Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.o (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.6 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.a.1519.5 |
$q$-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 \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.50928 | −1.44873 | −0.724367 | − | 0.689415i | \(-0.757868\pi\) | ||||
−0.724367 | + | 0.689415i | \(0.757868\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.52863 | −0.683625 | −0.341813 | − | 0.939768i | \(-0.611041\pi\) | ||||
−0.341813 | + | 0.939768i | \(0.611041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.415002i | − | 0.156856i | −0.996920 | − | 0.0784280i | \(-0.975010\pi\) | ||
0.996920 | − | 0.0784280i | \(-0.0249901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.29648 | 1.09883 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.53219i | − | 1.25700i | −0.777808 | − | 0.628502i | \(-0.783668\pi\) | ||
0.777808 | − | 0.628502i | \(-0.216332\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.83577 | 0.990391 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.133464 | 0.0323698 | 0.0161849 | − | 0.999869i | \(-0.494848\pi\) | ||||
0.0161849 | + | 0.999869i | \(0.494848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.33558 | + | 0.450279i | 0.994650 | + | 0.103301i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.04136i | 0.227242i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.38174i | 0.705142i | 0.935785 | + | 0.352571i | \(0.114693\pi\) | ||||
−0.935785 | + | 0.352571i | \(0.885307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.66328 | −0.532656 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.743957 | −0.143175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.02960i | − | 0.562582i | −0.959623 | − | 0.281291i | \(-0.909237\pi\) | ||
0.959623 | − | 0.281291i | \(-0.0907626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.01187 | −0.720554 | −0.360277 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360277 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.50928i | − | 0.436809i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.634385i | 0.107231i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.85333i | − | 0.304685i | −0.988328 | − | 0.152343i | \(-0.951318\pi\) | ||
0.988328 | − | 0.152343i | \(-0.0486817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.3725i | 1.82106i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.83030i | 0.910540i | 0.890354 | + | 0.455270i | \(0.150457\pi\) | ||||
−0.890354 | + | 0.455270i | \(0.849543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.93739i | 1.21044i | 0.796058 | + | 0.605220i | \(0.206915\pi\) | ||||
−0.796058 | + | 0.605220i | \(0.793085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.03911 | −0.751186 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1715i | 1.77540i | 0.460422 | + | 0.887700i | \(0.347698\pi\) | ||||
−0.460422 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82777 | 0.975396 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.334899 | −0.0468952 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.96262i | − | 0.819028i | −0.912304 | − | 0.409514i | \(-0.865698\pi\) | ||
0.912304 | − | 0.409514i | \(-0.134302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.52863i | − | 0.206121i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8792 | − | 1.12987i | −1.44098 | − | 0.149656i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.95715 | −1.03593 | −0.517966 | − | 0.855401i | \(-0.673311\pi\) | ||||
−0.517966 | + | 0.855401i | \(0.673311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.03402 | −0.388467 | −0.194233 | − | 0.980955i | \(-0.562222\pi\) | ||||
−0.194233 | + | 0.980955i | \(0.562222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.36805i | − | 0.172358i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92806i | 0.859320i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6481 | 1.54522 | 0.772608 | − | 0.634884i | \(-0.218952\pi\) | ||||
0.772608 | + | 0.634884i | \(0.218952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.48574i | − | 1.02156i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.95811 | 0.707098 | 0.353549 | − | 0.935416i | \(-0.384975\pi\) | ||||
0.353549 | + | 0.935416i | \(0.384975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3806 | 1.33200 | 0.665999 | − | 0.745953i | \(-0.268006\pi\) | ||||
0.665999 | + | 0.745953i | \(0.268006\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.68292 | 0.771677 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.415002 | 0.0472938 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.959216 | 0.107920 | 0.0539601 | − | 0.998543i | \(-0.482816\pi\) | ||||
0.0539601 | + | 0.998543i | \(0.482816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.02265 | −0.891406 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.0702i | − | 1.21511i | −0.794277 | − | 0.607555i | \(-0.792150\pi\) | ||
0.794277 | − | 0.607555i | \(-0.207850\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.204018 | −0.0221288 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.60210i | 0.815031i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.52486i | − | 1.00963i | −0.863227 | − | 0.504817i | \(-0.831560\pi\) | ||
0.863227 | − | 0.504817i | \(-0.168440\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.88087 | −0.197169 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0669 | 1.04389 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.62751 | − | 0.688311i | −0.679968 | − | 0.0706192i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.20133i | 0.934254i | 0.884190 | + | 0.467127i | \(0.154711\pi\) | ||||
−0.884190 | + | 0.467127i | \(0.845289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.29648i | 0.331309i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.6889 | −1.56110 | −0.780552 | − | 0.625091i | \(-0.785062\pi\) | ||||
−0.780552 | + | 0.625091i | \(0.785062\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8777 | −1.56448 | −0.782239 | − | 0.622979i | \(-0.785922\pi\) | ||||
−0.782239 | + | 0.622979i | \(0.785922\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.59185i | − | 0.155349i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.73531 | −0.554453 | −0.277227 | − | 0.960805i | \(-0.589415\pi\) | ||||
−0.277227 | + | 0.960805i | \(0.589415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.1730i | − | 1.83644i | −0.396069 | − | 0.918221i | \(-0.629626\pi\) | ||
0.396069 | − | 0.918221i | \(-0.370374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.65051i | 0.441407i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.09289i | 0.667243i | 0.942707 | + | 0.333621i | \(0.108271\pi\) | ||||
−0.942707 | + | 0.333621i | \(0.891729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.16944i | − | 0.482053i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 14.9403i | − | 1.38123i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.0553879i | − | 0.00507740i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 14.6298i | − | 1.31913i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7143 | 1.04776 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.67698 | 0.503751 | 0.251875 | − | 0.967760i | \(-0.418953\pi\) | ||||
0.251875 | + | 0.967760i | \(0.418953\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 19.9171i | − | 1.75361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.10480i | − | 0.708120i | −0.935223 | − | 0.354060i | \(-0.884801\pi\) | ||
0.935223 | − | 0.354060i | \(-0.115199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.186866 | − | 1.79927i | 0.0162034 | − | 0.156017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.13724 | 0.0978778 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.2712 | 1.04840 | 0.524200 | − | 0.851595i | \(-0.324364\pi\) | ||||
0.524200 | + | 0.851595i | \(0.324364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.4875i | − | 1.31363i | −0.754050 | − | 0.656817i | \(-0.771902\pi\) | ||
0.754050 | − | 0.656817i | \(-0.228098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 30.5418i | − | 2.57208i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.53219 | 0.379001 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.63114i | 0.384595i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.1328 | −1.41309 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.2811 | −1.16996 | −0.584979 | − | 0.811049i | \(-0.698897\pi\) | ||||
−0.584979 | + | 0.811049i | \(0.698897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.72230 | 0.302916 | 0.151458 | − | 0.988464i | \(-0.451603\pi\) | ||||
0.151458 | + | 0.988464i | \(0.451603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.439962 | 0.0355688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.13268 | 0.492589 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.37540 | 0.588621 | 0.294310 | − | 0.955710i | \(-0.404910\pi\) | ||||
0.294310 | + | 0.955710i | \(0.404910\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.9619i | 1.18655i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.40343 | 0.110606 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1527i | 1.18685i | 0.804888 | + | 0.593426i | \(0.202225\pi\) | ||||
−0.804888 | + | 0.593426i | \(0.797775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.83577i | 0.298614i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.67131 | 0.516241 | 0.258121 | − | 0.966113i | \(-0.416897\pi\) | ||||
0.258121 | + | 0.966113i | \(0.416897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.54077 | −0.580059 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.2922 | + | 1.48434i | 1.09295 | + | 0.113510i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.85272i | − | 0.216888i | −0.994103 | − | 0.108444i | \(-0.965413\pi\) | ||
0.994103 | − | 0.108444i | \(-0.0345869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.10527i | 0.0835503i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.9667 | 1.50079 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.93159 | −0.144374 | −0.0721869 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721869 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.4911i | − | 1.74608i | −0.487646 | − | 0.873042i | \(-0.662144\pi\) | ||
0.487646 | − | 0.873042i | \(-0.337856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.61321 | 0.562784 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.83306i | 0.208290i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.133464i | 0.00975986i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.308744i | 0.0224578i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.48832i | 0.324764i | 0.986728 | + | 0.162382i | \(0.0519176\pi\) | ||||
−0.986728 | + | 0.162382i | \(0.948082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 27.6742i | − | 1.99203i | −0.0891825 | − | 0.996015i | \(-0.528425\pi\) | ||
0.0891825 | − | 0.996015i | \(-0.471575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 17.3844i | − | 1.24492i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.0101 | 1.21192 | 0.605959 | − | 0.795496i | \(-0.292789\pi\) | ||||
0.605959 | + | 0.795496i | \(0.292789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.8516i | − | 1.69080i | −0.534135 | − | 0.845399i | \(-0.679363\pi\) | ||
0.534135 | − | 0.845399i | \(-0.320637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −31.7377 | −2.23860 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.25729 | −0.0882443 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.91238i | − | 0.622468i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.1479i | 0.774830i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.450279 | + | 4.33558i | −0.0311464 | + | 0.299898i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.36986 | 0.163148 | 0.0815738 | − | 0.996667i | \(-0.474005\pi\) | ||||
0.0815738 | + | 0.996667i | \(0.474005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.9506 | −1.02440 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 12.1334i | − | 0.827488i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.66494i | 0.113023i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.5571 | −1.92971 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.604885i | − | 0.0406890i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3913 | −1.23157 | −0.615786 | − | 0.787914i | \(-0.711161\pi\) | ||||
−0.615786 | + | 0.787914i | \(0.711161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.77946 | −0.585297 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8563 | −0.986050 | −0.493025 | − | 0.870015i | \(-0.664109\pi\) | ||||
−0.493025 | + | 0.870015i | \(0.664109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.16192 | 0.539355 | 0.269678 | − | 0.962951i | \(-0.413083\pi\) | ||||
0.269678 | + | 0.962951i | \(0.413083\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.04136 | −0.0685162 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0186 | −1.18044 | −0.590220 | − | 0.807242i | \(-0.700959\pi\) | ||||
−0.590220 | + | 0.807242i | \(0.700959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 18.6058i | − | 1.21371i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.40694 | −0.156348 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.14842i | − | 0.333024i | −0.986039 | − | 0.166512i | \(-0.946750\pi\) | ||
0.986039 | − | 0.166512i | \(-0.0532504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.7206i | − | 1.59239i | −0.605037 | − | 0.796197i | \(-0.706842\pi\) | ||
0.605037 | − | 0.796197i | \(-0.293158\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3629 | 1.43458 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.4372 | −0.666806 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.04075 | − | 19.6497i | 0.129850 | − | 1.25028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.7782i | 1.76037i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 18.8129i | − | 1.18746i | −0.804665 | − | 0.593729i | \(-0.797655\pi\) | ||
0.804665 | − | 0.593729i | \(-0.202345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.38174 | −0.212608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.511937 | 0.0320588 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.99648i | − | 0.561185i | −0.959827 | − | 0.280593i | \(-0.909469\pi\) | ||
0.959827 | − | 0.280593i | \(-0.0905310\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.769134 | −0.0477917 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 9.98701i | − | 0.618181i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3.49232i | − | 0.215346i | −0.994186 | − | 0.107673i | \(-0.965660\pi\) | ||
0.994186 | − | 0.107673i | \(-0.0343399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.11465i | 0.559908i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.9005i | 1.46269i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.24851i | − | 0.0761228i | −0.999275 | − | 0.0380614i | \(-0.987882\pi\) | ||
0.999275 | − | 0.0380614i | \(-0.0121183\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.56556i | 0.277338i | 0.990339 | + | 0.138669i | \(0.0442824\pi\) | ||||
−0.990339 | + | 0.138669i | \(0.955718\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.71962 | 0.285645 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.66328i | − | 0.160602i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9947 | −1.02111 | −0.510557 | − | 0.859844i | \(-0.670561\pi\) | ||||
−0.510557 | + | 0.859844i | \(0.670561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.2251 | −0.791764 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9487i | 0.712800i | 0.934334 | + | 0.356400i | \(0.115996\pi\) | ||||
−0.934334 | + | 0.356400i | \(0.884004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.3180i | − | 1.02945i | −0.857357 | − | 0.514723i | \(-0.827895\pi\) | ||
0.857357 | − | 0.514723i | \(-0.172105\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.6303 | + | 1.72716i | 0.985092 | + | 0.102308i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.41958 | 0.142824 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9822 | −0.998952 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 23.0887i | − | 1.35348i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4740i | 0.845578i | 0.906228 | + | 0.422789i | \(0.138949\pi\) | ||||
−0.906228 | + | 0.422789i | \(0.861051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1636 | 0.708190 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.743957i | − | 0.0431688i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.3267 | 0.886367 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.29403 | 0.189865 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.3678 | 2.26162 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.63790 | 0.265566 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.26094 | −0.186112 | −0.0930558 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930558 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.8416 | 2.26651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.0112i | − | 1.30485i | −0.757855 | − | 0.652423i | \(-0.773753\pi\) | ||
0.757855 | − | 0.652423i | \(-0.226247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.85527 | 0.330960 | 0.165480 | − | 0.986213i | \(-0.447083\pi\) | ||||
0.165480 | + | 0.986213i | \(0.447083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.09124i | 0.117828i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9747i | 1.17806i | 0.808112 | + | 0.589029i | \(0.200490\pi\) | ||||
−0.808112 | + | 0.589029i | \(0.799510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.02960 | 0.169625 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3915 | 0.803255 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.578644 | + | 0.0600960i | 0.0321966 | + | 0.00334383i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0705i | 0.669551i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 48.1104i | 2.66051i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.05121 | 0.278482 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.370803 | 0.0203812 | 0.0101906 | − | 0.999948i | \(-0.496756\pi\) | ||||
0.0101906 | + | 0.999948i | \(0.496756\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.10946i | − | 0.334796i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.3343 | −1.05635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.1742i | − | 1.31685i | −0.752646 | − | 0.658425i | \(-0.771223\pi\) | ||
0.752646 | − | 0.658425i | \(-0.228777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 17.7980i | − | 0.966657i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.01187i | − | 0.217255i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5.73855i | − | 0.309853i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9716i | 0.698366i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.61266i | − | 0.408669i | −0.978901 | − | 0.204335i | \(-0.934497\pi\) | ||
0.978901 | − | 0.204335i | \(-0.0655031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8541 | −0.955708 | −0.477854 | − | 0.878439i | \(-0.658585\pi\) | ||||
−0.477854 | + | 0.878439i | \(0.658585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.37176i | 0.179971i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9928 | 0.744764 | 0.372382 | − | 0.928080i | \(-0.378541\pi\) | ||||
0.372382 | + | 0.928080i | \(0.378541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.10776 | −0.483390 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.138984i | 0.00735579i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.3628i | − | 0.969150i | −0.874750 | − | 0.484575i | \(-0.838974\pi\) | ||
0.874750 | − | 0.484575i | \(-0.161026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5945 | + | 3.90444i | 0.978658 | + | 0.205497i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.50928 | 0.131703 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.3967 | −0.910587 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.3160i | − | 0.747291i | −0.927572 | − | 0.373645i | \(-0.878108\pi\) | ||
0.927572 | − | 0.373645i | \(-0.121892\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.2195i | 1.00053i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.47450 | −0.128469 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.18308i | 0.423704i | 0.977302 | + | 0.211852i | \(0.0679495\pi\) | ||||
−0.977302 | + | 0.211852i | \(0.932051\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.3946 | −1.51793 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.7307 | −0.707168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5333 | 0.951993 | 0.475996 | − | 0.879447i | \(-0.342088\pi\) | ||||
0.475996 | + | 0.879447i | \(0.342088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.2451 | −0.729801 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.03621 | −0.359534 | −0.179767 | − | 0.983709i | \(-0.557534\pi\) | ||||
−0.179767 | + | 0.983709i | \(0.557534\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.634385 | −0.0323313 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.1655i | 1.33007i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.2280 | 1.22841 | 0.614203 | − | 0.789148i | \(-0.289477\pi\) | ||||
0.614203 | + | 0.789148i | \(0.289477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.451342i | 0.0228253i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.3372i | 1.02588i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.46629 | −0.0737770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.81975 | 0.0913305 | 0.0456653 | − | 0.998957i | \(-0.485459\pi\) | ||||
0.0456653 | + | 0.998957i | \(0.485459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.468900 | + | 4.51488i | −0.0234744 | + | 0.226027i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1855i | 1.85695i | 0.371391 | + | 0.928477i | \(0.378881\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.1826i | 0.905739i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.2637 | 0.609388 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85333 | 0.0918660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.3614i | − | 1.10570i | −0.833281 | − | 0.552849i | \(-0.813541\pi\) | ||
0.833281 | − | 0.552849i | \(-0.186459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.7919 | −1.51885 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.30223i | 0.162492i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9222i | 0.830681i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.8625i | 1.90311i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9251i | 0.631433i | 0.948854 | + | 0.315717i | \(0.102245\pi\) | ||||
−0.948854 | + | 0.315717i | \(0.897755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.78793i | − | 0.233349i | −0.993170 | − | 0.116675i | \(-0.962776\pi\) | ||
0.993170 | − | 0.116675i | \(-0.0372235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.1232i | 1.95086i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.355453 | −0.0172420 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.25912i | 0.0609333i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.3725 | −0.549071 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.53476 | 0.459273 | 0.229637 | − | 0.973276i | \(-0.426246\pi\) | ||||
0.229637 | + | 0.973276i | \(0.426246\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.79089i | − | 0.134121i | −0.997749 | − | 0.0670607i | \(-0.978638\pi\) | ||
0.997749 | − | 0.0670607i | \(-0.0213621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 11.6208i | − | 0.557176i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.52273 | + | 14.6618i | −0.0728419 | + | 0.701370i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.02359 | −0.0965805 | −0.0482903 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482903 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.5076 | 1.07179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 32.1904i | − | 1.52941i | −0.644380 | − | 0.764705i | \(-0.722885\pi\) | ||
0.644380 | − | 0.764705i | \(-0.277115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.5600i | 0.690211i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 35.8354 | 1.69496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.30244i | 0.344624i | 0.985042 | + | 0.172312i | \(0.0551237\pi\) | ||||
−0.985042 | + | 0.172312i | \(0.944876\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.83030 | −0.274538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.34029 | −0.438845 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87516 | 0.134789 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.04532 | −0.189232 | −0.0946161 | − | 0.995514i | \(-0.530162\pi\) | ||||
−0.0946161 | + | 0.995514i | \(0.530162\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0992916 | −0.00463453 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.8447 | 1.11056 | 0.555280 | − | 0.831664i | \(-0.312611\pi\) | ||||
0.555280 | + | 0.831664i | \(0.312611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1537i | 1.02957i | 0.857320 | + | 0.514784i | \(0.172128\pi\) | ||||
−0.857320 | + | 0.514784i | \(0.827872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.3886 | −0.713630 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.9396i | 1.29289i | 0.762960 | + | 0.646446i | \(0.223745\pi\) | ||||
−0.762960 | + | 0.646446i | \(0.776255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.24900i | − | 0.242376i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.5069 | −0.852755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.93739 | −0.364962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.5469 | − | 1.19922i | −0.529807 | − | 0.0550239i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 19.6557i | − | 0.899971i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9541i | 1.04880i | 0.851472 | + | 0.524401i | \(0.175711\pi\) | ||||
−0.851472 | + | 0.524401i | \(0.824289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.39963 | −0.382990 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.52160 | −0.160238 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 14.0655i | − | 0.638680i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.18991 | 0.0539202 | 0.0269601 | − | 0.999637i | \(-0.491417\pi\) | ||||
0.0269601 | + | 0.999637i | \(0.491417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 38.0224i | − | 1.71943i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.54606i | − | 0.295420i | −0.989031 | − | 0.147710i | \(-0.952810\pi\) | ||
0.989031 | − | 0.147710i | \(-0.0471902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.404343i | − | 0.0182107i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.03911i | − | 0.226491i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.47263i | − | 0.110912i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.5231i | 1.45593i | 0.685613 | + | 0.727966i | \(0.259534\pi\) | ||||
−0.685613 | + | 0.727966i | \(0.740466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.7402 | −0.747896 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 40.2944i | − | 1.79664i | −0.439343 | − | 0.898319i | \(-0.644789\pi\) | ||
0.439343 | − | 0.898319i | \(-0.355211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.9826 | 1.06721 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.9219 | 0.840350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 22.6070i | − | 1.00204i | −0.865437 | − | 0.501018i | \(-0.832959\pi\) | ||
0.865437 | − | 0.501018i | \(-0.167041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.72297i | − | 0.208932i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.22549 | − | 0.334988i | −0.142409 | − | 0.0147901i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2712 | 1.06952 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.1715 | −0.535303 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.15827i | 0.314213i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.5795i | 0.901605i | 0.892624 | + | 0.450803i | \(0.148862\pi\) | ||||
−0.892624 | + | 0.450803i | \(0.851138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.64704 | 0.0720198 | 0.0360099 | − | 0.999351i | \(-0.488535\pi\) | ||||
0.0360099 | + | 0.999351i | \(0.488535\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.77342i | − | 0.121042i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.535441 | −0.0233242 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5638 | 0.502774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.2306 | −1.13831 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.4240 | 1.14455 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.76719 | 0.379038 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.84690 | 0.209159 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.82777i | 0.294093i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.8608 | −1.92872 | −0.964359 | − | 0.264598i | \(-0.914761\pi\) | ||||
−0.964359 | + | 0.264598i | \(0.914761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 58.9459i | 2.52961i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.3085i | 1.25544i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1854 | −1.54717 | −0.773587 | − | 0.633690i | \(-0.781540\pi\) | ||||
−0.773587 | + | 0.633690i | \(0.781540\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0016 | −0.426858 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.36416 | − | 13.1351i | 0.0581153 | − | 0.559572i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.398076i | − | 0.0169279i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 7.10893i | − | 0.301757i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.19813 | 0.135509 | 0.0677546 | − | 0.997702i | \(-0.478416\pi\) | ||||
0.0677546 | + | 0.997702i | \(0.478416\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.9738 | 1.52153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 0.334899i | − | 0.0141394i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.9130 | 0.881379 | 0.440690 | − | 0.897660i | \(-0.354734\pi\) | ||||
0.440690 | + | 0.897660i | \(0.354734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.8424i | − | 0.456144i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.32941i | 0.139822i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0229i | 0.797482i | 0.917064 | + | 0.398741i | \(0.130553\pi\) | ||||
−0.917064 | + | 0.398741i | \(0.869447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.5317i | − | 0.608134i | −0.952651 | − | 0.304067i | \(-0.901655\pi\) | ||
0.952651 | − | 0.304067i | \(-0.0983447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.2625i | − | 0.470496i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.00654i | − | 0.375599i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.52413 | −0.354864 | −0.177432 | − | 0.984133i | \(-0.556779\pi\) | ||||
−0.177432 | + | 0.984133i | \(0.556779\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 69.4422i | 2.88592i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.59415 | −0.190597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.96262 | 0.246946 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.8382i | 0.944244i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.9751i | 1.27848i | 0.769008 | + | 0.639239i | \(0.220751\pi\) | ||||
−0.769008 | + | 0.639239i | \(0.779249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.3938 | − | 1.80646i | −0.716699 | − | 0.0744339i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42.6831 | −1.75575 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5388 | −0.638102 | −0.319051 | − | 0.947737i | \(-0.603364\pi\) | ||||
−0.319051 | + | 0.947737i | \(0.603364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0846677i | 0.00347104i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 59.8505i | 2.44952i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.2889 | −0.951560 | −0.475780 | − | 0.879564i | \(-0.657834\pi\) | ||||
−0.475780 | + | 0.879564i | \(0.657834\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.656076i | − | 0.0267619i | −0.999910 | − | 0.0133809i | \(-0.995741\pi\) | ||
0.999910 | − | 0.0133809i | \(-0.00425941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.6943 | 1.69792 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.52863 | 0.0621478 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.9837 | −1.01406 | −0.507030 | − | 0.861929i | \(-0.669257\pi\) | ||||
−0.507030 | + | 0.861929i | \(0.669257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.15489 | 0.127842 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.1637 | 2.23168 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.0422 | −1.81924 | −0.909619 | − | 0.415444i | \(-0.863626\pi\) | ||||
−0.909619 | + | 0.415444i | \(0.863626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.3637i | 0.901790i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0816 | 1.37207 | 0.686037 | − | 0.727567i | \(-0.259349\pi\) | ||||
0.686037 | + | 0.727567i | \(0.259349\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.10524i | 0.124810i | 0.998051 | + | 0.0624051i | \(0.0198771\pi\) | ||||
−0.998051 | + | 0.0624051i | \(0.980123\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2.51587i | − | 0.100958i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.95283 | −0.158367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.59052 | −0.183621 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.12987 | − | 10.8792i | 0.0451229 | − | 0.434473i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.247353i | − | 0.00986260i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 39.7357i | − | 1.58185i | −0.611912 | − | 0.790926i | \(-0.709599\pi\) | ||
0.611912 | − | 0.790926i | \(-0.290401\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.94663 | −0.236357 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.67803 | −0.344377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 30.9448i | − | 1.22608i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.6408 | 0.776978 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.8914i | − | 0.509180i | −0.967049 | − | 0.254590i | \(-0.918060\pi\) | ||
0.967049 | − | 0.254590i | \(-0.0819405\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.01752i | − | 0.276744i | −0.990380 | − | 0.138372i | \(-0.955813\pi\) | ||
0.990380 | − | 0.138372i | \(-0.0441870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.4460i | 1.19881i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.511218i | 0.0200980i | 0.999950 | + | 0.0100490i | \(0.00319876\pi\) | ||||
−0.999950 | + | 0.0100490i | \(0.996801\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.95715i | − | 0.312345i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.17779i | − | 0.163740i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.3046 | 0.520648 | 0.260324 | − | 0.965521i | \(-0.416171\pi\) | ||||
0.260324 | + | 0.965521i | \(0.416171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3893i | 0.484089i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.5159 | 1.46364 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.8770 | −0.930116 | −0.465058 | − | 0.885280i | \(-0.653967\pi\) | ||||
−0.465058 | + | 0.885280i | \(0.653967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.2142i | − | 0.941823i | −0.882180 | − | 0.470912i | \(-0.843925\pi\) | ||
0.882180 | − | 0.470912i | \(-0.156075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.51783i | 0.0589475i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.285650 | + | 2.75043i | −0.0110770 | + | 0.106657i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.2453 | 0.396700 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.1489 | 1.78422 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.03402i | − | 0.117127i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3324i | 1.01504i | 0.861640 | + | 0.507520i | \(0.169438\pi\) | ||||
−0.861640 | + | 0.507520i | \(0.830562\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.98137 | 0.0762629 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 26.4383i | − | 1.01611i | −0.861326 | − | 0.508053i | \(-0.830365\pi\) | ||
0.861326 | − | 0.508053i | \(-0.169635\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.81857 | 0.146543 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.2787 | 1.42852 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1385 | −1.19148 | −0.595742 | − | 0.803176i | \(-0.703142\pi\) | ||||
−0.595742 | + | 0.803176i | \(0.703142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.7582 | −0.716713 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4805 | −0.781382 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.0237 | −1.02952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.3375i | − | 0.621509i | −0.950490 | − | 0.310755i | \(-0.899418\pi\) | ||
0.950490 | − | 0.310755i | \(-0.100582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.36805 | 0.0519678 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6747i | 0.898034i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.778136i | 0.0294740i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 45.2138 | 1.71014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.4417 | −0.545454 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.834513 | − | 8.03525i | 0.0314743 | − | 0.303055i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.6871i | 1.75834i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.51092i | 0.244868i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8931 | 0.709545 | 0.354773 | − | 0.934953i | \(-0.384558\pi\) | ||||
0.354773 | + | 0.934953i | \(0.384558\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.16204 | 0.118586 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 13.5671i | − | 0.508093i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.92806 | −0.259095 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9188i | 0.482463i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 20.0206i | − | 0.746644i | −0.927702 | − | 0.373322i | \(-0.878219\pi\) | ||
0.927702 | − | 0.373322i | \(-0.121781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.58928i | 0.245398i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 62.0309i | 2.30695i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.06867i | 0.299663i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.6848i | − | 1.17513i | −0.809178 | − | 0.587563i | \(-0.800087\pi\) | ||
0.809178 | − | 0.587563i | \(-0.199913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.0469 | −1.18692 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.05936i | 0.0391817i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.5971 | 1.13013 | 0.565065 | − | 0.825047i | \(-0.308851\pi\) | ||||
0.565065 | + | 0.825047i | \(0.308851\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.1897 | 0.966023 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.6481i | 0.465900i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1820i | 0.521695i | 0.965380 | + | 0.260847i | \(0.0840020\pi\) | ||||
−0.965380 | + | 0.260847i | \(0.915998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.12081 | + | 49.3065i | −0.188118 | + | 1.81132i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.3618 | −0.453511 | −0.226756 | − | 0.973952i | \(-0.572812\pi\) | ||||
−0.226756 | + | 0.973952i | \(0.572812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8306 | 0.799812 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 36.4927i | − | 1.33520i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.38016i | 0.0869693i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.04990 | −0.257255 | −0.128627 | − | 0.991693i | \(-0.541057\pi\) | ||||
−0.128627 | + | 0.991693i | \(0.541057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 47.2067i | 1.72031i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.69003 | −0.207081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0995 | 1.31206 | 0.656030 | − | 0.754735i | \(-0.272235\pi\) | ||||
0.656030 | + | 0.754735i | \(0.272235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.48574 | 0.308013 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.0883 | −1.45320 | −0.726600 | − | 0.687061i | \(-0.758901\pi\) | ||||
−0.726600 | + | 0.687061i | \(0.758901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.95683 | −0.288057 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.672541 | −0.0243158 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0633i | 1.30217i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7670 | −0.388267 | −0.194134 | − | 0.980975i | \(-0.562190\pi\) | ||||
−0.194134 | + | 0.980975i | \(0.562190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5747i | 0.813007i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7939i | 1.17952i | 0.807580 | + | 0.589758i | \(0.200777\pi\) | ||||
−0.807580 | + | 0.589758i | \(0.799223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.6848 | 0.383808 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.92997 | 0.0692374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.62526 | + | 25.2777i | −0.0940596 | + | 0.905668i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.95811i | 0.213198i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.25389i | 0.0805475i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2743 | −0.402396 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.4608 | 1.08581 | 0.542905 | − | 0.839794i | \(-0.317324\pi\) | ||||
0.542905 | + | 0.839794i | \(0.317324\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.76322i | 0.311979i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.94356 | 0.104661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.7508i | 0.488304i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 22.8712i | − | 0.811158i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11.8517i | − | 0.419808i | −0.977722 | − | 0.209904i | \(-0.932685\pi\) | ||
0.977722 | − | 0.209904i | \(-0.0673151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.62446i | 0.0574694i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 31.3985i | − | 1.10941i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3806i | 0.401612i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.14533 | −0.0756129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.13285i | 0.110282i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.9936 | 0.632622 | 0.316311 | − | 0.948655i | \(-0.397556\pi\) | ||||
0.316311 | + | 0.948655i | \(0.397556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.0359 | −1.61654 | −0.808269 | − | 0.588813i | \(-0.799596\pi\) | ||||
−0.808269 | + | 0.588813i | \(0.799596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.4563i | − | 0.401789i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 23.1629i | − | 0.811363i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.57404 | + | 34.4132i | −0.125040 | + | 1.20396i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.20025 | −0.216654 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.5384 | 1.41480 | 0.707401 | − | 0.706813i | \(-0.249868\pi\) | ||||
0.707401 | + | 0.706813i | \(0.249868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.5703i | − | 1.23990i | −0.784641 | − | 0.619951i | \(-0.787153\pi\) | ||
0.784641 | − | 0.619951i | \(-0.212847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.68292i | 0.232669i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.8547 | −1.24679 | −0.623396 | − | 0.781907i | \(-0.714247\pi\) | ||||
−0.623396 | + | 0.781907i | \(0.714247\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.8626i | − | 0.481466i | −0.970591 | − | 0.240733i | \(-0.922612\pi\) | ||
0.970591 | − | 0.240733i | \(-0.0773879\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.6445 | 1.47932 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.911263 | 0.0315734 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.1980 | −0.352916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.98466 | 0.103165 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0064 | −0.725221 | −0.362610 | − | 0.931941i | \(-0.618114\pi\) | ||||
−0.362610 | + | 0.931941i | \(0.618114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.8215 | 0.683501 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 29.9826i | − | 1.03266i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5271 | 0.396543 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.415002i | 0.0142596i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.4556i | 1.49139i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.26748 | 0.214846 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8177 | 0.507347 | 0.253673 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253673 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.8475 | − | 2.26900i | −0.747168 | − | 0.0775983i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.3717i | 1.17412i | 0.809545 | + | 0.587058i | \(0.199714\pi\) | ||||
−0.809545 | + | 0.587058i | \(0.800286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1368i | 1.36945i | 0.728801 | + | 0.684725i | \(0.240078\pi\) | ||||
−0.728801 | + | 0.684725i | \(0.759922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.07141 | −0.206913 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.1351 | −0.685408 | −0.342704 | − | 0.939443i | \(-0.611343\pi\) | ||||
−0.342704 | + | 0.939443i | \(0.611343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.36076i | 0.148270i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.6131 | 1.44722 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.959216i | 0.0325392i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 57.3238i | − | 1.94234i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.3320i | 1.02658i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.86147i | − | 0.164348i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 57.4953i | − | 1.94148i | −0.240133 | − | 0.970740i | \(-0.577191\pi\) | ||
0.240133 | − | 0.970740i | \(-0.422809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 36.3192i | − | 1.22502i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.3916 | 1.25976 | 0.629878 | − | 0.776694i | \(-0.283105\pi\) | ||||
0.629878 | + | 0.776694i | \(0.283105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8089i | 1.07046i | 0.844708 | + | 0.535228i | \(0.179774\pi\) | ||||
−0.844708 | + | 0.535228i | \(0.820226\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.5218 | −1.02598 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.0252 | 1.57895 | 0.789475 | − | 0.613782i | \(-0.210353\pi\) | ||||
0.789475 | + | 0.613782i | \(0.210353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.35596i | − | 0.0790163i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.02265i | − | 0.268769i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.48058 | + | 52.7706i | −0.183401 | + | 1.76590i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.95269 | 0.0986977 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −38.4590 | −1.28411 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1544i | 0.405371i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.795795i | − | 0.0265118i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.26564 | −0.275063 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.9093i | 1.19367i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.2406 | 0.439648 | 0.219824 | − | 0.975540i | \(-0.429452\pi\) | ||||
0.219824 | + | 0.975540i | \(0.429452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −51.7182 | −1.71538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.1712 | 0.734565 | 0.367283 | − | 0.930109i | \(-0.380288\pi\) | ||||
0.367283 | + | 0.930109i | \(0.380288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.0702 | 0.366370 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6378 | −0.384734 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.36351 | −0.111073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 17.5957i | − | 0.580430i | −0.956961 | − | 0.290215i | \(-0.906273\pi\) | ||
0.956961 | − | 0.290215i | \(-0.0937268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.18261 | 0.269626 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 27.0033i | − | 0.888824i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.93593i | 0.162292i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.3406 | −1.71909 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.3436 | 0.831495 | 0.415748 | − | 0.909480i | \(-0.363520\pi\) | ||||
0.415748 | + | 0.909480i | \(0.363520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.6024 | + | 3.07440i | 0.970178 | + | 0.100759i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57.7415i | 1.89037i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.204018i | − | 0.00667209i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.4346 | −0.765576 | −0.382788 | − | 0.923836i | \(-0.625036\pi\) | ||||
−0.382788 | + | 0.923836i | \(0.625036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.6925 | −0.479472 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 51.2071i | − | 1.66930i | −0.550779 | − | 0.834651i | \(-0.685669\pi\) | ||
0.550779 | − | 0.834651i | \(-0.314331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7166 | −0.642060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.471956i | − | 0.0153527i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 19.1234i | − | 0.621428i | −0.950504 | − | 0.310714i | \(-0.899432\pi\) | ||
0.950504 | − | 0.310714i | \(-0.100568\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 51.5790i | − | 1.67433i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 52.6315i | − | 1.70669i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.09795i | 0.0355660i | 0.999842 | + | 0.0177830i | \(0.00566080\pi\) | ||||
−0.999842 | + | 0.0177830i | \(0.994339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 6.86100i | − | 0.222017i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.60210 | −0.245741 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 5.09257i | − | 0.164448i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9049 | −0.480802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.9064 | −0.609249 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42.3037i | 1.36180i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.53586i | 0.210179i | 0.994463 | + | 0.105090i | \(0.0335129\pi\) | ||||
−0.994463 | + | 0.105090i | \(0.966487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.45198 | − | 0.150798i | −0.0466443 | − | 0.00484432i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.3985 | −0.847168 | −0.423584 | − | 0.905857i | \(-0.639228\pi\) | ||||
−0.423584 | + | 0.905857i | \(0.639228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.42735 | −0.206051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 30.2883i | − | 0.970001i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.7159i | 1.43059i | 0.698824 | + | 0.715293i | \(0.253707\pi\) | ||||
−0.698824 | + | 0.715293i | \(0.746293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.52486 | 0.304416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 63.2035i | − | 2.01793i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5385 | 0.463707 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.0022 | −0.828498 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.6749 | −0.403446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.8422 | −0.853533 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.4694 | −0.936125 | −0.468063 | − | 0.883695i | \(-0.655048\pi\) | ||||
−0.468063 | + | 0.883695i | \(0.655048\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.930449 | −0.0295269 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.4604i | 1.15587i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.5810 | 0.525126 | 0.262563 | − | 0.964915i | \(-0.415432\pi\) | ||||
0.262563 | + | 0.964915i | \(0.415432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.37880i | 0.0436232i |
(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 | 3344.2.o.a.1519.6 | yes | 36 | |
4.3 | odd | 2 | inner | 3344.2.o.a.1519.32 | yes | 36 | |
19.18 | odd | 2 | inner | 3344.2.o.a.1519.31 | yes | 36 | |
76.75 | even | 2 | inner | 3344.2.o.a.1519.5 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.a.1519.5 | ✓ | 36 | 76.75 | even | 2 | inner | |
3344.2.o.a.1519.6 | yes | 36 | 1.1 | even | 1 | trivial | |
3344.2.o.a.1519.31 | yes | 36 | 19.18 | odd | 2 | inner | |
3344.2.o.a.1519.32 | yes | 36 | 4.3 | odd | 2 | inner |