Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(476,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.476");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.o (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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 476.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.476 |
Dual form | 975.2.o.h.551.1 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.36603 | − | 3.36603i | 1.27224 | − | 1.27224i | 0.327327 | − | 0.944911i | \(-0.393852\pi\) |
0.944911 | − | 0.327327i | \(-0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | − | 3.46410i | − | 1.00000i | ||||||
\(13\) | −2.59808 | − | 2.50000i | −0.720577 | − | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83013 | − | 3.83013i | −0.878691 | − | 0.878691i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.83013 | + | 5.83013i | −1.27224 | + | 1.27224i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 6.73205 | + | 6.73205i | 1.27224 | + | 1.27224i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.830127 | + | 0.830127i | 0.149095 | + | 0.149095i | 0.777714 | − | 0.628619i | \(-0.216379\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000i | 1.00000i | ||||||||
\(37\) | 8.46410 | − | 8.46410i | 1.39149 | − | 1.39149i | 0.569495 | − | 0.821995i | \(-0.307139\pi\) |
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50000 | + | 4.33013i | 0.720577 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.1244i | − | 1.84895i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 6.92820 | 1.00000 | ||||||||
\(49\) | − | 15.6603i | − | 2.23718i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00000 | − | 5.19615i | 0.693375 | − | 0.720577i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.63397 | + | 6.63397i | 0.878691 | + | 0.878691i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.66025 | 1.10883 | 0.554416 | − | 0.832240i | \(-0.312942\pi\) | ||||
0.554416 | + | 0.832240i | \(0.312942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.0981 | − | 10.0981i | 1.27224 | − | 1.27224i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.29423 | − | 5.29423i | −0.646793 | − | 0.646793i | 0.305424 | − | 0.952217i | \(-0.401202\pi\) |
−0.952217 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9282 | + | 11.9282i | −1.39609 | + | 1.39609i | −0.585206 | + | 0.810885i | \(0.698986\pi\) |
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.66025 | − | 7.66025i | 0.878691 | − | 0.878691i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.3205 | 1.94871 | 0.974355 | − | 0.225018i | \(-0.0722440\pi\) | ||||
0.974355 | + | 0.225018i | \(0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | −11.6603 | − | 11.6603i | −1.27224 | − | 1.27224i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.1603 | + | 0.330127i | −1.79888 | + | 0.0346067i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.43782 | − | 1.43782i | −0.149095 | − | 0.149095i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.02628 | + | 7.02628i | 0.713411 | + | 0.713411i | 0.967247 | − | 0.253837i | \(-0.0816925\pi\) |
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410i | 0.341328i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | − | 10.3923i | − | 1.00000i | ||||||
\(109\) | 13.8301 | + | 13.8301i | 1.32469 | + | 1.32469i | 0.909935 | + | 0.414751i | \(0.136131\pi\) |
0.414751 | + | 0.909935i | \(0.363869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6603 | + | 14.6603i | −1.39149 | + | 1.39149i | ||||
\(112\) | −13.4641 | + | 13.4641i | −1.27224 | + | 1.27224i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.79423 | − | 7.50000i | −0.720577 | − | 0.693375i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.66025 | + | 1.66025i | −0.149095 | + | 0.149095i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 20.0000i | − | 1.77471i | −0.461084 | − | 0.887357i | \(-0.652539\pi\) | ||
0.461084 | − | 0.887357i | \(-0.347461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.0000i | 1.84895i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.7846 | −2.23581 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 27.1244i | 2.23718i | ||||||||
\(148\) | 16.9282 | + | 16.9282i | 1.39149 | + | 1.39149i | ||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.16987 | − | 7.16987i | 0.583476 | − | 0.583476i | −0.352381 | − | 0.935857i | \(-0.614628\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.66025 | + | 9.00000i | −0.693375 | + | 0.720577i | ||||
\(157\) | −25.0000 | −1.99522 | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) | ||||
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.90192 | − | 9.90192i | 0.775579 | − | 0.775579i | −0.203497 | − | 0.979076i | \(-0.565231\pi\) |
0.979076 | + | 0.203497i | \(0.0652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4904 | − | 11.4904i | −0.878691 | − | 0.878691i | ||||
\(172\) | 24.2487 | 1.84895 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.9808i | − | 1.93113i | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||
0.260153 | − | 0.965567i | \(-0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0000 | −1.10883 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.4904 | + | 17.4904i | −1.27224 | + | 1.27224i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 13.8564i | 1.00000i | ||||||||
\(193\) | −18.5622 | + | 18.5622i | −1.33613 | + | 1.33613i | −0.436365 | + | 0.899770i | \(0.643734\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.3205 | 2.23718 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000i | 0.779769i | 0.920864 | + | 0.389885i | \(0.127485\pi\) | ||||
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.16987 | + | 9.16987i | 0.646793 | + | 0.646793i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.3923 | + | 10.0000i | 0.720577 | + | 0.693375i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.9808 | 1.78859 | 0.894295 | − | 0.447478i | \(-0.147678\pi\) | ||||
0.894295 | + | 0.447478i | \(0.147678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.58846 | 0.379369 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.6603 | − | 20.6603i | 1.39609 | − | 1.39609i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.2224 | + | 17.2224i | 1.15330 | + | 1.15330i | 0.985887 | + | 0.167412i | \(0.0535411\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | −13.2679 | + | 13.2679i | −0.878691 | + | 0.878691i | ||||
\(229\) | −18.8301 | + | 18.8301i | −1.24433 | + | 1.24433i | −0.286143 | + | 0.958187i | \(0.592373\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.0000 | −1.94871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.49038 | + | 4.49038i | −0.289251 | + | 0.289251i | −0.836784 | − | 0.547533i | \(-0.815567\pi\) |
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 17.3205i | 1.10883i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.375644 | + | 19.5263i | 0.0239017 | + | 1.24243i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 20.1962 | + | 20.1962i | 1.27224 | + | 1.27224i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 56.9808i | − | 3.54061i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.5885 | − | 10.5885i | 0.646793 | − | 0.646793i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.33975 | + | 5.33975i | −0.324366 | + | 0.324366i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.526073 | + | 0.850439i | \(0.323664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.7224 | − | 0.571797i | 1.79888 | − | 0.0346067i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.9090i | 1.97731i | 0.150210 | + | 0.988654i | \(0.452005\pi\) | ||||
−0.150210 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.49038 | + | 2.49038i | 0.149095 | + | 0.149095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 25.0000i | − | 1.48610i | −0.669238 | − | 0.743048i | \(-0.733379\pi\) | ||
0.669238 | − | 0.743048i | \(-0.266621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1699 | − | 12.1699i | −0.713411 | − | 0.713411i | ||||
\(292\) | −23.8564 | − | 23.8564i | −1.39609 | − | 1.39609i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.8109 | − | 40.8109i | −2.35230 | − | 2.35230i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.3205 | + | 15.3205i | 0.878691 | + | 0.878691i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3660 | + | 18.3660i | −1.04820 | + | 1.04820i | −0.0494267 | + | 0.998778i | \(0.515739\pi\) |
−0.998778 | + | 0.0494267i | \(0.984261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.19615 | 0.293704 | 0.146852 | − | 0.989158i | \(-0.453086\pi\) | ||||
0.146852 | + | 0.989158i | \(0.453086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 34.6410i | 1.94871i | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.9545 | − | 23.9545i | −1.32469 | − | 1.32469i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6603 | − | 24.6603i | −1.35545 | − | 1.35545i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
−0.476011 | − | 0.879440i | \(-0.657918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.3923 | − | 25.3923i | 1.39149 | − | 1.39149i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 23.3205 | − | 23.3205i | 1.27224 | − | 1.27224i | ||||
\(337\) | 5.00000i | 0.272367i | 0.990684 | + | 0.136184i | \(0.0434837\pi\) | ||||
−0.990684 | + | 0.136184i | \(0.956516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −29.1506 | − | 29.1506i | −1.57399 | − | 1.57399i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3205 | − | 10.3205i | 0.552444 | − | 0.552444i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.927146 | + | 0.374701i | \(0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5000 | + | 12.9904i | 0.720577 | + | 0.693375i | ||||
\(352\) | 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 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3397i | 0.544197i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | −0.660254 | − | 34.3205i | −0.0346067 | − | 1.79888i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0000 | 1.82699 | 0.913493 | − | 0.406855i | \(-0.133375\pi\) | ||||
0.913493 | + | 0.406855i | \(0.133375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.87564 | − | 2.87564i | 0.149095 | − | 0.149095i | ||||
\(373\) | −29.4449 | −1.52460 | −0.762299 | − | 0.647225i | \(-0.775929\pi\) | ||||
−0.762299 | + | 0.647225i | \(0.775929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.50962 | + | 1.50962i | 0.0775439 | + | 0.0775439i | 0.744815 | − | 0.667271i | \(-0.232538\pi\) |
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.6410i | 1.77471i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 36.3731i | − | 1.84895i | ||||||
\(388\) | −14.0526 | + | 14.0526i | −0.713411 | + | 0.713411i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.97372 | − | 7.97372i | 0.400190 | − | 0.400190i | −0.478110 | − | 0.878300i | \(-0.658678\pi\) |
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.6603 | 2.23581 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0814157 | − | 4.23205i | −0.00405561 | − | 0.210813i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4904 | + | 28.4904i | 1.40876 | + | 1.40876i | 0.766426 | + | 0.642333i | \(0.222033\pi\) |
0.642333 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.92820 | −0.341328 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.7128 | 1.35710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3205 | + | 28.3205i | 1.38026 | + | 1.38026i | 0.844150 | + | 0.536107i | \(0.180106\pi\) |
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.1506 | − | 29.1506i | 1.41070 | − | 1.41070i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(432\) | 20.7846 | 1.00000 | ||||||||
\(433\) | 35.0000i | 1.68199i | 0.541041 | + | 0.840996i | \(0.318030\pi\) | ||||
−0.541041 | + | 0.840996i | \(0.681970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.6603 | + | 27.6603i | −1.32469 | + | 1.32469i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.66025i | − | 0.413331i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) | ||
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 46.9808i | − | 2.23718i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | −29.3205 | − | 29.3205i | −1.39149 | − | 1.39149i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.9282 | − | 26.9282i | −1.27224 | − | 1.27224i | ||||
\(449\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.4186 | + | 12.4186i | −0.583476 | + | 0.583476i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7846 | − | 15.7846i | −0.738373 | − | 0.738373i | 0.233890 | − | 0.972263i | \(-0.424854\pi\) |
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.05256 | − | 9.05256i | 0.420708 | − | 0.420708i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) |
0.885448 | + | 0.464739i | \(0.153852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 15.0000 | − | 15.5885i | 0.693375 | − | 0.720577i | ||||
\(469\) | −35.6410 | −1.64575 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 43.3013 | 1.99522 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.1506 | + | 0.830127i | −1.96750 | + | 0.0378505i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.68653 | − | 5.68653i | −0.257681 | − | 0.257681i | 0.566429 | − | 0.824110i | \(-0.308325\pi\) |
−0.824110 | + | 0.566429i | \(0.808325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.1506 | + | 17.1506i | −0.775579 | + | 0.775579i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.32051 | − | 3.32051i | −0.149095 | − | 0.149095i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1506 | − | 16.1506i | −0.723002 | − | 0.723002i | 0.246214 | − | 0.969216i | \(-0.420813\pi\) |
−0.969216 | + | 0.246214i | \(0.920813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.866025 | − | 22.5000i | −0.0384615 | − | 0.999260i | ||||
\(508\) | 40.0000 | 1.77471 | ||||||||
\(509\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 80.3013i | 3.55232i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.9019 | + | 19.9019i | 0.878691 | + | 0.878691i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −42.0000 | −1.84895 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.0000 | 1.53044 | 0.765222 | − | 0.643767i | \(-0.222629\pi\) | ||||
0.765222 | + | 0.643767i | \(0.222629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 51.5692i | − | 2.23581i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.1506 | + | 30.1506i | −1.29628 | + | 1.29628i | −0.365444 | + | 0.930834i | \(0.619083\pi\) |
−0.930834 | + | 0.365444i | \(0.880917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.0000i | 1.93113i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000 | 1.71028 | 0.855138 | − | 0.518400i | \(-0.173472\pi\) | ||||
0.855138 | + | 0.518400i | \(0.173472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.9808 | 1.10883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 58.3013 | − | 58.3013i | 2.47922 | − | 2.47922i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 32.0000i | − | 1.35710i | ||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.3109 | + | 31.5000i | −1.28201 | + | 1.33231i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.2942 | − | 30.2942i | 1.27224 | − | 1.27224i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.0000i | 1.96689i | 0.181210 | + | 0.983444i | \(0.441999\pi\) | ||||
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 24.0000i | − | 1.00000i | ||||||
\(577\) | −1.04552 | − | 1.04552i | −0.0435255 | − | 0.0435255i | 0.685009 | − | 0.728535i | \(-0.259798\pi\) |
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32.1506 | − | 32.1506i | 1.33613 | − | 1.33613i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | −54.2487 | −2.23718 | ||||||||
\(589\) | − | 6.35898i | − | 0.262017i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −33.8564 | + | 33.8564i | −1.39149 | + | 1.39149i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 19.0526i | − | 0.779769i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3013 | 1.76630 | 0.883148 | − | 0.469095i | \(-0.155420\pi\) | ||||
0.883148 | + | 0.469095i | \(0.155420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.8827 | − | 15.8827i | −0.646793 | − | 0.646793i | ||||
\(604\) | 14.3397 | + | 14.3397i | 0.583476 | + | 0.583476i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | 0.811775 | 0.405887 | − | 0.913923i | \(-0.366962\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.2487 | + | 29.2487i | 1.18134 | + | 1.18134i | 0.979396 | + | 0.201948i | \(0.0647272\pi\) |
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1699 | − | 20.1699i | 0.810696 | − | 0.810696i | −0.174042 | − | 0.984738i | \(-0.555683\pi\) |
0.984738 | + | 0.174042i | \(0.0556830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −18.0000 | − | 17.3205i | −0.720577 | − | 0.693375i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 50.0000i | − | 1.99522i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.50962 | − | 8.50962i | 0.338763 | − | 0.338763i | −0.517139 | − | 0.855901i | \(-0.673003\pi\) |
0.855901 | + | 0.517139i | \(0.173003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45.0000 | −1.78859 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.1506 | + | 40.6865i | −1.55120 | + | 1.61206i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.41154 | − | 4.41154i | −0.173974 | − | 0.173974i | 0.614749 | − | 0.788723i | \(-0.289257\pi\) |
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.67949 | −0.379369 | ||||||||
\(652\) | 19.8038 | + | 19.8038i | 0.775579 | + | 0.775579i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.7846 | + | 35.7846i | −1.39609 | + | 1.39609i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.3205 | − | 36.3205i | 1.41270 | − | 1.41270i | 0.673690 | − | 0.739014i | \(-0.264708\pi\) |
0.739014 | − | 0.673690i | \(-0.235292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.8301 | − | 29.8301i | −1.15330 | − | 1.15330i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.8564i | − | 0.534125i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) | ||
0.963679 | − | 0.267063i | \(-0.0860531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.9808 | + | 1.00000i | −0.999260 | + | 0.0384615i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.3013 | 1.81526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | 22.9808 | − | 22.9808i | 0.878691 | − | 0.878691i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.6147 | − | 32.6147i | 1.24433 | − | 1.24433i | ||||
\(688\) | 48.4974i | 1.84895i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.9808 | − | 21.9808i | −0.836188 | − | 0.836188i | 0.152167 | − | 0.988355i | \(-0.451375\pi\) |
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −64.8372 | −2.44538 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.15064 | − | 6.15064i | 0.230992 | − | 0.230992i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.813107 | + | 0.582115i | \(0.197775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 51.9615 | 1.94871 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6603 | + | 11.6603i | 0.434251 | + | 0.434251i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.77757 | − | 7.77757i | 0.289251 | − | 0.289251i | ||||
\(724\) | 51.9615 | 1.93113 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00000i | 0.185440i | 0.995692 | + | 0.0927199i | \(0.0295561\pi\) | ||||
−0.995692 | + | 0.0927199i | \(0.970444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 30.0000i | − | 1.10883i | ||||||
\(733\) | −14.6077 | − | 14.6077i | −0.539548 | − | 0.539548i | 0.383849 | − | 0.923396i | \(-0.374598\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9808 | + | 17.9808i | −0.661433 | + | 0.661433i | −0.955718 | − | 0.294285i | \(-0.904919\pi\) |
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.650635 | − | 33.8205i | −0.0239017 | − | 1.24243i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3205i | 0.632034i | 0.948753 | + | 0.316017i | \(0.102346\pi\) | ||||
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −34.9808 | − | 34.9808i | −1.27224 | − | 1.27224i | ||||
\(757\) | 1.73205 | 0.0629525 | 0.0314762 | − | 0.999505i | \(-0.489979\pi\) | ||||
0.0314762 | + | 0.999505i | \(0.489979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 93.1051 | 3.37063 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −1.00000 | ||||||||
\(769\) | −37.4904 | − | 37.4904i | −1.35194 | − | 1.35194i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
−0.468445 | − | 0.883493i | \(-0.655186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −37.1244 | − | 37.1244i | −1.33613 | − | 1.33613i | ||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 98.6936i | 3.54061i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 62.6410i | 2.23718i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6147 | + | 12.6147i | −0.449667 | + | 0.449667i | −0.895244 | − | 0.445577i | \(-0.852999\pi\) |
0.445577 | + | 0.895244i | \(0.352999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.5000 | − | 21.6506i | −0.798998 | − | 0.768837i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.0000 | −0.779769 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18.3397 | + | 18.3397i | −0.646793 | + | 0.646793i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.15064 | − | 3.15064i | −0.110634 | − | 0.110634i | 0.649623 | − | 0.760257i | \(-0.274927\pi\) |
−0.760257 | + | 0.649623i | \(0.774927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.24871 | − | 9.24871i | 0.324366 | − | 0.324366i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.4378 | + | 46.4378i | −1.62465 | + | 1.62465i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −51.4808 | + | 0.990381i | −1.79888 | + | 0.0346067i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 57.1577i | − | 1.99239i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) | ||
0.0871445 | − | 0.996196i | \(-0.472226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0000i | 1.59765i | 0.601566 | + | 0.798823i | \(0.294544\pi\) | ||||
−0.601566 | + | 0.798823i | \(0.705456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 57.0000i | − | 1.97731i | ||||||
\(832\) | −20.0000 | + | 20.7846i | −0.693375 | + | 0.720577i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.31347 | − | 4.31347i | −0.149095 | − | 0.149095i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 51.9615i | 1.78859i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.0263 | − | 37.0263i | −1.27224 | − | 1.27224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.3013i | 1.48610i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.8827 | + | 40.8827i | −1.39980 | + | 1.39980i | −0.599189 | + | 0.800608i | \(0.704510\pi\) |
−0.800608 | + | 0.599189i | \(0.795490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3205 | 0.590968 | 0.295484 | − | 0.955348i | \(-0.404519\pi\) | ||||
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.4449 | 1.00000 | ||||||||
\(868\) | 11.1769i | 0.379369i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.519238 | + | 26.9904i | 0.0175937 | + | 0.914534i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.0788 | + | 21.0788i | 0.713411 | + | 0.713411i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.3205 | + | 41.3205i | 1.39609 | + | 1.39609i | ||||
\(877\) | 39.3468 | + | 39.3468i | 1.32865 | + | 1.32865i | 0.906552 | + | 0.422095i | \(0.138705\pi\) |
0.422095 | + | 0.906552i | \(0.361295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.0000i | 1.85090i | 0.378873 | + | 0.925449i | \(0.376312\pi\) | ||||
−0.378873 | + | 0.925449i | \(0.623688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −67.3205 | − | 67.3205i | −2.25786 | − | 2.25786i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.4449 | + | 34.4449i | −1.15330 | + | 1.15330i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 70.6865 | + | 70.6865i | 2.35230 | + | 2.35230i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.0000i | 1.32818i | 0.747653 | + | 0.664089i | \(0.231180\pi\) | ||||
−0.747653 | + | 0.664089i | \(0.768820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −26.5359 | − | 26.5359i | −0.878691 | − | 0.878691i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37.6603 | − | 37.6603i | −1.24433 | − | 1.24433i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.6218 | −1.99973 | −0.999864 | − | 0.0164935i | \(-0.994750\pi\) | ||||
−0.999864 | + | 0.0164935i | \(0.994750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.8109 | − | 31.8109i | 1.04820 | − | 1.04820i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.3923i | 0.341328i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −59.9808 | + | 59.9808i | −1.96579 | + | 1.96579i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.2295 | 1.64093 | 0.820463 | − | 0.571700i | \(-0.193716\pi\) | ||||
0.820463 | + | 0.571700i | \(0.193716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.00000 | −0.293704 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | − | 60.0000i | − | 1.94871i | ||||||
\(949\) | 60.8109 | − | 1.16987i | 1.97400 | − | 0.0379757i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 29.6218i | − | 0.955541i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.98076 | − | 8.98076i | −0.289251 | − | 0.289251i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.4449 | + | 39.4449i | 1.26846 | + | 1.26846i | 0.946883 | + | 0.321578i | \(0.104213\pi\) |
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | − | 31.1769i | − | 1.00000i | ||||||
\(973\) | −53.8564 | + | 53.8564i | −1.72656 | + | 1.72656i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.6410 | −1.10883 | ||||||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.4904 | + | 41.4904i | 1.32469 | + | 1.32469i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −39.0526 | + | 0.751289i | −1.24243 | + | 0.0239017i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.0000 | 0.540023 | 0.270011 | − | 0.962857i | \(-0.412973\pi\) | ||||
0.270011 | + | 0.962857i | \(0.412973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.7128 | + | 42.7128i | 1.35545 | + | 1.35545i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0000 | −0.316703 | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.9808 | + | 43.9808i | −1.39149 | + | 1.39149i |
(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 | 975.2.o.h.476.1 | yes | 4 | |
3.2 | odd | 2 | CM | 975.2.o.h.476.1 | yes | 4 | |
5.2 | odd | 4 | 975.2.n.j.749.2 | 4 | |||
5.3 | odd | 4 | 975.2.n.e.749.1 | 4 | |||
5.4 | even | 2 | 975.2.o.e.476.2 | ✓ | 4 | ||
13.5 | odd | 4 | inner | 975.2.o.h.551.1 | yes | 4 | |
15.2 | even | 4 | 975.2.n.j.749.2 | 4 | |||
15.8 | even | 4 | 975.2.n.e.749.1 | 4 | |||
15.14 | odd | 2 | 975.2.o.e.476.2 | ✓ | 4 | ||
39.5 | even | 4 | inner | 975.2.o.h.551.1 | yes | 4 | |
65.18 | even | 4 | 975.2.n.j.824.1 | 4 | |||
65.44 | odd | 4 | 975.2.o.e.551.2 | yes | 4 | ||
65.57 | even | 4 | 975.2.n.e.824.2 | 4 | |||
195.44 | even | 4 | 975.2.o.e.551.2 | yes | 4 | ||
195.83 | odd | 4 | 975.2.n.j.824.1 | 4 | |||
195.122 | odd | 4 | 975.2.n.e.824.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.n.e.749.1 | 4 | 5.3 | odd | 4 | |||
975.2.n.e.749.1 | 4 | 15.8 | even | 4 | |||
975.2.n.e.824.2 | 4 | 65.57 | even | 4 | |||
975.2.n.e.824.2 | 4 | 195.122 | odd | 4 | |||
975.2.n.j.749.2 | 4 | 5.2 | odd | 4 | |||
975.2.n.j.749.2 | 4 | 15.2 | even | 4 | |||
975.2.n.j.824.1 | 4 | 65.18 | even | 4 | |||
975.2.n.j.824.1 | 4 | 195.83 | odd | 4 | |||
975.2.o.e.476.2 | ✓ | 4 | 5.4 | even | 2 | ||
975.2.o.e.476.2 | ✓ | 4 | 15.14 | odd | 2 | ||
975.2.o.e.551.2 | yes | 4 | 65.44 | odd | 4 | ||
975.2.o.e.551.2 | yes | 4 | 195.44 | even | 4 | ||
975.2.o.h.476.1 | yes | 4 | 1.1 | even | 1 | trivial | |
975.2.o.h.476.1 | yes | 4 | 3.2 | odd | 2 | CM | |
975.2.o.h.551.1 | yes | 4 | 13.5 | odd | 4 | inner | |
975.2.o.h.551.1 | yes | 4 | 39.5 | even | 4 | inner |