Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(0.767178 - 1.18804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.161 |
Dual form | 384.3.i.a.353.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.77809 | − | 1.13234i | 0.926031 | − | 0.377447i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.28651 | + | 6.28651i | 1.25730 | + | 1.25730i | 0.952376 | + | 0.304927i | \(0.0986321\pi\) |
0.304927 | + | 0.952376i | \(0.401368\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.64575i | − | 0.235107i | −0.993067 | − | 0.117554i | \(-0.962495\pi\) | ||
0.993067 | − | 0.117554i | \(-0.0375052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.43560 | − | 6.29150i | 0.715067 | − | 0.699056i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.75216 | − | 4.75216i | −0.432014 | − | 0.432014i | 0.457299 | − | 0.889313i | \(-0.348817\pi\) |
−0.889313 | + | 0.457299i | \(0.848817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.35425 | + | 9.35425i | 0.719558 | + | 0.719558i | 0.968515 | − | 0.248957i | \(-0.0800878\pi\) |
−0.248957 | + | 0.968515i | \(0.580088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.5830 | + | 10.3460i | 1.63887 | + | 0.689736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 11.4859i | − | 0.675644i | −0.941210 | − | 0.337822i | \(-0.890310\pi\) | ||
0.941210 | − | 0.337822i | \(-0.109690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.58301 | + | 8.58301i | 0.451737 | + | 0.451737i | 0.895931 | − | 0.444194i | \(-0.146510\pi\) |
−0.444194 | + | 0.895931i | \(0.646510\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.86355 | − | 4.57205i | −0.0887406 | − | 0.217717i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.2381 | −0.706004 | −0.353002 | − | 0.935623i | \(-0.614839\pi\) | ||||
−0.353002 | + | 0.935623i | \(0.614839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.0405i | 2.16162i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.7546 | − | 24.7657i | 0.398318 | − | 0.917248i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.7405 | + | 10.7405i | −0.370362 | + | 0.370362i | −0.867609 | − | 0.497247i | \(-0.834344\pi\) |
0.497247 | + | 0.867609i | \(0.334344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.35425 | 0.204976 | 0.102488 | − | 0.994734i | \(-0.467320\pi\) | ||||
0.102488 | + | 0.994734i | \(0.467320\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.5830 | − | 7.82087i | −0.563121 | − | 0.236996i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3460 | − | 10.3460i | 0.295601 | − | 0.295601i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.2288 | + | 27.2288i | −0.735912 | + | 0.735912i | −0.971784 | − | 0.235872i | \(-0.924205\pi\) |
0.235872 | + | 0.971784i | \(0.424205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.5792 | + | 15.3948i | 0.937928 | + | 0.394738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.98162 | −0.0483323 | −0.0241662 | − | 0.999708i | \(-0.507693\pi\) | ||||
−0.0241662 | + | 0.999708i | \(0.507693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.4170 | − | 19.4170i | 0.451558 | − | 0.451558i | −0.444313 | − | 0.895871i | \(-0.646552\pi\) |
0.895871 | + | 0.444313i | \(0.146552\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 80.0091 | + | 0.905893i | 1.77798 | + | 0.0201310i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 74.9474i | − | 1.59463i | −0.603566 | − | 0.797313i | \(-0.706254\pi\) | ||
0.603566 | − | 0.797313i | \(-0.293746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46.2915 | 0.944725 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0060 | − | 31.9090i | −0.255020 | − | 0.625667i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00671 | + | 4.00671i | 0.0755983 | + | 0.0755983i | 0.743895 | − | 0.668297i | \(-0.232976\pi\) |
−0.668297 | + | 0.743895i | \(0.732976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 59.7490i | − | 1.08635i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 33.5633 | + | 14.1255i | 0.588830 | + | 0.247816i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27.9694 | − | 27.9694i | −0.474058 | − | 0.474058i | 0.429167 | − | 0.903225i | \(-0.358807\pi\) |
−0.903225 | + | 0.429167i | \(0.858807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.2288 | − | 39.2288i | −0.643094 | − | 0.643094i | 0.308221 | − | 0.951315i | \(-0.400267\pi\) |
−0.951315 | + | 0.308221i | \(0.900267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.3542 | − | 10.5914i | −0.164353 | − | 0.168118i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 117.611i | 1.80940i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 68.6863 | + | 68.6863i | 1.02517 | + | 1.02517i | 0.999675 | + | 0.0254932i | \(0.00811562\pi\) |
0.0254932 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −45.1110 | + | 18.3871i | −0.653782 | + | 0.266479i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −40.6822 | −0.572988 | −0.286494 | − | 0.958082i | \(-0.592490\pi\) | ||||
−0.286494 | + | 0.958082i | \(0.592490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 59.0405i | − | 0.808774i | −0.914588 | − | 0.404387i | \(-0.867485\pi\) | ||
0.914588 | − | 0.404387i | \(-0.132515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.1923 | + | 150.130i | 0.815898 | + | 2.00173i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.82087 | + | 7.82087i | −0.101570 | + | 0.101570i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.3948 | 0.220187 | 0.110093 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110093 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.83399 | − | 80.9792i | 0.0226418 | − | 0.999744i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −75.1400 | + | 75.1400i | −0.905301 | + | 0.905301i | −0.995889 | − | 0.0905874i | \(-0.971126\pi\) |
0.0905874 | + | 0.995889i | \(0.471126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.2065 | − | 72.2065i | 0.849489 | − | 0.849489i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.6762 | + | 42.0000i | −0.203174 | + | 0.482759i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −78.8051 | −0.885450 | −0.442725 | − | 0.896657i | \(-0.645988\pi\) | ||||
−0.442725 | + | 0.896657i | \(0.645988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.3948 | − | 15.3948i | 0.169173 | − | 0.169173i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.6527 | − | 7.19518i | 0.189814 | − | 0.0773675i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107.914i | 1.13594i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −38.8340 | −0.400350 | −0.200175 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200175 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −60.4812 | − | 0.684791i | −0.610921 | − | 0.00691708i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −41.5332 | − | 41.5332i | −0.411220 | − | 0.411220i | 0.470943 | − | 0.882164i | \(-0.343914\pi\) |
−0.882164 | + | 0.470943i | \(0.843914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98.8118i | 0.959337i | 0.877450 | + | 0.479669i | \(0.159243\pi\) | ||||
−0.877450 | + | 0.479669i | \(0.840757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.0270 | − | 40.4575i | 0.162162 | − | 0.385310i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −98.8480 | − | 98.8480i | −0.923813 | − | 0.923813i | 0.0734837 | − | 0.997296i | \(-0.476588\pi\) |
−0.997296 | + | 0.0734837i | \(0.976588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −68.8523 | − | 68.8523i | −0.631672 | − | 0.631672i | 0.316815 | − | 0.948487i | \(-0.397387\pi\) |
−0.948487 | + | 0.316815i | \(0.897387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −44.8118 | + | 106.476i | −0.403710 | + | 0.959246i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.31160i | − | 0.0735540i | −0.999323 | − | 0.0367770i | \(-0.988291\pi\) | ||
0.999323 | − | 0.0367770i | \(-0.0117091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −102.081 | − | 102.081i | −0.887661 | − | 0.887661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 119.053 | + | 1.34796i | 1.01754 | + | 0.0115210i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.9030 | −0.158849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 75.8340i | − | 0.626727i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.50514 | + | 2.24388i | −0.0447572 | + | 0.0182429i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −182.564 | + | 182.564i | −1.46051 | + | 1.46051i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −195.933 | −1.54278 | −0.771391 | − | 0.636361i | \(-0.780439\pi\) | ||||
−0.771391 | + | 0.636361i | \(0.780439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.9555 | − | 75.9289i | 0.247717 | − | 0.588596i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 142.127 | − | 142.127i | 1.08494 | − | 1.08494i | 0.0888967 | − | 0.996041i | \(-0.471666\pi\) |
0.996041 | − | 0.0888967i | \(-0.0283341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.1255 | − | 14.1255i | 0.106207 | − | 0.106207i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 223.299 | − | 88.0810i | 1.65406 | − | 0.652452i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 50.4847 | 0.368501 | 0.184251 | − | 0.982879i | \(-0.441014\pi\) | ||||
0.184251 | + | 0.982879i | \(0.441014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −171.727 | + | 171.727i | −1.23544 | + | 1.23544i | −0.273601 | + | 0.961843i | \(0.588215\pi\) |
−0.961843 | + | 0.273601i | \(0.911785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −84.8661 | − | 208.211i | −0.601887 | − | 1.47667i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 88.9057i | − | 0.621718i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −135.041 | −0.931314 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 128.602 | − | 52.4178i | 0.874844 | − | 0.356584i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84.4952 | + | 84.4952i | 0.567082 | + | 0.567082i | 0.931310 | − | 0.364228i | \(-0.118667\pi\) |
−0.364228 | + | 0.931310i | \(0.618667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 30.1033i | − | 0.199359i | −0.995020 | − | 0.0996797i | \(-0.968218\pi\) | ||
0.995020 | − | 0.0996797i | \(-0.0317818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −72.2638 | − | 73.9190i | −0.472313 | − | 0.483130i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.9461 | + | 39.9461i | 0.257717 | + | 0.257717i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 181.265 | + | 181.265i | 1.15456 | + | 1.15456i | 0.985628 | + | 0.168928i | \(0.0540305\pi\) |
0.168928 | + | 0.985628i | \(0.445970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.6680 | + | 6.59405i | 0.0985407 | + | 0.0414720i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.7239i | 0.165987i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −200.081 | − | 200.081i | −1.22749 | − | 1.22749i | −0.964910 | − | 0.262581i | \(-0.915426\pi\) |
−0.262581 | − | 0.964910i | \(-0.584574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −67.6563 | − | 165.988i | −0.410038 | − | 1.00599i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −172.656 | −1.03387 | −0.516933 | − | 0.856026i | \(-0.672926\pi\) | ||||
−0.516933 | + | 0.856026i | \(0.672926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00394i | 0.0355263i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 109.237 | + | 1.23682i | 0.638812 | + | 0.00723287i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 40.8313 | − | 40.8313i | 0.236019 | − | 0.236019i | −0.579181 | − | 0.815199i | \(-0.696627\pi\) |
0.815199 | + | 0.579181i | \(0.196627\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 88.9373 | 0.508213 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −109.373 | − | 46.0307i | −0.617924 | − | 0.260060i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −152.613 | + | 152.613i | −0.852584 | + | 0.852584i | −0.990451 | − | 0.137866i | \(-0.955976\pi\) |
0.137866 | + | 0.990451i | \(0.455976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −166.601 | + | 166.601i | −0.920449 | + | 0.920449i | −0.997061 | − | 0.0766118i | \(-0.975590\pi\) |
0.0766118 | + | 0.997061i | \(0.475590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −153.402 | − | 64.5608i | −0.838260 | − | 0.352791i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −342.348 | −1.85053 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −54.5830 | + | 54.5830i | −0.291888 | + | 0.291888i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −40.7582 | − | 17.6994i | −0.215652 | − | 0.0936474i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3434i | 0.0750963i | 0.999295 | + | 0.0375482i | \(0.0119548\pi\) | ||||
−0.999295 | + | 0.0375482i | \(0.988045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 207.373 | 1.07447 | 0.537235 | − | 0.843433i | \(-0.319469\pi\) | ||||
0.537235 | + | 0.843433i | \(0.319469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 133.176 | + | 326.735i | 0.682954 | + | 1.67556i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −97.2608 | − | 97.2608i | −0.493710 | − | 0.493710i | 0.415763 | − | 0.909473i | \(-0.363514\pi\) |
−0.909473 | + | 0.415763i | \(0.863514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 82.7673i | 0.415916i | 0.978138 | + | 0.207958i | \(0.0666818\pi\) | ||||
−0.978138 | + | 0.207958i | \(0.933318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 268.593 | + | 113.041i | 1.33628 | + | 0.562391i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.6762 | + | 17.6762i | 0.0870748 | + | 0.0870748i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4575 | − | 12.4575i | −0.0607684 | − | 0.0607684i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −104.502 | + | 102.162i | −0.504840 | + | 0.493536i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 81.5756i | − | 0.390314i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 201.646 | + | 201.646i | 0.955667 | + | 0.955667i | 0.999058 | − | 0.0433911i | \(-0.0138162\pi\) |
−0.0433911 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −113.019 | + | 46.0661i | −0.530605 | + | 0.216273i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 244.130 | 1.13549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.4575i | − | 0.0481913i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −66.8541 | − | 164.020i | −0.305270 | − | 0.748950i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 107.442 | − | 107.442i | 0.486164 | − | 0.486164i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 233.261 | 1.04602 | 0.523008 | − | 0.852328i | \(-0.324810\pi\) | ||||
0.523008 | + | 0.852328i | \(0.324810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 339.996 | + | 347.783i | 1.51109 | + | 1.54570i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −94.3599 | + | 94.3599i | −0.415682 | + | 0.415682i | −0.883712 | − | 0.468030i | \(-0.844964\pi\) |
0.468030 | + | 0.883712i | \(0.344964\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 138.063 | − | 138.063i | 0.602894 | − | 0.602894i | −0.338185 | − | 0.941080i | \(-0.609813\pi\) |
0.941080 | + | 0.338185i | \(0.109813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.8712 | + | 30.5830i | −0.0557195 | + | 0.132394i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 396.796 | 1.70299 | 0.851493 | − | 0.524366i | \(-0.175697\pi\) | ||||
0.851493 | + | 0.524366i | \(0.175697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 471.158 | − | 471.158i | 2.00493 | − | 2.00493i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 48.3243 | − | 19.6968i | 0.203900 | − | 0.0831090i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 284.813i | − | 1.19168i | −0.803102 | − | 0.595842i | \(-0.796818\pi\) | ||
0.803102 | − | 0.595842i | \(-0.203182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −266.531 | −1.10594 | −0.552968 | − | 0.833202i | \(-0.686505\pi\) | ||||
−0.552968 | + | 0.833202i | \(0.686505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −86.6012 | − | 227.045i | −0.356383 | − | 0.934340i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 291.012 | + | 291.012i | 1.18780 | + | 1.18780i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 160.575i | 0.650102i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −123.662 | + | 293.830i | −0.496633 | + | 1.18004i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 153.945 | + | 153.945i | 0.613327 | + | 0.613327i | 0.943811 | − | 0.330485i | \(-0.107212\pi\) |
−0.330485 | + | 0.943811i | \(0.607212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 77.1660 | + | 77.1660i | 0.305004 | + | 0.305004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 118.834 | − | 282.359i | 0.466016 | − | 1.10729i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 240.167i | 0.934503i | 0.884125 | + | 0.467251i | \(0.154756\pi\) | ||||
−0.884125 | + | 0.467251i | \(0.845244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 44.8118 | + | 44.8118i | 0.173018 | + | 0.173018i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.54772 | + | 136.695i | −0.00592995 | + | 0.523737i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −140.707 | −0.535009 | −0.267505 | − | 0.963557i | \(-0.586199\pi\) | ||||
−0.267505 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 50.3765i | 0.190100i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −218.928 | + | 89.2343i | −0.819954 | + | 0.334211i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 229.830 | − | 229.830i | 0.854388 | − | 0.854388i | −0.136282 | − | 0.990670i | \(-0.543515\pi\) |
0.990670 | + | 0.136282i | \(0.0435152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 228.731 | 0.844025 | 0.422012 | − | 0.906590i | \(-0.361324\pi\) | ||||
0.422012 | + | 0.906590i | \(0.361324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.3360 | − | 60.2002i | 0.0928057 | − | 0.220514i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 256.809 | − | 256.809i | 0.933851 | − | 0.933851i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 103.265 | − | 103.265i | 0.372799 | − | 0.372799i | −0.495697 | − | 0.868496i | \(-0.665087\pi\) |
0.868496 | + | 0.495697i | \(0.165087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.8934 | − | 39.9778i | 0.146571 | − | 0.143290i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 283.552 | 1.00908 | 0.504540 | − | 0.863388i | \(-0.331662\pi\) | ||||
0.504540 | + | 0.863388i | \(0.331662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4758 | + | 23.4758i | −0.0829534 | + | 0.0829534i | −0.747366 | − | 0.664413i | \(-0.768682\pi\) |
0.664413 | + | 0.747366i | \(0.268682\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 122.196 | + | 299.796i | 0.428758 | + | 1.05192i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.26126i | 0.0113633i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 157.073 | 0.543506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −107.884 | + | 43.9734i | −0.370737 | + | 0.151111i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −381.409 | − | 381.409i | −1.30174 | − | 1.30174i | −0.927220 | − | 0.374516i | \(-0.877809\pi\) |
−0.374516 | − | 0.927220i | \(-0.622191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 351.660i | − | 1.19207i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −168.798 | + | 66.5830i | −0.568343 | + | 0.224185i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −151.895 | − | 151.895i | −0.508011 | − | 0.508011i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.9555 | − | 31.9555i | −0.106165 | − | 0.106165i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −162.413 | − | 68.3534i | −0.536017 | − | 0.225589i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 493.224i | − | 1.61713i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 209.055 | + | 209.055i | 0.680960 | + | 0.680960i | 0.960217 | − | 0.279256i | \(-0.0900879\pi\) |
−0.279256 | + | 0.960217i | \(0.590088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 111.889 | + | 274.508i | 0.362099 | + | 0.888376i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 111.176 | 0.357478 | 0.178739 | − | 0.983897i | \(-0.442798\pi\) | ||||
0.178739 | + | 0.983897i | \(0.442798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 282.280i | 0.901852i | 0.892561 | + | 0.450926i | \(0.148906\pi\) | ||||
−0.892561 | + | 0.450926i | \(0.851094\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.49088 | − | 131.675i | 0.00473294 | − | 0.418016i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −206.983 | + | 206.983i | −0.652943 | + | 0.652943i | −0.953701 | − | 0.300758i | \(-0.902760\pi\) |
0.300758 | + | 0.953701i | \(0.402760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 102.081 | 0.320003 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −386.539 | − | 162.679i | −1.20417 | − | 0.506789i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 98.5839 | − | 98.5839i | 0.305213 | − | 0.305213i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −505.508 | + | 505.508i | −1.55541 | + | 1.55541i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −269.242 | − | 113.314i | −0.823371 | − | 0.346525i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −123.345 | −0.374908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −127.431 | + | 127.431i | −0.384989 | + | 0.384989i | −0.872896 | − | 0.487907i | \(-0.837761\pi\) |
0.487907 | + | 0.872896i | \(0.337761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.92369 | + | 346.543i | −0.0117829 | + | 1.04067i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 863.594i | 2.57789i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 68.9595 | 0.204628 | 0.102314 | − | 0.994752i | \(-0.467375\pi\) | ||||
0.102314 | + | 0.994752i | \(0.467375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.41157 | − | 23.0904i | −0.0277627 | − | 0.0681133i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.1964 | − | 30.1964i | −0.0885525 | − | 0.0885525i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 156.826i | − | 0.457219i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −399.181 | − | 168.000i | −1.15705 | − | 0.486957i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 54.0628 | + | 54.0628i | 0.155801 | + | 0.155801i | 0.780703 | − | 0.624902i | \(-0.214861\pi\) |
−0.624902 | + | 0.780703i | \(0.714861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.107201 | − | 0.107201i | −0.000307168 | − | 0.000307168i | 0.706953 | − | 0.707260i | \(-0.250069\pi\) |
−0.707260 | + | 0.706953i | \(0.750069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 332.265 | − | 131.063i | 0.946625 | − | 0.373400i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 194.223i | − | 0.550208i | −0.961414 | − | 0.275104i | \(-0.911288\pi\) | ||
0.961414 | − | 0.275104i | \(-0.0887123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −255.749 | − | 255.749i | −0.720420 | − | 0.720420i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −52.5143 | + | 21.4047i | −0.147099 | + | 0.0599570i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 437.689 | 1.21919 | 0.609595 | − | 0.792713i | \(-0.291332\pi\) | ||||
0.609595 | + | 0.792713i | \(0.291332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 213.664i | − | 0.591867i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −85.8700 | − | 210.674i | −0.236556 | − | 0.580369i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 371.159 | − | 371.159i | 1.01687 | − | 1.01687i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −246.678 | −0.672148 | −0.336074 | − | 0.941836i | \(-0.609099\pi\) | ||||
−0.336074 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.7530 | + | 12.4674i | −0.0345608 | + | 0.0337870i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.59405 | − | 6.59405i | 0.0177737 | − | 0.0177737i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 349.678 | − | 349.678i | 0.937476 | − | 0.937476i | −0.0606816 | − | 0.998157i | \(-0.519327\pi\) |
0.998157 | + | 0.0606816i | \(0.0193274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −300.454 | + | 713.903i | −0.801212 | + | 1.90374i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −200.938 | −0.532993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −235.668 | + | 235.668i | −0.621815 | + | 0.621815i | −0.945995 | − | 0.324180i | \(-0.894912\pi\) |
0.324180 | + | 0.945995i | \(0.394912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −544.321 | + | 221.864i | −1.42866 | + | 0.582319i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 64.2130i | − | 0.167658i | −0.996480 | − | 0.0838290i | \(-0.973285\pi\) | ||
0.996480 | − | 0.0838290i | \(-0.0267149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −98.3320 | −0.255408 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.79801 | − | 247.122i | 0.00723000 | − | 0.638559i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 273.321 | + | 273.321i | 0.702624 | + | 0.702624i | 0.964973 | − | 0.262349i | \(-0.0844973\pi\) |
−0.262349 | + | 0.964973i | \(0.584497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 186.510i | 0.477007i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 233.905 | − | 555.778i | 0.595179 | − | 1.41419i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 109.352 | + | 109.352i | 0.276842 | + | 0.276842i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −141.678 | − | 141.678i | −0.356873 | − | 0.356873i | 0.505786 | − | 0.862659i | \(-0.331202\pi\) |
−0.862659 | + | 0.505786i | \(0.831202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.2470 | − | 55.2368i | 0.0582633 | − | 0.138438i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 194.801i | − | 0.485788i | −0.970053 | − | 0.242894i | \(-0.921903\pi\) | ||
0.970053 | − | 0.242894i | \(-0.0780967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59.4392 | + | 59.4392i | 0.147492 | + | 0.147492i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 520.607 | − | 497.548i | 1.28545 | − | 1.22851i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 258.791 | 0.635849 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 420.826i | 1.02891i | 0.857516 | + | 0.514457i | \(0.172007\pi\) | ||||
−0.857516 | + | 0.514457i | \(0.827993\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 140.251 | − | 57.1659i | 0.341244 | − | 0.139090i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −46.0307 | + | 46.0307i | −0.111454 | + | 0.111454i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −944.737 | −2.27648 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −282.620 | + | 671.526i | −0.677745 | + | 1.61038i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −186.421 | + | 186.421i | −0.444919 | + | 0.444919i | −0.893661 | − | 0.448742i | \(-0.851872\pi\) |
0.448742 | + | 0.893661i | \(0.351872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 186.889 | − | 186.889i | 0.443917 | − | 0.443917i | −0.449409 | − | 0.893326i | \(-0.648366\pi\) |
0.893326 | + | 0.449409i | \(0.148366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −471.532 | − | 482.332i | −1.11473 | − | 1.14026i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 620.706 | 1.46049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −64.5608 | + | 64.5608i | −0.151196 | + | 0.151196i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −100.672 | − | 246.988i | −0.234666 | − | 0.575731i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 128.395i | − | 0.297901i | −0.988845 | − | 0.148950i | \(-0.952411\pi\) | ||
0.988845 | − | 0.148950i | \(-0.0475895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 684.737 | 1.58138 | 0.790690 | − | 0.612217i | \(-0.209722\pi\) | ||||
0.790690 | + | 0.612217i | \(0.209722\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −375.155 | + | 152.912i | −0.862426 | + | 0.351522i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −139.372 | − | 139.372i | −0.318928 | − | 0.318928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 239.107i | − | 0.544663i | −0.962203 | − | 0.272332i | \(-0.912205\pi\) | ||
0.962203 | − | 0.272332i | \(-0.0877948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 297.914 | − | 291.243i | 0.675541 | − | 0.660415i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 310.189 | + | 310.189i | 0.700200 | + | 0.700200i | 0.964453 | − | 0.264253i | \(-0.0851255\pi\) |
−0.264253 | + | 0.964453i | \(0.585125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −495.409 | − | 495.409i | −1.11328 | − | 1.11328i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 330.413 | + | 139.058i | 0.739179 | + | 0.311092i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 545.902i | 1.21582i | 0.794007 | + | 0.607908i | \(0.207991\pi\) | ||||
−0.794007 | + | 0.607908i | \(0.792009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.41699 | + | 9.41699i | 0.0208803 | + | 0.0208803i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −34.0872 | − | 83.6297i | −0.0752477 | − | 0.184613i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 193.559 | 0.425404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 289.579i | − | 0.633652i | −0.948484 | − | 0.316826i | \(-0.897383\pi\) | ||
0.948484 | − | 0.316826i | \(-0.102617\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −284.457 | − | 123.526i | −0.619732 | − | 0.269121i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 160.511 | − | 160.511i | 0.348180 | − | 0.348180i | −0.511251 | − | 0.859431i | \(-0.670818\pi\) |
0.859431 | + | 0.511251i | \(0.170818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −197.573 | −0.426723 | −0.213361 | − | 0.976973i | \(-0.568441\pi\) | ||||
−0.213361 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 156.207 | + | 65.7413i | 0.335928 | + | 0.141379i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 52.7645 | − | 52.7645i | 0.112986 | − | 0.112986i | −0.648353 | − | 0.761339i | \(-0.724542\pi\) |
0.761339 | + | 0.648353i | \(0.224542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 113.041 | − | 113.041i | 0.241025 | − | 0.241025i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 708.826 | + | 298.318i | 1.50494 | + | 0.633371i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −184.545 | −0.390159 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −463.830 | + | 463.830i | −0.976484 | + | 0.976484i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 50.9938 | + | 0.577371i | 0.106905 | + | 0.00121042i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 175.985i | 0.367401i | 0.982982 | + | 0.183700i | \(0.0588076\pi\) | ||||
−0.982982 | + | 0.183700i | \(0.941192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −509.409 | −1.05906 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.2606 | + | 74.2414i | 0.0626513 | + | 0.153709i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −244.130 | − | 244.130i | −0.503362 | − | 0.503362i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 965.217i | 1.98196i | 0.133991 | + | 0.990982i | \(0.457221\pi\) | ||||
−0.133991 | + | 0.990982i | \(0.542779\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −782.404 | − | 329.284i | −1.60001 | − | 0.673382i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 600.614 | + | 600.614i | 1.22325 | + | 1.22325i | 0.966471 | + | 0.256775i | \(0.0826598\pi\) |
0.256775 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 123.365 | + | 123.365i | 0.250233 | + | 0.250233i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −375.911 | − | 384.521i | −0.759416 | − | 0.776810i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 66.9527i | 0.134714i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 51.6092 | + | 51.6092i | 0.103425 | + | 0.103425i | 0.756926 | − | 0.653501i | \(-0.226700\pi\) |
−0.653501 | + | 0.756926i | \(0.726700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −479.653 | + | 195.505i | −0.957391 | + | 0.390230i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −847.530 | −1.68495 | −0.842475 | − | 0.538735i | \(-0.818902\pi\) | ||||
−0.842475 | + | 0.538735i | \(0.818902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 522.199i | − | 1.03406i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.79851 | + | 16.6795i | 0.0134093 | + | 0.0328984i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −128.457 | + | 128.457i | −0.252372 | + | 0.252372i | −0.821942 | − | 0.569570i | \(-0.807110\pi\) |
0.569570 | + | 0.821942i | \(0.307110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −97.1660 | −0.190149 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 304.871 | − | 120.257i | 0.594290 | − | 0.234420i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −621.182 | + | 621.182i | −1.20618 | + | 1.20618i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −356.162 | + | 356.162i | −0.688901 | + | 0.688901i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 67.1981 | − | 159.668i | 0.129476 | − | 0.307645i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −676.366 | −1.29821 | −0.649103 | − | 0.760700i | \(-0.724856\pi\) | ||||
−0.649103 | + | 0.760700i | \(0.724856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 600.494 | − | 600.494i | 1.14817 | − | 1.14817i | 0.161260 | − | 0.986912i | \(-0.448444\pi\) |
0.986912 | − | 0.161260i | \(-0.0515559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 247.076 | − | 100.707i | 0.470621 | − | 0.191824i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 72.9845i | − | 0.138491i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −265.324 | −0.501558 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −355.970 | − | 4.03042i | −0.670376 | − | 0.00759025i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.5366 | − | 18.5366i | −0.0347779 | − | 0.0347779i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1242.82i | − | 2.32302i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −251.162 | + | 596.782i | −0.467714 | + | 1.11133i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −219.985 | − | 219.985i | −0.408135 | − | 0.408135i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.4797 | − | 43.4797i | −0.0803692 | − | 0.0803692i | 0.665779 | − | 0.746149i | \(-0.268099\pi\) |
−0.746149 | + | 0.665779i | \(0.768099\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −274.184 | + | 651.484i | −0.504943 | + | 1.19979i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 865.682i | − | 1.58841i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 125.498 | + | 125.498i | 0.229430 | + | 0.229430i | 0.812454 | − | 0.583025i | \(-0.198131\pi\) |
−0.583025 | + | 0.812454i | \(0.698131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −499.269 | − | 5.65291i | −0.909414 | − | 0.0102967i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −184.371 | −0.334612 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 28.6275i | − | 0.0517676i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −951.074 | + | 387.655i | −1.71365 | + | 0.698477i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −184.272 | + | 184.272i | −0.330829 | + | 0.330829i | −0.852901 | − | 0.522072i | \(-0.825159\pi\) |
0.522072 | + | 0.852901i | \(0.325159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 363.263 | 0.649844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −89.8301 | + | 213.443i | −0.160125 | + | 0.380469i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 523.489 | − | 523.489i | 0.929820 | − | 0.929820i | −0.0678736 | − | 0.997694i | \(-0.521621\pi\) |
0.997694 | + | 0.0678736i | \(0.0216215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 52.2510 | − | 52.2510i | 0.0924796 | − | 0.0924796i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −133.272 | − | 3.01829i | −0.235047 | − | 0.00532326i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 52.6214 | 0.0924805 | 0.0462403 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462403 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 114.561 | − | 114.561i | 0.200632 | − | 0.200632i | −0.599639 | − | 0.800271i | \(-0.704689\pi\) |
0.800271 | + | 0.599639i | \(0.204689\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2416 | + | 39.8473i | 0.0283449 | + | 0.0695415i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 877.515i | − | 1.52611i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 496.442 | 0.860384 | 0.430192 | − | 0.902737i | \(-0.358446\pi\) | ||||
0.430192 | + | 0.902737i | \(0.358446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 576.100 | − | 234.817i | 0.994992 | − | 0.405555i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 123.662 | + | 123.662i | 0.212843 | + | 0.212843i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 38.0810i | − | 0.0653191i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 739.951 | + | 756.899i | 1.26487 | + | 1.29384i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 115.260 | + | 115.260i | 0.196354 | + | 0.196354i | 0.798435 | − | 0.602081i | \(-0.205662\pi\) |
−0.602081 | + | 0.798435i | \(0.705662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.5385 | + | 54.5385i | 0.0925952 | + | 0.0925952i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −380.332 | − | 160.067i | −0.643540 | − | 0.270841i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 227.756i | − | 0.384074i | −0.981388 | − | 0.192037i | \(-0.938491\pi\) | ||
0.981388 | − | 0.192037i | \(-0.0615094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −118.834 | − | 118.834i | −0.199721 | − | 0.199721i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 93.7209 | + | 229.935i | 0.156986 | + | 0.385151i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 760.308 | 1.26930 | 0.634648 | − | 0.772802i | \(-0.281145\pi\) | ||||
0.634648 | + | 0.772802i | \(0.281145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 85.7856i | − | 0.142738i | −0.997450 | − | 0.0713690i | \(-0.977263\pi\) | ||
0.997450 | − | 0.0713690i | \(-0.0227368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 874.177 | + | 9.89776i | 1.44971 | + | 0.0164142i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 476.731 | − | 476.731i | 0.787986 | − | 0.787986i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 685.217 | 1.12886 | 0.564429 | − | 0.825482i | \(-0.309096\pi\) | ||||
0.564429 | + | 0.825482i | \(0.309096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 69.1216 | + | 29.0906i | 0.113500 | + | 0.0477678i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 701.077 | − | 701.077i | 1.14743 | − | 1.14743i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 544.727 | − | 544.727i | 0.888624 | − | 0.888624i | −0.105767 | − | 0.994391i | \(-0.533730\pi\) |
0.994391 | + | 0.105767i | \(0.0337296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −48.7143 | − | 20.5020i | −0.0792102 | − | 0.0333365i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 383.577 | 0.621681 | 0.310840 | − | 0.950462i | \(-0.399390\pi\) | ||||
0.310840 | + | 0.950462i | \(0.399390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −81.7634 | + | 81.7634i | −0.132089 | + | 0.132089i | −0.770060 | − | 0.637971i | \(-0.779774\pi\) |
0.637971 | + | 0.770060i | \(0.279774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −174.634 | + | 402.148i | −0.281214 | + | 0.647581i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 129.694i | 0.208176i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −944.365 | −1.51098 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −92.3715 | − | 226.625i | −0.147323 | − | 0.361443i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 312.748 | + | 312.748i | 0.497214 | + | 0.497214i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 944.242i | 1.49642i | 0.663461 | + | 0.748211i | \(0.269087\pi\) | ||||
−0.663461 | + | 0.748211i | \(0.730913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 788.523 | + | 331.859i | 1.24569 | + | 0.524263i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1231.74 | − | 1231.74i | −1.93974 | − | 1.93974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 433.022 | + | 433.022i | 0.679784 | + | 0.679784i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −261.814 | + | 255.952i | −0.409725 | + | 0.400551i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1102.48i | 1.71994i | 0.510344 | + | 0.859970i | \(0.329518\pi\) | ||||
−0.510344 | + | 0.859970i | \(0.670482\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −794.664 | − | 794.664i | −1.23587 | − | 1.23587i | −0.961674 | − | 0.274195i | \(-0.911588\pi\) |
−0.274195 | − | 0.961674i | \(-0.588412\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 678.217 | − | 276.439i | 1.05150 | − | 0.428588i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 768.446 | 1.18771 | 0.593853 | − | 0.804574i | \(-0.297606\pi\) | ||||
0.593853 | + | 0.804574i | \(0.297606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 265.830i | 0.409599i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.8415 | − | 29.0519i | −0.0181897 | − | 0.0446266i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −829.478 | + | 829.478i | −1.27026 | + | 1.27026i | −0.324305 | + | 0.945953i | \(0.605130\pi\) |
−0.945953 | + | 0.324305i | \(0.894870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1786.96 | 2.72819 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −371.454 | − | 379.961i | −0.565378 | − | 0.578328i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −653.956 | + | 653.956i | −0.992346 | + | 0.992346i | −0.999971 | − | 0.00762509i | \(-0.997573\pi\) |
0.00762509 | + | 0.999971i | \(0.497573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −734.342 | + | 734.342i | −1.11096 | + | 1.11096i | −0.117936 | + | 0.993021i | \(0.537628\pi\) |
−0.993021 | + | 0.117936i | \(0.962372\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 176.823 | − | 420.146i | 0.266702 | − | 0.633705i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 177.600 | 0.267068 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 174.405 | − | 174.405i | 0.261477 | − | 0.261477i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 648.022 | − | 264.132i | 0.968643 | − | 0.394816i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 372.842i | 0.555652i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 514.259 | 0.764129 | 0.382065 | − | 0.924136i | \(-0.375213\pi\) | ||||
0.382065 | + | 0.924136i | \(0.375213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1338.35 | + | 581.183i | 1.98274 | + | 0.861012i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 662.519 | + | 662.519i | 0.978610 | + | 0.978610i | 0.999776 | − | 0.0211661i | \(-0.00673787\pi\) |
−0.0211661 | + | 0.999776i | \(0.506738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 63.9111i | 0.0941253i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −155.293 | + | 368.988i | −0.228037 | + | 0.541833i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −280.446 | − | 280.446i | −0.410608 | − | 0.410608i | 0.471342 | − | 0.881950i | \(-0.343770\pi\) |
−0.881950 | + | 0.471342i | \(0.843770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 317.373 | + | 317.373i | 0.463318 | + | 0.463318i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 227.217 | − | 539.885i | 0.330738 | − | 0.785859i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 74.9595i | 0.108795i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 631.830 | + | 631.830i | 0.914371 | + | 0.914371i | 0.996612 | − | 0.0822418i | \(-0.0262080\pi\) |
−0.0822418 | + | 0.996612i | \(0.526208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.12700 | + | 99.5370i | −0.00162626 | + | 0.143632i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2159.13 | −3.10666 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.7608i | 0.0326554i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1102.34 | − | 449.309i | 1.57702 | − | 0.642788i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 160.480 | − | 160.480i | 0.228930 | − | 0.228930i | −0.583315 | − | 0.812246i | \(-0.698245\pi\) |
0.812246 | + | 0.583315i | \(0.198245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −467.409 | −0.664878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 775.409 | − | 1842.43i | 1.09987 | − | 2.61338i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −68.3534 | + | 68.3534i | −0.0966809 | + | 0.0966809i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 410.261 | − | 410.261i | 0.578648 | − | 0.578648i | −0.355883 | − | 0.934531i | \(-0.615820\pi\) |
0.934531 | + | 0.355883i | \(0.115820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 111.946 | − | 109.439i | 0.157448 | − | 0.153923i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −103.181 | −0.144714 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 558.907 | − | 558.907i | 0.781688 | − | 0.781688i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −322.505 | − | 791.236i | −0.449798 | − | 1.10354i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1069.18i | 1.48704i | 0.668716 | + | 0.743518i | \(0.266844\pi\) | ||||
−0.668716 | + | 0.743518i | \(0.733156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 162.620 | 0.225547 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −740.447 | + | 301.804i | −1.02413 | + | 0.417433i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −580.422 | − | 580.422i | −0.800582 | − | 0.800582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 148.864i | 0.204765i | 0.994745 | + | 0.102382i | \(0.0326466\pi\) | ||||
−0.994745 | + | 0.102382i | \(0.967353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −497.678 | − | 532.689i | −0.682686 | − | 0.730712i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −223.022 | − | 223.022i | −0.305092 | − | 0.305092i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 690.136 | + | 690.136i | 0.941522 | + | 0.941522i | 0.998382 | − | 0.0568598i | \(-0.0181088\pi\) |
−0.0568598 | + | 0.998382i | \(0.518109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1137.98 | + | 478.934i | 1.54828 | + | 0.651610i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 652.816i | − | 0.885775i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 535.593 | + | 535.593i | 0.724754 | + | 0.724754i | 0.969570 | − | 0.244815i | \(-0.0787274\pi\) |
−0.244815 | + | 0.969570i | \(0.578727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 181.826 | + | 446.093i | 0.245379 | + | 0.602014i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.5116 | −0.0276065 | −0.0138032 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138032 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1062.36i | 1.42599i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8278 | + | 956.315i | −0.0144950 | + | 1.28021i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −162.679 | + | 162.679i | −0.217195 | + | 0.217195i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8000 | −0.0210385 | −0.0105193 | − | 0.999945i | \(-0.503348\pi\) | ||||
−0.0105193 | + | 0.999945i | \(0.503348\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 601.992 | + | 253.355i | 0.799458 | + | 0.336461i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 189.245 | − | 189.245i | 0.250655 | − | 0.250655i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −810.497 | + | 810.497i | −1.07067 | + | 1.07067i | −0.0733640 | + | 0.997305i | \(0.523373\pi\) |
−0.997305 | + | 0.0733640i | \(0.976627\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 301.753 | + | 126.996i | 0.397566 | + | 0.167320i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −212.194 | −0.278836 | −0.139418 | − | 0.990234i | \(-0.544523\pi\) | ||||
−0.139418 | + | 0.990234i | \(0.544523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −113.314 | + | 113.314i | −0.148511 | + | 0.148511i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.4050 | − | 918.980i | 0.0136014 | − | 1.20128i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 523.266i | − | 0.682224i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −883.681 | −1.14913 | −0.574565 | − | 0.818459i | \(-0.694829\pi\) | ||||
−0.574565 | + | 0.818459i | \(0.694829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 271.951 | + | 667.207i | 0.352725 | + | 0.865378i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −515.805 | − | 515.805i | −0.667277 | − | 0.667277i | 0.289808 | − | 0.957085i | \(-0.406409\pi\) |
−0.957085 | + | 0.289808i | \(0.906409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 343.387i | 0.443080i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 175.233 | + | 73.7490i | 0.225526 | + | 0.0949151i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.0083 | − | 17.0083i | −0.0218335 | − | 0.0218335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 193.328 | + | 193.328i | 0.247539 | + | 0.247539i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 150.486 | + | 381.505i | 0.192192 | + | 0.487235i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2279.05i | 2.90325i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −279.150 | − | 279.150i | −0.354702 | − | 0.354702i | 0.507154 | − | 0.861856i | \(-0.330698\pi\) |
−0.861856 | + | 0.507154i | \(0.830698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −390.898 | + | 159.329i | −0.495435 | + | 0.201938i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.6788 | −0.0172931 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 733.911i | − | 0.925487i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 57.0434 | + | 139.951i | 0.0717527 | + | 0.176038i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −409.431 | + | 409.431i | −0.513715 | + | 0.513715i | −0.915663 | − | 0.401947i | \(-0.868333\pi\) |
0.401947 | + | 0.915663i | \(0.368333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −860.842 | −1.07740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −507.158 | + | 495.802i | −0.633156 | + | 0.618979i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −280.570 | + | 280.570i | −0.349402 | + | 0.349402i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −168.000 | + | 168.000i | −0.208696 | + | 0.208696i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 378.244 | − | 898.737i | 0.468704 | − | 1.11368i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −285.148 | −0.352470 | −0.176235 | − | 0.984348i | \(-0.556392\pi\) | ||||
−0.176235 | + | 0.984348i | \(0.556392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −819.150 | + | 819.150i | −1.01005 | + | 1.01005i | −0.0101007 | + | 0.999949i | \(0.503215\pi\) |
−0.999949 | + | 0.0101007i | \(0.996785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 635.435 | − | 259.001i | 0.781593 | − | 0.318575i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2515.62i | − | 3.08666i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 333.312 | 0.407971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.21840 | − | 195.931i | 0.00270867 | − | 0.239232i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 116.499 | + | 116.499i | 0.141899 | + | 0.141899i | 0.774488 | − | 0.632589i | \(-0.218008\pi\) |
−0.632589 | + | 0.774488i | \(0.718008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1551.22i | − | 1.88484i | −0.334429 | − | 0.942421i | \(-0.608543\pi\) | ||
0.334429 | − | 0.942421i | \(-0.391457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 422.644 | − | 1004.24i | 0.512296 | − | 1.21725i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 139.847 | + | 139.847i | 0.169102 | + | 0.169102i | 0.786584 | − | 0.617483i | \(-0.211847\pi\) |
−0.617483 | + | 0.786584i | \(0.711847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 454.593 | + | 454.593i | 0.548364 | + | 0.548364i | 0.925967 | − | 0.377604i | \(-0.123252\pi\) |
−0.377604 | + | 0.925967i | \(0.623252\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 169.949 | − | 403.812i | 0.204512 | − | 0.485936i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 531.701i | − | 0.638297i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1085.40 | − | 1085.40i | −1.29988 | − | 1.29988i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 68.3372 | − | 157.367i | 0.0816455 | − | 0.188014i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.1596 | −0.0407147 | −0.0203574 | − | 0.999793i | \(-0.506480\pi\) | ||||
−0.0203574 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 610.284i | 0.725664i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 787.733 | − | 321.077i | 0.934440 | − | 0.380875i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37.7438 | + | 37.7438i | −0.0446673 | + | 0.0446673i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −124.804 | −0.147348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.6353 | + | 91.8006i | −0.0455069 | + | 0.108128i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 442.143 | − | 442.143i | 0.519557 | − | 0.519557i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 514.933 | − | 514.933i | 0.603673 | − | 0.603673i | −0.337612 | − | 0.941285i | \(-0.609619\pi\) |
0.941285 | + | 0.337612i | \(0.109619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 678.944 | + | 694.494i | 0.794086 | + | 0.812274i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1165.96 | 1.36051 | 0.680254 | − | 0.732976i | \(-0.261869\pi\) | ||||
0.680254 | + | 0.732976i | \(0.261869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −246.162 | + | 246.162i | −0.286568 | + | 0.286568i | −0.835722 | − | 0.549153i | \(-0.814950\pi\) |
0.549153 | + | 0.835722i | \(0.314950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.69286 | + | 9.06009i | 0.00428904 | + | 0.0105228i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 196.851i | − | 0.228101i | −0.993475 | − | 0.114050i | \(-0.963617\pi\) | ||
0.993475 | − | 0.114050i | \(-0.0363825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 513.373 | 0.593494 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 436.364 | − | 177.861i | 0.503303 | − | 0.205145i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −82.6627 | − | 82.6627i | −0.0951239 | − | 0.0951239i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1285.02i | 1.47534i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −249.920 | + | 244.324i | −0.286277 | + | 0.279867i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 300.454 | + | 300.454i | 0.343376 | + | 0.343376i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1123.93 | − | 1123.93i | −1.28156 | − | 1.28156i | −0.939779 | − | 0.341782i | \(-0.888969\pi\) |
−0.341782 | − | 0.939779i | \(-0.611031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1491.47 | − | 627.704i | −1.69679 | − | 0.714112i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 776.024i | 0.880845i | 0.897791 | + | 0.440422i | \(0.145171\pi\) | ||||
−0.897791 | + | 0.440422i | \(0.854829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 157.587 | + | 157.587i | 0.178468 | + | 0.178468i | 0.790688 | − | 0.612220i | \(-0.209723\pi\) |
−0.612220 | + | 0.790688i | \(0.709723\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −398.199 | − | 976.945i | −0.449943 | − | 1.10389i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 469.259 | 0.529040 | 0.264520 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264520 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 322.458i | 0.362719i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −393.542 | + | 376.111i | −0.441685 | + | 0.422122i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 643.274 | − | 643.274i | 0.720352 | − | 0.720352i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1918.80 | −2.14391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −593.976 | − | 249.982i | −0.662181 | − | 0.278686i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −68.2478 | + | 68.2478i | −0.0759152 | + | 0.0759152i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.0208 | − | 46.0208i | 0.0510775 | − | 0.0510775i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −124.960 | − | 52.5909i | −0.138383 | − | 0.0582402i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2094.68 | −2.31457 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 684.081 | − | 684.081i | 0.754224 | − | 0.754224i | −0.221041 | − | 0.975265i | \(-0.570945\pi\) |
0.975265 | + | 0.221041i | \(0.0709454\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −528.598 | − | 5.98498i | −0.581516 | − | 0.00658414i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1109.61i | 1.21802i | 0.793164 | + | 0.609008i | \(0.208432\pi\) | ||||
−0.793164 | + | 0.609008i | \(0.791568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 714.154 | 0.782206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −558.498 | − | 1370.22i | −0.610381 | − | 1.49751i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −233.905 | − | 233.905i | −0.255077 | − | 0.255077i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 740.861i | − | 0.806160i | −0.915165 | − | 0.403080i | \(-0.867940\pi\) | ||
0.915165 | − | 0.403080i | \(-0.132060\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 817.496 | + | 344.052i | 0.887617 | + | 0.373564i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −380.551 | − | 380.551i | −0.412298 | − | 0.412298i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1471.46 | − | 1471.46i | −1.59076 | − | 1.59076i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 621.674 | + | 635.913i | 0.670630 | + | 0.685991i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 621.861i | − | 0.669388i | −0.942327 | − | 0.334694i | \(-0.891367\pi\) | ||
0.942327 | − | 0.334694i | \(-0.108633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 397.320 | + | 397.320i | 0.426767 | + | 0.426767i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 308.856 | − | 125.889i | 0.331036 | − | 0.134929i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −686.274 | −0.733983 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1036.08i | − | 1.10574i | −0.833267 | − | 0.552871i | \(-0.813532\pi\) | ||
0.833267 | − | 0.552871i | \(-0.186468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 319.637 | + | 784.199i | 0.340402 | + | 0.835143i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −904.283 | + | 904.283i | −0.960980 | + | 0.960980i | −0.999267 | − | 0.0382864i | \(-0.987810\pi\) |
0.0382864 | + | 0.999267i | \(0.487810\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.1778 | 0.0341228 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −144.959 | − | 367.494i | −0.153396 | − | 0.388883i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −895.943 | + | 895.943i | −0.946085 | + | 0.946085i | −0.998619 | − | 0.0525337i | \(-0.983270\pi\) |
0.0525337 | + | 0.998619i | \(0.483270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 552.280 | − | 552.280i | 0.581960 | − | 0.581960i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −340.642 | + | 809.393i | −0.358194 | + | 0.851097i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1165.12 | −1.22259 | −0.611293 | − | 0.791405i | \(-0.709350\pi\) | ||||
−0.611293 | + | 0.791405i | \(0.709350\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −90.1699 | + | 90.1699i | −0.0944188 | + | 0.0944188i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 283.591 | − | 115.591i | 0.296333 | − | 0.120784i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 83.0852i | − | 0.0866373i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −920.624 | −0.957985 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1258.05 | − | 14.2441i | −1.30638 | − | 0.0147914i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1303.65 | + | 1303.65i | 1.35093 | + | 1.35093i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 453.248i | 0.468716i | 0.972150 | + | 0.234358i | \(0.0752988\pi\) | ||||
−0.972150 | + | 0.234358i | \(0.924701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 162.245 | − | 385.506i | 0.167435 | − | 0.397839i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −678.155 | − | 678.155i | −0.698408 | − | 0.698408i | 0.265659 | − | 0.964067i | \(-0.414411\pi\) |
−0.964067 | + | 0.265659i | \(0.914411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 282.620 | + | 282.620i | 0.290462 | + | 0.290462i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −831.941 | + | 1976.76i | −0.853273 | + | 2.02744i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 544.399i | − | 0.557215i | −0.960405 | − | 0.278607i | \(-0.910127\pi\) | ||
0.960405 | − | 0.278607i | \(-0.0898728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 374.494 | + | 374.494i | 0.382527 | + | 0.382527i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −876.290 | − | 9.92169i | −0.893262 | − | 0.0101138i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 514.630 | 0.523530 | 0.261765 | − | 0.965132i | \(-0.415695\pi\) | ||||
0.261765 | + | 0.965132i | \(0.415695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1222.86i | − | 1.24148i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −342.663 | + | 139.669i | −0.347177 | + | 0.141508i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −315.295 | + | 315.295i | −0.318802 | + | 0.318802i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 939.282 | 0.947813 | 0.473906 | − | 0.880575i | \(-0.342844\pi\) | ||||
0.473906 | + | 0.880575i | \(0.342844\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −209.720 | + | 498.312i | −0.211199 | + | 0.501825i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −520.318 | + | 520.318i | −0.522932 | + | 0.522932i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −165.885 | + | 165.885i | −0.166384 | + | 0.166384i | −0.785388 | − | 0.619004i | \(-0.787537\pi\) |
0.619004 | + | 0.785388i | \(0.287537\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 381.505 | + | 967.172i | 0.381887 | + | 0.968141i |
(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 | 384.3.i.a.161.4 | 8 | ||
3.2 | odd | 2 | inner | 384.3.i.a.161.2 | 8 | ||
4.3 | odd | 2 | 384.3.i.b.161.1 | 8 | |||
8.3 | odd | 2 | 192.3.i.a.17.4 | 8 | |||
8.5 | even | 2 | 48.3.i.a.29.2 | yes | 8 | ||
12.11 | even | 2 | 384.3.i.b.161.3 | 8 | |||
16.3 | odd | 4 | 192.3.i.a.113.2 | 8 | |||
16.5 | even | 4 | inner | 384.3.i.a.353.2 | 8 | ||
16.11 | odd | 4 | 384.3.i.b.353.3 | 8 | |||
16.13 | even | 4 | 48.3.i.a.5.3 | yes | 8 | ||
24.5 | odd | 2 | 48.3.i.a.29.3 | yes | 8 | ||
24.11 | even | 2 | 192.3.i.a.17.2 | 8 | |||
48.5 | odd | 4 | inner | 384.3.i.a.353.4 | 8 | ||
48.11 | even | 4 | 384.3.i.b.353.1 | 8 | |||
48.29 | odd | 4 | 48.3.i.a.5.2 | ✓ | 8 | ||
48.35 | even | 4 | 192.3.i.a.113.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.a.5.2 | ✓ | 8 | 48.29 | odd | 4 | ||
48.3.i.a.5.3 | yes | 8 | 16.13 | even | 4 | ||
48.3.i.a.29.2 | yes | 8 | 8.5 | even | 2 | ||
48.3.i.a.29.3 | yes | 8 | 24.5 | odd | 2 | ||
192.3.i.a.17.2 | 8 | 24.11 | even | 2 | |||
192.3.i.a.17.4 | 8 | 8.3 | odd | 2 | |||
192.3.i.a.113.2 | 8 | 16.3 | odd | 4 | |||
192.3.i.a.113.4 | 8 | 48.35 | even | 4 | |||
384.3.i.a.161.2 | 8 | 3.2 | odd | 2 | inner | ||
384.3.i.a.161.4 | 8 | 1.1 | even | 1 | trivial | ||
384.3.i.a.353.2 | 8 | 16.5 | even | 4 | inner | ||
384.3.i.a.353.4 | 8 | 48.5 | odd | 4 | inner | ||
384.3.i.b.161.1 | 8 | 4.3 | odd | 2 | |||
384.3.i.b.161.3 | 8 | 12.11 | even | 2 | |||
384.3.i.b.353.1 | 8 | 48.11 | even | 4 | |||
384.3.i.b.353.3 | 8 | 16.11 | odd | 4 |