Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(207,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.207");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.s (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 943.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.943 |
Dual form | 1600.2.s.a.207.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | + | 3.00000i | −1.13389 | + | 1.13389i | −0.144370 | + | 0.989524i | \(0.546115\pi\) |
−0.989524 | + | 0.144370i | \(0.953885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.00000i | 0.301511 | + | 0.301511i | 0.841605 | − | 0.540094i | \(-0.181611\pi\) |
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.00000i | −0.242536 | + | 0.242536i | −0.817898 | − | 0.575363i | \(-0.804861\pi\) |
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 3.00000i | 0.688247 | + | 0.688247i | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | − | 6.00000i | 1.30931 | − | 1.30931i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.00000i | −0.208514 | − | 0.208514i | 0.595121 | − | 0.803636i | \(-0.297104\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.00000 | + | 7.00000i | −1.29987 | + | 1.29987i | −0.371391 | + | 0.928477i | \(0.621119\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.00000i | − | 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | − | 2.00000i | −0.348155 | − | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00000i | − | 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.00000 | − | 7.00000i | −1.02105 | − | 1.02105i | −0.999774 | − | 0.0212814i | \(-0.993225\pi\) |
−0.0212814 | − | 0.999774i | \(-0.506775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11.0000i | − | 1.57143i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 2.00000i | 0.280056 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | − | 6.00000i | −0.794719 | − | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | + | 3.00000i | −0.390567 | + | 0.390567i | −0.874889 | − | 0.484323i | \(-0.839066\pi\) |
0.484323 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.00000i | −0.128037 | − | 0.128037i | 0.640184 | − | 0.768221i | \(-0.278858\pi\) |
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | + | 3.00000i | −0.377964 | + | 0.377964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | + | 2.00000i | 0.240772 | + | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 3.00000i | −0.351123 | + | 0.351123i | −0.860527 | − | 0.509404i | \(-0.829866\pi\) |
0.509404 | + | 0.860527i | \(0.329866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.00000 | −0.219529 | −0.109764 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0000 | − | 14.0000i | 1.50096 | − | 1.50096i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 6.00000i | −0.628971 | − | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | − | 11.0000i | 1.11688 | − | 1.11688i | 0.124684 | − | 0.992196i | \(-0.460208\pi\) |
0.992196 | − | 0.124684i | \(-0.0397918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | + | 1.00000i | 0.100504 | + | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | + | 5.00000i | −0.497519 | + | 0.497519i | −0.910665 | − | 0.413146i | \(-0.864430\pi\) |
0.413146 | + | 0.910665i | \(0.364430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | − | 5.00000i | −0.492665 | − | 0.492665i | 0.416480 | − | 0.909145i | \(-0.363264\pi\) |
−0.909145 | + | 0.416480i | \(0.863264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | − | 5.00000i | 0.478913 | − | 0.478913i | −0.425871 | − | 0.904784i | \(-0.640032\pi\) |
0.904784 | + | 0.425871i | \(0.140032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000i | 1.13899i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0000 | − | 13.0000i | −1.22294 | − | 1.22294i | −0.966583 | − | 0.256354i | \(-0.917479\pi\) |
−0.256354 | − | 0.966583i | \(-0.582521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.00000i | − | 0.550019i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | − | 7.00000i | −0.621150 | − | 0.621150i | 0.324676 | − | 0.945825i | \(-0.394745\pi\) |
−0.945825 | + | 0.324676i | \(0.894745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.00000i | − | 0.704361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | − | 7.00000i | 0.611593 | − | 0.611593i | −0.331768 | − | 0.943361i | \(-0.607645\pi\) |
0.943361 | + | 0.331768i | \(0.107645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.0000 | −1.56080 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 9.00000i | 0.768922 | + | 0.768922i | 0.977917 | − | 0.208995i | \(-0.0670192\pi\) |
−0.208995 | + | 0.977917i | \(0.567019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.00000 | − | 9.00000i | 0.763370 | − | 0.763370i | −0.213560 | − | 0.976930i | \(-0.568506\pi\) |
0.976930 | + | 0.213560i | \(0.0685059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.0000 | + | 14.0000i | 1.17901 | + | 1.17901i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | + | 2.00000i | −0.167248 | + | 0.167248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.0000i | 1.81453i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.00000 | + | 1.00000i | 0.0819232 | + | 0.0819232i | 0.746881 | − | 0.664958i | \(-0.231550\pi\) |
−0.664958 | + | 0.746881i | \(0.731550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | + | 1.00000i | −0.0808452 | + | 0.0808452i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | −1.59617 | −0.798087 | − | 0.602542i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602542i | \(0.794154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0000 | −1.26888 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | + | 3.00000i | −0.232147 | + | 0.232147i | −0.813588 | − | 0.581441i | \(-0.802489\pi\) |
0.581441 | + | 0.813588i | \(0.302489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | + | 3.00000i | 0.229416 | + | 0.229416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | − | 6.00000i | 0.450988 | − | 0.450988i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.00000 | − | 5.00000i | −0.373718 | − | 0.373718i | 0.495112 | − | 0.868829i | \(-0.335127\pi\) |
−0.868829 | + | 0.495112i | \(0.835127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.00000 | − | 3.00000i | 0.222988 | − | 0.222988i | −0.586767 | − | 0.809756i | \(-0.699600\pi\) |
0.809756 | + | 0.586767i | \(0.199600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | + | 2.00000i | 0.147844 | + | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0000 | + | 12.0000i | −0.872872 | + | 0.872872i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.0000i | − | 1.30243i | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||
0.758891 | − | 0.651217i | \(-0.225741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0000 | + | 15.0000i | 1.07972 | + | 1.07972i | 0.996534 | + | 0.0831899i | \(0.0265108\pi\) |
0.0831899 | + | 0.996534i | \(0.473489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000i | 0.708881i | 0.935079 | + | 0.354441i | \(0.115329\pi\) | ||||
−0.935079 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000i | 0.564276i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 42.0000i | − | 2.94782i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | − | 1.00000i | −0.0695048 | − | 0.0695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000i | 0.415029i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0000 | − | 19.0000i | 1.30801 | − | 1.30801i | 0.385167 | − | 0.922847i | \(-0.374144\pi\) |
0.922847 | − | 0.385167i | \(-0.125856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | + | 6.00000i | 0.407307 | + | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | − | 6.00000i | 0.405442 | − | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | − | 2.00000i | −0.134535 | − | 0.134535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | + | 9.00000i | −0.602685 | + | 0.602685i | −0.941024 | − | 0.338340i | \(-0.890135\pi\) |
0.338340 | + | 0.941024i | \(0.390135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.0000i | − | 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.00000i | 0.0660819 | + | 0.0660819i | 0.739375 | − | 0.673293i | \(-0.235121\pi\) |
−0.673293 | + | 0.739375i | \(0.735121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | 0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | − | 9.00000i | 0.589610 | − | 0.589610i | −0.347916 | − | 0.937526i | \(-0.613111\pi\) |
0.937526 | + | 0.347916i | \(0.113111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | + | 6.00000i | −0.381771 | + | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0000 | − | 11.0000i | −0.694314 | − | 0.694314i | 0.268864 | − | 0.963178i | \(-0.413352\pi\) |
−0.963178 | + | 0.268864i | \(0.913352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.00000i | − | 0.125739i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0000 | + | 13.0000i | −0.810918 | + | 0.810918i | −0.984771 | − | 0.173854i | \(-0.944378\pi\) |
0.173854 | + | 0.984771i | \(0.444378\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.0000 | + | 18.0000i | 1.11847 | + | 1.11847i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.00000 | + | 7.00000i | −0.433289 | + | 0.433289i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.00000 | + | 7.00000i | 0.431638 | + | 0.431638i | 0.889185 | − | 0.457547i | \(-0.151272\pi\) |
−0.457547 | + | 0.889185i | \(0.651272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000 | 0.734388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00000 | − | 1.00000i | 0.0609711 | − | 0.0609711i | −0.675964 | − | 0.736935i | \(-0.736272\pi\) |
0.736935 | + | 0.675964i | \(0.236272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.0000i | 1.82237i | 0.411997 | + | 0.911185i | \(0.364831\pi\) | ||||
−0.411997 | + | 0.911185i | \(0.635169\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | + | 12.0000i | 0.726273 | + | 0.726273i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000i | 1.08152i | 0.841178 | + | 0.540758i | \(0.181862\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.00000i | − | 0.119737i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000i | 0.954480i | 0.878773 | + | 0.477240i | \(0.158363\pi\) | ||||
−0.878773 | + | 0.477240i | \(0.841637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000i | 0.713326i | 0.934233 | + | 0.356663i | \(0.116086\pi\) | ||||
−0.934233 | + | 0.356663i | \(0.883914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | + | 12.0000i | 0.708338 | + | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.0000 | + | 22.0000i | −1.28966 | + | 1.28966i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000 | + | 4.00000i | 0.232104 | + | 0.232104i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00000 | − | 2.00000i | 0.115663 | − | 0.115663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | − | 12.0000i | −0.691669 | − | 0.691669i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.0000 | − | 10.0000i | 0.574485 | − | 0.574485i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | + | 10.0000i | 0.568880 | + | 0.568880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0000 | − | 13.0000i | 0.734803 | − | 0.734803i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
0.971567 | + | 0.236764i | \(0.0760868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.00000 | −0.449325 | −0.224662 | − | 0.974437i | \(-0.572128\pi\) | ||||
−0.224662 | + | 0.974437i | \(0.572128\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.0000 | −0.783850 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.0000 | + | 10.0000i | −0.553001 | + | 0.553001i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.0000 | 2.31553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0000 | + | 21.0000i | 1.15426 | + | 1.15426i | 0.985689 | + | 0.168576i | \(0.0539168\pi\) |
0.168576 | + | 0.985689i | \(0.446083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.00000i | − | 0.328798i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 11.0000i | 0.599208 | − | 0.599208i | −0.340894 | − | 0.940102i | \(-0.610730\pi\) |
0.940102 | + | 0.340894i | \(0.110730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.0000 | + | 26.0000i | 1.41213 | + | 1.41213i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | − | 2.00000i | 0.108306 | − | 0.108306i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00000 | 0.107366 | 0.0536828 | − | 0.998558i | \(-0.482904\pi\) | ||||
0.0536828 | + | 0.998558i | \(0.482904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.00000 | + | 3.00000i | −0.160586 | + | 0.160586i | −0.782826 | − | 0.622240i | \(-0.786223\pi\) |
0.622240 | + | 0.782826i | \(0.286223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000i | 0.427008i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0000 | − | 13.0000i | −0.691920 | − | 0.691920i | 0.270734 | − | 0.962654i | \(-0.412734\pi\) |
−0.962654 | + | 0.270734i | \(0.912734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.0000i | 0.635107i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.0000i | − | 0.738892i | −0.929252 | − | 0.369446i | \(-0.879548\pi\) | ||
0.929252 | − | 0.369446i | \(-0.120452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.0000i | 0.944755i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0000 | + | 21.0000i | 1.09619 | + | 1.09619i | 0.994852 | + | 0.101339i | \(0.0323127\pi\) |
0.101339 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 24.0000i | −1.24602 | + | 1.24602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.0000 | − | 14.0000i | −0.721037 | − | 0.721037i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0000 | + | 15.0000i | −0.770498 | + | 0.770498i | −0.978194 | − | 0.207695i | \(-0.933404\pi\) |
0.207695 | + | 0.978194i | \(0.433404\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0000 | + | 14.0000i | 0.717242 | + | 0.717242i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.00000 | + | 5.00000i | −0.255488 | + | 0.255488i | −0.823216 | − | 0.567728i | \(-0.807823\pi\) |
0.567728 | + | 0.823216i | \(0.307823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.0000 | − | 23.0000i | −1.16615 | − | 1.16615i | −0.983105 | − | 0.183041i | \(-0.941406\pi\) |
−0.183041 | − | 0.983105i | \(-0.558594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.0000 | + | 14.0000i | −0.706207 | + | 0.706207i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0000 | 1.60603 | 0.803017 | − | 0.595956i | \(-0.203227\pi\) | ||||
0.803017 | + | 0.595956i | \(0.203227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 36.0000 | 1.80225 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | − | 6.00000i | 0.297409 | − | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.0000 | −1.87898 | −0.939490 | − | 0.342578i | \(-0.888700\pi\) | ||||
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | − | 18.0000i | −0.887875 | − | 0.887875i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 18.0000i | − | 0.885722i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.0000 | + | 18.0000i | −0.881464 | + | 0.881464i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0000 | − | 17.0000i | −0.830504 | − | 0.830504i | 0.157081 | − | 0.987586i | \(-0.449792\pi\) |
−0.987586 | + | 0.157081i | \(0.949792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | + | 5.00000i | −0.243685 | + | 0.243685i | −0.818373 | − | 0.574688i | \(-0.805124\pi\) |
0.574688 | + | 0.818373i | \(0.305124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.00000 | − | 7.00000i | −0.340352 | − | 0.340352i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | − | 4.00000i | 0.193122 | − | 0.193122i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.00000i | − | 0.0963366i | −0.998839 | − | 0.0481683i | \(-0.984662\pi\) | ||
0.998839 | − | 0.0481683i | \(-0.0153384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | − | 5.00000i | −0.240285 | − | 0.240285i | 0.576683 | − | 0.816968i | \(-0.304347\pi\) |
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.00000i | − | 0.287019i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0000i | 1.24091i | 0.784241 | + | 0.620456i | \(0.213053\pi\) | ||||
−0.784241 | + | 0.620456i | \(0.786947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 11.0000i | − | 0.523810i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.00000i | − | 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00000 | − | 2.00000i | −0.0945968 | − | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.0000i | − | 1.13263i | −0.824189 | − | 0.566315i | \(-0.808369\pi\) | ||
0.824189 | − | 0.566315i | \(-0.191631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | − | 4.00000i | 0.188353 | − | 0.188353i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000 | 0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | − | 7.00000i | −0.327446 | − | 0.327446i | 0.524168 | − | 0.851615i | \(-0.324376\pi\) |
−0.851615 | + | 0.524168i | \(0.824376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | + | 4.00000i | −0.186704 | + | 0.186704i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0000 | − | 21.0000i | −0.978068 | − | 0.978068i | 0.0216971 | − | 0.999765i | \(-0.493093\pi\) |
−0.999765 | + | 0.0216971i | \(0.993093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0000 | − | 19.0000i | 0.883005 | − | 0.883005i | −0.110834 | − | 0.993839i | \(-0.535352\pi\) |
0.993839 | + | 0.110834i | \(0.0353522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0000i | 1.29569i | 0.761774 | + | 0.647843i | \(0.224329\pi\) | ||||
−0.761774 | + | 0.647843i | \(0.775671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | + | 12.0000i | 0.554109 | + | 0.554109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.0000 | 1.84310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | + | 4.00000i | −0.183920 | + | 0.183920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.0000 | 1.46212 | 0.731059 | − | 0.682315i | \(-0.239027\pi\) | ||||
0.731059 | + | 0.682315i | \(0.239027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0000 | −0.546019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.0000 | + | 15.0000i | −0.679715 | + | 0.679715i | −0.959936 | − | 0.280221i | \(-0.909592\pi\) |
0.280221 | + | 0.959936i | \(0.409592\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.0000 | −1.26620 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | + | 9.00000i | 0.406164 | + | 0.406164i | 0.880399 | − | 0.474234i | \(-0.157275\pi\) |
−0.474234 | + | 0.880399i | \(0.657275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.0000i | − | 0.630528i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0000 | − | 29.0000i | −1.29822 | − | 1.29822i | −0.929568 | − | 0.368650i | \(-0.879820\pi\) |
−0.368650 | − | 0.929568i | \(-0.620180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | − | 6.00000i | 0.268060 | − | 0.268060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.0000 | − | 29.0000i | −1.29305 | − | 1.29305i | −0.932893 | − | 0.360153i | \(-0.882725\pi\) |
−0.360153 | − | 0.932893i | \(-0.617275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.0000 | −0.799408 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0000 | − | 17.0000i | 0.753512 | − | 0.753512i | −0.221621 | − | 0.975133i | \(-0.571135\pi\) |
0.975133 | + | 0.221621i | \(0.0711348\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 18.0000i | − | 0.796273i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.0000 | + | 12.0000i | 0.529813 | + | 0.529813i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 14.0000i | − | 0.615719i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.0000i | − | 0.526742i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.0000i | − | 0.700973i | −0.936568 | − | 0.350486i | \(-0.886016\pi\) | ||
0.936568 | − | 0.350486i | \(-0.113984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | + | 2.00000i | 0.0871214 | + | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.0000i | − | 0.913043i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | + | 3.00000i | −0.130189 | + | 0.130189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0000 | + | 10.0000i | 0.431532 | + | 0.431532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0000 | − | 11.0000i | 0.473804 | − | 0.473804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | + | 15.0000i | 0.644900 | + | 0.644900i | 0.951756 | − | 0.306856i | \(-0.0992769\pi\) |
−0.306856 | + | 0.951756i | \(0.599277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.00000 | + | 6.00000i | −0.257485 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 28.0000i | − | 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.00000i | −0.0426790 | − | 0.0426790i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.0000 | −1.78926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | − | 24.0000i | 1.02058 | − | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.0000 | −1.18640 | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||||
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.0000 | − | 33.0000i | 1.38587 | − | 1.38587i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.0000 | + | 25.0000i | 1.04622 | + | 1.04622i | 0.998879 | + | 0.0473385i | \(0.0150740\pi\) |
0.0473385 | + | 0.998879i | \(0.484926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.0000i | 1.50392i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00000 | + | 9.00000i | −0.374675 | + | 0.374675i | −0.869177 | − | 0.494502i | \(-0.835351\pi\) |
0.494502 | + | 0.869177i | \(0.335351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.0000 | − | 30.0000i | −1.24676 | − | 1.24676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | − | 6.00000i | 0.248922 | − | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | + | 8.00000i | 0.331326 | + | 0.331326i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.00000 | 0.0825488 | 0.0412744 | − | 0.999148i | \(-0.486858\pi\) | ||||
0.0412744 | + | 0.999148i | \(0.486858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | − | 6.00000i | 0.247226 | − | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 12.0000i | − | 0.493614i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.0000 | − | 17.0000i | −0.698106 | − | 0.698106i | 0.265896 | − | 0.964002i | \(-0.414332\pi\) |
−0.964002 | + | 0.265896i | \(0.914332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 20.0000i | − | 0.818546i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.0000i | − | 1.22577i | −0.790173 | − | 0.612883i | \(-0.790010\pi\) | ||
0.790173 | − | 0.612883i | \(-0.209990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0000i | 0.652654i | 0.945257 | + | 0.326327i | \(0.105811\pi\) | ||||
−0.945257 | + | 0.326327i | \(0.894189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0000 | − | 23.0000i | −0.933541 | − | 0.933541i | 0.0643840 | − | 0.997925i | \(-0.479492\pi\) |
−0.997925 | + | 0.0643840i | \(0.979492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 84.0000i | 3.40385i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.0000 | − | 14.0000i | 0.566379 | − | 0.566379i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.00000 | −0.323117 | −0.161558 | − | 0.986863i | \(-0.551652\pi\) | ||||
−0.161558 | + | 0.986863i | \(0.551652\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.0000 | + | 25.0000i | 1.00646 | + | 1.00646i | 0.999979 | + | 0.00648312i | \(0.00206366\pi\) |
0.00648312 | + | 0.999979i | \(0.497936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.00000 | + | 7.00000i | −0.281354 | + | 0.281354i | −0.833649 | − | 0.552295i | \(-0.813752\pi\) |
0.552295 | + | 0.833649i | \(0.313752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | − | 4.00000i | −0.160514 | − | 0.160514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | − | 18.0000i | 0.721155 | − | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | + | 6.00000i | 0.239236 | + | 0.239236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.0000 | + | 38.0000i | −1.51036 | + | 1.51036i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.0000 | 0.871672 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.0000 | + | 15.0000i | −0.589711 | + | 0.589711i | −0.937553 | − | 0.347842i | \(-0.886914\pi\) |
0.347842 | + | 0.937553i | \(0.386914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | − | 12.0000i | −0.470317 | − | 0.470317i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.00000i | 0.0782660i | 0.999234 | + | 0.0391330i | \(0.0124596\pi\) | ||||
−0.999234 | + | 0.0391330i | \(0.987540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | + | 3.00000i | −0.117041 | + | 0.117041i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0000 | + | 11.0000i | 0.428499 | + | 0.428499i | 0.888117 | − | 0.459618i | \(-0.152014\pi\) |
−0.459618 | + | 0.888117i | \(0.652014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0000 | + | 25.0000i | −0.972387 | + | 0.972387i | −0.999629 | − | 0.0272416i | \(-0.991328\pi\) |
0.0272416 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000 | + | 4.00000i | 0.155347 | + | 0.155347i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0000 | 0.542082 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0000 | − | 18.0000i | 0.695920 | − | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.00000i | − | 0.0772091i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.00000i | −0.0385472 | − | 0.0385472i | 0.687570 | − | 0.726118i | \(-0.258677\pi\) |
−0.726118 | + | 0.687570i | \(0.758677\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 42.0000i | − | 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.0000i | 2.53285i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000i | 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.00000i | − | 0.153056i | −0.997067 | − | 0.0765279i | \(-0.975617\pi\) | ||
0.997067 | − | 0.0765279i | \(-0.0243834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00000 | − | 2.00000i | −0.0763048 | − | 0.0763048i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0000i | 0.609551i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0000 | + | 21.0000i | −0.798878 | + | 0.798878i | −0.982919 | − | 0.184041i | \(-0.941082\pi\) |
0.184041 | + | 0.982919i | \(0.441082\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | −0.227921 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | + | 4.00000i | 0.151511 | + | 0.151511i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | + | 18.0000i | −0.680823 | + | 0.680823i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | − | 13.0000i | −0.491003 | − | 0.491003i | 0.417619 | − | 0.908622i | \(-0.362865\pi\) |
−0.908622 | + | 0.417619i | \(0.862865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | − | 18.0000i | 0.678883 | − | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 30.0000i | − | 1.12827i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00000 | + | 1.00000i | 0.0375558 | + | 0.0375558i | 0.725635 | − | 0.688080i | \(-0.241546\pi\) |
−0.688080 | + | 0.725635i | \(0.741546\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.00000 | + | 2.00000i | −0.0749006 | + | 0.0749006i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.0000 | 1.11726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.0000 | 1.04133 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00000 | + | 7.00000i | −0.259616 | + | 0.259616i | −0.824898 | − | 0.565282i | \(-0.808767\pi\) |
0.565282 | + | 0.824898i | \(0.308767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 4.00000i | −0.147945 | − | 0.147945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000i | 1.10808i | 0.832492 | + | 0.554038i | \(0.186914\pi\) | ||||
−0.832492 | + | 0.554038i | \(0.813086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.00000 | − | 4.00000i | 0.147342 | − | 0.147342i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0000 | − | 21.0000i | −0.772497 | − | 0.772497i | 0.206045 | − | 0.978543i | \(-0.433941\pi\) |
−0.978543 | + | 0.206045i | \(0.933941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | − | 12.0000i | 0.440831 | − | 0.440831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0000 | + | 31.0000i | 1.13728 | + | 1.13728i | 0.988936 | + | 0.148344i | \(0.0473942\pi\) |
0.148344 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.00000 | −0.0731762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | − | 18.0000i | 0.657706 | − | 0.657706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 50.0000i | − | 1.82453i | −0.409605 | − | 0.912263i | \(-0.634333\pi\) | ||
0.409605 | − | 0.912263i | \(-0.365667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0000 | + | 22.0000i | 0.801725 | + | 0.801725i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000i | 0.145191i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.0000i | 1.45000i | 0.688749 | + | 0.724999i | \(0.258160\pi\) | ||||
−0.688749 | + | 0.724999i | \(0.741840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0000i | 1.08607i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | − | 6.00000i | −0.216647 | − | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.00000i | − | 0.144244i | −0.997396 | − | 0.0721218i | \(-0.977023\pi\) | ||
0.997396 | − | 0.0721218i | \(-0.0229770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.0000 | − | 26.0000i | 0.936367 | − | 0.936367i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.0000 | −1.72644 | −0.863220 | − | 0.504828i | \(-0.831556\pi\) | ||||
−0.863220 | + | 0.504828i | \(0.831556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.0000 | − | 36.0000i | −1.29149 | − | 1.29149i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | − | 12.0000i | 0.429945 | − | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.0000 | + | 28.0000i | −1.00064 | + | 1.00064i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000i | 0.142585i | 0.997455 | + | 0.0712923i | \(0.0227123\pi\) | ||||
−0.997455 | + | 0.0712923i | \(0.977288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.0000 | − | 14.0000i | −0.498413 | − | 0.498413i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78.0000 | 2.77336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | − | 2.00000i | 0.0710221 | − | 0.0710221i |