Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (of order \(4\), degree \(2\), 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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.d.107.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22474 | + | 1.22474i | −0.462910 | + | 0.462910i | −0.899608 | − | 0.436698i | \(-0.856148\pi\) |
0.436698 | + | 0.899608i | \(0.356148\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 1.73205 | 0.462910 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.24264 | − | 4.24264i | −1.02899 | − | 1.02899i | −0.999567 | − | 0.0294245i | \(-0.990633\pi\) |
−0.0294245 | − | 0.999567i | \(-0.509367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | − | 4.24264i | 0.884652 | − | 0.884652i | −0.109351 | − | 0.994003i | \(-0.534877\pi\) |
0.994003 | + | 0.109351i | \(0.0348774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.22474 | − | 1.22474i | −0.231455 | − | 0.231455i | ||||
\(29\) | 10.3923 | 1.92980 | 0.964901 | − | 0.262613i | \(-0.0845842\pi\) | ||||
0.964901 | + | 0.262613i | \(0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000i | 1.02899i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.12372 | + | 6.12372i | −1.00673 | + | 1.00673i | −0.00675691 | + | 0.999977i | \(0.502151\pi\) |
−0.999977 | + | 0.00675691i | \(0.997849\pi\) | |||||||
\(38\) | 0.707107 | − | 0.707107i | 0.114708 | − | 0.114708i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.22474 | + | 1.22474i | 0.186772 | + | 0.186772i | 0.794299 | − | 0.607527i | \(-0.207838\pi\) |
−0.607527 | + | 0.794299i | \(0.707838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000i | 0.571429i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | − | 8.48528i | 1.16554 | − | 1.16554i | 0.182300 | − | 0.983243i | \(-0.441646\pi\) |
0.983243 | − | 0.182300i | \(-0.0583542\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.73205i | 0.231455i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.34847 | − | 7.34847i | −0.964901 | − | 0.964901i | ||||
\(59\) | 10.3923 | 1.35296 | 0.676481 | − | 0.736460i | \(-0.263504\pi\) | ||||
0.676481 | + | 0.736460i | \(0.263504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | −4.94975 | − | 4.94975i | −0.628619 | − | 0.628619i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34847 | − | 7.34847i | 0.897758 | − | 0.897758i | −0.0974792 | − | 0.995238i | \(-0.531078\pi\) |
0.995238 | + | 0.0974792i | \(0.0310779\pi\) | |||||||
\(68\) | 4.24264 | − | 4.24264i | 0.514496 | − | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.57321 | + | 8.57321i | 1.00342 | + | 1.00342i | 0.999994 | + | 0.00342468i | \(0.00109011\pi\) |
0.00342468 | + | 0.999994i | \(0.498910\pi\) | |||||||
\(74\) | 8.66025 | 1.00673 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.0000i | − | 1.46261i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) | ||
0.682048 | − | 0.731307i | \(-0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24264 | − | 4.24264i | 0.465690 | − | 0.465690i | −0.434825 | − | 0.900515i | \(-0.643190\pi\) |
0.900515 | + | 0.434825i | \(0.143190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.73205i | − | 0.186772i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.24264 | + | 4.24264i | 0.442326 | + | 0.442326i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.12372 | + | 6.12372i | −0.621770 | + | 0.621770i | −0.945984 | − | 0.324214i | \(-0.894900\pi\) |
0.324214 | + | 0.945984i | \(0.394900\pi\) | |||||||
\(98\) | 2.82843 | − | 2.82843i | 0.285714 | − | 0.285714i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.12372 | + | 6.12372i | 0.603388 | + | 0.603388i | 0.941210 | − | 0.337822i | \(-0.109690\pi\) |
−0.337822 | + | 0.941210i | \(0.609690\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | −12.7279 | − | 12.7279i | −1.23045 | − | 1.23045i | −0.963789 | − | 0.266666i | \(-0.914078\pi\) |
−0.266666 | − | 0.963789i | \(-0.585922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.00000i | − | 0.0957826i | −0.998853 | − | 0.0478913i | \(-0.984750\pi\) | ||
0.998853 | − | 0.0478913i | \(-0.0152501\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.22474 | − | 1.22474i | 0.115728 | − | 0.115728i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.3923i | 0.964901i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.34847 | − | 7.34847i | −0.676481 | − | 0.676481i | ||||
\(119\) | 10.3923 | 0.952661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −3.53553 | − | 3.53553i | −0.320092 | − | 0.320092i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.00000i | 0.628619i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847 | − | 7.34847i | 0.652071 | − | 0.652071i | −0.301420 | − | 0.953491i | \(-0.597461\pi\) |
0.953491 | + | 0.301420i | \(0.0974607\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.3923i | − | 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.22474 | − | 1.22474i | −0.106199 | − | 0.106199i | ||||
\(134\) | −10.3923 | −0.897758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 8.48528 | + | 8.48528i | 0.724947 | + | 0.724947i | 0.969608 | − | 0.244662i | \(-0.0786770\pi\) |
−0.244662 | + | 0.969608i | \(0.578677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.0000i | − | 0.933008i | −0.884519 | − | 0.466504i | \(-0.845513\pi\) | ||
0.884519 | − | 0.466504i | \(-0.154487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.34847 | − | 7.34847i | 0.616670 | − | 0.616670i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 12.1244i | − | 1.00342i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.12372 | − | 6.12372i | −0.503367 | − | 0.503367i | ||||
\(149\) | 10.3923 | 0.851371 | 0.425685 | − | 0.904871i | \(-0.360033\pi\) | ||||
0.425685 | + | 0.904871i | \(0.360033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 0.707107 | + | 0.707107i | 0.0573539 | + | 0.0573539i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.12372 | − | 6.12372i | 0.488726 | − | 0.488726i | −0.419178 | − | 0.907904i | \(-0.637682\pi\) |
0.907904 | + | 0.419178i | \(0.137682\pi\) | |||||||
\(158\) | −9.19239 | + | 9.19239i | −0.731307 | + | 0.731307i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34847 | + | 7.34847i | 0.575577 | + | 0.575577i | 0.933681 | − | 0.358105i | \(-0.116577\pi\) |
−0.358105 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 4.24264 | + | 4.24264i | 0.328305 | + | 0.328305i | 0.851942 | − | 0.523636i | \(-0.175425\pi\) |
−0.523636 | + | 0.851942i | \(0.675425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.22474 | + | 1.22474i | −0.0933859 | + | 0.0933859i | ||||
\(173\) | −4.24264 | + | 4.24264i | −0.322562 | + | 0.322562i | −0.849749 | − | 0.527187i | \(-0.823247\pi\) |
0.527187 | + | 0.849749i | \(0.323247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.34847 | + | 7.34847i | 0.550791 | + | 0.550791i | ||||
\(179\) | −20.7846 | −1.55351 | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.00000i | − | 0.442326i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.7846i | − | 1.50392i | −0.659208 | − | 0.751961i | \(-0.729108\pi\) | ||
0.659208 | − | 0.751961i | \(-0.270892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.22474 | + | 1.22474i | 0.0881591 | + | 0.0881591i | 0.749811 | − | 0.661652i | \(-0.230144\pi\) |
−0.661652 | + | 0.749811i | \(0.730144\pi\) | |||||||
\(194\) | 8.66025 | 0.621770 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.00000 | −0.285714 | ||||||||
\(197\) | −8.48528 | − | 8.48528i | −0.604551 | − | 0.604551i | 0.336966 | − | 0.941517i | \(-0.390599\pi\) |
−0.941517 | + | 0.336966i | \(0.890599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.0000i | − | 1.13421i | −0.823646 | − | 0.567105i | \(-0.808063\pi\) | ||
0.823646 | − | 0.567105i | \(-0.191937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.7279 | + | 12.7279i | −0.893325 | + | 0.893325i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 8.66025i | − | 0.603388i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 8.48528 | + | 8.48528i | 0.582772 | + | 0.582772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000i | 1.23045i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.57321 | + | 8.57321i | −0.581988 | + | 0.581988i | ||||
\(218\) | −0.707107 | + | 0.707107i | −0.0478913 | + | 0.0478913i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.57321 | − | 8.57321i | −0.574105 | − | 0.574105i | 0.359168 | − | 0.933273i | \(-0.383060\pi\) |
−0.933273 | + | 0.359168i | \(0.883060\pi\) | |||||||
\(224\) | −1.73205 | −0.115728 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9706 | + | 16.9706i | 1.12638 | + | 1.12638i | 0.990762 | + | 0.135614i | \(0.0433007\pi\) |
0.135614 | + | 0.990762i | \(0.456699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.0000i | 1.65205i | 0.563636 | + | 0.826023i | \(0.309402\pi\) | ||||
−0.563636 | + | 0.826023i | \(0.690598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.34847 | − | 7.34847i | 0.482451 | − | 0.482451i | ||||
\(233\) | −12.7279 | + | 12.7279i | −0.833834 | + | 0.833834i | −0.988039 | − | 0.154205i | \(-0.950718\pi\) |
0.154205 | + | 0.988039i | \(0.450718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.3923i | 0.676481i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.34847 | − | 7.34847i | −0.476331 | − | 0.476331i | ||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | −7.77817 | − | 7.77817i | −0.500000 | − | 0.500000i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000i | 0.320092i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.94975 | − | 4.94975i | 0.314309 | − | 0.314309i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923i | 0.655956i | 0.944685 | + | 0.327978i | \(0.106367\pi\) | ||||
−0.944685 | + | 0.327978i | \(0.893633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.3923 | −0.652071 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.48528 | + | 8.48528i | 0.529297 | + | 0.529297i | 0.920363 | − | 0.391066i | \(-0.127893\pi\) |
−0.391066 | + | 0.920363i | \(0.627893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.0000i | − | 0.932055i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.34847 | + | 7.34847i | −0.453990 | + | 0.453990i | ||||
\(263\) | −12.7279 | + | 12.7279i | −0.784837 | + | 0.784837i | −0.980643 | − | 0.195805i | \(-0.937268\pi\) |
0.195805 | + | 0.980643i | \(0.437268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.73205i | 0.106199i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.34847 | + | 7.34847i | 0.448879 | + | 0.448879i | ||||
\(269\) | −31.1769 | −1.90089 | −0.950445 | − | 0.310893i | \(-0.899372\pi\) | ||||
−0.950445 | + | 0.310893i | \(0.899372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | −0.0607457 | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | 4.24264 | + | 4.24264i | 0.257248 | + | 0.257248i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.0000i | − | 0.724947i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4722 | + | 13.4722i | −0.809466 | + | 0.809466i | −0.984553 | − | 0.175087i | \(-0.943979\pi\) |
0.175087 | + | 0.984553i | \(0.443979\pi\) | |||||||
\(278\) | −7.77817 | + | 7.77817i | −0.466504 | + | 0.466504i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.7846i | − | 1.23991i | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||
0.784639 | − | 0.619953i | \(-0.212848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8207 | + | 20.8207i | 1.23766 | + | 1.23766i | 0.960955 | + | 0.276705i | \(0.0892425\pi\) |
0.276705 | + | 0.960955i | \(0.410758\pi\) | |||||||
\(284\) | −10.3923 | −0.616670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.57321 | + | 8.57321i | −0.501709 | + | 0.501709i | ||||
\(293\) | −4.24264 | + | 4.24264i | −0.247858 | + | 0.247858i | −0.820091 | − | 0.572233i | \(-0.806077\pi\) |
0.572233 | + | 0.820091i | \(0.306077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.66025i | 0.503367i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.34847 | − | 7.34847i | −0.425685 | − | 0.425685i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 3.53553 | + | 3.53553i | 0.203447 | + | 0.203447i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8207 | − | 20.8207i | 1.18830 | − | 1.18830i | 0.210760 | − | 0.977538i | \(-0.432406\pi\) |
0.977538 | − | 0.210760i | \(-0.0675939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7846i | 1.17859i | 0.807919 | + | 0.589294i | \(0.200594\pi\) | ||||
−0.807919 | + | 0.589294i | \(0.799406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6969 | − | 14.6969i | −0.830720 | − | 0.830720i | 0.156895 | − | 0.987615i | \(-0.449852\pi\) |
−0.987615 | + | 0.156895i | \(0.949852\pi\) | |||||||
\(314\) | −8.66025 | −0.488726 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | 0.731307 | ||||||||
\(317\) | 4.24264 | + | 4.24264i | 0.238290 | + | 0.238290i | 0.816142 | − | 0.577851i | \(-0.196109\pi\) |
−0.577851 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.34847 | − | 7.34847i | 0.409514 | − | 0.409514i | ||||
\(323\) | 4.24264 | − | 4.24264i | 0.236067 | − | 0.236067i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 10.3923i | − | 0.575577i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | −0.714545 | −0.357272 | − | 0.934000i | \(-0.616293\pi\) | ||||
−0.357272 | + | 0.934000i | \(0.616293\pi\) | |||||||
\(332\) | 4.24264 | + | 4.24264i | 0.232845 | + | 0.232845i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.00000i | − | 0.328305i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6969 | + | 14.6969i | −0.800593 | + | 0.800593i | −0.983188 | − | 0.182595i | \(-0.941550\pi\) |
0.182595 | + | 0.983188i | \(0.441550\pi\) | |||||||
\(338\) | −9.19239 | + | 9.19239i | −0.500000 | + | 0.500000i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4722 | − | 13.4722i | −0.727430 | − | 0.727430i | ||||
\(344\) | 1.73205 | 0.0933859 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 12.7279 | + | 12.7279i | 0.683271 | + | 0.683271i | 0.960736 | − | 0.277465i | \(-0.0894943\pi\) |
−0.277465 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.0000i | 1.65939i | 0.558216 | + | 0.829696i | \(0.311486\pi\) | ||||
−0.558216 | + | 0.829696i | \(0.688514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.3923i | − | 0.550791i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.6969 | + | 14.6969i | 0.776757 | + | 0.776757i | ||||
\(359\) | −10.3923 | −0.548485 | −0.274242 | − | 0.961661i | \(-0.588427\pi\) | ||||
−0.274242 | + | 0.961661i | \(0.588427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 1.41421 | + | 1.41421i | 0.0743294 | + | 0.0743294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.34847 | + | 7.34847i | −0.383587 | + | 0.383587i | −0.872393 | − | 0.488806i | \(-0.837433\pi\) |
0.488806 | + | 0.872393i | \(0.337433\pi\) | |||||||
\(368\) | −4.24264 | + | 4.24264i | −0.221163 | + | 0.221163i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846i | 1.07908i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.57321 | − | 8.57321i | −0.443904 | − | 0.443904i | 0.449418 | − | 0.893322i | \(-0.351632\pi\) |
−0.893322 | + | 0.449418i | \(0.851632\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.6969 | + | 14.6969i | −0.751961 | + | 0.751961i | ||||
\(383\) | −4.24264 | + | 4.24264i | −0.216789 | + | 0.216789i | −0.807144 | − | 0.590355i | \(-0.798988\pi\) |
0.590355 | + | 0.807144i | \(0.298988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.73205i | − | 0.0881591i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.12372 | − | 6.12372i | −0.310885 | − | 0.310885i | ||||
\(389\) | −20.7846 | −1.05382 | −0.526911 | − | 0.849921i | \(-0.676650\pi\) | ||||
−0.526911 | + | 0.849921i | \(0.676650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 2.82843 | + | 2.82843i | 0.142857 | + | 0.142857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000i | 0.604551i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.12372 | + | 6.12372i | −0.307341 | + | 0.307341i | −0.843877 | − | 0.536536i | \(-0.819732\pi\) |
0.536536 | + | 0.843877i | \(0.319732\pi\) | |||||||
\(398\) | −11.3137 | + | 11.3137i | −0.567105 | + | 0.567105i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 20.7846i | − | 1.03793i | −0.854794 | − | 0.518967i | \(-0.826317\pi\) | ||
0.854794 | − | 0.518967i | \(-0.173683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0000 | 0.893325 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.0000i | 1.08783i | 0.839140 | + | 0.543915i | \(0.183059\pi\) | ||||
−0.839140 | + | 0.543915i | \(0.816941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.12372 | + | 6.12372i | −0.301694 | + | 0.301694i | ||||
\(413\) | −12.7279 | + | 12.7279i | −0.626300 | + | 0.626300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3923 | 0.507697 | 0.253849 | − | 0.967244i | \(-0.418303\pi\) | ||||
0.253849 | + | 0.967244i | \(0.418303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | 0.633581 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(422\) | 2.82843 | + | 2.82843i | 0.137686 | + | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.0000i | − | 0.582772i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.12372 | + | 6.12372i | −0.296348 | + | 0.296348i | ||||
\(428\) | 12.7279 | − | 12.7279i | 0.615227 | − | 0.615227i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.1769i | − | 1.50174i | −0.660451 | − | 0.750870i | \(-0.729635\pi\) | ||
0.660451 | − | 0.750870i | \(-0.270365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4722 | + | 13.4722i | 0.647432 | + | 0.647432i | 0.952372 | − | 0.304939i | \(-0.0986362\pi\) |
−0.304939 | + | 0.952372i | \(0.598636\pi\) | |||||||
\(434\) | 12.1244 | 0.581988 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | 0.0478913 | ||||||||
\(437\) | 4.24264 | + | 4.24264i | 0.202953 | + | 0.202953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.0000i | − | 1.47955i | −0.672855 | − | 0.739775i | \(-0.734932\pi\) | ||
0.672855 | − | 0.739775i | \(-0.265068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.24264 | + | 4.24264i | −0.201574 | + | 0.201574i | −0.800674 | − | 0.599100i | \(-0.795525\pi\) |
0.599100 | + | 0.800674i | \(0.295525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.1244i | 0.574105i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.22474 | + | 1.22474i | 0.0578638 | + | 0.0578638i | ||||
\(449\) | 31.1769 | 1.47133 | 0.735665 | − | 0.677346i | \(-0.236870\pi\) | ||||
0.735665 | + | 0.677346i | \(0.236870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 24.0000i | − | 1.12638i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6969 | − | 14.6969i | 0.687494 | − | 0.687494i | −0.274184 | − | 0.961677i | \(-0.588408\pi\) |
0.961677 | + | 0.274184i | \(0.0884076\pi\) | |||||||
\(458\) | 17.6777 | − | 17.6777i | 0.826023 | − | 0.826023i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3923i | 0.484018i | 0.970274 | + | 0.242009i | \(0.0778063\pi\) | ||||
−0.970274 | + | 0.242009i | \(0.922194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.57321 | + | 8.57321i | 0.398431 | + | 0.398431i | 0.877679 | − | 0.479248i | \(-0.159091\pi\) |
−0.479248 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(464\) | −10.3923 | −0.482451 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 4.24264 | + | 4.24264i | 0.196326 | + | 0.196326i | 0.798423 | − | 0.602097i | \(-0.205668\pi\) |
−0.602097 | + | 0.798423i | \(0.705668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000i | 0.831163i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.34847 | − | 7.34847i | 0.338241 | − | 0.338241i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.3923i | 0.476331i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.6969 | + | 14.6969i | 0.672222 | + | 0.672222i | ||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.3848 | − | 18.3848i | −0.837404 | − | 0.837404i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.0000i | 0.500000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0454 | − | 22.0454i | 0.998973 | − | 0.998973i | −0.00102669 | − | 0.999999i | \(-0.500327\pi\) |
0.999999 | + | 0.00102669i | \(0.000326807\pi\) | |||||||
\(488\) | 3.53553 | − | 3.53553i | 0.160046 | − | 0.160046i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.7846i | − | 0.937996i | −0.883199 | − | 0.468998i | \(-0.844615\pi\) | ||
0.883199 | − | 0.468998i | \(-0.155385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.0908 | − | 44.0908i | −1.98575 | − | 1.98575i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.00000 | −0.314309 | ||||||||
\(497\) | −12.7279 | − | 12.7279i | −0.570925 | − | 0.570925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.00000i | − | 0.313363i | −0.987649 | − | 0.156682i | \(-0.949920\pi\) | ||
0.987649 | − | 0.156682i | \(-0.0500796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.34847 | − | 7.34847i | 0.327978 | − | 0.327978i | ||||
\(503\) | 4.24264 | − | 4.24264i | 0.189170 | − | 0.189170i | −0.606167 | − | 0.795337i | \(-0.707294\pi\) |
0.795337 | + | 0.606167i | \(0.207294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34847 | + | 7.34847i | 0.326036 | + | 0.326036i | ||||
\(509\) | −20.7846 | −0.921262 | −0.460631 | − | 0.887592i | \(-0.652377\pi\) | ||||
−0.460631 | + | 0.887592i | \(0.652377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.0000 | −0.928985 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 12.0000i | − | 0.529297i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.6066 | + | 10.6066i | −0.466027 | + | 0.466027i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7846i | 0.910590i | 0.890341 | + | 0.455295i | \(0.150466\pi\) | ||||
−0.890341 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.9217 | − | 15.9217i | −0.696207 | − | 0.696207i | 0.267384 | − | 0.963590i | \(-0.413841\pi\) |
−0.963590 | + | 0.267384i | \(0.913841\pi\) | |||||||
\(524\) | 10.3923 | 0.453990 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0000 | 0.784837 | ||||||||
\(527\) | −29.6985 | − | 29.6985i | −1.29369 | − | 1.29369i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.0000i | − | 0.565217i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.22474 | − | 1.22474i | 0.0530994 | − | 0.0530994i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 10.3923i | − | 0.448879i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.0454 | + | 22.0454i | 0.950445 | + | 0.950445i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.0000 | −1.59075 | −0.795377 | − | 0.606115i | \(-0.792727\pi\) | ||||
−0.795377 | + | 0.606115i | \(0.792727\pi\) | |||||||
\(542\) | 0.707107 | + | 0.707107i | 0.0303728 | + | 0.0303728i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.00000i | − | 0.257248i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.22474 | + | 1.22474i | −0.0523663 | + | 0.0523663i | −0.732805 | − | 0.680439i | \(-0.761789\pi\) |
0.680439 | + | 0.732805i | \(0.261789\pi\) | |||||||
\(548\) | −8.48528 | + | 8.48528i | −0.362473 | + | 0.362473i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3923i | 0.442727i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9217 | + | 15.9217i | 0.677059 | + | 0.677059i | ||||
\(554\) | 19.0526 | 0.809466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.0000 | 0.466504 | ||||||||
\(557\) | 12.7279 | + | 12.7279i | 0.539299 | + | 0.539299i | 0.923323 | − | 0.384024i | \(-0.125462\pi\) |
−0.384024 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6969 | + | 14.6969i | −0.619953 | + | 0.619953i | ||||
\(563\) | 25.4558 | − | 25.4558i | 1.07284 | − | 1.07284i | 0.0757057 | − | 0.997130i | \(-0.475879\pi\) |
0.997130 | − | 0.0757057i | \(-0.0241210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 29.4449i | − | 1.23766i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.34847 | + | 7.34847i | 0.308335 | + | 0.308335i | ||||
\(569\) | 10.3923 | 0.435668 | 0.217834 | − | 0.975986i | \(-0.430101\pi\) | ||||
0.217834 | + | 0.975986i | \(0.430101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.0000 | −1.04622 | −0.523109 | − | 0.852266i | \(-0.675228\pi\) | ||||
−0.523109 | + | 0.852266i | \(0.675228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.1691 | + | 28.1691i | −1.17270 | + | 1.17270i | −0.191132 | + | 0.981564i | \(0.561216\pi\) |
−0.981564 | + | 0.191132i | \(0.938784\pi\) | |||||||
\(578\) | 13.4350 | − | 13.4350i | 0.558824 | − | 0.558824i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.1244 | 0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −29.6985 | − | 29.6985i | −1.22579 | − | 1.22579i | −0.965543 | − | 0.260245i | \(-0.916197\pi\) |
−0.260245 | − | 0.965543i | \(-0.583803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000i | 0.288430i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.12372 | − | 6.12372i | 0.251684 | − | 0.251684i | ||||
\(593\) | 29.6985 | − | 29.6985i | 1.21957 | − | 1.21957i | 0.251788 | − | 0.967782i | \(-0.418981\pi\) |
0.967782 | − | 0.251788i | \(-0.0810186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3923i | 0.425685i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.7846 | 0.849236 | 0.424618 | − | 0.905373i | \(-0.360408\pi\) | ||||
0.424618 | + | 0.905373i | \(0.360408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | 0.530281 | 0.265141 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265141 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(602\) | 2.12132 | + | 2.12132i | 0.0864586 | + | 0.0864586i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 5.00000i | − | 0.203447i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.2702 | − | 23.2702i | 0.944506 | − | 0.944506i | −0.0540328 | − | 0.998539i | \(-0.517208\pi\) |
0.998539 | + | 0.0540328i | \(0.0172076\pi\) | |||||||
\(608\) | −0.707107 | + | 0.707107i | −0.0286770 | + | 0.0286770i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.57321 | − | 8.57321i | −0.346269 | − | 0.346269i | 0.512449 | − | 0.858718i | \(-0.328738\pi\) |
−0.858718 | + | 0.512449i | \(0.828738\pi\) | |||||||
\(614\) | −29.4449 | −1.18830 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.9706 | − | 16.9706i | −0.683209 | − | 0.683209i | 0.277513 | − | 0.960722i | \(-0.410490\pi\) |
−0.960722 | + | 0.277513i | \(0.910490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.0000i | − | 0.522514i | −0.965269 | − | 0.261257i | \(-0.915863\pi\) | ||
0.965269 | − | 0.261257i | \(-0.0841370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.6969 | − | 14.6969i | 0.589294 | − | 0.589294i | ||||
\(623\) | 12.7279 | − | 12.7279i | 0.509933 | − | 0.509933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.7846i | 0.830720i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.12372 | + | 6.12372i | 0.244363 | + | 0.244363i | ||||
\(629\) | 51.9615 | 2.07184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −9.19239 | − | 9.19239i | −0.365654 | − | 0.365654i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 6.00000i | − | 0.238290i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.1769i | 1.23141i | 0.787975 | + | 0.615707i | \(0.211130\pi\) | ||||
−0.787975 | + | 0.615707i | \(0.788870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0454 | − | 22.0454i | −0.869386 | − | 0.869386i | 0.123018 | − | 0.992404i | \(-0.460743\pi\) |
−0.992404 | + | 0.123018i | \(0.960743\pi\) | |||||||
\(644\) | −10.3923 | −0.409514 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | −0.236067 | ||||||||
\(647\) | 16.9706 | + | 16.9706i | 0.667182 | + | 0.667182i | 0.957063 | − | 0.289881i | \(-0.0936157\pi\) |
−0.289881 | + | 0.957063i | \(0.593616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.34847 | + | 7.34847i | −0.287788 | + | 0.287788i | ||||
\(653\) | 8.48528 | − | 8.48528i | 0.332055 | − | 0.332055i | −0.521312 | − | 0.853366i | \(-0.674557\pi\) |
0.853366 | + | 0.521312i | \(0.174557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | −0.404827 | −0.202413 | − | 0.979300i | \(-0.564878\pi\) | ||||
−0.202413 | + | 0.979300i | \(0.564878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.0000 | −1.12797 | −0.563985 | − | 0.825785i | \(-0.690732\pi\) | ||||
−0.563985 | + | 0.825785i | \(0.690732\pi\) | |||||||
\(662\) | 9.19239 | + | 9.19239i | 0.357272 | + | 0.357272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.00000i | − | 0.232845i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0908 | − | 44.0908i | 1.70720 | − | 1.70720i | ||||
\(668\) | −4.24264 | + | 4.24264i | −0.164153 | + | 0.164153i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9217 | + | 15.9217i | 0.613736 | + | 0.613736i | 0.943917 | − | 0.330182i | \(-0.107110\pi\) |
−0.330182 | + | 0.943917i | \(0.607110\pi\) | |||||||
\(674\) | 20.7846 | 0.800593 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15.0000i | − | 0.575647i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.24264 | + | 4.24264i | −0.162340 | + | 0.162340i | −0.783603 | − | 0.621262i | \(-0.786620\pi\) |
0.621262 | + | 0.783603i | \(0.286620\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.0526i | 0.727430i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.22474 | − | 1.22474i | −0.0466930 | − | 0.0466930i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.0000 | −1.67384 | −0.836919 | − | 0.547326i | \(-0.815646\pi\) | ||||
−0.836919 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(692\) | −4.24264 | − | 4.24264i | −0.161281 | − | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 18.0000i | − | 0.683271i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 21.9203 | − | 21.9203i | 0.829696 | − | 0.829696i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.1769i | − | 1.17754i | −0.808302 | − | 0.588768i | \(-0.799613\pi\) | ||
0.808302 | − | 0.588768i | \(-0.200387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.12372 | − | 6.12372i | −0.230961 | − | 0.230961i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000i | 0.488225i | 0.969747 | + | 0.244113i | \(0.0784967\pi\) | ||||
−0.969747 | + | 0.244113i | \(0.921503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.34847 | + | 7.34847i | −0.275396 | + | 0.275396i | ||||
\(713\) | 29.6985 | − | 29.6985i | 1.11222 | − | 1.11222i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 20.7846i | − | 0.776757i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.34847 | + | 7.34847i | 0.274242 | + | 0.274242i | ||||
\(719\) | 51.9615 | 1.93784 | 0.968919 | − | 0.247378i | \(-0.0795691\pi\) | ||||
0.968919 | + | 0.247378i | \(0.0795691\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0000 | −0.558629 | ||||||||
\(722\) | −12.7279 | − | 12.7279i | −0.473684 | − | 0.473684i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2.00000i | − | 0.0743294i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.12372 | − | 6.12372i | 0.227116 | − | 0.227116i | −0.584371 | − | 0.811487i | \(-0.698659\pi\) |
0.811487 | + | 0.584371i | \(0.198659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.3923i | − | 0.384373i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6969 | − | 14.6969i | −0.542844 | − | 0.542844i | 0.381518 | − | 0.924362i | \(-0.375402\pi\) |
−0.924362 | + | 0.381518i | \(0.875402\pi\) | |||||||
\(734\) | 10.3923 | 0.383587 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.0000i | − | 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.6969 | − | 14.6969i | 0.539542 | − | 0.539542i | ||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.1244i | 0.443904i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.1769 | 1.13918 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0000 | −0.401396 | −0.200698 | − | 0.979653i | \(-0.564321\pi\) | ||||
−0.200698 | + | 0.979653i | \(0.564321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9217 | + | 15.9217i | −0.578683 | + | 0.578683i | −0.934540 | − | 0.355857i | \(-0.884189\pi\) |
0.355857 | + | 0.934540i | \(0.384189\pi\) | |||||||
\(758\) | 11.3137 | − | 11.3137i | 0.410932 | − | 0.410932i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5692i | 1.50688i | 0.657515 | + | 0.753442i | \(0.271608\pi\) | ||||
−0.657515 | + | 0.753442i | \(0.728392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22474 | + | 1.22474i | 0.0443387 | + | 0.0443387i | ||||
\(764\) | 20.7846 | 0.751961 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000i | 0.504853i | 0.967616 | + | 0.252426i | \(0.0812286\pi\) | ||||
−0.967616 | + | 0.252426i | \(0.918771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.22474 | + | 1.22474i | −0.0440795 | + | 0.0440795i | ||||
\(773\) | 4.24264 | − | 4.24264i | 0.152597 | − | 0.152597i | −0.626680 | − | 0.779277i | \(-0.715587\pi\) |
0.779277 | + | 0.626680i | \(0.215587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.66025i | 0.310885i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.6969 | + | 14.6969i | 0.526911 | + | 0.526911i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 25.4558 | + | 25.4558i | 0.910299 | + | 0.910299i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 4.00000i | − | 0.142857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.22474 | + | 1.22474i | −0.0436574 | + | 0.0436574i | −0.728598 | − | 0.684941i | \(-0.759828\pi\) |
0.684941 | + | 0.728598i | \(0.259828\pi\) | |||||||
\(788\) | 8.48528 | − | 8.48528i | 0.302276 | − | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.66025 | 0.307341 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | −8.48528 | − | 8.48528i | −0.300564 | − | 0.300564i | 0.540670 | − | 0.841235i | \(-0.318171\pi\) |
−0.841235 | + | 0.540670i | \(0.818171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.6969 | + | 14.6969i | −0.518967 | + | 0.518967i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.3923 | −0.365374 | −0.182687 | − | 0.983171i | \(-0.558479\pi\) | ||||
−0.182687 | + | 0.983171i | \(0.558479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0000 | 0.667180 | 0.333590 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333590 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(812\) | −12.7279 | − | 12.7279i | −0.446663 | − | 0.446663i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.22474 | + | 1.22474i | −0.0428484 | + | 0.0428484i | ||||
\(818\) | 15.5563 | − | 15.5563i | 0.543915 | − | 0.543915i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 20.7846i | − | 0.725388i | −0.931908 | − | 0.362694i | \(-0.881857\pi\) | ||
0.931908 | − | 0.362694i | \(-0.118143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0454 | + | 22.0454i | 0.768455 | + | 0.768455i | 0.977834 | − | 0.209380i | \(-0.0671445\pi\) |
−0.209380 | + | 0.977834i | \(0.567144\pi\) | |||||||
\(824\) | 8.66025 | 0.301694 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | 0.626300 | ||||||||
\(827\) | 8.48528 | + | 8.48528i | 0.295062 | + | 0.295062i | 0.839076 | − | 0.544014i | \(-0.183096\pi\) |
−0.544014 | + | 0.839076i | \(0.683096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0000i | 1.28506i | 0.766259 | + | 0.642532i | \(0.222116\pi\) | ||||
−0.766259 | + | 0.642532i | \(0.777884\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.9706 | − | 16.9706i | 0.587995 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.34847 | − | 7.34847i | −0.253849 | − | 0.253849i | ||||
\(839\) | −51.9615 | −1.79391 | −0.896956 | − | 0.442121i | \(-0.854226\pi\) | ||||
−0.896956 | + | 0.442121i | \(0.854226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.0000 | 2.72414 | ||||||||
\(842\) | −9.19239 | − | 9.19239i | −0.316791 | − | 0.316791i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.00000i | − | 0.137686i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.4722 | + | 13.4722i | −0.462910 | + | 0.462910i | ||||
\(848\) | −8.48528 | + | 8.48528i | −0.291386 | + | 0.291386i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.9615i | 1.78122i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.6969 | − | 14.6969i | −0.503214 | − | 0.503214i | 0.409221 | − | 0.912435i | \(-0.365800\pi\) |
−0.912435 | + | 0.409221i | \(0.865800\pi\) | |||||||
\(854\) | 8.66025 | 0.296348 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | −16.9706 | − | 16.9706i | −0.579703 | − | 0.579703i | 0.355118 | − | 0.934821i | \(-0.384441\pi\) |
−0.934821 | + | 0.355118i | \(0.884441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000i | 0.375315i | 0.982235 | + | 0.187658i | \(0.0600895\pi\) | ||||
−0.982235 | + | 0.187658i | \(0.939910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.0454 | + | 22.0454i | −0.750870 | + | 0.750870i | ||||
\(863\) | −4.24264 | + | 4.24264i | −0.144421 | + | 0.144421i | −0.775621 | − | 0.631199i | \(-0.782563\pi\) |
0.631199 | + | 0.775621i | \(0.282563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 19.0526i | − | 0.647432i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.57321 | − | 8.57321i | −0.290994 | − | 0.290994i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.707107 | − | 0.707107i | −0.0239457 | − | 0.0239457i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6.00000i | − | 0.202953i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.12372 | − | 6.12372i | 0.206783 | − | 0.206783i | −0.596115 | − | 0.802899i | \(-0.703290\pi\) |
0.802899 | + | 0.596115i | \(0.203290\pi\) | |||||||
\(878\) | −21.9203 | + | 21.9203i | −0.739775 | + | 0.739775i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.9615i | − | 1.75063i | −0.483555 | − | 0.875314i | \(-0.660655\pi\) | ||
0.483555 | − | 0.875314i | \(-0.339345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.8207 | + | 20.8207i | 0.700671 | + | 0.700671i | 0.964555 | − | 0.263883i | \(-0.0850034\pi\) |
−0.263883 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | 0.201574 | ||||||||
\(887\) | 8.48528 | + | 8.48528i | 0.284908 | + | 0.284908i | 0.835063 | − | 0.550155i | \(-0.185431\pi\) |
−0.550155 | + | 0.835063i | \(0.685431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000i | 0.603701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.57321 | − | 8.57321i | 0.287052 | − | 0.287052i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.73205i | − | 0.0578638i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0454 | − | 22.0454i | −0.735665 | − | 0.735665i | ||||
\(899\) | 72.7461 | 2.42622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.0000 | −2.39867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.12372 | + | 6.12372i | −0.203335 | + | 0.203335i | −0.801427 | − | 0.598092i | \(-0.795926\pi\) |
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(908\) | −16.9706 | + | 16.9706i | −0.563188 | + | 0.563188i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.9615i | 1.72156i | 0.508975 | + | 0.860781i | \(0.330024\pi\) | ||||
−0.508975 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −20.7846 | −0.687494 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.0000 | −0.826023 | ||||||||
\(917\) | 12.7279 | + | 12.7279i | 0.420313 | + | 0.420313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000i | 0.0329870i | 0.999864 | + | 0.0164935i | \(0.00525028\pi\) | ||||
−0.999864 | + | 0.0164935i | \(0.994750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.34847 | − | 7.34847i | 0.242009 | − | 0.242009i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 12.1244i | − | 0.398431i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.34847 | + | 7.34847i | 0.241225 | + | 0.241225i | ||||
\(929\) | −31.1769 | −1.02288 | −0.511441 | − | 0.859319i | \(-0.670888\pi\) | ||||
−0.511441 | + | 0.859319i | \(0.670888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | −12.7279 | − | 12.7279i | −0.416917 | − | 0.416917i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 6.00000i | − | 0.196326i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.6186 | + | 30.6186i | −1.00027 | + | 1.00027i | −0.000266809 | 1.00000i | \(0.500085\pi\) | |
−1.00000 | 0.000266809i | \(0.999915\pi\) | ||||||||
\(938\) | 12.7279 | − | 12.7279i | 0.415581 | − | 0.415581i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.7846i | − | 0.677559i | −0.940866 | − | 0.338779i | \(-0.889986\pi\) | ||
0.940866 | − | 0.338779i | \(-0.110014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −10.3923 | −0.338241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.6985 | − | 29.6985i | −0.965071 | − | 0.965071i | 0.0343392 | − | 0.999410i | \(-0.489067\pi\) |
−0.999410 | + | 0.0343392i | \(0.989067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.34847 | − | 7.34847i | 0.238165 | − | 0.238165i | ||||
\(953\) | −25.4558 | + | 25.4558i | −0.824596 | + | 0.824596i | −0.986763 | − | 0.162168i | \(-0.948151\pi\) |
0.162168 | + | 0.986763i | \(0.448151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 20.7846i | − | 0.672222i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.34847 | − | 7.34847i | −0.237418 | − | 0.237418i | ||||
\(959\) | −20.7846 | −0.671170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.0000i | 0.837404i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9217 | − | 15.9217i | 0.512007 | − | 0.512007i | −0.403134 | − | 0.915141i | \(-0.632079\pi\) |
0.915141 | + | 0.403134i | \(0.132079\pi\) | |||||||
\(968\) | 7.77817 | − | 7.77817i | 0.250000 | − | 0.250000i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.7846i | − | 0.667010i | −0.942748 | − | 0.333505i | \(-0.891769\pi\) | ||
0.942748 | − | 0.333505i | \(-0.108231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.4722 | + | 13.4722i | 0.431899 | + | 0.431899i | ||||
\(974\) | −31.1769 | −0.998973 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | −0.160046 | ||||||||
\(977\) | −12.7279 | − | 12.7279i | −0.407202 | − | 0.407202i | 0.473560 | − | 0.880762i | \(-0.342969\pi\) |
−0.880762 | + | 0.473560i | \(0.842969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.6969 | + | 14.6969i | −0.468998 | + | 0.468998i | ||||
\(983\) | 42.4264 | − | 42.4264i | 1.35319 | − | 1.35319i | 0.471127 | − | 0.882066i | \(-0.343847\pi\) |
0.882066 | − | 0.471127i | \(-0.156153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 62.3538i | 1.98575i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3923 | 0.330456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.0000 | 1.11181 | 0.555906 | − | 0.831245i | \(-0.312372\pi\) | ||||
0.555906 | + | 0.831245i | \(0.312372\pi\) | |||||||
\(992\) | 4.94975 | + | 4.94975i | 0.157155 | + | 0.157155i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.0000i | 0.570925i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | −4.94975 | + | 4.94975i | −0.156682 | + | 0.156682i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.2.f.d.593.1 | yes | 8 | |
3.2 | odd | 2 | inner | 1350.2.f.d.593.3 | yes | 8 | |
5.2 | odd | 4 | inner | 1350.2.f.d.107.3 | yes | 8 | |
5.3 | odd | 4 | inner | 1350.2.f.d.107.2 | yes | 8 | |
5.4 | even | 2 | inner | 1350.2.f.d.593.4 | yes | 8 | |
15.2 | even | 4 | inner | 1350.2.f.d.107.1 | ✓ | 8 | |
15.8 | even | 4 | inner | 1350.2.f.d.107.4 | yes | 8 | |
15.14 | odd | 2 | inner | 1350.2.f.d.593.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.2.f.d.107.1 | ✓ | 8 | 15.2 | even | 4 | inner | |
1350.2.f.d.107.2 | yes | 8 | 5.3 | odd | 4 | inner | |
1350.2.f.d.107.3 | yes | 8 | 5.2 | odd | 4 | inner | |
1350.2.f.d.107.4 | yes | 8 | 15.8 | even | 4 | inner | |
1350.2.f.d.593.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1350.2.f.d.593.2 | yes | 8 | 15.14 | odd | 2 | inner | |
1350.2.f.d.593.3 | yes | 8 | 3.2 | odd | 2 | inner | |
1350.2.f.d.593.4 | yes | 8 | 5.4 | even | 2 | inner |