Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(451,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(15.5708283941\) |
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: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 601.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.601 |
Dual form | 1950.2.i.o.451.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 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 | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −0.500000 | − | 0.866025i | −0.0821995 | − | 0.142374i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 5.00000 | 0.811107 | ||||||||
\(39\) | −1.00000 | + | 3.46410i | −0.160128 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | − | 5.19615i | −0.468521 | − | 0.811503i | 0.530831 | − | 0.847477i | \(-0.321880\pi\) |
−0.999353 | + | 0.0359748i | \(0.988546\pi\) | |||||||
\(42\) | 1.50000 | + | 2.59808i | 0.231455 | + | 0.400892i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | 9.00000 | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | − | 0.866025i | 0.485363 | − | 0.120096i | ||||
\(53\) | 13.0000 | 1.78569 | 0.892844 | − | 0.450367i | \(-0.148707\pi\) | ||||
0.892844 | + | 0.450367i | \(0.148707\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 5.00000 | + | 8.66025i | 0.635001 | + | 1.09985i | ||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | + | 3.46410i | −0.240772 | + | 0.417029i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | − | 1.73205i | 0.118678 | − | 0.205557i | −0.800566 | − | 0.599245i | \(-0.795468\pi\) |
0.919244 | + | 0.393688i | \(0.128801\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 16.0000 | 1.87266 | 0.936329 | − | 0.351123i | \(-0.114200\pi\) | ||||
0.936329 | + | 0.351123i | \(0.114200\pi\) | |||||||
\(74\) | 0.500000 | − | 0.866025i | 0.0581238 | − | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | 0 | ||||||||
\(81\) | −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 | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | −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 | 0.838308 | − | 0.545197i | \(-0.183545\pi\) |
−0.891308 | + | 0.453398i | \(0.850212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 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 | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.00000 | − | 10.3923i | 0.609208 | − | 1.05518i | −0.382164 | − | 0.924095i | \(-0.624821\pi\) |
0.991371 | − | 0.131084i | \(-0.0418458\pi\) | |||||||
\(98\) | 1.00000 | − | 1.73205i | 0.101015 | − | 0.174964i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | − | 3.46410i | −0.199007 | − | 0.344691i | 0.749199 | − | 0.662344i | \(-0.230438\pi\) |
−0.948207 | + | 0.317653i | \(0.897105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00000 | 0.886796 | 0.443398 | − | 0.896325i | \(-0.353773\pi\) | ||||
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(104\) | 2.50000 | + | 2.59808i | 0.245145 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.50000 | + | 11.2583i | 0.631336 | + | 1.09351i | ||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | −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 | 0 | ||||||||
\(111\) | −0.500000 | + | 0.866025i | −0.0474579 | + | 0.0821995i | ||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 8.00000 | − | 13.8564i | 0.752577 | − | 1.30350i | −0.193993 | − | 0.981003i | \(-0.562144\pi\) |
0.946570 | − | 0.322498i | \(-0.104523\pi\) | |||||||
\(114\) | −2.50000 | − | 4.33013i | −0.234146 | − | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.50000 | − | 0.866025i | 0.323575 | − | 0.0800641i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 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 | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.50000 | − | 2.59808i | 0.133631 | − | 0.231455i | ||||
\(127\) | 2.50000 | + | 4.33013i | 0.221839 | + | 0.384237i | 0.955366 | − | 0.295423i | \(-0.0954607\pi\) |
−0.733527 | + | 0.679660i | \(0.762127\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.00000 | − | 13.8564i | 0.683486 | − | 1.18383i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
0.973910 | − | 0.226935i | \(-0.0728704\pi\) | |||||||
\(138\) | −4.00000 | −0.340503 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −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 | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −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 | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | − | 2.59808i | −0.200160 | − | 0.208013i | ||||
\(157\) | −1.00000 | −0.0798087 | −0.0399043 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399043 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(158\) | −5.00000 | − | 8.66025i | −0.397779 | − | 0.688973i | ||||
\(159\) | −6.50000 | − | 11.2583i | −0.515484 | − | 0.892844i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | −6.50000 | − | 11.2583i | −0.502985 | − | 0.871196i | −0.999994 | − | 0.00345033i | \(-0.998902\pi\) |
0.497009 | − | 0.867745i | \(-0.334432\pi\) | |||||||
\(168\) | −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 | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | 0 | ||||||||
\(186\) | 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 | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −7.50000 | − | 12.9904i | −0.534353 | − | 0.925526i | −0.999194 | − | 0.0401324i | \(-0.987222\pi\) |
0.464841 | − | 0.885394i | \(-0.346111\pi\) | |||||||
\(198\) | 0.500000 | + | 0.866025i | 0.0355335 | + | 0.0615457i | ||||
\(199\) | 1.00000 | − | 1.73205i | 0.0708881 | − | 0.122782i | −0.828403 | − | 0.560133i | \(-0.810750\pi\) |
0.899291 | + | 0.437351i | \(0.144083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | 2.00000 | − | 3.46410i | 0.140720 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.50000 | + | 12.9904i | 0.516321 | + | 0.894295i | 0.999820 | + | 0.0189499i | \(0.00603229\pi\) |
−0.483499 | + | 0.875345i | \(0.660634\pi\) | |||||||
\(212\) | −6.50000 | + | 11.2583i | −0.446422 | + | 0.773225i | ||||
\(213\) | −2.00000 | −0.137038 | ||||||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −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 | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.00000 | −0.0671156 | ||||||||
\(223\) | 5.50000 | + | 9.52628i | 0.368307 | + | 0.637927i | 0.989301 | − | 0.145889i | \(-0.0466041\pi\) |
−0.620994 | + | 0.783815i | \(0.713271\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | −10.0000 | + | 17.3205i | −0.663723 | + | 1.14960i | 0.315906 | + | 0.948790i | \(0.397691\pi\) |
−0.979630 | + | 0.200812i | \(0.935642\pi\) | |||||||
\(228\) | 2.50000 | − | 4.33013i | 0.165567 | − | 0.286770i | ||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50000 | − | 2.59808i | −0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 2.50000 | + | 2.59808i | 0.163430 | + | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −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 | 0 | ||||||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | 10.0000 | 0.642824 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.00000 | + | 1.73205i | 0.0640184 | + | 0.110883i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −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 | 0 | ||||||||
\(251\) | −5.50000 | + | 9.52628i | −0.347157 | + | 0.601293i | −0.985743 | − | 0.168257i | \(-0.946186\pi\) |
0.638586 | + | 0.769550i | \(0.279520\pi\) | |||||||
\(252\) | 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 | −0.948523 | − | 0.316709i | \(-0.897422\pi\) |
0.199983 | − | 0.979799i | \(-0.435911\pi\) | |||||||
\(258\) | 1.00000 | + | 1.73205i | 0.0622573 | + | 0.107833i | ||||
\(259\) | 3.00000 | 0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.50000 | − | 12.9904i | −0.463352 | − | 0.802548i | ||||
\(263\) | 1.50000 | + | 2.59808i | 0.0924940 | + | 0.160204i | 0.908560 | − | 0.417755i | \(-0.137183\pi\) |
−0.816066 | + | 0.577959i | \(0.803849\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −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 | −0.381577 | − | 0.924337i | \(-0.624619\pi\) |
0.991288 | − | 0.131713i | \(-0.0420477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | + | 20.7846i | 0.728948 | + | 1.26258i | 0.957328 | + | 0.289003i | \(0.0933238\pi\) |
−0.228380 | + | 0.973572i | \(0.573343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.50000 | − | 7.79423i | −0.453921 | − | 0.471728i | ||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | 11.5000 | − | 19.9186i | 0.690968 | − | 1.19679i | −0.280553 | − | 0.959839i | \(-0.590518\pi\) |
0.971521 | − | 0.236953i | \(-0.0761488\pi\) | |||||||
\(278\) | 9.00000 | 0.539784 | ||||||||
\(279\) | −5.00000 | + | 8.66025i | −0.299342 | + | 0.518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.147734\pi\) |
−0.834772 | + | 0.550596i | \(0.814401\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −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 | \(-0.709349\pi\) |
0.991023 | + | 0.133689i | \(0.0426822\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −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 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0000 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671710\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671710\pi\) | |||||||
\(308\) | −1.50000 | + | 2.59808i | −0.0854704 | + | 0.148039i | ||||
\(309\) | −4.50000 | − | 7.79423i | −0.255996 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(-0.0893093\pi\) | ||||
0.960897 | + | 0.276907i | \(0.0893093\pi\) | |||||||
\(314\) | −0.500000 | − | 0.866025i | −0.0282166 | − | 0.0488726i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | − | 8.66025i | 0.281272 | − | 0.487177i | ||||
\(317\) | −19.0000 | −1.06715 | −0.533573 | − | 0.845754i | \(-0.679151\pi\) | ||||
−0.533573 | + | 0.845754i | \(0.679151\pi\) | |||||||
\(318\) | 6.50000 | − | 11.2583i | 0.364502 | − | 0.631336i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −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 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −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 | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | + | 24.2487i | −0.769510 | + | 1.33283i | 0.168320 | + | 0.985732i | \(0.446166\pi\) |
−0.937829 | + | 0.347097i | \(0.887167\pi\) | |||||||
\(332\) | 6.00000 | − | 10.3923i | 0.329293 | − | 0.570352i | ||||
\(333\) | 1.00000 | 0.0547997 | ||||||||
\(334\) | 6.50000 | − | 11.2583i | 0.355664 | − | 0.616028i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.50000 | − | 2.59808i | −0.0818317 | − | 0.141737i | ||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −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 | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | −0.483843 | ||||||||
\(347\) | −14.0000 | + | 24.2487i | −0.751559 | + | 1.30174i | 0.195507 | + | 0.980702i | \(0.437365\pi\) |
−0.947067 | + | 0.321037i | \(0.895969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | − | 31.1769i | −0.963518 | − | 1.66886i | −0.713545 | − | 0.700609i | \(-0.752912\pi\) |
−0.249973 | − | 0.968253i | \(-0.580422\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | − | 2.59808i | −0.133440 | − | 0.138675i | ||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −18.0000 | − | 31.1769i | −0.958043 | − | 1.65938i | −0.727245 | − | 0.686378i | \(-0.759200\pi\) |
−0.230799 | − | 0.973002i | \(-0.574134\pi\) | |||||||
\(354\) | 2.00000 | + | 3.46410i | 0.106299 | + | 0.184115i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | 0 | ||||||||
\(361\) | −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 | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −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 | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.00000 | −0.154303 | ||||||||
\(379\) | 0.500000 | + | 0.866025i | 0.0256833 | + | 0.0444847i | 0.878581 | − | 0.477593i | \(-0.158491\pi\) |
−0.852898 | + | 0.522077i | \(0.825157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.50000 | − | 4.33013i | 0.128079 | − | 0.221839i | ||||
\(382\) | 18.0000 | 0.920960 | ||||||||
\(383\) | −14.0000 | + | 24.2487i | −0.715367 | + | 1.23905i | 0.247451 | + | 0.968900i | \(0.420407\pi\) |
−0.962818 | + | 0.270151i | \(0.912926\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | \(0.632943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 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 | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | + | 0.866025i | −0.0251259 | + | 0.0435194i | ||||
\(397\) | −16.5000 | + | 28.5788i | −0.828111 | + | 1.43433i | 0.0714068 | + | 0.997447i | \(0.477251\pi\) |
−0.899518 | + | 0.436884i | \(0.856082\pi\) | |||||||
\(398\) | 2.00000 | 0.100251 | ||||||||
\(399\) | 7.50000 | − | 12.9904i | 0.375470 | − | 0.650332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5000 | − | 21.6506i | −0.624220 | − | 1.08118i | −0.988691 | − | 0.149966i | \(-0.952083\pi\) |
0.364471 | − | 0.931215i | \(-0.381250\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | −25.0000 | − | 25.9808i | −1.24534 | − | 1.29419i | ||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.500000 | + | 0.866025i | −0.0247841 | + | 0.0429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.50000 | + | 14.7224i | −0.420298 | + | 0.727977i | −0.995968 | − | 0.0897044i | \(-0.971408\pi\) |
0.575670 | + | 0.817682i | \(0.304741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −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 | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −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 | 0.973767 | + | 0.227547i | \(0.0730704\pi\) |
−0.289822 | + | 0.957080i | \(0.593596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | − | 31.1769i | −0.867029 | − | 1.50174i | −0.865018 | − | 0.501741i | \(-0.832693\pi\) |
−0.00201168 | − | 0.999998i | \(-0.500640\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 8.00000 | − | 13.8564i | 0.384455 | − | 0.665896i | −0.607238 | − | 0.794520i | \(-0.707723\pi\) |
0.991693 | + | 0.128624i | \(0.0410559\pi\) | |||||||
\(434\) | −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 | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0000 | 0.855206 | 0.427603 | − | 0.903967i | \(-0.359358\pi\) | ||||
0.427603 | + | 0.903967i | \(0.359358\pi\) | |||||||
\(444\) | −0.500000 | − | 0.866025i | −0.0237289 | − | 0.0410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −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 | −0.632990 | − | 0.774160i | \(-0.718173\pi\) |
0.986937 | + | 0.161106i | \(0.0515060\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.00000 | 0.234146 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | −5.00000 | − | 8.66025i | −0.233635 | − | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | − | 10.3923i | 0.279448 | − | 0.484018i | −0.691800 | − | 0.722089i | \(-0.743182\pi\) |
0.971248 | + | 0.238071i | \(0.0765153\pi\) | |||||||
\(462\) | 1.50000 | − | 2.59808i | 0.0697863 | − | 0.120873i | ||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.00000 | − | 8.66025i | −0.231621 | − | 0.401179i | ||||
\(467\) | 36.0000 | 1.66588 | 0.832941 | − | 0.553362i | \(-0.186655\pi\) | ||||
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(468\) | −1.00000 | + | 3.46410i | −0.0462250 | + | 0.160128i | ||||
\(469\) | 36.0000 | 1.66233 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 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 | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | 0.942821 | − | 0.333300i | \(-0.108162\pi\) |
−0.760056 | + | 0.649857i | \(0.774829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −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 | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 17.5000 | − | 30.3109i | 0.793001 | − | 1.37352i | −0.131100 | − | 0.991369i | \(-0.541851\pi\) |
0.924101 | − | 0.382148i | \(-0.124816\pi\) | |||||||
\(488\) | −1.00000 | + | 1.73205i | −0.0452679 | + | 0.0784063i | ||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5000 | − | 21.6506i | −0.564117 | − | 0.977079i | −0.997131 | − | 0.0756923i | \(-0.975883\pi\) |
0.433014 | − | 0.901387i | \(-0.357450\pi\) | |||||||
\(492\) | −3.00000 | − | 5.19615i | −0.135250 | − | 0.234261i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.5000 | − | 12.9904i | −0.562402 | − | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −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 | 0 | ||||||||
\(501\) | −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 | \(-0.840430\pi\) |
0.854663 | + | 0.519183i | \(0.173764\pi\) | |||||||
\(504\) | 1.50000 | + | 2.59808i | 0.0668153 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −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 | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 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 | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −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 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.124790\pi\) |
−0.792951 | + | 0.609285i | \(0.791456\pi\) | |||||||
\(524\) | 7.50000 | − | 12.9904i | 0.327639 | − | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −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 | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −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 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | 0 | ||||||||
\(541\) | −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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.00000 | − | 10.3923i | 0.128388 | − | 0.444750i | ||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 8.00000 | + | 13.8564i | 0.341743 | + | 0.591916i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 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 | 0 | ||||||||
\(556\) | 4.50000 | + | 7.79423i | 0.190843 | + | 0.330549i | ||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | −10.0000 | −0.423334 | ||||||||
\(559\) | 7.00000 | − | 1.73205i | 0.296068 | − | 0.0732579i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | + | 8.66025i | 0.210912 | + | 0.365311i | ||||
\(563\) | 12.0000 | − | 20.7846i | 0.505740 | − | 0.875967i | −0.494238 | − | 0.869326i | \(-0.664553\pi\) |
0.999978 | − | 0.00664037i | \(-0.00211371\pi\) | |||||||
\(564\) | 9.00000 | 0.378968 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −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 | 0.957977 | − | 0.286846i | \(-0.0926069\pi\) |
−0.727405 | + | 0.686209i | \(0.759274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | −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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0000 | 0.537025 | ||||||||
\(587\) | −9.00000 | − | 15.5885i | −0.371470 | − | 0.643404i | 0.618322 | − | 0.785925i | \(-0.287813\pi\) |
−0.989792 | + | 0.142520i | \(0.954479\pi\) | |||||||
\(588\) | −1.00000 | − | 1.73205i | −0.0412393 | − | 0.0714286i | ||||
\(589\) | 25.0000 | − | 43.3013i | 1.03011 | − | 1.78420i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −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 | \(-0.694963\pi\) | ||||
−0.574911 | + | 0.818216i | \(0.694963\pi\) | |||||||
\(594\) | 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 | 0 | ||||||||
\(601\) | 13.5000 | + | 23.3827i | 0.550676 | + | 0.953800i | 0.998226 | + | 0.0595404i | \(0.0189635\pi\) |
−0.447549 | + | 0.894259i | \(0.647703\pi\) | |||||||
\(602\) | 3.00000 | − | 5.19615i | 0.122271 | − | 0.211779i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 3.00000 | − | 5.19615i | 0.122068 | − | 0.211428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.00000 | −0.162489 | ||||||||
\(607\) | 18.5000 | − | 32.0429i | 0.750892 | − | 1.30058i | −0.196499 | − | 0.980504i | \(-0.562957\pi\) |
0.947391 | − | 0.320079i | \(-0.103709\pi\) | |||||||
\(608\) | −2.50000 | − | 4.33013i | −0.101388 | − | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5000 | − | 23.3827i | −0.910253 | − | 0.945962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5000 | + | 19.9186i | 0.464481 | + | 0.804504i | 0.999178 | − | 0.0405396i | \(-0.0129077\pi\) |
−0.534697 | + | 0.845044i | \(0.679574\pi\) | |||||||
\(614\) | −9.00000 | − | 15.5885i | −0.363210 | − | 0.629099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | −3.00000 | + | 5.19615i | −0.120775 | + | 0.209189i | −0.920074 | − | 0.391745i | \(-0.871871\pi\) |
0.799298 | + | 0.600935i | \(0.205205\pi\) | |||||||
\(618\) | 4.50000 | − | 7.79423i | 0.181017 | − | 0.313530i | ||||
\(619\) | −31.0000 | −1.24600 | −0.622998 | − | 0.782224i | \(-0.714085\pi\) | ||||
−0.622998 | + | 0.782224i | \(0.714085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −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 | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | − | 3.46410i | 0.0796187 | − | 0.137904i | −0.823467 | − | 0.567365i | \(-0.807963\pi\) |
0.903085 | + | 0.429461i | \(0.141296\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | 7.50000 | − | 12.9904i | 0.298098 | − | 0.516321i | ||||
\(634\) | −9.50000 | − | 16.4545i | −0.377293 | − | 0.653491i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | 0 | ||||||||
\(641\) | 4.50000 | − | 7.79423i | 0.177739 | − | 0.307854i | −0.763367 | − | 0.645966i | \(-0.776455\pi\) |
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(642\) | −6.00000 | −0.236801 | ||||||||
\(643\) | −22.0000 | + | 38.1051i | −0.867595 | + | 1.50272i | −0.00314839 | + | 0.999995i | \(0.501002\pi\) |
−0.864447 | + | 0.502724i | \(0.832331\pi\) | |||||||
\(644\) | −6.00000 | + | 10.3923i | −0.236433 | + | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.0000 | 1.17579 | ||||||||
\(652\) | −10.0000 | − | 17.3205i | −0.391630 | − | 0.678323i | ||||
\(653\) | 20.5000 | + | 35.5070i | 0.802227 | + | 1.38950i | 0.918147 | + | 0.396239i | \(0.129685\pi\) |
−0.115920 | + | 0.993259i | \(0.536982\pi\) | |||||||
\(654\) | −5.00000 | + | 8.66025i | −0.195515 | + | 0.338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −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 | −0.902348 | − | 0.431009i | \(-0.858158\pi\) |
0.824439 | + | 0.565951i | \(0.191491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | −28.0000 | −1.08825 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 1.50000 | − | 2.59808i | 0.0578638 | − | 0.100223i | ||||
\(673\) | −16.0000 | − | 27.7128i | −0.616755 | − | 1.06825i | −0.990074 | − | 0.140548i | \(-0.955114\pi\) |
0.373319 | − | 0.927703i | \(-0.378220\pi\) | |||||||
\(674\) | −1.00000 | − | 1.73205i | −0.0385186 | − | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 26.0000 | 0.999261 | 0.499631 | − | 0.866239i | \(-0.333469\pi\) | ||||
0.499631 | + | 0.866239i | \(0.333469\pi\) | |||||||
\(678\) | −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 | \(-0.999057\pi\) |
0.502564 | + | 0.864540i | \(0.332390\pi\) | |||||||
\(684\) | −5.00000 | −0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −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 | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5000 | − | 28.5788i | −0.627690 | − | 1.08719i | −0.988014 | − | 0.154363i | \(-0.950667\pi\) |
0.360325 | − | 0.932827i | \(-0.382666\pi\) | |||||||
\(692\) | −4.50000 | − | 7.79423i | −0.171064 | − | 0.296292i | ||||
\(693\) | −1.50000 | + | 2.59808i | −0.0569803 | + | 0.0986928i | ||||
\(694\) | −28.0000 | −1.06287 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 18.0000 | − | 31.1769i | 0.681310 | − | 1.18006i | ||||
\(699\) | 5.00000 | + | 8.66025i | 0.189117 | + | 0.327561i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 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 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | 0.306253 | + | 0.951950i | \(0.400925\pi\) |
−0.977539 | + | 0.210752i | \(0.932409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −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 | \(-0.259309\pi\) | ||||
0.686127 | + | 0.727482i | \(0.259309\pi\) | |||||||
\(728\) | −10.5000 | + | 2.59808i | −0.389156 | + | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.00000 | − | 1.73205i | 0.0369611 | − | 0.0640184i | ||||
\(733\) | 5.00000 | 0.184679 | 0.0923396 | − | 0.995728i | \(-0.470565\pi\) | ||||
0.0923396 | + | 0.995728i | \(0.470565\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | −0.984589 | − | 0.174883i | \(-0.944045\pi\) |
0.340841 | − | 0.940121i | \(-0.389288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 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 | \(-0.0215610\pi\) |
−0.557470 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(744\) | 5.00000 | + | 8.66025i | 0.183309 | + | 0.317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | 0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0000 | − | 38.1051i | −0.802791 | − | 1.39048i | −0.917772 | − | 0.397108i | \(-0.870014\pi\) |
0.114981 | − | 0.993368i | \(-0.463319\pi\) | |||||||
\(752\) | −4.50000 | − | 7.79423i | −0.164098 | − | 0.284226i | ||||
\(753\) | 11.0000 | 0.400862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.50000 | − | 2.59808i | −0.0545545 | − | 0.0944911i | ||||
\(757\) | 19.5000 | + | 33.7750i | 0.708740 | + | 1.22757i | 0.965325 | + | 0.261051i | \(0.0840692\pi\) |
−0.256585 | + | 0.966522i | \(0.582597\pi\) | |||||||
\(758\) | −0.500000 | + | 0.866025i | −0.0181608 | + | 0.0314555i | ||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5000 | + | 38.9711i | −0.815624 | + | 1.41270i | 0.0932544 | + | 0.995642i | \(0.470273\pi\) |
−0.908879 | + | 0.417061i | \(0.863060\pi\) | |||||||
\(762\) | 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 | 0.999364 | − | 0.0356685i | \(-0.0113561\pi\) |
−0.530572 | + | 0.847640i | \(0.678023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | + | 20.7846i | −0.432169 | + | 0.748539i | ||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | −18.5000 | + | 32.0429i | −0.665399 | + | 1.15250i | 0.313778 | + | 0.949496i | \(0.398405\pi\) |
−0.979177 | + | 0.203008i | \(0.934928\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −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 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | −0.0715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.50000 | + | 12.9904i | −0.267516 | + | 0.463352i | ||||
\(787\) | 8.00000 | − | 13.8564i | 0.285169 | − | 0.493928i | −0.687481 | − | 0.726202i | \(-0.741284\pi\) |
0.972650 | + | 0.232275i | \(0.0746169\pi\) | |||||||
\(788\) | 15.0000 | 0.534353 | ||||||||
\(789\) | 1.50000 | − | 2.59808i | 0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00000 | + | 1.73205i | 0.0354441 | + | 0.0613909i | ||||
\(797\) | −7.00000 | + | 12.1244i | −0.247953 | + | 0.429467i | −0.962958 | − | 0.269653i | \(-0.913091\pi\) |
0.715005 | + | 0.699119i | \(0.246424\pi\) | |||||||
\(798\) | 15.0000 | 0.530994 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 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 | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | 0.979739 | − | 0.200279i | \(-0.0641847\pi\) |
−0.663316 | + | 0.748340i | \(0.730851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 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 | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | −8.00000 | − | 13.8564i | −0.279032 | − | 0.483298i | ||||
\(823\) | −2.50000 | + | 4.33013i | −0.0871445 | + | 0.150939i | −0.906303 | − | 0.422628i | \(-0.861108\pi\) |
0.819159 | + | 0.573567i | \(0.194441\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | − | 10.3923i | 0.208767 | − | 0.361595i | ||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | −2.00000 | + | 3.46410i | −0.0695048 | + | 0.120386i | ||||
\(829\) | 22.0000 | + | 38.1051i | 0.764092 | + | 1.32345i | 0.940726 | + | 0.339169i | \(0.110146\pi\) |
−0.176634 | + | 0.984277i | \(0.556521\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −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 | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | 0.152493 | − | 0.988304i | \(-0.451270\pi\) |
0.779650 | − | 0.626215i | \(-0.215397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 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 | 0 | ||||||||
\(846\) | −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 | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | −3.00000 | + | 5.19615i | −0.102658 | + | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 2.50000 | + | 2.59808i | 0.0853486 | + | 0.0886969i | ||||
\(859\) | 19.0000 | 0.648272 | 0.324136 | − | 0.946011i | \(-0.394927\pi\) | ||||
0.324136 | + | 0.946011i | \(0.394927\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −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 | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576681i | \(0.195652\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | 19.0000 | − | 32.9090i | 0.641584 | − | 1.11126i | −0.343495 | − | 0.939155i | \(-0.611611\pi\) |
0.985079 | − | 0.172102i | \(-0.0550559\pi\) | |||||||
\(878\) | −5.00000 | + | 8.66025i | −0.168742 | + | 0.292269i | ||||
\(879\) | −13.0000 | −0.438479 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.50000 | − | 4.33013i | −0.0842271 | − | 0.145886i | 0.820834 | − | 0.571166i | \(-0.193509\pi\) |
−0.905062 | + | 0.425280i | \(0.860175\pi\) | |||||||
\(882\) | 1.00000 | + | 1.73205i | 0.0336718 | + | 0.0583212i | ||||
\(883\) | −42.0000 | −1.41341 | −0.706706 | − | 0.707507i | \(-0.749820\pi\) | ||||
−0.706706 | + | 0.707507i | \(0.749820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | + | 15.5885i | 0.302361 | + | 0.523704i | ||||
\(887\) | −6.50000 | − | 11.2583i | −0.218249 | − | 0.378018i | 0.736024 | − | 0.676955i | \(-0.236701\pi\) |
−0.954273 | + | 0.298938i | \(0.903368\pi\) | |||||||
\(888\) | 0.500000 | − | 0.866025i | 0.0167789 | − | 0.0290619i | ||||
\(889\) | −15.0000 | −0.503084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −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 | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 14.0000 | − | 3.46410i | 0.467446 | − | 0.115663i | ||||
\(898\) | 15.0000 | 0.500556 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 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 | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.00000 | + | 5.19615i | −0.0996683 | + | 0.172631i | ||||
\(907\) | 21.0000 | + | 36.3731i | 0.697294 | + | 1.20775i | 0.969401 | + | 0.245481i | \(0.0789459\pi\) |
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(908\) | −10.0000 | − | 17.3205i | −0.331862 | − | 0.574801i | ||||
\(909\) | 4.00000 | 0.132672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | 0.436650 | + | 0.899631i | \(0.356165\pi\) |
−0.997429 | + | 0.0716652i | \(0.977169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 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 | 0 | ||||||||
\(926\) | 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 | 0.439932 | + | 0.898031i | \(0.355003\pi\) |
−0.997684 | + | 0.0680235i | \(0.978331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −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 | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 18.0000 | + | 31.1769i | 0.587721 | + | 1.01796i | ||||
\(939\) | −17.0000 | − | 29.4449i | −0.554774 | − | 0.960897i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | + | 1.73205i | 0.0325128 | + | 0.0563138i | ||||
\(947\) | −19.0000 | − | 32.9090i | −0.617417 | − | 1.06940i | −0.989955 | − | 0.141381i | \(-0.954846\pi\) |
0.372538 | − | 0.928017i | \(-0.378488\pi\) | |||||||
\(948\) | −10.0000 | −0.324785 | ||||||||
\(949\) | −40.0000 | − | 41.5692i | −1.29845 | − | 1.34939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.50000 | + | 16.4545i | 0.308059 | + | 0.533573i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0000 | − | 19.0526i | 0.356325 | − | 0.617173i | −0.631019 | − | 0.775768i | \(-0.717363\pi\) |
0.987344 | + | 0.158595i | \(0.0506963\pi\) | |||||||
\(954\) | −13.0000 | −0.420891 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | 0 | ||||||||
\(961\) | 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 | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.00000 | − | 10.3923i | 0.193047 | − | 0.334367i | ||||
\(967\) | −7.00000 | −0.225105 | −0.112552 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112552 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(968\) | −5.00000 | + | 8.66025i | −0.160706 | + | 0.278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.5000 | + | 23.3827i | −0.433236 | + | 0.750386i | −0.997150 | − | 0.0754473i | \(-0.975962\pi\) |
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 13.5000 | + | 23.3827i | 0.432790 | + | 0.749614i | ||||
\(974\) | 35.0000 | 1.12147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 24.0000 | + | 41.5692i | 0.767828 | + | 1.32992i | 0.938738 | + | 0.344631i | \(0.111996\pi\) |
−0.170910 | + | 0.985287i | \(0.554671\pi\) | |||||||
\(978\) | 10.0000 | + | 17.3205i | 0.319765 | + | 0.553849i | ||||
\(979\) | −0.500000 | + | 0.866025i | −0.0159801 | + | 0.0276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 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 | \(-0.820530\pi\) | ||||
−0.845219 | + | 0.534421i | \(0.820530\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.0000 | 0.859419 | ||||||||
\(988\) | 5.00000 | − | 17.3205i | 0.159071 | − | 0.551039i | ||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0000 | − | 32.9090i | −0.603555 | − | 1.04539i | −0.992278 | − | 0.124033i | \(-0.960417\pi\) |
0.388723 | − | 0.921355i | \(-0.372916\pi\) | |||||||
\(992\) | 5.00000 | − | 8.66025i | 0.158750 | − | 0.274963i | ||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | −3.50000 | + | 6.06218i | −0.110846 | + | 0.191991i | −0.916112 | − | 0.400923i | \(-0.868689\pi\) |
0.805266 | + | 0.592914i | \(0.202023\pi\) | |||||||
\(998\) | 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 | 1950.2.i.o.601.1 | 2 | ||
5.2 | odd | 4 | 1950.2.z.i.1849.1 | 4 | |||
5.3 | odd | 4 | 1950.2.z.i.1849.2 | 4 | |||
5.4 | even | 2 | 390.2.i.b.211.1 | yes | 2 | ||
13.9 | even | 3 | inner | 1950.2.i.o.451.1 | 2 | ||
15.14 | odd | 2 | 1170.2.i.j.991.1 | 2 | |||
65.9 | even | 6 | 390.2.i.b.61.1 | ✓ | 2 | ||
65.22 | odd | 12 | 1950.2.z.i.1699.2 | 4 | |||
65.24 | odd | 12 | 5070.2.b.a.1351.2 | 2 | |||
65.29 | even | 6 | 5070.2.a.q.1.1 | 1 | |||
65.48 | odd | 12 | 1950.2.z.i.1699.1 | 4 | |||
65.49 | even | 6 | 5070.2.a.c.1.1 | 1 | |||
65.54 | odd | 12 | 5070.2.b.a.1351.1 | 2 | |||
195.74 | odd | 6 | 1170.2.i.j.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.b.61.1 | ✓ | 2 | 65.9 | even | 6 | ||
390.2.i.b.211.1 | yes | 2 | 5.4 | even | 2 | ||
1170.2.i.j.451.1 | 2 | 195.74 | odd | 6 | |||
1170.2.i.j.991.1 | 2 | 15.14 | odd | 2 | |||
1950.2.i.o.451.1 | 2 | 13.9 | even | 3 | inner | ||
1950.2.i.o.601.1 | 2 | 1.1 | even | 1 | trivial | ||
1950.2.z.i.1699.1 | 4 | 65.48 | odd | 12 | |||
1950.2.z.i.1699.2 | 4 | 65.22 | odd | 12 | |||
1950.2.z.i.1849.1 | 4 | 5.2 | odd | 4 | |||
1950.2.z.i.1849.2 | 4 | 5.3 | odd | 4 | |||
5070.2.a.c.1.1 | 1 | 65.49 | even | 6 | |||
5070.2.a.q.1.1 | 1 | 65.29 | even | 6 | |||
5070.2.b.a.1351.1 | 2 | 65.54 | odd | 12 | |||
5070.2.b.a.1351.2 | 2 | 65.24 | odd | 12 |