Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(31,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.z (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Character | \(\chi\) | \(=\) | 896.31 |
Dual form | 896.2.z.a.607.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.700587 | − | 2.61463i | −0.404484 | − | 1.50955i | −0.805005 | − | 0.593268i | \(-0.797838\pi\) |
0.400521 | − | 0.916287i | \(-0.368829\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.450647 | − | 0.120751i | −0.201536 | − | 0.0540013i | 0.156639 | − | 0.987656i | \(-0.449934\pi\) |
−0.358175 | + | 0.933655i | \(0.616601\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37326 | + | 1.16946i | 0.897008 | + | 0.442014i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.74737 | + | 2.16355i | −1.24912 | + | 0.721182i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.518581 | + | 1.93537i | 0.156358 | + | 0.583536i | 0.998985 | + | 0.0450390i | \(0.0143412\pi\) |
−0.842627 | + | 0.538497i | \(0.818992\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.51607 | − | 4.51607i | −1.25253 | − | 1.25253i | −0.954581 | − | 0.297952i | \(-0.903696\pi\) |
−0.297952 | − | 0.954581i | \(-0.596304\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.26287i | 0.326072i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.68066 | − | 2.70238i | −1.13523 | − | 0.655424i | −0.189983 | − | 0.981787i | \(-0.560843\pi\) |
−0.945244 | + | 0.326364i | \(0.894177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.90476 | − | 0.510379i | −0.436982 | − | 0.117089i | 0.0336198 | − | 0.999435i | \(-0.489296\pi\) |
−0.470602 | + | 0.882346i | \(0.655963\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.39503 | − | 7.02450i | 0.304420 | − | 1.53287i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.951245 | − | 1.64761i | −0.198348 | − | 0.343549i | 0.749645 | − | 0.661841i | \(-0.230224\pi\) |
−0.947993 | + | 0.318291i | \(0.896891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.14162 | − | 2.39117i | −0.828325 | − | 0.478234i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.54010 | + | 2.54010i | 0.488843 | + | 0.488843i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12415 | − | 1.12415i | 0.208749 | − | 0.208749i | −0.594986 | − | 0.803736i | \(-0.702843\pi\) |
0.803736 | + | 0.594986i | \(0.202843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.434075 | + | 0.751840i | −0.0779622 | + | 0.135035i | −0.902371 | − | 0.430961i | \(-0.858175\pi\) |
0.824408 | + | 0.565995i | \(0.191508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.69696 | − | 2.71179i | 0.817636 | − | 0.472062i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.928290 | − | 0.813586i | −0.156910 | − | 0.137521i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.11876 | + | 7.90732i | −0.348322 | + | 1.29996i | 0.540361 | + | 0.841433i | \(0.318288\pi\) |
−0.888683 | + | 0.458522i | \(0.848379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.64394 | + | 14.9717i | −1.38414 | + | 2.39740i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.24226 | −0.506356 | −0.253178 | − | 0.967420i | \(-0.581476\pi\) | ||||
−0.253178 | + | 0.967420i | \(0.581476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.35727 | − | 6.35727i | 0.969475 | − | 0.969475i | −0.0300731 | − | 0.999548i | \(-0.509574\pi\) |
0.999548 | + | 0.0300731i | \(0.00957401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.94999 | − | 0.522499i | 0.290688 | − | 0.0778895i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.49266 | − | 2.58536i | −0.217727 | − | 0.377114i | 0.736386 | − | 0.676562i | \(-0.236531\pi\) |
−0.954113 | + | 0.299448i | \(0.903198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.26473 | + | 5.55087i | 0.609246 | + | 0.792981i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.78650 | + | 14.1314i | −0.530217 | + | 1.97880i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.77976 | + | 1.81663i | −0.931272 | + | 0.249533i | −0.692397 | − | 0.721517i | \(-0.743445\pi\) |
−0.238875 | + | 0.971050i | \(0.576779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.934789i | − | 0.126047i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.33780i | 0.707009i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.29366 | + | 2.22228i | −1.07974 | + | 0.289316i | −0.754491 | − | 0.656311i | \(-0.772116\pi\) |
−0.325253 | + | 0.945627i | \(0.605449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.125856 | + | 0.469703i | −0.0161143 | + | 0.0601393i | −0.973515 | − | 0.228624i | \(-0.926577\pi\) |
0.957401 | + | 0.288763i | \(0.0932440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.4237 | + | 0.752254i | −1.43925 | + | 0.0947751i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.48984 | + | 2.58047i | 0.184792 | + | 0.320068i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85238 | − | 1.03224i | 0.470643 | − | 0.126108i | −0.0156996 | − | 0.999877i | \(-0.504998\pi\) |
0.486342 | + | 0.873768i | \(0.338331\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.64144 | + | 3.64144i | −0.438378 | + | 0.438378i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1916 | 1.44687 | 0.723437 | − | 0.690390i | \(-0.242561\pi\) | ||||
0.723437 | + | 0.690390i | \(0.242561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79109 | − | 13.4946i | 0.911878 | − | 1.57942i | 0.100470 | − | 0.994940i | \(-0.467965\pi\) |
0.811408 | − | 0.584480i | \(-0.198701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.35044 | + | 12.5040i | −0.386876 | + | 1.44384i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.03261 | + | 5.19960i | −0.117677 | + | 0.592549i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.07130 | + | 0.618516i | −0.120531 | + | 0.0695885i | −0.559053 | − | 0.829132i | \(-0.688835\pi\) |
0.438522 | + | 0.898720i | \(0.355502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.62878 | + | 2.82113i | −0.180976 | + | 0.313459i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.03560 | + | 9.03560i | −0.991786 | + | 0.991786i | −0.999967 | − | 0.00818066i | \(-0.997396\pi\) |
0.00818066 | + | 0.999967i | \(0.497396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.78301 | + | 1.78301i | 0.193395 | + | 0.193395i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.72680 | − | 2.15167i | −0.399554 | − | 0.230683i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.16364 | + | 2.01548i | 0.123345 | + | 0.213640i | 0.921085 | − | 0.389362i | \(-0.127304\pi\) |
−0.797740 | + | 0.603002i | \(0.793971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.43644 | − | 15.9992i | −0.569894 | − | 1.67717i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.26989 | + | 0.608215i | 0.235376 | + | 0.0630689i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.796746 | + | 0.460002i | 0.0817444 | + | 0.0471952i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.69704i | − | 0.476912i | −0.971153 | − | 0.238456i | \(-0.923359\pi\) | ||
0.971153 | − | 0.238456i | \(-0.0766414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.13058 | − | 6.13058i | −0.616146 | − | 0.616146i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.43509 | − | 5.35584i | −0.142797 | − | 0.532926i | −0.999844 | − | 0.0176866i | \(-0.994370\pi\) |
0.857047 | − | 0.515239i | \(-0.172297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.958115 | − | 0.553168i | 0.0944059 | − | 0.0545053i | −0.452054 | − | 0.891991i | \(-0.649308\pi\) |
0.546460 | + | 0.837485i | \(0.315975\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.47688 | + | 2.99712i | −0.144128 | + | 0.292489i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.97202 | + | 1.60020i | 0.577337 | + | 0.154697i | 0.535659 | − | 0.844434i | \(-0.320063\pi\) |
0.0416773 | + | 0.999131i | \(0.486730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.81979 | − | 10.5236i | −0.270087 | − | 1.00798i | −0.959063 | − | 0.283194i | \(-0.908606\pi\) |
0.688975 | − | 0.724785i | \(-0.258061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.1591 | 2.10324 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.81872 | −0.265163 | −0.132582 | − | 0.991172i | \(-0.542327\pi\) | ||||
−0.132582 | + | 0.991172i | \(0.542327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.229727 | + | 0.857352i | 0.0214221 | + | 0.0799485i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.6941 | + | 7.15267i | 2.46787 | + | 0.661264i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.94810 | − | 11.8873i | −0.728601 | − | 1.08971i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.04954 | − | 3.49271i | 0.549958 | − | 0.317519i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.27149 | + | 8.47731i | 0.204813 | + | 0.764373i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.22716 | + | 3.22716i | 0.288646 | + | 0.288646i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.34725i | − | 0.829434i | −0.909950 | − | 0.414717i | \(-0.863881\pi\) | ||
0.909950 | − | 0.414717i | \(-0.136119\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.0757 | − | 12.1681i | −1.85561 | − | 1.07134i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.9203 | + | 4.80174i | 1.56571 | + | 0.419530i | 0.934465 | − | 0.356056i | \(-0.115879\pi\) |
0.631242 | + | 0.775586i | \(0.282545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.92362 | − | 3.43880i | −0.340221 | − | 0.298182i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.837971 | − | 1.45141i | −0.0721211 | − | 0.124917i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1541 | − | 7.59453i | −1.12383 | − | 0.648844i | −0.181455 | − | 0.983399i | \(-0.558081\pi\) |
−0.942376 | + | 0.334555i | \(0.891414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.13113 | − | 1.13113i | −0.0959413 | − | 0.0959413i | 0.657507 | − | 0.753448i | \(-0.271611\pi\) |
−0.753448 | + | 0.657507i | \(0.771611\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.71402 | + | 5.71402i | −0.481207 | + | 0.481207i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.39833 | − | 11.0822i | 0.535055 | − | 0.926742i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.642337 | + | 0.370853i | −0.0533431 | + | 0.0307977i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.5256 | − | 15.0395i | 0.950618 | − | 1.24044i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.62960 | + | 9.81380i | −0.215425 | + | 0.803978i | 0.770591 | + | 0.637330i | \(0.219961\pi\) |
−0.986016 | + | 0.166648i | \(0.946706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.83900 | − | 10.1134i | 0.475171 | − | 0.823020i | −0.524425 | − | 0.851457i | \(-0.675720\pi\) |
0.999596 | + | 0.0284368i | \(0.00905293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 23.3869 | 1.89072 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.286400 | − | 0.286400i | 0.0230042 | − | 0.0230042i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.15127 | + | 0.576431i | −0.171690 | + | 0.0460042i | −0.343640 | − | 0.939101i | \(-0.611660\pi\) |
0.171950 | + | 0.985106i | \(0.444993\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.49962 | + | 16.4538i | 0.753369 | + | 1.30487i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.330743 | − | 5.02264i | −0.0260662 | − | 0.395839i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.79792 | − | 14.1740i | 0.297476 | − | 1.11020i | −0.641755 | − | 0.766910i | \(-0.721793\pi\) |
0.939231 | − | 0.343286i | \(-0.111540\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.44412 | + | 0.654901i | −0.190275 | + | 0.0509839i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.94995i | − | 0.460421i | −0.973141 | − | 0.230210i | \(-0.926059\pi\) | ||
0.973141 | − | 0.230210i | \(-0.0739415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.7898i | 2.13768i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.24207 | − | 2.20846i | 0.630287 | − | 0.168885i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.37723 | − | 8.87194i | 0.180737 | − | 0.674521i | −0.814766 | − | 0.579790i | \(-0.803134\pi\) |
0.995503 | − | 0.0947304i | \(-0.0301989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.03278 | − | 10.5183i | −0.531628 | − | 0.795111i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6209 | + | 20.1279i | 0.873478 | + | 1.51291i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.67501 | − | 0.984716i | 0.274683 | − | 0.0736011i | −0.118848 | − | 0.992912i | \(-0.537920\pi\) |
0.393531 | + | 0.919311i | \(0.371253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.13439 | − | 5.13439i | 0.381636 | − | 0.381636i | −0.490055 | − | 0.871691i | \(-0.663023\pi\) |
0.871691 | + | 0.490055i | \(0.163023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.31627 | 0.0973015 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.90963 | − | 3.30757i | 0.140398 | − | 0.243177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.80281 | − | 10.4602i | 0.204962 | − | 0.764927i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.05777 | + | 8.99887i | 0.222420 | + | 0.654572i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2400 | + | 8.79882i | −1.10273 | + | 0.636660i | −0.936936 | − | 0.349501i | \(-0.886351\pi\) |
−0.165791 | + | 0.986161i | \(0.553018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.28968 | − | 5.69790i | 0.236797 | − | 0.410144i | −0.722997 | − | 0.690851i | \(-0.757236\pi\) |
0.959793 | + | 0.280708i | \(0.0905692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.70321 | − | 5.70321i | 0.408415 | − | 0.408415i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8776 | − | 14.8776i | −1.05998 | − | 1.05998i | −0.998082 | − | 0.0619015i | \(-0.980284\pi\) |
−0.0619015 | − | 0.998082i | \(-0.519716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.43322 | − | 3.71422i | −0.456039 | − | 0.263294i | 0.254338 | − | 0.967115i | \(-0.418142\pi\) |
−0.710377 | + | 0.703821i | \(0.751476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.39785 | − | 9.34935i | −0.380735 | − | 0.659452i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.98255 | − | 1.35325i | 0.279520 | − | 0.0949796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.46112 | + | 0.391505i | 0.102049 | + | 0.0273439i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.12934 | + | 4.11612i | 0.495523 | + | 0.286090i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.95109i | − | 0.273303i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.11727 | − | 9.11727i | −0.627659 | − | 0.627659i | 0.319820 | − | 0.947478i | \(-0.396378\pi\) |
−0.947478 | + | 0.319820i | \(0.896378\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.54126 | − | 31.8764i | −0.585237 | − | 2.18414i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.63253 | + | 2.09724i | −0.247736 | + | 0.143031i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.90942 | + | 1.27668i | −0.129620 | + | 0.0866666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −40.7416 | − | 10.9167i | −2.75306 | − | 0.737681i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.93405 | + | 33.3423i | 0.600969 | + | 2.24285i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.72926 | −0.450624 | −0.225312 | − | 0.974287i | \(-0.572340\pi\) | ||||
−0.225312 | + | 0.974287i | \(0.572340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.6936 | 1.37957 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.00024 | − | 7.46500i | −0.132761 | − | 0.495469i | 0.867236 | − | 0.497896i | \(-0.165894\pi\) |
−0.999997 | + | 0.00242728i | \(0.999227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7233 | + | 3.94509i | 0.972941 | + | 0.260699i | 0.710069 | − | 0.704132i | \(-0.248664\pi\) |
0.262872 | + | 0.964831i | \(0.415330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3184 | − | 0.942877i | 0.942084 | − | 0.0620367i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7954 | + | 7.38741i | −0.838253 | + | 0.483965i | −0.856670 | − | 0.515865i | \(-0.827471\pi\) |
0.0184173 | + | 0.999830i | \(0.494137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.360479 | + | 1.34533i | 0.0235151 | + | 0.0877594i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.36773 | + | 2.36773i | 0.153800 | + | 0.153800i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.5488i | 1.84667i | 0.383998 | + | 0.923334i | \(0.374547\pi\) | ||||
−0.383998 | + | 0.923334i | \(0.625453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8792 | + | 11.4772i | 1.28053 | + | 0.739314i | 0.976945 | − | 0.213491i | \(-0.0684834\pi\) |
0.303584 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.9268 | + | 5.07143i | 1.21416 | + | 0.325332i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25162 | − | 3.01645i | −0.0799628 | − | 0.192714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.29713 | + | 10.9069i | 0.400676 | + | 0.693992i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.9549 | + | 17.2945i | 1.89832 | + | 1.09599i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2808 | + | 10.2808i | 0.648918 | + | 0.648918i | 0.952732 | − | 0.303813i | \(-0.0982599\pi\) |
−0.303813 | + | 0.952732i | \(0.598260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.69543 | − | 2.69543i | 0.169460 | − | 0.169460i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.41276 | − | 5.91107i | 0.213715 | − | 0.370165i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.17812 | − | 1.25754i | 0.135867 | − | 0.0784431i | −0.430526 | − | 0.902578i | \(-0.641672\pi\) |
0.566393 | + | 0.824135i | \(0.308338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2757 | + | 16.2883i | −0.887046 | + | 1.01211i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.78046 | + | 6.64475i | −0.110207 | + | 0.411300i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.54781 | − | 7.87703i | 0.280430 | − | 0.485718i | −0.691061 | − | 0.722797i | \(-0.742856\pi\) |
0.971491 | + | 0.237078i | \(0.0761897\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.27464 | 0.201159 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.45449 | − | 4.45449i | 0.272611 | − | 0.272611i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.50656 | + | 1.47548i | −0.335741 | + | 0.0899615i | −0.422751 | − | 0.906246i | \(-0.638935\pi\) |
0.0870099 | + | 0.996207i | \(0.472269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.76007 | − | 9.97673i | −0.349899 | − | 0.606043i | 0.636332 | − | 0.771415i | \(-0.280451\pi\) |
−0.986231 | + | 0.165372i | \(0.947118\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.0232 | + | 25.4231i | −2.30127 | + | 1.53868i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.48003 | − | 9.25560i | 0.149551 | − | 0.558134i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1829 | − | 5.40800i | 1.21268 | − | 0.324935i | 0.404864 | − | 0.914377i | \(-0.367319\pi\) |
0.807811 | + | 0.589442i | \(0.200652\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.75657i | − | 0.224900i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.8360i | − | 1.18331i | −0.806190 | − | 0.591657i | \(-0.798474\pi\) | ||
0.806190 | − | 0.591657i | \(-0.201526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.6531 | − | 5.26602i | 1.16825 | − | 0.313033i | 0.377996 | − | 0.925807i | \(-0.376613\pi\) |
0.790258 | + | 0.612775i | \(0.209947\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.644542 | − | 2.40546i | 0.0381794 | − | 0.142487i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.69473 | − | 3.79170i | −0.454206 | − | 0.223817i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.10572 | + | 10.5754i | 0.359160 | + | 0.622083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2810 | + | 3.29069i | −0.719926 | + | 0.192903i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.75509 | + | 6.75509i | −0.394636 | + | 0.394636i | −0.876336 | − | 0.481700i | \(-0.840020\pi\) |
0.481700 | + | 0.876336i | \(0.340020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00586 | 0.233230 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.59879 | + | 6.23329i | −0.208823 | + | 0.361692i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.14481 | + | 11.7366i | −0.181869 | + | 0.678745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.5220 | − | 7.65288i | 1.29815 | − | 0.441105i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9981 | + | 7.50446i | −0.746721 | + | 0.431120i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.113434 | − | 0.196473i | 0.00649520 | − | 0.0112500i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.36930 | + | 2.36930i | −0.135223 | + | 0.135223i | −0.771479 | − | 0.636255i | \(-0.780483\pi\) |
0.636255 | + | 0.771479i | \(0.280483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.11757 | − | 2.11757i | −0.120464 | − | 0.120464i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1239 | + | 7.57707i | 0.744186 | + | 0.429656i | 0.823589 | − | 0.567186i | \(-0.191968\pi\) |
−0.0794032 | + | 0.996843i | \(0.525301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.32791 | + | 5.76411i | 0.188105 | + | 0.325807i | 0.944618 | − | 0.328171i | \(-0.106432\pi\) |
−0.756514 | + | 0.653978i | \(0.773099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.23888 | + | 1.04041i | 0.295177 | + | 0.0586206i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6106 | + | 6.86233i | 1.43843 | + | 0.385427i | 0.891985 | − | 0.452065i | \(-0.149313\pi\) |
0.546449 | + | 0.837493i | \(0.315979\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.75861 | + | 1.59268i | 0.154453 | + | 0.0891732i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 16.7357i | − | 0.934094i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.53630 | + | 7.53630i | 0.419331 | + | 0.419331i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.90519 | + | 29.5026i | 0.438501 | + | 1.63651i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.5398 | + | 14.7454i | −1.41235 | + | 0.815423i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.518991 | − | 7.88134i | −0.0286129 | − | 0.434513i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.16331 | − | 2.45530i | −0.503661 | − | 0.134956i | −0.00196237 | − | 0.999998i | \(-0.500625\pi\) |
−0.501699 | + | 0.865043i | \(0.667291\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.16806 | − | 34.2157i | −0.502407 | − | 1.87501i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.86071 | −0.101661 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0354 | −0.873502 | −0.436751 | − | 0.899582i | \(-0.643871\pi\) | ||||
−0.436751 | + | 0.899582i | \(0.643871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.97476 | + | 7.36991i | 0.107254 | + | 0.400278i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.68019 | − | 0.450207i | −0.0909876 | − | 0.0243801i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.62978 | + | 18.1611i | 0.195990 | + | 0.980606i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.08071 | − | 1.20130i | 0.112022 | − | 0.0646758i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.821629 | + | 3.06636i | 0.0441074 | + | 0.164611i | 0.984467 | − | 0.175572i | \(-0.0561776\pi\) |
−0.940359 | + | 0.340183i | \(0.889511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.21348 | − | 2.21348i | −0.118485 | − | 0.118485i | 0.645378 | − | 0.763863i | \(-0.276700\pi\) |
−0.763863 | + | 0.645378i | \(0.776700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 22.9426i | − | 1.22458i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.11770 | − | 4.10941i | −0.378837 | − | 0.218722i | 0.298475 | − | 0.954417i | \(-0.403522\pi\) |
−0.677312 | + | 0.735696i | \(0.736855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.49410 | − | 1.47214i | −0.291597 | − | 0.0781331i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.5125 | + | 29.1094i | −1.35026 | + | 1.54063i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.3319 | − | 26.5556i | −0.809184 | − | 1.40155i | −0.913430 | − | 0.406997i | \(-0.866576\pi\) |
0.104245 | − | 0.994552i | \(-0.466757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0869 | − | 7.55570i | −0.688782 | − | 0.397668i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.3703 | − | 13.3703i | −0.701761 | − | 0.701761i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.14051 | + | 5.14051i | −0.269067 | + | 0.269067i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.91168 | − | 15.4355i | 0.465186 | − | 0.805726i | −0.534024 | − | 0.845469i | \(-0.679321\pi\) |
0.999210 | + | 0.0397435i | \(0.0126541\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.1500 | − | 7.01478i | 0.632502 | − | 0.365175i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.2146 | − | 3.61732i | −0.945656 | − | 0.187802i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.642914 | − | 2.39939i | 0.0332888 | − | 0.124236i | −0.947282 | − | 0.320401i | \(-0.896182\pi\) |
0.980571 | + | 0.196166i | \(0.0628490\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.17691 | − | 10.6987i | 0.318974 | − | 0.552480i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.1535 | −0.522931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.526070 | + | 0.526070i | −0.0270224 | + | 0.0270224i | −0.720489 | − | 0.693466i | \(-0.756083\pi\) |
0.693466 | + | 0.720489i | \(0.256083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.4396 | + | 6.54856i | −1.25208 | + | 0.335493i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.8928 | + | 20.5989i | 0.607692 | + | 1.05255i | 0.991620 | + | 0.129190i | \(0.0412377\pi\) |
−0.383928 | + | 0.923363i | \(0.625429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.09320 | − | 2.21850i | 0.0557145 | − | 0.113065i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.0688 | + | 37.5773i | −0.511826 | + | 1.91016i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.4190 | − | 6.27509i | 1.18739 | − | 0.318160i | 0.389535 | − | 0.921012i | \(-0.372636\pi\) |
0.797853 | + | 0.602852i | \(0.205969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2825i | 0.520009i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 50.2190i | − | 2.53321i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.557465 | − | 0.149372i | 0.0280491 | − | 0.00751574i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.09232 | + | 4.07659i | −0.0548219 | + | 0.204598i | −0.987904 | − | 0.155064i | \(-0.950442\pi\) |
0.933082 | + | 0.359662i | \(0.117108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.24235 | + | 12.6680i | −0.312508 | + | 0.634193i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.01163 | − | 15.6086i | −0.450019 | − | 0.779456i | 0.548367 | − | 0.836238i | \(-0.315250\pi\) |
−0.998387 | + | 0.0567812i | \(0.981916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.35568 | − | 1.43505i | 0.266785 | − | 0.0714849i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.07466 | − | 1.07466i | 0.0534002 | − | 0.0534002i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.4023 | −0.813034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9843 | + | 24.2215i | −0.691478 | + | 1.19768i | 0.279875 | + | 0.960036i | \(0.409707\pi\) |
−0.971354 | + | 0.237639i | \(0.923626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6412 | + | 39.7137i | −0.524894 | + | 1.95893i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.2819 | − | 4.42506i | −1.09642 | − | 0.217743i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.16292 | − | 2.98081i | 0.253438 | − | 0.146322i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.16503 | + | 3.74994i | −0.106022 | + | 0.183635i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4669 | − | 10.4669i | 0.511342 | − | 0.511342i | −0.403596 | − | 0.914937i | \(-0.632240\pi\) |
0.914937 | + | 0.403596i | \(0.132240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.3722 | − | 12.3722i | −0.602984 | − | 0.602984i | 0.338119 | − | 0.941103i | \(-0.390209\pi\) |
−0.941103 | + | 0.338119i | \(0.890209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.1871 | + | 6.45887i | 0.543935 | + | 0.314041i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.9237 | + | 22.3845i | 0.626891 | + | 1.08581i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.847989 | + | 0.967542i | −0.0410370 | + | 0.0468227i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.4585 | − | 8.96517i | −1.61539 | − | 0.432842i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8089 | − | 6.81786i | −0.568814 | − | 0.328405i | 0.187862 | − | 0.982195i | \(-0.439844\pi\) |
−0.756675 | + | 0.653791i | \(0.773178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.1575i | − | 0.920649i | −0.887751 | − | 0.460325i | \(-0.847733\pi\) | ||
0.887751 | − | 0.460325i | \(-0.152267\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.41965 | + | 1.41965i | 0.0680672 | + | 0.0680672i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.970991 | + | 3.62379i | 0.0464488 | + | 0.173349i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.42387 | + | 4.28617i | −0.354322 | + | 0.204568i | −0.666587 | − | 0.745427i | \(-0.732246\pi\) |
0.312265 | + | 0.949995i | \(0.398912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.9911 | − | 11.5742i | −1.33291 | − | 0.551154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.2310 | + | 5.42088i | 0.961204 | + | 0.257554i | 0.705110 | − | 0.709098i | \(-0.250898\pi\) |
0.256094 | + | 0.966652i | \(0.417564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.281020 | − | 1.04878i | −0.0133216 | − | 0.0497169i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.5017 | 1.30079 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4270 | −1.15278 | −0.576391 | − | 0.817174i | \(-0.695539\pi\) | ||||
−0.576391 | + | 0.817174i | \(0.695539\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.68138 | − | 6.27498i | −0.0791729 | − | 0.295477i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.5336 | − | 8.18145i | −1.43459 | − | 0.384398i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.518009 | + | 7.86644i | 0.0242846 | + | 0.368784i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.12783 | + | 1.80585i | −0.146314 | + | 0.0844743i | −0.571370 | − | 0.820693i | \(-0.693588\pi\) |
0.425056 | + | 0.905167i | \(0.360254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.02503 | − | 18.7537i | −0.234548 | − | 0.875347i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2872 | − | 25.2872i | −1.17774 | − | 1.17774i | −0.980318 | − | 0.197423i | \(-0.936743\pi\) |
−0.197423 | − | 0.980318i | \(-0.563257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.01165i | − | 0.372333i | −0.982518 | − | 0.186166i | \(-0.940394\pi\) | ||
0.982518 | − | 0.186166i | \(-0.0596064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.949477 | − | 0.548181i | −0.0440309 | − | 0.0254213i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.9002 | − | 4.79633i | −0.828321 | − | 0.221948i | −0.180340 | − | 0.983604i | \(-0.557720\pi\) |
−0.647981 | + | 0.761657i | \(0.724386\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3499 | + | 2.05542i | 0.477912 | + | 0.0949107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.01430 | + | 5.22093i | 0.138892 | + | 0.240568i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.6004 | + | 9.00692i | 0.717309 | + | 0.414139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.66840 | + | 6.66840i | 0.305967 | + | 0.305967i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.4759 | − | 21.4759i | 0.983314 | − | 0.983314i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6882 | − | 23.7087i | 0.625432 | − | 1.08328i | −0.363025 | − | 0.931779i | \(-0.618256\pi\) |
0.988457 | − | 0.151501i | \(-0.0484106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.2785 | − | 26.1415i | 2.06452 | − | 1.19195i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.9006 | + | 4.38357i | −0.586998 | + | 0.199459i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.567171 | + | 2.11671i | −0.0257539 | + | 0.0961148i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.68012 | − | 16.7665i | 0.438648 | − | 0.759761i | −0.558938 | − | 0.829210i | \(-0.688791\pi\) |
0.997585 | + | 0.0694492i | \(0.0221242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −39.7206 | −1.79623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1950 | + | 17.1950i | −0.775998 | + | 0.775998i | −0.979148 | − | 0.203149i | \(-0.934882\pi\) |
0.203149 | + | 0.979148i | \(0.434882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.29964 | + | 2.22388i | −0.373797 | + | 0.100159i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.02246 | + | 3.50300i | 0.0909027 | + | 0.157448i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.9338 | + | 14.2576i | 1.29786 | + | 0.639539i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.783708 | + | 2.92484i | −0.0350836 | + | 0.130934i | −0.981247 | − | 0.192757i | \(-0.938257\pi\) |
0.946163 | + | 0.323691i | \(0.104924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5569 | + | 4.16846i | −0.695031 | + | 0.186233i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.5673i | 1.54128i | 0.637272 | + | 0.770639i | \(0.280063\pi\) | ||||
−0.637272 | + | 0.770639i | \(0.719937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.58688i | 0.115115i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 72.6599 | − | 19.4692i | 3.22694 | − | 0.864656i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.08105 | − | 15.2307i | 0.180889 | − | 0.675088i | −0.814584 | − | 0.580046i | \(-0.803035\pi\) |
0.995473 | − | 0.0950424i | \(-0.0302987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.2717 | − | 22.9147i | 1.51609 | − | 1.01369i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.54187 | − | 6.13470i | −0.156377 | − | 0.270854i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.498567 | + | 0.133591i | −0.0219695 | + | 0.00588671i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.22957 | − | 4.22957i | 0.186016 | − | 0.186016i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.8623 | −1.09133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.72095 | − | 13.3731i | 0.338261 | − | 0.585885i | −0.645845 | − | 0.763469i | \(-0.723495\pi\) |
0.984106 | + | 0.177584i | \(0.0568281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.527773 | − | 1.96968i | 0.0230779 | − | 0.0861280i | −0.953426 | − | 0.301626i | \(-0.902471\pi\) |
0.976504 | + | 0.215498i | \(0.0691374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.5744 | + | 25.7571i | −0.985229 | + | 1.12413i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.06352 | − | 2.34607i | 0.177010 | − | 0.102197i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.69026 | − | 16.7840i | 0.421316 | − | 0.729740i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.2714 | − | 26.2714i | 1.14008 | − | 1.14008i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.6423 | + | 14.6423i | 0.634228 | + | 0.634228i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.49805 | − | 1.44225i | −0.108000 | − | 0.0623538i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.14933 | − | 8.91890i | −0.222210 | − | 0.384879i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.53138 | + | 11.1324i | −0.367473 | + | 0.479507i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.1819 | + | 5.40772i | 0.867686 | + | 0.232496i | 0.665087 | − | 0.746766i | \(-0.268394\pi\) |
0.202599 | + | 0.979262i | \(0.435061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.0216 | − | 9.82741i | −0.730466 | − | 0.421735i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.08293i | 0.217729i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0675 | + | 13.0675i | 0.558728 | + | 0.558728i | 0.928945 | − | 0.370217i | \(-0.120717\pi\) |
−0.370217 | + | 0.928945i | \(0.620717\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.544592 | − | 2.03245i | −0.0232426 | − | 0.0867427i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.71498 | + | 1.56749i | −0.115662 | + | 0.0667775i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.26581 | + | 0.215055i | −0.138876 | + | 0.00914507i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.98591 | − | 2.67572i | −0.423878 | − | 0.113578i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.13271 | − | 11.6914i | −0.132737 | − | 0.495381i | 0.867260 | − | 0.497856i | \(-0.165879\pi\) |
−0.999997 | + | 0.00247440i | \(0.999212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.4198 | −2.42860 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.3132 | −1.23760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.28930 | + | 27.2040i | 0.307207 | + | 1.14651i | 0.931029 | + | 0.364946i | \(0.118913\pi\) |
−0.623821 | + | 0.781567i | \(0.714421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.27025 | + | 0.340362i | 0.0534398 | + | 0.0143192i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.16472 | + | 4.79048i | −0.300890 | + | 0.201181i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.4277 | − | 11.7940i | 0.856375 | − | 0.494428i | −0.00642167 | − | 0.999979i | \(-0.502044\pi\) |
0.862797 | + | 0.505551i | \(0.168711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.83253 | − | 21.7673i | −0.244084 | − | 0.910933i | −0.973842 | − | 0.227227i | \(-0.927034\pi\) |
0.729758 | − | 0.683705i | \(-0.239633\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.6826 | + | 33.6826i | 1.40711 | + | 1.40711i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.09835i | 0.379427i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2893 | − | 9.40463i | −0.678132 | − | 0.391520i | 0.121019 | − | 0.992650i | \(-0.461384\pi\) |
−0.799151 | + | 0.601130i | \(0.794717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.2026 | − | 4.60942i | −0.714915 | − | 0.191561i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.0106 | + | 10.8771i | −1.32802 | + | 0.451256i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.03171 | − | 12.1793i | −0.291224 | − | 0.504414i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.1659 | − | 6.44666i | −0.461655 | − | 0.266537i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6185 | − | 12.6185i | −0.520820 | − | 0.520820i | 0.396999 | − | 0.917819i | \(-0.370052\pi\) |
−0.917819 | + | 0.396999i | \(0.870052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.21053 | − | 1.21053i | 0.0498791 | − | 0.0498791i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.4763 | + | 49.3223i | −1.17136 | + | 2.02885i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.0260 | + | 12.7167i | −0.904498 | + | 0.522212i | −0.878657 | − | 0.477454i | \(-0.841560\pi\) |
−0.0258409 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.14639 | + | 6.31671i | 0.0879934 | + | 0.258960i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.20427 | + | 19.4226i | −0.212997 | + | 0.794914i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.1003 | + | 36.5468i | −0.862135 | + | 1.49326i | 0.00772853 | + | 0.999970i | \(0.497540\pi\) |
−0.869864 | + | 0.493292i | \(0.835793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8695 | 1.21840 | 0.609202 | − | 0.793015i | \(-0.291490\pi\) | ||||
0.609202 | + | 0.793015i | \(0.291490\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.2030 | + | 12.2030i | −0.496944 | + | 0.496944i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.14796 | + | 0.843492i | −0.127983 | + | 0.0342928i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7137 | + | 25.4850i | 0.597212 | + | 1.03440i | 0.993231 | + | 0.116160i | \(0.0370584\pi\) |
−0.396018 | + | 0.918243i | \(0.629608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.32837 | − | 9.46480i | −0.256438 | − | 0.383533i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.93472 | + | 18.4166i | −0.199638 | + | 0.745058i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.1882 | − | 5.94532i | 0.896175 | − | 0.240129i | 0.218802 | − | 0.975769i | \(-0.429785\pi\) |
0.677373 | + | 0.735640i | \(0.263118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.09456i | − | 0.165108i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.2064i | 1.25632i | 0.778084 | + | 0.628161i | \(0.216192\pi\) | ||||
−0.778084 | + | 0.628161i | \(0.783808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7087 | + | 4.74503i | −0.711772 | + | 0.190719i | −0.596498 | − | 0.802615i | \(-0.703441\pi\) |
−0.115275 | + | 0.993334i | \(0.536775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.76883 | − | 6.60135i | 0.0709805 | − | 0.264903i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.404591 | + | 6.14408i | 0.0162096 | + | 0.246157i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.8912 | + | 18.8641i | 0.435648 | + | 0.754565i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3306 | + | 2.76808i | −0.412565 | + | 0.110547i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.2858 | − | 31.2858i | 1.24745 | − | 1.24745i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10970 | −0.322842 | −0.161421 | − | 0.986886i | \(-0.551608\pi\) | ||||
−0.161421 | + | 0.986886i | \(0.551608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.4508 | + | 30.2257i | −0.693608 | + | 1.20136i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.12869 | + | 4.21231i | −0.0447905 | + | 0.167160i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.80831 | − | 44.3279i | 0.230134 | − | 1.75634i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.6864 | + | 26.3770i | −1.80732 | + | 1.04346i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0435 | + | 24.3241i | −0.554685 | + | 0.960743i | 0.443242 | + | 0.896402i | \(0.353828\pi\) |
−0.997928 | + | 0.0643416i | \(0.979505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6759 | + | 21.6759i | −0.854812 | + | 0.854812i | −0.990721 | − | 0.135909i | \(-0.956605\pi\) |
0.135909 | + | 0.990721i | \(0.456605\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.02841 | + | 8.02841i | 0.316118 | + | 0.316118i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.8543 | + | 23.0099i | 1.56683 | + | 0.904612i | 0.996535 | + | 0.0831749i | \(0.0265060\pi\) |
0.570299 | + | 0.821437i | \(0.306827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.60188 | − | 14.8989i | −0.337653 | − | 0.584833i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.67575 | + | 4.09800i | 0.183257 | + | 0.160613i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.2593 | + | 7.84001i | 1.14501 | + | 0.306803i | 0.780962 | − | 0.624579i | \(-0.214729\pi\) |
0.364043 | + | 0.931382i | \(0.381396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.49594 | − | 4.32778i | −0.292890 | − | 0.169100i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 67.4255i | 2.63052i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.48634 | − | 7.48634i | −0.291626 | − | 0.291626i | 0.546096 | − | 0.837723i | \(-0.316113\pi\) |
−0.837723 | + | 0.546096i | \(0.816113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.73446 | − | 10.2052i | −0.106358 | − | 0.396934i | 0.892137 | − | 0.451764i | \(-0.149205\pi\) |
−0.998496 | + | 0.0548296i | \(0.982538\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 80.9187 | − | 46.7184i | 3.14262 | − | 1.81439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.35293 | + | 2.02347i | 0.0524645 | + | 0.0784667i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.92150 | − | 0.782813i | −0.113121 | − | 0.0303106i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.71443 | + | 17.5945i | 0.182270 | + | 0.680242i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.974316 | −0.0376130 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.2027 | 0.663115 | 0.331557 | − | 0.943435i | \(-0.392426\pi\) | ||||
0.331557 | + | 0.943435i | \(0.392426\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.44634 | − | 16.5940i | −0.171140 | − | 0.638702i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.3441 | − | 5.18323i | −0.743453 | − | 0.199208i | −0.132841 | − | 0.991137i | \(-0.542410\pi\) |
−0.610612 | + | 0.791930i | \(0.709077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.49301 | − | 11.1473i | 0.210802 | − | 0.427794i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.1168 | + | 10.4598i | −0.694238 | + | 0.400819i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.249364 | + | 0.930638i | 0.00954164 | + | 0.0356099i | 0.970533 | − | 0.240970i | \(-0.0774656\pi\) |
−0.960991 | + | 0.276580i | \(0.910799\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.01082 | + | 5.01082i | 0.191453 | + | 0.191453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 41.2597i | − | 1.57416i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.8219 | + | 22.4138i | 1.47900 | + | 0.853899i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.5048 | − | 8.97758i | −1.27458 | − | 0.341523i | −0.442797 | − | 0.896622i | \(-0.646014\pi\) |
−0.831784 | + | 0.555099i | \(0.812680\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.37999 | − | 21.7189i | −0.280343 | − | 0.825034i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.373156 | + | 0.646326i | 0.0141546 | + | 0.0245165i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.1759 | + | 8.76183i | 0.574829 | + | 0.331878i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.2796 | + | 28.2796i | 1.06963 | + | 1.06963i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.4969 | + | 32.4969i | −1.22739 | + | 1.22739i | −0.262444 | + | 0.964947i | \(0.584529\pi\) |
−0.964947 | + | 0.262444i | \(0.915471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.07146 | − | 13.9802i | 0.304421 | − | 0.527272i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.26498 | − | 1.88504i | 0.122966 | − | 0.0709945i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.85759 | − | 14.3891i | 0.107471 | − | 0.541157i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.21770 | − | 4.54454i | 0.0457319 | − | 0.170674i | −0.939283 | − | 0.343144i | \(-0.888508\pi\) |
0.985015 | + | 0.172470i | \(0.0551748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.67638 | − | 4.63562i | 0.100372 | − | 0.173849i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.65165 | 0.0618547 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.22157 | + | 4.22157i | −0.157878 | + | 0.157878i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 74.6444 | − | 20.0009i | 2.78765 | − | 0.746947i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.27548 | + | 16.0656i | 0.345917 | + | 0.599146i | 0.985520 | − | 0.169559i | \(-0.0542345\pi\) |
−0.639603 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.92076 | − | 0.192334i | 0.108775 | − | 0.00716289i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.0816 | − | 60.0174i | 0.598081 | − | 2.23207i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34384 | + | 1.96778i | −0.272743 | + | 0.0730813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.96613i | 0.221272i | 0.993861 | + | 0.110636i | \(0.0352887\pi\) | ||||
−0.993861 | + | 0.110636i | \(0.964711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.2669i | − | 1.60248i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.9360 | + | 12.5765i | −1.73599 | + | 0.465157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.59358 | + | 20.8755i | −0.206604 | + | 0.771055i | 0.782351 | + | 0.622838i | \(0.214020\pi\) |
−0.988955 | + | 0.148218i | \(0.952646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.01002 | + | 5.38579i | −0.258569 | + | 0.198658i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.99554 | + | 6.92048i | 0.147178 | + | 0.254919i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.9804 | − | 9.37297i | 1.28677 | − | 0.344790i | 0.450340 | − | 0.892857i | \(-0.351303\pi\) |
0.836434 | + | 0.548067i | \(0.184636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.1059 | − | 24.1059i | 0.885552 | − | 0.885552i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.2749 | −0.597067 | −0.298533 | − | 0.954399i | \(-0.596497\pi\) | ||||
−0.298533 | + | 0.954399i | \(0.596497\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.37004 | − | 4.10504i | 0.0868317 | − | 0.150397i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.3108 | − | 53.4087i | 0.523605 | − | 1.95412i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.3018 | + | 10.7817i | 0.449497 | + | 0.393955i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8511 | − | 9.15166i | 0.578416 | − | 0.333949i | −0.182087 | − | 0.983282i | \(-0.558285\pi\) |
0.760504 | + | 0.649334i | \(0.224952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.6778 | − | 34.0830i | 0.717101 | − | 1.24205i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.85253 | + | 3.85253i | −0.140208 | + | 0.140208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6944 | + | 16.6944i | 0.606767 | + | 0.606767i | 0.942100 | − | 0.335333i | \(-0.108849\pi\) |
−0.335333 | + | 0.942100i | \(0.608849\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.93593 | − | 5.15916i | −0.324354 | − | 0.187266i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.43390 | + | 7.67974i | 0.160729 | + | 0.278390i | 0.935130 | − | 0.354304i | \(-0.115282\pi\) |
−0.774401 | + | 0.632695i | \(0.781949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.61484 | − | 28.2729i | 0.203271 | − | 1.02355i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.5392 | − | 2.82398i | −0.381047 | − | 0.102101i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.4908 | + | 27.4188i | 1.71479 | + | 0.990036i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.14344i | − | 0.0412335i | −0.999787 | − | 0.0206167i | \(-0.993437\pi\) | ||
0.999787 | − | 0.0206167i | \(-0.00656298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.81396 | − | 4.81396i | −0.173370 | − | 0.173370i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.40701 | + | 5.25103i | 0.0506066 | + | 0.188866i | 0.986602 | − | 0.163146i | \(-0.0521641\pi\) |
−0.935995 | + | 0.352012i | \(0.885497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.59555 | − | 2.07589i | 0.129156 | − | 0.0745683i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 52.5892 | + | 25.9141i | 1.88663 | + | 0.929664i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.17573 | + | 1.65478i | 0.221269 | + | 0.0592888i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.32232 | + | 23.5952i | 0.226231 | + | 0.844304i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.71091 | 0.204091 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.03907 | 0.0370859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2008 | − | 49.2659i | −0.470556 | − | 1.75614i | −0.637778 | − | 0.770220i | \(-0.720146\pi\) |
0.167221 | − | 0.985919i | \(-0.446521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.7816 | − | 6.37227i | −0.846648 | − | 0.226859i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.68956 | − | 3.29639i | −0.237854 | − | 0.117206i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.68959 | − | 1.55283i | 0.0955101 | − | 0.0551428i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.29417 | − | 8.56196i | −0.0813658 | − | 0.303661i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.5433 | − | 26.5433i | −0.940211 | − | 0.940211i | 0.0581002 | − | 0.998311i | \(-0.481496\pi\) |
−0.998311 | + | 0.0581002i | \(0.981496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.1349i | 0.570813i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.72116 | − | 5.03516i | −0.308147 | − | 0.177909i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.1573 | + | 8.08063i | 1.06423 | + | 0.285159i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.457438 | + | 2.30338i | −0.0161226 | + | 0.0811833i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.71565 | + | 13.3639i | 0.271604 | + | 0.470432i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.6346 | + | 10.1813i | 0.620000 | + | 0.357957i | 0.776869 | − | 0.629662i | \(-0.216807\pi\) |
−0.156869 | + | 0.987619i | \(0.550140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8932 | + | 31.8932i | 1.11992 | + | 1.11992i | 0.991752 | + | 0.128171i | \(0.0409107\pi\) |
0.128171 | + | 0.991752i | \(0.459089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.0500 | + | 22.0500i | −0.773327 | + | 0.773327i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.42304 | + | 5.92889i | −0.119904 | + | 0.207680i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3537 | + | 8.86446i | −0.537158 | + | 0.310128i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 54.9873 | + | 48.1928i | 1.92141 | + | 1.68399i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.34443 | − | 23.6777i | 0.221422 | − | 0.826359i | −0.762384 | − | 0.647125i | \(-0.775971\pi\) |
0.983806 | − | 0.179234i | \(-0.0573620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.16976 | − | 8.95429i | 0.180207 | − | 0.312127i | −0.761744 | − | 0.647878i | \(-0.775657\pi\) |
0.941951 | + | 0.335751i | \(0.108990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.9374 | −0.903024 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0264 | − | 33.0264i | 1.14844 | − | 1.14844i | 0.161581 | − | 0.986859i | \(-0.448341\pi\) |
0.986859 | − | 0.161581i | \(-0.0516594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.2050 | + | 9.70111i | −1.25745 | + | 0.336934i | −0.825211 | − | 0.564824i | \(-0.808944\pi\) |
−0.432242 | + | 0.901758i | \(0.642277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.2798 | − | 48.9821i | −0.981015 | − | 1.69917i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.96118 | − | 37.5066i | −0.171895 | − | 1.29953i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.718460 | + | 2.68133i | −0.0248633 | + | 0.0927912i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.01235 | + | 0.807156i | −0.104122 | + | 0.0278994i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 41.5802i | − | 1.43551i | −0.696296 | − | 0.717754i | \(-0.745170\pi\) | ||
0.696296 | − | 0.717754i | \(-0.254830\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4726i | 0.912847i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −51.8636 | + | 13.8968i | −1.78628 | + | 0.478632i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.35563 | − | 12.5234i | 0.115437 | − | 0.430818i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.4417 | − | 1.21440i | 0.633665 | − | 0.0417272i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.5374 | − | 47.6961i | −0.945080 | − | 1.63693i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0436 | − | 4.03092i | 0.515688 | − | 0.138178i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.78632 | + | 3.78632i | −0.129641 | + | 0.129641i | −0.768950 | − | 0.639309i | \(-0.779221\pi\) |
0.639309 | + | 0.768950i | \(0.279221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.98094 | −0.136145 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.93943 | − | 17.2156i | 0.339524 | − | 0.588073i | −0.644819 | − | 0.764335i | \(-0.723067\pi\) |
0.984343 | + | 0.176262i | \(0.0564006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.31449 | + | 12.3699i | −0.113089 | + | 0.422054i | −0.999137 | − | 0.0415399i | \(-0.986774\pi\) |
0.886048 | + | 0.463594i | \(0.153440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.52304 | + | 22.7753i | −0.154145 | + | 0.776179i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.9940 | − | 12.1209i | 0.714643 | − | 0.412599i | −0.0981346 | − | 0.995173i | \(-0.531288\pi\) |
0.812778 | + | 0.582574i | \(0.197954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.14258 | + | 3.71106i | −0.0728500 | + | 0.126180i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.3732 | − | 23.3732i | 0.793794 | − | 0.793794i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.75262 | − | 1.75262i | −0.0594534 | − | 0.0594534i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0593 | − | 12.7359i | −0.747450 | − | 0.431541i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.1623 | + | 17.6016i | 0.343941 | + | 0.595723i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.88485 | + | 11.4329i | 0.131332 | + | 0.386503i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9270 | − | 5.60738i | −0.706656 | − | 0.189348i | −0.112446 | − | 0.993658i | \(-0.535868\pi\) |
−0.594210 | + | 0.804310i | \(0.702535\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.3946 | + | 12.9295i | 0.755349 | + | 0.436101i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.3375i | − | 0.516733i | −0.966047 | − | 0.258367i | \(-0.916816\pi\) | ||
0.966047 | − | 0.258367i | \(-0.0831842\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.7596 | + | 35.7596i | 1.20341 | + | 1.20341i | 0.973124 | + | 0.230282i | \(0.0739648\pi\) |
0.230282 | + | 0.973124i | \(0.426035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.80645 | − | 10.4738i | −0.0943378 | − | 0.352074i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0000 | + | 16.1658i | −0.940148 | + | 0.542795i | −0.890007 | − | 0.455947i | \(-0.849301\pi\) |
−0.0501414 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9312 | − | 22.1835i | 0.366622 | − | 0.744009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.30459 | − | 1.68931i | −0.211212 | − | 0.0565940i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.52364 | + | 5.68632i | 0.0509868 | + | 0.190285i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.77504 | −0.0593330 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.8900 | 1.09817 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.357216 | + | 1.33315i | 0.0119138 | + | 0.0444629i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.6430 | + | 9.81846i | 1.22075 | + | 0.327100i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.7881 | − | 53.5252i | −1.19095 | − | 1.78121i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.93378 | + | 1.69382i | −0.0975220 | + | 0.0563044i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.19408 | + | 30.5807i | 0.272080 | + | 1.01542i | 0.957773 | + | 0.287525i | \(0.0928325\pi\) |
−0.685693 | + | 0.727891i | \(0.740501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.9654 | + | 16.9654i | 0.562707 | + | 0.562707i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.17911i | − | 0.237854i | −0.992903 | − | 0.118927i | \(-0.962054\pi\) | ||
0.992903 | − | 0.118927i | \(-0.0379455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.1729 | − | 12.8015i | −0.733817 | − | 0.423669i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.593173 | − | 0.158940i | −0.0196097 | − | 0.00525441i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.9142 | + | 32.3529i | 1.21901 | + | 1.06839i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.18242 | + | 2.04801i | 0.0390044 | + | 0.0675576i | 0.884869 | − | 0.465841i | \(-0.154248\pi\) |
−0.845864 | + | 0.533398i | \(0.820915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.85475 | + | 4.53494i | 0.258823 | + | 0.149431i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.0580 | − | 55.0580i | −1.81226 | − | 1.81226i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.6828 | − | 27.6828i | 0.910206 | − | 0.910206i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.39361 | + | 4.14585i | −0.0786164 | + | 0.136168i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.6476 | + | 29.2414i | −1.66169 | + | 0.959379i | −0.689787 | + | 0.724012i | \(0.742296\pi\) |
−0.971906 | + | 0.235367i | \(0.924371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.29023 | − | 12.7497i | −0.173380 | − | 0.417854i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.6168 | − | 39.6224i | 0.347578 | − | 1.29718i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.52615 | + | 4.37543i | −0.0826141 | + | 0.143092i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.4613 | 0.439761 | 0.219881 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219881 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.7395 | − | 12.7395i | 0.415738 | − | 0.415738i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9193 | − | 3.99761i | 0.486355 | − | 0.130318i | −0.00730539 | − | 0.999973i | \(-0.502325\pi\) |
0.493660 | + | 0.869655i | \(0.335659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.08419 | + | 5.34197i | 0.100435 | + | 0.173959i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.291359 | − | 4.42454i | −0.00947790 | − | 0.143930i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.08357 | − | 30.1683i | 0.262681 | − | 0.980338i | −0.700974 | − | 0.713187i | \(-0.747251\pi\) |
0.963655 | − | 0.267151i | \(-0.0860823\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −96.1276 | + | 25.7573i | −3.12043 | + | 0.836118i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 71.7697i | − | 2.32729i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 15.7802i | − | 0.511170i | −0.966787 | − | 0.255585i | \(-0.917732\pi\) | ||
0.966787 | − | 0.255585i | \(-0.0822680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.93032 | − | 2.12492i | 0.256619 | − | 0.0687609i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.23163 | − | 8.32855i | 0.0721383 | − | 0.269224i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.3366 | − | 33.4070i | −0.721287 | − | 1.07877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1232 | + | 26.1941i | 0.487844 | + | 0.844970i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.8415 | + | 6.92420i | −0.832729 | + | 0.223129i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.17051 | + | 2.17051i | −0.0698712 | + | 0.0698712i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.7046 | 1.43760 | 0.718801 | − | 0.695216i | \(-0.244691\pi\) | ||||
0.718801 | + | 0.695216i | \(0.244691\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.4248 | − | 24.9844i | 0.463390 | − | 0.802615i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0660 | − | 56.2271i | 0.483491 | − | 1.80441i | −0.103269 | − | 0.994653i | \(-0.532930\pi\) |
0.586761 | − | 0.809761i | \(-0.300403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.36166 | − | 4.00728i | −0.0436527 | − | 0.128468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 71.5999 | − | 41.3382i | 2.29303 | − | 1.32388i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.4344 | − | 18.0729i | 0.333827 | − | 0.578204i | −0.649432 | − | 0.760420i | \(-0.724993\pi\) |
0.983259 | + | 0.182215i | \(0.0583267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.29726 | + | 3.29726i | −0.105381 | + | 0.105381i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.3351 | + | 33.3351i | 1.06431 | + | 1.06431i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.5230 | − | 21.0866i | −1.16490 | − | 0.672558i | −0.212430 | − | 0.977176i | \(-0.568138\pi\) |
−0.952474 | + | 0.304619i | \(0.901471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.90806 | + | 8.50102i | 0.156384 | + | 0.270865i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.2432 | + | 6.87853i | −0.644347 | + | 0.218946i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.5216 | − | 4.42695i | −0.525356 | − | 0.140769i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.7987 | − | 8.54402i | −0.470095 | − | 0.271410i | 0.246184 | − | 0.969223i | \(-0.420823\pi\) |
−0.716280 | + | 0.697813i | \(0.754156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.6788i | 0.814891i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45062 | + | 2.45062i | 0.0776898 | + | 0.0776898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.35325 | + | 27.4427i | 0.232880 | + | 0.869119i | 0.979093 | + | 0.203412i | \(0.0652031\pi\) |
−0.746214 | + | 0.665707i | \(0.768130\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.4673 | + | 14.7035i | −0.805749 | + | 0.465199i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 896.2.z.a.31.2 | 56 | ||
4.3 | odd | 2 | 896.2.z.b.31.13 | 56 | |||
7.5 | odd | 6 | inner | 896.2.z.a.159.2 | 56 | ||
8.3 | odd | 2 | 112.2.v.a.59.13 | yes | 56 | ||
8.5 | even | 2 | 448.2.z.a.143.13 | 56 | |||
16.3 | odd | 4 | inner | 896.2.z.a.479.2 | 56 | ||
16.5 | even | 4 | 112.2.v.a.3.7 | ✓ | 56 | ||
16.11 | odd | 4 | 448.2.z.a.367.13 | 56 | |||
16.13 | even | 4 | 896.2.z.b.479.13 | 56 | |||
28.19 | even | 6 | 896.2.z.b.159.13 | 56 | |||
56.3 | even | 6 | 784.2.j.a.587.8 | 56 | |||
56.5 | odd | 6 | 448.2.z.a.271.13 | 56 | |||
56.11 | odd | 6 | 784.2.j.a.587.7 | 56 | |||
56.19 | even | 6 | 112.2.v.a.75.7 | yes | 56 | ||
56.27 | even | 2 | 784.2.w.f.619.13 | 56 | |||
56.51 | odd | 6 | 784.2.w.f.411.7 | 56 | |||
112.5 | odd | 12 | 112.2.v.a.19.13 | yes | 56 | ||
112.19 | even | 12 | inner | 896.2.z.a.607.2 | 56 | ||
112.37 | even | 12 | 784.2.w.f.19.13 | 56 | |||
112.53 | even | 12 | 784.2.j.a.195.8 | 56 | |||
112.61 | odd | 12 | 896.2.z.b.607.13 | 56 | |||
112.69 | odd | 4 | 784.2.w.f.227.7 | 56 | |||
112.75 | even | 12 | 448.2.z.a.47.13 | 56 | |||
112.101 | odd | 12 | 784.2.j.a.195.7 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.v.a.3.7 | ✓ | 56 | 16.5 | even | 4 | ||
112.2.v.a.19.13 | yes | 56 | 112.5 | odd | 12 | ||
112.2.v.a.59.13 | yes | 56 | 8.3 | odd | 2 | ||
112.2.v.a.75.7 | yes | 56 | 56.19 | even | 6 | ||
448.2.z.a.47.13 | 56 | 112.75 | even | 12 | |||
448.2.z.a.143.13 | 56 | 8.5 | even | 2 | |||
448.2.z.a.271.13 | 56 | 56.5 | odd | 6 | |||
448.2.z.a.367.13 | 56 | 16.11 | odd | 4 | |||
784.2.j.a.195.7 | 56 | 112.101 | odd | 12 | |||
784.2.j.a.195.8 | 56 | 112.53 | even | 12 | |||
784.2.j.a.587.7 | 56 | 56.11 | odd | 6 | |||
784.2.j.a.587.8 | 56 | 56.3 | even | 6 | |||
784.2.w.f.19.13 | 56 | 112.37 | even | 12 | |||
784.2.w.f.227.7 | 56 | 112.69 | odd | 4 | |||
784.2.w.f.411.7 | 56 | 56.51 | odd | 6 | |||
784.2.w.f.619.13 | 56 | 56.27 | even | 2 | |||
896.2.z.a.31.2 | 56 | 1.1 | even | 1 | trivial | ||
896.2.z.a.159.2 | 56 | 7.5 | odd | 6 | inner | ||
896.2.z.a.479.2 | 56 | 16.3 | odd | 4 | inner | ||
896.2.z.a.607.2 | 56 | 112.19 | even | 12 | inner | ||
896.2.z.b.31.13 | 56 | 4.3 | odd | 2 | |||
896.2.z.b.159.13 | 56 | 28.19 | even | 6 | |||
896.2.z.b.479.13 | 56 | 16.13 | even | 4 | |||
896.2.z.b.607.13 | 56 | 112.61 | odd | 12 |