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.c.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 | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 1.50000 | − | 2.59808i | 0.353553 | − | 0.612372i | ||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | −4.50000 | + | 0.866025i | −0.981981 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | −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 | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | −1.50000 | − | 2.59808i | −0.273861 | − | 0.474342i | ||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 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 | \(0.0454735\pi\) | ||||
−0.989813 | + | 0.142374i | \(0.954527\pi\) | |||||||
\(38\) | −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 | \(\pi\) | |||||||||
\(42\) | −4.50000 | + | 0.866025i | −0.694365 | + | 0.133631i | ||||
\(43\) | −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 | \(0.0764641\pi\) | ||||
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(54\) | 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 | ||||||||
\(63\) | 6.00000 | − | 5.19615i | 0.755929 | − | 0.654654i | ||||
\(64\) | 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 | \(-0.678756\pi\) | ||
0.532524 | − | 0.846415i | \(-0.321244\pi\) | |||||||
\(68\) | −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 | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 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 | \(0.939113\pi\) | |||||||
\(84\) | −4.50000 | + | 0.866025i | −0.490990 | + | 0.0944911i | ||||
\(85\) | − | 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 | ||||
\(91\) | −5.50000 | + | 7.79423i | −0.576557 | + | 0.817057i | ||||
\(92\) | 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 | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 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 | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 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 | ||||
\(105\) | −1.50000 | − | 7.79423i | −0.146385 | − | 0.760639i | ||||
\(106\) | 3.46410i | 0.336463i | ||||||||
\(107\) | − | 10.3923i | − | 1.00466i | −0.864675 | − | 0.502331i | \(-0.832476\pi\) | ||
0.864675 | − | 0.502331i | \(-0.167524\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | − | 5.19615i | − | 0.497701i | −0.968542 | − | 0.248851i | \(-0.919947\pi\) | ||
0.968542 | − | 0.248851i | \(-0.0800528\pi\) | |||||||
\(110\) | 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 | \(0.105659\pi\) | ||||
−0.945413 | + | 0.325875i | \(0.894341\pi\) | |||||||
\(114\) | 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 | ||||||||
\(126\) | 6.00000 | − | 5.19615i | 0.534522 | − | 0.462910i | ||||
\(127\) | −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 | \(-0.272551\pi\) | ||||
0.655278 | + | 0.755388i | \(0.272551\pi\) | |||||||
\(132\) | 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 | ||||||||
\(147\) | −12.0000 | − | 1.73205i | −0.989743 | − | 0.142857i | ||||
\(148\) | 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 | \(-0.717630\pi\) | ||
0.631670 | − | 0.775238i | \(-0.282370\pi\) | |||||||
\(152\) | −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 | \(0.237293\pi\) | ||||
−0.734763 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(164\) | 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 | \(-0.0427919\pi\) | |||||||
\(168\) | −4.50000 | + | 0.866025i | −0.347183 | + | 0.0668153i | ||||
\(169\) | −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 | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | −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 | \(-0.850315\pi\) | ||
0.891455 | − | 0.453108i | \(-0.149685\pi\) | |||||||
\(180\) | 4.50000 | + | 2.59808i | 0.335410 | + | 0.193649i | ||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | −5.50000 | + | 7.79423i | −0.407687 | + | 0.577747i | ||||
\(183\) | 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 | \(0.270892\pi\) | ||||
−0.659208 | + | 0.751961i | \(0.729108\pi\) | |||||||
\(192\) | −1.50000 | + | 0.866025i | −0.108253 | + | 0.0625000i | ||||
\(193\) | − | 17.3205i | − | 1.24676i | −0.781920 | − | 0.623379i | \(-0.785760\pi\) | ||
0.781920 | − | 0.623379i | \(-0.214240\pi\) | |||||||
\(194\) | −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 | ||||||||
\(210\) | −1.50000 | − | 7.79423i | −0.103510 | − | 0.537853i | ||||
\(211\) | −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 | \(-0.424695\pi\) | ||||
0.234377 | + | 0.972146i | \(0.424695\pi\) | |||||||
\(224\) | 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 | \(-0.447172\pi\) | ||||
0.165205 | + | 0.986259i | \(0.447172\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.92820i | 0.454859i | ||||||||
\(233\) | − | 8.66025i | − | 0.567352i | −0.958920 | − | 0.283676i | \(-0.908446\pi\) | ||
0.958920 | − | 0.283676i | \(-0.0915540\pi\) | |||||||
\(234\) | 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 | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | −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 | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 6.00000 | − | 5.19615i | 0.377964 | − | 0.327327i | ||||
\(253\) | 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 | \(-0.727320\pi\) | ||||
−0.654972 | + | 0.755653i | \(0.727320\pi\) | |||||||
\(258\) | 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 | \(-0.859496\pi\) | ||
0.904152 | − | 0.427211i | \(-0.140504\pi\) | |||||||
\(264\) | 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 | \(-0.490331\pi\) | ||||
0.0303728 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 1.50000 | − | 16.4545i | 0.0907841 | − | 0.995871i | ||||
\(274\) | 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 | \(0.812132\pi\) | |||||||
\(294\) | −12.0000 | − | 1.73205i | −0.699854 | − | 0.101015i | ||||
\(295\) | 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 | \(-0.369180\pi\) | ||||
0.399511 | + | 0.916728i | \(0.369180\pi\) | |||||||
\(308\) | 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 | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | −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 | ||||||||
\(315\) | 9.00000 | + | 10.3923i | 0.507093 | + | 0.585540i | ||||
\(316\) | 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 | \(0.157918\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 3.46410i | 0.190117i | ||||||||
\(333\) | 4.50000 | + | 2.59808i | 0.246598 | + | 0.142374i | ||||
\(334\) | − | 3.46410i | − | 0.189547i | ||||||
\(335\) | 24.0000 | 1.31126 | ||||||||
\(336\) | −4.50000 | + | 0.866025i | −0.245495 | + | 0.0472456i | ||||
\(337\) | 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 | \(-0.862585\pi\) | ||
0.908255 | − | 0.418416i | \(-0.137415\pi\) | |||||||
\(348\) | −6.00000 | − | 10.3923i | −0.321634 | − | 0.557086i | ||||
\(349\) | −1.00000 | −0.0535288 | −0.0267644 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267644 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | 13.5000 | − | 2.59808i | 0.714496 | − | 0.137505i | ||||
\(358\) | − | 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 | ||||
\(364\) | −5.50000 | + | 7.79423i | −0.288278 | + | 0.408529i | ||||
\(365\) | 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 | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | − | 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 | \(0.0848622\pi\) | ||||
−0.964672 | + | 0.263455i | \(0.915138\pi\) | |||||||
\(390\) | 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 | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 6.92820i | 0.347279i | ||||||||
\(399\) | 9.00000 | − | 1.73205i | 0.450564 | − | 0.0867110i | ||||
\(400\) | 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 | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 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 | \(-0.270760\pi\) | ||||
0.659518 | + | 0.751689i | \(0.270760\pi\) | |||||||
\(420\) | −1.50000 | − | 7.79423i | −0.0731925 | − | 0.380319i | ||||
\(421\) | − | 32.9090i | − | 1.60388i | −0.597401 | − | 0.801942i | \(-0.703800\pi\) | ||
0.597401 | − | 0.801942i | \(-0.296200\pi\) | |||||||
\(422\) | −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 | ||||||||
\(441\) | 19.5000 | − | 7.79423i | 0.928571 | − | 0.371154i | ||||
\(442\) | 3.00000 | − | 10.3923i | 0.142695 | − | 0.494312i | ||||
\(443\) | 22.5167i | 1.06980i | 0.844916 | + | 0.534899i | \(0.179651\pi\) | ||||
−0.844916 | + | 0.534899i | \(0.820349\pi\) | |||||||
\(444\) | −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 | ||||||||
\(455\) | −13.5000 | − | 9.52628i | −0.632890 | − | 0.446599i | ||||
\(456\) | 3.00000 | − | 1.73205i | 0.140488 | − | 0.0811107i | ||||
\(457\) | − | 10.3923i | − | 0.486132i | −0.970010 | − | 0.243066i | \(-0.921847\pi\) | ||
0.970010 | − | 0.243066i | \(-0.0781531\pi\) | |||||||
\(458\) | 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 | \(0.190533\pi\) | ||||
−0.826139 | + | 0.563467i | \(0.809467\pi\) | |||||||
\(464\) | 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 | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 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 | ||||||||
\(483\) | −3.00000 | − | 15.5885i | −0.136505 | − | 0.709299i | ||||
\(484\) | −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 | \(0.185146\pi\) | ||||
−0.835555 | + | 0.549407i | \(0.814854\pi\) | |||||||
\(488\) | − | 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 | \(-0.693558\pi\) | ||
0.571292 | − | 0.820747i | \(-0.306442\pi\) | |||||||
\(492\) | 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 | \(-0.845974\pi\) | ||
0.885193 | − | 0.465223i | \(-0.154026\pi\) | |||||||
\(500\) | 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 | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 6.00000 | − | 5.19615i | 0.267261 | − | 0.231455i | ||||
\(505\) | 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 | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −9.00000 | + | 1.73205i | −0.392792 | + | 0.0755929i | ||||
\(526\) | − | 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 | \(0.134320\pi\) | ||||
−0.912280 | + | 0.409567i | \(0.865680\pi\) | |||||||
\(542\) | 1.00000 | 0.0429537 | ||||||||
\(543\) | −3.00000 | − | 5.19615i | −0.128742 | − | 0.222988i | ||||
\(544\) | −3.00000 | −0.128624 | ||||||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 1.50000 | − | 16.4545i | 0.0641941 | − | 0.704187i | ||||
\(547\) | 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 | \(-0.354084\pi\) | ||||
0.442522 | + | 0.896758i | \(0.354084\pi\) | |||||||
\(564\) | 10.5000 | + | 18.1865i | 0.442130 | + | 0.765791i | ||||
\(565\) | −12.0000 | −0.504844 | ||||||||
\(566\) | 10.3923i | 0.436821i | ||||||||
\(567\) | −4.50000 | − | 23.3827i | −0.188982 | − | 0.981981i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 32.9090i | 1.37962i | 0.723993 | + | 0.689808i | \(0.242305\pi\) | ||||
−0.723993 | + | 0.689808i | \(0.757695\pi\) | |||||||
\(570\) | 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 | \(-0.0931316\pi\) | ||||
0.957503 | + | 0.288425i | \(0.0931316\pi\) | |||||||
\(578\) | −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 | \(0.711951\pi\) | |||||||
\(588\) | −12.0000 | − | 1.73205i | −0.494872 | − | 0.0714286i | ||||
\(589\) | −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 | \(-0.835026\pi\) | ||
0.868672 | − | 0.495388i | \(-0.164974\pi\) | |||||||
\(600\) | −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 | ||||||||
\(609\) | −6.00000 | − | 31.1769i | −0.243132 | − | 1.26335i | ||||
\(610\) | 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 | \(0.0446825\pi\) | ||||
−0.990164 | + | 0.139914i | \(0.955317\pi\) | |||||||
\(614\) | 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 | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(620\) | 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 | ||||||
\(630\) | 9.00000 | + | 10.3923i | 0.358569 | + | 0.414039i | ||||
\(631\) | − | 22.5167i | − | 0.896374i | −0.893940 | − | 0.448187i | \(-0.852070\pi\) | ||
0.893940 | − | 0.448187i | \(-0.147930\pi\) | |||||||
\(632\) | 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 | ||||
\(637\) | −20.5000 | + | 14.7224i | −0.812240 | + | 0.583324i | ||||
\(638\) | 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 | \(0.239813\pi\) | ||||
−0.729370 | + | 0.684119i | \(0.760187\pi\) | |||||||
\(642\) | 9.00000 | + | 15.5885i | 0.355202 | + | 0.615227i | ||||
\(643\) | −40.0000 | −1.57745 | −0.788723 | − | 0.614749i | \(-0.789257\pi\) | ||||
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | −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 | \(-0.700758\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700758\pi\) | |||||||
\(648\) | −4.50000 | − | 7.79423i | −0.176777 | − | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.00000 | + | 6.92820i | −0.0784465 | + | 0.271746i | ||||
\(651\) | −36.0000 | + | 6.92820i | −1.41095 | + | 0.271538i | ||||
\(652\) | 17.3205i | 0.678323i | ||||||||
\(653\) | − | 41.5692i | − | 1.62673i | −0.581754 | − | 0.813365i | \(-0.697633\pi\) | ||
0.581754 | − | 0.813365i | \(-0.302367\pi\) | |||||||
\(654\) | 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 | \(0.156575\pi\) | ||||
−0.881439 | + | 0.472298i | \(0.843425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | 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 | ||||||||
\(672\) | −4.50000 | + | 0.866025i | −0.173591 | + | 0.0334077i | ||||
\(673\) | −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 | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | −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 | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 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 | \(0.255677\pi\) | ||||
−0.694383 | + | 0.719605i | \(0.744323\pi\) | |||||||
\(702\) | −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 | \(-0.774566\pi\) | ||
0.759519 | − | 0.650485i | \(-0.225434\pi\) | |||||||
\(710\) | 15.5885i | 0.585024i | ||||||||
\(711\) | 15.0000 | − | 25.9808i | 0.562544 | − | 0.974355i | ||||
\(712\) | 3.46410i | 0.129823i | ||||||||
\(713\) | 27.7128i | 1.03785i | ||||||||
\(714\) | 13.5000 | − | 2.59808i | 0.505225 | − | 0.0972306i | ||||
\(715\) | 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 | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 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 | \(0.719828\pi\) | |||||||
\(728\) | −5.50000 | + | 7.79423i | −0.203844 | + | 0.288873i | ||||
\(729\) | −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 | \(-0.614121\pi\) | ||||
−0.350891 | + | 0.936416i | \(0.614121\pi\) | |||||||
\(734\) | 34.6410i | 1.27862i | ||||||||
\(735\) | 3.00000 | − | 20.7846i | 0.110657 | − | 0.766652i | ||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.7846i | 0.764574i | 0.924044 | + | 0.382287i | \(0.124863\pi\) | ||||
−0.924044 | + | 0.382287i | \(0.875137\pi\) | |||||||
\(740\) | −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 | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | −1.50000 | − | 7.79423i | −0.0538122 | − | 0.279616i | ||||
\(778\) | 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 | \(-0.693188\pi\) | ||||
−0.570338 | + | 0.821410i | \(0.693188\pi\) | |||||||
\(788\) | −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 | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 9.00000 | − | 1.73205i | 0.318597 | − | 0.0613139i | ||||
\(799\) | 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 | \(-0.990307\pi\) | ||
0.999536 | − | 0.0304478i | \(-0.00969334\pi\) | |||||||
\(810\) | 13.5000 | − | 7.79423i | 0.474342 | − | 0.273861i | ||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −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 | ||||||||
\(819\) | 12.0000 | + | 25.9808i | 0.419314 | + | 0.907841i | ||||
\(820\) | 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 | \(-0.0574128\pi\) | |||||||
\(840\) | −1.50000 | − | 7.79423i | −0.0517549 | − | 0.268926i | ||||
\(841\) | −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 | \(-0.394544\pi\) | ||||
0.325274 | + | 0.945620i | \(0.394544\pi\) | |||||||
\(854\) | 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 | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 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 | \(-0.638705\pi\) | ||
0.422095 | − | 0.906552i | \(-0.361295\pi\) | |||||||
\(878\) | − | 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 | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 19.5000 | − | 7.79423i | 0.656599 | − | 0.262445i | ||||
\(883\) | 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 | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −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 | ||||||||
\(903\) | 49.5000 | − | 9.52628i | 1.64726 | − | 0.317015i | ||||
\(904\) | 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 | ||||
\(910\) | −13.5000 | − | 9.52628i | −0.447521 | − | 0.315793i | ||||
\(911\) | 6.92820i | 0.229542i | 0.993392 | + | 0.114771i | \(0.0366134\pi\) | ||||
−0.993392 | + | 0.114771i | \(0.963387\pi\) | |||||||
\(912\) | 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 | \(-0.991069\pi\) | ||
0.999606 | − | 0.0280533i | \(-0.00893082\pi\) | |||||||
\(954\) | 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 | ||||||||
\(966\) | −3.00000 | − | 15.5885i | −0.0965234 | − | 0.501550i | ||||
\(967\) | − | 43.3013i | − | 1.39247i | −0.717812 | − | 0.696237i | \(-0.754856\pi\) | ||
0.717812 | − | 0.696237i | \(-0.245144\pi\) | |||||||
\(968\) | −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 | \(-0.546129\pi\) | ||||
−0.144412 | + | 0.989518i | \(0.546129\pi\) | |||||||
\(972\) | 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 | ||||||
\(987\) | 10.5000 | + | 54.5596i | 0.334219 | + | 1.73665i | ||||
\(988\) | 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.c.545.2 | yes | 2 | |
3.2 | odd | 2 | 546.2.e.b.545.2 | yes | 2 | ||
7.6 | odd | 2 | 546.2.e.d.545.1 | yes | 2 | ||
13.12 | even | 2 | 546.2.e.a.545.2 | yes | 2 | ||
21.20 | even | 2 | 546.2.e.a.545.1 | ✓ | 2 | ||
39.38 | odd | 2 | 546.2.e.d.545.2 | yes | 2 | ||
91.90 | odd | 2 | 546.2.e.b.545.1 | yes | 2 | ||
273.272 | even | 2 | inner | 546.2.e.c.545.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.a.545.1 | ✓ | 2 | 21.20 | even | 2 | ||
546.2.e.a.545.2 | yes | 2 | 13.12 | even | 2 | ||
546.2.e.b.545.1 | yes | 2 | 91.90 | odd | 2 | ||
546.2.e.b.545.2 | yes | 2 | 3.2 | odd | 2 | ||
546.2.e.c.545.1 | yes | 2 | 273.272 | even | 2 | inner | |
546.2.e.c.545.2 | yes | 2 | 1.1 | even | 1 | trivial | |
546.2.e.d.545.1 | yes | 2 | 7.6 | odd | 2 | ||
546.2.e.d.545.2 | yes | 2 | 39.38 | odd | 2 |