Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.a.757.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | − | 2.00000i | − | 0.894427i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||
0.894427 | − | 0.447214i | \(-0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 2.00000i | 0.632456 | + | 0.632456i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.00000i | − | 1.38675i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) | ||
0.720577 | − | 0.693375i | \(-0.243877\pi\) | |||||||
\(14\) | 1.00000 | − | 1.00000i | 0.267261 | − | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.00000 | + | 5.00000i | 0.980581 | + | 0.980581i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 9.00000i | 1.67126i | 0.549294 | + | 0.835629i | \(0.314897\pi\) | ||||
−0.549294 | + | 0.835629i | \(0.685103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | + | 1.00000i | −0.171499 | + | 0.171499i | ||||
\(35\) | 2.00000i | 0.338062i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 4.00000 | + | 4.00000i | 0.648886 | + | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.00000 | − | 4.00000i | 0.632456 | − | 0.632456i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.00000i | − | 0.762493i | −0.924473 | − | 0.381246i | \(-0.875495\pi\) | ||
0.924473 | − | 0.381246i | \(-0.124505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.00000 | − | 5.00000i | 0.737210 | − | 0.737210i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | + | 1.00000i | −0.141421 | + | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.0000 | −1.38675 | ||||||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 2.00000i | −0.267261 | − | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.00000 | − | 9.00000i | −1.18176 | − | 1.18176i | ||||
\(59\) | − | 1.00000i | − | 0.130189i | −0.997879 | − | 0.0650945i | \(-0.979265\pi\) | ||
0.997879 | − | 0.0650945i | \(-0.0207349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.00000i | − | 0.768221i | −0.923287 | − | 0.384111i | \(-0.874508\pi\) | ||
0.923287 | − | 0.384111i | \(-0.125492\pi\) | |||||||
\(62\) | 7.00000 | − | 7.00000i | 0.889001 | − | 0.889001i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −10.0000 | −1.24035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00000i | 1.09952i | 0.835321 | + | 0.549762i | \(0.185282\pi\) | ||||
−0.835321 | + | 0.549762i | \(0.814718\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 2.00000i | −0.239046 | − | 0.239046i | ||||
\(71\) | −15.0000 | −1.78017 | −0.890086 | − | 0.455792i | \(-0.849356\pi\) | ||||
−0.890086 | + | 0.455792i | \(0.849356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 2.00000 | + | 2.00000i | 0.232495 | + | 0.232495i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0000 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 8.00000i | 0.894427i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | + | 2.00000i | −0.220863 | + | 0.220863i | ||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.00000i | − | 0.216930i | ||||||
\(86\) | 5.00000 | + | 5.00000i | 0.539164 | + | 0.539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0000 | −1.37800 | −0.688999 | − | 0.724763i | \(-0.741949\pi\) | ||||
−0.688999 | + | 0.724763i | \(0.741949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000i | 0.524142i | ||||||||
\(92\) | 10.0000i | 1.04257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | −1.00000 | + | 1.00000i | −0.101015 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 2.00000i | − | 0.200000i | ||||||
\(101\) | − | 8.00000i | − | 0.796030i | −0.917379 | − | 0.398015i | \(-0.869699\pi\) | ||
0.917379 | − | 0.398015i | \(-0.130301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | −0.295599 | −0.147799 | − | 0.989017i | \(-0.547219\pi\) | ||||
−0.147799 | + | 0.989017i | \(0.547219\pi\) | |||||||
\(104\) | 10.0000 | − | 10.0000i | 0.980581 | − | 0.980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | − | 9.00000i | −0.874157 | − | 0.874157i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.0000i | − | 1.53252i | −0.642529 | − | 0.766261i | \(-0.722115\pi\) | ||
0.642529 | − | 0.766261i | \(-0.277885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000i | 0.932505i | ||||||||
\(116\) | 18.0000 | 1.67126 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.00000 | + | 1.00000i | 0.0920575 | + | 0.0920575i | ||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 6.00000 | + | 6.00000i | 0.543214 | + | 0.543214i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0000i | 1.25724i | ||||||||
\(125\) | − | 12.0000i | − | 1.07331i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.0000 | − | 10.0000i | 0.877058 | − | 0.877058i | ||||
\(131\) | − | 13.0000i | − | 1.13582i | −0.823092 | − | 0.567908i | \(-0.807753\pi\) | ||
0.823092 | − | 0.567908i | \(-0.192247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000i | 0.346844i | ||||||||
\(134\) | −9.00000 | − | 9.00000i | −0.777482 | − | 0.777482i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 2.00000i | 0.171499 | + | 0.171499i | ||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000i | 1.69638i | 0.529694 | + | 0.848189i | \(0.322307\pi\) | ||||
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(140\) | 4.00000 | 0.338062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.0000 | − | 15.0000i | 1.25877 | − | 1.25877i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | − | 9.00000i | − | 0.737309i | −0.929567 | − | 0.368654i | \(-0.879819\pi\) | ||
0.929567 | − | 0.368654i | \(-0.120181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 8.00000 | − | 8.00000i | 0.648886 | − | 0.648886i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.0000i | 1.12451i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.0000i | 1.03751i | 0.854922 | + | 0.518756i | \(0.173605\pi\) | ||||
−0.854922 | + | 0.518756i | \(0.826395\pi\) | |||||||
\(158\) | 14.0000 | − | 14.0000i | 1.11378 | − | 1.11378i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00000 | − | 8.00000i | −0.632456 | − | 0.632456i | ||||
\(161\) | 5.00000 | 0.394055 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.0000i | − | 0.861586i | −0.902451 | − | 0.430793i | \(-0.858234\pi\) | ||
0.902451 | − | 0.430793i | \(-0.141766\pi\) | |||||||
\(164\) | − | 4.00000i | − | 0.312348i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | + | 4.00000i | 0.310460 | + | 0.310460i | ||||
\(167\) | −4.00000 | −0.309529 | −0.154765 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154765 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 2.00000 | + | 2.00000i | 0.153393 | + | 0.153393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.0000 | − | 13.0000i | 0.974391 | − | 0.974391i | ||||
\(179\) | − | 10.0000i | − | 0.747435i | −0.927543 | − | 0.373718i | \(-0.878083\pi\) | ||
0.927543 | − | 0.373718i | \(-0.121917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.0000i | − | 1.41226i | −0.708083 | − | 0.706129i | \(-0.750440\pi\) | ||
0.708083 | − | 0.706129i | \(-0.249560\pi\) | |||||||
\(182\) | −5.00000 | − | 5.00000i | −0.370625 | − | 0.370625i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0000 | − | 10.0000i | −0.737210 | − | 0.737210i | ||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | − | 8.00000i | 0.580381 | − | 0.580381i | ||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | 0.647834 | 0.323917 | − | 0.946085i | \(-0.395000\pi\) | ||||
0.323917 | + | 0.946085i | \(0.395000\pi\) | |||||||
\(194\) | 14.0000 | − | 14.0000i | 1.00514 | − | 1.00514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 2.00000i | − | 0.142857i | ||||||
\(197\) | 14.0000i | 0.997459i | 0.866758 | + | 0.498729i | \(0.166200\pi\) | ||||
−0.866758 | + | 0.498729i | \(0.833800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0000 | 0.921546 | 0.460773 | − | 0.887518i | \(-0.347572\pi\) | ||||
0.460773 | + | 0.887518i | \(0.347572\pi\) | |||||||
\(200\) | 2.00000 | + | 2.00000i | 0.141421 | + | 0.141421i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.00000 | + | 8.00000i | 0.562878 | + | 0.562878i | ||||
\(203\) | − | 9.00000i | − | 0.631676i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.00000i | − | 0.279372i | ||||||
\(206\) | 3.00000 | − | 3.00000i | 0.209020 | − | 0.209020i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.0000i | 1.38675i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000i | 0.0688428i | 0.999407 | + | 0.0344214i | \(0.0109588\pi\) | ||||
−0.999407 | + | 0.0344214i | \(0.989041\pi\) | |||||||
\(212\) | 18.0000 | 1.23625 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.0000 | −0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.00000 | 0.475191 | ||||||||
\(218\) | 16.0000 | + | 16.0000i | 1.08366 | + | 1.08366i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.00000i | − | 0.336336i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | −4.00000 | + | 4.00000i | −0.267261 | + | 0.267261i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | + | 6.00000i | −0.399114 | + | 0.399114i | ||||
\(227\) | 25.0000i | 1.65931i | 0.558278 | + | 0.829654i | \(0.311462\pi\) | ||||
−0.558278 | + | 0.829654i | \(0.688538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.0000i | − | 0.660819i | −0.943838 | − | 0.330409i | \(-0.892813\pi\) | ||
0.943838 | − | 0.330409i | \(-0.107187\pi\) | |||||||
\(230\) | −10.0000 | − | 10.0000i | −0.659380 | − | 0.659380i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.0000 | + | 18.0000i | −1.18176 | + | 1.18176i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | −0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.00000 | − | 1.00000i | 0.0648204 | − | 0.0648204i | ||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | −11.0000 | + | 11.0000i | −0.707107 | + | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | − | 2.00000i | − | 0.127775i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | −14.0000 | − | 14.0000i | −0.889001 | − | 0.889001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | + | 12.0000i | 0.758947 | + | 0.758947i | ||||
\(251\) | − | 12.0000i | − | 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | − | 8.00000i | 0.501965 | − | 0.501965i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000i | 0.124274i | ||||||||
\(260\) | 20.0000i | 1.24035i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.0000 | + | 13.0000i | 0.803143 | + | 0.803143i | ||||
\(263\) | −31.0000 | −1.91154 | −0.955771 | − | 0.294112i | \(-0.904976\pi\) | ||||
−0.955771 | + | 0.294112i | \(0.904976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | −4.00000 | − | 4.00000i | −0.245256 | − | 0.245256i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.0000 | 1.09952 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0000 | −0.911185 | −0.455593 | − | 0.890188i | \(-0.650573\pi\) | ||||
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | − | 12.0000i | 0.724947 | − | 0.724947i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0000i | 1.56219i | 0.624413 | + | 0.781094i | \(0.285338\pi\) | ||||
−0.624413 | + | 0.781094i | \(0.714662\pi\) | |||||||
\(278\) | −20.0000 | − | 20.0000i | −1.19952 | − | 1.19952i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.00000 | + | 4.00000i | −0.239046 | + | 0.239046i | ||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0000i | 0.951101i | 0.879688 | + | 0.475551i | \(0.157751\pi\) | ||||
−0.879688 | + | 0.475551i | \(0.842249\pi\) | |||||||
\(284\) | 30.0000i | 1.78017i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −18.0000 | + | 18.0000i | −1.05700 | + | 1.05700i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | −0.116445 | ||||||||
\(296\) | 4.00000 | − | 4.00000i | 0.232495 | − | 0.232495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.00000 | + | 9.00000i | 0.521356 | + | 0.521356i | ||||
\(299\) | 25.0000i | 1.44579i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000i | 0.288195i | ||||||||
\(302\) | −12.0000 | + | 12.0000i | −0.690522 | + | 0.690522i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.00000i | − | 0.342438i | −0.985233 | − | 0.171219i | \(-0.945229\pi\) | ||
0.985233 | − | 0.171219i | \(-0.0547706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.0000 | − | 14.0000i | −0.795147 | − | 0.795147i | ||||
\(311\) | 34.0000 | 1.92796 | 0.963982 | − | 0.265969i | \(-0.0856919\pi\) | ||||
0.963982 | + | 0.265969i | \(0.0856919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.0000 | 1.80875 | 0.904373 | − | 0.426742i | \(-0.140339\pi\) | ||||
0.904373 | + | 0.426742i | \(0.140339\pi\) | |||||||
\(314\) | −13.0000 | − | 13.0000i | −0.733632 | − | 0.733632i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.0000i | 1.57512i | ||||||||
\(317\) | − | 14.0000i | − | 0.786318i | −0.919470 | − | 0.393159i | \(-0.871382\pi\) | ||
0.919470 | − | 0.393159i | \(-0.128618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.0000 | 0.894427 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00000 | + | 5.00000i | −0.278639 | + | 0.278639i | ||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.00000i | − | 0.277350i | ||||||
\(326\) | 11.0000 | + | 11.0000i | 0.609234 | + | 0.609234i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.00000 | + | 4.00000i | 0.220863 | + | 0.220863i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0000i | 0.714545i | 0.934000 | + | 0.357272i | \(0.116293\pi\) | ||||
−0.934000 | + | 0.357272i | \(0.883707\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | − | 4.00000i | 0.218870 | − | 0.218870i | ||||
\(335\) | 18.0000 | 0.983445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0000 | 1.03500 | 0.517498 | − | 0.855684i | \(-0.326864\pi\) | ||||
0.517498 | + | 0.855684i | \(0.326864\pi\) | |||||||
\(338\) | 12.0000 | − | 12.0000i | 0.652714 | − | 0.652714i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | −0.216930 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 10.0000 | − | 10.0000i | 0.539164 | − | 0.539164i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 6.00000i | 0.322562 | + | 0.322562i | ||||
\(347\) | 16.0000i | 0.858925i | 0.903085 | + | 0.429463i | \(0.141297\pi\) | ||||
−0.903085 | + | 0.429463i | \(0.858703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.0000i | − | 1.23116i | −0.788074 | − | 0.615581i | \(-0.788921\pi\) | ||
0.788074 | − | 0.615581i | \(-0.211079\pi\) | |||||||
\(350\) | 1.00000 | − | 1.00000i | 0.0534522 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.0000 | −1.75641 | −0.878206 | − | 0.478282i | \(-0.841260\pi\) | ||||
−0.878206 | + | 0.478282i | \(0.841260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.0000i | 1.59223i | ||||||||
\(356\) | 26.0000i | 1.37800i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000 | + | 10.0000i | 0.528516 | + | 0.528516i | ||||
\(359\) | 1.00000 | 0.0527780 | 0.0263890 | − | 0.999652i | \(-0.491599\pi\) | ||||
0.0263890 | + | 0.999652i | \(0.491599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 19.0000 | + | 19.0000i | 0.998618 | + | 0.998618i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.0000 | 0.524142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0000 | 1.09619 | 0.548096 | − | 0.836416i | \(-0.315353\pi\) | ||||
0.548096 | + | 0.836416i | \(0.315353\pi\) | |||||||
\(368\) | 20.0000 | 1.04257 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.00000 | − | 4.00000i | 0.207950 | − | 0.207950i | ||||
\(371\) | − | 9.00000i | − | 0.467257i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.0000i | − | 1.13912i | −0.821951 | − | 0.569558i | \(-0.807114\pi\) | ||
0.821951 | − | 0.569558i | \(-0.192886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.0000 | 2.31762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.0000i | − | 0.821865i | −0.911666 | − | 0.410932i | \(-0.865203\pi\) | ||
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(380\) | 16.0000i | 0.820783i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | + | 4.00000i | −0.204658 | + | 0.204658i | ||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.00000 | + | 9.00000i | −0.458088 | + | 0.458088i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.0000i | 1.42148i | ||||||||
\(389\) | − | 10.0000i | − | 0.507020i | −0.967333 | − | 0.253510i | \(-0.918415\pi\) | ||
0.967333 | − | 0.253510i | \(-0.0815851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.00000 | −0.252861 | ||||||||
\(392\) | 2.00000 | + | 2.00000i | 0.101015 | + | 0.101015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0000 | − | 14.0000i | −0.705310 | − | 0.705310i | ||||
\(395\) | 28.0000i | 1.40883i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.0000i | − | 0.501886i | −0.968002 | − | 0.250943i | \(-0.919259\pi\) | ||
0.968002 | − | 0.250943i | \(-0.0807406\pi\) | |||||||
\(398\) | −13.0000 | + | 13.0000i | −0.651631 | + | 0.651631i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.0000i | 1.74347i | ||||||||
\(404\) | −16.0000 | −0.796030 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.00000 | + | 9.00000i | 0.446663 | + | 0.446663i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.0000 | −1.58230 | −0.791149 | − | 0.611623i | \(-0.790517\pi\) | ||||
−0.791149 | + | 0.611623i | \(0.790517\pi\) | |||||||
\(410\) | 4.00000 | + | 4.00000i | 0.197546 | + | 0.197546i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.00000i | 0.295599i | ||||||||
\(413\) | 1.00000i | 0.0492068i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | −20.0000 | − | 20.0000i | −0.980581 | − | 0.980581i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 15.0000i | − | 0.732798i | −0.930458 | − | 0.366399i | \(-0.880591\pi\) | ||
0.930458 | − | 0.366399i | \(-0.119409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.00000i | − | 0.194948i | −0.995238 | − | 0.0974740i | \(-0.968924\pi\) | ||
0.995238 | − | 0.0974740i | \(-0.0310763\pi\) | |||||||
\(422\) | −1.00000 | − | 1.00000i | −0.0486792 | − | 0.0486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | + | 18.0000i | −0.874157 | + | 0.874157i | ||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000i | 0.290360i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | − | 10.0000i | 0.482243 | − | 0.482243i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00000 | 0.384455 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(434\) | −7.00000 | + | 7.00000i | −0.336011 | + | 0.336011i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.0000 | −1.53252 | ||||||||
\(437\) | 20.0000i | 0.956730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.00000 | 0.429547 | 0.214773 | − | 0.976664i | \(-0.431099\pi\) | ||||
0.214773 | + | 0.976664i | \(0.431099\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.00000 | + | 5.00000i | 0.237826 | + | 0.237826i | ||||
\(443\) | 6.00000i | 0.285069i | 0.989790 | + | 0.142534i | \(0.0455251\pi\) | ||||
−0.989790 | + | 0.142534i | \(0.954475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0000i | 1.23252i | ||||||||
\(446\) | 16.0000 | − | 16.0000i | 0.757622 | − | 0.757622i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.0000 | − | 25.0000i | −1.17331 | − | 1.17331i | ||||
\(455\) | 10.0000 | 0.468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | 0.233890 | 0.116945 | − | 0.993138i | \(-0.462690\pi\) | ||||
0.116945 | + | 0.993138i | \(0.462690\pi\) | |||||||
\(458\) | 10.0000 | + | 10.0000i | 0.467269 | + | 0.467269i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.0000 | 0.932505 | ||||||||
\(461\) | 12.0000i | 0.558896i | 0.960161 | + | 0.279448i | \(0.0901514\pi\) | ||||
−0.960161 | + | 0.279448i | \(0.909849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | − | 36.0000i | − | 1.67126i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0000 | − | 10.0000i | 0.463241 | − | 0.463241i | ||||
\(467\) | − | 32.0000i | − | 1.48078i | −0.672176 | − | 0.740392i | \(-0.734640\pi\) | ||
0.672176 | − | 0.740392i | \(-0.265360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.00000i | − | 0.415581i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | − | 2.00000i | 0.0920575 | − | 0.0920575i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.00000i | − | 0.183533i | ||||||
\(476\) | 2.00000i | 0.0916698i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.0000 | + | 24.0000i | −1.09773 | + | 1.09773i | ||||
\(479\) | 26.0000 | 1.18797 | 0.593985 | − | 0.804476i | \(-0.297554\pi\) | ||||
0.593985 | + | 0.804476i | \(0.297554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0000 | −0.455961 | ||||||||
\(482\) | −26.0000 | + | 26.0000i | −1.18427 | + | 1.18427i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 22.0000i | − | 1.00000i | ||||||
\(485\) | 28.0000i | 1.27141i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 12.0000 | − | 12.0000i | 0.543214 | − | 0.543214i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | + | 2.00000i | 0.0903508 | + | 0.0903508i | ||||
\(491\) | − | 4.00000i | − | 0.180517i | −0.995918 | − | 0.0902587i | \(-0.971231\pi\) | ||
0.995918 | − | 0.0902587i | \(-0.0287694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000i | 0.405340i | ||||||||
\(494\) | 20.0000 | − | 20.0000i | 0.899843 | − | 0.899843i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.0000 | 1.25724 | ||||||||
\(497\) | 15.0000 | 0.672842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000i | 1.07439i | 0.843459 | + | 0.537194i | \(0.180516\pi\) | ||||
−0.843459 | + | 0.537194i | \(0.819484\pi\) | |||||||
\(500\) | −24.0000 | −1.07331 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | + | 12.0000i | 0.535586 | + | 0.535586i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.0000 | −0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000i | 0.709885i | ||||||||
\(509\) | − | 18.0000i | − | 0.797836i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) | ||
0.916987 | − | 0.398918i | \(-0.130614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000 | − | 6.00000i | 0.264649 | − | 0.264649i | ||||
\(515\) | 6.00000i | 0.264392i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.00000 | − | 2.00000i | −0.0878750 | − | 0.0878750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −20.0000 | − | 20.0000i | −0.877058 | − | 0.877058i | ||||
\(521\) | 39.0000 | 1.70862 | 0.854311 | − | 0.519763i | \(-0.173980\pi\) | ||||
0.854311 | + | 0.519763i | \(0.173980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.0000i | 1.57417i | 0.616844 | + | 0.787085i | \(0.288411\pi\) | ||||
−0.616844 | + | 0.787085i | \(0.711589\pi\) | |||||||
\(524\) | −26.0000 | −1.13582 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0000 | − | 31.0000i | 1.35166 | − | 1.35166i | ||||
\(527\) | −7.00000 | −0.304925 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | −18.0000 | + | 18.0000i | −0.781870 | + | 0.781870i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | − | 10.0000i | − | 0.433148i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18.0000 | + | 18.0000i | −0.777482 | + | 0.777482i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.0000i | − | 1.63375i | −0.576816 | − | 0.816874i | \(-0.695705\pi\) | ||
0.576816 | − | 0.816874i | \(-0.304295\pi\) | |||||||
\(542\) | 15.0000 | − | 15.0000i | 0.644305 | − | 0.644305i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | − | 4.00000i | 0.171499 | − | 0.171499i | ||||
\(545\) | −32.0000 | −1.37073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 28.0000i | − | 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | 24.0000i | 1.02523i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.0000 | 1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000 | 0.595341 | ||||||||
\(554\) | −26.0000 | − | 26.0000i | −1.10463 | − | 1.10463i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 40.0000 | 1.69638 | ||||||||
\(557\) | 33.0000i | 1.39825i | 0.714997 | + | 0.699127i | \(0.246428\pi\) | ||||
−0.714997 | + | 0.699127i | \(0.753572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.0000 | −1.05739 | ||||||||
\(560\) | − | 8.00000i | − | 0.338062i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0000 | − | 12.0000i | 0.506189 | − | 0.506189i | ||||
\(563\) | − | 15.0000i | − | 0.632175i | −0.948730 | − | 0.316087i | \(-0.897631\pi\) | ||
0.948730 | − | 0.316087i | \(-0.102369\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.0000i | − | 0.504844i | ||||||
\(566\) | −16.0000 | − | 16.0000i | −0.672530 | − | 0.672530i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30.0000 | − | 30.0000i | −1.25877 | − | 1.25877i | ||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19.0000i | − | 0.795125i | −0.917575 | − | 0.397563i | \(-0.869856\pi\) | ||
0.917575 | − | 0.397563i | \(-0.130144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.00000 | − | 2.00000i | 0.0834784 | − | 0.0834784i | ||||
\(575\) | −5.00000 | −0.208514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0000 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(578\) | 16.0000 | − | 16.0000i | 0.665512 | − | 0.665512i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 36.0000i | − | 1.49482i | ||||||
\(581\) | 4.00000i | 0.165948i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | − | 12.0000i | −0.495715 | − | 0.495715i | ||||
\(587\) | 23.0000i | 0.949312i | 0.880172 | + | 0.474656i | \(0.157427\pi\) | ||||
−0.880172 | + | 0.474656i | \(0.842573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000i | 1.15372i | ||||||||
\(590\) | 2.00000 | − | 2.00000i | 0.0823387 | − | 0.0823387i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000i | 0.328798i | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000i | 0.0819920i | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.0000 | − | 25.0000i | −1.02233 | − | 1.02233i | ||||
\(599\) | −35.0000 | −1.43006 | −0.715031 | − | 0.699093i | \(-0.753587\pi\) | ||||
−0.715031 | + | 0.699093i | \(0.753587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | −5.00000 | − | 5.00000i | −0.203785 | − | 0.203785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 24.0000i | − | 0.976546i | ||||||
\(605\) | − | 22.0000i | − | 0.894427i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00000 | 0.0405887 | 0.0202944 | − | 0.999794i | \(-0.493540\pi\) | ||||
0.0202944 | + | 0.999794i | \(0.493540\pi\) | |||||||
\(608\) | −16.0000 | − | 16.0000i | −0.648886 | − | 0.648886i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | − | 12.0000i | 0.485866 | − | 0.485866i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.0000i | − | 0.646234i | −0.946359 | − | 0.323117i | \(-0.895269\pi\) | ||
0.946359 | − | 0.323117i | \(-0.104731\pi\) | |||||||
\(614\) | 6.00000 | + | 6.00000i | 0.242140 | + | 0.242140i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.0000 | 1.85189 | 0.925945 | − | 0.377658i | \(-0.123271\pi\) | ||||
0.925945 | + | 0.377658i | \(0.123271\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 28.0000 | 1.12451 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −34.0000 | + | 34.0000i | −1.36328 | + | 1.36328i | ||||
\(623\) | 13.0000 | 0.520834 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −32.0000 | + | 32.0000i | −1.27898 | + | 1.27898i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.0000 | 1.03751 | ||||||||
\(629\) | − | 2.00000i | − | 0.0797452i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0000 | 1.35352 | 0.676759 | − | 0.736204i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736204i | \(0.263384\pi\) | |||||||
\(632\) | −28.0000 | − | 28.0000i | −1.11378 | − | 1.11378i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0000 | + | 14.0000i | 0.556011 | + | 0.556011i | ||||
\(635\) | 16.0000i | 0.634941i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.00000i | − | 0.198107i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0000 | + | 16.0000i | −0.632456 | + | 0.632456i | ||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.0000i | − | 0.552106i | −0.961142 | − | 0.276053i | \(-0.910973\pi\) | ||
0.961142 | − | 0.276053i | \(-0.0890266\pi\) | |||||||
\(644\) | − | 10.0000i | − | 0.394055i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00000 | + | 4.00000i | 0.157378 | + | 0.157378i | ||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.00000 | + | 5.00000i | 0.196116 | + | 0.196116i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.0000 | −0.861586 | ||||||||
\(653\) | − | 21.0000i | − | 0.821794i | −0.911682 | − | 0.410897i | \(-0.865216\pi\) | ||
0.911682 | − | 0.410897i | \(-0.134784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.0000 | −1.01590 | ||||||||
\(656\) | −8.00000 | −0.312348 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.0000i | − | 1.40236i | −0.712984 | − | 0.701180i | \(-0.752657\pi\) | ||
0.712984 | − | 0.701180i | \(-0.247343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000i | 0.855701i | 0.903850 | + | 0.427850i | \(0.140729\pi\) | ||||
−0.903850 | + | 0.427850i | \(0.859271\pi\) | |||||||
\(662\) | −13.0000 | − | 13.0000i | −0.505259 | − | 0.505259i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00000 | − | 8.00000i | 0.310460 | − | 0.310460i | ||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 45.0000i | − | 1.74241i | ||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.0000 | + | 18.0000i | −0.695401 | + | 0.695401i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.0000 | −1.42625 | −0.713123 | − | 0.701039i | \(-0.752720\pi\) | ||||
−0.713123 | + | 0.701039i | \(0.752720\pi\) | |||||||
\(674\) | −19.0000 | + | 19.0000i | −0.731853 | + | 0.731853i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.0000i | 0.923077i | ||||||||
\(677\) | − | 12.0000i | − | 0.461197i | −0.973049 | − | 0.230599i | \(-0.925932\pi\) | ||
0.973049 | − | 0.230599i | \(-0.0740685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | 0.537271 | ||||||||
\(680\) | 4.00000 | − | 4.00000i | 0.153393 | − | 0.153393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 46.0000i | − | 1.76014i | −0.474843 | − | 0.880071i | \(-0.657495\pi\) | ||
0.474843 | − | 0.880071i | \(-0.342505\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000i | 0.916993i | ||||||||
\(686\) | 1.00000 | − | 1.00000i | 0.0381802 | − | 0.0381802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.0000i | 0.762493i | ||||||||
\(689\) | 45.0000 | 1.71436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000i | 0.304334i | 0.988355 | + | 0.152167i | \(0.0486252\pi\) | ||||
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | − | 16.0000i | −0.607352 | − | 0.607352i | ||||
\(695\) | 40.0000 | 1.51729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | 0.0757554 | ||||||||
\(698\) | 23.0000 | + | 23.0000i | 0.870563 | + | 0.870563i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000i | 0.0755929i | ||||||||
\(701\) | 22.0000i | 0.830929i | 0.909610 | + | 0.415464i | \(0.136381\pi\) | ||||
−0.909610 | + | 0.415464i | \(0.863619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.0000 | − | 33.0000i | 1.24197 | − | 1.24197i | ||||
\(707\) | 8.00000i | 0.300871i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 16.0000i | − | 0.600893i | −0.953799 | − | 0.300446i | \(-0.902864\pi\) | ||
0.953799 | − | 0.300446i | \(-0.0971356\pi\) | |||||||
\(710\) | −30.0000 | − | 30.0000i | −1.12588 | − | 1.12588i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.0000 | − | 26.0000i | −0.974391 | − | 0.974391i | ||||
\(713\) | 35.0000 | 1.31076 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.0000 | −0.747435 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.00000 | + | 1.00000i | −0.0373197 | + | 0.0373197i | ||||
\(719\) | −14.0000 | −0.522112 | −0.261056 | − | 0.965324i | \(-0.584071\pi\) | ||||
−0.261056 | + | 0.965324i | \(0.584071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.00000 | 0.111726 | ||||||||
\(722\) | −3.00000 | + | 3.00000i | −0.111648 | + | 0.111648i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.0000 | −1.41226 | ||||||||
\(725\) | 9.00000i | 0.334252i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.0000 | −1.22390 | −0.611951 | − | 0.790896i | \(-0.709615\pi\) | ||||
−0.611951 | + | 0.790896i | \(0.709615\pi\) | |||||||
\(728\) | −10.0000 | + | 10.0000i | −0.370625 | + | 0.370625i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.00000i | − | 0.184932i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.0000i | 1.80986i | 0.425564 | + | 0.904928i | \(0.360076\pi\) | ||||
−0.425564 | + | 0.904928i | \(0.639924\pi\) | |||||||
\(734\) | −21.0000 | + | 21.0000i | −0.775124 | + | 0.775124i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.0000 | + | 20.0000i | −0.737210 | + | 0.737210i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.0000i | − | 1.17714i | −0.808447 | − | 0.588570i | \(-0.799691\pi\) | ||
0.808447 | − | 0.588570i | \(-0.200309\pi\) | |||||||
\(740\) | 8.00000i | 0.294086i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.00000 | + | 9.00000i | 0.330400 | + | 0.330400i | ||||
\(743\) | 23.0000 | 0.843788 | 0.421894 | − | 0.906645i | \(-0.361365\pi\) | ||||
0.421894 | + | 0.906645i | \(0.361365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | 22.0000 | + | 22.0000i | 0.805477 | + | 0.805477i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.0000 | −1.67856 | −0.839282 | − | 0.543696i | \(-0.817024\pi\) | ||||
−0.839282 | + | 0.543696i | \(0.817024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −45.0000 | + | 45.0000i | −1.63880 | + | 1.63880i | ||||
\(755\) | − | 24.0000i | − | 0.873449i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0000i | 0.872295i | 0.899875 | + | 0.436147i | \(0.143657\pi\) | ||||
−0.899875 | + | 0.436147i | \(0.856343\pi\) | |||||||
\(758\) | 16.0000 | + | 16.0000i | 0.581146 | + | 0.581146i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.0000 | − | 16.0000i | −0.580381 | − | 0.580381i | ||||
\(761\) | −11.0000 | −0.398750 | −0.199375 | − | 0.979923i | \(-0.563891\pi\) | ||||
−0.199375 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000i | 0.579239i | ||||||||
\(764\) | − | 8.00000i | − | 0.289430i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | − | 24.0000i | 0.867155 | − | 0.867155i | ||||
\(767\) | −5.00000 | −0.180540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 18.0000i | − | 0.647834i | ||||||
\(773\) | − | 32.0000i | − | 1.15096i | −0.817816 | − | 0.575480i | \(-0.804815\pi\) | ||
0.817816 | − | 0.575480i | \(-0.195185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.00000 | −0.251447 | ||||||||
\(776\) | −28.0000 | − | 28.0000i | −1.00514 | − | 1.00514i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0000 | + | 10.0000i | 0.358517 | + | 0.358517i | ||||
\(779\) | − | 8.00000i | − | 0.286630i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 5.00000 | − | 5.00000i | 0.178800 | − | 0.178800i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | 26.0000 | 0.927980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 48.0000i | − | 1.71102i | −0.517790 | − | 0.855508i | \(-0.673245\pi\) | ||
0.517790 | − | 0.855508i | \(-0.326755\pi\) | |||||||
\(788\) | 28.0000 | 0.997459 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −28.0000 | − | 28.0000i | −0.996195 | − | 0.996195i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0000 | −1.06533 | ||||||||
\(794\) | 10.0000 | + | 10.0000i | 0.354887 | + | 0.354887i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 26.0000i | − | 0.921546i | ||||||
\(797\) | 2.00000i | 0.0708436i | 0.999372 | + | 0.0354218i | \(0.0112775\pi\) | ||||
−0.999372 | + | 0.0354218i | \(0.988723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 4.00000i | 0.141421 | − | 0.141421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.0000 | + | 24.0000i | −0.847469 | + | 0.847469i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 10.0000i | − | 0.352454i | ||||||
\(806\) | −35.0000 | − | 35.0000i | −1.23282 | − | 1.23282i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.0000 | − | 16.0000i | 0.562878 | − | 0.562878i | ||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.0000i | − | 0.491606i | −0.969320 | − | 0.245803i | \(-0.920948\pi\) | ||
0.969320 | − | 0.245803i | \(-0.0790517\pi\) | |||||||
\(812\) | −18.0000 | −0.631676 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0000 | −0.770626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0000 | −0.699711 | ||||||||
\(818\) | 32.0000 | − | 32.0000i | 1.11885 | − | 1.11885i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.00000 | −0.279372 | ||||||||
\(821\) | − | 35.0000i | − | 1.22151i | −0.791820 | − | 0.610754i | \(-0.790866\pi\) | ||
0.791820 | − | 0.610754i | \(-0.209134\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.0000 | 1.53374 | 0.766872 | − | 0.641800i | \(-0.221812\pi\) | ||||
0.766872 | + | 0.641800i | \(0.221812\pi\) | |||||||
\(824\) | −6.00000 | − | 6.00000i | −0.209020 | − | 0.209020i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | − | 1.00000i | −0.0347945 | − | 0.0347945i | ||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.0000i | − | 1.18087i | −0.807086 | − | 0.590434i | \(-0.798956\pi\) | ||
0.807086 | − | 0.590434i | \(-0.201044\pi\) | |||||||
\(830\) | 8.00000 | − | 8.00000i | 0.277684 | − | 0.277684i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 40.0000 | 1.38675 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000i | 0.276851i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0000 | + | 15.0000i | 0.518166 | + | 0.518166i | ||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.0000 | −1.79310 | ||||||||
\(842\) | 4.00000 | + | 4.00000i | 0.137849 | + | 0.137849i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 24.0000i | 0.825625i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0000 | −0.377964 | ||||||||
\(848\) | − | 36.0000i | − | 1.23625i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.00000 | + | 1.00000i | −0.0342997 | + | 0.0342997i | ||||
\(851\) | 10.0000i | 0.342796i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.00000i | − | 0.308154i | −0.988059 | − | 0.154077i | \(-0.950760\pi\) | ||
0.988059 | − | 0.154077i | \(-0.0492404\pi\) | |||||||
\(854\) | −6.00000 | − | 6.00000i | −0.205316 | − | 0.205316i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | 0.307434 | 0.153717 | − | 0.988115i | \(-0.450876\pi\) | ||||
0.153717 | + | 0.988115i | \(0.450876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.00000i | − | 0.0682391i | −0.999418 | − | 0.0341196i | \(-0.989137\pi\) | ||
0.999418 | − | 0.0341196i | \(-0.0108627\pi\) | |||||||
\(860\) | 20.0000i | 0.681994i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | − | 12.0000i | 0.408722 | − | 0.408722i | ||||
\(863\) | −45.0000 | −1.53182 | −0.765909 | − | 0.642949i | \(-0.777711\pi\) | ||||
−0.765909 | + | 0.642949i | \(0.777711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | −8.00000 | + | 8.00000i | −0.271851 | + | 0.271851i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 14.0000i | − | 0.475191i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.0000 | 1.52477 | ||||||||
\(872\) | 32.0000 | − | 32.0000i | 1.08366 | − | 1.08366i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.0000 | − | 20.0000i | −0.676510 | − | 0.676510i | ||||
\(875\) | 12.0000i | 0.405674i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34.0000i | − | 1.14810i | −0.818821 | − | 0.574049i | \(-0.805372\pi\) | ||
0.818821 | − | 0.574049i | \(-0.194628\pi\) | |||||||
\(878\) | −9.00000 | + | 9.00000i | −0.303735 | + | 0.303735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.0000 | 1.58347 | 0.791735 | − | 0.610865i | \(-0.209178\pi\) | ||||
0.791735 | + | 0.610865i | \(0.209178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.0000i | − | 0.975928i | −0.872864 | − | 0.487964i | \(-0.837740\pi\) | ||
0.872864 | − | 0.487964i | \(-0.162260\pi\) | |||||||
\(884\) | −10.0000 | −0.336336 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 6.00000i | −0.201574 | − | 0.201574i | ||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | −26.0000 | − | 26.0000i | −0.871522 | − | 0.871522i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.0000i | 1.07144i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 8.00000 | + | 8.00000i | 0.267261 | + | 0.267261i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0000 | + | 30.0000i | −1.00111 | + | 1.00111i | ||||
\(899\) | − | 63.0000i | − | 2.10117i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000i | 0.299833i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.0000 | + | 12.0000i | 0.399114 | + | 0.399114i | ||||
\(905\) | −38.0000 | −1.26316 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 28.0000i | − | 0.929725i | −0.885383 | − | 0.464862i | \(-0.846104\pi\) | ||
0.885383 | − | 0.464862i | \(-0.153896\pi\) | |||||||
\(908\) | 50.0000 | 1.65931 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0000 | + | 10.0000i | −0.331497 | + | 0.331497i | ||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.00000 | + | 5.00000i | −0.165385 | + | 0.165385i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | 13.0000i | 0.429298i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0000 | 0.593765 | 0.296883 | − | 0.954914i | \(-0.404053\pi\) | ||||
0.296883 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(920\) | −20.0000 | + | 20.0000i | −0.659380 | + | 0.659380i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0000 | − | 12.0000i | −0.395199 | − | 0.395199i | ||||
\(923\) | 75.0000i | 2.46866i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.00000i | − | 0.0657596i | ||||||
\(926\) | −16.0000 | + | 16.0000i | −0.525793 | + | 0.525793i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36.0000 | + | 36.0000i | 1.18176 | + | 1.18176i | ||||
\(929\) | −14.0000 | −0.459325 | −0.229663 | − | 0.973270i | \(-0.573762\pi\) | ||||
−0.229663 | + | 0.973270i | \(0.573762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.00000i | − | 0.131095i | ||||||
\(932\) | 20.0000i | 0.655122i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.0000 | + | 32.0000i | 1.04707 | + | 1.04707i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 9.00000 | + | 9.00000i | 0.293860 | + | 0.293860i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0000i | 0.782378i | 0.920310 | + | 0.391189i | \(0.127936\pi\) | ||||
−0.920310 | + | 0.391189i | \(0.872064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0000 | −0.325645 | ||||||||
\(944\) | 4.00000i | 0.130189i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.00000 | + | 4.00000i | 0.129777 | + | 0.129777i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.00000 | − | 2.00000i | −0.0648204 | − | 0.0648204i | ||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.00000i | − | 0.258874i | ||||||
\(956\) | − | 48.0000i | − | 1.55243i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.0000 | + | 26.0000i | −0.840022 | + | 0.840022i | ||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 10.0000 | − | 10.0000i | 0.322413 | − | 0.322413i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 52.0000i | − | 1.67481i | ||||||
\(965\) | − | 18.0000i | − | 0.579441i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000 | 1.60789 | 0.803946 | − | 0.594703i | \(-0.202730\pi\) | ||||
0.803946 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(968\) | 22.0000 | + | 22.0000i | 0.707107 | + | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.0000 | − | 28.0000i | −0.899026 | − | 0.899026i | ||||
\(971\) | 33.0000i | 1.05902i | 0.848304 | + | 0.529510i | \(0.177624\pi\) | ||||
−0.848304 | + | 0.529510i | \(0.822376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 20.0000i | − | 0.641171i | ||||||
\(974\) | 16.0000 | − | 16.0000i | 0.512673 | − | 0.512673i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0000i | 0.768221i | ||||||||
\(977\) | −56.0000 | −1.79160 | −0.895799 | − | 0.444459i | \(-0.853396\pi\) | ||||
−0.895799 | + | 0.444459i | \(0.853396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.00000 | −0.127775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.00000 | + | 4.00000i | 0.127645 | + | 0.127645i | ||||
\(983\) | 62.0000 | 1.97749 | 0.988746 | − | 0.149601i | \(-0.0477989\pi\) | ||||
0.988746 | + | 0.149601i | \(0.0477989\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0000 | 0.892154 | ||||||||
\(986\) | −9.00000 | − | 9.00000i | −0.286618 | − | 0.286618i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40.0000i | 1.27257i | ||||||||
\(989\) | 25.0000i | 0.794954i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −28.0000 | + | 28.0000i | −0.889001 | + | 0.889001i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.0000 | + | 15.0000i | −0.475771 | + | 0.475771i | ||||
\(995\) | − | 26.0000i | − | 0.824255i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.0000i | 1.80521i | 0.430472 | + | 0.902604i | \(0.358347\pi\) | ||||
−0.430472 | + | 0.902604i | \(0.641653\pi\) | |||||||
\(998\) | −24.0000 | − | 24.0000i | −0.759707 | − | 0.759707i | ||||
\(999\) | 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 | 1512.2.c.a.757.2 | yes | 2 | |
3.2 | odd | 2 | 1512.2.c.b.757.1 | yes | 2 | ||
4.3 | odd | 2 | 6048.2.c.b.3025.1 | 2 | |||
8.3 | odd | 2 | 6048.2.c.b.3025.2 | 2 | |||
8.5 | even | 2 | inner | 1512.2.c.a.757.1 | ✓ | 2 | |
12.11 | even | 2 | 6048.2.c.a.3025.2 | 2 | |||
24.5 | odd | 2 | 1512.2.c.b.757.2 | yes | 2 | ||
24.11 | even | 2 | 6048.2.c.a.3025.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.a.757.1 | ✓ | 2 | 8.5 | even | 2 | inner | |
1512.2.c.a.757.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1512.2.c.b.757.1 | yes | 2 | 3.2 | odd | 2 | ||
1512.2.c.b.757.2 | yes | 2 | 24.5 | odd | 2 | ||
6048.2.c.a.3025.1 | 2 | 24.11 | even | 2 | |||
6048.2.c.a.3025.2 | 2 | 12.11 | even | 2 | |||
6048.2.c.b.3025.1 | 2 | 4.3 | odd | 2 | |||
6048.2.c.b.3025.2 | 2 | 8.3 | odd | 2 |