Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (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: | \(11.0672657201\) |
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 | 793.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.h.991.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 1.73205i | 0.316228 | + | 0.547723i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0.500000 | + | 2.59808i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | 0.799000 | − | 0.601331i | \(-0.205363\pi\) |
−0.920268 | + | 0.391289i | \(0.872029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 2.59808i | 0.344124 | − | 0.596040i | −0.641071 | − | 0.767482i | \(-0.721509\pi\) |
0.985194 | + | 0.171442i | \(0.0548427\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.50000 | − | 0.866025i | −0.472456 | − | 0.163663i | ||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −1.00000 | − | 5.19615i | −0.169031 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 1.50000 | + | 2.59808i | 0.243332 | + | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 1.73205i | 0.158114 | − | 0.273861i | ||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | −3.50000 | + | 6.06218i | −0.510527 | + | 0.884260i | 0.489398 | + | 0.872060i | \(0.337217\pi\) |
−0.999926 | + | 0.0121990i | \(0.996117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 2.00000 | − | 1.73205i | 0.267261 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.500000 | − | 0.866025i | 0.0656532 | − | 0.113715i | ||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | −0.500000 | + | 0.866025i | −0.0606339 | + | 0.105021i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.00000 | + | 1.73205i | 0.597614 | + | 0.207020i | ||||
\(71\) | 5.00000 | 0.593391 | 0.296695 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296695 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | + | 6.92820i | 0.468165 | + | 0.810885i | 0.999338 | − | 0.0363782i | \(-0.0115821\pi\) |
−0.531174 | + | 0.847263i | \(0.678249\pi\) | |||||||
\(74\) | 2.50000 | + | 4.33013i | 0.290619 | + | 0.503367i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | −2.50000 | − | 0.866025i | −0.284901 | − | 0.0986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(80\) | 1.00000 | + | 1.73205i | 0.111803 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.00000 | − | 8.66025i | 0.552158 | − | 0.956365i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.50000 | − | 6.06218i | −0.360997 | − | 0.625266i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 5.50000 | + | 4.33013i | 0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.00000 | − | 5.19615i | 0.295599 | − | 0.511992i | −0.679525 | − | 0.733652i | \(-0.737814\pi\) |
0.975124 | + | 0.221660i | \(0.0711475\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | 1.00000 | − | 1.73205i | 0.0966736 | − | 0.167444i | −0.813632 | − | 0.581380i | \(-0.802513\pi\) |
0.910306 | + | 0.413936i | \(0.135846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | + | 17.3205i | 0.957826 | + | 1.65900i | 0.727764 | + | 0.685828i | \(0.240560\pi\) |
0.230063 | + | 0.973176i | \(0.426107\pi\) | |||||||
\(110\) | 1.00000 | − | 1.73205i | 0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 2.59808i | 0.0472456 | + | 0.245495i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | − | 1.73205i | −0.0932505 | − | 0.161515i | ||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | −2.50000 | − | 0.866025i | −0.229175 | − | 0.0793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 7.00000 | + | 12.1244i | 0.633750 | + | 1.09769i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | − | 7.79423i | −0.130066 | − | 0.675845i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.500000 | − | 0.866025i | −0.0428746 | − | 0.0742611i | ||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0000 | −1.10265 | −0.551323 | − | 0.834292i | \(-0.685877\pi\) | ||||
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | −4.00000 | + | 3.46410i | −0.338062 | + | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.50000 | + | 4.33013i | −0.209795 | + | 0.363376i | ||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | + | 1.73205i | −0.0830455 | + | 0.143839i | ||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.00000 | −0.410997 | ||||||||
\(149\) | 5.50000 | − | 9.52628i | 0.450578 | − | 0.780423i | −0.547844 | − | 0.836580i | \(-0.684551\pi\) |
0.998422 | + | 0.0561570i | \(0.0178847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.50000 | + | 12.9904i | 0.610341 | + | 1.05714i | 0.991183 | + | 0.132502i | \(0.0423010\pi\) |
−0.380841 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(152\) | 1.50000 | − | 2.59808i | 0.121666 | − | 0.210732i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | − | 1.73205i | 0.161165 | − | 0.139573i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.500000 | − | 0.866025i | −0.0399043 | − | 0.0691164i | 0.845383 | − | 0.534160i | \(-0.179372\pi\) |
−0.885288 | + | 0.465044i | \(0.846039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | −0.500000 | − | 2.59808i | −0.0394055 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | + | 8.66025i | −0.391630 | + | 0.678323i | −0.992665 | − | 0.120900i | \(-0.961422\pi\) |
0.601035 | + | 0.799223i | \(0.294755\pi\) | |||||||
\(164\) | 5.00000 | + | 8.66025i | 0.390434 | + | 0.676252i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 1.00000 | − | 1.73205i | 0.0766965 | − | 0.132842i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.500000 | − | 0.866025i | −0.0381246 | − | 0.0660338i | ||||
\(173\) | −7.00000 | + | 12.1244i | −0.532200 | + | 0.921798i | 0.467093 | + | 0.884208i | \(0.345301\pi\) |
−0.999293 | + | 0.0375896i | \(0.988032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | + | 0.866025i | 0.188982 | + | 0.0654654i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | 3.50000 | + | 6.06218i | 0.261602 | + | 0.453108i | 0.966668 | − | 0.256034i | \(-0.0824158\pi\) |
−0.705066 | + | 0.709142i | \(0.749082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 1.00000 | + | 5.19615i | 0.0741249 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −5.00000 | − | 8.66025i | −0.367607 | − | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.500000 | + | 0.866025i | −0.0365636 | + | 0.0633300i | ||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | 4.00000 | − | 6.92820i | 0.289430 | − | 0.501307i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.973674 | + | 0.227946i | \(0.0732010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | − | 6.92820i | −0.287926 | − | 0.498703i | 0.685388 | − | 0.728178i | \(-0.259632\pi\) |
−0.973315 | + | 0.229475i | \(0.926299\pi\) | |||||||
\(194\) | −3.50000 | + | 6.06218i | −0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 27.0000 | 1.92367 | 0.961835 | − | 0.273629i | \(-0.0882242\pi\) | ||||
0.961835 | + | 0.273629i | \(0.0882242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.00000 | + | 1.73205i | 0.0708881 | + | 0.122782i | 0.899291 | − | 0.437351i | \(-0.144083\pi\) |
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.00000 | −0.633238 | ||||||||
\(203\) | −2.00000 | + | 1.73205i | −0.140372 | + | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | + | 17.3205i | −0.698430 | + | 1.20972i | ||||
\(206\) | 3.00000 | + | 5.19615i | 0.209020 | + | 0.362033i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −6.00000 | + | 10.3923i | −0.412082 | + | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.00000 | + | 1.73205i | 0.0683586 | + | 0.118401i | ||||
\(215\) | 1.00000 | − | 1.73205i | 0.0681994 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.00000 | + | 1.73205i | 0.339422 | + | 0.117579i | ||||
\(218\) | −20.0000 | −1.35457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00000 | + | 1.73205i | 0.0674200 | + | 0.116775i | ||||
\(221\) | −1.00000 | − | 1.73205i | −0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0000 | −1.74109 | −0.870544 | − | 0.492090i | \(-0.836233\pi\) | ||||
−0.870544 | + | 0.492090i | \(0.836233\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00000 | + | 8.66025i | −0.332595 | + | 0.576072i | ||||
\(227\) | 5.00000 | + | 8.66025i | 0.331862 | + | 0.574801i | 0.982877 | − | 0.184263i | \(-0.0589899\pi\) |
−0.651015 | + | 0.759065i | \(0.725657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 10.5000 | − | 18.1865i | 0.687878 | − | 1.19144i | −0.284645 | − | 0.958633i | \(-0.591876\pi\) |
0.972523 | − | 0.232806i | \(-0.0747909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | + | 12.1244i | 0.456630 | + | 0.790906i | ||||
\(236\) | 1.50000 | − | 2.59808i | 0.0976417 | − | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | − | 1.73205i | 0.129641 | − | 0.112272i | ||||
\(239\) | −22.0000 | −1.42306 | −0.711531 | − | 0.702655i | \(-0.751998\pi\) | ||||
−0.711531 | + | 0.702655i | \(0.751998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | + | 10.3923i | 0.386494 | + | 0.669427i | 0.991975 | − | 0.126432i | \(-0.0403527\pi\) |
−0.605481 | + | 0.795860i | \(0.707019\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.0000 | −0.896258 | ||||||||
\(245\) | −11.0000 | − | 8.66025i | −0.702764 | − | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 0.500000 | − | 0.866025i | 0.0313728 | − | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 12.9904i | −0.155342 | − | 0.807183i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 5.19615i | 0.184988 | + | 0.320408i | 0.943572 | − | 0.331166i | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0000 | −1.47431 | ||||||||
\(266\) | 7.50000 | + | 2.59808i | 0.459855 | + | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.00000 | + | 10.3923i | −0.366508 | + | 0.634811i | ||||
\(269\) | −6.00000 | − | 10.3923i | −0.365826 | − | 0.633630i | 0.623082 | − | 0.782157i | \(-0.285880\pi\) |
−0.988908 | + | 0.148527i | \(0.952547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0000 | + | 20.7846i | 0.721010 | + | 1.24883i | 0.960595 | + | 0.277951i | \(0.0896552\pi\) |
−0.239585 | + | 0.970875i | \(0.577011\pi\) | |||||||
\(278\) | 6.50000 | − | 11.2583i | 0.389844 | − | 0.675230i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | − | 5.19615i | −0.0597614 | − | 0.310530i | ||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(284\) | −2.50000 | − | 4.33013i | −0.148348 | − | 0.256946i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | −20.0000 | + | 17.3205i | −1.18056 | + | 1.02240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | −1.00000 | − | 1.73205i | −0.0587220 | − | 0.101710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000 | − | 6.92820i | 0.234082 | − | 0.405442i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 2.50000 | − | 4.33013i | 0.145310 | − | 0.251684i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.50000 | + | 9.52628i | 0.318606 | + | 0.551843i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 1.73205i | 0.115278 | − | 0.0998337i | ||||
\(302\) | −15.0000 | −0.863153 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.50000 | + | 2.59808i | 0.0860309 | + | 0.149010i | ||||
\(305\) | −14.0000 | − | 24.2487i | −0.801638 | − | 1.38848i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0.500000 | + | 2.59808i | 0.0284901 | + | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | + | 3.46410i | −0.113592 | + | 0.196748i | ||||
\(311\) | −6.50000 | − | 11.2583i | −0.368581 | − | 0.638401i | 0.620763 | − | 0.783998i | \(-0.286823\pi\) |
−0.989344 | + | 0.145597i | \(0.953490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.50000 | + | 6.06218i | −0.197832 | + | 0.342655i | −0.947825 | − | 0.318791i | \(-0.896723\pi\) |
0.749993 | + | 0.661445i | \(0.230057\pi\) | |||||||
\(314\) | 1.00000 | 0.0564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | + | 0.866025i | 0.0279946 | + | 0.0484881i | ||||
\(320\) | 1.00000 | − | 1.73205i | 0.0559017 | − | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.50000 | + | 0.866025i | 0.139320 | + | 0.0482617i | ||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | + | 1.73205i | 0.0554700 | + | 0.0960769i | ||||
\(326\) | −5.00000 | − | 8.66025i | −0.276924 | − | 0.479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.0000 | −0.552158 | ||||||||
\(329\) | 3.50000 | + | 18.1865i | 0.192961 | + | 1.00266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | − | 1.73205i | 0.0549650 | − | 0.0952021i | −0.837234 | − | 0.546845i | \(-0.815829\pi\) |
0.892199 | + | 0.451643i | \(0.149162\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.00000 | + | 1.73205i | −0.0547176 | + | 0.0947736i | ||||
\(335\) | −24.0000 | −1.31126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000 | + | 1.73205i | 0.0542326 | + | 0.0939336i | ||||
\(341\) | 1.00000 | − | 1.73205i | 0.0541530 | − | 0.0937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.00000 | − | 12.1244i | −0.376322 | − | 0.651809i | ||||
\(347\) | 16.0000 | + | 27.7128i | 0.858925 | + | 1.48770i | 0.872955 | + | 0.487800i | \(0.162201\pi\) |
−0.0140303 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | −0.856460 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | −2.00000 | + | 1.73205i | −0.106904 | + | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | − | 8.66025i | 0.265372 | − | 0.459639i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.00000 | −0.369961 | ||||||||
\(359\) | −5.00000 | + | 8.66025i | −0.263890 | + | 0.457071i | −0.967272 | − | 0.253741i | \(-0.918339\pi\) |
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | 5.00000 | − | 8.66025i | 0.262794 | − | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00000 | − | 1.73205i | −0.262071 | − | 0.0907841i | ||||
\(365\) | 16.0000 | 0.837478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | + | 27.7128i | 0.835193 | + | 1.44660i | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.0000 | 0.519875 | ||||||||
\(371\) | −30.0000 | − | 10.3923i | −1.55752 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | + | 22.5167i | −0.673114 | + | 1.16587i | 0.303902 | + | 0.952703i | \(0.401711\pi\) |
−0.977016 | + | 0.213165i | \(0.931623\pi\) | |||||||
\(374\) | −0.500000 | − | 0.866025i | −0.0258544 | − | 0.0447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.50000 | + | 6.06218i | −0.180499 | + | 0.312633i | ||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | + | 6.92820i | 0.204658 | + | 0.354478i | ||||
\(383\) | −12.5000 | + | 21.6506i | −0.638720 | + | 1.10630i | 0.346994 | + | 0.937867i | \(0.387203\pi\) |
−0.985714 | + | 0.168428i | \(0.946131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | + | 3.46410i | −0.203859 | + | 0.176547i | ||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.50000 | − | 6.06218i | −0.177686 | − | 0.307760i | ||||
\(389\) | 15.0000 | + | 25.9808i | 0.760530 | + | 1.31728i | 0.942578 | + | 0.333987i | \(0.108394\pi\) |
−0.182047 | + | 0.983290i | \(0.558272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | −0.0505722 | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.5000 | + | 23.3827i | −0.680120 | + | 1.17800i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5000 | − | 23.3827i | 0.677546 | − | 1.17354i | −0.298172 | − | 0.954512i | \(-0.596377\pi\) |
0.975718 | − | 0.219031i | \(-0.0702897\pi\) | |||||||
\(398\) | −2.00000 | −0.100251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 12.0000 | − | 20.7846i | 0.599251 | − | 1.03793i | −0.393680 | − | 0.919247i | \(-0.628798\pi\) |
0.992932 | − | 0.118686i | \(-0.0378683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | + | 3.46410i | 0.0996271 | + | 0.172559i | ||||
\(404\) | 4.50000 | − | 7.79423i | 0.223883 | − | 0.387777i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.500000 | − | 2.59808i | −0.0248146 | − | 0.128940i | ||||
\(407\) | −5.00000 | −0.247841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.00000 | − | 13.8564i | −0.395575 | − | 0.685155i | 0.597600 | − | 0.801795i | \(-0.296121\pi\) |
−0.993174 | + | 0.116639i | \(0.962788\pi\) | |||||||
\(410\) | −10.0000 | − | 17.3205i | −0.493865 | − | 0.855399i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.00000 | −0.295599 | ||||||||
\(413\) | 7.50000 | + | 2.59808i | 0.369051 | + | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.50000 | − | 2.59808i | 0.0733674 | − | 0.127076i | ||||
\(419\) | 29.0000 | 1.41674 | 0.708371 | − | 0.705840i | \(-0.249430\pi\) | ||||
0.708371 | + | 0.705840i | \(0.249430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | −0.828529 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(422\) | −2.00000 | + | 3.46410i | −0.0973585 | + | 0.168630i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | − | 10.3923i | −0.291386 | − | 0.504695i | ||||
\(425\) | 0.500000 | − | 0.866025i | 0.0242536 | − | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 36.3731i | −0.338754 | − | 1.76022i | ||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.00000 | + | 1.73205i | 0.0482243 | + | 0.0835269i | ||||
\(431\) | 8.00000 | + | 13.8564i | 0.385346 | + | 0.667440i | 0.991817 | − | 0.127666i | \(-0.0407486\pi\) |
−0.606471 | + | 0.795106i | \(0.707415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | −4.00000 | + | 3.46410i | −0.192006 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | − | 17.3205i | 0.478913 | − | 0.829502i | ||||
\(437\) | −1.50000 | − | 2.59808i | −0.0717547 | − | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5000 | + | 26.8468i | −0.739775 | + | 1.28133i | 0.212822 | + | 0.977091i | \(0.431735\pi\) |
−0.952597 | + | 0.304236i | \(0.901599\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −7.50000 | + | 12.9904i | −0.356336 | + | 0.617192i | −0.987346 | − | 0.158583i | \(-0.949307\pi\) |
0.631010 | + | 0.775775i | \(0.282641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 13.0000 | − | 22.5167i | 0.615568 | − | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | − | 1.73205i | 0.0944911 | − | 0.0818317i | ||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00000 | + | 8.66025i | 0.235441 | + | 0.407795i | ||||
\(452\) | −5.00000 | − | 8.66025i | −0.235180 | − | 0.407344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | −2.00000 | − | 10.3923i | −0.0937614 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0000 | + | 27.7128i | −0.748448 | + | 1.29635i | 0.200118 | + | 0.979772i | \(0.435868\pi\) |
−0.948566 | + | 0.316579i | \(0.897466\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | + | 1.73205i | −0.0466252 | + | 0.0807573i | ||||
\(461\) | 33.0000 | 1.53696 | 0.768482 | − | 0.639872i | \(-0.221013\pi\) | ||||
0.768482 | + | 0.639872i | \(0.221013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0.500000 | − | 0.866025i | 0.0232119 | − | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | −13.5000 | + | 23.3827i | −0.624705 | + | 1.08202i | 0.363892 | + | 0.931441i | \(0.381448\pi\) |
−0.988598 | + | 0.150581i | \(0.951886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0000 | − | 10.3923i | −1.38527 | − | 0.479872i | ||||
\(470\) | −14.0000 | −0.645772 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50000 | + | 2.59808i | 0.0690431 | + | 0.119586i | ||||
\(473\) | −0.500000 | − | 0.866025i | −0.0229900 | − | 0.0398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.00000 | 0.137649 | ||||||||
\(476\) | 0.500000 | + | 2.59808i | 0.0229175 | + | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.0000 | − | 19.0526i | 0.503128 | − | 0.871444i | ||||
\(479\) | 13.0000 | + | 22.5167i | 0.593985 | + | 1.02881i | 0.993689 | + | 0.112168i | \(0.0357796\pi\) |
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | −12.0000 | −0.546585 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.00000 | − | 12.1244i | 0.317854 | − | 0.550539i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.0000 | + | 29.4449i | 0.770344 | + | 1.33427i | 0.937375 | + | 0.348323i | \(0.113249\pi\) |
−0.167031 | + | 0.985952i | \(0.553418\pi\) | |||||||
\(488\) | 7.00000 | − | 12.1244i | 0.316875 | − | 0.548844i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.0000 | − | 5.19615i | 0.587280 | − | 0.234738i | ||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.500000 | + | 0.866025i | 0.0225189 | + | 0.0390038i | ||||
\(494\) | 3.00000 | + | 5.19615i | 0.134976 | + | 0.233786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 10.0000 | − | 8.66025i | 0.448561 | − | 0.388465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | + | 6.92820i | −0.179065 | + | 0.310149i | −0.941560 | − | 0.336844i | \(-0.890640\pi\) |
0.762496 | + | 0.646993i | \(0.223974\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.5000 | − | 18.1865i | 0.468638 | − | 0.811705i | ||||
\(503\) | −42.0000 | −1.87269 | −0.936344 | − | 0.351085i | \(-0.885813\pi\) | ||||
−0.936344 | + | 0.351085i | \(0.885813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0.500000 | − | 0.866025i | 0.0222277 | − | 0.0384995i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.500000 | + | 0.866025i | 0.0221839 | + | 0.0384237i | ||||
\(509\) | 10.0000 | − | 17.3205i | 0.443242 | − | 0.767718i | −0.554686 | − | 0.832060i | \(-0.687161\pi\) |
0.997928 | + | 0.0643419i | \(0.0204948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | + | 6.92820i | 0.884748 | + | 0.306486i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.00000 | + | 5.19615i | 0.132324 | + | 0.229192i | ||||
\(515\) | −6.00000 | − | 10.3923i | −0.264392 | − | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.00000 | 0.307860 | ||||||||
\(518\) | 12.5000 | + | 4.33013i | 0.549218 | + | 0.190255i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | − | 3.46410i | 0.0877058 | − | 0.151911i | ||||
\(521\) | −7.00000 | − | 12.1244i | −0.306676 | − | 0.531178i | 0.670957 | − | 0.741496i | \(-0.265883\pi\) |
−0.977633 | + | 0.210318i | \(0.932550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | − | 3.46410i | 0.0874539 | − | 0.151475i | −0.818980 | − | 0.573822i | \(-0.805460\pi\) |
0.906434 | + | 0.422347i | \(0.138794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | 1.00000 | − | 1.73205i | 0.0435607 | − | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 12.0000 | − | 20.7846i | 0.521247 | − | 0.902826i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | + | 5.19615i | −0.260133 | + | 0.225282i | ||||
\(533\) | −20.0000 | −0.866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.00000 | − | 3.46410i | −0.0864675 | − | 0.149766i | ||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | −6.50000 | + | 2.59808i | −0.279975 | + | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | − | 13.8564i | 0.343947 | − | 0.595733i | −0.641215 | − | 0.767361i | \(-0.721569\pi\) |
0.985162 | + | 0.171628i | \(0.0549027\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.500000 | + | 0.866025i | −0.0214373 | + | 0.0371305i | ||||
\(545\) | 40.0000 | 1.71341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.0000 | 1.66752 | 0.833760 | − | 0.552127i | \(-0.186184\pi\) | ||||
0.833760 | + | 0.552127i | \(0.186184\pi\) | |||||||
\(548\) | −3.00000 | + | 5.19615i | −0.128154 | + | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.500000 | + | 0.866025i | 0.0213201 | + | 0.0369274i | ||||
\(551\) | −1.50000 | + | 2.59808i | −0.0639021 | + | 0.110682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −24.0000 | −1.01966 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | + | 11.2583i | 0.275661 | + | 0.477460i | ||||
\(557\) | 17.5000 | + | 30.3109i | 0.741499 | + | 1.28431i | 0.951813 | + | 0.306680i | \(0.0992180\pi\) |
−0.210314 | + | 0.977634i | \(0.567449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 5.00000 | + | 1.73205i | 0.211289 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.50000 | + | 6.06218i | −0.147639 | + | 0.255718i | ||||
\(563\) | 19.0000 | + | 32.9090i | 0.800755 | + | 1.38695i | 0.919120 | + | 0.393977i | \(0.128901\pi\) |
−0.118366 | + | 0.992970i | \(0.537765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | − | 17.3205i | 0.420703 | − | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.00000 | 0.209795 | ||||||||
\(569\) | 7.50000 | − | 12.9904i | 0.314416 | − | 0.544585i | −0.664897 | − | 0.746935i | \(-0.731525\pi\) |
0.979313 | + | 0.202350i | \(0.0648579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.50000 | − | 6.06218i | −0.146470 | − | 0.253694i | 0.783450 | − | 0.621455i | \(-0.213458\pi\) |
−0.929921 | + | 0.367760i | \(0.880125\pi\) | |||||||
\(572\) | −1.00000 | + | 1.73205i | −0.0418121 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.00000 | − | 25.9808i | −0.208696 | − | 1.08442i | ||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | − | 12.1244i | −0.291414 | − | 0.504744i | 0.682730 | − | 0.730670i | \(-0.260792\pi\) |
−0.974144 | + | 0.225927i | \(0.927459\pi\) | |||||||
\(578\) | 8.00000 | + | 13.8564i | 0.332756 | + | 0.576351i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | −12.0000 | + | 10.3923i | −0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 4.00000 | + | 6.92820i | 0.165521 | + | 0.286691i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | −3.00000 | + | 5.19615i | −0.123508 | + | 0.213922i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50000 | + | 4.33013i | 0.102749 | + | 0.177967i | ||||
\(593\) | −7.50000 | + | 12.9904i | −0.307988 | + | 0.533451i | −0.977922 | − | 0.208970i | \(-0.932989\pi\) |
0.669934 | + | 0.742421i | \(0.266322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 3.46410i | −0.163984 | + | 0.142014i | ||||
\(596\) | −11.0000 | −0.450578 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.00000 | + | 1.73205i | 0.0408930 | + | 0.0708288i | ||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | 0.500000 | + | 2.59808i | 0.0203785 | + | 0.105890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.50000 | − | 12.9904i | 0.305171 | − | 0.528571i | ||||
\(605\) | 1.00000 | + | 1.73205i | 0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | − | 24.2487i | 0.568242 | − | 0.984225i | −0.428497 | − | 0.903543i | \(-0.640957\pi\) |
0.996740 | − | 0.0806818i | \(-0.0257098\pi\) | |||||||
\(608\) | −3.00000 | −0.121666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.0000 | 1.13369 | ||||||||
\(611\) | −7.00000 | + | 12.1244i | −0.283190 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.00000 | + | 12.1244i | 0.282727 | + | 0.489698i | 0.972056 | − | 0.234751i | \(-0.0754275\pi\) |
−0.689328 | + | 0.724449i | \(0.742094\pi\) | |||||||
\(614\) | 2.00000 | − | 3.46410i | 0.0807134 | − | 0.139800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50000 | − | 0.866025i | −0.100728 | − | 0.0348932i | ||||
\(617\) | 36.0000 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | − | 22.5167i | −0.522514 | − | 0.905021i | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
0.477143 | − | 0.878826i | \(-0.341672\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.0000 | 0.521253 | ||||||||
\(623\) | −3.00000 | − | 15.5885i | −0.120192 | − | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −3.50000 | − | 6.06218i | −0.139888 | − | 0.242293i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.500000 | + | 0.866025i | −0.0199522 | + | 0.0345582i | ||||
\(629\) | −5.00000 | −0.199363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | − | 5.19615i | −0.119145 | − | 0.206366i | ||||
\(635\) | −1.00000 | + | 1.73205i | −0.0396838 | + | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 13.8564i | 0.0792429 | − | 0.549011i | ||||
\(638\) | −1.00000 | −0.0395904 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 1.73205i | 0.0395285 | + | 0.0684653i | ||||
\(641\) | 6.00000 | + | 10.3923i | 0.236986 | + | 0.410471i | 0.959848 | − | 0.280521i | \(-0.0905072\pi\) |
−0.722862 | + | 0.690992i | \(0.757174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0000 | −1.26196 | −0.630978 | − | 0.775800i | \(-0.717346\pi\) | ||||
−0.630978 | + | 0.775800i | \(0.717346\pi\) | |||||||
\(644\) | −2.00000 | + | 1.73205i | −0.0788110 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50000 | − | 2.59808i | 0.0590167 | − | 0.102220i | ||||
\(647\) | −24.0000 | − | 41.5692i | −0.943537 | − | 1.63425i | −0.758654 | − | 0.651494i | \(-0.774142\pi\) |
−0.184884 | − | 0.982760i | \(-0.559191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50000 | − | 2.59808i | 0.0588802 | − | 0.101983i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.00000 | − | 8.66025i | 0.195217 | − | 0.338126i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.5000 | − | 6.06218i | −0.682221 | − | 0.236328i | ||||
\(659\) | 44.0000 | 1.71400 | 0.856998 | − | 0.515319i | \(-0.172327\pi\) | ||||
0.856998 | + | 0.515319i | \(0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50000 | − | 4.33013i | −0.0972387 | − | 0.168422i | 0.813302 | − | 0.581842i | \(-0.197668\pi\) |
−0.910541 | + | 0.413419i | \(0.864334\pi\) | |||||||
\(662\) | 1.00000 | + | 1.73205i | 0.0388661 | + | 0.0673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −15.0000 | − | 5.19615i | −0.581675 | − | 0.201498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.500000 | + | 0.866025i | −0.0193601 | + | 0.0335326i | ||||
\(668\) | −1.00000 | − | 1.73205i | −0.0386912 | − | 0.0670151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.0000 | − | 20.7846i | 0.463600 | − | 0.802980i | ||||
\(671\) | −14.0000 | −0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −3.50000 | + | 6.06218i | −0.134516 | + | 0.232988i | −0.925412 | − | 0.378962i | \(-0.876281\pi\) |
0.790897 | + | 0.611950i | \(0.209615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | − | 12.1244i | 0.537271 | − | 0.465290i | ||||
\(680\) | −2.00000 | −0.0766965 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000 | + | 1.73205i | 0.0382920 | + | 0.0663237i | ||||
\(683\) | 19.5000 | + | 33.7750i | 0.746147 | + | 1.29236i | 0.949657 | + | 0.313291i | \(0.101432\pi\) |
−0.203510 | + | 0.979073i | \(0.565235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 18.5000 | − | 0.866025i | 0.706333 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.500000 | + | 0.866025i | −0.0190623 | + | 0.0330169i | ||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | − | 15.5885i | 0.342376 | − | 0.593013i | −0.642497 | − | 0.766288i | \(-0.722102\pi\) |
0.984873 | + | 0.173275i | \(0.0554350\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | −13.0000 | + | 22.5167i | −0.493118 | + | 0.854106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.00000 | + | 8.66025i | 0.189389 | + | 0.328031i | ||||
\(698\) | 8.00000 | − | 13.8564i | 0.302804 | − | 0.524473i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.500000 | − | 2.59808i | −0.0188982 | − | 0.0981981i | ||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.50000 | − | 12.9904i | −0.282868 | − | 0.489942i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 22.5000 | + | 7.79423i | 0.846200 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.50000 | + | 7.79423i | −0.169001 | + | 0.292718i | −0.938069 | − | 0.346449i | \(-0.887387\pi\) |
0.769068 | + | 0.639167i | \(0.220721\pi\) | |||||||
\(710\) | 5.00000 | + | 8.66025i | 0.187647 | + | 0.325014i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 3.50000 | − | 6.06218i | 0.130801 | − | 0.226554i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | −11.5000 | + | 19.9186i | −0.428878 | + | 0.742838i | −0.996774 | − | 0.0802624i | \(-0.974424\pi\) |
0.567896 | + | 0.823100i | \(0.307758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | − | 15.5885i | −0.111726 | − | 0.580544i | ||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | + | 8.66025i | 0.185824 | + | 0.321856i | ||||
\(725\) | −0.500000 | − | 0.866025i | −0.0185695 | − | 0.0321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 4.00000 | − | 3.46410i | 0.148250 | − | 0.128388i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | + | 13.8564i | −0.296093 | + | 0.512849i | ||||
\(731\) | −0.500000 | − | 0.866025i | −0.0184932 | − | 0.0320311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.00000 | − | 8.66025i | 0.184679 | − | 0.319874i | −0.758789 | − | 0.651336i | \(-0.774209\pi\) |
0.943468 | + | 0.331463i | \(0.107542\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0000 | − | 31.1769i | −0.662141 | − | 1.14686i | −0.980052 | − | 0.198741i | \(-0.936315\pi\) |
0.317911 | − | 0.948120i | \(-0.397019\pi\) | |||||||
\(740\) | −5.00000 | + | 8.66025i | −0.183804 | + | 0.318357i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.0000 | − | 20.7846i | 0.881068 | − | 0.763027i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0000 | − | 19.0526i | −0.403009 | − | 0.698032i | ||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −1.00000 | − | 5.19615i | −0.0365392 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | −3.50000 | − | 6.06218i | −0.127632 | − | 0.221065i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.00000 | − | 1.73205i | 0.0364179 | − | 0.0630776i | ||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | 4.00000 | − | 6.92820i | 0.145287 | − | 0.251644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | − | 5.19615i | −0.108821 | − | 0.188484i | ||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.0000 | + | 17.3205i | 1.81012 | + | 0.627044i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.5000 | − | 21.6506i | −0.451643 | − | 0.782269i | ||||
\(767\) | 3.00000 | + | 5.19615i | 0.108324 | + | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.0000 | −0.721218 | −0.360609 | − | 0.932717i | \(-0.617431\pi\) | ||||
−0.360609 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(770\) | −1.00000 | − | 5.19615i | −0.0360375 | − | 0.187256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.00000 | + | 6.92820i | −0.143963 | + | 0.249351i | ||||
\(773\) | −18.0000 | − | 31.1769i | −0.647415 | − | 1.12136i | −0.983738 | − | 0.179609i | \(-0.942517\pi\) |
0.336323 | − | 0.941747i | \(-0.390817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | + | 1.73205i | −0.0359211 | + | 0.0622171i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | −15.0000 | + | 25.9808i | −0.537431 | + | 0.930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.50000 | − | 4.33013i | −0.0894570 | − | 0.154944i | ||||
\(782\) | 0.500000 | − | 0.866025i | 0.0178800 | − | 0.0309690i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5000 | + | 26.8468i | 0.552515 | + | 0.956985i | 0.998092 | + | 0.0617409i | \(0.0196653\pi\) |
−0.445577 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(788\) | −13.5000 | − | 23.3827i | −0.480918 | − | 0.832974i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0000 | − | 17.3205i | 0.711118 | − | 0.615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0000 | − | 24.2487i | 0.497155 | − | 0.861097i | ||||
\(794\) | 13.5000 | + | 23.3827i | 0.479097 | + | 0.829820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00000 | − | 1.73205i | 0.0354441 | − | 0.0613909i | ||||
\(797\) | 22.0000 | 0.779280 | 0.389640 | − | 0.920967i | \(-0.372599\pi\) | ||||
0.389640 | + | 0.920967i | \(0.372599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.00000 | 0.247642 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000 | + | 20.7846i | 0.423735 | + | 0.733930i | ||||
\(803\) | 4.00000 | − | 6.92820i | 0.141157 | − | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.00000 | − | 1.73205i | −0.176227 | − | 0.0610468i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.50000 | + | 7.79423i | 0.158309 | + | 0.274200i | ||||
\(809\) | −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 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 2.50000 | + | 0.866025i | 0.0877328 | + | 0.0303915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.50000 | − | 4.33013i | 0.0876250 | − | 0.151771i | ||||
\(815\) | 10.0000 | + | 17.3205i | 0.350285 | + | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.50000 | − | 2.59808i | 0.0524784 | − | 0.0908952i | ||||
\(818\) | 16.0000 | 0.559427 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | 15.0000 | − | 25.9808i | 0.523504 | − | 0.906735i | −0.476122 | − | 0.879379i | \(-0.657958\pi\) |
0.999626 | − | 0.0273557i | \(-0.00870868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0000 | − | 38.1051i | −0.766872 | − | 1.32826i | −0.939251 | − | 0.343230i | \(-0.888479\pi\) |
0.172379 | − | 0.985031i | \(-0.444854\pi\) | |||||||
\(824\) | 3.00000 | − | 5.19615i | 0.104510 | − | 0.181017i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | + | 5.19615i | −0.208767 | + | 0.180797i | ||||
\(827\) | 34.0000 | 1.18230 | 0.591148 | − | 0.806563i | \(-0.298675\pi\) | ||||
0.591148 | + | 0.806563i | \(0.298675\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.50000 | − | 6.06218i | −0.121560 | − | 0.210548i | 0.798823 | − | 0.601566i | \(-0.205456\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | −6.00000 | − | 10.3923i | −0.208263 | − | 0.360722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −6.50000 | + | 2.59808i | −0.225212 | + | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | − | 3.46410i | 0.0692129 | − | 0.119880i | ||||
\(836\) | 1.50000 | + | 2.59808i | 0.0518786 | + | 0.0898563i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.5000 | + | 25.1147i | −0.500894 | + | 0.867574i | ||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 8.50000 | − | 14.7224i | 0.292929 | − | 0.507369i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.00000 | − | 3.46410i | −0.0688428 | − | 0.119239i | ||||
\(845\) | −9.00000 | + | 15.5885i | −0.309609 | + | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.500000 | + | 2.59808i | 0.0171802 | + | 0.0892710i | ||||
\(848\) | 12.0000 | 0.412082 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.500000 | + | 0.866025i | 0.0171499 | + | 0.0297044i | ||||
\(851\) | −2.50000 | − | 4.33013i | −0.0856989 | − | 0.148435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 35.0000 | + | 12.1244i | 1.19768 | + | 0.414887i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.00000 | − | 1.73205i | 0.0341793 | − | 0.0592003i | ||||
\(857\) | 23.5000 | + | 40.7032i | 0.802745 | + | 1.39039i | 0.917803 | + | 0.397036i | \(0.129961\pi\) |
−0.115058 | + | 0.993359i | \(0.536706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | − | 22.5167i | 0.443554 | − | 0.768259i | −0.554396 | − | 0.832253i | \(-0.687051\pi\) |
0.997950 | + | 0.0639945i | \(0.0203840\pi\) | |||||||
\(860\) | −2.00000 | −0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | −22.0000 | + | 38.1051i | −0.748889 | + | 1.29711i | 0.199467 | + | 0.979905i | \(0.436079\pi\) |
−0.948356 | + | 0.317209i | \(0.897254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | + | 24.2487i | 0.476014 | + | 0.824481i | ||||
\(866\) | 9.50000 | − | 16.4545i | 0.322823 | − | 0.559146i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.00000 | − | 5.19615i | −0.0339422 | − | 0.176369i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | − | 20.7846i | −0.406604 | − | 0.704260i | ||||
\(872\) | 10.0000 | + | 17.3205i | 0.338643 | + | 0.586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.00000 | 0.101477 | ||||||||
\(875\) | 24.0000 | − | 20.7846i | 0.811348 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.00000 | − | 12.1244i | 0.236373 | − | 0.409410i | −0.723298 | − | 0.690536i | \(-0.757375\pi\) |
0.959671 | + | 0.281126i | \(0.0907079\pi\) | |||||||
\(878\) | −15.5000 | − | 26.8468i | −0.523100 | − | 0.906035i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0000 | 1.34611 | 0.673054 | − | 0.739594i | \(-0.264982\pi\) | ||||
0.673054 | + | 0.739594i | \(0.264982\pi\) | |||||||
\(884\) | −1.00000 | + | 1.73205i | −0.0336336 | + | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.50000 | − | 12.9904i | −0.251967 | − | 0.436420i | ||||
\(887\) | −22.0000 | + | 38.1051i | −0.738688 | + | 1.27944i | 0.214399 | + | 0.976746i | \(0.431221\pi\) |
−0.953086 | + | 0.302698i | \(0.902113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.00000 | + | 1.73205i | −0.0670778 | + | 0.0580911i | ||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0000 | + | 22.5167i | 0.435272 | + | 0.753914i | ||||
\(893\) | 10.5000 | + | 18.1865i | 0.351369 | + | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.0000 | 0.467968 | ||||||||
\(896\) | 0.500000 | + | 2.59808i | 0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | − | 10.3923i | 0.200223 | − | 0.346796i | ||||
\(899\) | −1.00000 | − | 1.73205i | −0.0333519 | − | 0.0577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | + | 10.3923i | −0.199889 | + | 0.346218i | ||||
\(902\) | −10.0000 | −0.332964 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | −10.0000 | + | 17.3205i | −0.332411 | + | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | + | 34.6410i | 0.664089 | + | 1.15024i | 0.979531 | + | 0.201291i | \(0.0645138\pi\) |
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(908\) | 5.00000 | − | 8.66025i | 0.165931 | − | 0.287401i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.0000 | + | 3.46410i | 0.331497 | + | 0.114834i | ||||
\(911\) | −45.0000 | −1.49092 | −0.745458 | − | 0.666552i | \(-0.767769\pi\) | ||||
−0.745458 | + | 0.666552i | \(0.767769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.00000 | + | 5.19615i | 0.0992855 | + | 0.171968i | ||||
\(914\) | −16.0000 | − | 27.7128i | −0.529233 | − | 0.916658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5000 | + | 49.3634i | −0.940128 | + | 1.62835i | −0.174905 | + | 0.984585i | \(0.555962\pi\) |
−0.765224 | + | 0.643765i | \(0.777372\pi\) | |||||||
\(920\) | −1.00000 | − | 1.73205i | −0.0329690 | − | 0.0571040i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.5000 | + | 28.5788i | −0.543399 | + | 0.941194i | ||||
\(923\) | 10.0000 | 0.329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | 0.164399 | ||||||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.500000 | + | 0.866025i | 0.0164133 | + | 0.0284287i | ||||
\(929\) | −18.0000 | + | 31.1769i | −0.590561 | + | 1.02288i | 0.403596 | + | 0.914937i | \(0.367760\pi\) |
−0.994157 | + | 0.107944i | \(0.965573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5000 | − | 12.9904i | −0.540766 | − | 0.425743i | ||||
\(932\) | −21.0000 | −0.687878 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.5000 | − | 23.3827i | −0.441733 | − | 0.765105i | ||||
\(935\) | 1.00000 | + | 1.73205i | 0.0327035 | + | 0.0566441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(938\) | 24.0000 | − | 20.7846i | 0.783628 | − | 0.678642i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.00000 | − | 12.1244i | 0.228315 | − | 0.395453i | ||||
\(941\) | −17.5000 | − | 30.3109i | −0.570484 | − | 0.988107i | −0.996516 | − | 0.0833989i | \(-0.973422\pi\) |
0.426033 | − | 0.904708i | \(-0.359911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.00000 | + | 8.66025i | −0.162822 | + | 0.282017i | ||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 26.5000 | − | 45.8993i | 0.861134 | − | 1.49153i | −0.00970072 | − | 0.999953i | \(-0.503088\pi\) |
0.870835 | − | 0.491575i | \(-0.163579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | + | 13.8564i | 0.259691 | + | 0.449798i | ||||
\(950\) | −1.50000 | + | 2.59808i | −0.0486664 | + | 0.0842927i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.50000 | − | 0.866025i | −0.0810255 | − | 0.0280680i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | − | 13.8564i | −0.258874 | − | 0.448383i | ||||
\(956\) | 11.0000 | + | 19.0526i | 0.355765 | + | 0.616204i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.0000 | −0.840022 | ||||||||
\(959\) | −15.0000 | − | 5.19615i | −0.484375 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 5.00000 | + | 8.66025i | 0.161206 | + | 0.279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.00000 | − | 10.3923i | 0.193247 | − | 0.334714i | ||||
\(965\) | −16.0000 | −0.515058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | −0.0321578 | −0.0160789 | − | 0.999871i | \(-0.505118\pi\) | ||||
−0.0160789 | + | 0.999871i | \(0.505118\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.00000 | + | 12.1244i | 0.224756 | + | 0.389290i | ||||
\(971\) | −2.00000 | + | 3.46410i | −0.0641831 | + | 0.111168i | −0.896331 | − | 0.443385i | \(-0.853777\pi\) |
0.832148 | + | 0.554553i | \(0.187111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.0000 | + | 22.5167i | −0.833522 | + | 0.721851i | ||||
\(974\) | −34.0000 | −1.08943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.00000 | + | 12.1244i | 0.224065 | + | 0.388091i | ||||
\(977\) | −14.0000 | − | 24.2487i | −0.447900 | − | 0.775785i | 0.550349 | − | 0.834934i | \(-0.314494\pi\) |
−0.998249 | + | 0.0591494i | \(0.981161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −2.00000 | + | 13.8564i | −0.0638877 | + | 0.442627i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.00000 | − | 5.19615i | 0.0957338 | − | 0.165816i | ||||
\(983\) | −19.5000 | − | 33.7750i | −0.621953 | − | 1.07725i | −0.989122 | − | 0.147100i | \(-0.953006\pi\) |
0.367168 | − | 0.930155i | \(-0.380327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | − | 46.7654i | 0.860292 | − | 1.49007i | ||||
\(986\) | −1.00000 | −0.0318465 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | 0.500000 | − | 0.866025i | 0.0158991 | − | 0.0275380i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | − | 13.8564i | −0.254128 | − | 0.440163i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.964658 | + | 0.263504i | \(0.915122\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.50000 | + | 12.9904i | 0.0792952 | + | 0.412030i | ||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | + | 36.3731i | 0.665077 | + | 1.15195i | 0.979265 | + | 0.202586i | \(0.0649345\pi\) |
−0.314188 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(998\) | −4.00000 | − | 6.92820i | −0.126618 | − | 0.219308i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.k.h.793.1 | ✓ | 2 | |
3.2 | odd | 2 | 1386.2.k.l.793.1 | yes | 2 | ||
7.2 | even | 3 | 9702.2.a.bi.1.1 | 1 | |||
7.4 | even | 3 | inner | 1386.2.k.h.991.1 | yes | 2 | |
7.5 | odd | 6 | 9702.2.a.ca.1.1 | 1 | |||
21.2 | odd | 6 | 9702.2.a.s.1.1 | 1 | |||
21.5 | even | 6 | 9702.2.a.f.1.1 | 1 | |||
21.11 | odd | 6 | 1386.2.k.l.991.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.h.793.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.h.991.1 | yes | 2 | 7.4 | even | 3 | inner | |
1386.2.k.l.793.1 | yes | 2 | 3.2 | odd | 2 | ||
1386.2.k.l.991.1 | yes | 2 | 21.11 | odd | 6 | ||
9702.2.a.f.1.1 | 1 | 21.5 | even | 6 | |||
9702.2.a.s.1.1 | 1 | 21.2 | odd | 6 | |||
9702.2.a.bi.1.1 | 1 | 7.2 | even | 3 | |||
9702.2.a.ca.1.1 | 1 | 7.5 | odd | 6 |