Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(10,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.10");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.r (of order \(6\), degree \(2\), not 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: | \(2.80274911095\) |
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: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 351.10 |
Dual form | 351.2.r.a.316.1 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.925615 | − | 0.378467i | \(-0.123549\pi\) |
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | + | 0.866025i | 0.670820 | + | 0.387298i | 0.796387 | − | 0.604787i | \(-0.206742\pi\) |
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | + | 2.59808i | −0.693375 | + | 0.720577i | ||||
\(14\) | −1.50000 | + | 2.59808i | −0.400892 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | − | 0.866025i | −0.344124 | − | 0.198680i | 0.317970 | − | 0.948101i | \(-0.396999\pi\) |
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 5.19615i | 0.639602 | + | 1.10782i | ||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | −6.00000 | + | 1.73205i | −1.17670 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.50000 | + | 0.866025i | −0.283473 | + | 0.163663i | ||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.50000 | − | 4.33013i | −1.34704 | − | 0.777714i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 4.50000 | − | 2.59808i | 0.795495 | − | 0.459279i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.50000 | − | 2.59808i | 0.771744 | − | 0.445566i | ||||
\(35\) | −1.50000 | + | 2.59808i | −0.253546 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.50000 | + | 2.59808i | −0.739795 | + | 0.427121i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | −1.50000 | − | 2.59808i | −0.243332 | − | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | − | 12.1244i | − | 1.89351i | −0.321960 | − | 0.946753i | \(-0.604342\pi\) | ||
0.321960 | − | 0.946753i | \(-0.395658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50000 | + | 2.59808i | 0.663489 | + | 0.383065i | ||||
\(47\) | 4.50000 | − | 2.59808i | 0.656392 | − | 0.378968i | −0.134509 | − | 0.990912i | \(-0.542946\pi\) |
0.790901 | + | 0.611944i | \(0.209612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | − | 3.46410i | − | 0.489898i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50000 | − | 0.866025i | −0.485363 | − | 0.120096i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.00000 | + | 5.19615i | −1.18176 | + | 0.682288i | ||||
\(59\) | −3.00000 | + | 1.73205i | −0.390567 | + | 0.225494i | −0.682406 | − | 0.730974i | \(-0.739066\pi\) |
0.291839 | + | 0.956467i | \(0.405733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(62\) | −7.50000 | − | 12.9904i | −0.952501 | − | 1.64978i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.00000 | + | 1.73205i | −0.744208 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.1244i | − | 1.48123i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) | ||
0.671932 | − | 0.740613i | \(-0.265465\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.50000 | + | 2.59808i | −0.537853 | + | 0.310530i | ||||
\(71\) | 7.50000 | + | 4.33013i | 0.890086 | + | 0.513892i | 0.873971 | − | 0.485979i | \(-0.161537\pi\) |
0.0161155 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | −9.00000 | −1.04623 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.73205i | − | 0.198680i | ||||||
\(77\) | −3.00000 | + | 5.19615i | −0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | + | 9.52628i | 0.618798 | + | 1.07179i | 0.989705 | + | 0.143120i | \(0.0457135\pi\) |
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(80\) | 7.50000 | − | 4.33013i | 0.838525 | − | 0.484123i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.5000 | − | 18.1865i | 1.15953 | − | 2.00837i | ||||
\(83\) | 4.50000 | − | 2.59808i | 0.493939 | − | 0.285176i | −0.232268 | − | 0.972652i | \(-0.574615\pi\) |
0.726207 | + | 0.687476i | \(0.241281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | − | 2.59808i | 0.488094 | − | 0.281801i | ||||
\(86\) | −1.50000 | − | 0.866025i | −0.161749 | − | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | −13.5000 | + | 7.79423i | −1.43100 | + | 0.826187i | −0.997197 | − | 0.0748225i | \(-0.976161\pi\) |
−0.433800 | + | 0.901009i | \(0.642828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50000 | − | 4.33013i | −0.471728 | − | 0.453921i | ||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000 | 0.928279 | ||||||||
\(95\) | −1.50000 | − | 2.59808i | −0.153897 | − | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.5885i | 1.58277i | 0.611319 | + | 0.791384i | \(0.290639\pi\) | ||||
−0.611319 | + | 0.791384i | \(0.709361\pi\) | |||||||
\(98\) | 6.00000 | + | 3.46410i | 0.606092 | + | 0.349927i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.50000 | − | 11.2583i | 0.640464 | − | 1.10932i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 4.50000 | + | 4.33013i | 0.441261 | + | 0.424604i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | − | 5.19615i | −0.874157 | − | 0.504695i | ||||
\(107\) | 7.50000 | + | 12.9904i | 0.725052 | + | 1.25583i | 0.958952 | + | 0.283567i | \(0.0915178\pi\) |
−0.233900 | + | 0.972261i | \(0.575149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 10.3923i | 0.990867i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.50000 | + | 4.33013i | 0.708683 | + | 0.409159i | ||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 2.59808i | 0.419627 | + | 0.242272i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 4.50000 | + | 2.59808i | 0.412514 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −7.50000 | − | 4.33013i | −0.679018 | − | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.66025i | − | 0.777714i | ||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50000 | + | 4.33013i | 0.221839 | + | 0.384237i | 0.955366 | − | 0.295423i | \(-0.0954607\pi\) |
−0.733527 | + | 0.679660i | \(0.762127\pi\) | |||||||
\(128\) | −10.5000 | − | 6.06218i | −0.928078 | − | 0.535826i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.5000 | − | 2.59808i | −0.920911 | − | 0.227866i | ||||
\(131\) | 7.50000 | − | 12.9904i | 0.655278 | − | 1.13497i | −0.326546 | − | 0.945181i | \(-0.605885\pi\) |
0.981824 | − | 0.189794i | \(-0.0607819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50000 | − | 2.59808i | 0.130066 | − | 0.225282i | ||||
\(134\) | 10.5000 | − | 18.1865i | 0.907062 | − | 1.57108i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50000 | − | 2.59808i | −0.385872 | − | 0.222783i | ||||
\(137\) | 5.19615i | 0.443937i | 0.975054 | + | 0.221969i | \(0.0712483\pi\) | ||||
−0.975054 | + | 0.221969i | \(0.928752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | + | 13.8564i | 0.678551 | + | 1.17529i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.50000 | + | 12.9904i | 0.629386 | + | 1.09013i | ||||
\(143\) | −12.0000 | + | 3.46410i | −1.00349 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 5.19615i | −0.747409 | + | 0.431517i | ||||
\(146\) | 6.00000 | − | 10.3923i | 0.496564 | − | 0.860073i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.50000 | − | 2.59808i | −0.369898 | − | 0.213561i | ||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5000 | + | 6.06218i | −0.854478 | + | 0.493333i | −0.862159 | − | 0.506637i | \(-0.830888\pi\) |
0.00768132 | + | 0.999970i | \(0.497555\pi\) | |||||||
\(152\) | −1.50000 | + | 2.59808i | −0.121666 | + | 0.210732i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.00000 | + | 5.19615i | −0.725241 | + | 0.418718i | ||||
\(155\) | −7.50000 | − | 12.9904i | −0.602414 | − | 1.04341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5000 | + | 19.9186i | −0.917800 | + | 1.58968i | −0.115050 | + | 0.993360i | \(0.536703\pi\) |
−0.802749 | + | 0.596316i | \(0.796630\pi\) | |||||||
\(158\) | 19.0526i | 1.51574i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.00000 | 0.711512 | ||||||||
\(161\) | 5.19615i | 0.409514i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5000 | + | 6.06218i | 0.822423 | + | 0.474826i | 0.851251 | − | 0.524758i | \(-0.175844\pi\) |
−0.0288280 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(164\) | 10.5000 | − | 6.06218i | 0.819912 | − | 0.473377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.00000 | 0.698535 | ||||||||
\(167\) | 5.19615i | 0.402090i | 0.979582 | + | 0.201045i | \(0.0644338\pi\) | ||||
−0.979582 | + | 0.201045i | \(0.935566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.500000 | − | 0.866025i | −0.0381246 | − | 0.0660338i | ||||
\(173\) | 21.0000 | 1.59660 | 0.798300 | − | 0.602260i | \(-0.205733\pi\) | ||||
0.798300 | + | 0.602260i | \(0.205733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | − | 1.73205i | 0.226779 | − | 0.130931i | ||||
\(176\) | 15.0000 | − | 8.66025i | 1.13067 | − | 0.652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.0000 | −2.02374 | ||||||||
\(179\) | 1.50000 | + | 2.59808i | 0.112115 | + | 0.194189i | 0.916623 | − | 0.399753i | \(-0.130904\pi\) |
−0.804508 | + | 0.593942i | \(0.797571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −3.00000 | − | 10.3923i | −0.222375 | − | 0.770329i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.19615i | − | 0.383065i | ||||||
\(185\) | −9.00000 | −0.661693 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 5.19615i | 0.658145 | − | 0.379980i | ||||
\(188\) | 4.50000 | + | 2.59808i | 0.328196 | + | 0.189484i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 5.19615i | − | 0.376969i | ||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.19615i | 0.374027i | 0.982357 | + | 0.187014i | \(0.0598809\pi\) | ||||
−0.982357 | + | 0.187014i | \(0.940119\pi\) | |||||||
\(194\) | −13.5000 | + | 23.3827i | −0.969244 | + | 1.67878i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | + | 3.46410i | 0.142857 | + | 0.247436i | ||||
\(197\) | −7.50000 | + | 4.33013i | −0.534353 | + | 0.308509i | −0.742787 | − | 0.669528i | \(-0.766497\pi\) |
0.208434 | + | 0.978036i | \(0.433163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50000 | + | 11.2583i | −0.460773 | + | 0.798082i | −0.999000 | − | 0.0447181i | \(-0.985761\pi\) |
0.538227 | + | 0.842800i | \(0.319094\pi\) | |||||||
\(200\) | −3.00000 | + | 1.73205i | −0.212132 | + | 0.122474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.00000 | + | 5.19615i | −0.633238 | + | 0.365600i | ||||
\(203\) | −9.00000 | − | 5.19615i | −0.631676 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5000 | − | 18.1865i | 0.733352 | − | 1.27020i | ||||
\(206\) | 19.5000 | − | 11.2583i | 1.35863 | − | 0.784405i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000 | + | 17.3205i | 0.346688 | + | 1.20096i | ||||
\(209\) | −3.00000 | − | 5.19615i | −0.207514 | − | 0.359425i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0000 | 0.894957 | 0.447478 | − | 0.894295i | \(-0.352322\pi\) | ||||
0.447478 | + | 0.894295i | \(0.352322\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.9808i | 1.77601i | ||||||||
\(215\) | −1.50000 | − | 0.866025i | −0.102299 | − | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.50000 | − | 12.9904i | 0.509133 | − | 0.881845i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | + | 5.19615i | −0.202260 | + | 0.350325i | ||||
\(221\) | 3.00000 | + | 10.3923i | 0.201802 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.00000 | + | 1.73205i | 0.200895 | + | 0.115987i | 0.597073 | − | 0.802187i | \(-0.296330\pi\) |
−0.396178 | + | 0.918174i | \(0.629664\pi\) | |||||||
\(224\) | 4.50000 | + | 7.79423i | 0.300669 | + | 0.520774i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3923i | 0.691286i | ||||||||
\(227\) | 12.1244i | 0.804722i | 0.915481 | + | 0.402361i | \(0.131810\pi\) | ||||
−0.915481 | + | 0.402361i | \(0.868190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.50000 | − | 4.33013i | −0.495614 | − | 0.286143i | 0.231287 | − | 0.972886i | \(-0.425707\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 4.50000 | + | 7.79423i | 0.296721 | + | 0.513936i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000 | + | 5.19615i | 0.590879 | + | 0.341144i | ||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | −3.00000 | − | 1.73205i | −0.195283 | − | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.50000 | + | 7.79423i | 0.291692 | + | 0.505225i | ||||
\(239\) | −4.50000 | − | 2.59808i | −0.291081 | − | 0.168056i | 0.347348 | − | 0.937736i | \(-0.387082\pi\) |
−0.638429 | + | 0.769681i | \(0.720415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.19615i | − | 0.334714i | −0.985896 | − | 0.167357i | \(-0.946477\pi\) | ||
0.985896 | − | 0.167357i | \(-0.0535232\pi\) | |||||||
\(242\) | 1.73205i | 0.111340i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.50000 | − | 4.33013i | −0.160046 | − | 0.277208i | ||||
\(245\) | 6.00000 | + | 3.46410i | 0.383326 | + | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | − | 1.73205i | 0.381771 | − | 0.110208i | ||||
\(248\) | −7.50000 | + | 12.9904i | −0.476250 | + | 0.824890i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5000 | − | 18.1865i | 0.664078 | − | 1.15022i | ||||
\(251\) | 4.50000 | − | 7.79423i | 0.284037 | − | 0.491967i | −0.688338 | − | 0.725390i | \(-0.741659\pi\) |
0.972375 | + | 0.233423i | \(0.0749927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | + | 5.19615i | 0.565825 | + | 0.326679i | ||||
\(254\) | 8.66025i | 0.543393i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.50000 | − | 7.79423i | −0.279616 | − | 0.484310i | ||||
\(260\) | −4.50000 | − | 4.33013i | −0.279078 | − | 0.268543i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.5000 | − | 12.9904i | 1.39005 | − | 0.802548i | ||||
\(263\) | 12.0000 | − | 20.7846i | 0.739952 | − | 1.28163i | −0.212565 | − | 0.977147i | \(-0.568182\pi\) |
0.952517 | − | 0.304487i | \(-0.0984850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | − | 5.19615i | −0.552866 | − | 0.319197i | ||||
\(266\) | 4.50000 | − | 2.59808i | 0.275913 | − | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.5000 | − | 6.06218i | 0.641390 | − | 0.370306i | ||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5000 | − | 7.79423i | 0.820067 | − | 0.473466i | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) |
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | −7.50000 | − | 12.9904i | −0.454754 | − | 0.787658i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.50000 | + | 7.79423i | −0.271855 | + | 0.470867i | ||||
\(275\) | − | 6.92820i | − | 0.417786i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0000 | 1.38194 | 0.690968 | − | 0.722885i | \(-0.257185\pi\) | ||||
0.690968 | + | 0.722885i | \(0.257185\pi\) | |||||||
\(278\) | 27.7128i | 1.66210i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.50000 | + | 2.59808i | 0.268926 | + | 0.155265i | ||||
\(281\) | −4.50000 | + | 2.59808i | −0.268447 | + | 0.154988i | −0.628182 | − | 0.778067i | \(-0.716201\pi\) |
0.359734 | + | 0.933055i | \(0.382867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.0000 | −1.36721 | −0.683604 | − | 0.729853i | \(-0.739588\pi\) | ||||
−0.683604 | + | 0.729853i | \(0.739588\pi\) | |||||||
\(284\) | 8.66025i | 0.513892i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.0000 | − | 5.19615i | −1.24176 | − | 0.307255i | ||||
\(287\) | 21.0000 | 1.23959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −18.0000 | −1.05700 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | − | 3.46410i | 0.351123 | − | 0.202721i | ||||
\(293\) | −12.0000 | + | 6.92820i | −0.701047 | + | 0.404750i | −0.807737 | − | 0.589542i | \(-0.799308\pi\) |
0.106690 | + | 0.994292i | \(0.465975\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 4.50000 | + | 7.79423i | 0.261557 | + | 0.453030i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.50000 | + | 7.79423i | −0.433736 | + | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.73205i | − | 0.0998337i | ||||||
\(302\) | −21.0000 | −1.20841 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.50000 | + | 4.33013i | −0.430155 | + | 0.248350i | ||||
\(305\) | −7.50000 | − | 4.33013i | −0.429449 | − | 0.247942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | −6.00000 | −0.341882 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 25.9808i | − | 1.47561i | ||||||
\(311\) | 13.5000 | − | 23.3827i | 0.765515 | − | 1.32591i | −0.174459 | − | 0.984664i | \(-0.555818\pi\) |
0.939974 | − | 0.341246i | \(-0.110849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | −34.5000 | + | 19.9186i | −1.94695 | + | 1.12407i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.50000 | + | 9.52628i | −0.309399 | + | 0.535895i | ||||
\(317\) | 7.50000 | − | 4.33013i | 0.421242 | − | 0.243204i | −0.274367 | − | 0.961625i | \(-0.588468\pi\) |
0.695609 | + | 0.718421i | \(0.255135\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | + | 10.3923i | −1.00781 | + | 0.581857i | ||||
\(320\) | −1.50000 | − | 0.866025i | −0.0838525 | − | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.50000 | + | 7.79423i | −0.250775 | + | 0.434355i | ||||
\(323\) | −4.50000 | + | 2.59808i | −0.250387 | + | 0.144561i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00000 | + | 1.73205i | 0.388290 | + | 0.0960769i | ||||
\(326\) | 10.5000 | + | 18.1865i | 0.581541 | + | 1.00726i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.0000 | −1.15953 | ||||||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5885i | 0.856819i | 0.903585 | + | 0.428410i | \(0.140926\pi\) | ||||
−0.903585 | + | 0.428410i | \(0.859074\pi\) | |||||||
\(332\) | 4.50000 | + | 2.59808i | 0.246970 | + | 0.142588i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.50000 | + | 7.79423i | −0.246229 | + | 0.426481i | ||||
\(335\) | 10.5000 | − | 18.1865i | 0.573676 | − | 0.993636i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5000 | − | 25.1147i | 0.789865 | − | 1.36809i | −0.136184 | − | 0.990684i | \(-0.543484\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 10.5000 | − | 19.9186i | 0.571125 | − | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.50000 | + | 2.59808i | 0.244047 | + | 0.140900i | ||||
\(341\) | −15.0000 | − | 25.9808i | −0.812296 | − | 1.40694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | 1.73205i | 0.0933859i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.5000 | + | 18.1865i | 1.69345 | + | 0.977714i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | − | 13.8564i | −1.28469 | − | 0.741716i | −0.306988 | − | 0.951713i | \(-0.599321\pi\) |
−0.977702 | + | 0.209997i | \(0.932655\pi\) | |||||||
\(350\) | 6.00000 | 0.320713 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.0000 | 0.959403 | ||||||||
\(353\) | −6.00000 | − | 3.46410i | −0.319348 | − | 0.184376i | 0.331754 | − | 0.943366i | \(-0.392360\pi\) |
−0.651102 | + | 0.758990i | \(0.725693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50000 | + | 12.9904i | 0.398059 | + | 0.689458i | ||||
\(356\) | −13.5000 | − | 7.79423i | −0.715499 | − | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.19615i | 0.274625i | ||||||||
\(359\) | − | 10.3923i | − | 0.548485i | −0.961661 | − | 0.274242i | \(-0.911573\pi\) | ||
0.961661 | − | 0.274242i | \(-0.0884271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | −33.0000 | − | 19.0526i | −1.73444 | − | 1.00138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50000 | − | 6.06218i | 0.0786214 | − | 0.317744i | ||||
\(365\) | 6.00000 | − | 10.3923i | 0.314054 | − | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 7.50000 | − | 12.9904i | 0.390965 | − | 0.677170i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.5000 | − | 7.79423i | −0.701832 | − | 0.405203i | ||||
\(371\) | − | 10.3923i | − | 0.539542i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.00000 | + | 12.1244i | 0.362446 | + | 0.627775i | 0.988363 | − | 0.152115i | \(-0.0486083\pi\) |
−0.625917 | + | 0.779890i | \(0.715275\pi\) | |||||||
\(374\) | 18.0000 | 0.930758 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | −6.00000 | − | 20.7846i | −0.309016 | − | 1.07046i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5000 | + | 6.06218i | −0.539349 | + | 0.311393i | −0.744815 | − | 0.667271i | \(-0.767462\pi\) |
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 1.50000 | − | 2.59808i | 0.0769484 | − | 0.133278i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.50000 | − | 2.59808i | −0.230240 | − | 0.132929i | ||||
\(383\) | 3.00000 | − | 1.73205i | 0.153293 | − | 0.0885037i | −0.421392 | − | 0.906879i | \(-0.638458\pi\) |
0.574684 | + | 0.818375i | \(0.305125\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | + | 5.19615i | −0.458682 | + | 0.264820i | ||||
\(386\) | −4.50000 | + | 7.79423i | −0.229044 | + | 0.396716i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.5000 | + | 7.79423i | −0.685359 | + | 0.395692i | ||||
\(389\) | 1.50000 | + | 2.59808i | 0.0760530 | + | 0.131728i | 0.901544 | − | 0.432688i | \(-0.142435\pi\) |
−0.825491 | + | 0.564416i | \(0.809102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | − | 6.92820i | − | 0.349927i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | 19.0526i | 0.958638i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.5000 | − | 12.9904i | −1.12924 | − | 0.651969i | −0.185498 | − | 0.982645i | \(-0.559390\pi\) |
−0.943744 | + | 0.330676i | \(0.892723\pi\) | |||||||
\(398\) | −19.5000 | + | 11.2583i | −0.977447 | + | 0.564329i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0000 | −0.500000 | ||||||||
\(401\) | 29.4449i | 1.47041i | 0.677847 | + | 0.735203i | \(0.262913\pi\) | ||||
−0.677847 | + | 0.735203i | \(0.737087\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.0000 | − | 8.66025i | 1.49441 | − | 0.431398i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.00000 | − | 15.5885i | −0.446663 | − | 0.773642i | ||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | − | 3.46410i | 0.296681 | − | 0.171289i | −0.344270 | − | 0.938871i | \(-0.611874\pi\) |
0.640951 | + | 0.767582i | \(0.278540\pi\) | |||||||
\(410\) | 31.5000 | − | 18.1865i | 1.55567 | − | 0.898169i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0000 | 0.640464 | ||||||||
\(413\) | −3.00000 | − | 5.19615i | −0.147620 | − | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.00000 | 0.441793 | ||||||||
\(416\) | −4.50000 | + | 18.1865i | −0.220631 | + | 0.891668i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 10.3923i | − | 0.508304i | ||||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.50000 | + | 4.33013i | −0.365528 | + | 0.211037i | −0.671503 | − | 0.741002i | \(-0.734351\pi\) |
0.305975 | + | 0.952039i | \(0.401018\pi\) | |||||||
\(422\) | 19.5000 | + | 11.2583i | 0.949245 | + | 0.548047i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.3923i | 0.504695i | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.66025i | − | 0.419099i | ||||||
\(428\) | −7.50000 | + | 12.9904i | −0.362526 | + | 0.627914i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.50000 | − | 2.59808i | −0.0723364 | − | 0.125290i | ||||
\(431\) | −19.5000 | + | 11.2583i | −0.939282 | + | 0.542295i | −0.889735 | − | 0.456477i | \(-0.849111\pi\) |
−0.0495468 | + | 0.998772i | \(0.515778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.50000 | − | 4.33013i | 0.120142 | − | 0.208093i | −0.799681 | − | 0.600425i | \(-0.794998\pi\) |
0.919824 | + | 0.392332i | \(0.128332\pi\) | |||||||
\(434\) | 22.5000 | − | 12.9904i | 1.08003 | − | 0.623558i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.50000 | − | 2.59808i | −0.215264 | − | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | 9.00000 | − | 5.19615i | 0.429058 | − | 0.247717i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.50000 | + | 18.1865i | −0.214043 | + | 0.865045i | ||||
\(443\) | 10.5000 | + | 18.1865i | 0.498870 | + | 0.864068i | 0.999999 | − | 0.00130426i | \(-0.000415158\pi\) |
−0.501129 | + | 0.865373i | \(0.667082\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0000 | −1.27992 | ||||||||
\(446\) | 3.00000 | + | 5.19615i | 0.142054 | + | 0.246045i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 1.73205i | − | 0.0818317i | ||||||
\(449\) | −13.5000 | − | 7.79423i | −0.637104 | − | 0.367832i | 0.146394 | − | 0.989226i | \(-0.453233\pi\) |
−0.783498 | + | 0.621394i | \(0.786567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0000 | − | 36.3731i | 0.988851 | − | 1.71274i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.5000 | + | 18.1865i | −0.492789 | + | 0.853536i | ||||
\(455\) | −3.00000 | − | 10.3923i | −0.140642 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | −7.50000 | − | 12.9904i | −0.350452 | − | 0.607001i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.19615i | 0.242272i | ||||||||
\(461\) | − | 1.73205i | − | 0.0806696i | −0.999186 | − | 0.0403348i | \(-0.987158\pi\) | ||
0.999186 | − | 0.0403348i | \(-0.0128425\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5000 | + | 12.9904i | 1.04566 | + | 0.603714i | 0.921432 | − | 0.388539i | \(-0.127020\pi\) |
0.124231 | + | 0.992253i | \(0.460353\pi\) | |||||||
\(464\) | 15.0000 | + | 25.9808i | 0.696358 | + | 1.20613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.0000 | + | 15.5885i | 1.25075 | + | 0.722121i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 13.5000 | + | 7.79423i | 0.622709 | + | 0.359521i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | −3.00000 | − | 1.73205i | −0.137940 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.46410i | 0.158944i | ||||||||
\(476\) | 5.19615i | 0.238165i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.50000 | − | 7.79423i | −0.205825 | − | 0.356500i | ||||
\(479\) | 21.0000 | + | 12.1244i | 0.959514 | + | 0.553976i | 0.896024 | − | 0.444006i | \(-0.146443\pi\) |
0.0634909 | + | 0.997982i | \(0.479777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | − | 18.1865i | 0.205182 | − | 0.829235i | ||||
\(482\) | 4.50000 | − | 7.79423i | 0.204969 | − | 0.355017i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | −13.5000 | + | 23.3827i | −0.613003 | + | 1.06175i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.50000 | − | 4.33013i | −0.339857 | − | 0.196217i | 0.320352 | − | 0.947299i | \(-0.396199\pi\) |
−0.660209 | + | 0.751082i | \(0.729532\pi\) | |||||||
\(488\) | 8.66025i | 0.392031i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000 | + | 10.3923i | 0.271052 | + | 0.469476i | ||||
\(491\) | 3.00000 | 0.135388 | 0.0676941 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676941 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 10.5000 | + | 2.59808i | 0.472417 | + | 0.116893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.5000 | + | 21.6506i | −1.68380 | + | 0.972142i | ||||
\(497\) | −7.50000 | + | 12.9904i | −0.336421 | + | 0.582698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.5000 | + | 12.9904i | 1.00724 | + | 0.581529i | 0.910382 | − | 0.413769i | \(-0.135788\pi\) |
0.0968564 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(500\) | 10.5000 | − | 6.06218i | 0.469574 | − | 0.271109i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.5000 | − | 7.79423i | 0.602534 | − | 0.347873i | ||||
\(503\) | 10.5000 | − | 18.1865i | 0.468172 | − | 0.810897i | −0.531167 | − | 0.847267i | \(-0.678246\pi\) |
0.999338 | + | 0.0363700i | \(0.0115795\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | + | 5.19615i | −0.400495 | + | 0.231226i | ||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.50000 | + | 4.33013i | −0.110920 | + | 0.192118i | ||||
\(509\) | 1.73205i | 0.0767718i | 0.999263 | + | 0.0383859i | \(0.0122216\pi\) | ||||
−0.999263 | + | 0.0383859i | \(0.987778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.50000 | − | 2.59808i | −0.198486 | − | 0.114596i | ||||
\(515\) | 19.5000 | − | 11.2583i | 0.859273 | − | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | − | 15.5885i | − | 0.684917i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | + | 10.3923i | 0.131559 | + | 0.455733i | ||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5000 | + | 21.6506i | 0.546587 | + | 0.946716i | 0.998505 | + | 0.0546569i | \(0.0174065\pi\) |
−0.451918 | + | 0.892059i | \(0.649260\pi\) | |||||||
\(524\) | 15.0000 | 0.655278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.0000 | − | 20.7846i | 1.56967 | − | 0.906252i | ||||
\(527\) | −22.5000 | + | 12.9904i | −0.980115 | + | 0.565870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −9.00000 | − | 15.5885i | −0.390935 | − | 0.677119i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.00000 | 0.130066 | ||||||||
\(533\) | 31.5000 | + | 30.3109i | 1.36442 | + | 1.31291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.9808i | 1.12325i | ||||||||
\(536\) | −21.0000 | −0.907062 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.50000 | − | 2.59808i | 0.194009 | − | 0.112011i | ||||
\(539\) | 12.0000 | + | 6.92820i | 0.516877 | + | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8564i | 0.595733i | 0.954607 | + | 0.297867i | \(0.0962751\pi\) | ||||
−0.954607 | + | 0.297867i | \(0.903725\pi\) | |||||||
\(542\) | 27.0000 | 1.15975 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 15.5885i | − | 0.668350i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.50000 | − | 14.7224i | −0.363434 | − | 0.629486i | 0.625090 | − | 0.780553i | \(-0.285062\pi\) |
−0.988524 | + | 0.151067i | \(0.951729\pi\) | |||||||
\(548\) | −4.50000 | + | 2.59808i | −0.192230 | + | 0.110984i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | − | 10.3923i | 0.255841 | − | 0.443129i | ||||
\(551\) | 9.00000 | − | 5.19615i | 0.383413 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5000 | + | 9.52628i | −0.701651 | + | 0.405099i | ||||
\(554\) | 34.5000 | + | 19.9186i | 1.46576 | + | 0.846260i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | 16.5000 | − | 9.52628i | 0.699127 | − | 0.403641i | −0.107895 | − | 0.994162i | \(-0.534411\pi\) |
0.807022 | + | 0.590521i | \(0.201078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.50000 | − | 2.59808i | 0.105739 | − | 0.109887i | ||||
\(560\) | 7.50000 | + | 12.9904i | 0.316933 | + | 0.548944i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.00000 | −0.379642 | ||||||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923i | 0.437208i | ||||||||
\(566\) | −34.5000 | − | 19.9186i | −1.45014 | − | 0.837241i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.50000 | − | 12.9904i | 0.314693 | − | 0.545064i | ||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50000 | − | 4.33013i | 0.104622 | − | 0.181210i | −0.808962 | − | 0.587861i | \(-0.799970\pi\) |
0.913584 | + | 0.406651i | \(0.133303\pi\) | |||||||
\(572\) | −9.00000 | − | 8.66025i | −0.376309 | − | 0.362103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31.5000 | + | 18.1865i | 1.31478 | + | 0.759091i | ||||
\(575\) | −3.00000 | − | 5.19615i | −0.125109 | − | 0.216695i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.92820i | − | 0.288425i | −0.989547 | − | 0.144212i | \(-0.953935\pi\) | ||
0.989547 | − | 0.144212i | \(-0.0460649\pi\) | |||||||
\(578\) | 13.8564i | 0.576351i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.00000 | − | 5.19615i | −0.373705 | − | 0.215758i | ||||
\(581\) | 4.50000 | + | 7.79423i | 0.186691 | + | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | − | 10.3923i | −0.745484 | − | 0.430405i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | −9.00000 | − | 5.19615i | −0.371470 | − | 0.214468i | 0.302631 | − | 0.953108i | \(-0.402135\pi\) |
−0.674100 | + | 0.738640i | \(0.735468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.50000 | + | 12.9904i | 0.309032 | + | 0.535259i | ||||
\(590\) | −9.00000 | − | 5.19615i | −0.370524 | − | 0.213922i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.9808i | 1.06780i | ||||||||
\(593\) | 27.7128i | 1.13803i | 0.822328 | + | 0.569014i | \(0.192675\pi\) | ||||
−0.822328 | + | 0.569014i | \(0.807325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | + | 7.79423i | 0.184482 | + | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.0000 | + | 5.19615i | −0.736075 | + | 0.212486i | ||||
\(599\) | 13.5000 | − | 23.3827i | 0.551595 | − | 0.955391i | −0.446565 | − | 0.894751i | \(-0.647353\pi\) |
0.998160 | − | 0.0606393i | \(-0.0193139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | + | 19.0526i | −0.448699 | + | 0.777170i | −0.998302 | − | 0.0582563i | \(-0.981446\pi\) |
0.549602 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(602\) | 1.50000 | − | 2.59808i | 0.0611354 | − | 0.105890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.5000 | − | 6.06218i | −0.427239 | − | 0.246667i | ||||
\(605\) | 1.73205i | 0.0704179i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | −9.00000 | −0.364998 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.50000 | − | 12.9904i | −0.303666 | − | 0.525965i | ||||
\(611\) | −4.50000 | + | 18.1865i | −0.182051 | + | 0.735748i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5000 | + | 6.06218i | −0.424091 | + | 0.244849i | −0.696826 | − | 0.717240i | \(-0.745405\pi\) |
0.272735 | + | 0.962089i | \(0.412072\pi\) | |||||||
\(614\) | 21.0000 | − | 36.3731i | 0.847491 | − | 1.46790i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.00000 | + | 5.19615i | 0.362620 | + | 0.209359i | ||||
\(617\) | 24.0000 | − | 13.8564i | 0.966204 | − | 0.557838i | 0.0681269 | − | 0.997677i | \(-0.478298\pi\) |
0.898077 | + | 0.439839i | \(0.144964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5000 | + | 12.9904i | −0.904351 | + | 0.522127i | −0.878609 | − | 0.477541i | \(-0.841528\pi\) |
−0.0257420 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(620\) | 7.50000 | − | 12.9904i | 0.301207 | − | 0.521706i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.5000 | − | 23.3827i | 1.62390 | − | 0.937560i | ||||
\(623\) | −13.5000 | − | 23.3827i | −0.540866 | − | 0.936808i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | − | 32.9090i | − | 1.31531i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.0000 | −0.917800 | ||||||||
\(629\) | 15.5885i | 0.621552i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.50000 | − | 4.33013i | −0.298570 | − | 0.172380i | 0.343230 | − | 0.939251i | \(-0.388479\pi\) |
−0.641800 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(632\) | 16.5000 | − | 9.52628i | 0.656335 | − | 0.378935i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.0000 | 0.595726 | ||||||||
\(635\) | 8.66025i | 0.343672i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.0000 | + | 10.3923i | −0.396214 | + | 0.411758i | ||||
\(638\) | −36.0000 | −1.42525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.5000 | − | 18.1865i | −0.415049 | − | 0.718886i | ||||
\(641\) | −39.0000 | −1.54041 | −0.770204 | − | 0.637798i | \(-0.779845\pi\) | ||||
−0.770204 | + | 0.637798i | \(0.779845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | + | 1.73205i | −0.118308 | + | 0.0683054i | −0.557986 | − | 0.829850i | \(-0.688426\pi\) |
0.439678 | + | 0.898155i | \(0.355093\pi\) | |||||||
\(644\) | −4.50000 | + | 2.59808i | −0.177325 | + | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.00000 | −0.354100 | ||||||||
\(647\) | −4.50000 | − | 7.79423i | −0.176913 | − | 0.306423i | 0.763908 | − | 0.645325i | \(-0.223278\pi\) |
−0.940822 | + | 0.338902i | \(0.889945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 9.00000 | + | 8.66025i | 0.353009 | + | 0.339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.1244i | 0.474826i | ||||||||
\(653\) | 45.0000 | 1.76099 | 0.880493 | − | 0.474059i | \(-0.157212\pi\) | ||||
0.880493 | + | 0.474059i | \(0.157212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5000 | − | 12.9904i | 0.879148 | − | 0.507576i | ||||
\(656\) | −52.5000 | − | 30.3109i | −2.04978 | − | 1.18344i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.5885i | 0.607701i | ||||||||
\(659\) | −39.0000 | −1.51922 | −0.759612 | − | 0.650376i | \(-0.774611\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.7654i | 1.81896i | 0.415745 | + | 0.909481i | \(0.363521\pi\) | ||||
−0.415745 | + | 0.909481i | \(0.636479\pi\) | |||||||
\(662\) | −13.5000 | + | 23.3827i | −0.524692 | + | 0.908794i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | − | 7.79423i | −0.174634 | − | 0.302475i | ||||
\(665\) | 4.50000 | − | 2.59808i | 0.174503 | − | 0.100749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | + | 15.5885i | −0.348481 | + | 0.603587i | ||||
\(668\) | −4.50000 | + | 2.59808i | −0.174110 | + | 0.100523i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 31.5000 | − | 18.1865i | 1.21695 | − | 0.702607i | ||||
\(671\) | −15.0000 | − | 8.66025i | −0.579069 | − | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | − | 29.4449i | 0.655302 | − | 1.13502i | −0.326516 | − | 0.945192i | \(-0.605875\pi\) |
0.981818 | − | 0.189824i | \(-0.0607919\pi\) | |||||||
\(674\) | 43.5000 | − | 25.1147i | 1.67556 | − | 0.967384i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | − | 6.92820i | 0.423077 | − | 0.266469i | ||||
\(677\) | −10.5000 | − | 18.1865i | −0.403548 | − | 0.698965i | 0.590603 | − | 0.806962i | \(-0.298890\pi\) |
−0.994151 | + | 0.107997i | \(0.965556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.0000 | −1.03616 | ||||||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 51.9615i | − | 1.98971i | ||||||
\(683\) | 19.5000 | + | 11.2583i | 0.746147 | + | 0.430788i | 0.824300 | − | 0.566153i | \(-0.191569\pi\) |
−0.0781532 | + | 0.996941i | \(0.524902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.50000 | + | 7.79423i | −0.171936 | + | 0.297802i | ||||
\(686\) | −16.5000 | + | 28.5788i | −0.629973 | + | 1.09115i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.50000 | + | 4.33013i | −0.0953116 | + | 0.165085i | ||||
\(689\) | 15.0000 | − | 15.5885i | 0.571454 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0000 | − | 8.66025i | −0.570627 | − | 0.329452i | 0.186773 | − | 0.982403i | \(-0.440197\pi\) |
−0.757400 | + | 0.652952i | \(0.773531\pi\) | |||||||
\(692\) | 10.5000 | + | 18.1865i | 0.399150 | + | 0.691348i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 20.7846i | − | 0.788973i | ||||||
\(695\) | 27.7128i | 1.05121i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.5000 | − | 18.1865i | −1.19315 | − | 0.688864i | ||||
\(698\) | −24.0000 | − | 41.5692i | −0.908413 | − | 1.57342i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.00000 | + | 1.73205i | 0.113389 | + | 0.0654654i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.00000 | 0.339441 | ||||||||
\(704\) | −3.00000 | − | 1.73205i | −0.113067 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | − | 10.3923i | −0.225813 | − | 0.391120i | ||||
\(707\) | −9.00000 | − | 5.19615i | −0.338480 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.1244i | − | 0.455340i | −0.973738 | − | 0.227670i | \(-0.926889\pi\) | ||
0.973738 | − | 0.227670i | \(-0.0731107\pi\) | |||||||
\(710\) | 25.9808i | 0.975041i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5000 | + | 23.3827i | 0.505934 | + | 0.876303i | ||||
\(713\) | −22.5000 | − | 12.9904i | −0.842632 | − | 0.486494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.0000 | − | 5.19615i | −0.785355 | − | 0.194325i | ||||
\(716\) | −1.50000 | + | 2.59808i | −0.0560576 | + | 0.0970947i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | − | 15.5885i | 0.335877 | − | 0.581756i | ||||
\(719\) | −19.5000 | + | 33.7750i | −0.727227 | + | 1.25959i | 0.230823 | + | 0.972996i | \(0.425858\pi\) |
−0.958051 | + | 0.286599i | \(0.907475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.5000 | + | 11.2583i | 0.726218 | + | 0.419282i | ||||
\(722\) | − | 27.7128i | − | 1.03136i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.0000 | − | 19.0526i | −0.408812 | − | 0.708083i | ||||
\(725\) | 12.0000 | 0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.500000 | − | 0.866025i | −0.0185440 | − | 0.0321191i | 0.856605 | − | 0.515974i | \(-0.172570\pi\) |
−0.875148 | + | 0.483854i | \(0.839236\pi\) | |||||||
\(728\) | −7.50000 | + | 7.79423i | −0.277968 | + | 0.288873i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0000 | − | 10.3923i | 0.666210 | − | 0.384636i | ||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5000 | + | 9.52628i | 0.609441 | + | 0.351861i | 0.772747 | − | 0.634714i | \(-0.218882\pi\) |
−0.163305 | + | 0.986576i | \(0.552216\pi\) | |||||||
\(734\) | −12.0000 | + | 6.92820i | −0.442928 | + | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.5000 | − | 7.79423i | 0.497617 | − | 0.287299i | ||||
\(737\) | 21.0000 | − | 36.3731i | 0.773545 | − | 1.33982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.5000 | + | 16.4545i | −1.04839 | + | 0.605288i | −0.922198 | − | 0.386718i | \(-0.873609\pi\) |
−0.126191 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(740\) | −4.50000 | − | 7.79423i | −0.165423 | − | 0.286522i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.00000 | − | 15.5885i | 0.330400 | − | 0.572270i | ||||
\(743\) | 12.1244i | 0.444799i | 0.974956 | + | 0.222400i | \(0.0713890\pi\) | ||||
−0.974956 | + | 0.222400i | \(0.928611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.2487i | 0.887808i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.00000 | + | 5.19615i | 0.329073 | + | 0.189990i | ||||
\(749\) | −22.5000 | + | 12.9904i | −0.822132 | + | 0.474658i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0000 | −0.693320 | −0.346660 | − | 0.937991i | \(-0.612684\pi\) | ||||
−0.346660 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(752\) | − | 25.9808i | − | 0.947421i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.00000 | − | 36.3731i | 0.327761 | − | 1.32463i | ||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.50000 | − | 6.06218i | −0.127210 | − | 0.220334i | 0.795385 | − | 0.606105i | \(-0.207269\pi\) |
−0.922595 | + | 0.385771i | \(0.873935\pi\) | |||||||
\(758\) | −21.0000 | −0.762754 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50000 | + | 2.59808i | −0.163232 | + | 0.0942421i | ||||
\(761\) | −12.0000 | + | 6.92820i | −0.435000 | + | 0.251147i | −0.701474 | − | 0.712695i | \(-0.747474\pi\) |
0.266475 | + | 0.963842i | \(0.414141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.50000 | − | 2.59808i | −0.0542681 | − | 0.0939951i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | 3.00000 | − | 12.1244i | 0.108324 | − | 0.437785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22.5167i | − | 0.811972i | −0.913879 | − | 0.405986i | \(-0.866928\pi\) | ||
0.913879 | − | 0.405986i | \(-0.133072\pi\) | |||||||
\(770\) | −18.0000 | −0.648675 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.50000 | + | 2.59808i | −0.161959 | + | 0.0935068i | ||||
\(773\) | −25.5000 | − | 14.7224i | −0.917171 | − | 0.529529i | −0.0344397 | − | 0.999407i | \(-0.510965\pi\) |
−0.882732 | + | 0.469878i | \(0.844298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3205i | 0.622171i | ||||||||
\(776\) | 27.0000 | 0.969244 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.19615i | 0.186291i | ||||||||
\(779\) | −10.5000 | + | 18.1865i | −0.376202 | + | 0.651600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | + | 25.9808i | 0.536742 | + | 0.929665i | ||||
\(782\) | 13.5000 | − | 7.79423i | 0.482759 | − | 0.278721i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.0000 | − | 17.3205i | 0.357143 | − | 0.618590i | ||||
\(785\) | −34.5000 | + | 19.9186i | −1.23136 | + | 0.710925i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.00000 | − | 1.73205i | 0.106938 | − | 0.0617409i | −0.445577 | − | 0.895244i | \(-0.647001\pi\) |
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(788\) | −7.50000 | − | 4.33013i | −0.267176 | − | 0.154254i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.5000 | + | 28.5788i | −0.587044 | + | 1.01679i | ||||
\(791\) | −9.00000 | + | 5.19615i | −0.320003 | + | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.5000 | − | 12.9904i | 0.443888 | − | 0.461302i | ||||
\(794\) | −22.5000 | − | 38.9711i | −0.798495 | − | 1.38303i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0000 | −0.460773 | ||||||||
\(797\) | 9.00000 | + | 15.5885i | 0.318796 | + | 0.552171i | 0.980237 | − | 0.197826i | \(-0.0633881\pi\) |
−0.661441 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.5885i | − | 0.551480i | ||||||
\(800\) | −9.00000 | − | 5.19615i | −0.318198 | − | 0.183712i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.5000 | + | 44.1673i | −0.900436 | + | 1.55960i | ||||
\(803\) | 12.0000 | − | 20.7846i | 0.423471 | − | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.50000 | + | 7.79423i | −0.158604 | + | 0.274710i | ||||
\(806\) | 52.5000 | + | 12.9904i | 1.84923 | + | 0.457567i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.00000 | + | 5.19615i | 0.316619 | + | 0.182800i | ||||
\(809\) | 13.5000 | + | 23.3827i | 0.474635 | + | 0.822091i | 0.999578 | − | 0.0290457i | \(-0.00924684\pi\) |
−0.524943 | + | 0.851137i | \(0.675914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | − | 10.3923i | − | 0.364698i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.0000 | − | 15.5885i | −0.946350 | − | 0.546375i | ||||
\(815\) | 10.5000 | + | 18.1865i | 0.367799 | + | 0.637046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.50000 | + | 0.866025i | 0.0524784 | + | 0.0302984i | ||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.0000 | 0.733352 | ||||||||
\(821\) | 24.0000 | + | 13.8564i | 0.837606 | + | 0.483592i | 0.856450 | − | 0.516231i | \(-0.172665\pi\) |
−0.0188439 | + | 0.999822i | \(0.505999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.0000 | − | 48.4974i | −0.976019 | − | 1.69051i | −0.676532 | − | 0.736413i | \(-0.736518\pi\) |
−0.299487 | − | 0.954100i | \(-0.596815\pi\) | |||||||
\(824\) | −19.5000 | − | 11.2583i | −0.679315 | − | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 10.3923i | − | 0.361595i | ||||||
\(827\) | 24.2487i | 0.843210i | 0.906780 | + | 0.421605i | \(0.138533\pi\) | ||||
−0.906780 | + | 0.421605i | \(0.861467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5000 | + | 25.1147i | 0.503606 | + | 0.872271i | 0.999991 | + | 0.00416865i | \(0.00132693\pi\) |
−0.496385 | + | 0.868102i | \(0.665340\pi\) | |||||||
\(830\) | 13.5000 | + | 7.79423i | 0.468592 | + | 0.270542i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | 6.00000 | − | 10.3923i | 0.207888 | − | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.50000 | + | 7.79423i | −0.155729 | + | 0.269730i | ||||
\(836\) | 3.00000 | − | 5.19615i | 0.103757 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.5000 | − | 7.79423i | −0.466350 | − | 0.269247i | ||||
\(839\) | 12.1244i | 0.418579i | 0.977854 | + | 0.209290i | \(0.0671151\pi\) | ||||
−0.977854 | + | 0.209290i | \(0.932885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −15.0000 | −0.516934 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.50000 | + | 11.2583i | 0.223739 | + | 0.387528i | ||||
\(845\) | 10.5000 | − | 19.9186i | 0.361211 | − | 0.685220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.50000 | + | 0.866025i | −0.0515406 | + | 0.0297570i | ||||
\(848\) | −15.0000 | + | 25.9808i | −0.515102 | + | 0.892183i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.00000 | − | 5.19615i | −0.308697 | − | 0.178227i | ||||
\(851\) | −13.5000 | + | 7.79423i | −0.462774 | + | 0.267183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.50000 | − | 2.59808i | 0.154077 | − | 0.0889564i | −0.420979 | − | 0.907070i | \(-0.638313\pi\) |
0.575056 | + | 0.818114i | \(0.304980\pi\) | |||||||
\(854\) | 7.50000 | − | 12.9904i | 0.256645 | − | 0.444522i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.5000 | − | 12.9904i | 0.769034 | − | 0.444002i | ||||
\(857\) | 1.50000 | + | 2.59808i | 0.0512390 | + | 0.0887486i | 0.890507 | − | 0.454969i | \(-0.150350\pi\) |
−0.839268 | + | 0.543718i | \(0.817016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.50000 | − | 4.33013i | 0.0852989 | − | 0.147742i | −0.820220 | − | 0.572049i | \(-0.806149\pi\) |
0.905519 | + | 0.424307i | \(0.139482\pi\) | |||||||
\(860\) | − | 1.73205i | − | 0.0590624i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.0000 | −1.32835 | ||||||||
\(863\) | − | 17.3205i | − | 0.589597i | −0.955559 | − | 0.294798i | \(-0.904747\pi\) | ||
0.955559 | − | 0.294798i | \(-0.0952525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.5000 | + | 18.1865i | 1.07103 | + | 0.618361i | ||||
\(866\) | 7.50000 | − | 4.33013i | 0.254860 | − | 0.147144i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0000 | 0.509133 | ||||||||
\(869\) | 38.1051i | 1.29263i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5000 | + | 30.3109i | 1.06734 | + | 1.02705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.50000 | − | 7.79423i | −0.152215 | − | 0.263644i | ||||
\(875\) | 21.0000 | 0.709930 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | −12.0000 | + | 6.92820i | −0.404980 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 30.0000 | 1.01130 | ||||||||
\(881\) | −4.50000 | − | 7.79423i | −0.151609 | − | 0.262594i | 0.780210 | − | 0.625517i | \(-0.215112\pi\) |
−0.931819 | + | 0.362923i | \(0.881779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0000 | 1.34611 | 0.673054 | − | 0.739594i | \(-0.264982\pi\) | ||||
0.673054 | + | 0.739594i | \(0.264982\pi\) | |||||||
\(884\) | −7.50000 | + | 7.79423i | −0.252252 | + | 0.262148i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.3731i | 1.22198i | ||||||||
\(887\) | 15.0000 | 0.503651 | 0.251825 | − | 0.967773i | \(-0.418969\pi\) | ||||
0.251825 | + | 0.967773i | \(0.418969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.50000 | + | 4.33013i | −0.251542 | + | 0.145228i | ||||
\(890\) | −40.5000 | − | 23.3827i | −1.35756 | − | 0.783789i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.46410i | 0.115987i | ||||||||
\(893\) | −9.00000 | −0.301174 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.19615i | 0.173688i | ||||||||
\(896\) | 10.5000 | − | 18.1865i | 0.350780 | − | 0.607569i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.5000 | − | 23.3827i | −0.450501 | − | 0.780290i | ||||
\(899\) | 45.0000 | − | 25.9808i | 1.50083 | − | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | 63.0000 | − | 36.3731i | 2.09767 | − | 1.21109i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000 | − | 5.19615i | 0.299336 | − | 0.172821i | ||||
\(905\) | −33.0000 | − | 19.0526i | −1.09696 | − | 0.633328i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | + | 3.46410i | −0.0664089 | + | 0.115024i | −0.897318 | − | 0.441384i | \(-0.854488\pi\) |
0.830909 | + | 0.556408i | \(0.187821\pi\) | |||||||
\(908\) | −10.5000 | + | 6.06218i | −0.348455 | + | 0.201180i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.50000 | − | 18.1865i | 0.149174 | − | 0.602878i | ||||
\(911\) | 22.5000 | + | 38.9711i | 0.745458 | + | 1.29117i | 0.949980 | + | 0.312310i | \(0.101103\pi\) |
−0.204522 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | 0.595713 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.66025i | − | 0.286143i | ||||||
\(917\) | 22.5000 | + | 12.9904i | 0.743015 | + | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5000 | + | 21.6506i | −0.412337 | + | 0.714189i | −0.995145 | − | 0.0984214i | \(-0.968621\pi\) |
0.582808 | + | 0.812610i | \(0.301954\pi\) | |||||||
\(920\) | 4.50000 | − | 7.79423i | 0.148361 | − | 0.256968i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.50000 | − | 2.59808i | 0.0493999 | − | 0.0855631i | ||||
\(923\) | −30.0000 | + | 8.66025i | −0.987462 | + | 0.285056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | + | 5.19615i | 0.295918 | + | 0.170848i | ||||
\(926\) | 22.5000 | + | 38.9711i | 0.739396 | + | 1.28067i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.1769i | 1.02343i | ||||||||
\(929\) | − | 57.1577i | − | 1.87528i | −0.347604 | − | 0.937641i | \(-0.613005\pi\) | ||
0.347604 | − | 0.937641i | \(-0.386995\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | − | 3.46410i | −0.196642 | − | 0.113531i | ||||
\(932\) | 9.00000 | + | 15.5885i | 0.294805 | + | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | + | 10.3923i | 0.588978 | + | 0.340047i | ||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 31.5000 | + | 18.1865i | 1.02851 | + | 0.593811i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | 13.5000 | + | 7.79423i | 0.440087 | + | 0.254085i | 0.703635 | − | 0.710562i | \(-0.251559\pi\) |
−0.263547 | + | 0.964646i | \(0.584893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.3731i | − | 1.18447i | ||||||
\(944\) | 17.3205i | 0.563735i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.00000 | − | 5.19615i | −0.0975384 | − | 0.168941i | ||||
\(947\) | −33.0000 | − | 19.0526i | −1.07236 | − | 0.619125i | −0.143532 | − | 0.989646i | \(-0.545846\pi\) |
−0.928824 | + | 0.370521i | \(0.879179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | + | 17.3205i | 0.584305 | + | 0.562247i | ||||
\(950\) | −3.00000 | + | 5.19615i | −0.0973329 | + | 0.168585i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.50000 | − | 7.79423i | 0.145846 | − | 0.252612i | ||||
\(953\) | 13.5000 | − | 23.3827i | 0.437308 | − | 0.757439i | −0.560173 | − | 0.828376i | \(-0.689265\pi\) |
0.997481 | + | 0.0709362i | \(0.0225987\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.50000 | − | 2.59808i | −0.145617 | − | 0.0840718i | ||||
\(956\) | − | 5.19615i | − | 0.168056i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.0000 | + | 36.3731i | 0.678479 | + | 1.17516i | ||||
\(959\) | −9.00000 | −0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0000 | + | 38.1051i | 0.709677 | + | 1.22920i | ||||
\(962\) | 22.5000 | − | 23.3827i | 0.725429 | − | 0.753888i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.50000 | − | 2.59808i | 0.144935 | − | 0.0836784i | ||||
\(965\) | −4.50000 | + | 7.79423i | −0.144860 | + | 0.250905i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5000 | + | 6.06218i | 0.337657 | + | 0.194946i | 0.659236 | − | 0.751936i | \(-0.270880\pi\) |
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(968\) | 1.50000 | − | 0.866025i | 0.0482118 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.5000 | + | 23.3827i | −1.30038 | + | 0.750773i | ||||
\(971\) | −13.5000 | + | 23.3827i | −0.433236 | + | 0.750386i | −0.997150 | − | 0.0754473i | \(-0.975962\pi\) |
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | + | 13.8564i | −0.769405 | + | 0.444216i | ||||
\(974\) | −7.50000 | − | 12.9904i | −0.240316 | − | 0.416239i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.5000 | + | 21.6506i | −0.400115 | + | 0.693020i | ||||
\(977\) | − | 25.9808i | − | 0.831198i | −0.909548 | − | 0.415599i | \(-0.863572\pi\) | ||
0.909548 | − | 0.415599i | \(-0.136428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.0000 | −1.72585 | ||||||||
\(980\) | 6.92820i | 0.221313i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.50000 | + | 2.59808i | 0.143601 | + | 0.0829079i | ||||
\(983\) | 4.50000 | − | 2.59808i | 0.143528 | − | 0.0828658i | −0.426517 | − | 0.904480i | \(-0.640259\pi\) |
0.570044 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0000 | −0.477940 | ||||||||
\(986\) | 31.1769i | 0.992875i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.50000 | + | 4.33013i | 0.143164 | + | 0.137760i | ||||
\(989\) | −3.00000 | −0.0953945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.5000 | + | 32.0429i | 0.587672 | + | 1.01788i | 0.994537 | + | 0.104389i | \(0.0332887\pi\) |
−0.406865 | + | 0.913488i | \(0.633378\pi\) | |||||||
\(992\) | −45.0000 | −1.42875 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.5000 | + | 12.9904i | −0.713657 | + | 0.412030i | ||||
\(995\) | −19.5000 | + | 11.2583i | −0.618192 | + | 0.356913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0000 | 0.728417 | 0.364209 | − | 0.931317i | \(-0.381339\pi\) | ||||
0.364209 | + | 0.931317i | \(0.381339\pi\) | |||||||
\(998\) | 22.5000 | + | 38.9711i | 0.712225 | + | 1.23361i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 351.2.r.a.10.1 | 2 | ||
3.2 | odd | 2 | 117.2.r.a.49.1 | yes | 2 | ||
9.2 | odd | 6 | 117.2.l.a.88.1 | yes | 2 | ||
9.7 | even | 3 | 351.2.l.a.127.1 | 2 | |||
13.4 | even | 6 | 351.2.l.a.199.1 | 2 | |||
39.17 | odd | 6 | 117.2.l.a.4.1 | ✓ | 2 | ||
117.43 | even | 6 | inner | 351.2.r.a.316.1 | 2 | ||
117.56 | odd | 6 | 117.2.r.a.43.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.l.a.4.1 | ✓ | 2 | 39.17 | odd | 6 | ||
117.2.l.a.88.1 | yes | 2 | 9.2 | odd | 6 | ||
117.2.r.a.43.1 | yes | 2 | 117.56 | odd | 6 | ||
117.2.r.a.49.1 | yes | 2 | 3.2 | odd | 2 | ||
351.2.l.a.127.1 | 2 | 9.7 | even | 3 | |||
351.2.l.a.199.1 | 2 | 13.4 | even | 6 | |||
351.2.r.a.10.1 | 2 | 1.1 | even | 1 | trivial | ||
351.2.r.a.316.1 | 2 | 117.43 | even | 6 | inner |