Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(61,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.i (of order \(3\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.61 |
Dual form | 390.2.i.b.211.1 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 1.50000 | + | 2.59808i | 0.566947 | + | 0.981981i | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.50000 | − | 2.59808i | 0.693375 | − | 0.720577i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.50000 | + | 4.33013i | 0.573539 | + | 0.993399i | 0.996199 | + | 0.0871106i | \(0.0277634\pi\) |
−0.422659 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 3.00000 | 0.654654 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 10.0000 | 1.79605 | 0.898027 | − | 0.439941i | \(-0.145001\pi\) | ||||
0.898027 | + | 0.439941i | \(0.145001\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | + | 2.59808i | 0.253546 | + | 0.439155i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | −1.50000 | + | 2.59808i | −0.231455 | + | 0.400892i | ||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50000 | − | 0.866025i | −0.485363 | − | 0.120096i | ||||
\(53\) | −13.0000 | −1.78569 | −0.892844 | − | 0.450367i | \(-0.851293\pi\) | ||||
−0.892844 | + | 0.450367i | \(0.851293\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −0.500000 | + | 0.866025i | −0.0674200 | + | 0.116775i | ||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | −5.00000 | + | 8.66025i | −0.635001 | + | 1.09985i | ||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | − | 2.59808i | 0.310087 | − | 0.322252i | ||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | − | 3.46410i | −0.240772 | − | 0.417029i | ||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | 1.00000 | + | 1.73205i | 0.118678 | + | 0.205557i | 0.919244 | − | 0.393688i | \(-0.128801\pi\) |
−0.800566 | + | 0.599245i | \(0.795468\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −16.0000 | −1.87266 | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 2.50000 | − | 4.33013i | 0.286770 | − | 0.496700i | ||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 3.50000 | + | 0.866025i | 0.396297 | + | 0.0980581i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.00000 | − | 5.19615i | −0.331295 | − | 0.573819i | ||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | −1.50000 | − | 2.59808i | −0.163663 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −0.500000 | + | 0.866025i | −0.0529999 | + | 0.0917985i | −0.891308 | − | 0.453398i | \(-0.850212\pi\) |
0.838308 | + | 0.545197i | \(0.183545\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 10.5000 | + | 2.59808i | 1.10070 | + | 0.272352i | ||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 5.00000 | − | 8.66025i | 0.518476 | − | 0.898027i | ||||
\(94\) | 4.50000 | − | 7.79423i | 0.464140 | − | 0.803913i | ||||
\(95\) | 2.50000 | + | 4.33013i | 0.256495 | + | 0.444262i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.00000 | − | 10.3923i | −0.609208 | − | 1.05518i | −0.991371 | − | 0.131084i | \(-0.958154\pi\) |
0.382164 | − | 0.924095i | \(-0.375179\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −2.00000 | + | 3.46410i | −0.199007 | + | 0.344691i | −0.948207 | − | 0.317653i | \(-0.897105\pi\) |
0.749199 | + | 0.662344i | \(0.230438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 2.50000 | − | 2.59808i | 0.245145 | − | 0.254762i | ||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | 6.50000 | − | 11.2583i | 0.631336 | − | 1.09351i | ||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | −0.500000 | − | 0.866025i | −0.0476731 | − | 0.0825723i | ||||
\(111\) | −0.500000 | − | 0.866025i | −0.0474579 | − | 0.0821995i | ||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | −8.00000 | − | 13.8564i | −0.752577 | − | 1.30350i | −0.946570 | − | 0.322498i | \(-0.895477\pi\) |
0.193993 | − | 0.981003i | \(-0.437856\pi\) | |||||||
\(114\) | −2.50000 | + | 4.33013i | −0.234146 | + | 0.405554i | ||||
\(115\) | 2.00000 | − | 3.46410i | 0.186501 | − | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.50000 | − | 0.866025i | −0.323575 | − | 0.0800641i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | −5.00000 | − | 8.66025i | −0.449013 | − | 0.777714i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.50000 | + | 2.59808i | 0.133631 | + | 0.231455i | ||||
\(127\) | −2.50000 | + | 4.33013i | −0.221839 | + | 0.384237i | −0.955366 | − | 0.295423i | \(-0.904539\pi\) |
0.733527 | + | 0.679660i | \(0.237873\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 1.00000 | + | 3.46410i | 0.0877058 | + | 0.303822i | ||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | 0.500000 | − | 0.866025i | 0.0435194 | − | 0.0753778i | ||||
\(133\) | −7.50000 | + | 12.9904i | −0.650332 | + | 1.12641i | ||||
\(134\) | 6.00000 | + | 10.3923i | 0.518321 | + | 0.897758i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.00000 | − | 13.8564i | −0.683486 | − | 1.18383i | −0.973910 | − | 0.226935i | \(-0.927130\pi\) |
0.290424 | − | 0.956898i | \(-0.406204\pi\) | |||||||
\(138\) | 4.00000 | 0.340503 | ||||||||
\(139\) | 4.50000 | + | 7.79423i | 0.381685 | + | 0.661098i | 0.991303 | − | 0.131597i | \(-0.0420106\pi\) |
−0.609618 | + | 0.792695i | \(0.708677\pi\) | |||||||
\(140\) | 1.50000 | − | 2.59808i | 0.126773 | − | 0.219578i | ||||
\(141\) | −4.50000 | + | 7.79423i | −0.378968 | + | 0.656392i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | 1.00000 | + | 3.46410i | 0.0836242 | + | 0.289683i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00000 | − | 13.8564i | 0.662085 | − | 1.14676i | ||||
\(147\) | 1.00000 | + | 1.73205i | 0.0824786 | + | 0.142857i | ||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | −6.00000 | −0.488273 | −0.244137 | − | 0.969741i | \(-0.578505\pi\) | ||||
−0.244137 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(152\) | 2.50000 | + | 4.33013i | 0.202777 | + | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.50000 | − | 2.59808i | 0.120873 | − | 0.209359i | ||||
\(155\) | 10.0000 | 0.803219 | ||||||||
\(156\) | −2.50000 | + | 2.59808i | −0.200160 | + | 0.208013i | ||||
\(157\) | 1.00000 | 0.0798087 | 0.0399043 | − | 0.999204i | \(-0.487295\pi\) | ||||
0.0399043 | + | 0.999204i | \(0.487295\pi\) | |||||||
\(158\) | 5.00000 | − | 8.66025i | 0.397779 | − | 0.688973i | ||||
\(159\) | −6.50000 | + | 11.2583i | −0.515484 | + | 0.892844i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 10.0000 | + | 17.3205i | 0.783260 | + | 1.35665i | 0.930033 | + | 0.367477i | \(0.119778\pi\) |
−0.146772 | + | 0.989170i | \(0.546888\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 6.50000 | − | 11.2583i | 0.502985 | − | 0.871196i | −0.497009 | − | 0.867745i | \(-0.665568\pi\) |
0.999994 | − | 0.00345033i | \(-0.00109828\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.50000 | − | 4.33013i | 0.191180 | − | 0.331133i | ||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.50000 | + | 2.59808i | 0.113389 | + | 0.196396i | ||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | −0.500000 | − | 0.866025i | −0.0374766 | − | 0.0649113i | ||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | −7.50000 | + | 7.79423i | −0.555937 | + | 0.577747i | ||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 0.500000 | − | 0.866025i | 0.0367607 | − | 0.0636715i | ||||
\(186\) | 5.00000 | + | 8.66025i | 0.366618 | + | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.50000 | + | 7.79423i | 0.328196 | + | 0.568453i | ||||
\(189\) | −1.50000 | − | 2.59808i | −0.109109 | − | 0.188982i | ||||
\(190\) | −5.00000 | −0.362738 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −8.00000 | + | 13.8564i | −0.575853 | + | 0.997406i | 0.420096 | + | 0.907480i | \(0.361996\pi\) |
−0.995948 | + | 0.0899262i | \(0.971337\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | −1.00000 | − | 3.46410i | −0.0716115 | − | 0.248069i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 7.50000 | − | 12.9904i | 0.534353 | − | 0.925526i | −0.464841 | − | 0.885394i | \(-0.653889\pi\) |
0.999194 | − | 0.0401324i | \(-0.0127780\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | 1.00000 | + | 1.73205i | 0.0708881 | + | 0.122782i | 0.899291 | − | 0.437351i | \(-0.144083\pi\) |
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −6.00000 | − | 10.3923i | −0.423207 | − | 0.733017i | ||||
\(202\) | −2.00000 | − | 3.46410i | −0.140720 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 4.50000 | − | 7.79423i | 0.313530 | − | 0.543050i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 1.00000 | + | 3.46410i | 0.0693375 | + | 0.240192i | ||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | −1.50000 | + | 2.59808i | −0.103510 | + | 0.179284i | ||||
\(211\) | 7.50000 | − | 12.9904i | 0.516321 | − | 0.894295i | −0.483499 | − | 0.875345i | \(-0.660634\pi\) |
0.999820 | − | 0.0189499i | \(-0.00603229\pi\) | |||||||
\(212\) | 6.50000 | + | 11.2583i | 0.446422 | + | 0.773225i | ||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 1.00000 | + | 1.73205i | 0.0681994 | + | 0.118125i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 15.0000 | + | 25.9808i | 1.01827 | + | 1.76369i | ||||
\(218\) | 5.00000 | − | 8.66025i | 0.338643 | − | 0.586546i | ||||
\(219\) | −8.00000 | + | 13.8564i | −0.540590 | + | 0.936329i | ||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.00000 | 0.0671156 | ||||||||
\(223\) | −5.50000 | + | 9.52628i | −0.368307 | + | 0.637927i | −0.989301 | − | 0.145889i | \(-0.953396\pi\) |
0.620994 | + | 0.783815i | \(0.286729\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | −2.50000 | − | 4.33013i | −0.165567 | − | 0.286770i | ||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 2.00000 | + | 3.46410i | 0.131876 | + | 0.228416i | ||||
\(231\) | −1.50000 | + | 2.59808i | −0.0986928 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 2.50000 | − | 2.59808i | 0.163430 | − | 0.169842i | ||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | −5.00000 | + | 8.66025i | −0.324785 | + | 0.562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.00000 | − | 1.73205i | 0.0640184 | − | 0.110883i | ||||
\(245\) | −1.00000 | + | 1.73205i | −0.0638877 | + | 0.110657i | ||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 17.5000 | + | 4.33013i | 1.11350 | + | 0.275519i | ||||
\(248\) | 10.0000 | 0.635001 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −5.50000 | − | 9.52628i | −0.347157 | − | 0.601293i | 0.638586 | − | 0.769550i | \(-0.279520\pi\) |
−0.985743 | + | 0.168257i | \(0.946186\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | 2.00000 | + | 3.46410i | 0.125739 | + | 0.217786i | ||||
\(254\) | −2.50000 | − | 4.33013i | −0.156864 | − | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 12.0000 | − | 20.7846i | 0.748539 | − | 1.29651i | −0.199983 | − | 0.979799i | \(-0.564089\pi\) |
0.948523 | − | 0.316709i | \(-0.102578\pi\) | |||||||
\(258\) | −1.00000 | + | 1.73205i | −0.0622573 | + | 0.107833i | ||||
\(259\) | 3.00000 | 0.186411 | ||||||||
\(260\) | −3.50000 | − | 0.866025i | −0.217061 | − | 0.0537086i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.50000 | − | 12.9904i | 0.463352 | − | 0.802548i | ||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | −13.0000 | −0.798584 | ||||||||
\(266\) | −7.50000 | − | 12.9904i | −0.459855 | − | 0.796491i | ||||
\(267\) | 0.500000 | + | 0.866025i | 0.0305995 | + | 0.0529999i | ||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | 10.0000 | + | 17.3205i | 0.609711 | + | 1.05605i | 0.991288 | + | 0.131713i | \(0.0420477\pi\) |
−0.381577 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.50000 | − | 7.79423i | 0.453921 | − | 0.471728i | ||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | −2.00000 | + | 3.46410i | −0.120386 | + | 0.208514i | ||||
\(277\) | −11.5000 | − | 19.9186i | −0.690968 | − | 1.19679i | −0.971521 | − | 0.236953i | \(-0.923851\pi\) |
0.280553 | − | 0.959839i | \(-0.409482\pi\) | |||||||
\(278\) | −9.00000 | −0.539784 | ||||||||
\(279\) | −5.00000 | − | 8.66025i | −0.299342 | − | 0.518476i | ||||
\(280\) | 1.50000 | + | 2.59808i | 0.0896421 | + | 0.155265i | ||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | −4.50000 | − | 7.79423i | −0.267971 | − | 0.464140i | ||||
\(283\) | −1.00000 | + | 1.73205i | −0.0594438 | + | 0.102960i | −0.894216 | − | 0.447636i | \(-0.852266\pi\) |
0.834772 | + | 0.550596i | \(0.185599\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 5.00000 | 0.296174 | ||||||||
\(286\) | −3.50000 | − | 0.866025i | −0.206959 | − | 0.0512092i | ||||
\(287\) | −18.0000 | −1.06251 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 8.00000 | + | 13.8564i | 0.468165 | + | 0.810885i | ||||
\(293\) | −6.50000 | − | 11.2583i | −0.379734 | − | 0.657719i | 0.611289 | − | 0.791407i | \(-0.290651\pi\) |
−0.991023 | + | 0.133689i | \(0.957318\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | −2.00000 | − | 3.46410i | −0.116445 | − | 0.201688i | ||||
\(296\) | 0.500000 | − | 0.866025i | 0.0290619 | − | 0.0503367i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −4.00000 | − | 13.8564i | −0.231326 | − | 0.801337i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −3.00000 | + | 5.19615i | −0.172917 | + | 0.299501i | ||||
\(302\) | 3.00000 | − | 5.19615i | 0.172631 | − | 0.299005i | ||||
\(303\) | 2.00000 | + | 3.46410i | 0.114897 | + | 0.199007i | ||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | 1.00000 | + | 1.73205i | 0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | 1.02731 | 0.513657 | − | 0.857996i | \(-0.328290\pi\) | ||||
0.513657 | + | 0.857996i | \(0.328290\pi\) | |||||||
\(308\) | 1.50000 | + | 2.59808i | 0.0854704 | + | 0.148039i | ||||
\(309\) | −4.50000 | + | 7.79423i | −0.255996 | + | 0.443398i | ||||
\(310\) | −5.00000 | + | 8.66025i | −0.283981 | + | 0.491869i | ||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | −1.00000 | − | 3.46410i | −0.0566139 | − | 0.196116i | ||||
\(313\) | −34.0000 | −1.92179 | −0.960897 | − | 0.276907i | \(-0.910691\pi\) | ||||
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | −0.500000 | + | 0.866025i | −0.0282166 | + | 0.0488726i | ||||
\(315\) | 1.50000 | − | 2.59808i | 0.0845154 | − | 0.146385i | ||||
\(316\) | 5.00000 | + | 8.66025i | 0.281272 | + | 0.487177i | ||||
\(317\) | 19.0000 | 1.06715 | 0.533573 | − | 0.845754i | \(-0.320849\pi\) | ||||
0.533573 | + | 0.845754i | \(0.320849\pi\) | |||||||
\(318\) | −6.50000 | − | 11.2583i | −0.364502 | − | 0.631336i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | −6.00000 | + | 10.3923i | −0.334367 | + | 0.579141i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.50000 | − | 2.59808i | 0.138675 | − | 0.144115i | ||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | −5.00000 | + | 8.66025i | −0.276501 | + | 0.478913i | ||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | −13.5000 | − | 23.3827i | −0.744279 | − | 1.28913i | ||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −6.00000 | − | 10.3923i | −0.329293 | − | 0.570352i | ||||
\(333\) | −1.00000 | −0.0547997 | ||||||||
\(334\) | 6.50000 | + | 11.2583i | 0.355664 | + | 0.616028i | ||||
\(335\) | 6.00000 | − | 10.3923i | 0.327815 | − | 0.567792i | ||||
\(336\) | −1.50000 | + | 2.59808i | −0.0818317 | + | 0.141737i | ||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 11.5000 | + | 6.06218i | 0.625518 | + | 0.329739i | ||||
\(339\) | −16.0000 | −0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | + | 8.66025i | −0.270765 | + | 0.468979i | ||||
\(342\) | 2.50000 | + | 4.33013i | 0.135185 | + | 0.234146i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 1.00000 | + | 1.73205i | 0.0539164 | + | 0.0933859i | ||||
\(345\) | −2.00000 | − | 3.46410i | −0.107676 | − | 0.186501i | ||||
\(346\) | −9.00000 | −0.483843 | ||||||||
\(347\) | 14.0000 | + | 24.2487i | 0.751559 | + | 1.30174i | 0.947067 | + | 0.321037i | \(0.104031\pi\) |
−0.195507 | + | 0.980702i | \(0.562635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | + | 31.1769i | −0.963518 | + | 1.66886i | −0.249973 | + | 0.968253i | \(0.580422\pi\) |
−0.713545 | + | 0.700609i | \(0.752912\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | −2.50000 | + | 2.59808i | −0.133440 | + | 0.138675i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 18.0000 | − | 31.1769i | 0.958043 | − | 1.65938i | 0.230799 | − | 0.973002i | \(-0.425866\pi\) |
0.727245 | − | 0.686378i | \(-0.240800\pi\) | |||||||
\(354\) | 2.00000 | − | 3.46410i | 0.106299 | − | 0.184115i | ||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | − | 10.3923i | −0.317110 | − | 0.549250i | ||||
\(359\) | 34.0000 | 1.79445 | 0.897226 | − | 0.441572i | \(-0.145579\pi\) | ||||
0.897226 | + | 0.441572i | \(0.145579\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | −3.00000 | + | 5.19615i | −0.157676 | + | 0.273104i | ||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | −3.00000 | − | 10.3923i | −0.157243 | − | 0.544705i | ||||
\(365\) | −16.0000 | −0.837478 | ||||||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0.500000 | + | 0.866025i | 0.0259938 | + | 0.0450225i | ||||
\(371\) | −19.5000 | − | 33.7750i | −1.01239 | − | 1.75351i | ||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.00000 | 0.154303 | ||||||||
\(379\) | 0.500000 | − | 0.866025i | 0.0256833 | − | 0.0444847i | −0.852898 | − | 0.522077i | \(-0.825157\pi\) |
0.878581 | + | 0.477593i | \(0.158491\pi\) | |||||||
\(380\) | 2.50000 | − | 4.33013i | 0.128247 | − | 0.222131i | ||||
\(381\) | 2.50000 | + | 4.33013i | 0.128079 | + | 0.221839i | ||||
\(382\) | −18.0000 | −0.920960 | ||||||||
\(383\) | 14.0000 | + | 24.2487i | 0.715367 | + | 1.23905i | 0.962818 | + | 0.270151i | \(0.0870736\pi\) |
−0.247451 | + | 0.968900i | \(0.579593\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | −8.00000 | − | 13.8564i | −0.407189 | − | 0.705273i | ||||
\(387\) | 1.00000 | − | 1.73205i | 0.0508329 | − | 0.0880451i | ||||
\(388\) | −6.00000 | + | 10.3923i | −0.304604 | + | 0.527589i | ||||
\(389\) | −16.0000 | −0.811232 | −0.405616 | − | 0.914044i | \(-0.632943\pi\) | ||||
−0.405616 | + | 0.914044i | \(0.632943\pi\) | |||||||
\(390\) | 3.50000 | + | 0.866025i | 0.177229 | + | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00000 | + | 1.73205i | −0.0505076 | + | 0.0874818i | ||||
\(393\) | −7.50000 | + | 12.9904i | −0.378325 | + | 0.655278i | ||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 16.5000 | + | 28.5788i | 0.828111 | + | 1.43433i | 0.899518 | + | 0.436884i | \(0.143918\pi\) |
−0.0714068 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(398\) | −2.00000 | −0.100251 | ||||||||
\(399\) | 7.50000 | + | 12.9904i | 0.375470 | + | 0.650332i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −12.5000 | + | 21.6506i | −0.624220 | + | 1.08118i | 0.364471 | + | 0.931215i | \(0.381250\pi\) |
−0.988691 | + | 0.149966i | \(0.952083\pi\) | |||||||
\(402\) | 12.0000 | 0.598506 | ||||||||
\(403\) | 25.0000 | − | 25.9808i | 1.24534 | − | 1.29419i | ||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.500000 | + | 0.866025i | 0.0247841 | + | 0.0429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.50000 | − | 14.7224i | −0.420298 | − | 0.727977i | 0.575670 | − | 0.817682i | \(-0.304741\pi\) |
−0.995968 | + | 0.0897044i | \(0.971408\pi\) | |||||||
\(410\) | −3.00000 | − | 5.19615i | −0.148159 | − | 0.256620i | ||||
\(411\) | −16.0000 | −0.789222 | ||||||||
\(412\) | 4.50000 | + | 7.79423i | 0.221699 | + | 0.383994i | ||||
\(413\) | 6.00000 | − | 10.3923i | 0.295241 | − | 0.511372i | ||||
\(414\) | 2.00000 | − | 3.46410i | 0.0982946 | − | 0.170251i | ||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | −3.50000 | − | 0.866025i | −0.171602 | − | 0.0424604i | ||||
\(417\) | 9.00000 | 0.440732 | ||||||||
\(418\) | 2.50000 | − | 4.33013i | 0.122279 | − | 0.211793i | ||||
\(419\) | 14.0000 | − | 24.2487i | 0.683945 | − | 1.18463i | −0.289822 | − | 0.957080i | \(-0.593596\pi\) |
0.973767 | − | 0.227547i | \(-0.0730704\pi\) | |||||||
\(420\) | −1.50000 | − | 2.59808i | −0.0731925 | − | 0.126773i | ||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 7.50000 | + | 12.9904i | 0.365094 | + | 0.632362i | ||||
\(423\) | 4.50000 | + | 7.79423i | 0.218797 | + | 0.378968i | ||||
\(424\) | −13.0000 | −0.631336 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.00000 | + | 1.73205i | −0.0484502 | + | 0.0839181i | ||||
\(427\) | −3.00000 | + | 5.19615i | −0.145180 | + | 0.251459i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 3.50000 | + | 0.866025i | 0.168982 | + | 0.0418121i | ||||
\(430\) | −2.00000 | −0.0964486 | ||||||||
\(431\) | −18.0000 | + | 31.1769i | −0.867029 | + | 1.50174i | −0.00201168 | + | 0.999998i | \(0.500640\pi\) |
−0.865018 | + | 0.501741i | \(0.832693\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −8.00000 | − | 13.8564i | −0.384455 | − | 0.665896i | 0.607238 | − | 0.794520i | \(-0.292277\pi\) |
−0.991693 | + | 0.128624i | \(0.958944\pi\) | |||||||
\(434\) | −30.0000 | −1.44005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | 20.0000 | 0.956730 | ||||||||
\(438\) | −8.00000 | − | 13.8564i | −0.382255 | − | 0.662085i | ||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | −0.500000 | + | 0.866025i | −0.0238366 | + | 0.0412861i | ||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0000 | −0.855206 | −0.427603 | − | 0.903967i | \(-0.640642\pi\) | ||||
−0.427603 | + | 0.903967i | \(0.640642\pi\) | |||||||
\(444\) | −0.500000 | + | 0.866025i | −0.0237289 | + | 0.0410997i | ||||
\(445\) | −0.500000 | + | 0.866025i | −0.0237023 | + | 0.0410535i | ||||
\(446\) | −5.50000 | − | 9.52628i | −0.260433 | − | 0.451082i | ||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 1.50000 | + | 2.59808i | 0.0708683 | + | 0.122748i | ||||
\(449\) | 7.50000 | + | 12.9904i | 0.353947 | + | 0.613054i | 0.986937 | − | 0.161106i | \(-0.0515060\pi\) |
−0.632990 | + | 0.774160i | \(0.718173\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −3.00000 | − | 5.19615i | −0.141264 | − | 0.244677i | ||||
\(452\) | −8.00000 | + | 13.8564i | −0.376288 | + | 0.651751i | ||||
\(453\) | −3.00000 | + | 5.19615i | −0.140952 | + | 0.244137i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 10.5000 | + | 2.59808i | 0.492248 | + | 0.121800i | ||||
\(456\) | 5.00000 | 0.234146 | ||||||||
\(457\) | −11.0000 | + | 19.0526i | −0.514558 | + | 0.891241i | 0.485299 | + | 0.874348i | \(0.338711\pi\) |
−0.999857 | + | 0.0168929i | \(0.994623\pi\) | |||||||
\(458\) | 5.00000 | − | 8.66025i | 0.233635 | − | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | −0.186501 | ||||||||
\(461\) | 6.00000 | + | 10.3923i | 0.279448 | + | 0.484018i | 0.971248 | − | 0.238071i | \(-0.0765153\pi\) |
−0.691800 | + | 0.722089i | \(0.743182\pi\) | |||||||
\(462\) | −1.50000 | − | 2.59808i | −0.0697863 | − | 0.120873i | ||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.00000 | − | 8.66025i | 0.231869 | − | 0.401610i | ||||
\(466\) | −5.00000 | + | 8.66025i | −0.231621 | + | 0.401179i | ||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 1.00000 | + | 3.46410i | 0.0462250 | + | 0.160128i | ||||
\(469\) | 36.0000 | 1.66233 | ||||||||
\(470\) | 4.50000 | − | 7.79423i | 0.207570 | − | 0.359521i | ||||
\(471\) | 0.500000 | − | 0.866025i | 0.0230388 | − | 0.0399043i | ||||
\(472\) | −2.00000 | − | 3.46410i | −0.0920575 | − | 0.159448i | ||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | −5.00000 | − | 8.66025i | −0.229658 | − | 0.397779i | ||||
\(475\) | 2.50000 | + | 4.33013i | 0.114708 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.50000 | + | 11.2583i | 0.297615 | + | 0.515484i | ||||
\(478\) | 1.00000 | − | 1.73205i | 0.0457389 | − | 0.0792222i | ||||
\(479\) | 4.00000 | − | 6.92820i | 0.182765 | − | 0.316558i | −0.760056 | − | 0.649857i | \(-0.774829\pi\) |
0.942821 | + | 0.333300i | \(0.108162\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −1.00000 | − | 3.46410i | −0.0455961 | − | 0.157949i | ||||
\(482\) | 15.0000 | 0.683231 | ||||||||
\(483\) | 6.00000 | − | 10.3923i | 0.273009 | − | 0.472866i | ||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | −6.00000 | − | 10.3923i | −0.272446 | − | 0.471890i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.5000 | − | 30.3109i | −0.793001 | − | 1.37352i | −0.924101 | − | 0.382148i | \(-0.875184\pi\) |
0.131100 | − | 0.991369i | \(-0.458149\pi\) | |||||||
\(488\) | 1.00000 | + | 1.73205i | 0.0452679 | + | 0.0784063i | ||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | −1.00000 | − | 1.73205i | −0.0451754 | − | 0.0782461i | ||||
\(491\) | −12.5000 | + | 21.6506i | −0.564117 | + | 0.977079i | 0.433014 | + | 0.901387i | \(0.357450\pi\) |
−0.997131 | + | 0.0756923i | \(0.975883\pi\) | |||||||
\(492\) | 3.00000 | − | 5.19615i | 0.135250 | − | 0.234261i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.5000 | + | 12.9904i | −0.562402 | + | 0.584465i | ||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | −5.00000 | + | 8.66025i | −0.224507 | + | 0.388857i | ||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 6.00000 | + | 10.3923i | 0.268866 | + | 0.465690i | ||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −6.50000 | − | 11.2583i | −0.290399 | − | 0.502985i | ||||
\(502\) | 11.0000 | 0.490954 | ||||||||
\(503\) | 0.500000 | + | 0.866025i | 0.0222939 | + | 0.0386142i | 0.876957 | − | 0.480569i | \(-0.159570\pi\) |
−0.854663 | + | 0.519183i | \(0.826236\pi\) | |||||||
\(504\) | 1.50000 | − | 2.59808i | 0.0668153 | − | 0.115728i | ||||
\(505\) | −2.00000 | + | 3.46410i | −0.0889988 | + | 0.154150i | ||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | −11.5000 | − | 6.06218i | −0.510733 | − | 0.269231i | ||||
\(508\) | 5.00000 | 0.221839 | ||||||||
\(509\) | −9.00000 | + | 15.5885i | −0.398918 | + | 0.690946i | −0.993593 | − | 0.113020i | \(-0.963948\pi\) |
0.594675 | + | 0.803966i | \(0.297281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | − | 41.5692i | −1.06170 | − | 1.83891i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.50000 | − | 4.33013i | −0.110378 | − | 0.191180i | ||||
\(514\) | 12.0000 | + | 20.7846i | 0.529297 | + | 0.916770i | ||||
\(515\) | −9.00000 | −0.396587 | ||||||||
\(516\) | −1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | ||||
\(517\) | 4.50000 | − | 7.79423i | 0.197910 | − | 0.342790i | ||||
\(518\) | −1.50000 | + | 2.59808i | −0.0659062 | + | 0.114153i | ||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 2.50000 | − | 2.59808i | 0.109632 | − | 0.113933i | ||||
\(521\) | 33.0000 | 1.44576 | 0.722878 | − | 0.690976i | \(-0.242819\pi\) | ||||
0.722878 | + | 0.690976i | \(0.242819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 5.19615i | −0.131181 | + | 0.227212i | −0.924132 | − | 0.382073i | \(-0.875210\pi\) |
0.792951 | + | 0.609285i | \(0.208544\pi\) | |||||||
\(524\) | 7.50000 | + | 12.9904i | 0.327639 | + | 0.567487i | ||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | −1.50000 | − | 2.59808i | −0.0654031 | − | 0.113282i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 6.50000 | − | 11.2583i | 0.282342 | − | 0.489031i | ||||
\(531\) | −2.00000 | + | 3.46410i | −0.0867926 | + | 0.150329i | ||||
\(532\) | 15.0000 | 0.650332 | ||||||||
\(533\) | 6.00000 | + | 20.7846i | 0.259889 | + | 0.900281i | ||||
\(534\) | −1.00000 | −0.0432742 | ||||||||
\(535\) | 3.00000 | − | 5.19615i | 0.129701 | − | 0.224649i | ||||
\(536\) | 6.00000 | − | 10.3923i | 0.259161 | − | 0.448879i | ||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | −20.0000 | −0.862261 | ||||||||
\(539\) | −1.00000 | − | 1.73205i | −0.0430730 | − | 0.0746047i | ||||
\(540\) | 0.500000 | + | 0.866025i | 0.0215166 | + | 0.0372678i | ||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 12.0000 | + | 20.7846i | 0.515444 | + | 0.892775i | ||||
\(543\) | 3.00000 | − | 5.19615i | 0.128742 | − | 0.222988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 3.00000 | + | 10.3923i | 0.128388 | + | 0.444750i | ||||
\(547\) | 34.0000 | 1.45374 | 0.726868 | − | 0.686778i | \(-0.240975\pi\) | ||||
0.726868 | + | 0.686778i | \(0.240975\pi\) | |||||||
\(548\) | −8.00000 | + | 13.8564i | −0.341743 | + | 0.591916i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.00000 | − | 3.46410i | −0.0851257 | − | 0.147442i | ||||
\(553\) | −15.0000 | − | 25.9808i | −0.637865 | − | 1.10481i | ||||
\(554\) | 23.0000 | 0.977176 | ||||||||
\(555\) | −0.500000 | − | 0.866025i | −0.0212238 | − | 0.0367607i | ||||
\(556\) | 4.50000 | − | 7.79423i | 0.190843 | − | 0.330549i | ||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | 10.0000 | 0.423334 | ||||||||
\(559\) | 7.00000 | + | 1.73205i | 0.296068 | + | 0.0732579i | ||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00000 | + | 8.66025i | −0.210912 | + | 0.365311i | ||||
\(563\) | −12.0000 | − | 20.7846i | −0.505740 | − | 0.875967i | −0.999978 | − | 0.00664037i | \(-0.997886\pi\) |
0.494238 | − | 0.869326i | \(-0.335447\pi\) | |||||||
\(564\) | 9.00000 | 0.378968 | ||||||||
\(565\) | −8.00000 | − | 13.8564i | −0.336563 | − | 0.582943i | ||||
\(566\) | −1.00000 | − | 1.73205i | −0.0420331 | − | 0.0728035i | ||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | 1.00000 | + | 1.73205i | 0.0419591 | + | 0.0726752i | ||||
\(569\) | 5.50000 | − | 9.52628i | 0.230572 | − | 0.399362i | −0.727405 | − | 0.686209i | \(-0.759274\pi\) |
0.957977 | + | 0.286846i | \(0.0926069\pi\) | |||||||
\(570\) | −2.50000 | + | 4.33013i | −0.104713 | + | 0.181369i | ||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 2.50000 | − | 2.59808i | 0.104530 | − | 0.108631i | ||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 9.00000 | − | 15.5885i | 0.375653 | − | 0.650650i | ||||
\(575\) | 2.00000 | − | 3.46410i | 0.0834058 | − | 0.144463i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 8.50000 | + | 14.7224i | 0.353553 | + | 0.612372i | ||||
\(579\) | 8.00000 | + | 13.8564i | 0.332469 | + | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | + | 31.1769i | 0.746766 | + | 1.29344i | ||||
\(582\) | 6.00000 | − | 10.3923i | 0.248708 | − | 0.430775i | ||||
\(583\) | 6.50000 | − | 11.2583i | 0.269202 | − | 0.466272i | ||||
\(584\) | −16.0000 | −0.662085 | ||||||||
\(585\) | −3.50000 | − | 0.866025i | −0.144707 | − | 0.0358057i | ||||
\(586\) | 13.0000 | 0.537025 | ||||||||
\(587\) | 9.00000 | − | 15.5885i | 0.371470 | − | 0.643404i | −0.618322 | − | 0.785925i | \(-0.712187\pi\) |
0.989792 | + | 0.142520i | \(0.0455206\pi\) | |||||||
\(588\) | 1.00000 | − | 1.73205i | 0.0412393 | − | 0.0714286i | ||||
\(589\) | 25.0000 | + | 43.3013i | 1.03011 | + | 1.78420i | ||||
\(590\) | 4.00000 | 0.164677 | ||||||||
\(591\) | −7.50000 | − | 12.9904i | −0.308509 | − | 0.534353i | ||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | 28.0000 | 1.14982 | 0.574911 | − | 0.818216i | \(-0.305037\pi\) | ||||
0.574911 | + | 0.818216i | \(0.305037\pi\) | |||||||
\(594\) | 0.500000 | + | 0.866025i | 0.0205152 | + | 0.0355335i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | − | 5.19615i | 0.122885 | − | 0.212843i | ||||
\(597\) | 2.00000 | 0.0818546 | ||||||||
\(598\) | 14.0000 | + | 3.46410i | 0.572503 | + | 0.141658i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | 13.5000 | − | 23.3827i | 0.550676 | − | 0.953800i | −0.447549 | − | 0.894259i | \(-0.647703\pi\) |
0.998226 | − | 0.0595404i | \(-0.0189635\pi\) | |||||||
\(602\) | −3.00000 | − | 5.19615i | −0.122271 | − | 0.211779i | ||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 3.00000 | + | 5.19615i | 0.122068 | + | 0.211428i | ||||
\(605\) | 5.00000 | + | 8.66025i | 0.203279 | + | 0.352089i | ||||
\(606\) | −4.00000 | −0.162489 | ||||||||
\(607\) | −18.5000 | − | 32.0429i | −0.750892 | − | 1.30058i | −0.947391 | − | 0.320079i | \(-0.896291\pi\) |
0.196499 | − | 0.980504i | \(-0.437043\pi\) | |||||||
\(608\) | 2.50000 | − | 4.33013i | 0.101388 | − | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | −22.5000 | + | 23.3827i | −0.910253 | + | 0.945962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5000 | + | 19.9186i | −0.464481 | + | 0.804504i | −0.999178 | − | 0.0405396i | \(-0.987092\pi\) |
0.534697 | + | 0.845044i | \(0.320426\pi\) | |||||||
\(614\) | −9.00000 | + | 15.5885i | −0.363210 | + | 0.629099i | ||||
\(615\) | 3.00000 | + | 5.19615i | 0.120972 | + | 0.209529i | ||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | 3.00000 | + | 5.19615i | 0.120775 | + | 0.209189i | 0.920074 | − | 0.391745i | \(-0.128129\pi\) |
−0.799298 | + | 0.600935i | \(0.794795\pi\) | |||||||
\(618\) | −4.50000 | − | 7.79423i | −0.181017 | − | 0.313530i | ||||
\(619\) | −31.0000 | −1.24600 | −0.622998 | − | 0.782224i | \(-0.714085\pi\) | ||||
−0.622998 | + | 0.782224i | \(0.714085\pi\) | |||||||
\(620\) | −5.00000 | − | 8.66025i | −0.200805 | − | 0.347804i | ||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | 6.00000 | − | 10.3923i | 0.240578 | − | 0.416693i | ||||
\(623\) | −3.00000 | −0.120192 | ||||||||
\(624\) | 3.50000 | + | 0.866025i | 0.140112 | + | 0.0346688i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.0000 | − | 29.4449i | 0.679457 | − | 1.17685i | ||||
\(627\) | −2.50000 | + | 4.33013i | −0.0998404 | + | 0.172929i | ||||
\(628\) | −0.500000 | − | 0.866025i | −0.0199522 | − | 0.0345582i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.50000 | + | 2.59808i | 0.0597614 | + | 0.103510i | ||||
\(631\) | 2.00000 | + | 3.46410i | 0.0796187 | + | 0.137904i | 0.903085 | − | 0.429461i | \(-0.141296\pi\) |
−0.823467 | + | 0.567365i | \(0.807963\pi\) | |||||||
\(632\) | −10.0000 | −0.397779 | ||||||||
\(633\) | −7.50000 | − | 12.9904i | −0.298098 | − | 0.516321i | ||||
\(634\) | −9.50000 | + | 16.4545i | −0.377293 | + | 0.653491i | ||||
\(635\) | −2.50000 | + | 4.33013i | −0.0992095 | + | 0.171836i | ||||
\(636\) | 13.0000 | 0.515484 | ||||||||
\(637\) | 2.00000 | + | 6.92820i | 0.0792429 | + | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | 22.0000 | + | 38.1051i | 0.867595 | + | 1.50272i | 0.864447 | + | 0.502724i | \(0.167669\pi\) |
0.00314839 | + | 0.999995i | \(0.498998\pi\) | |||||||
\(644\) | −6.00000 | − | 10.3923i | −0.236433 | − | 0.409514i | ||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.50000 | + | 7.79423i | −0.176913 | + | 0.306423i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) |
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 1.00000 | + | 3.46410i | 0.0392232 | + | 0.135873i | ||||
\(651\) | 30.0000 | 1.17579 | ||||||||
\(652\) | 10.0000 | − | 17.3205i | 0.391630 | − | 0.678323i | ||||
\(653\) | −20.5000 | + | 35.5070i | −0.802227 | + | 1.38950i | 0.115920 | + | 0.993259i | \(0.463018\pi\) |
−0.918147 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(654\) | −5.00000 | − | 8.66025i | −0.195515 | − | 0.338643i | ||||
\(655\) | −15.0000 | −0.586098 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 8.00000 | + | 13.8564i | 0.312110 | + | 0.540590i | ||||
\(658\) | 27.0000 | 1.05257 | ||||||||
\(659\) | −2.00000 | − | 3.46410i | −0.0779089 | − | 0.134942i | 0.824439 | − | 0.565951i | \(-0.191491\pi\) |
−0.902348 | + | 0.431009i | \(0.858158\pi\) | |||||||
\(660\) | 0.500000 | − | 0.866025i | 0.0194625 | − | 0.0337100i | ||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 28.0000 | 1.08825 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | −7.50000 | + | 12.9904i | −0.290838 | + | 0.503745i | ||||
\(666\) | 0.500000 | − | 0.866025i | 0.0193746 | − | 0.0335578i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −13.0000 | −0.502985 | ||||||||
\(669\) | 5.50000 | + | 9.52628i | 0.212642 | + | 0.368307i | ||||
\(670\) | 6.00000 | + | 10.3923i | 0.231800 | + | 0.401490i | ||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | −1.50000 | − | 2.59808i | −0.0578638 | − | 0.100223i | ||||
\(673\) | 16.0000 | − | 27.7128i | 0.616755 | − | 1.06825i | −0.373319 | − | 0.927703i | \(-0.621780\pi\) |
0.990074 | − | 0.140548i | \(-0.0448863\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | −26.0000 | −0.999261 | −0.499631 | − | 0.866239i | \(-0.666531\pi\) | ||||
−0.499631 | + | 0.866239i | \(0.666531\pi\) | |||||||
\(678\) | 8.00000 | − | 13.8564i | 0.307238 | − | 0.532152i | ||||
\(679\) | 18.0000 | − | 31.1769i | 0.690777 | − | 1.19646i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | −5.00000 | − | 8.66025i | −0.191460 | − | 0.331618i | ||||
\(683\) | 13.0000 | + | 22.5167i | 0.497431 | + | 0.861576i | 0.999996 | − | 0.00296369i | \(-0.000943372\pi\) |
−0.502564 | + | 0.864540i | \(0.667610\pi\) | |||||||
\(684\) | −5.00000 | −0.191180 | ||||||||
\(685\) | −8.00000 | − | 13.8564i | −0.305664 | − | 0.529426i | ||||
\(686\) | −7.50000 | + | 12.9904i | −0.286351 | + | 0.495975i | ||||
\(687\) | −5.00000 | + | 8.66025i | −0.190762 | + | 0.330409i | ||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | −32.5000 | + | 33.7750i | −1.23815 | + | 1.28672i | ||||
\(690\) | 4.00000 | 0.152277 | ||||||||
\(691\) | −16.5000 | + | 28.5788i | −0.627690 | + | 1.08719i | 0.360325 | + | 0.932827i | \(0.382666\pi\) |
−0.988014 | + | 0.154363i | \(0.950667\pi\) | |||||||
\(692\) | 4.50000 | − | 7.79423i | 0.171064 | − | 0.296292i | ||||
\(693\) | 1.50000 | + | 2.59808i | 0.0569803 | + | 0.0986928i | ||||
\(694\) | −28.0000 | −1.06287 | ||||||||
\(695\) | 4.50000 | + | 7.79423i | 0.170695 | + | 0.295652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −18.0000 | − | 31.1769i | −0.681310 | − | 1.18006i | ||||
\(699\) | 5.00000 | − | 8.66025i | 0.189117 | − | 0.327561i | ||||
\(700\) | 1.50000 | − | 2.59808i | 0.0566947 | − | 0.0981981i | ||||
\(701\) | 4.00000 | 0.151078 | 0.0755390 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755390 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(702\) | −1.00000 | − | 3.46410i | −0.0377426 | − | 0.130744i | ||||
\(703\) | 5.00000 | 0.188579 | ||||||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | −4.50000 | + | 7.79423i | −0.169480 | + | 0.293548i | ||||
\(706\) | 18.0000 | + | 31.1769i | 0.677439 | + | 1.17336i | ||||
\(707\) | −12.0000 | −0.451306 | ||||||||
\(708\) | 2.00000 | + | 3.46410i | 0.0751646 | + | 0.130189i | ||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | 5.00000 | + | 8.66025i | 0.187515 | + | 0.324785i | ||||
\(712\) | −0.500000 | + | 0.866025i | −0.0187383 | + | 0.0324557i | ||||
\(713\) | 20.0000 | − | 34.6410i | 0.749006 | − | 1.29732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00000 | + | 3.46410i | 0.0373979 | + | 0.129550i | ||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | −1.00000 | + | 1.73205i | −0.0373457 | + | 0.0646846i | ||||
\(718\) | −17.0000 | + | 29.4449i | −0.634434 | + | 1.09887i | ||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −13.5000 | − | 23.3827i | −0.502766 | − | 0.870817i | ||||
\(722\) | −3.00000 | − | 5.19615i | −0.111648 | − | 0.193381i | ||||
\(723\) | −15.0000 | −0.557856 | ||||||||
\(724\) | −3.00000 | − | 5.19615i | −0.111494 | − | 0.193113i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | + | 8.66025i | −0.185567 | + | 0.321412i | ||||
\(727\) | −37.0000 | −1.37225 | −0.686127 | − | 0.727482i | \(-0.740691\pi\) | ||||
−0.686127 | + | 0.727482i | \(0.740691\pi\) | |||||||
\(728\) | 10.5000 | + | 2.59808i | 0.389156 | + | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.00000 | − | 13.8564i | 0.296093 | − | 0.512849i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.00000 | − | 1.73205i | −0.0369611 | − | 0.0640184i | ||||
\(733\) | −5.00000 | −0.184679 | −0.0923396 | − | 0.995728i | \(-0.529435\pi\) | ||||
−0.0923396 | + | 0.995728i | \(0.529435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | + | 1.73205i | 0.0368856 | + | 0.0638877i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 6.00000 | + | 10.3923i | 0.221013 | + | 0.382805i | ||||
\(738\) | −3.00000 | + | 5.19615i | −0.110432 | + | 0.191273i | ||||
\(739\) | −17.5000 | + | 30.3109i | −0.643748 | + | 1.11500i | 0.340841 | + | 0.940121i | \(0.389288\pi\) |
−0.984589 | + | 0.174883i | \(0.944045\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 12.5000 | − | 12.9904i | 0.459199 | − | 0.477214i | ||||
\(742\) | 39.0000 | 1.43174 | ||||||||
\(743\) | −12.0000 | + | 20.7846i | −0.440237 | + | 0.762513i | −0.997707 | − | 0.0676840i | \(-0.978439\pi\) |
0.557470 | + | 0.830197i | \(0.311772\pi\) | |||||||
\(744\) | 5.00000 | − | 8.66025i | 0.183309 | − | 0.317500i | ||||
\(745\) | 3.00000 | + | 5.19615i | 0.109911 | + | 0.190372i | ||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | 0.657706 | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −22.0000 | + | 38.1051i | −0.802791 | + | 1.39048i | 0.114981 | + | 0.993368i | \(0.463319\pi\) |
−0.917772 | + | 0.397108i | \(0.870014\pi\) | |||||||
\(752\) | 4.50000 | − | 7.79423i | 0.164098 | − | 0.284226i | ||||
\(753\) | −11.0000 | −0.400862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | −1.50000 | + | 2.59808i | −0.0545545 | + | 0.0944911i | ||||
\(757\) | −19.5000 | + | 33.7750i | −0.708740 | + | 1.22757i | 0.256585 | + | 0.966522i | \(0.417403\pi\) |
−0.965325 | + | 0.261051i | \(0.915931\pi\) | |||||||
\(758\) | 0.500000 | + | 0.866025i | 0.0181608 | + | 0.0314555i | ||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 2.50000 | + | 4.33013i | 0.0906845 | + | 0.157070i | ||||
\(761\) | −22.5000 | − | 38.9711i | −0.815624 | − | 1.41270i | −0.908879 | − | 0.417061i | \(-0.863060\pi\) |
0.0932544 | − | 0.995642i | \(-0.470273\pi\) | |||||||
\(762\) | −5.00000 | −0.181131 | ||||||||
\(763\) | −15.0000 | − | 25.9808i | −0.543036 | − | 0.940567i | ||||
\(764\) | 9.00000 | − | 15.5885i | 0.325609 | − | 0.563971i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.0000 | −1.01168 | ||||||||
\(767\) | −14.0000 | − | 3.46410i | −0.505511 | − | 0.125081i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.0000 | − | 22.5167i | 0.468792 | − | 0.811972i | −0.530572 | − | 0.847640i | \(-0.678023\pi\) |
0.999364 | + | 0.0356685i | \(0.0113561\pi\) | |||||||
\(770\) | 1.50000 | − | 2.59808i | 0.0540562 | − | 0.0936282i | ||||
\(771\) | −12.0000 | − | 20.7846i | −0.432169 | − | 0.748539i | ||||
\(772\) | 16.0000 | 0.575853 | ||||||||
\(773\) | 18.5000 | + | 32.0429i | 0.665399 | + | 1.15250i | 0.979177 | + | 0.203008i | \(0.0650718\pi\) |
−0.313778 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 10.0000 | 0.359211 | ||||||||
\(776\) | −6.00000 | − | 10.3923i | −0.215387 | − | 0.373062i | ||||
\(777\) | 1.50000 | − | 2.59808i | 0.0538122 | − | 0.0932055i | ||||
\(778\) | 8.00000 | − | 13.8564i | 0.286814 | − | 0.496776i | ||||
\(779\) | −30.0000 | −1.07486 | ||||||||
\(780\) | −2.50000 | + | 2.59808i | −0.0895144 | + | 0.0930261i | ||||
\(781\) | −2.00000 | −0.0715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 1.00000 | 0.0356915 | ||||||||
\(786\) | −7.50000 | − | 12.9904i | −0.267516 | − | 0.463352i | ||||
\(787\) | −8.00000 | − | 13.8564i | −0.285169 | − | 0.493928i | 0.687481 | − | 0.726202i | \(-0.258716\pi\) |
−0.972650 | + | 0.232275i | \(0.925383\pi\) | |||||||
\(788\) | −15.0000 | −0.534353 | ||||||||
\(789\) | 1.50000 | + | 2.59808i | 0.0534014 | + | 0.0924940i | ||||
\(790\) | 5.00000 | − | 8.66025i | 0.177892 | − | 0.308118i | ||||
\(791\) | 24.0000 | − | 41.5692i | 0.853342 | − | 1.47803i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 7.00000 | + | 1.73205i | 0.248577 | + | 0.0615069i | ||||
\(794\) | −33.0000 | −1.17113 | ||||||||
\(795\) | −6.50000 | + | 11.2583i | −0.230531 | + | 0.399292i | ||||
\(796\) | 1.00000 | − | 1.73205i | 0.0354441 | − | 0.0613909i | ||||
\(797\) | 7.00000 | + | 12.1244i | 0.247953 | + | 0.429467i | 0.962958 | − | 0.269653i | \(-0.0869089\pi\) |
−0.715005 | + | 0.699119i | \(0.753576\pi\) | |||||||
\(798\) | −15.0000 | −0.530994 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 1.00000 | 0.0353333 | ||||||||
\(802\) | −12.5000 | − | 21.6506i | −0.441390 | − | 0.764511i | ||||
\(803\) | 8.00000 | − | 13.8564i | 0.282314 | − | 0.488982i | ||||
\(804\) | −6.00000 | + | 10.3923i | −0.211604 | + | 0.366508i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | 10.0000 | + | 34.6410i | 0.352235 | + | 1.22018i | ||||
\(807\) | 20.0000 | 0.704033 | ||||||||
\(808\) | −2.00000 | + | 3.46410i | −0.0703598 | + | 0.121867i | ||||
\(809\) | 9.00000 | − | 15.5885i | 0.316423 | − | 0.548061i | −0.663316 | − | 0.748340i | \(-0.730851\pi\) |
0.979739 | + | 0.200279i | \(0.0641847\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 33.0000 | 1.15879 | 0.579393 | − | 0.815048i | \(-0.303290\pi\) | ||||
0.579393 | + | 0.815048i | \(0.303290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | − | 20.7846i | −0.420858 | − | 0.728948i | ||||
\(814\) | −1.00000 | −0.0350500 | ||||||||
\(815\) | 10.0000 | + | 17.3205i | 0.350285 | + | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00000 | + | 8.66025i | −0.174928 | + | 0.302984i | ||||
\(818\) | 17.0000 | 0.594391 | ||||||||
\(819\) | −3.00000 | − | 10.3923i | −0.104828 | − | 0.363137i | ||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 8.00000 | − | 13.8564i | 0.279032 | − | 0.483298i | ||||
\(823\) | 2.50000 | + | 4.33013i | 0.0871445 | + | 0.150939i | 0.906303 | − | 0.422628i | \(-0.138892\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 0.500000 | + | 0.866025i | 0.0174078 | + | 0.0301511i | ||||
\(826\) | 6.00000 | + | 10.3923i | 0.208767 | + | 0.361595i | ||||
\(827\) | −30.0000 | −1.04320 | −0.521601 | − | 0.853189i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853189i | \(0.674665\pi\) | |||||||
\(828\) | 2.00000 | + | 3.46410i | 0.0695048 | + | 0.120386i | ||||
\(829\) | 22.0000 | − | 38.1051i | 0.764092 | − | 1.32345i | −0.176634 | − | 0.984277i | \(-0.556521\pi\) |
0.940726 | − | 0.339169i | \(-0.110146\pi\) | |||||||
\(830\) | −6.00000 | + | 10.3923i | −0.208263 | + | 0.360722i | ||||
\(831\) | −23.0000 | −0.797861 | ||||||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.50000 | + | 7.79423i | −0.155822 | + | 0.269892i | ||||
\(835\) | 6.50000 | − | 11.2583i | 0.224942 | − | 0.389611i | ||||
\(836\) | 2.50000 | + | 4.33013i | 0.0864643 | + | 0.149761i | ||||
\(837\) | −10.0000 | −0.345651 | ||||||||
\(838\) | 14.0000 | + | 24.2487i | 0.483622 | + | 0.837658i | ||||
\(839\) | 27.0000 | + | 46.7654i | 0.932144 | + | 1.61452i | 0.779650 | + | 0.626215i | \(0.215397\pi\) |
0.152493 | + | 0.988304i | \(0.451270\pi\) | |||||||
\(840\) | 3.00000 | 0.103510 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | −10.0000 | + | 17.3205i | −0.344623 | + | 0.596904i | ||||
\(843\) | 5.00000 | − | 8.66025i | 0.172209 | − | 0.298275i | ||||
\(844\) | −15.0000 | −0.516321 | ||||||||
\(845\) | −0.500000 | − | 12.9904i | −0.0172005 | − | 0.446883i | ||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | −15.0000 | + | 25.9808i | −0.515406 | + | 0.892710i | ||||
\(848\) | 6.50000 | − | 11.2583i | 0.223211 | − | 0.386613i | ||||
\(849\) | 1.00000 | + | 1.73205i | 0.0343199 | + | 0.0594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | − | 3.46410i | −0.0685591 | − | 0.118748i | ||||
\(852\) | −1.00000 | − | 1.73205i | −0.0342594 | − | 0.0593391i | ||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | −3.00000 | − | 5.19615i | −0.102658 | − | 0.177809i | ||||
\(855\) | 2.50000 | − | 4.33013i | 0.0854982 | − | 0.148087i | ||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | −2.50000 | + | 2.59808i | −0.0853486 | + | 0.0886969i | ||||
\(859\) | 19.0000 | 0.648272 | 0.324136 | − | 0.946011i | \(-0.394927\pi\) | ||||
0.324136 | + | 0.946011i | \(0.394927\pi\) | |||||||
\(860\) | 1.00000 | − | 1.73205i | 0.0340997 | − | 0.0590624i | ||||
\(861\) | −9.00000 | + | 15.5885i | −0.306719 | + | 0.531253i | ||||
\(862\) | −18.0000 | − | 31.1769i | −0.613082 | − | 1.06189i | ||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.50000 | + | 7.79423i | 0.153005 | + | 0.265012i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | −8.50000 | − | 14.7224i | −0.288675 | − | 0.500000i | ||||
\(868\) | 15.0000 | − | 25.9808i | 0.509133 | − | 0.881845i | ||||
\(869\) | 5.00000 | − | 8.66025i | 0.169613 | − | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | − | 41.5692i | −0.406604 | − | 1.40852i | ||||
\(872\) | −10.0000 | −0.338643 | ||||||||
\(873\) | −6.00000 | + | 10.3923i | −0.203069 | + | 0.351726i | ||||
\(874\) | −10.0000 | + | 17.3205i | −0.338255 | + | 0.585875i | ||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | −19.0000 | − | 32.9090i | −0.641584 | − | 1.11126i | −0.985079 | − | 0.172102i | \(-0.944944\pi\) |
0.343495 | − | 0.939155i | \(-0.388389\pi\) | |||||||
\(878\) | 5.00000 | + | 8.66025i | 0.168742 | + | 0.292269i | ||||
\(879\) | −13.0000 | −0.438479 | ||||||||
\(880\) | −0.500000 | − | 0.866025i | −0.0168550 | − | 0.0291937i | ||||
\(881\) | −2.50000 | + | 4.33013i | −0.0842271 | + | 0.145886i | −0.905062 | − | 0.425280i | \(-0.860175\pi\) |
0.820834 | + | 0.571166i | \(0.193509\pi\) | |||||||
\(882\) | −1.00000 | + | 1.73205i | −0.0336718 | + | 0.0583212i | ||||
\(883\) | 42.0000 | 1.41341 | 0.706706 | − | 0.707507i | \(-0.250180\pi\) | ||||
0.706706 | + | 0.707507i | \(0.250180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 9.00000 | − | 15.5885i | 0.302361 | − | 0.523704i | ||||
\(887\) | 6.50000 | − | 11.2583i | 0.218249 | − | 0.378018i | −0.736024 | − | 0.676955i | \(-0.763299\pi\) |
0.954273 | + | 0.298938i | \(0.0966323\pi\) | |||||||
\(888\) | −0.500000 | − | 0.866025i | −0.0167789 | − | 0.0290619i | ||||
\(889\) | −15.0000 | −0.503084 | ||||||||
\(890\) | −0.500000 | − | 0.866025i | −0.0167600 | − | 0.0290292i | ||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | 11.0000 | 0.368307 | ||||||||
\(893\) | −22.5000 | − | 38.9711i | −0.752934 | − | 1.30412i | ||||
\(894\) | −3.00000 | + | 5.19615i | −0.100335 | + | 0.173785i | ||||
\(895\) | −6.00000 | + | 10.3923i | −0.200558 | + | 0.347376i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | −14.0000 | − | 3.46410i | −0.467446 | − | 0.115663i | ||||
\(898\) | −15.0000 | −0.500556 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 3.00000 | + | 5.19615i | 0.0998337 | + | 0.172917i | ||||
\(904\) | −8.00000 | − | 13.8564i | −0.266076 | − | 0.460857i | ||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | −3.00000 | − | 5.19615i | −0.0996683 | − | 0.172631i | ||||
\(907\) | −21.0000 | + | 36.3731i | −0.697294 | + | 1.20775i | 0.272108 | + | 0.962267i | \(0.412279\pi\) |
−0.969401 | + | 0.245481i | \(0.921054\pi\) | |||||||
\(908\) | 10.0000 | − | 17.3205i | 0.331862 | − | 0.574801i | ||||
\(909\) | 4.00000 | 0.132672 | ||||||||
\(910\) | −7.50000 | + | 7.79423i | −0.248623 | + | 0.258376i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −2.50000 | + | 4.33013i | −0.0827833 | + | 0.143385i | ||||
\(913\) | −6.00000 | + | 10.3923i | −0.198571 | + | 0.343935i | ||||
\(914\) | −11.0000 | − | 19.0526i | −0.363848 | − | 0.630203i | ||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 5.00000 | + | 8.66025i | 0.165205 | + | 0.286143i | ||||
\(917\) | −22.5000 | − | 38.9711i | −0.743015 | − | 1.28694i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0000 | − | 29.4449i | −0.560778 | − | 0.971296i | −0.997429 | − | 0.0716652i | \(-0.977169\pi\) |
0.436650 | − | 0.899631i | \(-0.356165\pi\) | |||||||
\(920\) | 2.00000 | − | 3.46410i | 0.0659380 | − | 0.114208i | ||||
\(921\) | 9.00000 | − | 15.5885i | 0.296560 | − | 0.513657i | ||||
\(922\) | −12.0000 | −0.395199 | ||||||||
\(923\) | 7.00000 | + | 1.73205i | 0.230408 | + | 0.0570111i | ||||
\(924\) | 3.00000 | 0.0986928 | ||||||||
\(925\) | 0.500000 | − | 0.866025i | 0.0164399 | − | 0.0284747i | ||||
\(926\) | 8.00000 | − | 13.8564i | 0.262896 | − | 0.455350i | ||||
\(927\) | 4.50000 | + | 7.79423i | 0.147799 | + | 0.255996i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.0000 | − | 29.4449i | −0.557752 | − | 0.966055i | −0.997684 | − | 0.0680235i | \(-0.978331\pi\) |
0.439932 | − | 0.898031i | \(-0.355003\pi\) | |||||||
\(930\) | 5.00000 | + | 8.66025i | 0.163956 | + | 0.283981i | ||||
\(931\) | −10.0000 | −0.327737 | ||||||||
\(932\) | −5.00000 | − | 8.66025i | −0.163780 | − | 0.283676i | ||||
\(933\) | −6.00000 | + | 10.3923i | −0.196431 | + | 0.340229i | ||||
\(934\) | 18.0000 | − | 31.1769i | 0.588978 | − | 1.02014i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.50000 | − | 0.866025i | −0.114401 | − | 0.0283069i | ||||
\(937\) | −10.0000 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(938\) | −18.0000 | + | 31.1769i | −0.587721 | + | 1.01796i | ||||
\(939\) | −17.0000 | + | 29.4449i | −0.554774 | + | 0.960897i | ||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | 24.0000 | 0.782378 | 0.391189 | − | 0.920310i | \(-0.372064\pi\) | ||||
0.391189 | + | 0.920310i | \(0.372064\pi\) | |||||||
\(942\) | 0.500000 | + | 0.866025i | 0.0162909 | + | 0.0282166i | ||||
\(943\) | 12.0000 | + | 20.7846i | 0.390774 | + | 0.676840i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | −1.50000 | − | 2.59808i | −0.0487950 | − | 0.0845154i | ||||
\(946\) | 1.00000 | − | 1.73205i | 0.0325128 | − | 0.0563138i | ||||
\(947\) | 19.0000 | − | 32.9090i | 0.617417 | − | 1.06940i | −0.372538 | − | 0.928017i | \(-0.621512\pi\) |
0.989955 | − | 0.141381i | \(-0.0451542\pi\) | |||||||
\(948\) | 10.0000 | 0.324785 | ||||||||
\(949\) | −40.0000 | + | 41.5692i | −1.29845 | + | 1.34939i | ||||
\(950\) | −5.00000 | −0.162221 | ||||||||
\(951\) | 9.50000 | − | 16.4545i | 0.308059 | − | 0.533573i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.0000 | − | 19.0526i | −0.356325 | − | 0.617173i | 0.631019 | − | 0.775768i | \(-0.282637\pi\) |
−0.987344 | + | 0.158595i | \(0.949304\pi\) | |||||||
\(954\) | −13.0000 | −0.420891 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 1.00000 | + | 1.73205i | 0.0323423 | + | 0.0560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.00000 | + | 6.92820i | 0.129234 | + | 0.223840i | ||||
\(959\) | 24.0000 | − | 41.5692i | 0.775000 | − | 1.34234i | ||||
\(960\) | 0.500000 | − | 0.866025i | 0.0161374 | − | 0.0279508i | ||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 3.50000 | + | 0.866025i | 0.112845 | + | 0.0279218i | ||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −7.50000 | + | 12.9904i | −0.241559 | + | 0.418392i | ||||
\(965\) | −8.00000 | + | 13.8564i | −0.257529 | + | 0.446054i | ||||
\(966\) | 6.00000 | + | 10.3923i | 0.193047 | + | 0.334367i | ||||
\(967\) | 7.00000 | 0.225105 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(968\) | 5.00000 | + | 8.66025i | 0.160706 | + | 0.278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | −13.5000 | − | 23.3827i | −0.433236 | − | 0.750386i | 0.563914 | − | 0.825833i | \(-0.309295\pi\) |
−0.997150 | + | 0.0754473i | \(0.975962\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −13.5000 | + | 23.3827i | −0.432790 | + | 0.749614i | ||||
\(974\) | 35.0000 | 1.12147 | ||||||||
\(975\) | −1.00000 | − | 3.46410i | −0.0320256 | − | 0.110940i | ||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −24.0000 | + | 41.5692i | −0.767828 | + | 1.32992i | 0.170910 | + | 0.985287i | \(0.445329\pi\) |
−0.938738 | + | 0.344631i | \(0.888004\pi\) | |||||||
\(978\) | −10.0000 | + | 17.3205i | −0.319765 | + | 0.553849i | ||||
\(979\) | −0.500000 | − | 0.866025i | −0.0159801 | − | 0.0276783i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | 5.00000 | + | 8.66025i | 0.159638 | + | 0.276501i | ||||
\(982\) | −12.5000 | − | 21.6506i | −0.398891 | − | 0.690900i | ||||
\(983\) | 53.0000 | 1.69044 | 0.845219 | − | 0.534421i | \(-0.179470\pi\) | ||||
0.845219 | + | 0.534421i | \(0.179470\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | 7.50000 | − | 12.9904i | 0.238970 | − | 0.413908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.0000 | −0.859419 | ||||||||
\(988\) | −5.00000 | − | 17.3205i | −0.159071 | − | 0.551039i | ||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | −0.500000 | + | 0.866025i | −0.0158910 | + | 0.0275241i | ||||
\(991\) | −19.0000 | + | 32.9090i | −0.603555 | + | 1.04539i | 0.388723 | + | 0.921355i | \(0.372916\pi\) |
−0.992278 | + | 0.124033i | \(0.960417\pi\) | |||||||
\(992\) | −5.00000 | − | 8.66025i | −0.158750 | − | 0.274963i | ||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | −3.00000 | − | 5.19615i | −0.0951542 | − | 0.164812i | ||||
\(995\) | 1.00000 | + | 1.73205i | 0.0317021 | + | 0.0549097i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 3.50000 | + | 6.06218i | 0.110846 | + | 0.191991i | 0.916112 | − | 0.400923i | \(-0.131311\pi\) |
−0.805266 | + | 0.592914i | \(0.797977\pi\) | |||||||
\(998\) | −10.0000 | + | 17.3205i | −0.316544 | + | 0.548271i | ||||
\(999\) | −0.500000 | + | 0.866025i | −0.0158193 | + | 0.0273998i |
(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 | 390.2.i.b.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.i.j.451.1 | 2 | |||
5.2 | odd | 4 | 1950.2.z.i.1699.1 | 4 | |||
5.3 | odd | 4 | 1950.2.z.i.1699.2 | 4 | |||
5.4 | even | 2 | 1950.2.i.o.451.1 | 2 | |||
13.3 | even | 3 | inner | 390.2.i.b.211.1 | yes | 2 | |
13.4 | even | 6 | 5070.2.a.c.1.1 | 1 | |||
13.6 | odd | 12 | 5070.2.b.a.1351.1 | 2 | |||
13.7 | odd | 12 | 5070.2.b.a.1351.2 | 2 | |||
13.9 | even | 3 | 5070.2.a.q.1.1 | 1 | |||
39.29 | odd | 6 | 1170.2.i.j.991.1 | 2 | |||
65.3 | odd | 12 | 1950.2.z.i.1849.1 | 4 | |||
65.29 | even | 6 | 1950.2.i.o.601.1 | 2 | |||
65.42 | odd | 12 | 1950.2.z.i.1849.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.b.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
390.2.i.b.211.1 | yes | 2 | 13.3 | even | 3 | inner | |
1170.2.i.j.451.1 | 2 | 3.2 | odd | 2 | |||
1170.2.i.j.991.1 | 2 | 39.29 | odd | 6 | |||
1950.2.i.o.451.1 | 2 | 5.4 | even | 2 | |||
1950.2.i.o.601.1 | 2 | 65.29 | even | 6 | |||
1950.2.z.i.1699.1 | 4 | 5.2 | odd | 4 | |||
1950.2.z.i.1699.2 | 4 | 5.3 | odd | 4 | |||
1950.2.z.i.1849.1 | 4 | 65.3 | odd | 12 | |||
1950.2.z.i.1849.2 | 4 | 65.42 | odd | 12 | |||
5070.2.a.c.1.1 | 1 | 13.4 | even | 6 | |||
5070.2.a.q.1.1 | 1 | 13.9 | even | 3 | |||
5070.2.b.a.1351.1 | 2 | 13.6 | odd | 12 | |||
5070.2.b.a.1351.2 | 2 | 13.7 | odd | 12 |