Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(101,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bn (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: | \(4.35983195036\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.101 |
Dual form | 546.2.bn.c.173.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | − | 3.46410i | − | 1.09545i | ||||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | 2.50000 | − | 2.59808i | 0.693375 | − | 0.720577i | ||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | −3.00000 | − | 5.19615i | −0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | −3.00000 | − | 1.73205i | −0.670820 | − | 0.387298i | ||||
\(21\) | 1.50000 | + | 4.33013i | 0.327327 | + | 0.944911i | ||||
\(22\) | −3.00000 | + | 5.19615i | −0.639602 | + | 1.10782i | ||||
\(23\) | −3.00000 | − | 1.73205i | −0.625543 | − | 0.361158i | 0.153481 | − | 0.988152i | \(-0.450952\pi\) |
−0.779024 | + | 0.626994i | \(0.784285\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | 6.00000 | − | 3.46410i | 1.11417 | − | 0.643268i | 0.174265 | − | 0.984699i | \(-0.444245\pi\) |
0.939907 | + | 0.341431i | \(0.110912\pi\) | |||||||
\(30\) | −6.00000 | −1.09545 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 10.3923i | 1.80907i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | + | 6.92820i | −1.01419 | + | 1.17108i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 7.50000 | + | 4.33013i | 1.23299 | + | 0.711868i | 0.967653 | − | 0.252286i | \(-0.0811825\pi\) |
0.265340 | + | 0.964155i | \(0.414516\pi\) | |||||||
\(38\) | 2.50000 | − | 4.33013i | 0.405554 | − | 0.702439i | ||||
\(39\) | −4.50000 | − | 4.33013i | −0.720577 | − | 0.693375i | ||||
\(40\) | −3.00000 | + | 1.73205i | −0.474342 | + | 0.273861i | ||||
\(41\) | −9.00000 | + | 5.19615i | −1.40556 | + | 0.811503i | −0.994956 | − | 0.100309i | \(-0.968017\pi\) |
−0.410608 | + | 0.911812i | \(0.634683\pi\) | |||||||
\(42\) | 4.50000 | + | 0.866025i | 0.694365 | + | 0.133631i | ||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 3.00000 | + | 5.19615i | 0.452267 | + | 0.783349i | ||||
\(45\) | −9.00000 | + | 5.19615i | −1.34164 | + | 0.774597i | ||||
\(46\) | −3.00000 | + | 1.73205i | −0.442326 | + | 0.255377i | ||||
\(47\) | 6.00000 | − | 3.46410i | 0.875190 | − | 0.505291i | 0.00612051 | − | 0.999981i | \(-0.498052\pi\) |
0.869069 | + | 0.494690i | \(0.164718\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −3.50000 | − | 6.06218i | −0.494975 | − | 0.857321i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50000 | − | 0.866025i | −0.485363 | − | 0.120096i | ||||
\(53\) | −3.00000 | − | 1.73205i | −0.412082 | − | 0.237915i | 0.279602 | − | 0.960116i | \(-0.409797\pi\) |
−0.691684 | + | 0.722200i | \(0.743131\pi\) | |||||||
\(54\) | 4.50000 | + | 2.59808i | 0.612372 | + | 0.353553i | ||||
\(55\) | −18.0000 | + | 10.3923i | −2.42712 | + | 1.40130i | ||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | − | 8.66025i | − | 1.14708i | ||||||
\(58\) | − | 6.92820i | − | 0.909718i | ||||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | − | 5.19615i | − | 0.665299i | −0.943051 | − | 0.332650i | \(-0.892057\pi\) | ||
0.943051 | − | 0.332650i | \(-0.107943\pi\) | |||||||
\(62\) | −4.00000 | − | 6.92820i | −0.508001 | − | 0.879883i | ||||
\(63\) | 7.50000 | − | 2.59808i | 0.944911 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | − | 12.1244i | 0.372104 | − | 1.50384i | ||||
\(66\) | 9.00000 | + | 5.19615i | 1.10782 | + | 0.639602i | ||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | 3.00000 | + | 8.66025i | 0.358569 | + | 1.03510i | ||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 7.50000 | − | 4.33013i | 0.871857 | − | 0.503367i | ||||
\(75\) | −10.5000 | − | 6.06218i | −1.21244 | − | 0.700000i | ||||
\(76\) | −2.50000 | − | 4.33013i | −0.286770 | − | 0.496700i | ||||
\(77\) | 15.0000 | − | 5.19615i | 1.70941 | − | 0.592157i | ||||
\(78\) | −6.00000 | + | 1.73205i | −0.679366 | + | 0.196116i | ||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 3.46410i | 0.387298i | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 10.3923i | 1.14764i | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 3.00000 | − | 3.46410i | 0.327327 | − | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | 3.00000 | + | 1.73205i | 0.317999 | + | 0.183597i | 0.650500 | − | 0.759506i | \(-0.274559\pi\) |
−0.332501 | + | 0.943103i | \(0.607893\pi\) | |||||||
\(90\) | 10.3923i | 1.09545i | ||||||||
\(91\) | −4.00000 | + | 8.66025i | −0.419314 | + | 0.907841i | ||||
\(92\) | 3.46410i | 0.361158i | ||||||||
\(93\) | −12.0000 | − | 6.92820i | −1.24434 | − | 0.718421i | ||||
\(94\) | − | 6.92820i | − | 0.714590i | ||||||
\(95\) | 15.0000 | − | 8.66025i | 1.53897 | − | 0.888523i | ||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 3.50000 | − | 6.06218i | 0.355371 | − | 0.615521i | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | 18.0000 | 1.80907 | ||||||||
\(100\) | −7.00000 | −0.700000 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50000 | − | 2.59808i | 0.443398 | − | 0.255996i | −0.261640 | − | 0.965166i | \(-0.584263\pi\) |
0.705038 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(104\) | −2.50000 | + | 2.59808i | −0.245145 | + | 0.254762i | ||||
\(105\) | 12.0000 | + | 10.3923i | 1.17108 | + | 1.01419i | ||||
\(106\) | −3.00000 | + | 1.73205i | −0.291386 | + | 0.168232i | ||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 4.50000 | − | 2.59808i | 0.433013 | − | 0.250000i | ||||
\(109\) | 10.5000 | + | 6.06218i | 1.00572 | + | 0.580651i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 20.7846i | 1.98173i | ||||||||
\(111\) | 7.50000 | − | 12.9904i | 0.711868 | − | 1.23299i | ||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | −6.00000 | − | 3.46410i | −0.564433 | − | 0.325875i | 0.190490 | − | 0.981689i | \(-0.438992\pi\) |
−0.754923 | + | 0.655814i | \(0.772326\pi\) | |||||||
\(114\) | −7.50000 | − | 4.33013i | −0.702439 | − | 0.405554i | ||||
\(115\) | −12.0000 | −1.11901 | ||||||||
\(116\) | −6.00000 | − | 3.46410i | −0.557086 | − | 0.321634i | ||||
\(117\) | −7.50000 | + | 7.79423i | −0.693375 | + | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.00000 | + | 5.19615i | 0.273861 | + | 0.474342i | ||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | −4.50000 | − | 2.59808i | −0.407411 | − | 0.235219i | ||||
\(123\) | 9.00000 | + | 15.5885i | 0.811503 | + | 1.40556i | ||||
\(124\) | −8.00000 | −0.718421 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 1.50000 | − | 7.79423i | 0.133631 | − | 0.694365i | ||||
\(127\) | −0.500000 | − | 0.866025i | −0.0443678 | − | 0.0768473i | 0.842989 | − | 0.537931i | \(-0.180794\pi\) |
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | −9.00000 | − | 8.66025i | −0.789352 | − | 0.759555i | ||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 9.00000 | − | 5.19615i | 0.783349 | − | 0.452267i | ||||
\(133\) | −12.5000 | + | 4.33013i | −1.08389 | + | 0.375470i | ||||
\(134\) | 3.00000 | + | 1.73205i | 0.259161 | + | 0.149626i | ||||
\(135\) | 9.00000 | + | 15.5885i | 0.774597 | + | 1.34164i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 3.00000 | + | 5.19615i | 0.255377 | + | 0.442326i | ||||
\(139\) | 3.00000 | + | 1.73205i | 0.254457 | + | 0.146911i | 0.621803 | − | 0.783174i | \(-0.286400\pi\) |
−0.367347 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(140\) | 9.00000 | + | 1.73205i | 0.760639 | + | 0.146385i | ||||
\(141\) | −6.00000 | − | 10.3923i | −0.505291 | − | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0000 | + | 15.5885i | −1.25436 | + | 1.30357i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 12.0000 | − | 20.7846i | 0.996546 | − | 1.72607i | ||||
\(146\) | 3.50000 | + | 6.06218i | 0.289662 | + | 0.501709i | ||||
\(147\) | −7.50000 | − | 9.52628i | −0.618590 | − | 0.785714i | ||||
\(148\) | − | 8.66025i | − | 0.711868i | ||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | −10.5000 | + | 6.06218i | −0.857321 | + | 0.494975i | ||||
\(151\) | −3.00000 | − | 1.73205i | −0.244137 | − | 0.140952i | 0.372940 | − | 0.927855i | \(-0.378350\pi\) |
−0.617076 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(152\) | −5.00000 | −0.405554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | − | 15.5885i | 0.241747 | − | 1.25615i | ||||
\(155\) | − | 27.7128i | − | 2.22595i | ||||||
\(156\) | −1.50000 | + | 6.06218i | −0.120096 | + | 0.485363i | ||||
\(157\) | −16.5000 | − | 9.52628i | −1.31684 | − | 0.760280i | −0.333624 | − | 0.942706i | \(-0.608272\pi\) |
−0.983220 | + | 0.182426i | \(0.941605\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 3.00000 | + | 1.73205i | 0.237171 | + | 0.136931i | ||||
\(161\) | 9.00000 | + | 1.73205i | 0.709299 | + | 0.136505i | ||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | 1.73205i | 0.135665i | 0.997697 | + | 0.0678323i | \(0.0216083\pi\) | ||||
−0.997697 | + | 0.0678323i | \(0.978392\pi\) | |||||||
\(164\) | 9.00000 | + | 5.19615i | 0.702782 | + | 0.405751i | ||||
\(165\) | 18.0000 | + | 31.1769i | 1.40130 | + | 2.42712i | ||||
\(166\) | −3.00000 | − | 1.73205i | −0.232845 | − | 0.134433i | ||||
\(167\) | 3.00000 | − | 1.73205i | 0.232147 | − | 0.134030i | −0.379415 | − | 0.925227i | \(-0.623875\pi\) |
0.611562 | + | 0.791196i | \(0.290541\pi\) | |||||||
\(168\) | −1.50000 | − | 4.33013i | −0.115728 | − | 0.334077i | ||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.0000 | −1.14708 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | −3.50000 | + | 18.1865i | −0.264575 | + | 1.37477i | ||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | − | 1.73205i | 0.224860 | − | 0.129823i | ||||
\(179\) | 24.2487i | 1.81243i | 0.422813 | + | 0.906217i | \(0.361043\pi\) | ||||
−0.422813 | + | 0.906217i | \(0.638957\pi\) | |||||||
\(180\) | 9.00000 | + | 5.19615i | 0.670820 | + | 0.387298i | ||||
\(181\) | − | 15.5885i | − | 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | 5.50000 | + | 7.79423i | 0.407687 | + | 0.577747i | ||||
\(183\) | −9.00000 | −0.665299 | ||||||||
\(184\) | 3.00000 | + | 1.73205i | 0.221163 | + | 0.127688i | ||||
\(185\) | 30.0000 | 2.20564 | ||||||||
\(186\) | −12.0000 | + | 6.92820i | −0.879883 | + | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.00000 | − | 3.46410i | −0.437595 | − | 0.252646i | ||||
\(189\) | −4.50000 | − | 12.9904i | −0.327327 | − | 0.944911i | ||||
\(190\) | − | 17.3205i | − | 1.25656i | ||||||
\(191\) | − | 20.7846i | − | 1.50392i | −0.659208 | − | 0.751961i | \(-0.729108\pi\) | ||
0.659208 | − | 0.751961i | \(-0.270892\pi\) | |||||||
\(192\) | − | 1.73205i | − | 0.125000i | ||||||
\(193\) | 5.19615i | 0.374027i | 0.982357 | + | 0.187014i | \(0.0598809\pi\) | ||||
−0.982357 | + | 0.187014i | \(0.940119\pi\) | |||||||
\(194\) | −3.50000 | − | 6.06218i | −0.251285 | − | 0.435239i | ||||
\(195\) | −21.0000 | − | 5.19615i | −1.50384 | − | 0.372104i | ||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 6.00000 | + | 10.3923i | 0.427482 | + | 0.740421i | 0.996649 | − | 0.0818013i | \(-0.0260673\pi\) |
−0.569166 | + | 0.822222i | \(0.692734\pi\) | |||||||
\(198\) | 9.00000 | − | 15.5885i | 0.639602 | − | 1.10782i | ||||
\(199\) | −13.5000 | + | 7.79423i | −0.956990 | + | 0.552518i | −0.895245 | − | 0.445574i | \(-0.853000\pi\) |
−0.0617444 | + | 0.998092i | \(0.519666\pi\) | |||||||
\(200\) | −3.50000 | + | 6.06218i | −0.247487 | + | 0.428661i | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 3.00000 | − | 5.19615i | 0.211079 | − | 0.365600i | ||||
\(203\) | −12.0000 | + | 13.8564i | −0.842235 | + | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | + | 31.1769i | −1.25717 | + | 2.17749i | ||||
\(206\) | − | 5.19615i | − | 0.362033i | ||||||
\(207\) | 9.00000 | + | 5.19615i | 0.625543 | + | 0.361158i | ||||
\(208\) | 1.00000 | + | 3.46410i | 0.0693375 | + | 0.240192i | ||||
\(209\) | −30.0000 | −2.07514 | ||||||||
\(210\) | 15.0000 | − | 5.19615i | 1.03510 | − | 0.358569i | ||||
\(211\) | −2.50000 | − | 4.33013i | −0.172107 | − | 0.298098i | 0.767049 | − | 0.641588i | \(-0.221724\pi\) |
−0.939156 | + | 0.343490i | \(0.888391\pi\) | |||||||
\(212\) | 3.46410i | 0.237915i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.46410i | 0.236250i | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | −4.00000 | + | 20.7846i | −0.271538 | + | 1.41095i | ||||
\(218\) | 10.5000 | − | 6.06218i | 0.711150 | − | 0.410582i | ||||
\(219\) | 10.5000 | + | 6.06218i | 0.709524 | + | 0.409644i | ||||
\(220\) | 18.0000 | + | 10.3923i | 1.21356 | + | 0.700649i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.50000 | − | 12.9904i | −0.503367 | − | 0.871857i | ||||
\(223\) | 8.00000 | + | 13.8564i | 0.535720 | + | 0.927894i | 0.999128 | + | 0.0417488i | \(0.0132929\pi\) |
−0.463409 | + | 0.886145i | \(0.653374\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | −10.5000 | + | 18.1865i | −0.700000 | + | 1.21244i | ||||
\(226\) | −6.00000 | + | 3.46410i | −0.399114 | + | 0.230429i | ||||
\(227\) | −9.00000 | + | 5.19615i | −0.597351 | + | 0.344881i | −0.767999 | − | 0.640451i | \(-0.778747\pi\) |
0.170648 | + | 0.985332i | \(0.445414\pi\) | |||||||
\(228\) | −7.50000 | + | 4.33013i | −0.496700 | + | 0.286770i | ||||
\(229\) | 14.5000 | + | 25.1147i | 0.958187 | + | 1.65963i | 0.726900 | + | 0.686743i | \(0.240960\pi\) |
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | −6.00000 | + | 10.3923i | −0.395628 | + | 0.685248i | ||||
\(231\) | −9.00000 | − | 25.9808i | −0.592157 | − | 1.70941i | ||||
\(232\) | −6.00000 | + | 3.46410i | −0.393919 | + | 0.227429i | ||||
\(233\) | 6.00000 | − | 3.46410i | 0.393073 | − | 0.226941i | −0.290418 | − | 0.956900i | \(-0.593794\pi\) |
0.683491 | + | 0.729959i | \(0.260461\pi\) | |||||||
\(234\) | 3.00000 | + | 10.3923i | 0.196116 | + | 0.679366i | ||||
\(235\) | 12.0000 | − | 20.7846i | 0.782794 | − | 1.35584i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0000 | − | 6.92820i | 0.779484 | − | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 6.00000 | 0.387298 | ||||||||
\(241\) | 13.0000 | + | 22.5167i | 0.837404 | + | 1.45043i | 0.892058 | + | 0.451920i | \(0.149261\pi\) |
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | 12.5000 | − | 21.6506i | 0.803530 | − | 1.39176i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | −4.50000 | + | 2.59808i | −0.288083 | + | 0.166325i | ||||
\(245\) | 9.00000 | − | 22.5167i | 0.574989 | − | 1.43854i | ||||
\(246\) | 18.0000 | 1.14764 | ||||||||
\(247\) | 12.5000 | − | 12.9904i | 0.795356 | − | 0.826558i | ||||
\(248\) | −4.00000 | + | 6.92820i | −0.254000 | + | 0.439941i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | −6.00000 | − | 3.46410i | −0.379473 | − | 0.219089i | ||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | −6.00000 | − | 5.19615i | −0.377964 | − | 0.327327i | ||||
\(253\) | 18.0000 | + | 10.3923i | 1.13165 | + | 0.653359i | ||||
\(254\) | −1.00000 | −0.0627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 1.50000 | − | 0.866025i | 0.0933859 | − | 0.0539164i | ||||
\(259\) | −22.5000 | − | 4.33013i | −1.39808 | − | 0.269061i | ||||
\(260\) | −12.0000 | + | 3.46410i | −0.744208 | + | 0.214834i | ||||
\(261\) | −18.0000 | + | 10.3923i | −1.11417 | + | 0.643268i | ||||
\(262\) | 18.0000 | 1.11204 | ||||||||
\(263\) | − | 13.8564i | − | 0.854423i | −0.904152 | − | 0.427211i | \(-0.859496\pi\) | ||
0.904152 | − | 0.427211i | \(-0.140504\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | −2.50000 | + | 12.9904i | −0.153285 | + | 0.796491i | ||||
\(267\) | 3.00000 | − | 5.19615i | 0.183597 | − | 0.317999i | ||||
\(268\) | 3.00000 | − | 1.73205i | 0.183254 | − | 0.105802i | ||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 18.0000 | 1.09545 | ||||||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.0000 | + | 6.92820i | 0.907841 | + | 0.419314i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −21.0000 | + | 36.3731i | −1.26635 | + | 2.19338i | ||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | 3.00000 | − | 1.73205i | 0.179928 | − | 0.103882i | ||||
\(279\) | −12.0000 | + | 20.7846i | −0.718421 | + | 1.24434i | ||||
\(280\) | 6.00000 | − | 6.92820i | 0.358569 | − | 0.414039i | ||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | −12.0000 | −0.714590 | ||||||||
\(283\) | − | 1.73205i | − | 0.102960i | −0.998674 | − | 0.0514799i | \(-0.983606\pi\) | ||
0.998674 | − | 0.0514799i | \(-0.0163938\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.0000 | − | 25.9808i | −0.888523 | − | 1.53897i | ||||
\(286\) | 6.00000 | + | 20.7846i | 0.354787 | + | 1.22902i | ||||
\(287\) | 18.0000 | − | 20.7846i | 1.06251 | − | 1.22688i | ||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −12.0000 | − | 20.7846i | −0.704664 | − | 1.22051i | ||||
\(291\) | −10.5000 | − | 6.06218i | −0.615521 | − | 0.355371i | ||||
\(292\) | 7.00000 | 0.409644 | ||||||||
\(293\) | −6.00000 | − | 3.46410i | −0.350524 | − | 0.202375i | 0.314392 | − | 0.949293i | \(-0.398199\pi\) |
−0.664916 | + | 0.746918i | \(0.731533\pi\) | |||||||
\(294\) | −12.0000 | + | 1.73205i | −0.699854 | + | 0.101015i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.50000 | − | 4.33013i | −0.435929 | − | 0.251684i | ||||
\(297\) | − | 31.1769i | − | 1.80907i | ||||||
\(298\) | −9.00000 | + | 15.5885i | −0.521356 | + | 0.903015i | ||||
\(299\) | −12.0000 | + | 3.46410i | −0.693978 | + | 0.200334i | ||||
\(300\) | 12.1244i | 0.700000i | ||||||||
\(301\) | 0.500000 | − | 2.59808i | 0.0288195 | − | 0.149751i | ||||
\(302\) | −3.00000 | + | 1.73205i | −0.172631 | + | 0.0996683i | ||||
\(303\) | − | 10.3923i | − | 0.597022i | ||||||
\(304\) | −2.50000 | + | 4.33013i | −0.143385 | + | 0.248350i | ||||
\(305\) | −9.00000 | − | 15.5885i | −0.515339 | − | 0.892592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | −12.0000 | − | 10.3923i | −0.683763 | − | 0.592157i | ||||
\(309\) | −4.50000 | − | 7.79423i | −0.255996 | − | 0.443398i | ||||
\(310\) | −24.0000 | − | 13.8564i | −1.36311 | − | 0.786991i | ||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 4.50000 | + | 4.33013i | 0.254762 | + | 0.245145i | ||||
\(313\) | −28.5000 | + | 16.4545i | −1.61092 | + | 0.930062i | −0.621757 | + | 0.783210i | \(0.713581\pi\) |
−0.989158 | + | 0.146852i | \(0.953086\pi\) | |||||||
\(314\) | −16.5000 | + | 9.52628i | −0.931149 | + | 0.537599i | ||||
\(315\) | 18.0000 | − | 20.7846i | 1.01419 | − | 1.17108i | ||||
\(316\) | 4.00000 | − | 6.92820i | 0.225018 | − | 0.389742i | ||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 3.00000 | + | 5.19615i | 0.168232 | + | 0.291386i | ||||
\(319\) | −36.0000 | + | 20.7846i | −2.01561 | + | 1.16371i | ||||
\(320\) | 3.00000 | − | 1.73205i | 0.167705 | − | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.00000 | − | 6.92820i | 0.334367 | − | 0.386094i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | −7.00000 | − | 24.2487i | −0.388290 | − | 1.34508i | ||||
\(326\) | 1.50000 | + | 0.866025i | 0.0830773 | + | 0.0479647i | ||||
\(327\) | 10.5000 | − | 18.1865i | 0.580651 | − | 1.00572i | ||||
\(328\) | 9.00000 | − | 5.19615i | 0.496942 | − | 0.286910i | ||||
\(329\) | −12.0000 | + | 13.8564i | −0.661581 | + | 0.763928i | ||||
\(330\) | 36.0000 | 1.98173 | ||||||||
\(331\) | − | 19.0526i | − | 1.04722i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||
0.851957 | − | 0.523612i | \(-0.175416\pi\) | |||||||
\(332\) | −3.00000 | + | 1.73205i | −0.164646 | + | 0.0950586i | ||||
\(333\) | −22.5000 | − | 12.9904i | −1.23299 | − | 0.711868i | ||||
\(334\) | − | 3.46410i | − | 0.189547i | ||||||
\(335\) | 6.00000 | + | 10.3923i | 0.327815 | + | 0.567792i | ||||
\(336\) | −4.50000 | − | 0.866025i | −0.245495 | − | 0.0472456i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | −11.5000 | − | 6.06218i | −0.625518 | − | 0.329739i | ||||
\(339\) | −6.00000 | + | 10.3923i | −0.325875 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | + | 41.5692i | −1.29967 | + | 2.25110i | ||||
\(342\) | −7.50000 | + | 12.9904i | −0.405554 | + | 0.702439i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0.500000 | − | 0.866025i | 0.0269582 | − | 0.0466930i | ||||
\(345\) | 20.7846i | 1.11901i | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | 5.50000 | + | 9.52628i | 0.294408 | + | 0.509930i | 0.974847 | − | 0.222875i | \(-0.0715441\pi\) |
−0.680439 | + | 0.732805i | \(0.738211\pi\) | |||||||
\(350\) | 14.0000 | + | 12.1244i | 0.748331 | + | 0.648074i | ||||
\(351\) | 13.5000 | + | 12.9904i | 0.720577 | + | 0.693375i | ||||
\(352\) | −3.00000 | − | 5.19615i | −0.159901 | − | 0.276956i | ||||
\(353\) | 10.3923i | 0.553127i | 0.960996 | + | 0.276563i | \(0.0891955\pi\) | ||||
−0.960996 | + | 0.276563i | \(0.910804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 3.46410i | − | 0.183597i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.0000 | + | 12.1244i | 1.10988 | + | 0.640792i | ||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | 9.00000 | − | 5.19615i | 0.474342 | − | 0.273861i | ||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −13.5000 | − | 7.79423i | −0.709544 | − | 0.409656i | ||||
\(363\) | − | 43.3013i | − | 2.27273i | ||||||
\(364\) | 9.50000 | − | 0.866025i | 0.497935 | − | 0.0453921i | ||||
\(365\) | 24.2487i | 1.26924i | ||||||||
\(366\) | −4.50000 | + | 7.79423i | −0.235219 | + | 0.407411i | ||||
\(367\) | 1.73205i | 0.0904123i | 0.998978 | + | 0.0452062i | \(0.0143945\pi\) | ||||
−0.998978 | + | 0.0452062i | \(0.985606\pi\) | |||||||
\(368\) | 3.00000 | − | 1.73205i | 0.156386 | − | 0.0902894i | ||||
\(369\) | 27.0000 | − | 15.5885i | 1.40556 | − | 0.811503i | ||||
\(370\) | 15.0000 | − | 25.9808i | 0.779813 | − | 1.35068i | ||||
\(371\) | 9.00000 | + | 1.73205i | 0.467257 | + | 0.0899236i | ||||
\(372\) | 13.8564i | 0.718421i | ||||||||
\(373\) | −2.00000 | −0.103556 | −0.0517780 | − | 0.998659i | \(-0.516489\pi\) | ||||
−0.0517780 | + | 0.998659i | \(0.516489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | 6.00000 | − | 24.2487i | 0.309016 | − | 1.24887i | ||||
\(378\) | −13.5000 | − | 2.59808i | −0.694365 | − | 0.133631i | ||||
\(379\) | −15.0000 | + | 8.66025i | −0.770498 | + | 0.444847i | −0.833052 | − | 0.553194i | \(-0.813409\pi\) |
0.0625541 | + | 0.998042i | \(0.480075\pi\) | |||||||
\(380\) | −15.0000 | − | 8.66025i | −0.769484 | − | 0.444262i | ||||
\(381\) | −1.50000 | + | 0.866025i | −0.0768473 | + | 0.0443678i | ||||
\(382\) | −18.0000 | − | 10.3923i | −0.920960 | − | 0.531717i | ||||
\(383\) | − | 20.7846i | − | 1.06204i | −0.847358 | − | 0.531022i | \(-0.821808\pi\) | ||
0.847358 | − | 0.531022i | \(-0.178192\pi\) | |||||||
\(384\) | −1.50000 | − | 0.866025i | −0.0765466 | − | 0.0441942i | ||||
\(385\) | 36.0000 | − | 41.5692i | 1.83473 | − | 2.11856i | ||||
\(386\) | 4.50000 | + | 2.59808i | 0.229044 | + | 0.132239i | ||||
\(387\) | 1.50000 | − | 2.59808i | 0.0762493 | − | 0.132068i | ||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | 9.00000 | + | 5.19615i | 0.456318 | + | 0.263455i | 0.710495 | − | 0.703702i | \(-0.248471\pi\) |
−0.254177 | + | 0.967158i | \(0.581804\pi\) | |||||||
\(390\) | −15.0000 | + | 15.5885i | −0.759555 | + | 0.789352i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 27.0000 | − | 15.5885i | 1.36197 | − | 0.786334i | ||||
\(394\) | 12.0000 | 0.604551 | ||||||||
\(395\) | 24.0000 | + | 13.8564i | 1.20757 | + | 0.697191i | ||||
\(396\) | −9.00000 | − | 15.5885i | −0.452267 | − | 0.783349i | ||||
\(397\) | 11.0000 | 0.552074 | 0.276037 | − | 0.961147i | \(-0.410979\pi\) | ||||
0.276037 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(398\) | 15.5885i | 0.781379i | ||||||||
\(399\) | 7.50000 | + | 21.6506i | 0.375470 | + | 1.08389i | ||||
\(400\) | 3.50000 | + | 6.06218i | 0.175000 | + | 0.303109i | ||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 3.00000 | − | 5.19615i | 0.149626 | − | 0.259161i | ||||
\(403\) | −8.00000 | − | 27.7128i | −0.398508 | − | 1.38047i | ||||
\(404\) | −3.00000 | − | 5.19615i | −0.149256 | − | 0.258518i | ||||
\(405\) | 27.0000 | − | 15.5885i | 1.34164 | − | 0.774597i | ||||
\(406\) | 6.00000 | + | 17.3205i | 0.297775 | + | 0.859602i | ||||
\(407\) | −45.0000 | − | 25.9808i | −2.23057 | − | 1.28782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50000 | + | 16.4545i | 0.469745 | + | 0.813622i | 0.999402 | − | 0.0345902i | \(-0.0110126\pi\) |
−0.529657 | + | 0.848212i | \(0.677679\pi\) | |||||||
\(410\) | 18.0000 | + | 31.1769i | 0.888957 | + | 1.53972i | ||||
\(411\) | −9.00000 | + | 5.19615i | −0.443937 | + | 0.256307i | ||||
\(412\) | −4.50000 | − | 2.59808i | −0.221699 | − | 0.127998i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.00000 | − | 5.19615i | 0.442326 | − | 0.255377i | ||||
\(415\) | −6.00000 | − | 10.3923i | −0.294528 | − | 0.510138i | ||||
\(416\) | 3.50000 | + | 0.866025i | 0.171602 | + | 0.0424604i | ||||
\(417\) | 3.00000 | − | 5.19615i | 0.146911 | − | 0.254457i | ||||
\(418\) | −15.0000 | + | 25.9808i | −0.733674 | + | 1.27076i | ||||
\(419\) | −15.0000 | − | 25.9808i | −0.732798 | − | 1.26924i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.222885 | − | 0.974845i | \(-0.428453\pi\) | |||||||
\(420\) | 3.00000 | − | 15.5885i | 0.146385 | − | 0.760639i | ||||
\(421\) | 27.7128i | 1.35064i | 0.737525 | + | 0.675320i | \(0.235994\pi\) | ||||
−0.737525 | + | 0.675320i | \(0.764006\pi\) | |||||||
\(422\) | −5.00000 | −0.243396 | ||||||||
\(423\) | −18.0000 | + | 10.3923i | −0.875190 | + | 0.505291i | ||||
\(424\) | 3.00000 | + | 1.73205i | 0.145693 | + | 0.0841158i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.50000 | + | 12.9904i | 0.217770 | + | 0.628649i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.0000 | + | 25.9808i | 1.30357 | + | 1.25436i | ||||
\(430\) | 3.00000 | + | 1.73205i | 0.144673 | + | 0.0835269i | ||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | −4.50000 | − | 2.59808i | −0.216506 | − | 0.125000i | ||||
\(433\) | −18.0000 | − | 10.3923i | −0.865025 | − | 0.499422i | 0.000666943 | − | 1.00000i | \(-0.499788\pi\) |
−0.865692 | + | 0.500577i | \(0.833121\pi\) | |||||||
\(434\) | 16.0000 | + | 13.8564i | 0.768025 | + | 0.665129i | ||||
\(435\) | −36.0000 | − | 20.7846i | −1.72607 | − | 0.996546i | ||||
\(436\) | − | 12.1244i | − | 0.580651i | ||||||
\(437\) | −15.0000 | − | 8.66025i | −0.717547 | − | 0.414276i | ||||
\(438\) | 10.5000 | − | 6.06218i | 0.501709 | − | 0.289662i | ||||
\(439\) | 10.5000 | + | 6.06218i | 0.501138 | + | 0.289332i | 0.729183 | − | 0.684318i | \(-0.239900\pi\) |
−0.228046 | + | 0.973650i | \(0.573234\pi\) | |||||||
\(440\) | 18.0000 | − | 10.3923i | 0.858116 | − | 0.495434i | ||||
\(441\) | −16.5000 | + | 12.9904i | −0.785714 | + | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.0000 | − | 19.0526i | 1.56788 | − | 0.905214i | 0.571461 | − | 0.820629i | \(-0.306377\pi\) |
0.996416 | − | 0.0845852i | \(-0.0269565\pi\) | |||||||
\(444\) | −15.0000 | −0.711868 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 31.1769i | 1.47462i | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −15.0000 | + | 25.9808i | −0.707894 | + | 1.22611i | 0.257743 | + | 0.966213i | \(0.417021\pi\) |
−0.965637 | + | 0.259895i | \(0.916312\pi\) | |||||||
\(450\) | 10.5000 | + | 18.1865i | 0.494975 | + | 0.857321i | ||||
\(451\) | 54.0000 | − | 31.1769i | 2.54276 | − | 1.46806i | ||||
\(452\) | 6.92820i | 0.325875i | ||||||||
\(453\) | −3.00000 | + | 5.19615i | −0.140952 | + | 0.244137i | ||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 3.00000 | + | 32.9090i | 0.140642 | + | 1.54280i | ||||
\(456\) | 8.66025i | 0.405554i | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 29.0000 | 1.35508 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.00000 | + | 10.3923i | 0.279751 | + | 0.484544i | ||||
\(461\) | 18.0000 | + | 10.3923i | 0.838344 | + | 0.484018i | 0.856701 | − | 0.515814i | \(-0.172510\pi\) |
−0.0183573 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(462\) | −27.0000 | − | 5.19615i | −1.25615 | − | 0.241747i | ||||
\(463\) | 19.0526i | 0.885448i | 0.896658 | + | 0.442724i | \(0.145988\pi\) | ||||
−0.896658 | + | 0.442724i | \(0.854012\pi\) | |||||||
\(464\) | 6.92820i | 0.321634i | ||||||||
\(465\) | −48.0000 | −2.22595 | ||||||||
\(466\) | − | 6.92820i | − | 0.320943i | ||||||
\(467\) | −9.00000 | − | 15.5885i | −0.416470 | − | 0.721348i | 0.579111 | − | 0.815249i | \(-0.303400\pi\) |
−0.995582 | + | 0.0939008i | \(0.970066\pi\) | |||||||
\(468\) | 10.5000 | + | 2.59808i | 0.485363 | + | 0.120096i | ||||
\(469\) | −3.00000 | − | 8.66025i | −0.138527 | − | 0.399893i | ||||
\(470\) | −12.0000 | − | 20.7846i | −0.553519 | − | 0.958723i | ||||
\(471\) | −16.5000 | + | 28.5788i | −0.760280 | + | 1.31684i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | − | 13.8564i | − | 0.636446i | ||||||
\(475\) | 17.5000 | − | 30.3109i | 0.802955 | − | 1.39076i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | + | 5.19615i | 0.412082 | + | 0.237915i | ||||
\(478\) | 3.00000 | − | 5.19615i | 0.137217 | − | 0.237666i | ||||
\(479\) | 6.92820i | 0.316558i | 0.987394 | + | 0.158279i | \(0.0505945\pi\) | ||||
−0.987394 | + | 0.158279i | \(0.949406\pi\) | |||||||
\(480\) | 3.00000 | − | 5.19615i | 0.136931 | − | 0.237171i | ||||
\(481\) | 30.0000 | − | 8.66025i | 1.36788 | − | 0.394874i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 3.00000 | − | 15.5885i | 0.136505 | − | 0.709299i | ||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | − | 24.2487i | − | 1.10108i | ||||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | −13.5000 | + | 7.79423i | −0.611743 | + | 0.353190i | −0.773647 | − | 0.633616i | \(-0.781570\pi\) |
0.161904 | + | 0.986807i | \(0.448236\pi\) | |||||||
\(488\) | 5.19615i | 0.235219i | ||||||||
\(489\) | 3.00000 | 0.135665 | ||||||||
\(490\) | −15.0000 | − | 19.0526i | −0.677631 | − | 0.860707i | ||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 9.00000 | − | 15.5885i | 0.405751 | − | 0.702782i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.00000 | − | 17.3205i | −0.224961 | − | 0.779287i | ||||
\(495\) | 54.0000 | − | 31.1769i | 2.42712 | − | 1.40130i | ||||
\(496\) | 4.00000 | + | 6.92820i | 0.179605 | + | 0.311086i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | 7.50000 | − | 4.33013i | 0.335746 | − | 0.193843i | −0.322643 | − | 0.946521i | \(-0.604571\pi\) |
0.658389 | + | 0.752678i | \(0.271238\pi\) | |||||||
\(500\) | −6.00000 | + | 3.46410i | −0.268328 | + | 0.154919i | ||||
\(501\) | −3.00000 | − | 5.19615i | −0.134030 | − | 0.232147i | ||||
\(502\) | −6.00000 | − | 10.3923i | −0.267793 | − | 0.463831i | ||||
\(503\) | −15.0000 | + | 25.9808i | −0.668817 | + | 1.15842i | 0.309418 | + | 0.950926i | \(0.399866\pi\) |
−0.978235 | + | 0.207499i | \(0.933468\pi\) | |||||||
\(504\) | −7.50000 | + | 2.59808i | −0.334077 | + | 0.115728i | ||||
\(505\) | 18.0000 | − | 10.3923i | 0.800989 | − | 0.462451i | ||||
\(506\) | 18.0000 | − | 10.3923i | 0.800198 | − | 0.461994i | ||||
\(507\) | −22.5000 | + | 0.866025i | −0.999260 | + | 0.0384615i | ||||
\(508\) | −0.500000 | + | 0.866025i | −0.0221839 | + | 0.0384237i | ||||
\(509\) | 21.0000 | + | 12.1244i | 0.930809 | + | 0.537403i | 0.887067 | − | 0.461640i | \(-0.152739\pi\) |
0.0437414 | + | 0.999043i | \(0.486072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | − | 18.1865i | 0.154831 | − | 0.804525i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 25.9808i | 1.14708i | ||||||||
\(514\) | 9.00000 | + | 15.5885i | 0.396973 | + | 0.687577i | ||||
\(515\) | 9.00000 | − | 15.5885i | 0.396587 | − | 0.686909i | ||||
\(516\) | − | 1.73205i | − | 0.0762493i | ||||||
\(517\) | −36.0000 | + | 20.7846i | −1.58328 | + | 0.914106i | ||||
\(518\) | −15.0000 | + | 17.3205i | −0.659062 | + | 0.761019i | ||||
\(519\) | 10.3923i | 0.456172i | ||||||||
\(520\) | −3.00000 | + | 12.1244i | −0.131559 | + | 0.531688i | ||||
\(521\) | 6.00000 | − | 10.3923i | 0.262865 | − | 0.455295i | −0.704137 | − | 0.710064i | \(-0.748666\pi\) |
0.967002 | + | 0.254769i | \(0.0819994\pi\) | |||||||
\(522\) | 20.7846i | 0.909718i | ||||||||
\(523\) | 7.50000 | + | 4.33013i | 0.327952 | + | 0.189343i | 0.654932 | − | 0.755688i | \(-0.272697\pi\) |
−0.326979 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(524\) | 9.00000 | − | 15.5885i | 0.393167 | − | 0.680985i | ||||
\(525\) | 31.5000 | + | 6.06218i | 1.37477 | + | 0.264575i | ||||
\(526\) | −12.0000 | − | 6.92820i | −0.523225 | − | 0.302084i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −9.00000 | − | 5.19615i | −0.391675 | − | 0.226134i | ||||
\(529\) | −5.50000 | − | 9.52628i | −0.239130 | − | 0.414186i | ||||
\(530\) | −6.00000 | + | 10.3923i | −0.260623 | + | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0000 | + | 8.66025i | 0.433555 | + | 0.375470i | ||||
\(533\) | −9.00000 | + | 36.3731i | −0.389833 | + | 1.57549i | ||||
\(534\) | −3.00000 | − | 5.19615i | −0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.46410i | − | 0.149626i | ||||||
\(537\) | 42.0000 | 1.81243 | ||||||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | −33.0000 | + | 25.9808i | −1.42141 | + | 1.11907i | ||||
\(540\) | 9.00000 | − | 15.5885i | 0.387298 | − | 0.670820i | ||||
\(541\) | −1.50000 | + | 0.866025i | −0.0644900 | + | 0.0372333i | −0.531898 | − | 0.846808i | \(-0.678521\pi\) |
0.467408 | + | 0.884042i | \(0.345188\pi\) | |||||||
\(542\) | −0.500000 | − | 0.866025i | −0.0214768 | − | 0.0371990i | ||||
\(543\) | −27.0000 | −1.15868 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.0000 | 1.79908 | ||||||||
\(546\) | 13.5000 | − | 9.52628i | 0.577747 | − | 0.407687i | ||||
\(547\) | −25.0000 | −1.06892 | −0.534461 | − | 0.845193i | \(-0.679486\pi\) | ||||
−0.534461 | + | 0.845193i | \(0.679486\pi\) | |||||||
\(548\) | −3.00000 | + | 5.19615i | −0.128154 | + | 0.221969i | ||||
\(549\) | 15.5885i | 0.665299i | ||||||||
\(550\) | 21.0000 | + | 36.3731i | 0.895443 | + | 1.55095i | ||||
\(551\) | 30.0000 | − | 17.3205i | 1.27804 | − | 0.737878i | ||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | −16.0000 | − | 13.8564i | −0.680389 | − | 0.589234i | ||||
\(554\) | −17.0000 | −0.722261 | ||||||||
\(555\) | − | 51.9615i | − | 2.20564i | ||||||
\(556\) | − | 3.46410i | − | 0.146911i | ||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 12.0000 | + | 20.7846i | 0.508001 | + | 0.879883i | ||||
\(559\) | 1.00000 | + | 3.46410i | 0.0422955 | + | 0.146516i | ||||
\(560\) | −3.00000 | − | 8.66025i | −0.126773 | − | 0.365963i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | −9.00000 | − | 15.5885i | −0.379305 | − | 0.656975i | 0.611656 | − | 0.791123i | \(-0.290503\pi\) |
−0.990961 | + | 0.134148i | \(0.957170\pi\) | |||||||
\(564\) | −6.00000 | + | 10.3923i | −0.252646 | + | 0.437595i | ||||
\(565\) | −24.0000 | −1.00969 | ||||||||
\(566\) | −1.50000 | − | 0.866025i | −0.0630497 | − | 0.0364018i | ||||
\(567\) | −22.5000 | + | 7.79423i | −0.944911 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0000 | − | 13.8564i | −1.00613 | − | 0.580891i | −0.0960754 | − | 0.995374i | \(-0.530629\pi\) |
−0.910057 | + | 0.414483i | \(0.863962\pi\) | |||||||
\(570\) | −30.0000 | −1.25656 | ||||||||
\(571\) | −9.50000 | + | 16.4545i | −0.397563 | + | 0.688599i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) |
0.595862 | + | 0.803087i | \(0.296811\pi\) | |||||||
\(572\) | 21.0000 | + | 5.19615i | 0.878054 | + | 0.217262i | ||||
\(573\) | −36.0000 | −1.50392 | ||||||||
\(574\) | −9.00000 | − | 25.9808i | −0.375653 | − | 1.08442i | ||||
\(575\) | −21.0000 | + | 12.1244i | −0.875761 | + | 0.505621i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 18.5000 | − | 32.0429i | 0.770165 | − | 1.33397i | −0.167307 | − | 0.985905i | \(-0.553507\pi\) |
0.937472 | − | 0.348060i | \(-0.113160\pi\) | |||||||
\(578\) | −8.50000 | − | 14.7224i | −0.353553 | − | 0.612372i | ||||
\(579\) | 9.00000 | 0.374027 | ||||||||
\(580\) | −24.0000 | −0.996546 | ||||||||
\(581\) | 3.00000 | + | 8.66025i | 0.124461 | + | 0.359288i | ||||
\(582\) | −10.5000 | + | 6.06218i | −0.435239 | + | 0.251285i | ||||
\(583\) | 18.0000 | + | 10.3923i | 0.745484 | + | 0.430405i | ||||
\(584\) | 3.50000 | − | 6.06218i | 0.144831 | − | 0.250855i | ||||
\(585\) | −9.00000 | + | 36.3731i | −0.372104 | + | 1.50384i | ||||
\(586\) | −6.00000 | + | 3.46410i | −0.247858 | + | 0.143101i | ||||
\(587\) | 39.0000 | − | 22.5167i | 1.60970 | − | 0.929362i | 0.620266 | − | 0.784391i | \(-0.287025\pi\) |
0.989436 | − | 0.144971i | \(-0.0463088\pi\) | |||||||
\(588\) | −4.50000 | + | 11.2583i | −0.185577 | + | 0.464286i | ||||
\(589\) | 20.0000 | − | 34.6410i | 0.824086 | − | 1.42736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | − | 10.3923i | 0.740421 | − | 0.427482i | ||||
\(592\) | −7.50000 | + | 4.33013i | −0.308248 | + | 0.177967i | ||||
\(593\) | 6.00000 | − | 3.46410i | 0.246390 | − | 0.142254i | −0.371720 | − | 0.928345i | \(-0.621232\pi\) |
0.618110 | + | 0.786091i | \(0.287898\pi\) | |||||||
\(594\) | −27.0000 | − | 15.5885i | −1.10782 | − | 0.639602i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | + | 15.5885i | 0.368654 | + | 0.638528i | ||||
\(597\) | 13.5000 | + | 23.3827i | 0.552518 | + | 0.956990i | ||||
\(598\) | −3.00000 | + | 12.1244i | −0.122679 | + | 0.495802i | ||||
\(599\) | −24.0000 | − | 13.8564i | −0.980613 | − | 0.566157i | −0.0781581 | − | 0.996941i | \(-0.524904\pi\) |
−0.902455 | + | 0.430784i | \(0.858237\pi\) | |||||||
\(600\) | 10.5000 | + | 6.06218i | 0.428661 | + | 0.247487i | ||||
\(601\) | −1.50000 | + | 0.866025i | −0.0611863 | + | 0.0353259i | −0.530281 | − | 0.847822i | \(-0.677914\pi\) |
0.469095 | + | 0.883148i | \(0.344580\pi\) | |||||||
\(602\) | −2.00000 | − | 1.73205i | −0.0815139 | − | 0.0705931i | ||||
\(603\) | − | 10.3923i | − | 0.423207i | ||||||
\(604\) | 3.46410i | 0.140952i | ||||||||
\(605\) | 75.0000 | − | 43.3013i | 3.04918 | − | 1.76045i | ||||
\(606\) | −9.00000 | − | 5.19615i | −0.365600 | − | 0.211079i | ||||
\(607\) | 15.5885i | 0.632716i | 0.948640 | + | 0.316358i | \(0.102460\pi\) | ||||
−0.948640 | + | 0.316358i | \(0.897540\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 24.0000 | + | 20.7846i | 0.972529 | + | 0.842235i | ||||
\(610\) | −18.0000 | −0.728799 | ||||||||
\(611\) | 6.00000 | − | 24.2487i | 0.242734 | − | 0.980998i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 25.9808i | − | 1.04935i | −0.851302 | − | 0.524677i | \(-0.824186\pi\) | ||
0.851302 | − | 0.524677i | \(-0.175814\pi\) | |||||||
\(614\) | 2.00000 | − | 3.46410i | 0.0807134 | − | 0.139800i | ||||
\(615\) | 54.0000 | + | 31.1769i | 2.17749 | + | 1.25717i | ||||
\(616\) | −15.0000 | + | 5.19615i | −0.604367 | + | 0.209359i | ||||
\(617\) | 18.0000 | − | 31.1769i | 0.724653 | − | 1.25514i | −0.234464 | − | 0.972125i | \(-0.575334\pi\) |
0.959117 | − | 0.283011i | \(-0.0913331\pi\) | |||||||
\(618\) | −9.00000 | −0.362033 | ||||||||
\(619\) | −8.50000 | + | 14.7224i | −0.341644 | + | 0.591744i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | −24.0000 | + | 13.8564i | −0.963863 | + | 0.556487i | ||||
\(621\) | 9.00000 | − | 15.5885i | 0.361158 | − | 0.625543i | ||||
\(622\) | 3.00000 | + | 5.19615i | 0.120289 | + | 0.208347i | ||||
\(623\) | −9.00000 | − | 1.73205i | −0.360577 | − | 0.0693932i | ||||
\(624\) | 6.00000 | − | 1.73205i | 0.240192 | − | 0.0693375i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 32.9090i | 1.31531i | ||||||||
\(627\) | 51.9615i | 2.07514i | ||||||||
\(628\) | 19.0526i | 0.760280i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −9.00000 | − | 25.9808i | −0.358569 | − | 1.03510i | ||||
\(631\) | 22.5000 | + | 12.9904i | 0.895711 | + | 0.517139i | 0.875806 | − | 0.482663i | \(-0.160330\pi\) |
0.0199047 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | −7.50000 | + | 4.33013i | −0.298098 | + | 0.172107i | ||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | −3.00000 | − | 1.73205i | −0.119051 | − | 0.0687343i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 2.50000 | − | 25.1147i | 0.0990536 | − | 0.995082i | ||||
\(638\) | 41.5692i | 1.64574i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.46410i | − | 0.136931i | ||||||
\(641\) | −33.0000 | + | 19.0526i | −1.30342 | + | 0.752531i | −0.980989 | − | 0.194062i | \(-0.937834\pi\) |
−0.322432 | + | 0.946593i | \(0.604500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.50000 | − | 9.52628i | 0.216899 | − | 0.375680i | −0.736959 | − | 0.675937i | \(-0.763739\pi\) |
0.953858 | + | 0.300257i | \(0.0970725\pi\) | |||||||
\(644\) | −3.00000 | − | 8.66025i | −0.118217 | − | 0.341262i | ||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.0000 | 1.41531 | 0.707653 | − | 0.706560i | \(-0.249754\pi\) | ||||
0.707653 | + | 0.706560i | \(0.249754\pi\) | |||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −24.5000 | − | 6.06218i | −0.960969 | − | 0.237778i | ||||
\(651\) | 36.0000 | + | 6.92820i | 1.41095 | + | 0.271538i | ||||
\(652\) | 1.50000 | − | 0.866025i | 0.0587445 | − | 0.0339162i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −10.5000 | − | 18.1865i | −0.410582 | − | 0.711150i | ||||
\(655\) | 54.0000 | + | 31.1769i | 2.10995 | + | 1.21818i | ||||
\(656\) | − | 10.3923i | − | 0.405751i | ||||||
\(657\) | 10.5000 | − | 18.1865i | 0.409644 | − | 0.709524i | ||||
\(658\) | 6.00000 | + | 17.3205i | 0.233904 | + | 0.675224i | ||||
\(659\) | 24.0000 | + | 13.8564i | 0.934907 | + | 0.539769i | 0.888360 | − | 0.459147i | \(-0.151845\pi\) |
0.0465470 | + | 0.998916i | \(0.485178\pi\) | |||||||
\(660\) | 18.0000 | − | 31.1769i | 0.700649 | − | 1.21356i | ||||
\(661\) | −50.0000 | −1.94477 | −0.972387 | − | 0.233373i | \(-0.925024\pi\) | ||||
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | −16.5000 | − | 9.52628i | −0.641291 | − | 0.370249i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.46410i | 0.134433i | ||||||||
\(665\) | −30.0000 | + | 34.6410i | −1.16335 | + | 1.34332i | ||||
\(666\) | −22.5000 | + | 12.9904i | −0.871857 | + | 0.503367i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | −3.00000 | − | 1.73205i | −0.116073 | − | 0.0670151i | ||||
\(669\) | 24.0000 | − | 13.8564i | 0.927894 | − | 0.535720i | ||||
\(670\) | 12.0000 | 0.463600 | ||||||||
\(671\) | 31.1769i | 1.20357i | ||||||||
\(672\) | −3.00000 | + | 3.46410i | −0.115728 | + | 0.133631i | ||||
\(673\) | −0.500000 | − | 0.866025i | −0.0192736 | − | 0.0333828i | 0.856228 | − | 0.516599i | \(-0.172802\pi\) |
−0.875501 | + | 0.483216i | \(0.839469\pi\) | |||||||
\(674\) | 2.50000 | − | 4.33013i | 0.0962964 | − | 0.166790i | ||||
\(675\) | 31.5000 | + | 18.1865i | 1.21244 | + | 0.700000i | ||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 6.00000 | + | 10.3923i | 0.230429 | + | 0.399114i | ||||
\(679\) | −3.50000 | + | 18.1865i | −0.134318 | + | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | 24.0000 | + | 41.5692i | 0.919007 | + | 1.59177i | ||||
\(683\) | −9.00000 | − | 15.5885i | −0.344375 | − | 0.596476i | 0.640865 | − | 0.767654i | \(-0.278576\pi\) |
−0.985240 | + | 0.171178i | \(0.945243\pi\) | |||||||
\(684\) | 7.50000 | + | 12.9904i | 0.286770 | + | 0.496700i | ||||
\(685\) | −18.0000 | − | 10.3923i | −0.687745 | − | 0.397070i | ||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 43.5000 | − | 25.1147i | 1.65963 | − | 0.958187i | ||||
\(688\) | −0.500000 | − | 0.866025i | −0.0190623 | − | 0.0330169i | ||||
\(689\) | −12.0000 | + | 3.46410i | −0.457164 | + | 0.131972i | ||||
\(690\) | 18.0000 | + | 10.3923i | 0.685248 | + | 0.395628i | ||||
\(691\) | −8.50000 | + | 14.7224i | −0.323355 | + | 0.560068i | −0.981178 | − | 0.193105i | \(-0.938144\pi\) |
0.657823 | + | 0.753173i | \(0.271478\pi\) | |||||||
\(692\) | 3.00000 | + | 5.19615i | 0.114043 | + | 0.197528i | ||||
\(693\) | −45.0000 | + | 15.5885i | −1.70941 | + | 0.592157i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000 | 0.455186 | ||||||||
\(696\) | 6.00000 | + | 10.3923i | 0.227429 | + | 0.393919i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.0000 | 0.416356 | ||||||||
\(699\) | −6.00000 | − | 10.3923i | −0.226941 | − | 0.393073i | ||||
\(700\) | 17.5000 | − | 6.06218i | 0.661438 | − | 0.229129i | ||||
\(701\) | − | 13.8564i | − | 0.523349i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||
0.965156 | − | 0.261675i | \(-0.0842747\pi\) | |||||||
\(702\) | 18.0000 | − | 5.19615i | 0.679366 | − | 0.196116i | ||||
\(703\) | 37.5000 | + | 21.6506i | 1.41434 | + | 0.816569i | ||||
\(704\) | −6.00000 | −0.226134 | ||||||||
\(705\) | −36.0000 | − | 20.7846i | −1.35584 | − | 0.782794i | ||||
\(706\) | 9.00000 | + | 5.19615i | 0.338719 | + | 0.195560i | ||||
\(707\) | −15.0000 | + | 5.19615i | −0.564133 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 39.8372i | − | 1.49612i | −0.663633 | − | 0.748058i | \(-0.730986\pi\) | ||
0.663633 | − | 0.748058i | \(-0.269014\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | − | 20.7846i | −0.450035 | − | 0.779484i | ||||
\(712\) | −3.00000 | − | 1.73205i | −0.112430 | − | 0.0649113i | ||||
\(713\) | −24.0000 | + | 13.8564i | −0.898807 | + | 0.518927i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | + | 72.7461i | −0.673162 | + | 2.72055i | ||||
\(716\) | 21.0000 | − | 12.1244i | 0.784807 | − | 0.453108i | ||||
\(717\) | − | 10.3923i | − | 0.388108i | ||||||
\(718\) | 24.0000 | 0.895672 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | − | 10.3923i | − | 0.387298i | ||||||
\(721\) | −9.00000 | + | 10.3923i | −0.335178 | + | 0.387030i | ||||
\(722\) | 3.00000 | − | 5.19615i | 0.111648 | − | 0.193381i | ||||
\(723\) | 39.0000 | − | 22.5167i | 1.45043 | − | 0.837404i | ||||
\(724\) | −13.5000 | + | 7.79423i | −0.501724 | + | 0.289670i | ||||
\(725\) | − | 48.4974i | − | 1.80115i | ||||||
\(726\) | −37.5000 | − | 21.6506i | −1.39176 | − | 0.803530i | ||||
\(727\) | 10.3923i | 0.385429i | 0.981255 | + | 0.192715i | \(0.0617292\pi\) | ||||
−0.981255 | + | 0.192715i | \(0.938271\pi\) | |||||||
\(728\) | 4.00000 | − | 8.66025i | 0.148250 | − | 0.320970i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 21.0000 | + | 12.1244i | 0.777245 | + | 0.448743i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.50000 | + | 7.79423i | 0.166325 | + | 0.288083i | ||||
\(733\) | −23.0000 | − | 39.8372i | −0.849524 | − | 1.47142i | −0.881633 | − | 0.471935i | \(-0.843556\pi\) |
0.0321090 | − | 0.999484i | \(-0.489778\pi\) | |||||||
\(734\) | 1.50000 | + | 0.866025i | 0.0553660 | + | 0.0319656i | ||||
\(735\) | −39.0000 | − | 15.5885i | −1.43854 | − | 0.574989i | ||||
\(736\) | − | 3.46410i | − | 0.127688i | ||||||
\(737\) | − | 20.7846i | − | 0.765611i | ||||||
\(738\) | − | 31.1769i | − | 1.14764i | ||||||
\(739\) | 32.9090i | 1.21058i | 0.796007 | + | 0.605288i | \(0.206942\pi\) | ||||
−0.796007 | + | 0.605288i | \(0.793058\pi\) | |||||||
\(740\) | −15.0000 | − | 25.9808i | −0.551411 | − | 0.955072i | ||||
\(741\) | −22.5000 | − | 21.6506i | −0.826558 | − | 0.795356i | ||||
\(742\) | 6.00000 | − | 6.92820i | 0.220267 | − | 0.254342i | ||||
\(743\) | 15.0000 | + | 25.9808i | 0.550297 | + | 0.953142i | 0.998253 | + | 0.0590862i | \(0.0188187\pi\) |
−0.447956 | + | 0.894055i | \(0.647848\pi\) | |||||||
\(744\) | 12.0000 | + | 6.92820i | 0.439941 | + | 0.254000i | ||||
\(745\) | −54.0000 | + | 31.1769i | −1.97841 | + | 1.14223i | ||||
\(746\) | −1.00000 | + | 1.73205i | −0.0366126 | + | 0.0634149i | ||||
\(747\) | 10.3923i | 0.380235i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.00000 | + | 10.3923i | −0.219089 | + | 0.379473i | ||||
\(751\) | 8.50000 | − | 14.7224i | 0.310169 | − | 0.537229i | −0.668229 | − | 0.743955i | \(-0.732948\pi\) |
0.978399 | + | 0.206726i | \(0.0662809\pi\) | |||||||
\(752\) | 6.92820i | 0.252646i | ||||||||
\(753\) | −18.0000 | − | 10.3923i | −0.655956 | − | 0.378717i | ||||
\(754\) | −18.0000 | − | 17.3205i | −0.655521 | − | 0.630776i | ||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | −9.00000 | + | 10.3923i | −0.327327 | + | 0.377964i | ||||
\(757\) | −19.0000 | − | 32.9090i | −0.690567 | − | 1.19610i | −0.971652 | − | 0.236414i | \(-0.924028\pi\) |
0.281086 | − | 0.959683i | \(-0.409305\pi\) | |||||||
\(758\) | 17.3205i | 0.629109i | ||||||||
\(759\) | 18.0000 | − | 31.1769i | 0.653359 | − | 1.13165i | ||||
\(760\) | −15.0000 | + | 8.66025i | −0.544107 | + | 0.314140i | ||||
\(761\) | 3.46410i | 0.125574i | 0.998027 | + | 0.0627868i | \(0.0199988\pi\) | ||||
−0.998027 | + | 0.0627868i | \(0.980001\pi\) | |||||||
\(762\) | 1.73205i | 0.0627456i | ||||||||
\(763\) | −31.5000 | − | 6.06218i | −1.14038 | − | 0.219466i | ||||
\(764\) | −18.0000 | + | 10.3923i | −0.651217 | + | 0.375980i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | − | 10.3923i | −0.650366 | − | 0.375489i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.50000 | + | 0.866025i | −0.0541266 | + | 0.0312500i | ||||
\(769\) | −0.500000 | − | 0.866025i | −0.0180305 | − | 0.0312297i | 0.856869 | − | 0.515534i | \(-0.172406\pi\) |
−0.874900 | + | 0.484304i | \(0.839073\pi\) | |||||||
\(770\) | −18.0000 | − | 51.9615i | −0.648675 | − | 1.87256i | ||||
\(771\) | 27.0000 | + | 15.5885i | 0.972381 | + | 0.561405i | ||||
\(772\) | 4.50000 | − | 2.59808i | 0.161959 | − | 0.0935068i | ||||
\(773\) | −36.0000 | + | 20.7846i | −1.29483 | + | 0.747570i | −0.979506 | − | 0.201414i | \(-0.935446\pi\) |
−0.315324 | + | 0.948984i | \(0.602113\pi\) | |||||||
\(774\) | −1.50000 | − | 2.59808i | −0.0539164 | − | 0.0933859i | ||||
\(775\) | −28.0000 | − | 48.4974i | −1.00579 | − | 1.74208i | ||||
\(776\) | −3.50000 | + | 6.06218i | −0.125643 | + | 0.217620i | ||||
\(777\) | −7.50000 | + | 38.9711i | −0.269061 | + | 1.39808i | ||||
\(778\) | 9.00000 | − | 5.19615i | 0.322666 | − | 0.186291i | ||||
\(779\) | −45.0000 | + | 25.9808i | −1.61229 | + | 0.930857i | ||||
\(780\) | 6.00000 | + | 20.7846i | 0.214834 | + | 0.744208i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.0000 | + | 31.1769i | 0.643268 | + | 1.11417i | ||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −66.0000 | −2.35564 | ||||||||
\(786\) | − | 31.1769i | − | 1.11204i | ||||||
\(787\) | −26.5000 | − | 45.8993i | −0.944623 | − | 1.63614i | −0.756504 | − | 0.653989i | \(-0.773094\pi\) |
−0.188119 | − | 0.982146i | \(-0.560239\pi\) | |||||||
\(788\) | 6.00000 | − | 10.3923i | 0.213741 | − | 0.370211i | ||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 24.0000 | − | 13.8564i | 0.853882 | − | 0.492989i | ||||
\(791\) | 18.0000 | + | 3.46410i | 0.640006 | + | 0.123169i | ||||
\(792\) | −18.0000 | −0.639602 | ||||||||
\(793\) | −13.5000 | − | 12.9904i | −0.479399 | − | 0.461302i | ||||
\(794\) | 5.50000 | − | 9.52628i | 0.195188 | − | 0.338075i | ||||
\(795\) | 20.7846i | 0.737154i | ||||||||
\(796\) | 13.5000 | + | 7.79423i | 0.478495 | + | 0.276259i | ||||
\(797\) | 9.00000 | − | 15.5885i | 0.318796 | − | 0.552171i | −0.661441 | − | 0.749997i | \(-0.730055\pi\) |
0.980237 | + | 0.197826i | \(0.0633881\pi\) | |||||||
\(798\) | 22.5000 | + | 4.33013i | 0.796491 | + | 0.153285i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.00000 | 0.247487 | ||||||||
\(801\) | −9.00000 | − | 5.19615i | −0.317999 | − | 0.183597i | ||||
\(802\) | 3.00000 | + | 5.19615i | 0.105934 | + | 0.183483i | ||||
\(803\) | 21.0000 | − | 36.3731i | 0.741074 | − | 1.28358i | ||||
\(804\) | −3.00000 | − | 5.19615i | −0.105802 | − | 0.183254i | ||||
\(805\) | 30.0000 | − | 10.3923i | 1.05736 | − | 0.366281i | ||||
\(806\) | −28.0000 | − | 6.92820i | −0.986258 | − | 0.244036i | ||||
\(807\) | 18.0000 | − | 10.3923i | 0.633630 | − | 0.365826i | ||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | − | 6.92820i | − | 0.243583i | −0.992556 | − | 0.121791i | \(-0.961136\pi\) | ||
0.992556 | − | 0.121791i | \(-0.0388639\pi\) | |||||||
\(810\) | − | 31.1769i | − | 1.09545i | ||||||
\(811\) | 1.00000 | 0.0351147 | 0.0175574 | − | 0.999846i | \(-0.494411\pi\) | ||||
0.0175574 | + | 0.999846i | \(0.494411\pi\) | |||||||
\(812\) | 18.0000 | + | 3.46410i | 0.631676 | + | 0.121566i | ||||
\(813\) | −1.50000 | − | 0.866025i | −0.0526073 | − | 0.0303728i | ||||
\(814\) | −45.0000 | + | 25.9808i | −1.57725 | + | 0.910625i | ||||
\(815\) | 3.00000 | + | 5.19615i | 0.105085 | + | 0.182013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | + | 4.33013i | −0.0874639 | + | 0.151492i | ||||
\(818\) | 19.0000 | 0.664319 | ||||||||
\(819\) | 12.0000 | − | 25.9808i | 0.419314 | − | 0.907841i | ||||
\(820\) | 36.0000 | 1.25717 | ||||||||
\(821\) | −27.0000 | + | 46.7654i | −0.942306 | + | 1.63212i | −0.181250 | + | 0.983437i | \(0.558014\pi\) |
−0.761056 | + | 0.648686i | \(0.775319\pi\) | |||||||
\(822\) | 10.3923i | 0.362473i | ||||||||
\(823\) | −28.0000 | − | 48.4974i | −0.976019 | − | 1.69051i | −0.676532 | − | 0.736413i | \(-0.736518\pi\) |
−0.299487 | − | 0.954100i | \(-0.596815\pi\) | |||||||
\(824\) | −4.50000 | + | 2.59808i | −0.156765 | + | 0.0905083i | ||||
\(825\) | 63.0000 | + | 36.3731i | 2.19338 | + | 1.26635i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0000 | 1.66912 | 0.834562 | − | 0.550914i | \(-0.185721\pi\) | ||||
0.834562 | + | 0.550914i | \(0.185721\pi\) | |||||||
\(828\) | − | 10.3923i | − | 0.361158i | ||||||
\(829\) | − | 1.73205i | − | 0.0601566i | −0.999548 | − | 0.0300783i | \(-0.990424\pi\) | ||
0.999548 | − | 0.0300783i | \(-0.00957567\pi\) | |||||||
\(830\) | −12.0000 | −0.416526 | ||||||||
\(831\) | −25.5000 | + | 14.7224i | −0.884585 | + | 0.510716i | ||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.00000 | − | 5.19615i | −0.103882 | − | 0.179928i | ||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 15.0000 | + | 25.9808i | 0.518786 | + | 0.898563i | ||||
\(837\) | 36.0000 | + | 20.7846i | 1.24434 | + | 0.718421i | ||||
\(838\) | −30.0000 | −1.03633 | ||||||||
\(839\) | 18.0000 | + | 10.3923i | 0.621429 | + | 0.358782i | 0.777425 | − | 0.628975i | \(-0.216525\pi\) |
−0.155996 | + | 0.987758i | \(0.549859\pi\) | |||||||
\(840\) | −12.0000 | − | 10.3923i | −0.414039 | − | 0.358569i | ||||
\(841\) | 9.50000 | − | 16.4545i | 0.327586 | − | 0.567396i | ||||
\(842\) | 24.0000 | + | 13.8564i | 0.827095 | + | 0.477523i | ||||
\(843\) | 20.7846i | 0.715860i | ||||||||
\(844\) | −2.50000 | + | 4.33013i | −0.0860535 | + | 0.149049i | ||||
\(845\) | −24.0000 | − | 38.1051i | −0.825625 | − | 1.31086i | ||||
\(846\) | 20.7846i | 0.714590i | ||||||||
\(847\) | −62.5000 | + | 21.6506i | −2.14753 | + | 0.743925i | ||||
\(848\) | 3.00000 | − | 1.73205i | 0.103020 | − | 0.0594789i | ||||
\(849\) | −3.00000 | −0.102960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.0000 | − | 25.9808i | −0.514193 | − | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 13.5000 | + | 2.59808i | 0.461960 | + | 0.0889043i | ||||
\(855\) | −45.0000 | + | 25.9808i | −1.53897 | + | 0.888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000 | − | 20.7846i | 0.409912 | − | 0.709989i | −0.584967 | − | 0.811057i | \(-0.698893\pi\) |
0.994880 | + | 0.101068i | \(0.0322260\pi\) | |||||||
\(858\) | 36.0000 | − | 10.3923i | 1.22902 | − | 0.354787i | ||||
\(859\) | −1.50000 | + | 0.866025i | −0.0511793 | + | 0.0295484i | −0.525371 | − | 0.850873i | \(-0.676074\pi\) |
0.474192 | + | 0.880421i | \(0.342740\pi\) | |||||||
\(860\) | 3.00000 | − | 1.73205i | 0.102299 | − | 0.0590624i | ||||
\(861\) | −36.0000 | − | 31.1769i | −1.22688 | − | 1.06251i | ||||
\(862\) | 9.00000 | − | 15.5885i | 0.306541 | − | 0.530945i | ||||
\(863\) | −3.00000 | − | 5.19615i | −0.102121 | − | 0.176879i | 0.810437 | − | 0.585826i | \(-0.199230\pi\) |
−0.912558 | + | 0.408946i | \(0.865896\pi\) | |||||||
\(864\) | −4.50000 | + | 2.59808i | −0.153093 | + | 0.0883883i | ||||
\(865\) | −18.0000 | + | 10.3923i | −0.612018 | + | 0.353349i | ||||
\(866\) | −18.0000 | + | 10.3923i | −0.611665 | + | 0.353145i | ||||
\(867\) | −25.5000 | − | 14.7224i | −0.866025 | − | 0.500000i | ||||
\(868\) | 20.0000 | − | 6.92820i | 0.678844 | − | 0.235159i | ||||
\(869\) | −24.0000 | − | 41.5692i | −0.814144 | − | 1.41014i | ||||
\(870\) | −36.0000 | + | 20.7846i | −1.22051 | + | 0.704664i | ||||
\(871\) | 9.00000 | + | 8.66025i | 0.304953 | + | 0.293442i | ||||
\(872\) | −10.5000 | − | 6.06218i | −0.355575 | − | 0.205291i | ||||
\(873\) | −10.5000 | + | 18.1865i | −0.355371 | + | 0.615521i | ||||
\(874\) | −15.0000 | + | 8.66025i | −0.507383 | + | 0.292937i | ||||
\(875\) | 6.00000 | + | 17.3205i | 0.202837 | + | 0.585540i | ||||
\(876\) | − | 12.1244i | − | 0.409644i | ||||||
\(877\) | 27.7128i | 0.935795i | 0.883783 | + | 0.467898i | \(0.154988\pi\) | ||||
−0.883783 | + | 0.467898i | \(0.845012\pi\) | |||||||
\(878\) | 10.5000 | − | 6.06218i | 0.354358 | − | 0.204589i | ||||
\(879\) | −6.00000 | + | 10.3923i | −0.202375 | + | 0.350524i | ||||
\(880\) | − | 20.7846i | − | 0.700649i | ||||||
\(881\) | 18.0000 | + | 31.1769i | 0.606435 | + | 1.05038i | 0.991823 | + | 0.127622i | \(0.0407345\pi\) |
−0.385387 | + | 0.922755i | \(0.625932\pi\) | |||||||
\(882\) | 3.00000 | + | 20.7846i | 0.101015 | + | 0.699854i | ||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 38.1051i | − | 1.28017i | ||||||
\(887\) | −3.00000 | + | 5.19615i | −0.100730 | + | 0.174470i | −0.911986 | − | 0.410222i | \(-0.865451\pi\) |
0.811256 | + | 0.584692i | \(0.198785\pi\) | |||||||
\(888\) | −7.50000 | + | 12.9904i | −0.251684 | + | 0.435929i | ||||
\(889\) | 2.00000 | + | 1.73205i | 0.0670778 | + | 0.0580911i | ||||
\(890\) | 6.00000 | − | 10.3923i | 0.201120 | − | 0.348351i | ||||
\(891\) | −54.0000 | −1.80907 | ||||||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | 30.0000 | − | 17.3205i | 1.00391 | − | 0.579609i | ||||
\(894\) | 27.0000 | + | 15.5885i | 0.903015 | + | 0.521356i | ||||
\(895\) | 42.0000 | + | 72.7461i | 1.40391 | + | 2.43164i | ||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 6.00000 | + | 20.7846i | 0.200334 | + | 0.693978i | ||||
\(898\) | 15.0000 | + | 25.9808i | 0.500556 | + | 0.866989i | ||||
\(899\) | − | 55.4256i | − | 1.84855i | ||||||
\(900\) | 21.0000 | 0.700000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 62.3538i | − | 2.07616i | ||||||
\(903\) | −4.50000 | − | 0.866025i | −0.149751 | − | 0.0288195i | ||||
\(904\) | 6.00000 | + | 3.46410i | 0.199557 | + | 0.115214i | ||||
\(905\) | −27.0000 | − | 46.7654i | −0.897510 | − | 1.55453i | ||||
\(906\) | 3.00000 | + | 5.19615i | 0.0996683 | + | 0.172631i | ||||
\(907\) | −1.00000 | −0.0332045 | −0.0166022 | − | 0.999862i | \(-0.505285\pi\) | ||||
−0.0166022 | + | 0.999862i | \(0.505285\pi\) | |||||||
\(908\) | 9.00000 | + | 5.19615i | 0.298675 | + | 0.172440i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 30.0000 | + | 13.8564i | 0.994490 | + | 0.459335i | ||||
\(911\) | − | 13.8564i | − | 0.459083i | −0.973299 | − | 0.229542i | \(-0.926277\pi\) | ||
0.973299 | − | 0.229542i | \(-0.0737227\pi\) | |||||||
\(912\) | 7.50000 | + | 4.33013i | 0.248350 | + | 0.143385i | ||||
\(913\) | 20.7846i | 0.687870i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.0000 | + | 15.5885i | −0.892592 | + | 0.515339i | ||||
\(916\) | 14.5000 | − | 25.1147i | 0.479093 | − | 0.829814i | ||||
\(917\) | −36.0000 | − | 31.1769i | −1.18882 | − | 1.02955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0000 | 1.15454 | 0.577272 | − | 0.816552i | \(-0.304117\pi\) | ||||
0.577272 | + | 0.816552i | \(0.304117\pi\) | |||||||
\(920\) | 12.0000 | 0.395628 | ||||||||
\(921\) | − | 6.92820i | − | 0.228292i | ||||||
\(922\) | 18.0000 | − | 10.3923i | 0.592798 | − | 0.342252i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.0000 | + | 20.7846i | −0.592157 | + | 0.683763i | ||||
\(925\) | 52.5000 | − | 30.3109i | 1.72619 | − | 0.996616i | ||||
\(926\) | 16.5000 | + | 9.52628i | 0.542224 | + | 0.313053i | ||||
\(927\) | −13.5000 | + | 7.79423i | −0.443398 | + | 0.255996i | ||||
\(928\) | 6.00000 | + | 3.46410i | 0.196960 | + | 0.113715i | ||||
\(929\) | − | 27.7128i | − | 0.909228i | −0.890689 | − | 0.454614i | \(-0.849777\pi\) | ||
0.890689 | − | 0.454614i | \(-0.150223\pi\) | |||||||
\(930\) | −24.0000 | + | 41.5692i | −0.786991 | + | 1.36311i | ||||
\(931\) | 27.5000 | − | 21.6506i | 0.901276 | − | 0.709571i | ||||
\(932\) | −6.00000 | − | 3.46410i | −0.196537 | − | 0.113470i | ||||
\(933\) | 9.00000 | + | 5.19615i | 0.294647 | + | 0.170114i | ||||
\(934\) | −18.0000 | −0.588978 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.50000 | − | 7.79423i | 0.245145 | − | 0.254762i | ||||
\(937\) | − | 8.66025i | − | 0.282918i | −0.989944 | − | 0.141459i | \(-0.954821\pi\) | ||
0.989944 | − | 0.141459i | \(-0.0451794\pi\) | |||||||
\(938\) | −9.00000 | − | 1.73205i | −0.293860 | − | 0.0565535i | ||||
\(939\) | 28.5000 | + | 49.3634i | 0.930062 | + | 1.61092i | ||||
\(940\) | −24.0000 | −0.782794 | ||||||||
\(941\) | 12.0000 | + | 6.92820i | 0.391189 | + | 0.225853i | 0.682675 | − | 0.730722i | \(-0.260816\pi\) |
−0.291486 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(942\) | 16.5000 | + | 28.5788i | 0.537599 | + | 0.931149i | ||||
\(943\) | 36.0000 | 1.17232 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36.0000 | − | 31.1769i | −1.17108 | − | 1.01419i | ||||
\(946\) | −3.00000 | − | 5.19615i | −0.0975384 | − | 0.168941i | ||||
\(947\) | 24.0000 | − | 41.5692i | 0.779895 | − | 1.35082i | −0.152106 | − | 0.988364i | \(-0.548606\pi\) |
0.932002 | − | 0.362454i | \(-0.118061\pi\) | |||||||
\(948\) | −12.0000 | − | 6.92820i | −0.389742 | − | 0.225018i | ||||
\(949\) | 7.00000 | + | 24.2487i | 0.227230 | + | 0.787146i | ||||
\(950\) | −17.5000 | − | 30.3109i | −0.567775 | − | 0.983415i | ||||
\(951\) | 27.0000 | − | 15.5885i | 0.875535 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.0000 | + | 19.0526i | 1.06897 | + | 0.617173i | 0.927901 | − | 0.372826i | \(-0.121611\pi\) |
0.141074 | + | 0.989999i | \(0.454945\pi\) | |||||||
\(954\) | 9.00000 | − | 5.19615i | 0.291386 | − | 0.168232i | ||||
\(955\) | −36.0000 | − | 62.3538i | −1.16493 | − | 2.01772i | ||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | 36.0000 | + | 62.3538i | 1.16371 | + | 2.01561i | ||||
\(958\) | 6.00000 | + | 3.46410i | 0.193851 | + | 0.111920i | ||||
\(959\) | 12.0000 | + | 10.3923i | 0.387500 | + | 0.335585i | ||||
\(960\) | −3.00000 | − | 5.19615i | −0.0968246 | − | 0.167705i | ||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 7.50000 | − | 30.3109i | 0.241810 | − | 0.977262i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0000 | − | 22.5167i | 0.418702 | − | 0.725213i | ||||
\(965\) | 9.00000 | + | 15.5885i | 0.289720 | + | 0.501810i | ||||
\(966\) | −12.0000 | − | 10.3923i | −0.386094 | − | 0.334367i | ||||
\(967\) | 8.66025i | 0.278495i | 0.990258 | + | 0.139247i | \(0.0444684\pi\) | ||||
−0.990258 | + | 0.139247i | \(0.955532\pi\) | |||||||
\(968\) | −25.0000 | −0.803530 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.0000 | − | 12.1244i | −0.674269 | − | 0.389290i | ||||
\(971\) | −6.00000 | −0.192549 | −0.0962746 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962746 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | −9.00000 | − | 1.73205i | −0.288527 | − | 0.0555270i | ||||
\(974\) | 15.5885i | 0.499486i | ||||||||
\(975\) | −42.0000 | + | 12.1244i | −1.34508 | + | 0.388290i | ||||
\(976\) | 4.50000 | + | 2.59808i | 0.144041 | + | 0.0831624i | ||||
\(977\) | −36.0000 | −1.15174 | −0.575871 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575871 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(978\) | 1.50000 | − | 2.59808i | 0.0479647 | − | 0.0830773i | ||||
\(979\) | −18.0000 | − | 10.3923i | −0.575282 | − | 0.332140i | ||||
\(980\) | −24.0000 | + | 3.46410i | −0.766652 | + | 0.110657i | ||||
\(981\) | −31.5000 | − | 18.1865i | −1.00572 | − | 0.580651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.0000 | − | 17.3205i | −0.956851 | − | 0.552438i | −0.0616488 | − | 0.998098i | \(-0.519636\pi\) |
−0.895203 | + | 0.445659i | \(0.852969\pi\) | |||||||
\(984\) | −9.00000 | − | 15.5885i | −0.286910 | − | 0.496942i | ||||
\(985\) | 36.0000 | + | 20.7846i | 1.14706 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.0000 | + | 20.7846i | 0.763928 | + | 0.661581i | ||||
\(988\) | −17.5000 | − | 4.33013i | −0.556749 | − | 0.137760i | ||||
\(989\) | 3.00000 | − | 1.73205i | 0.0953945 | − | 0.0550760i | ||||
\(990\) | − | 62.3538i | − | 1.98173i | ||||||
\(991\) | 55.0000 | 1.74713 | 0.873566 | − | 0.486705i | \(-0.161801\pi\) | ||||
0.873566 | + | 0.486705i | \(0.161801\pi\) | |||||||
\(992\) | 8.00000 | 0.254000 | ||||||||
\(993\) | −33.0000 | −1.04722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.0000 | + | 46.7654i | −0.855958 | + | 1.48256i | ||||
\(996\) | 3.00000 | + | 5.19615i | 0.0950586 | + | 0.164646i | ||||
\(997\) | 37.5000 | − | 21.6506i | 1.18764 | − | 0.685682i | 0.229868 | − | 0.973222i | \(-0.426171\pi\) |
0.957769 | + | 0.287539i | \(0.0928372\pi\) | |||||||
\(998\) | − | 8.66025i | − | 0.274136i | ||||||
\(999\) | −22.5000 | + | 38.9711i | −0.711868 | + | 1.23299i |
(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.bn.c.101.1 | yes | 2 | |
3.2 | odd | 2 | 546.2.bn.b.101.1 | yes | 2 | ||
7.5 | odd | 6 | 546.2.bi.a.257.1 | yes | 2 | ||
13.4 | even | 6 | 546.2.bi.c.17.1 | yes | 2 | ||
21.5 | even | 6 | 546.2.bi.c.257.1 | yes | 2 | ||
39.17 | odd | 6 | 546.2.bi.a.17.1 | ✓ | 2 | ||
91.82 | odd | 6 | 546.2.bn.b.173.1 | yes | 2 | ||
273.173 | even | 6 | inner | 546.2.bn.c.173.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bi.a.17.1 | ✓ | 2 | 39.17 | odd | 6 | ||
546.2.bi.a.257.1 | yes | 2 | 7.5 | odd | 6 | ||
546.2.bi.c.17.1 | yes | 2 | 13.4 | even | 6 | ||
546.2.bi.c.257.1 | yes | 2 | 21.5 | even | 6 | ||
546.2.bn.b.101.1 | yes | 2 | 3.2 | odd | 2 | ||
546.2.bn.b.173.1 | yes | 2 | 91.82 | odd | 6 | ||
546.2.bn.c.101.1 | yes | 2 | 1.1 | even | 1 | trivial | |
546.2.bn.c.173.1 | yes | 2 | 273.173 | even | 6 | inner |