Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.4 | ||
Root | \(0.947217 - 0.807294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.m.337.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.67275 | − | 0.449358i | 0.965760 | − | 0.259437i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87447 | + | 3.24667i | 0.838287 | + | 1.45195i | 0.891326 | + | 0.453362i | \(0.149776\pi\) |
−0.0530397 | + | 0.998592i | \(0.516891\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.59615 | − | 1.50332i | 0.865385 | − | 0.501108i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.82552 | + | 3.16190i | −0.550416 | + | 0.953348i | 0.447829 | + | 0.894119i | \(0.352197\pi\) |
−0.998244 | + | 0.0592287i | \(0.981136\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77274 | + | 4.80253i | 0.769020 | + | 1.33198i | 0.938095 | + | 0.346378i | \(0.112588\pi\) |
−0.169076 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.59442 | + | 4.58854i | 1.18627 | + | 1.18476i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.20767 | −1.74812 | −0.874058 | − | 0.485821i | \(-0.838521\pi\) | ||||
−0.874058 | + | 0.485821i | \(0.838521\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.30555 | 0.758346 | 0.379173 | − | 0.925326i | \(-0.376208\pi\) | ||||
0.379173 | + | 0.925326i | \(0.376208\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.447217 | − | 1.67332i | 0.0975907 | − | 0.365148i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.49443 | − | 4.32048i | −0.520124 | − | 0.900881i | −0.999726 | − | 0.0233954i | \(-0.992552\pi\) |
0.479602 | − | 0.877486i | \(-0.340781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52724 | + | 7.84141i | −0.905449 | + | 1.56828i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.66717 | − | 3.68128i | 0.705748 | − | 0.708463i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.245497 | + | 0.425213i | −0.0455876 | + | 0.0789600i | −0.887919 | − | 0.460000i | \(-0.847849\pi\) |
0.842331 | + | 0.538960i | \(0.181183\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.94722 | − | 3.37268i | −0.349730 | − | 0.605751i | 0.636471 | − | 0.771301i | \(-0.280394\pi\) |
−0.986201 | + | 0.165550i | \(0.947060\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.63281 | + | 6.10936i | −0.284236 | + | 1.06350i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.74893 | 0.633685 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.89443 | 1.29784 | 0.648918 | − | 0.760858i | \(-0.275222\pi\) | ||||
0.648918 | + | 0.760858i | \(0.275222\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.79614 | + | 6.78745i | 1.08825 | + | 1.08686i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38215 | − | 4.12600i | −0.372029 | − | 0.644373i | 0.617849 | − | 0.786297i | \(-0.288004\pi\) |
−0.989878 | + | 0.141924i | \(0.954671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.801714 | + | 1.38861i | −0.122260 | + | 0.211761i | −0.920659 | − | 0.390369i | \(-0.872348\pi\) |
0.798398 | + | 0.602130i | \(0.205681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.74720 | + | 5.61092i | 1.45303 | + | 0.836427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.81995 | − | 8.34840i | 0.703062 | − | 1.21774i | −0.264324 | − | 0.964434i | \(-0.585149\pi\) |
0.967386 | − | 0.253305i | \(-0.0815177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.0566 | + | 3.23883i | −1.68826 | + | 0.453526i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.03647 | −1.10389 | −0.551947 | − | 0.833879i | \(-0.686115\pi\) | ||||
−0.551947 | + | 0.833879i | \(0.686115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6875 | −1.84562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.52935 | − | 1.48538i | 0.732380 | − | 0.196743i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.754503 | − | 1.30684i | −0.0982280 | − | 0.170136i | 0.812723 | − | 0.582650i | \(-0.197984\pi\) |
−0.910951 | + | 0.412514i | \(0.864651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04337 | − | 1.80717i | 0.133590 | − | 0.231385i | −0.791468 | − | 0.611211i | \(-0.790683\pi\) |
0.925058 | + | 0.379826i | \(0.124016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.00384004 | − | 3.00000i | −0.000483799 | − | 0.377964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.3948 | + | 18.0043i | −1.28932 | + | 2.23316i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.70172 | + | 2.94747i | 0.207898 | + | 0.360090i | 0.951052 | − | 0.309030i | \(-0.100004\pi\) |
−0.743154 | + | 0.669120i | \(0.766671\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.11398 | − | 6.10616i | −0.736037 | − | 0.735096i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7301 | 1.27343 | 0.636715 | − | 0.771099i | \(-0.280293\pi\) | ||||
0.636715 | + | 0.771099i | \(0.280293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.83567 | 1.15118 | 0.575589 | − | 0.817739i | \(-0.304773\pi\) | ||||
0.575589 | + | 0.817739i | \(0.304773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.04932 | + | 15.1510i | −0.467575 | + | 1.74949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.82552 | + | 3.16190i | 0.208038 | + | 0.360332i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.86391 | − | 3.22839i | 0.209706 | − | 0.363222i | −0.741916 | − | 0.670493i | \(-0.766083\pi\) |
0.951622 | + | 0.307271i | \(0.0994159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.48003 | − | 7.80572i | 0.497781 | − | 0.867303i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.69058 | + | 9.85637i | −0.624622 | + | 1.08188i | 0.363992 | + | 0.931402i | \(0.381414\pi\) |
−0.988614 | + | 0.150475i | \(0.951920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.5105 | − | 23.4009i | −1.46542 | − | 2.53819i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.219580 | + | 0.821588i | −0.0235415 | + | 0.0880835i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.14891 | 0.757783 | 0.378891 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378891 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.54548 | 0.581324 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.77274 | − | 4.76663i | −0.494910 | − | 0.494277i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.19615 | + | 10.7320i | 0.635711 | + | 1.10108i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.45316 | − | 9.44516i | 0.553685 | − | 0.959011i | −0.444320 | − | 0.895868i | \(-0.646555\pi\) |
0.998005 | − | 0.0631422i | \(-0.0201122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0140201 | + | 10.9531i | 0.00140908 | + | 1.10083i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.40171 | − | 11.0881i | 0.636994 | − | 1.10331i | −0.349095 | − | 0.937087i | \(-0.613511\pi\) |
0.986089 | − | 0.166218i | \(-0.0531557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.76717 | − | 8.25698i | −0.469723 | − | 0.813584i | 0.529678 | − | 0.848199i | \(-0.322313\pi\) |
−0.999401 | + | 0.0346149i | \(0.988980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.27101 | − | 1.68461i | 0.611988 | − | 0.164401i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.43223 | −0.815175 | −0.407587 | − | 0.913166i | \(-0.633630\pi\) | ||||
−0.407587 | + | 0.913166i | \(0.633630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5574 | 1.58591 | 0.792954 | − | 0.609281i | \(-0.208542\pi\) | ||||
0.792954 | + | 0.609281i | \(0.208542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.2054 | − | 3.54743i | 1.25340 | − | 0.336707i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0328150 | − | 0.0568372i | −0.00308697 | − | 0.00534679i | 0.864478 | − | 0.502671i | \(-0.167649\pi\) |
−0.867565 | + | 0.497324i | \(0.834316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.35144 | − | 16.1972i | 0.872026 | − | 1.51039i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.4182 | + | 8.29977i | 1.33296 | + | 0.767314i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.60383 | + | 6.24202i | −0.330363 | + | 0.572205i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.16507 | − | 2.01795i | −0.105915 | − | 0.183450i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.83877 | − | 5.83131i | −0.526465 | − | 0.525791i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.2000 | −1.35953 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.20080 | −0.284025 | −0.142012 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142012 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.717080 | + | 2.68305i | −0.0631354 | + | 0.236229i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.67061 | + | 13.2859i | 0.670184 | + | 1.16079i | 0.977852 | + | 0.209299i | \(0.0671182\pi\) |
−0.307668 | + | 0.951494i | \(0.599548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.65278 | − | 2.86269i | 0.143314 | − | 0.248227i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.8259 | + | 5.00566i | 1.62028 | + | 0.430819i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.342977 | + | 0.594054i | −0.0293025 | + | 0.0507535i | −0.880305 | − | 0.474409i | \(-0.842662\pi\) |
0.851002 | + | 0.525162i | \(0.175995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1004 | − | 17.4944i | −0.856702 | − | 1.48385i | −0.875057 | − | 0.484020i | \(-0.839176\pi\) |
0.0183546 | − | 0.999832i | \(-0.494157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31113 | − | 16.1306i | 0.363062 | − | 1.35844i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2468 | −1.69312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.84070 | −0.152862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.22553 | − | 1.22396i | −0.101080 | − | 0.100951i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.31652 | + | 7.47642i | 0.353623 | + | 0.612493i | 0.986881 | − | 0.161448i | \(-0.0516163\pi\) |
−0.633259 | + | 0.773940i | \(0.718283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.43836 | + | 9.41952i | −0.442568 | + | 0.766550i | −0.997879 | − | 0.0650926i | \(-0.979266\pi\) |
0.555311 | + | 0.831642i | \(0.312599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.7122 | + | 10.8355i | −1.51279 | + | 0.875995i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.29998 | − | 12.6439i | 0.586349 | − | 1.01559i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.49613 | + | 9.51958i | 0.438639 | + | 0.759745i | 0.997585 | − | 0.0694592i | \(-0.0221274\pi\) |
−0.558946 | + | 0.829204i | \(0.688794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.4430 | + | 3.61126i | −1.06610 | + | 0.286391i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.98886 | −0.393177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.79233 | −0.375364 | −0.187682 | − | 0.982230i | \(-0.560098\pi\) | ||||
−0.187682 | + | 0.982230i | \(0.560098\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.8957 | + | 6.15060i | −1.78243 | + | 0.478824i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.46719 | + | 2.54124i | 0.113534 | + | 0.196647i | 0.917193 | − | 0.398444i | \(-0.130450\pi\) |
−0.803659 | + | 0.595091i | \(0.797116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.87617 | + | 15.3740i | −0.682782 | + | 1.18261i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.58173 | − | 4.96932i | 0.656261 | − | 0.380013i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.99483 | − | 10.3834i | 0.455779 | − | 0.789432i | −0.542954 | − | 0.839763i | \(-0.682694\pi\) |
0.998733 | + | 0.0503306i | \(0.0160275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.52724 | + | 7.84141i | 0.342227 | + | 0.592755i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84933 | − | 1.84697i | −0.139004 | − | 0.138826i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.9266 | −1.86310 | −0.931552 | − | 0.363608i | \(-0.881545\pi\) | ||||
−0.931552 | + | 0.363608i | \(0.881545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4203 | −1.59216 | −0.796078 | − | 0.605194i | \(-0.793096\pi\) | ||||
−0.796078 | + | 0.605194i | \(0.793096\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.933226 | − | 3.49179i | 0.0689861 | − | 0.258120i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7978 | + | 25.6306i | 1.08796 | + | 1.88440i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1578 | − | 22.7899i | 0.962191 | − | 1.66656i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.35450 | − | 5.01651i | −0.0985252 | − | 0.364897i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.98003 | − | 15.5539i | 0.649772 | − | 1.12544i | −0.333405 | − | 0.942784i | \(-0.608198\pi\) |
0.983177 | − | 0.182655i | \(-0.0584691\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.68943 | − | 8.12233i | −0.337553 | − | 0.584658i | 0.646419 | − | 0.762983i | \(-0.276266\pi\) |
−0.983972 | + | 0.178324i | \(0.942932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.29747 | + | 34.7877i | −0.665806 | + | 2.49120i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.206917 | −0.0147422 | −0.00737110 | − | 0.999973i | \(-0.502346\pi\) | ||||
−0.00737110 | + | 0.999973i | \(0.502346\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.6169 | −0.894386 | −0.447193 | − | 0.894438i | \(-0.647576\pi\) | ||||
−0.447193 | + | 0.894438i | \(0.647576\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.17101 | + | 4.16568i | 0.294201 | + | 0.293824i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.245497 | + | 0.425213i | 0.0172305 | + | 0.0298441i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.93050 | − | 15.4681i | 0.623733 | − | 1.08034i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.9710 | − | 7.46669i | −0.901547 | − | 0.518971i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.03436 | + | 10.4518i | −0.417406 | + | 0.722968i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.96505 | − | 5.13561i | −0.204122 | − | 0.353550i | 0.745730 | − | 0.666248i | \(-0.232101\pi\) |
−0.949853 | + | 0.312698i | \(0.898767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.9487 | − | 4.82166i | 1.22983 | − | 0.330375i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.01114 | −0.409957 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.89443 | −0.264371 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.4526 | − | 4.41974i | 1.11176 | − | 0.298659i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.9850 | − | 34.6150i | −1.34434 | − | 2.32846i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.80500 | + | 3.12634i | −0.120871 | + | 0.209355i | −0.920112 | − | 0.391656i | \(-0.871902\pi\) |
0.799240 | + | 0.601012i | \(0.205236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0347696 | + | 27.1634i | 0.00231797 | + | 1.81090i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.30710 | + | 16.1204i | −0.617734 | + | 1.06995i | 0.372164 | + | 0.928167i | \(0.378616\pi\) |
−0.989898 | + | 0.141780i | \(0.954717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4965 | − | 19.9126i | −0.759712 | − | 1.31586i | −0.942997 | − | 0.332801i | \(-0.892006\pi\) |
0.183285 | − | 0.983060i | \(-0.441327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.47446 | + | 4.46874i | 0.294398 | + | 0.294021i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.07066 | −0.266678 | −0.133339 | − | 0.991071i | \(-0.542570\pi\) | ||||
−0.133339 | + | 0.991071i | \(0.542570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.1393 | 2.35747 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.66714 | − | 6.23783i | 0.108293 | − | 0.405191i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | + | 4.33013i | 0.161712 | + | 0.280093i | 0.935483 | − | 0.353373i | \(-0.114965\pi\) |
−0.773771 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.30843 | + | 12.6586i | −0.470777 | + | 0.815410i | −0.999441 | − | 0.0334208i | \(-0.989360\pi\) |
0.528664 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.98639 | − | 15.0701i | 0.255727 | − | 0.966749i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.87447 | − | 3.24667i | 0.119755 | − | 0.207422i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.16544 | + | 15.8750i | 0.583183 | + | 1.01010i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.08984 | + | 19.0443i | −0.322556 | + | 1.20688i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.74206 | −0.551794 | −0.275897 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275897 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.2145 | 1.14514 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −33.1151 | − | 33.0727i | −2.07375 | − | 2.07109i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.6399 | − | 18.4288i | −0.663699 | − | 1.14956i | −0.979636 | − | 0.200780i | \(-0.935652\pi\) |
0.315938 | − | 0.948780i | \(-0.397681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.94722 | − | 6.83678i | 0.245268 | − | 0.424817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.00188543 | + | 1.47298i | 0.000116705 | + | 0.0911751i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.80515 | − | 11.7869i | 0.419623 | − | 0.726809i | −0.576278 | − | 0.817254i | \(-0.695495\pi\) |
0.995901 | + | 0.0904446i | \(0.0288288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0641 | − | 26.0918i | −0.925380 | − | 1.60280i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9583 | − | 3.21242i | 0.731836 | − | 0.196597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9343 | −1.15445 | −0.577223 | − | 0.816587i | \(-0.695864\pi\) | ||||
−0.577223 | + | 0.816587i | \(0.695864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1669 | −0.860579 | −0.430290 | − | 0.902691i | \(-0.641589\pi\) | ||||
−0.430290 | + | 0.902691i | \(0.641589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.27617 | − | 2.49191i | 0.561420 | − | 0.150817i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.5292 | − | 28.6294i | −0.996746 | − | 1.72642i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.636090 | + | 1.10174i | −0.0382190 | + | 0.0661972i | −0.884502 | − | 0.466536i | \(-0.845502\pi\) |
0.846283 | + | 0.532733i | \(0.178835\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1255 | − | 5.82869i | −0.606198 | − | 0.348955i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.66891 | − | 8.08678i | 0.278524 | − | 0.482417i | −0.692494 | − | 0.721423i | \(-0.743488\pi\) |
0.971018 | + | 0.239006i | \(0.0768216\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.88983 | + | 8.46943i | 0.290670 | + | 0.503455i | 0.973968 | − | 0.226684i | \(-0.0727885\pi\) |
−0.683298 | + | 0.730139i | \(0.739455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.1871 | + | 15.1677i | 0.899607 | + | 0.898456i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.76429 | −0.281227 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.9505 | 2.05591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.87749 | − | 18.2498i | 0.285924 | − | 1.06982i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0672 | + | 20.9010i | 0.704972 | + | 1.22105i | 0.966702 | + | 0.255906i | \(0.0823738\pi\) |
−0.261729 | + | 0.965141i | \(0.584293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.82858 | − | 4.89925i | 0.164686 | − | 0.285245i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.94533 | + | 18.3155i | 0.286957 | + | 1.06277i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8328 | − | 23.9591i | 0.799971 | − | 1.38559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.801714 | + | 1.38861i | 0.0462100 | + | 0.0800382i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.72590 | − | 21.4242i | 0.328945 | − | 1.23079i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.82305 | 0.447947 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0425 | −1.14389 | −0.571944 | − | 0.820293i | \(-0.693810\pi\) | ||||
−0.571944 | + | 0.820293i | \(0.693810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6846 | − | 11.6697i | −0.664714 | − | 0.663863i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.56758 | + | 11.3754i | 0.372414 | + | 0.645039i | 0.989936 | − | 0.141514i | \(-0.0451970\pi\) |
−0.617523 | + | 0.786553i | \(0.711864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.29311 | + | 10.9000i | −0.355708 | + | 0.616104i | −0.987239 | − | 0.159247i | \(-0.949093\pi\) |
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.73280 | − | 5.63586i | 0.548381 | − | 0.317545i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.36679 | − | 9.29555i | 0.301429 | − | 0.522090i | −0.675031 | − | 0.737789i | \(-0.735870\pi\) |
0.976460 | + | 0.215699i | \(0.0692031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.896319 | − | 1.55247i | −0.0501842 | − | 0.0869217i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.1050 | + | 3.78909i | −0.787263 | + | 0.211487i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.8253 | −1.32568 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.2115 | −2.78523 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.6963 | − | 7.44020i | 1.53161 | − | 0.411444i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.81995 | − | 8.34840i | −0.265732 | − | 0.460262i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.61919 | + | 9.73273i | −0.308859 | + | 0.534959i | −0.978113 | − | 0.208074i | \(-0.933280\pi\) |
0.669254 | + | 0.743034i | \(0.266614\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.4952 | − | 11.8679i | 1.12313 | − | 0.650357i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.37963 | + | 11.0498i | −0.348557 | + | 0.603718i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.35453 | − | 2.34611i | −0.0737858 | − | 0.127801i | 0.826772 | − | 0.562537i | \(-0.190175\pi\) |
−0.900558 | + | 0.434737i | \(0.856841\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0804313 | − | 0.0803284i | −0.00436843 | − | 0.00436284i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2188 | 0.769989 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.36424 | − | 31.2959i | 0.450316 | − | 1.68491i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.77314 | − | 8.26733i | −0.256236 | − | 0.443813i | 0.708995 | − | 0.705214i | \(-0.249149\pi\) |
−0.965230 | + | 0.261400i | \(0.915816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.01114 | − | 1.75135i | 0.0541253 | − | 0.0937478i | −0.837693 | − | 0.546141i | \(-0.816096\pi\) |
0.891819 | + | 0.452393i | \(0.149430\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.8476 | + | 7.40446i | 1.48639 | + | 0.395221i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.93836 | + | 10.2855i | −0.316067 | + | 0.547444i | −0.979664 | − | 0.200646i | \(-0.935696\pi\) |
0.663597 | + | 0.748091i | \(0.269029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.1132 | + | 34.8371i | 1.06750 | + | 1.84896i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.22339 | + | 12.0607i | −0.170600 | + | 0.638321i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.9796 | 0.737817 | 0.368909 | − | 0.929466i | \(-0.379732\pi\) | ||||
0.368909 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.07331 | −0.424911 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.85564 | − | 2.85199i | −0.149882 | − | 0.149691i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4366 | + | 31.9332i | 0.965017 | + | 1.67146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.14299 | + | 1.97972i | −0.0596635 | + | 0.103340i | −0.894314 | − | 0.447439i | \(-0.852336\pi\) |
0.834651 | + | 0.550779i | \(0.185669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3871 | − | 7.13059i | −0.644848 | − | 0.371204i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.01824 | + | 6.95979i | −0.208616 | + | 0.361334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0527 | + | 29.5362i | 0.882957 | + | 1.52933i | 0.848038 | + | 0.529936i | \(0.177784\pi\) |
0.0349186 | + | 0.999390i | \(0.488883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.4257 | + | 6.83024i | −1.31298 | + | 0.352712i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.72279 | −0.140231 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.50473 | 0.334126 | 0.167063 | − | 0.985946i | \(-0.446572\pi\) | ||||
0.167063 | + | 0.985946i | \(0.446572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.35412 | + | 1.43831i | −0.274300 | + | 0.0736866i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.2348 | + | 19.4592i | 0.574069 | + | 0.994317i | 0.996142 | + | 0.0877552i | \(0.0279693\pi\) |
−0.422073 | + | 0.906562i | \(0.638697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.84376 | + | 11.8537i | −0.348790 | + | 0.604122i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.00615723 | + | 4.81028i | 0.000312989 | + | 0.244520i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.57316 | − | 4.45684i | 0.130464 | − | 0.225971i | −0.793391 | − | 0.608712i | \(-0.791687\pi\) |
0.923856 | + | 0.382741i | \(0.125020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.9790 | + | 31.1406i | 0.909238 | + | 1.57485i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.8011 | + | 18.7770i | 0.948390 | + | 0.947177i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.9753 | 0.703176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0214 | −1.05503 | −0.527517 | − | 0.849544i | \(-0.676877\pi\) | ||||
−0.527517 | + | 0.849544i | \(0.676877\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.47830 | − | 5.53125i | 0.0740076 | − | 0.276909i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.803852 | + | 1.39231i | 0.0401424 | + | 0.0695288i | 0.885399 | − | 0.464833i | \(-0.153885\pi\) |
−0.845256 | + | 0.534361i | \(0.820552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.7983 | − | 18.7031i | 0.537899 | − | 0.931669i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.7403 | − | 0.0863761i | 1.67657 | − | 0.00429207i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.4115 | + | 24.9614i | −0.714350 | + | 1.23729i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7055 | − | 18.5425i | −0.529354 | − | 0.916869i | −0.999414 | − | 0.0342340i | \(-0.989101\pi\) |
0.470059 | − | 0.882635i | \(-0.344232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.306771 | + | 1.14782i | −0.0151319 | + | 0.0566178i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.50901 | −0.0742534 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.6672 | −2.09445 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.7566 | − | 24.7249i | −1.21234 | − | 1.21078i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3497 | − | 30.0505i | −0.847587 | − | 1.46806i | −0.883355 | − | 0.468704i | \(-0.844721\pi\) |
0.0357681 | − | 0.999360i | \(-0.488612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6234 | − | 20.1323i | 0.566488 | − | 0.981186i | −0.430421 | − | 0.902628i | \(-0.641635\pi\) |
0.996910 | − | 0.0785583i | \(-0.0250317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0370176 | − | 28.9197i | −0.00179986 | − | 1.40612i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.6309 | − | 56.5183i | 1.58283 | − | 2.74154i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.04337 | − | 1.80717i | −0.0504923 | − | 0.0874552i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.8677 | + | 9.09807i | −1.63515 | + | 0.439259i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5201 | −0.506735 | −0.253368 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253368 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8296 | −1.43352 | −0.716758 | − | 0.697322i | \(-0.754375\pi\) | ||||
−0.716758 | + | 0.697322i | \(0.754375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.07902 | + | 0.827134i | −0.147628 | + | 0.0396580i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.24547 | − | 14.2816i | −0.394434 | − | 0.683180i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.28462 | − | 3.95708i | 0.109039 | − | 0.188861i | −0.806342 | − | 0.591449i | \(-0.798556\pi\) |
0.915381 | + | 0.402588i | \(0.131889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.59999 | − | 1.49667i | −0.123809 | − | 0.0712702i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.01455 | + | 8.68545i | −0.238248 | + | 0.412658i | −0.960212 | − | 0.279273i | \(-0.909907\pi\) |
0.721963 | + | 0.691931i | \(0.243240\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4004 | + | 23.2101i | 0.635239 | + | 1.10027i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5800 | + | 10.5665i | 0.500418 | + | 0.499778i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1908 | −0.858476 | −0.429238 | − | 0.903192i | \(-0.641218\pi\) | ||||
−0.429238 | + | 0.903192i | \(0.641218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3946 | 0.819082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.86426 | + | 18.2002i | −0.228543 | + | 0.855122i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.3948 | + | 18.0043i | 0.487316 | + | 0.844056i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.62708 | − | 4.55024i | 0.122890 | − | 0.212851i | −0.798016 | − | 0.602636i | \(-0.794117\pi\) |
0.920906 | + | 0.389784i | \(0.127451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.4318 | + | 26.5335i | −1.23373 | + | 1.23848i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.32763 | + | 7.49568i | −0.201558 | + | 0.349108i | −0.949031 | − | 0.315184i | \(-0.897934\pi\) |
0.747473 | + | 0.664293i | \(0.231267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.509788 | − | 0.882979i | −0.0236919 | − | 0.0410355i | 0.853936 | − | 0.520377i | \(-0.174209\pi\) |
−0.877628 | + | 0.479342i | \(0.840875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.52935 | − | 24.4304i | 0.302791 | − | 1.13293i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7167 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.40344 | 0.157156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4713 | + | 13.4541i | 0.620726 | + | 0.619932i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.92710 | − | 5.06988i | −0.134588 | − | 0.233113i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9650 | + | 25.9202i | −0.686643 | + | 1.18930i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.8639 | + | 12.0814i | −0.955293 | + | 0.553170i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3255 | + | 31.7407i | −0.837313 | + | 1.45027i | 0.0548199 | + | 0.998496i | \(0.482542\pi\) |
−0.892133 | + | 0.451773i | \(0.850792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.8892 | + | 37.9132i | 0.998062 | + | 1.72869i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.34509 | + | 2.24178i | −0.379715 | + | 0.102005i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.8871 | 1.85659 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.1877 | 1.59451 | 0.797253 | − | 0.603646i | \(-0.206286\pi\) | ||||
0.797253 | + | 0.603646i | \(0.206286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.01635 | + | 2.15347i | −0.362512 | + | 0.0973835i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.15489 | + | 15.8567i | 0.413154 | + | 0.715604i | 0.995233 | − | 0.0975285i | \(-0.0310937\pi\) |
−0.582079 | + | 0.813133i | \(0.697760\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.76946 | − | 3.06479i | 0.0796924 | − | 0.138031i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35.5349 | + | 20.5768i | −1.59718 | + | 0.924857i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.36505 | − | 9.29255i | 0.240656 | − | 0.416828i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2791 | + | 21.2679i | 0.549686 | + | 0.952084i | 0.998296 | + | 0.0583561i | \(0.0185859\pi\) |
−0.448610 | + | 0.893728i | \(0.648081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.59615 | + | 3.59155i | 0.160664 | + | 0.160459i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0176 | 0.758779 | 0.379390 | − | 0.925237i | \(-0.376134\pi\) | ||||
0.379390 | + | 0.925237i | \(0.376134\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.9991 | 2.13593 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.93914 | + | 29.7053i | −0.352590 | + | 1.31926i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3817 | + | 17.9817i | 0.460163 | + | 0.797025i | 0.998969 | − | 0.0454049i | \(-0.0144578\pi\) |
−0.538806 | + | 0.842430i | \(0.681124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91784 | − | 8.51794i | 0.217552 | − | 0.376812i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.1220 | − | 12.1687i | 0.535201 | − | 0.537260i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8718 | − | 30.9548i | 0.787525 | − | 1.36403i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.5979 | + | 30.4804i | 0.773953 | + | 1.34053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.36198 | − | 20.0625i | 0.235365 | − | 0.880648i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9915 | 1.31395 | 0.656977 | − | 0.753911i | \(-0.271835\pi\) | ||||
0.656977 | + | 0.753911i | \(0.271835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.57036 | −0.112394 | −0.0561970 | − | 0.998420i | \(-0.517898\pi\) | ||||
−0.0561970 | + | 0.998420i | \(0.517898\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.0965 | + | 11.0823i | 0.484292 | + | 0.483673i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0349 | + | 24.3091i | 0.611370 | + | 1.05892i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.944341 | + | 1.63565i | −0.0410583 | + | 0.0711151i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.92341 | − | 2.25849i | −0.170261 | − | 0.0980101i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2101 | − | 22.8806i | 0.572195 | − | 0.991070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8059 | − | 27.3767i | −0.683350 | − | 1.18360i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −41.6959 | + | 11.2010i | −1.79931 | + | 0.483358i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.65105 | 0.157262 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7962 | 1.06607 | 0.533036 | − | 0.846093i | \(-0.321051\pi\) | ||||
0.533036 | + | 0.846093i | \(0.321051\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.8307 | + | 9.62538i | −1.53764 | + | 0.413065i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.0362 | + | 53.7563i | 1.32945 | + | 2.30267i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.71955 | + | 9.90655i | −0.244550 | + | 0.423574i | −0.962005 | − | 0.273031i | \(-0.911974\pi\) |
0.717455 | + | 0.696605i | \(0.245307\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.00801317 | − | 6.26022i | −0.000341994 | − | 0.267180i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.811502 | + | 1.40556i | −0.0345712 | + | 0.0598790i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.86391 | − | 3.22839i | −0.0792615 | − | 0.137285i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.2704 | + | 36.2240i | 1.53959 | + | 1.53762i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8445 | 0.586609 | 0.293305 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293305 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.89178 | −0.376082 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.7687 | − | 44.0343i | 0.496877 | − | 1.85913i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.5194 | + | 30.3444i | 0.738353 | + | 1.27886i | 0.953237 | + | 0.302225i | \(0.0977293\pi\) |
−0.214884 | + | 0.976640i | \(0.568937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.123021 | − | 0.213079i | 0.00517553 | − | 0.00896429i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.51994 | − | 7.78268i | −0.189820 | − | 0.326842i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.72940 | + | 6.45951i | −0.156344 | + | 0.270797i | −0.933548 | − | 0.358453i | \(-0.883304\pi\) |
0.777203 | + | 0.629250i | \(0.216638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.4174 | + | 37.0961i | 0.896292 | + | 1.55242i | 0.832197 | + | 0.554480i | \(0.187083\pi\) |
0.0640949 | + | 0.997944i | \(0.479584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.03204 | − | 30.0529i | 0.335543 | − | 1.25548i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45.1715 | 1.88378 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.1386 | −0.671860 | −0.335930 | − | 0.941887i | \(-0.609051\pi\) | ||||
−0.335930 | + | 0.941887i | \(0.609051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.4941 | − | 11.4794i | −0.477677 | − | 0.477066i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.69058 | + | 9.85637i | 0.236085 | + | 0.408911i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6708 | − | 25.4105i | 0.607601 | − | 1.05240i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0798329 | + | 62.3688i | 0.00330068 | + | 2.57863i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9094 | − | 39.6802i | 0.945570 | − | 1.63778i | 0.190965 | − | 0.981597i | \(-0.438838\pi\) |
0.754605 | − | 0.656179i | \(-0.227829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.43663 | − | 11.1486i | −0.265217 | − | 0.459369i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.346119 | + | 0.0929797i | −0.0142374 | + | 0.00382467i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.4176 | −0.920579 | −0.460290 | − | 0.887769i | \(-0.652254\pi\) | ||||
−0.460290 | + | 0.887769i | \(0.652254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.0211 | −1.10776 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.1048 | + | 5.66949i | −0.863762 | + | 0.232037i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.622253 | + | 1.07777i | 0.0254246 | + | 0.0440366i | 0.878458 | − | 0.477820i | \(-0.158573\pi\) |
−0.853033 | + | 0.521857i | \(0.825240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9011 | − | 32.7377i | 0.770993 | − | 1.33540i | −0.166027 | − | 0.986121i | \(-0.553094\pi\) |
0.937019 | − | 0.349277i | \(-0.113573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.84893 | + | 5.09384i | 0.360356 | + | 0.207437i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.36775 | − | 7.56516i | 0.177574 | − | 0.307568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.01266 | + | 10.4142i | 0.244047 | + | 0.422701i | 0.961863 | − | 0.273531i | \(-0.0881917\pi\) |
−0.717817 | + | 0.696232i | \(0.754858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.601726 | + | 0.600956i | 0.0243832 | + | 0.0243520i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.4579 | 2.16267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5048 | −1.19169 | −0.595843 | − | 0.803101i | \(-0.703182\pi\) | ||||
−0.595843 | + | 0.803101i | \(0.703182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.98774 | − | 29.8872i | 0.322097 | − | 1.20517i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.26890 | + | 10.8581i | 0.252376 | + | 0.437129i | 0.964180 | − | 0.265250i | \(-0.0854546\pi\) |
−0.711803 | + | 0.702379i | \(0.752121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2153 | + | 26.3537i | −0.611555 | + | 1.05924i | 0.379423 | + | 0.925223i | \(0.376122\pi\) |
−0.990978 | + | 0.134022i | \(0.957211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.0524 | − | 6.66124i | −1.00532 | − | 0.267306i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.57445 | − | 6.19114i | 0.143207 | − | 0.248043i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.85564 | − | 10.1423i | −0.234226 | − | 0.405691i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.39734 | + | 20.1948i | −0.215549 | + | 0.806504i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.9005 | −2.26877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.6901 | 0.823660 | 0.411830 | − | 0.911261i | \(-0.364890\pi\) | ||||
0.411830 | + | 0.911261i | \(0.364890\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.26750 | − | 7.25820i | −0.288857 | − | 0.288488i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.99979 | − | 10.3919i | −0.238094 | − | 0.412391i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.77274 | − | 4.80253i | 0.109860 | − | 0.190283i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.8570 | − | 16.1308i | 1.10201 | − | 0.638126i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.24417 | − | 9.08317i | 0.207132 | − | 0.358764i | −0.743678 | − | 0.668538i | \(-0.766920\pi\) |
0.950810 | + | 0.309775i | \(0.100254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.2056 | − | 34.9971i | −0.796830 | − | 1.38015i | −0.921671 | − | 0.387972i | \(-0.873176\pi\) |
0.124841 | − | 0.992177i | \(-0.460158\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0551 | + | 2.70116i | −0.395920 | + | 0.106358i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.8906 | 0.664038 | 0.332019 | − | 0.943273i | \(-0.392270\pi\) | ||||
0.332019 | + | 0.943273i | \(0.392270\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.50945 | 0.216265 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.51440 | + | 1.75000i | −0.255319 | + | 0.0685878i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0982 | + | 33.0791i | 0.747372 | + | 1.29449i | 0.949079 | + | 0.315040i | \(0.102018\pi\) |
−0.201707 | + | 0.979446i | \(0.564649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.7566 | + | 49.8079i | −1.12361 | + | 1.94615i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.5349 | − | 14.7862i | 0.996212 | − | 0.576865i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.2864 | − | 26.4768i | 0.595472 | − | 1.03139i | −0.398008 | − | 0.917382i | \(-0.630298\pi\) |
0.993480 | − | 0.114006i | \(-0.0363684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0894 | − | 20.9395i | −0.470223 | − | 0.814451i | 0.529197 | − | 0.848499i | \(-0.322493\pi\) |
−0.999420 | + | 0.0340482i | \(0.989160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.9843 | − | 48.9217i | −1.90239 | − | 1.89996i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.3923 | 0.480553 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.44949 | 0.0948448 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.61445 | + | 6.04067i | −0.0624182 | + | 0.233546i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.80939 | + | 6.59806i | 0.147060 | + | 0.254715i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.5485 | + | 23.4667i | −0.522257 | + | 0.904575i | 0.477408 | + | 0.878682i | \(0.341576\pi\) |
−0.999665 | + | 0.0258933i | \(0.991757\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.2643 | + | 45.4219i | 0.472052 | + | 1.74829i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.72453 | + | 11.6472i | −0.258445 | + | 0.447640i | −0.965825 | − | 0.259193i | \(-0.916543\pi\) |
0.707381 | + | 0.706833i | \(0.249877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.45316 | − | 9.44516i | −0.209273 | − | 0.362472i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.32459 | + | 31.1475i | −0.318999 | + | 1.19358i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.4449 | −0.437925 | −0.218963 | − | 0.975733i | \(-0.570267\pi\) | ||||
−0.218963 | + | 0.975733i | \(0.570267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.57160 | −0.0982557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.1787 | − | 28.1426i | −1.07508 | − | 1.07371i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.2830 | − | 38.5954i | −0.848916 | − | 1.47037i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1416 | − | 31.4222i | 0.690139 | − | 1.19536i | −0.281653 | − | 0.959516i | \(-0.590883\pi\) |
0.971792 | − | 0.235840i | \(-0.0757840\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.49270 | + | 5.46442i | 0.360598 | + | 0.207576i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.8656 | − | 65.5851i | 1.43632 | − | 2.48779i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.1697 | + | 29.7388i | 0.650349 | + | 1.12644i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.80917 | + | 1.82918i | −0.257547 | + | 0.0691861i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.80688 | 0.181553 | 0.0907767 | − | 0.995871i | \(-0.471065\pi\) | ||||
0.0907767 | + | 0.995871i | \(0.471065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0955 | 0.984210 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 60.4519 | − | 16.2395i | 2.27675 | − | 0.611615i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.40171 | − | 11.0881i | −0.240761 | − | 0.417010i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.17770 | − | 10.7001i | 0.232008 | − | 0.401850i | −0.726391 | − | 0.687282i | \(-0.758804\pi\) |
0.958399 | + | 0.285432i | \(0.0921370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0143150 | − | 11.1834i | −0.000536853 | − | 0.419412i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.71438 | + | 16.8258i | −0.363807 | + | 0.630131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.9519 | − | 65.7347i | −1.41932 | − | 2.45834i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.12764 | + | 6.11980i | 0.228841 | + | 0.228548i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.4488 | 0.389673 | 0.194837 | − | 0.980836i | \(-0.437582\pi\) | ||||
0.194837 | + | 0.980836i | \(0.437582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.53433 | −0.355077 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.53691 | + | 24.4587i | −0.243110 | + | 0.909628i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.22285 | − | 3.85008i | −0.0825544 | − | 0.142988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.13266 | + | 15.8182i | −0.338711 | + | 0.586665i | −0.984191 | − | 0.177112i | \(-0.943324\pi\) |
0.645479 | + | 0.763778i | \(0.276658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.103681 | − | 26.9998i | −0.00384003 | − | 0.999993i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.77849 | − | 10.0086i | 0.213725 | − | 0.370183i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.3245 | + | 42.1313i | 0.898447 | + | 1.55616i | 0.829480 | + | 0.558537i | \(0.188637\pi\) |
0.0689673 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.67659 | − | 6.27316i | 0.0618418 | − | 0.231389i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4261 | −0.457722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.2935 | −1.92365 | −0.961823 | − | 0.273671i | \(-0.911762\pi\) | ||||
−0.961823 | + | 0.273671i | \(0.911762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.4650 | + | 22.4363i | 0.825273 | + | 0.824217i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.21154 | + | 9.02665i | 0.191193 | + | 0.331156i | 0.945646 | − | 0.325198i | \(-0.105431\pi\) |
−0.754453 | + | 0.656354i | \(0.772098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.1823 | + | 28.0286i | −0.592874 | + | 1.02689i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0437040 | + | 34.1434i | 0.00159905 | + | 1.24924i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.21612 | + | 7.30253i | −0.154054 | + | 0.266829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.10383 | + | 8.84010i | 0.186242 | + | 0.322580i | 0.943994 | − | 0.329962i | \(-0.107036\pi\) |
−0.757753 | + | 0.652542i | \(0.773703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6232 | + | 3.92832i | −0.532901 | + | 0.143156i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.7761 | −1.48399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.13207 | −0.222874 | −0.111437 | − | 0.993772i | \(-0.535545\pi\) | ||||
−0.111437 | + | 0.993772i | \(0.535545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.4683 | − | 8.18486i | 1.10593 | − | 0.297091i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.0967 | − | 27.8803i | −0.583505 | − | 1.01066i | −0.995060 | − | 0.0992757i | \(-0.968347\pi\) |
0.411555 | − | 0.911385i | \(-0.364986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.27869 | − | 14.3391i | 0.299709 | − | 0.519111i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −70.2546 | − | 40.4417i | −2.54006 | − | 1.46217i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.18408 | − | 7.24704i | 0.151078 | − | 0.261676i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.38520 | + | 9.32745i | 0.194195 | + | 0.336356i | 0.946636 | − | 0.322303i | \(-0.104457\pi\) |
−0.752441 | + | 0.658660i | \(0.771124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.0790 | − | 26.0456i | −0.939212 | − | 0.938011i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.6154 | −0.957289 | −0.478644 | − | 0.878009i | \(-0.658872\pi\) | ||||
−0.478644 | + | 0.878009i | \(0.658872\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.2621 | 1.26665 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.53052 | − | 13.2099i | 0.126657 | − | 0.473903i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.87431 | − | 13.6387i | −0.282127 | − | 0.488657i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5881 | + | 33.9275i | −0.700916 | + | 1.21402i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.665049 | + | 2.46307i | 0.0237669 | + | 0.0880230i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.6046 | + | 35.6882i | −0.735410 | + | 1.27377i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00251 | − | 6.93256i | −0.142674 | − | 0.247119i | 0.785829 | − | 0.618444i | \(-0.212237\pi\) |
−0.928503 | + | 0.371325i | \(0.878903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.08676 | − | 22.7744i | 0.216694 | − | 0.810789i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0656299 | −0.00233353 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.5720 | 0.410933 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.9229 | − | 36.8757i | −1.30952 | − | 1.30785i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.9675 | − | 20.7284i | −0.423912 | − | 0.734237i | 0.572406 | − | 0.819970i | \(-0.306010\pi\) |
−0.996318 | + | 0.0857334i | \(0.972677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.7406 | + | 60.1725i | −1.22903 | + | 2.12875i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.5597 | − | 10.7471i | 0.655774 | − | 0.379731i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.9552 | + | 31.0994i | −0.633627 | + | 1.09747i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.35144 | − | 16.1972i | −0.329595 | − | 0.570875i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.6723 | + | 8.50829i | −1.11492 | + | 0.299506i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9965 | 0.949148 | 0.474574 | − | 0.880216i | \(-0.342602\pi\) | ||||
0.474574 | + | 0.880216i | \(0.342602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.6011 | 1.46081 | 0.730406 | − | 0.683013i | \(-0.239331\pi\) | ||||
0.730406 | + | 0.683013i | \(0.239331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6977 | + | 6.36602i | −0.831113 | + | 0.223266i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.98306 | − | 15.5591i | −0.314663 | − | 0.545012i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.65011 | + | 4.59013i | −0.0927156 | + | 0.160588i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.3969 | − | 8.33665i | 0.503069 | − | 0.291306i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.33583 | + | 16.1701i | −0.325823 | + | 0.564341i | −0.981678 | − | 0.190545i | \(-0.938975\pi\) |
0.655856 | + | 0.754886i | \(0.272308\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.4756 | − | 37.1968i | −0.748591 | − | 1.29660i | −0.948498 | − | 0.316783i | \(-0.897397\pi\) |
0.199906 | − | 0.979815i | \(-0.435936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −40.5139 | − | 40.4621i | −1.41051 | − | 1.40871i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.4602 | −0.989657 | −0.494828 | − | 0.868991i | \(-0.664769\pi\) | ||||
−0.494828 | + | 0.868991i | \(0.664769\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.0061 | 1.11162 | 0.555809 | − | 0.831310i | \(-0.312409\pi\) | ||||
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.568941 | + | 2.12876i | −0.0197363 | + | 0.0738460i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.60383 | + | 6.24202i | 0.124865 | + | 0.216273i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.50038 | + | 9.52693i | −0.190348 | + | 0.329693i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.5566 | − | 5.19994i | −0.675974 | − | 0.179736i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.01191 | − | 3.48473i | 0.0694589 | − | 0.120306i | −0.829204 | − | 0.558946i | \(-0.811206\pi\) |
0.898663 | + | 0.438639i | \(0.144539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3795 | + | 24.9060i | 0.495844 | + | 0.858826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.17603 | − | 15.6251i | 0.143830 | − | 0.538158i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −66.5523 | −2.28947 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.33013 | −0.0800642 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.9852 | + | 11.9699i | 0.411332 | + | 0.410806i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.6921 | − | 34.1077i | −0.675036 | − | 1.16920i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1214 | + | 43.5116i | −0.860141 | + | 1.48981i | 0.0116510 | + | 0.999932i | \(0.496291\pi\) |
−0.871792 | + | 0.489876i | \(0.837042\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.2199 | + | 18.5472i | 1.10190 | + | 0.634301i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.37909 | − | 9.31685i | 0.183746 | − | 0.318258i | −0.759407 | − | 0.650616i | \(-0.774511\pi\) |
0.943153 | + | 0.332358i | \(0.107844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6126 | + | 37.4342i | 0.737413 | + | 1.27724i | 0.953656 | + | 0.300898i | \(0.0972863\pi\) |
−0.216243 | + | 0.976340i | \(0.569380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.96945 | + | 2.14087i | −0.271598 | + | 0.0729608i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.1446 | −1.50270 | −0.751349 | − | 0.659905i | \(-0.770597\pi\) | ||||
−0.751349 | + | 0.659905i | \(0.770597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.9484 | 1.52829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 58.4633 | − | 15.7053i | 1.98552 | − | 0.533380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.80522 | + | 11.7870i | 0.230851 | + | 0.399846i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.43685 | + | 16.3451i | −0.319756 | + | 0.553833i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0418807 | − | 32.7190i | −0.00141745 | − | 1.10737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.59999 | + | 13.1636i | −0.256927 | + | 0.445010i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.9631 | − | 18.9886i | −0.370196 | − | 0.641199i | 0.619399 | − | 0.785076i | \(-0.287376\pi\) |
−0.989596 | + | 0.143877i | \(0.954043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.5773 | + | 29.5395i | 0.997619 | + | 0.996343i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.6969 | 1.67433 | 0.837166 | − | 0.546949i | \(-0.184211\pi\) | ||||
0.837166 | + | 0.546949i | \(0.184211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8441 | −0.566848 | −0.283424 | − | 0.958995i | \(-0.591470\pi\) | ||||
−0.283424 | + | 0.958995i | \(0.591470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.52998 | − | 9.46624i | 0.0850443 | − | 0.318204i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.4950 | + | 18.1779i | 0.352387 | + | 0.610352i | 0.986667 | − | 0.162751i | \(-0.0520367\pi\) |
−0.634280 | + | 0.773103i | \(0.718703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.60040 | + | 2.77197i | −0.0536757 | + | 0.0929690i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.5025 | + | 28.4149i | 0.552855 | + | 0.951936i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.9326 | − | 27.5961i | 0.533164 | − | 0.923468i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.7241 | − | 80.9285i | −1.56181 | − | 2.70514i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.3725 | − | 46.2934i | 0.413106 | − | 1.54569i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.91214 | 0.0637735 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.9242 | 1.92974 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.96505 | + | 1.96253i | 0.0653927 | + | 0.0653090i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.1516 | − | 69.5446i | −1.33468 | − | 2.31174i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.55814 | − | 7.89494i | 0.151351 | − | 0.262147i | −0.780374 | − | 0.625314i | \(-0.784971\pi\) |
0.931724 | + | 0.363167i | \(0.118304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0491656 | − | 38.4102i | −0.00163072 | − | 1.27399i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.16079 | − | 15.8670i | 0.303511 | − | 0.525696i | −0.673418 | − | 0.739262i | \(-0.735175\pi\) |
0.976929 | + | 0.213566i | \(0.0685079\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.7766 | − | 35.9860i | −0.687603 | − | 1.19096i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.0860 | − | 3.51535i | 0.432609 | − | 0.116214i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3412 | 0.506612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.7097 | −1.83769 | −0.918847 | − | 0.394613i | \(-0.870879\pi\) | ||||
−0.918847 | + | 0.394613i | \(0.870879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.5261 | + | 9.00628i | −1.10472 | + | 0.296767i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7518 | + | 51.5316i | 0.979292 | + | 1.69618i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.7400 | + | 61.9035i | −1.17512 | + | 2.03538i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.7892 | − | 14.2698i | −0.814185 | − | 0.468681i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4420 | + | 18.0861i | −0.342592 | + | 0.593386i | −0.984913 | − | 0.173049i | \(-0.944638\pi\) |
0.642322 | + | 0.766435i | \(0.277971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.65278 | − | 2.86269i | −0.0541676 | − | 0.0938210i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0975 | + | 16.0769i | 0.527009 | + | 0.526335i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 98.6551 | 3.22637 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.56584 | −0.214497 | −0.107248 | − | 0.994232i | \(-0.534204\pi\) | ||||
−0.107248 | + | 0.994232i | \(0.534204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.62877 | + | 21.0608i | −0.183688 | + | 0.687292i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.21649 | − | 9.03523i | −0.170053 | − | 0.294540i | 0.768385 | − | 0.639988i | \(-0.221060\pi\) |
−0.938438 | + | 0.345447i | \(0.887727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8842 | + | 20.5840i | −0.387002 | + | 0.670307i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.7480 | − | 13.8009i | 0.447222 | − | 0.448942i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5391 | − | 26.9146i | 0.504954 | − | 0.874606i | −0.495029 | − | 0.868876i | \(-0.664843\pi\) |
0.999984 | − | 0.00573005i | \(-0.00182394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.2718 | + | 47.2361i | 0.885279 | + | 1.53335i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.80023 | − | 17.9607i | 0.155658 | − | 0.582415i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.2222 | 0.881814 | 0.440907 | − | 0.897553i | \(-0.354657\pi\) | ||||
0.440907 | + | 0.897553i | \(0.354657\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 67.3310 | 2.17878 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.19693 | − | 2.19412i | −0.0710166 | − | 0.0709258i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.342977 | + | 0.594054i | 0.0110753 | + | 0.0191830i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.91669 | − | 13.7121i | 0.255377 | − | 0.442326i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.8914 | + | 12.6764i | −0.705440 | + | 0.408491i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.5804 | − | 30.4501i | 0.565932 | − | 0.980223i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5710 | + | 37.3620i | 0.693675 | + | 1.20148i | 0.970625 | + | 0.240597i | \(0.0773431\pi\) |
−0.276950 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.8537 | + | 10.7061i | −1.28029 | + | 0.343930i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0357 | −0.578794 | −0.289397 | − | 0.957209i | \(-0.593455\pi\) | ||||
−0.289397 | + | 0.957209i | \(0.593455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.2007 | −0.647606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −83.9910 | + | 22.5629i | −2.68986 | + | 0.722592i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.6015 | − | 23.5586i | −0.435152 | − | 0.753705i | 0.562156 | − | 0.827031i | \(-0.309972\pi\) |
−0.997308 | + | 0.0733259i | \(0.976639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0505 | + | 22.6041i | −0.417096 | + | 0.722431i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.9855 | − | 24.8911i | 1.37242 | − | 0.794712i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.03965 | − | 15.6571i | 0.288320 | − | 0.499385i | −0.685089 | − | 0.728460i | \(-0.740237\pi\) |
0.973409 | + | 0.229074i | \(0.0735699\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.387858 | − | 0.671790i | −0.0123582 | − | 0.0214050i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.8140 | − | 11.7989i | −0.376043 | − | 0.375562i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.99927 | 0.254362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.2203 | 1.59530 | 0.797650 | − | 0.603121i | \(-0.206076\pi\) | ||||
0.797650 | + | 0.603121i | \(0.206076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.02600 | + | 18.8054i | −0.159495 | + | 0.596772i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6499 | − | 40.9628i | −0.749751 | − | 1.29861i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.3757 | − | 23.1673i | 0.423611 | − | 0.733716i | −0.572678 | − | 0.819780i | \(-0.694096\pi\) |
0.996290 | + | 0.0860640i | \(0.0274290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.9503 | − | 29.0616i | 0.915946 | − | 0.919470i |
(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 | 1008.2.r.m.673.4 | 8 | ||
3.2 | odd | 2 | 3024.2.r.l.2017.1 | 8 | |||
4.3 | odd | 2 | 504.2.r.d.169.1 | ✓ | 8 | ||
9.2 | odd | 6 | 9072.2.a.cl.1.4 | 4 | |||
9.4 | even | 3 | inner | 1008.2.r.m.337.4 | 8 | ||
9.5 | odd | 6 | 3024.2.r.l.1009.1 | 8 | |||
9.7 | even | 3 | 9072.2.a.ce.1.1 | 4 | |||
12.11 | even | 2 | 1512.2.r.d.505.1 | 8 | |||
36.7 | odd | 6 | 4536.2.a.x.1.1 | 4 | |||
36.11 | even | 6 | 4536.2.a.ba.1.4 | 4 | |||
36.23 | even | 6 | 1512.2.r.d.1009.1 | 8 | |||
36.31 | odd | 6 | 504.2.r.d.337.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.1 | ✓ | 8 | 4.3 | odd | 2 | ||
504.2.r.d.337.1 | yes | 8 | 36.31 | odd | 6 | ||
1008.2.r.m.337.4 | 8 | 9.4 | even | 3 | inner | ||
1008.2.r.m.673.4 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.d.505.1 | 8 | 12.11 | even | 2 | |||
1512.2.r.d.1009.1 | 8 | 36.23 | even | 6 | |||
3024.2.r.l.1009.1 | 8 | 9.5 | odd | 6 | |||
3024.2.r.l.2017.1 | 8 | 3.2 | odd | 2 | |||
4536.2.a.x.1.1 | 4 | 36.7 | odd | 6 | |||
4536.2.a.ba.1.4 | 4 | 36.11 | even | 6 | |||
9072.2.a.ce.1.1 | 4 | 9.7 | even | 3 | |||
9072.2.a.cl.1.4 | 4 | 9.2 | odd | 6 |