Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [61,2,Mod(14,61)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(61, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("61.14");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 61.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.487087452330\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 48.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 61.48 |
Dual form | 61.2.f.a.14.1 |
$q$-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 \(\left(\mathbb{Z}/61\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −1.06066 | − | 0.612372i | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 3.00000 | + | 1.73205i | 1.22474 | + | 0.707107i | ||||
\(7\) | −3.00000 | − | 1.73205i | −1.13389 | − | 0.654654i | −0.188982 | − | 0.981981i | \(-0.560519\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.50000 | − | 2.59808i | 1.42302 | − | 0.821584i | ||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | −1.00000 | − | 1.73205i | −0.288675 | − | 0.500000i | ||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 3.00000 | + | 5.19615i | 0.801784 | + | 1.38873i | ||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | −6.00000 | + | 3.46410i | −1.45521 | + | 0.840168i | −0.998770 | − | 0.0495842i | \(-0.984210\pi\) |
−0.456444 | + | 0.889752i | \(0.650877\pi\) | |||||||
\(18\) | −1.50000 | − | 0.866025i | −0.353553 | − | 0.204124i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | 6.00000 | + | 3.46410i | 1.30931 | + | 0.755929i | ||||
\(22\) | −3.00000 | + | 5.19615i | −0.639602 | + | 1.10782i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | − | 3.46410i | − | 0.707107i | ||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −3.00000 | + | 1.73205i | −0.588348 | + | 0.339683i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | − | 3.46410i | − | 0.654654i | ||||||
\(29\) | −1.50000 | + | 0.866025i | −0.278543 | + | 0.160817i | −0.632764 | − | 0.774345i | \(-0.718080\pi\) |
0.354221 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(30\) | −9.00000 | + | 5.19615i | −1.64317 | + | 0.948683i | ||||
\(31\) | −9.00000 | + | 5.19615i | −1.61645 | + | 0.933257i | −0.628619 | + | 0.777714i | \(0.716379\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −4.50000 | + | 2.59808i | −0.795495 | + | 0.459279i | ||||
\(33\) | 6.92820i | 1.20605i | ||||||||
\(34\) | 12.0000 | 2.05798 | ||||||||
\(35\) | 9.00000 | − | 5.19615i | 1.52128 | − | 0.878310i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | − | 1.73205i | − | 0.284747i | −0.989813 | − | 0.142374i | \(-0.954527\pi\) | ||
0.989813 | − | 0.142374i | \(-0.0454735\pi\) | |||||||
\(38\) | − | 3.46410i | − | 0.561951i | ||||||
\(39\) | −2.00000 | + | 3.46410i | −0.320256 | + | 0.554700i | ||||
\(40\) | −4.50000 | − | 2.59808i | −0.711512 | − | 0.410792i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | −6.00000 | − | 10.3923i | −0.925820 | − | 1.60357i | ||||
\(43\) | 3.00000 | + | 1.73205i | 0.457496 | + | 0.264135i | 0.710991 | − | 0.703201i | \(-0.248247\pi\) |
−0.253495 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(44\) | 3.00000 | − | 1.73205i | 0.452267 | − | 0.261116i | ||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | −5.00000 | + | 8.66025i | −0.721688 | + | 1.25000i | ||||
\(49\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | ||||
\(50\) | 6.92820i | 0.979796i | ||||||||
\(51\) | 12.0000 | − | 6.92820i | 1.68034 | − | 0.970143i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | − | 5.19615i | − | 0.713746i | −0.934153 | − | 0.356873i | \(-0.883843\pi\) | ||
0.934153 | − | 0.356873i | \(-0.116157\pi\) | |||||||
\(54\) | −6.00000 | − | 3.46410i | −0.816497 | − | 0.471405i | ||||
\(55\) | 9.00000 | + | 5.19615i | 1.21356 | + | 0.700649i | ||||
\(56\) | 3.00000 | − | 5.19615i | 0.400892 | − | 0.694365i | ||||
\(57\) | −2.00000 | − | 3.46410i | −0.264906 | − | 0.458831i | ||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | −3.00000 | − | 1.73205i | −0.390567 | − | 0.225494i | 0.291839 | − | 0.956467i | \(-0.405733\pi\) |
−0.682406 | + | 0.730974i | \(0.739066\pi\) | |||||||
\(60\) | 6.00000 | 0.774597 | ||||||||
\(61\) | −0.500000 | + | 7.79423i | −0.0640184 | + | 0.997949i | ||||
\(62\) | 18.0000 | 2.28600 | ||||||||
\(63\) | −3.00000 | − | 1.73205i | −0.377964 | − | 0.218218i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.00000 | + | 5.19615i | 0.372104 | + | 0.644503i | ||||
\(66\) | 6.00000 | − | 10.3923i | 0.738549 | − | 1.27920i | ||||
\(67\) | −3.00000 | − | 1.73205i | −0.366508 | − | 0.211604i | 0.305424 | − | 0.952217i | \(-0.401202\pi\) |
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | −6.00000 | − | 3.46410i | −0.727607 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.0000 | −2.15141 | ||||||||
\(71\) | −9.00000 | + | 5.19615i | −1.06810 | + | 0.616670i | −0.927663 | − | 0.373419i | \(-0.878185\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(72\) | 1.73205i | 0.204124i | ||||||||
\(73\) | 3.50000 | + | 6.06218i | 0.409644 | + | 0.709524i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | 4.00000 | + | 6.92820i | 0.461880 | + | 0.800000i | ||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −6.00000 | + | 10.3923i | −0.683763 | + | 1.18431i | ||||
\(78\) | 6.00000 | − | 3.46410i | 0.679366 | − | 0.392232i | ||||
\(79\) | −9.00000 | − | 5.19615i | −1.01258 | − | 0.584613i | −0.100633 | − | 0.994924i | \(-0.532087\pi\) |
−0.911946 | + | 0.410311i | \(0.865420\pi\) | |||||||
\(80\) | 7.50000 | + | 12.9904i | 0.838525 | + | 1.45237i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −4.50000 | − | 2.59808i | −0.496942 | − | 0.286910i | ||||
\(83\) | −3.00000 | + | 5.19615i | −0.329293 | + | 0.570352i | −0.982372 | − | 0.186938i | \(-0.940144\pi\) |
0.653079 | + | 0.757290i | \(0.273477\pi\) | |||||||
\(84\) | 6.92820i | 0.755929i | ||||||||
\(85\) | − | 20.7846i | − | 2.25441i | ||||||
\(86\) | −3.00000 | − | 5.19615i | −0.323498 | − | 0.560316i | ||||
\(87\) | 3.00000 | − | 1.73205i | 0.321634 | − | 0.185695i | ||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | − | 15.5885i | − | 1.65237i | −0.563397 | − | 0.826187i | \(-0.690506\pi\) | ||
0.563397 | − | 0.826187i | \(-0.309494\pi\) | |||||||
\(90\) | 4.50000 | − | 2.59808i | 0.474342 | − | 0.273861i | ||||
\(91\) | −6.00000 | + | 3.46410i | −0.628971 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.0000 | − | 10.3923i | 1.86651 | − | 1.07763i | ||||
\(94\) | 20.7846i | 2.14377i | ||||||||
\(95\) | −6.00000 | −0.615587 | ||||||||
\(96\) | 9.00000 | − | 5.19615i | 0.918559 | − | 0.530330i | ||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | − | 8.66025i | − | 0.874818i | ||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | 13.5000 | + | 7.79423i | 1.34330 | + | 0.775555i | 0.987290 | − | 0.158927i | \(-0.0508036\pi\) |
0.356010 | + | 0.934482i | \(0.384137\pi\) | |||||||
\(102\) | −24.0000 | −2.37635 | ||||||||
\(103\) | 4.00000 | + | 6.92820i | 0.394132 | + | 0.682656i | 0.992990 | − | 0.118199i | \(-0.0377120\pi\) |
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(104\) | 3.00000 | + | 1.73205i | 0.294174 | + | 0.169842i | ||||
\(105\) | −18.0000 | + | 10.3923i | −1.75662 | + | 1.01419i | ||||
\(106\) | −4.50000 | + | 7.79423i | −0.437079 | + | 0.757042i | ||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | 3.50000 | − | 6.06218i | 0.335239 | − | 0.580651i | −0.648292 | − | 0.761392i | \(-0.724516\pi\) |
0.983531 | + | 0.180741i | \(0.0578495\pi\) | |||||||
\(110\) | −9.00000 | − | 15.5885i | −0.858116 | − | 1.48630i | ||||
\(111\) | 3.46410i | 0.328798i | ||||||||
\(112\) | −15.0000 | + | 8.66025i | −1.41737 | + | 0.818317i | ||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 6.92820i | 0.648886i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.50000 | − | 0.866025i | −0.139272 | − | 0.0804084i | ||||
\(117\) | 1.00000 | − | 1.73205i | 0.0924500 | − | 0.160128i | ||||
\(118\) | 3.00000 | + | 5.19615i | 0.276172 | + | 0.478345i | ||||
\(119\) | 24.0000 | 2.20008 | ||||||||
\(120\) | 9.00000 | + | 5.19615i | 0.821584 | + | 0.474342i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 7.50000 | − | 11.2583i | 0.679018 | − | 1.01928i | ||||
\(123\) | −6.00000 | −0.541002 | ||||||||
\(124\) | −9.00000 | − | 5.19615i | −0.808224 | − | 0.466628i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 3.00000 | + | 5.19615i | 0.267261 | + | 0.462910i | ||||
\(127\) | 1.00000 | − | 1.73205i | 0.0887357 | − | 0.153695i | −0.818241 | − | 0.574875i | \(-0.805051\pi\) |
0.906977 | + | 0.421180i | \(0.138384\pi\) | |||||||
\(128\) | 10.5000 | + | 6.06218i | 0.928078 | + | 0.535826i | ||||
\(129\) | −6.00000 | − | 3.46410i | −0.528271 | − | 0.304997i | ||||
\(130\) | − | 10.3923i | − | 0.911465i | ||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −6.00000 | + | 3.46410i | −0.522233 | + | 0.301511i | ||||
\(133\) | − | 6.92820i | − | 0.600751i | ||||||
\(134\) | 3.00000 | + | 5.19615i | 0.259161 | + | 0.448879i | ||||
\(135\) | −6.00000 | + | 10.3923i | −0.516398 | + | 0.894427i | ||||
\(136\) | −6.00000 | − | 10.3923i | −0.514496 | − | 0.891133i | ||||
\(137\) | 1.50000 | − | 2.59808i | 0.128154 | − | 0.221969i | −0.794808 | − | 0.606861i | \(-0.792428\pi\) |
0.922961 | + | 0.384893i | \(0.125762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | − | 3.46410i | 0.508913 | − | 0.293821i | −0.223474 | − | 0.974710i | \(-0.571740\pi\) |
0.732387 | + | 0.680889i | \(0.238406\pi\) | |||||||
\(140\) | 9.00000 | + | 5.19615i | 0.760639 | + | 0.439155i | ||||
\(141\) | 12.0000 | + | 20.7846i | 1.01058 | + | 1.75038i | ||||
\(142\) | 18.0000 | 1.51053 | ||||||||
\(143\) | −6.00000 | − | 3.46410i | −0.501745 | − | 0.289683i | ||||
\(144\) | 2.50000 | − | 4.33013i | 0.208333 | − | 0.360844i | ||||
\(145\) | − | 5.19615i | − | 0.431517i | ||||||
\(146\) | − | 12.1244i | − | 1.00342i | ||||||
\(147\) | −5.00000 | − | 8.66025i | −0.412393 | − | 0.714286i | ||||
\(148\) | 1.50000 | − | 0.866025i | 0.123299 | − | 0.0711868i | ||||
\(149\) | −15.0000 | −1.22885 | −0.614424 | − | 0.788976i | \(-0.710612\pi\) | ||||
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(150\) | − | 13.8564i | − | 1.13137i | ||||||
\(151\) | −3.00000 | + | 1.73205i | −0.244137 | + | 0.140952i | −0.617076 | − | 0.786903i | \(-0.711683\pi\) |
0.372940 | + | 0.927855i | \(0.378350\pi\) | |||||||
\(152\) | −3.00000 | + | 1.73205i | −0.243332 | + | 0.140488i | ||||
\(153\) | −6.00000 | + | 3.46410i | −0.485071 | + | 0.280056i | ||||
\(154\) | 18.0000 | − | 10.3923i | 1.45048 | − | 0.837436i | ||||
\(155\) | − | 31.1769i | − | 2.50419i | ||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 12.0000 | − | 6.92820i | 0.957704 | − | 0.552931i | 0.0622385 | − | 0.998061i | \(-0.480176\pi\) |
0.895466 | + | 0.445130i | \(0.146843\pi\) | |||||||
\(158\) | 9.00000 | + | 15.5885i | 0.716002 | + | 1.24015i | ||||
\(159\) | 10.3923i | 0.824163i | ||||||||
\(160\) | − | 15.5885i | − | 1.23238i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 16.5000 | + | 9.52628i | 1.29636 | + | 0.748455i | ||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 1.50000 | + | 2.59808i | 0.117130 | + | 0.202876i | ||||
\(165\) | −18.0000 | − | 10.3923i | −1.40130 | − | 0.809040i | ||||
\(166\) | 9.00000 | − | 5.19615i | 0.698535 | − | 0.403300i | ||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | −6.00000 | + | 10.3923i | −0.462910 | + | 0.801784i | ||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | −18.0000 | + | 31.1769i | −1.38054 | + | 2.39116i | ||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 3.46410i | 0.264135i | ||||||||
\(173\) | −7.50000 | + | 4.33013i | −0.570214 | + | 0.329213i | −0.757235 | − | 0.653143i | \(-0.773450\pi\) |
0.187021 | + | 0.982356i | \(0.440117\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 13.8564i | 1.04745i | ||||||||
\(176\) | −15.0000 | − | 8.66025i | −1.13067 | − | 0.652791i | ||||
\(177\) | 6.00000 | + | 3.46410i | 0.450988 | + | 0.260378i | ||||
\(178\) | −13.5000 | + | 23.3827i | −1.01187 | + | 1.75261i | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | −3.00000 | −0.223607 | ||||||||
\(181\) | −19.5000 | − | 11.2583i | −1.44942 | − | 0.836825i | −0.450977 | − | 0.892536i | \(-0.648924\pi\) |
−0.998447 | + | 0.0557107i | \(0.982258\pi\) | |||||||
\(182\) | 12.0000 | 0.889499 | ||||||||
\(183\) | 1.00000 | − | 15.5885i | 0.0739221 | − | 1.15233i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.50000 | + | 2.59808i | 0.330847 | + | 0.191014i | ||||
\(186\) | −36.0000 | −2.63965 | ||||||||
\(187\) | 12.0000 | + | 20.7846i | 0.877527 | + | 1.51992i | ||||
\(188\) | 6.00000 | − | 10.3923i | 0.437595 | − | 0.757937i | ||||
\(189\) | −12.0000 | − | 6.92820i | −0.872872 | − | 0.503953i | ||||
\(190\) | 9.00000 | + | 5.19615i | 0.652929 | + | 0.376969i | ||||
\(191\) | 13.8564i | 1.00261i | 0.865269 | + | 0.501307i | \(0.167147\pi\) | ||||
−0.865269 | + | 0.501307i | \(0.832853\pi\) | |||||||
\(192\) | 2.00000 | 0.144338 | ||||||||
\(193\) | −10.5000 | + | 6.06218i | −0.755807 | + | 0.436365i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 1.73205i | 0.124354i | ||||||||
\(195\) | −6.00000 | − | 10.3923i | −0.429669 | − | 0.744208i | ||||
\(196\) | −2.50000 | + | 4.33013i | −0.178571 | + | 0.309295i | ||||
\(197\) | −1.50000 | − | 2.59808i | −0.106871 | − | 0.185105i | 0.807630 | − | 0.589689i | \(-0.200750\pi\) |
−0.914501 | + | 0.404584i | \(0.867416\pi\) | |||||||
\(198\) | −3.00000 | + | 5.19615i | −0.213201 | + | 0.369274i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 6.00000 | − | 3.46410i | 0.424264 | − | 0.244949i | ||||
\(201\) | 6.00000 | + | 3.46410i | 0.423207 | + | 0.244339i | ||||
\(202\) | −13.5000 | − | 23.3827i | −0.949857 | − | 1.64520i | ||||
\(203\) | 6.00000 | 0.421117 | ||||||||
\(204\) | 12.0000 | + | 6.92820i | 0.840168 | + | 0.485071i | ||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | − | 13.8564i | − | 0.965422i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.00000 | − | 8.66025i | −0.346688 | − | 0.600481i | ||||
\(209\) | 6.00000 | − | 3.46410i | 0.415029 | − | 0.239617i | ||||
\(210\) | 36.0000 | 2.48424 | ||||||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 4.50000 | − | 2.59808i | 0.309061 | − | 0.178437i | ||||
\(213\) | 18.0000 | − | 10.3923i | 1.23334 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.00000 | + | 5.19615i | −0.613795 | + | 0.354375i | ||||
\(216\) | 6.92820i | 0.471405i | ||||||||
\(217\) | 36.0000 | 2.44384 | ||||||||
\(218\) | −10.5000 | + | 6.06218i | −0.711150 | + | 0.410582i | ||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | 10.3923i | 0.700649i | ||||||||
\(221\) | 13.8564i | 0.932083i | ||||||||
\(222\) | 3.00000 | − | 5.19615i | 0.201347 | − | 0.348743i | ||||
\(223\) | −12.0000 | − | 6.92820i | −0.803579 | − | 0.463947i | 0.0411418 | − | 0.999153i | \(-0.486900\pi\) |
−0.844721 | + | 0.535207i | \(0.820234\pi\) | |||||||
\(224\) | 18.0000 | 1.20268 | ||||||||
\(225\) | −2.00000 | − | 3.46410i | −0.133333 | − | 0.230940i | ||||
\(226\) | −9.00000 | − | 5.19615i | −0.598671 | − | 0.345643i | ||||
\(227\) | 6.00000 | − | 3.46410i | 0.398234 | − | 0.229920i | −0.287488 | − | 0.957784i | \(-0.592820\pi\) |
0.685722 | + | 0.727864i | \(0.259487\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | −9.50000 | + | 16.4545i | −0.627778 | + | 1.08734i | 0.360219 | + | 0.932868i | \(0.382702\pi\) |
−0.987997 | + | 0.154475i | \(0.950631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 20.7846i | 0.789542 | − | 1.36753i | ||||
\(232\) | −1.50000 | − | 2.59808i | −0.0984798 | − | 0.170572i | ||||
\(233\) | − | 12.1244i | − | 0.794293i | −0.917755 | − | 0.397146i | \(-0.870000\pi\) | ||
0.917755 | − | 0.397146i | \(-0.130000\pi\) | |||||||
\(234\) | −3.00000 | + | 1.73205i | −0.196116 | + | 0.113228i | ||||
\(235\) | 36.0000 | 2.34838 | ||||||||
\(236\) | − | 3.46410i | − | 0.225494i | ||||||
\(237\) | 18.0000 | + | 10.3923i | 1.16923 | + | 0.675053i | ||||
\(238\) | −36.0000 | − | 20.7846i | −2.33353 | − | 1.34727i | ||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | −15.0000 | − | 25.9808i | −0.968246 | − | 1.67705i | ||||
\(241\) | −11.0000 | −0.708572 | −0.354286 | − | 0.935137i | \(-0.615276\pi\) | ||||
−0.354286 | + | 0.935137i | \(0.615276\pi\) | |||||||
\(242\) | 1.50000 | + | 0.866025i | 0.0964237 | + | 0.0556702i | ||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | −7.00000 | + | 3.46410i | −0.448129 | + | 0.221766i | ||||
\(245\) | −15.0000 | −0.958315 | ||||||||
\(246\) | 9.00000 | + | 5.19615i | 0.573819 | + | 0.331295i | ||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | −9.00000 | − | 15.5885i | −0.571501 | − | 0.989868i | ||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 4.50000 | + | 2.59808i | 0.284605 | + | 0.164317i | ||||
\(251\) | 12.0000 | + | 6.92820i | 0.757433 | + | 0.437304i | 0.828373 | − | 0.560176i | \(-0.189267\pi\) |
−0.0709402 | + | 0.997481i | \(0.522600\pi\) | |||||||
\(252\) | − | 3.46410i | − | 0.218218i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.00000 | + | 1.73205i | −0.188237 | + | 0.108679i | ||||
\(255\) | 41.5692i | 2.60317i | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 7.50000 | − | 12.9904i | 0.467837 | − | 0.810318i | −0.531487 | − | 0.847066i | \(-0.678367\pi\) |
0.999325 | + | 0.0367485i | \(0.0117000\pi\) | |||||||
\(258\) | 6.00000 | + | 10.3923i | 0.373544 | + | 0.646997i | ||||
\(259\) | −3.00000 | + | 5.19615i | −0.186411 | + | 0.322873i | ||||
\(260\) | −3.00000 | + | 5.19615i | −0.186052 | + | 0.322252i | ||||
\(261\) | −1.50000 | + | 0.866025i | −0.0928477 | + | 0.0536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 5.19615i | 0.184988 | + | 0.320408i | 0.943572 | − | 0.331166i | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | −12.0000 | −0.738549 | ||||||||
\(265\) | 13.5000 | + | 7.79423i | 0.829298 | + | 0.478796i | ||||
\(266\) | −6.00000 | + | 10.3923i | −0.367884 | + | 0.637193i | ||||
\(267\) | 31.1769i | 1.90800i | ||||||||
\(268\) | − | 3.46410i | − | 0.211604i | ||||||
\(269\) | −4.50000 | − | 7.79423i | −0.274370 | − | 0.475223i | 0.695606 | − | 0.718423i | \(-0.255136\pi\) |
−0.969976 | + | 0.243201i | \(0.921803\pi\) | |||||||
\(270\) | 18.0000 | − | 10.3923i | 1.09545 | − | 0.632456i | ||||
\(271\) | −10.0000 | −0.607457 | −0.303728 | − | 0.952759i | \(-0.598232\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598232\pi\) | |||||||
\(272\) | 34.6410i | 2.10042i | ||||||||
\(273\) | 12.0000 | − | 6.92820i | 0.726273 | − | 0.419314i | ||||
\(274\) | −4.50000 | + | 2.59808i | −0.271855 | + | 0.156956i | ||||
\(275\) | −12.0000 | + | 6.92820i | −0.723627 | + | 0.417786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −12.0000 | −0.719712 | ||||||||
\(279\) | −9.00000 | + | 5.19615i | −0.538816 | + | 0.311086i | ||||
\(280\) | 9.00000 | + | 15.5885i | 0.537853 | + | 0.931589i | ||||
\(281\) | − | 19.0526i | − | 1.13658i | −0.822828 | − | 0.568290i | \(-0.807605\pi\) | ||
0.822828 | − | 0.568290i | \(-0.192395\pi\) | |||||||
\(282\) | − | 41.5692i | − | 2.47541i | ||||||
\(283\) | −13.0000 | + | 22.5167i | −0.772770 | + | 1.33848i | 0.163270 | + | 0.986581i | \(0.447796\pi\) |
−0.936039 | + | 0.351895i | \(0.885537\pi\) | |||||||
\(284\) | −9.00000 | − | 5.19615i | −0.534052 | − | 0.308335i | ||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 6.00000 | + | 10.3923i | 0.354787 | + | 0.614510i | ||||
\(287\) | −9.00000 | − | 5.19615i | −0.531253 | − | 0.306719i | ||||
\(288\) | −4.50000 | + | 2.59808i | −0.265165 | + | 0.153093i | ||||
\(289\) | 15.5000 | − | 26.8468i | 0.911765 | − | 1.57922i | ||||
\(290\) | −4.50000 | + | 7.79423i | −0.264249 | + | 0.457693i | ||||
\(291\) | 1.00000 | + | 1.73205i | 0.0586210 | + | 0.101535i | ||||
\(292\) | −3.50000 | + | 6.06218i | −0.204822 | + | 0.354762i | ||||
\(293\) | −3.00000 | − | 5.19615i | −0.175262 | − | 0.303562i | 0.764990 | − | 0.644042i | \(-0.222744\pi\) |
−0.940252 | + | 0.340480i | \(0.889411\pi\) | |||||||
\(294\) | 17.3205i | 1.01015i | ||||||||
\(295\) | 9.00000 | − | 5.19615i | 0.524000 | − | 0.302532i | ||||
\(296\) | 3.00000 | 0.174371 | ||||||||
\(297\) | − | 13.8564i | − | 0.804030i | ||||||
\(298\) | 22.5000 | + | 12.9904i | 1.30339 | + | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | + | 6.92820i | −0.230940 | + | 0.400000i | ||||
\(301\) | −6.00000 | − | 10.3923i | −0.345834 | − | 0.599002i | ||||
\(302\) | 6.00000 | 0.345261 | ||||||||
\(303\) | −27.0000 | − | 15.5885i | −1.55111 | − | 0.895533i | ||||
\(304\) | 10.0000 | 0.573539 | ||||||||
\(305\) | −19.5000 | − | 12.9904i | −1.11657 | − | 0.743827i | ||||
\(306\) | 12.0000 | 0.685994 | ||||||||
\(307\) | −3.00000 | − | 1.73205i | −0.171219 | − | 0.0988534i | 0.411941 | − | 0.911210i | \(-0.364851\pi\) |
−0.583161 | + | 0.812357i | \(0.698184\pi\) | |||||||
\(308\) | −12.0000 | −0.683763 | ||||||||
\(309\) | −8.00000 | − | 13.8564i | −0.455104 | − | 0.788263i | ||||
\(310\) | −27.0000 | + | 46.7654i | −1.53350 | + | 2.65609i | ||||
\(311\) | 12.0000 | + | 6.92820i | 0.680458 | + | 0.392862i | 0.800027 | − | 0.599963i | \(-0.204818\pi\) |
−0.119570 | + | 0.992826i | \(0.538152\pi\) | |||||||
\(312\) | −6.00000 | − | 3.46410i | −0.339683 | − | 0.196116i | ||||
\(313\) | − | 20.7846i | − | 1.17482i | −0.809291 | − | 0.587408i | \(-0.800148\pi\) | ||
0.809291 | − | 0.587408i | \(-0.199852\pi\) | |||||||
\(314\) | −24.0000 | −1.35440 | ||||||||
\(315\) | 9.00000 | − | 5.19615i | 0.507093 | − | 0.292770i | ||||
\(316\) | − | 10.3923i | − | 0.584613i | ||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 9.00000 | − | 15.5885i | 0.504695 | − | 0.874157i | ||||
\(319\) | 3.00000 | + | 5.19615i | 0.167968 | + | 0.290929i | ||||
\(320\) | 1.50000 | − | 2.59808i | 0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | − | 6.92820i | −0.667698 | − | 0.385496i | ||||
\(324\) | −5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | ||||
\(325\) | −8.00000 | −0.443760 | ||||||||
\(326\) | −6.00000 | − | 3.46410i | −0.332309 | − | 0.191859i | ||||
\(327\) | −7.00000 | + | 12.1244i | −0.387101 | + | 0.670478i | ||||
\(328\) | 5.19615i | 0.286910i | ||||||||
\(329\) | 41.5692i | 2.29179i | ||||||||
\(330\) | 18.0000 | + | 31.1769i | 0.990867 | + | 1.71623i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | − | 1.73205i | − | 0.0949158i | ||||||
\(334\) | 27.0000 | − | 15.5885i | 1.47737 | − | 0.852962i | ||||
\(335\) | 9.00000 | − | 5.19615i | 0.491723 | − | 0.283896i | ||||
\(336\) | 30.0000 | − | 17.3205i | 1.63663 | − | 0.944911i | ||||
\(337\) | −24.0000 | + | 13.8564i | −1.30736 | + | 0.754807i | −0.981655 | − | 0.190664i | \(-0.938936\pi\) |
−0.325708 | + | 0.945470i | \(0.605603\pi\) | |||||||
\(338\) | − | 15.5885i | − | 0.847900i | ||||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 18.0000 | − | 10.3923i | 0.976187 | − | 0.563602i | ||||
\(341\) | 18.0000 | + | 31.1769i | 0.974755 | + | 1.68832i | ||||
\(342\) | − | 3.46410i | − | 0.187317i | ||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | −3.00000 | + | 5.19615i | −0.161749 | + | 0.280158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.0000 | 0.806405 | ||||||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | 3.00000 | + | 1.73205i | 0.160817 | + | 0.0928477i | ||||
\(349\) | 4.50000 | − | 2.59808i | 0.240879 | − | 0.139072i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 12.0000 | − | 20.7846i | 0.641427 | − | 1.11098i | ||||
\(351\) | 4.00000 | − | 6.92820i | 0.213504 | − | 0.369800i | ||||
\(352\) | 9.00000 | + | 15.5885i | 0.479702 | + | 0.830868i | ||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | − | 31.1769i | − | 1.65470i | ||||||
\(356\) | 13.5000 | − | 7.79423i | 0.715499 | − | 0.413093i | ||||
\(357\) | −48.0000 | −2.54043 | ||||||||
\(358\) | 10.3923i | 0.549250i | ||||||||
\(359\) | −15.0000 | − | 8.66025i | −0.791670 | − | 0.457071i | 0.0488803 | − | 0.998805i | \(-0.484435\pi\) |
−0.840550 | + | 0.541734i | \(0.817768\pi\) | |||||||
\(360\) | −4.50000 | − | 2.59808i | −0.237171 | − | 0.136931i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 19.5000 | + | 33.7750i | 1.02490 | + | 1.77517i | ||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | −6.00000 | − | 3.46410i | −0.314485 | − | 0.181568i | ||||
\(365\) | −21.0000 | −1.09919 | ||||||||
\(366\) | −15.0000 | + | 22.5167i | −0.784063 | + | 1.17696i | ||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | −4.50000 | − | 7.79423i | −0.233944 | − | 0.405203i | ||||
\(371\) | −9.00000 | + | 15.5885i | −0.467257 | + | 0.809312i | ||||
\(372\) | 18.0000 | + | 10.3923i | 0.933257 | + | 0.538816i | ||||
\(373\) | 25.5000 | + | 14.7224i | 1.32034 | + | 0.762299i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
0.336557 | + | 0.941663i | \(0.390737\pi\) | |||||||
\(374\) | − | 41.5692i | − | 2.14949i | ||||||
\(375\) | 6.00000 | 0.309839 | ||||||||
\(376\) | 18.0000 | − | 10.3923i | 0.928279 | − | 0.535942i | ||||
\(377\) | 3.46410i | 0.178410i | ||||||||
\(378\) | 12.0000 | + | 20.7846i | 0.617213 | + | 1.06904i | ||||
\(379\) | 8.00000 | − | 13.8564i | 0.410932 | − | 0.711756i | −0.584060 | − | 0.811711i | \(-0.698537\pi\) |
0.994992 | + | 0.0999550i | \(0.0318699\pi\) | |||||||
\(380\) | −3.00000 | − | 5.19615i | −0.153897 | − | 0.266557i | ||||
\(381\) | −2.00000 | + | 3.46410i | −0.102463 | + | 0.177471i | ||||
\(382\) | 12.0000 | − | 20.7846i | 0.613973 | − | 1.06343i | ||||
\(383\) | 18.0000 | − | 10.3923i | 0.919757 | − | 0.531022i | 0.0361995 | − | 0.999345i | \(-0.488475\pi\) |
0.883558 | + | 0.468323i | \(0.155141\pi\) | |||||||
\(384\) | −21.0000 | − | 12.1244i | −1.07165 | − | 0.618718i | ||||
\(385\) | −18.0000 | − | 31.1769i | −0.917365 | − | 1.58892i | ||||
\(386\) | 21.0000 | 1.06887 | ||||||||
\(387\) | 3.00000 | + | 1.73205i | 0.152499 | + | 0.0880451i | ||||
\(388\) | 0.500000 | − | 0.866025i | 0.0253837 | − | 0.0439658i | ||||
\(389\) | 29.4449i | 1.49291i | 0.665434 | + | 0.746457i | \(0.268247\pi\) | ||||
−0.665434 | + | 0.746457i | \(0.731753\pi\) | |||||||
\(390\) | 20.7846i | 1.05247i | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7.50000 | + | 4.33013i | −0.378807 | + | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.19615i | 0.261778i | ||||||||
\(395\) | 27.0000 | − | 15.5885i | 1.35852 | − | 0.784340i | ||||
\(396\) | 3.00000 | − | 1.73205i | 0.150756 | − | 0.0870388i | ||||
\(397\) | −28.5000 | + | 16.4545i | −1.43037 | + | 0.825827i | −0.997149 | − | 0.0754589i | \(-0.975958\pi\) |
−0.433225 | + | 0.901286i | \(0.642624\pi\) | |||||||
\(398\) | −6.00000 | + | 3.46410i | −0.300753 | + | 0.173640i | ||||
\(399\) | 13.8564i | 0.693688i | ||||||||
\(400\) | −20.0000 | −1.00000 | ||||||||
\(401\) | −1.50000 | + | 0.866025i | −0.0749064 | + | 0.0432472i | −0.536985 | − | 0.843592i | \(-0.680437\pi\) |
0.462079 | + | 0.886839i | \(0.347104\pi\) | |||||||
\(402\) | −6.00000 | − | 10.3923i | −0.299253 | − | 0.518321i | ||||
\(403\) | 20.7846i | 1.03536i | ||||||||
\(404\) | 15.5885i | 0.775555i | ||||||||
\(405\) | 16.5000 | − | 28.5788i | 0.819892 | − | 1.42009i | ||||
\(406\) | −9.00000 | − | 5.19615i | −0.446663 | − | 0.257881i | ||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 12.0000 | + | 20.7846i | 0.594089 | + | 1.02899i | ||||
\(409\) | 31.5000 | + | 18.1865i | 1.55757 | + | 0.899266i | 0.997488 | + | 0.0708321i | \(0.0225654\pi\) |
0.560087 | + | 0.828434i | \(0.310768\pi\) | |||||||
\(410\) | 13.5000 | − | 7.79423i | 0.666717 | − | 0.384930i | ||||
\(411\) | −3.00000 | + | 5.19615i | −0.147979 | + | 0.256307i | ||||
\(412\) | −4.00000 | + | 6.92820i | −0.197066 | + | 0.341328i | ||||
\(413\) | 6.00000 | + | 10.3923i | 0.295241 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | − | 15.5885i | −0.441793 | − | 0.765207i | ||||
\(416\) | 10.3923i | 0.509525i | ||||||||
\(417\) | −12.0000 | + | 6.92820i | −0.587643 | + | 0.339276i | ||||
\(418\) | −12.0000 | −0.586939 | ||||||||
\(419\) | − | 27.7128i | − | 1.35386i | −0.736048 | − | 0.676930i | \(-0.763310\pi\) | ||
0.736048 | − | 0.676930i | \(-0.236690\pi\) | |||||||
\(420\) | −18.0000 | − | 10.3923i | −0.878310 | − | 0.507093i | ||||
\(421\) | −18.0000 | − | 10.3923i | −0.877266 | − | 0.506490i | −0.00751023 | − | 0.999972i | \(-0.502391\pi\) |
−0.869756 | + | 0.493482i | \(0.835724\pi\) | |||||||
\(422\) | 3.00000 | − | 5.19615i | 0.146038 | − | 0.252945i | ||||
\(423\) | −6.00000 | − | 10.3923i | −0.291730 | − | 0.505291i | ||||
\(424\) | 9.00000 | 0.437079 | ||||||||
\(425\) | 24.0000 | + | 13.8564i | 1.16417 | + | 0.672134i | ||||
\(426\) | −36.0000 | −1.74421 | ||||||||
\(427\) | 15.0000 | − | 22.5167i | 0.725901 | − | 1.08966i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0000 | + | 6.92820i | 0.579365 | + | 0.334497i | ||||
\(430\) | 18.0000 | 0.868037 | ||||||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 10.0000 | − | 17.3205i | 0.481125 | − | 0.833333i | ||||
\(433\) | −34.5000 | − | 19.9186i | −1.65796 | − | 0.957226i | −0.973653 | − | 0.228036i | \(-0.926769\pi\) |
−0.684312 | − | 0.729190i | \(-0.739897\pi\) | |||||||
\(434\) | −54.0000 | − | 31.1769i | −2.59208 | − | 1.49654i | ||||
\(435\) | 10.3923i | 0.498273i | ||||||||
\(436\) | 7.00000 | 0.335239 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 24.2487i | 1.15865i | ||||||||
\(439\) | −10.0000 | − | 17.3205i | −0.477274 | − | 0.826663i | 0.522387 | − | 0.852709i | \(-0.325042\pi\) |
−0.999661 | + | 0.0260459i | \(0.991708\pi\) | |||||||
\(440\) | −9.00000 | + | 15.5885i | −0.429058 | + | 0.743151i | ||||
\(441\) | 2.50000 | + | 4.33013i | 0.119048 | + | 0.206197i | ||||
\(442\) | 12.0000 | − | 20.7846i | 0.570782 | − | 0.988623i | ||||
\(443\) | 3.00000 | − | 5.19615i | 0.142534 | − | 0.246877i | −0.785916 | − | 0.618333i | \(-0.787808\pi\) |
0.928450 | + | 0.371457i | \(0.121142\pi\) | |||||||
\(444\) | −3.00000 | + | 1.73205i | −0.142374 | + | 0.0821995i | ||||
\(445\) | 40.5000 | + | 23.3827i | 1.91988 | + | 1.10845i | ||||
\(446\) | 12.0000 | + | 20.7846i | 0.568216 | + | 0.984180i | ||||
\(447\) | 30.0000 | 1.41895 | ||||||||
\(448\) | 3.00000 | + | 1.73205i | 0.141737 | + | 0.0818317i | ||||
\(449\) | −15.0000 | + | 25.9808i | −0.707894 | + | 1.22611i | 0.257743 | + | 0.966213i | \(0.417021\pi\) |
−0.965637 | + | 0.259895i | \(0.916312\pi\) | |||||||
\(450\) | 6.92820i | 0.326599i | ||||||||
\(451\) | − | 10.3923i | − | 0.489355i | ||||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | 6.00000 | − | 3.46410i | 0.281905 | − | 0.162758i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | − | 20.7846i | − | 0.974398i | ||||||
\(456\) | 6.00000 | − | 3.46410i | 0.280976 | − | 0.162221i | ||||
\(457\) | −19.5000 | + | 11.2583i | −0.912172 | + | 0.526642i | −0.881129 | − | 0.472876i | \(-0.843216\pi\) |
−0.0310423 | + | 0.999518i | \(0.509883\pi\) | |||||||
\(458\) | 28.5000 | − | 16.4545i | 1.33172 | − | 0.768867i | ||||
\(459\) | −24.0000 | + | 13.8564i | −1.12022 | + | 0.646762i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0000 | 1.25752 | 0.628758 | − | 0.777601i | \(-0.283564\pi\) | ||||
0.628758 | + | 0.777601i | \(0.283564\pi\) | |||||||
\(462\) | −36.0000 | + | 20.7846i | −1.67487 | + | 0.966988i | ||||
\(463\) | −20.0000 | − | 34.6410i | −0.929479 | − | 1.60990i | −0.784195 | − | 0.620515i | \(-0.786924\pi\) |
−0.145284 | − | 0.989390i | \(-0.546410\pi\) | |||||||
\(464\) | 8.66025i | 0.402042i | ||||||||
\(465\) | 62.3538i | 2.89159i | ||||||||
\(466\) | −10.5000 | + | 18.1865i | −0.486403 | + | 0.842475i | ||||
\(467\) | 18.0000 | + | 10.3923i | 0.832941 | + | 0.480899i | 0.854858 | − | 0.518861i | \(-0.173644\pi\) |
−0.0219178 | + | 0.999760i | \(0.506977\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 6.00000 | + | 10.3923i | 0.277054 | + | 0.479872i | ||||
\(470\) | −54.0000 | − | 31.1769i | −2.49083 | − | 1.43808i | ||||
\(471\) | −24.0000 | + | 13.8564i | −1.10586 | + | 0.638470i | ||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 6.00000 | − | 10.3923i | 0.275880 | − | 0.477839i | ||||
\(474\) | −18.0000 | − | 31.1769i | −0.826767 | − | 1.43200i | ||||
\(475\) | 4.00000 | − | 6.92820i | 0.183533 | − | 0.317888i | ||||
\(476\) | 12.0000 | + | 20.7846i | 0.550019 | + | 0.952661i | ||||
\(477\) | − | 5.19615i | − | 0.237915i | ||||||
\(478\) | 9.00000 | − | 5.19615i | 0.411650 | − | 0.237666i | ||||
\(479\) | −6.00000 | −0.274147 | −0.137073 | − | 0.990561i | \(-0.543770\pi\) | ||||
−0.137073 | + | 0.990561i | \(0.543770\pi\) | |||||||
\(480\) | 31.1769i | 1.42302i | ||||||||
\(481\) | −3.00000 | − | 1.73205i | −0.136788 | − | 0.0789747i | ||||
\(482\) | 16.5000 | + | 9.52628i | 0.751554 | + | 0.433910i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | − | 0.866025i | −0.0227273 | − | 0.0393648i | ||||
\(485\) | 3.00000 | 0.136223 | ||||||||
\(486\) | −15.0000 | − | 8.66025i | −0.680414 | − | 0.392837i | ||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | −13.5000 | − | 0.866025i | −0.611116 | − | 0.0392031i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 22.5000 | + | 12.9904i | 1.01645 | + | 0.586846i | ||||
\(491\) | 30.0000 | 1.35388 | 0.676941 | − | 0.736038i | \(-0.263305\pi\) | ||||
0.676941 | + | 0.736038i | \(0.263305\pi\) | |||||||
\(492\) | −3.00000 | − | 5.19615i | −0.135250 | − | 0.234261i | ||||
\(493\) | 6.00000 | − | 10.3923i | 0.270226 | − | 0.468046i | ||||
\(494\) | −6.00000 | − | 3.46410i | −0.269953 | − | 0.155857i | ||||
\(495\) | 9.00000 | + | 5.19615i | 0.404520 | + | 0.233550i | ||||
\(496\) | 51.9615i | 2.33314i | ||||||||
\(497\) | 36.0000 | 1.61482 | ||||||||
\(498\) | −18.0000 | + | 10.3923i | −0.806599 | + | 0.465690i | ||||
\(499\) | 34.6410i | 1.55074i | 0.631504 | + | 0.775372i | \(0.282438\pi\) | ||||
−0.631504 | + | 0.775372i | \(0.717562\pi\) | |||||||
\(500\) | −1.50000 | − | 2.59808i | −0.0670820 | − | 0.116190i | ||||
\(501\) | 18.0000 | − | 31.1769i | 0.804181 | − | 1.39288i | ||||
\(502\) | −12.0000 | − | 20.7846i | −0.535586 | − | 0.927663i | ||||
\(503\) | −18.0000 | + | 31.1769i | −0.802580 | + | 1.39011i | 0.115332 | + | 0.993327i | \(0.463207\pi\) |
−0.917912 | + | 0.396783i | \(0.870127\pi\) | |||||||
\(504\) | 3.00000 | − | 5.19615i | 0.133631 | − | 0.231455i | ||||
\(505\) | −40.5000 | + | 23.3827i | −1.80223 | + | 1.04052i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | − | 15.5885i | −0.399704 | − | 0.692308i | ||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −13.5000 | − | 7.79423i | −0.598377 | − | 0.345473i | 0.170026 | − | 0.985440i | \(-0.445615\pi\) |
−0.768403 | + | 0.639966i | \(0.778948\pi\) | |||||||
\(510\) | 36.0000 | − | 62.3538i | 1.59411 | − | 2.76107i | ||||
\(511\) | − | 24.2487i | − | 1.07270i | ||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 4.00000 | + | 6.92820i | 0.176604 | + | 0.305888i | ||||
\(514\) | −22.5000 | + | 12.9904i | −0.992432 | + | 0.572981i | ||||
\(515\) | −24.0000 | −1.05757 | ||||||||
\(516\) | − | 6.92820i | − | 0.304997i | ||||||
\(517\) | −36.0000 | + | 20.7846i | −1.58328 | + | 0.914106i | ||||
\(518\) | 9.00000 | − | 5.19615i | 0.395437 | − | 0.228306i | ||||
\(519\) | 15.0000 | − | 8.66025i | 0.658427 | − | 0.380143i | ||||
\(520\) | −9.00000 | + | 5.19615i | −0.394676 | + | 0.227866i | ||||
\(521\) | 25.9808i | 1.13824i | 0.822255 | + | 0.569119i | \(0.192716\pi\) | ||||
−0.822255 | + | 0.569119i | \(0.807284\pi\) | |||||||
\(522\) | 3.00000 | 0.131306 | ||||||||
\(523\) | −18.0000 | + | 10.3923i | −0.787085 | + | 0.454424i | −0.838935 | − | 0.544231i | \(-0.816821\pi\) |
0.0518503 | + | 0.998655i | \(0.483488\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 27.7128i | − | 1.20949i | ||||||
\(526\) | − | 10.3923i | − | 0.453126i | ||||||
\(527\) | 36.0000 | − | 62.3538i | 1.56818 | − | 2.71618i | ||||
\(528\) | 30.0000 | + | 17.3205i | 1.30558 | + | 0.753778i | ||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −13.5000 | − | 23.3827i | −0.586403 | − | 1.01568i | ||||
\(531\) | −3.00000 | − | 1.73205i | −0.130189 | − | 0.0751646i | ||||
\(532\) | 6.00000 | − | 3.46410i | 0.260133 | − | 0.150188i | ||||
\(533\) | 3.00000 | − | 5.19615i | 0.129944 | − | 0.225070i | ||||
\(534\) | 27.0000 | − | 46.7654i | 1.16840 | − | 2.02374i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.00000 | − | 5.19615i | 0.129580 | − | 0.224440i | ||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | 15.5885i | 0.672066i | ||||||||
\(539\) | 15.0000 | − | 8.66025i | 0.646096 | − | 0.373024i | ||||
\(540\) | −12.0000 | −0.516398 | ||||||||
\(541\) | − | 13.8564i | − | 0.595733i | −0.954607 | − | 0.297867i | \(-0.903725\pi\) | ||
0.954607 | − | 0.297867i | \(-0.0962751\pi\) | |||||||
\(542\) | 15.0000 | + | 8.66025i | 0.644305 | + | 0.371990i | ||||
\(543\) | 39.0000 | + | 22.5167i | 1.67365 | + | 0.966282i | ||||
\(544\) | 18.0000 | − | 31.1769i | 0.771744 | − | 1.33670i | ||||
\(545\) | 10.5000 | + | 18.1865i | 0.449771 | + | 0.779026i | ||||
\(546\) | −24.0000 | −1.02711 | ||||||||
\(547\) | 33.0000 | + | 19.0526i | 1.41098 | + | 0.814629i | 0.995481 | − | 0.0949657i | \(-0.0302741\pi\) |
0.415498 | + | 0.909594i | \(0.363607\pi\) | |||||||
\(548\) | 3.00000 | 0.128154 | ||||||||
\(549\) | −0.500000 | + | 7.79423i | −0.0213395 | + | 0.332650i | ||||
\(550\) | 24.0000 | 1.02336 | ||||||||
\(551\) | −3.00000 | − | 1.73205i | −0.127804 | − | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | + | 31.1769i | 0.765438 | + | 1.32578i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.00000 | − | 5.19615i | −0.382029 | − | 0.220564i | ||||
\(556\) | 6.00000 | + | 3.46410i | 0.254457 | + | 0.146911i | ||||
\(557\) | 1.73205i | 0.0733893i | 0.999327 | + | 0.0366947i | \(0.0116829\pi\) | ||||
−0.999327 | + | 0.0366947i | \(0.988317\pi\) | |||||||
\(558\) | 18.0000 | 0.762001 | ||||||||
\(559\) | 6.00000 | − | 3.46410i | 0.253773 | − | 0.146516i | ||||
\(560\) | − | 51.9615i | − | 2.19578i | ||||||
\(561\) | −24.0000 | − | 41.5692i | −1.01328 | − | 1.75505i | ||||
\(562\) | −16.5000 | + | 28.5788i | −0.696010 | + | 1.20553i | ||||
\(563\) | −21.0000 | − | 36.3731i | −0.885044 | − | 1.53294i | −0.845663 | − | 0.533718i | \(-0.820794\pi\) |
−0.0393818 | − | 0.999224i | \(-0.512539\pi\) | |||||||
\(564\) | −12.0000 | + | 20.7846i | −0.505291 | + | 0.875190i | ||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 39.0000 | − | 22.5167i | 1.63929 | − | 0.946446i | ||||
\(567\) | 33.0000 | + | 19.0526i | 1.38587 | + | 0.800132i | ||||
\(568\) | −9.00000 | − | 15.5885i | −0.377632 | − | 0.654077i | ||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | −18.0000 | − | 10.3923i | −0.753937 | − | 0.435286i | ||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | − | 6.92820i | − | 0.289683i | ||||||
\(573\) | − | 27.7128i | − | 1.15772i | ||||||
\(574\) | 9.00000 | + | 15.5885i | 0.375653 | + | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 22.5167i | 0.937381i | 0.883362 | + | 0.468690i | \(0.155274\pi\) | ||||
−0.883362 | + | 0.468690i | \(0.844726\pi\) | |||||||
\(578\) | −46.5000 | + | 26.8468i | −1.93415 | + | 1.11668i | ||||
\(579\) | 21.0000 | − | 12.1244i | 0.872730 | − | 0.503871i | ||||
\(580\) | 4.50000 | − | 2.59808i | 0.186852 | − | 0.107879i | ||||
\(581\) | 18.0000 | − | 10.3923i | 0.746766 | − | 0.431145i | ||||
\(582\) | − | 3.46410i | − | 0.143592i | ||||||
\(583\) | −18.0000 | −0.745484 | ||||||||
\(584\) | −10.5000 | + | 6.06218i | −0.434493 | + | 0.250855i | ||||
\(585\) | 3.00000 | + | 5.19615i | 0.124035 | + | 0.214834i | ||||
\(586\) | 10.3923i | 0.429302i | ||||||||
\(587\) | − | 6.92820i | − | 0.285958i | −0.989726 | − | 0.142979i | \(-0.954332\pi\) | ||
0.989726 | − | 0.142979i | \(-0.0456681\pi\) | |||||||
\(588\) | 5.00000 | − | 8.66025i | 0.206197 | − | 0.357143i | ||||
\(589\) | −18.0000 | − | 10.3923i | −0.741677 | − | 0.428207i | ||||
\(590\) | −18.0000 | −0.741048 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | −7.50000 | − | 4.33013i | −0.308248 | − | 0.177967i | ||||
\(593\) | −1.50000 | + | 0.866025i | −0.0615976 | + | 0.0355634i | −0.530483 | − | 0.847696i | \(-0.677989\pi\) |
0.468885 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(594\) | −12.0000 | + | 20.7846i | −0.492366 | + | 0.852803i | ||||
\(595\) | −36.0000 | + | 62.3538i | −1.47586 | + | 2.55626i | ||||
\(596\) | −7.50000 | − | 12.9904i | −0.307212 | − | 0.532107i | ||||
\(597\) | −4.00000 | + | 6.92820i | −0.163709 | + | 0.283552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.3205i | 0.707697i | 0.935303 | + | 0.353848i | \(0.115127\pi\) | ||||
−0.935303 | + | 0.353848i | \(0.884873\pi\) | |||||||
\(600\) | −12.0000 | + | 6.92820i | −0.489898 | + | 0.282843i | ||||
\(601\) | −5.00000 | −0.203954 | −0.101977 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101977 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(602\) | 20.7846i | 0.847117i | ||||||||
\(603\) | −3.00000 | − | 1.73205i | −0.122169 | − | 0.0705346i | ||||
\(604\) | −3.00000 | − | 1.73205i | −0.122068 | − | 0.0704761i | ||||
\(605\) | 1.50000 | − | 2.59808i | 0.0609837 | − | 0.105627i | ||||
\(606\) | 27.0000 | + | 46.7654i | 1.09680 | + | 1.89971i | ||||
\(607\) | −22.0000 | −0.892952 | −0.446476 | − | 0.894795i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | −9.00000 | − | 5.19615i | −0.364998 | − | 0.210732i | ||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | 18.0000 | + | 36.3731i | 0.728799 | + | 1.47270i | ||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | −6.00000 | − | 3.46410i | −0.242536 | − | 0.140028i | ||||
\(613\) | −5.00000 | −0.201948 | −0.100974 | − | 0.994889i | \(-0.532196\pi\) | ||||
−0.100974 | + | 0.994889i | \(0.532196\pi\) | |||||||
\(614\) | 3.00000 | + | 5.19615i | 0.121070 | + | 0.209700i | ||||
\(615\) | 9.00000 | − | 15.5885i | 0.362915 | − | 0.628587i | ||||
\(616\) | −18.0000 | − | 10.3923i | −0.725241 | − | 0.418718i | ||||
\(617\) | −18.0000 | − | 10.3923i | −0.724653 | − | 0.418378i | 0.0918100 | − | 0.995777i | \(-0.470735\pi\) |
−0.816463 | + | 0.577398i | \(0.804068\pi\) | |||||||
\(618\) | 27.7128i | 1.11477i | ||||||||
\(619\) | −32.0000 | −1.28619 | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||||
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | 27.0000 | − | 15.5885i | 1.08435 | − | 0.626048i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | − | 20.7846i | −0.481156 | − | 0.833387i | ||||
\(623\) | −27.0000 | + | 46.7654i | −1.08173 | + | 1.87362i | ||||
\(624\) | 10.0000 | + | 17.3205i | 0.400320 | + | 0.693375i | ||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −18.0000 | + | 31.1769i | −0.719425 | + | 1.24608i | ||||
\(627\) | −12.0000 | + | 6.92820i | −0.479234 | + | 0.276686i | ||||
\(628\) | 12.0000 | + | 6.92820i | 0.478852 | + | 0.276465i | ||||
\(629\) | 6.00000 | + | 10.3923i | 0.239236 | + | 0.414368i | ||||
\(630\) | −18.0000 | −0.717137 | ||||||||
\(631\) | 15.0000 | + | 8.66025i | 0.597141 | + | 0.344759i | 0.767916 | − | 0.640551i | \(-0.221294\pi\) |
−0.170775 | + | 0.985310i | \(0.554627\pi\) | |||||||
\(632\) | 9.00000 | − | 15.5885i | 0.358001 | − | 0.620076i | ||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | − | 10.3923i | − | 0.412731i | ||||||
\(635\) | 3.00000 | + | 5.19615i | 0.119051 | + | 0.206203i | ||||
\(636\) | −9.00000 | + | 5.19615i | −0.356873 | + | 0.206041i | ||||
\(637\) | 10.0000 | 0.396214 | ||||||||
\(638\) | − | 10.3923i | − | 0.411435i | ||||||
\(639\) | −9.00000 | + | 5.19615i | −0.356034 | + | 0.205557i | ||||
\(640\) | −31.5000 | + | 18.1865i | −1.24515 | + | 0.718886i | ||||
\(641\) | 28.5000 | − | 16.4545i | 1.12568 | − | 0.649913i | 0.182837 | − | 0.983143i | \(-0.441472\pi\) |
0.942845 | + | 0.333230i | \(0.108139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.2487i | − | 0.956276i | −0.878285 | − | 0.478138i | \(-0.841312\pi\) | ||
0.878285 | − | 0.478138i | \(-0.158688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.0000 | − | 10.3923i | 0.708749 | − | 0.409197i | ||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | − | 13.8564i | − | 0.544752i | −0.962191 | − | 0.272376i | \(-0.912191\pi\) | ||
0.962191 | − | 0.272376i | \(-0.0878094\pi\) | |||||||
\(648\) | − | 19.0526i | − | 0.748455i | ||||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 12.0000 | + | 6.92820i | 0.470679 | + | 0.271746i | ||||
\(651\) | −72.0000 | −2.82190 | ||||||||
\(652\) | 2.00000 | + | 3.46410i | 0.0783260 | + | 0.135665i | ||||
\(653\) | 31.5000 | + | 18.1865i | 1.23269 | + | 0.711694i | 0.967590 | − | 0.252527i | \(-0.0812616\pi\) |
0.265100 | + | 0.964221i | \(0.414595\pi\) | |||||||
\(654\) | 21.0000 | − | 12.1244i | 0.821165 | − | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.50000 | − | 12.9904i | 0.292826 | − | 0.507189i | ||||
\(657\) | 3.50000 | + | 6.06218i | 0.136548 | + | 0.236508i | ||||
\(658\) | 36.0000 | − | 62.3538i | 1.40343 | − | 2.43081i | ||||
\(659\) | 9.00000 | + | 15.5885i | 0.350590 | + | 0.607240i | 0.986353 | − | 0.164644i | \(-0.0526477\pi\) |
−0.635763 | + | 0.771885i | \(0.719314\pi\) | |||||||
\(660\) | − | 20.7846i | − | 0.809040i | ||||||
\(661\) | −1.50000 | + | 0.866025i | −0.0583432 | + | 0.0336845i | −0.528888 | − | 0.848692i | \(-0.677391\pi\) |
0.470545 | + | 0.882376i | \(0.344057\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 27.7128i | − | 1.07628i | ||||||
\(664\) | −9.00000 | − | 5.19615i | −0.349268 | − | 0.201650i | ||||
\(665\) | 18.0000 | + | 10.3923i | 0.698010 | + | 0.402996i | ||||
\(666\) | −1.50000 | + | 2.59808i | −0.0581238 | + | 0.100673i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −18.0000 | −0.696441 | ||||||||
\(669\) | 24.0000 | + | 13.8564i | 0.927894 | + | 0.535720i | ||||
\(670\) | −18.0000 | −0.695401 | ||||||||
\(671\) | 27.0000 | + | 1.73205i | 1.04232 | + | 0.0668651i | ||||
\(672\) | −36.0000 | −1.38873 | ||||||||
\(673\) | −25.5000 | − | 14.7224i | −0.982953 | − | 0.567508i | −0.0797925 | − | 0.996811i | \(-0.525426\pi\) |
−0.903160 | + | 0.429303i | \(0.858759\pi\) | |||||||
\(674\) | 48.0000 | 1.84889 | ||||||||
\(675\) | −8.00000 | − | 13.8564i | −0.307920 | − | 0.533333i | ||||
\(676\) | −4.50000 | + | 7.79423i | −0.173077 | + | 0.299778i | ||||
\(677\) | −13.5000 | − | 7.79423i | −0.518847 | − | 0.299557i | 0.217616 | − | 0.976035i | \(-0.430172\pi\) |
−0.736463 | + | 0.676478i | \(0.763505\pi\) | |||||||
\(678\) | 18.0000 | + | 10.3923i | 0.691286 | + | 0.399114i | ||||
\(679\) | 3.46410i | 0.132940i | ||||||||
\(680\) | 36.0000 | 1.38054 | ||||||||
\(681\) | −12.0000 | + | 6.92820i | −0.459841 | + | 0.265489i | ||||
\(682\) | − | 62.3538i | − | 2.38765i | ||||||
\(683\) | 18.0000 | + | 31.1769i | 0.688751 | + | 1.19295i | 0.972242 | + | 0.233977i | \(0.0751739\pi\) |
−0.283491 | + | 0.958975i | \(0.591493\pi\) | |||||||
\(684\) | −1.00000 | + | 1.73205i | −0.0382360 | + | 0.0662266i | ||||
\(685\) | 4.50000 | + | 7.79423i | 0.171936 | + | 0.297802i | ||||
\(686\) | 6.00000 | − | 10.3923i | 0.229081 | − | 0.396780i | ||||
\(687\) | 19.0000 | − | 32.9090i | 0.724895 | − | 1.25556i | ||||
\(688\) | 15.0000 | − | 8.66025i | 0.571870 | − | 0.330169i | ||||
\(689\) | −9.00000 | − | 5.19615i | −0.342873 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | −7.50000 | − | 4.33013i | −0.285107 | − | 0.164607i | ||||
\(693\) | −6.00000 | + | 10.3923i | −0.227921 | + | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.7846i | 0.788405i | ||||||||
\(696\) | 3.00000 | + | 5.19615i | 0.113715 | + | 0.196960i | ||||
\(697\) | −18.0000 | + | 10.3923i | −0.681799 | + | 0.393637i | ||||
\(698\) | −9.00000 | −0.340655 | ||||||||
\(699\) | 24.2487i | 0.917170i | ||||||||
\(700\) | −12.0000 | + | 6.92820i | −0.453557 | + | 0.261861i | ||||
\(701\) | −10.5000 | + | 6.06218i | −0.396580 | + | 0.228965i | −0.685007 | − | 0.728536i | \(-0.740201\pi\) |
0.288428 | + | 0.957502i | \(0.406868\pi\) | |||||||
\(702\) | −12.0000 | + | 6.92820i | −0.452911 | + | 0.261488i | ||||
\(703\) | 3.00000 | − | 1.73205i | 0.113147 | − | 0.0653255i | ||||
\(704\) | 3.46410i | 0.130558i | ||||||||
\(705\) | −72.0000 | −2.71168 | ||||||||
\(706\) | −9.00000 | + | 5.19615i | −0.338719 | + | 0.195560i | ||||
\(707\) | −27.0000 | − | 46.7654i | −1.01544 | − | 1.75879i | ||||
\(708\) | 6.92820i | 0.260378i | ||||||||
\(709\) | − | 39.8372i | − | 1.49612i | −0.663633 | − | 0.748058i | \(-0.730986\pi\) | ||
0.663633 | − | 0.748058i | \(-0.269014\pi\) | |||||||
\(710\) | −27.0000 | + | 46.7654i | −1.01329 | + | 1.75507i | ||||
\(711\) | −9.00000 | − | 5.19615i | −0.337526 | − | 0.194871i | ||||
\(712\) | 27.0000 | 1.01187 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 72.0000 | + | 41.5692i | 2.69453 | + | 1.55569i | ||||
\(715\) | 18.0000 | − | 10.3923i | 0.673162 | − | 0.388650i | ||||
\(716\) | 3.00000 | − | 5.19615i | 0.112115 | − | 0.194189i | ||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | 15.0000 | + | 25.9808i | 0.559795 | + | 0.969593i | ||||
\(719\) | 15.0000 | − | 25.9808i | 0.559406 | − | 0.968919i | −0.438141 | − | 0.898906i | \(-0.644363\pi\) |
0.997546 | − | 0.0700124i | \(-0.0223039\pi\) | |||||||
\(720\) | 7.50000 | + | 12.9904i | 0.279508 | + | 0.484123i | ||||
\(721\) | − | 27.7128i | − | 1.03208i | ||||||
\(722\) | −22.5000 | + | 12.9904i | −0.837363 | + | 0.483452i | ||||
\(723\) | 22.0000 | 0.818189 | ||||||||
\(724\) | − | 22.5167i | − | 0.836825i | ||||||
\(725\) | 6.00000 | + | 3.46410i | 0.222834 | + | 0.128654i | ||||
\(726\) | −3.00000 | − | 1.73205i | −0.111340 | − | 0.0642824i | ||||
\(727\) | −5.00000 | + | 8.66025i | −0.185440 | + | 0.321191i | −0.943725 | − | 0.330732i | \(-0.892704\pi\) |
0.758285 | + | 0.651923i | \(0.226038\pi\) | |||||||
\(728\) | −6.00000 | − | 10.3923i | −0.222375 | − | 0.385164i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 31.5000 | + | 18.1865i | 1.16587 | + | 0.673114i | ||||
\(731\) | −24.0000 | −0.887672 | ||||||||
\(732\) | 14.0000 | − | 6.92820i | 0.517455 | − | 0.256074i | ||||
\(733\) | 41.0000 | 1.51437 | 0.757185 | − | 0.653201i | \(-0.226574\pi\) | ||||
0.757185 | + | 0.653201i | \(0.226574\pi\) | |||||||
\(734\) | 12.0000 | + | 6.92820i | 0.442928 | + | 0.255725i | ||||
\(735\) | 30.0000 | 1.10657 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | −4.50000 | − | 2.59808i | −0.165647 | − | 0.0956365i | ||||
\(739\) | 45.0000 | + | 25.9808i | 1.65535 | + | 0.955718i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 5.19615i | 0.191014i | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 27.0000 | − | 15.5885i | 0.991201 | − | 0.572270i | ||||
\(743\) | − | 27.7128i | − | 1.01668i | −0.861155 | − | 0.508342i | \(-0.830258\pi\) | ||
0.861155 | − | 0.508342i | \(-0.169742\pi\) | |||||||
\(744\) | 18.0000 | + | 31.1769i | 0.659912 | + | 1.14300i | ||||
\(745\) | 22.5000 | − | 38.9711i | 0.824336 | − | 1.42779i | ||||
\(746\) | −25.5000 | − | 44.1673i | −0.933621 | − | 1.61708i | ||||
\(747\) | −3.00000 | + | 5.19615i | −0.109764 | + | 0.190117i | ||||
\(748\) | −12.0000 | + | 20.7846i | −0.438763 | + | 0.759961i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.00000 | − | 5.19615i | −0.328634 | − | 0.189737i | ||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | −60.0000 | −2.18797 | ||||||||
\(753\) | −24.0000 | − | 13.8564i | −0.874609 | − | 0.504956i | ||||
\(754\) | 3.00000 | − | 5.19615i | 0.109254 | − | 0.189233i | ||||
\(755\) | − | 10.3923i | − | 0.378215i | ||||||
\(756\) | − | 13.8564i | − | 0.503953i | ||||||
\(757\) | −11.5000 | − | 19.9186i | −0.417975 | − | 0.723953i | 0.577761 | − | 0.816206i | \(-0.303927\pi\) |
−0.995736 | + | 0.0922527i | \(0.970593\pi\) | |||||||
\(758\) | −24.0000 | + | 13.8564i | −0.871719 | + | 0.503287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 10.3923i | − | 0.376969i | ||||||
\(761\) | −30.0000 | + | 17.3205i | −1.08750 | + | 0.627868i | −0.932910 | − | 0.360111i | \(-0.882739\pi\) |
−0.154590 | + | 0.987979i | \(0.549406\pi\) | |||||||
\(762\) | 6.00000 | − | 3.46410i | 0.217357 | − | 0.125491i | ||||
\(763\) | −21.0000 | + | 12.1244i | −0.760251 | + | 0.438931i | ||||
\(764\) | −12.0000 | + | 6.92820i | −0.434145 | + | 0.250654i | ||||
\(765\) | − | 20.7846i | − | 0.751469i | ||||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | −6.00000 | + | 3.46410i | −0.216647 | + | 0.125081i | ||||
\(768\) | 19.0000 | + | 32.9090i | 0.685603 | + | 1.18750i | ||||
\(769\) | − | 43.3013i | − | 1.56148i | −0.624854 | − | 0.780742i | \(-0.714841\pi\) | ||
0.624854 | − | 0.780742i | \(-0.285159\pi\) | |||||||
\(770\) | 62.3538i | 2.24708i | ||||||||
\(771\) | −15.0000 | + | 25.9808i | −0.540212 | + | 0.935674i | ||||
\(772\) | −10.5000 | − | 6.06218i | −0.377903 | − | 0.218183i | ||||
\(773\) | −39.0000 | −1.40273 | −0.701366 | − | 0.712801i | \(-0.747426\pi\) | ||||
−0.701366 | + | 0.712801i | \(0.747426\pi\) | |||||||
\(774\) | −3.00000 | − | 5.19615i | −0.107833 | − | 0.186772i | ||||
\(775\) | 36.0000 | + | 20.7846i | 1.29316 | + | 0.746605i | ||||
\(776\) | 1.50000 | − | 0.866025i | 0.0538469 | − | 0.0310885i | ||||
\(777\) | 6.00000 | − | 10.3923i | 0.215249 | − | 0.372822i | ||||
\(778\) | 25.5000 | − | 44.1673i | 0.914219 | − | 1.58347i | ||||
\(779\) | 3.00000 | + | 5.19615i | 0.107486 | + | 0.186171i | ||||
\(780\) | 6.00000 | − | 10.3923i | 0.214834 | − | 0.372104i | ||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00000 | + | 3.46410i | −0.214423 | + | 0.123797i | ||||
\(784\) | 25.0000 | 0.892857 | ||||||||
\(785\) | 41.5692i | 1.48367i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.00000 | − | 5.19615i | −0.320815 | − | 0.185223i | 0.330941 | − | 0.943652i | \(-0.392634\pi\) |
−0.651756 | + | 0.758429i | \(0.725967\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | −54.0000 | −1.92123 | ||||||||
\(791\) | −18.0000 | − | 10.3923i | −0.640006 | − | 0.369508i | ||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 13.0000 | + | 8.66025i | 0.461644 | + | 0.307535i | ||||
\(794\) | 57.0000 | 2.02285 | ||||||||
\(795\) | −27.0000 | − | 15.5885i | −0.957591 | − | 0.552866i | ||||
\(796\) | 4.00000 | 0.141776 | ||||||||
\(797\) | 10.5000 | + | 18.1865i | 0.371929 | + | 0.644200i | 0.989862 | − | 0.142031i | \(-0.0453631\pi\) |
−0.617933 | + | 0.786231i | \(0.712030\pi\) | |||||||
\(798\) | 12.0000 | − | 20.7846i | 0.424795 | − | 0.735767i | ||||
\(799\) | 72.0000 | + | 41.5692i | 2.54718 | + | 1.47061i | ||||
\(800\) | 18.0000 | + | 10.3923i | 0.636396 | + | 0.367423i | ||||
\(801\) | − | 15.5885i | − | 0.550791i | ||||||
\(802\) | 3.00000 | 0.105934 | ||||||||
\(803\) | 21.0000 | − | 12.1244i | 0.741074 | − | 0.427859i | ||||
\(804\) | 6.92820i | 0.244339i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.0000 | − | 31.1769i | 0.634023 | − | 1.09816i | ||||
\(807\) | 9.00000 | + | 15.5885i | 0.316815 | + | 0.548740i | ||||
\(808\) | −13.5000 | + | 23.3827i | −0.474928 | + | 0.822600i | ||||
\(809\) | 1.50000 | − | 2.59808i | 0.0527372 | − | 0.0913435i | −0.838452 | − | 0.544976i | \(-0.816539\pi\) |
0.891189 | + | 0.453632i | \(0.149872\pi\) | |||||||
\(810\) | −49.5000 | + | 28.5788i | −1.73925 | + | 1.00416i | ||||
\(811\) | −42.0000 | − | 24.2487i | −1.47482 | − | 0.851487i | −0.475222 | − | 0.879866i | \(-0.657632\pi\) |
−0.999597 | + | 0.0283784i | \(0.990966\pi\) | |||||||
\(812\) | 3.00000 | + | 5.19615i | 0.105279 | + | 0.182349i | ||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 9.00000 | + | 5.19615i | 0.315450 | + | 0.182125i | ||||
\(815\) | −6.00000 | + | 10.3923i | −0.210171 | + | 0.364027i | ||||
\(816\) | − | 69.2820i | − | 2.42536i | ||||||
\(817\) | 6.92820i | 0.242387i | ||||||||
\(818\) | −31.5000 | − | 54.5596i | −1.10137 | − | 1.90763i | ||||
\(819\) | −6.00000 | + | 3.46410i | −0.209657 | + | 0.121046i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 5.19615i | 0.181347i | 0.995881 | + | 0.0906735i | \(0.0289020\pi\) | ||||
−0.995881 | + | 0.0906735i | \(0.971098\pi\) | |||||||
\(822\) | 9.00000 | − | 5.19615i | 0.313911 | − | 0.181237i | ||||
\(823\) | 27.0000 | − | 15.5885i | 0.941161 | − | 0.543379i | 0.0508368 | − | 0.998707i | \(-0.483811\pi\) |
0.890324 | + | 0.455328i | \(0.150478\pi\) | |||||||
\(824\) | −12.0000 | + | 6.92820i | −0.418040 | + | 0.241355i | ||||
\(825\) | 24.0000 | − | 13.8564i | 0.835573 | − | 0.482418i | ||||
\(826\) | − | 20.7846i | − | 0.723189i | ||||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | 31.1769i | 1.08217i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | −30.0000 | − | 17.3205i | −1.03944 | − | 0.600120i | ||||
\(834\) | 24.0000 | 0.831052 | ||||||||
\(835\) | −27.0000 | − | 46.7654i | −0.934374 | − | 1.61838i | ||||
\(836\) | 6.00000 | + | 3.46410i | 0.207514 | + | 0.119808i | ||||
\(837\) | −36.0000 | + | 20.7846i | −1.24434 | + | 0.718421i | ||||
\(838\) | −24.0000 | + | 41.5692i | −0.829066 | + | 1.43598i | ||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | −18.0000 | − | 31.1769i | −0.621059 | − | 1.07571i | ||||
\(841\) | −13.0000 | + | 22.5167i | −0.448276 | + | 0.776437i | ||||
\(842\) | 18.0000 | + | 31.1769i | 0.620321 | + | 1.07443i | ||||
\(843\) | 38.1051i | 1.31241i | ||||||||
\(844\) | −3.00000 | + | 1.73205i | −0.103264 | + | 0.0596196i | ||||
\(845\) | −27.0000 | −0.928828 | ||||||||
\(846\) | 20.7846i | 0.714590i | ||||||||
\(847\) | 3.00000 | + | 1.73205i | 0.103081 | + | 0.0595140i | ||||
\(848\) | −22.5000 | − | 12.9904i | −0.772653 | − | 0.446092i | ||||
\(849\) | 26.0000 | − | 45.0333i | 0.892318 | − | 1.54554i | ||||
\(850\) | −24.0000 | − | 41.5692i | −0.823193 | − | 1.42581i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 18.0000 | + | 10.3923i | 0.616670 | + | 0.356034i | ||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | −42.0000 | + | 20.7846i | −1.43721 | + | 0.711235i | ||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | −0.717346 | −0.358673 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358673 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(858\) | −12.0000 | − | 20.7846i | −0.409673 | − | 0.709575i | ||||
\(859\) | −22.0000 | + | 38.1051i | −0.750630 | + | 1.30013i | 0.196887 | + | 0.980426i | \(0.436917\pi\) |
−0.947518 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(860\) | −9.00000 | − | 5.19615i | −0.306897 | − | 0.177187i | ||||
\(861\) | 18.0000 | + | 10.3923i | 0.613438 | + | 0.354169i | ||||
\(862\) | 20.7846i | 0.707927i | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | −18.0000 | + | 10.3923i | −0.612372 | + | 0.353553i | ||||
\(865\) | − | 25.9808i | − | 0.883372i | ||||||
\(866\) | 34.5000 | + | 59.7558i | 1.17236 | + | 2.03058i | ||||
\(867\) | −31.0000 | + | 53.6936i | −1.05282 | + | 1.82353i | ||||
\(868\) | 18.0000 | + | 31.1769i | 0.610960 | + | 1.05821i | ||||
\(869\) | −18.0000 | + | 31.1769i | −0.610608 | + | 1.05760i | ||||
\(870\) | 9.00000 | − | 15.5885i | 0.305129 | − | 0.528498i | ||||
\(871\) | −6.00000 | + | 3.46410i | −0.203302 | + | 0.117377i | ||||
\(872\) | 10.5000 | + | 6.06218i | 0.355575 | + | 0.205291i | ||||
\(873\) | −0.500000 | − | 0.866025i | −0.0169224 | − | 0.0293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.00000 | + | 5.19615i | 0.304256 | + | 0.175662i | ||||
\(876\) | 7.00000 | − | 12.1244i | 0.236508 | − | 0.409644i | ||||
\(877\) | − | 20.7846i | − | 0.701846i | −0.936404 | − | 0.350923i | \(-0.885868\pi\) | ||
0.936404 | − | 0.350923i | \(-0.114132\pi\) | |||||||
\(878\) | 34.6410i | 1.16908i | ||||||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 45.0000 | − | 25.9808i | 1.51695 | − | 0.875811i | ||||
\(881\) | −39.0000 | −1.31394 | −0.656972 | − | 0.753915i | \(-0.728163\pi\) | ||||
−0.656972 | + | 0.753915i | \(0.728163\pi\) | |||||||
\(882\) | − | 8.66025i | − | 0.291606i | ||||||
\(883\) | −9.00000 | + | 5.19615i | −0.302874 | + | 0.174864i | −0.643733 | − | 0.765250i | \(-0.722615\pi\) |
0.340859 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(884\) | −12.0000 | + | 6.92820i | −0.403604 | + | 0.233021i | ||||
\(885\) | −18.0000 | + | 10.3923i | −0.605063 | + | 0.349334i | ||||
\(886\) | −9.00000 | + | 5.19615i | −0.302361 | + | 0.174568i | ||||
\(887\) | − | 17.3205i | − | 0.581566i | −0.956789 | − | 0.290783i | \(-0.906084\pi\) | ||
0.956789 | − | 0.290783i | \(-0.0939157\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | −6.00000 | + | 3.46410i | −0.201234 | + | 0.116182i | ||||
\(890\) | −40.5000 | − | 70.1481i | −1.35756 | − | 2.35137i | ||||
\(891\) | 38.1051i | 1.27657i | ||||||||
\(892\) | − | 13.8564i | − | 0.463947i | ||||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | −45.0000 | − | 25.9808i | −1.50503 | − | 0.868927i | ||||
\(895\) | 18.0000 | 0.601674 | ||||||||
\(896\) | −21.0000 | − | 36.3731i | −0.701561 | − | 1.21514i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.0000 | − | 25.9808i | 1.50167 | − | 0.866989i | ||||
\(899\) | 9.00000 | − | 15.5885i | 0.300167 | − | 0.519904i | ||||
\(900\) | 2.00000 | − | 3.46410i | 0.0666667 | − | 0.115470i | ||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | −9.00000 | + | 15.5885i | −0.299667 | + | 0.519039i | ||||
\(903\) | 12.0000 | + | 20.7846i | 0.399335 | + | 0.691669i | ||||
\(904\) | 10.3923i | 0.345643i | ||||||||
\(905\) | 58.5000 | − | 33.7750i | 1.94461 | − | 1.12272i | ||||
\(906\) | −12.0000 | −0.398673 | ||||||||
\(907\) | − | 20.7846i | − | 0.690142i | −0.938577 | − | 0.345071i | \(-0.887855\pi\) | ||
0.938577 | − | 0.345071i | \(-0.112145\pi\) | |||||||
\(908\) | 6.00000 | + | 3.46410i | 0.199117 | + | 0.114960i | ||||
\(909\) | 13.5000 | + | 7.79423i | 0.447767 | + | 0.258518i | ||||
\(910\) | −18.0000 | + | 31.1769i | −0.596694 | + | 1.03350i | ||||
\(911\) | 9.00000 | + | 15.5885i | 0.298183 | + | 0.516469i | 0.975720 | − | 0.219020i | \(-0.0702860\pi\) |
−0.677537 | + | 0.735489i | \(0.736953\pi\) | |||||||
\(912\) | −20.0000 | −0.662266 | ||||||||
\(913\) | 18.0000 | + | 10.3923i | 0.595713 | + | 0.343935i | ||||
\(914\) | 39.0000 | 1.29001 | ||||||||
\(915\) | 39.0000 | + | 25.9808i | 1.28930 | + | 0.858898i | ||||
\(916\) | −19.0000 | −0.627778 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 48.0000 | 1.58424 | ||||||||
\(919\) | −22.0000 | − | 38.1051i | −0.725713 | − | 1.25697i | −0.958680 | − | 0.284487i | \(-0.908177\pi\) |
0.232967 | − | 0.972485i | \(-0.425157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | + | 3.46410i | 0.197707 | + | 0.114146i | ||||
\(922\) | −40.5000 | − | 23.3827i | −1.33380 | − | 0.770068i | ||||
\(923\) | 20.7846i | 0.684134i | ||||||||
\(924\) | 24.0000 | 0.789542 | ||||||||
\(925\) | −6.00000 | + | 3.46410i | −0.197279 | + | 0.113899i | ||||
\(926\) | 69.2820i | 2.27675i | ||||||||
\(927\) | 4.00000 | + | 6.92820i | 0.131377 | + | 0.227552i | ||||
\(928\) | 4.50000 | − | 7.79423i | 0.147720 | − | 0.255858i | ||||
\(929\) | 22.5000 | + | 38.9711i | 0.738201 | + | 1.27860i | 0.953305 | + | 0.302010i | \(0.0976578\pi\) |
−0.215104 | + | 0.976591i | \(0.569009\pi\) | |||||||
\(930\) | 54.0000 | − | 93.5307i | 1.77073 | − | 3.06699i | ||||
\(931\) | −5.00000 | + | 8.66025i | −0.163868 | + | 0.283828i | ||||
\(932\) | 10.5000 | − | 6.06218i | 0.343939 | − | 0.198573i | ||||
\(933\) | −24.0000 | − | 13.8564i | −0.785725 | − | 0.453638i | ||||
\(934\) | −18.0000 | − | 31.1769i | −0.588978 | − | 1.02014i | ||||
\(935\) | −72.0000 | −2.35465 | ||||||||
\(936\) | 3.00000 | + | 1.73205i | 0.0980581 | + | 0.0566139i | ||||
\(937\) | 2.50000 | − | 4.33013i | 0.0816714 | − | 0.141459i | −0.822297 | − | 0.569059i | \(-0.807308\pi\) |
0.903968 | + | 0.427600i | \(0.140641\pi\) | |||||||
\(938\) | − | 20.7846i | − | 0.678642i | ||||||
\(939\) | 41.5692i | 1.35656i | ||||||||
\(940\) | 18.0000 | + | 31.1769i | 0.587095 | + | 1.01688i | ||||
\(941\) | 34.5000 | − | 19.9186i | 1.12467 | − | 0.649327i | 0.182079 | − | 0.983284i | \(-0.441717\pi\) |
0.942588 | + | 0.333957i | \(0.108384\pi\) | |||||||
\(942\) | 48.0000 | 1.56392 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −15.0000 | + | 8.66025i | −0.488208 | + | 0.281867i | ||||
\(945\) | 36.0000 | − | 20.7846i | 1.17108 | − | 0.676123i | ||||
\(946\) | −18.0000 | + | 10.3923i | −0.585230 | + | 0.337883i | ||||
\(947\) | 15.0000 | − | 8.66025i | 0.487435 | − | 0.281420i | −0.236075 | − | 0.971735i | \(-0.575861\pi\) |
0.723510 | + | 0.690314i | \(0.242528\pi\) | |||||||
\(948\) | 20.7846i | 0.675053i | ||||||||
\(949\) | 14.0000 | 0.454459 | ||||||||
\(950\) | −12.0000 | + | 6.92820i | −0.389331 | + | 0.224781i | ||||
\(951\) | −6.00000 | − | 10.3923i | −0.194563 | − | 0.336994i | ||||
\(952\) | 41.5692i | 1.34727i | ||||||||
\(953\) | 32.9090i | 1.06603i | 0.846107 | + | 0.533013i | \(0.178940\pi\) | ||||
−0.846107 | + | 0.533013i | \(0.821060\pi\) | |||||||
\(954\) | −4.50000 | + | 7.79423i | −0.145693 | + | 0.252347i | ||||
\(955\) | −36.0000 | − | 20.7846i | −1.16493 | − | 0.672574i | ||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | −6.00000 | − | 10.3923i | −0.193952 | − | 0.335936i | ||||
\(958\) | 9.00000 | + | 5.19615i | 0.290777 | + | 0.167880i | ||||
\(959\) | −9.00000 | + | 5.19615i | −0.290625 | + | 0.167793i | ||||
\(960\) | −3.00000 | + | 5.19615i | −0.0968246 | + | 0.167705i | ||||
\(961\) | 38.5000 | − | 66.6840i | 1.24194 | − | 2.15110i | ||||
\(962\) | 3.00000 | + | 5.19615i | 0.0967239 | + | 0.167531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.50000 | − | 9.52628i | −0.177143 | − | 0.306821i | ||||
\(965\) | − | 36.3731i | − | 1.17089i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000 | 1.60789 | 0.803946 | − | 0.594703i | \(-0.202730\pi\) | ||||
0.803946 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(968\) | − | 1.73205i | − | 0.0556702i | ||||||
\(969\) | 24.0000 | + | 13.8564i | 0.770991 | + | 0.445132i | ||||
\(970\) | −4.50000 | − | 2.59808i | −0.144486 | − | 0.0834192i | ||||
\(971\) | −21.0000 | + | 36.3731i | −0.673922 | + | 1.16727i | 0.302861 | + | 0.953035i | \(0.402058\pi\) |
−0.976783 | + | 0.214232i | \(0.931275\pi\) | |||||||
\(972\) | 5.00000 | + | 8.66025i | 0.160375 | + | 0.277778i | ||||
\(973\) | −24.0000 | −0.769405 | ||||||||
\(974\) | −3.00000 | − | 1.73205i | −0.0961262 | − | 0.0554985i | ||||
\(975\) | 16.0000 | 0.512410 | ||||||||
\(976\) | 32.5000 | + | 21.6506i | 1.04030 | + | 0.693020i | ||||
\(977\) | −57.0000 | −1.82359 | −0.911796 | − | 0.410644i | \(-0.865304\pi\) | ||||
−0.911796 | + | 0.410644i | \(0.865304\pi\) | |||||||
\(978\) | 12.0000 | + | 6.92820i | 0.383718 | + | 0.221540i | ||||
\(979\) | −54.0000 | −1.72585 | ||||||||
\(980\) | −7.50000 | − | 12.9904i | −0.239579 | − | 0.414963i | ||||
\(981\) | 3.50000 | − | 6.06218i | 0.111746 | − | 0.193550i | ||||
\(982\) | −45.0000 | − | 25.9808i | −1.43601 | − | 0.829079i | ||||
\(983\) | 3.00000 | + | 1.73205i | 0.0956851 | + | 0.0552438i | 0.547079 | − | 0.837081i | \(-0.315740\pi\) |
−0.451394 | + | 0.892325i | \(0.649073\pi\) | |||||||
\(984\) | − | 10.3923i | − | 0.331295i | ||||||
\(985\) | 9.00000 | 0.286764 | ||||||||
\(986\) | −18.0000 | + | 10.3923i | −0.573237 | + | 0.330958i | ||||
\(987\) | − | 83.1384i | − | 2.64633i | ||||||
\(988\) | 2.00000 | + | 3.46410i | 0.0636285 | + | 0.110208i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −9.00000 | − | 15.5885i | −0.286039 | − | 0.495434i | ||||
\(991\) | 10.0000 | − | 17.3205i | 0.317660 | − | 0.550204i | −0.662339 | − | 0.749204i | \(-0.730436\pi\) |
0.979999 | + | 0.199000i | \(0.0637695\pi\) | |||||||
\(992\) | 27.0000 | − | 46.7654i | 0.857251 | − | 1.48480i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −54.0000 | − | 31.1769i | −1.71278 | − | 0.988872i | ||||
\(995\) | 6.00000 | + | 10.3923i | 0.190213 | + | 0.329458i | ||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | 6.00000 | + | 3.46410i | 0.190022 | + | 0.109709i | 0.591993 | − | 0.805943i | \(-0.298341\pi\) |
−0.401971 | + | 0.915652i | \(0.631675\pi\) | |||||||
\(998\) | 30.0000 | − | 51.9615i | 0.949633 | − | 1.64481i | ||||
\(999\) | − | 6.92820i | − | 0.219199i |
(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 | 61.2.f.a.48.1 | yes | 2 | |
3.2 | odd | 2 | 549.2.s.c.109.1 | 2 | |||
4.3 | odd | 2 | 976.2.ba.a.353.1 | 2 | |||
61.14 | even | 6 | inner | 61.2.f.a.14.1 | ✓ | 2 | |
61.21 | odd | 12 | 3721.2.a.b.1.1 | 2 | |||
61.40 | odd | 12 | 3721.2.a.b.1.2 | 2 | |||
183.14 | odd | 6 | 549.2.s.c.136.1 | 2 | |||
244.75 | odd | 6 | 976.2.ba.a.929.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
61.2.f.a.14.1 | ✓ | 2 | 61.14 | even | 6 | inner | |
61.2.f.a.48.1 | yes | 2 | 1.1 | even | 1 | trivial | |
549.2.s.c.109.1 | 2 | 3.2 | odd | 2 | |||
549.2.s.c.136.1 | 2 | 183.14 | odd | 6 | |||
976.2.ba.a.353.1 | 2 | 4.3 | odd | 2 | |||
976.2.ba.a.929.1 | 2 | 244.75 | odd | 6 | |||
3721.2.a.b.1.1 | 2 | 61.21 | odd | 12 | |||
3721.2.a.b.1.2 | 2 | 61.40 | odd | 12 |