Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(61,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.61 |
Dual form | 390.2.i.e.211.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −1.50000 | − | 2.59808i | −0.566947 | − | 0.981981i | −0.996866 | − | 0.0791130i | \(-0.974791\pi\) |
0.429919 | − | 0.902867i | \(-0.358542\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.50000 | + | 2.59808i | −0.693375 | + | 0.720577i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.50000 | − | 2.59808i | −0.344124 | − | 0.596040i | 0.641071 | − | 0.767482i | \(-0.278491\pi\) |
−0.985194 | + | 0.171442i | \(0.945157\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.50000 | + | 2.59808i | −0.283473 | + | 0.490990i | ||||
\(29\) | 2.00000 | − | 3.46410i | 0.371391 | − | 0.643268i | −0.618389 | − | 0.785872i | \(-0.712214\pi\) |
0.989780 | + | 0.142605i | \(0.0455477\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | + | 2.59808i | 0.253546 | + | 0.439155i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −4.50000 | + | 7.79423i | −0.739795 | + | 1.28136i | 0.212792 | + | 0.977098i | \(0.431744\pi\) |
−0.952587 | + | 0.304266i | \(0.901589\pi\) | |||||||
\(38\) | −3.00000 | −0.486664 | ||||||||
\(39\) | 1.00000 | + | 3.46410i | 0.160128 | + | 0.554700i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 5.00000 | − | 8.66025i | 0.780869 | − | 1.35250i | −0.150567 | − | 0.988600i | \(-0.548110\pi\) |
0.931436 | − | 0.363905i | \(-0.118557\pi\) | |||||||
\(42\) | −1.50000 | + | 2.59808i | −0.231455 | + | 0.400892i | ||||
\(43\) | 5.00000 | + | 8.66025i | 0.762493 | + | 1.32068i | 0.941562 | + | 0.336840i | \(0.109358\pi\) |
−0.179069 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −2.00000 | − | 3.46410i | −0.294884 | − | 0.510754i | ||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | + | 0.866025i | 0.485363 | + | 0.120096i | ||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −1.50000 | + | 2.59808i | −0.202260 | + | 0.350325i | ||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | −2.00000 | − | 3.46410i | −0.262613 | − | 0.454859i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 3.00000 | − | 5.19615i | 0.381000 | − | 0.659912i | ||||
\(63\) | −1.50000 | + | 2.59808i | −0.188982 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | − | 2.59808i | 0.310087 | − | 0.322252i | ||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | 4.00000 | − | 6.92820i | 0.488678 | − | 0.846415i | −0.511237 | − | 0.859440i | \(-0.670813\pi\) |
0.999915 | + | 0.0130248i | \(0.00414604\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | − | 3.46410i | −0.240772 | − | 0.417029i | ||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | 7.00000 | + | 12.1244i | 0.830747 | + | 1.43890i | 0.897447 | + | 0.441123i | \(0.145420\pi\) |
−0.0666994 | + | 0.997773i | \(0.521247\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | 4.50000 | + | 7.79423i | 0.523114 | + | 0.906061i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | −1.50000 | + | 2.59808i | −0.172062 | + | 0.298020i | ||||
\(77\) | −9.00000 | −1.02565 | ||||||||
\(78\) | 3.50000 | + | 0.866025i | 0.396297 | + | 0.0980581i | ||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −5.00000 | − | 8.66025i | −0.552158 | − | 0.956365i | ||||
\(83\) | 16.0000 | 1.75623 | 0.878114 | − | 0.478451i | \(-0.158802\pi\) | ||||
0.878114 | + | 0.478451i | \(0.158802\pi\) | |||||||
\(84\) | 1.50000 | + | 2.59808i | 0.163663 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.0000 | 1.07833 | ||||||||
\(87\) | −2.00000 | − | 3.46410i | −0.214423 | − | 0.371391i | ||||
\(88\) | −1.50000 | + | 2.59808i | −0.159901 | + | 0.276956i | ||||
\(89\) | 1.50000 | − | 2.59808i | 0.159000 | − | 0.275396i | −0.775509 | − | 0.631337i | \(-0.782506\pi\) |
0.934508 | + | 0.355942i | \(0.115840\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 10.5000 | + | 2.59808i | 1.10070 | + | 0.272352i | ||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 3.00000 | − | 5.19615i | 0.311086 | − | 0.538816i | ||||
\(94\) | −1.50000 | + | 2.59808i | −0.154713 | + | 0.267971i | ||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.00000 | − | 6.92820i | −0.406138 | − | 0.703452i | 0.588315 | − | 0.808632i | \(-0.299792\pi\) |
−0.994453 | + | 0.105180i | \(0.966458\pi\) | |||||||
\(98\) | 1.00000 | + | 1.73205i | 0.101015 | + | 0.174964i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0000 | −1.47799 | −0.738997 | − | 0.673709i | \(-0.764700\pi\) | ||||
−0.738997 | + | 0.673709i | \(0.764700\pi\) | |||||||
\(104\) | 2.50000 | − | 2.59808i | 0.245145 | − | 0.254762i | ||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | 4.50000 | − | 7.79423i | 0.437079 | − | 0.757042i | ||||
\(107\) | −1.00000 | + | 1.73205i | −0.0966736 | + | 0.167444i | −0.910306 | − | 0.413936i | \(-0.864154\pi\) |
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 1.50000 | + | 2.59808i | 0.143019 | + | 0.247717i | ||||
\(111\) | 4.50000 | + | 7.79423i | 0.427121 | + | 0.739795i | ||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 4.00000 | + | 6.92820i | 0.376288 | + | 0.651751i | 0.990519 | − | 0.137376i | \(-0.0438669\pi\) |
−0.614231 | + | 0.789127i | \(0.710534\pi\) | |||||||
\(114\) | −1.50000 | + | 2.59808i | −0.140488 | + | 0.243332i | ||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | 3.50000 | + | 0.866025i | 0.323575 | + | 0.0800641i | ||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −5.00000 | − | 8.66025i | −0.450835 | − | 0.780869i | ||||
\(124\) | −3.00000 | − | 5.19615i | −0.269408 | − | 0.466628i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.50000 | + | 2.59808i | 0.133631 | + | 0.231455i | ||||
\(127\) | −1.50000 | + | 2.59808i | −0.133103 | + | 0.230542i | −0.924871 | − | 0.380280i | \(-0.875828\pi\) |
0.791768 | + | 0.610822i | \(0.209161\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | −1.00000 | − | 3.46410i | −0.0877058 | − | 0.303822i | ||||
\(131\) | −3.00000 | −0.262111 | −0.131056 | − | 0.991375i | \(-0.541837\pi\) | ||||
−0.131056 | + | 0.991375i | \(0.541837\pi\) | |||||||
\(132\) | −1.50000 | + | 2.59808i | −0.130558 | + | 0.226134i | ||||
\(133\) | −4.50000 | + | 7.79423i | −0.390199 | + | 0.675845i | ||||
\(134\) | −4.00000 | − | 6.92820i | −0.345547 | − | 0.598506i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | −4.00000 | −0.340503 | ||||||||
\(139\) | 8.50000 | + | 14.7224i | 0.720961 | + | 1.24874i | 0.960615 | + | 0.277882i | \(0.0896325\pi\) |
−0.239655 | + | 0.970858i | \(0.577034\pi\) | |||||||
\(140\) | 1.50000 | − | 2.59808i | 0.126773 | − | 0.219578i | ||||
\(141\) | −1.50000 | + | 2.59808i | −0.126323 | + | 0.218797i | ||||
\(142\) | 14.0000 | 1.17485 | ||||||||
\(143\) | 3.00000 | + | 10.3923i | 0.250873 | + | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | −4.00000 | + | 6.92820i | −0.331042 | + | 0.573382i | ||||
\(147\) | 1.00000 | + | 1.73205i | 0.0824786 | + | 0.142857i | ||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | 1.00000 | + | 1.73205i | 0.0819232 | + | 0.141895i | 0.904076 | − | 0.427372i | \(-0.140560\pi\) |
−0.822153 | + | 0.569267i | \(0.807227\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 1.50000 | + | 2.59808i | 0.121666 | + | 0.210732i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.50000 | + | 7.79423i | −0.362620 | + | 0.628077i | ||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 2.50000 | − | 2.59808i | 0.200160 | − | 0.208013i | ||||
\(157\) | −17.0000 | −1.35675 | −0.678374 | − | 0.734717i | \(-0.737315\pi\) | ||||
−0.678374 | + | 0.734717i | \(0.737315\pi\) | |||||||
\(158\) | 3.00000 | − | 5.19615i | 0.238667 | − | 0.413384i | ||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | −10.0000 | −0.780869 | ||||||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 8.00000 | − | 13.8564i | 0.620920 | − | 1.07547i | ||||
\(167\) | −4.50000 | + | 7.79423i | −0.348220 | + | 0.603136i | −0.985933 | − | 0.167139i | \(-0.946547\pi\) |
0.637713 | + | 0.770274i | \(0.279881\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.50000 | + | 2.59808i | −0.114708 | + | 0.198680i | ||||
\(172\) | 5.00000 | − | 8.66025i | 0.381246 | − | 0.660338i | ||||
\(173\) | −6.50000 | − | 11.2583i | −0.494186 | − | 0.855955i | 0.505792 | − | 0.862656i | \(-0.331200\pi\) |
−0.999978 | + | 0.00670064i | \(0.997867\pi\) | |||||||
\(174\) | −4.00000 | −0.303239 | ||||||||
\(175\) | −1.50000 | − | 2.59808i | −0.113389 | − | 0.196396i | ||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | −1.50000 | − | 2.59808i | −0.112430 | − | 0.194734i | ||||
\(179\) | −2.00000 | + | 3.46410i | −0.149487 | + | 0.258919i | −0.931038 | − | 0.364922i | \(-0.881096\pi\) |
0.781551 | + | 0.623841i | \(0.214429\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 7.50000 | − | 7.79423i | 0.555937 | − | 0.577747i | ||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | −2.00000 | + | 3.46410i | −0.147442 | + | 0.255377i | ||||
\(185\) | 4.50000 | − | 7.79423i | 0.330847 | − | 0.573043i | ||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.50000 | + | 2.59808i | 0.109399 | + | 0.189484i | ||||
\(189\) | 1.50000 | + | 2.59808i | 0.109109 | + | 0.188982i | ||||
\(190\) | 3.00000 | 0.217643 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −4.00000 | + | 6.92820i | −0.287926 | + | 0.498703i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
0.685388 | + | 0.728178i | \(0.259632\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | −1.00000 | − | 3.46410i | −0.0716115 | − | 0.248069i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −5.50000 | + | 9.52628i | −0.391859 | + | 0.678719i | −0.992695 | − | 0.120653i | \(-0.961501\pi\) |
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(198\) | −1.50000 | + | 2.59808i | −0.106600 | + | 0.184637i | ||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0000 | −0.842235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | + | 8.66025i | −0.349215 | + | 0.604858i | ||||
\(206\) | −7.50000 | + | 12.9904i | −0.522550 | + | 0.905083i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | 1.50000 | − | 2.59808i | 0.103510 | − | 0.179284i | ||||
\(211\) | −4.50000 | + | 7.79423i | −0.309793 | + | 0.536577i | −0.978317 | − | 0.207114i | \(-0.933593\pi\) |
0.668524 | + | 0.743690i | \(0.266926\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | 14.0000 | 0.959264 | ||||||||
\(214\) | 1.00000 | + | 1.73205i | 0.0683586 | + | 0.118401i | ||||
\(215\) | −5.00000 | − | 8.66025i | −0.340997 | − | 0.590624i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.00000 | − | 15.5885i | −0.610960 | − | 1.05821i | ||||
\(218\) | −1.00000 | + | 1.73205i | −0.0677285 | + | 0.117309i | ||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.00000 | 0.604040 | ||||||||
\(223\) | 5.50000 | − | 9.52628i | 0.368307 | − | 0.637927i | −0.620994 | − | 0.783815i | \(-0.713271\pi\) |
0.989301 | + | 0.145889i | \(0.0466041\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | 8.00000 | + | 13.8564i | 0.530979 | + | 0.919682i | 0.999346 | + | 0.0361484i | \(0.0115089\pi\) |
−0.468368 | + | 0.883534i | \(0.655158\pi\) | |||||||
\(228\) | 1.50000 | + | 2.59808i | 0.0993399 | + | 0.172062i | ||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 2.00000 | + | 3.46410i | 0.131876 | + | 0.228416i | ||||
\(231\) | −4.50000 | + | 7.79423i | −0.296078 | + | 0.512823i | ||||
\(232\) | −2.00000 | + | 3.46410i | −0.131306 | + | 0.227429i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 2.50000 | − | 2.59808i | 0.163430 | − | 0.169842i | ||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 3.00000 | − | 5.19615i | 0.194871 | − | 0.337526i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.00000 | − | 5.19615i | 0.192055 | − | 0.332650i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | −10.0000 | −0.637577 | ||||||||
\(247\) | 10.5000 | + | 2.59808i | 0.668099 | + | 0.165312i | ||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 8.00000 | − | 13.8564i | 0.506979 | − | 0.878114i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 0.500000 | + | 0.866025i | 0.0315597 | + | 0.0546630i | 0.881374 | − | 0.472419i | \(-0.156619\pi\) |
−0.849814 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | −6.00000 | − | 10.3923i | −0.377217 | − | 0.653359i | ||||
\(254\) | 1.50000 | + | 2.59808i | 0.0941184 | + | 0.163018i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.00000 | + | 10.3923i | −0.374270 | + | 0.648254i | −0.990217 | − | 0.139533i | \(-0.955440\pi\) |
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(258\) | 5.00000 | − | 8.66025i | 0.311286 | − | 0.539164i | ||||
\(259\) | 27.0000 | 1.67770 | ||||||||
\(260\) | −3.50000 | − | 0.866025i | −0.217061 | − | 0.0537086i | ||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | −1.50000 | + | 2.59808i | −0.0926703 | + | 0.160510i | ||||
\(263\) | 15.5000 | − | 26.8468i | 0.955771 | − | 1.65544i | 0.223177 | − | 0.974778i | \(-0.428357\pi\) |
0.732594 | − | 0.680666i | \(-0.238309\pi\) | |||||||
\(264\) | 1.50000 | + | 2.59808i | 0.0923186 | + | 0.159901i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 4.50000 | + | 7.79423i | 0.275913 | + | 0.477895i | ||||
\(267\) | −1.50000 | − | 2.59808i | −0.0917985 | − | 0.159000i | ||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | 2.00000 | + | 3.46410i | 0.121942 | + | 0.211210i | 0.920534 | − | 0.390664i | \(-0.127754\pi\) |
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 6.00000 | − | 10.3923i | 0.364474 | − | 0.631288i | −0.624218 | − | 0.781251i | \(-0.714582\pi\) |
0.988692 | + | 0.149963i | \(0.0479155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.50000 | − | 7.79423i | 0.453921 | − | 0.471728i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | −2.00000 | + | 3.46410i | −0.120386 | + | 0.208514i | ||||
\(277\) | 15.5000 | + | 26.8468i | 0.931305 | + | 1.61307i | 0.781094 | + | 0.624413i | \(0.214662\pi\) |
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 17.0000 | 1.01959 | ||||||||
\(279\) | −3.00000 | − | 5.19615i | −0.179605 | − | 0.311086i | ||||
\(280\) | −1.50000 | − | 2.59808i | −0.0896421 | − | 0.155265i | ||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | −3.00000 | + | 5.19615i | −0.178331 | + | 0.308879i | −0.941309 | − | 0.337546i | \(-0.890403\pi\) |
0.762978 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(284\) | 7.00000 | − | 12.1244i | 0.415374 | − | 0.719448i | ||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | 10.5000 | + | 2.59808i | 0.620878 | + | 0.153627i | ||||
\(287\) | −30.0000 | −1.77084 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 2.00000 | + | 3.46410i | 0.117444 | + | 0.203419i | ||||
\(291\) | −8.00000 | −0.468968 | ||||||||
\(292\) | 4.00000 | + | 6.92820i | 0.234082 | + | 0.405442i | ||||
\(293\) | 0.500000 | + | 0.866025i | 0.0292103 | + | 0.0505937i | 0.880261 | − | 0.474490i | \(-0.157367\pi\) |
−0.851051 | + | 0.525084i | \(0.824034\pi\) | |||||||
\(294\) | 2.00000 | 0.116642 | ||||||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | 4.50000 | − | 7.79423i | 0.261557 | − | 0.453030i | ||||
\(297\) | −1.50000 | + | 2.59808i | −0.0870388 | + | 0.150756i | ||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | 4.00000 | + | 13.8564i | 0.231326 | + | 0.801337i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 15.0000 | − | 25.9808i | 0.864586 | − | 1.49751i | ||||
\(302\) | 7.00000 | − | 12.1244i | 0.402805 | − | 0.697678i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | 4.50000 | + | 7.79423i | 0.256411 | + | 0.444117i | ||||
\(309\) | −7.50000 | + | 12.9904i | −0.426660 | + | 0.738997i | ||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | −1.00000 | − | 3.46410i | −0.0566139 | − | 0.196116i | ||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | −8.50000 | + | 14.7224i | −0.479683 | + | 0.830835i | ||||
\(315\) | 1.50000 | − | 2.59808i | 0.0845154 | − | 0.146385i | ||||
\(316\) | −3.00000 | − | 5.19615i | −0.168763 | − | 0.292306i | ||||
\(317\) | 17.0000 | 0.954815 | 0.477408 | − | 0.878682i | \(-0.341577\pi\) | ||||
0.477408 | + | 0.878682i | \(0.341577\pi\) | |||||||
\(318\) | −4.50000 | − | 7.79423i | −0.252347 | − | 0.437079i | ||||
\(319\) | −6.00000 | − | 10.3923i | −0.335936 | − | 0.581857i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 1.00000 | + | 1.73205i | 0.0558146 | + | 0.0966736i | ||||
\(322\) | −6.00000 | + | 10.3923i | −0.334367 | + | 0.579141i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.50000 | + | 2.59808i | −0.138675 | + | 0.144115i | ||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | −1.00000 | + | 1.73205i | −0.0553001 | + | 0.0957826i | ||||
\(328\) | −5.00000 | + | 8.66025i | −0.276079 | + | 0.478183i | ||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | −8.00000 | − | 13.8564i | −0.439057 | − | 0.760469i | ||||
\(333\) | 9.00000 | 0.493197 | ||||||||
\(334\) | 4.50000 | + | 7.79423i | 0.246229 | + | 0.426481i | ||||
\(335\) | −4.00000 | + | 6.92820i | −0.218543 | + | 0.378528i | ||||
\(336\) | 1.50000 | − | 2.59808i | 0.0818317 | − | 0.141737i | ||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | −11.5000 | − | 6.06218i | −0.625518 | − | 0.329739i | ||||
\(339\) | 8.00000 | 0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.00000 | − | 15.5885i | 0.487377 | − | 0.844162i | ||||
\(342\) | 1.50000 | + | 2.59808i | 0.0811107 | + | 0.140488i | ||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −5.00000 | − | 8.66025i | −0.269582 | − | 0.466930i | ||||
\(345\) | 2.00000 | + | 3.46410i | 0.107676 | + | 0.186501i | ||||
\(346\) | −13.0000 | −0.698884 | ||||||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | −2.00000 | + | 3.46410i | −0.107211 | + | 0.185695i | ||||
\(349\) | −8.00000 | + | 13.8564i | −0.428230 | + | 0.741716i | −0.996716 | − | 0.0809766i | \(-0.974196\pi\) |
0.568486 | + | 0.822693i | \(0.307529\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 2.50000 | − | 2.59808i | 0.133440 | − | 0.138675i | ||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 4.00000 | − | 6.92820i | 0.212899 | − | 0.368751i | −0.739722 | − | 0.672913i | \(-0.765043\pi\) |
0.952620 | + | 0.304162i | \(0.0983763\pi\) | |||||||
\(354\) | −6.00000 | + | 10.3923i | −0.318896 | + | 0.552345i | ||||
\(355\) | −7.00000 | − | 12.1244i | −0.371521 | − | 0.643494i | ||||
\(356\) | −3.00000 | −0.159000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.00000 | + | 3.46410i | 0.105703 | + | 0.183083i | ||||
\(359\) | 30.0000 | 1.58334 | 0.791670 | − | 0.610949i | \(-0.209212\pi\) | ||||
0.791670 | + | 0.610949i | \(0.209212\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | −5.00000 | + | 8.66025i | −0.262794 | + | 0.455173i | ||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | −3.00000 | − | 10.3923i | −0.157243 | − | 0.544705i | ||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 3.00000 | − | 5.19615i | 0.156813 | − | 0.271607i | ||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | −4.50000 | − | 7.79423i | −0.233944 | − | 0.405203i | ||||
\(371\) | −13.5000 | − | 23.3827i | −0.700885 | − | 1.21397i | ||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 13.0000 | + | 22.5167i | 0.673114 | + | 1.16587i | 0.977016 | + | 0.213165i | \(0.0683772\pi\) |
−0.303902 | + | 0.952703i | \(0.598289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 4.00000 | + | 13.8564i | 0.206010 | + | 0.713641i | ||||
\(378\) | 3.00000 | 0.154303 | ||||||||
\(379\) | 16.5000 | − | 28.5788i | 0.847548 | − | 1.46800i | −0.0358418 | − | 0.999357i | \(-0.511411\pi\) |
0.883390 | − | 0.468639i | \(-0.155255\pi\) | |||||||
\(380\) | 1.50000 | − | 2.59808i | 0.0769484 | − | 0.133278i | ||||
\(381\) | 1.50000 | + | 2.59808i | 0.0768473 | + | 0.133103i | ||||
\(382\) | 6.00000 | 0.306987 | ||||||||
\(383\) | −2.00000 | − | 3.46410i | −0.102195 | − | 0.177007i | 0.810394 | − | 0.585886i | \(-0.199253\pi\) |
−0.912589 | + | 0.408879i | \(0.865920\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | 4.00000 | + | 6.92820i | 0.203595 | + | 0.352636i | ||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | −4.00000 | + | 6.92820i | −0.203069 | + | 0.351726i | ||||
\(389\) | 24.0000 | 1.21685 | 0.608424 | − | 0.793612i | \(-0.291802\pi\) | ||||
0.608424 | + | 0.793612i | \(0.291802\pi\) | |||||||
\(390\) | −3.50000 | − | 0.866025i | −0.177229 | − | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.00000 | − | 1.73205i | 0.0505076 | − | 0.0874818i | ||||
\(393\) | −1.50000 | + | 2.59808i | −0.0756650 | + | 0.131056i | ||||
\(394\) | 5.50000 | + | 9.52628i | 0.277086 | + | 0.479927i | ||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 11.5000 | + | 19.9186i | 0.577168 | + | 0.999685i | 0.995802 | + | 0.0915300i | \(0.0291757\pi\) |
−0.418634 | + | 0.908155i | \(0.637491\pi\) | |||||||
\(398\) | 10.0000 | 0.501255 | ||||||||
\(399\) | 4.50000 | + | 7.79423i | 0.225282 | + | 0.390199i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | −8.00000 | −0.399004 | ||||||||
\(403\) | −15.0000 | + | 15.5885i | −0.747203 | + | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | −6.00000 | + | 10.3923i | −0.297775 | + | 0.515761i | ||||
\(407\) | 13.5000 | + | 23.3827i | 0.669170 | + | 1.15904i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 5.00000 | + | 8.66025i | 0.246932 | + | 0.427699i | ||||
\(411\) | −12.0000 | −0.591916 | ||||||||
\(412\) | 7.50000 | + | 12.9904i | 0.369498 | + | 0.639990i | ||||
\(413\) | −18.0000 | + | 31.1769i | −0.885722 | + | 1.53412i | ||||
\(414\) | −2.00000 | + | 3.46410i | −0.0982946 | + | 0.170251i | ||||
\(415\) | −16.0000 | −0.785409 | ||||||||
\(416\) | −3.50000 | − | 0.866025i | −0.171602 | − | 0.0424604i | ||||
\(417\) | 17.0000 | 0.832494 | ||||||||
\(418\) | −4.50000 | + | 7.79423i | −0.220102 | + | 0.381228i | ||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | −1.50000 | − | 2.59808i | −0.0731925 | − | 0.126773i | ||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 4.50000 | + | 7.79423i | 0.219057 | + | 0.379417i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.00000 | − | 12.1244i | 0.339151 | − | 0.587427i | ||||
\(427\) | 9.00000 | − | 15.5885i | 0.435541 | − | 0.754378i | ||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 10.5000 | + | 2.59808i | 0.506945 | + | 0.125436i | ||||
\(430\) | −10.0000 | −0.482243 | ||||||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 8.00000 | + | 13.8564i | 0.384455 | + | 0.665896i | 0.991693 | − | 0.128624i | \(-0.0410559\pi\) |
−0.607238 | + | 0.794520i | \(0.707723\pi\) | |||||||
\(434\) | −18.0000 | −0.864028 | ||||||||
\(435\) | 2.00000 | + | 3.46410i | 0.0958927 | + | 0.166091i | ||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 4.00000 | + | 6.92820i | 0.191127 | + | 0.331042i | ||||
\(439\) | 15.0000 | − | 25.9808i | 0.715911 | − | 1.23999i | −0.246696 | − | 0.969093i | \(-0.579345\pi\) |
0.962607 | − | 0.270901i | \(-0.0873217\pi\) | |||||||
\(440\) | 1.50000 | − | 2.59808i | 0.0715097 | − | 0.123858i | ||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0000 | −0.475114 | −0.237557 | − | 0.971374i | \(-0.576347\pi\) | ||||
−0.237557 | + | 0.971374i | \(0.576347\pi\) | |||||||
\(444\) | 4.50000 | − | 7.79423i | 0.213561 | − | 0.369898i | ||||
\(445\) | −1.50000 | + | 2.59808i | −0.0711068 | + | 0.123161i | ||||
\(446\) | −5.50000 | − | 9.52628i | −0.260433 | − | 0.451082i | ||||
\(447\) | 2.00000 | 0.0945968 | ||||||||
\(448\) | −1.50000 | − | 2.59808i | −0.0708683 | − | 0.122748i | ||||
\(449\) | 17.5000 | + | 30.3109i | 0.825876 | + | 1.43046i | 0.901248 | + | 0.433304i | \(0.142652\pi\) |
−0.0753719 | + | 0.997155i | \(0.524014\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −15.0000 | − | 25.9808i | −0.706322 | − | 1.22339i | ||||
\(452\) | 4.00000 | − | 6.92820i | 0.188144 | − | 0.325875i | ||||
\(453\) | 7.00000 | − | 12.1244i | 0.328889 | − | 0.569652i | ||||
\(454\) | 16.0000 | 0.750917 | ||||||||
\(455\) | −10.5000 | − | 2.59808i | −0.492248 | − | 0.121800i | ||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | 21.0000 | − | 36.3731i | 0.982339 | − | 1.70146i | 0.329125 | − | 0.944286i | \(-0.393246\pi\) |
0.653213 | − | 0.757174i | \(-0.273421\pi\) | |||||||
\(458\) | −5.00000 | + | 8.66025i | −0.233635 | + | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | 16.0000 | + | 27.7128i | 0.745194 | + | 1.29071i | 0.950104 | + | 0.311933i | \(0.100977\pi\) |
−0.204910 | + | 0.978781i | \(0.565690\pi\) | |||||||
\(462\) | 4.50000 | + | 7.79423i | 0.209359 | + | 0.362620i | ||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | −3.00000 | + | 5.19615i | −0.139122 | + | 0.240966i | ||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | −1.00000 | − | 3.46410i | −0.0462250 | − | 0.160128i | ||||
\(469\) | −24.0000 | −1.10822 | ||||||||
\(470\) | 1.50000 | − | 2.59808i | 0.0691898 | − | 0.119840i | ||||
\(471\) | −8.50000 | + | 14.7224i | −0.391659 | + | 0.678374i | ||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | 30.0000 | 1.37940 | ||||||||
\(474\) | −3.00000 | − | 5.19615i | −0.137795 | − | 0.238667i | ||||
\(475\) | −1.50000 | − | 2.59808i | −0.0688247 | − | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.50000 | − | 7.79423i | −0.206041 | − | 0.356873i | ||||
\(478\) | −13.0000 | + | 22.5167i | −0.594606 | + | 1.02989i | ||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −9.00000 | − | 31.1769i | −0.410365 | − | 1.42154i | ||||
\(482\) | −7.00000 | −0.318841 | ||||||||
\(483\) | −6.00000 | + | 10.3923i | −0.273009 | + | 0.472866i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 4.00000 | + | 6.92820i | 0.181631 | + | 0.314594i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −14.5000 | − | 25.1147i | −0.657058 | − | 1.13806i | −0.981374 | − | 0.192109i | \(-0.938467\pi\) |
0.324316 | − | 0.945949i | \(-0.394866\pi\) | |||||||
\(488\) | −3.00000 | − | 5.19615i | −0.135804 | − | 0.235219i | ||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | −1.00000 | − | 1.73205i | −0.0451754 | − | 0.0782461i | ||||
\(491\) | −2.50000 | + | 4.33013i | −0.112823 | + | 0.195416i | −0.916908 | − | 0.399100i | \(-0.869323\pi\) |
0.804084 | + | 0.594515i | \(0.202656\pi\) | |||||||
\(492\) | −5.00000 | + | 8.66025i | −0.225417 | + | 0.390434i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7.50000 | − | 7.79423i | 0.337441 | − | 0.350679i | ||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | −3.00000 | + | 5.19615i | −0.134704 | + | 0.233314i | ||||
\(497\) | 21.0000 | − | 36.3731i | 0.941979 | − | 1.63156i | ||||
\(498\) | −8.00000 | − | 13.8564i | −0.358489 | − | 0.620920i | ||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 4.50000 | + | 7.79423i | 0.201045 | + | 0.348220i | ||||
\(502\) | 1.00000 | 0.0446322 | ||||||||
\(503\) | −10.5000 | − | 18.1865i | −0.468172 | − | 0.810897i | 0.531167 | − | 0.847267i | \(-0.321754\pi\) |
−0.999338 | + | 0.0363700i | \(0.988421\pi\) | |||||||
\(504\) | 1.50000 | − | 2.59808i | 0.0668153 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | −11.5000 | − | 6.06218i | −0.510733 | − | 0.269231i | ||||
\(508\) | 3.00000 | 0.133103 | ||||||||
\(509\) | −5.00000 | + | 8.66025i | −0.221621 | + | 0.383859i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733679 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 20.7846i | 0.530849 | + | 0.919457i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.50000 | + | 2.59808i | 0.0662266 | + | 0.114708i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | 15.0000 | 0.660979 | ||||||||
\(516\) | −5.00000 | − | 8.66025i | −0.220113 | − | 0.381246i | ||||
\(517\) | −4.50000 | + | 7.79423i | −0.197910 | + | 0.342790i | ||||
\(518\) | 13.5000 | − | 23.3827i | 0.593156 | − | 1.02738i | ||||
\(519\) | −13.0000 | −0.570637 | ||||||||
\(520\) | −2.50000 | + | 2.59808i | −0.109632 | + | 0.113933i | ||||
\(521\) | −35.0000 | −1.53338 | −0.766689 | − | 0.642019i | \(-0.778097\pi\) | ||||
−0.766689 | + | 0.642019i | \(0.778097\pi\) | |||||||
\(522\) | −2.00000 | + | 3.46410i | −0.0875376 | + | 0.151620i | ||||
\(523\) | −11.0000 | + | 19.0526i | −0.480996 | + | 0.833110i | −0.999762 | − | 0.0218062i | \(-0.993058\pi\) |
0.518766 | + | 0.854916i | \(0.326392\pi\) | |||||||
\(524\) | 1.50000 | + | 2.59808i | 0.0655278 | + | 0.113497i | ||||
\(525\) | −3.00000 | −0.130931 | ||||||||
\(526\) | −15.5000 | − | 26.8468i | −0.675832 | − | 1.17058i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | −4.50000 | + | 7.79423i | −0.195468 | + | 0.338560i | ||||
\(531\) | −6.00000 | + | 10.3923i | −0.260378 | + | 0.450988i | ||||
\(532\) | 9.00000 | 0.390199 | ||||||||
\(533\) | 10.0000 | + | 34.6410i | 0.433148 | + | 1.50047i | ||||
\(534\) | −3.00000 | −0.129823 | ||||||||
\(535\) | 1.00000 | − | 1.73205i | 0.0432338 | − | 0.0748831i | ||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 2.00000 | + | 3.46410i | 0.0863064 | + | 0.149487i | ||||
\(538\) | 4.00000 | 0.172452 | ||||||||
\(539\) | 3.00000 | + | 5.19615i | 0.129219 | + | 0.223814i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | −6.00000 | − | 10.3923i | −0.257722 | − | 0.446388i | ||||
\(543\) | −5.00000 | + | 8.66025i | −0.214571 | + | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | −3.00000 | − | 10.3923i | −0.128388 | − | 0.444750i | ||||
\(547\) | 22.0000 | 0.940652 | 0.470326 | − | 0.882493i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882493i | \(0.344136\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | −1.50000 | − | 2.59808i | −0.0639602 | − | 0.110782i | ||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 2.00000 | + | 3.46410i | 0.0851257 | + | 0.147442i | ||||
\(553\) | −9.00000 | − | 15.5885i | −0.382719 | − | 0.662889i | ||||
\(554\) | 31.0000 | 1.31706 | ||||||||
\(555\) | −4.50000 | − | 7.79423i | −0.191014 | − | 0.330847i | ||||
\(556\) | 8.50000 | − | 14.7224i | 0.360480 | − | 0.624370i | ||||
\(557\) | 4.50000 | − | 7.79423i | 0.190671 | − | 0.330252i | −0.754802 | − | 0.655953i | \(-0.772267\pi\) |
0.945473 | + | 0.325701i | \(0.105600\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | −35.0000 | − | 8.66025i | −1.48034 | − | 0.366290i | ||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | + | 25.9808i | −0.632737 | + | 1.09593i | ||||
\(563\) | −10.0000 | − | 17.3205i | −0.421450 | − | 0.729972i | 0.574632 | − | 0.818412i | \(-0.305145\pi\) |
−0.996082 | + | 0.0884397i | \(0.971812\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | −4.00000 | − | 6.92820i | −0.168281 | − | 0.291472i | ||||
\(566\) | 3.00000 | + | 5.19615i | 0.126099 | + | 0.218411i | ||||
\(567\) | 3.00000 | 0.125988 | ||||||||
\(568\) | −7.00000 | − | 12.1244i | −0.293713 | − | 0.508727i | ||||
\(569\) | 19.5000 | − | 33.7750i | 0.817483 | − | 1.41592i | −0.0900490 | − | 0.995937i | \(-0.528702\pi\) |
0.907532 | − | 0.419984i | \(-0.137964\pi\) | |||||||
\(570\) | 1.50000 | − | 2.59808i | 0.0628281 | − | 0.108821i | ||||
\(571\) | 23.0000 | 0.962520 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(572\) | 7.50000 | − | 7.79423i | 0.313591 | − | 0.325893i | ||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | −15.0000 | + | 25.9808i | −0.626088 | + | 1.08442i | ||||
\(575\) | 2.00000 | − | 3.46410i | 0.0834058 | − | 0.144463i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | −8.50000 | − | 14.7224i | −0.353553 | − | 0.612372i | ||||
\(579\) | 4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | ||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | −24.0000 | − | 41.5692i | −0.995688 | − | 1.72458i | ||||
\(582\) | −4.00000 | + | 6.92820i | −0.165805 | + | 0.287183i | ||||
\(583\) | 13.5000 | − | 23.3827i | 0.559113 | − | 0.968412i | ||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | −3.50000 | − | 0.866025i | −0.144707 | − | 0.0358057i | ||||
\(586\) | 1.00000 | 0.0413096 | ||||||||
\(587\) | −9.00000 | + | 15.5885i | −0.371470 | + | 0.643404i | −0.989792 | − | 0.142520i | \(-0.954479\pi\) |
0.618322 | + | 0.785925i | \(0.287813\pi\) | |||||||
\(588\) | 1.00000 | − | 1.73205i | 0.0412393 | − | 0.0714286i | ||||
\(589\) | −9.00000 | − | 15.5885i | −0.370839 | − | 0.642311i | ||||
\(590\) | 12.0000 | 0.494032 | ||||||||
\(591\) | 5.50000 | + | 9.52628i | 0.226240 | + | 0.391859i | ||||
\(592\) | −4.50000 | − | 7.79423i | −0.184949 | − | 0.320341i | ||||
\(593\) | 36.0000 | 1.47834 | 0.739171 | − | 0.673517i | \(-0.235217\pi\) | ||||
0.739171 | + | 0.673517i | \(0.235217\pi\) | |||||||
\(594\) | 1.50000 | + | 2.59808i | 0.0615457 | + | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.00000 | − | 1.73205i | 0.0409616 | − | 0.0709476i | ||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 14.0000 | + | 3.46410i | 0.572503 | + | 0.141658i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −10.5000 | + | 18.1865i | −0.428304 | + | 0.741844i | −0.996723 | − | 0.0808953i | \(-0.974222\pi\) |
0.568419 | + | 0.822739i | \(0.307555\pi\) | |||||||
\(602\) | −15.0000 | − | 25.9808i | −0.611354 | − | 1.05890i | ||||
\(603\) | −8.00000 | −0.325785 | ||||||||
\(604\) | −7.00000 | − | 12.1244i | −0.284826 | − | 0.493333i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.5000 | − | 23.3827i | −0.547948 | − | 0.949074i | −0.998415 | − | 0.0562808i | \(-0.982076\pi\) |
0.450467 | − | 0.892793i | \(-0.351258\pi\) | |||||||
\(608\) | 1.50000 | − | 2.59808i | 0.0608330 | − | 0.105366i | ||||
\(609\) | −6.00000 | + | 10.3923i | −0.243132 | + | 0.421117i | ||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | 7.50000 | − | 7.79423i | 0.303418 | − | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50000 | − | 6.06218i | 0.141364 | − | 0.244849i | −0.786647 | − | 0.617403i | \(-0.788185\pi\) |
0.928010 | + | 0.372554i | \(0.121518\pi\) | |||||||
\(614\) | 13.0000 | − | 22.5167i | 0.524637 | − | 0.908698i | ||||
\(615\) | 5.00000 | + | 8.66025i | 0.201619 | + | 0.349215i | ||||
\(616\) | 9.00000 | 0.362620 | ||||||||
\(617\) | 15.0000 | + | 25.9808i | 0.603877 | + | 1.04595i | 0.992228 | + | 0.124434i | \(0.0397116\pi\) |
−0.388351 | + | 0.921512i | \(0.626955\pi\) | |||||||
\(618\) | 7.50000 | + | 12.9904i | 0.301694 | + | 0.522550i | ||||
\(619\) | −23.0000 | −0.924448 | −0.462224 | − | 0.886763i | \(-0.652948\pi\) | ||||
−0.462224 | + | 0.886763i | \(0.652948\pi\) | |||||||
\(620\) | 3.00000 | + | 5.19615i | 0.120483 | + | 0.208683i | ||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | −2.00000 | + | 3.46410i | −0.0801927 | + | 0.138898i | ||||
\(623\) | −9.00000 | −0.360577 | ||||||||
\(624\) | −3.50000 | − | 0.866025i | −0.140112 | − | 0.0346688i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.0000 | − | 22.5167i | 0.519584 | − | 0.899947i | ||||
\(627\) | −4.50000 | + | 7.79423i | −0.179713 | + | 0.311272i | ||||
\(628\) | 8.50000 | + | 14.7224i | 0.339187 | + | 0.587489i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.50000 | − | 2.59808i | −0.0597614 | − | 0.103510i | ||||
\(631\) | −6.00000 | − | 10.3923i | −0.238856 | − | 0.413711i | 0.721530 | − | 0.692383i | \(-0.243439\pi\) |
−0.960386 | + | 0.278672i | \(0.910106\pi\) | |||||||
\(632\) | −6.00000 | −0.238667 | ||||||||
\(633\) | 4.50000 | + | 7.79423i | 0.178859 | + | 0.309793i | ||||
\(634\) | 8.50000 | − | 14.7224i | 0.337578 | − | 0.584702i | ||||
\(635\) | 1.50000 | − | 2.59808i | 0.0595257 | − | 0.103102i | ||||
\(636\) | −9.00000 | −0.356873 | ||||||||
\(637\) | −2.00000 | − | 6.92820i | −0.0792429 | − | 0.274505i | ||||
\(638\) | −12.0000 | −0.475085 | ||||||||
\(639\) | 7.00000 | − | 12.1244i | 0.276916 | − | 0.479632i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −17.5000 | − | 30.3109i | −0.691208 | − | 1.19721i | −0.971442 | − | 0.237276i | \(-0.923745\pi\) |
0.280234 | − | 0.959932i | \(-0.409588\pi\) | |||||||
\(642\) | 2.00000 | 0.0789337 | ||||||||
\(643\) | −14.0000 | − | 24.2487i | −0.552106 | − | 0.956276i | −0.998122 | − | 0.0612510i | \(-0.980491\pi\) |
0.446016 | − | 0.895025i | \(-0.352842\pi\) | |||||||
\(644\) | 6.00000 | + | 10.3923i | 0.236433 | + | 0.409514i | ||||
\(645\) | −10.0000 | −0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5000 | − | 38.9711i | 0.884566 | − | 1.53211i | 0.0383563 | − | 0.999264i | \(-0.487788\pi\) |
0.846210 | − | 0.532850i | \(-0.178879\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | 1.00000 | + | 3.46410i | 0.0392232 | + | 0.135873i | ||||
\(651\) | −18.0000 | −0.705476 | ||||||||
\(652\) | −10.0000 | + | 17.3205i | −0.391630 | + | 0.678323i | ||||
\(653\) | −1.50000 | + | 2.59808i | −0.0586995 | + | 0.101671i | −0.893882 | − | 0.448303i | \(-0.852029\pi\) |
0.835182 | + | 0.549973i | \(0.185362\pi\) | |||||||
\(654\) | 1.00000 | + | 1.73205i | 0.0391031 | + | 0.0677285i | ||||
\(655\) | 3.00000 | 0.117220 | ||||||||
\(656\) | 5.00000 | + | 8.66025i | 0.195217 | + | 0.338126i | ||||
\(657\) | 4.00000 | + | 6.92820i | 0.156055 | + | 0.270295i | ||||
\(658\) | 9.00000 | 0.350857 | ||||||||
\(659\) | −2.00000 | − | 3.46410i | −0.0779089 | − | 0.134942i | 0.824439 | − | 0.565951i | \(-0.191491\pi\) |
−0.902348 | + | 0.431009i | \(0.858158\pi\) | |||||||
\(660\) | 1.50000 | − | 2.59808i | 0.0583874 | − | 0.101130i | ||||
\(661\) | −15.0000 | + | 25.9808i | −0.583432 | + | 1.01053i | 0.411636 | + | 0.911348i | \(0.364957\pi\) |
−0.995069 | + | 0.0991864i | \(0.968376\pi\) | |||||||
\(662\) | 28.0000 | 1.08825 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.0000 | −0.620920 | ||||||||
\(665\) | 4.50000 | − | 7.79423i | 0.174503 | − | 0.302247i | ||||
\(666\) | 4.50000 | − | 7.79423i | 0.174371 | − | 0.302020i | ||||
\(667\) | −8.00000 | − | 13.8564i | −0.309761 | − | 0.536522i | ||||
\(668\) | 9.00000 | 0.348220 | ||||||||
\(669\) | −5.50000 | − | 9.52628i | −0.212642 | − | 0.368307i | ||||
\(670\) | 4.00000 | + | 6.92820i | 0.154533 | + | 0.267660i | ||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | −1.50000 | − | 2.59808i | −0.0578638 | − | 0.100223i | ||||
\(673\) | −24.0000 | + | 41.5692i | −0.925132 | + | 1.60238i | −0.133783 | + | 0.991011i | \(0.542713\pi\) |
−0.791349 | + | 0.611365i | \(0.790621\pi\) | |||||||
\(674\) | 3.00000 | − | 5.19615i | 0.115556 | − | 0.200148i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 4.00000 | − | 6.92820i | 0.153619 | − | 0.266076i | ||||
\(679\) | −12.0000 | + | 20.7846i | −0.460518 | + | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.0000 | 0.613121 | ||||||||
\(682\) | −9.00000 | − | 15.5885i | −0.344628 | − | 0.596913i | ||||
\(683\) | −15.0000 | − | 25.9808i | −0.573959 | − | 0.994126i | −0.996154 | − | 0.0876211i | \(-0.972074\pi\) |
0.422195 | − | 0.906505i | \(-0.361260\pi\) | |||||||
\(684\) | 3.00000 | 0.114708 | ||||||||
\(685\) | 6.00000 | + | 10.3923i | 0.229248 | + | 0.397070i | ||||
\(686\) | −7.50000 | + | 12.9904i | −0.286351 | + | 0.495975i | ||||
\(687\) | −5.00000 | + | 8.66025i | −0.190762 | + | 0.330409i | ||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | −22.5000 | + | 23.3827i | −0.857182 | + | 0.890809i | ||||
\(690\) | 4.00000 | 0.152277 | ||||||||
\(691\) | 3.50000 | − | 6.06218i | 0.133146 | − | 0.230616i | −0.791742 | − | 0.610856i | \(-0.790825\pi\) |
0.924888 | + | 0.380240i | \(0.124159\pi\) | |||||||
\(692\) | −6.50000 | + | 11.2583i | −0.247093 | + | 0.427977i | ||||
\(693\) | 4.50000 | + | 7.79423i | 0.170941 | + | 0.296078i | ||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −8.50000 | − | 14.7224i | −0.322423 | − | 0.558454i | ||||
\(696\) | 2.00000 | + | 3.46410i | 0.0758098 | + | 0.131306i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.00000 | + | 13.8564i | 0.302804 | + | 0.524473i | ||||
\(699\) | −3.00000 | + | 5.19615i | −0.113470 | + | 0.196537i | ||||
\(700\) | −1.50000 | + | 2.59808i | −0.0566947 | + | 0.0981981i | ||||
\(701\) | 24.0000 | 0.906467 | 0.453234 | − | 0.891392i | \(-0.350270\pi\) | ||||
0.453234 | + | 0.891392i | \(0.350270\pi\) | |||||||
\(702\) | −1.00000 | − | 3.46410i | −0.0377426 | − | 0.130744i | ||||
\(703\) | 27.0000 | 1.01832 | ||||||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 1.50000 | − | 2.59808i | 0.0564933 | − | 0.0978492i | ||||
\(706\) | −4.00000 | − | 6.92820i | −0.150542 | − | 0.260746i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000 | + | 10.3923i | 0.225494 | + | 0.390567i | ||||
\(709\) | 20.0000 | + | 34.6410i | 0.751116 | + | 1.30097i | 0.947282 | + | 0.320400i | \(0.103817\pi\) |
−0.196167 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(710\) | −14.0000 | −0.525411 | ||||||||
\(711\) | −3.00000 | − | 5.19615i | −0.112509 | − | 0.194871i | ||||
\(712\) | −1.50000 | + | 2.59808i | −0.0562149 | + | 0.0973670i | ||||
\(713\) | 12.0000 | − | 20.7846i | 0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | − | 10.3923i | −0.112194 | − | 0.388650i | ||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | −13.0000 | + | 22.5167i | −0.485494 | + | 0.840900i | ||||
\(718\) | 15.0000 | − | 25.9808i | 0.559795 | − | 0.969593i | ||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 22.5000 | + | 38.9711i | 0.837944 | + | 1.45136i | ||||
\(722\) | −5.00000 | − | 8.66025i | −0.186081 | − | 0.322301i | ||||
\(723\) | −7.00000 | −0.260333 | ||||||||
\(724\) | 5.00000 | + | 8.66025i | 0.185824 | + | 0.321856i | ||||
\(725\) | 2.00000 | − | 3.46410i | 0.0742781 | − | 0.128654i | ||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | −3.00000 | −0.111264 | −0.0556319 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556319 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(728\) | −10.5000 | − | 2.59808i | −0.389156 | − | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.00000 | − | 6.92820i | 0.148047 | − | 0.256424i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.00000 | − | 5.19615i | −0.110883 | − | 0.192055i | ||||
\(733\) | 53.0000 | 1.95760 | 0.978800 | − | 0.204819i | \(-0.0656606\pi\) | ||||
0.978800 | + | 0.204819i | \(0.0656606\pi\) | |||||||
\(734\) | 4.00000 | + | 6.92820i | 0.147643 | + | 0.255725i | ||||
\(735\) | −1.00000 | − | 1.73205i | −0.0368856 | − | 0.0638877i | ||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | −5.00000 | + | 8.66025i | −0.184053 | + | 0.318788i | ||||
\(739\) | −5.50000 | + | 9.52628i | −0.202321 | + | 0.350430i | −0.949276 | − | 0.314445i | \(-0.898182\pi\) |
0.746955 | + | 0.664875i | \(0.231515\pi\) | |||||||
\(740\) | −9.00000 | −0.330847 | ||||||||
\(741\) | 7.50000 | − | 7.79423i | 0.275519 | − | 0.286328i | ||||
\(742\) | −27.0000 | −0.991201 | ||||||||
\(743\) | −24.0000 | + | 41.5692i | −0.880475 | + | 1.52503i | −0.0296605 | + | 0.999560i | \(0.509443\pi\) |
−0.850814 | + | 0.525467i | \(0.823891\pi\) | |||||||
\(744\) | −3.00000 | + | 5.19615i | −0.109985 | + | 0.190500i | ||||
\(745\) | −1.00000 | − | 1.73205i | −0.0366372 | − | 0.0634574i | ||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | −8.00000 | − | 13.8564i | −0.292705 | − | 0.506979i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | 0.219235 | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | 12.0000 | − | 20.7846i | 0.437886 | − | 0.758441i | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 1.50000 | − | 2.59808i | 0.0546994 | − | 0.0947421i | ||||
\(753\) | 1.00000 | 0.0364420 | ||||||||
\(754\) | 14.0000 | + | 3.46410i | 0.509850 | + | 0.126155i | ||||
\(755\) | −14.0000 | −0.509512 | ||||||||
\(756\) | 1.50000 | − | 2.59808i | 0.0545545 | − | 0.0944911i | ||||
\(757\) | −8.50000 | + | 14.7224i | −0.308938 | + | 0.535096i | −0.978130 | − | 0.207993i | \(-0.933307\pi\) |
0.669193 | + | 0.743089i | \(0.266640\pi\) | |||||||
\(758\) | −16.5000 | − | 28.5788i | −0.599307 | − | 1.03803i | ||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | −1.50000 | − | 2.59808i | −0.0544107 | − | 0.0942421i | ||||
\(761\) | 15.5000 | + | 26.8468i | 0.561875 | + | 0.973195i | 0.997333 | + | 0.0729864i | \(0.0232530\pi\) |
−0.435458 | + | 0.900209i | \(0.643414\pi\) | |||||||
\(762\) | 3.00000 | 0.108679 | ||||||||
\(763\) | 3.00000 | + | 5.19615i | 0.108607 | + | 0.188113i | ||||
\(764\) | 3.00000 | − | 5.19615i | 0.108536 | − | 0.187990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | 42.0000 | + | 10.3923i | 1.51653 | + | 0.375244i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −23.0000 | + | 39.8372i | −0.829401 | + | 1.43657i | 0.0691074 | + | 0.997609i | \(0.477985\pi\) |
−0.898509 | + | 0.438956i | \(0.855348\pi\) | |||||||
\(770\) | 4.50000 | − | 7.79423i | 0.162169 | − | 0.280885i | ||||
\(771\) | 6.00000 | + | 10.3923i | 0.216085 | + | 0.374270i | ||||
\(772\) | 8.00000 | 0.287926 | ||||||||
\(773\) | 3.50000 | + | 6.06218i | 0.125886 | + | 0.218041i | 0.922079 | − | 0.387002i | \(-0.126489\pi\) |
−0.796193 | + | 0.605043i | \(0.793156\pi\) | |||||||
\(774\) | −5.00000 | − | 8.66025i | −0.179721 | − | 0.311286i | ||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 4.00000 | + | 6.92820i | 0.143592 | + | 0.248708i | ||||
\(777\) | 13.5000 | − | 23.3827i | 0.484310 | − | 0.838849i | ||||
\(778\) | 12.0000 | − | 20.7846i | 0.430221 | − | 0.745164i | ||||
\(779\) | −30.0000 | −1.07486 | ||||||||
\(780\) | −2.50000 | + | 2.59808i | −0.0895144 | + | 0.0930261i | ||||
\(781\) | 42.0000 | 1.50288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | + | 3.46410i | −0.0714742 | + | 0.123797i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 17.0000 | 0.606756 | ||||||||
\(786\) | 1.50000 | + | 2.59808i | 0.0535032 | + | 0.0926703i | ||||
\(787\) | 18.0000 | + | 31.1769i | 0.641631 | + | 1.11134i | 0.985069 | + | 0.172162i | \(0.0550751\pi\) |
−0.343438 | + | 0.939175i | \(0.611592\pi\) | |||||||
\(788\) | 11.0000 | 0.391859 | ||||||||
\(789\) | −15.5000 | − | 26.8468i | −0.551815 | − | 0.955771i | ||||
\(790\) | −3.00000 | + | 5.19615i | −0.106735 | + | 0.184871i | ||||
\(791\) | 12.0000 | − | 20.7846i | 0.426671 | − | 0.739016i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −21.0000 | − | 5.19615i | −0.745732 | − | 0.184521i | ||||
\(794\) | 23.0000 | 0.816239 | ||||||||
\(795\) | −4.50000 | + | 7.79423i | −0.159599 | + | 0.276433i | ||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | 21.0000 | + | 36.3731i | 0.743858 | + | 1.28840i | 0.950726 | + | 0.310031i | \(0.100340\pi\) |
−0.206868 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(798\) | 9.00000 | 0.318597 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −3.00000 | −0.106000 | ||||||||
\(802\) | −13.5000 | − | 23.3827i | −0.476702 | − | 0.825671i | ||||
\(803\) | −12.0000 | + | 20.7846i | −0.423471 | + | 0.733473i | ||||
\(804\) | −4.00000 | + | 6.92820i | −0.141069 | + | 0.244339i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | 6.00000 | + | 20.7846i | 0.211341 | + | 0.732107i | ||||
\(807\) | 4.00000 | 0.140807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.00000 | − | 8.66025i | 0.175791 | − | 0.304478i | −0.764644 | − | 0.644453i | \(-0.777085\pi\) |
0.940435 | + | 0.339975i | \(0.110418\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | −31.0000 | −1.08856 | −0.544279 | − | 0.838905i | \(-0.683197\pi\) | ||||
−0.544279 | + | 0.838905i | \(0.683197\pi\) | |||||||
\(812\) | 6.00000 | + | 10.3923i | 0.210559 | + | 0.364698i | ||||
\(813\) | −6.00000 | − | 10.3923i | −0.210429 | − | 0.364474i | ||||
\(814\) | 27.0000 | 0.946350 | ||||||||
\(815\) | 10.0000 | + | 17.3205i | 0.350285 | + | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0000 | − | 25.9808i | 0.524784 | − | 0.908952i | ||||
\(818\) | 7.00000 | 0.244749 | ||||||||
\(819\) | −3.00000 | − | 10.3923i | −0.104828 | − | 0.363137i | ||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | −25.0000 | + | 43.3013i | −0.872506 | + | 1.51122i | −0.0131101 | + | 0.999914i | \(0.504173\pi\) |
−0.859396 | + | 0.511311i | \(0.829160\pi\) | |||||||
\(822\) | −6.00000 | + | 10.3923i | −0.209274 | + | 0.362473i | ||||
\(823\) | 5.50000 | + | 9.52628i | 0.191718 | + | 0.332065i | 0.945820 | − | 0.324692i | \(-0.105261\pi\) |
−0.754102 | + | 0.656758i | \(0.771927\pi\) | |||||||
\(824\) | 15.0000 | 0.522550 | ||||||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 18.0000 | + | 31.1769i | 0.626300 | + | 1.08478i | ||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 2.00000 | + | 3.46410i | 0.0695048 | + | 0.120386i | ||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | −8.00000 | + | 13.8564i | −0.277684 | + | 0.480963i | ||||
\(831\) | 31.0000 | 1.07538 | ||||||||
\(832\) | −2.50000 | + | 2.59808i | −0.0866719 | + | 0.0900721i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.50000 | − | 14.7224i | 0.294331 | − | 0.509796i | ||||
\(835\) | 4.50000 | − | 7.79423i | 0.155729 | − | 0.269730i | ||||
\(836\) | 4.50000 | + | 7.79423i | 0.155636 | + | 0.269569i | ||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | 3.00000 | + | 5.19615i | 0.103572 | + | 0.179391i | 0.913154 | − | 0.407615i | \(-0.133640\pi\) |
−0.809582 | + | 0.587007i | \(0.800306\pi\) | |||||||
\(840\) | −3.00000 | −0.103510 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | −14.0000 | + | 24.2487i | −0.482472 | + | 0.835666i | ||||
\(843\) | −15.0000 | + | 25.9808i | −0.516627 | + | 0.894825i | ||||
\(844\) | 9.00000 | 0.309793 | ||||||||
\(845\) | 0.500000 | + | 12.9904i | 0.0172005 | + | 0.446883i | ||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 3.00000 | − | 5.19615i | 0.103081 | − | 0.178542i | ||||
\(848\) | −4.50000 | + | 7.79423i | −0.154531 | + | 0.267655i | ||||
\(849\) | 3.00000 | + | 5.19615i | 0.102960 | + | 0.178331i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | + | 31.1769i | 0.617032 | + | 1.06873i | ||||
\(852\) | −7.00000 | − | 12.1244i | −0.239816 | − | 0.415374i | ||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | −9.00000 | − | 15.5885i | −0.307974 | − | 0.533426i | ||||
\(855\) | 1.50000 | − | 2.59808i | 0.0512989 | − | 0.0888523i | ||||
\(856\) | 1.00000 | − | 1.73205i | 0.0341793 | − | 0.0592003i | ||||
\(857\) | −50.0000 | −1.70797 | −0.853984 | − | 0.520300i | \(-0.825820\pi\) | ||||
−0.853984 | + | 0.520300i | \(0.825820\pi\) | |||||||
\(858\) | 7.50000 | − | 7.79423i | 0.256046 | − | 0.266091i | ||||
\(859\) | −5.00000 | −0.170598 | −0.0852989 | − | 0.996355i | \(-0.527185\pi\) | ||||
−0.0852989 | + | 0.996355i | \(0.527185\pi\) | |||||||
\(860\) | −5.00000 | + | 8.66025i | −0.170499 | + | 0.295312i | ||||
\(861\) | −15.0000 | + | 25.9808i | −0.511199 | + | 0.885422i | ||||
\(862\) | −6.00000 | − | 10.3923i | −0.204361 | − | 0.353963i | ||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 6.50000 | + | 11.2583i | 0.221007 | + | 0.382795i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | −8.50000 | − | 14.7224i | −0.288675 | − | 0.500000i | ||||
\(868\) | −9.00000 | + | 15.5885i | −0.305480 | + | 0.529107i | ||||
\(869\) | 9.00000 | − | 15.5885i | 0.305304 | − | 0.528802i | ||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | 8.00000 | + | 27.7128i | 0.271070 | + | 0.939013i | ||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | −4.00000 | + | 6.92820i | −0.135379 | + | 0.234484i | ||||
\(874\) | −6.00000 | + | 10.3923i | −0.202953 | + | 0.351525i | ||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 19.0000 | + | 32.9090i | 0.641584 | + | 1.11126i | 0.985079 | + | 0.172102i | \(0.0550559\pi\) |
−0.343495 | + | 0.939155i | \(0.611611\pi\) | |||||||
\(878\) | −15.0000 | − | 25.9808i | −0.506225 | − | 0.876808i | ||||
\(879\) | 1.00000 | 0.0337292 | ||||||||
\(880\) | −1.50000 | − | 2.59808i | −0.0505650 | − | 0.0875811i | ||||
\(881\) | 11.5000 | − | 19.9186i | 0.387445 | − | 0.671074i | −0.604660 | − | 0.796484i | \(-0.706691\pi\) |
0.992105 | + | 0.125409i | \(0.0400244\pi\) | |||||||
\(882\) | 1.00000 | − | 1.73205i | 0.0336718 | − | 0.0583212i | ||||
\(883\) | 22.0000 | 0.740359 | 0.370179 | − | 0.928960i | \(-0.379296\pi\) | ||||
0.370179 | + | 0.928960i | \(0.379296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | −5.00000 | + | 8.66025i | −0.167978 | + | 0.290947i | ||||
\(887\) | −4.50000 | + | 7.79423i | −0.151095 | + | 0.261705i | −0.931630 | − | 0.363407i | \(-0.881613\pi\) |
0.780535 | + | 0.625112i | \(0.214947\pi\) | |||||||
\(888\) | −4.50000 | − | 7.79423i | −0.151010 | − | 0.261557i | ||||
\(889\) | 9.00000 | 0.301850 | ||||||||
\(890\) | 1.50000 | + | 2.59808i | 0.0502801 | + | 0.0870877i | ||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | −11.0000 | −0.368307 | ||||||||
\(893\) | 4.50000 | + | 7.79423i | 0.150587 | + | 0.260824i | ||||
\(894\) | 1.00000 | − | 1.73205i | 0.0334450 | − | 0.0579284i | ||||
\(895\) | 2.00000 | − | 3.46410i | 0.0668526 | − | 0.115792i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 14.0000 | + | 3.46410i | 0.467446 | + | 0.115663i | ||||
\(898\) | 35.0000 | 1.16797 | ||||||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −30.0000 | −0.998891 | ||||||||
\(903\) | −15.0000 | − | 25.9808i | −0.499169 | − | 0.864586i | ||||
\(904\) | −4.00000 | − | 6.92820i | −0.133038 | − | 0.230429i | ||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | −7.00000 | − | 12.1244i | −0.232559 | − | 0.402805i | ||||
\(907\) | 7.00000 | − | 12.1244i | 0.232431 | − | 0.402583i | −0.726092 | − | 0.687598i | \(-0.758665\pi\) |
0.958523 | + | 0.285015i | \(0.0919986\pi\) | |||||||
\(908\) | 8.00000 | − | 13.8564i | 0.265489 | − | 0.459841i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.50000 | + | 7.79423i | −0.248623 | + | 0.258376i | ||||
\(911\) | 28.0000 | 0.927681 | 0.463841 | − | 0.885919i | \(-0.346471\pi\) | ||||
0.463841 | + | 0.885919i | \(0.346471\pi\) | |||||||
\(912\) | 1.50000 | − | 2.59808i | 0.0496700 | − | 0.0860309i | ||||
\(913\) | 24.0000 | − | 41.5692i | 0.794284 | − | 1.37574i | ||||
\(914\) | −21.0000 | − | 36.3731i | −0.694618 | − | 1.20311i | ||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | 5.00000 | + | 8.66025i | 0.165205 | + | 0.286143i | ||||
\(917\) | 4.50000 | + | 7.79423i | 0.148603 | + | 0.257388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.00000 | − | 12.1244i | −0.230909 | − | 0.399946i | 0.727167 | − | 0.686461i | \(-0.240837\pi\) |
−0.958076 | + | 0.286515i | \(0.907503\pi\) | |||||||
\(920\) | 2.00000 | − | 3.46410i | 0.0659380 | − | 0.114208i | ||||
\(921\) | 13.0000 | − | 22.5167i | 0.428365 | − | 0.741949i | ||||
\(922\) | 32.0000 | 1.05386 | ||||||||
\(923\) | −49.0000 | − | 12.1244i | −1.61285 | − | 0.399078i | ||||
\(924\) | 9.00000 | 0.296078 | ||||||||
\(925\) | −4.50000 | + | 7.79423i | −0.147959 | + | 0.256273i | ||||
\(926\) | −12.0000 | + | 20.7846i | −0.394344 | + | 0.683025i | ||||
\(927\) | 7.50000 | + | 12.9904i | 0.246332 | + | 0.426660i | ||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | −1.00000 | − | 1.73205i | −0.0328089 | − | 0.0568267i | 0.849155 | − | 0.528144i | \(-0.177112\pi\) |
−0.881964 | + | 0.471317i | \(0.843779\pi\) | |||||||
\(930\) | 3.00000 | + | 5.19615i | 0.0983739 | + | 0.170389i | ||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 3.00000 | + | 5.19615i | 0.0982683 | + | 0.170206i | ||||
\(933\) | −2.00000 | + | 3.46410i | −0.0654771 | + | 0.113410i | ||||
\(934\) | 4.00000 | − | 6.92820i | 0.130884 | − | 0.226698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.50000 | − | 0.866025i | −0.114401 | − | 0.0283069i | ||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | −12.0000 | + | 20.7846i | −0.391814 | + | 0.678642i | ||||
\(939\) | 13.0000 | − | 22.5167i | 0.424239 | − | 0.734803i | ||||
\(940\) | −1.50000 | − | 2.59808i | −0.0489246 | − | 0.0847399i | ||||
\(941\) | −32.0000 | −1.04317 | −0.521585 | − | 0.853199i | \(-0.674659\pi\) | ||||
−0.521585 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(942\) | 8.50000 | + | 14.7224i | 0.276945 | + | 0.479683i | ||||
\(943\) | −20.0000 | − | 34.6410i | −0.651290 | − | 1.12807i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | −1.50000 | − | 2.59808i | −0.0487950 | − | 0.0845154i | ||||
\(946\) | 15.0000 | − | 25.9808i | 0.487692 | − | 0.844707i | ||||
\(947\) | −9.00000 | + | 15.5885i | −0.292461 | + | 0.506557i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) |
0.681930 | + | 0.731417i | \(0.261141\pi\) | |||||||
\(948\) | −6.00000 | −0.194871 | ||||||||
\(949\) | 20.0000 | − | 20.7846i | 0.649227 | − | 0.674697i | ||||
\(950\) | −3.00000 | −0.0973329 | ||||||||
\(951\) | 8.50000 | − | 14.7224i | 0.275631 | − | 0.477408i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.0000 | − | 29.4449i | −0.550684 | − | 0.953813i | −0.998225 | − | 0.0595495i | \(-0.981034\pi\) |
0.447541 | − | 0.894263i | \(-0.352300\pi\) | |||||||
\(954\) | −9.00000 | −0.291386 | ||||||||
\(955\) | −3.00000 | − | 5.19615i | −0.0970777 | − | 0.168144i | ||||
\(956\) | 13.0000 | + | 22.5167i | 0.420450 | + | 0.728241i | ||||
\(957\) | −12.0000 | −0.387905 | ||||||||
\(958\) | 6.00000 | + | 10.3923i | 0.193851 | + | 0.335760i | ||||
\(959\) | −18.0000 | + | 31.1769i | −0.581250 | + | 1.00676i | ||||
\(960\) | −0.500000 | + | 0.866025i | −0.0161374 | + | 0.0279508i | ||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −31.5000 | − | 7.79423i | −1.01560 | − | 0.251296i | ||||
\(963\) | 2.00000 | 0.0644491 | ||||||||
\(964\) | −3.50000 | + | 6.06218i | −0.112727 | + | 0.195250i | ||||
\(965\) | 4.00000 | − | 6.92820i | 0.128765 | − | 0.223027i | ||||
\(966\) | 6.00000 | + | 10.3923i | 0.193047 | + | 0.334367i | ||||
\(967\) | 25.0000 | 0.803946 | 0.401973 | − | 0.915652i | \(-0.368325\pi\) | ||||
0.401973 | + | 0.915652i | \(0.368325\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.00000 | 0.256865 | ||||||||
\(971\) | −7.50000 | − | 12.9904i | −0.240686 | − | 0.416881i | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 25.5000 | − | 44.1673i | 0.817492 | − | 1.41594i | ||||
\(974\) | −29.0000 | −0.929220 | ||||||||
\(975\) | 1.00000 | + | 3.46410i | 0.0320256 | + | 0.110940i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 22.0000 | − | 38.1051i | 0.703842 | − | 1.21909i | −0.263265 | − | 0.964723i | \(-0.584799\pi\) |
0.967108 | − | 0.254367i | \(-0.0818672\pi\) | |||||||
\(978\) | −10.0000 | + | 17.3205i | −0.319765 | + | 0.553849i | ||||
\(979\) | −4.50000 | − | 7.79423i | −0.143821 | − | 0.249105i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 1.00000 | + | 1.73205i | 0.0319275 | + | 0.0553001i | ||||
\(982\) | 2.50000 | + | 4.33013i | 0.0797782 | + | 0.138180i | ||||
\(983\) | 55.0000 | 1.75423 | 0.877114 | − | 0.480283i | \(-0.159466\pi\) | ||||
0.877114 | + | 0.480283i | \(0.159466\pi\) | |||||||
\(984\) | 5.00000 | + | 8.66025i | 0.159394 | + | 0.276079i | ||||
\(985\) | 5.50000 | − | 9.52628i | 0.175245 | − | 0.303533i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.00000 | 0.286473 | ||||||||
\(988\) | −3.00000 | − | 10.3923i | −0.0954427 | − | 0.330623i | ||||
\(989\) | 40.0000 | 1.27193 | ||||||||
\(990\) | 1.50000 | − | 2.59808i | 0.0476731 | − | 0.0825723i | ||||
\(991\) | −29.0000 | + | 50.2295i | −0.921215 | + | 1.59559i | −0.123678 | + | 0.992322i | \(0.539469\pi\) |
−0.797537 | + | 0.603269i | \(0.793864\pi\) | |||||||
\(992\) | 3.00000 | + | 5.19615i | 0.0952501 | + | 0.164978i | ||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | −21.0000 | − | 36.3731i | −0.666080 | − | 1.15368i | ||||
\(995\) | −5.00000 | − | 8.66025i | −0.158511 | − | 0.274549i | ||||
\(996\) | −16.0000 | −0.506979 | ||||||||
\(997\) | −23.5000 | − | 40.7032i | −0.744252 | − | 1.28908i | −0.950543 | − | 0.310592i | \(-0.899473\pi\) |
0.206291 | − | 0.978491i | \(-0.433861\pi\) | |||||||
\(998\) | 10.0000 | − | 17.3205i | 0.316544 | − | 0.548271i | ||||
\(999\) | 4.50000 | − | 7.79423i | 0.142374 | − | 0.246598i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 390.2.i.e.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.i.c.451.1 | 2 | |||
5.2 | odd | 4 | 1950.2.z.d.1699.2 | 4 | |||
5.3 | odd | 4 | 1950.2.z.d.1699.1 | 4 | |||
5.4 | even | 2 | 1950.2.i.f.451.1 | 2 | |||
13.3 | even | 3 | inner | 390.2.i.e.211.1 | yes | 2 | |
13.4 | even | 6 | 5070.2.a.r.1.1 | 1 | |||
13.6 | odd | 12 | 5070.2.b.b.1351.2 | 2 | |||
13.7 | odd | 12 | 5070.2.b.b.1351.1 | 2 | |||
13.9 | even | 3 | 5070.2.a.b.1.1 | 1 | |||
39.29 | odd | 6 | 1170.2.i.c.991.1 | 2 | |||
65.3 | odd | 12 | 1950.2.z.d.1849.2 | 4 | |||
65.29 | even | 6 | 1950.2.i.f.601.1 | 2 | |||
65.42 | odd | 12 | 1950.2.z.d.1849.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.e.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
390.2.i.e.211.1 | yes | 2 | 13.3 | even | 3 | inner | |
1170.2.i.c.451.1 | 2 | 3.2 | odd | 2 | |||
1170.2.i.c.991.1 | 2 | 39.29 | odd | 6 | |||
1950.2.i.f.451.1 | 2 | 5.4 | even | 2 | |||
1950.2.i.f.601.1 | 2 | 65.29 | even | 6 | |||
1950.2.z.d.1699.1 | 4 | 5.3 | odd | 4 | |||
1950.2.z.d.1699.2 | 4 | 5.2 | odd | 4 | |||
1950.2.z.d.1849.1 | 4 | 65.42 | odd | 12 | |||
1950.2.z.d.1849.2 | 4 | 65.3 | odd | 12 | |||
5070.2.a.b.1.1 | 1 | 13.9 | even | 3 | |||
5070.2.a.r.1.1 | 1 | 13.4 | even | 6 | |||
5070.2.b.b.1351.1 | 2 | 13.7 | odd | 12 | |||
5070.2.b.b.1351.2 | 2 | 13.6 | odd | 12 |