Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
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.z (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1849.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1849 |
Dual form | 1950.2.z.i.1699.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 2.59808 | + | 1.50000i | 0.981981 | + | 0.566947i | 0.902867 | − | 0.429919i | \(-0.141458\pi\) |
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 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 | \(0.881504\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 2.59808 | − | 2.50000i | 0.720577 | − | 0.693375i | ||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | 0.654654 | ||||||||
\(22\) | −0.866025 | − | 0.500000i | −0.184637 | − | 0.106600i | ||||
\(23\) | 3.46410 | − | 2.00000i | 0.722315 | − | 0.417029i | −0.0932891 | − | 0.995639i | \(-0.529738\pi\) |
0.815604 | + | 0.578610i | \(0.196405\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | − | 3.46410i | 0.196116 | − | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.59808 | − | 1.50000i | 0.490990 | − | 0.283473i | ||||
\(29\) | 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 | \(0.145001\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −0.866025 | − | 0.500000i | −0.150756 | − | 0.0870388i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −0.866025 | + | 0.500000i | −0.142374 | + | 0.0821995i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) |
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(38\) | 5.00000i | 0.811107i | ||||||||
\(39\) | 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 | \(0.988546\pi\) | |||||||
\(42\) | 2.59808 | − | 1.50000i | 0.400892 | − | 0.231455i | ||||
\(43\) | −1.73205 | − | 1.00000i | −0.264135 | − | 0.152499i | 0.362084 | − | 0.932145i | \(-0.382065\pi\) |
−0.626219 | + | 0.779647i | \(0.715399\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | − | 9.00000i | − | 1.31278i | −0.754420 | − | 0.656392i | \(-0.772082\pi\) | ||
0.754420 | − | 0.656392i | \(-0.227918\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.866025 | − | 3.50000i | −0.120096 | − | 0.485363i | ||||
\(53\) | 13.0000i | 1.78569i | 0.450367 | + | 0.892844i | \(0.351293\pi\) | ||||
−0.450367 | + | 0.892844i | \(0.648707\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | 5.00000i | 0.662266i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 8.66025 | − | 5.00000i | 1.09985 | − | 0.635001i | ||||
\(63\) | 2.59808 | − | 1.50000i | 0.327327 | − | 0.188982i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | 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 | \(0.128801\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 16.0000i | 1.87266i | 0.351123 | + | 0.936329i | \(0.385800\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −0.500000 | + | 0.866025i | −0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.50000 | + | 4.33013i | 0.286770 | + | 0.496700i | ||||
\(77\) | − | 3.00000i | − | 0.341882i | ||||||
\(78\) | −0.866025 | − | 3.50000i | −0.0980581 | − | 0.396297i | ||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.19615 | − | 3.00000i | −0.573819 | − | 0.331295i | ||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 1.50000 | − | 2.59808i | 0.163663 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.866025 | + | 0.500000i | −0.0923186 | + | 0.0533002i | ||||
\(89\) | 0.500000 | + | 0.866025i | 0.0529999 | + | 0.0917985i | 0.891308 | − | 0.453398i | \(-0.149788\pi\) |
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5000 | − | 2.59808i | 1.10070 | − | 0.272352i | ||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | 8.66025 | − | 5.00000i | 0.898027 | − | 0.518476i | ||||
\(94\) | −4.50000 | − | 7.79423i | −0.464140 | − | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.3923 | − | 6.00000i | −1.05518 | − | 0.609208i | −0.131084 | − | 0.991371i | \(-0.541846\pi\) |
−0.924095 | + | 0.382164i | \(0.875179\pi\) | |||||||
\(98\) | 1.73205 | + | 1.00000i | 0.174964 | + | 0.101015i | ||||
\(99\) | −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 | ||||||||
\(103\) | 9.00000i | 0.886796i | 0.896325 | + | 0.443398i | \(0.146227\pi\) | ||||
−0.896325 | + | 0.443398i | \(0.853773\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.50000 | + | 11.2583i | 0.631336 | + | 1.09351i | ||||
\(107\) | −5.19615 | + | 3.00000i | −0.502331 | + | 0.290021i | −0.729676 | − | 0.683793i | \(-0.760329\pi\) |
0.227345 | + | 0.973814i | \(0.426996\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.500000 | + | 0.866025i | −0.0474579 | + | 0.0821995i | ||||
\(112\) | − | 3.00000i | − | 0.283473i | ||||||
\(113\) | 13.8564 | + | 8.00000i | 1.30350 | + | 0.752577i | 0.981003 | − | 0.193993i | \(-0.0621440\pi\) |
0.322498 | + | 0.946570i | \(0.395477\pi\) | |||||||
\(114\) | 2.50000 | + | 4.33013i | 0.234146 | + | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.866025 | − | 3.50000i | −0.0800641 | − | 0.323575i | ||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | −5.19615 | − | 3.00000i | −0.468521 | − | 0.270501i | ||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.50000 | − | 2.59808i | 0.133631 | − | 0.231455i | ||||
\(127\) | 4.33013 | − | 2.50000i | 0.384237 | − | 0.221839i | −0.295423 | − | 0.955366i | \(-0.595461\pi\) |
0.679660 | + | 0.733527i | \(0.262127\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | −0.866025 | + | 0.500000i | −0.0753778 | + | 0.0435194i | ||||
\(133\) | −12.9904 | + | 7.50000i | −1.12641 | + | 0.650332i | ||||
\(134\) | −6.00000 | + | 10.3923i | −0.518321 | + | 0.897758i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.8564 | − | 8.00000i | −1.18383 | − | 0.683486i | −0.226935 | − | 0.973910i | \(-0.572870\pi\) |
−0.956898 | + | 0.290424i | \(0.906204\pi\) | |||||||
\(138\) | − | 4.00000i | − | 0.340503i | ||||||
\(139\) | −4.50000 | + | 7.79423i | −0.381685 | + | 0.661098i | −0.991303 | − | 0.131597i | \(-0.957989\pi\) |
0.609618 | + | 0.792695i | \(0.291323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | − | 7.79423i | −0.378968 | − | 0.656392i | ||||
\(142\) | − | 2.00000i | − | 0.167836i | ||||||
\(143\) | −3.46410 | − | 1.00000i | −0.289683 | − | 0.0836242i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00000 | + | 13.8564i | 0.662085 | + | 1.14676i | ||||
\(147\) | 1.73205 | + | 1.00000i | 0.142857 | + | 0.0824786i | ||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | −0.488273 | −0.244137 | − | 0.969741i | \(-0.578505\pi\) | ||||
−0.244137 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(152\) | 4.33013 | + | 2.50000i | 0.351220 | + | 0.202777i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | − | 2.59808i | −0.200160 | − | 0.208013i | ||||
\(157\) | 1.00000i | 0.0798087i | 0.999204 | + | 0.0399043i | \(0.0127053\pi\) | ||||
−0.999204 | + | 0.0399043i | \(0.987295\pi\) | |||||||
\(158\) | 8.66025 | − | 5.00000i | 0.688973 | − | 0.397779i | ||||
\(159\) | 6.50000 | + | 11.2583i | 0.515484 | + | 0.892844i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −17.3205 | − | 10.0000i | −1.35665 | − | 0.783260i | −0.367477 | − | 0.930033i | \(-0.619778\pi\) |
−0.989170 | + | 0.146772i | \(0.953112\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | −11.2583 | + | 6.50000i | −0.871196 | + | 0.502985i | −0.867745 | − | 0.497009i | \(-0.834432\pi\) |
−0.00345033 | + | 0.999994i | \(0.501098\pi\) | |||||||
\(168\) | − | 3.00000i | − | 0.231455i | ||||||
\(169\) | 0.500000 | − | 12.9904i | 0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.50000 | + | 4.33013i | 0.191180 | + | 0.331133i | ||||
\(172\) | −1.73205 | + | 1.00000i | −0.132068 | + | 0.0762493i | ||||
\(173\) | −7.79423 | − | 4.50000i | −0.592584 | − | 0.342129i | 0.173534 | − | 0.984828i | \(-0.444481\pi\) |
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | − | 4.00000i | − | 0.300658i | ||||||
\(178\) | 0.866025 | + | 0.500000i | 0.0649113 | + | 0.0374766i | ||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 7.79423 | − | 7.50000i | 0.577747 | − | 0.555937i | ||||
\(183\) | − | 2.00000i | − | 0.147844i | ||||||
\(184\) | −2.00000 | − | 3.46410i | −0.147442 | − | 0.255377i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.00000 | − | 8.66025i | 0.366618 | − | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.79423 | − | 4.50000i | −0.568453 | − | 0.328196i | ||||
\(189\) | 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 | \(-0.0590746\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −13.8564 | + | 8.00000i | −0.997406 | + | 0.575853i | −0.907480 | − | 0.420096i | \(-0.861996\pi\) |
−0.0899262 | + | 0.995948i | \(0.528663\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −12.9904 | + | 7.50000i | −0.925526 | + | 0.534353i | −0.885394 | − | 0.464841i | \(-0.846111\pi\) |
−0.0401324 | + | 0.999194i | \(0.512778\pi\) | |||||||
\(198\) | −0.866025 | + | 0.500000i | −0.0615457 | + | 0.0355335i | ||||
\(199\) | −1.00000 | + | 1.73205i | −0.0708881 | + | 0.122782i | −0.899291 | − | 0.437351i | \(-0.855917\pi\) |
0.828403 | + | 0.560133i | \(0.189250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | −3.46410 | − | 2.00000i | −0.243733 | − | 0.140720i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.50000 | + | 7.79423i | 0.313530 | + | 0.543050i | ||||
\(207\) | − | 4.00000i | − | 0.278019i | ||||||
\(208\) | −3.46410 | − | 1.00000i | −0.240192 | − | 0.0693375i | ||||
\(209\) | 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 | \(0.660634\pi\) | |||||||
\(212\) | 11.2583 | + | 6.50000i | 0.773225 | + | 0.446422i | ||||
\(213\) | − | 2.00000i | − | 0.137038i | ||||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 25.9808 | + | 15.0000i | 1.76369 | + | 1.01827i | ||||
\(218\) | 8.66025 | − | 5.00000i | 0.586546 | − | 0.338643i | ||||
\(219\) | 8.00000 | + | 13.8564i | 0.540590 | + | 0.936329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.00000i | 0.0671156i | ||||||||
\(223\) | −9.52628 | + | 5.50000i | −0.637927 | + | 0.368307i | −0.783815 | − | 0.620994i | \(-0.786729\pi\) |
0.145889 | + | 0.989301i | \(0.453396\pi\) | |||||||
\(224\) | −1.50000 | − | 2.59808i | −0.100223 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | 17.3205 | + | 10.0000i | 1.14960 | + | 0.663723i | 0.948790 | − | 0.315906i | \(-0.102309\pi\) |
0.200812 | + | 0.979630i | \(0.435642\pi\) | |||||||
\(228\) | 4.33013 | + | 2.50000i | 0.286770 | + | 0.165567i | ||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50000 | − | 2.59808i | −0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | −2.50000 | − | 2.59808i | −0.163430 | − | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 8.66025 | − | 5.00000i | 0.562544 | − | 0.324785i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | − | 10.0000i | − | 0.642824i | ||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −1.00000 | − | 1.73205i | −0.0640184 | − | 0.110883i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 4.33013 | + | 17.5000i | 0.275519 | + | 1.11350i | ||||
\(248\) | − | 10.0000i | − | 0.635001i | ||||||
\(249\) | −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 | \(0.279520\pi\) | |||||||
\(252\) | − | 3.00000i | − | 0.188982i | ||||||
\(253\) | −3.46410 | − | 2.00000i | −0.217786 | − | 0.125739i | ||||
\(254\) | 2.50000 | − | 4.33013i | 0.156864 | − | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −20.7846 | + | 12.0000i | −1.29651 | + | 0.748539i | −0.979799 | − | 0.199983i | \(-0.935911\pi\) |
−0.316709 | + | 0.948523i | \(0.602578\pi\) | |||||||
\(258\) | −1.73205 | + | 1.00000i | −0.107833 | + | 0.0622573i | ||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.9904 | + | 7.50000i | −0.802548 | + | 0.463352i | ||||
\(263\) | −2.59808 | + | 1.50000i | −0.160204 | + | 0.0924940i | −0.577959 | − | 0.816066i | \(-0.696151\pi\) |
0.417755 | + | 0.908560i | \(0.362817\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.50000 | + | 12.9904i | −0.459855 | + | 0.796491i | ||||
\(267\) | 0.866025 | + | 0.500000i | 0.0529999 | + | 0.0305995i | ||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | −10.0000 | + | 17.3205i | −0.609711 | + | 1.05605i | 0.381577 | + | 0.924337i | \(0.375381\pi\) |
−0.991288 | + | 0.131713i | \(0.957952\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 7.79423 | − | 7.50000i | 0.471728 | − | 0.453921i | ||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | −19.9186 | − | 11.5000i | −1.19679 | − | 0.690968i | −0.236953 | − | 0.971521i | \(-0.576149\pi\) |
−0.959839 | + | 0.280553i | \(0.909482\pi\) | |||||||
\(278\) | 9.00000i | 0.539784i | ||||||||
\(279\) | 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 | \(0.403589\pi\) | |||||||
\(282\) | −7.79423 | − | 4.50000i | −0.464140 | − | 0.267971i | ||||
\(283\) | −1.73205 | + | 1.00000i | −0.102960 | + | 0.0594438i | −0.550596 | − | 0.834772i | \(-0.685599\pi\) |
0.447636 | + | 0.894216i | \(0.352266\pi\) | |||||||
\(284\) | −1.00000 | − | 1.73205i | −0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.50000 | + | 0.866025i | −0.206959 | + | 0.0512092i | ||||
\(287\) | − | 18.0000i | − | 1.06251i | ||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −8.50000 | − | 14.7224i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 13.8564 | + | 8.00000i | 0.810885 | + | 0.468165i | ||||
\(293\) | 11.2583 | + | 6.50000i | 0.657719 | + | 0.379734i | 0.791407 | − | 0.611289i | \(-0.209349\pi\) |
−0.133689 | + | 0.991023i | \(0.542682\pi\) | |||||||
\(294\) | 2.00000 | 0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.500000 | + | 0.866025i | 0.0290619 | + | 0.0503367i | ||||
\(297\) | −0.866025 | + | 0.500000i | −0.0502519 | + | 0.0290129i | ||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 4.00000 | − | 13.8564i | 0.231326 | − | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | − | 5.19615i | −0.172917 | − | 0.299501i | ||||
\(302\) | −5.19615 | + | 3.00000i | −0.299005 | + | 0.172631i | ||||
\(303\) | −3.46410 | − | 2.00000i | −0.199007 | − | 0.114897i | ||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000i | 1.02731i | 0.857996 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(308\) | −2.59808 | − | 1.50000i | −0.148039 | − | 0.0854704i | ||||
\(309\) | 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 | \(0.610505\pi\) | |||||||
\(312\) | −3.46410 | − | 1.00000i | −0.196116 | − | 0.0566139i | ||||
\(313\) | 34.0000i | 1.92179i | 0.276907 | + | 0.960897i | \(0.410691\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | 0.500000 | + | 0.866025i | 0.0282166 | + | 0.0488726i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | − | 8.66025i | 0.281272 | − | 0.487177i | ||||
\(317\) | 19.0000i | 1.06715i | 0.845754 | + | 0.533573i | \(0.179151\pi\) | ||||
−0.845754 | + | 0.533573i | \(0.820849\pi\) | |||||||
\(318\) | 11.2583 | + | 6.50000i | 0.631336 | + | 0.364502i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | + | 5.19615i | −0.167444 | + | 0.290021i | ||||
\(322\) | 10.3923 | − | 6.00000i | 0.579141 | − | 0.334367i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | 8.66025 | − | 5.00000i | 0.478913 | − | 0.276501i | ||||
\(328\) | −5.19615 | + | 3.00000i | −0.286910 | + | 0.165647i | ||||
\(329\) | 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 | \(0.887167\pi\) | |||||||
\(332\) | −10.3923 | − | 6.00000i | −0.570352 | − | 0.329293i | ||||
\(333\) | 1.00000i | 0.0547997i | ||||||||
\(334\) | −6.50000 | + | 11.2583i | −0.355664 | + | 0.616028i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.50000 | − | 2.59808i | −0.0818317 | − | 0.141737i | ||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | −6.06218 | − | 11.5000i | −0.329739 | − | 0.625518i | ||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | − | 8.66025i | −0.270765 | − | 0.468979i | ||||
\(342\) | 4.33013 | + | 2.50000i | 0.234146 | + | 0.135185i | ||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | −1.00000 | + | 1.73205i | −0.0539164 | + | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | −0.483843 | ||||||||
\(347\) | 24.2487 | + | 14.0000i | 1.30174 | + | 0.751559i | 0.980702 | − | 0.195507i | \(-0.0626353\pi\) |
0.321037 | + | 0.947067i | \(0.395969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | + | 31.1769i | 0.963518 | + | 1.66886i | 0.713545 | + | 0.700609i | \(0.247088\pi\) |
0.249973 | + | 0.968253i | \(0.419578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | − | 2.59808i | −0.133440 | − | 0.138675i | ||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | 31.1769 | − | 18.0000i | 1.65938 | − | 0.958043i | 0.686378 | − | 0.727245i | \(-0.259200\pi\) |
0.973002 | − | 0.230799i | \(-0.0741338\pi\) | |||||||
\(354\) | −2.00000 | − | 3.46410i | −0.106299 | − | 0.184115i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.3923 | + | 6.00000i | 0.549250 | + | 0.317110i | ||||
\(359\) | −34.0000 | −1.79445 | −0.897226 | − | 0.441572i | \(-0.854421\pi\) | ||||
−0.897226 | + | 0.441572i | \(0.854421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 5.19615 | − | 3.00000i | 0.273104 | − | 0.157676i | ||||
\(363\) | − | 10.0000i | − | 0.524864i | ||||||
\(364\) | 3.00000 | − | 10.3923i | 0.157243 | − | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | −3.46410 | − | 2.00000i | −0.180579 | − | 0.104257i | ||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5000 | + | 33.7750i | −1.01239 | + | 1.75351i | ||||
\(372\) | − | 10.0000i | − | 0.518476i | ||||||
\(373\) | 8.66025 | + | 5.00000i | 0.448411 | + | 0.258890i | 0.707159 | − | 0.707055i | \(-0.249977\pi\) |
−0.258748 | + | 0.965945i | \(0.583310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | − | 3.00000i | − | 0.154303i | ||||||
\(379\) | −0.500000 | − | 0.866025i | −0.0256833 | − | 0.0444847i | 0.852898 | − | 0.522077i | \(-0.174843\pi\) |
−0.878581 | + | 0.477593i | \(0.841509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.50000 | − | 4.33013i | 0.128079 | − | 0.221839i | ||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | −24.2487 | − | 14.0000i | −1.23905 | − | 0.715367i | −0.270151 | − | 0.962818i | \(-0.587074\pi\) |
−0.968900 | + | 0.247451i | \(0.920407\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.00000 | + | 13.8564i | −0.407189 | + | 0.705273i | ||||
\(387\) | −1.73205 | + | 1.00000i | −0.0880451 | + | 0.0508329i | ||||
\(388\) | −10.3923 | + | 6.00000i | −0.527589 | + | 0.304604i | ||||
\(389\) | 16.0000 | 0.811232 | 0.405616 | − | 0.914044i | \(-0.367057\pi\) | ||||
0.405616 | + | 0.914044i | \(0.367057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.73205 | − | 1.00000i | 0.0874818 | − | 0.0505076i | ||||
\(393\) | −12.9904 | + | 7.50000i | −0.655278 | + | 0.378325i | ||||
\(394\) | −7.50000 | + | 12.9904i | −0.377845 | + | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | + | 0.866025i | −0.0251259 | + | 0.0435194i | ||||
\(397\) | 28.5788 | + | 16.5000i | 1.43433 | + | 0.828111i | 0.997447 | − | 0.0714068i | \(-0.0227489\pi\) |
0.436884 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(398\) | 2.00000i | 0.100251i | ||||||||
\(399\) | −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 | \(-0.381250\pi\) | |||||||
\(402\) | 12.0000i | 0.598506i | ||||||||
\(403\) | 25.9808 | − | 25.0000i | 1.29419 | − | 1.24534i | ||||
\(404\) | −4.00000 | −0.199007 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.866025 | + | 0.500000i | 0.0429273 | + | 0.0247841i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | − | 14.7224i | 0.420298 | − | 0.727977i | −0.575670 | − | 0.817682i | \(-0.695259\pi\) |
0.995968 | + | 0.0897044i | \(0.0285922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.0000 | −0.789222 | ||||||||
\(412\) | 7.79423 | + | 4.50000i | 0.383994 | + | 0.221699i | ||||
\(413\) | 10.3923 | − | 6.00000i | 0.511372 | − | 0.295241i | ||||
\(414\) | −2.00000 | − | 3.46410i | −0.0982946 | − | 0.170251i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.50000 | + | 0.866025i | −0.171602 | + | 0.0424604i | ||||
\(417\) | 9.00000i | 0.440732i | ||||||||
\(418\) | 4.33013 | − | 2.50000i | 0.211793 | − | 0.122279i | ||||
\(419\) | −14.0000 | − | 24.2487i | −0.683945 | − | 1.18463i | −0.973767 | − | 0.227547i | \(-0.926930\pi\) |
0.289822 | − | 0.957080i | \(-0.406404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 12.9904 | + | 7.50000i | 0.632362 | + | 0.365094i | ||||
\(423\) | −7.79423 | − | 4.50000i | −0.378968 | − | 0.218797i | ||||
\(424\) | 13.0000 | 0.631336 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.00000 | − | 1.73205i | −0.0484502 | − | 0.0839181i | ||||
\(427\) | 5.19615 | − | 3.00000i | 0.251459 | − | 0.145180i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | −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 | \(-0.500640\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 13.8564 | + | 8.00000i | 0.665896 | + | 0.384455i | 0.794520 | − | 0.607238i | \(-0.207723\pi\) |
−0.128624 | + | 0.991693i | \(0.541056\pi\) | |||||||
\(434\) | 30.0000 | 1.44005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | 20.0000i | 0.956730i | ||||||||
\(438\) | 13.8564 | + | 8.00000i | 0.662085 | + | 0.382255i | ||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0000i | 0.855206i | 0.903967 | + | 0.427603i | \(0.140642\pi\) | ||||
−0.903967 | + | 0.427603i | \(0.859358\pi\) | |||||||
\(444\) | 0.500000 | + | 0.866025i | 0.0237289 | + | 0.0410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.50000 | + | 9.52628i | −0.260433 | + | 0.451082i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | −2.59808 | − | 1.50000i | −0.122748 | − | 0.0708683i | ||||
\(449\) | −7.50000 | + | 12.9904i | −0.353947 | + | 0.613054i | −0.986937 | − | 0.161106i | \(-0.948494\pi\) |
0.632990 | + | 0.774160i | \(0.281827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | 13.8564 | − | 8.00000i | 0.651751 | − | 0.376288i | ||||
\(453\) | −5.19615 | + | 3.00000i | −0.244137 | + | 0.140952i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.00000 | 0.234146 | ||||||||
\(457\) | 19.0526 | − | 11.0000i | 0.891241 | − | 0.514558i | 0.0168929 | − | 0.999857i | \(-0.494623\pi\) |
0.874348 | + | 0.485299i | \(0.161289\pi\) | |||||||
\(458\) | 8.66025 | − | 5.00000i | 0.404667 | − | 0.233635i | ||||
\(459\) | 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 | \(0.0765153\pi\) | |||||||
\(462\) | −2.59808 | − | 1.50000i | −0.120873 | − | 0.0697863i | ||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.00000 | − | 8.66025i | −0.231621 | − | 0.401179i | ||||
\(467\) | − | 36.0000i | − | 1.66588i | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||
0.553362 | − | 0.832941i | \(-0.313345\pi\) | |||||||
\(468\) | −3.46410 | − | 1.00000i | −0.160128 | − | 0.0462250i | ||||
\(469\) | −36.0000 | −1.66233 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.500000 | + | 0.866025i | 0.0230388 | + | 0.0399043i | ||||
\(472\) | −3.46410 | − | 2.00000i | −0.159448 | − | 0.0920575i | ||||
\(473\) | 2.00000i | 0.0919601i | ||||||||
\(474\) | 5.00000 | − | 8.66025i | 0.229658 | − | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2583 | + | 6.50000i | 0.515484 | + | 0.297615i | ||||
\(478\) | 1.73205 | − | 1.00000i | 0.0792222 | − | 0.0457389i | ||||
\(479\) | −4.00000 | − | 6.92820i | −0.182765 | − | 0.316558i | 0.760056 | − | 0.649857i | \(-0.225171\pi\) |
−0.942821 | + | 0.333300i | \(0.891838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | + | 3.46410i | −0.0455961 | + | 0.157949i | ||||
\(482\) | 15.0000i | 0.683231i | ||||||||
\(483\) | 10.3923 | − | 6.00000i | 0.472866 | − | 0.273009i | ||||
\(484\) | −5.00000 | − | 8.66025i | −0.227273 | − | 0.393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −30.3109 | − | 17.5000i | −1.37352 | − | 0.793001i | −0.382148 | − | 0.924101i | \(-0.624816\pi\) |
−0.991369 | + | 0.131100i | \(0.958149\pi\) | |||||||
\(488\) | −1.73205 | − | 1.00000i | −0.0784063 | − | 0.0452679i | ||||
\(489\) | −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 | \(-0.357450\pi\) | |||||||
\(492\) | −5.19615 | + | 3.00000i | −0.234261 | + | 0.135250i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.5000 | + | 12.9904i | 0.562402 | + | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.00000 | − | 8.66025i | −0.224507 | − | 0.388857i | ||||
\(497\) | 5.19615 | − | 3.00000i | 0.233079 | − | 0.134568i | ||||
\(498\) | −10.3923 | − | 6.00000i | −0.465690 | − | 0.268866i | ||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.50000 | + | 11.2583i | −0.290399 | + | 0.502985i | ||||
\(502\) | 11.0000i | 0.490954i | ||||||||
\(503\) | −0.866025 | − | 0.500000i | −0.0386142 | − | 0.0222939i | 0.480569 | − | 0.876957i | \(-0.340430\pi\) |
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(504\) | −1.50000 | − | 2.59808i | −0.0668153 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | −6.06218 | − | 11.5000i | −0.269231 | − | 0.510733i | ||||
\(508\) | − | 5.00000i | − | 0.221839i | ||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | + | 41.5692i | −1.06170 | + | 1.83891i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.33013 | + | 2.50000i | 0.191180 | + | 0.110378i | ||||
\(514\) | −12.0000 | + | 20.7846i | −0.529297 | + | 0.916770i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | −7.79423 | + | 4.50000i | −0.342790 | + | 0.197910i | ||||
\(518\) | −2.59808 | + | 1.50000i | −0.114153 | + | 0.0659062i | ||||
\(519\) | −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 | ||||||||
\(523\) | −5.19615 | + | 3.00000i | −0.227212 | + | 0.131181i | −0.609285 | − | 0.792951i | \(-0.708544\pi\) |
0.382073 | + | 0.924132i | \(0.375210\pi\) | |||||||
\(524\) | −7.50000 | + | 12.9904i | −0.327639 | + | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.50000 | + | 2.59808i | −0.0654031 | + | 0.113282i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.00000i | 0.0435194i | ||||||||
\(529\) | −3.50000 | + | 6.06218i | −0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00000 | − | 3.46410i | −0.0867926 | − | 0.150329i | ||||
\(532\) | 15.0000i | 0.650332i | ||||||||
\(533\) | −20.7846 | − | 6.00000i | −0.900281 | − | 0.259889i | ||||
\(534\) | 1.00000 | 0.0432742 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 10.3923 | + | 6.00000i | 0.448461 | + | 0.258919i | ||||
\(538\) | 20.0000i | 0.862261i | ||||||||
\(539\) | 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 | \(0.513689\pi\) | |||||||
\(542\) | 20.7846 | + | 12.0000i | 0.892775 | + | 0.515444i | ||||
\(543\) | 5.19615 | − | 3.00000i | 0.222988 | − | 0.128742i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.00000 | − | 10.3923i | 0.128388 | − | 0.444750i | ||||
\(547\) | 34.0000i | 1.45374i | 0.686778 | + | 0.726868i | \(0.259025\pi\) | ||||
−0.686778 | + | 0.726868i | \(0.740975\pi\) | |||||||
\(548\) | −13.8564 | + | 8.00000i | −0.591916 | + | 0.341743i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −3.46410 | − | 2.00000i | −0.147442 | − | 0.0851257i | ||||
\(553\) | 25.9808 | + | 15.0000i | 1.10481 | + | 0.637865i | ||||
\(554\) | −23.0000 | −0.977176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.50000 | + | 7.79423i | 0.190843 | + | 0.330549i | ||||
\(557\) | −2.59808 | + | 1.50000i | −0.110084 | + | 0.0635570i | −0.554031 | − | 0.832496i | \(-0.686911\pi\) |
0.443947 | + | 0.896053i | \(0.353578\pi\) | |||||||
\(558\) | − | 10.0000i | − | 0.423334i | ||||||
\(559\) | −7.00000 | + | 1.73205i | −0.296068 | + | 0.0732579i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.66025 | − | 5.00000i | 0.365311 | − | 0.210912i | ||||
\(563\) | 20.7846 | + | 12.0000i | 0.875967 | + | 0.505740i | 0.869326 | − | 0.494238i | \(-0.164553\pi\) |
0.00664037 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(564\) | −9.00000 | −0.378968 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00000 | + | 1.73205i | −0.0420331 | + | 0.0728035i | ||||
\(567\) | − | 3.00000i | − | 0.125988i | ||||||
\(568\) | −1.73205 | − | 1.00000i | −0.0726752 | − | 0.0419591i | ||||
\(569\) | −5.50000 | − | 9.52628i | −0.230572 | − | 0.399362i | 0.727405 | − | 0.686209i | \(-0.240726\pi\) |
−0.957977 | + | 0.286846i | \(0.907393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | −2.59808 | + | 2.50000i | −0.108631 | + | 0.104530i | ||||
\(573\) | − | 18.0000i | − | 0.751961i | ||||||
\(574\) | −9.00000 | − | 15.5885i | −0.375653 | − | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | −14.7224 | − | 8.50000i | −0.612372 | − | 0.353553i | ||||
\(579\) | −8.00000 | + | 13.8564i | −0.332469 | + | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | − | 31.1769i | 0.746766 | − | 1.29344i | ||||
\(582\) | −10.3923 | + | 6.00000i | −0.430775 | + | 0.248708i | ||||
\(583\) | 11.2583 | − | 6.50000i | 0.466272 | − | 0.269202i | ||||
\(584\) | 16.0000 | 0.662085 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0000 | 0.537025 | ||||||||
\(587\) | −15.5885 | + | 9.00000i | −0.643404 | + | 0.371470i | −0.785925 | − | 0.618322i | \(-0.787813\pi\) |
0.142520 | + | 0.989792i | \(0.454479\pi\) | |||||||
\(588\) | 1.73205 | − | 1.00000i | 0.0714286 | − | 0.0412393i | ||||
\(589\) | −25.0000 | + | 43.3013i | −1.03011 | + | 1.78420i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.50000 | + | 12.9904i | −0.308509 | + | 0.534353i | ||||
\(592\) | 0.866025 | + | 0.500000i | 0.0355934 | + | 0.0205499i | ||||
\(593\) | − | 28.0000i | − | 1.14982i | −0.818216 | − | 0.574911i | \(-0.805037\pi\) | ||
0.818216 | − | 0.574911i | \(-0.194963\pi\) | |||||||
\(594\) | −0.500000 | + | 0.866025i | −0.0205152 | + | 0.0355335i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | + | 5.19615i | 0.122885 | + | 0.212843i | ||||
\(597\) | 2.00000i | 0.0818546i | ||||||||
\(598\) | −3.46410 | − | 14.0000i | −0.141658 | − | 0.572503i | ||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.5000 | + | 23.3827i | 0.550676 | + | 0.953800i | 0.998226 | + | 0.0595404i | \(0.0189635\pi\) |
−0.447549 | + | 0.894259i | \(0.647703\pi\) | |||||||
\(602\) | −5.19615 | − | 3.00000i | −0.211779 | − | 0.122271i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | −3.00000 | + | 5.19615i | −0.122068 | + | 0.211428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.00000 | −0.162489 | ||||||||
\(607\) | −32.0429 | − | 18.5000i | −1.30058 | − | 0.750892i | −0.320079 | − | 0.947391i | \(-0.603709\pi\) |
−0.980504 | + | 0.196499i | \(0.937043\pi\) | |||||||
\(608\) | 4.33013 | − | 2.50000i | 0.175610 | − | 0.101388i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5000 | − | 23.3827i | −0.910253 | − | 0.945962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.9186 | + | 11.5000i | −0.804504 | + | 0.464481i | −0.845044 | − | 0.534697i | \(-0.820426\pi\) |
0.0405396 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(614\) | 9.00000 | + | 15.5885i | 0.363210 | + | 0.629099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | 5.19615 | + | 3.00000i | 0.209189 | + | 0.120775i | 0.600935 | − | 0.799298i | \(-0.294795\pi\) |
−0.391745 | + | 0.920074i | \(0.628129\pi\) | |||||||
\(618\) | 7.79423 | + | 4.50000i | 0.313530 | + | 0.181017i | ||||
\(619\) | 31.0000 | 1.24600 | 0.622998 | − | 0.782224i | \(-0.285915\pi\) | ||||
0.622998 | + | 0.782224i | \(0.285915\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | −10.3923 | + | 6.00000i | −0.416693 | + | 0.240578i | ||||
\(623\) | 3.00000i | 0.120192i | ||||||||
\(624\) | −3.50000 | + | 0.866025i | −0.140112 | + | 0.0346688i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.0000 | + | 29.4449i | 0.679457 | + | 1.17685i | ||||
\(627\) | 4.33013 | − | 2.50000i | 0.172929 | − | 0.0998404i | ||||
\(628\) | 0.866025 | + | 0.500000i | 0.0345582 | + | 0.0199522i | ||||
\(629\) | 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 | \(0.141296\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | 12.9904 | + | 7.50000i | 0.516321 | + | 0.298098i | ||||
\(634\) | 9.50000 | + | 16.4545i | 0.377293 | + | 0.653491i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.0000 | 0.515484 | ||||||||
\(637\) | 6.92820 | + | 2.00000i | 0.274505 | + | 0.0792429i | ||||
\(638\) | 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 | \(0.109788\pi\) | |||||||
\(642\) | 6.00000i | 0.236801i | ||||||||
\(643\) | −38.1051 | − | 22.0000i | −1.50272 | − | 0.867595i | −0.999995 | − | 0.00314839i | \(-0.998998\pi\) |
−0.502724 | − | 0.864447i | \(-0.667669\pi\) | |||||||
\(644\) | 6.00000 | − | 10.3923i | 0.236433 | − | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.79423 | − | 4.50000i | 0.306423 | − | 0.176913i | −0.338902 | − | 0.940822i | \(-0.610055\pi\) |
0.645325 | + | 0.763908i | \(0.276722\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.0000 | 1.17579 | ||||||||
\(652\) | −17.3205 | + | 10.0000i | −0.678323 | + | 0.391630i | ||||
\(653\) | −35.5070 | + | 20.5000i | −1.38950 | + | 0.802227i | −0.993259 | − | 0.115920i | \(-0.963018\pi\) |
−0.396239 | + | 0.918147i | \(0.629685\pi\) | |||||||
\(654\) | 5.00000 | − | 8.66025i | 0.195515 | − | 0.338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | 13.8564 | + | 8.00000i | 0.540590 | + | 0.312110i | ||||
\(658\) | − | 27.0000i | − | 1.05257i | ||||||
\(659\) | 2.00000 | − | 3.46410i | 0.0779089 | − | 0.134942i | −0.824439 | − | 0.565951i | \(-0.808509\pi\) |
0.902348 | + | 0.431009i | \(0.141842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 28.0000i | 1.08825i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.500000 | + | 0.866025i | 0.0193746 | + | 0.0335578i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 13.0000i | 0.502985i | ||||||||
\(669\) | −5.50000 | + | 9.52628i | −0.212642 | + | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | −2.59808 | − | 1.50000i | −0.100223 | − | 0.0578638i | ||||
\(673\) | 27.7128 | − | 16.0000i | 1.06825 | − | 0.616755i | 0.140548 | − | 0.990074i | \(-0.455114\pi\) |
0.927703 | + | 0.373319i | \(0.121780\pi\) | |||||||
\(674\) | 1.00000 | + | 1.73205i | 0.0385186 | + | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | − | 26.0000i | − | 0.999261i | −0.866239 | − | 0.499631i | \(-0.833469\pi\) | ||
0.866239 | − | 0.499631i | \(-0.166531\pi\) | |||||||
\(678\) | 13.8564 | − | 8.00000i | 0.532152 | − | 0.307238i | ||||
\(679\) | −18.0000 | − | 31.1769i | −0.690777 | − | 1.19646i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | −8.66025 | − | 5.00000i | −0.331618 | − | 0.191460i | ||||
\(683\) | −22.5167 | − | 13.0000i | −0.861576 | − | 0.497431i | 0.00296369 | − | 0.999996i | \(-0.499057\pi\) |
−0.864540 | + | 0.502564i | \(0.832390\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | 8.66025 | − | 5.00000i | 0.330409 | − | 0.190762i | ||||
\(688\) | 2.00000i | 0.0762493i | ||||||||
\(689\) | 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 | \(-0.382666\pi\) | |||||||
\(692\) | −7.79423 | + | 4.50000i | −0.296292 | + | 0.171064i | ||||
\(693\) | −2.59808 | − | 1.50000i | −0.0986928 | − | 0.0569803i | ||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 31.1769 | + | 18.0000i | 1.18006 | + | 0.681310i | ||||
\(699\) | −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 | \(0.475932\pi\) | |||||||
\(702\) | −3.46410 | − | 1.00000i | −0.130744 | − | 0.0377426i | ||||
\(703\) | − | 5.00000i | − | 0.188579i | ||||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | − | 31.1769i | 0.677439 | − | 1.17336i | ||||
\(707\) | − | 12.0000i | − | 0.451306i | ||||||
\(708\) | −3.46410 | − | 2.00000i | −0.130189 | − | 0.0751646i | ||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 0.866025 | − | 0.500000i | 0.0324557 | − | 0.0187383i | ||||
\(713\) | 34.6410 | − | 20.0000i | 1.29732 | − | 0.749006i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | 1.73205 | − | 1.00000i | 0.0646846 | − | 0.0373457i | ||||
\(718\) | −29.4449 | + | 17.0000i | −1.09887 | + | 0.634434i | ||||
\(719\) | 18.0000 | − | 31.1769i | 0.671287 | − | 1.16270i | −0.306253 | − | 0.951950i | \(-0.599075\pi\) |
0.977539 | − | 0.210752i | \(-0.0675914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | + | 23.3827i | −0.502766 | + | 0.870817i | ||||
\(722\) | −5.19615 | − | 3.00000i | −0.193381 | − | 0.111648i | ||||
\(723\) | 15.0000i | 0.557856i | ||||||||
\(724\) | 3.00000 | − | 5.19615i | 0.111494 | − | 0.193113i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | − | 8.66025i | −0.185567 | − | 0.321412i | ||||
\(727\) | − | 37.0000i | − | 1.37225i | −0.727482 | − | 0.686127i | \(-0.759309\pi\) | ||
0.727482 | − | 0.686127i | \(-0.240691\pi\) | |||||||
\(728\) | −2.59808 | − | 10.5000i | −0.0962911 | − | 0.389156i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.73205 | − | 1.00000i | −0.0640184 | − | 0.0369611i | ||||
\(733\) | 5.00000i | 0.184679i | 0.995728 | + | 0.0923396i | \(0.0294345\pi\) | ||||
−0.995728 | + | 0.0923396i | \(0.970565\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 10.3923 | + | 6.00000i | 0.382805 | + | 0.221013i | ||||
\(738\) | −5.19615 | + | 3.00000i | −0.191273 | + | 0.110432i | ||||
\(739\) | 17.5000 | + | 30.3109i | 0.643748 | + | 1.11500i | 0.984589 | + | 0.174883i | \(0.0559548\pi\) |
−0.340841 | + | 0.940121i | \(0.610712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.5000 | + | 12.9904i | 0.459199 | + | 0.477214i | ||||
\(742\) | 39.0000i | 1.43174i | ||||||||
\(743\) | −20.7846 | + | 12.0000i | −0.762513 | + | 0.440237i | −0.830197 | − | 0.557470i | \(-0.811772\pi\) |
0.0676840 | + | 0.997707i | \(0.478439\pi\) | |||||||
\(744\) | −5.00000 | − | 8.66025i | −0.183309 | − | 0.317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | −10.3923 | − | 6.00000i | −0.380235 | − | 0.219529i | ||||
\(748\) | 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 | \(-0.463319\pi\) | |||||||
\(752\) | −7.79423 | + | 4.50000i | −0.284226 | + | 0.164098i | ||||
\(753\) | 11.0000i | 0.400862i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.50000 | − | 2.59808i | −0.0545545 | − | 0.0944911i | ||||
\(757\) | 33.7750 | − | 19.5000i | 1.22757 | − | 0.708740i | 0.261051 | − | 0.965325i | \(-0.415931\pi\) |
0.966522 | + | 0.256585i | \(0.0825975\pi\) | |||||||
\(758\) | −0.866025 | − | 0.500000i | −0.0314555 | − | 0.0181608i | ||||
\(759\) | −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 | \(0.863060\pi\) | |||||||
\(762\) | − | 5.00000i | − | 0.181131i | ||||||
\(763\) | 25.9808 | + | 15.0000i | 0.940567 | + | 0.543036i | ||||
\(764\) | −9.00000 | − | 15.5885i | −0.325609 | − | 0.563971i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.0000 | −1.01168 | ||||||||
\(767\) | −3.46410 | − | 14.0000i | −0.125081 | − | 0.505511i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −13.0000 | − | 22.5167i | −0.468792 | − | 0.811972i | 0.530572 | − | 0.847640i | \(-0.321977\pi\) |
−0.999364 | + | 0.0356685i | \(0.988644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | + | 20.7846i | −0.432169 | + | 0.748539i | ||||
\(772\) | 16.0000i | 0.575853i | ||||||||
\(773\) | −32.0429 | − | 18.5000i | −1.15250 | − | 0.665399i | −0.203008 | − | 0.979177i | \(-0.565072\pi\) |
−0.949496 | + | 0.313778i | \(0.898405\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | + | 10.3923i | −0.215387 | + | 0.373062i | ||||
\(777\) | −2.59808 | + | 1.50000i | −0.0932055 | + | 0.0538122i | ||||
\(778\) | 13.8564 | − | 8.00000i | 0.496776 | − | 0.286814i | ||||
\(779\) | 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 | ||||
\(787\) | −13.8564 | − | 8.00000i | −0.493928 | − | 0.285169i | 0.232275 | − | 0.972650i | \(-0.425383\pi\) |
−0.726202 | + | 0.687481i | \(0.758716\pi\) | |||||||
\(788\) | 15.0000i | 0.534353i | ||||||||
\(789\) | −1.50000 | + | 2.59808i | −0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | + | 41.5692i | 0.853342 | + | 1.47803i | ||||
\(792\) | 1.00000i | 0.0355335i | ||||||||
\(793\) | −1.73205 | − | 7.00000i | −0.0615069 | − | 0.248577i | ||||
\(794\) | 33.0000 | 1.17113 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00000 | + | 1.73205i | 0.0354441 | + | 0.0613909i | ||||
\(797\) | 12.1244 | + | 7.00000i | 0.429467 | + | 0.247953i | 0.699119 | − | 0.715005i | \(-0.253576\pi\) |
−0.269653 | + | 0.962958i | \(0.586909\pi\) | |||||||
\(798\) | 15.0000i | 0.530994i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00000 | 0.0353333 | ||||||||
\(802\) | −21.6506 | − | 12.5000i | −0.764511 | − | 0.441390i | ||||
\(803\) | 13.8564 | − | 8.00000i | 0.488982 | − | 0.282314i | ||||
\(804\) | 6.00000 | + | 10.3923i | 0.211604 | + | 0.366508i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0000 | − | 34.6410i | 0.352235 | − | 1.22018i | ||||
\(807\) | 20.0000i | 0.704033i | ||||||||
\(808\) | −3.46410 | + | 2.00000i | −0.121867 | + | 0.0703598i | ||||
\(809\) | −9.00000 | − | 15.5885i | −0.316423 | − | 0.548061i | 0.663316 | − | 0.748340i | \(-0.269149\pi\) |
−0.979739 | + | 0.200279i | \(0.935815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.0000 | 1.15879 | 0.579393 | − | 0.815048i | \(-0.303290\pi\) | ||||
0.579393 | + | 0.815048i | \(0.303290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.7846 | + | 12.0000i | 0.728948 | + | 0.420858i | ||||
\(814\) | 1.00000 | 0.0350500 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.66025 | − | 5.00000i | 0.302984 | − | 0.174928i | ||||
\(818\) | − | 17.0000i | − | 0.594391i | ||||||
\(819\) | 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 | \(0.935037\pi\) | |||||||
\(822\) | −13.8564 | + | 8.00000i | −0.483298 | + | 0.279032i | ||||
\(823\) | −4.33013 | − | 2.50000i | −0.150939 | − | 0.0871445i | 0.422628 | − | 0.906303i | \(-0.361108\pi\) |
−0.573567 | + | 0.819159i | \(0.694441\pi\) | |||||||
\(824\) | 9.00000 | 0.313530 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | − | 10.3923i | 0.208767 | − | 0.361595i | ||||
\(827\) | − | 30.0000i | − | 1.04320i | −0.853189 | − | 0.521601i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521601i | \(-0.174665\pi\) | |||||||
\(828\) | −3.46410 | − | 2.00000i | −0.120386 | − | 0.0695048i | ||||
\(829\) | −22.0000 | − | 38.1051i | −0.764092 | − | 1.32345i | −0.940726 | − | 0.339169i | \(-0.889854\pi\) |
0.176634 | − | 0.984277i | \(-0.443479\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.0000 | −0.797861 | ||||||||
\(832\) | −2.59808 | + | 2.50000i | −0.0900721 | + | 0.0866719i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.50000 | + | 7.79423i | 0.155822 | + | 0.269892i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.50000 | − | 4.33013i | 0.0864643 | − | 0.149761i | ||||
\(837\) | − | 10.0000i | − | 0.345651i | ||||||
\(838\) | −24.2487 | − | 14.0000i | −0.837658 | − | 0.483622i | ||||
\(839\) | −27.0000 | + | 46.7654i | −0.932144 | + | 1.61452i | −0.152493 | + | 0.988304i | \(0.548730\pi\) |
−0.779650 | + | 0.626215i | \(0.784603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | 17.3205 | − | 10.0000i | 0.596904 | − | 0.344623i | ||||
\(843\) | 8.66025 | − | 5.00000i | 0.298275 | − | 0.172209i | ||||
\(844\) | 15.0000 | 0.516321 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 25.9808 | − | 15.0000i | 0.892710 | − | 0.515406i | ||||
\(848\) | 11.2583 | − | 6.50000i | 0.386613 | − | 0.223211i | ||||
\(849\) | −1.00000 | + | 1.73205i | −0.0343199 | + | 0.0594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | + | 3.46410i | −0.0685591 | + | 0.118748i | ||||
\(852\) | −1.73205 | − | 1.00000i | −0.0593391 | − | 0.0342594i | ||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | 3.00000 | − | 5.19615i | 0.102658 | − | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | −2.59808 | + | 2.50000i | −0.0886969 | + | 0.0853486i | ||||
\(859\) | −19.0000 | −0.648272 | −0.324136 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | − | 15.5885i | −0.306719 | − | 0.531253i | ||||
\(862\) | −31.1769 | − | 18.0000i | −1.06189 | − | 0.613082i | ||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | −14.7224 | − | 8.50000i | −0.500000 | − | 0.288675i | ||||
\(868\) | 25.9808 | − | 15.0000i | 0.881845 | − | 0.509133i | ||||
\(869\) | −5.00000 | − | 8.66025i | −0.169613 | − | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | + | 41.5692i | −0.406604 | + | 1.40852i | ||||
\(872\) | − | 10.0000i | − | 0.338643i | ||||||
\(873\) | −10.3923 | + | 6.00000i | −0.351726 | + | 0.203069i | ||||
\(874\) | 10.0000 | + | 17.3205i | 0.338255 | + | 0.585875i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | −32.9090 | − | 19.0000i | −1.11126 | − | 0.641584i | −0.172102 | − | 0.985079i | \(-0.555056\pi\) |
−0.939155 | + | 0.343495i | \(0.888389\pi\) | |||||||
\(878\) | −8.66025 | − | 5.00000i | −0.292269 | − | 0.168742i | ||||
\(879\) | 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 | \(0.860175\pi\) | |||||||
\(882\) | 1.73205 | − | 1.00000i | 0.0583212 | − | 0.0336718i | ||||
\(883\) | − | 42.0000i | − | 1.41341i | −0.707507 | − | 0.706706i | \(-0.750180\pi\) | ||
0.707507 | − | 0.706706i | \(-0.249820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | + | 15.5885i | 0.302361 | + | 0.523704i | ||||
\(887\) | −11.2583 | + | 6.50000i | −0.378018 | + | 0.218249i | −0.676955 | − | 0.736024i | \(-0.736701\pi\) |
0.298938 | + | 0.954273i | \(0.403368\pi\) | |||||||
\(888\) | 0.866025 | + | 0.500000i | 0.0290619 | + | 0.0167789i | ||||
\(889\) | 15.0000 | 0.503084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 11.0000i | 0.368307i | ||||||||
\(893\) | 38.9711 | + | 22.5000i | 1.30412 | + | 0.752934i | ||||
\(894\) | 3.00000 | + | 5.19615i | 0.100335 | + | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | −3.46410 | − | 14.0000i | −0.115663 | − | 0.467446i | ||||
\(898\) | 15.0000i | 0.500556i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.00000i | 0.199778i | ||||||||
\(903\) | −5.19615 | − | 3.00000i | −0.172917 | − | 0.0998337i | ||||
\(904\) | 8.00000 | − | 13.8564i | 0.266076 | − | 0.460857i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.00000 | + | 5.19615i | −0.0996683 | + | 0.172631i | ||||
\(907\) | 36.3731 | − | 21.0000i | 1.20775 | − | 0.697294i | 0.245481 | − | 0.969401i | \(-0.421054\pi\) |
0.962267 | + | 0.272108i | \(0.0877207\pi\) | |||||||
\(908\) | 17.3205 | − | 10.0000i | 0.574801 | − | 0.331862i | ||||
\(909\) | −4.00000 | −0.132672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 4.33013 | − | 2.50000i | 0.143385 | − | 0.0827833i | ||||
\(913\) | −10.3923 | + | 6.00000i | −0.343935 | + | 0.198571i | ||||
\(914\) | 11.0000 | − | 19.0526i | 0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.00000 | − | 8.66025i | 0.165205 | − | 0.286143i | ||||
\(917\) | −38.9711 | − | 22.5000i | −1.28694 | − | 0.743015i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0000 | − | 29.4449i | 0.560778 | − | 0.971296i | −0.436650 | − | 0.899631i | \(-0.643835\pi\) |
0.997429 | − | 0.0716652i | \(-0.0228313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.00000 | + | 15.5885i | 0.296560 | + | 0.513657i | ||||
\(922\) | − | 12.0000i | − | 0.395199i | ||||||
\(923\) | −1.73205 | − | 7.00000i | −0.0570111 | − | 0.230408i | ||||
\(924\) | −3.00000 | −0.0986928 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.00000 | + | 13.8564i | 0.262896 | + | 0.455350i | ||||
\(927\) | 7.79423 | + | 4.50000i | 0.255996 | + | 0.147799i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.0000 | − | 29.4449i | 0.557752 | − | 0.966055i | −0.439932 | − | 0.898031i | \(-0.644997\pi\) |
0.997684 | − | 0.0680235i | \(-0.0216693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0000 | −0.327737 | ||||||||
\(932\) | −8.66025 | − | 5.00000i | −0.283676 | − | 0.163780i | ||||
\(933\) | −10.3923 | + | 6.00000i | −0.340229 | + | 0.196431i | ||||
\(934\) | −18.0000 | − | 31.1769i | −0.588978 | − | 1.02014i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.50000 | + | 0.866025i | −0.114401 | + | 0.0283069i | ||||
\(937\) | − | 10.0000i | − | 0.326686i | −0.986569 | − | 0.163343i | \(-0.947772\pi\) | ||
0.986569 | − | 0.163343i | \(-0.0522277\pi\) | |||||||
\(938\) | −31.1769 | + | 18.0000i | −1.01796 | + | 0.587721i | ||||
\(939\) | 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 | \(0.372064\pi\) | |||||||
\(942\) | 0.866025 | + | 0.500000i | 0.0282166 | + | 0.0162909i | ||||
\(943\) | −20.7846 | − | 12.0000i | −0.676840 | − | 0.390774i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | + | 1.73205i | 0.0325128 | + | 0.0563138i | ||||
\(947\) | −32.9090 | + | 19.0000i | −1.06940 | + | 0.617417i | −0.928017 | − | 0.372538i | \(-0.878488\pi\) |
−0.141381 | + | 0.989955i | \(0.545154\pi\) | |||||||
\(948\) | − | 10.0000i | − | 0.324785i | ||||||
\(949\) | 40.0000 | + | 41.5692i | 1.29845 | + | 1.34939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.50000 | + | 16.4545i | 0.308059 | + | 0.533573i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0526 | + | 11.0000i | 0.617173 | + | 0.356325i | 0.775768 | − | 0.631019i | \(-0.217363\pi\) |
−0.158595 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(954\) | 13.0000 | 0.420891 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.00000 | − | 1.73205i | 0.0323423 | − | 0.0560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.92820 | − | 4.00000i | −0.223840 | − | 0.129234i | ||||
\(959\) | −24.0000 | − | 41.5692i | −0.775000 | − | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0.866025 | + | 3.50000i | 0.0279218 | + | 0.112845i | ||||
\(963\) | 6.00000i | 0.193347i | ||||||||
\(964\) | 7.50000 | + | 12.9904i | 0.241559 | + | 0.418392i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.00000 | − | 10.3923i | 0.193047 | − | 0.334367i | ||||
\(967\) | 7.00000i | 0.225105i | 0.993646 | + | 0.112552i | \(0.0359026\pi\) | ||||
−0.993646 | + | 0.112552i | \(0.964097\pi\) | |||||||
\(968\) | −8.66025 | − | 5.00000i | −0.278351 | − | 0.160706i | ||||
\(969\) | 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 | \(0.309295\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | −23.3827 | + | 13.5000i | −0.749614 | + | 0.432790i | ||||
\(974\) | −35.0000 | −1.12147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 41.5692 | − | 24.0000i | 1.32992 | − | 0.767828i | 0.344631 | − | 0.938738i | \(-0.388004\pi\) |
0.985287 | + | 0.170910i | \(0.0546709\pi\) | |||||||
\(978\) | −17.3205 | + | 10.0000i | −0.553849 | + | 0.319765i | ||||
\(979\) | 0.500000 | − | 0.866025i | 0.0159801 | − | 0.0276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.00000 | − | 8.66025i | 0.159638 | − | 0.276501i | ||||
\(982\) | −21.6506 | − | 12.5000i | −0.690900 | − | 0.398891i | ||||
\(983\) | − | 53.0000i | − | 1.69044i | −0.534421 | − | 0.845219i | \(-0.679470\pi\) | ||
0.534421 | − | 0.845219i | \(-0.320530\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 27.0000i | − | 0.859419i | ||||||
\(988\) | 17.3205 | + | 5.00000i | 0.551039 | + | 0.159071i | ||||
\(989\) | −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 | \(-0.372916\pi\) | |||||||
\(992\) | −8.66025 | − | 5.00000i | −0.274963 | − | 0.158750i | ||||
\(993\) | 28.0000i | 0.888553i | ||||||||
\(994\) | 3.00000 | − | 5.19615i | 0.0951542 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 6.06218 | + | 3.50000i | 0.191991 | + | 0.110846i | 0.592914 | − | 0.805266i | \(-0.297977\pi\) |
−0.400923 | + | 0.916112i | \(0.631311\pi\) | |||||||
\(998\) | −17.3205 | + | 10.0000i | −0.548271 | + | 0.316544i | ||||
\(999\) | 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.z.i.1849.2 | 4 | ||
5.2 | odd | 4 | 1950.2.i.o.601.1 | 2 | |||
5.3 | odd | 4 | 390.2.i.b.211.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1950.2.z.i.1849.1 | 4 | ||
13.9 | even | 3 | inner | 1950.2.z.i.1699.1 | 4 | ||
15.8 | even | 4 | 1170.2.i.j.991.1 | 2 | |||
65.3 | odd | 12 | 5070.2.a.q.1.1 | 1 | |||
65.9 | even | 6 | inner | 1950.2.z.i.1699.2 | 4 | ||
65.22 | odd | 12 | 1950.2.i.o.451.1 | 2 | |||
65.23 | odd | 12 | 5070.2.a.c.1.1 | 1 | |||
65.28 | even | 12 | 5070.2.b.a.1351.1 | 2 | |||
65.48 | odd | 12 | 390.2.i.b.61.1 | ✓ | 2 | ||
65.63 | even | 12 | 5070.2.b.a.1351.2 | 2 | |||
195.113 | even | 12 | 1170.2.i.j.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.b.61.1 | ✓ | 2 | 65.48 | odd | 12 | ||
390.2.i.b.211.1 | yes | 2 | 5.3 | odd | 4 | ||
1170.2.i.j.451.1 | 2 | 195.113 | even | 12 | |||
1170.2.i.j.991.1 | 2 | 15.8 | even | 4 | |||
1950.2.i.o.451.1 | 2 | 65.22 | odd | 12 | |||
1950.2.i.o.601.1 | 2 | 5.2 | odd | 4 | |||
1950.2.z.i.1699.1 | 4 | 13.9 | even | 3 | inner | ||
1950.2.z.i.1699.2 | 4 | 65.9 | even | 6 | inner | ||
1950.2.z.i.1849.1 | 4 | 5.4 | even | 2 | inner | ||
1950.2.z.i.1849.2 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.a.c.1.1 | 1 | 65.23 | odd | 12 | |||
5070.2.a.q.1.1 | 1 | 65.3 | odd | 12 | |||
5070.2.b.a.1351.1 | 2 | 65.28 | even | 12 | |||
5070.2.b.a.1351.2 | 2 | 65.63 | even | 12 |