Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(161,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.j (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.9 | ||
Character | \(\chi\) | \(=\) | 1152.161 |
Dual form | 1152.3.j.a.737.9 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.900179 | + | 0.900179i | 0.180036 | + | 0.180036i | 0.791371 | − | 0.611336i | \(-0.209367\pi\) |
−0.611336 | + | 0.791371i | \(0.709367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.66460i | 1.09494i | 0.836824 | + | 0.547471i | \(0.184409\pi\) | ||||
−0.836824 | + | 0.547471i | \(0.815591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.57563 | − | 4.57563i | −0.415967 | − | 0.415967i | 0.467844 | − | 0.883811i | \(-0.345031\pi\) |
−0.883811 | + | 0.467844i | \(0.845031\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.9824 | − | 10.9824i | −0.844799 | − | 0.844799i | 0.144679 | − | 0.989479i | \(-0.453785\pi\) |
−0.989479 | + | 0.144679i | \(0.953785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.0435225i | − | 0.00256015i | −0.999999 | − | 0.00128007i | \(-0.999593\pi\) | ||
0.999999 | − | 0.00128007i | \(-0.000407460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.9849 | − | 12.9849i | −0.683414 | − | 0.683414i | 0.277354 | − | 0.960768i | \(-0.410543\pi\) |
−0.960768 | + | 0.277354i | \(0.910543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.3139 | 0.796256 | 0.398128 | − | 0.917330i | \(-0.369660\pi\) | ||||
0.398128 | + | 0.917330i | \(0.369660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 23.3794i | − | 0.935174i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.9759 | − | 34.9759i | 1.20607 | − | 1.20607i | 0.233774 | − | 0.972291i | \(-0.424892\pi\) |
0.972291 | − | 0.233774i | \(-0.0751077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.4592 | 1.24062 | 0.620310 | − | 0.784356i | \(-0.287007\pi\) | ||||
0.620310 | + | 0.784356i | \(0.287007\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.89951 | + | 6.89951i | −0.197129 | + | 0.197129i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.3885 | + | 11.3885i | −0.307797 | + | 0.307797i | −0.844054 | − | 0.536258i | \(-0.819838\pi\) |
0.536258 | + | 0.844054i | \(0.319838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −45.6887 | −1.11436 | −0.557179 | − | 0.830393i | \(-0.688116\pi\) | ||||
−0.557179 | + | 0.830393i | \(0.688116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.4657 | − | 51.4657i | 1.19688 | − | 1.19688i | 0.221781 | − | 0.975097i | \(-0.428813\pi\) |
0.975097 | − | 0.221781i | \(-0.0711869\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 56.5712i | 1.20364i | 0.798631 | + | 0.601822i | \(0.205558\pi\) | ||||
−0.798631 | + | 0.601822i | \(0.794442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.74608 | −0.198900 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 44.6596 | + | 44.6596i | 0.842634 | + | 0.842634i | 0.989201 | − | 0.146567i | \(-0.0468223\pi\) |
−0.146567 | + | 0.989201i | \(0.546822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.23778i | − | 0.149778i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20.7614 | + | 20.7614i | 0.351887 | + | 0.351887i | 0.860811 | − | 0.508924i | \(-0.169957\pi\) |
−0.508924 | + | 0.860811i | \(0.669957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.42706 | + | 2.42706i | 0.0397878 | + | 0.0397878i | 0.726721 | − | 0.686933i | \(-0.241043\pi\) |
−0.686933 | + | 0.726721i | \(0.741043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 19.7722i | − | 0.304188i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 18.9097 | + | 18.9097i | 0.282234 | + | 0.282234i | 0.833999 | − | 0.551766i | \(-0.186046\pi\) |
−0.551766 | + | 0.833999i | \(0.686046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 114.872 | 1.61791 | 0.808956 | − | 0.587869i | \(-0.200033\pi\) | ||||
0.808956 | + | 0.587869i | \(0.200033\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 127.648i | − | 1.74860i | −0.485388 | − | 0.874299i | \(-0.661322\pi\) | ||
0.485388 | − | 0.874299i | \(-0.338678\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35.0704 | − | 35.0704i | 0.455460 | − | 0.455460i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37.0284 | 0.468714 | 0.234357 | − | 0.972151i | \(-0.424701\pi\) | ||||
0.234357 | + | 0.972151i | \(0.424701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −84.4337 | + | 84.4337i | −1.01727 | + | 1.01727i | −0.0174254 | + | 0.999848i | \(0.505547\pi\) |
−0.999848 | + | 0.0174254i | \(0.994453\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0391780 | − | 0.0391780i | 0.000460918 | − | 0.000460918i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 136.172 | 1.53002 | 0.765012 | − | 0.644017i | \(-0.222733\pi\) | ||||
0.765012 | + | 0.644017i | \(0.222733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 84.1756 | − | 84.1756i | 0.925007 | − | 0.925007i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 23.3774i | − | 0.246078i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −173.475 | −1.78840 | −0.894202 | − | 0.447663i | \(-0.852256\pi\) | ||||
−0.894202 | + | 0.447663i | \(0.852256\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.4286 | − | 18.4286i | −0.182462 | − | 0.182462i | 0.609966 | − | 0.792428i | \(-0.291183\pi\) |
−0.792428 | + | 0.609966i | \(0.791183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 88.8974i | − | 0.863082i | −0.902093 | − | 0.431541i | \(-0.857970\pi\) | ||
0.902093 | − | 0.431541i | \(-0.142030\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 54.3773 | + | 54.3773i | 0.508199 | + | 0.508199i | 0.913973 | − | 0.405774i | \(-0.132998\pi\) |
−0.405774 | + | 0.913973i | \(0.632998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −122.019 | − | 122.019i | −1.11944 | − | 1.11944i | −0.991823 | − | 0.127620i | \(-0.959266\pi\) |
−0.127620 | − | 0.991823i | \(-0.540734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 162.624i | − | 1.43915i | −0.694415 | − | 0.719575i | \(-0.744337\pi\) | ||
0.694415 | − | 0.719575i | \(-0.255663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.4858 | + | 16.4858i | 0.143355 | + | 0.143355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.333582 | 0.00280321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 79.1271i | − | 0.653943i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 43.5501 | − | 43.5501i | 0.348401 | − | 0.348401i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.2712 | 0.285600 | 0.142800 | − | 0.989752i | \(-0.454389\pi\) | ||||
0.142800 | + | 0.989752i | \(0.454389\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 59.9003 | − | 59.9003i | 0.457254 | − | 0.457254i | −0.440499 | − | 0.897753i | \(-0.645198\pi\) |
0.897753 | + | 0.440499i | \(0.145198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 99.5238 | − | 99.5238i | 0.748299 | − | 0.748299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 98.5118 | 0.719064 | 0.359532 | − | 0.933133i | \(-0.382936\pi\) | ||||
0.359532 | + | 0.933133i | \(0.382936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.39960 | + | 3.39960i | −0.0244575 | + | 0.0244575i | −0.719230 | − | 0.694772i | \(-0.755505\pi\) |
0.694772 | + | 0.719230i | \(0.255505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 100.503i | 0.702817i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 62.9691 | 0.434270 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.03169 | + | 9.03169i | 0.0606154 | + | 0.0606154i | 0.736765 | − | 0.676149i | \(-0.236353\pi\) |
−0.676149 | + | 0.736765i | \(0.736353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 69.0548i | − | 0.457316i | −0.973507 | − | 0.228658i | \(-0.926566\pi\) | ||
0.973507 | − | 0.228658i | \(-0.0734338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 34.6202 | + | 34.6202i | 0.223356 | + | 0.223356i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −63.7071 | − | 63.7071i | −0.405778 | − | 0.405778i | 0.474486 | − | 0.880263i | \(-0.342634\pi\) |
−0.880263 | + | 0.474486i | \(0.842634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 140.369i | 0.871855i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 105.629 | + | 105.629i | 0.648033 | + | 0.648033i | 0.952517 | − | 0.304484i | \(-0.0984840\pi\) |
−0.304484 | + | 0.952517i | \(0.598484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −255.722 | −1.53127 | −0.765634 | − | 0.643276i | \(-0.777575\pi\) | ||||
−0.765634 | + | 0.643276i | \(0.777575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 72.2259i | 0.427372i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −56.9554 | + | 56.9554i | −0.329222 | + | 0.329222i | −0.852291 | − | 0.523069i | \(-0.824787\pi\) |
0.523069 | + | 0.852291i | \(0.324787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 179.193 | 1.02396 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 171.658 | − | 171.658i | 0.958982 | − | 0.958982i | −0.0402097 | − | 0.999191i | \(-0.512803\pi\) |
0.999191 | + | 0.0402097i | \(0.0128026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −55.5135 | + | 55.5135i | −0.306704 | + | 0.306704i | −0.843630 | − | 0.536925i | \(-0.819586\pi\) |
0.536925 | + | 0.843630i | \(0.319586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.5034 | −0.110829 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.199143 | + | 0.199143i | −0.00106494 | + | 0.00106494i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 101.947i | 0.533755i | 0.963730 | + | 0.266878i | \(0.0859920\pi\) | ||||
−0.963730 | + | 0.266878i | \(0.914008\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 81.5007 | 0.422284 | 0.211142 | − | 0.977455i | \(-0.432282\pi\) | ||||
0.211142 | + | 0.977455i | \(0.432282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −170.676 | − | 170.676i | −0.866377 | − | 0.866377i | 0.125692 | − | 0.992069i | \(-0.459885\pi\) |
−0.992069 | + | 0.125692i | \(0.959885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 187.424i | − | 0.941831i | −0.882178 | − | 0.470916i | \(-0.843924\pi\) | ||
0.882178 | − | 0.470916i | \(-0.156076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 268.076 | + | 268.076i | 1.32057 | + | 1.32057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −41.1280 | − | 41.1280i | −0.200624 | − | 0.200624i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 118.828i | 0.568555i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −111.675 | − | 111.675i | −0.529265 | − | 0.529265i | 0.391088 | − | 0.920353i | \(-0.372099\pi\) |
−0.920353 | + | 0.391088i | \(0.872099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 92.6567 | 0.430962 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 294.775i | 1.35841i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.477981 | + | 0.477981i | −0.00216281 | + | 0.00216281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 135.329 | 0.606857 | 0.303429 | − | 0.952854i | \(-0.401869\pi\) | ||||
0.303429 | + | 0.952854i | \(0.401869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.74050 | + | 6.74050i | −0.0296938 | + | 0.0296938i | −0.721798 | − | 0.692104i | \(-0.756684\pi\) |
0.692104 | + | 0.721798i | \(0.256684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 48.9527 | − | 48.9527i | 0.213767 | − | 0.213767i | −0.592098 | − | 0.805866i | \(-0.701700\pi\) |
0.805866 | + | 0.592098i | \(0.201700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 101.494 | 0.435595 | 0.217797 | − | 0.975994i | \(-0.430113\pi\) | ||||
0.217797 | + | 0.975994i | \(0.430113\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −50.9243 | + | 50.9243i | −0.216699 | + | 0.216699i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 47.7817i | − | 0.199923i | −0.994991 | − | 0.0999617i | \(-0.968128\pi\) | ||
0.994991 | − | 0.0999617i | \(-0.0318720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.2775 | −0.0758402 | −0.0379201 | − | 0.999281i | \(-0.512073\pi\) | ||||
−0.0379201 | + | 0.999281i | \(0.512073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.77322 | − | 8.77322i | −0.0358090 | − | 0.0358090i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 285.210i | 1.15470i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −300.658 | − | 300.658i | −1.19784 | − | 1.19784i | −0.974812 | − | 0.223027i | \(-0.928406\pi\) |
−0.223027 | − | 0.974812i | \(-0.571594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −83.7977 | − | 83.7977i | −0.331216 | − | 0.331216i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 170.456i | − | 0.663254i | −0.943411 | − | 0.331627i | \(-0.892402\pi\) | ||
0.943411 | − | 0.331627i | \(-0.107598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −87.2882 | − | 87.2882i | −0.337020 | − | 0.337020i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −294.979 | −1.12159 | −0.560797 | − | 0.827953i | \(-0.689505\pi\) | ||||
−0.560797 | + | 0.827953i | \(0.689505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 80.4033i | 0.303409i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −129.972 | + | 129.972i | −0.483165 | + | 0.483165i | −0.906141 | − | 0.422976i | \(-0.860986\pi\) |
0.422976 | + | 0.906141i | \(0.360986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −535.196 | −1.97489 | −0.987447 | − | 0.157953i | \(-0.949511\pi\) | ||||
−0.987447 | + | 0.157953i | \(0.949511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −106.975 | + | 106.975i | −0.389001 | + | 0.389001i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 62.0846 | − | 62.0846i | 0.224132 | − | 0.224132i | −0.586104 | − | 0.810236i | \(-0.699339\pi\) |
0.810236 | + | 0.586104i | \(0.199339\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 102.299 | 0.364055 | 0.182027 | − | 0.983293i | \(-0.441734\pi\) | ||||
0.182027 | + | 0.983293i | \(0.441734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −164.906 | + | 164.906i | −0.582705 | + | 0.582705i | −0.935646 | − | 0.352940i | \(-0.885182\pi\) |
0.352940 | + | 0.935646i | \(0.385182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 350.185i | − | 1.22016i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 288.998 | 0.999993 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 203.242 | + | 203.242i | 0.693658 | + | 0.693658i | 0.963035 | − | 0.269377i | \(-0.0868177\pi\) |
−0.269377 | + | 0.963035i | \(0.586818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.3779i | 0.126705i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −201.130 | − | 201.130i | −0.672677 | − | 0.672677i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 394.464 | + | 394.464i | 1.31051 | + | 1.31051i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.36957i | 0.0143265i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 133.116 | + | 133.116i | 0.433602 | + | 0.433602i | 0.889852 | − | 0.456250i | \(-0.150808\pi\) |
−0.456250 | + | 0.889852i | \(0.650808\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 260.983 | 0.839175 | 0.419587 | − | 0.907715i | \(-0.362175\pi\) | ||||
0.419587 | + | 0.907715i | \(0.362175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 157.967i | − | 0.504686i | −0.967638 | − | 0.252343i | \(-0.918799\pi\) | ||
0.967638 | − | 0.252343i | \(-0.0812011\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −136.209 | + | 136.209i | −0.429683 | + | 0.429683i | −0.888520 | − | 0.458838i | \(-0.848266\pi\) |
0.458838 | + | 0.888520i | \(0.348266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −320.074 | −1.00337 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.565134 | + | 0.565134i | −0.00174964 | + | 0.00174964i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −256.761 | + | 256.761i | −0.790035 | + | 0.790035i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −433.596 | −1.31792 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −432.414 | + | 432.414i | −1.30639 | + | 1.30639i | −0.382385 | + | 0.924003i | \(0.624897\pi\) |
−0.924003 | + | 0.382385i | \(0.875103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.0442i | 0.101624i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −383.585 | −1.13823 | −0.569117 | − | 0.822256i | \(-0.692715\pi\) | ||||
−0.569117 | + | 0.822256i | \(0.692715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −175.975 | − | 175.975i | −0.516057 | − | 0.516057i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 300.866i | 0.877159i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −111.739 | − | 111.739i | −0.322014 | − | 0.322014i | 0.527526 | − | 0.849539i | \(-0.323120\pi\) |
−0.849539 | + | 0.527526i | \(0.823120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 431.263 | + | 431.263i | 1.23571 | + | 1.23571i | 0.961738 | + | 0.273971i | \(0.0883374\pi\) |
0.273971 | + | 0.961738i | \(0.411663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 290.324i | 0.822448i | 0.911534 | + | 0.411224i | \(0.134899\pi\) | ||||
−0.911534 | + | 0.411224i | \(0.865101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 103.405 | + | 103.405i | 0.291282 | + | 0.291282i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 81.9699 | 0.228329 | 0.114164 | − | 0.993462i | \(-0.463581\pi\) | ||||
0.114164 | + | 0.993462i | \(0.463581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 23.7867i | − | 0.0658912i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 114.906 | − | 114.906i | 0.314810 | − | 0.314810i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −112.713 | −0.307121 | −0.153560 | − | 0.988139i | \(-0.549074\pi\) | ||||
−0.153560 | + | 0.988139i | \(0.549074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −342.298 | + | 342.298i | −0.922636 | + | 0.922636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.7139 | − | 32.7139i | 0.0877049 | − | 0.0877049i | −0.661893 | − | 0.749598i | \(-0.730247\pi\) |
0.749598 | + | 0.661893i | \(0.230247\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −768.238 | −2.03777 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 413.066 | − | 413.066i | 1.08988 | − | 1.08988i | 0.0943432 | − | 0.995540i | \(-0.469925\pi\) |
0.995540 | − | 0.0943432i | \(-0.0300751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 616.895i | − | 1.61069i | −0.592805 | − | 0.805346i | \(-0.701980\pi\) | ||
0.592805 | − | 0.805346i | \(-0.298020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 63.1393 | 0.163998 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 414.902 | + | 414.902i | 1.06659 | + | 1.06659i | 0.997619 | + | 0.0689668i | \(0.0219703\pi\) |
0.0689668 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.797066i | − | 0.00203853i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.3322 | + | 33.3322i | 0.0843854 | + | 0.0843854i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 252.200 | + | 252.200i | 0.635266 | + | 0.635266i | 0.949384 | − | 0.314118i | \(-0.101709\pi\) |
−0.314118 | + | 0.949384i | \(0.601709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 161.463i | 0.402651i | 0.979524 | + | 0.201325i | \(0.0645249\pi\) | ||||
−0.979524 | + | 0.201325i | \(0.935475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −422.375 | − | 422.375i | −1.04808 | − | 1.04808i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 104.219 | 0.256067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 156.176i | 0.381847i | 0.981605 | + | 0.190924i | \(0.0611483\pi\) | ||||
−0.981605 | + | 0.190924i | \(0.938852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −159.127 | + | 159.127i | −0.385296 | + | 0.385296i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −152.011 | −0.366291 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 530.843 | − | 530.843i | 1.26693 | − | 1.26693i | 0.319260 | − | 0.947667i | \(-0.396566\pi\) |
0.947667 | − | 0.319260i | \(-0.103434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −198.004 | + | 198.004i | −0.470318 | + | 0.470318i | −0.902017 | − | 0.431700i | \(-0.857914\pi\) |
0.431700 | + | 0.902017i | \(0.357914\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.01753 | −0.00239418 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.6024 | + | 18.6024i | −0.0435654 | + | 0.0435654i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 418.584i | 0.971192i | 0.874183 | + | 0.485596i | \(0.161397\pi\) | ||||
−0.874183 | + | 0.485596i | \(0.838603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 747.383 | 1.72606 | 0.863029 | − | 0.505154i | \(-0.168564\pi\) | ||||
0.863029 | + | 0.505154i | \(0.168564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −237.803 | − | 237.803i | −0.544172 | − | 0.544172i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 304.573i | 0.693789i | 0.937904 | + | 0.346894i | \(0.112764\pi\) | ||||
−0.937904 | + | 0.346894i | \(0.887236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −479.719 | − | 479.719i | −1.08289 | − | 1.08289i | −0.996239 | − | 0.0866493i | \(-0.972384\pi\) |
−0.0866493 | − | 0.996239i | \(-0.527616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 122.579 | + | 122.579i | 0.275459 | + | 0.275459i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 485.831i | − | 1.08203i | −0.841013 | − | 0.541015i | \(-0.818040\pi\) | ||
0.841013 | − | 0.541015i | \(-0.181960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 209.055 | + | 209.055i | 0.463536 | + | 0.463536i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 151.546 | 0.333069 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 413.632i | 0.905102i | 0.891738 | + | 0.452551i | \(0.149486\pi\) | ||||
−0.891738 | + | 0.452551i | \(0.850514\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −54.2195 | + | 54.2195i | −0.117613 | + | 0.117613i | −0.763464 | − | 0.645851i | \(-0.776503\pi\) |
0.645851 | + | 0.763464i | \(0.276503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −135.028 | −0.291637 | −0.145819 | − | 0.989311i | \(-0.546582\pi\) | ||||
−0.145819 | + | 0.989311i | \(0.546582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −583.642 | + | 583.642i | −1.24977 | + | 1.24977i | −0.293947 | + | 0.955822i | \(0.594969\pi\) |
−0.955822 | + | 0.293947i | \(0.905031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −144.935 | + | 144.935i | −0.309030 | + | 0.309030i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −470.977 | −0.995722 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −303.578 | + | 303.578i | −0.639111 | + | 0.639111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 51.0721i | − | 0.106622i | −0.998578 | − | 0.0533112i | \(-0.983022\pi\) | ||
0.998578 | − | 0.0533112i | \(-0.0169775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 250.146 | 0.520053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −156.159 | − | 156.159i | −0.321977 | − | 0.321977i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 490.285i | 1.00674i | 0.864070 | + | 0.503372i | \(0.167908\pi\) | ||||
−0.864070 | + | 0.503372i | \(0.832092\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −219.757 | − | 219.757i | −0.447570 | − | 0.447570i | 0.446976 | − | 0.894546i | \(-0.352501\pi\) |
−0.894546 | + | 0.446976i | \(0.852501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.52224 | − | 1.52224i | −0.00308770 | − | 0.00308770i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 880.446i | 1.77152i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −435.155 | − | 435.155i | −0.872054 | − | 0.872054i | 0.120642 | − | 0.992696i | \(-0.461505\pi\) |
−0.992696 | + | 0.120642i | \(0.961505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 46.8803 | 0.0932014 | 0.0466007 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466007 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 33.1781i | − | 0.0656993i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −166.731 | + | 166.731i | −0.327566 | + | 0.327566i | −0.851660 | − | 0.524094i | \(-0.824404\pi\) |
0.524094 | + | 0.851660i | \(0.324404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 978.368 | 1.91461 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 80.0236 | − | 80.0236i | 0.155386 | − | 0.155386i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 258.849 | − | 258.849i | 0.500676 | − | 0.500676i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 351.071 | 0.673840 | 0.336920 | − | 0.941533i | \(-0.390615\pi\) | ||||
0.336920 | + | 0.941533i | \(0.390615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −214.780 | + | 214.780i | −0.410670 | + | 0.410670i | −0.881972 | − | 0.471302i | \(-0.843784\pi\) |
0.471302 | + | 0.881972i | \(0.343784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.67384i | − | 0.00317617i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −193.601 | −0.365976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 501.771 | + | 501.771i | 0.941409 | + | 0.941409i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 97.8986i | 0.182988i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.5945 | + | 44.5945i | 0.0827356 | + | 0.0827356i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −579.728 | − | 579.728i | −1.07159 | − | 1.07159i | −0.997232 | − | 0.0743548i | \(-0.976310\pi\) |
−0.0743548 | − | 0.997232i | \(-0.523690\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 219.679i | − | 0.403080i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −100.142 | − | 100.142i | −0.183075 | − | 0.183075i | 0.609619 | − | 0.792694i | \(-0.291322\pi\) |
−0.792694 | + | 0.609619i | \(0.791322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −908.314 | −1.64848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 283.808i | 0.513215i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 644.771 | − | 644.771i | 1.15758 | − | 1.15758i | 0.172584 | − | 0.984995i | \(-0.444788\pi\) |
0.984995 | − | 0.172584i | \(-0.0552116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1130.43 | −2.02224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 418.555 | − | 418.555i | 0.743436 | − | 0.743436i | −0.229801 | − | 0.973238i | \(-0.573808\pi\) |
0.973238 | + | 0.229801i | \(0.0738076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 146.391 | − | 146.391i | 0.259098 | − | 0.259098i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 652.285 | 1.14637 | 0.573186 | − | 0.819426i | \(-0.305707\pi\) | ||||
0.573186 | + | 0.819426i | \(0.305707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.6933 | + | 13.6933i | −0.0239813 | + | 0.0239813i | −0.718996 | − | 0.695014i | \(-0.755398\pi\) |
0.695014 | + | 0.718996i | \(0.255398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 428.167i | − | 0.744638i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −269.997 | −0.467932 | −0.233966 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233966 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −647.150 | − | 647.150i | −1.11386 | − | 1.11386i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 408.692i | − | 0.701015i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 784.885 | + | 784.885i | 1.33711 | + | 1.33711i | 0.898844 | + | 0.438269i | \(0.144408\pi\) |
0.438269 | + | 0.898844i | \(0.355592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −499.388 | − | 499.388i | −0.847857 | − | 0.847857i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 451.885i | − | 0.762032i | −0.924569 | − | 0.381016i | \(-0.875574\pi\) | ||
0.924569 | − | 0.381016i | \(-0.124426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.300284 | + | 0.300284i | 0.000504679 | + | 0.000504679i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 664.313 | 1.10904 | 0.554518 | − | 0.832171i | \(-0.312902\pi\) | ||||
0.554518 | + | 0.832171i | \(0.312902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 496.693i | − | 0.826444i | −0.910630 | − | 0.413222i | \(-0.864403\pi\) | ||
0.910630 | − | 0.413222i | \(-0.135597\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 71.2286 | − | 71.2286i | 0.117733 | − | 0.117733i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 595.964 | 0.981819 | 0.490910 | − | 0.871210i | \(-0.336665\pi\) | ||||
0.490910 | + | 0.871210i | \(0.336665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 621.287 | − | 621.287i | 1.01684 | − | 1.01684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −228.109 | + | 228.109i | −0.372119 | + | 0.372119i | −0.868249 | − | 0.496129i | \(-0.834754\pi\) |
0.496129 | + | 0.868249i | \(0.334754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 199.680 | 0.323631 | 0.161815 | − | 0.986821i | \(-0.448265\pi\) | ||||
0.161815 | + | 0.986821i | \(0.448265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.72024 | − | 8.72024i | 0.0140876 | − | 0.0140876i | −0.700028 | − | 0.714116i | \(-0.746829\pi\) |
0.714116 | + | 0.700028i | \(0.246829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1043.70i | 1.67529i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −506.078 | −0.809725 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.495655 | + | 0.495655i | 0.000788005 | + | 0.000788005i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 558.798i | − | 0.885575i | −0.896627 | − | 0.442788i | \(-0.853990\pi\) | ||
0.896627 | − | 0.442788i | \(-0.146010\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.6506 | + | 32.6506i | 0.0514182 | + | 0.0514182i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 107.035 | + | 107.035i | 0.168030 | + | 0.168030i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 549.401i | 0.857100i | 0.903518 | + | 0.428550i | \(0.140975\pi\) | ||||
−0.903518 | + | 0.428550i | \(0.859025\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 615.401 | + | 615.401i | 0.957078 | + | 0.957078i | 0.999116 | − | 0.0420379i | \(-0.0133850\pi\) |
−0.0420379 | + | 0.999116i | \(0.513385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1040.44 | −1.60810 | −0.804051 | − | 0.594560i | \(-0.797326\pi\) | ||||
−0.804051 | + | 0.594560i | \(0.797326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 189.993i | − | 0.292747i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −359.946 | + | 359.946i | −0.551218 | + | 0.551218i | −0.926792 | − | 0.375574i | \(-0.877446\pi\) |
0.375574 | + | 0.926792i | \(0.377446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 107.842 | 0.164644 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −675.277 | + | 675.277i | −1.02470 | + | 1.02470i | −0.0250117 | + | 0.999687i | \(0.507962\pi\) |
−0.999687 | + | 0.0250117i | \(0.992038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 118.754 | − | 118.754i | 0.179659 | − | 0.179659i | −0.611548 | − | 0.791207i | \(-0.709453\pi\) |
0.791207 | + | 0.611548i | \(0.209453\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 179.178 | 0.269441 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 640.545 | − | 640.545i | 0.960337 | − | 0.960337i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.2106i | − | 0.0331008i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −226.637 | −0.336757 | −0.168378 | − | 0.985722i | \(-0.553853\pi\) | ||||
−0.168378 | + | 0.985722i | \(0.553853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 529.591 | + | 529.591i | 0.782261 | + | 0.782261i | 0.980212 | − | 0.197951i | \(-0.0634287\pi\) |
−0.197951 | + | 0.980212i | \(0.563429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1329.62i | − | 1.95820i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 582.521 | + | 582.521i | 0.852885 | + | 0.852885i | 0.990488 | − | 0.137602i | \(-0.0439395\pi\) |
−0.137602 | + | 0.990488i | \(0.543940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 88.6783 | + | 88.6783i | 0.129457 | + | 0.129457i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 980.938i | − | 1.42371i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 670.134 | + | 670.134i | 0.969803 | + | 0.969803i | 0.999557 | − | 0.0297546i | \(-0.00947258\pi\) |
−0.0297546 | + | 0.999557i | \(0.509473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.12050 | −0.00880647 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.98848i | 0.00285292i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −291.428 | + | 291.428i | −0.415732 | + | 0.415732i | −0.883730 | − | 0.467998i | \(-0.844976\pi\) |
0.467998 | + | 0.883730i | \(0.344976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 295.756 | 0.420705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 141.248 | − | 141.248i | 0.199785 | − | 0.199785i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 459.988 | − | 459.988i | 0.648784 | − | 0.648784i | −0.303915 | − | 0.952699i | \(-0.598294\pi\) |
0.952699 | + | 0.303915i | \(0.0982940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 704.338 | 0.987852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −90.4706 | + | 90.4706i | −0.126532 | + | 0.126532i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 285.232i | 0.396707i | 0.980131 | + | 0.198353i | \(0.0635594\pi\) | ||||
−0.980131 | + | 0.198353i | \(0.936441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 681.363 | 0.945025 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −817.714 | − | 817.714i | −1.12788 | − | 1.12788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 114.350i | 0.157290i | 0.996903 | + | 0.0786451i | \(0.0250594\pi\) | ||||
−0.996903 | + | 0.0786451i | \(0.974941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.23992 | − | 2.23992i | −0.00306418 | − | 0.00306418i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 158.553 | + | 158.553i | 0.216307 | + | 0.216307i | 0.806940 | − | 0.590633i | \(-0.201122\pi\) |
−0.590633 | + | 0.806940i | \(0.701122\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 173.047i | − | 0.234800i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 381.275 | + | 381.275i | 0.515933 | + | 0.515933i | 0.916338 | − | 0.400405i | \(-0.131131\pi\) |
−0.400405 | + | 0.916338i | \(0.631131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 445.947 | 0.600198 | 0.300099 | − | 0.953908i | \(-0.402980\pi\) | ||||
0.300099 | + | 0.953908i | \(0.402980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.2603i | 0.0218259i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −416.780 | + | 416.780i | −0.556449 | + | 0.556449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 774.061 | 1.03071 | 0.515353 | − | 0.856978i | \(-0.327661\pi\) | ||||
0.515353 | + | 0.856978i | \(0.327661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 62.1617 | − | 62.1617i | 0.0823333 | − | 0.0823333i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 431.310 | − | 431.310i | 0.569763 | − | 0.569763i | −0.362299 | − | 0.932062i | \(-0.618008\pi\) |
0.932062 | + | 0.362299i | \(0.118008\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1493.05 | 1.96195 | 0.980977 | − | 0.194123i | \(-0.0621861\pi\) | ||||
0.980977 | + | 0.194123i | \(0.0621861\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 935.229 | − | 935.229i | 1.22573 | − | 1.22573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 456.019i | − | 0.594548i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −823.023 | −1.07025 | −0.535126 | − | 0.844772i | \(-0.679736\pi\) | ||||
−0.535126 | + | 0.844772i | \(0.679736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −322.532 | − | 322.532i | −0.417247 | − | 0.417247i | 0.467007 | − | 0.884254i | \(-0.345332\pi\) |
−0.884254 | + | 0.467007i | \(0.845332\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 899.152i | − | 1.16020i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 593.261 | + | 593.261i | 0.761567 | + | 0.761567i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −525.611 | − | 525.611i | −0.672998 | − | 0.672998i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 114.696i | − | 0.146109i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −470.300 | − | 470.300i | −0.597586 | − | 0.597586i | 0.342083 | − | 0.939670i | \(-0.388867\pi\) |
−0.939670 | + | 0.342083i | \(0.888867\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1246.45 | 1.57579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 53.3098i | − | 0.0672255i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 775.967 | − | 775.967i | 0.973610 | − | 0.973610i | −0.0260505 | − | 0.999661i | \(-0.508293\pi\) |
0.999661 | + | 0.0260505i | \(0.00829308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.46212 | 0.00308150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −584.069 | + | 584.069i | −0.727359 | + | 0.727359i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −126.357 | + | 126.357i | −0.156965 | + | 0.156965i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −812.614 | −1.00447 | −0.502234 | − | 0.864732i | \(-0.667488\pi\) | ||||
−0.502234 | + | 0.864732i | \(0.667488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −229.002 | + | 229.002i | −0.282369 | + | 0.282369i | −0.834053 | − | 0.551684i | \(-0.813985\pi\) |
0.551684 | + | 0.834053i | \(0.313985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 190.171i | 0.233338i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1336.55 | −1.63592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 781.504 | + | 781.504i | 0.951893 | + | 0.951893i | 0.998895 | − | 0.0470014i | \(-0.0149665\pi\) |
−0.0470014 | + | 0.998895i | \(0.514967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 757.548i | 0.920472i | 0.887797 | + | 0.460236i | \(0.152235\pi\) | ||||
−0.887797 | + | 0.460236i | \(0.847765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 168.079 | + | 168.079i | 0.203240 | + | 0.203240i | 0.801387 | − | 0.598147i | \(-0.204096\pi\) |
−0.598147 | + | 0.801387i | \(0.704096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1044.13 | − | 1044.13i | −1.25950 | − | 1.25950i | −0.951331 | − | 0.308171i | \(-0.900283\pi\) |
−0.308171 | − | 0.951331i | \(-0.599717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.424174i | 0.000509212i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −230.195 | − | 230.195i | −0.275683 | − | 0.275683i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1052.57 | −1.25456 | −0.627278 | − | 0.778796i | \(-0.715831\pi\) | ||||
−0.627278 | + | 0.778796i | \(0.715831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1605.63i | − | 1.90919i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −65.0162 | + | 65.0162i | −0.0769423 | + | 0.0769423i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 606.478 | 0.716030 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −208.567 | + | 208.567i | −0.245085 | + | 0.245085i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 101.196 | − | 101.196i | 0.118636 | − | 0.118636i | −0.645296 | − | 0.763932i | \(-0.723266\pi\) |
0.763932 | + | 0.645296i | \(0.223266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 280.731 | 0.327574 | 0.163787 | − | 0.986496i | \(-0.447629\pi\) | ||||
0.163787 | + | 0.986496i | \(0.447629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 743.635 | − | 743.635i | 0.865699 | − | 0.865699i | −0.126294 | − | 0.991993i | \(-0.540308\pi\) |
0.991993 | + | 0.126294i | \(0.0403083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 98.7005i | − | 0.114369i | −0.998364 | − | 0.0571845i | \(-0.981788\pi\) | ||
0.998364 | − | 0.0571845i | \(-0.0182123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −102.540 | −0.118543 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −169.429 | − | 169.429i | −0.194970 | − | 0.194970i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 415.347i | − | 0.476862i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 333.794 | + | 333.794i | 0.381479 | + | 0.381479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −552.841 | − | 552.841i | −0.630378 | − | 0.630378i | 0.317785 | − | 0.948163i | \(-0.397061\pi\) |
−0.948163 | + | 0.317785i | \(0.897061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 316.248i | − | 0.358965i | −0.983761 | − | 0.179482i | \(-0.942558\pi\) | ||
0.983761 | − | 0.179482i | \(-0.0574423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 98.6469 | + | 98.6469i | 0.111718 | + | 0.111718i | 0.760756 | − | 0.649038i | \(-0.224828\pi\) |
−0.649038 | + | 0.760756i | \(0.724828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1426.43 | 1.60815 | 0.804074 | − | 0.594530i | \(-0.202662\pi\) | ||||
0.804074 | + | 0.594530i | \(0.202662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 278.004i | 0.312715i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 734.570 | − | 734.570i | 0.822586 | − | 0.822586i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 309.045 | 0.345302 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1345.15 | − | 1345.15i | 1.49627 | − | 1.49627i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.94370 | − | 1.94370i | 0.00215727 | − | 0.00215727i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −99.9442 | −0.110436 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −238.634 | + | 238.634i | −0.263103 | + | 0.263103i | −0.826313 | − | 0.563211i | \(-0.809566\pi\) |
0.563211 | + | 0.826313i | \(0.309566\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1309.38i | 1.43730i | 0.695374 | + | 0.718648i | \(0.255239\pi\) | ||||
−0.695374 | + | 0.718648i | \(0.744761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 772.676 | 0.846304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 459.112 | + | 459.112i | 0.500667 | + | 0.500667i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 511.000i | 0.556039i | 0.960575 | + | 0.278019i | \(0.0896779\pi\) | ||||
−0.960575 | + | 0.278019i | \(0.910322\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1261.57 | − | 1261.57i | −1.36681 | − | 1.36681i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 266.255 | + | 266.255i | 0.287844 | + | 0.287844i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 386.394i | − | 0.415924i | −0.978137 | − | 0.207962i | \(-0.933317\pi\) | ||
0.978137 | − | 0.207962i | \(-0.0666831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 126.551 | + | 126.551i | 0.135931 | + | 0.135931i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.358529 | −0.000383453 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 927.440i | − | 0.989797i | −0.868951 | − | 0.494898i | \(-0.835205\pi\) | ||
0.868951 | − | 0.494898i | \(-0.164795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 645.746 | − | 645.746i | 0.686234 | − | 0.686234i | −0.275164 | − | 0.961397i | \(-0.588732\pi\) |
0.961397 | + | 0.275164i | \(0.0887320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −836.737 | −0.887314 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1017.28 | + | 1017.28i | −1.07421 | + | 1.07421i | −0.0771972 | + | 0.997016i | \(0.524597\pi\) |
−0.997016 | + | 0.0771972i | \(0.975403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1401.88 | + | 1401.88i | −1.47721 | + | 1.47721i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −214.062 | −0.224619 | −0.112309 | − | 0.993673i | \(-0.535825\pi\) | ||||
−0.112309 | + | 0.993673i | \(0.535825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −91.7708 | + | 91.7708i | −0.0960951 | + | 0.0960951i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 755.054i | 0.787334i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 518.114 | 0.539140 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.3653 | + | 73.3653i | 0.0760262 | + | 0.0760262i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 440.861i | 0.455906i | 0.973672 | + | 0.227953i | \(0.0732033\pi\) | ||||
−0.973672 | + | 0.227953i | \(0.926797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 343.159 | + | 343.159i | 0.353407 | + | 0.353407i | 0.861376 | − | 0.507968i | \(-0.169603\pi\) |
−0.507968 | + | 0.861376i | \(0.669603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.0566 | − | 26.0566i | −0.0267796 | − | 0.0267796i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 388.323i | 0.397465i | 0.980054 | + | 0.198733i | \(0.0636825\pi\) | ||||
−0.980054 | + | 0.198733i | \(0.936317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −623.073 | − | 623.073i | −0.636439 | − | 0.636439i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1344.22 | −1.36746 | −0.683731 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683731 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 307.279i | − | 0.311958i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 942.538 | − | 942.538i | 0.953021 | − | 0.953021i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1058.38 | 1.06799 | 0.533997 | − | 0.845486i | \(-0.320689\pi\) | ||||
0.533997 | + | 0.845486i | \(0.320689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 168.716 | − | 168.716i | 0.169563 | − | 0.169563i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 554.656 | − | 554.656i | 0.556325 | − | 0.556325i | −0.371934 | − | 0.928259i | \(-0.621305\pi\) |
0.928259 | + | 0.371934i | \(0.121305\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1152.3.j.a.161.9 | 32 | ||
3.2 | odd | 2 | inner | 1152.3.j.a.161.8 | 32 | ||
4.3 | odd | 2 | 1152.3.j.b.161.9 | 32 | |||
8.3 | odd | 2 | 576.3.j.a.17.8 | 32 | |||
8.5 | even | 2 | 144.3.j.a.125.6 | yes | 32 | ||
12.11 | even | 2 | 1152.3.j.b.161.8 | 32 | |||
16.3 | odd | 4 | 576.3.j.a.305.9 | 32 | |||
16.5 | even | 4 | inner | 1152.3.j.a.737.8 | 32 | ||
16.11 | odd | 4 | 1152.3.j.b.737.8 | 32 | |||
16.13 | even | 4 | 144.3.j.a.53.11 | yes | 32 | ||
24.5 | odd | 2 | 144.3.j.a.125.11 | yes | 32 | ||
24.11 | even | 2 | 576.3.j.a.17.9 | 32 | |||
48.5 | odd | 4 | inner | 1152.3.j.a.737.9 | 32 | ||
48.11 | even | 4 | 1152.3.j.b.737.9 | 32 | |||
48.29 | odd | 4 | 144.3.j.a.53.6 | ✓ | 32 | ||
48.35 | even | 4 | 576.3.j.a.305.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.j.a.53.6 | ✓ | 32 | 48.29 | odd | 4 | ||
144.3.j.a.53.11 | yes | 32 | 16.13 | even | 4 | ||
144.3.j.a.125.6 | yes | 32 | 8.5 | even | 2 | ||
144.3.j.a.125.11 | yes | 32 | 24.5 | odd | 2 | ||
576.3.j.a.17.8 | 32 | 8.3 | odd | 2 | |||
576.3.j.a.17.9 | 32 | 24.11 | even | 2 | |||
576.3.j.a.305.8 | 32 | 48.35 | even | 4 | |||
576.3.j.a.305.9 | 32 | 16.3 | odd | 4 | |||
1152.3.j.a.161.8 | 32 | 3.2 | odd | 2 | inner | ||
1152.3.j.a.161.9 | 32 | 1.1 | even | 1 | trivial | ||
1152.3.j.a.737.8 | 32 | 16.5 | even | 4 | inner | ||
1152.3.j.a.737.9 | 32 | 48.5 | odd | 4 | inner | ||
1152.3.j.b.161.8 | 32 | 12.11 | even | 2 | |||
1152.3.j.b.161.9 | 32 | 4.3 | odd | 2 | |||
1152.3.j.b.737.8 | 32 | 16.11 | odd | 4 | |||
1152.3.j.b.737.9 | 32 | 48.11 | even | 4 |