Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(223,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.j (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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 671.1 | ||
Root | \(-1.40927 - 0.118126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.671 |
Dual form | 896.2.j.h.223.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.23450 | + | 2.23450i | −1.29009 | + | 1.29009i | −0.355364 | + | 0.934728i | \(0.615643\pi\) |
−0.934728 | + | 0.355364i | \(0.884357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.584038 | + | 0.584038i | −0.261190 | + | 0.261190i | −0.825537 | − | 0.564347i | \(-0.809128\pi\) |
0.564347 | + | 0.825537i | \(0.309128\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.82596 | + | 1.91465i | −0.690146 | + | 0.723670i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 6.98602i | − | 2.32867i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 2.00000i | 0.603023 | − | 0.603023i | −0.338091 | − | 0.941113i | \(-0.609781\pi\) |
0.941113 | + | 0.338091i | \(0.109781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.91203 | − | 2.91203i | −0.807651 | − | 0.807651i | 0.176627 | − | 0.984278i | \(-0.443481\pi\) |
−0.984278 | + | 0.176627i | \(0.943481\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.61007i | − | 0.673918i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.66123i | − | 0.645442i | −0.946494 | − | 0.322721i | \(-0.895402\pi\) | ||
0.946494 | − | 0.322721i | \(-0.104598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.319854 | + | 0.319854i | −0.0733795 | + | 0.0733795i | −0.742844 | − | 0.669465i | \(-0.766524\pi\) |
0.669465 | + | 0.742844i | \(0.266524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.198191 | − | 8.35840i | −0.0432489 | − | 1.82395i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.27830 | −0.683572 | −0.341786 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341786 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.31780i | 0.863560i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.90678 | + | 8.90678i | 1.71411 | + | 1.71411i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.04184 | − | 2.04184i | 0.379160 | − | 0.379160i | −0.491639 | − | 0.870799i | \(-0.663602\pi\) |
0.870799 | + | 0.491639i | \(0.163602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.52312 | 0.453166 | 0.226583 | − | 0.973992i | \(-0.427244\pi\) | ||||
0.226583 | + | 0.973992i | \(0.427244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.93802i | 1.55591i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0518018 | − | 2.18466i | −0.00875611 | − | 0.369275i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.70773 | − | 1.70773i | −0.280748 | − | 0.280748i | 0.552659 | − | 0.833407i | \(-0.313613\pi\) |
−0.833407 | + | 0.552659i | \(0.813613\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.0139 | 2.08389 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.9895 | 1.87245 | 0.936224 | − | 0.351405i | \(-0.114296\pi\) | ||||
0.936224 | + | 0.351405i | \(0.114296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.27830 | − | 3.27830i | 0.499936 | − | 0.499936i | −0.411482 | − | 0.911418i | \(-0.634989\pi\) |
0.911418 | + | 0.411482i | \(0.134989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.08010 | + | 4.08010i | 0.608226 | + | 0.608226i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.96799 | −1.45398 | −0.726991 | − | 0.686647i | \(-0.759082\pi\) | ||||
−0.726991 | + | 0.686647i | \(0.759082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.331777 | − | 6.99213i | −0.0473967 | − | 0.998876i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.94652 | + | 5.94652i | 0.832679 | + | 0.832679i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.37595 | + | 2.37595i | 0.326362 | + | 0.326362i | 0.851201 | − | 0.524840i | \(-0.175875\pi\) |
−0.524840 | + | 0.851201i | \(0.675875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.33615i | 0.315007i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.42943i | − | 0.189332i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.14916 | − | 4.14916i | −0.540174 | − | 0.540174i | 0.383406 | − | 0.923580i | \(-0.374751\pi\) |
−0.923580 | + | 0.383406i | \(0.874751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.52468 | + | 4.52468i | 0.579326 | + | 0.579326i | 0.934717 | − | 0.355392i | \(-0.115653\pi\) |
−0.355392 | + | 0.934717i | \(0.615653\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.3758 | + | 12.7562i | 1.68519 | + | 1.60713i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.40147 | 0.421901 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.37361 | + | 4.37361i | 0.534322 | + | 0.534322i | 0.921856 | − | 0.387534i | \(-0.126673\pi\) |
−0.387534 | + | 0.921856i | \(0.626673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.32537 | − | 7.32537i | 0.881871 | − | 0.881871i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.14114 | 0.610141 | 0.305071 | − | 0.952330i | \(-0.401320\pi\) | ||||
0.305071 | + | 0.952330i | \(0.401320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.99213 | −0.818367 | −0.409184 | − | 0.912452i | \(-0.634186\pi\) | ||||
−0.409184 | + | 0.912452i | \(0.634186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.64814 | − | 9.64814i | −1.11407 | − | 1.11407i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.177392 | + | 7.48121i | 0.0202157 | + | 0.852563i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.2248i | − | 1.26289i | −0.775420 | − | 0.631445i | \(-0.782462\pi\) | ||
0.775420 | − | 0.631445i | \(-0.217538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −18.8464 | −2.09405 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.39734 | − | 5.39734i | 0.592435 | − | 0.592435i | −0.345854 | − | 0.938288i | \(-0.612411\pi\) |
0.938288 | + | 0.345854i | \(0.112411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.55426 | + | 1.55426i | 0.168583 | + | 0.168583i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.12499i | 0.978301i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.05674 | −0.112014 | −0.0560071 | − | 0.998430i | \(-0.517837\pi\) | ||||
−0.0560071 | + | 0.998430i | \(0.517837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8927 | − | 0.258285i | 1.14187 | − | 0.0270756i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.63793 | + | 5.63793i | −0.584626 | + | 0.584626i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.373614i | − | 0.0383319i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2689i | − | 1.34726i | −0.739071 | − | 0.673628i | \(-0.764735\pi\) | ||
0.739071 | − | 0.673628i | \(-0.235265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.9720 | − | 13.9720i | −1.40424 | − | 1.40424i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.250803 | + | 0.250803i | −0.0249558 | + | 0.0249558i | −0.719475 | − | 0.694519i | \(-0.755617\pi\) |
0.694519 | + | 0.719475i | \(0.255617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.5179i | − | 1.23342i | −0.787189 | − | 0.616712i | \(-0.788464\pi\) | ||
0.787189 | − | 0.616712i | \(-0.211536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.99738 | + | 4.76588i | 0.487694 | + | 0.465102i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.88837 | − | 3.88837i | 0.375903 | − | 0.375903i | −0.493719 | − | 0.869622i | \(-0.664363\pi\) |
0.869622 | + | 0.493719i | \(0.164363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.26432 | − | 4.26432i | 0.408448 | − | 0.408448i | −0.472749 | − | 0.881197i | \(-0.656738\pi\) |
0.881197 | + | 0.472749i | \(0.156738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.63184 | 0.724382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.79072 | 0.732889 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.91465 | − | 1.91465i | 0.178542 | − | 0.178542i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.3435 | + | 20.3435i | −1.88076 | + | 1.88076i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.09532 | + | 4.85928i | 0.467087 | + | 0.445449i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.7906 | + | 26.7906i | −2.41563 | + | 2.41563i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.44195 | − | 5.44195i | −0.486743 | − | 0.486743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.02552i | − | 0.712150i | −0.934457 | − | 0.356075i | \(-0.884115\pi\) | ||
0.934457 | − | 0.356075i | \(-0.115885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.6507i | 1.28993i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.22664 | + | 9.22664i | −0.806135 | + | 0.806135i | −0.984047 | − | 0.177911i | \(-0.943066\pi\) |
0.177911 | + | 0.984047i | \(0.443066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0283697 | − | 1.19645i | −0.00245997 | − | 0.103745i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.4038 | −0.895417 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.02951i | − | 0.771443i | −0.922615 | − | 0.385722i | \(-0.873953\pi\) | ||
0.922615 | − | 0.385722i | \(-0.126047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33613 | − | 4.33613i | −0.367785 | − | 0.367785i | 0.498884 | − | 0.866669i | \(-0.333744\pi\) |
−0.866669 | + | 0.498884i | \(0.833744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.2735 | − | 22.2735i | 1.87577 | − | 1.87577i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.6481 | −0.974064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.38502i | 0.198065i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.3653 | + | 14.8826i | 1.34979 | + | 1.22750i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2620 | + | 13.2620i | 1.08646 | + | 1.08646i | 0.995890 | + | 0.0905743i | \(0.0288703\pi\) |
0.0905743 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7512 | −0.956300 | −0.478150 | − | 0.878278i | \(-0.658693\pi\) | ||||
−0.478150 | + | 0.878278i | \(0.658693\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.5914 | −1.50302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.47360 | + | 1.47360i | −0.118362 | + | 0.118362i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.90941 | − | 7.90941i | −0.631239 | − | 0.631239i | 0.317140 | − | 0.948379i | \(-0.397278\pi\) |
−0.948379 | + | 0.317140i | \(0.897278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6181 | −0.842073 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.98602 | − | 6.27679i | 0.471765 | − | 0.494681i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.65191 | − | 9.65191i | −0.755996 | − | 0.755996i | 0.219595 | − | 0.975591i | \(-0.429526\pi\) |
−0.975591 | + | 0.219595i | \(0.929526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.22015 | − | 5.22015i | −0.406388 | − | 0.406388i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.84557i | 0.607109i | 0.952814 | + | 0.303554i | \(0.0981734\pi\) | ||||
−0.952814 | + | 0.303554i | \(0.901827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.95982i | 0.304601i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.23450 | + | 2.23450i | 0.170877 | + | 0.170877i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.19669 | − | 2.19669i | −0.167011 | − | 0.167011i | 0.618653 | − | 0.785664i | \(-0.287679\pi\) |
−0.785664 | + | 0.618653i | \(0.787679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.26708 | − | 7.88411i | −0.624932 | − | 0.595982i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.5426 | 1.39375 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0302 | − | 10.0302i | −0.749692 | − | 0.749692i | 0.224729 | − | 0.974421i | \(-0.427850\pi\) |
−0.974421 | + | 0.224729i | \(0.927850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.03153 | − | 3.03153i | 0.225332 | − | 0.225332i | −0.585407 | − | 0.810739i | \(-0.699065\pi\) |
0.810739 | + | 0.585407i | \(0.199065\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.2208 | −1.49477 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.99475 | 0.146657 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.32245 | − | 5.32245i | −0.389216 | − | 0.389216i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −33.3168 | + | 0.789996i | −2.42344 | + | 0.0574637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2085i | 1.02809i | 0.857763 | + | 0.514046i | \(0.171854\pi\) | ||||
−0.857763 | + | 0.514046i | \(0.828146\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.2945 | −1.38885 | −0.694425 | − | 0.719565i | \(-0.744341\pi\) | ||||
−0.694425 | + | 0.719565i | \(0.744341\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.60061 | + | 7.60061i | −0.544291 | + | 0.544291i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.454953 | − | 0.454953i | −0.0324140 | − | 0.0324140i | 0.690714 | − | 0.723128i | \(-0.257296\pi\) |
−0.723128 | + | 0.690714i | \(0.757296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.6024i | − | 1.74402i | −0.489490 | − | 0.872009i | \(-0.662817\pi\) | ||
0.489490 | − | 0.872009i | \(-0.337183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5457 | −1.37865 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.181103 | + | 7.63771i | 0.0127109 | + | 0.536062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00234 | + | 7.00234i | −0.489064 | + | 0.489064i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.9022i | 1.59182i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.27941i | 0.0884990i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1092 | − | 10.1092i | −0.695946 | − | 0.695946i | 0.267588 | − | 0.963534i | \(-0.413774\pi\) |
−0.963534 | + | 0.267588i | \(0.913774\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4879 | + | 11.4879i | −0.787138 | + | 0.787138i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.82930i | 0.261156i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.60711 | + | 4.83090i | −0.312751 | + | 0.327943i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.6240 | − | 15.6240i | 1.05577 | − | 1.05577i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.74956 | + | 7.74956i | −0.521292 | + | 0.521292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1035 | 1.01140 | 0.505702 | − | 0.862708i | \(-0.331234\pi\) | ||||
0.505702 | + | 0.862708i | \(0.331234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 30.1642 | 2.01095 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.12502 | − | 7.12502i | 0.472904 | − | 0.472904i | −0.429949 | − | 0.902853i | \(-0.641469\pi\) |
0.902853 | + | 0.429949i | \(0.141469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7933 | − | 18.7933i | 1.24190 | − | 1.24190i | 0.282684 | − | 0.959213i | \(-0.408775\pi\) |
0.959213 | − | 0.282684i | \(-0.0912247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.1132 | − | 16.3204i | −1.12596 | − | 1.07380i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.47759i | 0.293337i | 0.989186 | + | 0.146668i | \(0.0468550\pi\) | ||||
−0.989186 | + | 0.146668i | \(0.953145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.82169 | − | 5.82169i | 0.379765 | − | 0.379765i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.0819 | + | 25.0819i | 1.62924 | + | 1.62924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.13871i | − | 0.591134i | −0.955322 | − | 0.295567i | \(-0.904491\pi\) | ||
0.955322 | − | 0.295567i | \(-0.0955086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.66969i | − | 0.622879i | −0.950266 | − | 0.311440i | \(-0.899189\pi\) | ||
0.950266 | − | 0.311440i | \(-0.100811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3921 | − | 15.3921i | 0.987403 | − | 0.987403i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.27744 | + | 3.88990i | 0.273276 | + | 0.248517i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.86285 | 0.118530 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.1207i | 1.52859i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9231 | − | 10.9231i | −0.689459 | − | 0.689459i | 0.272653 | − | 0.962112i | \(-0.412099\pi\) |
−0.962112 | + | 0.272653i | \(0.912099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.55659 | + | 6.55659i | −0.412209 | + | 0.412209i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.94599 | −0.434975 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.5888i | 1.47143i | 0.677293 | + | 0.735713i | \(0.263153\pi\) | ||||
−0.677293 | + | 0.735713i | \(0.736847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.38793 | − | 0.151468i | 0.396927 | − | 0.00941178i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.2643 | − | 14.2643i | −0.882939 | − | 0.882939i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.3595 | 1.56374 | 0.781868 | − | 0.623444i | \(-0.214267\pi\) | ||||
0.781868 | + | 0.623444i | \(0.214267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.77529 | −0.170485 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.36129 | − | 2.36129i | 0.144508 | − | 0.144508i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.74979 | − | 5.74979i | −0.350571 | − | 0.350571i | 0.509751 | − | 0.860322i | \(-0.329737\pi\) |
−0.860322 | + | 0.509751i | \(0.829737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7568 | 1.01790 | 0.508952 | − | 0.860795i | \(-0.330033\pi\) | ||||
0.508952 | + | 0.860795i | \(0.330033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −23.7628 | + | 24.9170i | −1.43819 | + | 1.50805i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.63560 | + | 8.63560i | 0.520746 | + | 0.520746i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.45729 | + | 5.45729i | 0.327897 | + | 0.327897i | 0.851786 | − | 0.523890i | \(-0.175520\pi\) |
−0.523890 | + | 0.851786i | \(0.675520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 17.6266i | − | 1.05528i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.11163i | − | 0.364589i | −0.983244 | − | 0.182295i | \(-0.941648\pi\) | ||
0.983244 | − | 0.182295i | \(-0.0583525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.03383 | + | 5.03383i | 0.299230 | + | 0.299230i | 0.840712 | − | 0.541482i | \(-0.182137\pi\) |
−0.541482 | + | 0.840712i | \(0.682137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.834841 | + | 0.834841i | 0.0494517 | + | 0.0494517i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.8923 | + | 22.9557i | −1.29226 | + | 1.35503i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.91788 | 0.583405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.6495 | + | 29.6495i | 1.73808 | + | 1.73808i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.6200 | + | 19.6200i | −1.14621 | + | 1.14621i | −0.158921 | + | 0.987291i | \(0.550801\pi\) |
−0.987291 | + | 0.158921i | \(0.949199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.84653 | 0.282176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.6271 | 2.06730 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.54649 | + | 9.54649i | 0.552088 | + | 0.552088i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.290772 | + | 12.2628i | 0.0167598 | + | 0.706817i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.12084i | − | 0.0643906i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.28517 | −0.302628 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.08795 | − | 3.08795i | 0.176238 | − | 0.176238i | −0.613475 | − | 0.789714i | \(-0.710229\pi\) |
0.789714 | + | 0.613475i | \(0.210229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.9713 | + | 27.9713i | 1.59123 | + | 1.59123i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.2122i | − | 1.14613i | −0.819511 | − | 0.573064i | \(-0.805755\pi\) | ||
0.819511 | − | 0.573064i | \(-0.194245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2311 | 0.860915 | 0.430457 | − | 0.902611i | \(-0.358352\pi\) | ||||
0.430457 | + | 0.902611i | \(0.358352\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.2621 | + | 0.361889i | −0.859920 | + | 0.0203901i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.3480 | − | 20.3480i | 1.14286 | − | 1.14286i | 0.154932 | − | 0.987925i | \(-0.450484\pi\) |
0.987925 | − | 0.154932i | \(-0.0495158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.16735i | − | 0.457284i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3772i | 0.969898i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.851203 | + | 0.851203i | 0.0473622 | + | 0.0473622i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5736 | − | 12.5736i | 0.697455 | − | 0.697455i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.0573i | 1.05387i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.2011 | − | 19.0852i | 1.00346 | − | 1.05220i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8186 | + | 20.8186i | −1.14429 | + | 1.14429i | −0.156636 | + | 0.987656i | \(0.550065\pi\) |
−0.987656 | + | 0.156636i | \(0.949935\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.9302 | + | 11.9302i | −0.653771 | + | 0.653771i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.10872 | −0.279119 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7954 | −0.751483 | −0.375741 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375741 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.4084 | + | 17.4084i | −0.945494 | + | 0.945494i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.04625 | − | 5.04625i | 0.273270 | − | 0.273270i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9933 | + | 12.1321i | 0.755567 | + | 0.655071i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.55659i | 0.460671i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.67743 | − | 3.67743i | 0.197415 | − | 0.197415i | −0.601476 | − | 0.798891i | \(-0.705420\pi\) |
0.798891 | + | 0.601476i | \(0.205420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8960 | − | 17.8960i | −0.957951 | − | 0.957951i | 0.0412000 | − | 0.999151i | \(-0.486882\pi\) |
−0.999151 | + | 0.0412000i | \(0.986882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 51.8736i | − | 2.76881i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.37978i | − | 0.233112i | −0.993184 | − | 0.116556i | \(-0.962815\pi\) | ||
0.993184 | − | 0.116556i | \(-0.0371854\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00262 | + | 3.00262i | −0.159363 | + | 0.159363i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.2436 | + | 0.527432i | −1.17726 | + | 0.0279147i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.3293 | −0.809052 | −0.404526 | − | 0.914527i | \(-0.632563\pi\) | ||||
−0.404526 | + | 0.914527i | \(0.632563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7954i | 0.989231i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.70351 | − | 6.70351i | −0.351843 | − | 0.351843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.08367 | − | 4.08367i | 0.213749 | − | 0.213749i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3152 | 1.37364 | 0.686821 | − | 0.726827i | \(-0.259006\pi\) | ||||
0.686821 | + | 0.726827i | \(0.259006\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 83.7590i | − | 4.36032i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.88749 | + | 0.210737i | −0.461415 | + | 0.0109409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6821 | − | 24.6821i | −1.27799 | − | 1.27799i | −0.941790 | − | 0.336200i | \(-0.890858\pi\) |
−0.336200 | − | 0.941790i | \(-0.609142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.3201 | 1.25589 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.8918 | −0.612458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8512 | − | 14.8512i | 0.762855 | − | 0.762855i | −0.213982 | − | 0.976838i | \(-0.568644\pi\) |
0.976838 | + | 0.213982i | \(0.0686435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.9331 | + | 17.9331i | 0.918739 | + | 0.918739i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4454 | 1.30020 | 0.650100 | − | 0.759849i | \(-0.274727\pi\) | ||||
0.650100 | + | 0.759849i | \(0.274727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.47292 | − | 4.26571i | −0.227961 | − | 0.217401i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.9022 | − | 22.9022i | −1.16419 | − | 1.16419i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.848867 | − | 0.848867i | −0.0430393 | − | 0.0430393i | 0.685260 | − | 0.728299i | \(-0.259689\pi\) |
−0.728299 | + | 0.685260i | \(0.759689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.72428i | 0.441206i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 41.2339i | − | 2.07998i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.55572 | + | 6.55572i | 0.329854 | + | 0.329854i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4575 | − | 15.4575i | −0.775787 | − | 0.775787i | 0.203324 | − | 0.979111i | \(-0.434825\pi\) |
−0.979111 | + | 0.203324i | \(0.934825\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.73686 | + | 2.61007i | 0.137014 | + | 0.130667i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.7348 | −1.08538 | −0.542692 | − | 0.839932i | \(-0.682595\pi\) | ||||
−0.542692 | + | 0.839932i | \(0.682595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.34741 | − | 7.34741i | −0.366000 | − | 0.366000i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0070 | − | 11.0070i | 0.546944 | − | 0.546944i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.83090 | −0.338595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.0142 | −1.33577 | −0.667883 | − | 0.744266i | \(-0.732799\pi\) | ||||
−0.667883 | + | 0.744266i | \(0.732799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1765 | + | 20.1765i | 0.995233 | + | 0.995233i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5204 | − | 0.368013i | 0.763707 | − | 0.0181087i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.30450i | 0.309476i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3782 | 0.948954 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.31859 | − | 1.31859i | 0.0644176 | − | 0.0644176i | −0.674164 | − | 0.738582i | \(-0.735496\pi\) |
0.738582 | + | 0.674164i | \(0.235496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.73490 | + | 9.73490i | 0.474450 | + | 0.474450i | 0.903351 | − | 0.428901i | \(-0.141099\pi\) |
−0.428901 | + | 0.903351i | \(0.641099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 69.6366i | 3.38585i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.4906 | 0.557378 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9250 | + | 0.401321i | −0.819060 | + | 0.0194213i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.0278 | − | 26.0278i | 1.25663 | − | 1.25663i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5262i | 1.08505i | 0.840040 | + | 0.542525i | \(0.182531\pi\) | ||||
−0.840040 | + | 0.542525i | \(0.817469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.16594i | 0.344373i | 0.985064 | + | 0.172187i | \(0.0550832\pi\) | ||||
−0.985064 | + | 0.172187i | \(0.944917\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.32934 | − | 5.32934i | −0.255522 | − | 0.255522i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.04858 | − | 1.04858i | 0.0501601 | − | 0.0501601i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4533i | 0.689820i | 0.938636 | + | 0.344910i | \(0.112091\pi\) | ||||
−0.938636 | + | 0.344910i | \(0.887909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −48.8472 | + | 2.31780i | −2.32606 | + | 0.110371i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5148 | − | 13.5148i | 0.642105 | − | 0.642105i | −0.308967 | − | 0.951073i | \(-0.599983\pi\) |
0.951073 | + | 0.308967i | \(0.0999834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.617176 | − | 0.617176i | 0.0292570 | − | 0.0292570i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −59.2679 | −2.80328 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2712 | 0.626306 | 0.313153 | − | 0.949703i | \(-0.398615\pi\) | ||||
0.313153 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9790 | − | 23.9790i | 1.12913 | − | 1.12913i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.2581 | − | 26.2581i | 1.23372 | − | 1.23372i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.21094 | + | 6.51263i | −0.291173 | + | 0.305317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 35.0713i | − | 1.64056i | −0.571959 | − | 0.820282i | \(-0.693817\pi\) | ||
0.571959 | − | 0.820282i | \(-0.306183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.7030 | − | 23.7030i | 1.10636 | − | 1.10636i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3005 | + | 16.3005i | 0.759188 | + | 0.759188i | 0.976175 | − | 0.216987i | \(-0.0696228\pi\) |
−0.216987 | + | 0.976175i | \(0.569623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.09532i | − | 0.0509037i | −0.999676 | − | 0.0254519i | \(-0.991898\pi\) | ||
0.999676 | − | 0.0254519i | \(-0.00810245\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 6.58554i | − | 0.305397i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5205 | + | 17.5205i | −0.810751 | + | 0.810751i | −0.984746 | − | 0.173995i | \(-0.944332\pi\) |
0.173995 | + | 0.984746i | \(0.444332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3600 | + | 0.387922i | −0.755433 | + | 0.0179126i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.3472 | 1.62871 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.1132i | − | 0.602945i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.38106 | − | 1.38106i | −0.0633675 | − | 0.0633675i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5984 | − | 16.5984i | 0.759990 | − | 0.759990i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.78311 | 0.355619 | 0.177810 | − | 0.984065i | \(-0.443099\pi\) | ||||
0.177810 | + | 0.984065i | \(0.443099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.94589i | 0.453493i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.649730 | + | 27.4013i | 0.0295638 | + | 1.24680i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.74956 | + | 7.74956i | 0.351890 | + | 0.351890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.6953 | −1.25499 | −0.627497 | − | 0.778619i | \(-0.715921\pi\) | ||||
−0.627497 | + | 0.778619i | \(0.715921\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 43.1345 | 1.95061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.2667 | + | 20.2667i | −0.914621 | + | 0.914621i | −0.996631 | − | 0.0820102i | \(-0.973866\pi\) |
0.0820102 | + | 0.996631i | \(0.473866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.43379 | − | 5.43379i | −0.244726 | − | 0.244726i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.3204 | 0.733548 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.38749 | + | 9.84349i | −0.421087 | + | 0.441541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.9852 | − | 19.9852i | −0.894662 | − | 0.894662i | 0.100295 | − | 0.994958i | \(-0.468021\pi\) |
−0.994958 | + | 0.100295i | \(0.968021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.5310 | − | 17.5310i | −0.783226 | − | 0.783226i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.04877i | 0.135938i | 0.997687 | + | 0.0679689i | \(0.0216519\pi\) | ||||
−0.997687 | + | 0.0679689i | \(0.978348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.292957i | − | 0.0130364i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.84823 | − | 8.84823i | −0.392964 | − | 0.392964i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.4653 | + | 16.4653i | 0.729813 | + | 0.729813i | 0.970582 | − | 0.240770i | \(-0.0773999\pi\) |
−0.240770 | + | 0.970582i | \(0.577400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7673 | − | 13.3875i | 0.564793 | − | 0.592228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.69773 | −0.251561 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.31092 | + | 7.31092i | 0.322158 | + | 0.322158i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.9360 | + | 19.9360i | −0.876784 | + | 0.876784i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.81702 | 0.430919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.8583 | −1.52717 | −0.763584 | − | 0.645708i | \(-0.776562\pi\) | ||||
−0.763584 | + | 0.645708i | \(0.776562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9307 | + | 31.9307i | 1.39623 | + | 1.39623i | 0.810515 | + | 0.585718i | \(0.199187\pi\) |
0.585718 | + | 0.810515i | \(0.300813\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 36.0899 | − | 0.855751i | 1.57509 | − | 0.0373480i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.71460i | − | 0.292493i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.2528 | −0.532729 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.9861 | + | 28.9861i | −1.25789 | + | 1.25789i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.9138 | − | 34.9138i | −1.51228 | − | 1.51228i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.54191i | 0.196364i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.8250 | 1.93434 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.6478 | − | 13.3207i | −0.630926 | − | 0.573764i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.5705 | + | 28.5705i | −1.22834 | + | 1.22834i | −0.263749 | + | 0.964591i | \(0.584959\pi\) |
−0.964591 | + | 0.263749i | \(0.915041\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5479i | 0.581398i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.98105i | 0.213365i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.86041 | + | 7.86041i | 0.336087 | + | 0.336087i | 0.854892 | − | 0.518805i | \(-0.173623\pi\) |
−0.518805 | + | 0.854892i | \(0.673623\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.6095 | − | 31.6095i | 1.34906 | − | 1.34906i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.30618i | 0.0556451i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.4916 | + | 20.4960i | 0.913916 | + | 0.871579i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.45729 | + | 4.45729i | −0.189201 | + | 0.189201i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.60077 | + | 5.60077i | −0.237312 | + | 0.237312i | −0.815736 | − | 0.578424i | \(-0.803668\pi\) |
0.578424 | + | 0.815736i | \(0.303668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.0930 | −0.807547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.7861 | 1.00425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.66644 | − | 2.66644i | 0.112377 | − | 0.112377i | −0.648682 | − | 0.761059i | \(-0.724680\pi\) |
0.761059 | + | 0.648682i | \(0.224680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.55008 | + | 4.55008i | −0.191423 | + | 0.191423i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.4127 | − | 36.0843i | 1.44520 | − | 1.51540i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3704i | 1.18935i | 0.803967 | + | 0.594675i | \(0.202719\pi\) | ||||
−0.803967 | + | 0.594675i | \(0.797281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.132484 | + | 0.132484i | −0.00554428 | + | 0.00554428i | −0.709873 | − | 0.704329i | \(-0.751248\pi\) |
0.704329 | + | 0.709873i | \(0.251248\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.7490 | − | 31.7490i | −1.32633 | − | 1.32633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.1550i | − | 0.590305i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.612944i | 0.0255172i | 0.999919 | + | 0.0127586i | \(0.00406130\pi\) | ||||
−0.999919 | + | 0.0127586i | \(0.995939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.1137 | − | 43.1137i | 1.79174 | − | 1.79174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.478722 | + | 20.1893i | 0.0198607 | + | 0.837594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.50380 | 0.393607 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 23.7628i | − | 0.982469i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1197 | + | 21.1197i | 0.871704 | + | 0.871704i | 0.992658 | − | 0.120954i | \(-0.0385954\pi\) |
−0.120954 | + | 0.992658i | \(0.538595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.807030 | + | 0.807030i | −0.0332531 | + | 0.0332531i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.03319 | 0.0836342 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.50150i | − | 0.143789i | −0.997412 | − | 0.0718947i | \(-0.977095\pi\) | ||
0.997412 | − | 0.0718947i | \(-0.0229046\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.81387 | + | 0.137856i | −0.238345 | + | 0.00565156i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 54.9742 | + | 54.9742i | 2.24994 | + | 2.24994i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.3759 | −0.587381 | −0.293691 | − | 0.955901i | \(-0.594884\pi\) | ||||
−0.293691 | + | 0.955901i | \(0.594884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.26571 | −0.174002 | −0.0870010 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0870010 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.5542 | − | 30.5542i | 1.24426 | − | 1.24426i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.75212 | − | 1.75212i | −0.0712336 | − | 0.0712336i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0435 | 0.529420 | 0.264710 | − | 0.964328i | \(-0.414724\pi\) | ||||
0.264710 | + | 0.964328i | \(0.414724\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.4712 | − | 16.6618i | −0.707967 | − | 0.675171i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.0271 | + | 29.0271i | 1.17431 | + | 1.17431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.3177 | − | 29.3177i | −1.18413 | − | 1.18413i | −0.978664 | − | 0.205467i | \(-0.934129\pi\) |
−0.205467 | − | 0.978664i | \(-0.565871\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 31.2935i | − | 1.26188i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2992i | 0.776956i | 0.921458 | + | 0.388478i | \(0.126999\pi\) | ||||
−0.921458 | + | 0.388478i | \(0.873001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.58436 | + | 1.58436i | 0.0636809 | + | 0.0636809i | 0.738230 | − | 0.674549i | \(-0.235662\pi\) |
−0.674549 | + | 0.738230i | \(0.735662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.1991 | − | 29.1991i | −1.17172 | − | 1.17172i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.92956 | − | 2.02329i | 0.0773061 | − | 0.0810613i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.2324 | −0.609295 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.85886 | − | 2.85886i | −0.114172 | − | 0.114172i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.54464 | + | 4.54464i | −0.181207 | + | 0.181207i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7915 | −0.549031 | −0.274515 | − | 0.961583i | \(-0.588517\pi\) | ||||
−0.274515 | + | 0.961583i | \(0.588517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.1781 | 1.79567 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.68721 | + | 4.68721i | 0.186006 | + | 0.186006i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.3951 | + | 21.3274i | −0.768464 | + | 0.845024i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 35.9161i | − | 1.42082i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.82159 | 0.269437 | 0.134718 | − | 0.990884i | \(-0.456987\pi\) | ||||
0.134718 | + | 0.990884i | \(0.456987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9875 | − | 32.9875i | 1.30090 | − | 1.30090i | 0.373112 | − | 0.927786i | \(-0.378291\pi\) |
0.927786 | − | 0.373112i | \(-0.121709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.55659 | − | 8.55659i | −0.336916 | − | 0.336916i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 20.4616i | − | 0.804430i | −0.915545 | − | 0.402215i | \(-0.868240\pi\) | ||
0.915545 | − | 0.402215i | \(-0.131760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.5966 | −0.651474 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.500062 | − | 21.0893i | −0.0195990 | − | 0.826554i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.37361 | + | 3.37361i | −0.132020 | + | 0.132020i | −0.770029 | − | 0.638009i | \(-0.779758\pi\) |
0.638009 | + | 0.770029i | \(0.279758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10.7774i | − | 0.421109i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 48.8472i | 1.90571i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8983 | + | 17.8983i | 0.697217 | + | 0.697217i | 0.963809 | − | 0.266592i | \(-0.0858977\pi\) |
−0.266592 | + | 0.963809i | \(0.585898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3379 | + | 15.3379i | −0.596577 | + | 0.596577i | −0.939400 | − | 0.342823i | \(-0.888617\pi\) |
0.342823 | + | 0.939400i | \(0.388617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 34.6329i | − | 1.34503i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.715340 | + | 0.682202i | 0.0277397 | + | 0.0264546i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.69375 | + | 6.69375i | −0.259183 | + | 0.259183i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.7488 | + | 33.7488i | −1.30480 | + | 1.30480i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0987 | 0.698693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.74723 | −0.260086 | −0.130043 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130043 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −38.4577 | + | 38.4577i | −1.48024 | + | 1.48024i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.4470 | − | 27.4470i | 1.05487 | − | 1.05487i | 0.0564681 | − | 0.998404i | \(-0.482016\pi\) |
0.998404 | − | 0.0564681i | \(-0.0179839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.4054 | + | 24.2285i | 0.974968 | + | 0.929803i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.8418i | 1.22018i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.1085 | + | 17.1085i | −0.654639 | + | 0.654639i | −0.954107 | − | 0.299467i | \(-0.903191\pi\) |
0.299467 | + | 0.954107i | \(0.403191\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.27358 | + | 5.27358i | 0.201493 | + | 0.201493i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 83.9875i | 3.20432i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.8377i | − | 0.527173i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0833 | + | 11.0833i | −0.421628 | + | 0.421628i | −0.885764 | − | 0.464136i | \(-0.846365\pi\) |
0.464136 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 52.2639 | − | 1.23926i | 1.98534 | − | 0.0470757i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.06493 | 0.192124 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 31.9068i | − | 1.20856i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0052 | − | 10.0052i | −0.378431 | − | 0.378431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.821691 | + | 0.821691i | −0.0310348 | + | 0.0310348i | −0.722454 | − | 0.691419i | \(-0.756986\pi\) |
0.691419 | + | 0.722454i | \(0.256986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09244 | 0.0412023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.0172i | 0.979864i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0222452 | − | 0.938155i | −0.000836617 | − | 0.0352830i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.61763 | − | 8.61763i | −0.323642 | − | 0.323642i | 0.526521 | − | 0.850162i | \(-0.323496\pi\) |
−0.850162 | + | 0.526521i | \(0.823496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −78.4168 | −2.94086 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.27155 | −0.309772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.80294 | − | 6.80294i | 0.254416 | − | 0.254416i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.4205 | + | 20.4205i | 0.762617 | + | 0.762617i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8866 | −0.853525 | −0.426763 | − | 0.904364i | \(-0.640346\pi\) | ||||
−0.426763 | + | 0.904364i | \(0.640346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9674 | + | 22.8571i | 0.892592 | + | 0.851242i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.6070 | + | 21.6070i | 0.803571 | + | 0.803571i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.81624 | + | 8.81624i | 0.327427 | + | 0.327427i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.6428i | − | 0.468896i | −0.972129 | − | 0.234448i | \(-0.924672\pi\) | ||
0.972129 | − | 0.234448i | \(-0.0753283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.2481i | 0.453633i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.72428 | − | 8.72428i | −0.322679 | − | 0.322679i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9017 | + | 16.9017i | 0.624280 | + | 0.624280i | 0.946623 | − | 0.322343i | \(-0.104471\pi\) |
−0.322343 | + | 0.946623i | \(0.604471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.2500 | + | 0.865961i | −0.673161 | + | 0.0319415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4945 | 0.644417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7651 | + | 14.7651i | 0.543143 | + | 0.543143i | 0.924449 | − | 0.381306i | \(-0.124526\pi\) |
−0.381306 | + | 0.924449i | \(0.624526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.16254 | + | 4.16254i | −0.152915 | + | 0.152915i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6332 | −0.390093 | −0.195046 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195046 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.4910 | −0.567547 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.7059 | − | 37.7059i | −1.37959 | − | 1.37959i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.344883 | + | 14.5449i | 0.0126017 | + | 0.531458i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9634i | 0.400060i | 0.979790 | + | 0.200030i | \(0.0641039\pi\) | ||||
−0.979790 | + | 0.200030i | \(0.935896\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.8154 | 1.77893 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.86316 | − | 6.86316i | 0.249776 | − | 0.249776i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8153 | + | 21.8153i | 0.792889 | + | 0.792889i | 0.981963 | − | 0.189073i | \(-0.0605484\pi\) |
−0.189073 | + | 0.981963i | \(0.560548\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 29.3015i | − | 1.06358i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.51842 | 0.345042 | 0.172521 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172521 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.378228 | + | 15.9511i | 0.0136928 | + | 0.577470i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.8581 | − | 10.8581i | 0.392575 | − | 0.392575i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.1649i | 0.872545i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36.0771i | − | 1.30098i | −0.759517 | − | 0.650488i | \(-0.774565\pi\) | ||
0.759517 | − | 0.650488i | \(-0.225435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.7092 | − | 52.7092i | −1.89827 | − | 1.89827i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.1103 | + | 24.1103i | −0.867188 | + | 0.867188i | −0.992160 | − | 0.124972i | \(-0.960116\pi\) |
0.124972 | + | 0.992160i | \(0.460116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8943i | 0.391336i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.9354 | + | 14.6123i | −0.499930 | + | 0.524214i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.83489 | + | 3.83489i | −0.137399 | + | 0.137399i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2823 | − | 10.2823i | 0.367929 | − | 0.367929i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.3724 | 1.29984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.23879 | 0.329747 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.65922 | − | 3.65922i | 0.130437 | − | 0.130437i | −0.638874 | − | 0.769311i | \(-0.720600\pi\) |
0.769311 | + | 0.638874i | \(0.220600\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −56.6660 | + | 56.6660i | −2.01736 | + | 2.01736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.2255 | + | 14.9165i | −0.505801 | + | 0.530370i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.3520i | − | 0.935786i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.20140 | − | 6.20140i | 0.219941 | − | 0.219941i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.56228 | + | 8.56228i | 0.303291 | + | 0.303291i | 0.842300 | − | 0.539009i | \(-0.181201\pi\) |
−0.539009 | + | 0.842300i | \(0.681201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.5271i | 0.938460i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.38240i | 0.260844i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.9843 | + | 13.9843i | −0.493494 | + | 0.493494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.169822 | + | 7.16195i | 0.00598543 | + | 0.252426i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.6959 | 0.904537 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.48515i | − | 0.333480i | −0.986001 | − | 0.166740i | \(-0.946676\pi\) | ||
0.986001 | − | 0.166740i | \(-0.0533241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.37320 | + | 8.37320i | 0.294023 | + | 0.294023i | 0.838667 | − | 0.544644i | \(-0.183335\pi\) |
−0.544644 | + | 0.838667i | \(0.683335\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.4432 | + | 37.4432i | −1.31319 | + | 1.31319i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.2742 | 0.394917 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.09715i | 0.0733700i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.80439 | − | 76.0970i | −0.0630503 | − | 2.65904i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.9813 | − | 29.9813i | −1.04635 | − | 1.04635i | −0.998872 | − | 0.0474808i | \(-0.984881\pi\) |
−0.0474808 | − | 0.998872i | \(-0.515119\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.25258 | −0.322525 | −0.161262 | − | 0.986912i | \(-0.551557\pi\) | ||||
−0.161262 | + | 0.986912i | \(0.551557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.5926 | −1.34362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.2363 | + | 18.2363i | −0.634137 | + | 0.634137i | −0.949103 | − | 0.314966i | \(-0.898007\pi\) |
0.314966 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.7233 | − | 32.7233i | −1.13653 | − | 1.13653i | −0.989068 | − | 0.147458i | \(-0.952891\pi\) |
−0.147458 | − | 0.989068i | \(-0.547109\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.3887 | −0.846034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6076 | + | 0.882932i | −0.644717 | + | 0.0305918i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.58212 | − | 4.58212i | −0.158571 | − | 0.158571i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.4729 | + | 22.4729i | 0.776778 | + | 0.776778i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1360i | 0.488028i | 0.969772 | + | 0.244014i | \(0.0784643\pi\) | ||||
−0.969772 | + | 0.244014i | \(0.921536\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6618i | 0.712476i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.6565 | + | 13.6565i | 0.470354 | + | 0.470354i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.31268 | − | 2.31268i | −0.0795588 | − | 0.0795588i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.74395 | − | 5.47787i | −0.197365 | − | 0.188222i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.4962 | −0.772069 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.59843 | + | 5.59843i | 0.191912 | + | 0.191912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.3648 | − | 11.3648i | 0.389122 | − | 0.389122i | −0.485252 | − | 0.874374i | \(-0.661272\pi\) |
0.874374 | + | 0.485252i | \(0.161272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61007 | −0.0892626 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.3289 | −0.523624 | −0.261812 | − | 0.965119i | \(-0.584320\pi\) | ||||
−0.261812 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9667 | − | 12.9667i | −0.442418 | − | 0.442418i | 0.450406 | − | 0.892824i | \(-0.351279\pi\) |
−0.892824 | + | 0.450406i | \(0.851279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.37622 | − | 100.213i | −0.0809813 | − | 3.41526i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 42.8175i | − | 1.45752i | −0.684767 | − | 0.728762i | \(-0.740096\pi\) | ||
0.684767 | − | 0.728762i | \(-0.259904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.56590 | 0.0872432 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.1616 | + | 22.1616i | −0.752646 | + | 0.752646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.4496 | − | 22.4496i | −0.761552 | − | 0.761552i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 25.4722i | − | 0.863092i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −92.6970 | −3.13732 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.3562 | − | 0.482679i | 0.688165 | − | 0.0163175i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6209 | − | 28.6209i | 0.966460 | − | 0.966460i | −0.0329952 | − | 0.999456i | \(-0.510505\pi\) |
0.999456 | + | 0.0329952i | \(0.0105046\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 87.6819i | − | 2.95744i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.93539i | − | 0.199969i | −0.994989 | − | 0.0999843i | \(-0.968121\pi\) | ||
0.994989 | − | 0.0999843i | \(-0.0318792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.96040 | − | 2.96040i | −0.0996254 | − | 0.0996254i | 0.655537 | − | 0.755163i | \(-0.272442\pi\) |
−0.755163 | + | 0.655537i | \(0.772442\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8296 | + | 10.8296i | −0.364033 | + | 0.364033i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0578i | 0.404860i | 0.979297 | + | 0.202430i | \(0.0648838\pi\) | ||||
−0.979297 | + | 0.202430i | \(0.935116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.3661 | + | 14.6542i | 0.515362 | + | 0.491488i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.6929 | + | 37.6929i | −1.26276 | + | 1.26276i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.18830 | − | 3.18830i | 0.106692 | − | 0.106692i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7160 | 0.391624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.6634 | −1.42449 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.15181 | − | 5.15181i | 0.171822 | − | 0.171822i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.32293 | − | 6.32293i | 0.210647 | − | 0.210647i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.0510 | − | 26.7516i | −0.933480 | − | 0.890237i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.54106i | 0.117709i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.21946 | − | 6.21946i | 0.206514 | − | 0.206514i | −0.596270 | − | 0.802784i | \(-0.703351\pi\) |
0.802784 | + | 0.596270i | \(0.203351\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.75212 | + | 1.75212i | 0.0581140 | + | 0.0581140i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.3682i | − | 0.873617i | −0.899554 | − | 0.436809i | \(-0.856109\pi\) | ||
0.899554 | − | 0.436809i | \(-0.143891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 21.5893i | − | 0.714503i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8097 | − | 11.8097i | 0.390418 | − | 0.390418i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.818365 | − | 34.5132i | −0.0270248 | − | 1.13973i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.0495 | −1.98085 | −0.990425 | − | 0.138053i | \(-0.955916\pi\) | ||||
−0.990425 | + | 0.138053i | \(0.955916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8001i | 0.454727i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.9712 | − | 14.9712i | −0.492781 | − | 0.492781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.37361 | − | 7.37361i | 0.242443 | − | 0.242443i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −87.4502 | −2.87224 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.1534i | 1.25177i | 0.779914 | + | 0.625887i | \(0.215263\pi\) | ||||
−0.779914 | + | 0.625887i | \(0.784737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.34258 | + | 2.13034i | 0.0767749 | + | 0.0698191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45.1642 | + | 45.1642i | 1.47861 | + | 1.47861i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.21703 | 0.203319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.2637 | 0.498643 | 0.249321 | − | 0.968421i | \(-0.419792\pi\) | ||||
0.249321 | + | 0.968421i | \(0.419792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.0341 | + | 34.0341i | −1.11066 | + | 1.11066i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.7177 | − | 35.7177i | −1.16436 | − | 1.16436i | −0.983510 | − | 0.180855i | \(-0.942114\pi\) |
−0.180855 | − | 0.983510i | \(-0.557886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.3052 | −1.27995 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.9969 | − | 19.9197i | 0.617969 | − | 0.647987i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.4222 | − | 26.4222i | −0.858607 | − | 0.858607i | 0.132567 | − | 0.991174i | \(-0.457678\pi\) |
−0.991174 | + | 0.132567i | \(0.957678\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.3613 | + | 20.3613i | 0.660955 | + | 0.660955i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 90.9354i | 2.94878i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.2788i | 1.69348i | 0.532010 | + | 0.846738i | \(0.321437\pi\) | ||||
−0.532010 | + | 0.846738i | \(0.678563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.29831 | − | 8.29831i | −0.268527 | − | 0.268527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.2500 | + | 18.2500i | 0.589938 | + | 0.589938i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.2884 | + | 16.4875i | 0.558270 | + | 0.532409i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.6338 | −0.794640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.1642 | − | 27.1642i | −0.875355 | − | 0.875355i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.2687 | − | 11.2687i | 0.362753 | − | 0.362753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6054 | 0.919888 | 0.459944 | − | 0.887948i | \(-0.347870\pi\) | ||||
0.459944 | + | 0.887948i | \(0.347870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.80403 | −0.122203 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.7842 | − | 32.7842i | −1.05209 | − | 1.05209i | −0.998566 | − | 0.0535273i | \(-0.982954\pi\) |
−0.0535273 | − | 0.998566i | \(-0.517046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.2197 | − | 0.384597i | 0.519981 | − | 0.0123296i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 56.1913i | 1.79956i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.2805 | 1.06474 | 0.532369 | − | 0.846512i | \(-0.321302\pi\) | ||||
0.532369 | + | 0.846512i | \(0.321302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.11348 | + | 2.11348i | −0.0675470 | + | 0.0675470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.7906 | − | 29.7906i | −0.951141 | − | 0.951141i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.1939i | 0.867350i | 0.901069 | + | 0.433675i | \(0.142783\pi\) | ||||
−0.901069 | + | 0.433675i | \(0.857217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.531420 | 0.0169324 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.97557 | + | 83.3165i | 0.0628831 | + | 2.65199i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.7472 | + | 10.7472i | −0.341742 | + | 0.341742i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4776i | 1.34935i | 0.738117 | + | 0.674673i | \(0.235715\pi\) | ||||
−0.738117 | + | 0.674673i | \(0.764285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 93.0384i | − | 2.95248i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3687 | + | 14.3687i | 0.455520 | + | 0.455520i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.9512 | + | 30.9512i | −0.980234 | + | 0.980234i | −0.999808 | − | 0.0195743i | \(-0.993769\pi\) |
0.0195743 | + | 0.999808i | \(0.493769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 30.4207i | − | 0.962468i |
(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 | 896.2.j.h.671.1 | 16 | ||
4.3 | odd | 2 | 896.2.j.g.671.8 | 16 | |||
7.6 | odd | 2 | inner | 896.2.j.h.671.8 | 16 | ||
8.3 | odd | 2 | 448.2.j.d.335.1 | 16 | |||
8.5 | even | 2 | 112.2.j.d.27.2 | yes | 16 | ||
16.3 | odd | 4 | inner | 896.2.j.h.223.8 | 16 | ||
16.5 | even | 4 | 448.2.j.d.111.8 | 16 | |||
16.11 | odd | 4 | 112.2.j.d.83.1 | yes | 16 | ||
16.13 | even | 4 | 896.2.j.g.223.1 | 16 | |||
28.27 | even | 2 | 896.2.j.g.671.1 | 16 | |||
56.5 | odd | 6 | 784.2.w.e.619.5 | 32 | |||
56.13 | odd | 2 | 112.2.j.d.27.1 | ✓ | 16 | ||
56.27 | even | 2 | 448.2.j.d.335.8 | 16 | |||
56.37 | even | 6 | 784.2.w.e.619.6 | 32 | |||
56.45 | odd | 6 | 784.2.w.e.411.6 | 32 | |||
56.53 | even | 6 | 784.2.w.e.411.5 | 32 | |||
112.11 | odd | 12 | 784.2.w.e.19.5 | 32 | |||
112.13 | odd | 4 | 896.2.j.g.223.8 | 16 | |||
112.27 | even | 4 | 112.2.j.d.83.2 | yes | 16 | ||
112.59 | even | 12 | 784.2.w.e.19.6 | 32 | |||
112.69 | odd | 4 | 448.2.j.d.111.1 | 16 | |||
112.75 | even | 12 | 784.2.w.e.227.5 | 32 | |||
112.83 | even | 4 | inner | 896.2.j.h.223.1 | 16 | ||
112.107 | odd | 12 | 784.2.w.e.227.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.1 | ✓ | 16 | 56.13 | odd | 2 | ||
112.2.j.d.27.2 | yes | 16 | 8.5 | even | 2 | ||
112.2.j.d.83.1 | yes | 16 | 16.11 | odd | 4 | ||
112.2.j.d.83.2 | yes | 16 | 112.27 | even | 4 | ||
448.2.j.d.111.1 | 16 | 112.69 | odd | 4 | |||
448.2.j.d.111.8 | 16 | 16.5 | even | 4 | |||
448.2.j.d.335.1 | 16 | 8.3 | odd | 2 | |||
448.2.j.d.335.8 | 16 | 56.27 | even | 2 | |||
784.2.w.e.19.5 | 32 | 112.11 | odd | 12 | |||
784.2.w.e.19.6 | 32 | 112.59 | even | 12 | |||
784.2.w.e.227.5 | 32 | 112.75 | even | 12 | |||
784.2.w.e.227.6 | 32 | 112.107 | odd | 12 | |||
784.2.w.e.411.5 | 32 | 56.53 | even | 6 | |||
784.2.w.e.411.6 | 32 | 56.45 | odd | 6 | |||
784.2.w.e.619.5 | 32 | 56.5 | odd | 6 | |||
784.2.w.e.619.6 | 32 | 56.37 | even | 6 | |||
896.2.j.g.223.1 | 16 | 16.13 | even | 4 | |||
896.2.j.g.223.8 | 16 | 112.13 | odd | 4 | |||
896.2.j.g.671.1 | 16 | 28.27 | even | 2 | |||
896.2.j.g.671.8 | 16 | 4.3 | odd | 2 | |||
896.2.j.h.223.1 | 16 | 112.83 | even | 4 | inner | ||
896.2.j.h.223.8 | 16 | 16.3 | odd | 4 | inner | ||
896.2.j.h.671.1 | 16 | 1.1 | even | 1 | trivial | ||
896.2.j.h.671.8 | 16 | 7.6 | odd | 2 | inner |