Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(545,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.e (of order \(2\), degree \(1\), 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: | \(4.35983195036\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.2 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.545 |
Dual form | 546.2.e.d.545.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 1.73205i | 0.547723i | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.50000 | + | 0.866025i | 0.433013 | + | 0.250000i | ||||
\(13\) | 1.00000 | + | 3.46410i | 0.277350 | + | 0.960769i | ||||
\(14\) | −2.50000 | − | 0.866025i | −0.668153 | − | 0.231455i | ||||
\(15\) | −1.50000 | + | 2.59808i | −0.387298 | + | 0.670820i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 1.50000 | + | 2.59808i | 0.353553 | + | 0.612372i | ||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | −3.00000 | − | 3.46410i | −0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.46410i | − | 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.50000 | − | 0.866025i | −0.472456 | − | 0.163663i | ||||
\(29\) | − | 6.92820i | − | 1.28654i | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||
0.765641 | − | 0.643268i | \(-0.222422\pi\) | |||||||
\(30\) | −1.50000 | + | 2.59808i | −0.273861 | + | 0.474342i | ||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 1.50000 | − | 4.33013i | 0.253546 | − | 0.731925i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | − | 1.73205i | − | 0.284747i | −0.989813 | − | 0.142374i | \(-0.954527\pi\) | ||
0.989813 | − | 0.142374i | \(-0.0454735\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | −1.50000 | + | 6.06218i | −0.240192 | + | 0.970725i | ||||
\(40\) | 1.73205i | 0.273861i | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | −3.00000 | − | 3.46410i | −0.462910 | − | 0.534522i | ||||
\(43\) | −11.0000 | −1.67748 | −0.838742 | − | 0.544529i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544529i | \(0.816708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.50000 | + | 2.59808i | −0.670820 | + | 0.387298i | ||||
\(46\) | − | 3.46410i | − | 0.510754i | ||||||
\(47\) | − | 12.1244i | − | 1.76852i | −0.466996 | − | 0.884260i | \(-0.654664\pi\) | ||
0.466996 | − | 0.884260i | \(-0.345336\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 4.50000 | + | 2.59808i | 0.630126 | + | 0.363803i | ||||
\(52\) | 1.00000 | + | 3.46410i | 0.138675 | + | 0.480384i | ||||
\(53\) | − | 3.46410i | − | 0.475831i | −0.971286 | − | 0.237915i | \(-0.923536\pi\) | ||
0.971286 | − | 0.237915i | \(-0.0764641\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | 3.00000 | + | 1.73205i | 0.397360 | + | 0.229416i | ||||
\(58\) | − | 6.92820i | − | 0.909718i | ||||||
\(59\) | − | 10.3923i | − | 1.35296i | −0.736460 | − | 0.676481i | \(-0.763504\pi\) | ||
0.736460 | − | 0.676481i | \(-0.236496\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | − | 6.92820i | − | 0.887066i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | −1.50000 | − | 7.79423i | −0.188982 | − | 0.981981i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | + | 1.73205i | −0.744208 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8564i | 1.69283i | 0.532524 | + | 0.846415i | \(0.321244\pi\) | ||||
−0.532524 | + | 0.846415i | \(0.678756\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | 1.50000 | − | 4.33013i | 0.179284 | − | 0.517549i | ||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | 1.50000 | + | 2.59808i | 0.176777 | + | 0.306186i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | − | 1.73205i | − | 0.201347i | ||||||
\(75\) | 3.00000 | + | 1.73205i | 0.346410 | + | 0.200000i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.50000 | + | 6.06218i | −0.169842 | + | 0.686406i | ||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 1.73205i | 0.193649i | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | −3.00000 | − | 3.46410i | −0.327327 | − | 0.377964i | ||||
\(85\) | 5.19615i | 0.563602i | ||||||||
\(86\) | −11.0000 | −1.18616 | ||||||||
\(87\) | 6.00000 | − | 10.3923i | 0.643268 | − | 1.11417i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410i | 0.367194i | 0.983002 | + | 0.183597i | \(0.0587741\pi\) | ||||
−0.983002 | + | 0.183597i | \(0.941226\pi\) | |||||||
\(90\) | −4.50000 | + | 2.59808i | −0.474342 | + | 0.273861i | ||||
\(91\) | 0.500000 | − | 9.52628i | 0.0524142 | − | 0.998625i | ||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | −12.0000 | − | 6.92820i | −1.24434 | − | 0.718421i | ||||
\(94\) | − | 12.1244i | − | 1.25053i | ||||||
\(95\) | 3.46410i | 0.355409i | ||||||||
\(96\) | 1.50000 | + | 0.866025i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 5.50000 | + | 4.33013i | 0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 4.50000 | + | 2.59808i | 0.445566 | + | 0.257248i | ||||
\(103\) | − | 3.46410i | − | 0.341328i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) | ||
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 1.00000 | + | 3.46410i | 0.0980581 | + | 0.339683i | ||||
\(105\) | 6.00000 | − | 5.19615i | 0.585540 | − | 0.507093i | ||||
\(106\) | − | 3.46410i | − | 0.336463i | ||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | 5.19615i | 0.497701i | 0.968542 | + | 0.248851i | \(0.0800528\pi\) | ||||
−0.968542 | + | 0.248851i | \(0.919947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.50000 | − | 2.59808i | 0.142374 | − | 0.246598i | ||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | 3.00000 | + | 1.73205i | 0.280976 | + | 0.162221i | ||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | − | 6.92820i | − | 0.643268i | ||||||
\(117\) | −7.50000 | + | 7.79423i | −0.693375 | + | 0.720577i | ||||
\(118\) | − | 10.3923i | − | 0.956689i | ||||||
\(119\) | −7.50000 | − | 2.59808i | −0.687524 | − | 0.238165i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 6.92820i | − | 0.627250i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.00000 | −0.718421 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −1.50000 | − | 7.79423i | −0.133631 | − | 0.694365i | ||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.5000 | − | 9.52628i | −1.45274 | − | 0.838742i | ||||
\(130\) | −6.00000 | + | 1.73205i | −0.526235 | + | 0.151911i | ||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | − | 1.73205i | −0.433555 | − | 0.150188i | ||||
\(134\) | 13.8564i | 1.19701i | ||||||||
\(135\) | −9.00000 | −0.774597 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 3.00000 | − | 5.19615i | 0.255377 | − | 0.442326i | ||||
\(139\) | − | 19.0526i | − | 1.61602i | −0.589171 | − | 0.808008i | \(-0.700546\pi\) | ||
0.589171 | − | 0.808008i | \(-0.299454\pi\) | |||||||
\(140\) | 1.50000 | − | 4.33013i | 0.126773 | − | 0.365963i | ||||
\(141\) | 10.5000 | − | 18.1865i | 0.884260 | − | 1.53158i | ||||
\(142\) | 9.00000 | 0.755263 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 4.50000 | + | 11.2583i | 0.371154 | + | 0.928571i | ||||
\(148\) | − | 1.73205i | − | 0.142374i | ||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 3.00000 | + | 1.73205i | 0.244949 | + | 0.141421i | ||||
\(151\) | 19.0526i | 1.55048i | 0.631670 | + | 0.775238i | \(0.282370\pi\) | ||||
−0.631670 | + | 0.775238i | \(0.717630\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 13.8564i | − | 1.11297i | ||||||
\(156\) | −1.50000 | + | 6.06218i | −0.120096 | + | 0.485363i | ||||
\(157\) | 10.3923i | 0.829396i | 0.909959 | + | 0.414698i | \(0.136113\pi\) | ||||
−0.909959 | + | 0.414698i | \(0.863887\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 1.73205i | 0.136931i | ||||||||
\(161\) | −3.00000 | + | 8.66025i | −0.236433 | + | 0.682524i | ||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | − | 17.3205i | − | 1.35665i | −0.734763 | − | 0.678323i | \(-0.762707\pi\) | ||
0.734763 | − | 0.678323i | \(-0.237293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.46410i | 0.268866i | ||||||||
\(167\) | − | 3.46410i | − | 0.268060i | −0.990977 | − | 0.134030i | \(-0.957208\pi\) | ||
0.990977 | − | 0.134030i | \(-0.0427919\pi\) | |||||||
\(168\) | −3.00000 | − | 3.46410i | −0.231455 | − | 0.267261i | ||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 5.19615i | 0.398527i | ||||||||
\(171\) | 3.00000 | + | 5.19615i | 0.229416 | + | 0.397360i | ||||
\(172\) | −11.0000 | −0.838742 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 6.00000 | − | 10.3923i | 0.454859 | − | 0.787839i | ||||
\(175\) | −5.00000 | − | 1.73205i | −0.377964 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00000 | − | 15.5885i | 0.676481 | − | 1.17170i | ||||
\(178\) | 3.46410i | 0.259645i | ||||||||
\(179\) | 12.1244i | 0.906217i | 0.891455 | + | 0.453108i | \(0.149685\pi\) | ||||
−0.891455 | + | 0.453108i | \(0.850315\pi\) | |||||||
\(180\) | −4.50000 | + | 2.59808i | −0.335410 | + | 0.193649i | ||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | 0.500000 | − | 9.52628i | 0.0370625 | − | 0.706135i | ||||
\(183\) | 6.00000 | − | 10.3923i | 0.443533 | − | 0.768221i | ||||
\(184\) | − | 3.46410i | − | 0.255377i | ||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | −12.0000 | − | 6.92820i | −0.879883 | − | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 12.1244i | − | 0.884260i | ||||||
\(189\) | 4.50000 | − | 12.9904i | 0.327327 | − | 0.944911i | ||||
\(190\) | 3.46410i | 0.251312i | ||||||||
\(191\) | − | 20.7846i | − | 1.50392i | −0.659208 | − | 0.751961i | \(-0.729108\pi\) | ||
0.659208 | − | 0.751961i | \(-0.270892\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | 17.3205i | 1.24676i | 0.781920 | + | 0.623379i | \(0.214240\pi\) | ||||
−0.781920 | + | 0.623379i | \(0.785760\pi\) | |||||||
\(194\) | 8.00000 | 0.574367 | ||||||||
\(195\) | −10.5000 | − | 2.59808i | −0.751921 | − | 0.186052i | ||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820i | 0.491127i | 0.969380 | + | 0.245564i | \(0.0789730\pi\) | ||||
−0.969380 | + | 0.245564i | \(0.921027\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | −12.0000 | + | 20.7846i | −0.846415 | + | 1.46603i | ||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | −6.00000 | + | 17.3205i | −0.421117 | + | 1.21566i | ||||
\(204\) | 4.50000 | + | 2.59808i | 0.315063 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.46410i | − | 0.241355i | ||||||
\(207\) | 9.00000 | − | 5.19615i | 0.625543 | − | 0.361158i | ||||
\(208\) | 1.00000 | + | 3.46410i | 0.0693375 | + | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | − | 5.19615i | 0.414039 | − | 0.358569i | ||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | − | 3.46410i | − | 0.237915i | ||||||
\(213\) | 13.5000 | + | 7.79423i | 0.925005 | + | 0.534052i | ||||
\(214\) | 10.3923i | 0.710403i | ||||||||
\(215\) | − | 19.0526i | − | 1.29937i | ||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 20.0000 | + | 6.92820i | 1.35769 | + | 0.470317i | ||||
\(218\) | 5.19615i | 0.351928i | ||||||||
\(219\) | −3.00000 | − | 1.73205i | −0.202721 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 10.3923i | 0.201802 | + | 0.699062i | ||||
\(222\) | 1.50000 | − | 2.59808i | 0.100673 | − | 0.174371i | ||||
\(223\) | −7.00000 | −0.468755 | −0.234377 | − | 0.972146i | \(-0.575305\pi\) | ||||
−0.234377 | + | 0.972146i | \(0.575305\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | 3.00000 | + | 5.19615i | 0.200000 | + | 0.346410i | ||||
\(226\) | − | 6.92820i | − | 0.460857i | ||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 3.00000 | + | 1.73205i | 0.198680 | + | 0.114708i | ||||
\(229\) | −5.00000 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.92820i | − | 0.454859i | ||||||
\(233\) | 8.66025i | 0.567352i | 0.958920 | + | 0.283676i | \(0.0915540\pi\) | ||||
−0.958920 | + | 0.283676i | \(0.908446\pi\) | |||||||
\(234\) | −7.50000 | + | 7.79423i | −0.490290 | + | 0.509525i | ||||
\(235\) | 21.0000 | 1.36989 | ||||||||
\(236\) | − | 10.3923i | − | 0.676481i | ||||||
\(237\) | 15.0000 | + | 8.66025i | 0.974355 | + | 0.562544i | ||||
\(238\) | −7.50000 | − | 2.59808i | −0.486153 | − | 0.168408i | ||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | −1.50000 | + | 2.59808i | −0.0968246 | + | 0.167705i | ||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | −7.50000 | + | 9.52628i | −0.479157 | + | 0.608612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | + | 6.92820i | 0.127257 | + | 0.440831i | ||||
\(248\) | −8.00000 | −0.508001 | ||||||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 12.1244i | 0.766812i | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −1.50000 | − | 7.79423i | −0.0944911 | − | 0.490990i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.00000 | −0.125491 | ||||||||
\(255\) | −4.50000 | + | 7.79423i | −0.281801 | + | 0.488094i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.0000 | 1.30994 | 0.654972 | − | 0.755653i | \(-0.272680\pi\) | ||||
0.654972 | + | 0.755653i | \(0.272680\pi\) | |||||||
\(258\) | −16.5000 | − | 9.52628i | −1.02725 | − | 0.593080i | ||||
\(259\) | −1.50000 | + | 4.33013i | −0.0932055 | + | 0.269061i | ||||
\(260\) | −6.00000 | + | 1.73205i | −0.372104 | + | 0.107417i | ||||
\(261\) | 18.0000 | − | 10.3923i | 1.11417 | − | 0.643268i | ||||
\(262\) | −15.0000 | −0.926703 | ||||||||
\(263\) | 13.8564i | 0.854423i | 0.904152 | + | 0.427211i | \(0.140504\pi\) | ||||
−0.904152 | + | 0.427211i | \(0.859496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −5.00000 | − | 1.73205i | −0.306570 | − | 0.106199i | ||||
\(267\) | −3.00000 | + | 5.19615i | −0.183597 | + | 0.317999i | ||||
\(268\) | 13.8564i | 0.846415i | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | −9.00000 | −0.547723 | ||||||||
\(271\) | −1.00000 | −0.0607457 | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 9.00000 | − | 13.8564i | 0.544705 | − | 0.838628i | ||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | ||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | − | 19.0526i | − | 1.14270i | ||||||
\(279\) | −12.0000 | − | 20.7846i | −0.718421 | − | 1.24434i | ||||
\(280\) | 1.50000 | − | 4.33013i | 0.0896421 | − | 0.258775i | ||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 10.5000 | − | 18.1865i | 0.625266 | − | 1.08299i | ||||
\(283\) | 10.3923i | 0.617758i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) | ||||
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(284\) | 9.00000 | 0.534052 | ||||||||
\(285\) | −3.00000 | + | 5.19615i | −0.177705 | + | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 12.0000 | 0.704664 | ||||||||
\(291\) | 12.0000 | + | 6.92820i | 0.703452 | + | 0.406138i | ||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | 19.0526i | 1.11306i | 0.830827 | + | 0.556531i | \(0.187868\pi\) | ||||
−0.830827 | + | 0.556531i | \(0.812132\pi\) | |||||||
\(294\) | 4.50000 | + | 11.2583i | 0.262445 | + | 0.656599i | ||||
\(295\) | 18.0000 | 1.04800 | ||||||||
\(296\) | − | 1.73205i | − | 0.100673i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 12.0000 | − | 3.46410i | 0.693978 | − | 0.200334i | ||||
\(300\) | 3.00000 | + | 1.73205i | 0.173205 | + | 0.100000i | ||||
\(301\) | 27.5000 | + | 9.52628i | 1.58507 | + | 0.549086i | ||||
\(302\) | 19.0526i | 1.09635i | ||||||||
\(303\) | −18.0000 | − | 10.3923i | −1.03407 | − | 0.597022i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 4.50000 | + | 7.79423i | 0.257248 | + | 0.445566i | ||||
\(307\) | −14.0000 | −0.799022 | −0.399511 | − | 0.916728i | \(-0.630820\pi\) | ||||
−0.399511 | + | 0.916728i | \(0.630820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.00000 | − | 5.19615i | 0.170664 | − | 0.295599i | ||||
\(310\) | − | 13.8564i | − | 0.786991i | ||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | −1.50000 | + | 6.06218i | −0.0849208 | + | 0.343203i | ||||
\(313\) | − | 8.66025i | − | 0.489506i | −0.969585 | − | 0.244753i | \(-0.921293\pi\) | ||
0.969585 | − | 0.244753i | \(-0.0787070\pi\) | |||||||
\(314\) | 10.3923i | 0.586472i | ||||||||
\(315\) | 13.5000 | − | 2.59808i | 0.760639 | − | 0.146385i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 3.00000 | − | 5.19615i | 0.168232 | − | 0.291386i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.73205i | 0.0968246i | ||||||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | −3.00000 | + | 8.66025i | −0.167183 | + | 0.482617i | ||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | 2.00000 | + | 6.92820i | 0.110940 | + | 0.384308i | ||||
\(326\) | − | 17.3205i | − | 0.959294i | ||||||
\(327\) | −4.50000 | + | 7.79423i | −0.248851 | + | 0.431022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5000 | + | 30.3109i | −0.578884 | + | 1.67109i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.3205i | − | 0.952021i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) | ||
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 3.46410i | 0.190117i | ||||||||
\(333\) | 4.50000 | − | 2.59808i | 0.246598 | − | 0.142374i | ||||
\(334\) | − | 3.46410i | − | 0.189547i | ||||||
\(335\) | −24.0000 | −1.31126 | ||||||||
\(336\) | −3.00000 | − | 3.46410i | −0.163663 | − | 0.188982i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | −11.0000 | + | 6.92820i | −0.598321 | + | 0.376845i | ||||
\(339\) | 6.00000 | − | 10.3923i | 0.325875 | − | 0.564433i | ||||
\(340\) | 5.19615i | 0.281801i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.00000 | + | 5.19615i | 0.162221 | + | 0.280976i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −11.0000 | −0.593080 | ||||||||
\(345\) | 9.00000 | + | 5.19615i | 0.484544 | + | 0.279751i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | 15.5885i | 0.836832i | 0.908255 | + | 0.418416i | \(0.137415\pi\) | ||||
−0.908255 | + | 0.418416i | \(0.862585\pi\) | |||||||
\(348\) | 6.00000 | − | 10.3923i | 0.321634 | − | 0.557086i | ||||
\(349\) | 1.00000 | 0.0535288 | 0.0267644 | − | 0.999642i | \(-0.491480\pi\) | ||||
0.0267644 | + | 0.999642i | \(0.491480\pi\) | |||||||
\(350\) | −5.00000 | − | 1.73205i | −0.267261 | − | 0.0925820i | ||||
\(351\) | −18.0000 | + | 5.19615i | −0.960769 | + | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3923i | 0.553127i | 0.960996 | + | 0.276563i | \(0.0891955\pi\) | ||||
−0.960996 | + | 0.276563i | \(0.910804\pi\) | |||||||
\(354\) | 9.00000 | − | 15.5885i | 0.478345 | − | 0.828517i | ||||
\(355\) | 15.5885i | 0.827349i | ||||||||
\(356\) | 3.46410i | 0.183597i | ||||||||
\(357\) | −9.00000 | − | 10.3923i | −0.476331 | − | 0.550019i | ||||
\(358\) | 12.1244i | 0.640792i | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −4.50000 | + | 2.59808i | −0.237171 | + | 0.136931i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 3.46410i | 0.182069i | ||||||||
\(363\) | −16.5000 | − | 9.52628i | −0.866025 | − | 0.500000i | ||||
\(364\) | 0.500000 | − | 9.52628i | 0.0262071 | − | 0.499313i | ||||
\(365\) | − | 3.46410i | − | 0.181319i | ||||||
\(366\) | 6.00000 | − | 10.3923i | 0.313625 | − | 0.543214i | ||||
\(367\) | 34.6410i | 1.80825i | 0.427272 | + | 0.904123i | \(0.359475\pi\) | ||||
−0.427272 | + | 0.904123i | \(0.640525\pi\) | |||||||
\(368\) | − | 3.46410i | − | 0.180579i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.00000 | 0.155963 | ||||||||
\(371\) | −3.00000 | + | 8.66025i | −0.155752 | + | 0.449618i | ||||
\(372\) | −12.0000 | − | 6.92820i | −0.622171 | − | 0.359211i | ||||
\(373\) | 16.0000 | 0.828449 | 0.414224 | − | 0.910175i | \(-0.364053\pi\) | ||||
0.414224 | + | 0.910175i | \(0.364053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5000 | + | 18.1865i | −0.542218 | + | 0.939149i | ||||
\(376\) | − | 12.1244i | − | 0.625266i | ||||||
\(377\) | 24.0000 | − | 6.92820i | 1.23606 | − | 0.356821i | ||||
\(378\) | 4.50000 | − | 12.9904i | 0.231455 | − | 0.668153i | ||||
\(379\) | − | 17.3205i | − | 0.889695i | −0.895606 | − | 0.444847i | \(-0.853258\pi\) | ||
0.895606 | − | 0.444847i | \(-0.146742\pi\) | |||||||
\(380\) | 3.46410i | 0.177705i | ||||||||
\(381\) | −3.00000 | − | 1.73205i | −0.153695 | − | 0.0887357i | ||||
\(382\) | − | 20.7846i | − | 1.06343i | ||||||
\(383\) | − | 5.19615i | − | 0.265511i | −0.991149 | − | 0.132755i | \(-0.957617\pi\) | ||
0.991149 | − | 0.132755i | \(-0.0423825\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3205i | 0.881591i | ||||||||
\(387\) | −16.5000 | − | 28.5788i | −0.838742 | − | 1.45274i | ||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | − | 10.3923i | − | 0.526911i | −0.964672 | − | 0.263455i | \(-0.915138\pi\) | ||
0.964672 | − | 0.263455i | \(-0.0848622\pi\) | |||||||
\(390\) | −10.5000 | − | 2.59808i | −0.531688 | − | 0.131559i | ||||
\(391\) | − | 10.3923i | − | 0.525561i | ||||||
\(392\) | 5.50000 | + | 4.33013i | 0.277792 | + | 0.218704i | ||||
\(393\) | −22.5000 | − | 12.9904i | −1.13497 | − | 0.655278i | ||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | 17.3205i | 0.871489i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 6.92820i | 0.347279i | ||||||||
\(399\) | −6.00000 | − | 6.92820i | −0.300376 | − | 0.346844i | ||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | −12.0000 | + | 20.7846i | −0.598506 | + | 1.03664i | ||||
\(403\) | −8.00000 | − | 27.7128i | −0.398508 | − | 1.38047i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | −13.5000 | − | 7.79423i | −0.670820 | − | 0.387298i | ||||
\(406\) | −6.00000 | + | 17.3205i | −0.297775 | + | 0.859602i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.50000 | + | 2.59808i | 0.222783 | + | 0.128624i | ||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.0000 | + | 15.5885i | 1.33181 | + | 0.768922i | ||||
\(412\) | − | 3.46410i | − | 0.170664i | ||||||
\(413\) | −9.00000 | + | 25.9808i | −0.442861 | + | 1.27843i | ||||
\(414\) | 9.00000 | − | 5.19615i | 0.442326 | − | 0.255377i | ||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 1.00000 | + | 3.46410i | 0.0490290 | + | 0.169842i | ||||
\(417\) | 16.5000 | − | 28.5788i | 0.808008 | − | 1.39951i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.0000 | −1.31904 | −0.659518 | − | 0.751689i | \(-0.729240\pi\) | ||||
−0.659518 | + | 0.751689i | \(0.729240\pi\) | |||||||
\(420\) | 6.00000 | − | 5.19615i | 0.292770 | − | 0.253546i | ||||
\(421\) | 32.9090i | 1.60388i | 0.597401 | + | 0.801942i | \(0.296200\pi\) | ||||
−0.597401 | + | 0.801942i | \(0.703800\pi\) | |||||||
\(422\) | −13.0000 | −0.632830 | ||||||||
\(423\) | 31.5000 | − | 18.1865i | 1.53158 | − | 0.884260i | ||||
\(424\) | − | 3.46410i | − | 0.168232i | ||||||
\(425\) | 6.00000 | 0.291043 | ||||||||
\(426\) | 13.5000 | + | 7.79423i | 0.654077 | + | 0.377632i | ||||
\(427\) | −6.00000 | + | 17.3205i | −0.290360 | + | 0.838198i | ||||
\(428\) | 10.3923i | 0.502331i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 19.0526i | − | 0.918796i | ||||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | 5.19615i | 0.249711i | 0.992175 | + | 0.124856i | \(0.0398468\pi\) | ||||
−0.992175 | + | 0.124856i | \(0.960153\pi\) | |||||||
\(434\) | 20.0000 | + | 6.92820i | 0.960031 | + | 0.332564i | ||||
\(435\) | 18.0000 | + | 10.3923i | 0.863034 | + | 0.498273i | ||||
\(436\) | 5.19615i | 0.248851i | ||||||||
\(437\) | − | 6.92820i | − | 0.331421i | ||||||
\(438\) | −3.00000 | − | 1.73205i | −0.143346 | − | 0.0827606i | ||||
\(439\) | − | 31.1769i | − | 1.48799i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||
0.668184 | − | 0.743996i | \(-0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 3.00000 | + | 10.3923i | 0.142695 | + | 0.494312i | ||||
\(443\) | − | 22.5167i | − | 1.06980i | −0.844916 | − | 0.534899i | \(-0.820349\pi\) | ||
0.844916 | − | 0.534899i | \(-0.179651\pi\) | |||||||
\(444\) | 1.50000 | − | 2.59808i | 0.0711868 | − | 0.123299i | ||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −7.00000 | −0.331460 | ||||||||
\(447\) | 9.00000 | + | 5.19615i | 0.425685 | + | 0.245770i | ||||
\(448\) | −2.50000 | − | 0.866025i | −0.118114 | − | 0.0409159i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.92820i | − | 0.325875i | ||||||
\(453\) | −16.5000 | + | 28.5788i | −0.775238 | + | 1.34275i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.5000 | + | 0.866025i | 0.773532 | + | 0.0405999i | ||||
\(456\) | 3.00000 | + | 1.73205i | 0.140488 | + | 0.0811107i | ||||
\(457\) | 10.3923i | 0.486132i | 0.970010 | + | 0.243066i | \(0.0781531\pi\) | ||||
−0.970010 | + | 0.243066i | \(0.921847\pi\) | |||||||
\(458\) | −5.00000 | −0.233635 | ||||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | 6.00000 | 0.279751 | ||||||||
\(461\) | 5.19615i | 0.242009i | 0.992652 | + | 0.121004i | \(0.0386115\pi\) | ||||
−0.992652 | + | 0.121004i | \(0.961388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | − | 6.92820i | − | 0.321634i | ||||||
\(465\) | 12.0000 | − | 20.7846i | 0.556487 | − | 0.963863i | ||||
\(466\) | 8.66025i | 0.401179i | ||||||||
\(467\) | 36.0000 | 1.66588 | 0.832941 | − | 0.553362i | \(-0.186655\pi\) | ||||
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(468\) | −7.50000 | + | 7.79423i | −0.346688 | + | 0.360288i | ||||
\(469\) | 12.0000 | − | 34.6410i | 0.554109 | − | 1.59957i | ||||
\(470\) | 21.0000 | 0.968658 | ||||||||
\(471\) | −9.00000 | + | 15.5885i | −0.414698 | + | 0.718278i | ||||
\(472\) | − | 10.3923i | − | 0.478345i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15.0000 | + | 8.66025i | 0.688973 | + | 0.397779i | ||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −7.50000 | − | 2.59808i | −0.343762 | − | 0.119083i | ||||
\(477\) | 9.00000 | − | 5.19615i | 0.412082 | − | 0.237915i | ||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | − | 32.9090i | − | 1.50365i | −0.659363 | − | 0.751825i | \(-0.729174\pi\) | ||
0.659363 | − | 0.751825i | \(-0.270826\pi\) | |||||||
\(480\) | −1.50000 | + | 2.59808i | −0.0684653 | + | 0.118585i | ||||
\(481\) | 6.00000 | − | 1.73205i | 0.273576 | − | 0.0789747i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | −12.0000 | + | 10.3923i | −0.546019 | + | 0.472866i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 13.8564i | 0.629187i | ||||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | − | 24.2487i | − | 1.09881i | −0.835555 | − | 0.549407i | \(-0.814854\pi\) | ||
0.835555 | − | 0.549407i | \(-0.185146\pi\) | |||||||
\(488\) | − | 6.92820i | − | 0.313625i | ||||||
\(489\) | 15.0000 | − | 25.9808i | 0.678323 | − | 1.17489i | ||||
\(490\) | −7.50000 | + | 9.52628i | −0.338815 | + | 0.430353i | ||||
\(491\) | 36.3731i | 1.64149i | 0.571292 | + | 0.820747i | \(0.306442\pi\) | ||||
−0.571292 | + | 0.820747i | \(0.693558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.7846i | − | 0.936092i | ||||||
\(494\) | 2.00000 | + | 6.92820i | 0.0899843 | + | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | −22.5000 | − | 7.79423i | −1.00926 | − | 0.349619i | ||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | 20.7846i | 0.930447i | 0.885193 | + | 0.465223i | \(0.154026\pi\) | ||||
−0.885193 | + | 0.465223i | \(0.845974\pi\) | |||||||
\(500\) | 12.1244i | 0.542218i | ||||||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | −1.50000 | − | 7.79423i | −0.0668153 | − | 0.347183i | ||||
\(505\) | − | 20.7846i | − | 0.924903i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.5000 | + | 0.866025i | −0.999260 | + | 0.0384615i | ||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | − | 27.7128i | − | 1.22835i | −0.789170 | − | 0.614174i | \(-0.789489\pi\) | ||
0.789170 | − | 0.614174i | \(-0.210511\pi\) | |||||||
\(510\) | −4.50000 | + | 7.79423i | −0.199263 | + | 0.345134i | ||||
\(511\) | 5.00000 | + | 1.73205i | 0.221187 | + | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.3923i | 0.458831i | ||||||||
\(514\) | 21.0000 | 0.926270 | ||||||||
\(515\) | 6.00000 | 0.264392 | ||||||||
\(516\) | −16.5000 | − | 9.52628i | −0.726372 | − | 0.419371i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.50000 | + | 4.33013i | −0.0659062 | + | 0.190255i | ||||
\(519\) | −9.00000 | − | 5.19615i | −0.395056 | − | 0.228086i | ||||
\(520\) | −6.00000 | + | 1.73205i | −0.263117 | + | 0.0759555i | ||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 18.0000 | − | 10.3923i | 0.787839 | − | 0.454859i | ||||
\(523\) | − | 17.3205i | − | 0.757373i | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||
0.925525 | − | 0.378686i | \(-0.123624\pi\) | |||||||
\(524\) | −15.0000 | −0.655278 | ||||||||
\(525\) | −6.00000 | − | 6.92820i | −0.261861 | − | 0.302372i | ||||
\(526\) | 13.8564i | 0.604168i | ||||||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | 27.0000 | − | 15.5885i | 1.17170 | − | 0.676481i | ||||
\(532\) | −5.00000 | − | 1.73205i | −0.216777 | − | 0.0750939i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | −18.0000 | −0.778208 | ||||||||
\(536\) | 13.8564i | 0.598506i | ||||||||
\(537\) | −10.5000 | + | 18.1865i | −0.453108 | + | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.00000 | −0.387298 | ||||||||
\(541\) | − | 19.0526i | − | 0.819133i | −0.912280 | − | 0.409567i | \(-0.865680\pi\) | ||
0.912280 | − | 0.409567i | \(-0.134320\pi\) | |||||||
\(542\) | −1.00000 | −0.0429537 | ||||||||
\(543\) | −3.00000 | + | 5.19615i | −0.128742 | + | 0.222988i | ||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | −9.00000 | −0.385518 | ||||||||
\(546\) | 9.00000 | − | 13.8564i | 0.385164 | − | 0.592999i | ||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | 18.0000 | 0.768922 | ||||||||
\(549\) | 18.0000 | − | 10.3923i | 0.768221 | − | 0.443533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8564i | − | 0.590303i | ||||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | −25.0000 | − | 8.66025i | −1.06311 | − | 0.368271i | ||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 4.50000 | + | 2.59808i | 0.191014 | + | 0.110282i | ||||
\(556\) | − | 19.0526i | − | 0.808008i | ||||||
\(557\) | −33.0000 | −1.39825 | −0.699127 | − | 0.714997i | \(-0.746428\pi\) | ||||
−0.699127 | + | 0.714997i | \(0.746428\pi\) | |||||||
\(558\) | −12.0000 | − | 20.7846i | −0.508001 | − | 0.879883i | ||||
\(559\) | −11.0000 | − | 38.1051i | −0.465250 | − | 1.61167i | ||||
\(560\) | 1.50000 | − | 4.33013i | 0.0633866 | − | 0.182981i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.0000 | 1.26547 | ||||||||
\(563\) | −21.0000 | −0.885044 | −0.442522 | − | 0.896758i | \(-0.645916\pi\) | ||||
−0.442522 | + | 0.896758i | \(0.645916\pi\) | |||||||
\(564\) | 10.5000 | − | 18.1865i | 0.442130 | − | 0.765791i | ||||
\(565\) | 12.0000 | 0.504844 | ||||||||
\(566\) | 10.3923i | 0.436821i | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | − | 32.9090i | − | 1.37962i | −0.723993 | − | 0.689808i | \(-0.757695\pi\) | ||
0.723993 | − | 0.689808i | \(-0.242305\pi\) | |||||||
\(570\) | −3.00000 | + | 5.19615i | −0.125656 | + | 0.217643i | ||||
\(571\) | 13.0000 | 0.544033 | 0.272017 | − | 0.962293i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962293i | \(0.412309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | − | 31.1769i | 0.751961 | − | 1.30243i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.92820i | − | 0.288926i | ||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −46.0000 | −1.91501 | −0.957503 | − | 0.288425i | \(-0.906868\pi\) | ||||
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −15.0000 | + | 25.9808i | −0.623379 | + | 1.07972i | ||||
\(580\) | 12.0000 | 0.498273 | ||||||||
\(581\) | 3.00000 | − | 8.66025i | 0.124461 | − | 0.359288i | ||||
\(582\) | 12.0000 | + | 6.92820i | 0.497416 | + | 0.287183i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | −13.5000 | − | 12.9904i | −0.558156 | − | 0.537086i | ||||
\(586\) | 19.0526i | 0.787054i | ||||||||
\(587\) | 38.1051i | 1.57277i | 0.617739 | + | 0.786383i | \(0.288049\pi\) | ||||
−0.617739 | + | 0.786383i | \(0.711951\pi\) | |||||||
\(588\) | 4.50000 | + | 11.2583i | 0.185577 | + | 0.464286i | ||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 18.0000 | 0.741048 | ||||||||
\(591\) | −22.5000 | − | 12.9904i | −0.925526 | − | 0.534353i | ||||
\(592\) | − | 1.73205i | − | 0.0711868i | ||||||
\(593\) | − | 48.4974i | − | 1.99155i | −0.0918243 | − | 0.995775i | \(-0.529270\pi\) | ||
0.0918243 | − | 0.995775i | \(-0.470730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | − | 12.9904i | 0.184482 | − | 0.532554i | ||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | −6.00000 | + | 10.3923i | −0.245564 | + | 0.425329i | ||||
\(598\) | 12.0000 | − | 3.46410i | 0.490716 | − | 0.141658i | ||||
\(599\) | 24.2487i | 0.990775i | 0.868672 | + | 0.495388i | \(0.164974\pi\) | ||||
−0.868672 | + | 0.495388i | \(0.835026\pi\) | |||||||
\(600\) | 3.00000 | + | 1.73205i | 0.122474 | + | 0.0707107i | ||||
\(601\) | − | 5.19615i | − | 0.211955i | −0.994369 | − | 0.105978i | \(-0.966203\pi\) | ||
0.994369 | − | 0.105978i | \(-0.0337972\pi\) | |||||||
\(602\) | 27.5000 | + | 9.52628i | 1.12082 | + | 0.388262i | ||||
\(603\) | −36.0000 | + | 20.7846i | −1.46603 | + | 0.846415i | ||||
\(604\) | 19.0526i | 0.775238i | ||||||||
\(605\) | − | 19.0526i | − | 0.774597i | ||||||
\(606\) | −18.0000 | − | 10.3923i | −0.731200 | − | 0.422159i | ||||
\(607\) | 24.2487i | 0.984225i | 0.870532 | + | 0.492112i | \(0.163775\pi\) | ||||
−0.870532 | + | 0.492112i | \(0.836225\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −24.0000 | + | 20.7846i | −0.972529 | + | 0.842235i | ||||
\(610\) | 12.0000 | 0.485866 | ||||||||
\(611\) | 42.0000 | − | 12.1244i | 1.69914 | − | 0.490499i | ||||
\(612\) | 4.50000 | + | 7.79423i | 0.181902 | + | 0.315063i | ||||
\(613\) | − | 6.92820i | − | 0.279827i | −0.990164 | − | 0.139914i | \(-0.955317\pi\) | ||
0.990164 | − | 0.139914i | \(-0.0446825\pi\) | |||||||
\(614\) | −14.0000 | −0.564994 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 3.00000 | − | 5.19615i | 0.120678 | − | 0.209020i | ||||
\(619\) | −40.0000 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(620\) | − | 13.8564i | − | 0.556487i | ||||||
\(621\) | 18.0000 | 0.722315 | ||||||||
\(622\) | 30.0000 | 1.20289 | ||||||||
\(623\) | 3.00000 | − | 8.66025i | 0.120192 | − | 0.346966i | ||||
\(624\) | −1.50000 | + | 6.06218i | −0.0600481 | + | 0.242681i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | − | 8.66025i | − | 0.346133i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3923i | 0.414698i | ||||||||
\(629\) | − | 5.19615i | − | 0.207184i | ||||||
\(630\) | 13.5000 | − | 2.59808i | 0.537853 | − | 0.103510i | ||||
\(631\) | 22.5167i | 0.896374i | 0.893940 | + | 0.448187i | \(0.147930\pi\) | ||||
−0.893940 | + | 0.448187i | \(0.852070\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | −19.5000 | − | 11.2583i | −0.775055 | − | 0.447478i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | − | 3.46410i | − | 0.137469i | ||||||
\(636\) | 3.00000 | − | 5.19615i | 0.118958 | − | 0.206041i | ||||
\(637\) | −9.50000 | + | 23.3827i | −0.376404 | + | 0.926456i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5000 | + | 23.3827i | 0.534052 | + | 0.925005i | ||||
\(640\) | 1.73205i | 0.0684653i | ||||||||
\(641\) | − | 34.6410i | − | 1.36824i | −0.729370 | − | 0.684119i | \(-0.760187\pi\) | ||
0.729370 | − | 0.684119i | \(-0.239813\pi\) | |||||||
\(642\) | −9.00000 | + | 15.5885i | −0.355202 | + | 0.615227i | ||||
\(643\) | 40.0000 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | −3.00000 | + | 8.66025i | −0.118217 | + | 0.341262i | ||||
\(645\) | 16.5000 | − | 28.5788i | 0.649687 | − | 1.12529i | ||||
\(646\) | 6.00000 | 0.236067 | ||||||||
\(647\) | 30.0000 | 1.17942 | 0.589711 | − | 0.807614i | \(-0.299242\pi\) | ||||
0.589711 | + | 0.807614i | \(0.299242\pi\) | |||||||
\(648\) | −4.50000 | + | 7.79423i | −0.176777 | + | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | + | 6.92820i | 0.0784465 | + | 0.271746i | ||||
\(651\) | 24.0000 | + | 27.7128i | 0.940634 | + | 1.08615i | ||||
\(652\) | − | 17.3205i | − | 0.678323i | ||||||
\(653\) | 41.5692i | 1.62673i | 0.581754 | + | 0.813365i | \(0.302367\pi\) | ||||
−0.581754 | + | 0.813365i | \(0.697633\pi\) | |||||||
\(654\) | −4.50000 | + | 7.79423i | −0.175964 | + | 0.304778i | ||||
\(655\) | − | 25.9808i | − | 1.01515i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | − | 5.19615i | −0.117041 | − | 0.202721i | ||||
\(658\) | −10.5000 | + | 30.3109i | −0.409333 | + | 1.18164i | ||||
\(659\) | − | 24.2487i | − | 0.944596i | −0.881439 | − | 0.472298i | \(-0.843425\pi\) | ||
0.881439 | − | 0.472298i | \(-0.156575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | − | 17.3205i | − | 0.673181i | ||||||
\(663\) | −4.50000 | + | 18.1865i | −0.174766 | + | 0.706306i | ||||
\(664\) | 3.46410i | 0.134433i | ||||||||
\(665\) | 3.00000 | − | 8.66025i | 0.116335 | − | 0.335830i | ||||
\(666\) | 4.50000 | − | 2.59808i | 0.174371 | − | 0.100673i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | − | 3.46410i | − | 0.134030i | ||||||
\(669\) | −10.5000 | − | 6.06218i | −0.405953 | − | 0.234377i | ||||
\(670\) | −24.0000 | −0.927201 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.00000 | − | 3.46410i | −0.115728 | − | 0.133631i | ||||
\(673\) | −17.0000 | −0.655302 | −0.327651 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327651 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(674\) | 5.00000 | 0.192593 | ||||||||
\(675\) | 10.3923i | 0.400000i | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 6.00000 | − | 10.3923i | 0.230429 | − | 0.399114i | ||||
\(679\) | −20.0000 | − | 6.92820i | −0.767530 | − | 0.265880i | ||||
\(680\) | 5.19615i | 0.199263i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0000 | −1.14792 | −0.573959 | − | 0.818884i | \(-0.694593\pi\) | ||||
−0.573959 | + | 0.818884i | \(0.694593\pi\) | |||||||
\(684\) | 3.00000 | + | 5.19615i | 0.114708 | + | 0.198680i | ||||
\(685\) | 31.1769i | 1.19121i | ||||||||
\(686\) | −10.0000 | − | 15.5885i | −0.381802 | − | 0.595170i | ||||
\(687\) | −7.50000 | − | 4.33013i | −0.286143 | − | 0.165205i | ||||
\(688\) | −11.0000 | −0.419371 | ||||||||
\(689\) | 12.0000 | − | 3.46410i | 0.457164 | − | 0.131972i | ||||
\(690\) | 9.00000 | + | 5.19615i | 0.342624 | + | 0.197814i | ||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.5885i | 0.591730i | ||||||||
\(695\) | 33.0000 | 1.25176 | ||||||||
\(696\) | 6.00000 | − | 10.3923i | 0.227429 | − | 0.393919i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.00000 | 0.0378506 | ||||||||
\(699\) | −7.50000 | + | 12.9904i | −0.283676 | + | 0.491341i | ||||
\(700\) | −5.00000 | − | 1.73205i | −0.188982 | − | 0.0654654i | ||||
\(701\) | − | 38.1051i | − | 1.43921i | −0.694383 | − | 0.719605i | \(-0.744323\pi\) | ||
0.694383 | − | 0.719605i | \(-0.255677\pi\) | |||||||
\(702\) | −18.0000 | + | 5.19615i | −0.679366 | + | 0.196116i | ||||
\(703\) | − | 3.46410i | − | 0.130651i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.5000 | + | 18.1865i | 1.18636 | + | 0.684944i | ||||
\(706\) | 10.3923i | 0.391120i | ||||||||
\(707\) | 30.0000 | + | 10.3923i | 1.12827 | + | 0.390843i | ||||
\(708\) | 9.00000 | − | 15.5885i | 0.338241 | − | 0.585850i | ||||
\(709\) | 34.6410i | 1.30097i | 0.759519 | + | 0.650485i | \(0.225434\pi\) | ||||
−0.759519 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(710\) | 15.5885i | 0.585024i | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | 3.46410i | 0.129823i | ||||||||
\(713\) | 27.7128i | 1.03785i | ||||||||
\(714\) | −9.00000 | − | 10.3923i | −0.336817 | − | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.1244i | 0.453108i | ||||||||
\(717\) | −22.5000 | − | 12.9904i | −0.840278 | − | 0.485135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | −4.50000 | + | 2.59808i | −0.167705 | + | 0.0968246i | ||||
\(721\) | −3.00000 | + | 8.66025i | −0.111726 | + | 0.322525i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 15.0000 | + | 8.66025i | 0.557856 | + | 0.322078i | ||||
\(724\) | 3.46410i | 0.128742i | ||||||||
\(725\) | − | 13.8564i | − | 0.514614i | ||||||
\(726\) | −16.5000 | − | 9.52628i | −0.612372 | − | 0.353553i | ||||
\(727\) | 41.5692i | 1.54172i | 0.637006 | + | 0.770859i | \(0.280172\pi\) | ||||
−0.637006 | + | 0.770859i | \(0.719828\pi\) | |||||||
\(728\) | 0.500000 | − | 9.52628i | 0.0185312 | − | 0.353067i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | − | 3.46410i | − | 0.128212i | ||||||
\(731\) | −33.0000 | −1.22055 | ||||||||
\(732\) | 6.00000 | − | 10.3923i | 0.221766 | − | 0.384111i | ||||
\(733\) | 19.0000 | 0.701781 | 0.350891 | − | 0.936416i | \(-0.385879\pi\) | ||||
0.350891 | + | 0.936416i | \(0.385879\pi\) | |||||||
\(734\) | 34.6410i | 1.27862i | ||||||||
\(735\) | −19.5000 | + | 7.79423i | −0.719268 | + | 0.287494i | ||||
\(736\) | − | 3.46410i | − | 0.127688i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.7846i | − | 0.764574i | −0.924044 | − | 0.382287i | \(-0.875137\pi\) | ||
0.924044 | − | 0.382287i | \(-0.124863\pi\) | |||||||
\(740\) | 3.00000 | 0.110282 | ||||||||
\(741\) | −3.00000 | + | 12.1244i | −0.110208 | + | 0.445399i | ||||
\(742\) | −3.00000 | + | 8.66025i | −0.110133 | + | 0.317928i | ||||
\(743\) | 33.0000 | 1.21065 | 0.605326 | − | 0.795977i | \(-0.293043\pi\) | ||||
0.605326 | + | 0.795977i | \(0.293043\pi\) | |||||||
\(744\) | −12.0000 | − | 6.92820i | −0.439941 | − | 0.254000i | ||||
\(745\) | 10.3923i | 0.380745i | ||||||||
\(746\) | 16.0000 | 0.585802 | ||||||||
\(747\) | −9.00000 | + | 5.19615i | −0.329293 | + | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00000 | − | 25.9808i | 0.328853 | − | 0.949316i | ||||
\(750\) | −10.5000 | + | 18.1865i | −0.383406 | + | 0.664078i | ||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | − | 12.1244i | − | 0.442130i | ||||||
\(753\) | 18.0000 | + | 10.3923i | 0.655956 | + | 0.378717i | ||||
\(754\) | 24.0000 | − | 6.92820i | 0.874028 | − | 0.252310i | ||||
\(755\) | −33.0000 | −1.20099 | ||||||||
\(756\) | 4.50000 | − | 12.9904i | 0.163663 | − | 0.472456i | ||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | − | 17.3205i | − | 0.629109i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.46410i | 0.125656i | ||||||||
\(761\) | 38.1051i | 1.38131i | 0.723185 | + | 0.690655i | \(0.242678\pi\) | ||||
−0.723185 | + | 0.690655i | \(0.757322\pi\) | |||||||
\(762\) | −3.00000 | − | 1.73205i | −0.108679 | − | 0.0627456i | ||||
\(763\) | 4.50000 | − | 12.9904i | 0.162911 | − | 0.470283i | ||||
\(764\) | − | 20.7846i | − | 0.751961i | ||||||
\(765\) | −13.5000 | + | 7.79423i | −0.488094 | + | 0.281801i | ||||
\(766\) | − | 5.19615i | − | 0.187745i | ||||||
\(767\) | 36.0000 | − | 10.3923i | 1.29988 | − | 0.375244i | ||||
\(768\) | 1.50000 | + | 0.866025i | 0.0541266 | + | 0.0312500i | ||||
\(769\) | 4.00000 | 0.144244 | 0.0721218 | − | 0.997396i | \(-0.477023\pi\) | ||||
0.0721218 | + | 0.997396i | \(0.477023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.5000 | + | 18.1865i | 1.13444 | + | 0.654972i | ||||
\(772\) | 17.3205i | 0.623379i | ||||||||
\(773\) | 15.5885i | 0.560678i | 0.959901 | + | 0.280339i | \(0.0904469\pi\) | ||||
−0.959901 | + | 0.280339i | \(0.909553\pi\) | |||||||
\(774\) | −16.5000 | − | 28.5788i | −0.593080 | − | 1.02725i | ||||
\(775\) | −16.0000 | −0.574737 | ||||||||
\(776\) | 8.00000 | 0.287183 | ||||||||
\(777\) | −6.00000 | + | 5.19615i | −0.215249 | + | 0.186411i | ||||
\(778\) | − | 10.3923i | − | 0.372582i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −10.5000 | − | 2.59808i | −0.375960 | − | 0.0930261i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 10.3923i | − | 0.371628i | ||||||
\(783\) | 36.0000 | 1.28654 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −22.5000 | − | 12.9904i | −0.802548 | − | 0.463352i | ||||
\(787\) | 32.0000 | 1.14068 | 0.570338 | − | 0.821410i | \(-0.306812\pi\) | ||||
0.570338 | + | 0.821410i | \(0.306812\pi\) | |||||||
\(788\) | −15.0000 | −0.534353 | ||||||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 17.3205i | 0.616236i | ||||||||
\(791\) | −6.00000 | + | 17.3205i | −0.213335 | + | 0.615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | − | 6.92820i | 0.852265 | − | 0.246028i | ||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | 9.00000 | + | 5.19615i | 0.319197 | + | 0.184289i | ||||
\(796\) | 6.92820i | 0.245564i | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | −6.00000 | − | 6.92820i | −0.212398 | − | 0.245256i | ||||
\(799\) | − | 36.3731i | − | 1.28679i | ||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | −9.00000 | + | 5.19615i | −0.317999 | + | 0.183597i | ||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −12.0000 | + | 20.7846i | −0.423207 | + | 0.733017i | ||||
\(805\) | −15.0000 | − | 5.19615i | −0.528681 | − | 0.183140i | ||||
\(806\) | −8.00000 | − | 27.7128i | −0.281788 | − | 0.976142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.0000 | −0.422159 | ||||||||
\(809\) | 1.73205i | 0.0608957i | 0.999536 | + | 0.0304478i | \(0.00969334\pi\) | ||||
−0.999536 | + | 0.0304478i | \(0.990307\pi\) | |||||||
\(810\) | −13.5000 | − | 7.79423i | −0.474342 | − | 0.273861i | ||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | −6.00000 | + | 17.3205i | −0.210559 | + | 0.607831i | ||||
\(813\) | −1.50000 | − | 0.866025i | −0.0526073 | − | 0.0303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.0000 | 1.05085 | ||||||||
\(816\) | 4.50000 | + | 2.59808i | 0.157532 | + | 0.0909509i | ||||
\(817\) | −22.0000 | −0.769683 | ||||||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 25.5000 | − | 12.9904i | 0.891042 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | −0.523504 | −0.261752 | − | 0.965135i | \(-0.584300\pi\) | ||||
−0.261752 | + | 0.965135i | \(0.584300\pi\) | |||||||
\(822\) | 27.0000 | + | 15.5885i | 0.941733 | + | 0.543710i | ||||
\(823\) | 38.0000 | 1.32460 | 0.662298 | − | 0.749240i | \(-0.269581\pi\) | ||||
0.662298 | + | 0.749240i | \(0.269581\pi\) | |||||||
\(824\) | − | 3.46410i | − | 0.120678i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00000 | + | 25.9808i | −0.313150 | + | 0.903986i | ||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | 9.00000 | − | 5.19615i | 0.312772 | − | 0.180579i | ||||
\(829\) | 27.7128i | 0.962506i | 0.876582 | + | 0.481253i | \(0.159818\pi\) | ||||
−0.876582 | + | 0.481253i | \(0.840182\pi\) | |||||||
\(830\) | −6.00000 | −0.208263 | ||||||||
\(831\) | −24.0000 | − | 13.8564i | −0.832551 | − | 0.480673i | ||||
\(832\) | 1.00000 | + | 3.46410i | 0.0346688 | + | 0.120096i | ||||
\(833\) | 16.5000 | + | 12.9904i | 0.571691 | + | 0.450090i | ||||
\(834\) | 16.5000 | − | 28.5788i | 0.571348 | − | 0.989604i | ||||
\(835\) | 6.00000 | 0.207639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 41.5692i | − | 1.43684i | ||||||
\(838\) | −27.0000 | −0.932700 | ||||||||
\(839\) | − | 10.3923i | − | 0.358782i | −0.983778 | − | 0.179391i | \(-0.942587\pi\) | ||
0.983778 | − | 0.179391i | \(-0.0574128\pi\) | |||||||
\(840\) | 6.00000 | − | 5.19615i | 0.207020 | − | 0.179284i | ||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 32.9090i | 1.13412i | ||||||||
\(843\) | 45.0000 | + | 25.9808i | 1.54988 | + | 0.894825i | ||||
\(844\) | −13.0000 | −0.447478 | ||||||||
\(845\) | −12.0000 | − | 19.0526i | −0.412813 | − | 0.655428i | ||||
\(846\) | 31.5000 | − | 18.1865i | 1.08299 | − | 0.625266i | ||||
\(847\) | 27.5000 | + | 9.52628i | 0.944911 | + | 0.327327i | ||||
\(848\) | − | 3.46410i | − | 0.118958i | ||||||
\(849\) | −9.00000 | + | 15.5885i | −0.308879 | + | 0.534994i | ||||
\(850\) | 6.00000 | 0.205798 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 13.5000 | + | 7.79423i | 0.462502 | + | 0.267026i | ||||
\(853\) | −19.0000 | −0.650548 | −0.325274 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325274 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(854\) | −6.00000 | + | 17.3205i | −0.205316 | + | 0.592696i | ||||
\(855\) | −9.00000 | + | 5.19615i | −0.307794 | + | 0.177705i | ||||
\(856\) | 10.3923i | 0.355202i | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3205i | 0.590968i | 0.955348 | + | 0.295484i | \(0.0954809\pi\) | ||||
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(860\) | − | 19.0526i | − | 0.649687i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.0000 | −1.12398 | ||||||||
\(863\) | −33.0000 | −1.12333 | −0.561667 | − | 0.827364i | \(-0.689840\pi\) | ||||
−0.561667 | + | 0.827364i | \(0.689840\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | − | 10.3923i | − | 0.353349i | ||||||
\(866\) | 5.19615i | 0.176572i | ||||||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | 20.0000 | + | 6.92820i | 0.678844 | + | 0.235159i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | + | 10.3923i | 0.610257 | + | 0.352332i | ||||
\(871\) | −48.0000 | + | 13.8564i | −1.62642 | + | 0.469506i | ||||
\(872\) | 5.19615i | 0.175964i | ||||||||
\(873\) | 12.0000 | + | 20.7846i | 0.406138 | + | 0.703452i | ||||
\(874\) | − | 6.92820i | − | 0.234350i | ||||||
\(875\) | 10.5000 | − | 30.3109i | 0.354965 | − | 1.02470i | ||||
\(876\) | −3.00000 | − | 1.73205i | −0.101361 | − | 0.0585206i | ||||
\(877\) | 53.6936i | 1.81310i | 0.422095 | + | 0.906552i | \(0.361295\pi\) | ||||
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | − | 31.1769i | − | 1.05217i | ||||||
\(879\) | −16.5000 | + | 28.5788i | −0.556531 | + | 0.963940i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | −3.00000 | + | 20.7846i | −0.101015 | + | 0.699854i | ||||
\(883\) | 17.0000 | 0.572096 | 0.286048 | − | 0.958215i | \(-0.407658\pi\) | ||||
0.286048 | + | 0.958215i | \(0.407658\pi\) | |||||||
\(884\) | 3.00000 | + | 10.3923i | 0.100901 | + | 0.349531i | ||||
\(885\) | 27.0000 | + | 15.5885i | 0.907595 | + | 0.524000i | ||||
\(886\) | − | 22.5167i | − | 0.756462i | ||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | 1.50000 | − | 2.59808i | 0.0503367 | − | 0.0871857i | ||||
\(889\) | 5.00000 | + | 1.73205i | 0.167695 | + | 0.0580911i | ||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.00000 | −0.234377 | ||||||||
\(893\) | − | 24.2487i | − | 0.811452i | ||||||
\(894\) | 9.00000 | + | 5.19615i | 0.301005 | + | 0.173785i | ||||
\(895\) | −21.0000 | −0.701953 | ||||||||
\(896\) | −2.50000 | − | 0.866025i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 21.0000 | + | 5.19615i | 0.701170 | + | 0.173494i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.4256i | 1.84855i | ||||||||
\(900\) | 3.00000 | + | 5.19615i | 0.100000 | + | 0.173205i | ||||
\(901\) | − | 10.3923i | − | 0.346218i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.0000 | + | 38.1051i | 1.09817 | + | 1.26806i | ||||
\(904\) | − | 6.92820i | − | 0.230429i | ||||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | −16.5000 | + | 28.5788i | −0.548176 | + | 0.949468i | ||||
\(907\) | 53.0000 | 1.75984 | 0.879918 | − | 0.475125i | \(-0.157597\pi\) | ||||
0.879918 | + | 0.475125i | \(0.157597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0000 | − | 31.1769i | −0.597022 | − | 1.03407i | ||||
\(910\) | 16.5000 | + | 0.866025i | 0.546970 | + | 0.0287085i | ||||
\(911\) | − | 6.92820i | − | 0.229542i | −0.993392 | − | 0.114771i | \(-0.963387\pi\) | ||
0.993392 | − | 0.114771i | \(-0.0366134\pi\) | |||||||
\(912\) | 3.00000 | + | 1.73205i | 0.0993399 | + | 0.0573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.3923i | 0.343747i | ||||||||
\(915\) | 18.0000 | + | 10.3923i | 0.595062 | + | 0.343559i | ||||
\(916\) | −5.00000 | −0.165205 | ||||||||
\(917\) | 37.5000 | + | 12.9904i | 1.23836 | + | 0.428980i | ||||
\(918\) | 15.5885i | 0.514496i | ||||||||
\(919\) | −52.0000 | −1.71532 | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | −21.0000 | − | 12.1244i | −0.691974 | − | 0.399511i | ||||
\(922\) | 5.19615i | 0.171126i | ||||||||
\(923\) | 9.00000 | + | 31.1769i | 0.296239 | + | 1.02620i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.46410i | − | 0.113899i | ||||||
\(926\) | − | 24.2487i | − | 0.796862i | ||||||
\(927\) | 9.00000 | − | 5.19615i | 0.295599 | − | 0.170664i | ||||
\(928\) | − | 6.92820i | − | 0.227429i | ||||||
\(929\) | − | 34.6410i | − | 1.13653i | −0.822844 | − | 0.568267i | \(-0.807614\pi\) | ||
0.822844 | − | 0.568267i | \(-0.192386\pi\) | |||||||
\(930\) | 12.0000 | − | 20.7846i | 0.393496 | − | 0.681554i | ||||
\(931\) | 11.0000 | + | 8.66025i | 0.360510 | + | 0.283828i | ||||
\(932\) | 8.66025i | 0.283676i | ||||||||
\(933\) | 45.0000 | + | 25.9808i | 1.47323 | + | 0.850572i | ||||
\(934\) | 36.0000 | 1.17796 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.50000 | + | 7.79423i | −0.245145 | + | 0.254762i | ||||
\(937\) | 34.6410i | 1.13167i | 0.824518 | + | 0.565836i | \(0.191447\pi\) | ||||
−0.824518 | + | 0.565836i | \(0.808553\pi\) | |||||||
\(938\) | 12.0000 | − | 34.6410i | 0.391814 | − | 1.13107i | ||||
\(939\) | 7.50000 | − | 12.9904i | 0.244753 | − | 0.423925i | ||||
\(940\) | 21.0000 | 0.684944 | ||||||||
\(941\) | − | 43.3013i | − | 1.41158i | −0.708421 | − | 0.705791i | \(-0.750592\pi\) | ||
0.708421 | − | 0.705791i | \(-0.249408\pi\) | |||||||
\(942\) | −9.00000 | + | 15.5885i | −0.293236 | + | 0.507899i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 10.3923i | − | 0.338241i | ||||||
\(945\) | 22.5000 | + | 7.79423i | 0.731925 | + | 0.253546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.0000 | 1.16984 | 0.584921 | − | 0.811090i | \(-0.301125\pi\) | ||||
0.584921 | + | 0.811090i | \(0.301125\pi\) | |||||||
\(948\) | 15.0000 | + | 8.66025i | 0.487177 | + | 0.281272i | ||||
\(949\) | −2.00000 | − | 6.92820i | −0.0649227 | − | 0.224899i | ||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | −9.00000 | − | 5.19615i | −0.291845 | − | 0.168497i | ||||
\(952\) | −7.50000 | − | 2.59808i | −0.243076 | − | 0.0842041i | ||||
\(953\) | 1.73205i | 0.0561066i | 0.999606 | + | 0.0280533i | \(0.00893082\pi\) | ||||
−0.999606 | + | 0.0280533i | \(0.991069\pi\) | |||||||
\(954\) | 9.00000 | − | 5.19615i | 0.291386 | − | 0.168232i | ||||
\(955\) | 36.0000 | 1.16493 | ||||||||
\(956\) | −15.0000 | −0.485135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 32.9090i | − | 1.06324i | ||||||
\(959\) | −45.0000 | − | 15.5885i | −1.45313 | − | 0.503378i | ||||
\(960\) | −1.50000 | + | 2.59808i | −0.0484123 | + | 0.0838525i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 6.00000 | − | 1.73205i | 0.193448 | − | 0.0558436i | ||||
\(963\) | −27.0000 | + | 15.5885i | −0.870063 | + | 0.502331i | ||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | −30.0000 | −0.965734 | ||||||||
\(966\) | −12.0000 | + | 10.3923i | −0.386094 | + | 0.334367i | ||||
\(967\) | 43.3013i | 1.39247i | 0.717812 | + | 0.696237i | \(0.245144\pi\) | ||||
−0.717812 | + | 0.696237i | \(0.754856\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 9.00000 | + | 5.19615i | 0.289122 | + | 0.166924i | ||||
\(970\) | 13.8564i | 0.444902i | ||||||||
\(971\) | 9.00000 | 0.288824 | 0.144412 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144412 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | −16.5000 | + | 47.6314i | −0.528966 | + | 1.52699i | ||||
\(974\) | − | 24.2487i | − | 0.776979i | ||||||
\(975\) | −3.00000 | + | 12.1244i | −0.0960769 | + | 0.388290i | ||||
\(976\) | − | 6.92820i | − | 0.221766i | ||||||
\(977\) | −24.0000 | −0.767828 | −0.383914 | − | 0.923369i | \(-0.625424\pi\) | ||||
−0.383914 | + | 0.923369i | \(0.625424\pi\) | |||||||
\(978\) | 15.0000 | − | 25.9808i | 0.479647 | − | 0.830773i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7.50000 | + | 9.52628i | −0.239579 | + | 0.304306i | ||||
\(981\) | −13.5000 | + | 7.79423i | −0.431022 | + | 0.248851i | ||||
\(982\) | 36.3731i | 1.16071i | ||||||||
\(983\) | 32.9090i | 1.04963i | 0.851215 | + | 0.524816i | \(0.175866\pi\) | ||||
−0.851215 | + | 0.524816i | \(0.824134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25.9808i | − | 0.827816i | ||||||
\(986\) | − | 20.7846i | − | 0.661917i | ||||||
\(987\) | −42.0000 | + | 36.3731i | −1.33687 | + | 1.15777i | ||||
\(988\) | 2.00000 | + | 6.92820i | 0.0636285 | + | 0.220416i | ||||
\(989\) | 38.1051i | 1.21167i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000 | 0.317660 | 0.158830 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158830 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(992\) | −8.00000 | −0.254000 | ||||||||
\(993\) | 15.0000 | − | 25.9808i | 0.476011 | − | 0.824475i | ||||
\(994\) | −22.5000 | − | 7.79423i | −0.713657 | − | 0.247218i | ||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | −3.00000 | + | 5.19615i | −0.0950586 | + | 0.164646i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 20.7846i | 0.657925i | ||||||||
\(999\) | 9.00000 | 0.284747 |
(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 | 546.2.e.d.545.2 | yes | 2 | |
3.2 | odd | 2 | 546.2.e.a.545.2 | yes | 2 | ||
7.6 | odd | 2 | 546.2.e.c.545.1 | yes | 2 | ||
13.12 | even | 2 | 546.2.e.b.545.2 | yes | 2 | ||
21.20 | even | 2 | 546.2.e.b.545.1 | yes | 2 | ||
39.38 | odd | 2 | 546.2.e.c.545.2 | yes | 2 | ||
91.90 | odd | 2 | 546.2.e.a.545.1 | ✓ | 2 | ||
273.272 | even | 2 | inner | 546.2.e.d.545.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.a.545.1 | ✓ | 2 | 91.90 | odd | 2 | ||
546.2.e.a.545.2 | yes | 2 | 3.2 | odd | 2 | ||
546.2.e.b.545.1 | yes | 2 | 21.20 | even | 2 | ||
546.2.e.b.545.2 | yes | 2 | 13.12 | even | 2 | ||
546.2.e.c.545.1 | yes | 2 | 7.6 | odd | 2 | ||
546.2.e.c.545.2 | yes | 2 | 39.38 | odd | 2 | ||
546.2.e.d.545.1 | yes | 2 | 273.272 | even | 2 | inner | |
546.2.e.d.545.2 | yes | 2 | 1.1 | even | 1 | trivial |