Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (of order \(6\), degree \(2\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} - 18 x^{9} + 11 x^{8} - 36 x^{7} + 180 x^{6} - 120 x^{5} + 31 x^{4} + 18 x^{3} + 162 x^{2} - 54 x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-1.17819 + 1.17819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.g.863.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.71294 | + | 1.56632i | −1.56632 | + | 0.904315i | −0.569726 | + | 0.821835i | \(0.692951\pi\) |
−0.996593 | + | 0.0824799i | \(0.973716\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | + | 0.866025i | −0.670820 | + | 0.387298i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.40671 | − | 5.90059i | 1.13557 | − | 1.96686i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.225929 | − | 0.391320i | 0.0626613 | − | 0.108533i | −0.832993 | − | 0.553284i | \(-0.813375\pi\) |
0.895654 | + | 0.444751i | \(0.146708\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.71294 | − | 4.69896i | 0.700479 | − | 1.21327i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.90671 | − | 5.03457i | −0.704980 | − | 1.22106i | −0.966699 | − | 0.255918i | \(-0.917622\pi\) |
0.261718 | − | 0.965144i | \(-0.415711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.16854 | + | 1.27407i | −0.956329 | + | 0.292292i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.13264 | − | 5.42589i | −0.683598 | − | 1.18403i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.70234 | − | 3.29225i | −1.18902 | − | 0.686481i | −0.230936 | − | 0.972969i | \(-0.574179\pi\) |
−0.958084 | + | 0.286488i | \(0.907512\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.9461i | 2.29902i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.90671 | − | 5.03457i | 0.539762 | − | 0.934896i | −0.459154 | − | 0.888357i | \(-0.651847\pi\) |
0.998916 | − | 0.0465391i | \(-0.0148192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.33708 | 1.49738 | 0.748692 | − | 0.662918i | \(-0.230682\pi\) | ||||
0.748692 | + | 0.662918i | \(0.230682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | − | 3.00000i | −0.292770 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.45186 | −0.567482 | −0.283741 | − | 0.958901i | \(-0.591576\pi\) | ||||
−0.283741 | + | 0.958901i | \(0.591576\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41551i | 0.226662i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.677786 | + | 0.391320i | −0.105852 | + | 0.0611139i | −0.551992 | − | 0.833850i | \(-0.686132\pi\) |
0.446139 | + | 0.894964i | \(0.352799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.276452 | − | 0.478830i | −0.0421586 | − | 0.0730209i | 0.844176 | − | 0.536066i | \(-0.180090\pi\) |
−0.886335 | + | 0.463045i | \(0.846757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.8012i | 1.75922i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.13883 | + | 4.69896i | 1.18717 | + | 0.685413i | 0.957662 | − | 0.287894i | \(-0.0929549\pi\) |
0.229508 | + | 0.973307i | \(0.426288\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.7715 | + | 9.10567i | 2.20845 | + | 1.27505i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.31342 | − | 7.47106i | 0.592493 | − | 1.02623i | −0.401402 | − | 0.915902i | \(-0.631477\pi\) |
0.993895 | − | 0.110327i | \(-0.0351897\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.31342 | − | 9.98575i | 1.23359 | − | 1.32264i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.506187 | − | 0.292247i | 0.0659000 | − | 0.0380474i | −0.466688 | − | 0.884422i | \(-0.654553\pi\) |
0.532588 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8979 | + | 6.29191i | 1.39533 | + | 0.805597i | 0.993899 | − | 0.110291i | \(-0.0351781\pi\) |
0.401435 | + | 0.915887i | \(0.368511\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.8012 | + | 6.81342i | 1.48681 | + | 0.858410i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.782640i | 0.0970745i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5523 | − | 7.24710i | −1.53351 | − | 0.885374i | −0.999196 | − | 0.0400897i | \(-0.987236\pi\) |
−0.534317 | − | 0.845284i | \(-0.679431\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.6268 | 2.48318 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.91970 | + | 8.52117i | 0.583861 | + | 1.01128i | 0.995016 | + | 0.0997116i | \(0.0317920\pi\) |
−0.411155 | + | 0.911565i | \(0.634875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 6.26527i | − | 0.723452i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.18765 | − | 5.52117i | −0.358639 | − | 0.621180i | 0.629095 | − | 0.777328i | \(-0.283426\pi\) |
−0.987734 | + | 0.156148i | \(0.950092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.49120 | − | 14.7072i | −0.943467 | − | 1.63413i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.33708 | 0.915114 | 0.457557 | − | 0.889180i | \(-0.348725\pi\) | ||||
0.457557 | + | 0.889180i | \(0.348725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.72013 | + | 5.03457i | 0.945831 | + | 0.546076i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.2113i | 1.95246i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.11804 | − | 5.26430i | −0.966510 | − | 0.558015i | −0.0683396 | − | 0.997662i | \(-0.521770\pi\) |
−0.898171 | + | 0.439647i | \(0.855103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.782640 | + | 0.451857i | 0.0820429 | + | 0.0473675i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.6180 | + | 13.0585i | −2.34538 | + | 1.35411i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.14943 | − | 5.52117i | 0.528321 | − | 0.566460i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.677786 | + | 0.391320i | −0.0688187 | + | 0.0397325i | −0.534015 | − | 0.845475i | \(-0.679317\pi\) |
0.465196 | + | 0.885208i | \(0.345984\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7201 | + | 8.49867i | 1.46471 | + | 0.845649i | 0.999223 | − | 0.0394071i | \(-0.0125469\pi\) |
0.465484 | + | 0.885056i | \(0.345880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3159 | −1.41059 | −0.705293 | − | 0.708916i | \(-0.749184\pi\) | ||||
−0.705293 | + | 0.708916i | \(0.749184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.39791 | + | 5.42589i | 0.917142 | + | 0.529512i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.6268i | − | 1.12401i | −0.827134 | − | 0.562004i | \(-0.810030\pi\) | ||
0.827134 | − | 0.562004i | \(-0.189970\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.17198 | + | 5.49404i | 0.303821 | + | 0.526233i | 0.976998 | − | 0.213248i | \(-0.0684042\pi\) |
−0.673177 | + | 0.739481i | \(0.735071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.36469 | − | 5.40671i | 0.888857 | − | 0.513182i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8306i | 1.58329i | 0.610984 | + | 0.791643i | \(0.290774\pi\) | ||||
−0.610984 | + | 0.791643i | \(0.709226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4047 | 1.06349 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.53935 | − | 2.66623i | −0.142313 | − | 0.246493i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0691 | − | 5.81342i | 0.923036 | − | 0.532915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.22586 | − | 2.12326i | 0.110532 | − | 0.191448i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.70234 | − | 9.87674i | 0.506001 | − | 0.876419i | −0.493975 | − | 0.869476i | \(-0.664457\pi\) |
0.999976 | − | 0.00694308i | \(-0.00221007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.198253 | + | 0.343384i | 0.0173214 | + | 0.0300016i | 0.874556 | − | 0.484924i | \(-0.161153\pi\) |
−0.857235 | + | 0.514926i | \(0.827819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.54814 | − | 8.33708i | −0.220952 | − | 0.722917i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.3456 | − | 17.9191i | −0.890406 | − | 1.54223i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.09329 | − | 5.35774i | 0.264278 | − | 0.457742i | −0.703096 | − | 0.711095i | \(-0.748200\pi\) |
0.967374 | + | 0.253352i | \(0.0815331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.61354 | − | 14.9191i | 0.730591 | − | 1.26542i | −0.226040 | − | 0.974118i | \(-0.572578\pi\) |
0.956631 | − | 0.291302i | \(-0.0940885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.4403 | −2.47932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0691i | 0.836196i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.13883 | + | 4.69896i | −0.671279 | + | 0.387563i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.7201 | − | 8.49867i | 1.20592 | − | 0.696238i | 0.244054 | − | 0.969762i | \(-0.421522\pi\) |
0.961865 | + | 0.273523i | \(0.0881891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.459470 | −0.0373911 | −0.0186956 | − | 0.999825i | \(-0.505951\pi\) | ||||
−0.0186956 | + | 0.999825i | \(0.505951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −39.6092 | −3.20222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5056 | + | 7.22013i | −1.00448 | + | 0.579935i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.54234 | + | 2.04517i | −0.282710 | + | 0.163222i | −0.634649 | − | 0.772800i | \(-0.718855\pi\) |
0.351940 | + | 0.936023i | \(0.385522\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.0247i | 2.14320i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.58449 | − | 11.4047i | 0.518931 | − | 0.898815i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.38767 | −0.578647 | −0.289324 | − | 0.957231i | \(-0.593430\pi\) | ||||
−0.289324 | + | 0.957231i | \(0.593430\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.71294 | − | 4.69896i | 0.209934 | − | 0.363616i | −0.741760 | − | 0.670666i | \(-0.766008\pi\) |
0.951693 | + | 0.307050i | \(0.0993418\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.39791 | + | 11.0815i | 0.492147 | + | 0.852424i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.68323 | + | 28.9373i | −0.511080 | + | 2.21289i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | − | 2.00000i | −0.261861 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.915505 | + | 1.58570i | −0.0688136 | + | 0.119189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.79582i | − | 0.507944i | −0.967212 | − | 0.253972i | \(-0.918263\pi\) | ||
0.967212 | − | 0.253972i | \(-0.0817371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.95186 | + | 3.38072i | −0.145080 | + | 0.251287i | −0.929403 | − | 0.369067i | \(-0.879677\pi\) |
0.784323 | + | 0.620353i | \(0.213011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −39.4206 | −2.91405 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.17779 | − | 2.98940i | 0.380678 | − | 0.219785i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.8921 | −1.73790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.4227i | − | 1.76716i | −0.468279 | − | 0.883581i | \(-0.655126\pi\) | ||
0.468279 | − | 0.883581i | \(-0.344874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2958 | − | 11.7178i | 1.46093 | − | 0.843466i | 0.461871 | − | 0.886947i | \(-0.347178\pi\) |
0.999054 | + | 0.0434813i | \(0.0138449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.22586 | − | 2.12326i | −0.0877859 | − | 0.152050i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.87298i | − | 0.347186i | −0.984818 | − | 0.173593i | \(-0.944462\pi\) | ||
0.984818 | − | 0.173593i | \(-0.0555377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.6844 | + | 13.0969i | 1.60806 | + | 0.928412i | 0.989804 | + | 0.142433i | \(0.0454926\pi\) |
0.618253 | + | 0.785979i | \(0.287841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 45.4051 | 3.20263 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0691 | + | 5.81342i | 0.706715 | + | 0.408022i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.677786 | − | 1.17396i | 0.0473386 | − | 0.0819929i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38.8524 | + | 22.4315i | −2.70043 | + | 1.55909i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3138 | + | 11.1508i | −1.32962 | + | 0.767654i | −0.985240 | − | 0.171178i | \(-0.945243\pi\) |
−0.344375 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.6937 | − | 15.4116i | −1.82902 | − | 1.05599i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.829357 | + | 0.478830i | 0.0565617 | + | 0.0326559i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.6742i | 1.13192i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.5647 | − | 7.83159i | −0.916619 | − | 0.529210i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.62684 | −0.176700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.66235 | − | 6.34338i | −0.245249 | − | 0.424784i | 0.716952 | − | 0.697122i | \(-0.245537\pi\) |
−0.962202 | + | 0.272338i | \(0.912203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.81342 | + | 11.8012i | 0.454228 | + | 0.786746i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.373165i | 0.0247678i | 0.999923 | + | 0.0123839i | \(0.00394202\pi\) | ||||
−0.999923 | + | 0.0123839i | \(0.996058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.5765i | − | 1.75623i | −0.478453 | − | 0.878113i | \(-0.658802\pi\) | ||
0.478453 | − | 0.878113i | \(-0.341198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.677786 | + | 1.17396i | 0.0444032 | + | 0.0769087i | 0.887373 | − | 0.461053i | \(-0.152528\pi\) |
−0.842970 | + | 0.537961i | \(0.819195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2777 | −1.06184 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.2958 | + | 9.98575i | 1.12348 | + | 0.648644i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.2713i | − | 0.858447i | −0.903198 | − | 0.429223i | \(-0.858787\pi\) | ||
0.903198 | − | 0.429223i | \(-0.141213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.07570 | − | 4.08516i | −0.455786 | − | 0.263148i | 0.254485 | − | 0.967077i | \(-0.418094\pi\) |
−0.710271 | + | 0.703929i | \(0.751427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0356 | + | 8.68078i | 0.964531 | + | 0.556872i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.50000 | + | 2.59808i | −0.287494 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.443224 | + | 1.91908i | −0.0282016 | + | 0.122108i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.6180 | + | 13.0585i | −1.43336 | + | 0.827551i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.43439 | − | 12.8767i | 0.469255 | − | 0.812773i | −0.530128 | − | 0.847918i | \(-0.677856\pi\) |
0.999382 | + | 0.0351451i | \(0.0111893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.5429 | −1.97530 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.10209 | − | 2.36834i | −0.255881 | − | 0.147733i | 0.366573 | − | 0.930389i | \(-0.380531\pi\) |
−0.622454 | + | 0.782656i | \(0.713864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.90371i | − | 0.428976i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.8046 | − | 34.3026i | −1.22588 | − | 2.12328i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.25347 | − | 1.30104i | 0.138955 | − | 0.0802258i | −0.428911 | − | 0.903347i | \(-0.641103\pi\) |
0.567866 | + | 0.823121i | \(0.307769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.9421i | 0.917887i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.9823 | 2.01848 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.67779 | + | 6.37011i | 0.224239 | + | 0.388393i | 0.956091 | − | 0.293071i | \(-0.0946772\pi\) |
−0.731852 | + | 0.681463i | \(0.761344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.6045 | + | 10.7413i | −1.13014 | + | 0.652487i | −0.943970 | − | 0.330030i | \(-0.892941\pi\) |
−0.186171 | + | 0.982517i | \(0.559608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.83101 | −0.171341 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.2900i | 1.03886i | 0.854514 | + | 0.519429i | \(0.173855\pi\) | ||||
−0.854514 | + | 0.519429i | \(0.826145\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.4020 | − | 49.1937i | 1.70038 | − | 2.94515i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.2958 | − | 13.4499i | −1.38971 | − | 0.802351i | −0.396430 | − | 0.918065i | \(-0.629751\pi\) |
−0.993283 | + | 0.115714i | \(0.963084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.93030 | − | 3.34338i | −0.114745 | − | 0.198744i | 0.802933 | − | 0.596069i | \(-0.203272\pi\) |
−0.917678 | + | 0.397326i | \(0.869938\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.32221 | + | 23.0443i | −0.315261 | + | 1.36503i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.782640 | − | 1.35557i | −0.0461978 | − | 0.0800169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.39791 | + | 14.5456i | −0.493995 | + | 0.855624i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.22586 | − | 2.12326i | 0.0718614 | − | 0.124468i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5246 | −1.02380 | −0.511898 | − | 0.859046i | \(-0.671057\pi\) | ||||
−0.511898 | + | 0.859046i | \(0.671057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.506187 | + | 0.876742i | −0.0294714 | + | 0.0510459i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.57664 | + | 1.48763i | −0.149011 | + | 0.0860316i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.957659 | − | 0.552905i | 0.0551986 | − | 0.0318689i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −53.2465 | −3.05893 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.7958 | −1.24803 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9340 | − | 14.9730i | 1.48013 | − | 0.854556i | 0.480387 | − | 0.877056i | \(-0.340496\pi\) |
0.999747 | + | 0.0225007i | \(0.00716279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.8382 | − | 22.4232i | 2.20943 | − | 1.27561i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.27126i | − | 0.0720867i | −0.999350 | − | 0.0360434i | \(-0.988525\pi\) | ||
0.999350 | − | 0.0360434i | \(-0.0114754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.07570 | − | 15.7196i | 0.512989 | − | 0.888523i | −0.486898 | − | 0.873459i | \(-0.661872\pi\) |
0.999887 | − | 0.0150637i | \(-0.00479510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.6024 | −1.32984 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4912 | − | 21.6354i | 0.701576 | − | 1.21517i | −0.266337 | − | 0.963880i | \(-0.585813\pi\) |
0.967913 | − | 0.251285i | \(-0.0808532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2113 | + | 31.5429i | 1.01646 | + | 1.76056i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5311 | + | 17.2835i | 1.03110 | + | 0.961677i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.451857 | + | 0.782640i | 0.0250645 | + | 0.0434130i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.2108 | − | 9.93668i | −0.951761 | − | 0.549499i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.39791 | + | 16.2777i | −0.518124 | + | 0.897417i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.7842i | − | 0.977509i | −0.872421 | − | 0.488755i | \(-0.837451\pi\) | ||
0.872421 | − | 0.488755i | \(-0.162549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.7595 | + | 20.3680i | −0.644415 | + | 1.11616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1047 | 1.37162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1180 | − | 6.99635i | 0.660112 | − | 0.381116i | −0.132208 | − | 0.991222i | \(-0.542207\pi\) |
0.792320 | + | 0.610106i | \(0.208873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.3620 | − | 45.6604i | −1.43179 | − | 2.47993i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.9403 | + | 17.8634i | −1.66577 | + | 0.961731i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.68997 | − | 8.12326i | −0.251771 | − | 0.436079i | 0.712243 | − | 0.701933i | \(-0.247679\pi\) |
−0.964013 | + | 0.265854i | \(0.914346\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.90236i | 0.530061i | 0.964240 | + | 0.265031i | \(0.0853821\pi\) | ||||
−0.964240 | + | 0.265031i | \(0.914618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.67473 | + | 2.69896i | 0.249519 | + | 0.144060i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.18658 | 0.169605 | 0.0848023 | − | 0.996398i | \(-0.472974\pi\) | ||||
0.0848023 | + | 0.996398i | \(0.472974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7591 | − | 8.52117i | −0.783332 | − | 0.452257i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.2113 | + | 31.5429i | −0.963846 | + | 1.66943i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.0562 | − | 12.1568i | 1.11130 | − | 0.641611i | 0.172137 | − | 0.985073i | \(-0.444933\pi\) |
0.939167 | + | 0.343462i | \(0.111600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7535 | − | 10.6220i | 0.829131 | − | 0.559055i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.8424 | − | 17.2295i | 1.56632 | − | 0.904315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50000 | − | 4.33013i | −0.392568 | − | 0.226649i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6029 | + | 6.69896i | 0.605668 | + | 0.349683i | 0.771268 | − | 0.636510i | \(-0.219623\pi\) |
−0.165600 | + | 0.986193i | \(0.552956\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.33245i | 0.277596i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.9421 | + | 8.62684i | 0.775756 | + | 0.447883i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8921 | −0.615750 | −0.307875 | − | 0.951427i | \(-0.599618\pi\) | ||||
−0.307875 | + | 0.951427i | \(0.599618\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.9906 | + | 32.8927i | 0.980671 | + | 1.69857i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.31342 | − | 2.27491i | −0.0676445 | − | 0.117164i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.80743i | − | 0.401041i | −0.979690 | − | 0.200520i | \(-0.935737\pi\) | ||
0.979690 | − | 0.200520i | \(-0.0642633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.7267i | 1.83034i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.68997 | + | 8.12326i | 0.239646 | + | 0.415079i | 0.960613 | − | 0.277891i | \(-0.0896353\pi\) |
−0.720967 | + | 0.692970i | \(0.756302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.76717 | −0.191496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2535 | + | 8.80660i | 0.773382 | + | 0.446513i | 0.834080 | − | 0.551644i | \(-0.185999\pi\) |
−0.0606975 | + | 0.998156i | \(0.519333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.2784i | 1.93582i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.07570 | − | 0.621055i | −0.0542618 | − | 0.0313281i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.56295 | + | 5.52117i | 0.481164 | + | 0.277800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.10209 | − | 2.36834i | 0.205878 | − | 0.118864i | −0.393516 | − | 0.919318i | \(-0.628742\pi\) |
0.599394 | + | 0.800454i | \(0.295408\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.9715 | + | 18.6268i | 0.999825 | + | 0.932508i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1604 | + | 9.90755i | −0.856948 | + | 0.494759i | −0.862989 | − | 0.505222i | \(-0.831410\pi\) |
0.00604076 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88359 | − | 3.26247i | 0.0938281 | − | 0.162515i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.4736 | + | 14.7072i | 1.26579 | + | 0.730806i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.5423 | + | 12.4375i | 1.06520 | + | 0.614994i | 0.926866 | − | 0.375392i | \(-0.122492\pi\) |
0.138334 | + | 0.990386i | \(0.455825\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.3803i | 0.955961i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.584495 | + | 1.01237i | 0.0287611 | + | 0.0498157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5056 | + | 7.22013i | −0.613877 | + | 0.354422i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 53.9662i | 2.64273i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4171 | 0.606613 | 0.303306 | − | 0.952893i | \(-0.401909\pi\) | ||||
0.303306 | + | 0.952893i | \(0.401909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0481 | + | 17.4039i | 0.489717 | + | 0.848214i | 0.999930 | − | 0.0118339i | \(-0.00376694\pi\) |
−0.510213 | + | 0.860048i | \(0.670434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 55.4533 | − | 32.0160i | 2.69623 | − | 1.55667i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6268 | 0.563984 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5838 | + | 21.7958i | −0.608974 | + | 1.05477i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.2186 | − | 26.3593i | 0.733053 | − | 1.26968i | −0.222520 | − | 0.974928i | \(-0.571428\pi\) |
0.955572 | − | 0.294756i | \(-0.0952385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6937 | − | 17.1437i | −1.42699 | − | 0.823873i | −0.430108 | − | 0.902778i | \(-0.641524\pi\) |
−0.996882 | + | 0.0789045i | \(0.974858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.7715 | − | 27.3170i | −0.756184 | − | 1.30975i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.9650 | + | 6.45868i | 1.33775 | + | 0.308961i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5035 | − | 30.3170i | −0.835398 | − | 1.44695i | −0.893706 | − | 0.448653i | \(-0.851904\pi\) |
0.0583085 | − | 0.998299i | \(-0.481429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.2201 | − | 17.7018i | 0.486673 | − | 0.842942i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.9124 | + | 32.7572i | −0.898556 | + | 1.55634i | −0.0692140 | + | 0.997602i | \(0.522049\pi\) |
−0.829342 | + | 0.558742i | \(0.811284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2361 | 0.864473 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.6232 | + | 46.1128i | −1.25924 | + | 2.18106i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 34.9441i | − | 1.64911i | −0.565779 | − | 0.824557i | \(-0.691425\pi\) | ||
0.565779 | − | 0.824557i | \(-0.308575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.24652 | − | 0.719676i | 0.0585664 | − | 0.0338133i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.56528 | −0.0733814 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.08468 | 0.0975173 | 0.0487586 | − | 0.998811i | \(-0.484473\pi\) | ||||
0.0487586 | + | 0.998811i | \(0.484473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 60.1432 | − | 34.7237i | 2.80725 | − | 1.62076i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.96664 | − | 2.29014i | 0.184745 | − | 0.106663i | −0.404775 | − | 0.914416i | \(-0.632650\pi\) |
0.589520 | + | 0.807754i | \(0.299317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.355572i | − | 0.0165248i | −0.999966 | − | 0.00826242i | \(-0.997370\pi\) | ||
0.999966 | − | 0.00826242i | \(-0.00263004\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.6180 | − | 39.1756i | 1.04889 | − | 1.81672i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2017 | −1.53639 | −0.768195 | − | 0.640216i | \(-0.778845\pi\) | ||||
−0.768195 | + | 0.640216i | \(0.778845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4942 | − | 25.1047i | 0.669280 | − | 1.15923i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.40678 | − | 11.0969i | 0.295209 | − | 0.511317i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.96179 | − | 8.49420i | 0.0900129 | − | 0.389741i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.3891 | − | 50.9034i | −1.34564 | − | 2.33071i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0242 | − | 8.09687i | −0.640782 | − | 0.369955i | 0.144134 | − | 0.989558i | \(-0.453960\pi\) |
−0.784916 | + | 0.619603i | \(0.787294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.779874 | + | 1.35078i | −0.0355592 | + | 0.0615903i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 41.2537i | 1.87711i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.677786 | − | 1.17396i | 0.0307767 | − | 0.0533068i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5730 | −0.841623 | −0.420811 | − | 0.907148i | \(-0.638255\pi\) | ||||
−0.420811 | + | 0.907148i | \(0.638255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0423 | − | 11.5715i | 0.906346 | − | 0.523279i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.53534 | + | 14.7836i | 0.385194 | + | 0.667176i | 0.991796 | − | 0.127830i | \(-0.0408011\pi\) |
−0.606602 | + | 0.795006i | \(0.707468\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.7958 | −1.52209 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.0423 | + | 9.83940i | −0.764453 | + | 0.441357i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.276452 | − | 0.478830i | −0.0123757 | − | 0.0214354i | 0.859771 | − | 0.510679i | \(-0.170606\pi\) |
−0.872147 | + | 0.489244i | \(0.837273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.9973i | 0.759385i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.4359 | + | 8.33459i | 0.643666 | + | 0.371621i | 0.786025 | − | 0.618194i | \(-0.212135\pi\) |
−0.142359 | + | 0.989815i | \(0.545469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.4403 | −1.31007 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.7144 | − | 20.0423i | −1.54172 | − | 0.890112i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.11804 | − | 10.5968i | 0.271177 | − | 0.469693i | −0.697986 | − | 0.716111i | \(-0.745920\pi\) |
0.969164 | + | 0.246418i | \(0.0792537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.66025 | + | 5.00000i | −0.383107 | + | 0.221187i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.2201 | − | 49.7976i | −0.671985 | − | 2.19862i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.4738 | − | 12.3979i | 0.946249 | − | 0.546317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.13883 | − | 4.69896i | −0.357255 | − | 0.206261i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.13056i | 0.137152i | 0.997646 | + | 0.0685761i | \(0.0218456\pi\) | ||||
−0.997646 | + | 0.0685761i | \(0.978154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.1620 | + | 12.7952i | 0.969077 | + | 0.559497i | 0.898955 | − | 0.438042i | \(-0.144328\pi\) |
0.0701222 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5305 | 0.546878 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.2335 | − | 41.9736i | −1.05563 | − | 1.82840i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1778 | + | 17.6284i | 0.442512 | + | 0.766454i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 3.98241i | − | 0.172822i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.353642i | 0.0153179i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0691 | + | 17.4403i | 0.435327 | + | 0.754008i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.6444 | + | 18.4367i | 0.459341 | + | 0.795602i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.1180 | − | 13.9246i | −1.03692 | − | 0.598663i | −0.117957 | − | 0.993019i | \(-0.537635\pi\) |
−0.918958 | + | 0.394355i | \(0.870968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12.2289i | − | 0.524793i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.51595 | − | 5.49404i | −0.407619 | − | 0.235339i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7379 | + | 11.9730i | 0.886688 | + | 0.511930i | 0.872858 | − | 0.487975i | \(-0.162264\pi\) |
0.0138304 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 74.2520 | − | 42.8694i | 3.16900 | − | 1.82962i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.70234 | + | 24.6902i | −0.242928 | + | 1.05184i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0423 | − | 6.37530i | 0.469568 | − | 0.271105i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.36469 | + | 16.2201i | −0.397509 | + | 0.688506i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.1340 | − | 16.8205i | −1.23445 | − | 0.712708i | −0.266493 | − | 0.963837i | \(-0.585865\pi\) |
−0.967954 | + | 0.251129i | \(0.919198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.249834 | −0.0105669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.91532i | − | 0.0807211i | −0.999185 | − | 0.0403605i | \(-0.987149\pi\) | ||
0.999185 | − | 0.0403605i | \(-0.0128506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.5757 | − | 25.2459i | −0.613204 | − | 1.06210i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.4144 | − | 16.9824i | 1.23529 | − | 0.713194i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 44.2306i | − | 1.85424i | −0.374762 | − | 0.927121i | \(-0.622275\pi\) | ||
0.374762 | − | 0.927121i | \(-0.377725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.8140 | 1.08028 | 0.540141 | − | 0.841575i | \(-0.318371\pi\) | ||||
0.540141 | + | 0.841575i | \(0.318371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.2537 | + | 66.2573i | 1.59807 | + | 2.76794i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.4047 | − | 6.58449i | 0.475608 | − | 0.274592i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.2361 | 1.46690 | 0.733449 | − | 0.679745i | \(-0.237910\pi\) | ||||
0.733449 | + | 0.679745i | \(0.237910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.7076 | + | 63.5795i | −1.52552 | + | 2.64227i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.6742i | 0.691761i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.61804 | + | 2.66623i | 0.190932 | + | 0.110235i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.21063 | − | 2.09687i | −0.0499680 | − | 0.0865470i | 0.839960 | − | 0.542649i | \(-0.182579\pi\) |
−0.889928 | + | 0.456102i | \(0.849245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.7535 | + | 10.6220i | −1.43199 | + | 0.437674i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.63264 | + | 13.2201i | 0.313965 | + | 0.543803i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.32221 | − | 4.02219i | 0.0953619 | − | 0.165172i | −0.814398 | − | 0.580307i | \(-0.802933\pi\) |
0.909760 | + | 0.415136i | \(0.136266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0691 | + | 17.4403i | −0.412794 | + | 0.714981i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −82.0555 | −3.35831 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.0467176 | + | 0.0809173i | −0.00190883 | + | 0.00330619i | −0.866978 | − | 0.498346i | \(-0.833941\pi\) |
0.865069 | + | 0.501652i | \(0.167274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.98342i | 0.366442i | 0.983072 | + | 0.183221i | \(0.0586523\pi\) | ||||
−0.983072 | + | 0.183221i | \(0.941348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −85.5244 | + | 49.3775i | −3.48282 | + | 2.01081i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.5000 | − | 9.52628i | 0.670820 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.84714 | 0.318506 | 0.159253 | − | 0.987238i | \(-0.449091\pi\) | ||||
0.159253 | + | 0.987238i | \(0.449091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.4227 | −1.47592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.67759 | − | 2.12326i | 0.148779 | − | 0.0858978i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2799 | − | 7.08979i | 0.495979 | − | 0.286354i | −0.231072 | − | 0.972937i | \(-0.574223\pi\) |
0.727052 | + | 0.686583i | \(0.240890\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.24652i | 0.171236i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.1180 | − | 26.1852i | 0.608629 | − | 1.05418i | −0.382837 | − | 0.923816i | \(-0.625053\pi\) |
0.991467 | − | 0.130361i | \(-0.0416137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.71658 | 0.189575 | 0.0947877 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947877 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.3294 | − | 68.1205i | 1.57823 | − | 2.73358i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.5286 | − | 18.2361i | 0.421820 | − | 0.730613i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0335 | + | 17.3786i | 0.400064 | + | 0.692930i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4150 | − | 10.0545i | −0.693278 | − | 0.400264i | 0.111561 | − | 0.993758i | \(-0.464415\pi\) |
−0.804839 | + | 0.593493i | \(0.797748\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.9315 | − | 60.5031i | 1.38840 | − | 2.40478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.7535i | 0.783893i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.677786 | − | 1.17396i | 0.0268549 | − | 0.0465140i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 67.0399 | 2.65206 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.45766 | − | 3.15098i | 0.215565 | − | 0.124456i | −0.388330 | − | 0.921520i | \(-0.626948\pi\) |
0.603895 | + | 0.797064i | \(0.293615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6780 | + | 27.1552i | 0.618282 | + | 1.07089i | 0.989799 | + | 0.142469i | \(0.0455042\pi\) |
−0.371518 | + | 0.928426i | \(0.621162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | −0.118125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.9648i | − | 0.549014i | −0.961585 | − | 0.274507i | \(-0.911485\pi\) | ||
0.961585 | − | 0.274507i | \(-0.0885146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.1171 | − | 45.2361i | −1.02361 | − | 1.77294i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.1078i | − | 0.786879i | −0.919351 | − | 0.393439i | \(-0.871285\pi\) | ||
0.919351 | − | 0.393439i | \(-0.128715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.594759 | − | 0.343384i | −0.0232392 | − | 0.0134171i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.0671 | 1.32908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.81566 | + | 4.51237i | 0.304455 | + | 0.175777i | 0.644442 | − | 0.764653i | \(-0.277090\pi\) |
−0.339988 | + | 0.940430i | \(0.610423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1720 | + | 21.0825i | −0.473435 | + | 0.820014i | −0.999538 | − | 0.0304073i | \(-0.990320\pi\) |
0.526102 | + | 0.850421i | \(0.323653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.12646 | − | 4.11446i | 0.276769 | − | 0.159792i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.0423 | + | 10.2989i | 0.428204 | + | 0.399373i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.1501 | + | 19.1392i | −1.28358 | + | 0.741073i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.8715 | + | 11.4728i | 0.768277 | + | 0.443565i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.2275i | − | 1.16518i | −0.812765 | − | 0.582592i | \(-0.802038\pi\) | ||
0.812765 | − | 0.582592i | \(-0.197962\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.6912 | − | 11.9461i | −0.796404 | − | 0.459804i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.9824 | −1.53665 | −0.768324 | − | 0.640061i | \(-0.778909\pi\) | ||||
−0.768324 | + | 0.640061i | \(0.778909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.782640 | − | 1.35557i | −0.0300350 | − | 0.0520221i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.584495 | − | 1.01237i | −0.0223979 | − | 0.0387943i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.3556i | 0.625829i | 0.949781 | + | 0.312914i | \(0.101305\pi\) | ||||
−0.949781 | + | 0.312914i | \(0.898695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7155i | 0.409417i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6273 | + | 72.1006i | 1.58818 | + | 2.75081i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.94905 | − | 3.37585i | −0.0742529 | − | 0.128610i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7846 | 0.790684 | 0.395342 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395342 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.8382i | 1.13183i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.94025 | + | 2.27491i | 0.149248 | + | 0.0861682i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.67759 | − | 2.12326i | −0.139099 | − | 0.0803090i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.2271 | + | 19.1837i | −1.25497 | + | 0.724557i | −0.972092 | − | 0.234599i | \(-0.924622\pi\) |
−0.282878 | + | 0.959156i | \(0.591289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3892 | − | 4.39791i | 0.542699 | − | 0.165870i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 44.1604 | − | 25.4960i | 1.66318 | − | 0.960235i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9973 | + | 29.4403i | −0.639251 | + | 1.10721i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.54234 | − | 5.50927i | −0.358370 | − | 0.206905i | 0.309995 | − | 0.950738i | \(-0.399672\pi\) |
−0.668366 | + | 0.743833i | \(0.733006\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.4376 | −1.62904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −47.5409 | − | 27.4477i | −1.78042 | − | 1.02793i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7870 | + | 36.0042i | 0.776306 | + | 1.34460i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.9994 | − | 6.92788i | 0.447504 | − | 0.258366i | −0.259272 | − | 0.965804i | \(-0.583483\pi\) |
0.706775 | + | 0.707438i | \(0.250149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 28.6318i | − | 1.06630i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.5946 | 0.951874 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.81342 | + | 10.0691i | 0.215905 | + | 0.373958i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6111 | + | 13.0545i | −0.838600 | + | 0.484166i | −0.856788 | − | 0.515669i | \(-0.827543\pi\) |
0.0181884 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.44025 | −0.127417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.60713 | + | 2.78364i | −0.0594420 | + | 0.102957i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2405i | 0.489050i | 0.969643 | + | 0.244525i | \(0.0786321\pi\) | ||||
−0.969643 | + | 0.244525i | \(0.921368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.13883 | − | 14.0969i | 0.300205 | − | 0.519971i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1850 | − | 34.9614i | −0.742517 | − | 1.28608i | −0.951346 | − | 0.308125i | \(-0.900299\pi\) |
0.208829 | − | 0.977952i | \(-0.433035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.80345 | − | 5.90059i | −0.0662516 | − | 0.216764i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.67936 | + | 13.3010i | 0.281728 | + | 0.487968i | 0.971811 | − | 0.235763i | \(-0.0757589\pi\) |
−0.690082 | + | 0.723731i | \(0.742426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7201 | + | 25.4960i | −0.539304 | + | 0.934101i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.4020 | − | 49.1937i | 1.03918 | − | 1.79990i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.2537 | 0.849671 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.21703 | − | 14.2323i | 0.299844 | − | 0.519345i | −0.676256 | − | 0.736666i | \(-0.736399\pi\) |
0.976100 | + | 0.217322i | \(0.0697321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.5785i | 1.69741i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.689205 | − | 0.397912i | 0.0250827 | − | 0.0144815i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0249 | + | 15.0255i | −0.945892 | + | 0.546111i | −0.891803 | − | 0.452425i | \(-0.850559\pi\) |
−0.0540898 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8981 | −1.33756 | −0.668778 | − | 0.743463i | \(-0.733182\pi\) | ||||
−0.668778 | + | 0.743463i | \(0.733182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9881 | + | 6.34397i | −0.397795 | + | 0.229667i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 59.4139 | − | 34.3026i | 2.14811 | − | 1.24021i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.264108i | − | 0.00953640i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.45766 | + | 2.52474i | −0.0525645 | + | 0.0910445i | −0.891110 | − | 0.453787i | \(-0.850073\pi\) |
0.838546 | + | 0.544831i | \(0.183406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8383 | 0.534389 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.87316 | − | 3.24442i | 0.0673731 | − | 0.116694i | −0.830371 | − | 0.557211i | \(-0.811872\pi\) |
0.897744 | + | 0.440517i | \(0.145205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.33708 | + | 14.4403i | −0.299477 | + | 0.518709i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.8134 | + | 18.7294i | 0.387929 | + | 0.671913i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.32681 | − | 2.49478i | 0.0833666 | − | 0.0893848i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 60.1432 | + | 34.7237i | 2.14934 | + | 1.24092i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.54234 | − | 6.13551i | 0.126432 | − | 0.218986i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.107890i | 0.00384585i | 0.999998 | + | 0.00192293i | \(0.000612087\pi\) | ||||
−0.999998 | + | 0.00192293i | \(0.999388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.07570 | + | 7.05932i | −0.145099 | + | 0.251318i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.6611 | −1.19685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.92430 | − | 2.84305i | 0.174867 | − | 0.100960i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.4041 | − | 40.5371i | −0.830059 | − | 1.43770i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.8981 | 1.73206 | 0.866030 | − | 0.499992i | \(-0.166664\pi\) | ||||
0.866030 | + | 0.499992i | \(0.166664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 54.6340i | − | 1.93281i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −62.1250 | + | 35.8679i | −2.19508 | + | 1.26733i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.8094i | 0.803924i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.9553 | − | 11.5212i | −0.702458 | − | 0.405564i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.98241 | −0.140014 | −0.0700070 | − | 0.997547i | \(-0.522302\pi\) | ||||
−0.0700070 | + | 0.997547i | \(0.522302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.7392 | − | 7.35499i | −0.447334 | − | 0.258269i | 0.259369 | − | 0.965778i | \(-0.416485\pi\) |
−0.706704 | + | 0.707510i | \(0.749819\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.6486 | − | 58.2811i | 1.18011 | − | 2.04401i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0815 | − | 6.39791i | 0.388168 | − | 0.224109i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.76247 | + | 1.64380i | 0.0616609 | + | 0.0575093i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.33245 | − | 3.07869i | 0.186331 | − | 0.107578i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0334 | − | 15.0304i | −0.908570 | − | 0.524563i | −0.0285995 | − | 0.999591i | \(-0.509105\pi\) |
−0.879971 | + | 0.475028i | \(0.842438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.3875 | + | 18.6990i | 1.12896 | + | 0.651805i | 0.943673 | − | 0.330880i | \(-0.107346\pi\) |
0.185286 | + | 0.982685i | \(0.440679\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.5117 | + | 16.4612i | 0.991449 | + | 0.572413i | 0.905707 | − | 0.423904i | \(-0.139341\pi\) |
0.0857418 | + | 0.996317i | \(0.472674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.80743 | −0.271163 | −0.135582 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135582 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.0817 | − | 46.9069i | −0.939454 | − | 1.62718i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.72013 | − | 15.1037i | −0.302134 | − | 0.523312i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.39791i | 0.325228i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 99.5953i | 3.44252i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.60713 | − | 2.78364i | −0.0554844 | − | 0.0961018i | 0.836949 | − | 0.547281i | \(-0.184337\pi\) |
−0.892434 | + | 0.451179i | \(0.851004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.39791 | − | 4.15331i | −0.0826866 | − | 0.143217i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 84.2670 | 2.90231 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.1937 | − | 11.0815i | −0.660285 | − | 0.381216i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.0000i | − | 0.755929i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.4736 | + | 6.04694i | 0.359453 | + | 0.207531i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6837 | + | 11.3644i | 0.674747 | + | 0.389566i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.8979 | − | 9.75601i | 0.578574 | − | 0.334040i | −0.181993 | − | 0.983300i | \(-0.558255\pi\) |
0.760566 | + | 0.649260i | \(0.224921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.0356 | − | 49.1937i | −0.514205 | − | 1.68239i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.50000 | + | 2.59808i | −0.153717 | + | 0.0887486i | −0.574886 | − | 0.818234i | \(-0.694953\pi\) |
0.421168 | + | 0.906982i | \(0.361620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.44499 | − | 7.69896i | 0.151661 | − | 0.262685i | −0.780177 | − | 0.625559i | \(-0.784871\pi\) |
0.931838 | + | 0.362874i | \(0.118204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.24652 | + | 2.45173i | 0.144721 | + | 0.0835546i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.43826 | 0.219161 | 0.109580 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109580 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.50000 | − | 2.59808i | −0.153005 | − | 0.0883372i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 52.6152i | − | 1.78691i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.67187 | + | 3.27465i | −0.192184 | + | 0.110957i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.33245i | 0.180476i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.2487 | 0.819756 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5699 | + | 47.7525i | 0.930969 | + | 1.61249i | 0.781668 | + | 0.623694i | \(0.214369\pi\) |
0.149301 | + | 0.988792i | \(0.452298\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.5431 | − | 27.4490i | 1.60359 | − | 0.925833i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.9472 | −1.21109 | −0.605546 | − | 0.795810i | \(-0.707045\pi\) | ||||
−0.605546 | + | 0.795810i | \(0.707045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.86448 | − | 4.96142i | 0.0963974 | − | 0.166965i | −0.813794 | − | 0.581154i | \(-0.802601\pi\) |
0.910191 | + | 0.414189i | \(0.135935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 3.17140i | − | 0.106606i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.26276 | + | 12.5795i | −0.243859 | + | 0.422377i | −0.961810 | − | 0.273717i | \(-0.911747\pi\) |
0.717951 | + | 0.696094i | \(0.245080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.7535 | + | 11.4047i | 0.662511 | + | 0.382501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.9139 | − | 9.21835i | −1.33567 | − | 0.308480i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.88536 | + | 10.1937i | 0.196726 | + | 0.340739i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.66019 | − | 8.07169i | 0.155599 | − | 0.269506i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.2335 | − | 41.9736i | 0.808232 | − | 1.39990i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.1514 | −1.67079 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.73205 | + | 3.00000i | −0.0576390 | + | 0.0998337i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6.76143i | − | 0.224758i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.11895 | + | 3.53277i | −0.203176 | + | 0.117304i | −0.598136 | − | 0.801394i | \(-0.704092\pi\) |
0.394960 | + | 0.918698i | \(0.370758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 100.294 | − | 57.9050i | 3.32655 | − | 1.92059i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.3251 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 59.1308 | − | 34.1392i | 1.95481 | − | 1.12861i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.686769 | + | 0.396506i | −0.0226791 | + | 0.0130938i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.7958i | 1.67560i | 0.545978 | + | 0.837800i | \(0.316158\pi\) | ||||
−0.545978 | + | 0.837800i | \(0.683842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.9051 | + | 81.2420i | −1.54557 | + | 2.67701i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.44600 | 0.146342 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.45186 | − | 5.97879i | 0.113496 | − | 0.196581i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48.7700 | + | 84.4722i | −1.60182 | + | 2.77443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.72892 | + | 6.45868i | 0.122342 | + | 0.211903i | 0.920691 | − | 0.390293i | \(-0.127626\pi\) |
−0.798349 | + | 0.602195i | \(0.794293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.5056 | + | 3.82221i | −0.409855 | + | 0.125268i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.99120 | + | 3.44887i | 0.0651891 | + | 0.112911i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.5847 | + | 33.9217i | −0.639804 | + | 1.10817i | 0.345672 | + | 0.938355i | \(0.387651\pi\) |
−0.985476 | + | 0.169817i | \(0.945682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.8617i | 1.85561i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.77126 | − | 4.79997i | 0.0903406 | − | 0.156475i | −0.817314 | − | 0.576193i | \(-0.804538\pi\) |
0.907654 | + | 0.419718i | \(0.137871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.15329 | 0.167814 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35.8382 | − | 20.6912i | 1.16582 | − | 0.673084i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.28108 | − | 5.68300i | −0.106621 | − | 0.184673i | 0.807778 | − | 0.589486i | \(-0.200670\pi\) |
−0.914399 | + | 0.404813i | \(0.867336\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.25929 | 0.0733395 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.2608i | 2.53778i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.1340 | − | 23.7487i | 1.33246 | − | 0.769297i | 0.346784 | − | 0.937945i | \(-0.387274\pi\) |
0.985676 | + | 0.168648i | \(0.0539402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1506 | + | 36.6340i | 0.684419 | + | 1.18545i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.7155 | + | 6.18658i | 0.346021 | + | 0.199775i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.5070 | 1.24216 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −68.6052 | − | 39.6092i | −2.21077 | − | 1.27639i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.2958 | + | 35.1534i | −0.653346 | + | 1.13163i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.3394 | + | 11.1656i | −0.621913 | + | 0.359061i | −0.777613 | − | 0.628743i | \(-0.783570\pi\) |
0.155701 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −77.3453 | − | 17.8634i | −2.48469 | − | 0.573854i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.4549 | + | 11.2323i | −0.624339 | + | 0.360462i | −0.778556 | − | 0.627575i | \(-0.784048\pi\) |
0.154218 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.8382 | + | 17.2271i | 0.956568 | + | 0.552275i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.45173 | − | 1.41551i | −0.0785181 | − | 0.0453324i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 28.3287i | − | 0.906315i | −0.891431 | − | 0.453157i | \(-0.850298\pi\) | ||
0.891431 | − | 0.453157i | \(-0.149702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.2241 | 1.38004 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.6811 | − | 20.2323i | −0.372570 | − | 0.645311i | 0.617390 | − | 0.786657i | \(-0.288190\pi\) |
−0.989960 | + | 0.141347i | \(0.954857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.22013 | + | 7.30947i | 0.134464 | + | 0.232899i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 58.8805i | − | 1.87419i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.64060i | 0.115764i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.85210 | − | 3.20794i | −0.0588340 | − | 0.101904i | 0.835108 | − | 0.550086i | \(-0.185405\pi\) |
−0.893942 | + | 0.448182i | \(0.852072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8558 | + | 48.2476i | 0.883976 | + | 1.53109i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.3689 | −1.43829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.29582 | + | 3.05755i | 0.167720 | + | 0.0968335i | 0.581511 | − | 0.813539i | \(-0.302462\pi\) |
−0.413790 | + | 0.910372i | \(0.635795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 41.2361i | − | 1.30465i |
(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 | 1216.2.s.g.31.1 | ✓ | 12 | |
4.3 | odd | 2 | inner | 1216.2.s.g.31.6 | yes | 12 | |
8.3 | odd | 2 | 1216.2.s.h.31.1 | yes | 12 | ||
8.5 | even | 2 | 1216.2.s.h.31.6 | yes | 12 | ||
19.8 | odd | 6 | 1216.2.s.h.863.1 | yes | 12 | ||
76.27 | even | 6 | 1216.2.s.h.863.6 | yes | 12 | ||
152.27 | even | 6 | inner | 1216.2.s.g.863.1 | yes | 12 | |
152.141 | odd | 6 | inner | 1216.2.s.g.863.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.g.31.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1216.2.s.g.31.6 | yes | 12 | 4.3 | odd | 2 | inner | |
1216.2.s.g.863.1 | yes | 12 | 152.27 | even | 6 | inner | |
1216.2.s.g.863.6 | yes | 12 | 152.141 | odd | 6 | inner | |
1216.2.s.h.31.1 | yes | 12 | 8.3 | odd | 2 | ||
1216.2.s.h.31.6 | yes | 12 | 8.5 | even | 2 | ||
1216.2.s.h.863.1 | yes | 12 | 19.8 | odd | 6 | ||
1216.2.s.h.863.6 | yes | 12 | 76.27 | even | 6 |