Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.5 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.41991 | − | 0.991901i | −0.819783 | − | 0.572674i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.11047 | − | 1.92339i | −0.496617 | − | 0.860166i | 0.503376 | − | 0.864068i | \(-0.332091\pi\) |
−0.999992 | + | 0.00390210i | \(0.998758\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.362456 | − | 2.62081i | 0.136995 | − | 0.990572i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.03226 | + | 2.81681i | 0.344088 | + | 0.938937i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.01582 | − | 0.586482i | −0.306280 | − | 0.176831i | 0.338980 | − | 0.940793i | \(-0.389918\pi\) |
−0.645261 | + | 0.763962i | \(0.723251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.12404 | − | 1.80366i | −0.866453 | − | 0.500247i | −0.000284763 | − | 1.00000i | \(-0.500091\pi\) |
−0.866168 | + | 0.499753i | \(0.833424\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.331050 | + | 3.83251i | −0.0854767 | + | 0.989549i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.71178 | + | 6.42899i | 0.900238 | + | 1.55926i | 0.827185 | + | 0.561930i | \(0.189941\pi\) |
0.0730533 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.05231 | − | 1.76225i | −0.700249 | − | 0.404289i | 0.107191 | − | 0.994238i | \(-0.465814\pi\) |
−0.807440 | + | 0.589950i | \(0.799148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.11423 | + | 3.36178i | −0.679581 | + | 0.733600i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.03374 | + | 2.90623i | −1.04961 | + | 0.605991i | −0.922539 | − | 0.385903i | \(-0.873890\pi\) |
−0.127068 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0337168 | − | 0.0583992i | 0.00674336 | − | 0.0116798i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.32828 | − | 5.02351i | 0.255628 | − | 0.966775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.04430 | + | 3.48968i | −1.12240 | + | 0.648017i | −0.942012 | − | 0.335579i | \(-0.891068\pi\) |
−0.180387 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.95031i | − | 1.42792i | −0.700187 | − | 0.713959i | \(-0.746900\pi\) | ||
0.700187 | − | 0.713959i | \(-0.253100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.860632 | + | 1.84034i | 0.149817 | + | 0.320362i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.44333 | + | 2.21318i | −0.920090 | + | 0.374096i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.54350 | + | 9.60163i | −0.911346 | + | 1.57850i | −0.0991818 | + | 0.995069i | \(0.531623\pi\) |
−0.812164 | + | 0.583429i | \(0.801711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.64678 | + | 5.65977i | 0.423825 | + | 0.906289i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.809022 | − | 1.40127i | 0.126348 | − | 0.218841i | −0.795911 | − | 0.605414i | \(-0.793008\pi\) |
0.922259 | + | 0.386572i | \(0.126341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.904302 | + | 1.56630i | 0.137905 | + | 0.238858i | 0.926703 | − | 0.375794i | \(-0.122630\pi\) |
−0.788799 | + | 0.614652i | \(0.789297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.27153 | − | 5.11343i | 0.636762 | − | 0.762265i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.52953 | −1.24416 | −0.622080 | − | 0.782954i | \(-0.713712\pi\) | ||||
−0.622080 | + | 0.782954i | \(0.713712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73725 | − | 1.89985i | −0.962465 | − | 0.271407i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.10654 | − | 12.8103i | 0.154947 | − | 1.79380i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.62611 | − | 5.55764i | 1.32225 | − | 0.763400i | 0.338161 | − | 0.941088i | \(-0.390195\pi\) |
0.984087 | + | 0.177688i | \(0.0568617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.60508i | 0.351269i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.58602 | + | 5.52983i | 0.342526 | + | 0.732444i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00276 | −0.521115 | −0.260557 | − | 0.965458i | \(-0.583906\pi\) | ||||
−0.260557 | + | 0.965458i | \(0.583906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.18688i | − | 1.04822i | −0.851650 | − | 0.524111i | \(-0.824398\pi\) | ||
0.851650 | − | 0.524111i | \(-0.175602\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.75647 | − | 1.68440i | 0.977223 | − | 0.212214i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.01166i | 0.993724i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.92669 | 1.21274 | 0.606369 | − | 0.795183i | \(-0.292625\pi\) | ||||
0.606369 | + | 0.795183i | \(0.292625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.0301 | + | 0.866397i | 1.20749 | + | 0.104302i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.67194i | − | 0.435779i | −0.975973 | − | 0.217890i | \(-0.930083\pi\) | ||
0.975973 | − | 0.217890i | \(-0.0699172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92803 | − | 3.99990i | 0.810865 | − | 0.468153i | −0.0363913 | − | 0.999338i | \(-0.511586\pi\) |
0.847256 | + | 0.531185i | \(0.178253\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.105801 | + | 0.0494776i | −0.0122168 | + | 0.00571318i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.90525 | + | 2.44969i | −0.217123 | + | 0.279168i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.51987 | −0.508525 | −0.254262 | − | 0.967135i | \(-0.581833\pi\) | ||||
−0.254262 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.86886 | + | 5.81539i | −0.763207 | + | 0.646155i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.390969 | + | 0.677179i | 0.0429145 | + | 0.0743300i | 0.886685 | − | 0.462374i | \(-0.153002\pi\) |
−0.843770 | + | 0.536704i | \(0.819669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.24363 | − | 14.2784i | 0.894147 | − | 1.54871i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0438 | + | 1.04033i | 1.29123 | + | 0.111535i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.75440 | + | 3.03870i | −0.185966 | + | 0.322102i | −0.943901 | − | 0.330227i | \(-0.892875\pi\) |
0.757936 | + | 0.652329i | \(0.226208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.85938 | + | 7.53375i | −0.614230 | + | 0.789752i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.88592 | + | 11.2887i | −0.817732 | + | 1.17058i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.82772i | 0.803107i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.49226 | − | 2.01626i | 0.354585 | − | 0.204720i | −0.312118 | − | 0.950043i | \(-0.601038\pi\) |
0.666703 | + | 0.745324i | \(0.267705\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.603418 | − | 3.46677i | 0.0606458 | − | 0.348424i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13904 | − | 1.97288i | 0.113339 | − | 0.196309i | −0.803775 | − | 0.594933i | \(-0.797179\pi\) |
0.917115 | + | 0.398624i | \(0.130512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68427 | − | 4.43651i | 0.757153 | − | 0.437143i | −0.0711195 | − | 0.997468i | \(-0.522657\pi\) |
0.828273 | + | 0.560325i | \(0.189324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.92427 | + | 2.25673i | 0.968509 | + | 0.220234i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.574764 | + | 0.331840i | 0.0555646 | + | 0.0320802i | 0.527525 | − | 0.849540i | \(-0.323120\pi\) |
−0.471960 | + | 0.881620i | \(0.656453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.03435 | − | 13.9159i | −0.769551 | − | 1.33290i | −0.937807 | − | 0.347158i | \(-0.887147\pi\) |
0.168256 | − | 0.985743i | \(-0.446187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.3951 | − | 8.13480i | 1.65107 | − | 0.772121i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.86666 | − | 2.80977i | −0.457817 | − | 0.264321i | 0.253309 | − | 0.967385i | \(-0.418481\pi\) |
−0.711126 | + | 0.703065i | \(0.751814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1796 | + | 6.45456i | 1.04250 | + | 0.601891i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.85575 | − | 10.6617i | 0.171564 | − | 0.985674i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.1945 | − | 7.39763i | 1.66789 | − | 0.678139i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.81208 | − | 8.33476i | −0.437462 | − | 0.757706i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.53865 | + | 1.18720i | −0.228903 | + | 0.107046i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.2545 | −1.00663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.74425 | 0.687191 | 0.343595 | − | 0.939118i | \(-0.388355\pi\) | ||||
0.343595 | + | 0.939118i | \(0.388355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.269588 | − | 3.12097i | 0.0237359 | − | 0.274786i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.81293 | − | 13.5324i | −0.682619 | − | 1.18233i | −0.974179 | − | 0.225778i | \(-0.927507\pi\) |
0.291559 | − | 0.956553i | \(-0.405826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.72486 | + | 7.36078i | −0.496408 | + | 0.638261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1372 | + | 3.02366i | −0.958536 | + | 0.260235i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.931541 | + | 0.537826i | 0.0795870 | + | 0.0459496i | 0.539265 | − | 0.842136i | \(-0.318702\pi\) |
−0.459678 | + | 0.888085i | \(0.652035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.81776 | − | 3.35889i | −0.493456 | − | 0.284897i | 0.232551 | − | 0.972584i | \(-0.425293\pi\) |
−0.726007 | + | 0.687687i | \(0.758626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1111 | + | 8.46045i | 1.01994 | + | 0.712498i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.11563 | + | 3.66439i | 0.176918 | + | 0.306431i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.4240 | + | 7.75036i | 1.11480 | + | 0.643633i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.68180 | + | 9.38030i | 0.633584 | + | 0.773674i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2105 | − | 8.78176i | 1.24609 | − | 0.719430i | 0.275762 | − | 0.961226i | \(-0.411070\pi\) |
0.970327 | + | 0.241796i | \(0.0777365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.848028 | + | 1.46883i | −0.0690115 | + | 0.119531i | −0.898466 | − | 0.439042i | \(-0.855318\pi\) |
0.829455 | + | 0.558574i | \(0.188651\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.2777 | + | 17.0918i | −1.15428 | + | 1.38179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2915 | + | 8.82858i | −1.22825 | + | 0.709128i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.88233i | − | 0.629078i | −0.949244 | − | 0.314539i | \(-0.898150\pi\) | ||
0.949244 | − | 0.314539i | \(-0.101850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.1808 | − | 1.65683i | −1.52114 | − | 0.131395i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.79216 | + | 14.2458i | 0.456486 | + | 1.12273i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.69385 | + | 9.86204i | −0.445977 | + | 0.772455i | −0.998120 | − | 0.0612949i | \(-0.980477\pi\) |
0.552143 | + | 0.833750i | \(0.313810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.58398 | − | 3.69897i | 0.201163 | − | 0.287964i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.05638 | + | 13.9541i | −0.623422 | + | 1.07980i | 0.365422 | + | 0.930842i | \(0.380925\pi\) |
−0.988844 | + | 0.148956i | \(0.952409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.00641296 | + | 0.0111076i | 0.000493305 | + | 0.000854429i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.81314 | − | 10.4169i | 0.138654 | − | 0.796601i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.90364 | 0.524874 | 0.262437 | − | 0.964949i | \(-0.415474\pi\) | ||||
0.262437 | + | 0.964949i | \(0.415474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.140832 | − | 0.109532i | −0.0106459 | − | 0.00827986i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.68354 | + | 3.97034i | 0.427201 | + | 0.298429i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.28759 | − | 3.05279i | 0.395213 | − | 0.228176i | −0.289203 | − | 0.957268i | \(-0.593390\pi\) |
0.684416 | + | 0.729091i | \(0.260057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.46329i | − | 0.406083i | −0.979170 | − | 0.203041i | \(-0.934917\pi\) | ||
0.979170 | − | 0.203041i | \(-0.0650826\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.12057 | + | 11.6246i | −0.600290 | + | 0.859315i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.6236 | 1.81036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.70756i | − | 0.636760i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.6842 | − | 5.30196i | −0.922640 | − | 0.385661i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.01636i | − | 0.435328i | −0.976024 | − | 0.217664i | \(-0.930156\pi\) | ||
0.976024 | − | 0.217664i | \(-0.0698438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.78034 | −0.416078 | −0.208039 | − | 0.978121i | \(-0.566708\pi\) | ||||
−0.208039 | + | 0.978121i | \(0.566708\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.94677 | − | 11.3758i | 0.569080 | − | 0.814638i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.95354i | − | 0.566666i | −0.959022 | − | 0.283333i | \(-0.908560\pi\) | ||
0.959022 | − | 0.283333i | \(-0.0914402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5229 | + | 8.96214i | −1.10039 | + | 0.635309i | −0.936323 | − | 0.351141i | \(-0.885794\pi\) |
−0.164065 | + | 0.986450i | \(0.552461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0950 | − | 9.84629i | −0.994182 | − | 0.694504i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.95498 | + | 17.1058i | 0.488144 | + | 1.20059i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.59358 | −0.250986 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.3825 | − | 11.1791i | −0.930145 | − | 0.777001i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.06706 | + | 3.58026i | 0.142982 | + | 0.247651i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00200 | + | 6.93166i | −0.275509 | + | 0.477195i | −0.970263 | − | 0.242052i | \(-0.922180\pi\) |
0.694755 | + | 0.719247i | \(0.255513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.64220 | + | 5.21381i | −0.249559 | + | 0.357244i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00840 | − | 3.47865i | 0.136972 | − | 0.237242i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.8362 | − | 2.88164i | −1.41446 | − | 0.195618i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.8047 | − | 1.19244i | −0.932832 | − | 0.0805776i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 26.7792i | − | 1.80136i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.2405 | − | 8.22177i | 0.953616 | − | 0.550570i | 0.0594134 | − | 0.998233i | \(-0.481077\pi\) |
0.894202 | + | 0.447663i | \(0.147744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.199304 | + | 0.0346904i | 0.0132869 | + | 0.00231269i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.99649 | + | 13.8503i | −0.530746 | + | 0.919279i | 0.468610 | + | 0.883405i | \(0.344755\pi\) |
−0.999356 | + | 0.0358740i | \(0.988578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3898 | + | 7.73058i | −0.884820 | + | 0.510851i | −0.872245 | − | 0.489070i | \(-0.837336\pi\) |
−0.0125754 | + | 0.999921i | \(0.504003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.13511 | − | 1.58851i | 0.337866 | − | 0.104516i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5268 | − | 9.54175i | −1.08271 | − | 0.625101i | −0.151081 | − | 0.988521i | \(-0.548275\pi\) |
−0.931625 | + | 0.363421i | \(0.881609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.47178 | + | 16.4056i | 0.617871 | + | 1.07018i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.41778 | + | 4.48326i | 0.416880 | + | 0.291219i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.37626 | + | 4.25868i | 0.477130 | + | 0.275471i | 0.719220 | − | 0.694783i | \(-0.244499\pi\) |
−0.242089 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6047 | + | 11.3188i | 1.26285 | + | 0.729107i | 0.973625 | − | 0.228154i | \(-0.0732690\pi\) |
0.289225 | + | 0.957261i | \(0.406602\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5214 | − | 1.44408i | 0.995700 | − | 0.0926377i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.82736 | + | 15.0681i | 0.244521 | + | 0.962664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.35703 | + | 11.0107i | 0.404488 | + | 0.700594i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.116555 | − | 1.34933i | 0.00738635 | − | 0.0855105i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.74235 | −0.488693 | −0.244346 | − | 0.969688i | \(-0.578573\pi\) | ||||
−0.244346 | + | 0.969688i | \(0.578573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.81781 | 0.428632 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.8679 | + | 12.0971i | −1.61991 | + | 0.757549i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8945 | − | 20.6019i | −0.741958 | − | 1.28511i | −0.951603 | − | 0.307331i | \(-0.900564\pi\) |
0.209645 | − | 0.977778i | \(-0.432769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.1547 | + | 18.0086i | 1.43877 | + | 1.11900i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0691 | − | 13.4234i | −0.994652 | − | 0.830887i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.7831 | − | 10.2671i | −1.09655 | − | 0.633094i | −0.161238 | − | 0.986916i | \(-0.551549\pi\) |
−0.935313 | + | 0.353822i | \(0.884882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.3790 | − | 12.3432i | −1.31330 | − | 0.758235i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.50517 | − | 2.57448i | 0.336911 | − | 0.157556i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.17188 | − | 10.6900i | −0.376306 | − | 0.651782i | 0.614215 | − | 0.789138i | \(-0.289473\pi\) |
−0.990522 | + | 0.137357i | \(0.956139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3900 | − | 14.6589i | −1.54233 | − | 0.890467i | −0.998691 | − | 0.0511505i | \(-0.983711\pi\) |
−0.543643 | − | 0.839317i | \(-0.682955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.7925 | − | 4.88529i | 0.955806 | − | 0.295671i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0685002 | + | 0.0395486i | −0.00413072 | + | 0.00238487i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24115 | − | 2.14974i | 0.0745735 | − | 0.129165i | −0.826327 | − | 0.563190i | \(-0.809574\pi\) |
0.900901 | + | 0.434025i | \(0.142907\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.3945 | − | 8.20683i | 1.34073 | − | 0.491330i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0970 | − | 11.6030i | 1.19889 | − | 0.692178i | 0.238581 | − | 0.971123i | \(-0.423318\pi\) |
0.960307 | + | 0.278944i | \(0.0899845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.3000i | 1.62282i | 0.584480 | + | 0.811408i | \(0.301298\pi\) | ||||
−0.584480 | + | 0.811408i | \(0.698702\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.76432 | − | 11.1146i | 0.459919 | − | 0.658373i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.37922 | − | 2.62819i | −0.199469 | − | 0.155137i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0546 | + | 33.0035i | −1.12086 | + | 1.94138i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.95861 | − | 0.601081i | −0.407921 | − | 0.0352360i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.15628 | + | 7.19888i | −0.242812 | + | 0.420563i | −0.961514 | − | 0.274755i | \(-0.911403\pi\) |
0.718702 | + | 0.695318i | \(0.244737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.44494 | + | 7.69886i | 0.258794 | + | 0.448245i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.29549 | + | 4.32396i | −0.249250 | + | 0.250901i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.9675 | 1.21258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.43273 | − | 1.80229i | 0.255498 | − | 0.103882i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.57424 | + | 1.67149i | −0.205335 | + | 0.0960245i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.7465 | + | 9.09127i | −0.901645 | + | 0.520565i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.4908i | − | 1.28362i | −0.766864 | − | 0.641810i | \(-0.778184\pi\) | ||
0.766864 | − | 0.641810i | \(-0.221816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3115 | − | 1.32260i | −0.871042 | − | 0.0752401i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.67799 | 0.548789 | 0.274394 | − | 0.961617i | \(-0.411523\pi\) | ||||
0.274394 | + | 0.961617i | \(0.411523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4969i | 1.38465i | 0.721587 | + | 0.692324i | \(0.243413\pi\) | ||||
−0.721587 | + | 0.692324i | \(0.756587\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.8531 | − | 13.0482i | −0.667845 | − | 0.735185i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.18619i | − | 0.515948i | −0.966152 | − | 0.257974i | \(-0.916945\pi\) | ||
0.966152 | − | 0.257974i | \(-0.0830549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.18654 | 0.458358 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.486958 | − | 1.04129i | −0.0271794 | − | 0.0581192i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 26.1644i | − | 1.45582i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.210665 | + | 0.121628i | −0.0116856 | + | 0.00674668i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.39518 | + | 27.7285i | −0.132454 | + | 1.53339i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.09157 | + | 22.3542i | −0.170444 | + | 1.23243i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.7197 | 1.41368 | 0.706842 | − | 0.707372i | \(-0.250119\pi\) | ||||
0.706842 | + | 0.707372i | \(0.250119\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.7683 | − | 5.70358i | −1.79569 | − | 0.312554i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0233 | − | 19.0929i | −0.602266 | − | 1.04316i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.80657 | − | 15.2534i | 0.479724 | − | 0.830907i | −0.520005 | − | 0.854163i | \(-0.674070\pi\) |
0.999730 | + | 0.0232560i | \(0.00740329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.12319 | + | 8.81685i | 0.223941 | + | 0.478865i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.66272 | + | 8.07606i | −0.252500 | + | 0.437343i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.42110 | + | 16.9684i | −0.400702 | + | 0.916209i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.47173 | − | 20.2539i | −0.509941 | − | 1.09044i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.35297i | 0.448411i | 0.974542 | + | 0.224206i | \(0.0719787\pi\) | ||||
−0.974542 | + | 0.224206i | \(0.928021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4062 | − | 9.47211i | 0.878203 | − | 0.507031i | 0.00813729 | − | 0.999967i | \(-0.497410\pi\) |
0.870065 | + | 0.492936i | \(0.164076\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.2103 | + | 13.2979i | −0.705115 | + | 0.709788i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7486 | − | 22.0811i | 0.678537 | − | 1.17526i | −0.296884 | − | 0.954913i | \(-0.595948\pi\) |
0.975421 | − | 0.220347i | \(-0.0707191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.06257 | + | 4.07758i | −0.374842 | + | 0.216415i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.1722 | − | 7.54319i | −1.75566 | − | 0.399228i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4128 | + | 10.0533i | 0.919013 | + | 0.530592i | 0.883320 | − | 0.468771i | \(-0.155303\pi\) |
0.0356928 | + | 0.999363i | \(0.488636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.28892 | − | 5.69658i | −0.173101 | − | 0.299820i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.43456 | + | 16.6077i | −0.0752950 | + | 0.871677i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.3867 | − | 8.88353i | −0.805378 | − | 0.464985i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.1654 | − | 11.6425i | −1.05263 | − | 0.607735i | −0.129244 | − | 0.991613i | \(-0.541255\pi\) |
−0.923384 | + | 0.383878i | \(0.874588\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.78223 | + | 0.832384i | 0.248953 | + | 0.0433322i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0765 | − | 27.2426i | −0.575061 | − | 1.41436i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5625 | + | 21.7588i | 0.650460 | + | 1.12663i | 0.983011 | + | 0.183545i | \(0.0587573\pi\) |
−0.332551 | + | 0.943085i | \(0.607909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.9803 | + | 11.1633i | 0.825217 | + | 0.576471i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.1768 | 1.29667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3000 | 1.65914 | 0.829569 | − | 0.558404i | \(-0.188586\pi\) | ||||
0.829569 | + | 0.558404i | \(0.188586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9961 | − | 7.68153i | −0.563347 | − | 0.393536i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.77182 | + | 8.26503i | 0.243828 | + | 0.422323i | 0.961802 | − | 0.273748i | \(-0.0882633\pi\) |
−0.717973 | + | 0.696071i | \(0.754930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.82741 | + | 0.944226i | 0.347957 | + | 0.0481222i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.47849 | + | 4.16408i | −0.176821 | + | 0.211672i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7953 | + | 6.81005i | 0.598048 | + | 0.345283i | 0.768273 | − | 0.640122i | \(-0.221116\pi\) |
−0.170225 | + | 0.985405i | \(0.554450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.3682 | − | 21.5746i | −1.88979 | − | 1.09107i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.32917 | + | 26.9644i | −0.117491 | + | 1.36017i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.01917 | + | 8.69346i | 0.252542 | + | 0.437415i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.59589 | + | 1.49874i | 0.130284 | + | 0.0752196i | 0.563726 | − | 0.825962i | \(-0.309368\pi\) |
−0.433441 | + | 0.901182i | \(0.642701\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.4299 | − | 4.77313i | 0.772462 | − | 0.238955i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2875 | − | 6.51682i | 0.563669 | − | 0.325434i | −0.190948 | − | 0.981600i | \(-0.561156\pi\) |
0.754617 | + | 0.656166i | \(0.227823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3397 | + | 24.8371i | −0.714311 | + | 1.23722i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.8129 | + | 6.75367i | 0.934821 | + | 0.335593i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2624 | − | 6.50233i | 0.558255 | − | 0.322309i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.8723i | 1.62543i | 0.582662 | + | 0.812714i | \(0.302011\pi\) | ||||
−0.582662 | + | 0.812714i | \(0.697989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.789231 | − | 1.68766i | −0.0389299 | − | 0.0832461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.45082 | + | 10.4905i | −0.0713903 | + | 0.516201i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.868319 | − | 1.50397i | 0.0426241 | − | 0.0738271i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.92899 | + | 10.5399i | 0.241374 | + | 0.516144i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.0687 | + | 19.1716i | −0.540742 | + | 0.936593i | 0.458119 | + | 0.888891i | \(0.348523\pi\) |
−0.998862 | + | 0.0477024i | \(0.984810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1963 | + | 21.1245i | 0.594409 | + | 1.02955i | 0.993630 | + | 0.112692i | \(0.0359472\pi\) |
−0.399221 | + | 0.916855i | \(0.630719\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.80473 | − | 24.0261i | −0.428101 | − | 1.16819i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.500597 | 0.0242825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4562 | − | 2.96738i | −1.03834 | − | 0.143602i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.630707 | − | 7.30158i | 0.0304508 | − | 0.352524i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2611 | − | 7.07897i | 0.590598 | − | 0.340982i | −0.174736 | − | 0.984615i | \(-0.555907\pi\) |
0.765334 | + | 0.643634i | \(0.222574\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.90220i | 0.427813i | 0.976854 | + | 0.213906i | \(0.0686187\pi\) | ||||
−0.976854 | + | 0.213906i | \(0.931381\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3733 | − | 24.3201i | −0.545306 | − | 1.16606i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.4861 | 0.979981 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.1624i | − | 0.771389i | −0.922626 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922626 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.60310 | − | 20.9387i | −0.0763382 | − | 0.997082i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4477i | 0.828963i | 0.910058 | + | 0.414482i | \(0.136037\pi\) | ||||
−0.910058 | + | 0.414482i | \(0.863963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.79281 | 0.369415 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.3080 | − | 2.61799i | −1.43352 | − | 0.123827i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.14988i | 0.431809i | 0.976414 | + | 0.215905i | \(0.0692700\pi\) | ||||
−0.976414 | + | 0.215905i | \(0.930730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.64364 | + | 0.948954i | −0.0773958 | + | 0.0446845i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.66105 | − | 1.24444i | 0.125027 | − | 0.0584687i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.9970 | + | 2.90387i | 0.984354 | + | 0.136135i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.1151 | 0.660279 | 0.330139 | − | 0.943932i | \(-0.392904\pi\) | ||||
0.330139 | + | 0.943932i | \(0.392904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 37.2264 | − | 10.1067i | 1.73758 | − | 0.471739i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5323 | + | 30.3668i | 0.816561 | + | 1.41432i | 0.908202 | + | 0.418532i | \(0.137455\pi\) |
−0.0916412 | + | 0.995792i | \(0.529211\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9985 | − | 27.7103i | 0.743515 | − | 1.28781i | −0.207370 | − | 0.978263i | \(-0.566490\pi\) |
0.950885 | − | 0.309543i | \(-0.100176\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.4696 | + | 2.63195i | 1.41300 | + | 0.122054i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.02671 | − | 13.9027i | 0.371432 | − | 0.643339i | −0.618354 | − | 0.785899i | \(-0.712200\pi\) |
0.989786 | + | 0.142561i | \(0.0455337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.59798 | − | 26.0159i | 0.166139 | − | 1.20130i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.81849 | + | 11.1922i | −0.360257 | + | 0.515708i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.12143i | − | 0.0975434i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.205828 | + | 0.118835i | −0.00944406 | + | 0.00545253i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.5915 | + | 21.3780i | 1.17176 | + | 0.978831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.7481 | − | 27.2764i | 0.719547 | − | 1.24629i | −0.241632 | − | 0.970368i | \(-0.577683\pi\) |
0.961179 | − | 0.275925i | \(-0.0889840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6362 | − | 19.9972i | 1.57928 | − | 0.911796i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.90613 | − | 25.9730i | 0.268738 | − | 1.18181i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.75609 | − | 4.47798i | −0.352186 | − | 0.203335i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7924 | + | 18.6930i | 0.489052 | + | 0.847062i | 0.999921 | − | 0.0125963i | \(-0.00400964\pi\) |
−0.510869 | + | 0.859659i | \(0.670676\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.8669 | − | 8.35543i | 0.807969 | − | 0.377846i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9290 | − | 16.7022i | −1.30555 | − | 0.753758i | −0.324197 | − | 0.945990i | \(-0.605094\pi\) |
−0.981349 | + | 0.192232i | \(0.938427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.8702 | − | 25.9058i | −2.02085 | − | 1.16674i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.33803 | + | 2.68913i | −0.329820 | + | 0.120868i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.62344 | − | 1.33091i | −0.431670 | − | 0.0596997i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0722 | − | 27.8378i | −0.719489 | − | 1.24619i | −0.961202 | − | 0.275844i | \(-0.911043\pi\) |
0.241713 | − | 0.970348i | \(-0.422291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.2804 | − | 11.8223i | 1.12944 | − | 0.528183i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7295 | 0.968872 | 0.484436 | − | 0.874827i | \(-0.339025\pi\) | ||||
0.484436 | + | 0.874827i | \(0.339025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.05949 | −0.225145 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.00191182 | − | 0.0221327i | 8.49067e−5 | − | 0.000982950i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.9432 | + | 20.6862i | 0.529373 | + | 0.916901i | 0.999413 | + | 0.0342559i | \(0.0109061\pi\) |
−0.470040 | + | 0.882645i | \(0.655761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.97186 | − | 19.6068i | −0.352654 | − | 0.867354i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9070 | + | 12.9926i | −0.569859 | + | 0.573636i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.0663 | − | 9.85322i | −0.752030 | − | 0.434185i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.66444 | + | 5.00242i | 0.381062 | + | 0.220006i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.80251 | − | 6.84772i | −0.430283 | − | 0.300582i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.5098 | − | 23.3996i | −0.591874 | − | 1.02516i | −0.993980 | − | 0.109562i | \(-0.965055\pi\) |
0.402106 | − | 0.915593i | \(-0.368278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.2136 | + | 15.7118i | 1.18997 | + | 0.687028i | 0.958299 | − | 0.285766i | \(-0.0922482\pi\) |
0.231669 | + | 0.972795i | \(0.425582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0913232 | + | 0.295217i | 0.00398567 | + | 0.0128843i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.1125 | − | 29.5098i | 2.22649 | − | 1.28547i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.39234 | − | 9.33981i | 0.234450 | − | 0.406079i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.13190 | − | 11.2750i | −0.179309 | − | 0.489294i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.05483 | + | 2.91841i | −0.218949 | + | 0.126410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.47399i | − | 0.0637263i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.5359 | − | 0.910090i | −0.454660 | − | 0.0392733i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.72959 | + | 5.88118i | 0.246791 | + | 0.253320i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0969057 | + | 0.167846i | −0.00416630 | + | 0.00721624i | −0.868101 | − | 0.496388i | \(-0.834660\pi\) |
0.863935 | + | 0.503604i | \(0.167993\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.41904 | + | 7.75735i | −0.232553 | + | 0.332900i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.8438 | + | 30.9064i | −0.764344 | + | 1.32388i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.987053 | + | 1.70963i | 0.0422033 | + | 0.0730983i | 0.886355 | − | 0.463005i | \(-0.153229\pi\) |
−0.844152 | + | 0.536104i | \(0.819896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.0609 | − | 8.45102i | 0.984215 | − | 0.360681i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5988 | 1.04794 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63825 | + | 11.8457i | −0.0696655 | + | 0.503730i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.9631 | − | 24.4241i | −1.48410 | − | 1.03675i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3383 | − | 10.5876i | 0.777018 | − | 0.448612i | −0.0583543 | − | 0.998296i | \(-0.518585\pi\) |
0.835373 | + | 0.549684i | \(0.185252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.52423i | − | 0.275946i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.63704 | + | 12.3639i | −0.364656 | + | 0.522005i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.1289 | −1.43836 | −0.719182 | − | 0.694822i | \(-0.755483\pi\) | ||||
−0.719182 | + | 0.694822i | \(0.755483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4806i | 0.525064i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.7514 | + | 20.1098i | 0.535507 | + | 0.844531i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.0389i | − | 0.462773i | −0.972862 | − | 0.231387i | \(-0.925674\pi\) | ||
0.972862 | − | 0.231387i | \(-0.0743262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.3233 | 1.72933 | 0.864663 | − | 0.502353i | \(-0.167532\pi\) | ||||
0.864663 | + | 0.502353i | \(0.167532\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.96763 | + | 8.54266i | −0.249301 | + | 0.356875i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.391955i | 0.0163456i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5253 | − | 7.23151i | 0.521437 | − | 0.301052i | −0.216085 | − | 0.976374i | \(-0.569329\pi\) |
0.737522 | + | 0.675323i | \(0.235996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.20754 | + | 5.73352i | 0.341094 | + | 0.238277i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.91646 | − | 0.779208i | 0.0795083 | − | 0.0323270i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.0378 | −0.539972 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.5673 | + | 8.27015i | −0.933044 | + | 0.341929i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.248251 | + | 0.429983i | 0.0102464 | + | 0.0177473i | 0.871103 | − | 0.491100i | \(-0.163405\pi\) |
−0.860857 | + | 0.508847i | \(0.830072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0105 | + | 24.2669i | −0.577292 | + | 0.999898i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.88912 | + | 11.2933i | −0.324515 | + | 0.464543i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2302 | + | 21.1834i | −0.502236 | + | 0.869898i | 0.497761 | + | 0.867314i | \(0.334156\pi\) |
−0.999997 | + | 0.00258345i | \(0.999178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.4329 | − | 26.7802i | −1.41161 | − | 1.09788i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.9306 | + | 2.67177i | 1.26590 | + | 0.109348i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8348i | 0.769570i | 0.923006 | + | 0.384785i | \(0.125724\pi\) | ||||
−0.923006 | + | 0.384785i | \(0.874276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.37572 | − | 3.68102i | 0.260071 | − | 0.150152i | −0.364296 | − | 0.931283i | \(-0.618690\pi\) |
0.624367 | + | 0.781131i | \(0.285357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2470 | + | 27.9616i | 0.417289 | + | 1.13868i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6873 | + | 18.5110i | −0.434502 | + | 0.752579i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1081 | + | 14.4961i | −1.01910 | + | 0.588380i | −0.913845 | − | 0.406064i | \(-0.866901\pi\) |
−0.105260 | + | 0.994445i | \(0.533568\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.09184 | − | 31.1873i | 0.287376 | − | 1.26377i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.6466 | + | 15.3844i | 1.07801 | + | 0.622387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4334 | + | 21.5352i | 0.502179 | + | 0.869799i | 0.999997 | + | 0.00251771i | \(0.000801413\pi\) |
−0.497818 | + | 0.867282i | \(0.665865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.10254 | + | 3.56447i | 0.205754 | + | 0.143733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.4629 | − | 21.6292i | −1.50820 | − | 0.870759i | −0.999954 | − | 0.00954684i | \(-0.996961\pi\) |
−0.508245 | − | 0.861213i | \(-0.669706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.45380 | − | 3.72610i | −0.259400 | − | 0.149765i | 0.364661 | − | 0.931140i | \(-0.381185\pi\) |
−0.624061 | + | 0.781376i | \(0.714518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.91327 | + | 29.1473i | 0.317548 | + | 1.16964i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.32796 | + | 5.69933i | 0.293588 | + | 0.228339i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.3291 | + | 21.3547i | 0.493166 | + | 0.854188i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.616227 | − | 7.13395i | 0.0246097 | − | 0.284902i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −82.3050 | −3.28171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.67068 | −0.384984 | −0.192492 | − | 0.981299i | \(-0.561657\pi\) | ||||
−0.192492 | + | 0.981299i | \(0.561657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5580 | − | 5.87272i | 0.499135 | − | 0.233420i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.59975 | − | 14.8952i | −0.341271 | − | 0.591098i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6207 | + | 18.0870i | 0.698159 | + | 0.716631i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3432 | − | 3.79041i | 0.409169 | − | 0.149946i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8113 | − | 15.4795i | −1.05898 | − | 0.611404i | −0.133832 | − | 0.991004i | \(-0.542728\pi\) |
−0.925151 | + | 0.379600i | \(0.876062\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.99262 | − | 4.03719i | −0.275762 | − | 0.159211i | 0.355741 | − | 0.934585i | \(-0.384228\pi\) |
−0.631503 | + | 0.775373i | \(0.717562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.30221 | + | 2.94722i | −0.248149 | + | 0.116047i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.54355 | − | 7.86966i | −0.178625 | − | 0.309388i | 0.762785 | − | 0.646653i | \(-0.223832\pi\) |
−0.941410 | + | 0.337265i | \(0.890498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.06607 | + | 2.34755i | 0.159607 | + | 0.0921492i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.7272 | + | 24.7591i | 1.04752 | + | 0.970387i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.8326 | − | 10.2957i | 0.697844 | − | 0.402900i | −0.108700 | − | 0.994075i | \(-0.534669\pi\) |
0.806544 | + | 0.591174i | \(0.201335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3520 | + | 30.0546i | −0.678000 | + | 1.17433i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.4185 | + | 15.3860i | 0.718575 | + | 0.600265i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7687 | + | 24.1152i | −1.62708 | + | 0.939395i | −0.642121 | + | 0.766604i | \(0.721945\pi\) |
−0.984959 | + | 0.172791i | \(0.944722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5213i | 1.07046i | 0.844708 | + | 0.535228i | \(0.179774\pi\) | ||||
−0.844708 | + | 0.535228i | \(0.820226\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.5623 | + | 38.0239i | −1.03159 | + | 1.47673i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.5149 | + | 2.83720i | 0.795535 | + | 0.110022i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.2836 | − | 35.1323i | 0.785385 | − | 1.36033i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.3754 | − | 2.45105i | −1.09706 | − | 0.0947631i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.80146 | + | 8.31637i | −0.185358 | + | 0.321050i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5734 | − | 30.4380i | −0.677404 | − | 1.17330i | −0.975760 | − | 0.218844i | \(-0.929771\pi\) |
0.298355 | − | 0.954455i | \(-0.403562\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.248584 | − | 0.246947i | −0.00956799 | − | 0.00950500i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.8855 | −1.68666 | −0.843329 | − | 0.537397i | \(-0.819408\pi\) | ||||
−0.843329 | + | 0.537397i | \(0.819408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.01843 | − | 9.88334i | −0.154213 | − | 0.379288i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.0924 | − | 11.7344i | 0.961544 | − | 0.449665i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.9331 | + | 10.3537i | −0.686190 | + | 0.396172i | −0.802183 | − | 0.597078i | \(-0.796328\pi\) |
0.115993 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.38896i | − | 0.0912773i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6802 | + | 2.30462i | 1.01791 | + | 0.0879267i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.0965 | −1.52755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.3226i | − | 0.697023i | −0.937304 | − | 0.348512i | \(-0.886687\pi\) | ||
0.937304 | − | 0.348512i | \(-0.113313\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.86702 | − | 2.83799i | −0.336830 | − | 0.107806i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.9198i | 0.565939i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0116 | 0.454973 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.0020 | + | 29.9413i | 0.529605 | + | 1.13248i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.62840i | − | 0.0992734i | −0.998767 | − | 0.0496367i | \(-0.984194\pi\) | ||
0.998767 | − | 0.0496367i | \(-0.0158064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.8410 | − | 19.5381i | 1.27634 | − | 0.736894i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.82370 | − | 32.6895i | 0.106347 | − | 1.23116i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.75769 | − | 3.70030i | −0.178931 | − | 0.139164i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3327 | −0.613387 | −0.306693 | − | 0.951808i | \(-0.599223\pi\) | ||||
−0.306693 | + | 0.951808i | \(0.599223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.66570 | − | 12.7316i | −0.174977 | − | 0.477473i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.1054 | + | 40.0198i | 0.865305 | + | 1.49875i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.69869 | − | 8.13838i | 0.175721 | − | 0.304358i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.24940 | − | 13.3634i | −0.233388 | − | 0.499067i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.15485 | + | 5.46436i | −0.117656 | + | 0.203786i | −0.918838 | − | 0.394634i | \(-0.870871\pi\) |
0.801182 | + | 0.598420i | \(0.204205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.84204 | − | 21.7470i | −0.329295 | − | 0.809901i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.6097 | − | 35.5175i | −0.617722 | − | 1.32091i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.470643i | 0.0174792i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.3318 | + | 8.27447i | −0.531537 | + | 0.306883i | −0.741642 | − | 0.670796i | \(-0.765953\pi\) |
0.210105 | + | 0.977679i | \(0.432619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4713 | − | 13.3453i | −0.869309 | − | 0.494269i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.71314 | + | 11.6275i | −0.248294 | + | 0.430058i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2433 | − | 9.95544i | 0.636897 | − | 0.367713i | −0.146521 | − | 0.989208i | \(-0.546808\pi\) |
0.783418 | + | 0.621495i | \(0.213474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.51156 | − | 25.1916i | 0.350839 | − | 0.929207i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.0837 | − | 5.82183i | −0.371438 | − | 0.214450i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.1545 | − | 41.8368i | −0.888536 | − | 1.53899i | −0.841606 | − | 0.540092i | \(-0.818389\pi\) |
−0.0469307 | − | 0.998898i | \(-0.514944\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.89514 | − | 21.9397i | 0.0696197 | − | 0.805975i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.17819 | − | 4.14433i | −0.263342 | − | 0.152041i | 0.362516 | − | 0.931978i | \(-0.381918\pi\) |
−0.625858 | + | 0.779937i | \(0.715251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.7815 | − | 19.5037i | −1.23766 | − | 0.714562i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50390 | + | 1.80031i | −0.0550249 | + | 0.0658701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.07802 | − | 1.38607i | 0.0393898 | − | 0.0506458i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5114 | + | 21.6705i | 0.456549 | + | 0.790767i | 0.998776 | − | 0.0494658i | \(-0.0157519\pi\) |
−0.542227 | + | 0.840232i | \(0.682419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.9934 | + | 7.67964i | 0.400622 | + | 0.279862i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.76683 | 0.137089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7744 | −0.682368 | −0.341184 | − | 0.939997i | \(-0.610828\pi\) | ||||
−0.341184 | + | 0.939997i | \(0.610828\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.68065 | − | 6.76259i | −0.351385 | − | 0.245467i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5963 | + | 20.0854i | 0.420367 | + | 0.728097i | 0.995975 | − | 0.0896289i | \(-0.0285681\pi\) |
−0.575609 | + | 0.817725i | \(0.695235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.3830 | + | 16.0126i | −1.42576 | + | 0.579694i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.7291 | + | 8.48168i | 1.76180 | + | 0.306656i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5048 | + | 7.21963i | 0.451521 | + | 0.260686i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.8202 | − | 16.0620i | −1.00322 | − | 0.579210i | −0.0940211 | − | 0.995570i | \(-0.529972\pi\) |
−0.909200 | + | 0.416360i | \(0.863305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.54595 | + | 41.0509i | −0.127704 | + | 1.47841i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.14023 | + | 14.0993i | 0.292784 | + | 0.507116i | 0.974467 | − | 0.224531i | \(-0.0720851\pi\) |
−0.681683 | + | 0.731647i | \(0.738752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.464292 | − | 0.268059i | −0.0166779 | − | 0.00962896i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.0148 | − | 48.5377i | −0.538652 | − | 1.74128i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.93878 | + | 2.85141i | −0.176950 | + | 0.102162i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.15353 | + | 3.73002i | −0.0770593 | + | 0.133471i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.50192 | + | 34.9989i | 0.339571 | + | 1.25076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1608 | + | 8.75308i | −0.541112 | + | 0.312411i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.922766i | 0.0328931i | 0.999865 | + | 0.0164465i | \(0.00523533\pi\) | ||||
−0.999865 | + | 0.0164465i | \(0.994765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.0664 | + | 32.2173i | 0.536377 | + | 1.14697i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.12780 | + | 11.7362i | −0.324547 | + | 0.417290i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7664 | + | 25.5761i | −0.524369 | + | 0.908235i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.1130 | + | 38.7320i | 0.642401 | + | 1.37368i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.98084 | − | 5.16296i | 0.105587 | − | 0.182881i | −0.808391 | − | 0.588646i | \(-0.799661\pi\) |
0.913978 | + | 0.405764i | \(0.132995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.6597 | − | 54.8362i | −1.12004 | − | 1.93997i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.3705 | − | 1.80506i | −0.366422 | − | 0.0637786i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.38348 | −0.331136 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.9683 | − | 26.9601i | 0.739034 | − | 0.950220i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.83994 | + | 21.3007i | −0.0647691 | + | 0.749820i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0267 | − | 10.4077i | 0.633784 | − | 0.365916i | −0.148432 | − | 0.988923i | \(-0.547423\pi\) |
0.782216 | + | 0.623007i | \(0.214089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.7101i | 0.411198i | 0.978636 | + | 0.205599i | \(0.0659142\pi\) | ||||
−0.978636 | + | 0.205599i | \(0.934086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.5112 | + | 45.9987i | 0.754432 | + | 1.61324i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.2914 | 0.885919 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.37444i | − | 0.223013i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.2696 | − | 8.72795i | −0.952877 | − | 0.304979i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 0.558286i | − | 0.0194843i | −0.999953 | − | 0.00974215i | \(-0.996899\pi\) | ||
0.999953 | − | 0.00974215i | \(-0.00310107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.4087 | 1.44341 | 0.721707 | − | 0.692198i | \(-0.243358\pi\) | ||||
0.721707 | + | 0.692198i | \(0.243358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.136492 | + | 0.0117901i | 0.00475204 | + | 0.000410479i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.83309i | 0.307157i | 0.988136 | + | 0.153578i | \(0.0490797\pi\) | ||||
−0.988136 | + | 0.153578i | \(0.950920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.60753 | + | 4.39221i | −0.264220 | + | 0.152548i | −0.626258 | − | 0.779616i | \(-0.715414\pi\) |
0.362038 | + | 0.932163i | \(0.382081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.89464 | + | 1.82132i | −0.135104 | + | 0.0631810i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.7931 | − | 50.3655i | −0.443253 | − | 1.74506i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7855 | 1.23841 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −39.9385 | − | 10.5602i | −1.38048 | − | 0.365015i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.6778 | − | 20.2265i | −0.403161 | − | 0.698295i | 0.590944 | − | 0.806712i | \(-0.298755\pi\) |
−0.994106 | + | 0.108417i | \(0.965422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.85573 | − | 17.0706i | 0.339853 | − | 0.588642i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.0449 | − | 3.45906i | −1.37922 | − | 0.119136i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0142428 | − | 0.0246693i | 0.000489967 | − | 0.000848648i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.5880 | + | 9.59054i | −0.810492 | + | 0.329535i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0789 | − | 38.7634i | 0.929345 | − | 1.33036i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 64.4428i | − | 2.20907i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8754 | − | 8.01099i | 0.475086 | − | 0.274291i | −0.243280 | − | 0.969956i | \(-0.578223\pi\) |
0.718366 | + | 0.695665i | \(0.244890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0492 | + | 8.08027i | −0.754067 | + | 0.276340i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.41205 | + | 14.5701i | −0.287350 | + | 0.497705i | −0.973176 | − | 0.230060i | \(-0.926108\pi\) |
0.685826 | + | 0.727765i | \(0.259441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.2188 | + | 23.7977i | −1.40637 | + | 0.811966i | −0.995036 | − | 0.0995201i | \(-0.968269\pi\) |
−0.411331 | + | 0.911486i | \(0.634936\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.19127 | + | 7.08363i | 0.0746782 | + | 0.241409i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.7300 | + | 25.8249i | 1.52263 | + | 0.879089i | 0.999642 | + | 0.0267477i | \(0.00851508\pi\) |
0.522985 | + | 0.852342i | \(0.324818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.66628 | − | 13.2784i | −0.260661 | − | 0.451478i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 59.7919 | − | 27.9616i | 2.03064 | − | 0.949625i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.59136 | + | 2.65082i | 0.155751 | + | 0.0899230i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.0114 | − | 17.9044i | −1.05078 | − | 0.606668i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.28435 | + | 7.75573i | 0.314228 | + | 0.262492i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.07924 | + | 29.4958i | −0.137904 | + | 0.997138i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.15280 | − | 12.3890i | −0.241533 | − | 0.418347i | 0.719618 | − | 0.694370i | \(-0.244317\pi\) |
−0.961151 | + | 0.276023i | \(0.910983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0421 | − | 6.09912i | 0.439899 | − | 0.205718i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4054 | 0.350566 | 0.175283 | − | 0.984518i | \(-0.443916\pi\) | ||||
0.175283 | + | 0.984518i | \(0.443916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.9042 | 1.51115 | 0.755574 | − | 0.655064i | \(-0.227358\pi\) | ||||
0.755574 | + | 0.655064i | \(0.227358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.32511 | − | 15.3406i | 0.0445432 | − | 0.515668i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.474260 | + | 0.821442i | 0.0159241 | + | 0.0275813i | 0.873878 | − | 0.486146i | \(-0.161598\pi\) |
−0.857954 | + | 0.513727i | \(0.828264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.80695 | − | 20.2962i | 0.0941419 | − | 0.680712i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.3881 | − | 1.87891i | 0.348015 | − | 0.0629458i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.0348 | + | 15.0312i | 0.871221 | + | 0.503000i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.7434 | − | 6.78006i | −0.392539 | − | 0.226632i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.7718 | − | 20.7976i | −0.994052 | − | 0.694413i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.7440 | + | 48.0541i | 0.925316 | + | 1.60269i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.4600 | + | 41.2574i | 2.38068 | + | 1.37448i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.08175 | − | 1.83775i | −0.268944 | − | 0.0611566i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.5080 | + | 6.06681i | −0.349299 | + | 0.201668i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5275 | + | 30.3585i | −0.581990 | + | 1.00804i | 0.413253 | + | 0.910616i | \(0.364393\pi\) |
−0.995243 | + | 0.0974205i | \(0.968941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.73303 | + | 1.17194i | 0.223321 | + | 0.0388707i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8316 | + | 24.7288i | −1.41907 | + | 0.819303i | −0.996218 | − | 0.0868934i | \(-0.972306\pi\) |
−0.422857 | + | 0.906196i | \(0.638973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.917186i | − | 0.0303544i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.3763 | + | 2.71026i | 1.03727 | + | 0.0895986i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.2976 | + | 15.5713i | −1.26470 | + | 0.514209i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.34526 | − | 14.4544i | 0.275285 | − | 0.476807i | −0.694922 | − | 0.719085i | \(-0.744561\pi\) |
0.970207 | + | 0.242278i | \(0.0778945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3087 | + | 31.9349i | −0.735096 | + | 1.05229i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.62295 | + | 11.4713i | −0.217997 | + | 0.377582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.373818 | + | 0.647472i | 0.0122911 | + | 0.0212888i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.4290 | + | 17.0655i | 0.670977 | + | 0.560504i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6372 | −0.348995 | −0.174498 | − | 0.984658i | \(-0.555830\pi\) | ||||
−0.174498 | + | 0.984658i | \(0.555830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.2162 | + | 17.6717i | 0.564238 | + | 0.579166i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.7418 | − | 9.59961i | −0.449888 | − | 0.314277i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.7480 | + | 9.66948i | −0.547719 | + | 0.316226i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.7085i | − | 0.872528i | −0.899819 | − | 0.436264i | \(-0.856301\pi\) | ||
0.899819 | − | 0.436264i | \(-0.143699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2985 | − | 34.7833i | 0.792952 | − | 1.13511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.59067 | 0.214850 | 0.107425 | − | 0.994213i | \(-0.465739\pi\) | ||||
0.107425 | + | 0.994213i | \(0.465739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.40482i | 0.306263i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.88768 | + | 30.2843i | 0.126466 | + | 0.985150i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28.7413i | − | 0.933965i | −0.884267 | − | 0.466983i | \(-0.845341\pi\) | ||
0.884267 | − | 0.466983i | \(-0.154659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.8579 | −0.936768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.11179 | + | 13.0435i | −0.295470 | + | 0.422965i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.2616i | − | 0.591550i | −0.955258 | − | 0.295775i | \(-0.904422\pi\) | ||
0.955258 | − | 0.295775i | \(-0.0955778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.5718 | + | 6.68098i | −0.374455 | + | 0.216191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.6241 | − | 8.12024i | −0.375754 | − | 0.262490i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.74718 | − | 2.24645i | 0.0564194 | − | 0.0725417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.2075 | −1.03895 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.341423 | + | 1.96155i | −0.0110022 | + | 0.0632101i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.41889 | + | 11.1178i | 0.206631 | + | 0.357896i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5899 | − | 21.8064i | 0.404865 | − | 0.701247i | −0.589441 | − | 0.807812i | \(-0.700652\pi\) |
0.994306 | + | 0.106565i | \(0.0339851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.9525 | + | 37.1509i | −0.833714 | + | 1.19346i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.7214 | − | 41.0866i | 0.761255 | − | 1.31853i | −0.180949 | − | 0.983492i | \(-0.557917\pi\) |
0.942204 | − | 0.335040i | \(-0.108750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.9117 | + | 14.0298i | −0.349812 | + | 0.449774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.419767 | + | 0.0362593i | 0.0134433 | + | 0.00116123i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.3422i | 1.77055i | 0.465064 | + | 0.885277i | \(0.346031\pi\) | ||||
−0.465064 | + | 0.885277i | \(0.653969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.56429 | − | 2.05784i | 0.113915 | − | 0.0657690i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.9049 | − | 36.9961i | 0.986717 | − | 1.18120i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.6750 | + | 21.9537i | −0.404268 | + | 0.700213i | −0.994236 | − | 0.107214i | \(-0.965807\pi\) |
0.589968 | + | 0.807427i | \(0.299140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2977 | + | 8.83216i | −0.487427 | + | 0.281416i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.5629 | − | 28.6744i | 0.845508 | − | 0.912716i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.10404 | − | 5.25622i | −0.289492 | − | 0.167138i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9683 | − | 22.4618i | −0.411953 | − | 0.713523i | 0.583151 | − | 0.812364i | \(-0.301820\pi\) |
−0.995103 | + | 0.0988413i | \(0.968486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.5196 | − | 25.5114i | −1.15891 | − | 0.809580i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.4753 | + | 19.9043i | 1.09294 | + | 0.631010i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7943 | − | 7.96414i | −0.436869 | − | 0.252227i | 0.265399 | − | 0.964139i | \(-0.414496\pi\) |
−0.702269 | + | 0.711912i | \(0.747830\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.8706 | + | 40.6015i | 1.29309 | + | 1.28457i |
(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 | 504.2.bs.a.257.5 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.20 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.20 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.13 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.13 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.20 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.20 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.20 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.12 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.20 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.12 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.5 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.20 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.20 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.20 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.20 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.5 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.5 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.13 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.13 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.20 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.20 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.12 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.12 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.20 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.20 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.20 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.20 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.20 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.20 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.20 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.20 | 48 | 36.7 | odd | 6 |