Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
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 | 949.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.949 |
Dual form | 1050.2.o.d.499.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.59808 | + | 0.500000i | −0.981981 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.19615 | − | 3.00000i | −1.26025 | − | 0.727607i | −0.287129 | − | 0.957892i | \(-0.592701\pi\) |
−0.973123 | + | 0.230285i | \(0.926034\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.50000 | + | 4.33013i | 0.490290 | + | 0.849208i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.866025 | + | 2.50000i | −0.163663 | + | 0.472456i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.866025 | − | 0.500000i | 0.142374 | − | 0.0821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | −6.06218 | − | 3.50000i | −0.983415 | − | 0.567775i | ||||
\(39\) | 2.50000 | − | 4.33013i | 0.400320 | − | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 2.59808 | − | 0.500000i | 0.400892 | − | 0.0771517i | ||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −5.19615 | + | 3.00000i | −0.757937 | + | 0.437595i | −0.828554 | − | 0.559908i | \(-0.810836\pi\) |
0.0706177 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 4.33013 | + | 2.50000i | 0.600481 | + | 0.346688i | ||||
\(53\) | 5.19615 | + | 3.00000i | 0.713746 | + | 0.412082i | 0.812447 | − | 0.583036i | \(-0.198135\pi\) |
−0.0987002 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | + | 2.59808i | 0.0668153 | + | 0.347183i | ||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | −1.73205 | − | 2.00000i | −0.218218 | − | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2583 | − | 6.50000i | −1.37542 | − | 0.794101i | −0.383819 | − | 0.923408i | \(-0.625391\pi\) |
−0.991605 | + | 0.129307i | \(0.958725\pi\) | |||||||
\(68\) | −5.19615 | + | 3.00000i | −0.630126 | + | 0.363803i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | −4.33013 | − | 2.50000i | −0.506803 | − | 0.292603i | 0.224716 | − | 0.974424i | \(-0.427855\pi\) |
−0.731519 | + | 0.681822i | \(0.761188\pi\) | |||||||
\(74\) | 0.500000 | − | 0.866025i | 0.0581238 | − | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 5.00000i | − | 0.566139i | ||||||
\(79\) | −3.50000 | − | 6.06218i | −0.393781 | − | 0.682048i | 0.599164 | − | 0.800626i | \(-0.295500\pi\) |
−0.992945 | + | 0.118578i | \(0.962166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 18.0000i | − | 1.97576i | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||
0.155230 | − | 0.987878i | \(-0.450388\pi\) | |||||||
\(84\) | 2.00000 | − | 1.73205i | 0.218218 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | − | 12.9904i | −0.262071 | − | 1.36176i | ||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 6.92820 | − | 4.00000i | 0.718421 | − | 0.414781i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 7.00000i | 0.710742i | 0.934725 | + | 0.355371i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | 4.33013 | − | 5.50000i | 0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 5.19615 | + | 3.00000i | 0.514496 | + | 0.297044i | ||||
\(103\) | −11.2583 | + | 6.50000i | −1.10932 | + | 0.640464i | −0.938652 | − | 0.344865i | \(-0.887925\pi\) |
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 15.5885 | − | 9.00000i | 1.50699 | − | 0.870063i | 0.507026 | − | 0.861931i | \(-0.330745\pi\) |
0.999967 | − | 0.00813215i | \(-0.00258857\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −3.50000 | + | 6.06218i | −0.335239 | + | 0.580651i | −0.983531 | − | 0.180741i | \(-0.942150\pi\) |
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 1.73205 | + | 2.00000i | 0.163663 | + | 0.188982i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 3.50000 | + | 6.06218i | 0.327805 | + | 0.567775i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.33013 | + | 2.50000i | −0.400320 | + | 0.231125i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 15.0000 | + | 5.19615i | 1.37505 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0.866025 | + | 0.500000i | 0.0784063 | + | 0.0452679i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.50000 | − | 0.866025i | −0.222718 | − | 0.0771517i | ||||
\(127\) | − | 11.0000i | − | 0.976092i | −0.872818 | − | 0.488046i | \(-0.837710\pi\) | ||
0.872818 | − | 0.488046i | \(-0.162290\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1244 | + | 14.0000i | 1.05131 | + | 1.21395i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | 5.19615 | − | 3.00000i | 0.442326 | − | 0.255377i | ||||
\(139\) | −11.0000 | −0.933008 | −0.466504 | − | 0.884519i | \(-0.654487\pi\) | ||||
−0.466504 | + | 0.884519i | \(0.654487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 10.3923 | − | 6.00000i | 0.872103 | − | 0.503509i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.00000 | −0.413803 | ||||||||
\(147\) | −6.92820 | − | 1.00000i | −0.571429 | − | 0.0824786i | ||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | −6.06218 | + | 3.50000i | −0.491708 | + | 0.283887i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | − | 4.33013i | −0.200160 | − | 0.346688i | ||||
\(157\) | −0.866025 | − | 0.500000i | −0.0691164 | − | 0.0399043i | 0.465044 | − | 0.885288i | \(-0.346039\pi\) |
−0.534160 | + | 0.845383i | \(0.679372\pi\) | |||||||
\(158\) | −6.06218 | − | 3.50000i | −0.482281 | − | 0.278445i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | − | 10.3923i | 0.945732 | − | 0.819028i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −0.866025 | + | 0.500000i | −0.0678323 | + | 0.0391630i | −0.533533 | − | 0.845780i | \(-0.679136\pi\) |
0.465700 | + | 0.884943i | \(0.345802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | − | 15.5885i | −0.698535 | − | 1.20990i | ||||
\(167\) | 6.00000i | 0.464294i | 0.972681 | + | 0.232147i | \(0.0745750\pi\) | ||||
−0.972681 | + | 0.232147i | \(0.925425\pi\) | |||||||
\(168\) | 0.866025 | − | 2.50000i | 0.0668153 | − | 0.192879i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | − | 6.06218i | 0.267652 | − | 0.463586i | ||||
\(172\) | 6.92820 | + | 4.00000i | 0.528271 | + | 0.304997i | ||||
\(173\) | 15.5885 | − | 9.00000i | 1.18517 | − | 0.684257i | 0.227964 | − | 0.973670i | \(-0.426793\pi\) |
0.957205 | + | 0.289412i | \(0.0934598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19615 | − | 3.00000i | 0.390567 | − | 0.225494i | ||||
\(178\) | −5.19615 | − | 3.00000i | −0.389468 | − | 0.224860i | ||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −8.66025 | − | 10.0000i | −0.641941 | − | 0.741249i | ||||
\(183\) | − | 1.00000i | − | 0.0739221i | ||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | − | 6.92820i | 0.293294 | − | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | − | 20.7846i | −0.868290 | − | 1.50392i | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 8.66025 | + | 5.00000i | 0.623379 | + | 0.359908i | 0.778183 | − | 0.628037i | \(-0.216141\pi\) |
−0.154805 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(194\) | 3.50000 | + | 6.06218i | 0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50000 | − | 9.52628i | 0.389885 | − | 0.675300i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.992434 | + | 0.122782i | \(0.0391815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.50000 | + | 11.2583i | 0.458475 | + | 0.794101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.50000 | + | 11.2583i | −0.452876 | + | 0.784405i | ||||
\(207\) | −5.19615 | − | 3.00000i | −0.361158 | − | 0.208514i | ||||
\(208\) | 4.33013 | − | 2.50000i | 0.300240 | − | 0.173344i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | −10.3923 | − | 6.00000i | −0.712069 | − | 0.411113i | ||||
\(214\) | 9.00000 | − | 15.5885i | 0.615227 | − | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 6.92820 | − | 20.0000i | 0.470317 | − | 1.35769i | ||||
\(218\) | 7.00000i | 0.474100i | ||||||||
\(219\) | 2.50000 | + | 4.33013i | 0.168934 | + | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | − | 25.9808i | 1.00901 | − | 1.74766i | ||||
\(222\) | −0.866025 | + | 0.500000i | −0.0581238 | + | 0.0335578i | ||||
\(223\) | 17.0000i | 1.13840i | 0.822198 | + | 0.569202i | \(0.192748\pi\) | ||||
−0.822198 | + | 0.569202i | \(0.807252\pi\) | |||||||
\(224\) | 2.50000 | + | 0.866025i | 0.167038 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | − | 5.19615i | −0.199557 | − | 0.345643i | ||||
\(227\) | 10.3923 | + | 6.00000i | 0.689761 | + | 0.398234i | 0.803523 | − | 0.595274i | \(-0.202957\pi\) |
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(228\) | 6.06218 | + | 3.50000i | 0.401478 | + | 0.231793i | ||||
\(229\) | 2.50000 | + | 4.33013i | 0.165205 | + | 0.286143i | 0.936728 | − | 0.350058i | \(-0.113838\pi\) |
−0.771523 | + | 0.636201i | \(0.780505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.7846 | − | 12.0000i | 1.36165 | − | 0.786146i | 0.371802 | − | 0.928312i | \(-0.378740\pi\) |
0.989843 | + | 0.142166i | \(0.0454066\pi\) | |||||||
\(234\) | −2.50000 | + | 4.33013i | −0.163430 | + | 0.283069i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | 7.00000i | 0.454699i | ||||||||
\(238\) | 15.5885 | − | 3.00000i | 1.01045 | − | 0.194461i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 9.52628 | + | 5.50000i | 0.612372 | + | 0.353553i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.3109 | − | 17.5000i | 1.92864 | − | 1.11350i | ||||
\(248\) | 6.92820 | + | 4.00000i | 0.439941 | + | 0.254000i | ||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | −2.59808 | + | 0.500000i | −0.163663 | + | 0.0314970i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.50000 | − | 9.52628i | −0.345101 | − | 0.597732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 20.7846 | − | 12.0000i | 1.29651 | − | 0.748539i | 0.316709 | − | 0.948523i | \(-0.397422\pi\) |
0.979799 | + | 0.199983i | \(0.0640888\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | −2.00000 | + | 1.73205i | −0.124274 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.19615 | − | 3.00000i | −0.321019 | − | 0.185341i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.5000 | + | 6.06218i | 1.07299 | + | 0.371696i | ||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | −11.2583 | + | 6.50000i | −0.687712 | + | 0.397051i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | − | 17.3205i | −0.607457 | − | 1.05215i | −0.991658 | − | 0.128897i | \(-0.958856\pi\) |
0.384201 | − | 0.923249i | \(-0.374477\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | −4.33013 | + | 12.5000i | −0.262071 | + | 0.756534i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | ||||
\(277\) | −16.4545 | − | 9.50000i | −0.988654 | − | 0.570800i | −0.0837823 | − | 0.996484i | \(-0.526700\pi\) |
−0.904872 | + | 0.425684i | \(0.860033\pi\) | |||||||
\(278\) | −9.52628 | + | 5.50000i | −0.571348 | + | 0.329868i | ||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 5.19615 | − | 3.00000i | 0.309426 | − | 0.178647i | ||||
\(283\) | −4.33013 | − | 2.50000i | −0.257399 | − | 0.148610i | 0.365748 | − | 0.930714i | \(-0.380813\pi\) |
−0.623148 | + | 0.782104i | \(0.714146\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.50000 | − | 6.06218i | 0.205174 | − | 0.355371i | ||||
\(292\) | −4.33013 | + | 2.50000i | −0.253402 | + | 0.146301i | ||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | −6.50000 | + | 2.59808i | −0.379088 | + | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.500000 | − | 0.866025i | −0.0290619 | − | 0.0503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.3923 | + | 6.00000i | 0.602010 | + | 0.347571i | ||||
\(299\) | −15.0000 | − | 25.9808i | −0.867472 | − | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 20.7846i | −0.230556 | − | 1.19800i | ||||
\(302\) | − | 1.00000i | − | 0.0575435i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | + | 6.06218i | −0.200739 | + | 0.347690i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0000 | 0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | + | 15.5885i | −0.510343 | + | 0.883940i | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | −4.33013 | − | 2.50000i | −0.245145 | − | 0.141535i | ||||
\(313\) | 12.1244 | − | 7.00000i | 0.685309 | − | 0.395663i | −0.116543 | − | 0.993186i | \(-0.537181\pi\) |
0.801852 | + | 0.597522i | \(0.203848\pi\) | |||||||
\(314\) | −1.00000 | −0.0564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.00000 | −0.393781 | ||||||||
\(317\) | 15.5885 | − | 9.00000i | 0.875535 | − | 0.505490i | 0.00635137 | − | 0.999980i | \(-0.497978\pi\) |
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(318\) | −5.19615 | − | 3.00000i | −0.291386 | − | 0.168232i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 5.19615 | − | 15.0000i | 0.289570 | − | 0.835917i | ||||
\(323\) | 42.0000i | 2.33694i | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.500000 | + | 0.866025i | −0.0276924 | + | 0.0479647i | ||||
\(327\) | 6.06218 | − | 3.50000i | 0.335239 | − | 0.193550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | − | 10.3923i | 0.661581 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | + | 16.4545i | 0.522167 | + | 0.904420i | 0.999667 | + | 0.0257885i | \(0.00820965\pi\) |
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(332\) | −15.5885 | − | 9.00000i | −0.855528 | − | 0.493939i | ||||
\(333\) | 0.866025 | + | 0.500000i | 0.0474579 | + | 0.0273998i | ||||
\(334\) | 3.00000 | + | 5.19615i | 0.164153 | + | 0.284321i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 2.59808i | −0.0272772 | − | 0.141737i | ||||
\(337\) | 34.0000i | 1.85210i | 0.377403 | + | 0.926049i | \(0.376817\pi\) | ||||
−0.377403 | + | 0.926049i | \(0.623183\pi\) | |||||||
\(338\) | −10.3923 | + | 6.00000i | −0.565267 | + | 0.326357i | ||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 7.00000i | − | 0.378517i | ||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.00000 | − | 15.5885i | 0.483843 | − | 0.838041i | ||||
\(347\) | 15.5885 | + | 9.00000i | 0.836832 | + | 0.483145i | 0.856186 | − | 0.516667i | \(-0.172828\pi\) |
−0.0193540 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7846 | + | 12.0000i | 1.10625 | + | 0.638696i | 0.937856 | − | 0.347024i | \(-0.112808\pi\) |
0.168397 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | −10.3923 | − | 12.0000i | −0.550019 | − | 0.635107i | ||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | 15.0000 | + | 25.9808i | 0.791670 | + | 1.37121i | 0.924932 | + | 0.380131i | \(0.124121\pi\) |
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | −8.66025 | + | 5.00000i | −0.455173 | + | 0.262794i | ||||
\(363\) | − | 11.0000i | − | 0.577350i | ||||||
\(364\) | −12.5000 | − | 4.33013i | −0.655178 | − | 0.226960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.500000 | − | 0.866025i | −0.0261354 | − | 0.0452679i | ||||
\(367\) | 6.92820 | + | 4.00000i | 0.361649 | + | 0.208798i | 0.669804 | − | 0.742538i | \(-0.266378\pi\) |
−0.308155 | + | 0.951336i | \(0.599711\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.0000 | − | 5.19615i | −0.778761 | − | 0.269771i | ||||
\(372\) | − | 8.00000i | − | 0.414781i | ||||||
\(373\) | −11.2583 | + | 6.50000i | −0.582934 | + | 0.336557i | −0.762299 | − | 0.647225i | \(-0.775929\pi\) |
0.179364 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.73205 | + | 2.00000i | 0.0890871 | + | 0.102869i | ||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50000 | + | 9.52628i | −0.281774 | + | 0.488046i | ||||
\(382\) | −20.7846 | − | 12.0000i | −1.06343 | − | 0.613973i | ||||
\(383\) | −5.19615 | + | 3.00000i | −0.265511 | + | 0.153293i | −0.626846 | − | 0.779143i | \(-0.715654\pi\) |
0.361335 | + | 0.932436i | \(0.382321\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −6.92820 | + | 4.00000i | −0.352180 | + | 0.203331i | ||||
\(388\) | 6.06218 | + | 3.50000i | 0.307760 | + | 0.177686i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | −2.59808 | − | 6.50000i | −0.131223 | − | 0.328300i | ||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 6.00000 | + | 10.3923i | 0.302276 | + | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1244 | + | 7.00000i | −0.608504 | + | 0.351320i | −0.772380 | − | 0.635161i | \(-0.780934\pi\) |
0.163876 | + | 0.986481i | \(0.447600\pi\) | |||||||
\(398\) | − | 11.0000i | − | 0.551380i | ||||||
\(399\) | −3.50000 | − | 18.1865i | −0.175219 | − | 0.910465i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | + | 31.1769i | 0.898877 | + | 1.55690i | 0.828932 | + | 0.559350i | \(0.188949\pi\) |
0.0699455 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(402\) | 11.2583 | + | 6.50000i | 0.561514 | + | 0.324191i | ||||
\(403\) | −34.6410 | − | 20.0000i | −1.72559 | − | 0.996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.19615 | − | 3.00000i | 0.257248 | − | 0.148522i | ||||
\(409\) | 2.50000 | − | 4.33013i | 0.123617 | − | 0.214111i | −0.797574 | − | 0.603220i | \(-0.793884\pi\) |
0.921192 | + | 0.389109i | \(0.127217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | + | 15.5885i | 0.443937 | + | 0.768922i | ||||
\(412\) | 13.0000i | 0.640464i | ||||||||
\(413\) | 5.19615 | − | 15.0000i | 0.255686 | − | 0.738102i | ||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | − | 4.33013i | 0.122573 | − | 0.212302i | ||||
\(417\) | 9.52628 | + | 5.50000i | 0.466504 | + | 0.269336i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | −11.2583 | + | 6.50000i | −0.548047 | + | 0.316415i | ||||
\(423\) | −5.19615 | − | 3.00000i | −0.252646 | − | 0.145865i | ||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | −1.73205 | − | 2.00000i | −0.0838198 | − | 0.0967868i | ||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 34.0000i | − | 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | −4.00000 | − | 20.7846i | −0.192006 | − | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50000 | + | 6.06218i | 0.167620 | + | 0.290326i | ||||
\(437\) | 36.3731 | + | 21.0000i | 1.73996 | + | 1.00457i | ||||
\(438\) | 4.33013 | + | 2.50000i | 0.206901 | + | 0.119455i | ||||
\(439\) | 2.50000 | + | 4.33013i | 0.119318 | + | 0.206666i | 0.919498 | − | 0.393095i | \(-0.128596\pi\) |
−0.800179 | + | 0.599761i | \(0.795262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | − | 30.0000i | − | 1.42695i | ||||||
\(443\) | −36.3731 | + | 21.0000i | −1.72814 | + | 0.997740i | −0.830473 | + | 0.557059i | \(0.811930\pi\) |
−0.897664 | + | 0.440681i | \(0.854737\pi\) | |||||||
\(444\) | −0.500000 | + | 0.866025i | −0.0237289 | + | 0.0410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.50000 | + | 14.7224i | 0.402487 | + | 0.697127i | ||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | 2.59808 | − | 0.500000i | 0.122748 | − | 0.0236228i | ||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.19615 | − | 3.00000i | −0.244406 | − | 0.141108i | ||||
\(453\) | −0.866025 | + | 0.500000i | −0.0406894 | + | 0.0234920i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.00000 | 0.327805 | ||||||||
\(457\) | −25.1147 | + | 14.5000i | −1.17482 | + | 0.678281i | −0.954810 | − | 0.297217i | \(-0.903942\pi\) |
−0.220008 | + | 0.975498i | \(0.570608\pi\) | |||||||
\(458\) | 4.33013 | + | 2.50000i | 0.202334 | + | 0.116817i | ||||
\(459\) | −3.00000 | + | 5.19615i | −0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 31.0000i | − | 1.44069i | −0.693615 | − | 0.720346i | \(-0.743983\pi\) | ||
0.693615 | − | 0.720346i | \(-0.256017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | − | 20.7846i | 0.555889 | − | 0.962828i | ||||
\(467\) | −25.9808 | + | 15.0000i | −1.20225 | + | 0.694117i | −0.961054 | − | 0.276360i | \(-0.910872\pi\) |
−0.241192 | + | 0.970477i | \(0.577538\pi\) | |||||||
\(468\) | 5.00000i | 0.231125i | ||||||||
\(469\) | 32.5000 | + | 11.2583i | 1.50071 | + | 0.519861i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.500000 | + | 0.866025i | 0.0230388 | + | 0.0399043i | ||||
\(472\) | 5.19615 | + | 3.00000i | 0.239172 | + | 0.138086i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.50000 | + | 6.06218i | 0.160760 | + | 0.278445i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | − | 10.3923i | 0.550019 | − | 0.476331i | ||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 10.3923 | − | 6.00000i | 0.475333 | − | 0.274434i | ||||
\(479\) | 9.00000 | − | 15.5885i | 0.411220 | − | 0.712255i | −0.583803 | − | 0.811895i | \(-0.698436\pi\) |
0.995023 | + | 0.0996406i | \(0.0317693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | 5.00000i | 0.227744i | ||||||||
\(483\) | −15.5885 | + | 3.00000i | −0.709299 | + | 0.136505i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −34.6410 | − | 20.0000i | −1.56973 | − | 0.906287i | −0.996199 | − | 0.0871056i | \(-0.972238\pi\) |
−0.573535 | − | 0.819181i | \(-0.694428\pi\) | |||||||
\(488\) | 0.866025 | − | 0.500000i | 0.0392031 | − | 0.0226339i | ||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 17.5000 | − | 30.3109i | 0.787362 | − | 1.36375i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −31.1769 | + | 6.00000i | −1.39848 | + | 0.269137i | ||||
\(498\) | 18.0000i | 0.806599i | ||||||||
\(499\) | 2.50000 | + | 4.33013i | 0.111915 | + | 0.193843i | 0.916542 | − | 0.399937i | \(-0.130968\pi\) |
−0.804627 | + | 0.593780i | \(0.797635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | −20.7846 | + | 12.0000i | −0.927663 | + | 0.535586i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | −2.00000 | + | 1.73205i | −0.0890871 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.3923 | + | 6.00000i | 0.461538 | + | 0.266469i | ||||
\(508\) | −9.52628 | − | 5.50000i | −0.422660 | − | 0.244023i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5000 | + | 4.33013i | 0.552967 | + | 0.191554i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.06218 | + | 3.50000i | −0.267652 | + | 0.154529i | ||||
\(514\) | 12.0000 | − | 20.7846i | 0.529297 | − | 0.916770i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | − | 6.92820i | −0.176090 | − | 0.304997i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.866025 | + | 2.50000i | −0.0380510 | + | 0.109844i | ||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0000 | + | 36.3731i | −0.920027 | + | 1.59353i | −0.120656 | + | 0.992694i | \(0.538500\pi\) |
−0.799370 | + | 0.600839i | \(0.794833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7128 | − | 16.0000i | 1.21180 | − | 0.699631i | 0.248646 | − | 0.968594i | \(-0.420014\pi\) |
0.963150 | + | 0.268963i | \(0.0866810\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.5692 | − | 24.0000i | 1.81078 | − | 1.04546i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 18.1865 | − | 3.50000i | 0.788486 | − | 0.151744i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.00000 | + | 5.19615i | 0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.50000 | + | 11.2583i | −0.280757 | + | 0.486286i | ||||
\(537\) | −10.3923 | + | 6.00000i | −0.448461 | + | 0.258919i | ||||
\(538\) | 24.0000i | 1.03471i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5000 | + | 37.2391i | 0.924357 | + | 1.60103i | 0.792592 | + | 0.609753i | \(0.208731\pi\) |
0.131765 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(542\) | −17.3205 | − | 10.0000i | −0.743980 | − | 0.429537i | ||||
\(543\) | 8.66025 | + | 5.00000i | 0.371647 | + | 0.214571i | ||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.50000 | + | 12.9904i | 0.106990 | + | 0.555937i | ||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | −15.5885 | + | 9.00000i | −0.665906 | + | 0.384461i | ||||
\(549\) | −0.500000 | + | 0.866025i | −0.0213395 | + | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 6.00000i | − | 0.255377i | ||||||
\(553\) | 12.1244 | + | 14.0000i | 0.515580 | + | 0.595341i | ||||
\(554\) | −19.0000 | −0.807233 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.50000 | + | 9.52628i | −0.233252 | + | 0.404004i | ||||
\(557\) | −10.3923 | − | 6.00000i | −0.440336 | − | 0.254228i | 0.263404 | − | 0.964686i | \(-0.415155\pi\) |
−0.703740 | + | 0.710457i | \(0.748488\pi\) | |||||||
\(558\) | −6.92820 | + | 4.00000i | −0.293294 | + | 0.169334i | ||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.5885 | + | 9.00000i | −0.657559 | + | 0.379642i | ||||
\(563\) | 10.3923 | + | 6.00000i | 0.437983 | + | 0.252870i | 0.702742 | − | 0.711445i | \(-0.251959\pi\) |
−0.264758 | + | 0.964315i | \(0.585292\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.00000 | −0.210166 | ||||||||
\(567\) | 0.866025 | − | 2.50000i | 0.0363696 | − | 0.104990i | ||||
\(568\) | − | 12.0000i | − | 0.503509i | ||||||
\(569\) | −18.0000 | − | 31.1769i | −0.754599 | − | 1.30700i | −0.945573 | − | 0.325409i | \(-0.894498\pi\) |
0.190974 | − | 0.981595i | \(-0.438835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | + | 4.33013i | −0.104622 | + | 0.181210i | −0.913584 | − | 0.406651i | \(-0.866697\pi\) |
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0000i | 1.00261i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 12.1244 | + | 7.00000i | 0.504744 | + | 0.291414i | 0.730670 | − | 0.682730i | \(-0.239208\pi\) |
−0.225927 | + | 0.974144i | \(0.572541\pi\) | |||||||
\(578\) | 16.4545 | + | 9.50000i | 0.684416 | + | 0.395148i | ||||
\(579\) | −5.00000 | − | 8.66025i | −0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.00000 | + | 46.7654i | 0.373383 | + | 1.94015i | ||||
\(582\) | − | 7.00000i | − | 0.290159i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.50000 | + | 4.33013i | −0.103451 | + | 0.179182i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | − | 20.7846i | −0.495715 | − | 0.858604i | ||||
\(587\) | 30.0000i | 1.23823i | 0.785299 | + | 0.619116i | \(0.212509\pi\) | ||||
−0.785299 | + | 0.619116i | \(0.787491\pi\) | |||||||
\(588\) | −4.33013 | + | 5.50000i | −0.178571 | + | 0.226816i | ||||
\(589\) | 56.0000 | 2.30744 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | − | 10.3923i | 0.246807 | − | 0.427482i | ||||
\(592\) | −0.866025 | − | 0.500000i | −0.0355934 | − | 0.0205499i | ||||
\(593\) | −5.19615 | + | 3.00000i | −0.213380 | + | 0.123195i | −0.602881 | − | 0.797831i | \(-0.705981\pi\) |
0.389501 | + | 0.921026i | \(0.372647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | −9.52628 | + | 5.50000i | −0.389885 | + | 0.225100i | ||||
\(598\) | −25.9808 | − | 15.0000i | −1.06243 | − | 0.613396i | ||||
\(599\) | −15.0000 | + | 25.9808i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | −13.8564 | − | 16.0000i | −0.564745 | − | 0.652111i | ||||
\(603\) | − | 13.0000i | − | 0.529401i | ||||||
\(604\) | −0.500000 | − | 0.866025i | −0.0203447 | − | 0.0352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2391 | − | 21.5000i | 1.51149 | − | 0.872658i | 0.511578 | − | 0.859237i | \(-0.329061\pi\) |
0.999910 | − | 0.0134214i | \(-0.00427228\pi\) | |||||||
\(608\) | 7.00000i | 0.283887i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | − | 25.9808i | −0.606835 | − | 1.05107i | ||||
\(612\) | −5.19615 | − | 3.00000i | −0.210042 | − | 0.121268i | ||||
\(613\) | −32.9090 | − | 19.0000i | −1.32918 | − | 0.767403i | −0.344008 | − | 0.938967i | \(-0.611785\pi\) |
−0.985173 | + | 0.171564i | \(0.945118\pi\) | |||||||
\(614\) | 14.0000 | + | 24.2487i | 0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 48.0000i | − | 1.93241i | −0.257780 | − | 0.966204i | \(-0.582991\pi\) | ||
0.257780 | − | 0.966204i | \(-0.417009\pi\) | |||||||
\(618\) | 11.2583 | − | 6.50000i | 0.452876 | − | 0.261468i | ||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | 18.0000i | 0.721734i | ||||||||
\(623\) | 10.3923 | + | 12.0000i | 0.416359 | + | 0.480770i | ||||
\(624\) | −5.00000 | −0.200160 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.00000 | − | 12.1244i | 0.279776 | − | 0.484587i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.866025 | + | 0.500000i | −0.0345582 | + | 0.0199522i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | −6.06218 | + | 3.50000i | −0.241140 | + | 0.139223i | ||||
\(633\) | 11.2583 | + | 6.50000i | 0.447478 | + | 0.258352i | ||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 12.9904 | + | 32.5000i | 0.514698 | + | 1.28770i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | − | 20.7846i | 0.473972 | − | 0.820943i | −0.525584 | − | 0.850741i | \(-0.676153\pi\) |
0.999556 | + | 0.0297987i | \(0.00948663\pi\) | |||||||
\(642\) | −15.5885 | + | 9.00000i | −0.615227 | + | 0.355202i | ||||
\(643\) | 11.0000i | 0.433798i | 0.976194 | + | 0.216899i | \(0.0695942\pi\) | ||||
−0.976194 | + | 0.216899i | \(0.930406\pi\) | |||||||
\(644\) | −3.00000 | − | 15.5885i | −0.118217 | − | 0.614271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.0000 | + | 36.3731i | 0.826234 | + | 1.43108i | ||||
\(647\) | −10.3923 | − | 6.00000i | −0.408564 | − | 0.235884i | 0.281609 | − | 0.959529i | \(-0.409132\pi\) |
−0.690172 | + | 0.723645i | \(0.742465\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0000 | + | 13.8564i | −0.627089 | + | 0.543075i | ||||
\(652\) | 1.00000i | 0.0391630i | ||||||||
\(653\) | −31.1769 | + | 18.0000i | −1.22005 | + | 0.704394i | −0.964928 | − | 0.262515i | \(-0.915448\pi\) |
−0.255119 | + | 0.966910i | \(0.582115\pi\) | |||||||
\(654\) | 3.50000 | − | 6.06218i | 0.136861 | − | 0.237050i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.00000i | − | 0.195069i | ||||||
\(658\) | 5.19615 | − | 15.0000i | 0.202567 | − | 0.584761i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | + | 30.3109i | −0.680671 | + | 1.17896i | 0.294105 | + | 0.955773i | \(0.404978\pi\) |
−0.974776 | + | 0.223184i | \(0.928355\pi\) | |||||||
\(662\) | 16.4545 | + | 9.50000i | 0.639522 | + | 0.369228i | ||||
\(663\) | −25.9808 | + | 15.0000i | −1.00901 | + | 0.582552i | ||||
\(664\) | −18.0000 | −0.698535 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.19615 | + | 3.00000i | 0.201045 | + | 0.116073i | ||||
\(669\) | 8.50000 | − | 14.7224i | 0.328629 | − | 0.569202i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.73205 | − | 2.00000i | −0.0668153 | − | 0.0771517i | ||||
\(673\) | − | 1.00000i | − | 0.0385472i | −0.999814 | − | 0.0192736i | \(-0.993865\pi\) | ||
0.999814 | − | 0.0192736i | \(-0.00613535\pi\) | |||||||
\(674\) | 17.0000 | + | 29.4449i | 0.654816 | + | 1.13417i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | −36.3731 | + | 21.0000i | −1.39793 | + | 0.807096i | −0.994176 | − | 0.107772i | \(-0.965628\pi\) |
−0.403755 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −3.50000 | − | 18.1865i | −0.134318 | − | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | − | 10.3923i | −0.229920 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7846 | − | 12.0000i | −0.795301 | − | 0.459167i | 0.0465244 | − | 0.998917i | \(-0.485185\pi\) |
−0.841825 | + | 0.539750i | \(0.818519\pi\) | |||||||
\(684\) | −3.50000 | − | 6.06218i | −0.133826 | − | 0.231793i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 5.00000i | − | 0.190762i | ||||||
\(688\) | 6.92820 | − | 4.00000i | 0.264135 | − | 0.152499i | ||||
\(689\) | −15.0000 | + | 25.9808i | −0.571454 | + | 0.989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.50000 | + | 6.06218i | 0.133146 | + | 0.230616i | 0.924888 | − | 0.380240i | \(-0.124159\pi\) |
−0.791742 | + | 0.610856i | \(0.790825\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −22.5167 | + | 13.0000i | −0.852268 | + | 0.492057i | ||||
\(699\) | −24.0000 | −0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 4.33013 | − | 2.50000i | 0.163430 | − | 0.0943564i | ||||
\(703\) | −6.06218 | − | 3.50000i | −0.228639 | − | 0.132005i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −3.50000 | − | 6.06218i | −0.131445 | − | 0.227670i | 0.792789 | − | 0.609497i | \(-0.208628\pi\) |
−0.924234 | + | 0.381827i | \(0.875295\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50000 | − | 6.06218i | 0.131260 | − | 0.227349i | ||||
\(712\) | −5.19615 | + | 3.00000i | −0.194734 | + | 0.112430i | ||||
\(713\) | − | 48.0000i | − | 1.79761i | ||||||
\(714\) | −15.0000 | − | 5.19615i | −0.561361 | − | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | − | 10.3923i | −0.224231 | − | 0.388379i | ||||
\(717\) | −10.3923 | − | 6.00000i | −0.388108 | − | 0.224074i | ||||
\(718\) | 25.9808 | + | 15.0000i | 0.969593 | + | 0.559795i | ||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.0000 | − | 22.5167i | 0.968291 | − | 0.838564i | ||||
\(722\) | 30.0000i | 1.11648i | ||||||||
\(723\) | 4.33013 | − | 2.50000i | 0.161039 | − | 0.0929760i | ||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.50000 | − | 9.52628i | −0.204124 | − | 0.353553i | ||||
\(727\) | 37.0000i | 1.37225i | 0.727482 | + | 0.686127i | \(0.240691\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759309\pi\) | |||||||
\(728\) | −12.9904 | + | 2.50000i | −0.481456 | + | 0.0926562i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | − | 41.5692i | 0.887672 | − | 1.53749i | ||||
\(732\) | −0.866025 | − | 0.500000i | −0.0320092 | − | 0.0184805i | ||||
\(733\) | 35.5070 | − | 20.5000i | 1.31148 | − | 0.757185i | 0.329141 | − | 0.944281i | \(-0.393241\pi\) |
0.982342 | + | 0.187096i | \(0.0599076\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5000 | + | 21.6506i | −0.459820 | + | 0.796431i | −0.998951 | − | 0.0457903i | \(-0.985419\pi\) |
0.539131 | + | 0.842222i | \(0.318753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.0000 | −1.28576 | ||||||||
\(742\) | −15.5885 | + | 3.00000i | −0.572270 | + | 0.110133i | ||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | −4.00000 | − | 6.92820i | −0.146647 | − | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.50000 | + | 11.2583i | −0.237982 | + | 0.412197i | ||||
\(747\) | 15.5885 | − | 9.00000i | 0.570352 | − | 0.329293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.0000 | + | 31.1769i | −1.31541 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | + | 21.6506i | 0.456131 | + | 0.790043i | 0.998752 | − | 0.0499348i | \(-0.0159013\pi\) |
−0.542621 | + | 0.839978i | \(0.682568\pi\) | |||||||
\(752\) | 5.19615 | + | 3.00000i | 0.189484 | + | 0.109399i | ||||
\(753\) | 20.7846 | + | 12.0000i | 0.757433 | + | 0.437304i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.50000 | + | 0.866025i | 0.0909241 | + | 0.0314970i | ||||
\(757\) | − | 29.0000i | − | 1.05402i | −0.849858 | − | 0.527011i | \(-0.823312\pi\) | ||
0.849858 | − | 0.527011i | \(-0.176688\pi\) | |||||||
\(758\) | −9.52628 | + | 5.50000i | −0.346010 | + | 0.199769i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | − | 15.5885i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(762\) | 11.0000i | 0.398488i | ||||||||
\(763\) | 6.06218 | − | 17.5000i | 0.219466 | − | 0.633543i | ||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | + | 5.19615i | −0.108394 | + | 0.187745i | ||||
\(767\) | −25.9808 | − | 15.0000i | −0.938111 | − | 0.541619i | ||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 8.66025 | − | 5.00000i | 0.311689 | − | 0.179954i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | −4.00000 | + | 6.92820i | −0.143777 | + | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 2.59808 | − | 0.500000i | 0.0932055 | − | 0.0179374i | ||||
\(778\) | 12.0000i | 0.430221i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 31.1769 | − | 18.0000i | 1.11488 | − | 0.643679i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | ||||
\(787\) | 19.9186 | + | 11.5000i | 0.710021 | + | 0.409931i | 0.811069 | − | 0.584951i | \(-0.198886\pi\) |
−0.101048 | + | 0.994882i | \(0.532220\pi\) | |||||||
\(788\) | 10.3923 | + | 6.00000i | 0.370211 | + | 0.213741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | + | 15.5885i | 0.106668 | + | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.33013 | + | 2.50000i | −0.153767 | + | 0.0887776i | ||||
\(794\) | −7.00000 | + | 12.1244i | −0.248421 | + | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.50000 | − | 9.52628i | −0.194942 | − | 0.337650i | ||||
\(797\) | − | 54.0000i | − | 1.91278i | −0.292096 | − | 0.956389i | \(-0.594353\pi\) | ||
0.292096 | − | 0.956389i | \(-0.405647\pi\) | |||||||
\(798\) | −12.1244 | − | 14.0000i | −0.429198 | − | 0.495595i | ||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | − | 5.19615i | 0.106000 | − | 0.183597i | ||||
\(802\) | 31.1769 | + | 18.0000i | 1.10090 | + | 0.635602i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0000 | 0.458475 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −40.0000 | −1.40894 | ||||||||
\(807\) | 20.7846 | − | 12.0000i | 0.731653 | − | 0.422420i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0000 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000i | 0.701431i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 48.4974 | − | 28.0000i | 1.69671 | − | 0.979596i | ||||
\(818\) | − | 5.00000i | − | 0.174821i | ||||||
\(819\) | 10.0000 | − | 8.66025i | 0.349428 | − | 0.302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 15.5885 | + | 9.00000i | 0.543710 | + | 0.313911i | ||||
\(823\) | −4.33013 | − | 2.50000i | −0.150939 | − | 0.0871445i | 0.422628 | − | 0.906303i | \(-0.361108\pi\) |
−0.573567 | + | 0.819159i | \(0.694441\pi\) | |||||||
\(824\) | 6.50000 | + | 11.2583i | 0.226438 | + | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 15.5885i | −0.104383 | − | 0.542392i | ||||
\(827\) | 24.0000i | 0.834562i | 0.908778 | + | 0.417281i | \(0.137017\pi\) | ||||
−0.908778 | + | 0.417281i | \(0.862983\pi\) | |||||||
\(828\) | −5.19615 | + | 3.00000i | −0.180579 | + | 0.104257i | ||||
\(829\) | −3.50000 | + | 6.06218i | −0.121560 | + | 0.210548i | −0.920383 | − | 0.391018i | \(-0.872123\pi\) |
0.798823 | + | 0.601566i | \(0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.50000 | + | 16.4545i | 0.329551 | + | 0.570800i | ||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | −41.5692 | − | 6.00000i | −1.44029 | − | 0.207888i | ||||
\(834\) | 11.0000 | 0.380899 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.92820 | + | 4.00000i | 0.239474 | + | 0.138260i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.0000 | 0.621429 | 0.310715 | − | 0.950503i | \(-0.399432\pi\) | ||||
0.310715 | + | 0.950503i | \(0.399432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 4.33013 | − | 2.50000i | 0.149226 | − | 0.0861557i | ||||
\(843\) | 15.5885 | + | 9.00000i | 0.536895 | + | 0.309976i | ||||
\(844\) | −6.50000 | + | 11.2583i | −0.223739 | + | 0.387528i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | −19.0526 | − | 22.0000i | −0.654654 | − | 0.755929i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 2.50000 | + | 4.33013i | 0.0857998 | + | 0.148610i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | + | 5.19615i | −0.102839 | + | 0.178122i | ||||
\(852\) | −10.3923 | + | 6.00000i | −0.356034 | + | 0.205557i | ||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | −2.50000 | − | 0.866025i | −0.0855482 | − | 0.0296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | − | 15.5885i | −0.307614 | − | 0.532803i | ||||
\(857\) | 15.5885 | + | 9.00000i | 0.532492 | + | 0.307434i | 0.742030 | − | 0.670366i | \(-0.233863\pi\) |
−0.209539 | + | 0.977800i | \(0.567196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | − | 3.46410i | −0.0682391 | − | 0.118194i | 0.829887 | − | 0.557931i | \(-0.188405\pi\) |
−0.898126 | + | 0.439738i | \(0.855071\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 18.0000i | − | 0.613082i | ||||||
\(863\) | 25.9808 | − | 15.0000i | 0.884395 | − | 0.510606i | 0.0122903 | − | 0.999924i | \(-0.496088\pi\) |
0.872105 | + | 0.489319i | \(0.162754\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.0000 | − | 29.4449i | −0.577684 | − | 1.00058i | ||||
\(867\) | − | 19.0000i | − | 0.645274i | ||||||
\(868\) | −13.8564 | − | 16.0000i | −0.470317 | − | 0.543075i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5000 | − | 56.2917i | 1.10122 | − | 1.90737i | ||||
\(872\) | 6.06218 | + | 3.50000i | 0.205291 | + | 0.118525i | ||||
\(873\) | −6.06218 | + | 3.50000i | −0.205174 | + | 0.118457i | ||||
\(874\) | 42.0000 | 1.42067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.00000 | 0.168934 | ||||||||
\(877\) | −40.7032 | + | 23.5000i | −1.37445 | + | 0.793539i | −0.991485 | − | 0.130224i | \(-0.958430\pi\) |
−0.382965 | + | 0.923763i | \(0.625097\pi\) | |||||||
\(878\) | 4.33013 | + | 2.50000i | 0.146135 | + | 0.0843709i | ||||
\(879\) | −12.0000 | + | 20.7846i | −0.404750 | + | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0000 | −0.404290 | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202145 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(882\) | 6.92820 | + | 1.00000i | 0.233285 | + | 0.0336718i | ||||
\(883\) | − | 25.0000i | − | 0.841317i | −0.907219 | − | 0.420658i | \(-0.861799\pi\) | ||
0.907219 | − | 0.420658i | \(-0.138201\pi\) | |||||||
\(884\) | −15.0000 | − | 25.9808i | −0.504505 | − | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.0000 | + | 36.3731i | −0.705509 | + | 1.22198i | ||||
\(887\) | 5.19615 | − | 3.00000i | 0.174470 | − | 0.100730i | −0.410222 | − | 0.911986i | \(-0.634549\pi\) |
0.584692 | + | 0.811256i | \(0.301215\pi\) | |||||||
\(888\) | 1.00000i | 0.0335578i | ||||||||
\(889\) | 5.50000 | + | 28.5788i | 0.184464 | + | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.7224 | + | 8.50000i | 0.492943 | + | 0.284601i | ||||
\(893\) | 36.3731 | + | 21.0000i | 1.21718 | + | 0.702738i | ||||
\(894\) | −6.00000 | − | 10.3923i | −0.200670 | − | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | 30.0000i | 1.00167i | ||||||||
\(898\) | −5.19615 | + | 3.00000i | −0.173398 | + | 0.100111i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.92820 | + | 20.0000i | −0.230556 | + | 0.665558i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.500000 | + | 0.866025i | −0.0166114 | + | 0.0287718i | ||||
\(907\) | −6.06218 | − | 3.50000i | −0.201291 | − | 0.116216i | 0.395966 | − | 0.918265i | \(-0.370410\pi\) |
−0.597258 | + | 0.802049i | \(0.703743\pi\) | |||||||
\(908\) | 10.3923 | − | 6.00000i | 0.344881 | − | 0.199117i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 6.06218 | − | 3.50000i | 0.200739 | − | 0.115897i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −14.5000 | + | 25.1147i | −0.479617 | + | 0.830722i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.00000 | 0.165205 | ||||||||
\(917\) | 10.3923 | + | 12.0000i | 0.343184 | + | 0.396275i | ||||
\(918\) | 6.00000i | 0.198030i | ||||||||
\(919\) | 4.00000 | + | 6.92820i | 0.131948 | + | 0.228540i | 0.924427 | − | 0.381358i | \(-0.124544\pi\) |
−0.792480 | + | 0.609898i | \(0.791210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | 5.19615 | − | 3.00000i | 0.171126 | − | 0.0987997i | ||||
\(923\) | 60.0000i | 1.97492i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.5000 | − | 26.8468i | −0.509362 | − | 0.882240i | ||||
\(927\) | −11.2583 | − | 6.50000i | −0.369772 | − | 0.213488i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | − | 31.1769i | −0.590561 | − | 1.02288i | −0.994157 | − | 0.107944i | \(-0.965573\pi\) |
0.403596 | − | 0.914937i | \(-0.367760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.5000 | − | 30.3109i | −1.26179 | − | 0.993399i | ||||
\(932\) | − | 24.0000i | − | 0.786146i | ||||||
\(933\) | 15.5885 | − | 9.00000i | 0.510343 | − | 0.294647i | ||||
\(934\) | −15.0000 | + | 25.9808i | −0.490815 | + | 0.850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | + | 4.33013i | 0.0817151 | + | 0.141535i | ||||
\(937\) | 10.0000i | 0.326686i | 0.986569 | + | 0.163343i | \(0.0522277\pi\) | ||||
−0.986569 | + | 0.163343i | \(0.947772\pi\) | |||||||
\(938\) | 33.7750 | − | 6.50000i | 1.10279 | − | 0.212233i | ||||
\(939\) | −14.0000 | −0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | − | 5.19615i | 0.0977972 | − | 0.169390i | −0.812975 | − | 0.582298i | \(-0.802154\pi\) |
0.910773 | + | 0.412908i | \(0.135487\pi\) | |||||||
\(942\) | 0.866025 | + | 0.500000i | 0.0282166 | + | 0.0162909i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.3731 | + | 21.0000i | −1.18197 | + | 0.682408i | −0.956469 | − | 0.291835i | \(-0.905734\pi\) |
−0.225497 | + | 0.974244i | \(0.572401\pi\) | |||||||
\(948\) | 6.06218 | + | 3.50000i | 0.196890 | + | 0.113675i | ||||
\(949\) | 12.5000 | − | 21.6506i | 0.405767 | − | 0.702809i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 5.19615 | − | 15.0000i | 0.168408 | − | 0.486153i | ||||
\(953\) | − | 12.0000i | − | 0.388718i | −0.980930 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980930 | − | 0.194359i | \(-0.0622627\pi\) | |||||||
\(954\) | 3.00000 | + | 5.19615i | 0.0971286 | + | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.00000 | − | 10.3923i | 0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.0000i | − | 0.581554i | ||||||
\(959\) | 45.0000 | + | 15.5885i | 1.45313 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 4.33013 | + | 2.50000i | 0.139609 | + | 0.0806032i | ||||
\(963\) | 15.5885 | + | 9.00000i | 0.502331 | + | 0.290021i | ||||
\(964\) | 2.50000 | + | 4.33013i | 0.0805196 | + | 0.139464i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0000 | + | 10.3923i | −0.386094 | + | 0.334367i | ||||
\(967\) | − | 41.0000i | − | 1.31847i | −0.751936 | − | 0.659236i | \(-0.770880\pi\) | ||
0.751936 | − | 0.659236i | \(-0.229120\pi\) | |||||||
\(968\) | 9.52628 | − | 5.50000i | 0.306186 | − | 0.176777i | ||||
\(969\) | 21.0000 | − | 36.3731i | 0.674617 | − | 1.16847i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 28.5788 | − | 5.50000i | 0.916195 | − | 0.176322i | ||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.500000 | − | 0.866025i | 0.0160046 | − | 0.0277208i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0.866025 | − | 0.500000i | 0.0276924 | − | 0.0159882i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.00000 | −0.223493 | ||||||||
\(982\) | −5.19615 | + | 3.00000i | −0.165816 | + | 0.0957338i | ||||
\(983\) | 25.9808 | + | 15.0000i | 0.828658 | + | 0.478426i | 0.853393 | − | 0.521268i | \(-0.174541\pi\) |
−0.0247352 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.5885 | + | 3.00000i | −0.496186 | + | 0.0954911i | ||||
\(988\) | − | 35.0000i | − | 1.11350i | ||||||
\(989\) | −24.0000 | − | 41.5692i | −0.763156 | − | 1.32182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | + | 27.7128i | −0.508257 | + | 0.880327i | 0.491698 | + | 0.870766i | \(0.336377\pi\) |
−0.999954 | + | 0.00956046i | \(0.996957\pi\) | |||||||
\(992\) | 6.92820 | − | 4.00000i | 0.219971 | − | 0.127000i | ||||
\(993\) | − | 19.0000i | − | 0.602947i | ||||||
\(994\) | −24.0000 | + | 20.7846i | −0.761234 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.00000 | + | 15.5885i | 0.285176 | + | 0.493939i | ||||
\(997\) | −11.2583 | − | 6.50000i | −0.356555 | − | 0.205857i | 0.311014 | − | 0.950405i | \(-0.399332\pi\) |
−0.667568 | + | 0.744548i | \(0.732665\pi\) | |||||||
\(998\) | 4.33013 | + | 2.50000i | 0.137068 | + | 0.0791361i | ||||
\(999\) | −0.500000 | − | 0.866025i | −0.0158193 | − | 0.0273998i |
(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 | 1050.2.o.d.949.2 | 4 | ||
5.2 | odd | 4 | 1050.2.i.n.151.1 | yes | 2 | ||
5.3 | odd | 4 | 1050.2.i.g.151.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.d.949.1 | 4 | ||
7.2 | even | 3 | inner | 1050.2.o.d.499.1 | 4 | ||
35.2 | odd | 12 | 1050.2.i.n.751.1 | yes | 2 | ||
35.3 | even | 12 | 7350.2.a.cv.1.1 | 1 | |||
35.9 | even | 6 | inner | 1050.2.o.d.499.2 | 4 | ||
35.17 | even | 12 | 7350.2.a.k.1.1 | 1 | |||
35.18 | odd | 12 | 7350.2.a.bv.1.1 | 1 | |||
35.23 | odd | 12 | 1050.2.i.g.751.1 | yes | 2 | ||
35.32 | odd | 12 | 7350.2.a.bf.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.g.151.1 | ✓ | 2 | 5.3 | odd | 4 | ||
1050.2.i.g.751.1 | yes | 2 | 35.23 | odd | 12 | ||
1050.2.i.n.151.1 | yes | 2 | 5.2 | odd | 4 | ||
1050.2.i.n.751.1 | yes | 2 | 35.2 | odd | 12 | ||
1050.2.o.d.499.1 | 4 | 7.2 | even | 3 | inner | ||
1050.2.o.d.499.2 | 4 | 35.9 | even | 6 | inner | ||
1050.2.o.d.949.1 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.d.949.2 | 4 | 1.1 | even | 1 | trivial | ||
7350.2.a.k.1.1 | 1 | 35.17 | even | 12 | |||
7350.2.a.bf.1.1 | 1 | 35.32 | odd | 12 | |||
7350.2.a.bv.1.1 | 1 | 35.18 | odd | 12 | |||
7350.2.a.cv.1.1 | 1 | 35.3 | even | 12 |