Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.249 |
Dual form | 1400.2.bh.e.849.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205 | + | 1.00000i | 1.00000 | + | 0.577350i | 0.908248 | − | 0.418432i | \(-0.137420\pi\) |
0.0917517 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.00000i | − | 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73205 | − | 1.00000i | −0.420084 | − | 0.242536i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 5.19615i | −0.218218 | − | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.06218 | − | 3.50000i | 1.26405 | − | 0.729800i | 0.290196 | − | 0.956967i | \(-0.406280\pi\) |
0.973856 | + | 0.227167i | \(0.0729463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73205 | − | 1.00000i | 0.301511 | − | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.33013 | − | 2.50000i | 0.711868 | − | 0.410997i | −0.0998840 | − | 0.994999i | \(-0.531847\pi\) |
0.811752 | + | 0.584002i | \(0.198514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | − | 5.19615i | 0.480384 | − | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.79423 | − | 4.50000i | 1.13691 | − | 0.656392i | 0.191243 | − | 0.981543i | \(-0.438748\pi\) |
0.945662 | + | 0.325150i | \(0.105415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.52628 | − | 5.50000i | −1.30854 | − | 0.755483i | −0.326683 | − | 0.945134i | \(-0.605931\pi\) |
−0.981852 | + | 0.189651i | \(0.939264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 10.0000i | − | 1.32453i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.866025 | − | 2.50000i | 0.109109 | − | 0.314970i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.0000 | 1.68540 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3923 | − | 6.00000i | −1.21633 | − | 0.702247i | −0.252197 | − | 0.967676i | \(-0.581153\pi\) |
−0.964130 | + | 0.265429i | \(0.914486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.59808 | + | 0.500000i | −0.296078 | + | 0.0569803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3923 | + | 6.00000i | 1.11417 | + | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 5.19615i | −0.628971 | + | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | + | 4.00000i | −0.718421 | + | 0.414781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3205 | − | 10.0000i | 1.70664 | − | 0.985329i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
0.938652 | − | 0.344865i | \(-0.112075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | \(-0.863630\pi\) |
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.0000i | 1.88144i | 0.339182 | + | 0.940721i | \(0.389850\pi\) | ||||
−0.339182 | + | 0.940721i | \(0.610150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.59808 | − | 1.50000i | 0.240192 | − | 0.138675i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | + | 5.19615i | 0.0916698 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.66025 | − | 5.00000i | −0.780869 | − | 0.450835i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0000i | − | 1.50851i | −0.656584 | − | 0.754253i | \(-0.727999\pi\) | ||
0.656584 | − | 0.754253i | \(-0.272001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | + | 10.3923i | −0.528271 | + | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.50000 | − | 6.06218i | −0.305796 | − | 0.529655i | 0.671642 | − | 0.740876i | \(-0.265589\pi\) |
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33013 | + | 12.5000i | −0.375470 | + | 1.08389i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0000 | 1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.59808 | − | 1.50000i | −0.217262 | − | 0.125436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.66025 | + | 11.0000i | −0.714286 | + | 0.907265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.33013 | + | 2.50000i | 0.345582 | + | 0.199522i | 0.662738 | − | 0.748852i | \(-0.269394\pi\) |
−0.317156 | + | 0.948373i | \(0.602728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.0000 | − | 19.0526i | −0.872357 | − | 1.51097i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.5000 | − | 6.06218i | −1.37919 | − | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410 | − | 2.00000i | 0.271329 | − | 0.156652i | −0.358162 | − | 0.933659i | \(-0.616597\pi\) |
0.629492 | + | 0.777007i | \(0.283263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.00000i | − | 0.386912i | −0.981109 | − | 0.193456i | \(-0.938030\pi\) | ||
0.981109 | − | 0.193456i | \(-0.0619696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.50000 | − | 4.33013i | 0.191180 | − | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4545 | − | 9.50000i | 1.25101 | − | 0.722272i | 0.279701 | − | 0.960087i | \(-0.409765\pi\) |
0.971310 | + | 0.237816i | \(0.0764314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8564 | − | 8.00000i | 1.04151 | − | 0.601317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0000i | 1.77413i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73205 | + | 1.00000i | −0.126660 | + | 0.0731272i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | + | 6.92820i | −0.581914 | + | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3205 | + | 10.0000i | 1.24676 | + | 0.719816i | 0.970461 | − | 0.241257i | \(-0.0775596\pi\) |
0.276296 | + | 0.961073i | \(0.410893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.0000i | 1.92367i | 0.273629 | + | 0.961835i | \(0.411776\pi\) | ||||
−0.273629 | + | 0.961835i | \(0.588224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3923 | − | 12.0000i | −0.729397 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.06218 | + | 3.50000i | 0.421350 | + | 0.243267i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | − | 4.00000i | −0.474713 | − | 0.274075i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3923 | − | 2.00000i | 0.705476 | − | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | − | 20.7846i | −0.810885 | − | 1.40449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.0000i | − | 1.07144i | −0.844396 | − | 0.535720i | \(-0.820040\pi\) | ||
0.844396 | − | 0.535720i | \(-0.179960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.92820 | − | 4.00000i | −0.459841 | − | 0.265489i | 0.252136 | − | 0.967692i | \(-0.418867\pi\) |
−0.711977 | + | 0.702202i | \(0.752200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | − | 24.2487i | −0.925146 | − | 1.60240i | −0.791326 | − | 0.611394i | \(-0.790609\pi\) |
−0.133820 | − | 0.991006i | \(-0.542724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | − | 1.73205i | −0.328976 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.73205 | − | 1.00000i | 0.113470 | − | 0.0655122i | −0.442191 | − | 0.896921i | \(-0.645799\pi\) |
0.555661 | + | 0.831409i | \(0.312465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28.0000i | 1.81880i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.66025 | − | 5.00000i | 0.555556 | − | 0.320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9904 | + | 7.50000i | −0.826558 | + | 0.477214i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | − | 6.92820i | 0.253490 | − | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.0000 | 1.83046 | 0.915232 | − | 0.402928i | \(-0.132007\pi\) | ||||
0.915232 | + | 0.402928i | \(0.132007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.00000i | − | 0.440086i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3923 | + | 6.00000i | −0.648254 | + | 0.374270i | −0.787787 | − | 0.615948i | \(-0.788773\pi\) |
0.139533 | + | 0.990217i | \(0.455440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5000 | − | 4.33013i | −0.776712 | − | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.92820 | − | 4.00000i | −0.427211 | − | 0.246651i | 0.270947 | − | 0.962594i | \(-0.412663\pi\) |
−0.698158 | + | 0.715944i | \(0.745997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000i | 0.734388i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.5885 | + | 3.00000i | −0.943456 | + | 0.181568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73205 | + | 1.00000i | 0.104069 | + | 0.0600842i | 0.551131 | − | 0.834419i | \(-0.314196\pi\) |
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0526 | + | 11.0000i | 1.13256 | + | 0.653882i | 0.944577 | − | 0.328291i | \(-0.106473\pi\) |
0.187980 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.66025 | + | 10.0000i | 0.511199 | + | 0.590281i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 10.3923i | 0.351726 | − | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0000i | 1.22683i | 0.789760 | + | 0.613417i | \(0.210205\pi\) | ||||
−0.789760 | + | 0.613417i | \(0.789795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.46410 | − | 2.00000i | −0.201008 | − | 0.116052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5000 | − | 18.1865i | −0.607231 | − | 1.05175i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | − | 10.3923i | 0.691669 | − | 0.599002i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.7846 | + | 12.0000i | −1.19404 | + | 0.689382i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000i | 0.342438i | 0.985233 | + | 0.171219i | \(0.0547706\pi\) | ||||
−0.985233 | + | 0.171219i | \(0.945229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.0000 | 2.27552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.00000 | − | 3.46410i | 0.113410 | − | 0.196431i | −0.803733 | − | 0.594990i | \(-0.797156\pi\) |
0.917143 | + | 0.398559i | \(0.130489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8564 | − | 8.00000i | 0.783210 | − | 0.452187i | −0.0543564 | − | 0.998522i | \(-0.517311\pi\) |
0.837567 | + | 0.546335i | \(0.183977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.73205 | + | 1.00000i | −0.0972817 | + | 0.0561656i | −0.547852 | − | 0.836576i | \(-0.684554\pi\) |
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0000i | 0.556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.92820 | + | 4.00000i | −0.383131 | + | 0.221201i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5000 | − | 7.79423i | −1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5000 | + | 23.3827i | 0.742027 | + | 1.28523i | 0.951571 | + | 0.307429i | \(0.0994688\pi\) |
−0.209544 | + | 0.977799i | \(0.567198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.33013 | + | 2.50000i | 0.237289 | + | 0.136999i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000i | 1.41631i | 0.706057 | + | 0.708155i | \(0.250472\pi\) | ||||
−0.706057 | + | 0.708155i | \(0.749528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.0000 | + | 34.6410i | −1.08625 | + | 1.88144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.92820 | + | 4.00000i | 0.371925 | + | 0.214731i | 0.674299 | − | 0.738458i | \(-0.264446\pi\) |
−0.302374 | + | 0.953189i | \(0.597779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0000 | −0.640513 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.3205 | − | 10.0000i | −0.921878 | − | 0.532246i | −0.0376440 | − | 0.999291i | \(-0.511985\pi\) |
−0.884234 | + | 0.467045i | \(0.845319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.46410 | + | 10.0000i | −0.183340 | + | 0.529256i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0000 | + | 25.9808i | 0.791670 | + | 1.37121i | 0.924932 | + | 0.380131i | \(0.124121\pi\) |
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.0000i | 1.04973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4545 | + | 9.50000i | 0.858917 | + | 0.495896i | 0.863649 | − | 0.504093i | \(-0.168173\pi\) |
−0.00473247 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.50000 | − | 4.33013i | −0.130145 | − | 0.225417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.50000 | + | 28.5788i | 0.285546 | + | 1.48374i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1244 | − | 7.00000i | 0.627775 | − | 0.362446i | −0.152115 | − | 0.988363i | \(-0.548608\pi\) |
0.779890 | + | 0.625917i | \(0.215275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 18.0000i | − | 0.927047i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0000 | 1.07870 | 0.539349 | − | 0.842082i | \(-0.318670\pi\) | ||||
0.539349 | + | 0.842082i | \(0.318670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.0000 | − | 29.4449i | 0.870936 | − | 1.50851i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.19615 | + | 3.00000i | −0.264135 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.00000 | + | 13.8564i | −0.405616 | + | 0.702548i | −0.994393 | − | 0.105748i | \(-0.966276\pi\) |
0.588777 | + | 0.808296i | \(0.299610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0000 | −0.708010 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.0000i | − | 0.706207i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5885 | + | 9.00000i | −0.782362 | + | 0.451697i | −0.837267 | − | 0.546795i | \(-0.815848\pi\) |
0.0549046 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.0000 | + | 17.3205i | −1.00125 | + | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.50000 | − | 11.2583i | −0.324595 | − | 0.562214i | 0.656836 | − | 0.754034i | \(-0.271895\pi\) |
−0.981430 | + | 0.191820i | \(0.938561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3923 | + | 6.00000i | 0.517678 | + | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.00000i | − | 0.247841i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | + | 5.19615i | −0.148340 | + | 0.256933i | −0.930614 | − | 0.366002i | \(-0.880726\pi\) |
0.782274 | + | 0.622935i | \(0.214060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0000 | − | 20.7846i | −0.591916 | − | 1.02523i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.7846 | + | 4.00000i | −1.02274 | + | 0.196827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.92820 | − | 4.00000i | −0.339276 | − | 0.195881i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.00000 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.79423 | + | 4.50000i | 0.378968 | + | 0.218797i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3923 | − | 30.0000i | 0.502919 | − | 1.45180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | − | 13.8564i | 0.385346 | − | 0.667440i | −0.606471 | − | 0.795106i | \(-0.707415\pi\) |
0.991817 | + | 0.127666i | \(0.0407486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000i | 1.15337i | 0.816968 | + | 0.576683i | \(0.195653\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.3109 | − | 17.5000i | −1.44997 | − | 0.837139i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.7128 | + | 16.0000i | −1.31668 | + | 0.760183i | −0.983192 | − | 0.182573i | \(-0.941557\pi\) |
−0.333483 | + | 0.942756i | \(0.608224\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.0000i | 0.945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.0000 | −0.613508 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.50000 | + | 4.33013i | −0.117720 | + | 0.203898i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3205 | − | 10.0000i | 0.813788 | − | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0526 | − | 11.0000i | 0.891241 | − | 0.514558i | 0.0168929 | − | 0.999857i | \(-0.494623\pi\) |
0.874348 | + | 0.485299i | \(0.161289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | + | 6.92820i | −0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.00000i | 0.418265i | 0.977887 | + | 0.209133i | \(0.0670641\pi\) | ||||
−0.977887 | + | 0.209133i | \(0.932936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.66025 | − | 5.00000i | 0.400749 | − | 0.231372i | −0.286058 | − | 0.958212i | \(-0.592345\pi\) |
0.686807 | + | 0.726840i | \(0.259012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | + | 10.3923i | 0.0923514 | + | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.19615 | + | 3.00000i | 0.238919 | + | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.0000i | − | 0.503655i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | + | 13.8564i | −0.365529 | + | 0.633115i | −0.988861 | − | 0.148842i | \(-0.952445\pi\) |
0.623332 | + | 0.781958i | \(0.285779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | − | 12.9904i | −0.341971 | − | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.2487 | − | 28.0000i | −1.10335 | − | 1.27404i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.92820 | − | 4.00000i | −0.313947 | − | 0.181257i | 0.334744 | − | 0.942309i | \(-0.391350\pi\) |
−0.648691 | + | 0.761052i | \(0.724683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3923 | − | 6.00000i | −0.468046 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.92820 | + | 8.00000i | 0.310772 | + | 0.358849i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.00000 | − | 8.66025i | 0.223384 | − | 0.386912i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000i | 0.713405i | 0.934218 | + | 0.356702i | \(0.116099\pi\) | ||||
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.92820 | + | 4.00000i | 0.307692 | + | 0.177646i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 31.1769i | 0.265424 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.3205 | + | 10.0000i | −0.764719 | + | 0.441511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.00000i | − | 0.395820i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.0000 | 1.66801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.2487 | − | 14.0000i | 1.06032 | − | 0.612177i | 0.134801 | − | 0.990873i | \(-0.456961\pi\) |
0.925521 | + | 0.378695i | \(0.123627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.92820 | − | 4.00000i | 0.301797 | − | 0.174243i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | − | 22.5167i | 0.565217 | − | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0000i | 0.649722i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.5885 | − | 9.00000i | 0.672692 | − | 0.388379i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50000 | + | 4.33013i | 0.236902 | + | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | + | 34.6410i | 0.859867 | + | 1.48933i | 0.872055 | + | 0.489408i | \(0.162787\pi\) |
−0.0121878 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.46410 | + | 2.00000i | 0.148659 | + | 0.0858282i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00000 | + | 10.3923i | −0.256074 | + | 0.443533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1244 | − | 35.0000i | 0.515580 | − | 1.48835i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.1865 | + | 10.5000i | 0.770588 | + | 0.444899i | 0.833084 | − | 0.553146i | \(-0.186573\pi\) |
−0.0624962 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.19615 | − | 3.00000i | −0.218992 | − | 0.126435i | 0.386492 | − | 0.922293i | \(-0.373687\pi\) |
−0.605483 | + | 0.795858i | \(0.707020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28.5788 | + | 5.50000i | −1.20020 | + | 0.230978i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.50000 | − | 9.52628i | −0.230572 | − | 0.399362i | 0.727405 | − | 0.686209i | \(-0.240726\pi\) |
−0.957977 | + | 0.286846i | \(0.907393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0000 | + | 24.2487i | −0.585882 | + | 1.01478i | 0.408883 | + | 0.912587i | \(0.365918\pi\) |
−0.994765 | + | 0.102190i | \(0.967415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.46410 | − | 2.00000i | −0.144212 | − | 0.0832611i | 0.426158 | − | 0.904649i | \(-0.359867\pi\) |
−0.570370 | + | 0.821388i | \(0.693200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.0000 | + | 34.6410i | 0.831172 | + | 1.43963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | + | 6.92820i | −0.331896 | + | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.52628 | + | 5.50000i | −0.394538 | + | 0.227787i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | + | 46.7654i | −1.11063 | + | 1.92367i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.3923 | + | 6.00000i | −0.426761 | + | 0.246390i | −0.697966 | − | 0.716131i | \(-0.745911\pi\) |
0.271205 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.92820 | + | 4.00000i | −0.283552 | + | 0.163709i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0000 | − | 29.4449i | 0.694601 | − | 1.20308i | −0.275714 | − | 0.961240i | \(-0.588914\pi\) |
0.970315 | − | 0.241845i | \(-0.0777525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.5788 | + | 16.5000i | −1.15998 | + | 0.669714i | −0.951299 | − | 0.308270i | \(-0.900250\pi\) |
−0.208680 | + | 0.977984i | \(0.566917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00000 | − | 31.1769i | −0.243132 | − | 1.26335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.5000 | − | 23.3827i | −0.546152 | − | 0.945962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5070 | + | 20.5000i | 1.43412 | + | 0.827987i | 0.997431 | − | 0.0716275i | \(-0.0228193\pi\) |
0.436684 | + | 0.899615i | \(0.356153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.0000i | − | 1.69086i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||
0.534089 | − | 0.845428i | \(-0.320655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5000 | − | 30.3109i | 0.703384 | − | 1.21830i | −0.263887 | − | 0.964554i | \(-0.585005\pi\) |
0.967271 | − | 0.253744i | \(-0.0816620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.0000 | − | 24.2487i | −0.561801 | − | 0.973067i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.19615 | − | 15.0000i | 0.208179 | − | 0.600962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.66025 | − | 5.00000i | −0.345857 | − | 0.199681i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5167 | − | 13.0000i | −0.894957 | − | 0.516704i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.7846 | + | 3.00000i | 0.823516 | + | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00000 | − | 3.46410i | −0.0791188 | − | 0.137038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5000 | + | 30.3109i | −0.691208 | + | 1.19721i | 0.280234 | + | 0.959932i | \(0.409588\pi\) |
−0.971442 | + | 0.237276i | \(0.923745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 34.0000i | − | 1.34083i | −0.741987 | − | 0.670415i | \(-0.766116\pi\) | ||
0.741987 | − | 0.670415i | \(-0.233884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9186 | + | 11.5000i | 0.783080 | + | 0.452112i | 0.837521 | − | 0.546405i | \(-0.184004\pi\) |
−0.0544405 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | − | 6.92820i | −0.157014 | − | 0.271956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.0000 | + | 6.92820i | 0.783862 | + | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.9711 | − | 22.5000i | 1.52506 | − | 0.880493i | 0.525500 | − | 0.850794i | \(-0.323878\pi\) |
0.999559 | − | 0.0296993i | \(-0.00945498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0000i | − | 0.468165i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0000 | 0.623272 | 0.311636 | − | 0.950202i | \(-0.399123\pi\) | ||||
0.311636 | + | 0.950202i | \(0.399123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | − | 31.1769i | 0.700119 | − | 1.21264i | −0.268306 | − | 0.963334i | \(-0.586464\pi\) |
0.968424 | − | 0.249308i | \(-0.0802030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3923 | + | 6.00000i | −0.403604 | + | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.3731 | − | 21.0000i | 1.40837 | − | 0.813123i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | − | 27.7128i | 0.618596 | − | 1.07144i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.0000i | − | 1.61898i | −0.587133 | − | 0.809491i | \(-0.699743\pi\) | ||
0.587133 | − | 0.809491i | \(-0.300257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1865 | + | 10.5000i | −0.698965 | + | 0.403548i | −0.806962 | − | 0.590603i | \(-0.798890\pi\) |
0.107997 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 10.3923i | −0.460518 | + | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00000 | − | 13.8564i | −0.306561 | − | 0.530979i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.1769 | + | 18.0000i | 1.19295 | + | 0.688751i | 0.958975 | − | 0.283491i | \(-0.0914927\pi\) |
0.233977 | + | 0.972242i | \(0.424826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 56.0000i | − | 2.13653i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.5000 | + | 28.5788i | −0.628600 | + | 1.08877i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.73205 | − | 2.00000i | −0.0657952 | − | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.66025 | + | 5.00000i | 0.328031 | + | 0.189389i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.00000 | 0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6506 | − | 12.5000i | −0.816569 | − | 0.471446i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1769 | − | 6.00000i | 1.17253 | − | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.00000 | − | 15.5885i | −0.338002 | − | 0.585437i | 0.646055 | − | 0.763291i | \(-0.276418\pi\) |
−0.984057 | + | 0.177854i | \(0.943084\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.00000 | + | 12.1244i | −0.262521 | + | 0.454699i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0000i | 1.04861i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3923 | − | 6.00000i | −0.388108 | − | 0.224074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.0000 | − | 17.3205i | −1.86210 | − | 0.645049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.8372 | + | 23.0000i | −1.48156 | + | 0.855379i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.0000i | − | 1.52061i | −0.649569 | − | 0.760303i | \(-0.725051\pi\) | ||
0.649569 | − | 0.760303i | \(-0.274949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.8468 | − | 15.5000i | 0.991609 | − | 0.572506i | 0.0858539 | − | 0.996308i | \(-0.472638\pi\) |
0.905755 | + | 0.423802i | \(0.139305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.46410 | + | 2.00000i | −0.127602 | + | 0.0736709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5000 | + | 35.5070i | −0.754105 | + | 1.30615i | 0.191714 | + | 0.981451i | \(0.438596\pi\) |
−0.945818 | + | 0.324697i | \(0.894738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30.0000 | −1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.00000i | − | 0.110059i | −0.998485 | − | 0.0550297i | \(-0.982475\pi\) | ||
0.998485 | − | 0.0550297i | \(-0.0175253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46410 | − | 2.00000i | 0.126745 | − | 0.0731762i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | + | 10.3923i | 1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.00000 | − | 15.5885i | −0.328415 | − | 0.568831i | 0.653783 | − | 0.756682i | \(-0.273181\pi\) |
−0.982197 | + | 0.187851i | \(0.939848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50.2295 | + | 29.0000i | 1.83046 | + | 1.05682i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000i | 0.218074i | 0.994038 | + | 0.109037i | \(0.0347767\pi\) | ||||
−0.994038 | + | 0.109037i | \(0.965223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.00000 | − | 12.1244i | 0.254084 | − | 0.440086i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | + | 2.59808i | 0.0543750 | + | 0.0941802i | 0.891932 | − | 0.452170i | \(-0.149350\pi\) |
−0.837557 | + | 0.546350i | \(0.816017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3923 | − | 2.00000i | 0.376227 | − | 0.0724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7846 | − | 12.0000i | −0.750489 | − | 0.433295i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0000 | 1.47850 | 0.739249 | − | 0.673432i | \(-0.235181\pi\) | ||||
0.739249 | + | 0.673432i | \(0.235181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.9904 | − | 7.50000i | −0.467232 | − | 0.269756i | 0.247849 | − | 0.968799i | \(-0.420276\pi\) |
−0.715080 | + | 0.699043i | \(0.753610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.3205 | − | 20.0000i | −0.621370 | − | 0.717496i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.5000 | + | 21.6506i | 0.447859 | + | 0.775715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | + | 3.46410i | −0.0715656 | + | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 24.0000i | − | 0.857690i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5885 | − | 9.00000i | −0.555668 | − | 0.320815i | 0.195737 | − | 0.980656i | \(-0.437290\pi\) |
−0.751405 | + | 0.659841i | \(0.770624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.00000 | − | 13.8564i | −0.284808 | − | 0.493301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.0000 | − | 34.6410i | 1.42224 | − | 1.23169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.1769 | − | 18.0000i | 1.10712 | − | 0.639199i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3923 | + | 6.00000i | −0.366736 | + | 0.211735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.7846 | + | 12.0000i | −0.731653 | + | 0.422420i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.5000 | − | 47.6314i | 0.966849 | − | 1.67463i | 0.262284 | − | 0.964991i | \(-0.415524\pi\) |
0.704564 | − | 0.709640i | \(-0.251142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.00000 | −0.175574 | −0.0877869 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877869 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000i | 0.561144i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.9808 | − | 15.0000i | 0.908952 | − | 0.524784i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.50000 | − | 2.59808i | −0.262071 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | − | 25.9808i | −0.523504 | − | 0.906735i | −0.999626 | − | 0.0273557i | \(-0.991291\pi\) |
0.476122 | − | 0.879379i | \(-0.342042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.46410 | − | 2.00000i | −0.120751 | − | 0.0697156i | 0.438408 | − | 0.898776i | \(-0.355543\pi\) |
−0.559159 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.0000i | 0.486828i | 0.969923 | + | 0.243414i | \(0.0782673\pi\) | ||||
−0.969923 | + | 0.243414i | \(0.921733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000 | − | 32.9090i | 0.659897 | − | 1.14298i | −0.320745 | − | 0.947166i | \(-0.603933\pi\) |
0.980642 | − | 0.195810i | \(-0.0627335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.66025 | − | 11.0000i | 0.300060 | − | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.8564 | + | 8.00000i | 0.478947 | + | 0.276520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.0000 | 0.483334 | 0.241667 | − | 0.970359i | \(-0.422306\pi\) | ||||
0.241667 | + | 0.970359i | \(0.422306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.19615 | − | 3.00000i | −0.178965 | − | 0.103325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66025 | − | 25.0000i | 0.297570 | − | 0.859010i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0000 | + | 38.1051i | 0.755038 | + | 1.30776i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.5000 | − | 30.3109i | 0.599892 | − | 1.03904i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000i | 0.787505i | 0.919216 | + | 0.393753i | \(0.128823\pi\) | ||||
−0.919216 | + | 0.393753i | \(0.871177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.3731 | − | 21.0000i | −1.24248 | − | 0.717346i | −0.272882 | − | 0.962048i | \(-0.587977\pi\) |
−0.969599 | + | 0.244701i | \(0.921310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | + | 34.6410i | 0.682391 | + | 1.18194i | 0.974249 | + | 0.225475i | \(0.0723932\pi\) |
−0.291858 | + | 0.956462i | \(0.594273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | + | 25.9808i | 0.170400 | + | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.2583 | + | 6.50000i | −0.383238 | + | 0.221263i | −0.679226 | − | 0.733929i | \(-0.737684\pi\) |
0.295988 | + | 0.955192i | \(0.404351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 26.0000i | − | 0.883006i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.0000 | 0.474917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 10.3923i | −0.203302 | + | 0.352130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.19615 | − | 3.00000i | 0.175863 | − | 0.101535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.79423 | + | 4.50000i | −0.263192 | + | 0.151954i | −0.625790 | − | 0.779992i | \(-0.715223\pi\) |
0.362598 | + | 0.931946i | \(0.381890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0000 | + | 36.3731i | −0.708312 | + | 1.22683i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.0000 | + | 29.4449i | −1.14032 | + | 0.987549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.50000 | − | 9.52628i | −0.184257 | − | 0.319142i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.9711 | − | 22.5000i | −1.30412 | − | 0.752934i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 42.0000i | − | 1.40234i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0000 | + | 19.0526i | 0.366463 | + | 0.634733i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.1769 | − | 6.00000i | 1.03750 | − | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0526 | + | 11.0000i | 0.632630 | + | 0.365249i | 0.781770 | − | 0.623567i | \(-0.214317\pi\) |
−0.149140 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0000 | 1.39152 | 0.695761 | − | 0.718273i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718273i | \(0.255067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46410 | − | 2.00000i | −0.114645 | − | 0.0661903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.06218 | + | 17.5000i | −0.200191 | + | 0.577901i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.00000 | − | 15.5885i | −0.296883 | − | 0.514216i | 0.678538 | − | 0.734565i | \(-0.262614\pi\) |
−0.975421 | + | 0.220349i | \(0.929280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | + | 10.3923i | −0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000i | 0.394985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.3205 | + | 10.0000i | 0.568880 | + | 0.328443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.5000 | − | 26.8468i | −0.508539 | − | 0.880815i | −0.999951 | − | 0.00988764i | \(-0.996853\pi\) |
0.491413 | − | 0.870927i | \(-0.336481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.5000 | − | 12.9904i | 1.06514 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.92820 | − | 4.00000i | 0.226819 | − | 0.130954i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.0000i | 1.24141i | 0.784046 | + | 0.620703i | \(0.213153\pi\) | ||||
−0.784046 | + | 0.620703i | \(0.786847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.0000 | 1.04428 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.3109 | + | 17.5000i | −0.987058 | + | 0.569878i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.1244 | + | 7.00000i | −0.393989 | + | 0.227469i | −0.683887 | − | 0.729588i | \(-0.739712\pi\) |
0.289898 | + | 0.957057i | \(0.406379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | + | 31.1769i | −0.584305 | + | 1.01205i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.00000 | −0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20.0000i | − | 0.647864i | −0.946080 | − | 0.323932i | \(-0.894995\pi\) | ||
0.946080 | − | 0.323932i | \(-0.105005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3923 | − | 6.00000i | 0.335936 | − | 0.193952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 31.1769i | 0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3923 | − | 6.00000i | −0.334887 | − | 0.193347i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000i | 0.257263i | 0.991692 | + | 0.128631i | \(0.0410584\pi\) | ||||
−0.991692 | + | 0.128631i | \(0.958942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0000 | + | 17.3205i | −0.321246 | + | 0.556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.50000 | − | 6.06218i | −0.112320 | − | 0.194545i | 0.804385 | − | 0.594108i | \(-0.202495\pi\) |
−0.916705 | + | 0.399564i | \(0.869162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.92820 | + | 8.00000i | 0.222108 | + | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5885 | + | 9.00000i | 0.498719 | + | 0.287936i | 0.728184 | − | 0.685381i | \(-0.240364\pi\) |
−0.229465 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.59808 | + | 1.50000i | 0.0828658 | + | 0.0478426i | 0.540860 | − | 0.841112i | \(-0.318099\pi\) |
−0.457995 | + | 0.888955i | \(0.651432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.1769 | − | 36.0000i | −0.992372 | − | 1.14589i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.0000 | + | 36.3731i | 0.667761 | + | 1.15660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.0000i | 1.71364i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8372 | + | 23.0000i | 1.26166 | + | 0.728417i | 0.973395 | − | 0.229135i | \(-0.0735896\pi\) |
0.288261 | + | 0.957552i | \(0.406923\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | − | 17.3205i | −0.316386 | − | 0.547997i |
(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 | 1400.2.bh.e.249.2 | 4 | ||
5.2 | odd | 4 | 280.2.q.c.81.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1400.2.q.a.1201.1 | 2 | |||
5.4 | even | 2 | inner | 1400.2.bh.e.249.1 | 4 | ||
7.2 | even | 3 | inner | 1400.2.bh.e.849.1 | 4 | ||
15.2 | even | 4 | 2520.2.bi.e.361.1 | 2 | |||
20.7 | even | 4 | 560.2.q.c.81.1 | 2 | |||
35.2 | odd | 12 | 280.2.q.c.121.1 | yes | 2 | ||
35.3 | even | 12 | 9800.2.a.g.1.1 | 1 | |||
35.9 | even | 6 | inner | 1400.2.bh.e.849.2 | 4 | ||
35.12 | even | 12 | 1960.2.q.c.961.1 | 2 | |||
35.17 | even | 12 | 1960.2.a.m.1.1 | 1 | |||
35.18 | odd | 12 | 9800.2.a.bi.1.1 | 1 | |||
35.23 | odd | 12 | 1400.2.q.a.401.1 | 2 | |||
35.27 | even | 4 | 1960.2.q.c.361.1 | 2 | |||
35.32 | odd | 12 | 1960.2.a.a.1.1 | 1 | |||
105.2 | even | 12 | 2520.2.bi.e.1801.1 | 2 | |||
140.67 | even | 12 | 3920.2.a.bf.1.1 | 1 | |||
140.87 | odd | 12 | 3920.2.a.i.1.1 | 1 | |||
140.107 | even | 12 | 560.2.q.c.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.c.81.1 | ✓ | 2 | 5.2 | odd | 4 | ||
280.2.q.c.121.1 | yes | 2 | 35.2 | odd | 12 | ||
560.2.q.c.81.1 | 2 | 20.7 | even | 4 | |||
560.2.q.c.401.1 | 2 | 140.107 | even | 12 | |||
1400.2.q.a.401.1 | 2 | 35.23 | odd | 12 | |||
1400.2.q.a.1201.1 | 2 | 5.3 | odd | 4 | |||
1400.2.bh.e.249.1 | 4 | 5.4 | even | 2 | inner | ||
1400.2.bh.e.249.2 | 4 | 1.1 | even | 1 | trivial | ||
1400.2.bh.e.849.1 | 4 | 7.2 | even | 3 | inner | ||
1400.2.bh.e.849.2 | 4 | 35.9 | even | 6 | inner | ||
1960.2.a.a.1.1 | 1 | 35.32 | odd | 12 | |||
1960.2.a.m.1.1 | 1 | 35.17 | even | 12 | |||
1960.2.q.c.361.1 | 2 | 35.27 | even | 4 | |||
1960.2.q.c.961.1 | 2 | 35.12 | even | 12 | |||
2520.2.bi.e.361.1 | 2 | 15.2 | even | 4 | |||
2520.2.bi.e.1801.1 | 2 | 105.2 | even | 12 | |||
3920.2.a.i.1.1 | 1 | 140.87 | odd | 12 | |||
3920.2.a.bf.1.1 | 1 | 140.67 | even | 12 | |||
9800.2.a.g.1.1 | 1 | 35.3 | even | 12 | |||
9800.2.a.bi.1.1 | 1 | 35.18 | odd | 12 |