Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(111,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(3.57729801055\) |
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 | 111.8 | ||
Root | \(1.40927 + 0.118126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.111 |
Dual form | 448.2.j.d.335.8 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.23450 | + | 2.23450i | 1.29009 | + | 1.29009i | 0.934728 | + | 0.355364i | \(0.115643\pi\) |
0.355364 | + | 0.934728i | \(0.384357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.584038 | − | 0.584038i | −0.261190 | − | 0.261190i | 0.564347 | − | 0.825537i | \(-0.309128\pi\) |
−0.825537 | + | 0.564347i | \(0.809128\pi\) | |||||||
\(6\) | 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 | 0.941113 | − | 0.338091i | \(-0.109781\pi\) |
−0.338091 | + | 0.941113i | \(0.609781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.91203 | + | 2.91203i | −0.807651 | + | 0.807651i | −0.984278 | − | 0.176627i | \(-0.943481\pi\) |
0.176627 | + | 0.984278i | \(0.443481\pi\) | |||||||
\(14\) | 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 | \(-0.233476\pi\) |
−0.669465 | + | 0.742844i | \(0.733476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.35840 | − | 0.198191i | 1.82395 | − | 0.0432489i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.27830 | 0.683572 | 0.341786 | − | 0.939778i | \(-0.388968\pi\) | ||||
0.341786 | + | 0.939778i | \(0.388968\pi\) | |||||||
\(24\) | 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 | \(-0.336398\pi\) |
−0.870799 | + | 0.491639i | \(0.836398\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −2.18466 | + | 0.0518018i | −0.369275 | + | 0.00875611i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70773 | − | 1.70773i | 0.280748 | − | 0.280748i | −0.552659 | − | 0.833407i | \(-0.686387\pi\) |
0.833407 | + | 0.552659i | \(0.186387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.0139 | −2.08389 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.9895 | −1.87245 | −0.936224 | − | 0.351405i | \(-0.885704\pi\) | ||||
−0.936224 | + | 0.351405i | \(0.885704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.27830 | + | 3.27830i | 0.499936 | + | 0.499936i | 0.911418 | − | 0.411482i | \(-0.134989\pi\) |
−0.411482 | + | 0.911418i | \(0.634989\pi\) | |||||||
\(44\) | 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 | \(-0.824125\pi\) |
0.524840 | + | 0.851201i | \(0.324125\pi\) | |||||||
\(54\) | 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 | \(-0.625249\pi\) |
0.923580 | + | 0.383406i | \(0.125249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.52468 | − | 4.52468i | 0.579326 | − | 0.579326i | −0.355392 | − | 0.934717i | \(-0.615653\pi\) |
0.934717 | + | 0.355392i | \(0.115653\pi\) | |||||||
\(62\) | 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 | −0.387534 | − | 0.921856i | \(-0.626673\pi\) |
0.921856 | + | 0.387534i | \(0.126673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.32537 | + | 7.32537i | 0.881871 | + | 0.881871i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.14114 | −0.610141 | −0.305071 | − | 0.952330i | \(-0.598680\pi\) | ||||
−0.305071 | + | 0.952330i | \(0.598680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.99213 | 0.818367 | 0.409184 | − | 0.912452i | \(-0.365814\pi\) | ||||
0.409184 | + | 0.912452i | \(0.365814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.64814 | − | 9.64814i | 1.11407 | − | 1.11407i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.48121 | − | 0.177392i | 0.852563 | − | 0.0202157i | ||||
\(78\) | 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 | \(-0.387589\pi\) |
−0.938288 | + | 0.345854i | \(0.887589\pi\) | |||||||
\(84\) | 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 | \(-0.482163\pi\) | ||||
0.0560071 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.258285 | + | 10.8927i | 0.0270756 | + | 1.14187i | ||||
\(92\) | 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 | 0.694519 | − | 0.719475i | \(-0.255617\pi\) |
−0.719475 | + | 0.694519i | \(0.755617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5179i | 1.23342i | 0.787189 | + | 0.616712i | \(0.211536\pi\) | ||||
−0.787189 | + | 0.616712i | \(0.788464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.99738 | − | 4.76588i | −0.487694 | − | 0.465102i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.88837 | + | 3.88837i | 0.375903 | + | 0.375903i | 0.869622 | − | 0.493719i | \(-0.164363\pi\) |
−0.493719 | + | 0.869622i | \(0.664363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.26432 | − | 4.26432i | −0.408448 | − | 0.408448i | 0.472749 | − | 0.881197i | \(-0.343262\pi\) |
−0.881197 | + | 0.472749i | \(0.843262\pi\) | |||||||
\(110\) | 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 | \(-0.0569341\pi\) |
−0.177911 | + | 0.984047i | \(0.556934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19645 | − | 0.0283697i | 0.103745 | − | 0.00245997i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.4038 | 0.895417 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.02951i | 0.771443i | 0.922615 | + | 0.385722i | \(0.126047\pi\) | ||||
−0.922615 | + | 0.385722i | \(0.873953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.33613 | − | 4.33613i | 0.367785 | − | 0.367785i | −0.498884 | − | 0.866669i | \(-0.666256\pi\) |
0.866669 | + | 0.498884i | \(0.166256\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 14.8826 | − | 16.3653i | 1.22750 | − | 1.34979i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2620 | + | 13.2620i | −1.08646 | + | 1.08646i | −0.0905743 | + | 0.995890i | \(0.528870\pi\) |
−0.995890 | + | 0.0905743i | \(0.971130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7512 | 0.956300 | 0.478150 | − | 0.878278i | \(-0.341307\pi\) | ||||
0.478150 | + | 0.878278i | \(0.341307\pi\) | |||||||
\(152\) | 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 | −0.948379 | − | 0.317140i | \(-0.897278\pi\) |
0.317140 | + | 0.948379i | \(0.397278\pi\) | |||||||
\(158\) | 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 | −0.975591 | − | 0.219595i | \(-0.929526\pi\) |
0.219595 | + | 0.975591i | \(0.429526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.22015 | − | 5.22015i | 0.406388 | − | 0.406388i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.84557i | − | 0.607109i | −0.952814 | − | 0.303554i | \(-0.901827\pi\) | ||
0.952814 | − | 0.303554i | \(-0.0981734\pi\) | |||||||
\(168\) | 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 | −0.785664 | − | 0.618653i | \(-0.787679\pi\) |
0.618653 | + | 0.785664i | \(0.287679\pi\) | |||||||
\(174\) | 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 | −0.974421 | − | 0.224729i | \(-0.927850\pi\) |
0.224729 | + | 0.974421i | \(0.427850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.03153 | + | 3.03153i | 0.225332 | + | 0.225332i | 0.810739 | − | 0.585407i | \(-0.199065\pi\) |
−0.585407 | + | 0.810739i | \(0.699065\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 0.789996 | + | 33.3168i | 0.0574637 | + | 2.42344i | ||||
\(190\) | 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 | \(-0.742704\pi\) |
0.723128 | + | 0.690714i | \(0.242704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6024i | 1.74402i | 0.489490 | + | 0.872009i | \(0.337183\pi\) | ||||
−0.489490 | + | 0.872009i | \(0.662817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5457 | 1.37865 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.63771 | + | 0.181103i | −0.536062 | + | 0.0127109i | ||||
\(204\) | 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 | −0.963534 | − | 0.267588i | \(-0.913774\pi\) |
0.267588 | + | 0.963534i | \(0.413774\pi\) | |||||||
\(212\) | 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 | \(-0.358531\pi\) |
−0.902853 | + | 0.429949i | \(0.858531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7933 | + | 18.7933i | 1.24190 | + | 1.24190i | 0.959213 | + | 0.282684i | \(0.0912247\pi\) |
0.282684 | + | 0.959213i | \(0.408775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.1132 | + | 16.3204i | 1.12596 | + | 1.07380i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.47759i | − | 0.293337i | −0.989186 | − | 0.146668i | \(-0.953145\pi\) | ||
0.989186 | − | 0.146668i | \(-0.0468550\pi\) | |||||||
\(234\) | 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 | ||||||||
\(245\) | −3.88990 | + | 4.27744i | −0.248517 | + | 0.273276i | ||||
\(246\) | 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 | \(-0.587901\pi\) |
0.962112 | + | 0.272653i | \(0.0879012\pi\) | |||||||
\(252\) | 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 | ||||||||
\(259\) | −0.151468 | − | 6.38793i | −0.00941178 | − | 0.396927i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.2643 | − | 14.2643i | 0.882939 | − | 0.882939i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.3595 | −1.56374 | −0.781868 | − | 0.623444i | \(-0.785733\pi\) | ||||
−0.781868 | + | 0.623444i | \(0.785733\pi\) | |||||||
\(264\) | 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 | −0.860322 | − | 0.509751i | \(-0.829737\pi\) |
0.509751 | + | 0.860322i | \(0.329737\pi\) | |||||||
\(270\) | 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 | \(-0.824480\pi\) |
0.523890 | + | 0.851786i | \(0.324480\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.6266i | 1.05528i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.11163i | 0.364589i | 0.983244 | + | 0.182295i | \(0.0583525\pi\) | ||||
−0.983244 | + | 0.182295i | \(0.941648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.03383 | + | 5.03383i | −0.299230 | + | 0.299230i | −0.840712 | − | 0.541482i | \(-0.817863\pi\) |
0.541482 | + | 0.840712i | \(0.317863\pi\) | |||||||
\(284\) | 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 | −0.987291 | − | 0.158921i | \(-0.949199\pi\) |
−0.158921 | − | 0.987291i | \(-0.550801\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 12.2628 | − | 0.290772i | 0.706817 | − | 0.0167598i | ||||
\(302\) | 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 | \(-0.289771\pi\) |
−0.789714 | + | 0.613475i | \(0.789771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.9713 | + | 27.9713i | −1.59123 | + | 1.59123i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2122i | 1.14613i | 0.819511 | + | 0.573064i | \(0.194245\pi\) | ||||
−0.819511 | + | 0.573064i | \(0.805755\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.2311 | −0.860915 | −0.430457 | − | 0.902611i | \(-0.641648\pi\) | ||||
−0.430457 | + | 0.902611i | \(0.641648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.361889 | − | 15.2621i | −0.0203901 | − | 0.859920i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.3480 | − | 20.3480i | −1.14286 | − | 1.14286i | −0.987925 | − | 0.154932i | \(-0.950484\pi\) |
−0.154932 | − | 0.987925i | \(-0.549516\pi\) | |||||||
\(318\) | 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 | −0.987656 | − | 0.156636i | \(-0.949935\pi\) |
−0.156636 | − | 0.987656i | \(-0.550065\pi\) | |||||||
\(332\) | 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 | 0.798891 | − | 0.601476i | \(-0.205420\pi\) |
−0.601476 | + | 0.798891i | \(0.705420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8960 | + | 17.8960i | −0.957951 | + | 0.957951i | −0.999151 | − | 0.0412000i | \(-0.986882\pi\) |
0.0412000 | + | 0.999151i | \(0.486882\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | −0.527432 | − | 22.2436i | −0.0279147 | − | 1.17726i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.3293 | 0.809052 | 0.404526 | − | 0.914527i | \(-0.367437\pi\) | ||||
0.404526 | + | 0.914527i | \(0.367437\pi\) | |||||||
\(360\) | 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 | ||||||||
\(371\) | 0.210737 | + | 8.88749i | 0.0109409 | + | 0.461415i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6821 | − | 24.6821i | 1.27799 | − | 1.27799i | 0.336200 | − | 0.941790i | \(-0.390858\pi\) |
0.941790 | − | 0.336200i | \(-0.109142\pi\) | |||||||
\(374\) | 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 | 0.976838 | − | 0.213982i | \(-0.0686435\pi\) |
−0.213982 | + | 0.976838i | \(0.568644\pi\) | |||||||
\(380\) | 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 | \(-0.740311\pi\) |
0.728299 | + | 0.685260i | \(0.240311\pi\) | |||||||
\(390\) | 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 | −0.979111 | − | 0.203324i | \(-0.934825\pi\) |
0.203324 | + | 0.979111i | \(0.434825\pi\) | |||||||
\(398\) | 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 | \(-0.267201\pi\) | ||||
0.667883 | + | 0.744266i | \(0.267201\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.1765 | + | 20.1765i | −0.995233 | + | 0.995233i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.368013 | − | 15.5204i | −0.0181087 | − | 0.763707i | ||||
\(414\) | 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 | \(-0.264504\pi\) |
−0.738582 | + | 0.674164i | \(0.764504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.73490 | + | 9.73490i | −0.474450 | + | 0.474450i | −0.903351 | − | 0.428901i | \(-0.858901\pi\) |
0.428901 | + | 0.903351i | \(0.358901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 69.6366i | − | 3.38585i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4906 | −0.557378 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.401321 | − | 16.9250i | −0.0194213 | − | 0.819060i | ||||
\(428\) | 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 | \(-0.887909\pi\) | ||
0.938636 | − | 0.344910i | \(-0.112091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.8472 | − | 2.31780i | 2.32606 | − | 0.110371i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5148 | + | 13.5148i | 0.642105 | + | 0.642105i | 0.951073 | − | 0.308967i | \(-0.0999834\pi\) |
−0.308967 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(444\) | 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 | \(0.306183\pi\) | ||||
−0.571959 | + | 0.820282i | \(0.693817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.7030 | + | 23.7030i | 1.10636 | + | 1.10636i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3005 | − | 16.3005i | 0.759188 | − | 0.759188i | −0.216987 | − | 0.976175i | \(-0.569623\pi\) |
0.976175 | + | 0.216987i | \(0.0696228\pi\) | |||||||
\(462\) | 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 | \(-0.0556678\pi\) |
−0.173995 | + | 0.984746i | \(0.555668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.387922 | − | 16.3600i | −0.0179126 | − | 0.755433i | ||||
\(470\) | 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 | ||||||||
\(483\) | 27.4013 | − | 0.649730i | 1.24680 | − | 0.0295638i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.74956 | + | 7.74956i | −0.351890 | + | 0.351890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.6953 | 1.25499 | 0.627497 | − | 0.778619i | \(-0.284079\pi\) | ||||
0.627497 | + | 0.778619i | \(0.284079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −43.1345 | −1.95061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.2667 | − | 20.2667i | −0.914621 | − | 0.914621i | 0.0820102 | − | 0.996631i | \(-0.473866\pi\) |
−0.996631 | + | 0.0820102i | \(0.973866\pi\) | |||||||
\(492\) | 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 | −0.994958 | − | 0.100295i | \(-0.968021\pi\) |
0.100295 | + | 0.994958i | \(0.468021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5310 | − | 17.5310i | 0.783226 | − | 0.783226i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.04877i | − | 0.135938i | −0.997687 | − | 0.0679689i | \(-0.978348\pi\) | ||
0.997687 | − | 0.0679689i | \(-0.0216519\pi\) | |||||||
\(504\) | 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 | −0.240770 | − | 0.970582i | \(-0.577400\pi\) |
0.970582 | + | 0.240770i | \(0.0773999\pi\) | |||||||
\(510\) | 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 | \(-0.223438\pi\) | ||||
0.763584 | + | 0.645708i | \(0.223438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9307 | + | 31.9307i | −1.39623 | + | 1.39623i | −0.585718 | + | 0.810515i | \(0.699187\pi\) |
−0.810515 | + | 0.585718i | \(0.800813\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.855751 | − | 36.0899i | −0.0373480 | − | 1.57509i | ||||
\(526\) | 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 | ||||||||
\(539\) | 13.3207 | − | 14.6478i | 0.573764 | − | 0.630926i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5705 | + | 28.5705i | 1.22834 | + | 1.22834i | 0.964591 | + | 0.263749i | \(0.0849592\pi\) |
0.263749 | + | 0.964591i | \(0.415041\pi\) | |||||||
\(542\) | 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 | −0.518805 | − | 0.854892i | \(-0.673623\pi\) |
0.854892 | + | 0.518805i | \(0.173623\pi\) | |||||||
\(548\) | 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 | \(-0.196332\pi\) |
−0.578424 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(558\) | 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 | \(-0.275320\pi\) |
−0.761059 | + | 0.648682i | \(0.775320\pi\) | |||||||
\(564\) | 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 | \(-0.797281\pi\) | ||
0.803967 | − | 0.594675i | \(-0.202719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.132484 | − | 0.132484i | −0.00554428 | − | 0.00554428i | 0.704329 | − | 0.709873i | \(-0.251248\pi\) |
−0.709873 | + | 0.704329i | \(0.751248\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −20.1893 | + | 0.478722i | −0.837594 | + | 0.0198607i | ||||
\(582\) | 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 | \(-0.961405\pi\) |
0.120954 | + | 0.992658i | \(0.461405\pi\) | |||||||
\(588\) | 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 | ||||||||
\(595\) | 0.137856 | + | 5.81387i | 0.00565156 | + | 0.238345i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −54.9742 | + | 54.9742i | −2.24994 | + | 2.24994i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.3759 | 0.587381 | 0.293691 | − | 0.955901i | \(-0.405116\pi\) | ||||
0.293691 | + | 0.955901i | \(0.405116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.26571 | 0.174002 | 0.0870010 | − | 0.996208i | \(-0.472272\pi\) | ||||
0.0870010 | + | 0.996208i | \(0.472272\pi\) | |||||||
\(602\) | 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 | 0.205467 | − | 0.978664i | \(-0.434129\pi\) |
0.978664 | − | 0.205467i | \(-0.0658712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.2935i | 1.26188i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.2992i | − | 0.776956i | −0.921458 | − | 0.388478i | \(-0.873001\pi\) | ||
0.921458 | − | 0.388478i | \(-0.126999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.58436 | + | 1.58436i | −0.0636809 | + | 0.0636809i | −0.738230 | − | 0.674549i | \(-0.764338\pi\) |
0.674549 | + | 0.738230i | \(0.264338\pi\) | |||||||
\(620\) | 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 | \(-0.411483\pi\) | ||||
0.274515 | + | 0.961583i | \(0.411483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45.1781 | −1.79567 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.68721 | + | 4.68721i | −0.186006 | + | 0.186006i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.3274 | + | 19.3951i | 0.845024 | + | 0.768464i | ||||
\(638\) | 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 | −0.927786 | − | 0.373112i | \(-0.878291\pi\) |
−0.373112 | − | 0.927786i | \(-0.621709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.55659 | − | 8.55659i | 0.336916 | − | 0.336916i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.4616i | 0.804430i | 0.915545 | + | 0.402215i | \(0.131760\pi\) | ||||
−0.915545 | + | 0.402215i | \(0.868240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.5966 | 0.651474 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0893 | − | 0.500062i | 0.826554 | − | 0.0195990i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.37361 | + | 3.37361i | 0.132020 | + | 0.132020i | 0.770029 | − | 0.638009i | \(-0.220242\pi\) |
−0.638009 | + | 0.770029i | \(0.720242\pi\) | |||||||
\(654\) | 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 | −0.266592 | − | 0.963809i | \(-0.585898\pi\) |
0.963809 | + | 0.266592i | \(0.0858977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3379 | − | 15.3379i | −0.596577 | − | 0.596577i | 0.342823 | − | 0.939400i | \(-0.388617\pi\) |
−0.939400 | + | 0.342823i | \(0.888617\pi\) | |||||||
\(662\) | 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 | 0.998404 | + | 0.0564681i | \(0.0179839\pi\) |
0.0564681 | + | 0.998404i | \(0.482016\pi\) | |||||||
\(678\) | 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 | 0.299467 | − | 0.954107i | \(-0.403191\pi\) |
−0.954107 | + | 0.299467i | \(0.903191\pi\) | |||||||
\(684\) | 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 | \(-0.153635\pi\) |
−0.464136 | + | 0.885764i | \(0.653635\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.23926 | + | 52.2639i | 0.0470757 | + | 1.98534i | ||||
\(694\) | 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 | \(-0.243014\pi\) |
−0.691419 | + | 0.722454i | \(0.743014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09244 | 0.0412023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.0172i | 0.979864i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.938155 | + | 0.0222452i | −0.0352830 | + | 0.000836617i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.61763 | − | 8.61763i | 0.323642 | − | 0.323642i | −0.526521 | − | 0.850162i | \(-0.676504\pi\) |
0.850162 | + | 0.526521i | \(0.176504\pi\) | |||||||
\(710\) | 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 | \(0.0753283\pi\) | ||||
−0.972129 | + | 0.234448i | \(0.924672\pi\) | |||||||
\(728\) | 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 | −0.322343 | − | 0.946623i | \(-0.604471\pi\) |
0.946623 | + | 0.322343i | \(0.104471\pi\) | |||||||
\(734\) | 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 | −0.381306 | − | 0.924449i | \(-0.624526\pi\) |
0.924449 | + | 0.381306i | \(0.124526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.16254 | − | 4.16254i | −0.152915 | − | 0.152915i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6332 | 0.390093 | 0.195046 | − | 0.980794i | \(-0.437514\pi\) | ||||
0.195046 | + | 0.980794i | \(0.437514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.4910 | 0.567547 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.7059 | − | 37.7059i | 1.37959 | − | 1.37959i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5449 | − | 0.344883i | 0.531458 | − | 0.0126017i | ||||
\(750\) | 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 | \(-0.939452\pi\) |
0.189073 | + | 0.981963i | \(0.439452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.3015i | 1.06358i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.51842 | −0.345042 | −0.172521 | − | 0.985006i | \(-0.555191\pi\) | ||||
−0.172521 | + | 0.985006i | \(0.555191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.9511 | + | 0.378228i | −0.577470 | + | 0.0136928i | ||||
\(764\) | 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 | 0.124972 | − | 0.992160i | \(-0.460116\pi\) |
−0.992160 | + | 0.124972i | \(0.960116\pi\) | |||||||
\(774\) | 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 | \(-0.279400\pi\) |
−0.769311 | + | 0.638874i | \(0.779400\pi\) | |||||||
\(788\) | 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 | −0.539009 | − | 0.842300i | \(-0.681201\pi\) |
0.842300 | + | 0.539009i | \(0.181201\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | −7.16195 | + | 0.169822i | −0.252426 | + | 0.00598543i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.6959 | −0.904537 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.48515i | 0.333480i | 0.986001 | + | 0.166740i | \(0.0533241\pi\) | ||||
−0.986001 | + | 0.166740i | \(0.946676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.37320 | + | 8.37320i | −0.294023 | + | 0.294023i | −0.838667 | − | 0.544644i | \(-0.816665\pi\) |
0.544644 | + | 0.838667i | \(0.316665\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | −76.0970 | + | 1.80439i | −2.65904 | + | 0.0630503i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.9813 | − | 29.9813i | 1.04635 | − | 1.04635i | 0.0474808 | − | 0.998872i | \(-0.484881\pi\) |
0.998872 | − | 0.0474808i | \(-0.0151193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.25258 | 0.322525 | 0.161262 | − | 0.986912i | \(-0.448443\pi\) | ||||
0.161262 | + | 0.986912i | \(0.448443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.5926 | 1.34362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.2363 | − | 18.2363i | −0.634137 | − | 0.634137i | 0.314966 | − | 0.949103i | \(-0.398007\pi\) |
−0.949103 | + | 0.314966i | \(0.898007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.7233 | + | 32.7233i | −1.13653 | + | 1.13653i | −0.147458 | + | 0.989068i | \(0.547109\pi\) |
−0.989068 | + | 0.147458i | \(0.952891\pi\) | |||||||
\(830\) | 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 | \(-0.921536\pi\) | ||
0.969772 | − | 0.244014i | \(-0.0784643\pi\) | |||||||
\(840\) | 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 | 0.874374 | − | 0.485252i | \(-0.161272\pi\) |
−0.485252 | + | 0.874374i | \(0.661272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.61007 | 0.0892626 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.3289 | 0.523624 | 0.261812 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261812 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9667 | − | 12.9667i | 0.442418 | − | 0.442418i | −0.450406 | − | 0.892824i | \(-0.648721\pi\) |
0.892824 | + | 0.450406i | \(0.148721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −100.213 | + | 2.37622i | −3.41526 | + | 0.0809813i | ||||
\(862\) | 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 | ||||||||
\(875\) | 0.482679 | + | 20.3562i | 0.0163175 | + | 0.688165i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.6209 | − | 28.6209i | −0.966460 | − | 0.966460i | 0.0329952 | − | 0.999456i | \(-0.489495\pi\) |
−0.999456 | + | 0.0329952i | \(0.989495\pi\) | |||||||
\(878\) | 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 | −0.755163 | − | 0.655537i | \(-0.772442\pi\) |
0.655537 | + | 0.755163i | \(0.272442\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8296 | − | 10.8296i | −0.364033 | − | 0.364033i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.0578i | − | 0.404860i | −0.979297 | − | 0.202430i | \(-0.935116\pi\) | ||
0.979297 | − | 0.202430i | \(-0.0648838\pi\) | |||||||
\(888\) | 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 | 0.802784 | − | 0.596270i | \(-0.203351\pi\) |
−0.596270 | + | 0.802784i | \(0.703351\pi\) | |||||||
\(908\) | 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 | ||||||||
\(917\) | 34.5132 | − | 0.818365i | 1.13973 | − | 0.0270248i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 60.0495 | 1.98085 | 0.990425 | − | 0.138053i | \(-0.0440843\pi\) | ||||
0.990425 | + | 0.138053i | \(0.0440843\pi\) | |||||||
\(920\) | 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 | ||||||||
\(931\) | 2.13034 | − | 2.34258i | 0.0698191 | − | 0.0767749i | ||||
\(932\) | 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 | \(-0.580208\pi\) | ||||
−0.249321 | + | 0.968421i | \(0.580208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.0341 | − | 34.0341i | −1.11066 | − | 1.11066i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.7177 | + | 35.7177i | −1.16436 | + | 1.16436i | −0.180855 | + | 0.983510i | \(0.557886\pi\) |
−0.983510 | + | 0.180855i | \(0.942114\pi\) | |||||||
\(942\) | 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 | −0.991174 | − | 0.132567i | \(-0.957678\pi\) |
0.132567 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(948\) | 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 | \(-0.678563\pi\) | ||
0.532010 | − | 0.846738i | \(-0.321437\pi\) | |||||||
\(954\) | 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 | \(-0.652130\pi\) | ||||
−0.459944 | + | 0.887948i | \(0.652130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.80403 | 0.122203 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.7842 | − | 32.7842i | 1.05209 | − | 1.05209i | 0.0535273 | − | 0.998566i | \(-0.482954\pi\) |
0.998566 | − | 0.0535273i | \(-0.0170464\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.384597 | − | 16.2197i | −0.0123296 | − | 0.519981i | ||||
\(974\) | 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 | \(-0.857217\pi\) | ||
0.901069 | − | 0.433675i | \(-0.142783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.531420 | −0.0169324 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −83.3165 | + | 1.97557i | −2.65199 | + | 0.0628831i | ||||
\(988\) | 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 | 0.0195743 | − | 0.999808i | \(-0.493769\pi\) |
−0.999808 | + | 0.0195743i | \(0.993769\pi\) | |||||||
\(998\) | 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 | 448.2.j.d.111.8 | 16 | ||
4.3 | odd | 2 | 112.2.j.d.83.1 | yes | 16 | ||
7.6 | odd | 2 | inner | 448.2.j.d.111.1 | 16 | ||
8.3 | odd | 2 | 896.2.j.h.223.8 | 16 | |||
8.5 | even | 2 | 896.2.j.g.223.1 | 16 | |||
16.3 | odd | 4 | 896.2.j.g.671.8 | 16 | |||
16.5 | even | 4 | 112.2.j.d.27.2 | yes | 16 | ||
16.11 | odd | 4 | inner | 448.2.j.d.335.1 | 16 | ||
16.13 | even | 4 | 896.2.j.h.671.1 | 16 | |||
28.3 | even | 6 | 784.2.w.e.19.6 | 32 | |||
28.11 | odd | 6 | 784.2.w.e.19.5 | 32 | |||
28.19 | even | 6 | 784.2.w.e.227.5 | 32 | |||
28.23 | odd | 6 | 784.2.w.e.227.6 | 32 | |||
28.27 | even | 2 | 112.2.j.d.83.2 | yes | 16 | ||
56.13 | odd | 2 | 896.2.j.g.223.8 | 16 | |||
56.27 | even | 2 | 896.2.j.h.223.1 | 16 | |||
112.5 | odd | 12 | 784.2.w.e.619.5 | 32 | |||
112.13 | odd | 4 | 896.2.j.h.671.8 | 16 | |||
112.27 | even | 4 | inner | 448.2.j.d.335.8 | 16 | ||
112.37 | even | 12 | 784.2.w.e.619.6 | 32 | |||
112.53 | even | 12 | 784.2.w.e.411.5 | 32 | |||
112.69 | odd | 4 | 112.2.j.d.27.1 | ✓ | 16 | ||
112.83 | even | 4 | 896.2.j.g.671.1 | 16 | |||
112.101 | odd | 12 | 784.2.w.e.411.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.1 | ✓ | 16 | 112.69 | odd | 4 | ||
112.2.j.d.27.2 | yes | 16 | 16.5 | even | 4 | ||
112.2.j.d.83.1 | yes | 16 | 4.3 | odd | 2 | ||
112.2.j.d.83.2 | yes | 16 | 28.27 | even | 2 | ||
448.2.j.d.111.1 | 16 | 7.6 | odd | 2 | inner | ||
448.2.j.d.111.8 | 16 | 1.1 | even | 1 | trivial | ||
448.2.j.d.335.1 | 16 | 16.11 | odd | 4 | inner | ||
448.2.j.d.335.8 | 16 | 112.27 | even | 4 | inner | ||
784.2.w.e.19.5 | 32 | 28.11 | odd | 6 | |||
784.2.w.e.19.6 | 32 | 28.3 | even | 6 | |||
784.2.w.e.227.5 | 32 | 28.19 | even | 6 | |||
784.2.w.e.227.6 | 32 | 28.23 | odd | 6 | |||
784.2.w.e.411.5 | 32 | 112.53 | even | 12 | |||
784.2.w.e.411.6 | 32 | 112.101 | odd | 12 | |||
784.2.w.e.619.5 | 32 | 112.5 | odd | 12 | |||
784.2.w.e.619.6 | 32 | 112.37 | even | 12 | |||
896.2.j.g.223.1 | 16 | 8.5 | even | 2 | |||
896.2.j.g.223.8 | 16 | 56.13 | odd | 2 | |||
896.2.j.g.671.1 | 16 | 112.83 | even | 4 | |||
896.2.j.g.671.8 | 16 | 16.3 | odd | 4 | |||
896.2.j.h.223.1 | 16 | 56.27 | even | 2 | |||
896.2.j.h.223.8 | 16 | 8.3 | odd | 2 | |||
896.2.j.h.671.1 | 16 | 16.13 | even | 4 | |||
896.2.j.h.671.8 | 16 | 112.13 | odd | 4 |