Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(197,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.bc (of order \(12\), degree \(4\), 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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 197.2 | ||
Character | \(\chi\) | \(=\) | 572.197 |
Dual form | 572.2.bc.a.241.2 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.56324 | − | 2.70762i | −0.902539 | − | 1.56324i | −0.824188 | − | 0.566317i | \(-0.808368\pi\) |
−0.0783509 | − | 0.996926i | \(-0.524965\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.477789 | − | 0.477789i | 0.213674 | − | 0.213674i | −0.592152 | − | 0.805826i | \(-0.701722\pi\) |
0.805826 | + | 0.592152i | \(0.201722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02740 | + | 3.83429i | 0.388319 | + | 1.44923i | 0.832868 | + | 0.553471i | \(0.186697\pi\) |
−0.444549 | + | 0.895754i | \(0.646636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.38745 | + | 5.86724i | −1.12915 | + | 1.95575i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.12228 | + | 3.12098i | 0.338380 | + | 0.941009i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.33231 | + | 1.37685i | 0.924216 | + | 0.381870i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.04057 | − | 0.546769i | −0.526873 | − | 0.141175i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.99621 | + | 3.45753i | −0.484152 | + | 0.838575i | −0.999834 | − | 0.0182044i | \(-0.994205\pi\) |
0.515683 | + | 0.856780i | \(0.327538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.12208 | + | 1.90835i | −1.63392 | + | 0.437807i | −0.955047 | − | 0.296453i | \(-0.904196\pi\) |
−0.678869 | + | 0.734260i | \(0.737530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.77572 | − | 8.77572i | 1.91502 | − | 1.91502i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.01091 | + | 1.16100i | −0.419303 | + | 0.242085i | −0.694779 | − | 0.719223i | \(-0.744498\pi\) |
0.275476 | + | 0.961308i | \(0.411165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.54344i | 0.908687i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.8022 | 2.27133 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.62932 | − | 4.40479i | 1.41673 | − | 0.817949i | 0.420719 | − | 0.907191i | \(-0.361778\pi\) |
0.996010 | + | 0.0892417i | \(0.0284444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.95758 | − | 2.95758i | 0.531197 | − | 0.531197i | −0.389732 | − | 0.920928i | \(-0.627432\pi\) |
0.920928 | + | 0.389732i | \(0.127432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.69600 | − | 7.91755i | 1.16562 | − | 1.37827i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.32286 | + | 1.34110i | 0.392635 | + | 0.226688i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.14913 | + | 4.28860i | −0.188915 | + | 0.705042i | 0.804843 | + | 0.593488i | \(0.202250\pi\) |
−0.993758 | + | 0.111554i | \(0.964417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.48122 | − | 11.1750i | −0.237185 | − | 1.78943i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.299301 | − | 1.11701i | 0.0467429 | − | 0.174447i | −0.938608 | − | 0.344985i | \(-0.887884\pi\) |
0.985351 | + | 0.170538i | \(0.0545506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.498991 | − | 0.864278i | 0.0760955 | − | 0.131801i | −0.825467 | − | 0.564451i | \(-0.809088\pi\) |
0.901562 | + | 0.432650i | \(0.142421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.18482 | + | 4.42179i | 0.176622 | + | 0.659162i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.42186 | − | 8.42186i | −1.22845 | − | 1.22845i | −0.964549 | − | 0.263905i | \(-0.914989\pi\) |
−0.263905 | − | 0.964549i | \(-0.585011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.58407 | + | 4.37866i | −1.08344 | + | 0.625523i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.4822 | 1.74786 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.84262 | 1.07727 | 0.538633 | − | 0.842540i | \(-0.318941\pi\) | ||||
0.538633 | + | 0.842540i | \(0.318941\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.02738 | + | 0.954954i | 0.273372 | + | 0.128766i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.3006 | + | 16.3006i | 2.15907 | + | 2.15907i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.51724 | + | 1.47834i | −0.718284 | + | 0.192464i | −0.599406 | − | 0.800445i | \(-0.704596\pi\) |
−0.118878 | + | 0.992909i | \(0.537930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.61754 | + | 3.24329i | 0.719252 | + | 0.415260i | 0.814477 | − | 0.580195i | \(-0.197024\pi\) |
−0.0952254 | + | 0.995456i | \(0.530357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25.9770 | − | 6.96051i | −3.27279 | − | 0.876942i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24998 | − | 0.934296i | 0.279076 | − | 0.115885i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.15648 | − | 1.38168i | −0.629964 | − | 0.168798i | −0.0703109 | − | 0.997525i | \(-0.522399\pi\) |
−0.559654 | + | 0.828727i | \(0.689066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.28708 | + | 3.62984i | 0.756875 | + | 0.436982i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.78241 | + | 6.65206i | 0.211534 | + | 0.789455i | 0.987358 | + | 0.158506i | \(0.0506676\pi\) |
−0.775824 | + | 0.630949i | \(0.782666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.78927 | + | 3.78927i | −0.443500 | + | 0.443500i | −0.893187 | − | 0.449686i | \(-0.851536\pi\) |
0.449686 | + | 0.893187i | \(0.351536\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3019 | − | 7.10249i | 1.42050 | − | 0.820125i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.8137 | + | 7.50962i | −1.23234 | + | 0.855801i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5491i | 1.74941i | 0.484658 | + | 0.874704i | \(0.338944\pi\) | ||||
−0.484658 | + | 0.874704i | \(0.661056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.28734 | − | 14.3541i | −0.920815 | − | 1.59490i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.95729 | − | 2.95729i | −0.324605 | − | 0.324605i | 0.525926 | − | 0.850530i | \(-0.323719\pi\) |
−0.850530 | + | 0.525926i | \(0.823719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.698206 | + | 2.60574i | 0.0757310 | + | 0.282632i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.8530 | − | 13.7715i | −2.55731 | − | 1.47646i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.236225 | + | 0.881602i | −0.0250398 | + | 0.0934497i | −0.977315 | − | 0.211791i | \(-0.932070\pi\) |
0.952275 | + | 0.305241i | \(0.0987370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85565 | + | 14.1916i | −0.194525 | + | 1.48769i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.6314 | − | 3.38457i | −1.30981 | − | 0.350964i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.49106 | + | 4.31464i | −0.255577 | + | 0.442673i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.56447 | − | 13.3028i | −0.361917 | − | 1.35069i | −0.871552 | − | 0.490303i | \(-0.836886\pi\) |
0.509635 | − | 0.860391i | \(-0.329780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.1132 | − | 3.98747i | −2.22246 | − | 0.400756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.01454 | + | 5.22134i | 0.299958 | + | 0.519543i | 0.976126 | − | 0.217205i | \(-0.0696939\pi\) |
−0.676168 | + | 0.736748i | \(0.736361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.5179i | − | 1.03636i | −0.855272 | − | 0.518180i | \(-0.826610\pi\) | ||
0.855272 | − | 0.518180i | \(-0.173390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.38588i | − | 0.818378i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6909 | − | 6.74973i | 1.13020 | − | 0.652521i | 0.186215 | − | 0.982509i | \(-0.440378\pi\) |
0.943985 | + | 0.329988i | \(0.107045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.07100 | − | 2.07100i | −0.198366 | − | 0.198366i | 0.600933 | − | 0.799299i | \(-0.294796\pi\) |
−0.799299 | + | 0.600933i | \(0.794796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.4083 | − | 3.59273i | 1.27266 | − | 0.341007i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.34851 | − | 7.53184i | 0.409073 | − | 0.708536i | −0.585713 | − | 0.810519i | \(-0.699185\pi\) |
0.994786 | + | 0.101983i | \(0.0325187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.406078 | + | 1.51550i | −0.0378669 | + | 0.141321i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.3664 | + | 14.8874i | −1.79042 | + | 1.37634i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.3081 | − | 4.10179i | −1.40329 | − | 0.376010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.48097 | + | 7.00522i | −0.770998 | + | 0.636838i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.49230 | + | 0.935759i | −0.314890 | + | 0.0843746i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.55975 | + | 4.55975i | 0.407836 | + | 0.407836i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.81666 | + | 10.0747i | 0.516145 | + | 0.893989i | 0.999824 | + | 0.0187438i | \(0.00596668\pi\) |
−0.483680 | + | 0.875245i | \(0.660700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.12018 | −0.274716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.54354i | 0.571712i | 0.958273 | + | 0.285856i | \(0.0922779\pi\) | ||||
−0.958273 | + | 0.285856i | \(0.907722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6344 | − | 25.3475i | −1.26896 | − | 2.19791i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.63896 | − | 5.63896i | 0.485325 | − | 0.485325i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3940 | − | 4.66071i | 1.48607 | − | 0.398192i | 0.577663 | − | 0.816275i | \(-0.303965\pi\) |
0.908409 | + | 0.418084i | \(0.137298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9003 | + | 10.3347i | 1.51828 | + | 0.876582i | 0.999769 | + | 0.0215139i | \(0.00684861\pi\) |
0.518516 | + | 0.855068i | \(0.326485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.63774 | + | 35.9686i | −0.811645 | + | 3.02910i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.557335 | + | 11.9453i | −0.0466067 | + | 0.998913i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.54065 | − | 5.74977i | 0.127944 | − | 0.477492i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 23.7115 | + | 13.6898i | 1.95569 | + | 1.12912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.83951 | − | 2.10059i | 0.642237 | − | 0.172087i | 0.0770207 | − | 0.997029i | \(-0.475459\pi\) |
0.565217 | + | 0.824943i | \(0.308793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.56303 | − | 6.56303i | 0.534092 | − | 0.534092i | −0.387695 | − | 0.921788i | \(-0.626729\pi\) |
0.921788 | + | 0.387695i | \(0.126729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5241 | − | 23.4245i | −1.09336 | − | 1.89376i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.82620i | − | 0.227006i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2293 | −1.13562 | −0.567811 | − | 0.823159i | \(-0.692210\pi\) | ||||
−0.567811 | + | 0.823159i | \(0.692210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2599 | − | 21.2348i | −0.972275 | − | 1.68403i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.51760 | − | 6.51760i | −0.513659 | − | 0.513659i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8434 | + | 3.17343i | −0.927646 | + | 0.248562i | −0.690850 | − | 0.722998i | \(-0.742764\pi\) |
−0.236795 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.583639 | − | 6.98219i | −0.0454362 | − | 0.543563i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.36037 | + | 0.900408i | 0.260033 | + | 0.0696757i | 0.386480 | − | 0.922298i | \(-0.373691\pi\) |
−0.126447 | + | 0.991973i | \(0.540357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.20856 | + | 9.17619i | 0.708351 | + | 0.705861i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9289 | − | 48.2514i | 0.988700 | − | 3.68988i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.305153 | − | 0.528541i | 0.0232004 | − | 0.0401842i | −0.854192 | − | 0.519958i | \(-0.825948\pi\) |
0.877392 | + | 0.479773i | \(0.159281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.4209 | + | 4.66790i | −1.31689 | + | 0.352860i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.6276 | + | 12.6276i | 0.949146 | + | 0.949146i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7499 | − | 11.4026i | 1.47617 | − | 0.852270i | 0.476536 | − | 0.879155i | \(-0.341892\pi\) |
0.999639 | + | 0.0268853i | \(0.00855888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.40584i | − | 0.476142i | −0.971248 | − | 0.238071i | \(-0.923485\pi\) | ||
0.971248 | − | 0.238071i | \(-0.0765152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.2802i | − | 1.49915i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50001 | + | 2.59809i | 0.110283 | + | 0.191015i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.0312 | − | 2.34979i | −0.952935 | − | 0.171834i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.1255 | + | 45.2531i | 0.882002 | + | 3.29168i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.22458 | + | 7.31719i | −0.305680 | + | 0.529453i | −0.977413 | − | 0.211340i | \(-0.932217\pi\) |
0.671732 | + | 0.740794i | \(0.265550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.3129 | − | 5.17489i | −1.39018 | − | 0.372497i | −0.515369 | − | 0.856968i | \(-0.672345\pi\) |
−0.874807 | + | 0.484472i | \(0.839012\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.04699 | − | 4.63156i | −0.433034 | − | 0.331673i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.761372 | + | 2.84148i | −0.0542455 | + | 0.202447i | −0.987730 | − | 0.156170i | \(-0.950085\pi\) |
0.933485 | + | 0.358617i | \(0.116752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8089 | + | 6.81790i | 0.837114 | + | 0.483308i | 0.856282 | − | 0.516508i | \(-0.172769\pi\) |
−0.0191684 | + | 0.999816i | \(0.506102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.31979 | + | 16.1217i | 0.304694 | + | 1.13713i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.7276 | + | 24.7276i | 1.73554 | + | 1.73554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.390690 | − | 0.676696i | −0.0272870 | − | 0.0472625i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 15.7313i | − | 1.09340i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.9489 | − | 20.0861i | −0.964865 | − | 1.38939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.15337 | + | 5.28470i | −0.630144 | + | 0.363814i | −0.780808 | − | 0.624771i | \(-0.785192\pi\) |
0.150664 | + | 0.988585i | \(0.451859\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.2249 | − | 15.2249i | 1.04319 | − | 1.04319i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.174530 | − | 0.651355i | −0.0119029 | − | 0.0444221i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.3788 | + | 8.30161i | 0.976098 | + | 0.563550i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.1834 | + | 4.33634i | 1.09357 | + | 0.293022i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4125 | + | 8.77309i | −0.767687 | + | 0.590142i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19284 | + | 0.319621i | 0.0798785 | + | 0.0214034i | 0.298537 | − | 0.954398i | \(-0.403501\pi\) |
−0.218658 | + | 0.975801i | \(0.570168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.6574 | − | 15.3907i | −1.77716 | − | 1.02605i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.2552 | − | 7.30300i | 1.80899 | − | 0.484717i | 0.813668 | − | 0.581330i | \(-0.197468\pi\) |
0.995322 | + | 0.0966131i | \(0.0308010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.79059 | − | 5.79059i | −0.382653 | − | 0.382653i | 0.489404 | − | 0.872057i | \(-0.337214\pi\) |
−0.872057 | + | 0.489404i | \(0.837214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 37.2376 | + | 17.5400i | 2.45006 | + | 1.15405i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.46751 | 0.161652 | 0.0808261 | − | 0.996728i | \(-0.474244\pi\) | ||||
0.0808261 | + | 0.996728i | \(0.474244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.04774 | −0.524977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 42.1009 | − | 24.3070i | 2.73475 | − | 1.57891i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.61060 | − | 8.61060i | −0.556974 | − | 0.556974i | 0.371471 | − | 0.928445i | \(-0.378854\pi\) |
−0.928445 | + | 0.371471i | \(0.878854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.64691 | − | 6.14636i | −0.106087 | − | 0.395922i | 0.892379 | − | 0.451286i | \(-0.149035\pi\) |
−0.998466 | + | 0.0553645i | \(0.982368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.20694 | + | 14.2148i | −0.526475 | + | 0.911882i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.53151 | + | 5.71566i | −0.0978444 | + | 0.365160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3605 | − | 3.44682i | −1.67728 | − | 0.219316i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.38424 | + | 12.6302i | −0.214468 | + | 0.800404i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.54880 | + | 0.894197i | 0.0977591 | + | 0.0564412i | 0.548082 | − | 0.836424i | \(-0.315358\pi\) |
−0.450323 | + | 0.892866i | \(0.648691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.88025 | − | 4.97303i | −0.369688 | − | 0.312652i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.96387 | − | 5.96387i | 0.373472 | − | 0.373472i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.3333 | + | 9.43002i | −1.01884 | + | 0.588229i | −0.913768 | − | 0.406236i | \(-0.866841\pi\) |
−0.105074 | + | 0.994464i | \(0.533508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.6244 | −1.09512 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 59.6841i | 3.69435i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.37420 | − | 1.94810i | 0.208062 | − | 0.120125i | −0.392348 | − | 0.919817i | \(-0.628337\pi\) |
0.600411 | + | 0.799692i | \(0.295004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.74712 | − | 3.74712i | 0.230184 | − | 0.230184i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.75632 | − | 0.738553i | 0.168684 | − | 0.0451987i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.36252 | − | 16.2164i | 0.570843 | − | 0.988729i | −0.425637 | − | 0.904894i | \(-0.639950\pi\) |
0.996480 | − | 0.0838349i | \(-0.0267168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.59616 | − | 1.23154i | −0.279197 | − | 0.0748106i | 0.116503 | − | 0.993190i | \(-0.462831\pi\) |
−0.395700 | + | 0.918380i | \(0.629498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 41.3263 | − | 17.1605i | 2.50118 | − | 1.03860i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.1799 | + | 5.09901i | −0.855083 | + | 0.307482i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8710 | + | 18.8291i | −0.653173 | + | 1.13133i | 0.329175 | + | 0.944269i | \(0.393229\pi\) |
−0.982348 | + | 0.187060i | \(0.940104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.33417 | + | 27.3715i | 0.439085 | + | 1.63869i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.54703 | + | 7.54703i | −0.450218 | + | 0.450218i | −0.895427 | − | 0.445209i | \(-0.853129\pi\) |
0.445209 | + | 0.895427i | \(0.353129\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.48163 | + | 2.56626i | 0.0880738 | + | 0.152548i | 0.906697 | − | 0.421783i | \(-0.138596\pi\) |
−0.818623 | + | 0.574331i | \(0.805262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.5765 | 0.922673 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.59042 | 0.270964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.530302 | + | 0.918510i | 0.0311942 | + | 0.0540300i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.4467 | + | 30.4467i | −1.78482 | + | 1.78482i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.07010 | − | 26.3860i | −0.413040 | − | 1.54149i | −0.788730 | − | 0.614740i | \(-0.789261\pi\) |
0.375690 | − | 0.926746i | \(-0.377406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.92974 | + | 3.34241i | −0.112354 | + | 0.194603i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2454 | + | 36.8344i | 0.768575 | + | 2.13735i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.29949 | + | 1.10008i | −0.479972 | + | 0.0636194i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.82656 | + | 1.02532i | 0.220559 | + | 0.0590986i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.42492 | − | 16.3244i | 0.541448 | − | 0.937815i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.23360 | − | 1.13439i | 0.242415 | − | 0.0649550i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.41011 | − | 7.41011i | 0.422917 | − | 0.422917i | −0.463290 | − | 0.886207i | \(-0.653331\pi\) |
0.886207 | + | 0.463290i | \(0.153331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.4784 | + | 16.4420i | −1.62008 | + | 0.935354i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.7397i | − | 0.665700i | −0.942980 | − | 0.332850i | \(-0.891990\pi\) | ||
0.942980 | − | 0.332850i | \(-0.108010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.34977 | 0.358910 | 0.179455 | − | 0.983766i | \(-0.442567\pi\) | ||||
0.179455 | + | 0.983766i | \(0.442567\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.7372 | + | 9.08586i | −0.886689 | + | 0.511930i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.63617 | + | 5.63617i | −0.316559 | + | 0.316559i | −0.847444 | − | 0.530885i | \(-0.821860\pi\) |
0.530885 | + | 0.847444i | \(0.321860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.3095 | + | 18.8675i | 1.24909 | + | 1.05638i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.5514 | − | 21.1029i | −2.04010 | − | 1.17785i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.61895 | − | 28.4343i | 0.423930 | − | 1.58213i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.25564 | + | 15.1401i | −0.347000 | + | 0.839823i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.37000 | + | 8.84495i | −0.131061 | + | 0.489127i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.6393 | − | 40.9444i | 1.30328 | − | 2.25734i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29309 | + | 8.55794i | 0.126040 | + | 0.470387i | 0.999875 | − | 0.0158360i | \(-0.00504097\pi\) |
−0.873835 | + | 0.486223i | \(0.838374\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.2697 | − | 21.2697i | −1.16557 | − | 1.16557i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.12386 | + | 1.80356i | −0.170675 | + | 0.0985391i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0009 | 0.708206 | 0.354103 | − | 0.935206i | \(-0.384786\pi\) | ||||
0.354103 | + | 0.935206i | \(0.384786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.1911 | −1.47682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5498 | + | 5.91130i | 0.679608 | + | 0.320115i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.93263 | − | 4.93263i | −0.266337 | − | 0.266337i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.73820 | − | 1.26960i | 0.255096 | − | 0.0683527i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.6763 | − | 15.9789i | −1.48574 | − | 0.857793i | −0.485873 | − | 0.874030i | \(-0.661498\pi\) |
−0.999868 | + | 0.0162365i | \(0.994832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.645630 | − | 0.172996i | −0.0345598 | − | 0.00926027i | 0.241498 | − | 0.970401i | \(-0.422361\pi\) |
−0.276058 | + | 0.961141i | \(0.589028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39.3286 | + | 16.2499i | 2.09920 | + | 0.867354i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.0160 | + | 4.55942i | 0.905670 | + | 0.242674i | 0.681450 | − | 0.731865i | \(-0.261350\pi\) |
0.224220 | + | 0.974538i | \(0.428016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.02990 | + | 2.32666i | 0.213885 | + | 0.123487i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.8242 | + | 47.8605i | 0.678728 | + | 2.53305i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.65365 | + | 7.65365i | −0.403944 | + | 0.403944i | −0.879620 | − | 0.475676i | \(-0.842203\pi\) |
0.475676 | + | 0.879620i | \(0.342203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.6277 | − | 17.6829i | 1.61198 | − | 0.930679i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.2253 | + | 12.0124i | 1.69139 | + | 0.630485i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.62094i | 0.189529i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.84759 | − | 11.8604i | −0.357442 | − | 0.619107i | 0.630091 | − | 0.776521i | \(-0.283018\pi\) |
−0.987533 | + | 0.157414i | \(0.949684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.53988 | + | 5.53988i | 0.288394 | + | 0.288394i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.05747 | + | 30.0709i | 0.418323 | + | 1.56120i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.48769 | − | 4.32302i | −0.387698 | − | 0.223837i | 0.293464 | − | 0.955970i | \(-0.405192\pi\) |
−0.681162 | + | 0.732133i | \(0.738525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.21805 | − | 19.4740i | 0.269459 | − | 1.00564i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.4880 | − | 4.17368i | 1.62171 | − | 0.214955i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.95447 | + | 0.791648i | 0.151761 | + | 0.0406642i | 0.333900 | − | 0.942609i | \(-0.391635\pi\) |
−0.182139 | + | 0.983273i | \(0.558302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.1857 | − | 31.4985i | 0.931681 | − | 1.61372i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.63995 | + | 6.12037i | 0.0837975 | + | 0.312736i | 0.995084 | − | 0.0990369i | \(-0.0315762\pi\) |
−0.911286 | + | 0.411773i | \(0.864910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.57865 | + | 8.75468i | −0.0804556 | + | 0.446180i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.38062 | + | 5.85541i | 0.171847 | + | 0.297647i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9676i | 0.708183i | 0.935211 | + | 0.354092i | \(0.115210\pi\) | ||||
−0.935211 | + | 0.354092i | \(0.884790\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.27038i | − | 0.468823i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7174 | − | 10.2291i | 0.893724 | − | 0.515992i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.42918 | + | 7.42918i | 0.373802 | + | 0.373802i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.18194 | − | 2.46029i | 0.460828 | − | 0.123479i | −0.0209333 | − | 0.999781i | \(-0.506664\pi\) |
0.481762 | + | 0.876302i | \(0.339997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −45.7542 | + | 79.2485i | −2.29057 | + | 3.96739i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.28094 | − | 23.4408i | 0.313655 | − | 1.17058i | −0.611580 | − | 0.791183i | \(-0.709466\pi\) |
0.925235 | − | 0.379395i | \(-0.123868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.9277 | − | 5.78342i | 0.693789 | − | 0.288093i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8178 | − | 2.89863i | −0.537542 | − | 0.144034i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6743 | + | 1.22662i | −0.727376 | + | 0.0608011i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9059 | + | 5.60172i | −1.03373 | + | 0.276987i | −0.735513 | − | 0.677510i | \(-0.763059\pi\) |
−0.298218 | + | 0.954498i | \(0.596392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.8105 | − | 39.8105i | −1.96371 | − | 1.96371i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3368 | − | 19.6359i | −0.557846 | − | 0.966218i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.82592 | −0.138719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 64.6229i | − | 3.16460i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.69305 | − | 4.66449i | −0.131564 | − | 0.227875i | 0.792716 | − | 0.609592i | \(-0.208667\pi\) |
−0.924280 | + | 0.381716i | \(0.875333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8300 | − | 14.8300i | 0.722769 | − | 0.722769i | −0.246400 | − | 0.969168i | \(-0.579248\pi\) |
0.969168 | + | 0.246400i | \(0.0792476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 77.9417 | − | 20.8844i | 3.78966 | − | 1.01544i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.7091 | − | 9.06964i | −0.762003 | − | 0.439942i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.66427 | + | 24.8714i | −0.322507 | + | 1.20361i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.2144 | − | 17.1643i | 1.60361 | − | 0.828700i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.72236 | − | 6.42795i | 0.0829633 | − | 0.309623i | −0.911957 | − | 0.410285i | \(-0.865429\pi\) |
0.994921 | + | 0.100662i | \(0.0320959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.94600 | − | 5.16498i | −0.429917 | − | 0.248213i | 0.269394 | − | 0.963030i | \(-0.413177\pi\) |
−0.699311 | + | 0.714817i | \(0.746510\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.9766 | + | 4.81680i | −0.861910 | + | 0.230948i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.1062 | − | 12.1062i | 0.579120 | − | 0.579120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3656 | + | 24.8819i | 0.685631 | + | 1.18755i | 0.973238 | + | 0.229800i | \(0.0738070\pi\) |
−0.287607 | + | 0.957749i | \(0.592860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 59.3301i | − | 2.82524i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.79772 | −0.132924 | −0.0664618 | − | 0.997789i | \(-0.521171\pi\) | ||||
−0.0664618 | + | 0.997789i | \(0.521171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.308354 | + | 0.534086i | 0.0146174 | + | 0.0253181i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.9426 | − | 17.9426i | −0.848658 | − | 0.848658i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.42731 | − | 2.52604i | 0.444902 | − | 0.119211i | −0.0294108 | − | 0.999567i | \(-0.509363\pi\) |
0.474313 | + | 0.880356i | \(0.342696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.82205 | − | 0.319483i | 0.179973 | − | 0.0150439i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.0298 | − | 7.51056i | −1.31695 | − | 0.352877i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.89399 | + | 7.66721i | 0.276314 | + | 0.359444i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0751127 | − | 0.280324i | 0.00351362 | − | 0.0131130i | −0.964147 | − | 0.265370i | \(-0.914506\pi\) |
0.967660 | + | 0.252257i | \(0.0811727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.5597 | + | 40.8065i | −1.09967 | + | 1.90469i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.775606 | − | 0.207823i | 0.0361236 | − | 0.00967929i | −0.240712 | − | 0.970597i | \(-0.577381\pi\) |
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1917 | + | 16.1917i | 0.752492 | + | 0.752492i | 0.974944 | − | 0.222452i | \(-0.0714060\pi\) |
−0.222452 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.65225 | + | 4.41803i | −0.354865 | + | 0.204881i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.1802i | − | 1.21147i | −0.795665 | − | 0.605737i | \(-0.792878\pi\) | ||
0.795665 | − | 0.605737i | \(-0.207122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 21.1910i | − | 0.978508i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.2439 | + | 38.5275i | 1.02494 | + | 1.77525i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.25740 | + | 0.587377i | 0.149775 | + | 0.0270076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.67049 | − | 32.3587i | −0.397829 | − | 1.48472i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.5665 | + | 46.0146i | −1.21640 | + | 2.10686i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.54595 | + | 0.950135i | 0.162019 | + | 0.0434128i | 0.338917 | − | 0.940816i | \(-0.389940\pi\) |
−0.176898 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.73402 | + | 12.7088i | −0.443833 | + | 0.579470i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.45857 | + | 27.8358i | −0.339377 | + | 1.26657i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.05899 | − | 4.65286i | −0.365940 | − | 0.211275i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1039 | − | 37.7084i | −0.457853 | − | 1.70873i | −0.679563 | − | 0.733617i | \(-0.737831\pi\) |
0.221711 | − | 0.975112i | \(-0.428836\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.1065 | + | 27.1065i | 1.22580 | + | 1.22580i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4238 | − | 26.7148i | −0.696066 | − | 1.20562i | −0.969820 | − | 0.243821i | \(-0.921599\pi\) |
0.273755 | − | 0.961800i | \(-0.411734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.1715i | 1.58405i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.4706 | + | 8.66027i | −0.560512 | + | 0.389250i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.6747 | + | 13.6686i | −1.06196 | + | 0.613120i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.99551 | − | 7.99551i | 0.357928 | − | 0.357928i | −0.505121 | − | 0.863049i | \(-0.668552\pi\) |
0.863049 | + | 0.505121i | \(0.168552\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.81511 | − | 10.5061i | −0.125770 | − | 0.469380i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07284 | − | 0.619403i | −0.0478355 | − | 0.0276178i | 0.475892 | − | 0.879504i | \(-0.342125\pi\) |
−0.523727 | + | 0.851886i | \(0.675459\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.93501 | + | 1.05438i | 0.175106 | + | 0.0469195i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.4504 | − | 39.2778i | 0.464118 | − | 1.74439i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.15268 | + | 1.91655i | 0.317037 | + | 0.0849498i | 0.413828 | − | 0.910355i | \(-0.364191\pi\) |
−0.0967916 | + | 0.995305i | \(0.530858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.4222 | − | 10.6361i | −0.814952 | − | 0.470513i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −84.0562 | + | 22.5228i | −3.71117 | + | 0.994405i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.02534 | − | 5.02534i | −0.221443 | − | 0.221443i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.8327 | − | 35.7361i | 0.740302 | − | 1.57167i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.90812 | −0.0837570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0187 | −0.920847 | −0.460424 | − | 0.887699i | \(-0.652302\pi\) | ||||
−0.460424 | + | 0.887699i | \(0.652302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6969 | + | 6.17584i | −0.467741 | + | 0.270050i | −0.715294 | − | 0.698824i | \(-0.753707\pi\) |
0.247553 | + | 0.968874i | \(0.420374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 39.8719 | + | 39.8719i | 1.74015 | + | 1.74015i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.32199 | + | 16.1299i | 0.188269 | + | 0.702628i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.80417 | + | 15.2493i | −0.382790 | + | 0.663011i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0156 | − | 37.3788i | 0.434641 | − | 1.62210i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.53531 | − | 3.31011i | 0.109817 | − | 0.143377i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.36083 | − | 8.81072i | 0.102067 | − | 0.380921i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −61.7477 | − | 35.6500i | −2.66461 | − | 1.53841i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.1772 | − | 18.7556i | −0.955238 | − | 0.807861i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.4117 | + | 24.4117i | −1.04954 | + | 1.04954i | −0.0508347 | + | 0.998707i | \(0.516188\pi\) |
−0.998707 | + | 0.0508347i | \(0.983812\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3446 | + | 10.0139i | −0.744326 | + | 0.429737i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97900 | −0.0847712 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 19.0377i | − | 0.813992i | −0.913430 | − | 0.406996i | \(-0.866576\pi\) | ||
0.913430 | − | 0.406996i | \(-0.133424\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38.0583 | + | 21.9730i | −1.62429 | + | 0.937784i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.9307 | + | 45.9307i | −1.95671 | + | 1.95671i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −59.6197 | + | 15.9750i | −2.53529 | + | 0.679328i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.68975 | − | 8.12288i | 0.199069 | − | 0.344797i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.25675 | + | 2.21239i | 0.349850 | + | 0.0937420i | 0.429464 | − | 0.903084i | \(-0.358702\pi\) |
−0.0796147 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.85278 | − | 2.19301i | 0.120660 | − | 0.0927542i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.0086 | + | 38.9567i | 0.591442 | + | 1.64475i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.69347 | − | 8.12933i | 0.197806 | − | 0.342610i | −0.750011 | − | 0.661426i | \(-0.769952\pi\) |
0.947817 | + | 0.318815i | \(0.103285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.52096 | − | 5.67630i | −0.0639872 | − | 0.238804i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 46.5234 | − | 46.5234i | 1.95380 | − | 1.95380i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0039 | + | 31.1836i | 0.754761 | + | 1.30728i | 0.945493 | + | 0.325642i | \(0.105580\pi\) |
−0.190732 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8778 | 0.622618 | 0.311309 | − | 0.950309i | \(-0.399233\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.4162 | 1.10355 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.27492 | − | 9.13643i | −0.219979 | − | 0.381016i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9357 | + | 16.9357i | −0.705043 | + | 0.705043i | −0.965489 | − | 0.260445i | \(-0.916131\pi\) |
0.260445 | + | 0.965489i | \(0.416131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.1792 | + | 60.3816i | 0.672385 | + | 2.50938i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.30080 | − | 14.3774i | 0.344375 | − | 0.596475i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.80162 | + | 24.4766i | 0.364526 | + | 1.01372i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.13998 | + | 16.3661i | −0.0884773 | + | 0.676655i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.2901 | + | 9.72391i | 1.49785 | + | 0.401349i | 0.912380 | − | 0.409343i | \(-0.134242\pi\) |
0.585473 | + | 0.810692i | \(0.300909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4200 | + | 26.7082i | −0.635370 | + | 1.10049i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.88384 | − | 2.38042i | 0.365432 | − | 0.0979173i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.2367 | + | 23.2367i | −0.954216 | + | 0.954216i | −0.998997 | − | 0.0447806i | \(-0.985741\pi\) |
0.0447806 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.27383 | + | 5.35425i | −0.380190 | + | 0.219503i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 42.6321i | − | 1.74482i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.5864 | −1.20887 | −0.604434 | − | 0.796656i | \(-0.706600\pi\) | ||||
−0.604434 | + | 0.796656i | \(0.706600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.97969 | + | 2.29767i | −0.162335 | + | 0.0937240i | −0.578966 | − | 0.815351i | \(-0.696544\pi\) |
0.416632 | + | 0.909075i | \(0.363210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.5740 | − | 25.5740i | 1.04145 | − | 1.04145i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.705099 | + | 7.39913i | −0.0286664 | + | 0.300818i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7384 | + | 16.0148i | 1.12587 | + | 0.650020i | 0.942893 | − | 0.333097i | \(-0.108094\pi\) |
0.182976 | + | 0.983117i | \(0.441427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.2976 | − | 105.608i | 1.14668 | − | 4.27945i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4686 | − | 39.6599i | −0.666247 | − | 1.60447i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.28313 | − | 34.6451i | 0.374942 | − | 1.39930i | −0.478487 | − | 0.878095i | \(-0.658815\pi\) |
0.853429 | − | 0.521209i | \(-0.174519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.22149 | + | 2.11568i | −0.0492551 | + | 0.0853124i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.25696 | + | 4.69102i | 0.0506031 | + | 0.188854i | 0.986601 | − | 0.163153i | \(-0.0521663\pi\) |
−0.935998 | + | 0.352006i | \(0.885500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.70022 | + | 7.70022i | 0.309498 | + | 0.309498i | 0.844715 | − | 0.535217i | \(-0.179770\pi\) |
−0.535217 | + | 0.844715i | \(0.679770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.7331 | + | 13.7023i | −0.952378 | + | 0.549856i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.62302 | −0.145153 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.3600 | −0.734399 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.5800 | + | 69.1677i | −1.30112 | + | 2.76229i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.5341 | − | 12.5341i | −0.499767 | − | 0.499767i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.20198 | − | 0.590020i | 0.0876596 | − | 0.0234883i | −0.214723 | − | 0.976675i | \(-0.568885\pi\) |
0.302382 | + | 0.953187i | \(0.402218\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.6179 | + | 16.5225i | 1.13746 | + | 0.656712i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.59274 | + | 2.03447i | 0.301309 | + | 0.0807354i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.3012 | + | 4.14892i | −1.24020 | + | 0.164386i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.0671 | − | 12.0757i | −1.78283 | − | 0.477707i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.4377 | + | 22.7694i | 1.55770 | + | 0.899337i | 0.997477 | + | 0.0709934i | \(0.0226169\pi\) |
0.560220 | + | 0.828344i | \(0.310716\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.89343 | + | 7.06639i | 0.0746697 | + | 0.278671i | 0.993158 | − | 0.116777i | \(-0.0372561\pi\) |
−0.918489 | + | 0.395448i | \(0.870589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.49079 | + | 1.49079i | −0.0586997 | + | 0.0586997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.5341 | − | 17.6288i | 1.20042 | − | 0.693061i | 0.239770 | − | 0.970830i | \(-0.422928\pi\) |
0.960648 | + | 0.277768i | \(0.0895948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8058 | − | 15.5601i | −0.424163 | − | 0.610786i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 51.9097i | − | 2.03450i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.2159 | − | 36.7471i | −0.830244 | − | 1.43802i | −0.897845 | − | 0.440312i | \(-0.854868\pi\) |
0.0676008 | − | 0.997712i | \(-0.478466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12643 | + | 3.12643i | 0.122160 | + | 0.122160i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.39659 | − | 35.0685i | −0.366596 | − | 1.36815i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4581 | + | 10.6568i | 0.719027 | + | 0.415131i | 0.814395 | − | 0.580312i | \(-0.197069\pi\) |
−0.0953673 | + | 0.995442i | \(0.530403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.75930 | − | 10.2978i | 0.107324 | − | 0.400540i | −0.891274 | − | 0.453465i | \(-0.850188\pi\) |
0.998598 | + | 0.0529250i | \(0.0168544\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.5947 | + | 17.1862i | 1.61540 | + | 0.667456i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.1029 | − | 5.11860i | −0.740778 | − | 0.198491i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.2279 | + | 17.7153i | −0.396026 | + | 0.685938i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.999289 | − | 3.72940i | −0.0386347 | − | 0.144187i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.81777 | + | 21.1721i | −0.147383 | + | 0.817339i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1774 | − | 34.9483i | −0.777782 | − | 1.34716i | −0.933218 | − | 0.359311i | \(-0.883012\pi\) |
0.155436 | − | 0.987846i | \(-0.450322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 53.6225i | 2.06393i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8030i | 0.607360i | 0.952774 | + | 0.303680i | \(0.0982154\pi\) | ||||
−0.952774 | + | 0.303680i | \(0.901785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.3446 | − | 27.3344i | 1.81692 | − | 1.04900i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −62.3802 | − | 62.3802i | −2.39041 | − | 2.39041i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.4823 | + | 8.43566i | −1.20464 | + | 0.322782i | −0.804656 | − | 0.593742i | \(-0.797650\pi\) |
−0.399981 | + | 0.916523i | \(0.630983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.08383 | − | 10.5375i | 0.232451 | − | 0.402618i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.62659 | + | 24.7308i | −0.252820 | + | 0.943538i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.1340 | + | 10.7981i | 0.995627 | + | 0.411376i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1523 | + | 5.13185i | 0.728589 | + | 0.195225i | 0.604001 | − | 0.796984i | \(-0.293572\pi\) |
0.124588 | + | 0.992209i | \(0.460239\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.42987 | − | 88.8851i | −0.282237 | − | 3.37647i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.4904 | − | 3.61474i | 0.511720 | − | 0.137115i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.26462 | + | 3.26462i | 0.123656 | + | 0.123656i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.85732 | − | 6.68108i | −0.145897 | − | 0.252702i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.8917 | 1.77108 | 0.885538 | − | 0.464566i | \(-0.153790\pi\) | ||||
0.885538 | + | 0.464566i | \(0.153790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.7367i | − | 1.23469i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.5806 | + | 21.7902i | 0.473812 | + | 0.820666i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9230 | + | 16.9230i | −0.636455 | + | 0.636455i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0355 | − | 7.51209i | 1.05290 | − | 0.282123i | 0.309448 | − | 0.950916i | \(-0.399856\pi\) |
0.743448 | + | 0.668794i | \(0.233189\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −91.2302 | − | 52.6718i | −3.42140 | − | 1.97535i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.51367 | + | 9.38116i | −0.0941379 | + | 0.351327i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.44103 | + | 5.97361i | 0.203483 | + | 0.223400i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.85374 | + | 36.7747i | −0.367995 | + | 1.37337i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.9746 | + | 23.6567i | 1.52809 | + | 0.882245i | 0.999442 | + | 0.0334064i | \(0.0106356\pi\) |
0.528652 | + | 0.848839i | \(0.322698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.3287 | − | 10.8060i | 1.50192 | − | 0.402438i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0674 | + | 14.0674i | −0.523174 | + | 0.523174i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.0129 | + | 34.6633i | 0.743260 | + | 1.28736i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.6158i | − | 0.838775i | −0.907807 | − | 0.419387i | \(-0.862245\pi\) | ||
0.907807 | − | 0.419387i | \(-0.137755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59371 | 0.0590262 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.99218 | + | 3.45056i | 0.0736835 | + | 0.127624i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7102 | + | 20.7102i | 0.764949 | + | 0.764949i | 0.977213 | − | 0.212263i | \(-0.0680834\pi\) |
−0.212263 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.8699 | − | 4.78823i | 0.659142 | − | 0.176617i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.47484 | − | 17.6439i | −0.0543266 | − | 0.649921i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.3783 | + | 8.67575i | 1.19106 | + | 0.319143i | 0.799303 | − | 0.600928i | \(-0.205202\pi\) |
0.391753 | + | 0.920070i | \(0.371869\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.8752 | + | 76.7622i | 1.17096 | + | 2.81993i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.6411 | + | 43.4452i | −0.427070 | + | 1.59385i | 0.332289 | + | 0.943177i | \(0.392179\pi\) |
−0.759360 | + | 0.650671i | \(0.774488\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.74199 | − | 4.74927i | 0.100459 | − | 0.174000i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.3688 | − | 7.33345i | 1.00137 | − | 0.268317i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.8916 | + | 37.8916i | 1.38453 | + | 1.38453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.76965 | − | 4.48581i | 0.283519 | − | 0.163690i | −0.351497 | − | 0.936189i | \(-0.614327\pi\) |
0.635015 | + | 0.772500i | \(0.280994\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.59139i | − | 0.203762i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 6.27149i | − | 0.228243i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6233 | − | 21.8641i | −0.458800 | − | 0.794665i | 0.540098 | − | 0.841602i | \(-0.318387\pi\) |
−0.998898 | + | 0.0469373i | \(0.985054\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.27279 | + | 23.6955i | −0.155093 | + | 0.860093i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.78957 | − | 25.3390i | −0.246122 | − | 0.918539i | −0.972816 | − | 0.231578i | \(-0.925611\pi\) |
0.726695 | − | 0.686961i | \(-0.241056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.81308 | − | 10.0686i | 0.210448 | − | 0.364506i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.6536 | − | 4.73028i | −0.638269 | − | 0.171024i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.4206 | − | 2.67014i | −0.737345 | − | 0.0964130i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.72684 | − | 32.5690i | 0.314698 | − | 1.17447i | −0.609573 | − | 0.792730i | \(-0.708659\pi\) |
0.924271 | − | 0.381738i | \(-0.124674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.0658 | + | 29.4828i | 1.83909 | + | 1.06180i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.71139 | + | 21.3152i | 0.205424 | + | 0.766654i | 0.989320 | + | 0.145761i | \(0.0465631\pi\) |
−0.783895 | + | 0.620893i | \(0.786770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4376 | + | 13.4376i | 0.482692 | + | 0.482692i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.5511 | + | 47.7200i | 0.988392 | + | 1.71195i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.52657i | 0.305496i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.7606 | + | 13.0284i | −0.671305 | + | 0.466191i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 90.0428 | − | 51.9862i | 3.21787 | − | 1.85784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.79860 | + | 6.79860i | −0.242653 | + | 0.242653i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.92094 | − | 10.9011i | −0.104120 | − | 0.388582i | 0.894124 | − | 0.447820i | \(-0.147799\pi\) |
−0.998244 | + | 0.0592383i | \(0.981133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5494 | − | 6.09070i | −0.375568 | − | 0.216835i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.3469 | + | 8.93527i | 1.18568 | + | 0.317702i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.2538 | + | 18.5421i | 0.506169 | + | 0.658451i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.0034 | − | 4.28810i | −0.567583 | − | 0.152083i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.3013 | − | 15.1851i | −0.931639 | − | 0.537882i | −0.0443097 | − | 0.999018i | \(-0.514109\pi\) |
−0.887330 | + | 0.461136i | \(0.847442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.9306 | − | 12.3071i | 1.62491 | − | 0.435393i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.37238 | − | 4.37238i | −0.154490 | − | 0.154490i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.0788 | − | 7.57359i | −0.567410 | − | 0.267266i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.22808 | −0.219511 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58.5436 | −2.06083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5827 | + | 10.7287i | −0.653332 | + | 0.377201i | −0.789732 | − | 0.613453i | \(-0.789780\pi\) |
0.136400 | + | 0.990654i | \(0.456447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5160 | + | 21.5160i | 0.755528 | + | 0.755528i | 0.975505 | − | 0.219977i | \(-0.0705984\pi\) |
−0.219977 | + | 0.975505i | \(0.570598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.85039 | + | 14.3698i | 0.135039 | + | 0.503972i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.14241 | + | 7.17487i | −0.145102 | + | 0.251325i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.90451 | + | 7.10771i | −0.0666302 | + | 0.248667i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −76.9797 | − | 58.9610i | −2.68989 | − | 2.06026i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.38546 | − | 5.17061i | 0.0483529 | − | 0.180455i | −0.937526 | − | 0.347915i | \(-0.886890\pi\) |
0.985879 | + | 0.167460i | \(0.0535564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.78358 | + | 3.91650i | 0.236461 | + | 0.136521i | 0.613549 | − | 0.789657i | \(-0.289741\pi\) |
−0.377088 | + | 0.926177i | \(0.623075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 35.9729 | + | 30.4229i | 1.25241 | + | 1.05919i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.4534 | + | 26.4534i | −0.919874 | + | 0.919874i | −0.997020 | − | 0.0771459i | \(-0.975419\pi\) |
0.0771459 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.76096 | + | 2.74874i | −0.165355 | + | 0.0954677i | −0.580394 | − | 0.814336i | \(-0.697101\pi\) |
0.415039 | + | 0.909804i | \(0.363768\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 67.9758 | 2.35806 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 34.9629i | − | 1.21139i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.03575 | − | 1.17534i | 0.0704501 | − | 0.0406744i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.9059 | − | 34.9059i | 1.20653 | − | 1.20653i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7209 | + | 4.21239i | −0.542744 | + | 0.145428i | −0.519767 | − | 0.854308i | \(-0.673981\pi\) |
−0.0229774 | + | 0.999736i | \(0.507315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3044 | − | 42.0964i | 0.838082 | − | 1.45160i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.2323 | + | 8.63662i | 1.11014 | + | 0.297461i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.78403 | − | 0.0154668i | 0.302180 | − | 0.000532075i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.5734 | − | 25.3214i | −1.22232 | − | 0.870053i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.63230 | − | 8.02337i | 0.158980 | − | 0.275361i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.66827 | − | 9.95812i | −0.0914672 | − | 0.341360i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.85064 | + | 3.85064i | −0.131843 | + | 0.131843i | −0.769949 | − | 0.638106i | \(-0.779718\pi\) |
0.638106 | + | 0.769949i | \(0.279718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.8767 | − | 29.2313i | −0.577171 | − | 0.999689i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.3553 | 0.831960 | 0.415980 | − | 0.909374i | \(-0.363439\pi\) | ||||
0.415980 | + | 0.909374i | \(0.363439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5586 | 0.872049 | 0.436024 | − | 0.899935i | \(-0.356386\pi\) | ||||
0.436024 | + | 0.899935i | \(0.356386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.17595 | − | 12.4291i | −0.244556 | − | 0.423583i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.8076 | + | 10.8076i | −0.367894 | + | 0.367894i | −0.866709 | − | 0.498815i | \(-0.833769\pi\) |
0.498815 | + | 0.866709i | \(0.333769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.106732 | − | 0.398330i | −0.00362901 | − | 0.0135436i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.65798 | − | 2.87171i | 0.0563080 | − | 0.0975284i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.5283 | + | 17.4504i | −1.64621 | + | 0.591965i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.2806 | − | 11.7039i | −0.517764 | − | 0.396571i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 90.1252 | + | 24.1490i | 3.05027 | + | 0.817319i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.7987 | + | 22.1681i | −0.432676 | + | 0.749417i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.7625 | + | 9.85048i | −1.24138 | + | 0.332627i | −0.819001 | − | 0.573792i | \(-0.805472\pi\) |
−0.422380 | + | 0.906419i | \(0.638805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −60.3908 | + | 60.3908i | −2.03693 | + | 2.03693i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.69048 | − | 1.55335i | 0.0906447 | − | 0.0523337i | −0.453992 | − | 0.891006i | \(-0.650001\pi\) |
0.544637 | + | 0.838672i | \(0.316667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.1708i | 0.880717i | 0.897822 | + | 0.440359i | \(0.145149\pi\) | ||||
−0.897822 | + | 0.440359i | \(0.854851\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0666 | 0.405615 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.37977 | + | 4.83806i | −0.281365 | + | 0.162446i | −0.634041 | − | 0.773299i | \(-0.718605\pi\) |
0.352676 | + | 0.935745i | \(0.385272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.6535 | + | 32.6535i | −1.09516 | + | 1.09516i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.4980 | − | 41.9739i | 1.18923 | − | 1.40618i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 76.0530 | + | 43.9092i | 2.54502 | + | 1.46937i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.98824 | − | 14.8843i | 0.133312 | − | 0.497527i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9527 | + | 20.7521i | 0.532646 | + | 0.692893i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.53680 | − | 35.5918i | 0.318070 | − | 1.18705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.6555 | + | 27.1161i | −0.521561 | + | 0.903369i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.20566 | − | 11.9637i | −0.106678 | − | 0.398126i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.06064 | − | 3.06064i | −0.101739 | − | 0.101739i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.9116 | − | 25.3524i | 1.45806 | − | 0.841812i | 0.459145 | − | 0.888361i | \(-0.348156\pi\) |
0.998916 | + | 0.0465497i | \(0.0148226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40.8465 | −1.35479 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.0275 | −1.69062 | −0.845309 | − | 0.534278i | \(-0.820584\pi\) | ||||
−0.845309 | + | 0.534278i | \(0.820584\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.91072 | − | 12.5485i | 0.195616 | − | 0.415296i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.68964 | − | 9.68964i | −0.320330 | − | 0.320330i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.0898 | + | 6.72280i | −0.828539 | + | 0.222006i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.05177 | − | 3.49399i | −0.199629 | − | 0.115256i | 0.396853 | − | 0.917882i | \(-0.370102\pi\) |
−0.596483 | + | 0.802626i | \(0.703436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6475 | − | 8.47993i | −1.04282 | − | 0.279423i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.21935 | + | 24.6208i | −0.105966 | + | 0.810405i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.4850 | − | 5.22099i | −0.640663 | − | 0.171665i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 61.7111 | + | 35.6289i | 2.02686 | + | 1.17021i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.71476 | − | 13.8637i | −0.121877 | − | 0.454852i | 0.877832 | − | 0.478969i | \(-0.158989\pi\) |
−0.999709 | + | 0.0241169i | \(0.992323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.6583 | − | 45.6583i | 1.49639 | − | 1.49639i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.7867 | + | 18.3521i | −1.04065 | + | 0.600820i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.34886 | + | 5.10345i | −0.240334 | + | 0.166901i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.1866i | 1.80287i | 0.432916 | + | 0.901434i | \(0.357485\pi\) | ||||
−0.432916 | + | 0.901434i | \(0.642515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.92623 | − | 17.1927i | −0.323930 | − | 0.561064i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.16199 | − | 3.16199i | −0.103078 | − | 0.103078i | 0.653687 | − | 0.756765i | \(-0.273221\pi\) |
−0.756765 | + | 0.653687i | \(0.773221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.694975 | + | 2.59368i | 0.0226315 | + | 0.0844620i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.4149 | + | 15.8280i | 0.891805 | + | 0.514884i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8897 | − | 40.6408i | 0.353866 | − | 1.32065i | −0.528039 | − | 0.849220i | \(-0.677072\pi\) |
0.881905 | − | 0.471427i | \(-0.156261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.8443 | + | 7.40975i | −0.579250 | + | 0.240531i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0713 | + | 6.44988i | 0.780564 | + | 0.209152i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9812 | − | 36.3404i | 0.679646 | − | 1.17718i | −0.295441 | − | 0.955361i | \(-0.595467\pi\) |
0.975087 | − | 0.221821i | \(-0.0712000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.47761 | + | 5.51453i | 0.0478145 | + | 0.178446i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.2108 | − | 89.9000i | 0.524022 | − | 2.90605i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.7411 | + | 61.9053i | 1.15414 | + | 1.99903i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5055i | 0.435660i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 91.4577i | 2.94718i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.7000 | + | 6.75501i | −0.376637 | + | 0.217451i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7354 | − | 20.7354i | −0.666806 | − | 0.666806i | 0.290169 | − | 0.956975i | \(-0.406288\pi\) |
−0.956975 | + | 0.290169i | \(0.906288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −88.8994 | + | 23.8205i | −2.85586 | + | 0.765226i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.46895 | − | 6.00840i | 0.111324 | − | 0.192819i | −0.804980 | − | 0.593301i | \(-0.797824\pi\) |
0.916304 | + | 0.400483i | \(0.131158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.2357 | + | 79.2529i | −0.680787 | + | 2.54073i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 50.7727 | − | 6.72984i | 1.62603 | − | 0.215527i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.5433 | − | 3.89685i | −0.465280 | − | 0.124671i | 0.0185602 | − | 0.999828i | \(-0.494092\pi\) |
−0.483840 | + | 0.875156i | \(0.660758\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.01657 | + | 0.252154i | −0.0964100 | + | 0.00805887i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.1665 | − | 5.13564i | 0.611939 | − | 0.163969i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.5129 | − | 10.5129i | −0.335310 | − | 0.335310i | 0.519289 | − | 0.854599i | \(-0.326197\pi\) |
−0.854599 | + | 0.519289i | \(0.826197\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.993852 | + | 1.72140i | 0.0316668 | + | 0.0548484i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −147.816 | −4.70502 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.31731i | 0.0736863i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.7336 | − | 23.7874i | −0.436263 | − | 0.755630i | 0.561135 | − | 0.827725i | \(-0.310365\pi\) |
−0.997398 | + | 0.0720944i | \(0.977032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.5869 | − | 19.5869i | 0.621573 | − | 0.621573i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.89970 | − | 2.38467i | 0.282139 | − | 0.0755990i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.7236 | + | 26.3985i | 1.44808 | + | 0.836049i | 0.998367 | − | 0.0571244i | \(-0.0181932\pi\) |
0.449712 | + | 0.893173i | \(0.351526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.5622 | + | 50.6149i | −0.429090 | + | 1.60139i |
(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 | 572.2.bc.a.197.2 | yes | 56 | |
11.10 | odd | 2 | inner | 572.2.bc.a.197.1 | ✓ | 56 | |
13.7 | odd | 12 | inner | 572.2.bc.a.241.1 | yes | 56 | |
143.98 | even | 12 | inner | 572.2.bc.a.241.2 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.bc.a.197.1 | ✓ | 56 | 11.10 | odd | 2 | inner | |
572.2.bc.a.197.2 | yes | 56 | 1.1 | even | 1 | trivial | |
572.2.bc.a.241.1 | yes | 56 | 13.7 | odd | 12 | inner | |
572.2.bc.a.241.2 | yes | 56 | 143.98 | even | 12 | inner |