Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 551.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.551 |
Dual form | 630.2.t.a.311.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | 1.26795i | 0.382301i | 0.981561 | + | 0.191151i | \(0.0612219\pi\) | ||||
−0.981561 | + | 0.191151i | \(0.938778\pi\) | |||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | 1.73205 | + | 2.00000i | 0.462910 | + | 0.534522i | ||||
\(15\) | −0.866025 | − | 1.50000i | −0.223607 | − | 0.387298i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | 4.09808 | + | 2.36603i | 0.940163 | + | 0.542803i | 0.890011 | − | 0.455938i | \(-0.150696\pi\) |
0.0501517 | + | 0.998742i | \(0.484030\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −3.46410 | + | 3.00000i | −0.755929 | + | 0.654654i | ||||
\(22\) | 0.633975 | + | 1.09808i | 0.135164 | + | 0.234111i | ||||
\(23\) | 9.46410i | 1.97340i | 0.162547 | + | 0.986701i | \(0.448029\pi\) | ||||
−0.162547 | + | 0.986701i | \(0.551971\pi\) | |||||||
\(24\) | 1.50000 | − | 0.866025i | 0.306186 | − | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.73205 | − | 3.00000i | 0.339683 | − | 0.588348i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 2.50000 | + | 0.866025i | 0.472456 | + | 0.163663i | ||||
\(29\) | −0.401924 | − | 0.232051i | −0.0746354 | − | 0.0430908i | 0.462218 | − | 0.886766i | \(-0.347054\pi\) |
−0.536853 | + | 0.843676i | \(0.680387\pi\) | |||||||
\(30\) | −1.50000 | − | 0.866025i | −0.273861 | − | 0.158114i | ||||
\(31\) | −1.90192 | − | 1.09808i | −0.341596 | − | 0.197220i | 0.319382 | − | 0.947626i | \(-0.396525\pi\) |
−0.660977 | + | 0.750406i | \(0.729858\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −1.90192 | + | 1.09808i | −0.331082 | + | 0.191151i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.500000 | − | 2.59808i | −0.0845154 | − | 0.439155i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 2.09808 | − | 3.63397i | 0.344922 | − | 0.597422i | −0.640418 | − | 0.768027i | \(-0.721239\pi\) |
0.985340 | + | 0.170605i | \(0.0545722\pi\) | |||||||
\(38\) | 4.73205 | 0.767640 | ||||||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −4.50000 | − | 7.79423i | −0.702782 | − | 1.21725i | −0.967486 | − | 0.252924i | \(-0.918608\pi\) |
0.264704 | − | 0.964330i | \(-0.414726\pi\) | |||||||
\(42\) | −1.50000 | + | 4.33013i | −0.231455 | + | 0.668153i | ||||
\(43\) | 3.59808 | − | 6.23205i | 0.548701 | − | 0.950379i | −0.449662 | − | 0.893199i | \(-0.648456\pi\) |
0.998364 | − | 0.0571802i | \(-0.0182110\pi\) | |||||||
\(44\) | 1.09808 | + | 0.633975i | 0.165541 | + | 0.0955753i | ||||
\(45\) | 1.50000 | − | 2.59808i | 0.223607 | − | 0.387298i | ||||
\(46\) | 4.73205 | + | 8.19615i | 0.697703 | + | 1.20846i | ||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 0.866025 | − | 1.50000i | 0.125000 | − | 0.216506i | ||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 3.46410i | − | 0.480384i | ||||||
\(53\) | 9.29423 | − | 5.36603i | 1.27666 | − | 0.737080i | 0.300428 | − | 0.953805i | \(-0.402871\pi\) |
0.976233 | + | 0.216724i | \(0.0695373\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | − | 1.26795i | − | 0.170970i | ||||||
\(56\) | 2.59808 | − | 0.500000i | 0.347183 | − | 0.0668153i | ||||
\(57\) | 8.19615i | 1.08561i | ||||||||
\(58\) | −0.464102 | −0.0609395 | ||||||||
\(59\) | −4.09808 | + | 7.09808i | −0.533524 | + | 0.924091i | 0.465709 | + | 0.884938i | \(0.345799\pi\) |
−0.999233 | + | 0.0391530i | \(0.987534\pi\) | |||||||
\(60\) | −1.73205 | −0.223607 | ||||||||
\(61\) | 0.803848 | − | 0.464102i | 0.102922 | − | 0.0594221i | −0.447655 | − | 0.894206i | \(-0.647741\pi\) |
0.550578 | + | 0.834784i | \(0.314408\pi\) | |||||||
\(62\) | −2.19615 | −0.278912 | ||||||||
\(63\) | −7.50000 | − | 2.59808i | −0.944911 | − | 0.327327i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.00000 | + | 1.73205i | −0.372104 | + | 0.214834i | ||||
\(66\) | −1.09808 | + | 1.90192i | −0.135164 | + | 0.234111i | ||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.1962 | + | 8.19615i | −1.70902 | + | 0.986701i | ||||
\(70\) | −1.73205 | − | 2.00000i | −0.207020 | − | 0.239046i | ||||
\(71\) | − | 1.26795i | − | 0.150478i | −0.997166 | − | 0.0752389i | \(-0.976028\pi\) | ||
0.997166 | − | 0.0752389i | \(-0.0239720\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 6.00000 | − | 3.46410i | 0.702247 | − | 0.405442i | −0.105937 | − | 0.994373i | \(-0.533784\pi\) |
0.808184 | + | 0.588930i | \(0.200451\pi\) | |||||||
\(74\) | − | 4.19615i | − | 0.487793i | ||||||
\(75\) | 0.866025 | + | 1.50000i | 0.100000 | + | 0.173205i | ||||
\(76\) | 4.09808 | − | 2.36603i | 0.470082 | − | 0.271402i | ||||
\(77\) | −3.29423 | + | 0.633975i | −0.375412 | + | 0.0722481i | ||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | 8.29423 | + | 14.3660i | 0.933174 | + | 1.61630i | 0.777859 | + | 0.628439i | \(0.216306\pi\) |
0.155315 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −7.79423 | − | 4.50000i | −0.860729 | − | 0.496942i | ||||
\(83\) | 0.401924 | − | 0.696152i | 0.0441169 | − | 0.0764127i | −0.843124 | − | 0.537720i | \(-0.819286\pi\) |
0.887241 | + | 0.461307i | \(0.152619\pi\) | |||||||
\(84\) | 0.866025 | + | 4.50000i | 0.0944911 | + | 0.490990i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.19615i | − | 0.775981i | ||||||
\(87\) | − | 0.803848i | − | 0.0861815i | ||||||
\(88\) | 1.26795 | 0.135164 | ||||||||
\(89\) | 8.19615 | − | 14.1962i | 0.868790 | − | 1.50479i | 0.00555677 | − | 0.999985i | \(-0.498231\pi\) |
0.863234 | − | 0.504805i | \(-0.168435\pi\) | |||||||
\(90\) | − | 3.00000i | − | 0.316228i | ||||||
\(91\) | 6.00000 | + | 6.92820i | 0.628971 | + | 0.726273i | ||||
\(92\) | 8.19615 | + | 4.73205i | 0.854508 | + | 0.493350i | ||||
\(93\) | − | 3.80385i | − | 0.394441i | ||||||
\(94\) | −7.79423 | − | 4.50000i | −0.803913 | − | 0.464140i | ||||
\(95\) | −4.09808 | − | 2.36603i | −0.420454 | − | 0.242749i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | −13.3923 | − | 7.73205i | −1.35978 | − | 0.785071i | −0.370188 | − | 0.928957i | \(-0.620707\pi\) |
−0.989594 | + | 0.143886i | \(0.954040\pi\) | |||||||
\(98\) | −4.33013 | + | 5.50000i | −0.437409 | + | 0.555584i | ||||
\(99\) | −3.29423 | − | 1.90192i | −0.331082 | − | 0.191151i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −0.803848 | −0.0799858 | −0.0399929 | − | 0.999200i | \(-0.512734\pi\) | ||||
−0.0399929 | + | 0.999200i | \(0.512734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.1244i | − | 1.19465i | −0.802000 | − | 0.597324i | \(-0.796231\pi\) | ||
0.802000 | − | 0.597324i | \(-0.203769\pi\) | |||||||
\(104\) | −1.73205 | − | 3.00000i | −0.169842 | − | 0.294174i | ||||
\(105\) | 3.46410 | − | 3.00000i | 0.338062 | − | 0.292770i | ||||
\(106\) | 5.36603 | − | 9.29423i | 0.521194 | − | 0.902735i | ||||
\(107\) | −1.79423 | − | 1.03590i | −0.173455 | − | 0.100144i | 0.410759 | − | 0.911744i | \(-0.365264\pi\) |
−0.584214 | + | 0.811600i | \(0.698597\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | −1.59808 | − | 2.76795i | −0.153068 | − | 0.265121i | 0.779286 | − | 0.626669i | \(-0.215582\pi\) |
−0.932354 | + | 0.361547i | \(0.882249\pi\) | |||||||
\(110\) | −0.633975 | − | 1.09808i | −0.0604471 | − | 0.104697i | ||||
\(111\) | 7.26795 | 0.689843 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | −16.0981 | + | 9.29423i | −1.51438 | + | 0.874327i | −0.514522 | + | 0.857477i | \(0.672030\pi\) |
−0.999858 | + | 0.0168501i | \(0.994636\pi\) | |||||||
\(114\) | 4.09808 | + | 7.09808i | 0.383820 | + | 0.664796i | ||||
\(115\) | − | 9.46410i | − | 0.882532i | ||||||
\(116\) | −0.401924 | + | 0.232051i | −0.0373177 | + | 0.0215454i | ||||
\(117\) | 10.3923i | 0.960769i | ||||||||
\(118\) | 8.19615i | 0.754517i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.50000 | + | 0.866025i | −0.136931 | + | 0.0790569i | ||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 0.464102 | − | 0.803848i | 0.0420178 | − | 0.0727769i | ||||
\(123\) | 7.79423 | − | 13.5000i | 0.702782 | − | 1.21725i | ||||
\(124\) | −1.90192 | + | 1.09808i | −0.170798 | + | 0.0986102i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.79423 | + | 1.50000i | −0.694365 | + | 0.133631i | ||||
\(127\) | 9.39230 | 0.833432 | 0.416716 | − | 0.909037i | \(-0.363181\pi\) | ||||
0.416716 | + | 0.909037i | \(0.363181\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 12.4641 | 1.09740 | ||||||||
\(130\) | −1.73205 | + | 3.00000i | −0.151911 | + | 0.263117i | ||||
\(131\) | −16.3923 | −1.43220 | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(132\) | 2.19615i | 0.191151i | ||||||||
\(133\) | −4.09808 | + | 11.8301i | −0.355348 | + | 1.02580i | ||||
\(134\) | − | 4.00000i | − | 0.345547i | ||||||
\(135\) | 5.19615 | 0.447214 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.7321i | − | 0.916901i | −0.888720 | − | 0.458450i | \(-0.848405\pi\) | ||
0.888720 | − | 0.458450i | \(-0.151595\pi\) | |||||||
\(138\) | −8.19615 | + | 14.1962i | −0.697703 | + | 1.20846i | ||||
\(139\) | 13.9019 | − | 8.02628i | 1.17915 | − | 0.680780i | 0.223329 | − | 0.974743i | \(-0.428308\pi\) |
0.955817 | + | 0.293963i | \(0.0949742\pi\) | |||||||
\(140\) | −2.50000 | − | 0.866025i | −0.211289 | − | 0.0731925i | ||||
\(141\) | 7.79423 | − | 13.5000i | 0.656392 | − | 1.13691i | ||||
\(142\) | −0.633975 | − | 1.09808i | −0.0532020 | − | 0.0921485i | ||||
\(143\) | 2.19615 | + | 3.80385i | 0.183651 | + | 0.318094i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0.401924 | + | 0.232051i | 0.0333780 | + | 0.0192708i | ||||
\(146\) | 3.46410 | − | 6.00000i | 0.286691 | − | 0.496564i | ||||
\(147\) | −9.52628 | − | 7.50000i | −0.785714 | − | 0.618590i | ||||
\(148\) | −2.09808 | − | 3.63397i | −0.172461 | − | 0.298711i | ||||
\(149\) | 12.0000i | 0.983078i | 0.870855 | + | 0.491539i | \(0.163566\pi\) | ||||
−0.870855 | + | 0.491539i | \(0.836434\pi\) | |||||||
\(150\) | 1.50000 | + | 0.866025i | 0.122474 | + | 0.0707107i | ||||
\(151\) | 6.19615 | 0.504236 | 0.252118 | − | 0.967697i | \(-0.418873\pi\) | ||||
0.252118 | + | 0.967697i | \(0.418873\pi\) | |||||||
\(152\) | 2.36603 | − | 4.09808i | 0.191910 | − | 0.332398i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.53590 | + | 2.19615i | −0.204349 | + | 0.176971i | ||||
\(155\) | 1.90192 | + | 1.09808i | 0.152766 | + | 0.0881996i | ||||
\(156\) | 5.19615 | − | 3.00000i | 0.416025 | − | 0.240192i | ||||
\(157\) | 0.294229 | + | 0.169873i | 0.0234820 | + | 0.0135573i | 0.511695 | − | 0.859167i | \(-0.329018\pi\) |
−0.488213 | + | 0.872724i | \(0.662351\pi\) | |||||||
\(158\) | 14.3660 | + | 8.29423i | 1.14290 | + | 0.659853i | ||||
\(159\) | 16.0981 | + | 9.29423i | 1.27666 | + | 0.737080i | ||||
\(160\) | 0.866025 | + | 0.500000i | 0.0684653 | + | 0.0395285i | ||||
\(161\) | −24.5885 | + | 4.73205i | −1.93784 | + | 0.372938i | ||||
\(162\) | −7.79423 | − | 4.50000i | −0.612372 | − | 0.353553i | ||||
\(163\) | −6.19615 | + | 10.7321i | −0.485320 | + | 0.840599i | −0.999858 | − | 0.0168687i | \(-0.994630\pi\) |
0.514538 | + | 0.857468i | \(0.327964\pi\) | |||||||
\(164\) | −9.00000 | −0.702782 | ||||||||
\(165\) | 1.90192 | − | 1.09808i | 0.148065 | − | 0.0854851i | ||||
\(166\) | − | 0.803848i | − | 0.0623907i | ||||||
\(167\) | −5.19615 | − | 9.00000i | −0.402090 | − | 0.696441i | 0.591888 | − | 0.806020i | \(-0.298383\pi\) |
−0.993978 | + | 0.109580i | \(0.965050\pi\) | |||||||
\(168\) | 3.00000 | + | 3.46410i | 0.231455 | + | 0.267261i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.2942 | + | 7.09808i | −0.940163 | + | 0.542803i | ||||
\(172\) | −3.59808 | − | 6.23205i | −0.274351 | − | 0.475189i | ||||
\(173\) | −1.09808 | − | 1.90192i | −0.0834852 | − | 0.144601i | 0.821260 | − | 0.570555i | \(-0.193272\pi\) |
−0.904745 | + | 0.425954i | \(0.859938\pi\) | |||||||
\(174\) | −0.401924 | − | 0.696152i | −0.0304698 | − | 0.0527752i | ||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | 1.09808 | − | 0.633975i | 0.0827706 | − | 0.0477876i | ||||
\(177\) | −14.1962 | −1.06705 | ||||||||
\(178\) | − | 16.3923i | − | 1.22866i | ||||||
\(179\) | 5.70577 | − | 3.29423i | 0.426469 | − | 0.246222i | −0.271372 | − | 0.962475i | \(-0.587477\pi\) |
0.697841 | + | 0.716252i | \(0.254144\pi\) | |||||||
\(180\) | −1.50000 | − | 2.59808i | −0.111803 | − | 0.193649i | ||||
\(181\) | 7.39230i | 0.549466i | 0.961521 | + | 0.274733i | \(0.0885894\pi\) | ||||
−0.961521 | + | 0.274733i | \(0.911411\pi\) | |||||||
\(182\) | 8.66025 | + | 3.00000i | 0.641941 | + | 0.222375i | ||||
\(183\) | 1.39230 | + | 0.803848i | 0.102922 | + | 0.0594221i | ||||
\(184\) | 9.46410 | 0.697703 | ||||||||
\(185\) | −2.09808 | + | 3.63397i | −0.154254 | + | 0.267175i | ||||
\(186\) | −1.90192 | − | 3.29423i | −0.139456 | − | 0.241545i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | −2.59808 | − | 13.5000i | −0.188982 | − | 0.981981i | ||||
\(190\) | −4.73205 | −0.343299 | ||||||||
\(191\) | 3.00000 | − | 1.73205i | 0.217072 | − | 0.125327i | −0.387522 | − | 0.921861i | \(-0.626669\pi\) |
0.604594 | + | 0.796534i | \(0.293335\pi\) | |||||||
\(192\) | −0.866025 | − | 1.50000i | −0.0625000 | − | 0.108253i | ||||
\(193\) | −12.0981 | + | 20.9545i | −0.870839 | + | 1.50834i | −0.00970797 | + | 0.999953i | \(0.503090\pi\) |
−0.861131 | + | 0.508384i | \(0.830243\pi\) | |||||||
\(194\) | −15.4641 | −1.11026 | ||||||||
\(195\) | −5.19615 | − | 3.00000i | −0.372104 | − | 0.214834i | ||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | − | 6.33975i | − | 0.451688i | −0.974163 | − | 0.225844i | \(-0.927486\pi\) | ||
0.974163 | − | 0.225844i | \(-0.0725140\pi\) | |||||||
\(198\) | −3.80385 | −0.270328 | ||||||||
\(199\) | 6.00000 | − | 3.46410i | 0.425329 | − | 0.245564i | −0.272026 | − | 0.962290i | \(-0.587694\pi\) |
0.697355 | + | 0.716726i | \(0.254360\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 6.92820 | 0.488678 | ||||||||
\(202\) | −0.696152 | + | 0.401924i | −0.0489811 | + | 0.0282793i | ||||
\(203\) | 0.401924 | − | 1.16025i | 0.0282095 | − | 0.0814339i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | −6.06218 | − | 10.5000i | −0.422372 | − | 0.731570i | ||||
\(207\) | −24.5885 | − | 14.1962i | −1.70902 | − | 0.986701i | ||||
\(208\) | −3.00000 | − | 1.73205i | −0.208013 | − | 0.120096i | ||||
\(209\) | −3.00000 | + | 5.19615i | −0.207514 | + | 0.359425i | ||||
\(210\) | 1.50000 | − | 4.33013i | 0.103510 | − | 0.298807i | ||||
\(211\) | −5.29423 | − | 9.16987i | −0.364470 | − | 0.631280i | 0.624221 | − | 0.781248i | \(-0.285416\pi\) |
−0.988691 | + | 0.149968i | \(0.952083\pi\) | |||||||
\(212\) | − | 10.7321i | − | 0.737080i | ||||||
\(213\) | 1.90192 | − | 1.09808i | 0.130318 | − | 0.0752389i | ||||
\(214\) | −2.07180 | −0.141625 | ||||||||
\(215\) | −3.59808 | + | 6.23205i | −0.245387 | + | 0.425022i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 1.90192 | − | 5.49038i | 0.129111 | − | 0.372711i | ||||
\(218\) | −2.76795 | − | 1.59808i | −0.187469 | − | 0.108235i | ||||
\(219\) | 10.3923 | + | 6.00000i | 0.702247 | + | 0.405442i | ||||
\(220\) | −1.09808 | − | 0.633975i | −0.0740323 | − | 0.0427426i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.29423 | − | 3.63397i | 0.422441 | − | 0.243896i | ||||
\(223\) | −8.89230 | − | 5.13397i | −0.595473 | − | 0.343796i | 0.171786 | − | 0.985134i | \(-0.445046\pi\) |
−0.767259 | + | 0.641338i | \(0.778380\pi\) | |||||||
\(224\) | 0.866025 | − | 2.50000i | 0.0578638 | − | 0.167038i | ||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | −9.29423 | + | 16.0981i | −0.618243 | + | 1.07083i | ||||
\(227\) | 4.39230 | 0.291528 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(228\) | 7.09808 | + | 4.09808i | 0.470082 | + | 0.271402i | ||||
\(229\) | 27.9282i | 1.84555i | 0.385342 | + | 0.922774i | \(0.374083\pi\) | ||||
−0.385342 | + | 0.922774i | \(0.625917\pi\) | |||||||
\(230\) | −4.73205 | − | 8.19615i | −0.312022 | − | 0.540438i | ||||
\(231\) | −3.80385 | − | 4.39230i | −0.250275 | − | 0.288992i | ||||
\(232\) | −0.232051 | + | 0.401924i | −0.0152349 | + | 0.0263876i | ||||
\(233\) | −4.09808 | − | 2.36603i | −0.268474 | − | 0.155003i | 0.359720 | − | 0.933060i | \(-0.382872\pi\) |
−0.628194 | + | 0.778057i | \(0.716206\pi\) | |||||||
\(234\) | 5.19615 | + | 9.00000i | 0.339683 | + | 0.588348i | ||||
\(235\) | 4.50000 | + | 7.79423i | 0.293548 | + | 0.508439i | ||||
\(236\) | 4.09808 | + | 7.09808i | 0.266762 | + | 0.462045i | ||||
\(237\) | −14.3660 | + | 24.8827i | −0.933174 | + | 1.61630i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.2942 | − | 10.5622i | 1.18336 | − | 0.683210i | 0.226567 | − | 0.973996i | \(-0.427250\pi\) |
0.956788 | + | 0.290785i | \(0.0939165\pi\) | |||||||
\(240\) | −0.866025 | + | 1.50000i | −0.0559017 | + | 0.0968246i | ||||
\(241\) | 20.6603i | 1.33084i | 0.746467 | + | 0.665422i | \(0.231748\pi\) | ||||
−0.746467 | + | 0.665422i | \(0.768252\pi\) | |||||||
\(242\) | 8.13397 | − | 4.69615i | 0.522872 | − | 0.301880i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | − | 0.928203i | − | 0.0594221i | ||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | − | 15.5885i | − | 0.993884i | ||||||
\(247\) | 16.3923 | 1.04302 | ||||||||
\(248\) | −1.09808 | + | 1.90192i | −0.0697279 | + | 0.120772i | ||||
\(249\) | 1.39230 | 0.0882337 | ||||||||
\(250\) | −0.866025 | + | 0.500000i | −0.0547723 | + | 0.0316228i | ||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | −6.00000 | + | 5.19615i | −0.377964 | + | 0.327327i | ||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 8.13397 | − | 4.69615i | 0.510371 | − | 0.294663i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.60770 | 0.474555 | 0.237277 | − | 0.971442i | \(-0.423745\pi\) | ||||
0.237277 | + | 0.971442i | \(0.423745\pi\) | |||||||
\(258\) | 10.7942 | − | 6.23205i | 0.672019 | − | 0.387991i | ||||
\(259\) | 10.4904 | + | 3.63397i | 0.651841 | + | 0.225804i | ||||
\(260\) | 3.46410i | 0.214834i | ||||||||
\(261\) | 1.20577 | − | 0.696152i | 0.0746354 | − | 0.0430908i | ||||
\(262\) | −14.1962 | + | 8.19615i | −0.877041 | + | 0.506360i | ||||
\(263\) | 10.2679i | 0.633149i | 0.948568 | + | 0.316574i | \(0.102533\pi\) | ||||
−0.948568 | + | 0.316574i | \(0.897467\pi\) | |||||||
\(264\) | 1.09808 | + | 1.90192i | 0.0675819 | + | 0.117055i | ||||
\(265\) | −9.29423 | + | 5.36603i | −0.570940 | + | 0.329632i | ||||
\(266\) | 2.36603 | + | 12.2942i | 0.145070 | + | 0.753808i | ||||
\(267\) | 28.3923 | 1.73758 | ||||||||
\(268\) | −2.00000 | − | 3.46410i | −0.122169 | − | 0.211604i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 4.50000 | − | 2.59808i | 0.273861 | − | 0.158114i | ||||
\(271\) | 21.2942 | + | 12.2942i | 1.29353 | + | 0.746821i | 0.979279 | − | 0.202518i | \(-0.0649124\pi\) |
0.314254 | + | 0.949339i | \(0.398246\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.19615 | + | 15.0000i | −0.314485 | + | 0.907841i | ||||
\(274\) | −5.36603 | − | 9.29423i | −0.324173 | − | 0.561485i | ||||
\(275\) | 1.26795i | 0.0764602i | ||||||||
\(276\) | 16.3923i | 0.986701i | ||||||||
\(277\) | −13.8038 | −0.829393 | −0.414696 | − | 0.909960i | \(-0.636112\pi\) | ||||
−0.414696 | + | 0.909960i | \(0.636112\pi\) | |||||||
\(278\) | 8.02628 | − | 13.9019i | 0.481384 | − | 0.833782i | ||||
\(279\) | 5.70577 | − | 3.29423i | 0.341596 | − | 0.197220i | ||||
\(280\) | −2.59808 | + | 0.500000i | −0.155265 | + | 0.0298807i | ||||
\(281\) | 2.30385 | + | 1.33013i | 0.137436 | + | 0.0793487i | 0.567141 | − | 0.823620i | \(-0.308049\pi\) |
−0.429705 | + | 0.902969i | \(0.641383\pi\) | |||||||
\(282\) | − | 15.5885i | − | 0.928279i | ||||||
\(283\) | −9.40192 | − | 5.42820i | −0.558886 | − | 0.322673i | 0.193812 | − | 0.981039i | \(-0.437915\pi\) |
−0.752698 | + | 0.658365i | \(0.771248\pi\) | |||||||
\(284\) | −1.09808 | − | 0.633975i | −0.0651588 | − | 0.0376195i | ||||
\(285\) | − | 8.19615i | − | 0.485498i | ||||||
\(286\) | 3.80385 | + | 2.19615i | 0.224926 | + | 0.129861i | ||||
\(287\) | 18.0000 | − | 15.5885i | 1.06251 | − | 0.920158i | ||||
\(288\) | 2.59808 | − | 1.50000i | 0.153093 | − | 0.0883883i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0.464102 | 0.0272530 | ||||||||
\(291\) | − | 26.7846i | − | 1.57014i | ||||||
\(292\) | − | 6.92820i | − | 0.405442i | ||||||
\(293\) | 2.19615 | + | 3.80385i | 0.128301 | + | 0.222223i | 0.923018 | − | 0.384756i | \(-0.125714\pi\) |
−0.794718 | + | 0.606979i | \(0.792381\pi\) | |||||||
\(294\) | −12.0000 | − | 1.73205i | −0.699854 | − | 0.101015i | ||||
\(295\) | 4.09808 | − | 7.09808i | 0.238599 | − | 0.413266i | ||||
\(296\) | −3.63397 | − | 2.09808i | −0.211220 | − | 0.121948i | ||||
\(297\) | − | 6.58846i | − | 0.382301i | ||||||
\(298\) | 6.00000 | + | 10.3923i | 0.347571 | + | 0.602010i | ||||
\(299\) | 16.3923 | + | 28.3923i | 0.947991 | + | 1.64197i | ||||
\(300\) | 1.73205 | 0.100000 | ||||||||
\(301\) | 17.9904 | + | 6.23205i | 1.03695 | + | 0.359209i | ||||
\(302\) | 5.36603 | − | 3.09808i | 0.308780 | − | 0.178274i | ||||
\(303\) | −0.696152 | − | 1.20577i | −0.0399929 | − | 0.0692698i | ||||
\(304\) | − | 4.73205i | − | 0.271402i | ||||||
\(305\) | −0.803848 | + | 0.464102i | −0.0460282 | + | 0.0265744i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.7846i | − | 1.01502i | −0.861645 | − | 0.507511i | \(-0.830566\pi\) | ||
0.861645 | − | 0.507511i | \(-0.169434\pi\) | |||||||
\(308\) | −1.09808 | + | 3.16987i | −0.0625687 | + | 0.180620i | ||||
\(309\) | 18.1865 | − | 10.5000i | 1.03460 | − | 0.597324i | ||||
\(310\) | 2.19615 | 0.124733 | ||||||||
\(311\) | −13.0981 | + | 22.6865i | −0.742724 | + | 1.28644i | 0.208527 | + | 0.978017i | \(0.433133\pi\) |
−0.951251 | + | 0.308419i | \(0.900200\pi\) | |||||||
\(312\) | 3.00000 | − | 5.19615i | 0.169842 | − | 0.294174i | ||||
\(313\) | 8.49038 | − | 4.90192i | 0.479905 | − | 0.277073i | −0.240472 | − | 0.970656i | \(-0.577302\pi\) |
0.720377 | + | 0.693583i | \(0.243969\pi\) | |||||||
\(314\) | 0.339746 | 0.0191730 | ||||||||
\(315\) | 7.50000 | + | 2.59808i | 0.422577 | + | 0.146385i | ||||
\(316\) | 16.5885 | 0.933174 | ||||||||
\(317\) | −23.7846 | + | 13.7321i | −1.33588 | + | 0.771269i | −0.986193 | − | 0.165599i | \(-0.947044\pi\) |
−0.349684 | + | 0.936868i | \(0.613711\pi\) | |||||||
\(318\) | 18.5885 | 1.04239 | ||||||||
\(319\) | 0.294229 | − | 0.509619i | 0.0164736 | − | 0.0285332i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | − | 3.58846i | − | 0.200288i | ||||||
\(322\) | −18.9282 | + | 16.3923i | −1.05483 | + | 0.913507i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 3.00000 | − | 1.73205i | 0.166410 | − | 0.0960769i | ||||
\(326\) | 12.3923i | 0.686346i | ||||||||
\(327\) | 2.76795 | − | 4.79423i | 0.153068 | − | 0.265121i | ||||
\(328\) | −7.79423 | + | 4.50000i | −0.430364 | + | 0.248471i | ||||
\(329\) | 18.0000 | − | 15.5885i | 0.992372 | − | 0.859419i | ||||
\(330\) | 1.09808 | − | 1.90192i | 0.0604471 | − | 0.104697i | ||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | −0.401924 | − | 0.696152i | −0.0220584 | − | 0.0382063i | ||||
\(333\) | 6.29423 | + | 10.9019i | 0.344922 | + | 0.597422i | ||||
\(334\) | −9.00000 | − | 5.19615i | −0.492458 | − | 0.284321i | ||||
\(335\) | −2.00000 | + | 3.46410i | −0.109272 | + | 0.189264i | ||||
\(336\) | 4.33013 | + | 1.50000i | 0.236228 | + | 0.0818317i | ||||
\(337\) | −5.00000 | − | 8.66025i | −0.272367 | − | 0.471754i | 0.697100 | − | 0.716974i | \(-0.254473\pi\) |
−0.969468 | + | 0.245220i | \(0.921140\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | −27.8827 | − | 16.0981i | −1.51438 | − | 0.874327i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.39230 | − | 2.41154i | 0.0753975 | − | 0.130592i | ||||
\(342\) | −7.09808 | + | 12.2942i | −0.383820 | + | 0.664796i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −6.23205 | − | 3.59808i | −0.336010 | − | 0.193995i | ||||
\(345\) | 14.1962 | − | 8.19615i | 0.764295 | − | 0.441266i | ||||
\(346\) | −1.90192 | − | 1.09808i | −0.102248 | − | 0.0590329i | ||||
\(347\) | 23.5981 | + | 13.6244i | 1.26681 | + | 0.731394i | 0.974383 | − | 0.224894i | \(-0.0722035\pi\) |
0.292428 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(348\) | −0.696152 | − | 0.401924i | −0.0373177 | − | 0.0215454i | ||||
\(349\) | 3.80385 | + | 2.19615i | 0.203615 | + | 0.117557i | 0.598341 | − | 0.801242i | \(-0.295827\pi\) |
−0.394725 | + | 0.918799i | \(0.629160\pi\) | |||||||
\(350\) | 1.73205 | + | 2.00000i | 0.0925820 | + | 0.106904i | ||||
\(351\) | −15.5885 | + | 9.00000i | −0.832050 | + | 0.480384i | ||||
\(352\) | 0.633975 | − | 1.09808i | 0.0337910 | − | 0.0585277i | ||||
\(353\) | 30.5885 | 1.62806 | 0.814030 | − | 0.580823i | \(-0.197269\pi\) | ||||
0.814030 | + | 0.580823i | \(0.197269\pi\) | |||||||
\(354\) | −12.2942 | + | 7.09808i | −0.653431 | + | 0.377258i | ||||
\(355\) | 1.26795i | 0.0672958i | ||||||||
\(356\) | −8.19615 | − | 14.1962i | −0.434395 | − | 0.752395i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.29423 | − | 5.70577i | 0.174105 | − | 0.301559i | ||||
\(359\) | 22.6865 | + | 13.0981i | 1.19735 | + | 0.691290i | 0.959963 | − | 0.280125i | \(-0.0903760\pi\) |
0.237386 | + | 0.971415i | \(0.423709\pi\) | |||||||
\(360\) | −2.59808 | − | 1.50000i | −0.136931 | − | 0.0790569i | ||||
\(361\) | 1.69615 | + | 2.93782i | 0.0892712 | + | 0.154622i | ||||
\(362\) | 3.69615 | + | 6.40192i | 0.194265 | + | 0.336478i | ||||
\(363\) | 8.13397 | + | 14.0885i | 0.426923 | + | 0.739452i | ||||
\(364\) | 9.00000 | − | 1.73205i | 0.471728 | − | 0.0907841i | ||||
\(365\) | −6.00000 | + | 3.46410i | −0.314054 | + | 0.181319i | ||||
\(366\) | 1.60770 | 0.0840356 | ||||||||
\(367\) | − | 18.8038i | − | 0.981553i | −0.871286 | − | 0.490776i | \(-0.836713\pi\) | ||
0.871286 | − | 0.490776i | \(-0.163287\pi\) | |||||||
\(368\) | 8.19615 | − | 4.73205i | 0.427254 | − | 0.246675i | ||||
\(369\) | 27.0000 | 1.40556 | ||||||||
\(370\) | 4.19615i | 0.218148i | ||||||||
\(371\) | 18.5885 | + | 21.4641i | 0.965065 | + | 1.11436i | ||||
\(372\) | −3.29423 | − | 1.90192i | −0.170798 | − | 0.0986102i | ||||
\(373\) | −0.196152 | −0.0101564 | −0.00507819 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507819 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.866025 | − | 1.50000i | −0.0447214 | − | 0.0774597i | ||||
\(376\) | −7.79423 | + | 4.50000i | −0.401957 | + | 0.232070i | ||||
\(377\) | −1.60770 | −0.0828005 | ||||||||
\(378\) | −9.00000 | − | 10.3923i | −0.462910 | − | 0.534522i | ||||
\(379\) | −30.3923 | −1.56115 | −0.780574 | − | 0.625063i | \(-0.785073\pi\) | ||||
−0.780574 | + | 0.625063i | \(0.785073\pi\) | |||||||
\(380\) | −4.09808 | + | 2.36603i | −0.210227 | + | 0.121375i | ||||
\(381\) | 8.13397 | + | 14.0885i | 0.416716 | + | 0.721774i | ||||
\(382\) | 1.73205 | − | 3.00000i | 0.0886194 | − | 0.153493i | ||||
\(383\) | −1.39230 | −0.0711435 | −0.0355717 | − | 0.999367i | \(-0.511325\pi\) | ||||
−0.0355717 | + | 0.999367i | \(0.511325\pi\) | |||||||
\(384\) | −1.50000 | − | 0.866025i | −0.0765466 | − | 0.0441942i | ||||
\(385\) | 3.29423 | − | 0.633975i | 0.167889 | − | 0.0323103i | ||||
\(386\) | 24.1962i | 1.23155i | ||||||||
\(387\) | 10.7942 | + | 18.6962i | 0.548701 | + | 0.950379i | ||||
\(388\) | −13.3923 | + | 7.73205i | −0.679891 | + | 0.392535i | ||||
\(389\) | 30.7128i | 1.55720i | 0.627520 | + | 0.778601i | \(0.284070\pi\) | ||||
−0.627520 | + | 0.778601i | \(0.715930\pi\) | |||||||
\(390\) | −6.00000 | −0.303822 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.59808 | + | 6.50000i | 0.131223 | + | 0.328300i | ||||
\(393\) | −14.1962 | − | 24.5885i | −0.716101 | − | 1.24032i | ||||
\(394\) | −3.16987 | − | 5.49038i | −0.159696 | − | 0.276601i | ||||
\(395\) | −8.29423 | − | 14.3660i | −0.417328 | − | 0.722833i | ||||
\(396\) | −3.29423 | + | 1.90192i | −0.165541 | + | 0.0955753i | ||||
\(397\) | −0.509619 | − | 0.294229i | −0.0255770 | − | 0.0147669i | 0.487157 | − | 0.873314i | \(-0.338034\pi\) |
−0.512734 | + | 0.858548i | \(0.671367\pi\) | |||||||
\(398\) | 3.46410 | − | 6.00000i | 0.173640 | − | 0.300753i | ||||
\(399\) | −21.2942 | + | 4.09808i | −1.06604 | + | 0.205160i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | − | 27.5885i | − | 1.37770i | −0.724903 | − | 0.688851i | \(-0.758115\pi\) | ||
0.724903 | − | 0.688851i | \(-0.241885\pi\) | |||||||
\(402\) | 6.00000 | − | 3.46410i | 0.299253 | − | 0.172774i | ||||
\(403\) | −7.60770 | −0.378966 | ||||||||
\(404\) | −0.401924 | + | 0.696152i | −0.0199965 | + | 0.0346349i | ||||
\(405\) | 4.50000 | + | 7.79423i | 0.223607 | + | 0.387298i | ||||
\(406\) | −0.232051 | − | 1.20577i | −0.0115165 | − | 0.0598414i | ||||
\(407\) | 4.60770 | + | 2.66025i | 0.228395 | + | 0.131864i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.8923 | − | 17.2583i | −1.47808 | − | 0.853370i | −0.478386 | − | 0.878149i | \(-0.658778\pi\) |
−0.999693 | + | 0.0247799i | \(0.992111\pi\) | |||||||
\(410\) | 7.79423 | + | 4.50000i | 0.384930 | + | 0.222239i | ||||
\(411\) | 16.0981 | − | 9.29423i | 0.794060 | − | 0.458450i | ||||
\(412\) | −10.5000 | − | 6.06218i | −0.517298 | − | 0.298662i | ||||
\(413\) | −20.4904 | − | 7.09808i | −1.00827 | − | 0.349273i | ||||
\(414\) | −28.3923 | −1.39541 | ||||||||
\(415\) | −0.401924 | + | 0.696152i | −0.0197297 | + | 0.0341728i | ||||
\(416\) | −3.46410 | −0.169842 | ||||||||
\(417\) | 24.0788 | + | 13.9019i | 1.17915 | + | 0.680780i | ||||
\(418\) | 6.00000i | 0.293470i | ||||||||
\(419\) | −5.19615 | − | 9.00000i | −0.253849 | − | 0.439679i | 0.710734 | − | 0.703461i | \(-0.248363\pi\) |
−0.964582 | + | 0.263783i | \(0.915030\pi\) | |||||||
\(420\) | −0.866025 | − | 4.50000i | −0.0422577 | − | 0.219578i | ||||
\(421\) | −10.9904 | + | 19.0359i | −0.535638 | + | 0.927753i | 0.463494 | + | 0.886100i | \(0.346596\pi\) |
−0.999132 | + | 0.0416527i | \(0.986738\pi\) | |||||||
\(422\) | −9.16987 | − | 5.29423i | −0.446382 | − | 0.257719i | ||||
\(423\) | 27.0000 | 1.31278 | ||||||||
\(424\) | −5.36603 | − | 9.29423i | −0.260597 | − | 0.451368i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.09808 | − | 1.90192i | 0.0532020 | − | 0.0921485i | ||||
\(427\) | 1.60770 | + | 1.85641i | 0.0778018 | + | 0.0898378i | ||||
\(428\) | −1.79423 | + | 1.03590i | −0.0867273 | + | 0.0500720i | ||||
\(429\) | −3.80385 | + | 6.58846i | −0.183651 | + | 0.318094i | ||||
\(430\) | 7.19615i | 0.347029i | ||||||||
\(431\) | −2.41154 | + | 1.39230i | −0.116160 | + | 0.0670650i | −0.556954 | − | 0.830543i | \(-0.688030\pi\) |
0.440794 | + | 0.897608i | \(0.354697\pi\) | |||||||
\(432\) | 2.59808 | + | 4.50000i | 0.125000 | + | 0.216506i | ||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | −1.09808 | − | 5.70577i | −0.0527093 | − | 0.273886i | ||||
\(435\) | 0.803848i | 0.0385415i | ||||||||
\(436\) | −3.19615 | −0.153068 | ||||||||
\(437\) | −22.3923 | + | 38.7846i | −1.07117 | + | 1.85532i | ||||
\(438\) | 12.0000 | 0.573382 | ||||||||
\(439\) | −10.6865 | + | 6.16987i | −0.510040 | + | 0.294472i | −0.732850 | − | 0.680390i | \(-0.761810\pi\) |
0.222810 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(440\) | −1.26795 | −0.0604471 | ||||||||
\(441\) | 3.00000 | − | 20.7846i | 0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 3.63397 | − | 6.29423i | 0.172461 | − | 0.298711i | ||||
\(445\) | −8.19615 | + | 14.1962i | −0.388535 | + | 0.672962i | ||||
\(446\) | −10.2679 | −0.486201 | ||||||||
\(447\) | −18.0000 | + | 10.3923i | −0.851371 | + | 0.491539i | ||||
\(448\) | −0.500000 | − | 2.59808i | −0.0236228 | − | 0.122748i | ||||
\(449\) | − | 21.5885i | − | 1.01882i | −0.860523 | − | 0.509411i | \(-0.829863\pi\) | ||
0.860523 | − | 0.509411i | \(-0.170137\pi\) | |||||||
\(450\) | 3.00000i | 0.141421i | ||||||||
\(451\) | 9.88269 | − | 5.70577i | 0.465358 | − | 0.268674i | ||||
\(452\) | 18.5885i | 0.874327i | ||||||||
\(453\) | 5.36603 | + | 9.29423i | 0.252118 | + | 0.436681i | ||||
\(454\) | 3.80385 | − | 2.19615i | 0.178523 | − | 0.103071i | ||||
\(455\) | −6.00000 | − | 6.92820i | −0.281284 | − | 0.324799i | ||||
\(456\) | 8.19615 | 0.383820 | ||||||||
\(457\) | 9.19615 | + | 15.9282i | 0.430178 | + | 0.745090i | 0.996888 | − | 0.0788271i | \(-0.0251175\pi\) |
−0.566710 | + | 0.823917i | \(0.691784\pi\) | |||||||
\(458\) | 13.9641 | + | 24.1865i | 0.652500 | + | 1.13016i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.19615 | − | 4.73205i | −0.382148 | − | 0.220633i | ||||
\(461\) | 2.59808 | − | 4.50000i | 0.121004 | − | 0.209586i | −0.799160 | − | 0.601119i | \(-0.794722\pi\) |
0.920164 | + | 0.391533i | \(0.128055\pi\) | |||||||
\(462\) | −5.49038 | − | 1.90192i | −0.255436 | − | 0.0884855i | ||||
\(463\) | 11.6962 | + | 20.2583i | 0.543566 | + | 0.941484i | 0.998696 | + | 0.0510591i | \(0.0162597\pi\) |
−0.455129 | + | 0.890425i | \(0.650407\pi\) | |||||||
\(464\) | 0.464102i | 0.0215454i | ||||||||
\(465\) | 3.80385i | 0.176399i | ||||||||
\(466\) | −4.73205 | −0.219208 | ||||||||
\(467\) | 8.59808 | − | 14.8923i | 0.397872 | − | 0.689134i | −0.595592 | − | 0.803287i | \(-0.703082\pi\) |
0.993463 | + | 0.114154i | \(0.0364156\pi\) | |||||||
\(468\) | 9.00000 | + | 5.19615i | 0.416025 | + | 0.240192i | ||||
\(469\) | 10.0000 | + | 3.46410i | 0.461757 | + | 0.159957i | ||||
\(470\) | 7.79423 | + | 4.50000i | 0.359521 | + | 0.207570i | ||||
\(471\) | 0.588457i | 0.0271147i | ||||||||
\(472\) | 7.09808 | + | 4.09808i | 0.326715 | + | 0.188629i | ||||
\(473\) | 7.90192 | + | 4.56218i | 0.363331 | + | 0.209769i | ||||
\(474\) | 28.7321i | 1.31971i | ||||||||
\(475\) | 4.09808 | + | 2.36603i | 0.188033 | + | 0.108561i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.1962i | 1.47416i | ||||||||
\(478\) | 10.5622 | − | 18.2942i | 0.483103 | − | 0.836759i | ||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 1.73205i | 0.0790569i | ||||||||
\(481\) | − | 14.5359i | − | 0.662780i | ||||||
\(482\) | 10.3301 | + | 17.8923i | 0.470524 | + | 0.814972i | ||||
\(483\) | −28.3923 | − | 32.7846i | −1.29189 | − | 1.49175i | ||||
\(484\) | 4.69615 | − | 8.13397i | 0.213461 | − | 0.369726i | ||||
\(485\) | 13.3923 | + | 7.73205i | 0.608113 | + | 0.351094i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | −17.0000 | − | 29.4449i | −0.770344 | − | 1.33427i | −0.937375 | − | 0.348323i | \(-0.886751\pi\) |
0.167031 | − | 0.985952i | \(-0.446582\pi\) | |||||||
\(488\) | −0.464102 | − | 0.803848i | −0.0210089 | − | 0.0363885i | ||||
\(489\) | −21.4641 | −0.970640 | ||||||||
\(490\) | 4.33013 | − | 5.50000i | 0.195615 | − | 0.248465i | ||||
\(491\) | 2.49038 | − | 1.43782i | 0.112389 | − | 0.0648880i | −0.442752 | − | 0.896644i | \(-0.645998\pi\) |
0.555141 | + | 0.831756i | \(0.312664\pi\) | |||||||
\(492\) | −7.79423 | − | 13.5000i | −0.351391 | − | 0.608627i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 14.1962 | − | 8.19615i | 0.638715 | − | 0.368762i | ||||
\(495\) | 3.29423 | + | 1.90192i | 0.148065 | + | 0.0854851i | ||||
\(496\) | 2.19615i | 0.0986102i | ||||||||
\(497\) | 3.29423 | − | 0.633975i | 0.147766 | − | 0.0284376i | ||||
\(498\) | 1.20577 | − | 0.696152i | 0.0540319 | − | 0.0311953i | ||||
\(499\) | −5.80385 | −0.259816 | −0.129908 | − | 0.991526i | \(-0.541468\pi\) | ||||
−0.129908 | + | 0.991526i | \(0.541468\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | −15.5885 | + | 9.00000i | −0.695747 | + | 0.401690i | ||||
\(503\) | 13.3923 | 0.597133 | 0.298567 | − | 0.954389i | \(-0.403491\pi\) | ||||
0.298567 | + | 0.954389i | \(0.403491\pi\) | |||||||
\(504\) | −2.59808 | + | 7.50000i | −0.115728 | + | 0.334077i | ||||
\(505\) | 0.803848 | 0.0357707 | ||||||||
\(506\) | −10.3923 | + | 6.00000i | −0.461994 | + | 0.266733i | ||||
\(507\) | −1.73205 | −0.0769231 | ||||||||
\(508\) | 4.69615 | − | 8.13397i | 0.208358 | − | 0.360887i | ||||
\(509\) | −21.5885 | −0.956892 | −0.478446 | − | 0.878117i | \(-0.658800\pi\) | ||||
−0.478446 | + | 0.878117i | \(0.658800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 13.8564i | 0.530849 | + | 0.612971i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −21.2942 | − | 12.2942i | −0.940163 | − | 0.542803i | ||||
\(514\) | 6.58846 | − | 3.80385i | 0.290604 | − | 0.167781i | ||||
\(515\) | 12.1244i | 0.534263i | ||||||||
\(516\) | 6.23205 | − | 10.7942i | 0.274351 | − | 0.475189i | ||||
\(517\) | 9.88269 | − | 5.70577i | 0.434640 | − | 0.250940i | ||||
\(518\) | 10.9019 | − | 2.09808i | 0.479003 | − | 0.0921842i | ||||
\(519\) | 1.90192 | − | 3.29423i | 0.0834852 | − | 0.144601i | ||||
\(520\) | 1.73205 | + | 3.00000i | 0.0759555 | + | 0.131559i | ||||
\(521\) | 10.5000 | + | 18.1865i | 0.460013 | + | 0.796766i | 0.998961 | − | 0.0455727i | \(-0.0145113\pi\) |
−0.538948 | + | 0.842339i | \(0.681178\pi\) | |||||||
\(522\) | 0.696152 | − | 1.20577i | 0.0304698 | − | 0.0527752i | ||||
\(523\) | −28.5788 | − | 16.5000i | −1.24967 | − | 0.721495i | −0.278623 | − | 0.960401i | \(-0.589878\pi\) |
−0.971043 | + | 0.238906i | \(0.923211\pi\) | |||||||
\(524\) | −8.19615 | + | 14.1962i | −0.358051 | + | 0.620162i | ||||
\(525\) | −3.46410 | + | 3.00000i | −0.151186 | + | 0.130931i | ||||
\(526\) | 5.13397 | + | 8.89230i | 0.223852 | + | 0.387723i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.90192 | + | 1.09808i | 0.0827706 | + | 0.0477876i | ||||
\(529\) | −66.5692 | −2.89431 | ||||||||
\(530\) | −5.36603 | + | 9.29423i | −0.233085 | + | 0.403715i | ||||
\(531\) | −12.2942 | − | 21.2942i | −0.533524 | − | 0.924091i | ||||
\(532\) | 8.19615 | + | 9.46410i | 0.355348 | + | 0.410321i | ||||
\(533\) | −27.0000 | − | 15.5885i | −1.16950 | − | 0.675211i | ||||
\(534\) | 24.5885 | − | 14.1962i | 1.06405 | − | 0.614328i | ||||
\(535\) | 1.79423 | + | 1.03590i | 0.0775713 | + | 0.0447858i | ||||
\(536\) | −3.46410 | − | 2.00000i | −0.149626 | − | 0.0863868i | ||||
\(537\) | 9.88269 | + | 5.70577i | 0.426469 | + | 0.246222i | ||||
\(538\) | 15.5885 | + | 9.00000i | 0.672066 | + | 0.388018i | ||||
\(539\) | −3.29423 | − | 8.24167i | −0.141892 | − | 0.354994i | ||||
\(540\) | 2.59808 | − | 4.50000i | 0.111803 | − | 0.193649i | ||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 24.5885 | 1.05616 | ||||||||
\(543\) | −11.0885 | + | 6.40192i | −0.475851 | + | 0.274733i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.59808 | + | 2.76795i | 0.0684541 | + | 0.118566i | ||||
\(546\) | 3.00000 | + | 15.5885i | 0.128388 | + | 0.667124i | ||||
\(547\) | 12.7942 | − | 22.1603i | 0.547042 | − | 0.947504i | −0.451434 | − | 0.892305i | \(-0.649087\pi\) |
0.998475 | − | 0.0551993i | \(-0.0175794\pi\) | |||||||
\(548\) | −9.29423 | − | 5.36603i | −0.397030 | − | 0.229225i | ||||
\(549\) | 2.78461i | 0.118844i | ||||||||
\(550\) | 0.633975 | + | 1.09808i | 0.0270328 | + | 0.0468221i | ||||
\(551\) | −1.09808 | − | 1.90192i | −0.0467796 | − | 0.0810247i | ||||
\(552\) | 8.19615 | + | 14.1962i | 0.348851 | + | 0.604228i | ||||
\(553\) | −33.1769 | + | 28.7321i | −1.41083 | + | 1.22181i | ||||
\(554\) | −11.9545 | + | 6.90192i | −0.507897 | + | 0.293235i | ||||
\(555\) | −7.26795 | −0.308507 | ||||||||
\(556\) | − | 16.0526i | − | 0.680780i | ||||||
\(557\) | 7.60770 | − | 4.39230i | 0.322348 | − | 0.186108i | −0.330090 | − | 0.943949i | \(-0.607079\pi\) |
0.652439 | + | 0.757841i | \(0.273746\pi\) | |||||||
\(558\) | 3.29423 | − | 5.70577i | 0.139456 | − | 0.241545i | ||||
\(559\) | − | 24.9282i | − | 1.05435i | ||||||
\(560\) | −2.00000 | + | 1.73205i | −0.0845154 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.66025 | 0.112216 | ||||||||
\(563\) | −17.1962 | + | 29.7846i | −0.724731 | + | 1.25527i | 0.234353 | + | 0.972152i | \(0.424703\pi\) |
−0.959084 | + | 0.283120i | \(0.908631\pi\) | |||||||
\(564\) | −7.79423 | − | 13.5000i | −0.328196 | − | 0.568453i | ||||
\(565\) | 16.0981 | − | 9.29423i | 0.677251 | − | 0.391011i | ||||
\(566\) | −10.8564 | −0.456329 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | −1.26795 | −0.0532020 | ||||||||
\(569\) | 5.19615 | − | 3.00000i | 0.217834 | − | 0.125767i | −0.387113 | − | 0.922032i | \(-0.626528\pi\) |
0.604947 | + | 0.796266i | \(0.293194\pi\) | |||||||
\(570\) | −4.09808 | − | 7.09808i | −0.171650 | − | 0.297306i | ||||
\(571\) | −21.1962 | + | 36.7128i | −0.887031 | + | 1.53638i | −0.0436638 | + | 0.999046i | \(0.513903\pi\) |
−0.843368 | + | 0.537337i | \(0.819430\pi\) | |||||||
\(572\) | 4.39230 | 0.183651 | ||||||||
\(573\) | 5.19615 | + | 3.00000i | 0.217072 | + | 0.125327i | ||||
\(574\) | 7.79423 | − | 22.5000i | 0.325325 | − | 0.939132i | ||||
\(575\) | 9.46410i | 0.394680i | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −20.7846 | + | 12.0000i | −0.865275 | + | 0.499567i | −0.865775 | − | 0.500433i | \(-0.833174\pi\) |
0.000500448 | 1.00000i | \(0.499841\pi\) | ||||||||
\(578\) | − | 17.0000i | − | 0.707107i | ||||||
\(579\) | −41.9090 | −1.74168 | ||||||||
\(580\) | 0.401924 | − | 0.232051i | 0.0166890 | − | 0.00963539i | ||||
\(581\) | 2.00962 | + | 0.696152i | 0.0833730 | + | 0.0288813i | ||||
\(582\) | −13.3923 | − | 23.1962i | −0.555129 | − | 0.961511i | ||||
\(583\) | 6.80385 | + | 11.7846i | 0.281787 | + | 0.488069i | ||||
\(584\) | −3.46410 | − | 6.00000i | −0.143346 | − | 0.248282i | ||||
\(585\) | − | 10.3923i | − | 0.429669i | ||||||
\(586\) | 3.80385 | + | 2.19615i | 0.157135 | + | 0.0907222i | ||||
\(587\) | 20.5981 | − | 35.6769i | 0.850174 | − | 1.47254i | −0.0308777 | − | 0.999523i | \(-0.509830\pi\) |
0.881051 | − | 0.473021i | \(-0.156836\pi\) | |||||||
\(588\) | −11.2583 | + | 4.50000i | −0.464286 | + | 0.185577i | ||||
\(589\) | −5.19615 | − | 9.00000i | −0.214104 | − | 0.370839i | ||||
\(590\) | − | 8.19615i | − | 0.337430i | ||||||
\(591\) | 9.50962 | − | 5.49038i | 0.391173 | − | 0.225844i | ||||
\(592\) | −4.19615 | −0.172461 | ||||||||
\(593\) | 7.39230 | − | 12.8038i | 0.303566 | − | 0.525791i | −0.673375 | − | 0.739301i | \(-0.735156\pi\) |
0.976941 | + | 0.213510i | \(0.0684895\pi\) | |||||||
\(594\) | −3.29423 | − | 5.70577i | −0.135164 | − | 0.234111i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3923 | + | 6.00000i | 0.425685 | + | 0.245770i | ||||
\(597\) | 10.3923 | + | 6.00000i | 0.425329 | + | 0.245564i | ||||
\(598\) | 28.3923 | + | 16.3923i | 1.16105 | + | 0.670331i | ||||
\(599\) | 14.1962 | + | 8.19615i | 0.580039 | + | 0.334886i | 0.761149 | − | 0.648577i | \(-0.224636\pi\) |
−0.181110 | + | 0.983463i | \(0.557969\pi\) | |||||||
\(600\) | 1.50000 | − | 0.866025i | 0.0612372 | − | 0.0353553i | ||||
\(601\) | −3.58846 | − | 2.07180i | −0.146376 | − | 0.0845104i | 0.425023 | − | 0.905182i | \(-0.360266\pi\) |
−0.571399 | + | 0.820672i | \(0.693599\pi\) | |||||||
\(602\) | 18.6962 | − | 3.59808i | 0.761998 | − | 0.146647i | ||||
\(603\) | 6.00000 | + | 10.3923i | 0.244339 | + | 0.423207i | ||||
\(604\) | 3.09808 | − | 5.36603i | 0.126059 | − | 0.218340i | ||||
\(605\) | −9.39230 | −0.381851 | ||||||||
\(606\) | −1.20577 | − | 0.696152i | −0.0489811 | − | 0.0282793i | ||||
\(607\) | − | 18.1244i | − | 0.735645i | −0.929896 | − | 0.367822i | \(-0.880103\pi\) | ||
0.929896 | − | 0.367822i | \(-0.119897\pi\) | |||||||
\(608\) | −2.36603 | − | 4.09808i | −0.0959550 | − | 0.166199i | ||||
\(609\) | 2.08846 | − | 0.401924i | 0.0846286 | − | 0.0162868i | ||||
\(610\) | −0.464102 | + | 0.803848i | −0.0187909 | + | 0.0325468i | ||||
\(611\) | −27.0000 | − | 15.5885i | −1.09230 | − | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3923 | − | 30.1244i | −0.702469 | − | 1.21671i | −0.967597 | − | 0.252498i | \(-0.918748\pi\) |
0.265129 | − | 0.964213i | \(-0.414586\pi\) | |||||||
\(614\) | −8.89230 | − | 15.4019i | −0.358864 | − | 0.621571i | ||||
\(615\) | −7.79423 | + | 13.5000i | −0.314294 | + | 0.544373i | ||||
\(616\) | 0.633975 | + | 3.29423i | 0.0255436 | + | 0.132728i | ||||
\(617\) | 26.1962 | − | 15.1244i | 1.05462 | − | 0.608884i | 0.130679 | − | 0.991425i | \(-0.458284\pi\) |
0.923938 | + | 0.382541i | \(0.124951\pi\) | |||||||
\(618\) | 10.5000 | − | 18.1865i | 0.422372 | − | 0.731570i | ||||
\(619\) | − | 4.39230i | − | 0.176542i | −0.996097 | − | 0.0882708i | \(-0.971866\pi\) | ||
0.996097 | − | 0.0882708i | \(-0.0281341\pi\) | |||||||
\(620\) | 1.90192 | − | 1.09808i | 0.0763831 | − | 0.0440998i | ||||
\(621\) | − | 49.1769i | − | 1.97340i | ||||||
\(622\) | 26.1962i | 1.05037i | ||||||||
\(623\) | 40.9808 | + | 14.1962i | 1.64186 | + | 0.568757i | ||||
\(624\) | − | 6.00000i | − | 0.240192i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.90192 | − | 8.49038i | 0.195920 | − | 0.339344i | ||||
\(627\) | −10.3923 | −0.415029 | ||||||||
\(628\) | 0.294229 | − | 0.169873i | 0.0117410 | − | 0.00677867i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 7.79423 | − | 1.50000i | 0.310530 | − | 0.0597614i | ||||
\(631\) | −8.39230 | −0.334092 | −0.167046 | − | 0.985949i | \(-0.553423\pi\) | ||||
−0.167046 | + | 0.985949i | \(0.553423\pi\) | |||||||
\(632\) | 14.3660 | − | 8.29423i | 0.571450 | − | 0.329927i | ||||
\(633\) | 9.16987 | − | 15.8827i | 0.364470 | − | 0.631280i | ||||
\(634\) | −13.7321 | + | 23.7846i | −0.545369 | + | 0.944608i | ||||
\(635\) | −9.39230 | −0.372722 | ||||||||
\(636\) | 16.0981 | − | 9.29423i | 0.638330 | − | 0.368540i | ||||
\(637\) | −15.0000 | + | 19.0526i | −0.594322 | + | 0.754890i | ||||
\(638\) | − | 0.588457i | − | 0.0232972i | ||||||
\(639\) | 3.29423 | + | 1.90192i | 0.130318 | + | 0.0752389i | ||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | − | 44.7846i | − | 1.76889i | −0.466648 | − | 0.884443i | \(-0.654539\pi\) | ||
0.466648 | − | 0.884443i | \(-0.345461\pi\) | |||||||
\(642\) | −1.79423 | − | 3.10770i | −0.0708126 | − | 0.122651i | ||||
\(643\) | 31.7942 | − | 18.3564i | 1.25384 | − | 0.723906i | 0.281972 | − | 0.959423i | \(-0.409012\pi\) |
0.971870 | + | 0.235517i | \(0.0756782\pi\) | |||||||
\(644\) | −8.19615 | + | 23.6603i | −0.322974 | + | 0.932345i | ||||
\(645\) | −12.4641 | −0.490774 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6962 | + | 21.9904i | 0.499137 | + | 0.864531i | 1.00000 | 0.000995924i | \(-0.000317013\pi\) | |
−0.500862 | + | 0.865527i | \(0.666984\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | −9.00000 | − | 5.19615i | −0.353281 | − | 0.203967i | ||||
\(650\) | 1.73205 | − | 3.00000i | 0.0679366 | − | 0.117670i | ||||
\(651\) | 9.88269 | − | 1.90192i | 0.387333 | − | 0.0745423i | ||||
\(652\) | 6.19615 | + | 10.7321i | 0.242660 | + | 0.420300i | ||||
\(653\) | − | 22.1436i | − | 0.866546i | −0.901263 | − | 0.433273i | \(-0.857359\pi\) | ||
0.901263 | − | 0.433273i | \(-0.142641\pi\) | |||||||
\(654\) | − | 5.53590i | − | 0.216471i | ||||||
\(655\) | 16.3923 | 0.640500 | ||||||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | 20.7846i | 0.810885i | ||||||||
\(658\) | 7.79423 | − | 22.5000i | 0.303851 | − | 0.877141i | ||||
\(659\) | −17.7058 | − | 10.2224i | −0.689719 | − | 0.398209i | 0.113788 | − | 0.993505i | \(-0.463702\pi\) |
−0.803507 | + | 0.595296i | \(0.797035\pi\) | |||||||
\(660\) | − | 2.19615i | − | 0.0854851i | ||||||
\(661\) | −35.3827 | − | 20.4282i | −1.37623 | − | 0.794565i | −0.384524 | − | 0.923115i | \(-0.625634\pi\) |
−0.991703 | + | 0.128550i | \(0.958968\pi\) | |||||||
\(662\) | 6.92820 | + | 4.00000i | 0.269272 | + | 0.155464i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.696152 | − | 0.401924i | −0.0270160 | − | 0.0155977i | ||||
\(665\) | 4.09808 | − | 11.8301i | 0.158917 | − | 0.458753i | ||||
\(666\) | 10.9019 | + | 6.29423i | 0.422441 | + | 0.243896i | ||||
\(667\) | 2.19615 | − | 3.80385i | 0.0850354 | − | 0.147286i | ||||
\(668\) | −10.3923 | −0.402090 | ||||||||
\(669\) | − | 17.7846i | − | 0.687593i | ||||||
\(670\) | 4.00000i | 0.154533i | ||||||||
\(671\) | 0.588457 | + | 1.01924i | 0.0227171 | + | 0.0393472i | ||||
\(672\) | 4.50000 | − | 0.866025i | 0.173591 | − | 0.0334077i | ||||
\(673\) | −13.4904 | + | 23.3660i | −0.520016 | + | 0.900694i | 0.479713 | + | 0.877425i | \(0.340741\pi\) |
−0.999729 | + | 0.0232688i | \(0.992593\pi\) | |||||||
\(674\) | −8.66025 | − | 5.00000i | −0.333581 | − | 0.192593i | ||||
\(675\) | −5.19615 | −0.200000 | ||||||||
\(676\) | 0.500000 | + | 0.866025i | 0.0192308 | + | 0.0333087i | ||||
\(677\) | −14.4904 | − | 25.0981i | −0.556911 | − | 0.964597i | −0.997752 | − | 0.0670125i | \(-0.978653\pi\) |
0.440842 | − | 0.897585i | \(-0.354680\pi\) | |||||||
\(678\) | −32.1962 | −1.23649 | ||||||||
\(679\) | 13.3923 | − | 38.6603i | 0.513949 | − | 1.48364i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.80385 | + | 6.58846i | 0.145764 | + | 0.252470i | ||||
\(682\) | − | 2.78461i | − | 0.106628i | ||||||
\(683\) | −36.7750 | + | 21.2321i | −1.40716 | + | 0.812422i | −0.995113 | − | 0.0987426i | \(-0.968518\pi\) |
−0.412043 | + | 0.911164i | \(0.635185\pi\) | |||||||
\(684\) | 14.1962i | 0.542803i | ||||||||
\(685\) | 10.7321i | 0.410051i | ||||||||
\(686\) | −16.4545 | − | 8.50000i | −0.628235 | − | 0.324532i | ||||
\(687\) | −41.8923 | + | 24.1865i | −1.59829 | + | 0.922774i | ||||
\(688\) | −7.19615 | −0.274351 | ||||||||
\(689\) | 18.5885 | − | 32.1962i | 0.708164 | − | 1.22658i | ||||
\(690\) | 8.19615 | − | 14.1962i | 0.312022 | − | 0.540438i | ||||
\(691\) | 16.3923 | − | 9.46410i | 0.623593 | − | 0.360031i | −0.154674 | − | 0.987966i | \(-0.549433\pi\) |
0.778266 | + | 0.627934i | \(0.216099\pi\) | |||||||
\(692\) | −2.19615 | −0.0834852 | ||||||||
\(693\) | 3.29423 | − | 9.50962i | 0.125137 | − | 0.361241i | ||||
\(694\) | 27.2487 | 1.03435 | ||||||||
\(695\) | −13.9019 | + | 8.02628i | −0.527330 | + | 0.304454i | ||||
\(696\) | −0.803848 | −0.0304698 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 4.39230 | 0.166251 | ||||||||
\(699\) | − | 8.19615i | − | 0.310007i | ||||||
\(700\) | 2.50000 | + | 0.866025i | 0.0944911 | + | 0.0327327i | ||||
\(701\) | 9.67949i | 0.365589i | 0.983151 | + | 0.182795i | \(0.0585144\pi\) | ||||
−0.983151 | + | 0.182795i | \(0.941486\pi\) | |||||||
\(702\) | −9.00000 | + | 15.5885i | −0.339683 | + | 0.588348i | ||||
\(703\) | 17.1962 | − | 9.92820i | 0.648565 | − | 0.374449i | ||||
\(704\) | − | 1.26795i | − | 0.0477876i | ||||||
\(705\) | −7.79423 | + | 13.5000i | −0.293548 | + | 0.508439i | ||||
\(706\) | 26.4904 | − | 15.2942i | 0.996979 | − | 0.575606i | ||||
\(707\) | −0.401924 | − | 2.08846i | −0.0151159 | − | 0.0785445i | ||||
\(708\) | −7.09808 | + | 12.2942i | −0.266762 | + | 0.462045i | ||||
\(709\) | 2.60770 | + | 4.51666i | 0.0979340 | + | 0.169627i | 0.910829 | − | 0.412783i | \(-0.135443\pi\) |
−0.812895 | + | 0.582410i | \(0.802110\pi\) | |||||||
\(710\) | 0.633975 | + | 1.09808i | 0.0237926 | + | 0.0412101i | ||||
\(711\) | −49.7654 | −1.86635 | ||||||||
\(712\) | −14.1962 | − | 8.19615i | −0.532023 | − | 0.307164i | ||||
\(713\) | 10.3923 | − | 18.0000i | 0.389195 | − | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.19615 | − | 3.80385i | −0.0821314 | − | 0.142256i | ||||
\(716\) | − | 6.58846i | − | 0.246222i | ||||||
\(717\) | 31.6865 | + | 18.2942i | 1.18336 | + | 0.683210i | ||||
\(718\) | 26.1962 | 0.977632 | ||||||||
\(719\) | −20.7846 | + | 36.0000i | −0.775135 | + | 1.34257i | 0.159583 | + | 0.987184i | \(0.448985\pi\) |
−0.934718 | + | 0.355389i | \(0.884348\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 31.5000 | − | 6.06218i | 1.17312 | − | 0.225767i | ||||
\(722\) | 2.93782 | + | 1.69615i | 0.109334 | + | 0.0631243i | ||||
\(723\) | −30.9904 | + | 17.8923i | −1.15254 | + | 0.665422i | ||||
\(724\) | 6.40192 | + | 3.69615i | 0.237926 | + | 0.137366i | ||||
\(725\) | −0.401924 | − | 0.232051i | −0.0149271 | − | 0.00861815i | ||||
\(726\) | 14.0885 | + | 8.13397i | 0.522872 | + | 0.301880i | ||||
\(727\) | −0.215390 | − | 0.124356i | −0.00798838 | − | 0.00461210i | 0.496000 | − | 0.868322i | \(-0.334801\pi\) |
−0.503989 | + | 0.863710i | \(0.668135\pi\) | |||||||
\(728\) | 6.92820 | − | 6.00000i | 0.256776 | − | 0.222375i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −3.46410 | + | 6.00000i | −0.128212 | + | 0.222070i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.39230 | − | 0.803848i | 0.0514611 | − | 0.0297111i | ||||
\(733\) | − | 4.05256i | − | 0.149685i | −0.997195 | − | 0.0748423i | \(-0.976155\pi\) | ||
0.997195 | − | 0.0748423i | \(-0.0238454\pi\) | |||||||
\(734\) | −9.40192 | − | 16.2846i | −0.347031 | − | 0.601076i | ||||
\(735\) | 9.52628 | + | 7.50000i | 0.351382 | + | 0.276642i | ||||
\(736\) | 4.73205 | − | 8.19615i | 0.174426 | − | 0.302114i | ||||
\(737\) | 4.39230 | + | 2.53590i | 0.161793 | + | 0.0934110i | ||||
\(738\) | 23.3827 | − | 13.5000i | 0.860729 | − | 0.496942i | ||||
\(739\) | 14.5885 | + | 25.2679i | 0.536645 | + | 0.929497i | 0.999082 | + | 0.0428442i | \(0.0136419\pi\) |
−0.462437 | + | 0.886652i | \(0.653025\pi\) | |||||||
\(740\) | 2.09808 | + | 3.63397i | 0.0771268 | + | 0.133588i | ||||
\(741\) | 14.1962 | + | 24.5885i | 0.521509 | + | 0.903280i | ||||
\(742\) | 26.8301 | + | 9.29423i | 0.984965 | + | 0.341202i | ||||
\(743\) | 38.6769 | − | 22.3301i | 1.41892 | − | 0.819213i | 0.422714 | − | 0.906263i | \(-0.361077\pi\) |
0.996204 | + | 0.0870500i | \(0.0277440\pi\) | |||||||
\(744\) | −3.80385 | −0.139456 | ||||||||
\(745\) | − | 12.0000i | − | 0.439646i | ||||||
\(746\) | −0.169873 | + | 0.0980762i | −0.00621949 | + | 0.00359083i | ||||
\(747\) | 1.20577 | + | 2.08846i | 0.0441169 | + | 0.0764127i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.79423 | − | 5.17949i | 0.0655597 | − | 0.189255i | ||||
\(750\) | −1.50000 | − | 0.866025i | −0.0547723 | − | 0.0316228i | ||||
\(751\) | −42.3923 | −1.54692 | −0.773459 | − | 0.633847i | \(-0.781475\pi\) | ||||
−0.773459 | + | 0.633847i | \(0.781475\pi\) | |||||||
\(752\) | −4.50000 | + | 7.79423i | −0.164098 | + | 0.284226i | ||||
\(753\) | −15.5885 | − | 27.0000i | −0.568075 | − | 0.983935i | ||||
\(754\) | −1.39230 | + | 0.803848i | −0.0507048 | + | 0.0292744i | ||||
\(755\) | −6.19615 | −0.225501 | ||||||||
\(756\) | −12.9904 | − | 4.50000i | −0.472456 | − | 0.163663i | ||||
\(757\) | 22.5885 | 0.820991 | 0.410496 | − | 0.911863i | \(-0.365356\pi\) | ||||
0.410496 | + | 0.911863i | \(0.365356\pi\) | |||||||
\(758\) | −26.3205 | + | 15.1962i | −0.956004 | + | 0.551949i | ||||
\(759\) | −10.3923 | − | 18.0000i | −0.377217 | − | 0.653359i | ||||
\(760\) | −2.36603 | + | 4.09808i | −0.0858248 | + | 0.148653i | ||||
\(761\) | −33.0000 | −1.19625 | −0.598125 | − | 0.801403i | \(-0.704087\pi\) | ||||
−0.598125 | + | 0.801403i | \(0.704087\pi\) | |||||||
\(762\) | 14.0885 | + | 8.13397i | 0.510371 | + | 0.294663i | ||||
\(763\) | 6.39230 | − | 5.53590i | 0.231417 | − | 0.200413i | ||||
\(764\) | − | 3.46410i | − | 0.125327i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20577 | + | 0.696152i | −0.0435663 | + | 0.0251530i | ||||
\(767\) | 28.3923i | 1.02519i | ||||||||
\(768\) | −1.73205 | −0.0625000 | ||||||||
\(769\) | 13.5000 | − | 7.79423i | 0.486822 | − | 0.281067i | −0.236433 | − | 0.971648i | \(-0.575978\pi\) |
0.723255 | + | 0.690581i | \(0.242645\pi\) | |||||||
\(770\) | 2.53590 | − | 2.19615i | 0.0913874 | − | 0.0791438i | ||||
\(771\) | 6.58846 | + | 11.4115i | 0.237277 | + | 0.410977i | ||||
\(772\) | 12.0981 | + | 20.9545i | 0.435419 | + | 0.754168i | ||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | 18.6962 | + | 10.7942i | 0.672019 | + | 0.387991i | ||||
\(775\) | −1.90192 | − | 1.09808i | −0.0683191 | − | 0.0394441i | ||||
\(776\) | −7.73205 | + | 13.3923i | −0.277564 | + | 0.480756i | ||||
\(777\) | 3.63397 | + | 18.8827i | 0.130368 | + | 0.677413i | ||||
\(778\) | 15.3564 | + | 26.5981i | 0.550554 | + | 0.953587i | ||||
\(779\) | − | 42.5885i | − | 1.52589i | ||||||
\(780\) | −5.19615 | + | 3.00000i | −0.186052 | + | 0.107417i | ||||
\(781\) | 1.60770 | 0.0575279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.08846 | + | 1.20577i | 0.0746354 | + | 0.0430908i | ||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | −0.294229 | − | 0.169873i | −0.0105015 | − | 0.00606303i | ||||
\(786\) | −24.5885 | − | 14.1962i | −0.877041 | − | 0.506360i | ||||
\(787\) | −33.9904 | − | 19.6244i | −1.21163 | − | 0.699533i | −0.248513 | − | 0.968629i | \(-0.579942\pi\) |
−0.963113 | + | 0.269096i | \(0.913275\pi\) | |||||||
\(788\) | −5.49038 | − | 3.16987i | −0.195587 | − | 0.112922i | ||||
\(789\) | −15.4019 | + | 8.89230i | −0.548323 | + | 0.316574i | ||||
\(790\) | −14.3660 | − | 8.29423i | −0.511120 | − | 0.295095i | ||||
\(791\) | −32.1962 | − | 37.1769i | −1.14476 | − | 1.32186i | ||||
\(792\) | −1.90192 | + | 3.29423i | −0.0675819 | + | 0.117055i | ||||
\(793\) | 1.60770 | − | 2.78461i | 0.0570909 | − | 0.0988844i | ||||
\(794\) | −0.588457 | −0.0208836 | ||||||||
\(795\) | −16.0981 | − | 9.29423i | −0.570940 | − | 0.329632i | ||||
\(796\) | − | 6.92820i | − | 0.245564i | ||||||
\(797\) | 21.5885 | + | 37.3923i | 0.764702 | + | 1.32450i | 0.940404 | + | 0.340060i | \(0.110447\pi\) |
−0.175701 | + | 0.984444i | \(0.556219\pi\) | |||||||
\(798\) | −16.3923 | + | 14.1962i | −0.580281 | + | 0.502538i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 24.5885 | + | 42.5885i | 0.868790 | + | 1.50479i | ||||
\(802\) | −13.7942 | − | 23.8923i | −0.487091 | − | 0.843667i | ||||
\(803\) | 4.39230 | + | 7.60770i | 0.155001 | + | 0.268470i | ||||
\(804\) | 3.46410 | − | 6.00000i | 0.122169 | − | 0.211604i | ||||
\(805\) | 24.5885 | − | 4.73205i | 0.866629 | − | 0.166783i | ||||
\(806\) | −6.58846 | + | 3.80385i | −0.232069 | + | 0.133985i | ||||
\(807\) | −15.5885 | + | 27.0000i | −0.548740 | + | 0.950445i | ||||
\(808\) | 0.803848i | 0.0282793i | ||||||||
\(809\) | −6.48076 | + | 3.74167i | −0.227851 | + | 0.131550i | −0.609580 | − | 0.792724i | \(-0.708662\pi\) |
0.381729 | + | 0.924274i | \(0.375329\pi\) | |||||||
\(810\) | 7.79423 | + | 4.50000i | 0.273861 | + | 0.158114i | ||||
\(811\) | 51.4641i | 1.80715i | 0.428431 | + | 0.903575i | \(0.359067\pi\) | ||||
−0.428431 | + | 0.903575i | \(0.640933\pi\) | |||||||
\(812\) | −0.803848 | − | 0.928203i | −0.0282095 | − | 0.0325735i | ||||
\(813\) | 42.5885i | 1.49364i | ||||||||
\(814\) | 5.32051 | 0.186484 | ||||||||
\(815\) | 6.19615 | − | 10.7321i | 0.217042 | − | 0.375927i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.4904 | − | 17.0263i | 1.03174 | − | 0.595674i | ||||
\(818\) | −34.5167 | −1.20685 | ||||||||
\(819\) | −27.0000 | + | 5.19615i | −0.943456 | + | 0.181568i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 16.2058 | − | 9.35641i | 0.565585 | − | 0.326541i | −0.189799 | − | 0.981823i | \(-0.560784\pi\) |
0.755384 | + | 0.655282i | \(0.227450\pi\) | |||||||
\(822\) | 9.29423 | − | 16.0981i | 0.324173 | − | 0.561485i | ||||
\(823\) | −25.6962 | + | 44.5070i | −0.895712 | + | 1.55142i | −0.0627901 | + | 0.998027i | \(0.520000\pi\) |
−0.832921 | + | 0.553391i | \(0.813333\pi\) | |||||||
\(824\) | −12.1244 | −0.422372 | ||||||||
\(825\) | −1.90192 | + | 1.09808i | −0.0662165 | + | 0.0382301i | ||||
\(826\) | −21.2942 | + | 4.09808i | −0.740921 | + | 0.142590i | ||||
\(827\) | 37.6410i | 1.30891i | 0.756103 | + | 0.654453i | \(0.227101\pi\) | ||||
−0.756103 | + | 0.654453i | \(0.772899\pi\) | |||||||
\(828\) | −24.5885 | + | 14.1962i | −0.854508 | + | 0.493350i | ||||
\(829\) | −6.18653 | + | 3.57180i | −0.214867 | + | 0.124054i | −0.603571 | − | 0.797309i | \(-0.706256\pi\) |
0.388704 | + | 0.921363i | \(0.372923\pi\) | |||||||
\(830\) | 0.803848i | 0.0279020i | ||||||||
\(831\) | −11.9545 | − | 20.7058i | −0.414696 | − | 0.718275i | ||||
\(832\) | −3.00000 | + | 1.73205i | −0.104006 | + | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 27.8038 | 0.962769 | ||||||||
\(835\) | 5.19615 | + | 9.00000i | 0.179820 | + | 0.311458i | ||||
\(836\) | 3.00000 | + | 5.19615i | 0.103757 | + | 0.179713i | ||||
\(837\) | 9.88269 | + | 5.70577i | 0.341596 | + | 0.197220i | ||||
\(838\) | −9.00000 | − | 5.19615i | −0.310900 | − | 0.179498i | ||||
\(839\) | 7.09808 | − | 12.2942i | 0.245053 | − | 0.424444i | −0.717094 | − | 0.696977i | \(-0.754528\pi\) |
0.962146 | + | 0.272533i | \(0.0878614\pi\) | |||||||
\(840\) | −3.00000 | − | 3.46410i | −0.103510 | − | 0.119523i | ||||
\(841\) | −14.3923 | − | 24.9282i | −0.496286 | − | 0.859593i | ||||
\(842\) | 21.9808i | 0.757507i | ||||||||
\(843\) | 4.60770i | 0.158697i | ||||||||
\(844\) | −10.5885 | −0.364470 | ||||||||
\(845\) | 0.500000 | − | 0.866025i | 0.0172005 | − | 0.0297922i | ||||
\(846\) | 23.3827 | − | 13.5000i | 0.803913 | − | 0.464140i | ||||
\(847\) | 4.69615 | + | 24.4019i | 0.161362 | + | 0.838460i | ||||
\(848\) | −9.29423 | − | 5.36603i | −0.319165 | − | 0.184270i | ||||
\(849\) | − | 18.8038i | − | 0.645346i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.3923 | + | 19.8564i | 1.17895 | + | 0.680669i | ||||
\(852\) | − | 2.19615i | − | 0.0752389i | ||||||
\(853\) | 38.7846 | + | 22.3923i | 1.32796 | + | 0.766698i | 0.984984 | − | 0.172646i | \(-0.0552318\pi\) |
0.342976 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(854\) | 2.32051 | + | 0.803848i | 0.0794062 | + | 0.0275071i | ||||
\(855\) | 12.2942 | − | 7.09808i | 0.420454 | − | 0.242749i | ||||
\(856\) | −1.03590 | + | 1.79423i | −0.0354063 | + | 0.0613255i | ||||
\(857\) | −48.5885 | −1.65975 | −0.829875 | − | 0.557949i | \(-0.811588\pi\) | ||||
−0.829875 | + | 0.557949i | \(0.811588\pi\) | |||||||
\(858\) | 7.60770i | 0.259722i | ||||||||
\(859\) | 26.1962i | 0.893801i | 0.894584 | + | 0.446901i | \(0.147472\pi\) | ||||
−0.894584 | + | 0.446901i | \(0.852528\pi\) | |||||||
\(860\) | 3.59808 | + | 6.23205i | 0.122693 | + | 0.212511i | ||||
\(861\) | 38.9711 | + | 13.5000i | 1.32813 | + | 0.460079i | ||||
\(862\) | −1.39230 | + | 2.41154i | −0.0474221 | + | 0.0821375i | ||||
\(863\) | 4.60770 | + | 2.66025i | 0.156848 | + | 0.0905561i | 0.576370 | − | 0.817189i | \(-0.304469\pi\) |
−0.419522 | + | 0.907745i | \(0.637802\pi\) | |||||||
\(864\) | 4.50000 | + | 2.59808i | 0.153093 | + | 0.0883883i | ||||
\(865\) | 1.09808 | + | 1.90192i | 0.0373357 | + | 0.0646673i | ||||
\(866\) | −9.00000 | − | 15.5885i | −0.305832 | − | 0.529717i | ||||
\(867\) | 29.4449 | 1.00000 | ||||||||
\(868\) | −3.80385 | − | 4.39230i | −0.129111 | − | 0.149085i | ||||
\(869\) | −18.2154 | + | 10.5167i | −0.617915 | + | 0.356753i | ||||
\(870\) | 0.401924 | + | 0.696152i | 0.0136265 | + | 0.0236018i | ||||
\(871\) | − | 13.8564i | − | 0.469506i | ||||||
\(872\) | −2.76795 | + | 1.59808i | −0.0937346 | + | 0.0541177i | ||||
\(873\) | 40.1769 | − | 23.1962i | 1.35978 | − | 0.785071i | ||||
\(874\) | 44.7846i | 1.51486i | ||||||||
\(875\) | −0.500000 | − | 2.59808i | −0.0169031 | − | 0.0878310i | ||||
\(876\) | 10.3923 | − | 6.00000i | 0.351123 | − | 0.202721i | ||||
\(877\) | −41.7654 | −1.41032 | −0.705158 | − | 0.709050i | \(-0.749124\pi\) | ||||
−0.705158 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(878\) | −6.16987 | + | 10.6865i | −0.208223 | + | 0.360653i | ||||
\(879\) | −3.80385 | + | 6.58846i | −0.128301 | + | 0.222223i | ||||
\(880\) | −1.09808 | + | 0.633975i | −0.0370161 | + | 0.0213713i | ||||
\(881\) | 4.39230 | 0.147981 | 0.0739903 | − | 0.997259i | \(-0.476427\pi\) | ||||
0.0739903 | + | 0.997259i | \(0.476427\pi\) | |||||||
\(882\) | −7.79423 | − | 19.5000i | −0.262445 | − | 0.656599i | ||||
\(883\) | −44.3731 | −1.49327 | −0.746636 | − | 0.665232i | \(-0.768332\pi\) | ||||
−0.746636 | + | 0.665232i | \(0.768332\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1962 | 0.477198 | ||||||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | −28.6077 | −0.960552 | −0.480276 | − | 0.877117i | \(-0.659464\pi\) | ||||
−0.480276 | + | 0.877117i | \(0.659464\pi\) | |||||||
\(888\) | − | 7.26795i | − | 0.243896i | ||||||
\(889\) | 4.69615 | + | 24.4019i | 0.157504 | + | 0.818414i | ||||
\(890\) | 16.3923i | 0.549471i | ||||||||
\(891\) | 9.88269 | − | 5.70577i | 0.331082 | − | 0.191151i | ||||
\(892\) | −8.89230 | + | 5.13397i | −0.297736 | + | 0.171898i | ||||
\(893\) | − | 42.5885i | − | 1.42517i | ||||||
\(894\) | −10.3923 | + | 18.0000i | −0.347571 | + | 0.602010i | ||||
\(895\) | −5.70577 | + | 3.29423i | −0.190723 | + | 0.110114i | ||||
\(896\) | −1.73205 | − | 2.00000i | −0.0578638 | − | 0.0668153i | ||||
\(897\) | −28.3923 | + | 49.1769i | −0.947991 | + | 1.64197i | ||||
\(898\) | −10.7942 | − | 18.6962i | −0.360208 | − | 0.623899i | ||||
\(899\) | 0.509619 | + | 0.882686i | 0.0169967 | + | 0.0294392i | ||||
\(900\) | 1.50000 | + | 2.59808i | 0.0500000 | + | 0.0866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 5.70577 | − | 9.88269i | 0.189981 | − | 0.329057i | ||||
\(903\) | 6.23205 | + | 32.3827i | 0.207390 | + | 1.07763i | ||||
\(904\) | 9.29423 | + | 16.0981i | 0.309121 | + | 0.535414i | ||||
\(905\) | − | 7.39230i | − | 0.245729i | ||||||
\(906\) | 9.29423 | + | 5.36603i | 0.308780 | + | 0.178274i | ||||
\(907\) | 33.1962 | 1.10226 | 0.551130 | − | 0.834419i | \(-0.314197\pi\) | ||||
0.551130 | + | 0.834419i | \(0.314197\pi\) | |||||||
\(908\) | 2.19615 | − | 3.80385i | 0.0728819 | − | 0.126235i | ||||
\(909\) | 1.20577 | − | 2.08846i | 0.0399929 | − | 0.0692698i | ||||
\(910\) | −8.66025 | − | 3.00000i | −0.287085 | − | 0.0994490i | ||||
\(911\) | 4.90192 | + | 2.83013i | 0.162408 | + | 0.0937663i | 0.579001 | − | 0.815327i | \(-0.303443\pi\) |
−0.416593 | + | 0.909093i | \(0.636776\pi\) | |||||||
\(912\) | 7.09808 | − | 4.09808i | 0.235041 | − | 0.135701i | ||||
\(913\) | 0.882686 | + | 0.509619i | 0.0292126 | + | 0.0168659i | ||||
\(914\) | 15.9282 | + | 9.19615i | 0.526858 | + | 0.304182i | ||||
\(915\) | −1.39230 | − | 0.803848i | −0.0460282 | − | 0.0265744i | ||||
\(916\) | 24.1865 | + | 13.9641i | 0.799146 | + | 0.461387i | ||||
\(917\) | −8.19615 | − | 42.5885i | −0.270661 | − | 1.40639i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2942 | − | 23.0263i | 0.438536 | − | 0.759567i | −0.559041 | − | 0.829140i | \(-0.688830\pi\) |
0.997577 | + | 0.0695733i | \(0.0221638\pi\) | |||||||
\(920\) | −9.46410 | −0.312022 | ||||||||
\(921\) | 26.6769 | − | 15.4019i | 0.879034 | − | 0.507511i | ||||
\(922\) | − | 5.19615i | − | 0.171126i | ||||||
\(923\) | −2.19615 | − | 3.80385i | −0.0722872 | − | 0.125205i | ||||
\(924\) | −5.70577 | + | 1.09808i | −0.187706 | + | 0.0361241i | ||||
\(925\) | 2.09808 | − | 3.63397i | 0.0689843 | − | 0.119484i | ||||
\(926\) | 20.2583 | + | 11.6962i | 0.665730 | + | 0.384359i | ||||
\(927\) | 31.5000 | + | 18.1865i | 1.03460 | + | 0.597324i | ||||
\(928\) | 0.232051 | + | 0.401924i | 0.00761744 | + | 0.0131938i | ||||
\(929\) | 16.2846 | + | 28.2058i | 0.534281 | + | 0.925401i | 0.999198 | + | 0.0400471i | \(0.0127508\pi\) |
−0.464917 | + | 0.885354i | \(0.653916\pi\) | |||||||
\(930\) | 1.90192 | + | 3.29423i | 0.0623665 | + | 0.108022i | ||||
\(931\) | −32.7846 | − | 4.73205i | −1.07447 | − | 0.155087i | ||||
\(932\) | −4.09808 | + | 2.36603i | −0.134237 | + | 0.0775017i | ||||
\(933\) | −45.3731 | −1.48545 | ||||||||
\(934\) | − | 17.1962i | − | 0.562675i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3923 | 0.339683 | ||||||||
\(937\) | − | 11.4115i | − | 0.372799i | −0.982474 | − | 0.186399i | \(-0.940318\pi\) | ||
0.982474 | − | 0.186399i | \(-0.0596818\pi\) | |||||||
\(938\) | 10.3923 | − | 2.00000i | 0.339321 | − | 0.0653023i | ||||
\(939\) | 14.7058 | + | 8.49038i | 0.479905 | + | 0.277073i | ||||
\(940\) | 9.00000 | 0.293548 | ||||||||
\(941\) | 12.9904 | − | 22.5000i | 0.423474 | − | 0.733479i | −0.572802 | − | 0.819694i | \(-0.694144\pi\) |
0.996277 | + | 0.0862145i | \(0.0274771\pi\) | |||||||
\(942\) | 0.294229 | + | 0.509619i | 0.00958649 | + | 0.0166043i | ||||
\(943\) | 73.7654 | − | 42.5885i | 2.40213 | − | 1.38687i | ||||
\(944\) | 8.19615 | 0.266762 | ||||||||
\(945\) | 2.59808 | + | 13.5000i | 0.0845154 | + | 0.439155i | ||||
\(946\) | 9.12436 | 0.296658 | ||||||||
\(947\) | −51.5885 | + | 29.7846i | −1.67640 | + | 0.967870i | −0.712474 | + | 0.701699i | \(0.752425\pi\) |
−0.963926 | + | 0.266171i | \(0.914241\pi\) | |||||||
\(948\) | 14.3660 | + | 24.8827i | 0.466587 | + | 0.808152i | ||||
\(949\) | 12.0000 | − | 20.7846i | 0.389536 | − | 0.674697i | ||||
\(950\) | 4.73205 | 0.153528 | ||||||||
\(951\) | −41.1962 | − | 23.7846i | −1.33588 | − | 0.771269i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.73205i | − | 0.153286i | −0.997059 | − | 0.0766431i | \(-0.975580\pi\) | ||
0.997059 | − | 0.0766431i | \(-0.0244202\pi\) | |||||||
\(954\) | 16.0981 | + | 27.8827i | 0.521194 | + | 0.902735i | ||||
\(955\) | −3.00000 | + | 1.73205i | −0.0970777 | + | 0.0560478i | ||||
\(956\) | − | 21.1244i | − | 0.683210i | ||||||
\(957\) | 1.01924 | 0.0329473 | ||||||||
\(958\) | 9.00000 | − | 5.19615i | 0.290777 | − | 0.167880i | ||||
\(959\) | 27.8827 | − | 5.36603i | 0.900379 | − | 0.173278i | ||||
\(960\) | 0.866025 | + | 1.50000i | 0.0279508 | + | 0.0484123i | ||||
\(961\) | −13.0885 | − | 22.6699i | −0.422208 | − | 0.731286i | ||||
\(962\) | −7.26795 | − | 12.5885i | −0.234328 | − | 0.405868i | ||||
\(963\) | 5.38269 | − | 3.10770i | 0.173455 | − | 0.100144i | ||||
\(964\) | 17.8923 | + | 10.3301i | 0.576272 | + | 0.332711i | ||||
\(965\) | 12.0981 | − | 20.9545i | 0.389451 | − | 0.674549i | ||||
\(966\) | −40.9808 | − | 14.1962i | −1.31853 | − | 0.456754i | ||||
\(967\) | 8.00000 | + | 13.8564i | 0.257263 | + | 0.445592i | 0.965508 | − | 0.260375i | \(-0.0838461\pi\) |
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(968\) | − | 9.39230i | − | 0.301880i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.4641 | 0.496522 | ||||||||
\(971\) | −13.3923 | + | 23.1962i | −0.429780 | + | 0.744400i | −0.996853 | − | 0.0792670i | \(-0.974742\pi\) |
0.567074 | + | 0.823667i | \(0.308075\pi\) | |||||||
\(972\) | −7.79423 | − | 13.5000i | −0.250000 | − | 0.433013i | ||||
\(973\) | 27.8038 | + | 32.1051i | 0.891350 | + | 1.02924i | ||||
\(974\) | −29.4449 | − | 17.0000i | −0.943474 | − | 0.544715i | ||||
\(975\) | 5.19615 | + | 3.00000i | 0.166410 | + | 0.0960769i | ||||
\(976\) | −0.803848 | − | 0.464102i | −0.0257305 | − | 0.0148555i | ||||
\(977\) | −16.3923 | − | 9.46410i | −0.524436 | − | 0.302783i | 0.214312 | − | 0.976765i | \(-0.431249\pi\) |
−0.738748 | + | 0.673982i | \(0.764583\pi\) | |||||||
\(978\) | −18.5885 | + | 10.7321i | −0.594393 | + | 0.343173i | ||||
\(979\) | 18.0000 | + | 10.3923i | 0.575282 | + | 0.332140i | ||||
\(980\) | 1.00000 | − | 6.92820i | 0.0319438 | − | 0.221313i | ||||
\(981\) | 9.58846 | 0.306136 | ||||||||
\(982\) | 1.43782 | − | 2.49038i | 0.0458827 | − | 0.0794713i | ||||
\(983\) | −10.6077 | −0.338333 | −0.169166 | − | 0.985587i | \(-0.554108\pi\) | ||||
−0.169166 | + | 0.985587i | \(0.554108\pi\) | |||||||
\(984\) | −13.5000 | − | 7.79423i | −0.430364 | − | 0.248471i | ||||
\(985\) | 6.33975i | 0.202001i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.9711 | + | 13.5000i | 1.24047 | + | 0.429710i | ||||
\(988\) | 8.19615 | − | 14.1962i | 0.260754 | − | 0.451640i | ||||
\(989\) | 58.9808 | + | 34.0526i | 1.87548 | + | 1.08281i | ||||
\(990\) | 3.80385 | 0.120894 | ||||||||
\(991\) | 22.2942 | + | 38.6147i | 0.708200 | + | 1.22664i | 0.965524 | + | 0.260313i | \(0.0838256\pi\) |
−0.257325 | + | 0.966325i | \(0.582841\pi\) | |||||||
\(992\) | 1.09808 | + | 1.90192i | 0.0348640 | + | 0.0603861i | ||||
\(993\) | −6.92820 | + | 12.0000i | −0.219860 | + | 0.380808i | ||||
\(994\) | 2.53590 | − | 2.19615i | 0.0804338 | − | 0.0696577i | ||||
\(995\) | −6.00000 | + | 3.46410i | −0.190213 | + | 0.109819i | ||||
\(996\) | 0.696152 | − | 1.20577i | 0.0220584 | − | 0.0382063i | ||||
\(997\) | 13.5167i | 0.428077i | 0.976825 | + | 0.214038i | \(0.0686618\pi\) | ||||
−0.976825 | + | 0.214038i | \(0.931338\pi\) | |||||||
\(998\) | −5.02628 | + | 2.90192i | −0.159104 | + | 0.0918588i | ||||
\(999\) | −10.9019 | + | 18.8827i | −0.344922 | + | 0.597422i |
(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 | 630.2.t.a.551.2 | yes | 4 | |
3.2 | odd | 2 | 1890.2.t.a.1601.1 | 4 | |||
7.3 | odd | 6 | 630.2.bk.a.101.2 | yes | 4 | ||
9.4 | even | 3 | 1890.2.bk.a.341.2 | 4 | |||
9.5 | odd | 6 | 630.2.bk.a.131.1 | yes | 4 | ||
21.17 | even | 6 | 1890.2.bk.a.521.1 | 4 | |||
63.31 | odd | 6 | 1890.2.t.a.1151.1 | 4 | |||
63.59 | even | 6 | inner | 630.2.t.a.311.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.a.311.2 | ✓ | 4 | 63.59 | even | 6 | inner | |
630.2.t.a.551.2 | yes | 4 | 1.1 | even | 1 | trivial | |
630.2.bk.a.101.2 | yes | 4 | 7.3 | odd | 6 | ||
630.2.bk.a.131.1 | yes | 4 | 9.5 | odd | 6 | ||
1890.2.t.a.1151.1 | 4 | 63.31 | odd | 6 | |||
1890.2.t.a.1601.1 | 4 | 3.2 | odd | 2 | |||
1890.2.bk.a.341.2 | 4 | 9.4 | even | 3 | |||
1890.2.bk.a.521.1 | 4 | 21.17 | even | 6 |