 | 0.511592 | ||||||||
\(659\) | −30.7386 | −1.19741 | −0.598704 | − | 0.800971i | \(-0.704317\pi\) | ||||
−0.598704 | + | 0.800971i | \(0.704317\pi\) | |||||||
\(660\) | −2.56155 | −0.0997083 | ||||||||
\(661\) | 26.4924 | 1.03044 | 0.515218 | − | 0.857059i | \(-0.327711\pi\) | ||||
0.515218 | + | 0.857059i | \(0.327711\pi\) | |||||||
\(662\) | −6.24621 | −0.242766 | ||||||||
\(663\) | 6.24621 | 0.242583 | ||||||||
\(664\) | 14.2462 | 0.552860 | ||||||||
\(665\) | −19.6847 | −0.763338 | ||||||||
\(666\) | −3.12311 | −0.121018 | ||||||||
\(667\) | 10.2462 | 0.396735 | ||||||||
\(668\) | −6.56155 | −0.253874 | ||||||||
\(669\) | 21.1231 | 0.816666 | ||||||||
\(670\) | −15.3693 | −0.593769 | ||||||||
\(671\) | 15.3693 | 0.593326 | ||||||||
\(672\) | −2.56155 | −0.0988140 | ||||||||
\(673\) | 11.7538 | 0.453075 | 0.226538 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226538 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 32.4233 | 1.24613 | 0.623064 | − | 0.782171i | \(-0.285888\pi\) | ||||
0.623064 | + | 0.782171i | \(0.285888\pi\) | |||||||
\(678\) | 1.68466 | 0.0646989 | ||||||||
\(679\) | −15.3693 | −0.589820 | ||||||||
\(680\) | −3.12311 | −0.119766 | ||||||||
\(681\) | −7.68466 | −0.294477 | ||||||||
\(682\) | 2.56155 | 0.0980869 | ||||||||
\(683\) | 31.6847 | 1.21238 | 0.606190 | − | 0.795320i | \(-0.292697\pi\) | ||||
0.606190 | + | 0.795320i | \(0.292697\pi\) | |||||||
\(684\) | −7.68466 | −0.293830 | ||||||||
\(685\) | 20.2462 | 0.773568 | ||||||||
\(686\) | −19.0540 | −0.727484 | ||||||||
\(687\) | 16.5616 | 0.631863 | ||||||||
\(688\) | 12.8078 | 0.488291 | ||||||||
\(689\) | 14.8769 | 0.566765 | ||||||||
\(690\) | −1.43845 | −0.0547607 | ||||||||
\(691\) | 15.0540 | 0.572680 | 0.286340 | − | 0.958128i | \(-0.407561\pi\) | ||||
0.286340 | + | 0.958128i | \(0.407561\pi\) | |||||||
\(692\) | 8.24621 | 0.313474 | ||||||||
\(693\) | 6.56155 | 0.249253 | ||||||||
\(694\) | 14.2462 | 0.540779 | ||||||||
\(695\) | −17.1231 | −0.649516 | ||||||||
\(696\) | −7.12311 | −0.270001 | ||||||||
\(697\) | −22.2462 | −0.842635 | ||||||||
\(698\) | 5.36932 | 0.203232 | ||||||||
\(699\) | 17.0540 | 0.645041 | ||||||||
\(700\) | 2.56155 | 0.0968176 | ||||||||
\(701\) | 5.19224 | 0.196108 | 0.0980540 | − | 0.995181i | \(-0.468738\pi\) | ||||
0.0980540 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | 2.56155 | 0.0965422 | ||||||||
\(705\) | −5.12311 | −0.192947 | ||||||||
\(706\) | −0.246211 | −0.00926628 | ||||||||
\(707\) | −1.43845 | −0.0540984 | ||||||||
\(708\) | 13.1231 | 0.493197 | ||||||||
\(709\) | 17.0540 | 0.640475 | 0.320238 | − | 0.947337i | \(-0.396237\pi\) | ||||
0.320238 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(710\) | −7.68466 | −0.288400 | ||||||||
\(711\) | −4.31534 | −0.161838 | ||||||||
\(712\) | −13.6847 | −0.512854 | ||||||||
\(713\) | 1.43845 | 0.0538703 | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 5.12311 | 0.191593 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −24.0000 | −0.896296 | ||||||||
\(718\) | −31.6847 | −1.18246 | ||||||||
\(719\) | −34.8769 | −1.30069 | −0.650344 | − | 0.759640i | \(-0.725375\pi\) | ||||
−0.650344 | + | 0.759640i | \(0.725375\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −4.49242 | −0.167307 | ||||||||
\(722\) | 40.0540 | 1.49065 | ||||||||
\(723\) | −12.2462 | −0.455441 | ||||||||
\(724\) | −13.0540 | −0.485147 | ||||||||
\(725\) | 7.12311 | 0.264546 | ||||||||
\(726\) | 4.43845 | 0.164726 | ||||||||
\(727\) | 23.0540 | 0.855025 | 0.427512 | − | 0.904010i | \(-0.359390\pi\) | ||||
0.427512 | + | 0.904010i | \(0.359390\pi\) | |||||||
\(728\) | 5.12311 | 0.189875 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.8078 | −0.400013 | ||||||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | −6.49242 | −0.239803 | −0.119902 | − | 0.992786i | \(-0.538258\pi\) | ||||
−0.119902 | + | 0.992786i | \(0.538258\pi\) | |||||||
\(734\) | 15.3693 | 0.567292 | ||||||||
\(735\) | 0.438447 | 0.0161724 | ||||||||
\(736\) | 1.43845 | 0.0530219 | ||||||||
\(737\) | −39.3693 | −1.45019 | ||||||||
\(738\) | 7.12311 | 0.262205 | ||||||||
\(739\) | 52.9848 | 1.94908 | 0.974540 | − | 0.224216i | \(-0.0719821\pi\) | ||||
0.974540 | + | 0.224216i | \(0.0719821\pi\) | |||||||
\(740\) | −3.12311 | −0.114808 | ||||||||
\(741\) | 15.3693 | 0.564606 | ||||||||
\(742\) | 19.0540 | 0.699493 | ||||||||
\(743\) | −50.4233 | −1.84985 | −0.924926 | − | 0.380148i | \(-0.875873\pi\) | ||||
−0.924926 | + | 0.380148i | \(0.875873\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 17.0540 | 0.624809 | ||||||||
\(746\) | −5.68466 | −0.208130 | ||||||||
\(747\) | 14.2462 | 0.521242 | ||||||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | −6.56155 | −0.239754 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 45.1231 | 1.64657 | 0.823283 | − | 0.567631i | \(-0.192140\pi\) | ||||
0.823283 | + | 0.567631i | \(0.192140\pi\) | |||||||
\(752\) | 5.12311 | 0.186820 | ||||||||
\(753\) | −16.4924 | −0.601017 | ||||||||
\(754\) | 14.2462 | 0.518816 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.56155 | −0.0931628 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | −7.05398 | −0.256212 | ||||||||
\(759\) | −3.68466 | −0.133745 | ||||||||
\(760\) | −7.68466 | −0.278752 | ||||||||
\(761\) | −20.4233 | −0.740344 | −0.370172 | − | 0.928963i | \(-0.620701\pi\) | ||||
−0.370172 | + | 0.928963i | \(0.620701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7538 | 0.497921 | ||||||||
\(764\) | −14.2462 | −0.515410 | ||||||||
\(765\) | −3.12311 | −0.112916 | ||||||||
\(766\) | −10.2462 | −0.370211 | ||||||||
\(767\) | −26.2462 | −0.947696 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −20.5616 | −0.741469 | −0.370734 | − | 0.928739i | \(-0.620894\pi\) | ||||
−0.370734 | + | 0.928739i | \(0.620894\pi\) | |||||||
\(770\) | 6.56155 | 0.236462 | ||||||||
\(771\) | 1.68466 | 0.0606715 | ||||||||
\(772\) | 14.4924 | 0.521594 | ||||||||
\(773\) | −11.4384 | −0.411412 | −0.205706 | − | 0.978614i | \(-0.565949\pi\) | ||||
−0.205706 | + | 0.978614i | \(0.565949\pi\) | |||||||
\(774\) | 12.8078 | 0.460366 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | 7.75379 | 0.277987 | ||||||||
\(779\) | −54.7386 | −1.96122 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | −19.6847 | −0.704372 | ||||||||
\(782\) | −4.49242 | −0.160649 | ||||||||
\(783\) | −7.12311 | −0.254559 | ||||||||
\(784\) | −0.438447 | −0.0156588 | ||||||||
\(785\) | 17.0540 | 0.608682 | ||||||||
\(786\) | 15.3693 | 0.548205 | ||||||||
\(787\) | −17.9309 | −0.639166 | −0.319583 | − | 0.947558i | \(-0.603543\pi\) | ||||
−0.319583 | + | 0.947558i | \(0.603543\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 20.4924 | 0.729550 | ||||||||
\(790\) | −4.31534 | −0.153533 | ||||||||
\(791\) | −4.31534 | −0.153436 | ||||||||
\(792\) | 2.56155 | 0.0910208 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 9.05398 | 0.321314 | ||||||||
\(795\) | −7.43845 | −0.263815 | ||||||||
\(796\) | −16.8078 | −0.595735 | ||||||||
\(797\) | −26.9848 | −0.955852 | −0.477926 | − | 0.878400i | \(-0.658611\pi\) | ||||
−0.477926 | + | 0.878400i | \(0.658611\pi\) | |||||||
\(798\) | 19.6847 | 0.696829 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −13.6847 | −0.483524 | ||||||||
\(802\) | −13.6847 | −0.483222 | ||||||||
\(803\) | −27.6847 | −0.976970 | ||||||||
\(804\) | 15.3693 | 0.542034 | ||||||||
\(805\) | 3.68466 | 0.129867 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | 0.246211 | 0.00866705 | ||||||||
\(808\) | −0.561553 | −0.0197554 | ||||||||
\(809\) | −37.6847 | −1.32492 | −0.662461 | − | 0.749096i | \(-0.730488\pi\) | ||||
−0.662461 | + | 0.749096i | \(0.730488\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −24.6695 | −0.866263 | −0.433132 | − | 0.901331i | \(-0.642592\pi\) | ||||
−0.433132 | + | 0.901331i | \(0.642592\pi\) | |||||||
\(812\) | 18.2462 | 0.640316 | ||||||||
\(813\) | −27.0540 | −0.948824 | ||||||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | −15.3693 | −0.538364 | ||||||||
\(816\) | 3.12311 | 0.109331 | ||||||||
\(817\) | −98.4233 | −3.44340 | ||||||||
\(818\) | −37.3693 | −1.30659 | ||||||||
\(819\) | 5.12311 | 0.179016 | ||||||||
\(820\) | 7.12311 | 0.248750 | ||||||||
\(821\) | 19.6155 | 0.684587 | 0.342293 | − | 0.939593i | \(-0.388796\pi\) | ||||
0.342293 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(822\) | −20.2462 | −0.706168 | ||||||||
\(823\) | −25.6155 | −0.892901 | −0.446451 | − | 0.894808i | \(-0.647312\pi\) | ||||
−0.446451 | + | 0.894808i | \(0.647312\pi\) | |||||||
\(824\) | −1.75379 | −0.0610961 | ||||||||
\(825\) | −2.56155 | −0.0891818 | ||||||||
\(826\) | −33.6155 | −1.16963 | ||||||||
\(827\) | 1.75379 | 0.0609852 | 0.0304926 | − | 0.999535i | \(-0.490292\pi\) | ||||
0.0304926 | + | 0.999535i | \(0.490292\pi\) | |||||||
\(828\) | 1.43845 | 0.0499895 | ||||||||
\(829\) | 24.4233 | 0.848256 | 0.424128 | − | 0.905602i | \(-0.360581\pi\) | ||||
0.424128 | + | 0.905602i | \(0.360581\pi\) | |||||||
\(830\) | 14.2462 | 0.494493 | ||||||||
\(831\) | 5.36932 | 0.186260 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 1.36932 | 0.0474440 | ||||||||
\(834\) | 17.1231 | 0.592925 | ||||||||
\(835\) | −6.56155 | −0.227072 | ||||||||
\(836\) | −19.6847 | −0.680808 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 5.75379 | 0.198761 | ||||||||
\(839\) | 6.06913 | 0.209530 | 0.104765 | − | 0.994497i | \(-0.466591\pi\) | ||||
0.104765 | + | 0.994497i | \(0.466591\pi\) | |||||||
\(840\) | −2.56155 | −0.0883820 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | −14.4924 | −0.499442 | ||||||||
\(843\) | −4.87689 | −0.167969 | ||||||||
\(844\) | −23.6847 | −0.815260 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 5.12311 | 0.176136 | ||||||||
\(847\) | −11.3693 | −0.390654 | ||||||||
\(848\) | 7.43845 | 0.255437 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.12311 | −0.107122 | ||||||||
\(851\) | −4.49242 | −0.153998 | ||||||||
\(852\) | 7.68466 | 0.263272 | ||||||||
\(853\) | 47.7926 | 1.63639 | 0.818194 | − | 0.574942i | \(-0.194976\pi\) | ||||
0.818194 | + | 0.574942i | \(0.194976\pi\) | |||||||
\(854\) | 15.3693 | 0.525927 | ||||||||
\(855\) | −7.68466 | −0.262810 | ||||||||
\(856\) | −2.56155 | −0.0875521 | ||||||||
\(857\) | 29.2311 | 0.998514 | 0.499257 | − | 0.866454i | \(-0.333606\pi\) | ||||
0.499257 | + | 0.866454i | \(0.333606\pi\) | |||||||
\(858\) | −5.12311 | −0.174900 | ||||||||
\(859\) | 26.7386 | 0.912310 | 0.456155 | − | 0.889900i | \(-0.349226\pi\) | ||||
0.456155 | + | 0.889900i | \(0.349226\pi\) | |||||||
\(860\) | 12.8078 | 0.436741 | ||||||||
\(861\) | −18.2462 | −0.621829 | ||||||||
\(862\) | −30.2462 | −1.03019 | ||||||||
\(863\) | 39.5464 | 1.34618 | 0.673088 | − | 0.739563i | \(-0.264968\pi\) | ||||
0.673088 | + | 0.739563i | \(0.264968\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 8.24621 | 0.280380 | ||||||||
\(866\) | 35.3002 | 1.19955 | ||||||||
\(867\) | 7.24621 | 0.246094 | ||||||||
\(868\) | 2.56155 | 0.0869448 | ||||||||
\(869\) | −11.0540 | −0.374980 | ||||||||
\(870\) | −7.12311 | −0.241496 | ||||||||
\(871\) | −30.7386 | −1.04154 | ||||||||
\(872\) | 5.36932 | 0.181828 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | −11.0540 | −0.373906 | ||||||||
\(875\) | 2.56155 | 0.0865963 | ||||||||
\(876\) | 10.8078 | 0.365161 | ||||||||
\(877\) | −50.0000 | −1.68838 | −0.844190 | − | 0.536044i | \(-0.819918\pi\) | ||||
−0.844190 | + | 0.536044i | \(0.819918\pi\) | |||||||
\(878\) | 9.61553 | 0.324508 | ||||||||
\(879\) | −26.4924 | −0.893567 | ||||||||
\(880\) | 2.56155 | 0.0863499 | ||||||||
\(881\) | 9.50758 | 0.320318 | 0.160159 | − | 0.987091i | \(-0.448799\pi\) | ||||
0.160159 | + | 0.987091i | \(0.448799\pi\) | |||||||
\(882\) | −0.438447 | −0.0147633 | ||||||||
\(883\) | 30.4233 | 1.02383 | 0.511913 | − | 0.859038i | \(-0.328937\pi\) | ||||
0.511913 | + | 0.859038i | \(0.328937\pi\) | |||||||
\(884\) | −6.24621 | −0.210083 | ||||||||
\(885\) | 13.1231 | 0.441128 | ||||||||
\(886\) | 23.0540 | 0.774513 | ||||||||
\(887\) | −32.6307 | −1.09563 | −0.547816 | − | 0.836599i | \(-0.684540\pi\) | ||||
−0.547816 | + | 0.836599i | \(0.684540\pi\) | |||||||
\(888\) | 3.12311 | 0.104805 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13.6847 | −0.458711 | ||||||||
\(891\) | 2.56155 | 0.0858152 | ||||||||
\(892\) | −21.1231 | −0.707254 | ||||||||
\(893\) | −39.3693 | −1.31744 | ||||||||
\(894\) | −17.0540 | −0.570370 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 2.56155 | 0.0855755 | ||||||||
\(897\) | −2.87689 | −0.0960567 | ||||||||
\(898\) | 10.4924 | 0.350137 | ||||||||
\(899\) | 7.12311 | 0.237569 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −23.2311 | −0.773939 | ||||||||
\(902\) | 18.2462 | 0.607532 | ||||||||
\(903\) | −32.8078 | −1.09177 | ||||||||
\(904\) | −1.68466 | −0.0560309 | ||||||||
\(905\) | −13.0540 | −0.433929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | 7.68466 | 0.255024 | ||||||||
\(909\) | −0.561553 | −0.0186255 | ||||||||
\(910\) | 5.12311 | 0.169829 | ||||||||
\(911\) | −11.5076 | −0.381263 | −0.190632 | − | 0.981662i | \(-0.561054\pi\) | ||||
−0.190632 | + | 0.981662i | \(0.561054\pi\) | |||||||
\(912\) | 7.68466 | 0.254464 | ||||||||
\(913\) | 36.4924 | 1.20772 | ||||||||
\(914\) | −24.7386 | −0.818281 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −16.5616 | −0.547209 | ||||||||
\(917\) | −39.3693 | −1.30009 | ||||||||
\(918\) | 3.12311 | 0.103078 | ||||||||
\(919\) | −1.61553 | −0.0532914 | −0.0266457 | − | 0.999645i | \(-0.508483\pi\) | ||||
−0.0266457 | + | 0.999645i | \(0.508483\pi\) | |||||||
\(920\) | 1.43845 | 0.0474242 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.36932 | 0.308562 | ||||||||
\(923\) | −15.3693 | −0.505887 | ||||||||
\(924\) | −6.56155 | −0.215859 | ||||||||
\(925\) | −3.12311 | −0.102687 | ||||||||
\(926\) | 30.7386 | 1.01013 | ||||||||
\(927\) | −1.75379 | −0.0576020 | ||||||||
\(928\) | 7.12311 | 0.233827 | ||||||||
\(929\) | 7.43845 | 0.244048 | 0.122024 | − | 0.992527i | \(-0.461062\pi\) | ||||
0.122024 | + | 0.992527i | \(0.461062\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | 3.36932 | 0.110425 | ||||||||
\(932\) | −17.0540 | −0.558622 | ||||||||
\(933\) | 1.75379 | 0.0574165 | ||||||||
\(934\) | −9.75379 | −0.319154 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 41.3693 | 1.35148 | 0.675738 | − | 0.737142i | \(-0.263825\pi\) | ||||
0.675738 | + | 0.737142i | \(0.263825\pi\) | |||||||
\(938\) | −39.3693 | −1.28545 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | 5.12311 | 0.167097 | ||||||||
\(941\) | 2.63068 | 0.0857578 | 0.0428789 | − | 0.999080i | \(-0.486347\pi\) | ||||
0.0428789 | + | 0.999080i | \(0.486347\pi\) | |||||||
\(942\) | −17.0540 | −0.555649 | ||||||||
\(943\) | 10.2462 | 0.333663 | ||||||||
\(944\) | −13.1231 | −0.427121 | ||||||||
\(945\) | −2.56155 | −0.0833273 | ||||||||
\(946\) | 32.8078 | 1.06667 | ||||||||
\(947\) | −9.12311 | −0.296461 | −0.148231 | − | 0.988953i | \(-0.547358\pi\) | ||||
−0.148231 | + | 0.988953i | \(0.547358\pi\) | |||||||
\(948\) | 4.31534 | 0.140156 | ||||||||
\(949\) | −21.6155 | −0.701670 | ||||||||
\(950\) | −7.68466 | −0.249323 | ||||||||
\(951\) | −16.8769 | −0.547271 | ||||||||
\(952\) | −8.00000 | −0.259281 | ||||||||
\(953\) | 16.1080 | 0.521788 | 0.260894 | − | 0.965367i | \(-0.415983\pi\) | ||||
0.260894 | + | 0.965367i | \(0.415983\pi\) | |||||||
\(954\) | 7.43845 | 0.240829 | ||||||||
\(955\) | −14.2462 | −0.460997 | ||||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | −18.2462 | −0.589816 | ||||||||
\(958\) | 10.5616 | 0.341228 | ||||||||
\(959\) | 51.8617 | 1.67470 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −6.24621 | −0.201386 | ||||||||
\(963\) | −2.56155 | −0.0825449 | ||||||||
\(964\) | 12.2462 | 0.394424 | ||||||||
\(965\) | 14.4924 | 0.466528 | ||||||||
\(966\) | −3.68466 | −0.118552 | ||||||||
\(967\) | −42.2462 | −1.35855 | −0.679273 | − | 0.733885i | \(-0.737705\pi\) | ||||
−0.679273 | + | 0.733885i | \(0.737705\pi\) | |||||||
\(968\) | −4.43845 | −0.142657 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | −6.00000 | −0.192648 | ||||||||
\(971\) | −37.1231 | −1.19134 | −0.595669 | − | 0.803230i | \(-0.703113\pi\) | ||||
−0.595669 | + | 0.803230i | \(0.703113\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −43.8617 | −1.40614 | ||||||||
\(974\) | 24.0000 | 0.769010 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 42.9848 | 1.37521 | 0.687604 | − | 0.726086i | \(-0.258663\pi\) | ||||
0.687604 | + | 0.726086i | \(0.258663\pi\) | |||||||
\(978\) | 15.3693 | 0.491457 | ||||||||
\(979\) | −35.0540 | −1.12033 | ||||||||
\(980\) | −0.438447 | −0.0140057 | ||||||||
\(981\) | 5.36932 | 0.171429 | ||||||||
\(982\) | −25.9309 | −0.827487 | ||||||||
\(983\) | 40.9848 | 1.30721 | 0.653607 | − | 0.756834i | \(-0.273255\pi\) | ||||
0.653607 | + | 0.756834i | \(0.273255\pi\) | |||||||
\(984\) | −7.12311 | −0.227076 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | −22.2462 | −0.708464 | ||||||||
\(987\) | −13.1231 | −0.417713 | ||||||||
\(988\) | −15.3693 | −0.488963 | ||||||||
\(989\) | 18.4233 | 0.585827 | ||||||||
\(990\) | 2.56155 | 0.0814115 | ||||||||
\(991\) | 35.6847 | 1.13356 | 0.566780 | − | 0.823869i | \(-0.308189\pi\) | ||||
0.566780 | + | 0.823869i | \(0.308189\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 6.24621 | 0.198218 | ||||||||
\(994\) | −19.6847 | −0.624359 | ||||||||
\(995\) | −16.8078 | −0.532842 | ||||||||
\(996\) | −14.2462 | −0.451408 | ||||||||
\(997\) | −29.5076 | −0.934514 | −0.467257 | − | 0.884121i | \(-0.654758\pi\) | ||||
−0.467257 | + | 0.884121i | \(0.654758\pi\) | |||||||
\(998\) | 20.0000 | 0.633089 | ||||||||
\(999\) | 3.12311 | 0.0988107 |
(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 | 930.2.a.p.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.a.be.1.2 | 2 | |||
4.3 | odd | 2 | 7440.2.a.bl.1.1 | 2 | |||
5.2 | odd | 4 | 4650.2.d.bd.3349.4 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bd.3349.1 | 4 | |||
5.4 | even | 2 | 4650.2.a.ce.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.p.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2790.2.a.be.1.2 | 2 | 3.2 | odd | 2 | |||
4650.2.a.ce.1.1 | 2 | 5.4 | even | 2 | |||
4650.2.d.bd.3349.1 | 4 | 5.3 | odd | 4 | |||
4650.2.d.bd.3349.4 | 4 | 5.2 | odd | 4 | |||
7440.2.a.bl.1.1 | 2 | 4.3 | odd | 2 |