Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.353 |
Dual form | 462.2.k.d.89.4 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.358719 | + | 0.621320i | 0.160424 | + | 0.277863i | 0.935021 | − | 0.354593i | \(-0.115380\pi\) |
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0.621320 | + | 0.358719i | 0.196479 | + | 0.113437i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | ||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 2.09077 | − | 1.62132i | 0.558782 | − | 0.433316i | ||||
\(15\) | − | 1.24264i | − | 0.320848i | ||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.31552 | − | 5.74264i | 0.804131 | − | 1.39279i | −0.112746 | − | 0.993624i | \(-0.535965\pi\) |
0.916876 | − | 0.399171i | \(-0.130702\pi\) | |||||||
\(18\) | 2.59808 | + | 1.50000i | 0.612372 | + | 0.353553i | ||||
\(19\) | 1.24264 | − | 0.717439i | 0.285081 | − | 0.164592i | −0.350640 | − | 0.936510i | \(-0.614036\pi\) |
0.635722 | + | 0.771918i | \(0.280703\pi\) | |||||||
\(20\) | 0.717439 | 0.160424 | ||||||||
\(21\) | −4.24264 | − | 1.73205i | −0.925820 | − | 0.377964i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.27231 | + | 3.62132i | −1.30787 | + | 0.755097i | −0.981740 | − | 0.190228i | \(-0.939077\pi\) |
−0.326127 | + | 0.945326i | \(0.605744\pi\) | |||||||
\(24\) | −0.866025 | + | 1.50000i | −0.176777 | + | 0.306186i | ||||
\(25\) | 2.24264 | − | 3.88437i | 0.448528 | − | 0.776874i | ||||
\(26\) | −1.73205 | − | 3.00000i | −0.339683 | − | 0.588348i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | −0.621320 | − | 1.07616i | −0.113437 | − | 0.196479i | ||||
\(31\) | −7.24264 | − | 4.18154i | −1.30082 | − | 0.751027i | −0.320273 | − | 0.947325i | \(-0.603774\pi\) |
−0.980544 | + | 0.196299i | \(0.937108\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −0.866025 | − | 1.50000i | −0.150756 | − | 0.261116i | ||||
\(34\) | − | 6.63103i | − | 1.13721i | ||||||
\(35\) | 1.16320 | + | 1.50000i | 0.196616 | + | 0.253546i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0.717439 | − | 1.24264i | 0.116384 | − | 0.201583i | ||||
\(39\) | −3.00000 | + | 5.19615i | −0.480384 | + | 0.832050i | ||||
\(40\) | 0.621320 | − | 0.358719i | 0.0982394 | − | 0.0567185i | ||||
\(41\) | 5.19615 | 0.811503 | 0.405751 | − | 0.913984i | \(-0.367010\pi\) | ||||
0.405751 | + | 0.913984i | \(0.367010\pi\) | |||||||
\(42\) | −4.54026 | + | 0.621320i | −0.700577 | + | 0.0958718i | ||||
\(43\) | 12.4853 | 1.90399 | 0.951994 | − | 0.306117i | \(-0.0990300\pi\) | ||||
0.951994 | + | 0.306117i | \(0.0990300\pi\) | |||||||
\(44\) | 0.866025 | − | 0.500000i | 0.130558 | − | 0.0753778i | ||||
\(45\) | −1.07616 | + | 1.86396i | −0.160424 | + | 0.277863i | ||||
\(46\) | −3.62132 | + | 6.27231i | −0.533935 | + | 0.924802i | ||||
\(47\) | 0.358719 | + | 0.621320i | 0.0523246 | + | 0.0906289i | 0.891001 | − | 0.454001i | \(-0.150004\pi\) |
−0.838677 | + | 0.544630i | \(0.816670\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | − | 4.48528i | − | 0.634315i | ||||||
\(51\) | −9.94655 | + | 5.74264i | −1.39279 | + | 0.804131i | ||||
\(52\) | −3.00000 | − | 1.73205i | −0.416025 | − | 0.240192i | ||||
\(53\) | 7.34847 | + | 4.24264i | 1.00939 | + | 0.582772i | 0.911013 | − | 0.412378i | \(-0.135302\pi\) |
0.0983769 | + | 0.995149i | \(0.468635\pi\) | |||||||
\(54\) | −2.59808 | − | 4.50000i | −0.353553 | − | 0.612372i | ||||
\(55\) | 0.717439i | 0.0967394i | ||||||||
\(56\) | −0.358719 | − | 2.62132i | −0.0479359 | − | 0.350289i | ||||
\(57\) | −2.48528 | −0.329184 | ||||||||
\(58\) | 4.24264 | + | 7.34847i | 0.557086 | + | 0.964901i | ||||
\(59\) | −6.63103 | + | 11.4853i | −0.863287 | + | 1.49526i | 0.00545184 | + | 0.999985i | \(0.498265\pi\) |
−0.868738 | + | 0.495271i | \(0.835069\pi\) | |||||||
\(60\) | −1.07616 | − | 0.621320i | −0.138931 | − | 0.0802121i | ||||
\(61\) | −3.62132 | + | 2.09077i | −0.463663 | + | 0.267696i | −0.713583 | − | 0.700571i | \(-0.752929\pi\) |
0.249920 | + | 0.968266i | \(0.419596\pi\) | |||||||
\(62\) | −8.36308 | −1.06211 | ||||||||
\(63\) | 4.86396 | + | 6.27231i | 0.612801 | + | 0.790237i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.15232 | − | 1.24264i | 0.266962 | − | 0.154131i | ||||
\(66\) | −1.50000 | − | 0.866025i | −0.184637 | − | 0.106600i | ||||
\(67\) | −6.74264 | + | 11.6786i | −0.823745 | + | 1.42677i | 0.0791303 | + | 0.996864i | \(0.474786\pi\) |
−0.902875 | + | 0.429903i | \(0.858548\pi\) | |||||||
\(68\) | −3.31552 | − | 5.74264i | −0.402065 | − | 0.696397i | ||||
\(69\) | 12.5446 | 1.51019 | ||||||||
\(70\) | 1.75736 | + | 0.717439i | 0.210045 | + | 0.0857504i | ||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 2.59808 | − | 1.50000i | 0.306186 | − | 0.176777i | ||||
\(73\) | 1.24264 | + | 0.717439i | 0.145440 | + | 0.0839699i | 0.570954 | − | 0.820982i | \(-0.306573\pi\) |
−0.425514 | + | 0.904952i | \(0.639907\pi\) | |||||||
\(74\) | −3.46410 | − | 2.00000i | −0.402694 | − | 0.232495i | ||||
\(75\) | −6.72792 | + | 3.88437i | −0.776874 | + | 0.448528i | ||||
\(76\) | − | 1.43488i | − | 0.164592i | ||||||
\(77\) | 2.44949 | + | 1.00000i | 0.279145 | + | 0.113961i | ||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | −1.62132 | − | 2.80821i | −0.182413 | − | 0.315948i | 0.760289 | − | 0.649585i | \(-0.225057\pi\) |
−0.942702 | + | 0.333637i | \(0.891724\pi\) | |||||||
\(80\) | 0.358719 | − | 0.621320i | 0.0401061 | − | 0.0694657i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 4.50000 | − | 2.59808i | 0.496942 | − | 0.286910i | ||||
\(83\) | −6.63103 | −0.727850 | −0.363925 | − | 0.931428i | \(-0.618564\pi\) | ||||
−0.363925 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(84\) | −3.62132 | + | 2.80821i | −0.395118 | + | 0.306401i | ||||
\(85\) | 4.75736 | 0.516008 | ||||||||
\(86\) | 10.8126 | − | 6.24264i | 1.16595 | − | 0.673161i | ||||
\(87\) | 7.34847 | − | 12.7279i | 0.787839 | − | 1.36458i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 5.91359 | + | 10.2426i | 0.626839 | + | 1.08572i | 0.988182 | + | 0.153285i | \(0.0489851\pi\) |
−0.361343 | + | 0.932433i | \(0.617682\pi\) | |||||||
\(90\) | 2.15232i | 0.226874i | ||||||||
\(91\) | −1.24264 | − | 9.08052i | −0.130264 | − | 0.951897i | ||||
\(92\) | 7.24264i | 0.755097i | ||||||||
\(93\) | 7.24264 | + | 12.5446i | 0.751027 | + | 1.30082i | ||||
\(94\) | 0.621320 | + | 0.358719i | 0.0640843 | + | 0.0369991i | ||||
\(95\) | 0.891519 | + | 0.514719i | 0.0914679 | + | 0.0528090i | ||||
\(96\) | 0.866025 | + | 1.50000i | 0.0883883 | + | 0.153093i | ||||
\(97\) | 10.0951i | 1.02501i | 0.858686 | + | 0.512503i | \(0.171282\pi\) | ||||
−0.858686 | + | 0.512503i | \(0.828718\pi\) | |||||||
\(98\) | 4.89898 | − | 5.00000i | 0.494872 | − | 0.505076i | ||||
\(99\) | 3.00000i | 0.301511i | ||||||||
\(100\) | −2.24264 | − | 3.88437i | −0.224264 | − | 0.388437i | ||||
\(101\) | −5.91359 | + | 10.2426i | −0.588424 | + | 1.01918i | 0.406015 | + | 0.913867i | \(0.366918\pi\) |
−0.994439 | + | 0.105314i | \(0.966415\pi\) | |||||||
\(102\) | −5.74264 | + | 9.94655i | −0.568606 | + | 0.984855i | ||||
\(103\) | 1.75736 | − | 1.01461i | 0.173158 | − | 0.0999727i | −0.410916 | − | 0.911673i | \(-0.634791\pi\) |
0.584074 | + | 0.811700i | \(0.301458\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | −0.445759 | − | 3.25736i | −0.0435017 | − | 0.317886i | ||||
\(106\) | 8.48528 | 0.824163 | ||||||||
\(107\) | −12.9904 | + | 7.50000i | −1.25583 | + | 0.725052i | −0.972261 | − | 0.233900i | \(-0.924851\pi\) |
−0.283567 | + | 0.958952i | \(0.591518\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | −5.62132 | + | 9.73641i | −0.538425 | + | 0.932579i | 0.460564 | + | 0.887626i | \(0.347647\pi\) |
−0.998989 | + | 0.0449528i | \(0.985686\pi\) | |||||||
\(110\) | 0.358719 | + | 0.621320i | 0.0342026 | + | 0.0592406i | ||||
\(111\) | 6.92820i | 0.657596i | ||||||||
\(112\) | −1.62132 | − | 2.09077i | −0.153200 | − | 0.197559i | ||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | −2.15232 | + | 1.24264i | −0.201583 | + | 0.116384i | ||||
\(115\) | −4.50000 | − | 2.59808i | −0.419627 | − | 0.242272i | ||||
\(116\) | 7.34847 | + | 4.24264i | 0.682288 | + | 0.393919i | ||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | 13.2621i | 1.22087i | ||||||||
\(119\) | 6.63103 | − | 16.2426i | 0.607866 | − | 1.48896i | ||||
\(120\) | −1.24264 | −0.113437 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −2.09077 | + | 3.62132i | −0.189289 | + | 0.327859i | ||||
\(123\) | −7.79423 | − | 4.50000i | −0.702782 | − | 0.405751i | ||||
\(124\) | −7.24264 | + | 4.18154i | −0.650408 | + | 0.375513i | ||||
\(125\) | 6.80511 | 0.608668 | ||||||||
\(126\) | 7.34847 | + | 3.00000i | 0.654654 | + | 0.267261i | ||||
\(127\) | 6.75736 | 0.599619 | 0.299809 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299809 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −18.7279 | − | 10.8126i | −1.64890 | − | 0.951994i | ||||
\(130\) | 1.24264 | − | 2.15232i | 0.108987 | − | 0.188771i | ||||
\(131\) | −6.63103 | − | 11.4853i | −0.579356 | − | 1.00347i | −0.995553 | − | 0.0941995i | \(-0.969971\pi\) |
0.416198 | − | 0.909274i | \(-0.363362\pi\) | |||||||
\(132\) | −1.73205 | −0.150756 | ||||||||
\(133\) | 3.00000 | − | 2.32640i | 0.260133 | − | 0.201724i | ||||
\(134\) | 13.4853i | 1.16495i | ||||||||
\(135\) | 3.22848 | − | 1.86396i | 0.277863 | − | 0.160424i | ||||
\(136\) | −5.74264 | − | 3.31552i | −0.492427 | − | 0.284303i | ||||
\(137\) | 2.15232 | + | 1.24264i | 0.183885 | + | 0.106166i | 0.589117 | − | 0.808048i | \(-0.299476\pi\) |
−0.405232 | + | 0.914214i | \(0.632809\pi\) | |||||||
\(138\) | 10.8640 | − | 6.27231i | 0.924802 | − | 0.533935i | ||||
\(139\) | 3.46410i | 0.293821i | 0.989150 | + | 0.146911i | \(0.0469330\pi\) | ||||
−0.989150 | + | 0.146911i | \(0.953067\pi\) | |||||||
\(140\) | 1.88064 | − | 0.257359i | 0.158943 | − | 0.0217508i | ||||
\(141\) | − | 1.24264i | − | 0.104649i | ||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 1.73205 | − | 3.00000i | 0.144841 | − | 0.250873i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | −5.27208 | + | 3.04384i | −0.437822 | + | 0.252777i | ||||
\(146\) | 1.43488 | 0.118751 | ||||||||
\(147\) | −11.7426 | − | 3.01834i | −0.968517 | − | 0.248949i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | −3.88437 | + | 6.72792i | −0.317157 | + | 0.549333i | ||||
\(151\) | 4.62132 | − | 8.00436i | 0.376078 | − | 0.651386i | −0.614410 | − | 0.788987i | \(-0.710606\pi\) |
0.990488 | + | 0.137601i | \(0.0439392\pi\) | |||||||
\(152\) | −0.717439 | − | 1.24264i | −0.0581920 | − | 0.100791i | ||||
\(153\) | 19.8931 | 1.60826 | ||||||||
\(154\) | 2.62132 | − | 0.358719i | 0.211232 | − | 0.0289064i | ||||
\(155\) | − | 6.00000i | − | 0.481932i | ||||||
\(156\) | 3.00000 | + | 5.19615i | 0.240192 | + | 0.416025i | ||||
\(157\) | −7.75736 | − | 4.47871i | −0.619105 | − | 0.357440i | 0.157416 | − | 0.987532i | \(-0.449684\pi\) |
−0.776520 | + | 0.630092i | \(0.783017\pi\) | |||||||
\(158\) | −2.80821 | − | 1.62132i | −0.223409 | − | 0.128985i | ||||
\(159\) | −7.34847 | − | 12.7279i | −0.582772 | − | 1.00939i | ||||
\(160\) | − | 0.717439i | − | 0.0567185i | ||||||
\(161\) | −15.1427 | + | 11.7426i | −1.19341 | + | 0.925450i | ||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 6.50000 | + | 11.2583i | 0.509119 | + | 0.881820i | 0.999944 | + | 0.0105623i | \(0.00336213\pi\) |
−0.490825 | + | 0.871258i | \(0.663305\pi\) | |||||||
\(164\) | 2.59808 | − | 4.50000i | 0.202876 | − | 0.351391i | ||||
\(165\) | 0.621320 | − | 1.07616i | 0.0483697 | − | 0.0837788i | ||||
\(166\) | −5.74264 | + | 3.31552i | −0.445715 | + | 0.257334i | ||||
\(167\) | −11.8272 | −0.915215 | −0.457607 | − | 0.889154i | \(-0.651293\pi\) | ||||
−0.457607 | + | 0.889154i | \(0.651293\pi\) | |||||||
\(168\) | −1.73205 | + | 4.24264i | −0.133631 | + | 0.327327i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.11999 | − | 2.37868i | 0.315989 | − | 0.182436i | ||||
\(171\) | 3.72792 | + | 2.15232i | 0.285081 | + | 0.164592i | ||||
\(172\) | 6.24264 | − | 10.8126i | 0.475997 | − | 0.824451i | ||||
\(173\) | −0.717439 | − | 1.24264i | −0.0545459 | − | 0.0944762i | 0.837463 | − | 0.546494i | \(-0.184038\pi\) |
−0.892009 | + | 0.452018i | \(0.850704\pi\) | |||||||
\(174\) | − | 14.6969i | − | 1.11417i | ||||||
\(175\) | 4.48528 | − | 10.9867i | 0.339055 | − | 0.830513i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 19.8931 | − | 11.4853i | 1.49526 | − | 0.863287i | ||||
\(178\) | 10.2426 | + | 5.91359i | 0.767718 | + | 0.443242i | ||||
\(179\) | 2.15232 | + | 1.24264i | 0.160872 | + | 0.0928793i | 0.578275 | − | 0.815842i | \(-0.303726\pi\) |
−0.417403 | + | 0.908722i | \(0.637060\pi\) | |||||||
\(180\) | 1.07616 | + | 1.86396i | 0.0802121 | + | 0.138931i | ||||
\(181\) | − | 2.86976i | − | 0.213307i | −0.994296 | − | 0.106654i | \(-0.965986\pi\) | ||
0.994296 | − | 0.106654i | \(-0.0340136\pi\) | |||||||
\(182\) | −5.61642 | − | 7.24264i | −0.416317 | − | 0.536860i | ||||
\(183\) | 7.24264 | 0.535391 | ||||||||
\(184\) | 3.62132 | + | 6.27231i | 0.266967 | + | 0.462401i | ||||
\(185\) | 1.43488 | − | 2.48528i | 0.105494 | − | 0.182722i | ||||
\(186\) | 12.5446 | + | 7.24264i | 0.919816 | + | 0.531056i | ||||
\(187\) | 5.74264 | − | 3.31552i | 0.419943 | − | 0.242454i | ||||
\(188\) | 0.717439 | 0.0523246 | ||||||||
\(189\) | −1.86396 | − | 13.6208i | −0.135583 | − | 0.990766i | ||||
\(190\) | 1.02944 | 0.0746832 | ||||||||
\(191\) | −15.5885 | + | 9.00000i | −1.12794 | + | 0.651217i | −0.943416 | − | 0.331611i | \(-0.892408\pi\) |
−0.184525 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | −0.242641 | + | 0.420266i | −0.0174657 | + | 0.0302514i | −0.874626 | − | 0.484798i | \(-0.838893\pi\) |
0.857160 | + | 0.515049i | \(0.172226\pi\) | |||||||
\(194\) | 5.04757 | + | 8.74264i | 0.362394 | + | 0.627685i | ||||
\(195\) | −4.30463 | −0.308261 | ||||||||
\(196\) | 1.74264 | − | 6.77962i | 0.124474 | − | 0.484258i | ||||
\(197\) | − | 8.48528i | − | 0.604551i | −0.953221 | − | 0.302276i | \(-0.902254\pi\) | ||
0.953221 | − | 0.302276i | \(-0.0977463\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | −5.48528 | − | 3.16693i | −0.388841 | − | 0.224498i | 0.292817 | − | 0.956169i | \(-0.405407\pi\) |
−0.681658 | + | 0.731671i | \(0.738741\pi\) | |||||||
\(200\) | −3.88437 | − | 2.24264i | −0.274666 | − | 0.158579i | ||||
\(201\) | 20.2279 | − | 11.6786i | 1.42677 | − | 0.823745i | ||||
\(202\) | 11.8272i | 0.832158i | ||||||||
\(203\) | 3.04384 | + | 22.2426i | 0.213635 | + | 1.56113i | ||||
\(204\) | 11.4853i | 0.804131i | ||||||||
\(205\) | 1.86396 | + | 3.22848i | 0.130185 | + | 0.225486i | ||||
\(206\) | 1.01461 | − | 1.75736i | 0.0706914 | − | 0.122441i | ||||
\(207\) | −18.8169 | − | 10.8640i | −1.30787 | − | 0.755097i | ||||
\(208\) | −3.00000 | + | 1.73205i | −0.208013 | + | 0.120096i | ||||
\(209\) | 1.43488 | 0.0992526 | ||||||||
\(210\) | −2.01472 | − | 2.59808i | −0.139029 | − | 0.179284i | ||||
\(211\) | −4.48528 | −0.308780 | −0.154390 | − | 0.988010i | \(-0.549341\pi\) | ||||
−0.154390 | + | 0.988010i | \(0.549341\pi\) | |||||||
\(212\) | 7.34847 | − | 4.24264i | 0.504695 | − | 0.291386i | ||||
\(213\) | −5.19615 | + | 9.00000i | −0.356034 | + | 0.616670i | ||||
\(214\) | −7.50000 | + | 12.9904i | −0.512689 | + | 0.888004i | ||||
\(215\) | 4.47871 | + | 7.75736i | 0.305446 | + | 0.529048i | ||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | −20.4853 | − | 8.36308i | −1.39063 | − | 0.567723i | ||||
\(218\) | 11.2426i | 0.761448i | ||||||||
\(219\) | −1.24264 | − | 2.15232i | −0.0839699 | − | 0.145440i | ||||
\(220\) | 0.621320 | + | 0.358719i | 0.0418894 | + | 0.0241849i | ||||
\(221\) | −19.8931 | − | 11.4853i | −1.33815 | − | 0.772584i | ||||
\(222\) | 3.46410 | + | 6.00000i | 0.232495 | + | 0.402694i | ||||
\(223\) | 13.2621i | 0.888093i | 0.896004 | + | 0.444047i | \(0.146458\pi\) | ||||
−0.896004 | + | 0.444047i | \(0.853542\pi\) | |||||||
\(224\) | −2.44949 | − | 1.00000i | −0.163663 | − | 0.0668153i | ||||
\(225\) | 13.4558 | 0.897056 | ||||||||
\(226\) | −9.00000 | − | 15.5885i | −0.598671 | − | 1.03693i | ||||
\(227\) | 1.16320 | − | 2.01472i | 0.0772042 | − | 0.133722i | −0.824838 | − | 0.565368i | \(-0.808734\pi\) |
0.902043 | + | 0.431647i | \(0.142067\pi\) | |||||||
\(228\) | −1.24264 | + | 2.15232i | −0.0822959 | + | 0.142541i | ||||
\(229\) | 6.00000 | − | 3.46410i | 0.396491 | − | 0.228914i | −0.288478 | − | 0.957487i | \(-0.593149\pi\) |
0.684969 | + | 0.728572i | \(0.259816\pi\) | |||||||
\(230\) | −5.19615 | −0.342624 | ||||||||
\(231\) | −2.80821 | − | 3.62132i | −0.184767 | − | 0.238265i | ||||
\(232\) | 8.48528 | 0.557086 | ||||||||
\(233\) | −6.90271 | + | 3.98528i | −0.452212 | + | 0.261084i | −0.708764 | − | 0.705446i | \(-0.750747\pi\) |
0.256552 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(234\) | 5.19615 | − | 9.00000i | 0.339683 | − | 0.588348i | ||||
\(235\) | −0.257359 | + | 0.445759i | −0.0167883 | + | 0.0290781i | ||||
\(236\) | 6.63103 | + | 11.4853i | 0.431643 | + | 0.747628i | ||||
\(237\) | 5.61642i | 0.364826i | ||||||||
\(238\) | −2.37868 | − | 17.3821i | −0.154187 | − | 1.12671i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −1.07616 | + | 0.621320i | −0.0694657 | + | 0.0401061i | ||||
\(241\) | 12.0000 | + | 6.92820i | 0.772988 | + | 0.446285i | 0.833939 | − | 0.551856i | \(-0.186080\pi\) |
−0.0609515 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(242\) | 0.866025 | + | 0.500000i | 0.0556702 | + | 0.0321412i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 4.18154i | 0.267696i | ||||||||
\(245\) | 3.58719 | + | 3.51472i | 0.229177 | + | 0.224547i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −2.48528 | − | 4.30463i | −0.158135 | − | 0.273897i | ||||
\(248\) | −4.18154 | + | 7.24264i | −0.265528 | + | 0.459908i | ||||
\(249\) | 9.94655 | + | 5.74264i | 0.630337 | + | 0.363925i | ||||
\(250\) | 5.89340 | − | 3.40256i | 0.372731 | − | 0.215196i | ||||
\(251\) | 14.6969 | 0.927663 | 0.463831 | − | 0.885924i | \(-0.346474\pi\) | ||||
0.463831 | + | 0.885924i | \(0.346474\pi\) | |||||||
\(252\) | 7.86396 | − | 1.07616i | 0.495383 | − | 0.0677916i | ||||
\(253\) | −7.24264 | −0.455341 | ||||||||
\(254\) | 5.85204 | − | 3.37868i | 0.367190 | − | 0.211997i | ||||
\(255\) | −7.13604 | − | 4.11999i | −0.446876 | − | 0.258004i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.91359 | − | 10.2426i | −0.368880 | − | 0.638918i | 0.620511 | − | 0.784198i | \(-0.286925\pi\) |
−0.989391 | + | 0.145279i | \(0.953592\pi\) | |||||||
\(258\) | −21.6251 | −1.34632 | ||||||||
\(259\) | −6.48528 | − | 8.36308i | −0.402976 | − | 0.519657i | ||||
\(260\) | − | 2.48528i | − | 0.154131i | ||||||
\(261\) | −22.0454 | + | 12.7279i | −1.36458 | + | 0.787839i | ||||
\(262\) | −11.4853 | − | 6.63103i | −0.709563 | − | 0.409666i | ||||
\(263\) | 19.8931 | + | 11.4853i | 1.22666 | + | 0.708213i | 0.966330 | − | 0.257307i | \(-0.0828351\pi\) |
0.260331 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(264\) | −1.50000 | + | 0.866025i | −0.0923186 | + | 0.0533002i | ||||
\(265\) | 6.08767i | 0.373963i | ||||||||
\(266\) | 1.43488 | − | 3.51472i | 0.0879780 | − | 0.215501i | ||||
\(267\) | − | 20.4853i | − | 1.25368i | ||||||
\(268\) | 6.74264 | + | 11.6786i | 0.411872 | + | 0.713384i | ||||
\(269\) | 4.11999 | − | 7.13604i | 0.251200 | − | 0.435092i | −0.712656 | − | 0.701514i | \(-0.752508\pi\) |
0.963857 | + | 0.266422i | \(0.0858413\pi\) | |||||||
\(270\) | 1.86396 | − | 3.22848i | 0.113437 | − | 0.196479i | ||||
\(271\) | −18.7279 | + | 10.8126i | −1.13764 | + | 0.656817i | −0.945845 | − | 0.324618i | \(-0.894764\pi\) |
−0.191795 | + | 0.981435i | \(0.561431\pi\) | |||||||
\(272\) | −6.63103 | −0.402065 | ||||||||
\(273\) | −6.00000 | + | 14.6969i | −0.363137 | + | 0.889499i | ||||
\(274\) | 2.48528 | 0.150141 | ||||||||
\(275\) | 3.88437 | − | 2.24264i | 0.234236 | − | 0.135236i | ||||
\(276\) | 6.27231 | − | 10.8640i | 0.377549 | − | 0.653934i | ||||
\(277\) | −5.75736 | + | 9.97204i | −0.345926 | + | 0.599162i | −0.985522 | − | 0.169550i | \(-0.945769\pi\) |
0.639595 | + | 0.768712i | \(0.279102\pi\) | |||||||
\(278\) | 1.73205 | + | 3.00000i | 0.103882 | + | 0.179928i | ||||
\(279\) | − | 25.0892i | − | 1.50205i | ||||||
\(280\) | 1.50000 | − | 1.16320i | 0.0896421 | − | 0.0695144i | ||||
\(281\) | − | 0.514719i | − | 0.0307055i | −0.999882 | − | 0.0153528i | \(-0.995113\pi\) | ||
0.999882 | − | 0.0153528i | \(-0.00488713\pi\) | |||||||
\(282\) | −0.621320 | − | 1.07616i | −0.0369991 | − | 0.0640843i | ||||
\(283\) | 21.2132 | + | 12.2474i | 1.26099 | + | 0.728035i | 0.973267 | − | 0.229677i | \(-0.0737670\pi\) |
0.287727 | + | 0.957712i | \(0.407100\pi\) | |||||||
\(284\) | −5.19615 | − | 3.00000i | −0.308335 | − | 0.178017i | ||||
\(285\) | −0.891519 | − | 1.54416i | −0.0528090 | − | 0.0914679i | ||||
\(286\) | − | 3.46410i | − | 0.204837i | ||||||
\(287\) | 13.6208 | − | 1.86396i | 0.804009 | − | 0.110026i | ||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | −13.4853 | − | 23.3572i | −0.793252 | − | 1.37395i | ||||
\(290\) | −3.04384 | + | 5.27208i | −0.178740 | + | 0.309587i | ||||
\(291\) | 8.74264 | − | 15.1427i | 0.512503 | − | 0.887681i | ||||
\(292\) | 1.24264 | − | 0.717439i | 0.0727200 | − | 0.0419849i | ||||
\(293\) | −22.2195 | −1.29808 | −0.649038 | − | 0.760756i | \(-0.724828\pi\) | ||||
−0.649038 | + | 0.760756i | \(0.724828\pi\) | |||||||
\(294\) | −11.6786 | + | 3.25736i | −0.681110 | + | 0.189973i | ||||
\(295\) | −9.51472 | −0.553968 | ||||||||
\(296\) | −3.46410 | + | 2.00000i | −0.201347 | + | 0.116248i | ||||
\(297\) | 2.59808 | − | 4.50000i | 0.150756 | − | 0.261116i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5446 | + | 21.7279i | 0.725474 | + | 1.25656i | ||||
\(300\) | 7.76874i | 0.448528i | ||||||||
\(301\) | 32.7279 | − | 4.47871i | 1.88641 | − | 0.258149i | ||||
\(302\) | − | 9.24264i | − | 0.531854i | ||||||
\(303\) | 17.7408 | − | 10.2426i | 1.01918 | − | 0.588424i | ||||
\(304\) | −1.24264 | − | 0.717439i | −0.0712703 | − | 0.0411479i | ||||
\(305\) | −2.59808 | − | 1.50000i | −0.148765 | − | 0.0858898i | ||||
\(306\) | 17.2279 | − | 9.94655i | 0.984855 | − | 0.568606i | ||||
\(307\) | 4.05845i | 0.231628i | 0.993271 | + | 0.115814i | \(0.0369476\pi\) | ||||
−0.993271 | + | 0.115814i | \(0.963052\pi\) | |||||||
\(308\) | 2.09077 | − | 1.62132i | 0.119133 | − | 0.0923833i | ||||
\(309\) | −3.51472 | −0.199945 | ||||||||
\(310\) | −3.00000 | − | 5.19615i | −0.170389 | − | 0.295122i | ||||
\(311\) | 14.3382 | − | 24.8345i | 0.813046 | − | 1.40824i | −0.0976768 | − | 0.995218i | \(-0.531141\pi\) |
0.910723 | − | 0.413018i | \(-0.135526\pi\) | |||||||
\(312\) | 5.19615 | + | 3.00000i | 0.294174 | + | 0.169842i | ||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −8.95743 | −0.505497 | ||||||||
\(315\) | −2.15232 | + | 5.27208i | −0.121269 | + | 0.297048i | ||||
\(316\) | −3.24264 | −0.182413 | ||||||||
\(317\) | 14.5123 | − | 8.37868i | 0.815092 | − | 0.470594i | −0.0336291 | − | 0.999434i | \(-0.510706\pi\) |
0.848721 | + | 0.528841i | \(0.177373\pi\) | |||||||
\(318\) | −12.7279 | − | 7.34847i | −0.713746 | − | 0.412082i | ||||
\(319\) | −4.24264 | + | 7.34847i | −0.237542 | + | 0.411435i | ||||
\(320\) | −0.358719 | − | 0.621320i | −0.0200530 | − | 0.0347329i | ||||
\(321\) | 25.9808 | 1.45010 | ||||||||
\(322\) | −7.24264 | + | 17.7408i | −0.403617 | + | 0.988655i | ||||
\(323\) | − | 9.51472i | − | 0.529413i | ||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | −13.4558 | − | 7.76874i | −0.746396 | − | 0.430932i | ||||
\(326\) | 11.2583 | + | 6.50000i | 0.623541 | + | 0.360002i | ||||
\(327\) | 16.8640 | − | 9.73641i | 0.932579 | − | 0.538425i | ||||
\(328\) | − | 5.19615i | − | 0.286910i | ||||||
\(329\) | 1.16320 | + | 1.50000i | 0.0641292 | + | 0.0826977i | ||||
\(330\) | − | 1.24264i | − | 0.0684051i | ||||||
\(331\) | −9.50000 | − | 16.4545i | −0.522167 | − | 0.904420i | −0.999667 | − | 0.0257885i | \(-0.991790\pi\) |
0.477500 | − | 0.878632i | \(-0.341543\pi\) | |||||||
\(332\) | −3.31552 | + | 5.74264i | −0.181963 | + | 0.315168i | ||||
\(333\) | 6.00000 | − | 10.3923i | 0.328798 | − | 0.569495i | ||||
\(334\) | −10.2426 | + | 5.91359i | −0.560452 | + | 0.323577i | ||||
\(335\) | −9.67487 | −0.528594 | ||||||||
\(336\) | 0.621320 | + | 4.54026i | 0.0338958 | + | 0.247691i | ||||
\(337\) | 13.5147 | 0.736194 | 0.368097 | − | 0.929787i | \(-0.380009\pi\) | ||||
0.368097 | + | 0.929787i | \(0.380009\pi\) | |||||||
\(338\) | 0.866025 | − | 0.500000i | 0.0471056 | − | 0.0271964i | ||||
\(339\) | −15.5885 | + | 27.0000i | −0.846649 | + | 1.46644i | ||||
\(340\) | 2.37868 | − | 4.11999i | 0.129002 | − | 0.223438i | ||||
\(341\) | −4.18154 | − | 7.24264i | −0.226443 | − | 0.392211i | ||||
\(342\) | 4.30463 | 0.232768 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | − | 12.4853i | − | 0.673161i | ||||||
\(345\) | 4.50000 | + | 7.79423i | 0.242272 | + | 0.419627i | ||||
\(346\) | −1.24264 | − | 0.717439i | −0.0668048 | − | 0.0385698i | ||||
\(347\) | −15.1427 | − | 8.74264i | −0.812903 | − | 0.469330i | 0.0350602 | − | 0.999385i | \(-0.488838\pi\) |
−0.847963 | + | 0.530056i | \(0.822171\pi\) | |||||||
\(348\) | −7.34847 | − | 12.7279i | −0.393919 | − | 0.682288i | ||||
\(349\) | − | 18.8785i | − | 1.01054i | −0.862961 | − | 0.505271i | \(-0.831393\pi\) | ||
0.862961 | − | 0.505271i | \(-0.168607\pi\) | |||||||
\(350\) | −1.60896 | − | 11.7574i | −0.0860024 | − | 0.628457i | ||||
\(351\) | −18.0000 | −0.960769 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 2.15232 | − | 3.72792i | 0.114556 | − | 0.198417i | −0.803046 | − | 0.595917i | \(-0.796789\pi\) |
0.917602 | + | 0.397500i | \(0.130122\pi\) | |||||||
\(354\) | 11.4853 | − | 19.8931i | 0.610436 | − | 1.05731i | ||||
\(355\) | 3.72792 | − | 2.15232i | 0.197858 | − | 0.114233i | ||||
\(356\) | 11.8272 | 0.626839 | ||||||||
\(357\) | −24.0131 | + | 18.6213i | −1.27091 | + | 0.985545i | ||||
\(358\) | 2.48528 | 0.131351 | ||||||||
\(359\) | −7.34847 | + | 4.24264i | −0.387837 | + | 0.223918i | −0.681223 | − | 0.732076i | \(-0.738551\pi\) |
0.293385 | + | 0.955994i | \(0.405218\pi\) | |||||||
\(360\) | 1.86396 | + | 1.07616i | 0.0982394 | + | 0.0567185i | ||||
\(361\) | −8.47056 | + | 14.6714i | −0.445819 | + | 0.772181i | ||||
\(362\) | −1.43488 | − | 2.48528i | −0.0754155 | − | 0.130623i | ||||
\(363\) | − | 1.73205i | − | 0.0909091i | ||||||
\(364\) | −8.48528 | − | 3.46410i | −0.444750 | − | 0.181568i | ||||
\(365\) | 1.02944i | 0.0538832i | ||||||||
\(366\) | 6.27231 | − | 3.62132i | 0.327859 | − | 0.189289i | ||||
\(367\) | 3.72792 | + | 2.15232i | 0.194596 | + | 0.112350i | 0.594132 | − | 0.804367i | \(-0.297496\pi\) |
−0.399536 | + | 0.916717i | \(0.630829\pi\) | |||||||
\(368\) | 6.27231 | + | 3.62132i | 0.326967 | + | 0.188774i | ||||
\(369\) | 7.79423 | + | 13.5000i | 0.405751 | + | 0.702782i | ||||
\(370\) | − | 2.86976i | − | 0.149191i | ||||||
\(371\) | 20.7846 | + | 8.48528i | 1.07908 | + | 0.440534i | ||||
\(372\) | 14.4853 | 0.751027 | ||||||||
\(373\) | 3.86396 | + | 6.69258i | 0.200068 | + | 0.346528i | 0.948550 | − | 0.316627i | \(-0.102550\pi\) |
−0.748482 | + | 0.663155i | \(0.769217\pi\) | |||||||
\(374\) | 3.31552 | − | 5.74264i | 0.171441 | − | 0.296945i | ||||
\(375\) | −10.2077 | − | 5.89340i | −0.527122 | − | 0.304334i | ||||
\(376\) | 0.621320 | − | 0.358719i | 0.0320422 | − | 0.0184995i | ||||
\(377\) | 29.3939 | 1.51386 | ||||||||
\(378\) | −8.42463 | − | 10.8640i | −0.433316 | − | 0.558782i | ||||
\(379\) | −33.9706 | −1.74495 | −0.872475 | − | 0.488658i | \(-0.837487\pi\) | ||||
−0.872475 | + | 0.488658i | \(0.837487\pi\) | |||||||
\(380\) | 0.891519 | − | 0.514719i | 0.0457340 | − | 0.0264045i | ||||
\(381\) | −10.1360 | − | 5.85204i | −0.519285 | − | 0.299809i | ||||
\(382\) | −9.00000 | + | 15.5885i | −0.460480 | + | 0.797575i | ||||
\(383\) | 8.78335 | + | 15.2132i | 0.448808 | + | 0.777358i | 0.998309 | − | 0.0581349i | \(-0.0185154\pi\) |
−0.549501 | + | 0.835493i | \(0.685182\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 0.257359 | + | 1.88064i | 0.0131162 | + | 0.0958462i | ||||
\(386\) | 0.485281i | 0.0247002i | ||||||||
\(387\) | 18.7279 | + | 32.4377i | 0.951994 | + | 1.64890i | ||||
\(388\) | 8.74264 | + | 5.04757i | 0.443840 | + | 0.256251i | ||||
\(389\) | 1.96768 | + | 1.13604i | 0.0997652 | + | 0.0575995i | 0.549052 | − | 0.835788i | \(-0.314989\pi\) |
−0.449287 | + | 0.893387i | \(0.648322\pi\) | |||||||
\(390\) | −3.72792 | + | 2.15232i | −0.188771 | + | 0.108987i | ||||
\(391\) | 48.0262i | 2.42879i | ||||||||
\(392\) | −1.88064 | − | 6.74264i | −0.0949865 | − | 0.340555i | ||||
\(393\) | 22.9706i | 1.15871i | ||||||||
\(394\) | −4.24264 | − | 7.34847i | −0.213741 | − | 0.370211i | ||||
\(395\) | 1.16320 | − | 2.01472i | 0.0585269 | − | 0.101371i | ||||
\(396\) | 2.59808 | + | 1.50000i | 0.130558 | + | 0.0753778i | ||||
\(397\) | −21.2132 | + | 12.2474i | −1.06466 | + | 0.614682i | −0.926718 | − | 0.375758i | \(-0.877382\pi\) |
−0.137943 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(398\) | −6.33386 | −0.317488 | ||||||||
\(399\) | −6.51472 | + | 0.891519i | −0.326144 | + | 0.0446318i | ||||
\(400\) | −4.48528 | −0.224264 | ||||||||
\(401\) | 7.34847 | − | 4.24264i | 0.366965 | − | 0.211867i | −0.305167 | − | 0.952299i | \(-0.598712\pi\) |
0.672132 | + | 0.740432i | \(0.265379\pi\) | |||||||
\(402\) | 11.6786 | − | 20.2279i | 0.582475 | − | 1.00888i | ||||
\(403\) | −14.4853 | + | 25.0892i | −0.721563 | + | 1.24978i | ||||
\(404\) | 5.91359 | + | 10.2426i | 0.294212 | + | 0.509590i | ||||
\(405\) | −6.45695 | −0.320848 | ||||||||
\(406\) | 13.7574 | + | 17.7408i | 0.682766 | + | 0.880460i | ||||
\(407\) | − | 4.00000i | − | 0.198273i | ||||||
\(408\) | 5.74264 | + | 9.94655i | 0.284303 | + | 0.492427i | ||||
\(409\) | 4.75736 | + | 2.74666i | 0.235236 | + | 0.135814i | 0.612985 | − | 0.790094i | \(-0.289968\pi\) |
−0.377749 | + | 0.925908i | \(0.623302\pi\) | |||||||
\(410\) | 3.22848 | + | 1.86396i | 0.159443 | + | 0.0920545i | ||||
\(411\) | −2.15232 | − | 3.72792i | −0.106166 | − | 0.183885i | ||||
\(412\) | − | 2.02922i | − | 0.0999727i | ||||||
\(413\) | −13.2621 | + | 32.4853i | −0.652583 | + | 1.59850i | ||||
\(414\) | −21.7279 | −1.06787 | ||||||||
\(415\) | −2.37868 | − | 4.11999i | −0.116765 | − | 0.202243i | ||||
\(416\) | −1.73205 | + | 3.00000i | −0.0849208 | + | 0.147087i | ||||
\(417\) | 3.00000 | − | 5.19615i | 0.146911 | − | 0.254457i | ||||
\(418\) | 1.24264 | − | 0.717439i | 0.0607795 | − | 0.0350911i | ||||
\(419\) | 1.43488 | 0.0700984 | 0.0350492 | − | 0.999386i | \(-0.488841\pi\) | ||||
0.0350492 | + | 0.999386i | \(0.488841\pi\) | |||||||
\(420\) | −3.04384 | − | 1.24264i | −0.148524 | − | 0.0606347i | ||||
\(421\) | −0.485281 | −0.0236512 | −0.0118256 | − | 0.999930i | \(-0.503764\pi\) | ||||
−0.0118256 | + | 0.999930i | \(0.503764\pi\) | |||||||
\(422\) | −3.88437 | + | 2.24264i | −0.189088 | + | 0.109170i | ||||
\(423\) | −1.07616 | + | 1.86396i | −0.0523246 | + | 0.0906289i | ||||
\(424\) | 4.24264 | − | 7.34847i | 0.206041 | − | 0.356873i | ||||
\(425\) | −14.8710 | − | 25.7574i | −0.721350 | − | 1.24942i | ||||
\(426\) | 10.3923i | 0.503509i | ||||||||
\(427\) | −8.74264 | + | 6.77962i | −0.423086 | + | 0.328089i | ||||
\(428\) | 15.0000i | 0.725052i | ||||||||
\(429\) | −5.19615 | + | 3.00000i | −0.250873 | + | 0.144841i | ||||
\(430\) | 7.75736 | + | 4.47871i | 0.374093 | + | 0.215983i | ||||
\(431\) | −22.9369 | − | 13.2426i | −1.10483 | − | 0.637876i | −0.167347 | − | 0.985898i | \(-0.553520\pi\) |
−0.937486 | + | 0.348023i | \(0.886853\pi\) | |||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | − | 9.25460i | − | 0.444748i | −0.974961 | − | 0.222374i | \(-0.928619\pi\) | ||
0.974961 | − | 0.222374i | \(-0.0713805\pi\) | |||||||
\(434\) | −21.9223 | + | 3.00000i | −1.05230 | + | 0.144005i | ||||
\(435\) | 10.5442 | 0.505554 | ||||||||
\(436\) | 5.62132 | + | 9.73641i | 0.269212 | + | 0.466290i | ||||
\(437\) | −5.19615 | + | 9.00000i | −0.248566 | + | 0.430528i | ||||
\(438\) | −2.15232 | − | 1.24264i | −0.102842 | − | 0.0593757i | ||||
\(439\) | −13.3492 | + | 7.70719i | −0.637125 | + | 0.367844i | −0.783506 | − | 0.621384i | \(-0.786571\pi\) |
0.146381 | + | 0.989228i | \(0.453237\pi\) | |||||||
\(440\) | 0.717439 | 0.0342026 | ||||||||
\(441\) | 15.0000 | + | 14.6969i | 0.714286 | + | 0.699854i | ||||
\(442\) | −22.9706 | −1.09260 | ||||||||
\(443\) | 31.1769 | − | 18.0000i | 1.48126 | − | 0.855206i | 0.481486 | − | 0.876454i | \(-0.340097\pi\) |
0.999774 | + | 0.0212481i | \(0.00676401\pi\) | |||||||
\(444\) | 6.00000 | + | 3.46410i | 0.284747 | + | 0.164399i | ||||
\(445\) | −4.24264 | + | 7.34847i | −0.201120 | + | 0.348351i | ||||
\(446\) | 6.63103 | + | 11.4853i | 0.313988 | + | 0.543844i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.62132 | + | 0.358719i | −0.123846 | + | 0.0169479i | ||||
\(449\) | − | 20.4853i | − | 0.966760i | −0.875411 | − | 0.483380i | \(-0.839409\pi\) | ||
0.875411 | − | 0.483380i | \(-0.160591\pi\) | |||||||
\(450\) | 11.6531 | − | 6.72792i | 0.549333 | − | 0.317157i | ||||
\(451\) | 4.50000 | + | 2.59808i | 0.211897 | + | 0.122339i | ||||
\(452\) | −15.5885 | − | 9.00000i | −0.733219 | − | 0.423324i | ||||
\(453\) | −13.8640 | + | 8.00436i | −0.651386 | + | 0.376078i | ||||
\(454\) | − | 2.32640i | − | 0.109183i | ||||||
\(455\) | 5.19615 | − | 4.02944i | 0.243599 | − | 0.188903i | ||||
\(456\) | 2.48528i | 0.116384i | ||||||||
\(457\) | 6.48528 | + | 11.2328i | 0.303369 | + | 0.525450i | 0.976897 | − | 0.213712i | \(-0.0685553\pi\) |
−0.673528 | + | 0.739162i | \(0.735222\pi\) | |||||||
\(458\) | 3.46410 | − | 6.00000i | 0.161867 | − | 0.280362i | ||||
\(459\) | −29.8396 | − | 17.2279i | −1.39279 | − | 0.804131i | ||||
\(460\) | −4.50000 | + | 2.59808i | −0.209814 | + | 0.121136i | ||||
\(461\) | −13.2621 | −0.617676 | −0.308838 | − | 0.951115i | \(-0.599940\pi\) | ||||
−0.308838 | + | 0.951115i | \(0.599940\pi\) | |||||||
\(462\) | −4.24264 | − | 1.73205i | −0.197386 | − | 0.0805823i | ||||
\(463\) | 21.4558 | 0.997138 | 0.498569 | − | 0.866850i | \(-0.333859\pi\) | ||||
0.498569 | + | 0.866850i | \(0.333859\pi\) | |||||||
\(464\) | 7.34847 | − | 4.24264i | 0.341144 | − | 0.196960i | ||||
\(465\) | −5.19615 | + | 9.00000i | −0.240966 | + | 0.417365i | ||||
\(466\) | −3.98528 | + | 6.90271i | −0.184615 | + | 0.319762i | ||||
\(467\) | 15.5885 | + | 27.0000i | 0.721348 | + | 1.24941i | 0.960460 | + | 0.278419i | \(0.0898104\pi\) |
−0.239112 | + | 0.970992i | \(0.576856\pi\) | |||||||
\(468\) | − | 10.3923i | − | 0.480384i | ||||||
\(469\) | −13.4853 | + | 33.0321i | −0.622692 | + | 1.52528i | ||||
\(470\) | 0.514719i | 0.0237422i | ||||||||
\(471\) | 7.75736 | + | 13.4361i | 0.357440 | + | 0.619105i | ||||
\(472\) | 11.4853 | + | 6.63103i | 0.528653 | + | 0.305218i | ||||
\(473\) | 10.8126 | + | 6.24264i | 0.497163 | + | 0.287037i | ||||
\(474\) | 2.80821 | + | 4.86396i | 0.128985 | + | 0.223409i | ||||
\(475\) | − | 6.43583i | − | 0.295296i | ||||||
\(476\) | −10.7510 | − | 13.8640i | −0.492772 | − | 0.635454i | ||||
\(477\) | 25.4558i | 1.16554i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.78335 | + | 15.2132i | −0.401321 | + | 0.695109i | −0.993886 | − | 0.110414i | \(-0.964782\pi\) |
0.592564 | + | 0.805523i | \(0.298116\pi\) | |||||||
\(480\) | −0.621320 | + | 1.07616i | −0.0283593 | + | 0.0491197i | ||||
\(481\) | −12.0000 | + | 6.92820i | −0.547153 | + | 0.315899i | ||||
\(482\) | 13.8564 | 0.631142 | ||||||||
\(483\) | 32.8835 | − | 4.50000i | 1.49625 | − | 0.204757i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.27231 | + | 3.62132i | −0.284811 | + | 0.164436i | ||||
\(486\) | 7.79423 | − | 13.5000i | 0.353553 | − | 0.612372i | ||||
\(487\) | 9.48528 | − | 16.4290i | 0.429819 | − | 0.744469i | −0.567038 | − | 0.823692i | \(-0.691911\pi\) |
0.996857 | + | 0.0792232i | \(0.0252440\pi\) | |||||||
\(488\) | 2.09077 | + | 3.62132i | 0.0946447 | + | 0.163929i | ||||
\(489\) | − | 22.5167i | − | 1.01824i | ||||||
\(490\) | 4.86396 | + | 1.25024i | 0.219731 | + | 0.0564800i | ||||
\(491\) | − | 13.9706i | − | 0.630483i | −0.949012 | − | 0.315241i | \(-0.897915\pi\) | ||
0.949012 | − | 0.315241i | \(-0.102085\pi\) | |||||||
\(492\) | −7.79423 | + | 4.50000i | −0.351391 | + | 0.202876i | ||||
\(493\) | 48.7279 | + | 28.1331i | 2.19460 | + | 1.26705i | ||||
\(494\) | −4.30463 | − | 2.48528i | −0.193675 | − | 0.111818i | ||||
\(495\) | −1.86396 | + | 1.07616i | −0.0837788 | + | 0.0483697i | ||||
\(496\) | 8.36308i | 0.375513i | ||||||||
\(497\) | −2.15232 | − | 15.7279i | −0.0965446 | − | 0.705494i | ||||
\(498\) | 11.4853 | 0.514668 | ||||||||
\(499\) | −10.4853 | − | 18.1610i | −0.469386 | − | 0.813000i | 0.530002 | − | 0.847997i | \(-0.322191\pi\) |
−0.999387 | + | 0.0349967i | \(0.988858\pi\) | |||||||
\(500\) | 3.40256 | − | 5.89340i | 0.152167 | − | 0.263561i | ||||
\(501\) | 17.7408 | + | 10.2426i | 0.792599 | + | 0.457607i | ||||
\(502\) | 12.7279 | − | 7.34847i | 0.568075 | − | 0.327978i | ||||
\(503\) | 2.86976 | 0.127956 | 0.0639780 | − | 0.997951i | \(-0.479621\pi\) | ||||
0.0639780 | + | 0.997951i | \(0.479621\pi\) | |||||||
\(504\) | 6.27231 | − | 4.86396i | 0.279391 | − | 0.216658i | ||||
\(505\) | −8.48528 | −0.377590 | ||||||||
\(506\) | −6.27231 | + | 3.62132i | −0.278838 | + | 0.160987i | ||||
\(507\) | −1.50000 | − | 0.866025i | −0.0666173 | − | 0.0384615i | ||||
\(508\) | 3.37868 | − | 5.85204i | 0.149905 | − | 0.259643i | ||||
\(509\) | −6.63103 | − | 11.4853i | −0.293915 | − | 0.509076i | 0.680817 | − | 0.732454i | \(-0.261625\pi\) |
−0.974732 | + | 0.223378i | \(0.928292\pi\) | |||||||
\(510\) | −8.23999 | −0.364873 | ||||||||
\(511\) | 3.51472 | + | 1.43488i | 0.155482 | + | 0.0634753i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.72792 | − | 6.45695i | −0.164592 | − | 0.285081i | ||||
\(514\) | −10.2426 | − | 5.91359i | −0.451784 | − | 0.260837i | ||||
\(515\) | 1.26080 | + | 0.727922i | 0.0555574 | + | 0.0320761i | ||||
\(516\) | −18.7279 | + | 10.8126i | −0.824451 | + | 0.475997i | ||||
\(517\) | 0.717439i | 0.0315529i | ||||||||
\(518\) | −9.79796 | − | 4.00000i | −0.430498 | − | 0.175750i | ||||
\(519\) | 2.48528i | 0.109092i | ||||||||
\(520\) | −1.24264 | − | 2.15232i | −0.0544934 | − | 0.0943853i | ||||
\(521\) | −18.4582 | + | 31.9706i | −0.808669 | + | 1.40066i | 0.105117 | + | 0.994460i | \(0.466478\pi\) |
−0.913786 | + | 0.406196i | \(0.866855\pi\) | |||||||
\(522\) | −12.7279 | + | 22.0454i | −0.557086 | + | 0.964901i | ||||
\(523\) | −31.2426 | + | 18.0379i | −1.36615 | + | 0.788744i | −0.990433 | − | 0.137992i | \(-0.955935\pi\) |
−0.375712 | + | 0.926736i | \(0.622602\pi\) | |||||||
\(524\) | −13.2621 | −0.579356 | ||||||||
\(525\) | −16.2426 | + | 12.5956i | −0.708887 | + | 0.549717i | ||||
\(526\) | 22.9706 | 1.00156 | ||||||||
\(527\) | −48.0262 | + | 27.7279i | −2.09205 | + | 1.20785i | ||||
\(528\) | −0.866025 | + | 1.50000i | −0.0376889 | + | 0.0652791i | ||||
\(529\) | 14.7279 | − | 25.5095i | 0.640344 | − | 1.10911i | ||||
\(530\) | 3.04384 | + | 5.27208i | 0.132216 | + | 0.229004i | ||||
\(531\) | −39.7862 | −1.72657 | ||||||||
\(532\) | −0.514719 | − | 3.76127i | −0.0223159 | − | 0.163072i | ||||
\(533\) | − | 18.0000i | − | 0.779667i | ||||||
\(534\) | −10.2426 | − | 17.7408i | −0.443242 | − | 0.767718i | ||||
\(535\) | −9.31981 | − | 5.38079i | −0.402930 | − | 0.232632i | ||||
\(536\) | 11.6786 | + | 6.74264i | 0.504439 | + | 0.291238i | ||||
\(537\) | −2.15232 | − | 3.72792i | −0.0928793 | − | 0.160872i | ||||
\(538\) | − | 8.23999i | − | 0.355251i | ||||||
\(539\) | 6.77962 | + | 1.74264i | 0.292019 | + | 0.0750608i | ||||
\(540\) | − | 3.72792i | − | 0.160424i | ||||||
\(541\) | −7.62132 | − | 13.2005i | −0.327666 | − | 0.567534i | 0.654382 | − | 0.756164i | \(-0.272929\pi\) |
−0.982048 | + | 0.188630i | \(0.939595\pi\) | |||||||
\(542\) | −10.8126 | + | 18.7279i | −0.464440 | + | 0.804433i | ||||
\(543\) | −2.48528 | + | 4.30463i | −0.106654 | + | 0.184730i | ||||
\(544\) | −5.74264 | + | 3.31552i | −0.246214 | + | 0.142152i | ||||
\(545\) | −8.06591 | −0.345506 | ||||||||
\(546\) | 2.15232 | + | 15.7279i | 0.0921107 | + | 0.673093i | ||||
\(547\) | 39.4558 | 1.68701 | 0.843505 | − | 0.537121i | \(-0.180488\pi\) | ||||
0.843505 | + | 0.537121i | \(0.180488\pi\) | |||||||
\(548\) | 2.15232 | − | 1.24264i | 0.0919424 | − | 0.0530830i | ||||
\(549\) | −10.8640 | − | 6.27231i | −0.463663 | − | 0.267696i | ||||
\(550\) | 2.24264 | − | 3.88437i | 0.0956265 | − | 0.165630i | ||||
\(551\) | 6.08767 | + | 10.5442i | 0.259344 | + | 0.449196i | ||||
\(552\) | − | 12.5446i | − | 0.533935i | ||||||
\(553\) | −5.25736 | − | 6.77962i | −0.223566 | − | 0.288299i | ||||
\(554\) | 11.5147i | 0.489214i | ||||||||
\(555\) | −4.30463 | + | 2.48528i | −0.182722 | + | 0.105494i | ||||
\(556\) | 3.00000 | + | 1.73205i | 0.127228 | + | 0.0734553i | ||||
\(557\) | 38.5254 | + | 22.2426i | 1.63237 | + | 0.942451i | 0.983359 | + | 0.181675i | \(0.0581518\pi\) |
0.649014 | + | 0.760776i | \(0.275182\pi\) | |||||||
\(558\) | −12.5446 | − | 21.7279i | −0.531056 | − | 0.919816i | ||||
\(559\) | − | 43.2503i | − | 1.82929i | ||||||
\(560\) | 0.717439 | − | 1.75736i | 0.0303173 | − | 0.0742620i | ||||
\(561\) | −11.4853 | −0.484909 | ||||||||
\(562\) | −0.257359 | − | 0.445759i | −0.0108560 | − | 0.0188032i | ||||
\(563\) | −3.76127 | + | 6.51472i | −0.158519 | + | 0.274563i | −0.934335 | − | 0.356397i | \(-0.884005\pi\) |
0.775816 | + | 0.630959i | \(0.217339\pi\) | |||||||
\(564\) | −1.07616 | − | 0.621320i | −0.0453144 | − | 0.0261623i | ||||
\(565\) | 11.1838 | − | 6.45695i | 0.470505 | − | 0.271646i | ||||
\(566\) | 24.4949 | 1.02960 | ||||||||
\(567\) | −9.00000 | + | 22.0454i | −0.377964 | + | 0.925820i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | 34.5900 | − | 19.9706i | 1.45009 | − | 0.837210i | 0.451604 | − | 0.892219i | \(-0.350852\pi\) |
0.998486 | + | 0.0550091i | \(0.0175188\pi\) | |||||||
\(570\) | −1.54416 | − | 0.891519i | −0.0646776 | − | 0.0373416i | ||||
\(571\) | 10.4853 | − | 18.1610i | 0.438795 | − | 0.760016i | −0.558801 | − | 0.829301i | \(-0.688739\pi\) |
0.997597 | + | 0.0692856i | \(0.0220720\pi\) | |||||||
\(572\) | −1.73205 | − | 3.00000i | −0.0724207 | − | 0.125436i | ||||
\(573\) | 31.1769 | 1.30243 | ||||||||
\(574\) | 10.8640 | − | 8.42463i | 0.453453 | − | 0.351637i | ||||
\(575\) | 32.4853i | 1.35473i | ||||||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | 9.25736 | + | 5.34474i | 0.385389 | + | 0.222504i | 0.680160 | − | 0.733063i | \(-0.261910\pi\) |
−0.294771 | + | 0.955568i | \(0.595243\pi\) | |||||||
\(578\) | −23.3572 | − | 13.4853i | −0.971531 | − | 0.560914i | ||||
\(579\) | 0.727922 | − | 0.420266i | 0.0302514 | − | 0.0174657i | ||||
\(580\) | 6.08767i | 0.252777i | ||||||||
\(581\) | −17.3821 | + | 2.37868i | −0.721129 | + | 0.0986843i | ||||
\(582\) | − | 17.4853i | − | 0.724788i | ||||||
\(583\) | 4.24264 | + | 7.34847i | 0.175712 | + | 0.304342i | ||||
\(584\) | 0.717439 | − | 1.24264i | 0.0296878 | − | 0.0514208i | ||||
\(585\) | 6.45695 | + | 3.72792i | 0.266962 | + | 0.154131i | ||||
\(586\) | −19.2426 | + | 11.1097i | −0.794906 | + | 0.458939i | ||||
\(587\) | 22.2195 | 0.917096 | 0.458548 | − | 0.888670i | \(-0.348370\pi\) | ||||
0.458548 | + | 0.888670i | \(0.348370\pi\) | |||||||
\(588\) | −8.48528 | + | 8.66025i | −0.349927 | + | 0.357143i | ||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | −8.23999 | + | 4.75736i | −0.339235 | + | 0.195857i | ||||
\(591\) | −7.34847 | + | 12.7279i | −0.302276 | + | 0.523557i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | −22.2195 | − | 38.4853i | −0.912445 | − | 1.58040i | −0.810600 | − | 0.585601i | \(-0.800859\pi\) |
−0.101845 | − | 0.994800i | \(-0.532475\pi\) | |||||||
\(594\) | − | 5.19615i | − | 0.213201i | ||||||
\(595\) | 12.4706 | − | 1.70656i | 0.511243 | − | 0.0699620i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.48528 | + | 9.50079i | 0.224498 | + | 0.388841i | ||||
\(598\) | 21.7279 | + | 12.5446i | 0.888521 | + | 0.512988i | ||||
\(599\) | 1.96768 | + | 1.13604i | 0.0803971 | + | 0.0464173i | 0.539660 | − | 0.841883i | \(-0.318553\pi\) |
−0.459263 | + | 0.888301i | \(0.651886\pi\) | |||||||
\(600\) | 3.88437 | + | 6.72792i | 0.158579 | + | 0.274666i | ||||
\(601\) | 9.79796i | 0.399667i | 0.979830 | + | 0.199834i | \(0.0640401\pi\) | ||||
−0.979830 | + | 0.199834i | \(0.935960\pi\) | |||||||
\(602\) | 26.1039 | − | 20.2426i | 1.06391 | − | 0.825028i | ||||
\(603\) | −40.4558 | −1.64749 | ||||||||
\(604\) | −4.62132 | − | 8.00436i | −0.188039 | − | 0.325693i | ||||
\(605\) | −0.358719 | + | 0.621320i | −0.0145840 | + | 0.0252603i | ||||
\(606\) | 10.2426 | − | 17.7408i | 0.416079 | − | 0.720670i | ||||
\(607\) | 19.8640 | − | 11.4685i | 0.806253 | − | 0.465491i | −0.0393998 | − | 0.999224i | \(-0.512545\pi\) |
0.845653 | + | 0.533733i | \(0.179211\pi\) | |||||||
\(608\) | −1.43488 | −0.0581920 | ||||||||
\(609\) | 14.6969 | − | 36.0000i | 0.595550 | − | 1.45879i | ||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | 2.15232 | − | 1.24264i | 0.0870734 | − | 0.0502719i | ||||
\(612\) | 9.94655 | − | 17.2279i | 0.402065 | − | 0.696397i | ||||
\(613\) | 17.1066 | − | 29.6295i | 0.690929 | − | 1.19672i | −0.280605 | − | 0.959823i | \(-0.590535\pi\) |
0.971534 | − | 0.236901i | \(-0.0761317\pi\) | |||||||
\(614\) | 2.02922 | + | 3.51472i | 0.0818928 | + | 0.141843i | ||||
\(615\) | − | 6.45695i | − | 0.260369i | ||||||
\(616\) | 1.00000 | − | 2.44949i | 0.0402911 | − | 0.0986928i | ||||
\(617\) | − | 8.48528i | − | 0.341605i | −0.985305 | − | 0.170802i | \(-0.945364\pi\) | ||
0.985305 | − | 0.170802i | \(-0.0546359\pi\) | |||||||
\(618\) | −3.04384 | + | 1.75736i | −0.122441 | + | 0.0706914i | ||||
\(619\) | 29.2279 | + | 16.8747i | 1.17477 | + | 0.678253i | 0.954799 | − | 0.297253i | \(-0.0960705\pi\) |
0.219971 | + | 0.975506i | \(0.429404\pi\) | |||||||
\(620\) | −5.19615 | − | 3.00000i | −0.208683 | − | 0.120483i | ||||
\(621\) | 18.8169 | + | 32.5919i | 0.755097 | + | 1.30787i | ||||
\(622\) | − | 28.6764i | − | 1.14982i | ||||||
\(623\) | 19.1757 | + | 24.7279i | 0.768256 | + | 0.990703i | ||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | −8.77208 | − | 15.1937i | −0.350883 | − | 0.607747i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.15232 | − | 1.24264i | −0.0859553 | − | 0.0496263i | ||||
\(628\) | −7.75736 | + | 4.47871i | −0.309552 | + | 0.178720i | ||||
\(629\) | −26.5241 | −1.05759 | ||||||||
\(630\) | 0.772078 | + | 5.64191i | 0.0307603 | + | 0.224779i | ||||
\(631\) | 6.97056 | 0.277494 | 0.138747 | − | 0.990328i | \(-0.455693\pi\) | ||||
0.138747 | + | 0.990328i | \(0.455693\pi\) | |||||||
\(632\) | −2.80821 | + | 1.62132i | −0.111705 | + | 0.0644927i | ||||
\(633\) | 6.72792 | + | 3.88437i | 0.267411 | + | 0.154390i | ||||
\(634\) | 8.37868 | − | 14.5123i | 0.332760 | − | 0.576357i | ||||
\(635\) | 2.42400 | + | 4.19848i | 0.0961934 | + | 0.166612i | ||||
\(636\) | −14.6969 | −0.582772 | ||||||||
\(637\) | −6.51472 | − | 23.3572i | −0.258123 | − | 0.925446i | ||||
\(638\) | 8.48528i | 0.335936i | ||||||||
\(639\) | 15.5885 | − | 9.00000i | 0.616670 | − | 0.356034i | ||||
\(640\) | −0.621320 | − | 0.358719i | −0.0245598 | − | 0.0141796i | ||||
\(641\) | −25.0892 | − | 14.4853i | −0.990966 | − | 0.572134i | −0.0854028 | − | 0.996347i | \(-0.527218\pi\) |
−0.905563 | + | 0.424212i | \(0.860551\pi\) | |||||||
\(642\) | 22.5000 | − | 12.9904i | 0.888004 | − | 0.512689i | ||||
\(643\) | − | 43.8446i | − | 1.72906i | −0.502578 | − | 0.864532i | \(-0.667615\pi\) | ||
0.502578 | − | 0.864532i | \(-0.332385\pi\) | |||||||
\(644\) | 2.59808 | + | 18.9853i | 0.102379 | + | 0.748125i | ||||
\(645\) | − | 15.5147i | − | 0.610891i | ||||||
\(646\) | −4.75736 | − | 8.23999i | −0.187176 | − | 0.324198i | ||||
\(647\) | 4.83743 | − | 8.37868i | 0.190179 | − | 0.329400i | −0.755130 | − | 0.655575i | \(-0.772426\pi\) |
0.945309 | + | 0.326175i | \(0.105760\pi\) | |||||||
\(648\) | 7.79423 | + | 4.50000i | 0.306186 | + | 0.176777i | ||||
\(649\) | −11.4853 | + | 6.63103i | −0.450837 | + | 0.260291i | ||||
\(650\) | −15.5375 | −0.609430 | ||||||||
\(651\) | 23.4853 | + | 30.2854i | 0.920461 | + | 1.18698i | ||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | 0.184640 | − | 0.106602i | 0.00722551 | − | 0.00417165i | −0.496383 | − | 0.868104i | \(-0.665339\pi\) |
0.503608 | + | 0.863932i | \(0.332005\pi\) | |||||||
\(654\) | 9.73641 | − | 16.8640i | 0.380724 | − | 0.659433i | ||||
\(655\) | 4.75736 | − | 8.23999i | 0.185885 | − | 0.321963i | ||||
\(656\) | −2.59808 | − | 4.50000i | −0.101438 | − | 0.175695i | ||||
\(657\) | 4.30463i | 0.167940i | ||||||||
\(658\) | 1.75736 | + | 0.717439i | 0.0685090 | + | 0.0279687i | ||||
\(659\) | 25.9706i | 1.01167i | 0.862630 | + | 0.505835i | \(0.168815\pi\) | ||||
−0.862630 | + | 0.505835i | \(0.831185\pi\) | |||||||
\(660\) | −0.621320 | − | 1.07616i | −0.0241849 | − | 0.0418894i | ||||
\(661\) | −6.51472 | − | 3.76127i | −0.253393 | − | 0.146297i | 0.367924 | − | 0.929856i | \(-0.380069\pi\) |
−0.621317 | + | 0.783559i | \(0.713402\pi\) | |||||||
\(662\) | −16.4545 | − | 9.50000i | −0.639522 | − | 0.369228i | ||||
\(663\) | 19.8931 | + | 34.4558i | 0.772584 | + | 1.33815i | ||||
\(664\) | 6.63103i | 0.257334i | ||||||||
\(665\) | 2.52160 | + | 1.02944i | 0.0977833 | + | 0.0399199i | ||||
\(666\) | − | 12.0000i | − | 0.464991i | ||||||
\(667\) | −30.7279 | − | 53.2223i | −1.18979 | − | 2.06078i | ||||
\(668\) | −5.91359 | + | 10.2426i | −0.228804 | + | 0.396300i | ||||
\(669\) | 11.4853 | − | 19.8931i | 0.444047 | − | 0.769111i | ||||
\(670\) | −8.37868 | + | 4.83743i | −0.323697 | + | 0.186886i | ||||
\(671\) | −4.18154 | −0.161427 | ||||||||
\(672\) | 2.80821 | + | 3.62132i | 0.108329 | + | 0.139695i | ||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 11.7041 | − | 6.75736i | 0.450825 | − | 0.260284i | ||||
\(675\) | −20.1838 | − | 11.6531i | −0.776874 | − | 0.448528i | ||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | −25.8067 | − | 44.6985i | −0.991831 | − | 1.71790i | −0.606382 | − | 0.795173i | \(-0.707380\pi\) |
−0.385449 | − | 0.922729i | \(-0.625953\pi\) | |||||||
\(678\) | 31.1769i | 1.19734i | ||||||||
\(679\) | 3.62132 | + | 26.4626i | 0.138974 | + | 1.01554i | ||||
\(680\) | − | 4.75736i | − | 0.182436i | ||||||
\(681\) | −3.48960 | + | 2.01472i | −0.133722 | + | 0.0772042i | ||||
\(682\) | −7.24264 | − | 4.18154i | −0.277335 | − | 0.160119i | ||||
\(683\) | −20.7846 | − | 12.0000i | −0.795301 | − | 0.459167i | 0.0465244 | − | 0.998917i | \(-0.485185\pi\) |
−0.841825 | + | 0.539750i | \(0.818519\pi\) | |||||||
\(684\) | 3.72792 | − | 2.15232i | 0.142541 | − | 0.0822959i | ||||
\(685\) | 1.78304i | 0.0681264i | ||||||||
\(686\) | 11.0482 | − | 14.8640i | 0.421822 | − | 0.567509i | ||||
\(687\) | −12.0000 | −0.457829 | ||||||||
\(688\) | −6.24264 | − | 10.8126i | −0.237998 | − | 0.412225i | ||||
\(689\) | 14.6969 | − | 25.4558i | 0.559909 | − | 0.969790i | ||||
\(690\) | 7.79423 | + | 4.50000i | 0.296721 | + | 0.171312i | ||||
\(691\) | 8.74264 | − | 5.04757i | 0.332586 | − | 0.192018i | −0.324403 | − | 0.945919i | \(-0.605163\pi\) |
0.656989 | + | 0.753901i | \(0.271830\pi\) | |||||||
\(692\) | −1.43488 | −0.0545459 | ||||||||
\(693\) | 1.07616 | + | 7.86396i | 0.0408799 | + | 0.298727i | ||||
\(694\) | −17.4853 | −0.663732 | ||||||||
\(695\) | −2.15232 | + | 1.24264i | −0.0816420 | + | 0.0471360i | ||||
\(696\) | −12.7279 | − | 7.34847i | −0.482451 | − | 0.278543i | ||||
\(697\) | 17.2279 | − | 29.8396i | 0.652554 | − | 1.13026i | ||||
\(698\) | −9.43924 | − | 16.3492i | −0.357280 | − | 0.618828i | ||||
\(699\) | 13.8054 | 0.522169 | ||||||||
\(700\) | −7.27208 | − | 9.37769i | −0.274859 | − | 0.354443i | ||||
\(701\) | 2.48528i | 0.0938678i | 0.998898 | + | 0.0469339i | \(0.0149450\pi\) | ||||
−0.998898 | + | 0.0469339i | \(0.985055\pi\) | |||||||
\(702\) | −15.5885 | + | 9.00000i | −0.588348 | + | 0.339683i | ||||
\(703\) | −4.97056 | − | 2.86976i | −0.187468 | − | 0.108235i | ||||
\(704\) | −0.866025 | − | 0.500000i | −0.0326396 | − | 0.0188445i | ||||
\(705\) | 0.772078 | − | 0.445759i | 0.0290781 | − | 0.0167883i | ||||
\(706\) | − | 4.30463i | − | 0.162007i | ||||||
\(707\) | −11.8272 | + | 28.9706i | −0.444807 | + | 1.08955i | ||||
\(708\) | − | 22.9706i | − | 0.863287i | ||||||
\(709\) | 2.75736 | + | 4.77589i | 0.103555 | + | 0.179362i | 0.913147 | − | 0.407631i | \(-0.133645\pi\) |
−0.809592 | + | 0.586993i | \(0.800312\pi\) | |||||||
\(710\) | 2.15232 | − | 3.72792i | 0.0807750 | − | 0.139906i | ||||
\(711\) | 4.86396 | − | 8.42463i | 0.182413 | − | 0.315948i | ||||
\(712\) | 10.2426 | − | 5.91359i | 0.383859 | − | 0.221621i | ||||
\(713\) | 60.5708 | 2.26839 | ||||||||
\(714\) | −11.4853 | + | 28.1331i | −0.429826 | + | 1.05285i | ||||
\(715\) | 2.48528 | 0.0929443 | ||||||||
\(716\) | 2.15232 | − | 1.24264i | 0.0804359 | − | 0.0464397i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.24264 | + | 7.34847i | −0.158334 | + | 0.274242i | ||||
\(719\) | −16.6646 | − | 28.8640i | −0.621485 | − | 1.07644i | −0.989209 | − | 0.146509i | \(-0.953196\pi\) |
0.367724 | − | 0.929935i | \(-0.380137\pi\) | |||||||
\(720\) | 2.15232 | 0.0802121 | ||||||||
\(721\) | 4.24264 | − | 3.29002i | 0.158004 | − | 0.122527i | ||||
\(722\) | 16.9411i | 0.630483i | ||||||||
\(723\) | −12.0000 | − | 20.7846i | −0.446285 | − | 0.772988i | ||||
\(724\) | −2.48528 | − | 1.43488i | −0.0923648 | − | 0.0533268i | ||||
\(725\) | 32.9600 | + | 19.0294i | 1.22410 | + | 0.706736i | ||||
\(726\) | −0.866025 | − | 1.50000i | −0.0321412 | − | 0.0556702i | ||||
\(727\) | − | 21.6251i | − | 0.802032i | −0.916071 | − | 0.401016i | \(-0.868657\pi\) | ||
0.916071 | − | 0.401016i | \(-0.131343\pi\) | |||||||
\(728\) | −9.08052 | + | 1.24264i | −0.336546 | + | 0.0460553i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0.514719 | + | 0.891519i | 0.0190506 | + | 0.0329966i | ||||
\(731\) | 41.3951 | − | 71.6985i | 1.53105 | − | 2.65186i | ||||
\(732\) | 3.62132 | − | 6.27231i | 0.133848 | − | 0.231831i | ||||
\(733\) | −7.86396 | + | 4.54026i | −0.290462 | + | 0.167698i | −0.638150 | − | 0.769912i | \(-0.720300\pi\) |
0.347688 | + | 0.937610i | \(0.386967\pi\) | |||||||
\(734\) | 4.30463 | 0.158887 | ||||||||
\(735\) | −2.33696 | − | 8.37868i | −0.0861999 | − | 0.309052i | ||||
\(736\) | 7.24264 | 0.266967 | ||||||||
\(737\) | −11.6786 | + | 6.74264i | −0.430187 | + | 0.248368i | ||||
\(738\) | 13.5000 | + | 7.79423i | 0.496942 | + | 0.286910i | ||||
\(739\) | −7.00000 | + | 12.1244i | −0.257499 | + | 0.446002i | −0.965571 | − | 0.260138i | \(-0.916232\pi\) |
0.708072 | + | 0.706140i | \(0.249565\pi\) | |||||||
\(740\) | −1.43488 | − | 2.48528i | −0.0527472 | − | 0.0913608i | ||||
\(741\) | 8.60927i | 0.316269i | ||||||||
\(742\) | 22.2426 | − | 3.04384i | 0.816553 | − | 0.111743i | ||||
\(743\) | − | 12.0000i | − | 0.440237i | −0.975473 | − | 0.220119i | \(-0.929356\pi\) | ||
0.975473 | − | 0.220119i | \(-0.0706445\pi\) | |||||||
\(744\) | 12.5446 | − | 7.24264i | 0.459908 | − | 0.265528i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.69258 | + | 3.86396i | 0.245033 | + | 0.141470i | ||||
\(747\) | −9.94655 | − | 17.2279i | −0.363925 | − | 0.630337i | ||||
\(748\) | − | 6.63103i | − | 0.242454i | ||||||
\(749\) | −31.3616 | + | 24.3198i | −1.14593 | + | 0.888626i | ||||
\(750\) | −11.7868 | −0.430393 | ||||||||
\(751\) | 1.72792 | + | 2.99285i | 0.0630528 | + | 0.109211i | 0.895829 | − | 0.444400i | \(-0.146583\pi\) |
−0.832776 | + | 0.553610i | \(0.813250\pi\) | |||||||
\(752\) | 0.358719 | − | 0.621320i | 0.0130812 | − | 0.0226572i | ||||
\(753\) | −22.0454 | − | 12.7279i | −0.803379 | − | 0.463831i | ||||
\(754\) | 25.4558 | − | 14.6969i | 0.927047 | − | 0.535231i | ||||
\(755\) | 6.63103 | 0.241328 | ||||||||
\(756\) | −12.7279 | − | 5.19615i | −0.462910 | − | 0.188982i | ||||
\(757\) | 19.9411 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(758\) | −29.4194 | + | 16.9853i | −1.06856 | + | 0.616933i | ||||
\(759\) | 10.8640 | + | 6.27231i | 0.394337 | + | 0.227670i | ||||
\(760\) | 0.514719 | − | 0.891519i | 0.0186708 | − | 0.0323388i | ||||
\(761\) | −7.07679 | − | 12.2574i | −0.256533 | − | 0.444329i | 0.708777 | − | 0.705432i | \(-0.249247\pi\) |
−0.965311 | + | 0.261103i | \(0.915914\pi\) | |||||||
\(762\) | −11.7041 | −0.423994 | ||||||||
\(763\) | −11.2426 | + | 27.5387i | −0.407011 | + | 0.996969i | ||||
\(764\) | 18.0000i | 0.651217i | ||||||||
\(765\) | 7.13604 | + | 12.3600i | 0.258004 | + | 0.446876i | ||||
\(766\) | 15.2132 | + | 8.78335i | 0.549675 | + | 0.317355i | ||||
\(767\) | 39.7862 | + | 22.9706i | 1.43660 | + | 0.829419i | ||||
\(768\) | 1.50000 | − | 0.866025i | 0.0541266 | − | 0.0312500i | ||||
\(769\) | 27.9590i | 1.00823i | 0.863637 | + | 0.504114i | \(0.168181\pi\) | ||||
−0.863637 | + | 0.504114i | \(0.831819\pi\) | |||||||
\(770\) | 1.16320 | + | 1.50000i | 0.0419188 | + | 0.0540562i | ||||
\(771\) | 20.4853i | 0.737759i | ||||||||
\(772\) | 0.242641 | + | 0.420266i | 0.00873283 | + | 0.0151257i | ||||
\(773\) | −20.2518 | + | 35.0772i | −0.728407 | + | 1.26164i | 0.229149 | + | 0.973391i | \(0.426406\pi\) |
−0.957556 | + | 0.288247i | \(0.906928\pi\) | |||||||
\(774\) | 32.4377 | + | 18.7279i | 1.16595 | + | 0.673161i | ||||
\(775\) | −32.4853 | + | 18.7554i | −1.16691 | + | 0.673713i | ||||
\(776\) | 10.0951 | 0.362394 | ||||||||
\(777\) | 2.48528 | + | 18.1610i | 0.0891590 | + | 0.651524i | ||||
\(778\) | 2.27208 | 0.0814579 | ||||||||
\(779\) | 6.45695 | − | 3.72792i | 0.231344 | − | 0.133567i | ||||
\(780\) | −2.15232 | + | 3.72792i | −0.0770653 | + | 0.133481i | ||||
\(781\) | 3.00000 | − | 5.19615i | 0.107348 | − | 0.185933i | ||||
\(782\) | 24.0131 | + | 41.5919i | 0.858706 | + | 1.48732i | ||||
\(783\) | 44.0908 | 1.57568 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | − | 6.42641i | − | 0.229368i | ||||||
\(786\) | 11.4853 | + | 19.8931i | 0.409666 | + | 0.709563i | ||||
\(787\) | 9.72792 | + | 5.61642i | 0.346763 | + | 0.200204i | 0.663259 | − | 0.748390i | \(-0.269173\pi\) |
−0.316496 | + | 0.948594i | \(0.602506\pi\) | |||||||
\(788\) | −7.34847 | − | 4.24264i | −0.261778 | − | 0.151138i | ||||
\(789\) | −19.8931 | − | 34.4558i | −0.708213 | − | 1.22666i | ||||
\(790\) | − | 2.32640i | − | 0.0827695i | ||||||
\(791\) | −6.45695 | − | 47.1838i | −0.229583 | − | 1.67766i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | 7.24264 | + | 12.5446i | 0.257194 | + | 0.445473i | ||||
\(794\) | −12.2474 | + | 21.2132i | −0.434646 | + | 0.752828i | ||||
\(795\) | 5.27208 | − | 9.13151i | 0.186981 | − | 0.323861i | ||||
\(796\) | −5.48528 | + | 3.16693i | −0.194421 | + | 0.112249i | ||||
\(797\) | −36.1990 | −1.28223 | −0.641117 | − | 0.767443i | \(-0.721529\pi\) | ||||
−0.641117 | + | 0.767443i | \(0.721529\pi\) | |||||||
\(798\) | −5.19615 | + | 4.02944i | −0.183942 | + | 0.142641i | ||||
\(799\) | 4.75736 | 0.168303 | ||||||||
\(800\) | −3.88437 | + | 2.24264i | −0.137333 | + | 0.0792893i | ||||
\(801\) | −17.7408 | + | 30.7279i | −0.626839 | + | 1.08572i | ||||
\(802\) | 4.24264 | − | 7.34847i | 0.149813 | − | 0.259483i | ||||
\(803\) | 0.717439 | + | 1.24264i | 0.0253179 | + | 0.0438518i | ||||
\(804\) | − | 23.3572i | − | 0.823745i | ||||||
\(805\) | −12.7279 | − | 5.19615i | −0.448600 | − | 0.183140i | ||||
\(806\) | 28.9706i | 1.02044i | ||||||||
\(807\) | −12.3600 | + | 7.13604i | −0.435092 | + | 0.251200i | ||||
\(808\) | 10.2426 | + | 5.91359i | 0.360335 | + | 0.208039i | ||||
\(809\) | −2.59808 | − | 1.50000i | −0.0913435 | − | 0.0527372i | 0.453632 | − | 0.891189i | \(-0.350128\pi\) |
−0.544976 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(810\) | −5.59188 | + | 3.22848i | −0.196479 | + | 0.113437i | ||||
\(811\) | 36.9164i | 1.29631i | 0.761508 | + | 0.648156i | \(0.224459\pi\) | ||||
−0.761508 | + | 0.648156i | \(0.775541\pi\) | |||||||
\(812\) | 20.7846 | + | 8.48528i | 0.729397 | + | 0.297775i | ||||
\(813\) | 37.4558 | 1.31363 | ||||||||
\(814\) | −2.00000 | − | 3.46410i | −0.0701000 | − | 0.121417i | ||||
\(815\) | −4.66335 | + | 8.07716i | −0.163350 | + | 0.282931i | ||||
\(816\) | 9.94655 | + | 5.74264i | 0.348199 | + | 0.201033i | ||||
\(817\) | 15.5147 | − | 8.95743i | 0.542791 | − | 0.313381i | ||||
\(818\) | 5.49333 | 0.192070 | ||||||||
\(819\) | 21.7279 | − | 16.8493i | 0.759235 | − | 0.588761i | ||||
\(820\) | 3.72792 | 0.130185 | ||||||||
\(821\) | −12.5446 | + | 7.24264i | −0.437810 | + | 0.252770i | −0.702668 | − | 0.711518i | \(-0.748008\pi\) |
0.264858 | + | 0.964287i | \(0.414675\pi\) | |||||||
\(822\) | −3.72792 | − | 2.15232i | −0.130026 | − | 0.0750707i | ||||
\(823\) | 15.2426 | − | 26.4010i | 0.531325 | − | 0.920282i | −0.468007 | − | 0.883725i | \(-0.655028\pi\) |
0.999332 | − | 0.0365570i | \(-0.0116390\pi\) | |||||||
\(824\) | −1.01461 | − | 1.75736i | −0.0353457 | − | 0.0612205i | ||||
\(825\) | −7.76874 | −0.270473 | ||||||||
\(826\) | 4.75736 | + | 34.7641i | 0.165530 | + | 1.20960i | ||||
\(827\) | − | 0.514719i | − | 0.0178985i | −0.999960 | − | 0.00894926i | \(-0.997151\pi\) | ||
0.999960 | − | 0.00894926i | \(-0.00284868\pi\) | |||||||
\(828\) | −18.8169 | + | 10.8640i | −0.653934 | + | 0.377549i | ||||
\(829\) | 4.97056 | + | 2.86976i | 0.172635 | + | 0.0996707i | 0.583828 | − | 0.811878i | \(-0.301554\pi\) |
−0.411193 | + | 0.911548i | \(0.634888\pi\) | |||||||
\(830\) | −4.11999 | − | 2.37868i | −0.143007 | − | 0.0825652i | ||||
\(831\) | 17.2721 | − | 9.97204i | 0.599162 | − | 0.345926i | ||||
\(832\) | 3.46410i | 0.120096i | ||||||||
\(833\) | 11.5555 | − | 44.9558i | 0.400374 | − | 1.55763i | ||||
\(834\) | − | 6.00000i | − | 0.207763i | ||||||
\(835\) | −4.24264 | − | 7.34847i | −0.146823 | − | 0.254304i | ||||
\(836\) | 0.717439 | − | 1.24264i | 0.0248131 | − | 0.0429776i | ||||
\(837\) | −21.7279 | + | 37.6339i | −0.751027 | + | 1.30082i | ||||
\(838\) | 1.24264 | − | 0.717439i | 0.0429263 | − | 0.0247835i | ||||
\(839\) | −39.0687 | −1.34880 | −0.674401 | − | 0.738365i | \(-0.735598\pi\) | ||||
−0.674401 | + | 0.738365i | \(0.735598\pi\) | |||||||
\(840\) | −3.25736 | + | 0.445759i | −0.112390 | + | 0.0153802i | ||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | −0.420266 | + | 0.242641i | −0.0144833 | + | 0.00836195i | ||||
\(843\) | −0.445759 | + | 0.772078i | −0.0153528 | + | 0.0265918i | ||||
\(844\) | −2.24264 | + | 3.88437i | −0.0771949 | + | 0.133705i | ||||
\(845\) | 0.358719 | + | 0.621320i | 0.0123403 | + | 0.0213741i | ||||
\(846\) | 2.15232i | 0.0739982i | ||||||||
\(847\) | 1.62132 | + | 2.09077i | 0.0557092 | + | 0.0718397i | ||||
\(848\) | − | 8.48528i | − | 0.291386i | ||||||
\(849\) | −21.2132 | − | 36.7423i | −0.728035 | − | 1.26099i | ||||
\(850\) | −25.7574 | − | 14.8710i | −0.883470 | − | 0.510072i | ||||
\(851\) | 25.0892 | + | 14.4853i | 0.860048 | + | 0.496549i | ||||
\(852\) | 5.19615 | + | 9.00000i | 0.178017 | + | 0.308335i | ||||
\(853\) | 13.9795i | 0.478649i | 0.970940 | + | 0.239324i | \(0.0769260\pi\) | ||||
−0.970940 | + | 0.239324i | \(0.923074\pi\) | |||||||
\(854\) | −4.18154 | + | 10.2426i | −0.143089 | + | 0.350496i | ||||
\(855\) | 3.08831i | 0.105618i | ||||||||
\(856\) | 7.50000 | + | 12.9904i | 0.256345 | + | 0.444002i | ||||
\(857\) | −11.5555 | + | 20.0147i | −0.394728 | + | 0.683690i | −0.993066 | − | 0.117554i | \(-0.962495\pi\) |
0.598338 | + | 0.801244i | \(0.295828\pi\) | |||||||
\(858\) | −3.00000 | + | 5.19615i | −0.102418 | + | 0.177394i | ||||
\(859\) | 26.4411 | − | 15.2658i | 0.902160 | − | 0.520862i | 0.0242594 | − | 0.999706i | \(-0.492277\pi\) |
0.877900 | + | 0.478844i | \(0.158944\pi\) | |||||||
\(860\) | 8.95743 | 0.305446 | ||||||||
\(861\) | −22.0454 | − | 9.00000i | −0.751305 | − | 0.306719i | ||||
\(862\) | −26.4853 | −0.902092 | ||||||||
\(863\) | 28.3177 | − | 16.3492i | 0.963946 | − | 0.556535i | 0.0665610 | − | 0.997782i | \(-0.478797\pi\) |
0.897385 | + | 0.441248i | \(0.145464\pi\) | |||||||
\(864\) | −2.59808 | + | 4.50000i | −0.0883883 | + | 0.153093i | ||||
\(865\) | 0.514719 | − | 0.891519i | 0.0175010 | − | 0.0303125i | ||||
\(866\) | −4.62730 | − | 8.01472i | −0.157242 | − | 0.272351i | ||||
\(867\) | 46.7144i | 1.58650i | ||||||||
\(868\) | −17.4853 | + | 13.5592i | −0.593489 | + | 0.460230i | ||||
\(869\) | − | 3.24264i | − | 0.109999i | ||||||
\(870\) | 9.13151 | − | 5.27208i | 0.309587 | − | 0.178740i | ||||
\(871\) | 40.4558 | + | 23.3572i | 1.37079 | + | 0.791428i | ||||
\(872\) | 9.73641 | + | 5.62132i | 0.329717 | + | 0.190362i | ||||
\(873\) | −26.2279 | + | 15.1427i | −0.887681 | + | 0.512503i | ||||
\(874\) | 10.3923i | 0.351525i | ||||||||
\(875\) | 17.8384 | − | 2.44113i | 0.603047 | − | 0.0825251i | ||||
\(876\) | −2.48528 | −0.0839699 | ||||||||
\(877\) | −26.3492 | − | 45.6382i | −0.889751 | − | 1.54109i | −0.840170 | − | 0.542323i | \(-0.817545\pi\) |
−0.0495808 | − | 0.998770i | \(-0.515789\pi\) | |||||||
\(878\) | −7.70719 | + | 13.3492i | −0.260105 | + | 0.450515i | ||||
\(879\) | 33.3292 | + | 19.2426i | 1.12417 | + | 0.649038i | ||||
\(880\) | 0.621320 | − | 0.358719i | 0.0209447 | − | 0.0120924i | ||||
\(881\) | −39.7862 | −1.34043 | −0.670215 | − | 0.742167i | \(-0.733798\pi\) | ||||
−0.670215 | + | 0.742167i | \(0.733798\pi\) | |||||||
\(882\) | 20.3389 | + | 5.22792i | 0.684845 | + | 0.176033i | ||||
\(883\) | −18.4558 | −0.621089 | −0.310544 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310544 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(884\) | −19.8931 | + | 11.4853i | −0.669077 | + | 0.386292i | ||||
\(885\) | 14.2721 | + | 8.23999i | 0.479751 | + | 0.276984i | ||||
\(886\) | 18.0000 | − | 31.1769i | 0.604722 | − | 1.04741i | ||||
\(887\) | −2.32640 | − | 4.02944i | −0.0781128 | − | 0.135295i | 0.824323 | − | 0.566120i | \(-0.191556\pi\) |
−0.902436 | + | 0.430825i | \(0.858223\pi\) | |||||||
\(888\) | 6.92820 | 0.232495 | ||||||||
\(889\) | 17.7132 | − | 2.42400i | 0.594082 | − | 0.0812982i | ||||
\(890\) | 8.48528i | 0.284427i | ||||||||
\(891\) | −7.79423 | + | 4.50000i | −0.261116 | + | 0.150756i | ||||
\(892\) | 11.4853 | + | 6.63103i | 0.384556 | + | 0.222023i | ||||
\(893\) | 0.891519 | + | 0.514719i | 0.0298335 | + | 0.0172244i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78304i | 0.0596004i | ||||||||
\(896\) | −2.09077 | + | 1.62132i | −0.0698477 | + | 0.0541645i | ||||
\(897\) | − | 43.4558i | − | 1.45095i | ||||||
\(898\) | −10.2426 | − | 17.7408i | −0.341801 | − | 0.592017i | ||||
\(899\) | 35.4815 | − | 61.4558i | 1.18338 | − | 2.04967i | ||||
\(900\) | 6.72792 | − | 11.6531i | 0.224264 | − | 0.388437i | ||||
\(901\) | 48.7279 | − | 28.1331i | 1.62336 | − | 0.937249i | ||||
\(902\) | 5.19615 | 0.173013 | ||||||||
\(903\) | −52.9706 | − | 21.6251i | −1.76275 | − | 0.719640i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 1.78304 | − | 1.02944i | 0.0592702 | − | 0.0342197i | ||||
\(906\) | −8.00436 | + | 13.8640i | −0.265927 | + | 0.460599i | ||||
\(907\) | 0.227922 | − | 0.394773i | 0.00756803 | − | 0.0131082i | −0.862217 | − | 0.506540i | \(-0.830924\pi\) |
0.869785 | + | 0.493432i | \(0.164258\pi\) | |||||||
\(908\) | −1.16320 | − | 2.01472i | −0.0386021 | − | 0.0668608i | ||||
\(909\) | −35.4815 | −1.17685 | ||||||||
\(910\) | 2.48528 | − | 6.08767i | 0.0823863 | − | 0.201804i | ||||
\(911\) | 27.7279i | 0.918667i | 0.888264 | + | 0.459334i | \(0.151912\pi\) | ||||
−0.888264 | + | 0.459334i | \(0.848088\pi\) | |||||||
\(912\) | 1.24264 | + | 2.15232i | 0.0411479 | + | 0.0712703i | ||||
\(913\) | −5.74264 | − | 3.31552i | −0.190054 | − | 0.109728i | ||||
\(914\) | 11.2328 | + | 6.48528i | 0.371549 | + | 0.214514i | ||||
\(915\) | 2.59808 | + | 4.50000i | 0.0858898 | + | 0.148765i | ||||
\(916\) | − | 6.92820i | − | 0.228914i | ||||||
\(917\) | −21.5020 | − | 27.7279i | −0.710060 | − | 0.915657i | ||||
\(918\) | −34.4558 | −1.13721 | ||||||||
\(919\) | −0.136039 | − | 0.235626i | −0.00448751 | − | 0.00777260i | 0.863773 | − | 0.503881i | \(-0.168095\pi\) |
−0.868260 | + | 0.496109i | \(0.834762\pi\) | |||||||
\(920\) | −2.59808 | + | 4.50000i | −0.0856560 | + | 0.148361i | ||||
\(921\) | 3.51472 | − | 6.08767i | 0.115814 | − | 0.200596i | ||||
\(922\) | −11.4853 | + | 6.63103i | −0.378248 | + | 0.218381i | ||||
\(923\) | −20.7846 | −0.684134 | ||||||||
\(924\) | −4.54026 | + | 0.621320i | −0.149364 | + | 0.0204399i | ||||
\(925\) | −17.9411 | −0.589901 | ||||||||
\(926\) | 18.5813 | − | 10.7279i | 0.610620 | − | 0.352541i | ||||
\(927\) | 5.27208 | + | 3.04384i | 0.173158 | + | 0.0999727i | ||||
\(928\) | 4.24264 | − | 7.34847i | 0.139272 | − | 0.241225i | ||||
\(929\) | 0.717439 | + | 1.24264i | 0.0235384 | + | 0.0407697i | 0.877555 | − | 0.479477i | \(-0.159173\pi\) |
−0.854016 | + | 0.520246i | \(0.825840\pi\) | |||||||
\(930\) | 10.3923i | 0.340777i | ||||||||
\(931\) | 7.02944 | − | 7.17439i | 0.230381 | − | 0.235131i | ||||
\(932\) | 7.97056i | 0.261084i | ||||||||
\(933\) | −43.0147 | + | 24.8345i | −1.40824 | + | 0.813046i | ||||
\(934\) | 27.0000 | + | 15.5885i | 0.883467 | + | 0.510070i | ||||
\(935\) | 4.11999 | + | 2.37868i | 0.134738 | + | 0.0777911i | ||||
\(936\) | −5.19615 | − | 9.00000i | −0.169842 | − | 0.294174i | ||||
\(937\) | − | 52.4539i | − | 1.71359i | −0.515654 | − | 0.856797i | \(-0.672451\pi\) | ||
0.515654 | − | 0.856797i | \(-0.327549\pi\) | |||||||
\(938\) | 4.83743 | + | 35.3492i | 0.157948 | + | 1.15419i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.257359 | + | 0.445759i | 0.00839414 | + | 0.0145391i | ||||
\(941\) | 5.19615 | − | 9.00000i | 0.169390 | − | 0.293392i | −0.768816 | − | 0.639470i | \(-0.779154\pi\) |
0.938205 | + | 0.346079i | \(0.112487\pi\) | |||||||
\(942\) | 13.4361 | + | 7.75736i | 0.437773 | + | 0.252748i | ||||
\(943\) | −32.5919 | + | 18.8169i | −1.06134 | + | 0.612764i | ||||
\(944\) | 13.2621 | 0.431643 | ||||||||
\(945\) | 7.79423 | − | 6.04416i | 0.253546 | − | 0.196616i | ||||
\(946\) | 12.4853 | 0.405932 | ||||||||
\(947\) | 0.891519 | − | 0.514719i | 0.0289705 | − | 0.0167261i | −0.485445 | − | 0.874267i | \(-0.661342\pi\) |
0.514415 | + | 0.857541i | \(0.328009\pi\) | |||||||
\(948\) | 4.86396 | + | 2.80821i | 0.157974 | + | 0.0912064i | ||||
\(949\) | 2.48528 | − | 4.30463i | 0.0806756 | − | 0.139734i | ||||
\(950\) | −3.21792 | − | 5.57359i | −0.104403 | − | 0.180831i | ||||
\(951\) | −29.0246 | −0.941187 | ||||||||
\(952\) | −16.2426 | − | 6.63103i | −0.526427 | − | 0.214913i | ||||
\(953\) | − | 7.97056i | − | 0.258192i | −0.991632 | − | 0.129096i | \(-0.958792\pi\) | ||
0.991632 | − | 0.129096i | \(-0.0412075\pi\) | |||||||
\(954\) | 12.7279 | + | 22.0454i | 0.412082 | + | 0.713746i | ||||
\(955\) | −11.1838 | − | 6.45695i | −0.361898 | − | 0.208942i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.7279 | − | 7.34847i | 0.411435 | − | 0.237542i | ||||
\(958\) | 17.5667i | 0.567554i | ||||||||
\(959\) | 6.08767 | + | 2.48528i | 0.196581 | + | 0.0802539i | ||||
\(960\) | 1.24264i | 0.0401061i | ||||||||
\(961\) | 19.4706 | + | 33.7240i | 0.628083 | + | 1.08787i | ||||
\(962\) | −6.92820 | + | 12.0000i | −0.223374 | + | 0.386896i | ||||
\(963\) | −38.9711 | − | 22.5000i | −1.25583 | − | 0.725052i | ||||
\(964\) | 12.0000 | − | 6.92820i | 0.386494 | − | 0.223142i | ||||
\(965\) | −0.348160 | −0.0112077 | ||||||||
\(966\) | 26.2279 | − | 20.3389i | 0.843870 | − | 0.654392i | ||||
\(967\) | −40.2132 | −1.29317 | −0.646585 | − | 0.762842i | \(-0.723803\pi\) | ||||
−0.646585 | + | 0.762842i | \(0.723803\pi\) | |||||||
\(968\) | 0.866025 | − | 0.500000i | 0.0278351 | − | 0.0160706i | ||||
\(969\) | −8.23999 | + | 14.2721i | −0.264707 | + | 0.458485i | ||||
\(970\) | −3.62132 | + | 6.27231i | −0.116274 | + | 0.201392i | ||||
\(971\) | 2.32640 | + | 4.02944i | 0.0746576 | + | 0.129311i | 0.900937 | − | 0.433949i | \(-0.142880\pi\) |
−0.826280 | + | 0.563260i | \(0.809547\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | 1.24264 | + | 9.08052i | 0.0398372 | + | 0.291108i | ||||
\(974\) | − | 18.9706i | − | 0.607856i | ||||||
\(975\) | 13.4558 | + | 23.3062i | 0.430932 | + | 0.746396i | ||||
\(976\) | 3.62132 | + | 2.09077i | 0.115916 | + | 0.0669239i | ||||
\(977\) | −30.2854 | − | 17.4853i | −0.968916 | − | 0.559404i | −0.0700102 | − | 0.997546i | \(-0.522303\pi\) |
−0.898905 | + | 0.438143i | \(0.855637\pi\) | |||||||
\(978\) | −11.2583 | − | 19.5000i | −0.360002 | − | 0.623541i | ||||
\(979\) | 11.8272i | 0.377998i | ||||||||
\(980\) | 4.83743 | − | 1.34924i | 0.154526 | − | 0.0431000i | ||||
\(981\) | −33.7279 | −1.07685 | ||||||||
\(982\) | −6.98528 | − | 12.0989i | −0.222909 | − | 0.386090i | ||||
\(983\) | 20.9692 | − | 36.3198i | 0.668815 | − | 1.15842i | −0.309421 | − | 0.950925i | \(-0.600135\pi\) |
0.978236 | − | 0.207497i | \(-0.0665316\pi\) | |||||||
\(984\) | −4.50000 | + | 7.79423i | −0.143455 | + | 0.248471i | ||||
\(985\) | 5.27208 | − | 3.04384i | 0.167982 | − | 0.0969847i | ||||
\(986\) | 56.2662 | 1.79188 | ||||||||
\(987\) | −0.445759 | − | 3.25736i | −0.0141887 | − | 0.103683i | ||||
\(988\) | −4.97056 | −0.158135 | ||||||||
\(989\) | −78.3116 | + | 45.2132i | −2.49016 | + | 1.43770i | ||||
\(990\) | −1.07616 | + | 1.86396i | −0.0342026 | + | 0.0592406i | ||||
\(991\) | 4.00000 | − | 6.92820i | 0.127064 | − | 0.220082i | −0.795474 | − | 0.605988i | \(-0.792778\pi\) |
0.922538 | + | 0.385906i | \(0.126111\pi\) | |||||||
\(992\) | 4.18154 | + | 7.24264i | 0.132764 | + | 0.229954i | ||||
\(993\) | 32.9090i | 1.04433i | ||||||||
\(994\) | −9.72792 | − | 12.5446i | −0.308551 | − | 0.397891i | ||||
\(995\) | − | 4.54416i | − | 0.144059i | ||||||
\(996\) | 9.94655 | − | 5.74264i | 0.315168 | − | 0.181963i | ||||
\(997\) | 17.4853 | + | 10.0951i | 0.553764 | + | 0.319716i | 0.750639 | − | 0.660713i | \(-0.229746\pi\) |
−0.196874 | + | 0.980429i | \(0.563079\pi\) | |||||||
\(998\) | −18.1610 | − | 10.4853i | −0.574878 | − | 0.331906i | ||||
\(999\) | −18.0000 | + | 10.3923i | −0.569495 | + | 0.328798i |
(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 | 462.2.k.d.353.4 | yes | 8 | |
3.2 | odd | 2 | inner | 462.2.k.d.353.1 | yes | 8 | |
7.5 | odd | 6 | inner | 462.2.k.d.89.1 | ✓ | 8 | |
21.5 | even | 6 | inner | 462.2.k.d.89.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.d.89.1 | ✓ | 8 | 7.5 | odd | 6 | inner | |
462.2.k.d.89.4 | yes | 8 | 21.5 | even | 6 | inner | |
462.2.k.d.353.1 | yes | 8 | 3.2 | odd | 2 | inner | |
462.2.k.d.353.4 | yes | 8 | 1.1 | even | 1 | trivial |