Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,2,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.39738203537\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.2.b.c.99.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.61803i | − 1.14412i | −0.820211 | − | 0.572061i | \(-0.806144\pi\) | ||||
0.820211 | − | 0.572061i | \(-0.193856\pi\) | |||||||
\(3\) | 1.23607i | 0.713644i | 0.934172 | + | 0.356822i | \(0.116140\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | 1.47214 | 0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.23607 | 1.27722 | 0.638611 | − | 0.769529i | \(-0.279509\pi\) | ||||
0.638611 | + | 0.769529i | \(0.279509\pi\) | |||||||
\(12\) | − 0.763932i | − 0.220528i | ||||||||
\(13\) | − 3.23607i | − 0.897524i | −0.893651 | − | 0.448762i | \(-0.851865\pi\) | ||||
0.893651 | − | 0.448762i | \(-0.148135\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 6.47214i | 1.56972i | 0.619671 | + | 0.784862i | \(0.287266\pi\) | ||||
−0.619671 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(18\) | − 2.38197i | − 0.561435i | ||||||||
\(19\) | −4.47214 | −1.02598 | −0.512989 | − | 0.858395i | \(-0.671462\pi\) | ||||
−0.512989 | + | 0.858395i | \(0.671462\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.23607 | 0.269732 | ||||||||
\(22\) | − 6.85410i | − 1.46130i | ||||||||
\(23\) | 1.76393i | 0.367805i | 0.982944 | + | 0.183903i | \(0.0588731\pi\) | ||||
−0.982944 | + | 0.183903i | \(0.941127\pi\) | |||||||
\(24\) | 2.76393 | 0.564185 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.23607 | −1.02688 | ||||||||
\(27\) | 5.52786i | 1.06384i | ||||||||
\(28\) | 0.618034i | 0.116797i | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.70820 | −1.74364 | −0.871822 | − | 0.489822i | \(-0.837062\pi\) | ||||
−0.871822 | + | 0.489822i | \(0.837062\pi\) | |||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | 5.23607i | 0.911482i | ||||||||
\(34\) | 10.4721 | 1.79596 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.909830 | −0.151638 | ||||||||
\(37\) | − 3.00000i | − 0.493197i | −0.969118 | − | 0.246598i | \(-0.920687\pi\) | ||||
0.969118 | − | 0.246598i | \(-0.0793129\pi\) | |||||||
\(38\) | 7.23607i | 1.17385i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.23607 | 1.44243 | 0.721216 | − | 0.692711i | \(-0.243584\pi\) | ||||
0.721216 | + | 0.692711i | \(0.243584\pi\) | |||||||
\(42\) | − 2.00000i | − 0.308607i | ||||||||
\(43\) | 6.23607i | 0.950991i | 0.879718 | + | 0.475496i | \(0.157731\pi\) | ||||
−0.879718 | + | 0.475496i | \(0.842269\pi\) | |||||||
\(44\) | −2.61803 | −0.394683 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.85410 | 0.420814 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | − 6.00000i | − 0.866025i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − 0.472136i | − 0.0648529i | −0.999474 | − | 0.0324264i | \(-0.989677\pi\) | ||||
0.999474 | − | 0.0324264i | \(-0.0103235\pi\) | |||||||
\(54\) | 8.94427 | 1.21716 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | − 5.52786i | − 0.732183i | ||||||||
\(58\) | 8.09017i | 1.06229i | ||||||||
\(59\) | 1.70820 | 0.222389 | 0.111195 | − | 0.993799i | \(-0.464532\pi\) | ||||
0.111195 | + | 0.993799i | \(0.464532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.70820 | 0.474787 | 0.237393 | − | 0.971414i | \(-0.423707\pi\) | ||||
0.237393 | + | 0.971414i | \(0.423707\pi\) | |||||||
\(62\) | 15.7082i | 1.99494i | ||||||||
\(63\) | − 1.47214i | − 0.185472i | ||||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.47214 | 1.04285 | ||||||||
\(67\) | − 0.236068i | − 0.0288403i | −0.999896 | − | 0.0144201i | \(-0.995410\pi\) | ||||
0.999896 | − | 0.0144201i | \(-0.00459023\pi\) | |||||||
\(68\) | − 4.00000i | − 0.485071i | ||||||||
\(69\) | −2.18034 | −0.262482 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.70820 | −0.558761 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(72\) | − 3.29180i | − 0.387942i | ||||||||
\(73\) | − 13.2361i | − 1.54916i | −0.632473 | − | 0.774582i | \(-0.717960\pi\) | ||||
0.632473 | − | 0.774582i | \(-0.282040\pi\) | |||||||
\(74\) | −4.85410 | −0.564278 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.76393 | 0.317045 | ||||||||
\(77\) | − 4.23607i | − 0.482745i | ||||||||
\(78\) | − 6.47214i | − 0.732825i | ||||||||
\(79\) | −11.1803 | −1.25789 | −0.628943 | − | 0.777451i | \(-0.716512\pi\) | ||||
−0.628943 | + | 0.777451i | \(0.716512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | − 14.9443i | − 1.65032i | ||||||||
\(83\) | 5.70820i | 0.626557i | 0.949661 | + | 0.313278i | \(0.101427\pi\) | ||||
−0.949661 | + | 0.313278i | \(0.898573\pi\) | |||||||
\(84\) | −0.763932 | −0.0833518 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.0902 | 1.08805 | ||||||||
\(87\) | − 6.18034i | − 0.662602i | ||||||||
\(88\) | − 9.47214i | − 1.00973i | ||||||||
\(89\) | −12.7639 | −1.35297 | −0.676487 | − | 0.736455i | \(-0.736499\pi\) | ||||
−0.676487 | + | 0.736455i | \(0.736499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | −0.339232 | ||||||||
\(92\) | − 1.09017i | − 0.113658i | ||||||||
\(93\) | − 12.0000i | − 1.24434i | ||||||||
\(94\) | 3.23607 | 0.333775 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.18034 | −0.426654 | ||||||||
\(97\) | − 0.763932i | − 0.0775655i | −0.999248 | − | 0.0387828i | \(-0.987652\pi\) | ||||
0.999248 | − | 0.0387828i | \(-0.0123480\pi\) | |||||||
\(98\) | 1.61803i | 0.163446i | ||||||||
\(99\) | 6.23607 | 0.626748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.23607 | 0.919023 | 0.459512 | − | 0.888172i | \(-0.348024\pi\) | ||||
0.459512 | + | 0.888172i | \(0.348024\pi\) | |||||||
\(102\) | 12.9443i | 1.28167i | ||||||||
\(103\) | − 0.472136i | − 0.0465209i | −0.999729 | − | 0.0232605i | \(-0.992595\pi\) | ||||
0.999729 | − | 0.0232605i | \(-0.00740471\pi\) | |||||||
\(104\) | −7.23607 | −0.709555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.763932 | −0.0741996 | ||||||||
\(107\) | − 8.00000i | − 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | − 3.41641i | − 0.328744i | ||||||||
\(109\) | 18.4164 | 1.76397 | 0.881986 | − | 0.471276i | \(-0.156206\pi\) | ||||
0.881986 | + | 0.471276i | \(0.156206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.70820 | 0.351967 | ||||||||
\(112\) | 4.85410i | 0.458670i | ||||||||
\(113\) | 12.4164i | 1.16804i | 0.811740 | + | 0.584019i | \(0.198521\pi\) | ||||
−0.811740 | + | 0.584019i | \(0.801479\pi\) | |||||||
\(114\) | −8.94427 | −0.837708 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.09017 | 0.286915 | ||||||||
\(117\) | − 4.76393i | − 0.440426i | ||||||||
\(118\) | − 2.76393i | − 0.254441i | ||||||||
\(119\) | 6.47214 | 0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | − 6.00000i | − 0.543214i | ||||||||
\(123\) | 11.4164i | 1.02938i | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.38197 | −0.212202 | ||||||||
\(127\) | 17.6525i | 1.56640i | 0.621767 | + | 0.783202i | \(0.286415\pi\) | ||||
−0.621767 | + | 0.783202i | \(0.713585\pi\) | |||||||
\(128\) | 13.6180i | 1.20368i | ||||||||
\(129\) | −7.70820 | −0.678670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.944272 | 0.0825014 | 0.0412507 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412507 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(132\) | − 3.23607i | − 0.281664i | ||||||||
\(133\) | 4.47214i | 0.387783i | ||||||||
\(134\) | −0.381966 | −0.0329968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.4721 | 1.24098 | ||||||||
\(137\) | − 6.94427i | − 0.593289i | −0.954988 | − | 0.296645i | \(-0.904132\pi\) | ||||
0.954988 | − | 0.296645i | \(-0.0958677\pi\) | |||||||
\(138\) | 3.52786i | 0.300312i | ||||||||
\(139\) | 20.6525 | 1.75172 | 0.875860 | − | 0.482565i | \(-0.160295\pi\) | ||||
0.875860 | + | 0.482565i | \(0.160295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.47214 | −0.208191 | ||||||||
\(142\) | 7.61803i | 0.639291i | ||||||||
\(143\) | − 13.7082i | − 1.14634i | ||||||||
\(144\) | −7.14590 | −0.595492 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.4164 | −1.77243 | ||||||||
\(147\) | − 1.23607i | − 0.101949i | ||||||||
\(148\) | 1.85410i | 0.152406i | ||||||||
\(149\) | 13.9443 | 1.14236 | 0.571180 | − | 0.820825i | \(-0.306486\pi\) | ||||
0.571180 | + | 0.820825i | \(0.306486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7639 | −1.28285 | −0.641425 | − | 0.767185i | \(-0.721657\pi\) | ||||
−0.641425 | + | 0.767185i | \(0.721657\pi\) | |||||||
\(152\) | 10.0000i | 0.811107i | ||||||||
\(153\) | 9.52786i | 0.770282i | ||||||||
\(154\) | −6.85410 | −0.552319 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.47214 | −0.197929 | ||||||||
\(157\) | − 5.23607i | − 0.417884i | −0.977928 | − | 0.208942i | \(-0.932998\pi\) | ||||
0.977928 | − | 0.208942i | \(-0.0670019\pi\) | |||||||
\(158\) | 18.0902i | 1.43918i | ||||||||
\(159\) | 0.583592 | 0.0462819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.76393 | 0.139017 | ||||||||
\(162\) | 3.90983i | 0.307185i | ||||||||
\(163\) | − 10.4721i | − 0.820241i | −0.912031 | − | 0.410120i | \(-0.865487\pi\) | ||||
0.912031 | − | 0.410120i | \(-0.134513\pi\) | |||||||
\(164\) | −5.70820 | −0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.23607 | 0.716858 | ||||||||
\(167\) | − 0.763932i | − 0.0591148i | −0.999563 | − | 0.0295574i | \(-0.990590\pi\) | ||||
0.999563 | − | 0.0295574i | \(-0.00940979\pi\) | |||||||
\(168\) | − 2.76393i | − 0.213242i | ||||||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.58359 | −0.503460 | ||||||||
\(172\) | − 3.85410i | − 0.293873i | ||||||||
\(173\) | − 20.4721i | − 1.55647i | −0.627975 | − | 0.778234i | \(-0.716116\pi\) | ||||
0.627975 | − | 0.778234i | \(-0.283884\pi\) | |||||||
\(174\) | −10.0000 | −0.758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.5623 | −1.54994 | ||||||||
\(177\) | 2.11146i | 0.158707i | ||||||||
\(178\) | 20.6525i | 1.54797i | ||||||||
\(179\) | −3.41641 | −0.255354 | −0.127677 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127677 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1803 | −1.05402 | −0.527008 | − | 0.849860i | \(-0.676686\pi\) | ||||
−0.527008 | + | 0.849860i | \(0.676686\pi\) | |||||||
\(182\) | 5.23607i | 0.388123i | ||||||||
\(183\) | 4.58359i | 0.338829i | ||||||||
\(184\) | 3.94427 | 0.290776 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −19.4164 | −1.42368 | ||||||||
\(187\) | 27.4164i | 2.00489i | ||||||||
\(188\) | − 1.23607i | − 0.0901495i | ||||||||
\(189\) | 5.52786 | 0.402093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.47214 | −0.178877 | −0.0894387 | − | 0.995992i | \(-0.528507\pi\) | ||||
−0.0894387 | + | 0.995992i | \(0.528507\pi\) | |||||||
\(192\) | − 5.23607i | − 0.377881i | ||||||||
\(193\) | − 14.4164i | − 1.03772i | −0.854861 | − | 0.518858i | \(-0.826357\pi\) | ||||
0.854861 | − | 0.518858i | \(-0.173643\pi\) | |||||||
\(194\) | −1.23607 | −0.0887445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | − 7.47214i | − 0.532368i | −0.963922 | − | 0.266184i | \(-0.914237\pi\) | ||||
0.963922 | − | 0.266184i | \(-0.0857628\pi\) | |||||||
\(198\) | − 10.0902i | − 0.717077i | ||||||||
\(199\) | −2.76393 | −0.195930 | −0.0979650 | − | 0.995190i | \(-0.531233\pi\) | ||||
−0.0979650 | + | 0.995190i | \(0.531233\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.291796 | 0.0205817 | ||||||||
\(202\) | − 14.9443i | − 1.05148i | ||||||||
\(203\) | 5.00000i | 0.350931i | ||||||||
\(204\) | 4.94427 | 0.346168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.763932 | −0.0532257 | ||||||||
\(207\) | 2.59675i | 0.180486i | ||||||||
\(208\) | 15.7082i | 1.08917i | ||||||||
\(209\) | −18.9443 | −1.31040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0.291796i | 0.0200406i | ||||||||
\(213\) | − 5.81966i | − 0.398757i | ||||||||
\(214\) | −12.9443 | −0.884852 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.3607 | 0.841038 | ||||||||
\(217\) | 9.70820i | 0.659036i | ||||||||
\(218\) | − 29.7984i | − 2.01820i | ||||||||
\(219\) | 16.3607 | 1.10555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.9443 | 1.40886 | ||||||||
\(222\) | − 6.00000i | − 0.402694i | ||||||||
\(223\) | − 2.18034i | − 0.146006i | −0.997332 | − | 0.0730032i | \(-0.976742\pi\) | ||||
0.997332 | − | 0.0730032i | \(-0.0232583\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0902 | 1.33638 | ||||||||
\(227\) | 5.41641i | 0.359500i | 0.983712 | + | 0.179750i | \(0.0575288\pi\) | ||||
−0.983712 | + | 0.179750i | \(0.942471\pi\) | |||||||
\(228\) | 3.41641i | 0.226257i | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.23607 | 0.344508 | ||||||||
\(232\) | 11.1803i | 0.734025i | ||||||||
\(233\) | − 9.94427i | − 0.651471i | −0.945461 | − | 0.325735i | \(-0.894388\pi\) | ||||
0.945461 | − | 0.325735i | \(-0.105612\pi\) | |||||||
\(234\) | −7.70820 | −0.503901 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.05573 | −0.0687220 | ||||||||
\(237\) | − 13.8197i | − 0.897683i | ||||||||
\(238\) | − 10.4721i | − 0.678808i | ||||||||
\(239\) | 14.4721 | 0.936125 | 0.468062 | − | 0.883695i | \(-0.344952\pi\) | ||||
0.468062 | + | 0.883695i | \(0.344952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4721 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(242\) | − 11.2361i | − 0.722282i | ||||||||
\(243\) | 13.5967i | 0.872232i | ||||||||
\(244\) | −2.29180 | −0.146717 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.4721 | 1.17774 | ||||||||
\(247\) | 14.4721i | 0.920840i | ||||||||
\(248\) | 21.7082i | 1.37847i | ||||||||
\(249\) | −7.05573 | −0.447139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.47214 | −0.156040 | −0.0780199 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780199 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(252\) | 0.909830i | 0.0573139i | ||||||||
\(253\) | 7.47214i | 0.469769i | ||||||||
\(254\) | 28.5623 | 1.79216 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | − 18.6525i | − 1.16351i | −0.813364 | − | 0.581755i | \(-0.802366\pi\) | ||||
0.813364 | − | 0.581755i | \(-0.197634\pi\) | |||||||
\(258\) | 12.4721i | 0.776481i | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.36068 | −0.455615 | ||||||||
\(262\) | − 1.52786i | − 0.0943918i | ||||||||
\(263\) | 11.7639i | 0.725395i | 0.931907 | + | 0.362698i | \(0.118144\pi\) | ||||
−0.931907 | + | 0.362698i | \(0.881856\pi\) | |||||||
\(264\) | 11.7082 | 0.720590 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.23607 | 0.443672 | ||||||||
\(267\) | − 15.7771i | − 0.965542i | ||||||||
\(268\) | 0.145898i | 0.00891214i | ||||||||
\(269\) | −1.70820 | −0.104151 | −0.0520755 | − | 0.998643i | \(-0.516584\pi\) | ||||
−0.0520755 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2918 | 0.625182 | 0.312591 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312591 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(272\) | − 31.4164i | − 1.90490i | ||||||||
\(273\) | − 4.00000i | − 0.242091i | ||||||||
\(274\) | −11.2361 | −0.678796 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.34752 | 0.0811114 | ||||||||
\(277\) | − 15.8885i | − 0.954650i | −0.878727 | − | 0.477325i | \(-0.841606\pi\) | ||||
0.878727 | − | 0.477325i | \(-0.158394\pi\) | |||||||
\(278\) | − 33.4164i | − 2.00418i | ||||||||
\(279\) | −14.2918 | −0.855627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3607 | 1.75151 | 0.875756 | − | 0.482755i | \(-0.160364\pi\) | ||||
0.875756 | + | 0.482755i | \(0.160364\pi\) | |||||||
\(282\) | 4.00000i | 0.238197i | ||||||||
\(283\) | − 9.41641i | − 0.559747i | −0.960037 | − | 0.279874i | \(-0.909707\pi\) | ||||
0.960037 | − | 0.279874i | \(-0.0902926\pi\) | |||||||
\(284\) | 2.90983 | 0.172667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.1803 | −1.31155 | ||||||||
\(287\) | − 9.23607i | − 0.545188i | ||||||||
\(288\) | 4.97871i | 0.293374i | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.944272 | 0.0553542 | ||||||||
\(292\) | 8.18034i | 0.478718i | ||||||||
\(293\) | 9.12461i | 0.533066i | 0.963826 | + | 0.266533i | \(0.0858781\pi\) | ||||
−0.963826 | + | 0.266533i | \(0.914122\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.70820 | −0.389906 | ||||||||
\(297\) | 23.4164i | 1.35876i | ||||||||
\(298\) | − 22.5623i | − 1.30700i | ||||||||
\(299\) | 5.70820 | 0.330114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.23607 | 0.359441 | ||||||||
\(302\) | 25.5066i | 1.46774i | ||||||||
\(303\) | 11.4164i | 0.655855i | ||||||||
\(304\) | 21.7082 | 1.24505 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 15.4164 | 0.881297 | ||||||||
\(307\) | − 31.4164i | − 1.79303i | −0.443014 | − | 0.896515i | \(-0.646091\pi\) | ||||
0.443014 | − | 0.896515i | \(-0.353909\pi\) | |||||||
\(308\) | 2.61803i | 0.149176i | ||||||||
\(309\) | 0.583592 | 0.0331994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3607 | −1.15455 | −0.577274 | − | 0.816550i | \(-0.695884\pi\) | ||||
−0.577274 | + | 0.816550i | \(0.695884\pi\) | |||||||
\(312\) | − 8.94427i | − 0.506370i | ||||||||
\(313\) | 28.4721i | 1.60934i | 0.593722 | + | 0.804670i | \(0.297658\pi\) | ||||
−0.593722 | + | 0.804670i | \(0.702342\pi\) | |||||||
\(314\) | −8.47214 | −0.478110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.90983 | 0.388708 | ||||||||
\(317\) | 19.3607i | 1.08740i | 0.839278 | + | 0.543702i | \(0.182978\pi\) | ||||
−0.839278 | + | 0.543702i | \(0.817022\pi\) | |||||||
\(318\) | − 0.944272i | − 0.0529521i | ||||||||
\(319\) | −21.1803 | −1.18587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.88854 | 0.551925 | ||||||||
\(322\) | − 2.85410i | − 0.159053i | ||||||||
\(323\) | − 28.9443i | − 1.61050i | ||||||||
\(324\) | 1.49342 | 0.0829679 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.9443 | −0.938456 | ||||||||
\(327\) | 22.7639i | 1.25885i | ||||||||
\(328\) | − 20.6525i | − 1.14034i | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.2918 | −0.620653 | −0.310327 | − | 0.950630i | \(-0.600438\pi\) | ||||
−0.310327 | + | 0.950630i | \(0.600438\pi\) | |||||||
\(332\) | − 3.52786i | − 0.193617i | ||||||||
\(333\) | − 4.41641i | − 0.242018i | ||||||||
\(334\) | −1.23607 | −0.0676346 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | −0.327327 | ||||||||
\(337\) | 7.52786i | 0.410069i | 0.978755 | + | 0.205034i | \(0.0657306\pi\) | ||||
−0.978755 | + | 0.205034i | \(0.934269\pi\) | |||||||
\(338\) | − 4.09017i | − 0.222476i | ||||||||
\(339\) | −15.3475 | −0.833563 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.1246 | −2.22702 | ||||||||
\(342\) | 10.6525i | 0.576020i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 13.9443 | 0.751825 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.1246 | −1.78079 | ||||||||
\(347\) | − 15.7639i | − 0.846252i | −0.906071 | − | 0.423126i | \(-0.860933\pi\) | ||||
0.906071 | − | 0.423126i | \(-0.139067\pi\) | |||||||
\(348\) | 3.81966i | 0.204755i | ||||||||
\(349\) | 4.47214 | 0.239388 | 0.119694 | − | 0.992811i | \(-0.461809\pi\) | ||||
0.119694 | + | 0.992811i | \(0.461809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8885 | 0.954820 | ||||||||
\(352\) | 14.3262i | 0.763591i | ||||||||
\(353\) | 20.1803i | 1.07409i | 0.843553 | + | 0.537046i | \(0.180460\pi\) | ||||
−0.843553 | + | 0.537046i | \(0.819540\pi\) | |||||||
\(354\) | 3.41641 | 0.181580 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.88854 | 0.418092 | ||||||||
\(357\) | 8.00000i | 0.423405i | ||||||||
\(358\) | 5.52786i | 0.292157i | ||||||||
\(359\) | −10.1246 | −0.534357 | −0.267178 | − | 0.963647i | \(-0.586091\pi\) | ||||
−0.267178 | + | 0.963647i | \(0.586091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 22.9443i | 1.20592i | ||||||||
\(363\) | 8.58359i | 0.450522i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.41641 | 0.387662 | ||||||||
\(367\) | − 3.12461i | − 0.163103i | −0.996669 | − | 0.0815517i | \(-0.974012\pi\) | ||||
0.996669 | − | 0.0815517i | \(-0.0259876\pi\) | |||||||
\(368\) | − 8.56231i | − 0.446341i | ||||||||
\(369\) | 13.5967 | 0.707818 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.472136 | −0.0245121 | ||||||||
\(372\) | 7.41641i | 0.384523i | ||||||||
\(373\) | 15.8328i | 0.819792i | 0.912132 | + | 0.409896i | \(0.134435\pi\) | ||||
−0.912132 | + | 0.409896i | \(0.865565\pi\) | |||||||
\(374\) | 44.3607 | 2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.47214 | 0.230633 | ||||||||
\(377\) | 16.1803i | 0.833330i | ||||||||
\(378\) | − 8.94427i | − 0.460044i | ||||||||
\(379\) | −11.1803 | −0.574295 | −0.287148 | − | 0.957886i | \(-0.592707\pi\) | ||||
−0.287148 | + | 0.957886i | \(0.592707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.8197 | −1.11786 | ||||||||
\(382\) | 4.00000i | 0.204658i | ||||||||
\(383\) | − 28.7639i | − 1.46977i | −0.678193 | − | 0.734884i | \(-0.737237\pi\) | ||||
0.678193 | − | 0.734884i | \(-0.262763\pi\) | |||||||
\(384\) | −16.8328 | −0.858996 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.3262 | −1.18727 | ||||||||
\(387\) | 9.18034i | 0.466663i | ||||||||
\(388\) | 0.472136i | 0.0239691i | ||||||||
\(389\) | 32.8885 | 1.66752 | 0.833758 | − | 0.552131i | \(-0.186185\pi\) | ||||
0.833758 | + | 0.552131i | \(0.186185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4164 | −0.577353 | ||||||||
\(392\) | 2.23607i | 0.112938i | ||||||||
\(393\) | 1.16718i | 0.0588767i | ||||||||
\(394\) | −12.0902 | −0.609094 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.85410 | −0.193676 | ||||||||
\(397\) | − 26.9443i | − 1.35229i | −0.736767 | − | 0.676147i | \(-0.763648\pi\) | ||||
0.736767 | − | 0.676147i | \(-0.236352\pi\) | |||||||
\(398\) | 4.47214i | 0.224168i | ||||||||
\(399\) | −5.52786 | −0.276739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4721 | 0.572891 | 0.286446 | − | 0.958097i | \(-0.407526\pi\) | ||||
0.286446 | + | 0.958097i | \(0.407526\pi\) | |||||||
\(402\) | − 0.472136i | − 0.0235480i | ||||||||
\(403\) | 31.4164i | 1.56496i | ||||||||
\(404\) | −5.70820 | −0.283994 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.09017 | 0.401508 | ||||||||
\(407\) | − 12.7082i | − 0.629922i | ||||||||
\(408\) | 17.8885i | 0.885615i | ||||||||
\(409\) | −15.5279 | −0.767803 | −0.383902 | − | 0.923374i | \(-0.625420\pi\) | ||||
−0.383902 | + | 0.923374i | \(0.625420\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.58359 | 0.423397 | ||||||||
\(412\) | 0.291796i | 0.0143758i | ||||||||
\(413\) | − 1.70820i | − 0.0840552i | ||||||||
\(414\) | 4.20163 | 0.206499 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.9443 | 0.536587 | ||||||||
\(417\) | 25.5279i | 1.25010i | ||||||||
\(418\) | 30.6525i | 1.49926i | ||||||||
\(419\) | 3.81966 | 0.186603 | 0.0933013 | − | 0.995638i | \(-0.470258\pi\) | ||||
0.0933013 | + | 0.995638i | \(0.470258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | − 19.4164i | − 0.945176i | ||||||||
\(423\) | 2.94427i | 0.143155i | ||||||||
\(424\) | −1.05573 | −0.0512707 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.41641 | −0.456226 | ||||||||
\(427\) | − 3.70820i | − 0.179453i | ||||||||
\(428\) | 4.94427i | 0.238990i | ||||||||
\(429\) | 16.9443 | 0.818077 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.4721 | 1.27512 | 0.637559 | − | 0.770402i | \(-0.279944\pi\) | ||||
0.637559 | + | 0.770402i | \(0.279944\pi\) | |||||||
\(432\) | − 26.8328i | − 1.29099i | ||||||||
\(433\) | 16.3607i | 0.786244i | 0.919486 | + | 0.393122i | \(0.128605\pi\) | ||||
−0.919486 | + | 0.393122i | \(0.871395\pi\) | |||||||
\(434\) | 15.7082 | 0.754018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3820 | −0.545097 | ||||||||
\(437\) | − 7.88854i | − 0.377360i | ||||||||
\(438\) | − 26.4721i | − 1.26489i | ||||||||
\(439\) | 21.7082 | 1.03608 | 0.518038 | − | 0.855358i | \(-0.326663\pi\) | ||||
0.518038 | + | 0.855358i | \(0.326663\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | − 33.8885i | − 1.61191i | ||||||||
\(443\) | 7.41641i | 0.352364i | 0.984358 | + | 0.176182i | \(0.0563748\pi\) | ||||
−0.984358 | + | 0.176182i | \(0.943625\pi\) | |||||||
\(444\) | −2.29180 | −0.108764 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.52786 | −0.167049 | ||||||||
\(447\) | 17.2361i | 0.815238i | ||||||||
\(448\) | 4.23607i | 0.200135i | ||||||||
\(449\) | −29.4721 | −1.39088 | −0.695438 | − | 0.718586i | \(-0.744790\pi\) | ||||
−0.695438 | + | 0.718586i | \(0.744790\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.1246 | 1.84231 | ||||||||
\(452\) | − 7.67376i | − 0.360943i | ||||||||
\(453\) | − 19.4853i | − 0.915499i | ||||||||
\(454\) | 8.76393 | 0.411312 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.3607 | −0.578842 | ||||||||
\(457\) | 21.4721i | 1.00442i | 0.864744 | + | 0.502212i | \(0.167480\pi\) | ||||
−0.864744 | + | 0.502212i | \(0.832520\pi\) | |||||||
\(458\) | 7.23607i | 0.338119i | ||||||||
\(459\) | −35.7771 | −1.66993 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18034 | 0.380996 | 0.190498 | − | 0.981688i | \(-0.438990\pi\) | ||||
0.190498 | + | 0.981688i | \(0.438990\pi\) | |||||||
\(462\) | − 8.47214i | − 0.394159i | ||||||||
\(463\) | 21.8885i | 1.01725i | 0.860989 | + | 0.508623i | \(0.169845\pi\) | ||||
−0.860989 | + | 0.508623i | \(0.830155\pi\) | |||||||
\(464\) | 24.2705 | 1.12673 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0902 | −0.745363 | ||||||||
\(467\) | 10.9443i | 0.506441i | 0.967409 | + | 0.253220i | \(0.0814897\pi\) | ||||
−0.967409 | + | 0.253220i | \(0.918510\pi\) | |||||||
\(468\) | 2.94427i | 0.136099i | ||||||||
\(469\) | −0.236068 | −0.0109006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.47214 | 0.298220 | ||||||||
\(472\) | − 3.81966i | − 0.175814i | ||||||||
\(473\) | 26.4164i | 1.21463i | ||||||||
\(474\) | −22.3607 | −1.02706 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | − 0.695048i | − 0.0318241i | ||||||||
\(478\) | − 23.4164i | − 1.07104i | ||||||||
\(479\) | 3.81966 | 0.174525 | 0.0872624 | − | 0.996185i | \(-0.472188\pi\) | ||||
0.0872624 | + | 0.996185i | \(0.472188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.70820 | −0.442656 | ||||||||
\(482\) | 20.1803i | 0.919189i | ||||||||
\(483\) | 2.18034i | 0.0992089i | ||||||||
\(484\) | −4.29180 | −0.195082 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0000 | 0.997940 | ||||||||
\(487\) | − 10.2361i | − 0.463841i | −0.972735 | − | 0.231920i | \(-0.925499\pi\) | ||||
0.972735 | − | 0.231920i | \(-0.0745008\pi\) | |||||||
\(488\) | − 8.29180i | − 0.375352i | ||||||||
\(489\) | 12.9443 | 0.585360 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2361 | −0.461947 | −0.230974 | − | 0.972960i | \(-0.574191\pi\) | ||||
−0.230974 | + | 0.972960i | \(0.574191\pi\) | |||||||
\(492\) | − 7.05573i | − 0.318097i | ||||||||
\(493\) | − 32.3607i | − 1.45745i | ||||||||
\(494\) | 23.4164 | 1.05355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.1246 | 2.11596 | ||||||||
\(497\) | 4.70820i | 0.211192i | ||||||||
\(498\) | 11.4164i | 0.511581i | ||||||||
\(499\) | −28.9443 | −1.29572 | −0.647862 | − | 0.761758i | \(-0.724337\pi\) | ||||
−0.647862 | + | 0.761758i | \(0.724337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.944272 | 0.0421870 | ||||||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | − 43.8885i | − 1.95689i | −0.206499 | − | 0.978447i | \(-0.566207\pi\) | ||||
0.206499 | − | 0.978447i | \(-0.433793\pi\) | |||||||
\(504\) | −3.29180 | −0.146628 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.0902 | 0.537474 | ||||||||
\(507\) | 3.12461i | 0.138769i | ||||||||
\(508\) | − 10.9098i | − 0.484045i | ||||||||
\(509\) | −9.34752 | −0.414322 | −0.207161 | − | 0.978307i | \(-0.566422\pi\) | ||||
−0.207161 | + | 0.978307i | \(0.566422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2361 | −0.585529 | ||||||||
\(512\) | 5.29180i | 0.233867i | ||||||||
\(513\) | − 24.7214i | − 1.09147i | ||||||||
\(514\) | −30.1803 | −1.33120 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.76393 | 0.209720 | ||||||||
\(517\) | 8.47214i | 0.372604i | ||||||||
\(518\) | 4.85410i | 0.213277i | ||||||||
\(519\) | 25.3050 | 1.11076 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 11.9098i | 0.521279i | ||||||||
\(523\) | − 28.3607i | − 1.24013i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) | ||||
0.784552 | − | 0.620063i | \(-0.212893\pi\) | |||||||
\(524\) | −0.583592 | −0.0254943 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.0344 | 0.829941 | ||||||||
\(527\) | − 62.8328i | − 2.73704i | ||||||||
\(528\) | − 25.4164i | − 1.10611i | ||||||||
\(529\) | 19.8885 | 0.864719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.51471 | 0.109129 | ||||||||
\(532\) | − 2.76393i | − 0.119832i | ||||||||
\(533\) | − 29.8885i | − 1.29462i | ||||||||
\(534\) | −25.5279 | −1.10470 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.527864 | −0.0228003 | ||||||||
\(537\) | − 4.22291i | − 0.182232i | ||||||||
\(538\) | 2.76393i | 0.119162i | ||||||||
\(539\) | −4.23607 | −0.182460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.94427 | −0.0835908 | −0.0417954 | − | 0.999126i | \(-0.513308\pi\) | ||||
−0.0417954 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(542\) | − 16.6525i | − 0.715285i | ||||||||
\(543\) | − 17.5279i | − 0.752193i | ||||||||
\(544\) | −21.8885 | −0.938464 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.47214 | −0.276982 | ||||||||
\(547\) | 14.2361i | 0.608690i | 0.952562 | + | 0.304345i | \(0.0984376\pi\) | ||||
−0.952562 | + | 0.304345i | \(0.901562\pi\) | |||||||
\(548\) | 4.29180i | 0.183336i | ||||||||
\(549\) | 5.45898 | 0.232984 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3607 | 0.952597 | ||||||||
\(552\) | 4.87539i | 0.207510i | ||||||||
\(553\) | 11.1803i | 0.475436i | ||||||||
\(554\) | −25.7082 | −1.09224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.7639 | −0.541311 | ||||||||
\(557\) | 44.8885i | 1.90199i | 0.309208 | + | 0.950994i | \(0.399936\pi\) | ||||
−0.309208 | + | 0.950994i | \(0.600064\pi\) | |||||||
\(558\) | 23.1246i | 0.978943i | ||||||||
\(559\) | 20.1803 | 0.853537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.8885 | −1.43078 | ||||||||
\(562\) | − 47.5066i | − 2.00394i | ||||||||
\(563\) | − 9.41641i | − 0.396854i | −0.980116 | − | 0.198427i | \(-0.936417\pi\) | ||||
0.980116 | − | 0.198427i | \(-0.0635833\pi\) | |||||||
\(564\) | 1.52786 | 0.0643347 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.2361 | −0.640420 | ||||||||
\(567\) | 2.41641i | 0.101480i | ||||||||
\(568\) | 10.5279i | 0.441739i | ||||||||
\(569\) | −13.9443 | −0.584574 | −0.292287 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292287 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5967 | −0.527157 | −0.263579 | − | 0.964638i | \(-0.584903\pi\) | ||||
−0.263579 | + | 0.964638i | \(0.584903\pi\) | |||||||
\(572\) | 8.47214i | 0.354238i | ||||||||
\(573\) | − 3.05573i | − 0.127655i | ||||||||
\(574\) | −14.9443 | −0.623762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.23607 | −0.259836 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 40.2705i | 1.67503i | ||||||||
\(579\) | 17.8197 | 0.740560 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.70820 | 0.236816 | ||||||||
\(582\) | − 1.52786i | − 0.0633320i | ||||||||
\(583\) | − 2.00000i | − 0.0828315i | ||||||||
\(584\) | −29.5967 | −1.22472 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7639 | 0.609892 | ||||||||
\(587\) | 29.2361i | 1.20670i | 0.797476 | + | 0.603351i | \(0.206168\pi\) | ||||
−0.797476 | + | 0.603351i | \(0.793832\pi\) | |||||||
\(588\) | 0.763932i | 0.0315040i | ||||||||
\(589\) | 43.4164 | 1.78894 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.23607 | 0.379921 | ||||||||
\(592\) | 14.5623i | 0.598507i | ||||||||
\(593\) | 25.3050i | 1.03915i | 0.854425 | + | 0.519575i | \(0.173910\pi\) | ||||
−0.854425 | + | 0.519575i | \(0.826090\pi\) | |||||||
\(594\) | 37.8885 | 1.55459 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.61803 | −0.353008 | ||||||||
\(597\) | − 3.41641i | − 0.139824i | ||||||||
\(598\) | − 9.23607i | − 0.377691i | ||||||||
\(599\) | −11.1803 | −0.456816 | −0.228408 | − | 0.973565i | \(-0.573352\pi\) | ||||
−0.228408 | + | 0.973565i | \(0.573352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0557 | −0.777299 | −0.388650 | − | 0.921386i | \(-0.627058\pi\) | ||||
−0.388650 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(602\) | − 10.0902i | − 0.411245i | ||||||||
\(603\) | − 0.347524i | − 0.0141523i | ||||||||
\(604\) | 9.74265 | 0.396423 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.4721 | 0.750379 | ||||||||
\(607\) | − 33.1246i | − 1.34449i | −0.740330 | − | 0.672243i | \(-0.765331\pi\) | ||||
0.740330 | − | 0.672243i | \(-0.234669\pi\) | |||||||
\(608\) | − 15.1246i | − 0.613384i | ||||||||
\(609\) | −6.18034 | −0.250440 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.47214 | 0.261835 | ||||||||
\(612\) | − 5.88854i | − 0.238030i | ||||||||
\(613\) | − 17.5836i | − 0.710195i | −0.934829 | − | 0.355097i | \(-0.884448\pi\) | ||||
0.934829 | − | 0.355097i | \(-0.115552\pi\) | |||||||
\(614\) | −50.8328 | −2.05145 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47214 | −0.381643 | ||||||||
\(617\) | − 11.9443i | − 0.480858i | −0.970667 | − | 0.240429i | \(-0.922712\pi\) | ||||
0.970667 | − | 0.240429i | \(-0.0772882\pi\) | |||||||
\(618\) | − 0.944272i | − 0.0379842i | ||||||||
\(619\) | −1.70820 | −0.0686585 | −0.0343293 | − | 0.999411i | \(-0.510929\pi\) | ||||
−0.0343293 | + | 0.999411i | \(0.510929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.75078 | −0.391285 | ||||||||
\(622\) | 32.9443i | 1.32094i | ||||||||
\(623\) | 12.7639i | 0.511376i | ||||||||
\(624\) | −19.4164 | −0.777278 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 46.0689 | 1.84128 | ||||||||
\(627\) | − 23.4164i | − 0.935161i | ||||||||
\(628\) | 3.23607i | 0.129133i | ||||||||
\(629\) | 19.4164 | 0.774183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.65248 | −0.145403 | −0.0727014 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0727014 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(632\) | 25.0000i | 0.994447i | ||||||||
\(633\) | 14.8328i | 0.589551i | ||||||||
\(634\) | 31.3262 | 1.24412 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.360680 | −0.0143019 | ||||||||
\(637\) | 3.23607i | 0.128218i | ||||||||
\(638\) | 34.2705i | 1.35678i | ||||||||
\(639\) | −6.93112 | −0.274191 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.83282 | −0.388373 | −0.194186 | − | 0.980965i | \(-0.562207\pi\) | ||||
−0.194186 | + | 0.980965i | \(0.562207\pi\) | |||||||
\(642\) | − 16.0000i | − 0.631470i | ||||||||
\(643\) | 9.52786i | 0.375742i | 0.982194 | + | 0.187871i | \(0.0601587\pi\) | ||||
−0.982194 | + | 0.187871i | \(0.939841\pi\) | |||||||
\(644\) | −1.09017 | −0.0429587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.8328 | −1.84261 | ||||||||
\(647\) | − 15.8885i | − 0.624643i | −0.949976 | − | 0.312322i | \(-0.898893\pi\) | ||||
0.949976 | − | 0.312322i | \(-0.101107\pi\) | |||||||
\(648\) | 5.40325i | 0.212260i | ||||||||
\(649\) | 7.23607 | 0.284041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 6.47214i | 0.253468i | ||||||||
\(653\) | 42.9443i | 1.68054i | 0.542169 | + | 0.840270i | \(0.317603\pi\) | ||||
−0.542169 | + | 0.840270i | \(0.682397\pi\) | |||||||
\(654\) | 36.8328 | 1.44028 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −44.8328 | −1.75043 | ||||||||
\(657\) | − 19.4853i | − 0.760194i | ||||||||
\(658\) | − 3.23607i | − 0.126155i | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.7214 | 1.81725 | 0.908625 | − | 0.417613i | \(-0.137133\pi\) | ||||
0.908625 | + | 0.417613i | \(0.137133\pi\) | |||||||
\(662\) | 18.2705i | 0.710104i | ||||||||
\(663\) | 25.8885i | 1.00543i | ||||||||
\(664\) | 12.7639 | 0.495337 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.14590 | −0.276898 | ||||||||
\(667\) | − 8.81966i | − 0.341499i | ||||||||
\(668\) | 0.472136i | 0.0182675i | ||||||||
\(669\) | 2.69505 | 0.104197 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.7082 | 0.606408 | ||||||||
\(672\) | 4.18034i | 0.161260i | ||||||||
\(673\) | 28.4721i | 1.09752i | 0.835980 | + | 0.548760i | \(0.184900\pi\) | ||||
−0.835980 | + | 0.548760i | \(0.815100\pi\) | |||||||
\(674\) | 12.1803 | 0.469169 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | − 30.3607i | − 1.16686i | −0.812165 | − | 0.583428i | \(-0.801711\pi\) | ||||
0.812165 | − | 0.583428i | \(-0.198289\pi\) | |||||||
\(678\) | 24.8328i | 0.953699i | ||||||||
\(679\) | −0.763932 | −0.0293170 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.69505 | −0.256555 | ||||||||
\(682\) | 66.5410i | 2.54799i | ||||||||
\(683\) | − 26.1246i | − 0.999630i | −0.866132 | − | 0.499815i | \(-0.833401\pi\) | ||||
0.866132 | − | 0.499815i | \(-0.166599\pi\) | |||||||
\(684\) | 4.06888 | 0.155578 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.61803 | 0.0617768 | ||||||||
\(687\) | − 5.52786i | − 0.210901i | ||||||||
\(688\) | − 30.2705i | − 1.15405i | ||||||||
\(689\) | −1.52786 | −0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1803 | 0.691613 | 0.345806 | − | 0.938306i | \(-0.387605\pi\) | ||||
0.345806 | + | 0.938306i | \(0.387605\pi\) | |||||||
\(692\) | 12.6525i | 0.480975i | ||||||||
\(693\) | − 6.23607i | − 0.236889i | ||||||||
\(694\) | −25.5066 | −0.968216 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.8197 | −0.523833 | ||||||||
\(697\) | 59.7771i | 2.26422i | ||||||||
\(698\) | − 7.23607i | − 0.273889i | ||||||||
\(699\) | 12.2918 | 0.464918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.9443 | −1.77306 | −0.886530 | − | 0.462670i | \(-0.846891\pi\) | ||||
−0.886530 | + | 0.462670i | \(0.846891\pi\) | |||||||
\(702\) | − 28.9443i | − 1.09243i | ||||||||
\(703\) | 13.4164i | 0.506009i | ||||||||
\(704\) | −17.9443 | −0.676300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.6525 | 1.22889 | ||||||||
\(707\) | − 9.23607i | − 0.347358i | ||||||||
\(708\) | − 1.30495i | − 0.0490431i | ||||||||
\(709\) | 47.8885 | 1.79849 | 0.899246 | − | 0.437443i | \(-0.144116\pi\) | ||||
0.899246 | + | 0.437443i | \(0.144116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.4590 | −0.617260 | ||||||||
\(712\) | 28.5410i | 1.06962i | ||||||||
\(713\) | − 17.1246i | − 0.641322i | ||||||||
\(714\) | 12.9443 | 0.484427 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.11146 | 0.0789088 | ||||||||
\(717\) | 17.8885i | 0.668060i | ||||||||
\(718\) | 16.3820i | 0.611370i | ||||||||
\(719\) | 6.18034 | 0.230488 | 0.115244 | − | 0.993337i | \(-0.463235\pi\) | ||||
0.115244 | + | 0.993337i | \(0.463235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.472136 | −0.0175833 | ||||||||
\(722\) | − 1.61803i | − 0.0602170i | ||||||||
\(723\) | − 15.4164i | − 0.573342i | ||||||||
\(724\) | 8.76393 | 0.325709 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.8885 | 0.515452 | ||||||||
\(727\) | 20.9443i | 0.776780i | 0.921495 | + | 0.388390i | \(0.126969\pi\) | ||||
−0.921495 | + | 0.388390i | \(0.873031\pi\) | |||||||
\(728\) | 7.23607i | 0.268187i | ||||||||
\(729\) | −24.0557 | −0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.3607 | −1.49279 | ||||||||
\(732\) | − 2.83282i | − 0.104704i | ||||||||
\(733\) | 4.00000i | 0.147743i | 0.997268 | + | 0.0738717i | \(0.0235355\pi\) | ||||
−0.997268 | + | 0.0738717i | \(0.976464\pi\) | |||||||
\(734\) | −5.05573 | −0.186610 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.96556 | −0.219893 | ||||||||
\(737\) | − 1.00000i | − 0.0368355i | ||||||||
\(738\) | − 22.0000i | − 0.809831i | ||||||||
\(739\) | 5.65248 | 0.207930 | 0.103965 | − | 0.994581i | \(-0.466847\pi\) | ||||
0.103965 | + | 0.994581i | \(0.466847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.8885 | −0.657152 | ||||||||
\(742\) | 0.763932i | 0.0280448i | ||||||||
\(743\) | − 1.52786i | − 0.0560519i | −0.999607 | − | 0.0280259i | \(-0.991078\pi\) | ||||
0.999607 | − | 0.0280259i | \(-0.00892210\pi\) | |||||||
\(744\) | −26.8328 | −0.983739 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.6180 | 0.937943 | ||||||||
\(747\) | 8.40325i | 0.307459i | ||||||||
\(748\) | − 16.9443i | − 0.619544i | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9443 | 0.764267 | 0.382134 | − | 0.924107i | \(-0.375189\pi\) | ||||
0.382134 | + | 0.924107i | \(0.375189\pi\) | |||||||
\(752\) | − 9.70820i | − 0.354022i | ||||||||
\(753\) | − 3.05573i | − 0.111357i | ||||||||
\(754\) | 26.1803 | 0.953432 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.41641 | −0.124254 | ||||||||
\(757\) | − 46.4164i | − 1.68703i | −0.537103 | − | 0.843517i | \(-0.680481\pi\) | ||||
0.537103 | − | 0.843517i | \(-0.319519\pi\) | |||||||
\(758\) | 18.0902i | 0.657065i | ||||||||
\(759\) | −9.23607 | −0.335248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.7771 | −1.58692 | −0.793459 | − | 0.608624i | \(-0.791722\pi\) | ||||
−0.793459 | + | 0.608624i | \(0.791722\pi\) | |||||||
\(762\) | 35.3050i | 1.27896i | ||||||||
\(763\) | − 18.4164i | − 0.666719i | ||||||||
\(764\) | 1.52786 | 0.0552762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46.5410 | −1.68160 | ||||||||
\(767\) | − 5.52786i | − 0.199600i | ||||||||
\(768\) | 16.7639i | 0.604916i | ||||||||
\(769\) | −33.0132 | −1.19048 | −0.595242 | − | 0.803546i | \(-0.702944\pi\) | ||||
−0.595242 | + | 0.803546i | \(0.702944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.0557 | 0.830332 | ||||||||
\(772\) | 8.90983i | 0.320672i | ||||||||
\(773\) | 27.8197i | 1.00060i | 0.865851 | + | 0.500302i | \(0.166778\pi\) | ||||
−0.865851 | + | 0.500302i | \(0.833222\pi\) | |||||||
\(774\) | 14.8541 | 0.533920 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.70820 | −0.0613209 | ||||||||
\(777\) | − 3.70820i | − 0.133031i | ||||||||
\(778\) | − 53.2148i | − 1.90784i | ||||||||
\(779\) | −41.3050 | −1.47990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.9443 | −0.713662 | ||||||||
\(782\) | 18.4721i | 0.660562i | ||||||||
\(783\) | − 27.6393i | − 0.987749i | ||||||||
\(784\) | 4.85410 | 0.173361 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.88854 | 0.0673621 | ||||||||
\(787\) | − 45.2361i | − 1.61249i | −0.591581 | − | 0.806246i | \(-0.701496\pi\) | ||||
0.591581 | − | 0.806246i | \(-0.298504\pi\) | |||||||
\(788\) | 4.61803i | 0.164511i | ||||||||
\(789\) | −14.5410 | −0.517674 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4164 | 0.441477 | ||||||||
\(792\) | − 13.9443i | − 0.495488i | ||||||||
\(793\) | − 12.0000i | − 0.426132i | ||||||||
\(794\) | −43.5967 | −1.54719 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.70820 | 0.0605457 | ||||||||
\(797\) | 8.58359i | 0.304046i | 0.988377 | + | 0.152023i | \(0.0485789\pi\) | ||||
−0.988377 | + | 0.152023i | \(0.951421\pi\) | |||||||
\(798\) | 8.94427i | 0.316624i | ||||||||
\(799\) | −12.9443 | −0.457935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.7902 | −0.663921 | ||||||||
\(802\) | − 18.5623i | − 0.655458i | ||||||||
\(803\) | − 56.0689i | − 1.97863i | ||||||||
\(804\) | −0.180340 | −0.00636010 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.8328 | 1.79051 | ||||||||
\(807\) | − 2.11146i | − 0.0743268i | ||||||||
\(808\) | − 20.6525i | − 0.726552i | ||||||||
\(809\) | −20.5279 | −0.721721 | −0.360861 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360861 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7214 | 1.64061 | 0.820304 | − | 0.571927i | \(-0.193804\pi\) | ||||
0.820304 | + | 0.571927i | \(0.193804\pi\) | |||||||
\(812\) | − 3.09017i | − 0.108444i | ||||||||
\(813\) | 12.7214i | 0.446158i | ||||||||
\(814\) | −20.5623 | −0.720708 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 38.8328 | 1.35942 | ||||||||
\(817\) | − 27.8885i | − 0.975697i | ||||||||
\(818\) | 25.1246i | 0.878461i | ||||||||
\(819\) | −4.76393 | −0.166465 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.8328 | −0.866671 | −0.433336 | − | 0.901233i | \(-0.642664\pi\) | ||||
−0.433336 | + | 0.901233i | \(0.642664\pi\) | |||||||
\(822\) | − 13.8885i | − 0.484419i | ||||||||
\(823\) | − 0.347524i | − 0.0121139i | −0.999982 | − | 0.00605697i | \(-0.998072\pi\) | ||||
0.999982 | − | 0.00605697i | \(-0.00192800\pi\) | |||||||
\(824\) | −1.05573 | −0.0367780 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.76393 | −0.0961695 | ||||||||
\(827\) | 25.5410i | 0.888148i | 0.895990 | + | 0.444074i | \(0.146467\pi\) | ||||
−0.895990 | + | 0.444074i | \(0.853533\pi\) | |||||||
\(828\) | − 1.60488i | − 0.0557734i | ||||||||
\(829\) | 52.3607 | 1.81856 | 0.909281 | − | 0.416183i | \(-0.136632\pi\) | ||||
0.909281 | + | 0.416183i | \(0.136632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.6393 | 0.681280 | ||||||||
\(832\) | 13.7082i | 0.475246i | ||||||||
\(833\) | − 6.47214i | − 0.224246i | ||||||||
\(834\) | 41.3050 | 1.43027 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.7082 | 0.404937 | ||||||||
\(837\) | − 53.6656i | − 1.85496i | ||||||||
\(838\) | − 6.18034i | − 0.213496i | ||||||||
\(839\) | −0.652476 | −0.0225260 | −0.0112630 | − | 0.999937i | \(-0.503585\pi\) | ||||
−0.0112630 | + | 0.999937i | \(0.503585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 21.0344i | 0.724895i | ||||||||
\(843\) | 36.2918i | 1.24996i | ||||||||
\(844\) | −7.41641 | −0.255283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.76393 | 0.163787 | ||||||||
\(847\) | − 6.94427i | − 0.238608i | ||||||||
\(848\) | 2.29180i | 0.0787006i | ||||||||
\(849\) | 11.6393 | 0.399460 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.29180 | 0.181400 | ||||||||
\(852\) | 3.59675i | 0.123223i | ||||||||
\(853\) | 0.583592i | 0.0199818i | 0.999950 | + | 0.00999091i | \(0.00318026\pi\) | ||||
−0.999950 | + | 0.00999091i | \(0.996820\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.8885 | −0.611418 | ||||||||
\(857\) | 38.1803i | 1.30422i | 0.758126 | + | 0.652108i | \(0.226115\pi\) | ||||
−0.758126 | + | 0.652108i | \(0.773885\pi\) | |||||||
\(858\) | − 27.4164i | − 0.935981i | ||||||||
\(859\) | 22.3607 | 0.762937 | 0.381468 | − | 0.924382i | \(-0.375419\pi\) | ||||
0.381468 | + | 0.924382i | \(0.375419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4164 | 0.389070 | ||||||||
\(862\) | − 42.8328i | − 1.45889i | ||||||||
\(863\) | 49.6525i | 1.69019i | 0.534616 | + | 0.845095i | \(0.320456\pi\) | ||||
−0.534616 | + | 0.845095i | \(0.679544\pi\) | |||||||
\(864\) | −18.6950 | −0.636018 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.4721 | 0.899560 | ||||||||
\(867\) | − 30.7639i | − 1.04480i | ||||||||
\(868\) | − 6.00000i | − 0.203653i | ||||||||
\(869\) | −47.3607 | −1.60660 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.763932 | −0.0258848 | ||||||||
\(872\) | − 41.1803i | − 1.39454i | ||||||||
\(873\) | − 1.12461i | − 0.0380623i | ||||||||
\(874\) | −12.7639 | −0.431746 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.1115 | −0.341634 | ||||||||
\(877\) | 14.3607i | 0.484926i | 0.970161 | + | 0.242463i | \(0.0779553\pi\) | ||||
−0.970161 | + | 0.242463i | \(0.922045\pi\) | |||||||
\(878\) | − 35.1246i | − 1.18540i | ||||||||
\(879\) | −11.2786 | −0.380419 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.1803 | 0.949420 | 0.474710 | − | 0.880142i | \(-0.342553\pi\) | ||||
0.474710 | + | 0.880142i | \(0.342553\pi\) | |||||||
\(882\) | 2.38197i | 0.0802050i | ||||||||
\(883\) | − 50.5967i | − 1.70272i | −0.524585 | − | 0.851358i | \(-0.675780\pi\) | ||||
0.524585 | − | 0.851358i | \(-0.324220\pi\) | |||||||
\(884\) | −12.9443 | −0.435363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 52.6525i | 1.76790i | 0.467584 | + | 0.883949i | \(0.345124\pi\) | ||||
−0.467584 | + | 0.883949i | \(0.654876\pi\) | |||||||
\(888\) | − 8.29180i | − 0.278254i | ||||||||
\(889\) | 17.6525 | 0.592045 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2361 | −0.342921 | ||||||||
\(892\) | 1.34752i | 0.0451184i | ||||||||
\(893\) | − 8.94427i | − 0.299309i | ||||||||
\(894\) | 27.8885 | 0.932732 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.6180 | 0.454947 | ||||||||
\(897\) | 7.05573i | 0.235584i | ||||||||
\(898\) | 47.6869i | 1.59133i | ||||||||
\(899\) | 48.5410 | 1.61893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.05573 | 0.101801 | ||||||||
\(902\) | − 63.3050i | − 2.10782i | ||||||||
\(903\) | 7.70820i | 0.256513i | ||||||||
\(904\) | 27.7639 | 0.923415 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −31.5279 | −1.04744 | ||||||||
\(907\) | 18.8328i | 0.625333i | 0.949863 | + | 0.312667i | \(0.101222\pi\) | ||||
−0.949863 | + | 0.312667i | \(0.898778\pi\) | |||||||
\(908\) | − 3.34752i | − 0.111091i | ||||||||
\(909\) | 13.5967 | 0.450976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.1803 | 0.767999 | 0.383999 | − | 0.923333i | \(-0.374546\pi\) | ||||
0.383999 | + | 0.923333i | \(0.374546\pi\) | |||||||
\(912\) | 26.8328i | 0.888523i | ||||||||
\(913\) | 24.1803i | 0.800252i | ||||||||
\(914\) | 34.7426 | 1.14918 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.76393 | 0.0913229 | ||||||||
\(917\) | − 0.944272i | − 0.0311826i | ||||||||
\(918\) | 57.8885i | 1.91061i | ||||||||
\(919\) | 32.2361 | 1.06337 | 0.531685 | − | 0.846942i | \(-0.321559\pi\) | ||||
0.531685 | + | 0.846942i | \(0.321559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.8328 | 1.27958 | ||||||||
\(922\) | − 13.2361i | − 0.435907i | ||||||||
\(923\) | 15.2361i | 0.501501i | ||||||||
\(924\) | −3.23607 | −0.106459 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.4164 | 1.16386 | ||||||||
\(927\) | − 0.695048i | − 0.0228284i | ||||||||
\(928\) | − 16.9098i | − 0.555092i | ||||||||
\(929\) | −51.7082 | −1.69649 | −0.848246 | − | 0.529603i | \(-0.822341\pi\) | ||||
−0.848246 | + | 0.529603i | \(0.822341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.47214 | 0.146568 | ||||||||
\(932\) | 6.14590i | 0.201316i | ||||||||
\(933\) | − 25.1672i | − 0.823937i | ||||||||
\(934\) | 17.7082 | 0.579430 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.6525 | −0.348187 | ||||||||
\(937\) | − 30.7639i | − 1.00501i | −0.864573 | − | 0.502507i | \(-0.832411\pi\) | ||||
0.864573 | − | 0.502507i | \(-0.167589\pi\) | |||||||
\(938\) | 0.381966i | 0.0124716i | ||||||||
\(939\) | −35.1935 | −1.14850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.763932 | −0.0249035 | −0.0124517 | − | 0.999922i | \(-0.503964\pi\) | ||||
−0.0124517 | + | 0.999922i | \(0.503964\pi\) | |||||||
\(942\) | − 10.4721i | − 0.341201i | ||||||||
\(943\) | 16.2918i | 0.530534i | ||||||||
\(944\) | −8.29180 | −0.269875 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.7426 | 1.38968 | ||||||||
\(947\) | 18.8328i | 0.611984i | 0.952034 | + | 0.305992i | \(0.0989881\pi\) | ||||
−0.952034 | + | 0.305992i | \(0.901012\pi\) | |||||||
\(948\) | 8.54102i | 0.277399i | ||||||||
\(949\) | −42.8328 | −1.39041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.9311 | −0.776020 | ||||||||
\(952\) | − 14.4721i | − 0.469045i | ||||||||
\(953\) | − 5.47214i | − 0.177260i | −0.996065 | − | 0.0886299i | \(-0.971751\pi\) | ||||
0.996065 | − | 0.0886299i | \(-0.0282489\pi\) | |||||||
\(954\) | −1.12461 | −0.0364107 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.94427 | −0.289278 | ||||||||
\(957\) | − 26.1803i | − 0.846290i | ||||||||
\(958\) | − 6.18034i | − 0.199678i | ||||||||
\(959\) | −6.94427 | −0.224242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.2492 | 2.04030 | ||||||||
\(962\) | 15.7082i | 0.506453i | ||||||||
\(963\) | − 11.7771i | − 0.379511i | ||||||||
\(964\) | 7.70820 | 0.248265 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.52786 | 0.113507 | ||||||||
\(967\) | 49.8885i | 1.60431i | 0.597118 | + | 0.802154i | \(0.296313\pi\) | ||||
−0.597118 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(968\) | − 15.5279i | − 0.499084i | ||||||||
\(969\) | 35.7771 | 1.14933 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | − 8.40325i | − 0.269534i | ||||||||
\(973\) | − 20.6525i | − 0.662088i | ||||||||
\(974\) | −16.5623 | −0.530691 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0000 | −0.576166 | ||||||||
\(977\) | 2.52786i | 0.0808735i | 0.999182 | + | 0.0404368i | \(0.0128749\pi\) | ||||
−0.999182 | + | 0.0404368i | \(0.987125\pi\) | |||||||
\(978\) | − 20.9443i | − 0.669724i | ||||||||
\(979\) | −54.0689 | −1.72805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1115 | 0.865602 | ||||||||
\(982\) | 16.5623i | 0.528524i | ||||||||
\(983\) | 32.5410i | 1.03790i | 0.854805 | + | 0.518949i | \(0.173676\pi\) | ||||
−0.854805 | + | 0.518949i | \(0.826324\pi\) | |||||||
\(984\) | 25.5279 | 0.813799 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −52.3607 | −1.66750 | ||||||||
\(987\) | 2.47214i | 0.0786890i | ||||||||
\(988\) | − 8.94427i | − 0.284555i | ||||||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.18034 | −0.291623 | −0.145812 | − | 0.989312i | \(-0.546579\pi\) | ||||
−0.145812 | + | 0.989312i | \(0.546579\pi\) | |||||||
\(992\) | − 32.8328i | − 1.04244i | ||||||||
\(993\) | − 13.9574i | − 0.442926i | ||||||||
\(994\) | 7.61803 | 0.241629 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.36068 | 0.138173 | ||||||||
\(997\) | 18.5836i | 0.588548i | 0.955721 | + | 0.294274i | \(0.0950779\pi\) | ||||
−0.955721 | + | 0.294274i | \(0.904922\pi\) | |||||||
\(998\) | 46.8328i | 1.48247i | ||||||||
\(999\) | 16.5836 | 0.524682 |
(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 | 175.2.b.c.99.1 | 4 | ||
3.2 | odd | 2 | 1575.2.d.k.1324.4 | 4 | |||
4.3 | odd | 2 | 2800.2.g.s.449.2 | 4 | |||
5.2 | odd | 4 | 175.2.a.e.1.2 | yes | 2 | ||
5.3 | odd | 4 | 175.2.a.d.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 175.2.b.c.99.4 | 4 | ||
7.6 | odd | 2 | 1225.2.b.k.99.1 | 4 | |||
15.2 | even | 4 | 1575.2.a.n.1.1 | 2 | |||
15.8 | even | 4 | 1575.2.a.s.1.2 | 2 | |||
15.14 | odd | 2 | 1575.2.d.k.1324.1 | 4 | |||
20.3 | even | 4 | 2800.2.a.bh.1.2 | 2 | |||
20.7 | even | 4 | 2800.2.a.bp.1.1 | 2 | |||
20.19 | odd | 2 | 2800.2.g.s.449.3 | 4 | |||
35.13 | even | 4 | 1225.2.a.n.1.1 | 2 | |||
35.27 | even | 4 | 1225.2.a.u.1.2 | 2 | |||
35.34 | odd | 2 | 1225.2.b.k.99.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.a.d.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
175.2.a.e.1.2 | yes | 2 | 5.2 | odd | 4 | ||
175.2.b.c.99.1 | 4 | 1.1 | even | 1 | trivial | ||
175.2.b.c.99.4 | 4 | 5.4 | even | 2 | inner | ||
1225.2.a.n.1.1 | 2 | 35.13 | even | 4 | |||
1225.2.a.u.1.2 | 2 | 35.27 | even | 4 | |||
1225.2.b.k.99.1 | 4 | 7.6 | odd | 2 | |||
1225.2.b.k.99.4 | 4 | 35.34 | odd | 2 | |||
1575.2.a.n.1.1 | 2 | 15.2 | even | 4 | |||
1575.2.a.s.1.2 | 2 | 15.8 | even | 4 | |||
1575.2.d.k.1324.1 | 4 | 15.14 | odd | 2 | |||
1575.2.d.k.1324.4 | 4 | 3.2 | odd | 2 | |||
2800.2.a.bh.1.2 | 2 | 20.3 | even | 4 | |||
2800.2.a.bp.1.1 | 2 | 20.7 | even | 4 | |||
2800.2.g.s.449.2 | 4 | 4.3 | odd | 2 | |||
2800.2.g.s.449.3 | 4 | 20.19 | odd | 2 |