Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
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, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\), 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: | \(8\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.947217 - 0.807294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.337 |
Dual form | 504.2.r.d.169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.0530397 | − | 0.998592i | \(-0.516891\pi\) |
0.891326 | − | 0.453362i | \(-0.149776\pi\) | |||||||
\(6\) | 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 | 0.998244 | + | 0.0592287i | \(0.0188641\pi\) |
−0.447829 | + | 0.894119i | \(0.647803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77274 | − | 4.80253i | 0.769020 | − | 1.33198i | −0.169076 | − | 0.985603i | \(-0.554078\pi\) |
0.938095 | − | 0.346378i | \(-0.112588\pi\) | |||||||
\(14\) | 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 | \(-0.623792\pi\) | ||||
−0.379173 | + | 0.925326i | \(0.623792\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.447217 | + | 1.67332i | 0.0975907 | + | 0.365148i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.49443 | − | 4.32048i | 0.520124 | − | 0.900881i | −0.479602 | − | 0.877486i | \(-0.659219\pi\) |
0.999726 | − | 0.0233954i | \(-0.00744767\pi\) | |||||||
\(24\) | 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 | 0.842331 | − | 0.538960i | \(-0.181183\pi\) |
−0.887919 | + | 0.460000i | \(0.847849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.94722 | − | 3.37268i | 0.349730 | − | 0.605751i | −0.636471 | − | 0.771301i | \(-0.719606\pi\) |
0.986201 | + | 0.165550i | \(0.0529398\pi\) | |||||||
\(32\) | 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 | −0.989878 | − | 0.141924i | \(-0.954671\pi\) |
0.617849 | + | 0.786297i | \(0.288004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.801714 | + | 1.38861i | 0.122260 | + | 0.211761i | 0.920659 | − | 0.390369i | \(-0.127652\pi\) |
−0.798398 | + | 0.602130i | \(0.794319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.74720 | − | 5.61092i | 1.45303 | − | 0.836427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.81995 | − | 8.34840i | −0.703062 | − | 1.21774i | −0.967386 | − | 0.253305i | \(-0.918482\pi\) |
0.264324 | − | 0.964434i | \(-0.414851\pi\) | |||||||
\(48\) | 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 | \(-0.802016\pi\) |
0.910951 | + | 0.412514i | \(0.135349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04337 | + | 1.80717i | 0.133590 | + | 0.231385i | 0.925058 | − | 0.379826i | \(-0.124016\pi\) |
−0.791468 | + | 0.611211i | \(0.790683\pi\) | |||||||
\(62\) | 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 | \(-0.899996\pi\) |
0.743154 | + | 0.669120i | \(0.233329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.11398 | + | 6.10616i | −0.736037 | + | 0.735096i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7301 | −1.27343 | −0.636715 | − | 0.771099i | \(-0.719707\pi\) | ||||
−0.636715 | + | 0.771099i | \(0.719707\pi\) | |||||||
\(72\) | 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 | \(-0.233917\pi\) |
−0.951622 | + | 0.307271i | \(0.900584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.48003 | + | 7.80572i | 0.497781 | + | 0.867303i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.69058 | + | 9.85637i | 0.624622 | + | 1.08188i | 0.988614 | + | 0.150475i | \(0.0480802\pi\) |
−0.363992 | + | 0.931402i | \(0.618586\pi\) | |||||||
\(84\) | 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 | 0.998005 | + | 0.0631422i | \(0.0201122\pi\) |
−0.444320 | + | 0.895868i | \(0.646555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0140201 | + | 10.9531i | −0.00140908 | + | 1.10083i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.40171 | + | 11.0881i | 0.636994 | + | 1.10331i | 0.986089 | + | 0.166218i | \(0.0531557\pi\) |
−0.349095 | + | 0.937087i | \(0.613511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.76717 | − | 8.25698i | 0.469723 | − | 0.813584i | −0.529678 | − | 0.848199i | \(-0.677687\pi\) |
0.999401 | + | 0.0346149i | \(0.0110205\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.27101 | + | 1.68461i | 0.611988 | + | 0.164401i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.43223 | 0.815175 | 0.407587 | − | 0.913166i | \(-0.366370\pi\) | ||||
0.407587 | + | 0.913166i | \(0.366370\pi\) | |||||||
\(108\) | 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 | −0.867565 | − | 0.497324i | \(-0.834316\pi\) |
0.864478 | + | 0.502671i | \(0.167649\pi\) | |||||||
\(114\) | 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 | \(-0.454643\pi\) | ||||
0.142012 | + | 0.989865i | \(0.454643\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.717080 | − | 2.68305i | −0.0631354 | − | 0.236229i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.67061 | + | 13.2859i | −0.670184 | + | 1.16079i | 0.307668 | + | 0.951494i | \(0.400452\pi\) |
−0.977852 | + | 0.209299i | \(0.932882\pi\) | |||||||
\(132\) | 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 | 0.851002 | − | 0.525162i | \(-0.175995\pi\) |
−0.880305 | + | 0.474409i | \(0.842662\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1004 | − | 17.4944i | 0.856702 | − | 1.48385i | −0.0183546 | − | 0.999832i | \(-0.505843\pi\) |
0.875057 | − | 0.484020i | \(-0.160824\pi\) | |||||||
\(140\) | 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 | −0.633259 | − | 0.773940i | \(-0.718283\pi\) |
0.986881 | + | 0.161448i | \(0.0516163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.43836 | + | 9.41952i | 0.442568 | + | 0.766550i | 0.997879 | − | 0.0650926i | \(-0.0207343\pi\) |
−0.555311 | + | 0.831642i | \(0.687401\pi\) | |||||||
\(152\) | 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 | −0.558946 | − | 0.829204i | \(-0.688794\pi\) |
0.997585 | + | 0.0694592i | \(0.0221274\pi\) | |||||||
\(158\) | 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 | \(-0.439902\pi\) | ||||
0.187682 | + | 0.982230i | \(0.439902\pi\) | |||||||
\(164\) | 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 | \(-0.869550\pi\) |
0.803659 | + | 0.595091i | \(0.202884\pi\) | |||||||
\(168\) | 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 | 0.998733 | − | 0.0503306i | \(-0.0160275\pi\) |
−0.542954 | + | 0.839763i | \(0.682694\pi\) | |||||||
\(174\) | 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 | \(-0.118455\pi\) | ||||
0.931552 | + | 0.363608i | \(0.118455\pi\) | |||||||
\(180\) | 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 | −0.983177 | − | 0.182655i | \(-0.941531\pi\) |
0.333405 | − | 0.942784i | \(-0.391802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.68943 | + | 8.12233i | −0.337553 | + | 0.584658i | −0.983972 | − | 0.178324i | \(-0.942932\pi\) |
0.646419 | + | 0.762983i | \(0.276266\pi\) | |||||||
\(194\) | 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 | \(-0.352424\pi\) | ||||
0.447193 | + | 0.894438i | \(0.352424\pi\) | |||||||
\(200\) | 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 | \(-0.767899\pi\) |
0.949853 | + | 0.312698i | \(0.101233\pi\) | |||||||
\(212\) | 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 | \(-0.128098\pi\) |
−0.799240 | + | 0.601012i | \(0.794764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0347696 | − | 27.1634i | 0.00231797 | − | 1.81090i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.30710 | + | 16.1204i | 0.617734 | + | 1.06995i | 0.989898 | + | 0.141780i | \(0.0452826\pi\) |
−0.372164 | + | 0.928167i | \(0.621384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4965 | + | 19.9126i | −0.759712 | + | 1.31586i | 0.183285 | + | 0.983060i | \(0.441327\pi\) |
−0.942997 | + | 0.332801i | \(0.892006\pi\) | |||||||
\(230\) | 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 | \(-0.885035\pi\) |
0.773771 | + | 0.633465i | \(0.218368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.30843 | − | 12.6586i | −0.470777 | − | 0.815410i | 0.528664 | − | 0.848831i | \(-0.322693\pi\) |
−0.999441 | + | 0.0334208i | \(0.989360\pi\) | |||||||
\(242\) | 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 | \(-0.411025\pi\) | ||||
0.275897 | + | 0.961187i | \(0.411025\pi\) | |||||||
\(252\) | 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 | 0.315938 | + | 0.948780i | \(0.397681\pi\) |
−0.979636 | + | 0.200780i | \(0.935652\pi\) | |||||||
\(258\) | 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 | \(-0.304505\pi\) |
−0.995901 | + | 0.0904446i | \(0.971171\pi\) | |||||||
\(264\) | 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 | \(-0.358411\pi\) | ||||
0.430290 | + | 0.902691i | \(0.358411\pi\) | |||||||
\(272\) | 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 | 0.846283 | − | 0.532733i | \(-0.178835\pi\) |
−0.884502 | + | 0.466536i | \(0.845502\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.1255 | − | 5.82869i | 0.606198 | − | 0.348955i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.66891 | + | 8.08678i | 0.278524 | + | 0.482417i | 0.971018 | − | 0.239006i | \(-0.0768216\pi\) |
−0.692494 | + | 0.721423i | \(0.743488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.88983 | + | 8.46943i | −0.290670 | + | 0.503455i | −0.973968 | − | 0.226684i | \(-0.927212\pi\) |
0.683298 | + | 0.730139i | \(0.260545\pi\) | |||||||
\(284\) | 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 | −0.261729 | − | 0.965141i | \(-0.584293\pi\) |
0.966702 | − | 0.255906i | \(-0.0823738\pi\) | |||||||
\(294\) | 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 | \(-0.306190\pi\) | ||||
0.571944 | + | 0.820293i | \(0.306190\pi\) | |||||||
\(308\) | 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 | \(-0.954803\pi\) |
0.617523 | + | 0.786553i | \(0.288136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.29311 | − | 10.9000i | −0.355708 | − | 0.616104i | 0.631531 | − | 0.775351i | \(-0.282427\pi\) |
−0.987239 | + | 0.159247i | \(0.949093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.73280 | − | 5.63586i | −0.548381 | − | 0.317545i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.36679 | + | 9.29555i | 0.301429 | + | 0.522090i | 0.976460 | − | 0.215699i | \(-0.0692031\pi\) |
−0.675031 | + | 0.737789i | \(0.735870\pi\) | |||||||
\(318\) | 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 | \(-0.0667196\pi\) |
−0.669254 | + | 0.743034i | \(0.733386\pi\) | |||||||
\(332\) | 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 | −0.900558 | − | 0.434737i | \(-0.856841\pi\) |
0.826772 | + | 0.562537i | \(0.190175\pi\) | |||||||
\(338\) | 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 | \(-0.750851\pi\) |
0.965230 | + | 0.261400i | \(0.0841843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.01114 | + | 1.75135i | 0.0541253 | + | 0.0937478i | 0.891819 | − | 0.452393i | \(-0.149430\pi\) |
−0.837693 | + | 0.546141i | \(0.816096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.8476 | + | 7.40446i | −1.48639 | + | 0.395221i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.93836 | − | 10.2855i | −0.316067 | − | 0.547444i | 0.663597 | − | 0.748091i | \(-0.269029\pi\) |
−0.979664 | + | 0.200646i | \(0.935696\pi\) | |||||||
\(354\) | 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 | \(-0.620268\pi\) | ||||
−0.368909 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(360\) | 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 | \(-0.147664\pi\) |
−0.834651 | + | 0.550779i | \(0.814331\pi\) | |||||||
\(368\) | 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 | 0.0349186 | − | 0.999390i | \(-0.488883\pi\) |
0.848038 | − | 0.529936i | \(-0.177784\pi\) | |||||||
\(374\) | 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 | \(-0.553428\pi\) | ||||
−0.167063 | + | 0.985946i | \(0.553428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.35412 | − | 1.43831i | −0.274300 | − | 0.0736866i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2348 | + | 19.4592i | −0.574069 | + | 0.994317i | 0.422073 | + | 0.906562i | \(0.361303\pi\) |
−0.996142 | + | 0.0877552i | \(0.972031\pi\) | |||||||
\(384\) | 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 | 0.923856 | − | 0.382741i | \(-0.125020\pi\) |
−0.793391 | + | 0.608712i | \(0.791687\pi\) | |||||||
\(390\) | 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 | −0.845256 | − | 0.534361i | \(-0.820552\pi\) |
0.885399 | + | 0.464833i | \(0.153885\pi\) | |||||||
\(402\) | 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 | 0.470059 | + | 0.882635i | \(0.344232\pi\) |
−0.999414 | + | 0.0342340i | \(0.989101\pi\) | |||||||
\(410\) | 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 | −0.0357681 | − | 0.999360i | \(-0.511388\pi\) |
0.883355 | − | 0.468704i | \(-0.155279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6234 | + | 20.1323i | 0.566488 | + | 0.981186i | 0.996910 | + | 0.0785583i | \(0.0250317\pi\) |
−0.430421 | + | 0.902628i | \(0.641635\pi\) | |||||||
\(422\) | 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 | \(-0.418462\pi\) | ||||
0.253368 | + | 0.967370i | \(0.418462\pi\) | |||||||
\(432\) | 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 | \(-0.201444\pi\) |
−0.915381 | + | 0.402588i | \(0.868111\pi\) | |||||||
\(440\) | 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 | \(-0.0900934\pi\) |
−0.721963 | + | 0.691931i | \(0.756760\pi\) | |||||||
\(444\) | 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 | 0.920906 | − | 0.389784i | \(-0.127451\pi\) |
−0.798016 | + | 0.602636i | \(0.794117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.4318 | + | 26.5335i | 1.23373 | + | 1.23848i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.32763 | − | 7.49568i | −0.201558 | − | 0.349108i | 0.747473 | − | 0.664293i | \(-0.231267\pi\) |
−0.949031 | + | 0.315184i | \(0.897934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.509788 | − | 0.882979i | 0.0236919 | − | 0.0410355i | −0.853936 | − | 0.520377i | \(-0.825791\pi\) |
0.877628 | + | 0.479342i | \(0.159125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.52935 | + | 24.4304i | 0.302791 | + | 1.13293i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7167 | 0.866104 | 0.433052 | − | 0.901369i | \(-0.357437\pi\) | ||||
0.433052 | + | 0.901369i | \(0.357437\pi\) | |||||||
\(468\) | 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 | 0.892133 | + | 0.451773i | \(0.149208\pi\) |
−0.0548199 | + | 0.998496i | \(0.517458\pi\) | |||||||
\(480\) | 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 | \(-0.793714\pi\) | ||||
−0.797253 | + | 0.603646i | \(0.793714\pi\) | |||||||
\(488\) | 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 | \(-0.968906\pi\) |
0.582079 | + | 0.813133i | \(0.302240\pi\) | |||||||
\(492\) | 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 | 0.448610 | + | 0.893728i | \(0.351919\pi\) |
−0.998296 | + | 0.0583561i | \(0.981414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.59615 | − | 3.59155i | 0.160664 | − | 0.160459i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0176 | −0.758779 | −0.379390 | − | 0.925237i | \(-0.623866\pi\) | ||||
−0.379390 | + | 0.925237i | \(0.623866\pi\) | |||||||
\(504\) | 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 | −0.538806 | − | 0.842430i | \(-0.681124\pi\) |
0.998969 | + | 0.0454049i | \(0.0144578\pi\) | |||||||
\(510\) | 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 | \(-0.482102\pi\) | ||||
0.0561970 | + | 0.998420i | \(0.482102\pi\) | |||||||
\(524\) | 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 | \(-0.0880263\pi\) |
−0.717455 | + | 0.696605i | \(0.754693\pi\) | |||||||
\(548\) | 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 | 0.214884 | + | 0.976640i | \(0.431063\pi\) |
−0.953237 | + | 0.302225i | \(0.902271\pi\) | |||||||
\(564\) | 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 | 0.777203 | − | 0.629250i | \(-0.216638\pi\) |
−0.933548 | + | 0.358453i | \(0.883304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4174 | + | 37.0961i | −0.896292 | + | 1.55242i | −0.0640949 | + | 0.997944i | \(0.520416\pi\) |
−0.832197 | + | 0.554480i | \(0.812917\pi\) | |||||||
\(572\) | 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 | −0.754605 | − | 0.656179i | \(-0.772171\pi\) |
−0.190965 | − | 0.981597i | \(-0.561162\pi\) | |||||||
\(588\) | 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 | \(-0.841427\pi\) |
0.853033 | + | 0.521857i | \(0.174760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9011 | + | 32.7377i | 0.770993 | + | 1.33540i | 0.937019 | + | 0.349277i | \(0.113573\pi\) |
−0.166027 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(602\) | 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 | \(-0.911808\pi\) |
0.717817 | + | 0.696232i | \(0.245142\pi\) | |||||||
\(608\) | 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 | −0.711803 | − | 0.702379i | \(-0.752121\pi\) |
0.964180 | + | 0.265250i | \(0.0854546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2153 | + | 26.3537i | 0.611555 | + | 1.05924i | 0.990978 | + | 0.134022i | \(0.0427891\pi\) |
−0.379423 | + | 0.925223i | \(0.623878\pi\) | |||||||
\(620\) | 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 | \(-0.635110\pi\) | ||||
−0.411830 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(632\) | 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 | 0.950810 | − | 0.309775i | \(-0.100254\pi\) |
−0.743678 | + | 0.668538i | \(0.766920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.2056 | − | 34.9971i | 0.796830 | − | 1.38015i | −0.124841 | − | 0.992177i | \(-0.539842\pi\) |
0.921671 | − | 0.387972i | \(-0.126824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0551 | − | 2.70116i | −0.395920 | − | 0.106358i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.8906 | −0.664038 | −0.332019 | − | 0.943273i | \(-0.607730\pi\) | ||||
−0.332019 | + | 0.943273i | \(0.607730\pi\) | |||||||
\(648\) | 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 | −0.201707 | − | 0.979446i | \(-0.564649\pi\) |
0.949079 | − | 0.315040i | \(-0.102018\pi\) | |||||||
\(654\) | 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 | −0.993480 | − | 0.114006i | \(-0.963632\pi\) |
0.398008 | − | 0.917382i | \(-0.369702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0894 | + | 20.9395i | −0.470223 | + | 0.814451i | −0.999420 | − | 0.0340482i | \(-0.989160\pi\) |
0.529197 | + | 0.848499i | \(0.322493\pi\) | |||||||
\(662\) | 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 | −0.999665 | − | 0.0258933i | \(-0.991757\pi\) |
0.477408 | − | 0.878682i | \(-0.341576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.2643 | + | 45.4219i | −0.472052 | + | 1.74829i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.72453 | − | 11.6472i | −0.258445 | − | 0.447640i | 0.707381 | − | 0.706833i | \(-0.249877\pi\) |
−0.965825 | + | 0.259193i | \(0.916543\pi\) | |||||||
\(678\) | 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 | \(-0.429733\pi\) | ||||
0.218963 | + | 0.975733i | \(0.429733\pi\) | |||||||
\(684\) | 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 | −0.971792 | − | 0.235840i | \(-0.924216\pi\) |
0.281653 | − | 0.959516i | \(-0.409117\pi\) | |||||||
\(692\) | 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 | 0.958399 | − | 0.285432i | \(-0.0921370\pi\) |
−0.726391 | + | 0.687282i | \(0.758804\pi\) | |||||||
\(710\) | 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 | \(-0.562418\pi\) | ||||
−0.194837 | + | 0.980836i | \(0.562418\pi\) | |||||||
\(720\) | 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 | \(-0.0566756\pi\) |
−0.645479 | + | 0.763778i | \(0.723342\pi\) | |||||||
\(728\) | 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 | 0.0689673 | − | 0.997619i | \(-0.478030\pi\) |
0.829480 | − | 0.558537i | \(-0.188637\pi\) | |||||||
\(734\) | 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 | \(-0.0882379\pi\) | ||||
0.961823 | + | 0.273671i | \(0.0882379\pi\) | |||||||
\(740\) | 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 | \(-0.894569\pi\) |
0.754453 | + | 0.656354i | \(0.227902\pi\) | |||||||
\(744\) | 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 | \(-0.892964\pi\) |
0.757753 | + | 0.652542i | \(0.226297\pi\) | |||||||
\(752\) | 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 | 0.411555 | + | 0.911385i | \(0.364986\pi\) |
−0.995060 | + | 0.0992757i | \(0.968347\pi\) | |||||||
\(762\) | 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 | −0.752441 | − | 0.658660i | \(-0.771124\pi\) |
0.946636 | + | 0.322303i | \(0.104457\pi\) | |||||||
\(770\) | 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 | \(-0.787763\pi\) |
0.928503 | + | 0.371325i | \(0.121097\pi\) | |||||||
\(788\) | 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 | −0.996318 | − | 0.0857334i | \(-0.972677\pi\) |
0.572406 | + | 0.819970i | \(0.306010\pi\) | |||||||
\(798\) | 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 | \(-0.760669\pi\) | ||||
−0.730406 | + | 0.683013i | \(0.760669\pi\) | |||||||
\(812\) | 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 | 0.655856 | − | 0.754886i | \(-0.272308\pi\) |
−0.981678 | + | 0.190545i | \(0.938975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4756 | − | 37.1968i | 0.748591 | − | 1.29660i | −0.199906 | − | 0.979815i | \(-0.564064\pi\) |
0.948498 | − | 0.316783i | \(-0.102603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −40.5139 | + | 40.4621i | −1.41051 | + | 1.40871i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.4602 | 0.989657 | 0.494828 | − | 0.868991i | \(-0.335231\pi\) | ||||
0.494828 | + | 0.868991i | \(0.335231\pi\) | |||||||
\(828\) | 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 | \(-0.188794\pi\) |
−0.898663 | + | 0.438639i | \(0.855461\pi\) | |||||||
\(840\) | 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 | −0.871792 | − | 0.489876i | \(-0.837042\pi\) |
0.0116510 | − | 0.999932i | \(-0.496291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.2199 | + | 18.5472i | −1.10190 | + | 0.634301i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.37909 | + | 9.31685i | 0.183746 | + | 0.318258i | 0.943153 | − | 0.332358i | \(-0.107844\pi\) |
−0.759407 | + | 0.650616i | \(0.774511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6126 | + | 37.4342i | −0.737413 | + | 1.27724i | 0.216243 | + | 0.976340i | \(0.430620\pi\) |
−0.953656 | + | 0.300898i | \(0.902714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.96945 | − | 2.14087i | −0.271598 | − | 0.0729608i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1446 | 1.50270 | 0.751349 | − | 0.659905i | \(-0.229403\pi\) | ||||
0.751349 | + | 0.659905i | \(0.229403\pi\) | |||||||
\(864\) | 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 | −0.989596 | − | 0.143877i | \(-0.954043\pi\) |
0.619399 | + | 0.785076i | \(0.287376\pi\) | |||||||
\(878\) | 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 | \(-0.408530\pi\) | ||||
0.283424 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(884\) | 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 | \(-0.947963\pi\) |
0.634280 | + | 0.773103i | \(0.281297\pi\) | |||||||
\(888\) | 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 | \(-0.215029\pi\) |
−0.931724 | + | 0.363167i | \(0.881696\pi\) | |||||||
\(908\) | 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 | \(-0.264825\pi\) |
−0.976929 | + | 0.213566i | \(0.931492\pi\) | |||||||
\(912\) | 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 | \(-0.129121\pi\) | ||||
0.918847 | + | 0.394613i | \(0.129121\pi\) | |||||||
\(920\) | 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 | 0.642322 | − | 0.766435i | \(-0.277971\pi\) |
−0.984913 | + | 0.173049i | \(0.944638\pi\) | |||||||
\(930\) | 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 | −0.938438 | − | 0.345447i | \(-0.887727\pi\) |
0.768385 | + | 0.639988i | \(0.221060\pi\) | |||||||
\(942\) | 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 | −0.999984 | − | 0.00573005i | \(-0.998176\pi\) |
0.495029 | − | 0.868876i | \(-0.335157\pi\) | |||||||
\(948\) | 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 | 0.276950 | + | 0.960884i | \(0.410676\pi\) |
−0.970625 | + | 0.240597i | \(0.922657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.8537 | − | 10.7061i | −1.28029 | − | 0.343930i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0357 | 0.578794 | 0.289397 | − | 0.957209i | \(-0.406545\pi\) | ||||
0.289397 | + | 0.957209i | \(0.406545\pi\) | |||||||
\(972\) | 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 | −0.997308 | − | 0.0733259i | \(-0.976639\pi\) |
0.562156 | + | 0.827031i | \(0.309972\pi\) | |||||||
\(978\) | 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 | \(-0.259763\pi\) |
−0.973409 | + | 0.229074i | \(0.926430\pi\) | |||||||
\(984\) | 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 | \(-0.793924\pi\) | ||||
−0.797650 | + | 0.603121i | \(0.793924\pi\) | |||||||
\(992\) | 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 | 0.996290 | − | 0.0860640i | \(-0.0274290\pi\) |
−0.572678 | + | 0.819780i | \(0.694096\pi\) | |||||||
\(998\) | 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 | 504.2.r.d.337.1 | yes | 8 | |
3.2 | odd | 2 | 1512.2.r.d.1009.1 | 8 | |||
4.3 | odd | 2 | 1008.2.r.m.337.4 | 8 | |||
9.2 | odd | 6 | 1512.2.r.d.505.1 | 8 | |||
9.4 | even | 3 | 4536.2.a.x.1.1 | 4 | |||
9.5 | odd | 6 | 4536.2.a.ba.1.4 | 4 | |||
9.7 | even | 3 | inner | 504.2.r.d.169.1 | ✓ | 8 | |
12.11 | even | 2 | 3024.2.r.l.1009.1 | 8 | |||
36.7 | odd | 6 | 1008.2.r.m.673.4 | 8 | |||
36.11 | even | 6 | 3024.2.r.l.2017.1 | 8 | |||
36.23 | even | 6 | 9072.2.a.cl.1.4 | 4 | |||
36.31 | odd | 6 | 9072.2.a.ce.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
504.2.r.d.337.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1008.2.r.m.337.4 | 8 | 4.3 | odd | 2 | |||
1008.2.r.m.673.4 | 8 | 36.7 | odd | 6 | |||
1512.2.r.d.505.1 | 8 | 9.2 | odd | 6 | |||
1512.2.r.d.1009.1 | 8 | 3.2 | odd | 2 | |||
3024.2.r.l.1009.1 | 8 | 12.11 | even | 2 | |||
3024.2.r.l.2017.1 | 8 | 36.11 | even | 6 | |||
4536.2.a.x.1.1 | 4 | 9.4 | even | 3 | |||
4536.2.a.ba.1.4 | 4 | 9.5 | odd | 6 | |||
9072.2.a.ce.1.1 | 4 | 36.31 | odd | 6 | |||
9072.2.a.cl.1.4 | 4 | 36.23 | even | 6 |