Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,2,Mod(43,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.934249703649\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.49 |
Dual form | 117.2.r.a.43.1 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 1.50000 | + | 2.59808i | 0.612372 | + | 1.06066i | ||||
\(7\) | 1.73205i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | −3.00000 | − | 1.73205i | −0.904534 | − | 0.522233i | −0.0258656 | − | 0.999665i | \(-0.508234\pi\) |
−0.878668 | + | 0.477432i | \(0.841568\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | −2.50000 | + | 2.59808i | −0.693375 | + | 0.720577i | ||||
\(14\) | 1.50000 | − | 2.59808i | 0.400892 | − | 0.694365i | ||||
\(15\) | 1.50000 | + | 2.59808i | 0.387298 | + | 0.670820i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | − | 5.19615i | − | 1.22474i | ||||||
\(19\) | −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 | ||||||
\(21\) | 1.50000 | − | 2.59808i | 0.327327 | − | 0.566947i | ||||
\(22\) | 3.00000 | + | 5.19615i | 0.639602 | + | 1.10782i | ||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 1.50000 | − | 2.59808i | 0.306186 | − | 0.530330i | ||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 6.00000 | − | 1.73205i | 1.17670 | − | 0.339683i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −1.50000 | + | 0.866025i | −0.283473 | + | 0.163663i | ||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | − | 5.19615i | − | 0.948683i | ||||||
\(31\) | −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 | ||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 4.50000 | − | 2.59808i | 0.771744 | − | 0.445566i | ||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −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 | ||||
\(39\) | 6.00000 | − | 1.73205i | 0.960769 | − | 0.277350i | ||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 12.1244i | 1.89351i | 0.321960 | + | 0.946753i | \(0.395658\pi\) | ||||
−0.321960 | + | 0.946753i | \(0.604342\pi\) | |||||||
\(42\) | −4.50000 | + | 2.59808i | −0.694365 | + | 0.400892i | ||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | − | 3.46410i | − | 0.522233i | ||||||
\(45\) | − | 5.19615i | − | 0.774597i | ||||||
\(46\) | 4.50000 | + | 2.59808i | 0.663489 | + | 0.383065i | ||||
\(47\) | −4.50000 | + | 2.59808i | −0.656392 | + | 0.378968i | −0.790901 | − | 0.611944i | \(-0.790388\pi\) |
0.134509 | + | 0.990912i | \(0.457054\pi\) | |||||||
\(48\) | −7.50000 | + | 4.33013i | −1.08253 | + | 0.625000i | ||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 3.46410i | 0.489898i | ||||||||
\(51\) | 4.50000 | − | 2.59808i | 0.630126 | − | 0.363803i | ||||
\(52\) | −3.50000 | − | 0.866025i | −0.485363 | − | 0.120096i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −4.50000 | + | 7.79423i | −0.612372 | + | 1.06066i | ||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 1.50000 | + | 2.59808i | 0.198680 | + | 0.344124i | ||||
\(58\) | −9.00000 | + | 5.19615i | −1.18176 | + | 0.682288i | ||||
\(59\) | 3.00000 | − | 1.73205i | 0.390567 | − | 0.225494i | −0.291839 | − | 0.956467i | \(-0.594267\pi\) |
0.682406 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | −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 | ||||
\(63\) | −4.50000 | + | 2.59808i | −0.566947 | + | 0.327327i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.00000 | − | 1.73205i | 0.744208 | − | 0.214834i | ||||
\(66\) | − | 10.3923i | − | 1.27920i | ||||||
\(67\) | − | 12.1244i | − | 1.48123i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) | ||
0.671932 | − | 0.740613i | \(-0.265465\pi\) | |||||||
\(68\) | −3.00000 | −0.363803 | ||||||||
\(69\) | 4.50000 | + | 2.59808i | 0.541736 | + | 0.312772i | ||||
\(70\) | −4.50000 | + | 2.59808i | −0.537853 | + | 0.310530i | ||||
\(71\) | −7.50000 | − | 4.33013i | −0.890086 | − | 0.513892i | −0.0161155 | − | 0.999870i | \(-0.505130\pi\) |
−0.873971 | + | 0.485979i | \(0.838463\pi\) | |||||||
\(72\) | −4.50000 | + | 2.59808i | −0.530330 | + | 0.306186i | ||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 9.00000 | 1.04623 | ||||||||
\(75\) | 3.46410i | 0.400000i | ||||||||
\(76\) | − | 1.73205i | − | 0.198680i | ||||||
\(77\) | 3.00000 | − | 5.19615i | 0.341882 | − | 0.592157i | ||||
\(78\) | −10.5000 | − | 2.59808i | −1.18889 | − | 0.294174i | ||||
\(79\) | 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 | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 10.5000 | − | 18.1865i | 1.15953 | − | 2.00837i | ||||
\(83\) | −4.50000 | + | 2.59808i | −0.493939 | + | 0.285176i | −0.726207 | − | 0.687476i | \(-0.758719\pi\) |
0.232268 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | 4.50000 | − | 2.59808i | 0.488094 | − | 0.281801i | ||||
\(86\) | 1.50000 | + | 0.866025i | 0.161749 | + | 0.0933859i | ||||
\(87\) | −9.00000 | + | 5.19615i | −0.964901 | + | 0.557086i | ||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | 13.5000 | − | 7.79423i | 1.43100 | − | 0.826187i | 0.433800 | − | 0.901009i | \(-0.357172\pi\) |
0.997197 | + | 0.0748225i | \(0.0238390\pi\) | |||||||
\(90\) | −4.50000 | + | 7.79423i | −0.474342 | + | 0.821584i | ||||
\(91\) | −4.50000 | − | 4.33013i | −0.471728 | − | 0.453921i | ||||
\(92\) | −1.50000 | − | 2.59808i | −0.156386 | − | 0.270868i | ||||
\(93\) | 7.50000 | + | 12.9904i | 0.777714 | + | 1.34704i | ||||
\(94\) | 9.00000 | 0.928279 | ||||||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 9.00000 | 0.918559 | ||||||||
\(97\) | 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 | ||||
\(99\) | − | 10.3923i | − | 1.04447i | ||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | −9.00000 | −0.891133 | ||||||||
\(103\) | 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 | ||||
\(105\) | −4.50000 | + | 2.59808i | −0.439155 | + | 0.253546i | ||||
\(106\) | −9.00000 | − | 5.19615i | −0.874157 | − | 0.504695i | ||||
\(107\) | −7.50000 | − | 12.9904i | −0.725052 | − | 1.25583i | −0.958952 | − | 0.283567i | \(-0.908482\pi\) |
0.233900 | − | 0.972261i | \(-0.424851\pi\) | |||||||
\(108\) | 4.50000 | − | 2.59808i | 0.433013 | − | 0.250000i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | − | 10.3923i | − | 0.990867i | ||||||
\(111\) | 9.00000 | 0.854242 | ||||||||
\(112\) | 7.50000 | + | 4.33013i | 0.708683 | + | 0.409159i | ||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | − | 5.19615i | − | 0.486664i | ||||||
\(115\) | 4.50000 | + | 2.59808i | 0.419627 | + | 0.242272i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | −10.5000 | − | 2.59808i | −0.970725 | − | 0.240192i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | −4.50000 | − | 2.59808i | −0.412514 | − | 0.238165i | ||||
\(120\) | −4.50000 | + | 2.59808i | −0.410792 | + | 0.237171i | ||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 7.50000 | + | 4.33013i | 0.679018 | + | 0.392031i | ||||
\(123\) | 10.5000 | − | 18.1865i | 0.946753 | − | 1.63982i | ||||
\(124\) | − | 8.66025i | − | 0.777714i | ||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 9.00000 | 0.801784 | ||||||||
\(127\) | 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 | ||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | −10.5000 | − | 2.59808i | −0.920911 | − | 0.227866i | ||||
\(131\) | −7.50000 | + | 12.9904i | −0.655278 | + | 1.13497i | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | −3.00000 | + | 5.19615i | −0.261116 | + | 0.452267i | ||||
\(133\) | 1.50000 | − | 2.59808i | 0.130066 | − | 0.225282i | ||||
\(134\) | −10.5000 | + | 18.1865i | −0.907062 | + | 1.57108i | ||||
\(135\) | −4.50000 | + | 7.79423i | −0.387298 | + | 0.670820i | ||||
\(136\) | −4.50000 | − | 2.59808i | −0.385872 | − | 0.222783i | ||||
\(137\) | − | 5.19615i | − | 0.443937i | −0.975054 | − | 0.221969i | \(-0.928752\pi\) | ||
0.975054 | − | 0.221969i | \(-0.0712483\pi\) | |||||||
\(138\) | −4.50000 | − | 7.79423i | −0.383065 | − | 0.663489i | ||||
\(139\) | 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 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 7.50000 | + | 12.9904i | 0.629386 | + | 1.09013i | ||||
\(143\) | 12.0000 | − | 3.46410i | 1.00349 | − | 0.289683i | ||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | −9.00000 | + | 5.19615i | −0.747409 | + | 0.431517i | ||||
\(146\) | −6.00000 | + | 10.3923i | −0.496564 | + | 0.860073i | ||||
\(147\) | −6.00000 | − | 3.46410i | −0.494872 | − | 0.285714i | ||||
\(148\) | −4.50000 | − | 2.59808i | −0.369898 | − | 0.213561i | ||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 3.00000 | − | 5.19615i | 0.244949 | − | 0.424264i | ||||
\(151\) | −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 | ||||
\(153\) | −9.00000 | −0.727607 | ||||||||
\(154\) | −9.00000 | + | 5.19615i | −0.725241 | + | 0.418718i | ||||
\(155\) | 7.50000 | + | 12.9904i | 0.602414 | + | 1.04341i | ||||
\(156\) | 4.50000 | + | 4.33013i | 0.360288 | + | 0.346688i | ||||
\(157\) | −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 | ||||||
\(159\) | −9.00000 | − | 5.19615i | −0.713746 | − | 0.412082i | ||||
\(160\) | 9.00000 | 0.711512 | ||||||||
\(161\) | − | 5.19615i | − | 0.409514i | ||||||
\(162\) | 13.5000 | − | 7.79423i | 1.06066 | − | 0.612372i | ||||
\(163\) | 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 | ||||
\(165\) | − | 10.3923i | − | 0.809040i | ||||||
\(166\) | 9.00000 | 0.698535 | ||||||||
\(167\) | − | 5.19615i | − | 0.402090i | −0.979582 | − | 0.201045i | \(-0.935566\pi\) | ||
0.979582 | − | 0.201045i | \(-0.0644338\pi\) | |||||||
\(168\) | 4.50000 | + | 2.59808i | 0.347183 | + | 0.200446i | ||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | − | 5.19615i | − | 0.397360i | ||||||
\(172\) | −0.500000 | − | 0.866025i | −0.0381246 | − | 0.0660338i | ||||
\(173\) | −21.0000 | −1.59660 | −0.798300 | − | 0.602260i | \(-0.794267\pi\) | ||||
−0.798300 | + | 0.602260i | \(0.794267\pi\) | |||||||
\(174\) | 18.0000 | 1.36458 | ||||||||
\(175\) | 3.00000 | − | 1.73205i | 0.226779 | − | 0.130931i | ||||
\(176\) | −15.0000 | + | 8.66025i | −1.13067 | + | 0.652791i | ||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | −27.0000 | −2.02374 | ||||||||
\(179\) | −1.50000 | − | 2.59808i | −0.112115 | − | 0.194189i | 0.804508 | − | 0.593942i | \(-0.202429\pi\) |
−0.916623 | + | 0.399753i | \(0.869096\pi\) | |||||||
\(180\) | 4.50000 | − | 2.59808i | 0.335410 | − | 0.193649i | ||||
\(181\) | −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 | ||||
\(183\) | 7.50000 | + | 4.33013i | 0.554416 | + | 0.320092i | ||||
\(184\) | − | 5.19615i | − | 0.383065i | ||||||
\(185\) | 9.00000 | 0.661693 | ||||||||
\(186\) | − | 25.9808i | − | 1.90500i | ||||||
\(187\) | 9.00000 | − | 5.19615i | 0.658145 | − | 0.379980i | ||||
\(188\) | −4.50000 | − | 2.59808i | −0.328196 | − | 0.189484i | ||||
\(189\) | 9.00000 | 0.654654 | ||||||||
\(190\) | − | 5.19615i | − | 0.376969i | ||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | 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 | ||||
\(195\) | −10.5000 | − | 2.59808i | −0.751921 | − | 0.186052i | ||||
\(196\) | 2.00000 | + | 3.46410i | 0.142857 | + | 0.247436i | ||||
\(197\) | 7.50000 | − | 4.33013i | 0.534353 | − | 0.308509i | −0.208434 | − | 0.978036i | \(-0.566837\pi\) |
0.742787 | + | 0.669528i | \(0.233503\pi\) | |||||||
\(198\) | −9.00000 | + | 15.5885i | −0.639602 | + | 1.10782i | ||||
\(199\) | −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 | ||||
\(201\) | −10.5000 | + | 18.1865i | −0.740613 | + | 1.28278i | ||||
\(202\) | −9.00000 | + | 5.19615i | −0.633238 | + | 0.365600i | ||||
\(203\) | 9.00000 | + | 5.19615i | 0.631676 | + | 0.364698i | ||||
\(204\) | 4.50000 | + | 2.59808i | 0.315063 | + | 0.181902i | ||||
\(205\) | 10.5000 | − | 18.1865i | 0.733352 | − | 1.27020i | ||||
\(206\) | −19.5000 | + | 11.2583i | −1.35863 | + | 0.784405i | ||||
\(207\) | −4.50000 | − | 7.79423i | −0.312772 | − | 0.541736i | ||||
\(208\) | 5.00000 | + | 17.3205i | 0.346688 | + | 1.20096i | ||||
\(209\) | 3.00000 | + | 5.19615i | 0.207514 | + | 0.359425i | ||||
\(210\) | 9.00000 | 0.621059 | ||||||||
\(211\) | 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 | ||||
\(213\) | 7.50000 | + | 12.9904i | 0.513892 | + | 0.890086i | ||||
\(214\) | 25.9808i | 1.77601i | ||||||||
\(215\) | 1.50000 | + | 0.866025i | 0.102299 | + | 0.0590624i | ||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 7.50000 | − | 12.9904i | 0.509133 | − | 0.881845i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | −3.00000 | + | 5.19615i | −0.202260 | + | 0.350325i | ||||
\(221\) | −3.00000 | − | 10.3923i | −0.201802 | − | 0.699062i | ||||
\(222\) | −13.5000 | − | 7.79423i | −0.906061 | − | 0.523114i | ||||
\(223\) | 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 | ||||
\(225\) | 3.00000 | − | 5.19615i | 0.200000 | − | 0.346410i | ||||
\(226\) | 10.3923i | 0.691286i | ||||||||
\(227\) | − | 12.1244i | − | 0.804722i | −0.915481 | − | 0.402361i | \(-0.868190\pi\) | ||
0.915481 | − | 0.402361i | \(-0.131810\pi\) | |||||||
\(228\) | −1.50000 | + | 2.59808i | −0.0993399 | + | 0.172062i | ||||
\(229\) | −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 | ||||
\(231\) | −9.00000 | + | 5.19615i | −0.592157 | + | 0.341882i | ||||
\(232\) | 9.00000 | + | 5.19615i | 0.590879 | + | 0.341144i | ||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 13.5000 | + | 12.9904i | 0.882523 | + | 0.849208i | ||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | 3.00000 | + | 1.73205i | 0.195283 | + | 0.112747i | ||||
\(237\) | − | 19.0526i | − | 1.23760i | ||||||
\(238\) | 4.50000 | + | 7.79423i | 0.291692 | + | 0.505225i | ||||
\(239\) | 4.50000 | + | 2.59808i | 0.291081 | + | 0.168056i | 0.638429 | − | 0.769681i | \(-0.279585\pi\) |
−0.347348 | + | 0.937736i | \(0.612918\pi\) | |||||||
\(240\) | 15.0000 | 0.968246 | ||||||||
\(241\) | − | 5.19615i | − | 0.334714i | −0.985896 | − | 0.167357i | \(-0.946477\pi\) | ||
0.985896 | − | 0.167357i | \(-0.0535232\pi\) | |||||||
\(242\) | − | 1.73205i | − | 0.111340i | ||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | −2.50000 | − | 4.33013i | −0.160046 | − | 0.277208i | ||||
\(245\) | −6.00000 | − | 3.46410i | −0.383326 | − | 0.221313i | ||||
\(246\) | −31.5000 | + | 18.1865i | −2.00837 | + | 1.15953i | ||||
\(247\) | 6.00000 | − | 1.73205i | 0.381771 | − | 0.110208i | ||||
\(248\) | 7.50000 | − | 12.9904i | 0.476250 | − | 0.824890i | ||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | 10.5000 | − | 18.1865i | 0.664078 | − | 1.15022i | ||||
\(251\) | −4.50000 | + | 7.79423i | −0.284037 | + | 0.491967i | −0.972375 | − | 0.233423i | \(-0.925007\pi\) |
0.688338 | + | 0.725390i | \(0.258341\pi\) | |||||||
\(252\) | −4.50000 | − | 2.59808i | −0.283473 | − | 0.163663i | ||||
\(253\) | 9.00000 | + | 5.19615i | 0.565825 | + | 0.326679i | ||||
\(254\) | − | 8.66025i | − | 0.543393i | ||||||
\(255\) | −9.00000 | −0.563602 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 3.00000 | 0.187135 | 0.0935674 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935674 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(258\) | −1.50000 | − | 2.59808i | −0.0933859 | − | 0.161749i | ||||
\(259\) | −4.50000 | − | 7.79423i | −0.279616 | − | 0.484310i | ||||
\(260\) | 4.50000 | + | 4.33013i | 0.279078 | + | 0.268543i | ||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 22.5000 | − | 12.9904i | 1.39005 | − | 0.802548i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | −9.00000 | + | 5.19615i | −0.553912 | + | 0.319801i | ||||
\(265\) | −9.00000 | − | 5.19615i | −0.552866 | − | 0.319197i | ||||
\(266\) | −4.50000 | + | 2.59808i | −0.275913 | + | 0.159298i | ||||
\(267\) | −27.0000 | −1.65237 | ||||||||
\(268\) | 10.5000 | − | 6.06218i | 0.641390 | − | 0.370306i | ||||
\(269\) | −1.50000 | + | 2.59808i | −0.0914566 | + | 0.158408i | −0.908124 | − | 0.418701i | \(-0.862486\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(270\) | 13.5000 | − | 7.79423i | 0.821584 | − | 0.474342i | ||||
\(271\) | 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 | ||||
\(273\) | 3.00000 | + | 10.3923i | 0.181568 | + | 0.628971i | ||||
\(274\) | −4.50000 | + | 7.79423i | −0.271855 | + | 0.470867i | ||||
\(275\) | 6.92820i | 0.417786i | ||||||||
\(276\) | 5.19615i | 0.312772i | ||||||||
\(277\) | 23.0000 | 1.38194 | 0.690968 | − | 0.722885i | \(-0.257185\pi\) | ||||
0.690968 | + | 0.722885i | \(0.257185\pi\) | |||||||
\(278\) | − | 27.7128i | − | 1.66210i | ||||||
\(279\) | − | 25.9808i | − | 1.55543i | ||||||
\(280\) | 4.50000 | + | 2.59808i | 0.268926 | + | 0.155265i | ||||
\(281\) | 4.50000 | − | 2.59808i | 0.268447 | − | 0.154988i | −0.359734 | − | 0.933055i | \(-0.617133\pi\) |
0.628182 | + | 0.778067i | \(0.283799\pi\) | |||||||
\(282\) | −13.5000 | − | 7.79423i | −0.803913 | − | 0.464140i | ||||
\(283\) | −23.0000 | −1.36721 | −0.683604 | − | 0.729853i | \(-0.739588\pi\) | ||||
−0.683604 | + | 0.729853i | \(0.739588\pi\) | |||||||
\(284\) | − | 8.66025i | − | 0.513892i | ||||||
\(285\) | − | 5.19615i | − | 0.307794i | ||||||
\(286\) | −21.0000 | − | 5.19615i | −1.24176 | − | 0.307255i | ||||
\(287\) | −21.0000 | −1.23959 | ||||||||
\(288\) | −13.5000 | − | 7.79423i | −0.795495 | − | 0.459279i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 18.0000 | 1.05700 | ||||||||
\(291\) | 13.5000 | − | 23.3827i | 0.791384 | − | 1.37072i | ||||
\(292\) | 6.00000 | − | 3.46410i | 0.351123 | − | 0.202721i | ||||
\(293\) | 12.0000 | − | 6.92820i | 0.701047 | − | 0.404750i | −0.106690 | − | 0.994292i | \(-0.534025\pi\) |
0.807737 | + | 0.589542i | \(0.200692\pi\) | |||||||
\(294\) | 6.00000 | + | 10.3923i | 0.349927 | + | 0.606092i | ||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | −4.50000 | − | 7.79423i | −0.261557 | − | 0.453030i | ||||
\(297\) | −9.00000 | + | 15.5885i | −0.522233 | + | 0.904534i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.50000 | − | 7.79423i | 0.433736 | − | 0.450752i | ||||
\(300\) | −3.00000 | + | 1.73205i | −0.173205 | + | 0.100000i | ||||
\(301\) | − | 1.73205i | − | 0.0998337i | ||||||
\(302\) | 21.0000 | 1.20841 | ||||||||
\(303\) | −9.00000 | + | 5.19615i | −0.517036 | + | 0.298511i | ||||
\(304\) | −7.50000 | + | 4.33013i | −0.430155 | + | 0.248350i | ||||
\(305\) | 7.50000 | + | 4.33013i | 0.429449 | + | 0.247942i | ||||
\(306\) | 13.5000 | + | 7.79423i | 0.771744 | + | 0.445566i | ||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | 6.00000 | 0.341882 | ||||||||
\(309\) | −19.5000 | + | 11.2583i | −1.10932 | + | 0.640464i | ||||
\(310\) | − | 25.9808i | − | 1.47561i | ||||||
\(311\) | −13.5000 | + | 23.3827i | −0.765515 | + | 1.32591i | 0.174459 | + | 0.984664i | \(0.444182\pi\) |
−0.939974 | + | 0.341246i | \(0.889151\pi\) | |||||||
\(312\) | 3.00000 | + | 10.3923i | 0.169842 | + | 0.588348i | ||||
\(313\) | −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 | ||||
\(315\) | 9.00000 | 0.507093 | ||||||||
\(316\) | −5.50000 | + | 9.52628i | −0.309399 | + | 0.535895i | ||||
\(317\) | −7.50000 | + | 4.33013i | −0.421242 | + | 0.243204i | −0.695609 | − | 0.718421i | \(-0.744865\pi\) |
0.274367 | + | 0.961625i | \(0.411532\pi\) | |||||||
\(318\) | 9.00000 | + | 15.5885i | 0.504695 | + | 0.874157i | ||||
\(319\) | −18.0000 | + | 10.3923i | −1.00781 | + | 0.581857i | ||||
\(320\) | 1.50000 | + | 0.866025i | 0.0838525 | + | 0.0484123i | ||||
\(321\) | 25.9808i | 1.45010i | ||||||||
\(322\) | −4.50000 | + | 7.79423i | −0.250775 | + | 0.434355i | ||||
\(323\) | 4.50000 | − | 2.59808i | 0.250387 | − | 0.144561i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 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 | ||||
\(330\) | −9.00000 | + | 15.5885i | −0.495434 | + | 0.858116i | ||||
\(331\) | 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 | ||||
\(333\) | −13.5000 | − | 7.79423i | −0.739795 | − | 0.427121i | ||||
\(334\) | −4.50000 | + | 7.79423i | −0.246229 | + | 0.426481i | ||||
\(335\) | −10.5000 | + | 18.1865i | −0.573676 | + | 0.993636i | ||||
\(336\) | −7.50000 | − | 12.9904i | −0.409159 | − | 0.708683i | ||||
\(337\) | 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 | ||||
\(339\) | 10.3923i | 0.564433i | ||||||||
\(340\) | 4.50000 | + | 2.59808i | 0.244047 | + | 0.140900i | ||||
\(341\) | 15.0000 | + | 25.9808i | 0.812296 | + | 1.40694i | ||||
\(342\) | −4.50000 | + | 7.79423i | −0.243332 | + | 0.421464i | ||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | − | 1.73205i | − | 0.0933859i | ||||||
\(345\) | −4.50000 | − | 7.79423i | −0.242272 | − | 0.419627i | ||||
\(346\) | 31.5000 | + | 18.1865i | 1.69345 | + | 0.977714i | ||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | −9.00000 | − | 5.19615i | −0.482451 | − | 0.278543i | ||||
\(349\) | −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 | ||||||||
\(351\) | 13.5000 | + | 12.9904i | 0.720577 | + | 0.693375i | ||||
\(352\) | 18.0000 | 0.959403 | ||||||||
\(353\) | 6.00000 | + | 3.46410i | 0.319348 | + | 0.184376i | 0.651102 | − | 0.758990i | \(-0.274307\pi\) |
−0.331754 | + | 0.943366i | \(0.607640\pi\) | |||||||
\(354\) | 9.00000 | + | 5.19615i | 0.478345 | + | 0.276172i | ||||
\(355\) | 7.50000 | + | 12.9904i | 0.398059 | + | 0.689458i | ||||
\(356\) | 13.5000 | + | 7.79423i | 0.715499 | + | 0.413093i | ||||
\(357\) | 4.50000 | + | 7.79423i | 0.238165 | + | 0.412514i | ||||
\(358\) | 5.19615i | 0.274625i | ||||||||
\(359\) | 10.3923i | 0.548485i | 0.961661 | + | 0.274242i | \(0.0884271\pi\) | ||||
−0.961661 | + | 0.274242i | \(0.911573\pi\) | |||||||
\(360\) | 9.00000 | 0.474342 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | 33.0000 | + | 19.0526i | 1.73444 | + | 1.00138i | ||||
\(363\) | − | 1.73205i | − | 0.0909091i | ||||||
\(364\) | 1.50000 | − | 6.06218i | 0.0786214 | − | 0.317744i | ||||
\(365\) | −6.00000 | + | 10.3923i | −0.314054 | + | 0.543958i | ||||
\(366\) | −7.50000 | − | 12.9904i | −0.392031 | − | 0.679018i | ||||
\(367\) | −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 | ||||
\(369\) | −31.5000 | + | 18.1865i | −1.63982 | + | 0.946753i | ||||
\(370\) | −13.5000 | − | 7.79423i | −0.701832 | − | 0.405203i | ||||
\(371\) | 10.3923i | 0.539542i | ||||||||
\(372\) | −7.50000 | + | 12.9904i | −0.388857 | + | 0.673520i | ||||
\(373\) | 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 | ||||||||
\(375\) | 10.5000 | − | 18.1865i | 0.542218 | − | 0.939149i | ||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | 6.00000 | + | 20.7846i | 0.309016 | + | 1.07046i | ||||
\(378\) | −13.5000 | − | 7.79423i | −0.694365 | − | 0.400892i | ||||
\(379\) | −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 | ||||
\(381\) | − | 8.66025i | − | 0.443678i | ||||||
\(382\) | −4.50000 | − | 2.59808i | −0.230240 | − | 0.132929i | ||||
\(383\) | −3.00000 | + | 1.73205i | −0.153293 | + | 0.0885037i | −0.574684 | − | 0.818375i | \(-0.694875\pi\) |
0.421392 | + | 0.906879i | \(0.361542\pi\) | |||||||
\(384\) | −10.5000 | − | 18.1865i | −0.535826 | − | 0.928078i | ||||
\(385\) | −9.00000 | + | 5.19615i | −0.458682 | + | 0.264820i | ||||
\(386\) | 4.50000 | − | 7.79423i | 0.229044 | − | 0.396716i | ||||
\(387\) | −1.50000 | − | 2.59808i | −0.0762493 | − | 0.132068i | ||||
\(388\) | −13.5000 | + | 7.79423i | −0.685359 | + | 0.395692i | ||||
\(389\) | −1.50000 | − | 2.59808i | −0.0760530 | − | 0.131728i | 0.825491 | − | 0.564416i | \(-0.190898\pi\) |
−0.901544 | + | 0.432688i | \(0.857565\pi\) | |||||||
\(390\) | 13.5000 | + | 12.9904i | 0.683599 | + | 0.657794i | ||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | 6.92820i | 0.349927i | ||||||||
\(393\) | 22.5000 | − | 12.9904i | 1.13497 | − | 0.655278i | ||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | − | 19.0526i | − | 0.958638i | ||||||
\(396\) | 9.00000 | − | 5.19615i | 0.452267 | − | 0.261116i | ||||
\(397\) | −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 | ||||
\(399\) | −4.50000 | + | 2.59808i | −0.225282 | + | 0.130066i | ||||
\(400\) | −10.0000 | −0.500000 | ||||||||
\(401\) | − | 29.4449i | − | 1.47041i | −0.677847 | − | 0.735203i | \(-0.737087\pi\) | ||
0.677847 | − | 0.735203i | \(-0.262913\pi\) | |||||||
\(402\) | 31.5000 | − | 18.1865i | 1.57108 | − | 0.907062i | ||||
\(403\) | 30.0000 | − | 8.66025i | 1.49441 | − | 0.431398i | ||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 13.5000 | − | 7.79423i | 0.670820 | − | 0.387298i | ||||
\(406\) | −9.00000 | − | 15.5885i | −0.446663 | − | 0.773642i | ||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | 4.50000 | + | 7.79423i | 0.222783 | + | 0.385872i | ||||
\(409\) | 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 | ||||
\(411\) | −4.50000 | + | 7.79423i | −0.221969 | + | 0.384461i | ||||
\(412\) | 13.0000 | 0.640464 | ||||||||
\(413\) | 3.00000 | + | 5.19615i | 0.147620 | + | 0.255686i | ||||
\(414\) | 15.5885i | 0.766131i | ||||||||
\(415\) | 9.00000 | 0.441793 | ||||||||
\(416\) | 4.50000 | − | 18.1865i | 0.220631 | − | 0.891668i | ||||
\(417\) | − | 27.7128i | − | 1.35710i | ||||||
\(418\) | − | 10.3923i | − | 0.508304i | ||||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | −4.50000 | − | 2.59808i | −0.219578 | − | 0.126773i | ||||
\(421\) | −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 | ||||
\(423\) | −13.5000 | − | 7.79423i | −0.656392 | − | 0.378968i | ||||
\(424\) | 10.3923i | 0.504695i | ||||||||
\(425\) | 6.00000 | 0.291043 | ||||||||
\(426\) | − | 25.9808i | − | 1.25877i | ||||||
\(427\) | − | 8.66025i | − | 0.419099i | ||||||
\(428\) | 7.50000 | − | 12.9904i | 0.362526 | − | 0.627914i | ||||
\(429\) | −21.0000 | − | 5.19615i | −1.01389 | − | 0.250873i | ||||
\(430\) | −1.50000 | − | 2.59808i | −0.0723364 | − | 0.125290i | ||||
\(431\) | 19.5000 | − | 11.2583i | 0.939282 | − | 0.542295i | 0.0495468 | − | 0.998772i | \(-0.484222\pi\) |
0.889735 | + | 0.456477i | \(0.150889\pi\) | |||||||
\(432\) | −22.5000 | − | 12.9904i | −1.08253 | − | 0.625000i | ||||
\(433\) | 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 | ||||
\(435\) | 18.0000 | 0.863034 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.50000 | + | 2.59808i | 0.215264 | + | 0.124283i | ||||
\(438\) | 18.0000 | − | 10.3923i | 0.860073 | − | 0.496564i | ||||
\(439\) | −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 | ||||
\(441\) | 6.00000 | + | 10.3923i | 0.285714 | + | 0.494872i | ||||
\(442\) | −4.50000 | + | 18.1865i | −0.214043 | + | 0.865045i | ||||
\(443\) | −10.5000 | − | 18.1865i | −0.498870 | − | 0.864068i | 0.501129 | − | 0.865373i | \(-0.332918\pi\) |
−0.999999 | + | 0.00130426i | \(0.999585\pi\) | |||||||
\(444\) | 4.50000 | + | 7.79423i | 0.213561 | + | 0.369898i | ||||
\(445\) | −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 | 0.783498 | − | 0.621394i | \(-0.213433\pi\) |
−0.146394 | + | 0.989226i | \(0.546767\pi\) | |||||||
\(450\) | −9.00000 | + | 5.19615i | −0.424264 | + | 0.244949i | ||||
\(451\) | 21.0000 | − | 36.3731i | 0.988851 | − | 1.71274i | ||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | 21.0000 | 0.986666 | ||||||||
\(454\) | −10.5000 | + | 18.1865i | −0.492789 | + | 0.853536i | ||||
\(455\) | 3.00000 | + | 10.3923i | 0.140642 | + | 0.487199i | ||||
\(456\) | −4.50000 | + | 2.59808i | −0.210732 | + | 0.121666i | ||||
\(457\) | 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 | ||||
\(459\) | 13.5000 | + | 7.79423i | 0.630126 | + | 0.363803i | ||||
\(460\) | 5.19615i | 0.242272i | ||||||||
\(461\) | 1.73205i | 0.0806696i | 0.999186 | + | 0.0403348i | \(0.0128425\pi\) | ||||
−0.999186 | + | 0.0403348i | \(0.987158\pi\) | |||||||
\(462\) | 18.0000 | 0.837436 | ||||||||
\(463\) | 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 | ||||
\(465\) | − | 25.9808i | − | 1.20483i | ||||||
\(466\) | 27.0000 | + | 15.5885i | 1.25075 | + | 0.722121i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −3.00000 | − | 10.3923i | −0.138675 | − | 0.480384i | ||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | −13.5000 | − | 7.79423i | −0.622709 | − | 0.359521i | ||||
\(471\) | 34.5000 | − | 19.9186i | 1.58968 | − | 0.917800i | ||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | 3.00000 | + | 1.73205i | 0.137940 | + | 0.0796398i | ||||
\(474\) | −16.5000 | + | 28.5788i | −0.757870 | + | 1.31267i | ||||
\(475\) | 3.46410i | 0.158944i | ||||||||
\(476\) | − | 5.19615i | − | 0.238165i | ||||||
\(477\) | 9.00000 | + | 15.5885i | 0.412082 | + | 0.713746i | ||||
\(478\) | −4.50000 | − | 7.79423i | −0.205825 | − | 0.356500i | ||||
\(479\) | −21.0000 | − | 12.1244i | −0.959514 | − | 0.553976i | −0.0634909 | − | 0.997982i | \(-0.520223\pi\) |
−0.896024 | + | 0.444006i | \(0.853557\pi\) | |||||||
\(480\) | −13.5000 | − | 7.79423i | −0.616188 | − | 0.355756i | ||||
\(481\) | 4.50000 | − | 18.1865i | 0.205182 | − | 0.829235i | ||||
\(482\) | −4.50000 | + | 7.79423i | −0.204969 | + | 0.355017i | ||||
\(483\) | −4.50000 | + | 7.79423i | −0.204757 | + | 0.354650i | ||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 13.5000 | − | 23.3827i | 0.613003 | − | 1.06175i | ||||
\(486\) | −27.0000 | −1.22474 | ||||||||
\(487\) | −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 | ||||||
\(489\) | −10.5000 | − | 18.1865i | −0.474826 | − | 0.822423i | ||||
\(490\) | 6.00000 | + | 10.3923i | 0.271052 | + | 0.469476i | ||||
\(491\) | −3.00000 | −0.135388 | −0.0676941 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676941 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(492\) | 21.0000 | 0.946753 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | −10.5000 | − | 2.59808i | −0.472417 | − | 0.116893i | ||||
\(495\) | −9.00000 | + | 15.5885i | −0.404520 | + | 0.700649i | ||||
\(496\) | −37.5000 | + | 21.6506i | −1.68380 | + | 0.972142i | ||||
\(497\) | 7.50000 | − | 12.9904i | 0.336421 | − | 0.582698i | ||||
\(498\) | −13.5000 | − | 7.79423i | −0.604949 | − | 0.349268i | ||||
\(499\) | 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 | ||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | 13.5000 | − | 7.79423i | 0.602534 | − | 0.347873i | ||||
\(503\) | −10.5000 | + | 18.1865i | −0.468172 | + | 0.810897i | −0.999338 | − | 0.0363700i | \(-0.988421\pi\) |
0.531167 | + | 0.847267i | \(0.321754\pi\) | |||||||
\(504\) | −4.50000 | − | 7.79423i | −0.200446 | − | 0.347183i | ||||
\(505\) | −9.00000 | + | 5.19615i | −0.400495 | + | 0.231226i | ||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | −10.5000 | + | 19.9186i | −0.466321 | + | 0.884615i | ||||
\(508\) | −2.50000 | + | 4.33013i | −0.110920 | + | 0.192118i | ||||
\(509\) | − | 1.73205i | − | 0.0767718i | −0.999263 | − | 0.0383859i | \(-0.987778\pi\) | ||
0.999263 | − | 0.0383859i | \(-0.0122216\pi\) | |||||||
\(510\) | 13.5000 | + | 7.79423i | 0.597790 | + | 0.345134i | ||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | −4.50000 | + | 7.79423i | −0.198680 | + | 0.344124i | ||||
\(514\) | −4.50000 | − | 2.59808i | −0.198486 | − | 0.114596i | ||||
\(515\) | −19.5000 | + | 11.2583i | −0.859273 | + | 0.496101i | ||||
\(516\) | 1.73205i | 0.0762493i | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 15.5885i | 0.684917i | ||||||||
\(519\) | 31.5000 | + | 18.1865i | 1.38270 | + | 0.798300i | ||||
\(520\) | 3.00000 | + | 10.3923i | 0.131559 | + | 0.455733i | ||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | −27.0000 | − | 15.5885i | −1.18176 | − | 0.682288i | ||||
\(523\) | 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 | ||||||||
\(525\) | −6.00000 | −0.261861 | ||||||||
\(526\) | 36.0000 | − | 20.7846i | 1.56967 | − | 0.906252i | ||||
\(527\) | 22.5000 | − | 12.9904i | 0.980115 | − | 0.565870i | ||||
\(528\) | 30.0000 | 1.30558 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 9.00000 | + | 15.5885i | 0.390935 | + | 0.677119i | ||||
\(531\) | 9.00000 | + | 5.19615i | 0.390567 | + | 0.225494i | ||||
\(532\) | 3.00000 | 0.130066 | ||||||||
\(533\) | −31.5000 | − | 30.3109i | −1.36442 | − | 1.31291i | ||||
\(534\) | 40.5000 | + | 23.3827i | 1.75261 | + | 1.01187i | ||||
\(535\) | 25.9808i | 1.12325i | ||||||||
\(536\) | 21.0000 | 0.907062 | ||||||||
\(537\) | 5.19615i | 0.224231i | ||||||||
\(538\) | 4.50000 | − | 2.59808i | 0.194009 | − | 0.112011i | ||||
\(539\) | −12.0000 | − | 6.92820i | −0.516877 | − | 0.298419i | ||||
\(540\) | −9.00000 | −0.387298 | ||||||||
\(541\) | 13.8564i | 0.595733i | 0.954607 | + | 0.297867i | \(0.0962751\pi\) | ||||
−0.954607 | + | 0.297867i | \(0.903725\pi\) | |||||||
\(542\) | −27.0000 | −1.15975 | ||||||||
\(543\) | 33.0000 | + | 19.0526i | 1.41617 | + | 0.817624i | ||||
\(544\) | − | 15.5885i | − | 0.668350i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.50000 | − | 18.1865i | 0.192582 | − | 0.778312i | ||||
\(547\) | −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 | ||||
\(549\) | −7.50000 | − | 12.9904i | −0.320092 | − | 0.554416i | ||||
\(550\) | 6.00000 | − | 10.3923i | 0.255841 | − | 0.443129i | ||||
\(551\) | −9.00000 | + | 5.19615i | −0.383413 | + | 0.221364i | ||||
\(552\) | −4.50000 | + | 7.79423i | −0.191533 | + | 0.331744i | ||||
\(553\) | −16.5000 | + | 9.52628i | −0.701651 | + | 0.405099i | ||||
\(554\) | −34.5000 | − | 19.9186i | −1.46576 | − | 0.846260i | ||||
\(555\) | −13.5000 | − | 7.79423i | −0.573043 | − | 0.330847i | ||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | −16.5000 | + | 9.52628i | −0.699127 | + | 0.403641i | −0.807022 | − | 0.590521i | \(-0.798922\pi\) |
0.107895 | + | 0.994162i | \(0.465589\pi\) | |||||||
\(558\) | −22.5000 | + | 38.9711i | −0.952501 | + | 1.64978i | ||||
\(559\) | 2.50000 | − | 2.59808i | 0.105739 | − | 0.109887i | ||||
\(560\) | −7.50000 | − | 12.9904i | −0.316933 | − | 0.548944i | ||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | −9.00000 | −0.379642 | ||||||||
\(563\) | −12.0000 | − | 20.7846i | −0.505740 | − | 0.875967i | −0.999978 | − | 0.00664037i | \(-0.997886\pi\) |
0.494238 | − | 0.869326i | \(-0.335447\pi\) | |||||||
\(564\) | 4.50000 | + | 7.79423i | 0.189484 | + | 0.328196i | ||||
\(565\) | 10.3923i | 0.437208i | ||||||||
\(566\) | 34.5000 | + | 19.9186i | 1.45014 | + | 0.837241i | ||||
\(567\) | −13.5000 | − | 7.79423i | −0.566947 | − | 0.327327i | ||||
\(568\) | 7.50000 | − | 12.9904i | 0.314693 | − | 0.545064i | ||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | −4.50000 | + | 7.79423i | −0.188484 | + | 0.326464i | ||||
\(571\) | 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 | ||||
\(573\) | −4.50000 | − | 2.59808i | −0.187990 | − | 0.108536i | ||||
\(574\) | 31.5000 | + | 18.1865i | 1.31478 | + | 0.759091i | ||||
\(575\) | 3.00000 | + | 5.19615i | 0.125109 | + | 0.216695i | ||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | − | 6.92820i | − | 0.288425i | −0.989547 | − | 0.144212i | \(-0.953935\pi\) | ||
0.989547 | − | 0.144212i | \(-0.0460649\pi\) | |||||||
\(578\) | − | 13.8564i | − | 0.576351i | ||||||
\(579\) | 4.50000 | − | 7.79423i | 0.187014 | − | 0.323917i | ||||
\(580\) | −9.00000 | − | 5.19615i | −0.373705 | − | 0.215758i | ||||
\(581\) | −4.50000 | − | 7.79423i | −0.186691 | − | 0.323359i | ||||
\(582\) | −40.5000 | + | 23.3827i | −1.67878 | + | 0.969244i | ||||
\(583\) | −18.0000 | − | 10.3923i | −0.745484 | − | 0.430405i | ||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 13.5000 | + | 12.9904i | 0.558156 | + | 0.537086i | ||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | 9.00000 | + | 5.19615i | 0.371470 | + | 0.214468i | 0.674100 | − | 0.738640i | \(-0.264532\pi\) |
−0.302631 | + | 0.953108i | \(0.597865\pi\) | |||||||
\(588\) | − | 6.92820i | − | 0.285714i | ||||||
\(589\) | 7.50000 | + | 12.9904i | 0.309032 | + | 0.535259i | ||||
\(590\) | 9.00000 | + | 5.19615i | 0.370524 | + | 0.213922i | ||||
\(591\) | −15.0000 | −0.617018 | ||||||||
\(592\) | 25.9808i | 1.06780i | ||||||||
\(593\) | − | 27.7128i | − | 1.13803i | −0.822328 | − | 0.569014i | \(-0.807325\pi\) | ||
0.822328 | − | 0.569014i | \(-0.192675\pi\) | |||||||
\(594\) | 27.0000 | − | 15.5885i | 1.10782 | − | 0.639602i | ||||
\(595\) | 4.50000 | + | 7.79423i | 0.184482 | + | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.5000 | − | 11.2583i | 0.798082 | − | 0.460773i | ||||
\(598\) | −18.0000 | + | 5.19615i | −0.736075 | + | 0.212486i | ||||
\(599\) | −13.5000 | + | 23.3827i | −0.551595 | + | 0.955391i | 0.446565 | + | 0.894751i | \(0.352647\pi\) |
−0.998160 | + | 0.0606393i | \(0.980686\pi\) | |||||||
\(600\) | −6.00000 | −0.244949 | ||||||||
\(601\) | −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 | ||||
\(603\) | 31.5000 | − | 18.1865i | 1.28278 | − | 0.740613i | ||||
\(604\) | −10.5000 | − | 6.06218i | −0.427239 | − | 0.246667i | ||||
\(605\) | − | 1.73205i | − | 0.0704179i | ||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | −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 | ||||||||
\(609\) | −9.00000 | − | 15.5885i | −0.364698 | − | 0.631676i | ||||
\(610\) | −7.50000 | − | 12.9904i | −0.303666 | − | 0.525965i | ||||
\(611\) | 4.50000 | − | 18.1865i | 0.182051 | − | 0.735748i | ||||
\(612\) | −4.50000 | − | 7.79423i | −0.181902 | − | 0.315063i | ||||
\(613\) | −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 | ||||
\(615\) | −31.5000 | + | 18.1865i | −1.27020 | + | 0.733352i | ||||
\(616\) | 9.00000 | + | 5.19615i | 0.362620 | + | 0.209359i | ||||
\(617\) | −24.0000 | + | 13.8564i | −0.966204 | + | 0.557838i | −0.898077 | − | 0.439839i | \(-0.855036\pi\) |
−0.0681269 | + | 0.997677i | \(0.521702\pi\) | |||||||
\(618\) | 39.0000 | 1.56881 | ||||||||
\(619\) | −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 | ||||
\(621\) | 15.5885i | 0.625543i | ||||||||
\(622\) | 40.5000 | − | 23.3827i | 1.62390 | − | 0.937560i | ||||
\(623\) | 13.5000 | + | 23.3827i | 0.540866 | + | 0.936808i | ||||
\(624\) | 7.50000 | − | 30.3109i | 0.300240 | − | 1.21341i | ||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 32.9090i | 1.31531i | ||||||||
\(627\) | − | 10.3923i | − | 0.415029i | ||||||
\(628\) | −23.0000 | −0.917800 | ||||||||
\(629\) | − | 15.5885i | − | 0.621552i | ||||||
\(630\) | −13.5000 | − | 7.79423i | −0.537853 | − | 0.310530i | ||||
\(631\) | −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 | ||||
\(633\) | −19.5000 | − | 11.2583i | −0.775055 | − | 0.447478i | ||||
\(634\) | 15.0000 | 0.595726 | ||||||||
\(635\) | − | 8.66025i | − | 0.343672i | ||||||
\(636\) | − | 10.3923i | − | 0.412082i | ||||||
\(637\) | −10.0000 | + | 10.3923i | −0.396214 | + | 0.411758i | ||||
\(638\) | 36.0000 | 1.42525 | ||||||||
\(639\) | − | 25.9808i | − | 1.02778i | ||||||
\(640\) | −10.5000 | − | 18.1865i | −0.415049 | − | 0.718886i | ||||
\(641\) | 39.0000 | 1.54041 | 0.770204 | − | 0.637798i | \(-0.220155\pi\) | ||||
0.770204 | + | 0.637798i | \(0.220155\pi\) | |||||||
\(642\) | 22.5000 | − | 38.9711i | 0.888004 | − | 1.53807i | ||||
\(643\) | −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 | ||||
\(645\) | −1.50000 | − | 2.59808i | −0.0590624 | − | 0.102299i | ||||
\(646\) | −9.00000 | −0.354100 | ||||||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | −13.5000 | − | 7.79423i | −0.530330 | − | 0.306186i | ||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | −9.00000 | − | 8.66025i | −0.353009 | − | 0.339683i | ||||
\(651\) | −22.5000 | + | 12.9904i | −0.881845 | + | 0.509133i | ||||
\(652\) | 12.1244i | 0.474826i | ||||||||
\(653\) | −45.0000 | −1.76099 | −0.880493 | − | 0.474059i | \(-0.842788\pi\) | ||||
−0.880493 | + | 0.474059i | \(0.842788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5000 | − | 12.9904i | 0.879148 | − | 0.507576i | ||||
\(656\) | 52.5000 | + | 30.3109i | 2.04978 | + | 1.18344i | ||||
\(657\) | 18.0000 | − | 10.3923i | 0.702247 | − | 0.405442i | ||||
\(658\) | 15.5885i | 0.607701i | ||||||||
\(659\) | 39.0000 | 1.51922 | 0.759612 | − | 0.650376i | \(-0.225389\pi\) | ||||
0.759612 | + | 0.650376i | \(0.225389\pi\) | |||||||
\(660\) | 9.00000 | − | 5.19615i | 0.350325 | − | 0.202260i | ||||
\(661\) | 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 | ||||
\(663\) | −4.50000 | + | 18.1865i | −0.174766 | + | 0.706306i | ||||
\(664\) | −4.50000 | − | 7.79423i | −0.174634 | − | 0.302475i | ||||
\(665\) | −4.50000 | + | 2.59808i | −0.174503 | + | 0.100749i | ||||
\(666\) | 13.5000 | + | 23.3827i | 0.523114 | + | 0.906061i | ||||
\(667\) | −9.00000 | + | 15.5885i | −0.348481 | + | 0.603587i | ||||
\(668\) | 4.50000 | − | 2.59808i | 0.174110 | − | 0.100523i | ||||
\(669\) | −3.00000 | − | 5.19615i | −0.115987 | − | 0.200895i | ||||
\(670\) | 31.5000 | − | 18.1865i | 1.21695 | − | 0.702607i | ||||
\(671\) | 15.0000 | + | 8.66025i | 0.579069 | + | 0.334325i | ||||
\(672\) | 15.5885i | 0.601338i | ||||||||
\(673\) | 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 | ||||
\(675\) | −9.00000 | + | 5.19615i | −0.346410 | + | 0.200000i | ||||
\(676\) | 11.0000 | − | 6.92820i | 0.423077 | − | 0.266469i | ||||
\(677\) | 10.5000 | + | 18.1865i | 0.403548 | + | 0.698965i | 0.994151 | − | 0.107997i | \(-0.0344436\pi\) |
−0.590603 | + | 0.806962i | \(0.701110\pi\) | |||||||
\(678\) | 9.00000 | − | 15.5885i | 0.345643 | − | 0.598671i | ||||
\(679\) | −27.0000 | −1.03616 | ||||||||
\(680\) | 4.50000 | + | 7.79423i | 0.172567 | + | 0.298895i | ||||
\(681\) | −10.5000 | + | 18.1865i | −0.402361 | + | 0.696909i | ||||
\(682\) | − | 51.9615i | − | 1.98971i | ||||||
\(683\) | −19.5000 | − | 11.2583i | −0.746147 | − | 0.430788i | 0.0781532 | − | 0.996941i | \(-0.475098\pi\) |
−0.824300 | + | 0.566153i | \(0.808431\pi\) | |||||||
\(684\) | 4.50000 | − | 2.59808i | 0.172062 | − | 0.0993399i | ||||
\(685\) | −4.50000 | + | 7.79423i | −0.171936 | + | 0.297802i | ||||
\(686\) | 16.5000 | − | 28.5788i | 0.629973 | − | 1.09115i | ||||
\(687\) | 7.50000 | + | 12.9904i | 0.286143 | + | 0.495614i | ||||
\(688\) | −2.50000 | + | 4.33013i | −0.0953116 | + | 0.165085i | ||||
\(689\) | −15.0000 | + | 15.5885i | −0.571454 | + | 0.593873i | ||||
\(690\) | 15.5885i | 0.593442i | ||||||||
\(691\) | −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 | ||||
\(693\) | 18.0000 | 0.683763 | ||||||||
\(694\) | − | 20.7846i | − | 0.788973i | ||||||
\(695\) | − | 27.7128i | − | 1.05121i | ||||||
\(696\) | −9.00000 | − | 15.5885i | −0.341144 | − | 0.590879i | ||||
\(697\) | −31.5000 | − | 18.1865i | −1.19315 | − | 0.688864i | ||||
\(698\) | 24.0000 | + | 41.5692i | 0.908413 | + | 1.57342i | ||||
\(699\) | 27.0000 | + | 15.5885i | 1.02123 | + | 0.589610i | ||||
\(700\) | 3.00000 | + | 1.73205i | 0.113389 | + | 0.0654654i | ||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | −9.00000 | − | 31.1769i | −0.339683 | − | 1.17670i | ||||
\(703\) | 9.00000 | 0.339441 | ||||||||
\(704\) | 3.00000 | + | 1.73205i | 0.113067 | + | 0.0652791i | ||||
\(705\) | −13.5000 | − | 7.79423i | −0.508439 | − | 0.293548i | ||||
\(706\) | −6.00000 | − | 10.3923i | −0.225813 | − | 0.391120i | ||||
\(707\) | 9.00000 | + | 5.19615i | 0.338480 | + | 0.195421i | ||||
\(708\) | −3.00000 | − | 5.19615i | −0.112747 | − | 0.195283i | ||||
\(709\) | − | 12.1244i | − | 0.455340i | −0.973738 | − | 0.227670i | \(-0.926889\pi\) | ||
0.973738 | − | 0.227670i | \(-0.0731107\pi\) | |||||||
\(710\) | − | 25.9808i | − | 0.975041i | ||||||
\(711\) | −16.5000 | + | 28.5788i | −0.618798 | + | 1.07179i | ||||
\(712\) | 13.5000 | + | 23.3827i | 0.505934 | + | 0.876303i | ||||
\(713\) | 22.5000 | + | 12.9904i | 0.842632 | + | 0.486494i | ||||
\(714\) | − | 15.5885i | − | 0.583383i | ||||||
\(715\) | −21.0000 | − | 5.19615i | −0.785355 | − | 0.194325i | ||||
\(716\) | 1.50000 | − | 2.59808i | 0.0560576 | − | 0.0970947i | ||||
\(717\) | −4.50000 | − | 7.79423i | −0.168056 | − | 0.291081i | ||||
\(718\) | 9.00000 | − | 15.5885i | 0.335877 | − | 0.581756i | ||||
\(719\) | 19.5000 | − | 33.7750i | 0.727227 | − | 1.25959i | −0.230823 | − | 0.972996i | \(-0.574142\pi\) |
0.958051 | − | 0.286599i | \(-0.0925247\pi\) | |||||||
\(720\) | −22.5000 | − | 12.9904i | −0.838525 | − | 0.484123i | ||||
\(721\) | 19.5000 | + | 11.2583i | 0.726218 | + | 0.419282i | ||||
\(722\) | 27.7128i | 1.03136i | ||||||||
\(723\) | −4.50000 | + | 7.79423i | −0.167357 | + | 0.289870i | ||||
\(724\) | −11.0000 | − | 19.0526i | −0.408812 | − | 0.708083i | ||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | −1.50000 | + | 2.59808i | −0.0556702 | + | 0.0964237i | ||||
\(727\) | −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 | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 18.0000 | − | 10.3923i | 0.666210 | − | 0.384636i | ||||
\(731\) | 1.50000 | − | 2.59808i | 0.0554795 | − | 0.0960933i | ||||
\(732\) | 8.66025i | 0.320092i | ||||||||
\(733\) | 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 | ||||
\(735\) | 6.00000 | + | 10.3923i | 0.221313 | + | 0.383326i | ||||
\(736\) | 13.5000 | − | 7.79423i | 0.497617 | − | 0.287299i | ||||
\(737\) | −21.0000 | + | 36.3731i | −0.773545 | + | 1.33982i | ||||
\(738\) | 63.0000 | 2.31906 | ||||||||
\(739\) | −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 | ||||
\(741\) | −10.5000 | − | 2.59808i | −0.385727 | − | 0.0954427i | ||||
\(742\) | 9.00000 | − | 15.5885i | 0.330400 | − | 0.572270i | ||||
\(743\) | − | 12.1244i | − | 0.444799i | −0.974956 | − | 0.222400i | \(-0.928611\pi\) | ||
0.974956 | − | 0.222400i | \(-0.0713890\pi\) | |||||||
\(744\) | −22.5000 | + | 12.9904i | −0.824890 | + | 0.476250i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 24.2487i | − | 0.887808i | ||||||
\(747\) | −13.5000 | − | 7.79423i | −0.493939 | − | 0.285176i | ||||
\(748\) | 9.00000 | + | 5.19615i | 0.329073 | + | 0.189990i | ||||
\(749\) | 22.5000 | − | 12.9904i | 0.822132 | − | 0.474658i | ||||
\(750\) | −31.5000 | + | 18.1865i | −1.15022 | + | 0.664078i | ||||
\(751\) | −19.0000 | −0.693320 | −0.346660 | − | 0.937991i | \(-0.612684\pi\) | ||||
−0.346660 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(752\) | 25.9808i | 0.947421i | ||||||||
\(753\) | 13.5000 | − | 7.79423i | 0.491967 | − | 0.284037i | ||||
\(754\) | 9.00000 | − | 36.3731i | 0.327761 | − | 1.32463i | ||||
\(755\) | 21.0000 | 0.764268 | ||||||||
\(756\) | 4.50000 | + | 7.79423i | 0.163663 | + | 0.283473i | ||||
\(757\) | −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 | ||||||||
\(759\) | −9.00000 | − | 15.5885i | −0.326679 | − | 0.565825i | ||||
\(760\) | −4.50000 | + | 2.59808i | −0.163232 | + | 0.0942421i | ||||
\(761\) | 12.0000 | − | 6.92820i | 0.435000 | − | 0.251147i | −0.266475 | − | 0.963842i | \(-0.585859\pi\) |
0.701474 | + | 0.712695i | \(0.252526\pi\) | |||||||
\(762\) | −7.50000 | + | 12.9904i | −0.271696 | + | 0.470592i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.50000 | + | 2.59808i | 0.0542681 | + | 0.0939951i | ||||
\(765\) | 13.5000 | + | 7.79423i | 0.488094 | + | 0.281801i | ||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | −3.00000 | + | 12.1244i | −0.108324 | + | 0.437785i | ||||
\(768\) | 32.9090i | 1.18750i | ||||||||
\(769\) | − | 22.5167i | − | 0.811972i | −0.913879 | − | 0.405986i | \(-0.866928\pi\) | ||
0.913879 | − | 0.405986i | \(-0.133072\pi\) | |||||||
\(770\) | 18.0000 | 0.648675 | ||||||||
\(771\) | −4.50000 | − | 2.59808i | −0.162064 | − | 0.0935674i | ||||
\(772\) | −4.50000 | + | 2.59808i | −0.161959 | + | 0.0935068i | ||||
\(773\) | 25.5000 | + | 14.7224i | 0.917171 | + | 0.529529i | 0.882732 | − | 0.469878i | \(-0.155702\pi\) |
0.0344397 | + | 0.999407i | \(0.489035\pi\) | |||||||
\(774\) | 5.19615i | 0.186772i | ||||||||
\(775\) | 17.3205i | 0.622171i | ||||||||
\(776\) | −27.0000 | −0.969244 | ||||||||
\(777\) | 15.5885i | 0.559233i | ||||||||
\(778\) | 5.19615i | 0.186291i | ||||||||
\(779\) | 10.5000 | − | 18.1865i | 0.376202 | − | 0.651600i | ||||
\(780\) | −3.00000 | − | 10.3923i | −0.107417 | − | 0.372104i | ||||
\(781\) | 15.0000 | + | 25.9808i | 0.536742 | + | 0.929665i | ||||
\(782\) | −13.5000 | + | 7.79423i | −0.482759 | + | 0.278721i | ||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | 10.0000 | − | 17.3205i | 0.357143 | − | 0.618590i | ||||
\(785\) | 34.5000 | − | 19.9186i | 1.23136 | − | 0.710925i | ||||
\(786\) | −45.0000 | −1.60510 | ||||||||
\(787\) | 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 | ||||
\(789\) | 36.0000 | − | 20.7846i | 1.28163 | − | 0.739952i | ||||
\(790\) | −16.5000 | + | 28.5788i | −0.587044 | + | 1.01679i | ||||
\(791\) | 9.00000 | − | 5.19615i | 0.320003 | − | 0.184754i | ||||
\(792\) | 18.0000 | 0.639602 | ||||||||
\(793\) | 12.5000 | − | 12.9904i | 0.443888 | − | 0.461302i | ||||
\(794\) | 22.5000 | + | 38.9711i | 0.798495 | + | 1.38303i | ||||
\(795\) | 9.00000 | + | 15.5885i | 0.319197 | + | 0.552866i | ||||
\(796\) | −13.0000 | −0.460773 | ||||||||
\(797\) | −9.00000 | − | 15.5885i | −0.318796 | − | 0.552171i | 0.661441 | − | 0.749997i | \(-0.269945\pi\) |
−0.980237 | + | 0.197826i | \(0.936612\pi\) | |||||||
\(798\) | 9.00000 | 0.318597 | ||||||||
\(799\) | − | 15.5885i | − | 0.551480i | ||||||
\(800\) | 9.00000 | + | 5.19615i | 0.318198 | + | 0.183712i | ||||
\(801\) | 40.5000 | + | 23.3827i | 1.43100 | + | 0.826187i | ||||
\(802\) | −25.5000 | + | 44.1673i | −0.900436 | + | 1.55960i | ||||
\(803\) | −12.0000 | + | 20.7846i | −0.423471 | + | 0.733473i | ||||
\(804\) | −21.0000 | −0.740613 | ||||||||
\(805\) | −4.50000 | + | 7.79423i | −0.158604 | + | 0.274710i | ||||
\(806\) | −52.5000 | − | 12.9904i | −1.84923 | − | 0.457567i | ||||
\(807\) | 4.50000 | − | 2.59808i | 0.158408 | − | 0.0914566i | ||||
\(808\) | 9.00000 | + | 5.19615i | 0.316619 | + | 0.182800i | ||||
\(809\) | −13.5000 | − | 23.3827i | −0.474635 | − | 0.822091i | 0.524943 | − | 0.851137i | \(-0.324086\pi\) |
−0.999578 | + | 0.0290457i | \(0.990753\pi\) | |||||||
\(810\) | −27.0000 | −0.948683 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | 10.3923i | 0.364698i | ||||||||
\(813\) | −27.0000 | −0.946931 | ||||||||
\(814\) | −27.0000 | − | 15.5885i | −0.946350 | − | 0.546375i | ||||
\(815\) | −10.5000 | − | 18.1865i | −0.367799 | − | 0.637046i | ||||
\(816\) | − | 25.9808i | − | 0.909509i | ||||||
\(817\) | 1.50000 | + | 0.866025i | 0.0524784 | + | 0.0302984i | ||||
\(818\) | −12.0000 | −0.419570 | ||||||||
\(819\) | 4.50000 | − | 18.1865i | 0.157243 | − | 0.635489i | ||||
\(820\) | 21.0000 | 0.733352 | ||||||||
\(821\) | −24.0000 | − | 13.8564i | −0.837606 | − | 0.483592i | 0.0188439 | − | 0.999822i | \(-0.494001\pi\) |
−0.856450 | + | 0.516231i | \(0.827335\pi\) | |||||||
\(822\) | 13.5000 | − | 7.79423i | 0.470867 | − | 0.271855i | ||||
\(823\) | −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 | ||||
\(825\) | 6.00000 | − | 10.3923i | 0.208893 | − | 0.361814i | ||||
\(826\) | − | 10.3923i | − | 0.361595i | ||||||
\(827\) | − | 24.2487i | − | 0.843210i | −0.906780 | − | 0.421605i | \(-0.861467\pi\) | ||
0.906780 | − | 0.421605i | \(-0.138533\pi\) | |||||||
\(828\) | 4.50000 | − | 7.79423i | 0.156386 | − | 0.270868i | ||||
\(829\) | 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 | ||||
\(831\) | −34.5000 | − | 19.9186i | −1.19679 | − | 0.690968i | ||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | −6.00000 | + | 10.3923i | −0.207888 | + | 0.360072i | ||||
\(834\) | −24.0000 | + | 41.5692i | −0.831052 | + | 1.43942i | ||||
\(835\) | −4.50000 | + | 7.79423i | −0.155729 | + | 0.269730i | ||||
\(836\) | −3.00000 | + | 5.19615i | −0.103757 | + | 0.179713i | ||||
\(837\) | −22.5000 | + | 38.9711i | −0.777714 | + | 1.34704i | ||||
\(838\) | −13.5000 | − | 7.79423i | −0.466350 | − | 0.269247i | ||||
\(839\) | − | 12.1244i | − | 0.418579i | −0.977854 | − | 0.209290i | \(-0.932885\pi\) | ||
0.977854 | − | 0.209290i | \(-0.0671151\pi\) | |||||||
\(840\) | −4.50000 | − | 7.79423i | −0.155265 | − | 0.268926i | ||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 15.0000 | 0.516934 | ||||||||
\(843\) | −9.00000 | −0.309976 | ||||||||
\(844\) | 6.50000 | + | 11.2583i | 0.223739 | + | 0.387528i | ||||
\(845\) | −10.5000 | + | 19.9186i | −0.361211 | + | 0.685220i | ||||
\(846\) | 13.5000 | + | 23.3827i | 0.464140 | + | 0.803913i | ||||
\(847\) | −1.50000 | + | 0.866025i | −0.0515406 | + | 0.0297570i | ||||
\(848\) | 15.0000 | − | 25.9808i | 0.515102 | − | 0.892183i | ||||
\(849\) | 34.5000 | + | 19.9186i | 1.18404 | + | 0.683604i | ||||
\(850\) | −9.00000 | − | 5.19615i | −0.308697 | − | 0.178227i | ||||
\(851\) | 13.5000 | − | 7.79423i | 0.462774 | − | 0.267183i | ||||
\(852\) | −7.50000 | + | 12.9904i | −0.256946 | + | 0.445043i | ||||
\(853\) | 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 | ||||
\(855\) | −4.50000 | + | 7.79423i | −0.153897 | + | 0.266557i | ||||
\(856\) | 22.5000 | − | 12.9904i | 0.769034 | − | 0.444002i | ||||
\(857\) | −1.50000 | − | 2.59808i | −0.0512390 | − | 0.0887486i | 0.839268 | − | 0.543718i | \(-0.182984\pi\) |
−0.890507 | + | 0.454969i | \(0.849650\pi\) | |||||||
\(858\) | 27.0000 | + | 25.9808i | 0.921765 | + | 0.886969i | ||||
\(859\) | 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 | ||||||||
\(861\) | 31.5000 | + | 18.1865i | 1.07352 | + | 0.619795i | ||||
\(862\) | −39.0000 | −1.32835 | ||||||||
\(863\) | 17.3205i | 0.589597i | 0.955559 | + | 0.294798i | \(0.0952525\pi\) | ||||
−0.955559 | + | 0.294798i | \(0.904747\pi\) | |||||||
\(864\) | 13.5000 | + | 23.3827i | 0.459279 | + | 0.795495i | ||||
\(865\) | 31.5000 | + | 18.1865i | 1.07103 | + | 0.618361i | ||||
\(866\) | −7.50000 | + | 4.33013i | −0.254860 | + | 0.147144i | ||||
\(867\) | − | 13.8564i | − | 0.470588i | ||||||
\(868\) | 15.0000 | 0.509133 | ||||||||
\(869\) | − | 38.1051i | − | 1.29263i | ||||||
\(870\) | −27.0000 | − | 15.5885i | −0.915386 | − | 0.528498i | ||||
\(871\) | 31.5000 | + | 30.3109i | 1.06734 | + | 1.02705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −40.5000 | + | 23.3827i | −1.37072 | + | 0.791384i | ||||
\(874\) | −4.50000 | − | 7.79423i | −0.152215 | − | 0.263644i | ||||
\(875\) | −21.0000 | −0.709930 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | 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 | ||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 30.0000 | 1.01130 | ||||||||
\(881\) | 4.50000 | + | 7.79423i | 0.151609 | + | 0.262594i | 0.931819 | − | 0.362923i | \(-0.118221\pi\) |
−0.780210 | + | 0.625517i | \(0.784888\pi\) | |||||||
\(882\) | − | 20.7846i | − | 0.699854i | ||||||
\(883\) | 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 | ||||
\(885\) | 9.00000 | + | 5.19615i | 0.302532 | + | 0.174667i | ||||
\(886\) | 36.3731i | 1.22198i | ||||||||
\(887\) | −15.0000 | −0.503651 | −0.251825 | − | 0.967773i | \(-0.581031\pi\) | ||||
−0.251825 | + | 0.967773i | \(0.581031\pi\) | |||||||
\(888\) | 15.5885i | 0.523114i | ||||||||
\(889\) | −7.50000 | + | 4.33013i | −0.251542 | + | 0.145228i | ||||
\(890\) | 40.5000 | + | 23.3827i | 1.35756 | + | 0.783789i | ||||
\(891\) | 27.0000 | − | 15.5885i | 0.904534 | − | 0.522233i | ||||
\(892\) | 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 | ||||
\(897\) | −18.0000 | + | 5.19615i | −0.601003 | + | 0.173494i | ||||
\(898\) | −13.5000 | − | 23.3827i | −0.450501 | − | 0.780290i | ||||
\(899\) | −45.0000 | + | 25.9808i | −1.50083 | + | 0.866507i | ||||
\(900\) | 6.00000 | 0.200000 | ||||||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | −63.0000 | + | 36.3731i | −2.09767 | + | 1.21109i | ||||
\(903\) | −1.50000 | + | 2.59808i | −0.0499169 | + | 0.0864586i | ||||
\(904\) | 9.00000 | − | 5.19615i | 0.299336 | − | 0.172821i | ||||
\(905\) | 33.0000 | + | 19.0526i | 1.09696 | + | 0.633328i | ||||
\(906\) | −31.5000 | − | 18.1865i | −1.04652 | − | 0.604207i | ||||
\(907\) | −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 | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 4.50000 | − | 18.1865i | 0.149174 | − | 0.602878i | ||||
\(911\) | −22.5000 | − | 38.9711i | −0.745458 | − | 1.29117i | −0.949980 | − | 0.312310i | \(-0.898897\pi\) |
0.204522 | − | 0.978862i | \(-0.434436\pi\) | |||||||
\(912\) | 15.0000 | 0.496700 | ||||||||
\(913\) | 18.0000 | 0.595713 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.50000 | − | 12.9904i | −0.247942 | − | 0.429449i | ||||
\(916\) | − | 8.66025i | − | 0.286143i | ||||||
\(917\) | −22.5000 | − | 12.9904i | −0.743015 | − | 0.428980i | ||||
\(918\) | −13.5000 | − | 23.3827i | −0.445566 | − | 0.771744i | ||||
\(919\) | −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 | ||||
\(921\) | −21.0000 | + | 36.3731i | −0.691974 | + | 1.19853i | ||||
\(922\) | 1.50000 | − | 2.59808i | 0.0493999 | − | 0.0855631i | ||||
\(923\) | 30.0000 | − | 8.66025i | 0.987462 | − | 0.285056i | ||||
\(924\) | −9.00000 | − | 5.19615i | −0.296078 | − | 0.170941i | ||||
\(925\) | 9.00000 | + | 5.19615i | 0.295918 | + | 0.170848i | ||||
\(926\) | −22.5000 | − | 38.9711i | −0.739396 | − | 1.28067i | ||||
\(927\) | 39.0000 | 1.28093 | ||||||||
\(928\) | 31.1769i | 1.02343i | ||||||||
\(929\) | 57.1577i | 1.87528i | 0.347604 | + | 0.937641i | \(0.386995\pi\) | ||||
−0.347604 | + | 0.937641i | \(0.613005\pi\) | |||||||
\(930\) | −22.5000 | + | 38.9711i | −0.737804 | + | 1.27791i | ||||
\(931\) | −6.00000 | − | 3.46410i | −0.196642 | − | 0.113531i | ||||
\(932\) | −9.00000 | − | 15.5885i | −0.294805 | − | 0.510617i | ||||
\(933\) | 40.5000 | − | 23.3827i | 1.32591 | − | 0.765515i | ||||
\(934\) | 18.0000 | + | 10.3923i | 0.588978 | + | 0.340047i | ||||
\(935\) | −18.0000 | −0.588663 | ||||||||
\(936\) | 4.50000 | − | 18.1865i | 0.147087 | − | 0.594445i | ||||
\(937\) | −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 | ||||
\(939\) | 32.9090i | 1.07394i | ||||||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | −13.5000 | − | 7.79423i | −0.440087 | − | 0.254085i | 0.263547 | − | 0.964646i | \(-0.415107\pi\) |
−0.703635 | + | 0.710562i | \(0.748441\pi\) | |||||||
\(942\) | −69.0000 | −2.24814 | ||||||||
\(943\) | − | 36.3731i | − | 1.18447i | ||||||
\(944\) | − | 17.3205i | − | 0.563735i | ||||||
\(945\) | −13.5000 | − | 7.79423i | −0.439155 | − | 0.253546i | ||||
\(946\) | −3.00000 | − | 5.19615i | −0.0975384 | − | 0.168941i | ||||
\(947\) | 33.0000 | + | 19.0526i | 1.07236 | + | 0.619125i | 0.928824 | − | 0.370521i | \(-0.120821\pi\) |
0.143532 | + | 0.989646i | \(0.454154\pi\) | |||||||
\(948\) | 16.5000 | − | 9.52628i | 0.535895 | − | 0.309399i | ||||
\(949\) | 18.0000 | + | 17.3205i | 0.584305 | + | 0.562247i | ||||
\(950\) | 3.00000 | − | 5.19615i | 0.0973329 | − | 0.168585i | ||||
\(951\) | 15.0000 | 0.486408 | ||||||||
\(952\) | 4.50000 | − | 7.79423i | 0.145846 | − | 0.252612i | ||||
\(953\) | −13.5000 | + | 23.3827i | −0.437308 | + | 0.757439i | −0.997481 | − | 0.0709362i | \(-0.977401\pi\) |
0.560173 | + | 0.828376i | \(0.310735\pi\) | |||||||
\(954\) | − | 31.1769i | − | 1.00939i | ||||||
\(955\) | −4.50000 | − | 2.59808i | −0.145617 | − | 0.0840718i | ||||
\(956\) | 5.19615i | 0.168056i | ||||||||
\(957\) | 36.0000 | 1.16371 | ||||||||
\(958\) | 21.0000 | + | 36.3731i | 0.678479 | + | 1.17516i | ||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | −1.50000 | − | 2.59808i | −0.0484123 | − | 0.0838525i | ||||
\(961\) | 22.0000 | + | 38.1051i | 0.709677 | + | 1.22920i | ||||
\(962\) | −22.5000 | + | 23.3827i | −0.725429 | + | 0.753888i | ||||
\(963\) | 22.5000 | − | 38.9711i | 0.725052 | − | 1.25583i | ||||
\(964\) | 4.50000 | − | 2.59808i | 0.144935 | − | 0.0836784i | ||||
\(965\) | 4.50000 | − | 7.79423i | 0.144860 | − | 0.250905i | ||||
\(966\) | 13.5000 | − | 7.79423i | 0.434355 | − | 0.250775i | ||||
\(967\) | 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 | ||||
\(969\) | −9.00000 | −0.289122 | ||||||||
\(970\) | −40.5000 | + | 23.3827i | −1.30038 | + | 0.750773i | ||||
\(971\) | 13.5000 | − | 23.3827i | 0.433236 | − | 0.750386i | −0.563914 | − | 0.825833i | \(-0.690705\pi\) |
0.997150 | + | 0.0754473i | \(0.0240385\pi\) | |||||||
\(972\) | 13.5000 | + | 7.79423i | 0.433013 | + | 0.250000i | ||||
\(973\) | −24.0000 | + | 13.8564i | −0.769405 | + | 0.444216i | ||||
\(974\) | 7.50000 | + | 12.9904i | 0.240316 | + | 0.416239i | ||||
\(975\) | −9.00000 | − | 8.66025i | −0.288231 | − | 0.277350i | ||||
\(976\) | −12.5000 | + | 21.6506i | −0.400115 | + | 0.693020i | ||||
\(977\) | 25.9808i | 0.831198i | 0.909548 | + | 0.415599i | \(0.136428\pi\) | ||||
−0.909548 | + | 0.415599i | \(0.863572\pi\) | |||||||
\(978\) | 36.3731i | 1.16308i | ||||||||
\(979\) | −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 | −0.570044 | − | 0.821614i | \(-0.693074\pi\) |
0.426517 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(984\) | 31.5000 | + | 18.1865i | 1.00418 | + | 0.579766i | ||||
\(985\) | −15.0000 | −0.477940 | ||||||||
\(986\) | − | 31.1769i | − | 0.992875i | ||||||
\(987\) | 15.5885i | 0.496186i | ||||||||
\(988\) | 4.50000 | + | 4.33013i | 0.143164 | + | 0.137760i | ||||
\(989\) | 3.00000 | 0.0953945 | ||||||||
\(990\) | 27.0000 | − | 15.5885i | 0.858116 | − | 0.495434i | ||||
\(991\) | 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 | ||||||||
\(993\) | 13.5000 | − | 23.3827i | 0.428410 | − | 0.742027i | ||||
\(994\) | −22.5000 | + | 12.9904i | −0.713657 | + | 0.412030i | ||||
\(995\) | 19.5000 | − | 11.2583i | 0.618192 | − | 0.356913i | ||||
\(996\) | 4.50000 | + | 7.79423i | 0.142588 | + | 0.246970i | ||||
\(997\) | 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 | ||||
\(999\) | 13.5000 | + | 23.3827i | 0.427121 | + | 0.739795i |
(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 | 117.2.r.a.49.1 | yes | 2 | |
3.2 | odd | 2 | 351.2.r.a.10.1 | 2 | |||
9.2 | odd | 6 | 351.2.l.a.127.1 | 2 | |||
9.7 | even | 3 | 117.2.l.a.88.1 | yes | 2 | ||
13.4 | even | 6 | 117.2.l.a.4.1 | ✓ | 2 | ||
39.17 | odd | 6 | 351.2.l.a.199.1 | 2 | |||
117.43 | even | 6 | inner | 117.2.r.a.43.1 | yes | 2 | |
117.56 | odd | 6 | 351.2.r.a.316.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.l.a.4.1 | ✓ | 2 | 13.4 | even | 6 | ||
117.2.l.a.88.1 | yes | 2 | 9.7 | even | 3 | ||
117.2.r.a.43.1 | yes | 2 | 117.43 | even | 6 | inner | |
117.2.r.a.49.1 | yes | 2 | 1.1 | even | 1 | trivial | |
351.2.l.a.127.1 | 2 | 9.2 | odd | 6 | |||
351.2.l.a.199.1 | 2 | 39.17 | odd | 6 | |||
351.2.r.a.10.1 | 2 | 3.2 | odd | 2 | |||
351.2.r.a.316.1 | 2 | 117.56 | odd | 6 |