Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.69760 | + | 0.343722i | −0.980111 | + | 0.198448i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0262870 | − | 0.0455305i | −0.0117559 | − | 0.0203618i | 0.860088 | − | 0.510146i | \(-0.170409\pi\) |
−0.871844 | + | 0.489785i | \(0.837075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10354 | + | 1.60471i | −0.795065 | + | 0.606525i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.76371 | − | 1.16701i | 0.921237 | − | 0.389003i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.15187 | + | 1.24238i | 0.648812 | + | 0.374592i | 0.788001 | − | 0.615674i | \(-0.211116\pi\) |
−0.139189 | + | 0.990266i | \(0.544449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.51752 | − | 1.45349i | −0.698235 | − | 0.403126i | 0.108455 | − | 0.994101i | \(-0.465410\pi\) |
−0.806690 | + | 0.590975i | \(0.798743\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0602747 | + | 0.0682572i | 0.0155629 | + | 0.0176239i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.88651 | − | 4.99959i | −0.700082 | − | 1.21258i | −0.968437 | − | 0.249258i | \(-0.919813\pi\) |
0.268355 | − | 0.963320i | \(-0.413520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.92807 | − | 1.69052i | −0.671745 | − | 0.387832i | 0.124993 | − | 0.992158i | \(-0.460109\pi\) |
−0.796737 | + | 0.604326i | \(0.793443\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.01941 | − | 3.44720i | 0.658888 | − | 0.752241i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.47404 | + | 4.31514i | −1.55845 | + | 0.899769i | −0.561039 | + | 0.827789i | \(0.689598\pi\) |
−0.997406 | + | 0.0719794i | \(0.977068\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49862 | − | 4.32773i | 0.499724 | − | 0.865547i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.29056 | + | 2.93106i | −0.825718 | + | 0.564083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.23728 | + | 3.60109i | −1.15823 | + | 0.668706i | −0.950880 | − | 0.309560i | \(-0.899818\pi\) |
−0.207353 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.92107i | − | 1.78188i | −0.454125 | − | 0.890938i | \(-0.650048\pi\) | ||
0.454125 | − | 0.890938i | \(-0.349952\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.08005 | − | 1.36942i | −0.710245 | − | 0.238386i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.128359 | + | 0.0535922i | 0.0216967 | + | 0.00905873i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.770828 | + | 1.33511i | −0.126723 | + | 0.219491i | −0.922405 | − | 0.386223i | \(-0.873779\pi\) |
0.795682 | + | 0.605715i | \(0.207113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.77335 | + | 1.60212i | 0.764348 | + | 0.256545i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.392450 | + | 0.679743i | −0.0612904 | + | 0.106158i | −0.895042 | − | 0.445981i | \(-0.852855\pi\) |
0.833752 | + | 0.552139i | \(0.186188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.03075 | − | 3.51736i | −0.309686 | − | 0.536392i | 0.668608 | − | 0.743615i | \(-0.266891\pi\) |
−0.978294 | + | 0.207223i | \(0.933557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.125784 | − | 0.0951558i | −0.0187508 | − | 0.0141850i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.31552 | 0.191888 | 0.0959441 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959441 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.84979 | − | 6.75117i | 0.264256 | − | 0.964453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.61862 | + | 7.49515i | 0.926792 | + | 1.04953i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.710864 | + | 0.410417i | −0.0976447 | + | 0.0563752i | −0.548027 | − | 0.836461i | \(-0.684621\pi\) |
0.450382 | + | 0.892836i | \(0.351288\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.130634i | − | 0.0176147i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.55176 | + | 1.86339i | 0.735349 | + | 0.246812i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.64150 | −0.604271 | −0.302136 | − | 0.953265i | \(-0.597700\pi\) | ||||
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.62413i | 0.720097i | 0.932934 | + | 0.360048i | \(0.117240\pi\) | ||||
−0.932934 | + | 0.360048i | \(0.882760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.94087 | + | 6.88981i | −0.496503 | + | 0.868035i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.152832i | 0.0189565i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9012 | −1.69830 | −0.849149 | − | 0.528153i | \(-0.822885\pi\) | ||||
−0.849149 | + | 0.528153i | \(0.822885\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.2047 | − | 9.89439i | 1.34889 | − | 1.19114i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.51362i | − | 0.416990i | −0.978023 | − | 0.208495i | \(-0.933143\pi\) | ||
0.978023 | − | 0.208495i | \(-0.0668565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.75829 | − | 3.90190i | 0.790998 | − | 0.456683i | −0.0493159 | − | 0.998783i | \(-0.515704\pi\) |
0.840314 | + | 0.542100i | \(0.182371\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.75412 | + | 8.20560i | −0.318019 | + | 0.947501i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.52021 | + | 0.839727i | −0.743047 | + | 0.0956958i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0014 | 1.68779 | 0.843895 | − | 0.536508i | \(-0.180257\pi\) | ||||
0.843895 | + | 0.536508i | \(0.180257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.27619 | − | 6.45054i | 0.697354 | − | 0.716727i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.14086 | + | 5.44013i | 0.344754 | + | 0.597132i | 0.985309 | − | 0.170781i | \(-0.0546290\pi\) |
−0.640555 | + | 0.767912i | \(0.721296\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.151756 | + | 0.262848i | −0.0164602 | + | 0.0285099i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.35064 | − | 8.25712i | 1.00249 | − | 0.885256i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.93120 | + | 13.7372i | −0.840706 | + | 1.45615i | 0.0485931 | + | 0.998819i | \(0.484526\pi\) |
−0.889299 | + | 0.457326i | \(0.848807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.62815 | − | 0.982418i | 0.799648 | − | 0.102985i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.41009 | + | 16.8420i | 0.353610 | + | 1.74644i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.177755i | 0.0182373i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.57451 | + | 0.909044i | −0.159867 | + | 0.0922995i | −0.577799 | − | 0.816179i | \(-0.696088\pi\) |
0.417932 | + | 0.908478i | \(0.362755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.39700 | + | 0.922336i | 0.743427 | + | 0.0926982i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.667947 | − | 1.15692i | 0.0664632 | − | 0.115118i | −0.830879 | − | 0.556453i | \(-0.812162\pi\) |
0.897342 | + | 0.441336i | \(0.145495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.62845 | + | 3.82694i | −0.653120 | + | 0.377079i | −0.789651 | − | 0.613557i | \(-0.789738\pi\) |
0.136530 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.236324 | − | 0.0468583i | −0.0230628 | − | 0.00457290i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.9289 | + | 6.30978i | 1.05653 | + | 0.609989i | 0.924471 | − | 0.381252i | \(-0.124507\pi\) |
0.132062 | + | 0.991242i | \(0.457840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.12613 | + | 8.87871i | 0.490994 | + | 0.850426i | 0.999946 | − | 0.0103684i | \(-0.00330042\pi\) |
−0.508952 | + | 0.860795i | \(0.669967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.849651 | − | 2.53144i | 0.0806453 | − | 0.240274i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4379 | + | 7.75836i | 1.26413 | + | 0.729845i | 0.973871 | − | 0.227104i | \(-0.0729257\pi\) |
0.290258 | + | 0.956949i | \(0.406259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.392940 | + | 0.226864i | 0.0366419 | + | 0.0211552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.65394 | − | 1.07906i | −0.800057 | − | 0.0997594i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.0948 | + | 5.88482i | 1.29207 | + | 0.539461i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.41298 | − | 4.17940i | −0.219362 | − | 0.379946i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.432581 | − | 1.28883i | 0.0390046 | − | 0.116210i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.525595 | −0.0470107 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.05269 | −0.625825 | −0.312912 | − | 0.949782i | \(-0.601305\pi\) | ||||
−0.312912 | + | 0.949782i | \(0.601305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.65640 | + | 5.27306i | 0.409973 | + | 0.464267i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.84958 | − | 3.20357i | −0.161599 | − | 0.279898i | 0.773843 | − | 0.633377i | \(-0.218332\pi\) |
−0.935442 | + | 0.353479i | \(0.884998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.87212 | − | 1.14263i | 0.769310 | − | 0.0990782i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.246239 | + | 0.118302i | 0.0211928 | + | 0.0101818i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.54459 | − | 2.04647i | −0.302835 | − | 0.174842i | 0.340881 | − | 0.940107i | \(-0.389275\pi\) |
−0.643716 | + | 0.765265i | \(0.722608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1602 | − | 7.02072i | −1.03142 | − | 0.595489i | −0.114027 | − | 0.993478i | \(-0.536375\pi\) |
−0.917391 | + | 0.397988i | \(0.869708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.23323 | + | 0.452173i | −0.188072 | + | 0.0380799i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.61158 | − | 6.25544i | −0.302016 | − | 0.523106i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.327919 | + | 0.189324i | 0.0272322 | + | 0.0157225i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.819682 | + | 12.0966i | −0.0676062 | + | 0.997712i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.55913 | + | 3.78692i | −0.537345 | + | 0.310236i | −0.744002 | − | 0.668177i | \(-0.767075\pi\) |
0.206657 | + | 0.978413i | \(0.433742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.34413 | − | 10.9883i | 0.516278 | − | 0.894219i | −0.483544 | − | 0.875320i | \(-0.660651\pi\) |
0.999821 | − | 0.0188990i | \(-0.00601609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.8120 | − | 10.4488i | −1.11664 | − | 0.844738i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.451711 | + | 0.260795i | −0.0362823 | + | 0.0209476i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.09592i | − | 0.0874639i | −0.999043 | − | 0.0437319i | \(-0.986075\pi\) | ||
0.999043 | − | 0.0437319i | \(-0.0139247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.06569 | − | 0.941066i | 0.0845151 | − | 0.0746314i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.79741 | − | 21.0708i | 0.693333 | − | 1.66061i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.43585 | − | 7.68311i | 0.347442 | − | 0.601788i | −0.638352 | − | 0.769745i | \(-0.720384\pi\) |
0.985794 | + | 0.167957i | \(0.0537169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0449018 | + | 0.221765i | 0.00349560 | + | 0.0172643i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.68302 | − | 8.11124i | 0.362383 | − | 0.627666i | −0.625969 | − | 0.779848i | \(-0.715296\pi\) |
0.988353 | + | 0.152181i | \(0.0486298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.27472 | − | 3.93994i | −0.174979 | − | 0.303072i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.0652 | − | 1.25503i | −0.769703 | − | 0.0959746i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.9351 | −1.74372 | −0.871861 | − | 0.489753i | \(-0.837087\pi\) | ||||
−0.871861 | + | 0.489753i | \(0.837087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.68882 | + | 13.1131i | 0.127663 | + | 0.991260i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.87942 | − | 1.59539i | 0.592253 | − | 0.119916i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5254 | + | 6.07685i | −0.786706 | + | 0.454205i | −0.838802 | − | 0.544437i | \(-0.816743\pi\) |
0.0520958 | + | 0.998642i | \(0.483410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.1883i | 1.79790i | 0.438048 | + | 0.898952i | \(0.355670\pi\) | ||||
−0.438048 | + | 0.898952i | \(0.644330\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.93314 | − | 9.54755i | −0.142902 | − | 0.705775i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0810510 | 0.00595899 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.3446i | − | 1.04898i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.32185 | − | 13.0507i | 0.314368 | − | 0.949301i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5335i | 0.906889i | 0.891284 | + | 0.453445i | \(0.149805\pi\) | ||||
−0.891284 | + | 0.453445i | \(0.850195\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.97733 | −0.214313 | −0.107157 | − | 0.994242i | \(-0.534175\pi\) | ||||
−0.107157 | + | 0.994242i | \(0.534175\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0525317 | − | 0.259448i | −0.00376187 | − | 0.0185794i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.95974i | 0.638355i | 0.947695 | + | 0.319178i | \(0.103407\pi\) | ||||
−0.947695 | + | 0.319178i | \(0.896593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.95927 | + | 3.44059i | −0.422442 | + | 0.243897i | −0.696121 | − | 0.717924i | \(-0.745092\pi\) |
0.273680 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.5987 | − | 4.77814i | 1.66452 | − | 0.337024i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.34166 | − | 17.5841i | 0.515284 | − | 1.23416i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0412654 | 0.00288210 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.6203 | + | 20.6481i | −1.08568 | + | 1.43514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.20054 | − | 7.27555i | −0.290557 | − | 0.503260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.51329 | − | 9.54930i | 0.379550 | − | 0.657401i | −0.611446 | − | 0.791286i | \(-0.709412\pi\) |
0.990997 | + | 0.133885i | \(0.0427453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.20771 | + | 5.96473i | 0.0827509 | + | 0.408697i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.106765 | + | 0.184922i | −0.00728128 | + | 0.0126116i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.9205 | + | 20.8694i | 1.08075 | + | 1.41671i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.1317 | + | 8.94685i | −0.684638 | + | 0.604572i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.7821i | 1.12889i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.55863 | + | 3.20928i | −0.372234 | + | 0.214909i | −0.674434 | − | 0.738335i | \(-0.735612\pi\) |
0.302200 | + | 0.953244i | \(0.402279\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.85496 | − | 14.8765i | 0.123664 | − | 0.991767i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1083 | − | 20.9722i | 0.803658 | − | 1.39198i | −0.113535 | − | 0.993534i | \(-0.536218\pi\) |
0.917193 | − | 0.398443i | \(-0.130449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.51981 | + | 5.49626i | −0.629087 | + | 0.363203i | −0.780398 | − | 0.625283i | \(-0.784984\pi\) |
0.151312 | + | 0.988486i | \(0.451650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7801 | − | 3.66666i | 0.709278 | − | 0.241249i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3691 | − | 10.6054i | −1.20340 | − | 0.694783i | −0.242090 | − | 0.970254i | \(-0.577833\pi\) |
−0.961309 | + | 0.275471i | \(0.911166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0345811 | − | 0.0598962i | −0.00225582 | − | 0.00390720i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.4664 | + | 5.15632i | −1.65422 | + | 0.334939i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.14539 | − | 0.661293i | −0.0740893 | − | 0.0427755i | 0.462498 | − | 0.886620i | \(-0.346953\pi\) |
−0.536587 | + | 0.843845i | \(0.680287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.20494 | + | 1.85037i | 0.206448 | + | 0.119193i | 0.599660 | − | 0.800255i | \(-0.295303\pi\) |
−0.393212 | + | 0.919448i | \(0.628636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.43728 | + | 13.1077i | −0.541252 | + | 0.840861i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.356009 | + | 0.0932463i | −0.0227446 | + | 0.00595729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.91431 | + | 8.51184i | 0.312690 | + | 0.541595i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.20182 | − | 8.15559i | −0.456397 | − | 0.516840i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.6932 | 1.68486 | 0.842429 | − | 0.538807i | \(-0.181125\pi\) | ||||
0.842429 | + | 0.538807i | \(0.181125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.4442 | −1.34818 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.167274 | − | 0.498374i | 0.0104751 | − | 0.0312094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.888958 | + | 1.53972i | 0.0554517 | + | 0.0960451i | 0.892419 | − | 0.451208i | \(-0.149007\pi\) |
−0.836967 | + | 0.547253i | \(0.815673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.521004 | − | 4.04542i | −0.0323736 | − | 0.251370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0355 | + | 17.2313i | −0.806879 | + | 1.06659i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4352 | − | 9.48887i | −1.01344 | − | 0.585109i | −0.101241 | − | 0.994862i | \(-0.532281\pi\) |
−0.912196 | + | 0.409753i | \(0.865615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0373730 | + | 0.0215773i | 0.00229580 | + | 0.00132548i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.74223 | − | 26.0465i | 0.535016 | − | 1.59402i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.17800 | + | 12.4327i | 0.437651 | + | 0.758033i | 0.997508 | − | 0.0705560i | \(-0.0224773\pi\) |
−0.559857 | + | 0.828589i | \(0.689144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0202 | − | 6.36254i | −0.669432 | − | 0.386497i | 0.126429 | − | 0.991976i | \(-0.459648\pi\) |
−0.795861 | + | 0.605479i | \(0.792982\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.6119 | + | 4.28972i | −0.763307 | + | 0.259626i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.7534 | − | 6.20847i | 0.648454 | − | 0.374385i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4763 | − | 21.6095i | 0.749625 | − | 1.29839i | −0.198377 | − | 0.980126i | \(-0.563567\pi\) |
0.948002 | − | 0.318264i | \(-0.103100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.5780 | − | 27.4189i | −0.693154 | − | 1.64153i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.13275 | − | 5.27279i | 0.544814 | − | 0.314549i | −0.202214 | − | 0.979341i | \(-0.564814\pi\) |
0.747028 | + | 0.664793i | \(0.231480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 15.3438i | − | 0.912094i | −0.889956 | − | 0.456047i | \(-0.849265\pi\) | ||
0.889956 | − | 0.456047i | \(-0.150735\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0610983 | − | 0.301757i | −0.00361915 | − | 0.0178746i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.265258 | − | 2.05964i | −0.0156577 | − | 0.121577i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.16392 | + | 14.1403i | −0.480230 | + | 0.831783i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.36043 | − | 2.08439i | 0.138371 | − | 0.122189i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.55166 | − | 2.68756i | 0.0906490 | − | 0.157009i | −0.817135 | − | 0.576446i | \(-0.804439\pi\) |
0.907784 | + | 0.419437i | \(0.137773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.122011 | + | 0.211329i | 0.00710376 | + | 0.0123041i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8742 | + | 0.976755i | −0.747037 | + | 0.0566771i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.0881 | 1.45088 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.91612 | + | 4.14015i | 0.571555 | + | 0.238634i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.736250 | + | 2.19358i | −0.0422965 | + | 0.126018i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.256069 | − | 0.147842i | 0.0146625 | − | 0.00846539i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1272i | 1.26286i | 0.775431 | + | 0.631432i | \(0.217533\pi\) | ||||
−0.775431 | + | 0.631432i | \(0.782467\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.93707 | − | 8.77496i | 0.565300 | − | 0.499190i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.33250 | −0.472493 | −0.236246 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236246 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6015i | 1.33403i | 0.745043 | + | 0.667017i | \(0.232429\pi\) | ||||
−0.745043 | + | 0.667017i | \(0.767571\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.417290 | − | 0.00168300i | 0.0235116 | − | 9.48263e-5i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.0871i | − | 0.959708i | −0.877348 | − | 0.479854i | \(-0.840690\pi\) | ||
0.877348 | − | 0.479854i | \(-0.159310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.8957 | −1.00197 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.7217 | − | 6.95501i | −1.15657 | − | 0.388191i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5188i | 1.08606i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.5806 | + | 7.26344i | −0.697849 | + | 0.402903i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.7539 | − | 13.3106i | −0.649994 | − | 0.736076i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.76725 | + | 2.11103i | −0.152564 | + | 0.116385i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3681 | 1.06457 | 0.532283 | − | 0.846567i | \(-0.321334\pi\) | ||||
0.532283 | + | 0.846567i | \(0.321334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.572258 | + | 4.58943i | −0.0313595 | + | 0.251499i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.365420 | + | 0.632927i | 0.0199651 | + | 0.0345805i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.58170 | − | 7.93573i | 0.249581 | − | 0.432287i | −0.713829 | − | 0.700320i | \(-0.753040\pi\) |
0.963410 | + | 0.268033i | \(0.0863738\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.4789 | − | 8.55171i | −1.38382 | − | 0.464465i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3257 | − | 21.3488i | 0.667476 | − | 1.15610i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.94258 | + | 17.1698i | 0.374864 | + | 0.927080i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.745035 | − | 0.250063i | −0.0401113 | − | 0.0134629i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.8514i | − | 0.689900i | −0.938621 | − | 0.344950i | \(-0.887896\pi\) | ||
0.938621 | − | 0.344950i | \(-0.112104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3111 | + | 9.99458i | −0.926643 | + | 0.534998i | −0.885748 | − | 0.464166i | \(-0.846354\pi\) |
−0.0408947 | + | 0.999163i | \(0.513021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.0618 | − | 1.14273i | 0.803942 | − | 0.0609944i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.52912 | + | 6.11262i | −0.187836 | + | 0.325342i | −0.944529 | − | 0.328429i | \(-0.893481\pi\) |
0.756692 | + | 0.653771i | \(0.226814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.159977 | + | 0.0923626i | −0.00849068 | + | 0.00490210i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.9501 | − | 5.14539i | −1.37343 | − | 0.272323i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.3683 | − | 14.0690i | −1.28611 | − | 0.742536i | −0.308151 | − | 0.951337i | \(-0.599710\pi\) |
−0.977958 | + | 0.208802i | \(0.933044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.78428 | − | 6.55457i | −0.199173 | − | 0.344978i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.53283 | + | 6.26557i | 0.290398 | + | 0.328857i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.355310 | − | 0.205139i | −0.0185978 | − | 0.0107374i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.2547 | + | 18.0449i | 1.63148 | + | 0.941936i | 0.983637 | + | 0.180163i | \(0.0576624\pi\) |
0.647844 | + | 0.761773i | \(0.275671\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.291352 | + | 2.33661i | −0.0151672 | + | 0.121639i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.836731 | − | 2.00406i | 0.0434409 | − | 0.104046i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.59811 | + | 6.23211i | 0.186303 | + | 0.322686i | 0.944015 | − | 0.329903i | \(-0.107016\pi\) |
−0.757712 | + | 0.652589i | \(0.773683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.892252 | − | 0.180659i | 0.0460757 | − | 0.00932917i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.9366 | 1.07829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.1915 | −1.44810 | −0.724051 | − | 0.689746i | \(-0.757722\pi\) | ||||
−0.724051 | + | 0.689746i | \(0.757722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.9727 | − | 2.42416i | 0.613378 | − | 0.124194i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.20827 | + | 3.82483i | 0.112837 | + | 0.195440i | 0.916913 | − | 0.399087i | \(-0.130673\pi\) |
−0.804076 | + | 0.594527i | \(0.797340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.209630 | + | 0.274794i | 0.0106837 | + | 0.0140048i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.71718 | − | 7.35106i | −0.493952 | − | 0.373675i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6573 | + | 6.15300i | 0.540347 | + | 0.311970i | 0.745220 | − | 0.666819i | \(-0.232345\pi\) |
−0.204873 | + | 0.978789i | \(0.565678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.1478 | + | 24.9114i | 2.18208 | + | 1.25982i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.24100 | + | 4.80265i | 0.213930 | + | 0.242262i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.394342 | − | 0.683021i | −0.0198415 | − | 0.0343665i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.201000 | − | 0.116048i | −0.0100879 | − | 0.00582426i | 0.494948 | − | 0.868923i | \(-0.335187\pi\) |
−0.505035 | + | 0.863099i | \(0.668521\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6686 | + | 4.98927i | −0.734348 | + | 0.249776i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.2036 | − | 17.4381i | 1.50830 | − | 0.870816i | 0.508344 | − | 0.861154i | \(-0.330258\pi\) |
0.999953 | − | 0.00966170i | \(-0.00307546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.4202 | + | 24.9765i | −0.718321 | + | 1.24417i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.458678 | − | 0.116192i | −0.0227919 | − | 0.00577363i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.31744 | + | 1.91532i | −0.164439 | + | 0.0949390i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.67860i | 0.330235i | 0.986274 | + | 0.165118i | \(0.0528004\pi\) | ||||
−0.986274 | + | 0.165118i | \(0.947200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.72073 | + | 2.25574i | 0.331509 | + | 0.111267i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.76359 | − | 7.44827i | 0.480435 | − | 0.366505i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.165128 | − | 0.286009i | 0.00810580 | − | 0.0140397i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.0564 | + | 7.73864i | 1.12908 | + | 0.378963i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.8635 | − | 25.7443i | 0.726128 | − | 1.25769i | −0.232380 | − | 0.972625i | \(-0.574651\pi\) |
0.958508 | − | 0.285066i | \(-0.0920154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2147 | − | 26.3526i | −0.741518 | − | 1.28435i | −0.951804 | − | 0.306707i | \(-0.900773\pi\) |
0.210286 | − | 0.977640i | \(-0.432560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.63571 | − | 1.53522i | 0.176774 | − | 0.0746450i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.8492 | −1.39939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.02512 | − | 11.8306i | −0.436756 | − | 0.572523i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.28116 | + | 9.37787i | 0.399818 | + | 0.452768i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.8782 | + | 12.6314i | −1.05384 | + | 0.608432i | −0.923721 | − | 0.383066i | \(-0.874868\pi\) |
−0.130115 | + | 0.991499i | \(0.541535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.7303i | − | 0.996234i | −0.867110 | − | 0.498117i | \(-0.834025\pi\) | ||
0.867110 | − | 0.498117i | \(-0.165975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.621751 | − | 0.208684i | −0.0298107 | − | 0.0100056i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.1793 | 1.39584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 36.0015i | − | 1.71826i | −0.511761 | − | 0.859128i | \(-0.671007\pi\) | ||
0.511761 | − | 0.859128i | \(-0.328993\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.76638 | − | 20.8170i | −0.131732 | − | 0.991285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.35336i | − | 0.111811i | −0.998436 | − | 0.0559057i | \(-0.982195\pi\) | ||
0.998436 | − | 0.0559057i | \(-0.0178046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.833951 | 0.0395331 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.83315 | − | 8.68320i | 0.465092 | − | 0.410701i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3789i | 1.48086i | 0.672132 | + | 0.740431i | \(0.265379\pi\) | ||||
−0.672132 | + | 0.740431i | \(0.734621\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.68900 | + | 0.975145i | −0.0795319 | + | 0.0459178i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.99287 | + | 20.8345i | −0.328554 | + | 0.978889i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.245251 | − | 0.321488i | −0.0114976 | − | 0.0150716i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9821 | 0.841168 | 0.420584 | − | 0.907254i | \(-0.361825\pi\) | ||||
0.420584 | + | 0.907254i | \(0.361825\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.0389 | + | 12.9905i | 1.26207 | + | 0.606342i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.53192 | − | 4.38541i | −0.117923 | − | 0.204249i | 0.801021 | − | 0.598636i | \(-0.204290\pi\) |
−0.918945 | + | 0.394387i | \(0.870957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8461 | + | 22.2501i | −0.597008 | + | 1.03405i | 0.396252 | + | 0.918142i | \(0.370311\pi\) |
−0.993260 | + | 0.115906i | \(0.963023\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.677184 | − | 0.597990i | 0.0314037 | − | 0.0277311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.1382 | + | 33.1484i | −0.885612 | + | 1.53392i | −0.0406007 | + | 0.999175i | \(0.512927\pi\) |
−0.845011 | + | 0.534749i | \(0.820406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.2417 | − | 22.3074i | 1.35026 | − | 1.03006i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.376692 | + | 1.86044i | 0.0173570 | + | 0.0857243i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.0918i | − | 0.464024i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.6322 | + | 8.44793i | −0.671373 | + | 0.387617i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.48566 | + | 1.96386i | −0.0680238 | + | 0.0899189i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.90031 | + | 8.48758i | −0.223901 | + | 0.387808i | −0.955989 | − | 0.293402i | \(-0.905213\pi\) |
0.732088 | + | 0.681210i | \(0.238546\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.88115 | − | 2.24078i | 0.176965 | − | 0.102171i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.69201 | + | 38.7937i | −0.349998 | + | 1.76517i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0827784 | + | 0.0477921i | 0.00375877 | + | 0.00217013i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3631 | + | 30.0737i | 0.786796 | + | 1.36277i | 0.927920 | + | 0.372778i | \(0.121595\pi\) |
−0.141125 | + | 0.989992i | \(0.545072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.88945 | + | 14.5676i | −0.221109 | + | 0.658768i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3641 | + | 13.4893i | 1.05441 | + | 0.608763i | 0.923880 | − | 0.382682i | \(-0.124999\pi\) |
0.130528 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0080 | + | 20.7892i | 1.62172 | + | 0.936299i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.152451 | − | 0.361034i | −0.00685216 | − | 0.0162273i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.63835 | + | 7.39105i | 0.252915 | + | 0.331534i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.47273 | − | 4.28289i | −0.110694 | − | 0.191728i | 0.805356 | − | 0.592791i | \(-0.201974\pi\) |
−0.916050 | + | 0.401063i | \(0.868641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.16190 | + | 15.3793i | −0.230617 | + | 0.687097i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0173 | 0.669587 | 0.334794 | − | 0.942291i | \(-0.391333\pi\) | ||||
0.334794 | + | 0.942291i | \(0.391333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0702334 | −0.00312534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.21582 | + | 5.90657i | 0.231643 | + | 0.262320i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4297 | + | 21.5289i | 0.550938 | + | 0.954252i | 0.998207 | + | 0.0598530i | \(0.0190632\pi\) |
−0.447269 | + | 0.894399i | \(0.647603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.95492 | + | 19.0529i | −0.351905 | + | 0.842852i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5181 | − | 1.32908i | 0.773441 | − | 0.0586803i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.348484 | + | 0.201197i | 0.0153561 | + | 0.00886582i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.83082 | + | 1.63438i | 0.124499 | + | 0.0718798i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.9347 | − | 7.88330i | 1.70904 | − | 0.346038i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.60577 | − | 14.9056i | −0.377025 | − | 0.653027i | 0.613603 | − | 0.789615i | \(-0.289720\pi\) |
−0.990628 | + | 0.136588i | \(0.956386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.4139 | + | 13.5180i | 1.02382 | + | 0.591101i | 0.915207 | − | 0.402984i | \(-0.132027\pi\) |
0.108609 | + | 0.994085i | \(0.465360\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.37422 | − | 21.6804i | −0.321837 | − | 0.946211i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −49.6012 | + | 28.6373i | −2.16066 | + | 1.24746i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.7409 | − | 44.5845i | 1.11917 | − | 1.93846i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8277 | + | 5.41666i | −0.556677 | + | 0.235063i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.97600 | − | 1.14085i | 0.0855902 | − | 0.0494155i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.663461i | − | 0.0286839i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.7792 | − | 13.9339i | 0.680923 | − | 0.601292i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.3680 | − | 12.2295i | 0.532729 | − | 0.526761i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.4779 | − | 33.7367i | 0.837419 | − | 1.45045i | −0.0546263 | − | 0.998507i | \(-0.517397\pi\) |
0.892045 | − | 0.451946i | \(-0.149270\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.31406 | − | 41.0622i | −0.356791 | − | 1.76215i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.269501 | − | 0.466790i | 0.0115442 | − | 0.0199951i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.14413 | − | 1.98170i | −0.0489196 | − | 0.0847313i | 0.840529 | − | 0.541767i | \(-0.182244\pi\) |
−0.889448 | + | 0.457036i | \(0.848911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.56341 | + | 15.5435i | 0.280119 | + | 0.663379i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3509 | 1.03738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.5561 | + | 24.0730i | −1.34190 | + | 1.02369i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.137592 | + | 0.0278590i | −0.00584048 | + | 0.00118255i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.2838 | − | 20.3711i | 1.49502 | − | 0.863151i | 0.495038 | − | 0.868871i | \(-0.335154\pi\) |
0.999984 | + | 0.00572024i | \(0.00182082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8067i | 0.499370i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.93056 | + | 24.3514i | 0.208168 | + | 1.02812i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.4287 | −0.987403 | −0.493701 | − | 0.869631i | \(-0.664356\pi\) | ||||
−0.493701 | + | 0.869631i | \(0.664356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.815776i | − | 0.0343200i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.85096 | + | 23.6405i | −0.119729 | + | 0.992807i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.67098i | − | 0.279662i | −0.990175 | − | 0.139831i | \(-0.955344\pi\) | ||
0.990175 | − | 0.139831i | \(-0.0446560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.69555 | 0.112805 | 0.0564026 | − | 0.998408i | \(-0.482037\pi\) | ||||
0.0564026 | + | 0.998408i | \(0.482037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.30803 | − | 21.2768i | −0.179970 | − | 0.888852i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 43.1275i | 1.79854i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.9482 | + | 16.1359i | −1.16350 | + | 0.671747i | −0.952140 | − | 0.305662i | \(-0.901122\pi\) |
−0.211359 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.05433 | − | 1.02338i | 0.210051 | − | 0.0425300i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.3368 | − | 6.40337i | −0.636277 | − | 0.265656i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.03958 | −0.0844708 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.178356 | + | 0.422383i | 0.00737411 | + | 0.0174634i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.93933 | − | 6.82313i | −0.162594 | − | 0.281621i | 0.773204 | − | 0.634157i | \(-0.218653\pi\) |
−0.935798 | + | 0.352536i | \(0.885319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7718 | + | 29.0495i | −0.691068 | + | 1.19697i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.07966 | − | 15.2101i | −0.126680 | − | 0.625659i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.7133 | − | 18.5559i | 0.439941 | − | 0.762001i | −0.557743 | − | 0.830014i | \(-0.688333\pi\) |
0.997684 | + | 0.0680127i | \(0.0216658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.102572 | − | 0.796438i | −0.00420504 | − | 0.0326508i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.93387 | − | 7.88909i | 0.365639 | − | 0.322879i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.55531i | 0.0635482i | 0.999495 | + | 0.0317741i | \(0.0101157\pi\) | ||||
−0.999495 | + | 0.0317741i | \(0.989884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.4367 | + | 14.6859i | −1.03758 | + | 0.599050i | −0.919148 | − | 0.393912i | \(-0.871121\pi\) |
−0.118436 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.4188 | + | 16.2228i | −1.56454 | + | 0.660643i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.126860 | + | 0.219728i | −0.00515759 | + | 0.00893322i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.8433 | − | 17.2300i | 1.21130 | − | 0.699345i | 0.248258 | − | 0.968694i | \(-0.420142\pi\) |
0.963043 | + | 0.269349i | \(0.0868085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.41918 | + | 32.3743i | −0.260118 | + | 1.31187i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.31185 | − | 1.91210i | −0.133983 | − | 0.0773552i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9007 | − | 25.8087i | −0.601832 | − | 1.04240i | −0.992544 | − | 0.121891i | \(-0.961104\pi\) |
0.390711 | − | 0.920513i | \(-0.372229\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0700522 | + | 0.0141838i | −0.00282478 | + | 0.000571947i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.9008 | − | 6.29358i | −0.438850 | − | 0.253370i | 0.264260 | − | 0.964451i | \(-0.414872\pi\) |
−0.703110 | + | 0.711082i | \(0.748206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.0926 | − | 21.4154i | −1.49088 | − | 0.860759i | −0.490933 | − | 0.871197i | \(-0.663344\pi\) |
−0.999946 | + | 0.0104377i | \(0.996678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.4198 | − | 40.4212i | 0.779291 | − | 1.62205i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.36071 | − | 41.6242i | −0.214772 | − | 1.66764i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4793 | − | 21.6147i | −0.499171 | − | 0.864589i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.63162 | + | 10.9072i | 0.384650 | + | 0.435590i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.90002 | 0.354867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2015 | 0.844018 | 0.422009 | − | 0.906592i | \(-0.361325\pi\) | ||||
0.422009 | + | 0.906592i | \(0.361325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.07707 | + | 18.1060i | −0.241542 | + | 0.719647i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.185394 | + | 0.321112i | 0.00735714 | + | 0.0127429i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.4697 | + | 14.3076i | −0.573309 | + | 0.566886i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.10042 | − | 9.71063i | −0.162210 | − | 0.384147i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7877 | + | 6.22827i | 0.426088 | + | 0.246002i | 0.697679 | − | 0.716411i | \(-0.254216\pi\) |
−0.271591 | + | 0.962413i | \(0.587550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.57692 | − | 2.64249i | −0.180496 | − | 0.104209i | 0.407030 | − | 0.913415i | \(-0.366565\pi\) |
−0.587526 | + | 0.809205i | \(0.699898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.117682 | − | 0.350621i | 0.00463373 | − | 0.0138057i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3799 | − | 30.1028i | −0.683273 | − | 1.18346i | −0.973976 | − | 0.226650i | \(-0.927223\pi\) |
0.290704 | − | 0.956813i | \(-0.406111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.98788 | − | 5.76651i | −0.392059 | − | 0.226355i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.1999 | − | 29.9557i | −1.34040 | − | 1.17406i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.3498 | + | 15.2131i | −1.03115 | + | 0.595333i | −0.917313 | − | 0.398166i | \(-0.869647\pi\) |
−0.113834 | + | 0.993500i | \(0.536313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0972401 | + | 0.168425i | −0.00379949 | + | 0.00658090i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.1244 | − | 18.6707i | 0.551045 | − | 0.728413i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.3127 | + | 19.2331i | −1.29768 | + | 0.749215i | −0.980003 | − | 0.198984i | \(-0.936236\pi\) |
−0.317676 | + | 0.948199i | \(0.602903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.9551i | − | 1.70965i | −0.518914 | − | 0.854827i | \(-0.673663\pi\) | ||
0.518914 | − | 0.854827i | \(-0.326337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.76838 | − | 28.4893i | −0.224025 | − | 1.10643i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.285246 | − | 0.373915i | −0.0110614 | − | 0.0144998i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0784 | − | 53.8294i | 1.20336 | − | 2.08428i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.33325 | − | 7.35871i | 0.322182 | − | 0.284504i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.98732 | + | 12.1024i | −0.269742 | + | 0.467208i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.65619 | − | 8.06477i | −0.179483 | − | 0.310874i | 0.762221 | − | 0.647317i | \(-0.224109\pi\) |
−0.941704 | + | 0.336444i | \(0.890776\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.96440 | + | 25.8920i | 0.0756099 | + | 0.996583i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.54128 | −0.212969 | −0.106484 | − | 0.994314i | \(-0.533959\pi\) | ||||
−0.106484 | + | 0.994314i | \(0.533959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.85330 | − | 4.43885i | 0.0711230 | − | 0.170348i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.3465 | + | 39.7644i | −0.511439 | + | 1.52378i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.8479 | + | 14.9233i | −0.989041 | + | 0.571023i | −0.904988 | − | 0.425438i | \(-0.860120\pi\) |
−0.0840538 | + | 0.996461i | \(0.526787\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.215183i | 0.00822170i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.2717 | − | 12.6026i | 0.544498 | − | 0.480821i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.38615 | 0.0909052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.2898i | 1.22836i | 0.789165 | + | 0.614181i | \(0.210513\pi\) | ||||
−0.789165 | + | 0.614181i | \(0.789487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.0400 | + | 9.92990i | −0.647296 | + | 0.377206i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.738215i | 0.0280021i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.53125 | 0.171633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.8287 | + | 11.6899i | 1.31734 | + | 0.442152i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.6043i | − | 1.04260i | −0.853373 | − | 0.521301i | \(-0.825447\pi\) | ||
0.853373 | − | 0.521301i | \(-0.174553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.51407 | − | 2.60620i | 0.170251 | − | 0.0982947i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0792926 | + | 0.0897937i | 0.00298633 | + | 0.00338182i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.451467 | + | 3.50549i | 0.0169791 | + | 0.131838i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.4354 | −1.48103 | −0.740514 | − | 0.672041i | \(-0.765418\pi\) | ||||
−0.740514 | + | 0.672041i | \(0.765418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.4595 | − | 17.5068i | 1.55485 | − | 0.656555i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.8108 | + | 74.1504i | 1.60328 | + | 2.77696i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.189875 | + | 0.328874i | −0.00710094 | + | 0.0122992i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.17172 | + | 0.728915i | 0.0811044 | + | 0.0272218i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.51750 | − | 4.36045i | 0.0938871 | − | 0.162617i | −0.815257 | − | 0.579100i | \(-0.803404\pi\) |
0.909144 | + | 0.416483i | \(0.136737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.80209 | − | 18.6869i | 0.290565 | − | 0.695936i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.07672 | − | 2.03959i | −0.225996 | − | 0.0758530i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.9910i | 1.33667i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.3848 | + | 8.88245i | −0.570592 | + | 0.329432i | −0.757386 | − | 0.652968i | \(-0.773524\pi\) |
0.186793 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.81773 | − | 25.1518i | 0.363620 | − | 0.931548i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.7236 | + | 20.3058i | −0.433611 | + | 0.751037i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.6113 | − | 6.12644i | 0.391938 | − | 0.226285i | −0.291062 | − | 0.956704i | \(-0.594008\pi\) |
0.682999 | + | 0.730419i | \(0.260675\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.572311 | − | 0.280663i | 0.0211100 | − | 0.0103524i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.9135 | − | 17.2706i | −1.10188 | − | 0.636169i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.09505 | − | 7.09284i | −0.150639 | − | 0.260914i | 0.780824 | − | 0.624752i | \(-0.214800\pi\) |
−0.931463 | + | 0.363837i | \(0.881466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.2683 | − | 12.7606i | −0.413950 | − | 0.468771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9393 | − | 12.0893i | −0.768190 | − | 0.443514i | 0.0640389 | − | 0.997947i | \(-0.479602\pi\) |
−0.832228 | + | 0.554433i | \(0.812935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.344840 | + | 0.199094i | 0.0126340 | + | 0.00729422i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.0291 | + | 11.3695i | 0.549886 | + | 0.415989i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.1147 | + | 4.26479i | −1.20999 | + | 0.155832i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.15243 | + | 10.6563i | 0.224505 | + | 0.388855i | 0.956171 | − | 0.292809i | \(-0.0945900\pi\) |
−0.731666 | + | 0.681664i | \(0.761257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.3144 | + | 9.17504i | −1.65135 | + | 0.334357i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.667073 | −0.0242773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3788 | −1.06779 | −0.533895 | − | 0.845551i | \(-0.679272\pi\) | ||||
−0.533895 | + | 0.845551i | \(0.679272\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.4037 | − | 7.37084i | 1.32137 | − | 0.267545i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1690 | − | 21.0774i | −0.441127 | − | 0.764055i | 0.556646 | − | 0.830750i | \(-0.312088\pi\) |
−0.997773 | + | 0.0666951i | \(0.978755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0308 | − | 10.4508i | −0.906176 | − | 0.378344i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.112662 | + | 0.903537i | −0.00407332 | + | 0.0326674i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.6851 | + | 6.74638i | 0.421923 | + | 0.243597i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0120 | + | 9.24453i | 0.577407 | + | 0.333366i | 0.760102 | − | 0.649803i | \(-0.225149\pi\) |
−0.182695 | + | 0.983170i | \(0.558482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.03833 | − | 2.30828i | −0.0734088 | − | 0.0831306i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.77378 | − | 16.9287i | −0.351538 | − | 0.608882i | 0.634981 | − | 0.772528i | \(-0.281008\pi\) |
−0.986519 | + | 0.163646i | \(0.947675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.9357 | − | 24.7890i | −1.54230 | − | 0.890445i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.27496 | + | 6.68844i | 0.0816137 | + | 0.239947i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.29824 | − | 1.32689i | 0.0823430 | − | 0.0475407i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.36526 | − | 7.56084i | 0.156201 | − | 0.270548i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.2063 | − | 33.7326i | 0.579168 | − | 1.20550i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0498977 | + | 0.0288084i | −0.00178093 | + | 0.00102822i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19.3435i | − | 0.689520i | −0.938691 | − | 0.344760i | \(-0.887960\pi\) | ||
0.938691 | − | 0.344760i | \(-0.112040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.1620 | + | 10.4592i | 1.10940 | + | 0.372357i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.7171 | + | 5.24389i | −1.44773 | + | 0.186451i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.17463 | − | 14.1589i | 0.290290 | − | 0.502797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0708611 | − | 0.0237838i | −0.00251318 | − | 0.000843523i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.07573 | − | 7.05937i | 0.144370 | − | 0.250056i | −0.784768 | − | 0.619790i | \(-0.787218\pi\) |
0.929138 | + | 0.369734i | \(0.120551\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.79726 | − | 6.57705i | −0.134338 | − | 0.232679i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.88807 | + | 47.2215i | −0.208045 | + | 1.66849i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.3906 | 0.684279 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.19062 | + | 0.153338i | −0.0419638 | + | 0.00540445i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.4588 | − | 18.6385i | −0.579377 | − | 0.656106i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.27457 | + | 3.04527i | −0.185444 | + | 0.107066i | −0.589848 | − | 0.807514i | \(-0.700812\pi\) |
0.404404 | + | 0.914580i | \(0.367479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.909185i | 0.0319258i | 0.999873 | + | 0.0159629i | \(0.00508137\pi\) | ||||
−0.999873 | + | 0.0159629i | \(0.994919\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.8949 | + | 7.01316i | 0.732817 | + | 0.245962i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.466421 | −0.0163380 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.7321i | 0.480425i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.9355 | − | 11.6172i | 0.696603 | − | 0.405939i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 35.8604i | − | 1.25154i | −0.780009 | − | 0.625768i | \(-0.784786\pi\) | ||
0.780009 | − | 0.625768i | \(-0.215214\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.26442 | −0.218364 | −0.109182 | − | 0.994022i | \(-0.534823\pi\) | ||||
−0.109182 | + | 0.994022i | \(0.534823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.1210 | + | 14.2357i | −0.561261 | + | 0.495623i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 21.2516i | − | 0.738990i | −0.929233 | − | 0.369495i | \(-0.879531\pi\) | ||
0.929233 | − | 0.369495i | \(-0.120469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3259 | − | 12.3125i | 0.740678 | − | 0.427631i | −0.0816377 | − | 0.996662i | \(-0.526015\pi\) |
0.822316 | + | 0.569031i | \(0.192682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.7521 | + | 40.9727i | −0.477054 | + | 1.42133i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.0925 | + | 10.2392i | −1.35447 | + | 0.354766i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.492411 | −0.0170406 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.0793 | + | 42.5669i | 1.00513 | + | 1.47133i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.92909 | + | 12.0015i | 0.239219 | + | 0.414339i | 0.960490 | − | 0.278313i | \(-0.0897753\pi\) |
−0.721272 | + | 0.692652i | \(0.756442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4358 | − | 19.8073i | 0.394336 | − | 0.683011i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.6914 | + | 12.0902i | −0.471557 | + | 0.416410i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.119591 | + | 0.207138i | −0.00411407 | + | 0.00712578i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.7825 | + | 4.91941i | 0.404853 | + | 0.169033i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.27401 | + | 26.0477i | 0.181003 | + | 0.893954i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.3049i | − | 0.456087i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.86165 | + | 3.96158i | −0.234938 | + | 0.135642i | −0.612848 | − | 0.790201i | \(-0.709976\pi\) |
0.377910 | + | 0.925842i | \(0.376643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.207441 | + | 0.491263i | 0.00709434 | + | 0.0168008i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.8942 | + | 37.9219i | −0.747892 | + | 1.29539i | 0.200939 | + | 0.979604i | \(0.435601\pi\) |
−0.948831 | + | 0.315784i | \(0.897733\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.6923 | − | 25.2257i | 1.49076 | − | 0.860691i | 0.490817 | − | 0.871263i | \(-0.336698\pi\) |
0.999944 | + | 0.0105716i | \(0.00336509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.15825 | + | 3.40528i | 0.0394729 | + | 0.116051i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.5324 | − | 10.1223i | −0.596810 | − | 0.344568i | 0.170976 | − | 0.985275i | \(-0.445308\pi\) |
−0.767786 | + | 0.640707i | \(0.778641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.602895 | + | 1.04424i | 0.0204990 | + | 0.0355054i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.99874 | − | 26.8108i | 0.305613 | − | 0.910541i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.2810 | + | 18.6375i | 1.09506 | + | 0.632233i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.9965 | + | 20.2052i | 1.18581 | + | 0.684629i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.29063 | + | 4.34980i | −0.111371 | + | 0.147218i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.10561 | − | 0.843429i | 0.0373765 | − | 0.0285131i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3916 | − | 38.7834i | −0.756111 | − | 1.30962i | −0.944820 | − | 0.327589i | \(-0.893764\pi\) |
0.188710 | − | 0.982033i | \(-0.439569\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.71033 | + | 5.09574i | −0.0576880 | + | 0.171875i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.83016 | −0.297496 | −0.148748 | − | 0.988875i | \(-0.547524\pi\) | ||||
−0.148748 | + | 0.988875i | \(0.547524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.5994 | 0.424005 | 0.212002 | − | 0.977269i | \(-0.432002\pi\) | ||||
0.212002 | + | 0.977269i | \(0.432002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.279765 | − | 0.316815i | −0.00940420 | − | 0.0106496i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.45185 | − | 16.3711i | −0.317362 | − | 0.549687i | 0.662575 | − | 0.748996i | \(-0.269464\pi\) |
−0.979937 | + | 0.199308i | \(0.936130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.8356 | − | 11.3175i | 0.497571 | − | 0.379578i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.5195 | − | 6.08329i | 0.720932 | − | 0.203798i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.85193 | − | 2.22391i | −0.128900 | − | 0.0744204i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.553363 | + | 0.319484i | 0.0184969 | + | 0.0106792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.5896 | + | 8.62333i | −1.42202 | + | 0.287925i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.7267 | + | 61.8804i | 1.19155 | + | 2.06383i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.10384 | + | 2.36935i | 0.136719 | + | 0.0789345i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2567 | − | 3.61994i | −0.607544 | − | 0.120464i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.10131 | − | 0.635839i | 0.0366086 | − | 0.0211360i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.32064 | − | 10.9477i | 0.209873 | − | 0.363511i | −0.741801 | − | 0.670620i | \(-0.766028\pi\) |
0.951674 | + | 0.307109i | \(0.0993615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.495880 | − | 3.97689i | 0.0164473 | − | 0.131905i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.36161 | + | 5.40493i | −0.310164 | + | 0.179073i | −0.647000 | − | 0.762490i | \(-0.723977\pi\) |
0.336836 | + | 0.941563i | \(0.390643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.6086i | 0.516568i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.383888 | + | 0.338993i | −0.0126909 | + | 0.0112068i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.03150 | + | 3.77080i | 0.298246 | + | 0.124523i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.46198 | − | 12.9245i | 0.246148 | − | 0.426341i | −0.716306 | − | 0.697787i | \(-0.754168\pi\) |
0.962454 | + | 0.271446i | \(0.0875017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.60560 | − | 37.5632i | −0.250613 | − | 1.23775i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.10702 | + | 8.84561i | −0.168100 | + | 0.291157i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.85201 | + | 6.67187i | 0.126653 | + | 0.219370i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.8530 | + | 18.3120i | −0.454994 | + | 0.601445i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.5241 | 0.870227 | 0.435114 | − | 0.900376i | \(-0.356708\pi\) | ||||
0.435114 | + | 0.900376i | \(0.356708\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.8293 | + | 16.6408i | −0.551558 | + | 0.545379i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.1453 | − | 2.86407i | 0.463096 | − | 0.0937653i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.653116 | + | 0.377077i | −0.0213592 | + | 0.0123317i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.3437i | − | 1.35064i | −0.737525 | − | 0.675320i | \(-0.764006\pi\) | ||
0.737525 | − | 0.675320i | \(-0.235994\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.11235 | − | 40.0659i | −0.264736 | − | 1.30750i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.2975 | −1.47666 | −0.738328 | − | 0.674442i | \(-0.764384\pi\) | ||||
−0.738328 | + | 0.674442i | \(0.764384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.77391i | − | 0.220589i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.707814 | + | 0.146289i | −0.0230252 | + | 0.00475878i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 15.7268i | − | 0.511053i | −0.966802 | − | 0.255526i | \(-0.917751\pi\) | ||
0.966802 | − | 0.255526i | \(-0.0822487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.6855 | −0.736403 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.87322 | + | 29.0071i | 0.190452 | + | 0.940621i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0501i | 1.29735i | 0.761065 | + | 0.648676i | \(0.224677\pi\) | ||||
−0.761065 | + | 0.648676i | \(0.775323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.570654 | − | 0.329467i | 0.0184659 | − | 0.0106613i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.3798 | − | 6.15116i | 0.982040 | − | 0.198839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.7402 | − | 1.38321i | 0.346819 | − | 0.0446663i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −67.4275 | −2.17508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.5678 | + | 4.68434i | 1.21060 | + | 0.150951i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0782652 | + | 0.135559i | 0.00251945 | + | 0.00436381i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9257 | − | 18.9239i | 0.351348 | − | 0.608553i | −0.635138 | − | 0.772399i | \(-0.719057\pi\) |
0.986486 | + | 0.163846i | \(0.0523900\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.70906 | − | 33.1352i | −0.215526 | − | 1.06446i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.2295 | − | 28.1102i | 0.520828 | − | 0.902100i | −0.478879 | − | 0.877881i | \(-0.658957\pi\) |
0.999707 | − | 0.0242194i | \(-0.00771003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.8458 | − | 4.74531i | 1.18122 | − | 0.152128i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.8603 | − | 16.6547i | 0.604014 | − | 0.533377i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.2114i | 1.73438i | 0.497980 | + | 0.867189i | \(0.334075\pi\) | ||||
−0.497980 | + | 0.867189i | \(0.665925\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.1338 | + | 19.7071i | −1.09092 | + | 0.629843i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.5286 | + | 18.5560i | 0.783139 | + | 0.592446i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.50399 | − | 14.7293i | 0.271235 | − | 0.469793i | −0.697943 | − | 0.716153i | \(-0.745901\pi\) |
0.969178 | + | 0.246360i | \(0.0792346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.407941 | − | 0.235525i | 0.0129981 | − | 0.00750445i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.97209 | − | 4.53486i | 0.126433 | − | 0.144346i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.3558 | + | 17.5259i | 0.965258 | + | 0.557292i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.21588 | + | 9.03416i | 0.165688 | + | 0.286980i | 0.936899 | − | 0.349599i | \(-0.113682\pi\) |
−0.771212 | + | 0.636579i | \(0.780349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.8793 | + | 6.65724i | −1.04339 | + | 0.211261i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.313303 | + | 0.180886i | 0.00993237 | + | 0.00573446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.6171 | + | 9.01654i | 0.494599 | + | 0.285557i | 0.726480 | − | 0.687187i | \(-0.241155\pi\) |
−0.231881 | + | 0.972744i | \(0.574488\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.606022 | − | 7.98772i | −0.0191737 | − | 0.252720i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.bs.a.257.2 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.10 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.23 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.6 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.6 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.10 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.10 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.10 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.19 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.10 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.19 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.2 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.10 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.10 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.10 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.2 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.2 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.6 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.6 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.23 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.23 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.19 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.19 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.10 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.10 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.10 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.10 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.10 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.10 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.10 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.10 | 48 | 36.7 | odd | 6 |