Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.i (of order \(3\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 133.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.133 |
Dual form | 429.2.i.a.100.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 1.73205i | 0.258199 | + | 0.447214i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 2.00000 | − | 3.46410i | 0.447214 | − | 0.774597i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | + | 1.73205i | 0.188982 | + | 0.327327i | ||||
\(29\) | 4.00000 | + | 6.92820i | 0.742781 | + | 1.28654i | 0.951224 | + | 0.308500i | \(0.0998271\pi\) |
−0.208443 | + | 0.978035i | \(0.566840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 1.73205i | −0.169031 | + | 0.292770i | ||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | −5.00000 | − | 8.66025i | −0.821995 | − | 1.42374i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
0.0821995 | − | 0.996616i | \(-0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 3.46410i | 0.160128 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | + | 6.92820i | 0.624695 | + | 1.08200i | 0.988600 | + | 0.150567i | \(0.0481100\pi\) |
−0.363905 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | − | 6.06218i | 0.533745 | − | 0.924473i | −0.465478 | − | 0.885059i | \(-0.654118\pi\) |
0.999223 | − | 0.0394140i | \(-0.0125491\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 2.00000 | − | 3.46410i | 0.288675 | − | 0.500000i | ||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 5.00000 | − | 5.19615i | 0.693375 | − | 0.720577i | ||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | + | 6.92820i | −0.520756 | + | 0.901975i | 0.478953 | + | 0.877841i | \(0.341016\pi\) |
−0.999709 | + | 0.0241347i | \(0.992317\pi\) | |||||||
\(60\) | 4.00000 | 0.516398 | ||||||||
\(61\) | −6.50000 | + | 11.2583i | −0.832240 | + | 1.44148i | 0.0640184 | + | 0.997949i | \(0.479608\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 7.00000 | + | 1.73205i | 0.868243 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 2.00000 | − | 3.46410i | 0.240772 | − | 0.417029i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0000 | −1.52153 | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −4.00000 | − | 6.92820i | −0.458831 | − | 0.794719i | ||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | −0.787562 | −0.393781 | − | 0.919204i | \(-0.628833\pi\) | ||||
−0.393781 | + | 0.919204i | \(0.628833\pi\) | |||||||
\(80\) | −4.00000 | − | 6.92820i | −0.447214 | − | 0.774597i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −1.00000 | + | 1.73205i | −0.109109 | + | 0.188982i | ||||
\(85\) | −2.00000 | + | 3.46410i | −0.216930 | + | 0.375735i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.00000 | + | 6.92820i | −0.428845 | + | 0.742781i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.00000 | − | 6.92820i | −0.423999 | − | 0.734388i | 0.572327 | − | 0.820025i | \(-0.306041\pi\) |
−0.996326 | + | 0.0856373i | \(0.972707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 2.59808i | −0.262071 | + | 0.272352i | ||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.50000 | − | 6.06218i | 0.355371 | − | 0.615521i | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.00000 | + | 1.73205i | −0.100000 | + | 0.173205i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0000 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | −1.00000 | + | 1.73205i | −0.0962250 | + | 0.166667i | ||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | − | 8.66025i | 0.474579 | − | 0.821995i | ||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | −8.00000 | + | 13.8564i | −0.752577 | + | 1.30350i | 0.193993 | + | 0.981003i | \(0.437856\pi\) |
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | 16.0000 | 1.48556 | ||||||||
\(117\) | −2.50000 | + | 2.59808i | −0.231125 | + | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | − | 1.73205i | −0.0916698 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | + | 6.92820i | −0.360668 | + | 0.624695i | ||||
\(124\) | −3.00000 | + | 5.19615i | −0.269408 | + | 0.466628i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.500000 | − | 0.866025i | −0.0443678 | − | 0.0768473i | 0.842989 | − | 0.537931i | \(-0.180794\pi\) |
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.00000 | 0.616316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 1.00000 | + | 1.73205i | 0.0870388 | + | 0.150756i | ||||
\(133\) | 2.00000 | + | 3.46410i | 0.173422 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 2.00000 | + | 3.46410i | 0.169031 | + | 0.292770i | ||||
\(141\) | 4.00000 | + | 6.92820i | 0.336861 | + | 0.583460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | + | 3.46410i | 0.0836242 | + | 0.289683i | ||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 8.00000 | + | 13.8564i | 0.664364 | + | 1.15071i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | + | 5.19615i | −0.247436 | + | 0.428571i | ||||
\(148\) | −20.0000 | −1.64399 | ||||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | − | 1.73205i | −0.0808452 | − | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 7.00000 | + | 1.73205i | 0.560449 | + | 0.138675i | ||||
\(157\) | 23.0000 | 1.83560 | 0.917800 | − | 0.397043i | \(-0.129964\pi\) | ||||
0.917800 | + | 0.397043i | \(0.129964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.00000 | − | 8.66025i | −0.396526 | − | 0.686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 16.0000 | 1.24939 | ||||||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.00000 | + | 12.1244i | 0.541676 | + | 0.938211i | 0.998808 | + | 0.0488118i | \(0.0155435\pi\) |
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 3.46410i | 0.152944 | + | 0.264906i | ||||
\(172\) | −7.00000 | − | 12.1244i | −0.533745 | − | 0.924473i | ||||
\(173\) | −5.00000 | + | 8.66025i | −0.380143 | + | 0.658427i | −0.991082 | − | 0.133250i | \(-0.957459\pi\) |
0.610939 | + | 0.791677i | \(0.290792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | + | 20.7846i | 0.896922 | + | 1.55351i | 0.831408 | + | 0.555663i | \(0.187536\pi\) |
0.0655145 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(180\) | 2.00000 | + | 3.46410i | 0.149071 | + | 0.258199i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0000 | − | 17.3205i | −0.735215 | − | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 8.00000 | − | 13.8564i | 0.583460 | − | 1.01058i | ||||
\(189\) | 0.500000 | − | 0.866025i | 0.0363696 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −4.00000 | − | 6.92820i | −0.288675 | − | 0.500000i | ||||
\(193\) | 1.50000 | + | 2.59808i | 0.107972 | + | 0.187014i | 0.914949 | − | 0.403570i | \(-0.132231\pi\) |
−0.806976 | + | 0.590584i | \(0.798898\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000 | + | 6.92820i | 0.143223 | + | 0.496139i | ||||
\(196\) | 12.0000 | 0.857143 | ||||||||
\(197\) | −10.0000 | − | 17.3205i | −0.712470 | − | 1.23404i | −0.963927 | − | 0.266167i | \(-0.914243\pi\) |
0.251457 | − | 0.967869i | \(-0.419090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.50000 | − | 9.52628i | 0.387940 | − | 0.671932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 8.00000 | + | 13.8564i | 0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | −4.00000 | − | 13.8564i | −0.277350 | − | 0.960769i | ||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.50000 | + | 12.9904i | 0.516321 | + | 0.894295i | 0.999820 | + | 0.0189499i | \(0.00603229\pi\) |
−0.483499 | + | 0.875345i | \(0.660634\pi\) | |||||||
\(212\) | −10.0000 | + | 17.3205i | −0.686803 | + | 1.18958i | ||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.00000 | − | 12.1244i | 0.477396 | − | 0.826874i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | − | 2.59808i | 0.101827 | − | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.50000 | − | 11.2583i | −0.439229 | − | 0.760767i | ||||
\(220\) | 4.00000 | 0.269680 | ||||||||
\(221\) | −5.00000 | + | 5.19615i | −0.336336 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | − | 20.7846i | 0.796468 | − | 1.37952i | −0.125435 | − | 0.992102i | \(-0.540033\pi\) |
0.921903 | − | 0.387421i | \(-0.126634\pi\) | |||||||
\(228\) | 4.00000 | − | 6.92820i | 0.264906 | − | 0.458831i | ||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.500000 | − | 0.866025i | −0.0328976 | − | 0.0569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.00000 | 0.524097 | 0.262049 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262049 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 8.00000 | + | 13.8564i | 0.520756 | + | 0.901975i | ||||
\(237\) | −3.50000 | − | 6.06218i | −0.227349 | − | 0.393781i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | 4.00000 | − | 6.92820i | 0.258199 | − | 0.447214i | ||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 13.0000 | + | 22.5167i | 0.832240 | + | 1.44148i | ||||
\(245\) | 6.00000 | + | 10.3923i | 0.383326 | + | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | − | 10.3923i | 0.636285 | − | 0.661247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | − | 15.5885i | 0.568075 | − | 0.983935i | −0.428681 | − | 0.903456i | \(-0.641022\pi\) |
0.996756 | − | 0.0804789i | \(-0.0256450\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 2.00000 | − | 3.46410i | 0.125739 | − | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000 | 0.621370 | ||||||||
\(260\) | 10.0000 | − | 10.3923i | 0.620174 | − | 0.644503i | ||||
\(261\) | −8.00000 | −0.495188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 5.19615i | 0.184988 | + | 0.320408i | 0.943572 | − | 0.331166i | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.0000 | −1.22859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000 | − | 6.92820i | 0.244796 | − | 0.423999i | ||||
\(268\) | −22.0000 | −1.34386 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.50000 | + | 14.7224i | 0.516338 | + | 0.894324i | 0.999820 | + | 0.0189696i | \(0.00603859\pi\) |
−0.483482 | + | 0.875354i | \(0.660628\pi\) | |||||||
\(272\) | 8.00000 | 0.485071 | ||||||||
\(273\) | −3.50000 | − | 0.866025i | −0.211830 | − | 0.0524142i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | −4.00000 | − | 6.92820i | −0.240772 | − | 0.417029i | ||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50000 | − | 2.59808i | 0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.50000 | + | 2.59808i | 0.0891657 | + | 0.154440i | 0.907159 | − | 0.420789i | \(-0.138247\pi\) |
−0.817993 | + | 0.575228i | \(0.804913\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.00000 | 0.410347 | ||||||||
\(292\) | −13.0000 | + | 22.5167i | −0.760767 | + | 1.31769i | ||||
\(293\) | 8.00000 | − | 13.8564i | 0.467365 | − | 0.809500i | −0.531940 | − | 0.846782i | \(-0.678537\pi\) |
0.999305 | + | 0.0372823i | \(0.0118701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | + | 13.8564i | −0.465778 | + | 0.806751i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | − | 13.8564i | −0.231326 | − | 0.801337i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 3.50000 | + | 6.06218i | 0.201737 | + | 0.349418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | + | 5.19615i | −0.172345 | + | 0.298511i | ||||
\(304\) | −16.0000 | −0.917663 | ||||||||
\(305\) | −13.0000 | + | 22.5167i | −0.744378 | + | 1.28930i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.00000 | 0.513657 | 0.256829 | − | 0.966457i | \(-0.417322\pi\) | ||||
0.256829 | + | 0.966457i | \(0.417322\pi\) | |||||||
\(308\) | −1.00000 | + | 1.73205i | −0.0569803 | + | 0.0986928i | ||||
\(309\) | 5.50000 | + | 9.52628i | 0.312884 | + | 0.541931i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.00000 | −0.508710 | −0.254355 | − | 0.967111i | \(-0.581863\pi\) | ||||
−0.254355 | + | 0.967111i | \(0.581863\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | − | 1.73205i | −0.0563436 | − | 0.0975900i | ||||
\(316\) | −7.00000 | + | 12.1244i | −0.393781 | + | 0.682048i | ||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | −16.0000 | −0.894427 | ||||||||
\(321\) | 4.00000 | − | 6.92820i | 0.223258 | − | 0.386695i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | + | 6.92820i | 0.222566 | + | 0.385496i | ||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | −3.50000 | − | 0.866025i | −0.194145 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.50000 | − | 4.33013i | −0.138250 | − | 0.239457i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | + | 6.92820i | −0.220527 | + | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.5000 | − | 19.9186i | 0.632097 | − | 1.09482i | −0.355025 | − | 0.934857i | \(-0.615528\pi\) |
0.987122 | − | 0.159968i | \(-0.0511390\pi\) | |||||||
\(332\) | −6.00000 | + | 10.3923i | −0.329293 | + | 0.570352i | ||||
\(333\) | 10.0000 | 0.547997 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0000 | − | 19.0526i | −0.600994 | − | 1.04095i | ||||
\(336\) | 2.00000 | + | 3.46410i | 0.109109 | + | 0.188982i | ||||
\(337\) | 7.00000 | 0.381314 | 0.190657 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190657 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0000 | −0.869001 | ||||||||
\(340\) | 4.00000 | + | 6.92820i | 0.216930 | + | 0.375735i | ||||
\(341\) | −1.50000 | − | 2.59808i | −0.0812296 | − | 0.140694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | − | 6.92820i | 0.215353 | − | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00000 | − | 15.5885i | 0.483145 | − | 0.836832i | −0.516667 | − | 0.856186i | \(-0.672828\pi\) |
0.999813 | + | 0.0193540i | \(0.00616095\pi\) | |||||||
\(348\) | 8.00000 | + | 13.8564i | 0.428845 | + | 0.742781i | ||||
\(349\) | 5.50000 | + | 9.52628i | 0.294408 | + | 0.509930i | 0.974847 | − | 0.222875i | \(-0.0715441\pi\) |
−0.680439 | + | 0.732805i | \(0.738211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.50000 | − | 0.866025i | −0.186816 | − | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 10.3923i | 0.318447 | − | 0.551566i | ||||
\(356\) | −16.0000 | −0.847998 | ||||||||
\(357\) | 1.00000 | − | 1.73205i | 0.0529256 | − | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 2.00000 | + | 6.92820i | 0.104828 | + | 0.363137i | ||||
\(365\) | −26.0000 | −1.36090 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.50000 | − | 7.79423i | −0.234898 | − | 0.406855i | 0.724345 | − | 0.689438i | \(-0.242142\pi\) |
−0.959243 | + | 0.282582i | \(0.908809\pi\) | |||||||
\(368\) | −8.00000 | + | 13.8564i | −0.417029 | + | 0.722315i | ||||
\(369\) | −8.00000 | −0.416463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.00000 | − | 8.66025i | 0.259587 | − | 0.449618i | ||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | −14.5000 | + | 25.1147i | −0.750782 | + | 1.30039i | 0.196663 | + | 0.980471i | \(0.436990\pi\) |
−0.947444 | + | 0.319921i | \(0.896344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | + | 27.7128i | 0.412021 | + | 1.42728i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5000 | + | 25.1147i | 0.744815 | + | 1.29006i | 0.950281 | + | 0.311393i | \(0.100796\pi\) |
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | −8.00000 | − | 13.8564i | −0.410391 | − | 0.710819i | ||||
\(381\) | 0.500000 | − | 0.866025i | 0.0256158 | − | 0.0443678i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | − | 13.8564i | 0.408781 | − | 0.708029i | −0.585973 | − | 0.810331i | \(-0.699287\pi\) |
0.994753 | + | 0.102302i | \(0.0326207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.50000 | + | 6.06218i | 0.177915 | + | 0.308158i | ||||
\(388\) | −7.00000 | − | 12.1244i | −0.355371 | − | 0.615521i | ||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | − | 15.5885i | −0.453990 | − | 0.786334i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0000 | −0.704416 | ||||||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.50000 | + | 2.59808i | −0.0752828 | + | 0.130394i | −0.901209 | − | 0.433384i | \(-0.857319\pi\) |
0.825926 | + | 0.563778i | \(0.190653\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.5000 | − | 2.59808i | −0.523042 | − | 0.129419i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | −1.00000 | − | 1.73205i | −0.0496904 | − | 0.0860663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.00000 | − | 8.66025i | 0.247841 | − | 0.429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5000 | − | 28.5788i | 0.815872 | − | 1.41313i | −0.0928272 | − | 0.995682i | \(-0.529590\pi\) |
0.908700 | − | 0.417450i | \(-0.137076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 11.0000 | − | 19.0526i | 0.541931 | − | 0.938652i | ||||
\(413\) | −4.00000 | − | 6.92820i | −0.196827 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.00000 | 0.440732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0000 | − | 22.5167i | −0.635092 | − | 1.10001i | −0.986496 | − | 0.163787i | \(-0.947629\pi\) |
0.351404 | − | 0.936224i | \(-0.385704\pi\) | |||||||
\(420\) | −2.00000 | + | 3.46410i | −0.0975900 | + | 0.169031i | ||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.00000 | + | 6.92820i | −0.194487 | + | 0.336861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50000 | − | 11.2583i | −0.314557 | − | 0.544829i | ||||
\(428\) | −16.0000 | −0.773389 | ||||||||
\(429\) | −2.50000 | + | 2.59808i | −0.120701 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0000 | + | 19.0526i | 0.529851 | + | 0.917729i | 0.999394 | + | 0.0348195i | \(0.0110856\pi\) |
−0.469542 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | 10.5000 | − | 18.1865i | 0.504598 | − | 0.873989i | −0.495388 | − | 0.868672i | \(-0.664974\pi\) |
0.999986 | − | 0.00531724i | \(-0.00169254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | + | 13.8564i | −0.383571 | + | 0.664364i | ||||
\(436\) | −5.00000 | + | 8.66025i | −0.239457 | + | 0.414751i | ||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5000 | − | 18.1865i | −0.501138 | − | 0.867996i | −0.999999 | − | 0.00131415i | \(-0.999582\pi\) |
0.498861 | − | 0.866682i | \(-0.333752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | −10.0000 | − | 17.3205i | −0.474579 | − | 0.821995i | ||||
\(445\) | −8.00000 | − | 13.8564i | −0.379236 | − | 0.656857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 4.00000 | − | 6.92820i | 0.188982 | − | 0.327327i | ||||
\(449\) | 6.00000 | − | 10.3923i | 0.283158 | − | 0.490443i | −0.689003 | − | 0.724758i | \(-0.741951\pi\) |
0.972161 | + | 0.234315i | \(0.0752847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | + | 6.92820i | −0.188353 | + | 0.326236i | ||||
\(452\) | 16.0000 | + | 27.7128i | 0.752577 | + | 1.30350i | ||||
\(453\) | 2.00000 | + | 3.46410i | 0.0939682 | + | 0.162758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.00000 | + | 5.19615i | −0.234404 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.5000 | + | 32.0429i | 0.865393 | + | 1.49891i | 0.866656 | + | 0.498906i | \(0.166265\pi\) |
−0.00126243 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | −16.0000 | −0.746004 | ||||||||
\(461\) | 1.00000 | − | 1.73205i | 0.0465746 | − | 0.0806696i | −0.841798 | − | 0.539792i | \(-0.818503\pi\) |
0.888373 | + | 0.459123i | \(0.151836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0000 | −1.25480 | −0.627398 | − | 0.778699i | \(-0.715880\pi\) | ||||
−0.627398 | + | 0.778699i | \(0.715880\pi\) | |||||||
\(464\) | 16.0000 | − | 27.7128i | 0.742781 | − | 1.28654i | ||||
\(465\) | −3.00000 | − | 5.19615i | −0.139122 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.00000 | −0.0925490 | −0.0462745 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462745 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(468\) | 2.00000 | + | 6.92820i | 0.0924500 | + | 0.320256i | ||||
\(469\) | 11.0000 | 0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5000 | + | 19.9186i | 0.529892 | + | 0.917800i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.00000 | 0.321860 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | 5.00000 | − | 8.66025i | 0.228934 | − | 0.396526i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0000 | − | 34.6410i | −0.455961 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.00000 | + | 3.46410i | 0.0910032 | + | 0.157622i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 7.00000 | − | 12.1244i | 0.317854 | − | 0.550539i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | − | 27.7128i | 0.725029 | − | 1.25579i | −0.233933 | − | 0.972253i | \(-0.575160\pi\) |
0.958962 | − | 0.283535i | \(-0.0915071\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0000 | + | 25.9808i | 0.676941 | + | 1.17250i | 0.975898 | + | 0.218229i | \(0.0700279\pi\) |
−0.298957 | + | 0.954267i | \(0.596639\pi\) | |||||||
\(492\) | 8.00000 | + | 13.8564i | 0.360668 | + | 0.624695i | ||||
\(493\) | −16.0000 | −0.720604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 6.00000 | + | 10.3923i | 0.269408 | + | 0.466628i | ||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | −12.0000 | + | 20.7846i | −0.536656 | + | 0.929516i | ||||
\(501\) | −7.00000 | + | 12.1244i | −0.312737 | + | 0.541676i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0000 | + | 31.1769i | −0.802580 | + | 1.39011i | 0.115332 | + | 0.993327i | \(0.463207\pi\) |
−0.917912 | + | 0.396783i | \(0.870127\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | + | 10.3923i | 0.266996 | + | 0.462451i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.500000 | + | 12.9904i | 0.0222058 | + | 0.576923i | ||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.50000 | − | 11.2583i | 0.287543 | − | 0.498039i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0000 | 0.969436 | ||||||||
\(516\) | 7.00000 | − | 12.1244i | 0.308158 | − | 0.533745i | ||||
\(517\) | 4.00000 | + | 6.92820i | 0.175920 | + | 0.304702i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.0000 | −0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | −18.0000 | + | 31.1769i | −0.786334 | + | 1.36197i | ||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | − | 6.92820i | −0.173585 | − | 0.300658i | ||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | 8.00000 | + | 27.7128i | 0.346518 | + | 1.20038i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | − | 13.8564i | −0.345870 | − | 0.599065i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | + | 20.7846i | −0.517838 | + | 0.896922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.00000 | + | 5.19615i | −0.129219 | + | 0.223814i | ||||
\(540\) | −2.00000 | + | 3.46410i | −0.0860663 | + | 0.149071i | ||||
\(541\) | −21.0000 | −0.902861 | −0.451430 | − | 0.892306i | \(-0.649086\pi\) | ||||
−0.451430 | + | 0.892306i | \(0.649086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00000 | − | 1.73205i | −0.0429141 | − | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | −0.0213785 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | −2.00000 | − | 3.46410i | −0.0854358 | − | 0.147979i | ||||
\(549\) | −6.50000 | − | 11.2583i | −0.277413 | − | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.0000 | 1.36325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.50000 | − | 6.06218i | 0.148835 | − | 0.257790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.0000 | − | 17.3205i | 0.424476 | − | 0.735215i | ||||
\(556\) | −9.00000 | − | 15.5885i | −0.381685 | − | 0.661098i | ||||
\(557\) | 3.00000 | + | 5.19615i | 0.127114 | + | 0.220168i | 0.922557 | − | 0.385860i | \(-0.126095\pi\) |
−0.795443 | + | 0.606028i | \(0.792762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5000 | − | 18.1865i | 0.740171 | − | 0.769208i | ||||
\(560\) | 8.00000 | 0.338062 | ||||||||
\(561\) | −1.00000 | − | 1.73205i | −0.0422200 | − | 0.0731272i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | 16.0000 | 0.673722 | ||||||||
\(565\) | −16.0000 | + | 27.7128i | −0.673125 | + | 1.16589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 7.00000 | + | 1.73205i | 0.292685 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.00000 | + | 3.46410i | 0.0834058 | + | 0.144463i | ||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50000 | + | 2.59808i | −0.0623379 | + | 0.107972i | ||||
\(580\) | 32.0000 | 1.32873 | ||||||||
\(581\) | 3.00000 | − | 5.19615i | 0.124461 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.00000 | − | 8.66025i | −0.207079 | − | 0.358671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.00000 | + | 5.19615i | −0.206725 | + | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000 | + | 20.7846i | 0.495293 | + | 0.857873i | 0.999985 | − | 0.00542667i | \(-0.00172737\pi\) |
−0.504692 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(588\) | 6.00000 | + | 10.3923i | 0.247436 | + | 0.428571i | ||||
\(589\) | −6.00000 | + | 10.3923i | −0.247226 | + | 0.428207i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | − | 17.3205i | 0.411345 | − | 0.712470i | ||||
\(592\) | −20.0000 | + | 34.6410i | −0.821995 | + | 1.42374i | ||||
\(593\) | 36.0000 | 1.47834 | 0.739171 | − | 0.673517i | \(-0.235217\pi\) | ||||
0.739171 | + | 0.673517i | \(0.235217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | − | 3.46410i | −0.0819920 | − | 0.142014i | ||||
\(596\) | −10.0000 | − | 17.3205i | −0.409616 | − | 0.709476i | ||||
\(597\) | 7.00000 | 0.286491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0000 | + | 39.8372i | 0.938190 | + | 1.62499i | 0.768845 | + | 0.639435i | \(0.220832\pi\) |
0.169344 | + | 0.985557i | \(0.445835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.0000 | 0.447955 | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.00000 | − | 6.92820i | −0.162088 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.0000 | + | 6.92820i | 1.13276 | + | 0.280285i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | −6.50000 | − | 11.2583i | −0.262533 | − | 0.454720i | 0.704382 | − | 0.709821i | \(-0.251224\pi\) |
−0.966914 | + | 0.255102i | \(0.917891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | + | 13.8564i | −0.322591 | + | 0.558744i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | + | 20.7846i | −0.483102 | + | 0.836757i | −0.999812 | − | 0.0194037i | \(-0.993823\pi\) |
0.516710 | + | 0.856161i | \(0.327157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0000 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | −6.00000 | + | 10.3923i | −0.240966 | + | 0.417365i | ||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.00000 | 0.320513 | ||||||||
\(624\) | 10.0000 | − | 10.3923i | 0.400320 | − | 0.416025i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000 | + | 3.46410i | 0.0798723 | + | 0.138343i | ||||
\(628\) | 23.0000 | − | 39.8372i | 0.917800 | − | 1.58968i | ||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5000 | − | 28.5788i | 0.656855 | − | 1.13771i | −0.324571 | − | 0.945861i | \(-0.605220\pi\) |
0.981425 | − | 0.191844i | \(-0.0614468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.50000 | + | 12.9904i | −0.298098 | + | 0.516321i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00000 | − | 1.73205i | −0.0396838 | − | 0.0687343i | ||||
\(636\) | −20.0000 | −0.793052 | ||||||||
\(637\) | 6.00000 | + | 20.7846i | 0.237729 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0000 | − | 41.5692i | 0.947943 | − | 1.64189i | 0.198194 | − | 0.980163i | \(-0.436492\pi\) |
0.749749 | − | 0.661723i | \(-0.230174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5000 | − | 32.0429i | 0.729569 | − | 1.26365i | −0.227497 | − | 0.973779i | \(-0.573054\pi\) |
0.957066 | − | 0.289871i | \(-0.0936125\pi\) | |||||||
\(644\) | 4.00000 | − | 6.92820i | 0.157622 | − | 0.273009i | ||||
\(645\) | 14.0000 | 0.551249 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00000 | − | 15.5885i | −0.353827 | − | 0.612845i | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.00000 | 0.117579 | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | −13.0000 | − | 22.5167i | −0.508729 | − | 0.881145i | −0.999949 | − | 0.0101092i | \(-0.996782\pi\) |
0.491220 | − | 0.871036i | \(-0.336551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | −1.40664 | ||||||||
\(656\) | 16.0000 | − | 27.7128i | 0.624695 | − | 1.08200i | ||||
\(657\) | 6.50000 | − | 11.2583i | 0.253589 | − | 0.439229i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.00000 | + | 3.46410i | −0.0779089 | + | 0.134942i | −0.902348 | − | 0.431009i | \(-0.858158\pi\) |
0.824439 | + | 0.565951i | \(0.191491\pi\) | |||||||
\(660\) | 2.00000 | + | 3.46410i | 0.0778499 | + | 0.134840i | ||||
\(661\) | 8.50000 | + | 14.7224i | 0.330612 | + | 0.572636i | 0.982632 | − | 0.185565i | \(-0.0594116\pi\) |
−0.652020 | + | 0.758202i | \(0.726078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.00000 | − | 1.73205i | −0.271857 | − | 0.0672673i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000 | + | 6.92820i | 0.155113 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | − | 27.7128i | 0.619522 | − | 1.07304i | ||||
\(668\) | 28.0000 | 1.08335 | ||||||||
\(669\) | −2.00000 | + | 3.46410i | −0.0773245 | + | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0000 | −0.501859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.5000 | − | 42.4352i | −0.944406 | − | 1.63576i | −0.756937 | − | 0.653488i | \(-0.773305\pi\) |
−0.187469 | − | 0.982271i | \(-0.560028\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 22.0000 | − | 13.8564i | 0.846154 | − | 0.532939i | ||||
\(677\) | 30.0000 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | + | 6.06218i | 0.134318 | + | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000 | 0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.0000 | + | 22.5167i | −0.497431 | + | 0.861576i | −0.999996 | − | 0.00296369i | \(-0.999057\pi\) |
0.502564 | + | 0.864540i | \(0.332390\pi\) | |||||||
\(684\) | 8.00000 | 0.305888 | ||||||||
\(685\) | 2.00000 | − | 3.46410i | 0.0764161 | − | 0.132357i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.00000 | + | 5.19615i | 0.114457 | + | 0.198246i | ||||
\(688\) | −28.0000 | −1.06749 | ||||||||
\(689\) | −35.0000 | − | 8.66025i | −1.33339 | − | 0.329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50000 | + | 2.59808i | 0.0570627 | + | 0.0988355i | 0.893146 | − | 0.449768i | \(-0.148493\pi\) |
−0.836083 | + | 0.548603i | \(0.815160\pi\) | |||||||
\(692\) | 10.0000 | + | 17.3205i | 0.380143 | + | 0.658427i | ||||
\(693\) | 0.500000 | − | 0.866025i | 0.0189934 | − | 0.0328976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.00000 | − | 15.5885i | 0.341389 | − | 0.591304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.00000 | + | 6.92820i | 0.151294 | + | 0.262049i | ||||
\(700\) | −1.00000 | − | 1.73205i | −0.0377964 | − | 0.0654654i | ||||
\(701\) | 38.0000 | 1.43524 | 0.717620 | − | 0.696435i | \(-0.245231\pi\) | ||||
0.717620 | + | 0.696435i | \(0.245231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.0000 | −1.50863 | ||||||||
\(704\) | −4.00000 | − | 6.92820i | −0.150756 | − | 0.261116i | ||||
\(705\) | 8.00000 | + | 13.8564i | 0.301297 | + | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | −8.00000 | + | 13.8564i | −0.300658 | + | 0.520756i | ||||
\(709\) | −6.50000 | + | 11.2583i | −0.244113 | + | 0.422815i | −0.961882 | − | 0.273466i | \(-0.911830\pi\) |
0.717769 | + | 0.696281i | \(0.245163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50000 | − | 6.06218i | 0.131260 | − | 0.227349i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | + | 6.92820i | 0.0747958 | + | 0.259100i | ||||
\(716\) | 48.0000 | 1.79384 | ||||||||
\(717\) | −9.00000 | − | 15.5885i | −0.336111 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.00000 | + | 13.8564i | −0.298350 | + | 0.516757i | −0.975759 | − | 0.218850i | \(-0.929769\pi\) |
0.677409 | + | 0.735607i | \(0.263103\pi\) | |||||||
\(720\) | 8.00000 | 0.298142 | ||||||||
\(721\) | −5.50000 | + | 9.52628i | −0.204831 | + | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000 | 0.371904 | ||||||||
\(724\) | −2.00000 | + | 3.46410i | −0.0743294 | + | 0.128742i | ||||
\(725\) | −4.00000 | − | 6.92820i | −0.148556 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.00000 | −0.185440 | −0.0927199 | − | 0.995692i | \(-0.529556\pi\) | ||||
−0.0927199 | + | 0.995692i | \(0.529556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.00000 | + | 12.1244i | 0.258904 | + | 0.448435i | ||||
\(732\) | −13.0000 | + | 22.5167i | −0.480494 | + | 0.832240i | ||||
\(733\) | −1.00000 | −0.0369358 | −0.0184679 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184679 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.00000 | + | 10.3923i | −0.221313 | + | 0.383326i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.50000 | − | 9.52628i | 0.202595 | − | 0.350905i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0000 | + | 17.3205i | 0.367856 | + | 0.637145i | 0.989230 | − | 0.146369i | \(-0.0467586\pi\) |
−0.621374 | + | 0.783514i | \(0.713425\pi\) | |||||||
\(740\) | −40.0000 | −1.47043 | ||||||||
\(741\) | 14.0000 | + | 3.46410i | 0.514303 | + | 0.127257i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0000 | − | 17.3205i | 0.366372 | − | 0.634574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.00000 | − | 5.19615i | 0.109764 | − | 0.190117i | ||||
\(748\) | −2.00000 | + | 3.46410i | −0.0731272 | + | 0.126660i | ||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | − | 41.5692i | −0.875772 | − | 1.51688i | −0.855938 | − | 0.517079i | \(-0.827019\pi\) |
−0.0198348 | − | 0.999803i | \(-0.506314\pi\) | |||||||
\(752\) | −16.0000 | − | 27.7128i | −0.583460 | − | 1.01058i | ||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | −1.00000 | − | 1.73205i | −0.0363696 | − | 0.0629941i | ||||
\(757\) | 27.0000 | + | 46.7654i | 0.981332 | + | 1.69972i | 0.657222 | + | 0.753697i | \(0.271731\pi\) |
0.324109 | + | 0.946020i | \(0.394935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.00000 | + | 12.1244i | −0.253750 | + | 0.439508i | −0.964555 | − | 0.263881i | \(-0.914997\pi\) |
0.710805 | + | 0.703389i | \(0.248331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.50000 | − | 4.33013i | 0.0905061 | − | 0.156761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | − | 3.46410i | −0.0723102 | − | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.0000 | + | 20.7846i | −0.722158 | + | 0.750489i | ||||
\(768\) | −16.0000 | −0.577350 | ||||||||
\(769\) | 15.0000 | + | 25.9808i | 0.540914 | + | 0.936890i | 0.998852 | + | 0.0479061i | \(0.0152548\pi\) |
−0.457938 | + | 0.888984i | \(0.651412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | + | 10.3923i | −0.216085 | + | 0.374270i | ||||
\(772\) | 6.00000 | 0.215945 | ||||||||
\(773\) | −15.0000 | + | 25.9808i | −0.539513 | + | 0.934463i | 0.459418 | + | 0.888220i | \(0.348058\pi\) |
−0.998930 | + | 0.0462427i | \(0.985275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | 0.107763 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00000 | + | 8.66025i | 0.179374 | + | 0.310685i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.0000 | 1.14652 | ||||||||
\(780\) | 14.0000 | + | 3.46410i | 0.501280 | + | 0.124035i | ||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.00000 | − | 6.92820i | −0.142948 | − | 0.247594i | ||||
\(784\) | 12.0000 | − | 20.7846i | 0.428571 | − | 0.742307i | ||||
\(785\) | 46.0000 | 1.64181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5000 | − | 44.1673i | 0.908977 | − | 1.57439i | 0.0934886 | − | 0.995620i | \(-0.470198\pi\) |
0.815488 | − | 0.578774i | \(-0.196469\pi\) | |||||||
\(788\) | −40.0000 | −1.42494 | ||||||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.00000 | − | 13.8564i | −0.284447 | − | 0.492677i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.5000 | + | 33.7750i | −1.15411 | + | 1.19939i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.0000 | − | 17.3205i | −0.354663 | − | 0.614295i | ||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | −13.0000 | + | 22.5167i | −0.460484 | + | 0.797581i | −0.998985 | − | 0.0450436i | \(-0.985657\pi\) |
0.538501 | + | 0.842625i | \(0.318991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | + | 13.8564i | −0.283020 | + | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | 0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.50000 | − | 11.2583i | −0.229380 | − | 0.397298i | ||||
\(804\) | −11.0000 | − | 19.0526i | −0.387940 | − | 0.671932i | ||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | − | 10.3923i | −0.210949 | − | 0.365374i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.0000 | −1.58016 | −0.790082 | − | 0.613001i | \(-0.789962\pi\) | ||||
−0.790082 | + | 0.613001i | \(0.789962\pi\) | |||||||
\(812\) | −8.00000 | + | 13.8564i | −0.280745 | + | 0.486265i | ||||
\(813\) | −8.50000 | + | 14.7224i | −0.298108 | + | 0.516338i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000 | − | 1.73205i | 0.0350285 | − | 0.0606711i | ||||
\(816\) | 4.00000 | + | 6.92820i | 0.140028 | + | 0.242536i | ||||
\(817\) | −14.0000 | − | 24.2487i | −0.489798 | − | 0.848355i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | − | 3.46410i | −0.0349428 | − | 0.121046i | ||||
\(820\) | 32.0000 | 1.11749 | ||||||||
\(821\) | −27.0000 | − | 46.7654i | −0.942306 | − | 1.63212i | −0.761056 | − | 0.648686i | \(-0.775319\pi\) |
−0.181250 | − | 0.983437i | \(-0.558014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0000 | + | 24.2487i | −0.488009 | + | 0.845257i | −0.999905 | − | 0.0137907i | \(-0.995610\pi\) |
0.511896 | + | 0.859048i | \(0.328943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.500000 | − | 0.866025i | 0.0174078 | − | 0.0301511i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0000 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(828\) | 4.00000 | − | 6.92820i | 0.139010 | − | 0.240772i | ||||
\(829\) | −14.5000 | − | 25.1147i | −0.503606 | − | 0.872271i | −0.999991 | − | 0.00416865i | \(-0.998673\pi\) |
0.496385 | − | 0.868102i | \(-0.334660\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | −28.0000 | − | 6.92820i | −0.970725 | − | 0.240192i | ||||
\(833\) | −12.0000 | −0.415775 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.0000 | + | 24.2487i | 0.484490 | + | 0.839161i | ||||
\(836\) | 4.00000 | − | 6.92820i | 0.138343 | − | 0.239617i | ||||
\(837\) | 3.00000 | 0.103695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.0000 | + | 43.3013i | −0.863096 | + | 1.49493i | 0.00582968 | + | 0.999983i | \(0.498144\pi\) |
−0.868926 | + | 0.494943i | \(0.835189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | + | 30.3109i | −0.603448 | + | 1.04520i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | + | 20.7846i | 0.413302 | + | 0.715860i | ||||
\(844\) | 30.0000 | 1.03264 | ||||||||
\(845\) | 23.0000 | + | 12.1244i | 0.791224 | + | 0.417091i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.500000 | − | 0.866025i | −0.0171802 | − | 0.0297570i | ||||
\(848\) | 20.0000 | + | 34.6410i | 0.686803 | + | 1.18958i | ||||
\(849\) | −1.50000 | + | 2.59808i | −0.0514799 | + | 0.0891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0000 | + | 34.6410i | −0.685591 | + | 1.18748i | ||||
\(852\) | 6.00000 | − | 10.3923i | 0.205557 | − | 0.356034i | ||||
\(853\) | −11.0000 | −0.376633 | −0.188316 | − | 0.982108i | \(-0.560303\pi\) | ||||
−0.188316 | + | 0.982108i | \(0.560303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | + | 6.92820i | 0.136797 | + | 0.236940i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0000 | −0.888143 | −0.444072 | − | 0.895991i | \(-0.646466\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0000 | 1.05771 | 0.528853 | − | 0.848713i | \(-0.322622\pi\) | ||||
0.528853 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(860\) | −14.0000 | − | 24.2487i | −0.477396 | − | 0.826874i | ||||
\(861\) | −4.00000 | − | 6.92820i | −0.136320 | − | 0.236113i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.0000 | −1.02121 | −0.510606 | − | 0.859815i | \(-0.670579\pi\) | ||||
−0.510606 | + | 0.859815i | \(0.670579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | + | 17.3205i | −0.340010 | + | 0.588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.50000 | + | 11.2583i | −0.220752 | + | 0.382353i | ||||
\(868\) | −3.00000 | − | 5.19615i | −0.101827 | − | 0.176369i | ||||
\(869\) | −3.50000 | − | 6.06218i | −0.118729 | − | 0.205645i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0000 | − | 38.1051i | −0.372721 | − | 1.29114i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.50000 | + | 6.06218i | 0.118457 | + | 0.205174i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | − | 10.3923i | 0.202837 | − | 0.351324i | ||||
\(876\) | −26.0000 | −0.878459 | ||||||||
\(877\) | −19.0000 | + | 32.9090i | −0.641584 | + | 1.11126i | 0.343495 | + | 0.939155i | \(0.388389\pi\) |
−0.985079 | + | 0.172102i | \(0.944944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.0000 | 0.539667 | ||||||||
\(880\) | 4.00000 | − | 6.92820i | 0.134840 | − | 0.233550i | ||||
\(881\) | 3.00000 | + | 5.19615i | 0.101073 | + | 0.175063i | 0.912127 | − | 0.409908i | \(-0.134439\pi\) |
−0.811054 | + | 0.584971i | \(0.801106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0000 | 0.437485 | 0.218742 | − | 0.975783i | \(-0.429805\pi\) | ||||
0.218742 | + | 0.975783i | \(0.429805\pi\) | |||||||
\(884\) | 4.00000 | + | 13.8564i | 0.134535 | + | 0.466041i | ||||
\(885\) | −16.0000 | −0.537834 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | 16.0000 | − | 27.7128i | 0.535420 | − | 0.927374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | + | 41.5692i | 0.802232 | + | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.0000 | − | 10.3923i | 0.333890 | − | 0.346989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | − | 20.7846i | −0.400222 | − | 0.693206i | ||||
\(900\) | −1.00000 | − | 1.73205i | −0.0333333 | − | 0.0577350i | ||||
\(901\) | 10.0000 | − | 17.3205i | 0.333148 | − | 0.577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.50000 | + | 6.06218i | −0.116473 | + | 0.201737i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | −0.132964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0000 | − | 24.2487i | −0.464862 | − | 0.805165i | 0.534333 | − | 0.845274i | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | −24.0000 | − | 41.5692i | −0.796468 | − | 1.37952i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.0000 | 0.927681 | 0.463841 | − | 0.885919i | \(-0.346471\pi\) | ||||
0.463841 | + | 0.885919i | \(0.346471\pi\) | |||||||
\(912\) | −8.00000 | − | 13.8564i | −0.264906 | − | 0.458831i | ||||
\(913\) | −3.00000 | − | 5.19615i | −0.0992855 | − | 0.171968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.0000 | −0.859533 | ||||||||
\(916\) | 6.00000 | − | 10.3923i | 0.198246 | − | 0.343371i | ||||
\(917\) | 9.00000 | − | 15.5885i | 0.297206 | − | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0000 | + | 45.0333i | −0.857661 | + | 1.48551i | 0.0164935 | + | 0.999864i | \(0.494750\pi\) |
−0.874154 | + | 0.485648i | \(0.838584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.50000 | + | 7.79423i | 0.148280 | + | 0.256829i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.0000 | − | 15.5885i | 0.493731 | − | 0.513100i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 5.00000 | + | 8.66025i | 0.164399 | + | 0.284747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.50000 | + | 9.52628i | −0.180644 | + | 0.312884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0000 | + | 41.5692i | −0.787414 | + | 1.36384i | 0.140132 | + | 0.990133i | \(0.455247\pi\) |
−0.927546 | + | 0.373709i | \(0.878086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000 | 0.786568 | ||||||||
\(932\) | 8.00000 | − | 13.8564i | 0.262049 | − | 0.453882i | ||||
\(933\) | −8.00000 | − | 13.8564i | −0.261908 | − | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.0000 | −1.76410 | −0.882052 | − | 0.471153i | \(-0.843838\pi\) | ||||
−0.882052 | + | 0.471153i | \(0.843838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.50000 | − | 7.79423i | −0.146852 | − | 0.254355i | ||||
\(940\) | 16.0000 | − | 27.7128i | 0.521862 | − | 0.903892i | ||||
\(941\) | −18.0000 | −0.586783 | −0.293392 | − | 0.955992i | \(-0.594784\pi\) | ||||
−0.293392 | + | 0.955992i | \(0.594784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | − | 27.7128i | 0.521032 | − | 0.902453i | ||||
\(944\) | 32.0000 | 1.04151 | ||||||||
\(945\) | 1.00000 | − | 1.73205i | 0.0325300 | − | 0.0563436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.0000 | + | 31.1769i | 0.584921 | + | 1.01311i | 0.994885 | + | 0.101012i | \(0.0322080\pi\) |
−0.409964 | + | 0.912102i | \(0.634459\pi\) | |||||||
\(948\) | −14.0000 | −0.454699 | ||||||||
\(949\) | −45.5000 | − | 11.2583i | −1.47699 | − | 0.365461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.00000 | + | 12.1244i | 0.226991 | + | 0.393159i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0000 | + | 20.7846i | −0.388718 | + | 0.673280i | −0.992277 | − | 0.124039i | \(-0.960415\pi\) |
0.603559 | + | 0.797318i | \(0.293749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0000 | + | 31.1769i | −0.582162 | + | 1.00833i | ||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00000 | + | 1.73205i | 0.0322917 | + | 0.0559308i | ||||
\(960\) | −8.00000 | − | 13.8564i | −0.258199 | − | 0.447214i | ||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.00000 | 0.257796 | ||||||||
\(964\) | −10.0000 | − | 17.3205i | −0.322078 | − | 0.557856i | ||||
\(965\) | 3.00000 | + | 5.19615i | 0.0965734 | + | 0.167270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | + | 6.92820i | −0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0000 | + | 27.7128i | −0.513464 | + | 0.889346i | 0.486414 | + | 0.873729i | \(0.338305\pi\) |
−0.999878 | + | 0.0156178i | \(0.995028\pi\) | |||||||
\(972\) | −1.00000 | − | 1.73205i | −0.0320750 | − | 0.0555556i | ||||
\(973\) | 4.50000 | + | 7.79423i | 0.144263 | + | 0.249871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | − | 3.46410i | −0.0320256 | − | 0.110940i | ||||
\(976\) | 52.0000 | 1.66448 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | − | 6.92820i | 0.127841 | − | 0.221426i | ||||
\(980\) | 24.0000 | 0.766652 | ||||||||
\(981\) | 2.50000 | − | 4.33013i | 0.0798189 | − | 0.138250i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.0000 | −1.46717 | −0.733586 | − | 0.679597i | \(-0.762155\pi\) | ||||
−0.733586 | + | 0.679597i | \(0.762155\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0000 | − | 34.6410i | −0.637253 | − | 1.10375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | −8.00000 | − | 27.7128i | −0.254514 | − | 0.881662i | ||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0000 | + | 24.2487i | 0.444725 | + | 0.770286i | 0.998033 | − | 0.0626908i | \(-0.0199682\pi\) |
−0.553308 | + | 0.832977i | \(0.686635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.0000 | 0.729883 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.00000 | − | 12.1244i | 0.221915 | − | 0.384368i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 1.50000 | − | 2.59808i | 0.0475055 | − | 0.0822819i | −0.841295 | − | 0.540576i | \(-0.818206\pi\) |
0.888800 | + | 0.458295i | \(0.151540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.00000 | + | 8.66025i | 0.158193 | + | 0.273998i |
(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 | 429.2.i.a.133.1 | yes | 2 | |
13.3 | even | 3 | 5577.2.a.e.1.1 | 1 | |||
13.9 | even | 3 | inner | 429.2.i.a.100.1 | ✓ | 2 | |
13.10 | even | 6 | 5577.2.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.a.100.1 | ✓ | 2 | 13.9 | even | 3 | inner | |
429.2.i.a.133.1 | yes | 2 | 1.1 | even | 1 | trivial | |
5577.2.a.b.1.1 | 1 | 13.10 | even | 6 | |||
5577.2.a.e.1.1 | 1 | 13.3 | even | 3 |