Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(257,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.v (of order \(4\), 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: | \(9.58204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.593 |
Dual form | 1200.2.v.j.257.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.414214 | − | 0.414214i | 0.156558 | − | 0.156558i | −0.624482 | − | 0.781040i | \(-0.714690\pi\) |
0.781040 | + | 0.624482i | \(0.214690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.82843i | − | 1.45583i | −0.685670 | − | 0.727913i | \(-0.740491\pi\) | ||
0.685670 | − | 0.727913i | \(-0.259509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.82843 | + | 1.82843i | 0.507114 | + | 0.507114i | 0.913640 | − | 0.406525i | \(-0.133260\pi\) |
−0.406525 | + | 0.913640i | \(0.633260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.82843 | + | 3.82843i | 0.928530 | + | 0.928530i | 0.997611 | − | 0.0690811i | \(-0.0220067\pi\) |
−0.0690811 | + | 0.997611i | \(0.522007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82843i | 1.10772i | 0.832611 | + | 0.553859i | \(0.186845\pi\) | ||||
−0.832611 | + | 0.553859i | \(0.813155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 0.171573i | 0.218218 | + | 0.0374403i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.58579 | + | 1.58579i | −0.330659 | + | 0.330659i | −0.852837 | − | 0.522178i | \(-0.825120\pi\) |
0.522178 | + | 0.852837i | \(0.325120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.82843 | − | 4.82843i | 1.18868 | − | 0.840521i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.171573 | − | 0.171573i | 0.0282064 | − | 0.0282064i | −0.692863 | − | 0.721069i | \(-0.743651\pi\) |
0.721069 | + | 0.692863i | \(0.243651\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.757359 | + | 4.41421i | −0.121275 | + | 0.706840i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41421 | + | 2.41421i | 0.368164 | + | 0.368164i | 0.866807 | − | 0.498643i | \(-0.166168\pi\) |
−0.498643 | + | 0.866807i | \(0.666168\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.41421 | − | 6.41421i | −0.935609 | − | 0.935609i | 0.0624395 | − | 0.998049i | \(-0.480112\pi\) |
−0.998049 | + | 0.0624395i | \(0.980112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685i | 0.950979i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.58579 | + | 9.24264i | −0.222055 | + | 1.29423i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | + | 3.00000i | −0.412082 | + | 0.412082i | −0.882463 | − | 0.470381i | \(-0.844116\pi\) |
0.470381 | + | 0.882463i | \(0.344116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.82843 | + | 4.82843i | −0.904447 | + | 0.639541i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6569 | 1.49251 | 0.746254 | − | 0.665662i | \(-0.231851\pi\) | ||||
0.746254 | + | 0.665662i | \(0.231851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.757359 | + | 1.58579i | 0.0954183 | + | 0.199790i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.07107 | + | 4.07107i | −0.497360 | + | 0.497360i | −0.910615 | − | 0.413255i | \(-0.864392\pi\) |
0.413255 | + | 0.910615i | \(0.364392\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.82843 | − | 0.656854i | −0.460888 | − | 0.0790760i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.48528i | − | 0.769661i | −0.922987 | − | 0.384831i | \(-0.874260\pi\) | ||
0.922987 | − | 0.384831i | \(-0.125740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.65685 | − | 6.65685i | −0.779126 | − | 0.779126i | 0.200556 | − | 0.979682i | \(-0.435725\pi\) |
−0.979682 | + | 0.200556i | \(0.935725\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | − | 2.00000i | −0.227921 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.82843i | − | 0.543240i | −0.962405 | − | 0.271620i | \(-0.912441\pi\) | ||
0.962405 | − | 0.271620i | \(-0.0875595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.24264 | − | 5.24264i | 0.575455 | − | 0.575455i | −0.358193 | − | 0.933648i | \(-0.616607\pi\) |
0.933648 | + | 0.358193i | \(0.116607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.65685 | + | 10.8284i | 0.820901 | + | 1.16093i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.34315 | −0.460373 | −0.230186 | − | 0.973147i | \(-0.573934\pi\) | ||||
−0.230186 | + | 0.973147i | \(0.573934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.51472 | 0.158786 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.65685 | + | 8.00000i | 0.586588 | + | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.00000i | −0.101535 | + | 0.101535i | −0.756049 | − | 0.654515i | \(-0.772873\pi\) |
0.654515 | + | 0.756049i | \(0.272873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6569 | + | 4.82843i | 1.37257 | + | 0.485275i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.65685i | − | 0.164863i | −0.996597 | − | 0.0824316i | \(-0.973731\pi\) | ||
0.996597 | − | 0.0824316i | \(-0.0262686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.41421 | − | 8.41421i | −0.829077 | − | 0.829077i | 0.158312 | − | 0.987389i | \(-0.449395\pi\) |
−0.987389 | + | 0.158312i | \(0.949395\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4142 | + | 12.4142i | 1.20013 | + | 1.20013i | 0.974127 | + | 0.226000i | \(0.0725649\pi\) |
0.226000 | + | 0.974127i | \(0.427435\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.414214 | + | 0.0710678i | 0.0393154 | + | 0.00674546i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.48528 | + | 7.48528i | −0.704156 | + | 0.704156i | −0.965300 | − | 0.261144i | \(-0.915900\pi\) |
0.261144 | + | 0.965300i | \(0.415900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.00000 | + | 3.34315i | −0.647150 | + | 0.309074i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.17157 | 0.290738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | + | 5.65685i | −0.721336 | + | 0.510061i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.41421 | − | 8.41421i | 0.746641 | − | 0.746641i | −0.227206 | − | 0.973847i | \(-0.572959\pi\) |
0.973847 | + | 0.227206i | \(0.0729591\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | + | 5.82843i | −0.0880451 | + | 0.513164i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.17157i | 0.277102i | 0.990355 | + | 0.138551i | \(0.0442444\pi\) | ||||
−0.990355 | + | 0.138551i | \(0.955756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 2.00000i | 0.173422 | + | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.17157 | − | 4.17157i | −0.356402 | − | 0.356402i | 0.506083 | − | 0.862485i | \(-0.331093\pi\) |
−0.862485 | + | 0.506083i | \(0.831093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.17157i | − | 0.269009i | −0.990913 | − | 0.134505i | \(-0.957056\pi\) | ||
0.990913 | − | 0.134505i | \(-0.0429443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.65685 | − | 15.4853i | 0.223747 | − | 1.30410i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.82843 | − | 8.82843i | 0.738270 | − | 0.738270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.41421 | + | 6.65685i | −0.776471 | + | 0.549048i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.31371 | −0.763009 | −0.381504 | − | 0.924367i | \(-0.624594\pi\) | ||||
−0.381504 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.34315 | 0.190682 | 0.0953412 | − | 0.995445i | \(-0.469606\pi\) | ||||
0.0953412 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.6569 | + | 7.00000i | −1.18494 | + | 0.565916i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4853 | − | 11.4853i | 0.916625 | − | 0.916625i | −0.0801570 | − | 0.996782i | \(-0.525542\pi\) |
0.996782 | + | 0.0801570i | \(0.0255422\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.24264 | − | 1.24264i | −0.574379 | − | 0.0985478i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.31371i | 0.103535i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.41421 | + | 2.41421i | 0.189096 | + | 0.189096i | 0.795305 | − | 0.606209i | \(-0.207311\pi\) |
−0.606209 | + | 0.795305i | \(0.707311\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.757359 | − | 0.757359i | −0.0586062 | − | 0.0586062i | 0.677196 | − | 0.735802i | \(-0.263195\pi\) |
−0.735802 | + | 0.677196i | \(0.763195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.31371i | − | 0.485670i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.6569 | − | 4.82843i | −1.04437 | − | 0.369239i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6569 | − | 10.6569i | 0.810226 | − | 0.810226i | −0.174442 | − | 0.984667i | \(-0.555812\pi\) |
0.984667 | + | 0.174442i | \(0.0558121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | − | 5.65685i | −0.300658 | − | 0.425195i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3137 | 1.28692 | 0.643459 | − | 0.765481i | \(-0.277499\pi\) | ||||
0.643459 | + | 0.765481i | \(0.277499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6569 | + | 16.4853i | 0.861699 | + | 1.21863i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.4853 | − | 18.4853i | 1.35178 | − | 1.35178i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.48528 | + | 2.65685i | −0.108038 | + | 0.193258i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.1421i | 1.74686i | 0.486946 | + | 0.873432i | \(0.338111\pi\) | ||||
−0.486946 | + | 0.873432i | \(0.661889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.34315 | − | 3.34315i | −0.240645 | − | 0.240645i | 0.576472 | − | 0.817117i | \(-0.304429\pi\) |
−0.817117 | + | 0.576472i | \(0.804429\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.34315 | + | 3.34315i | 0.238189 | + | 0.238189i | 0.816100 | − | 0.577911i | \(-0.196132\pi\) |
−0.577911 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.51472i | − | 0.107376i | −0.998558 | − | 0.0536878i | \(-0.982902\pi\) | ||
0.998558 | − | 0.0536878i | \(-0.0170976\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.82843 | − | 1.68629i | −0.693244 | − | 0.118942i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.17157 | − | 3.17157i | 0.222601 | − | 0.222601i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.89949 | − | 6.07107i | −0.201529 | − | 0.421968i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.3137 | 1.61264 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9706 | 0.892930 | 0.446465 | − | 0.894801i | \(-0.352683\pi\) | ||||
0.446465 | + | 0.894801i | \(0.352683\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.17157 | − | 6.48528i | 0.628426 | − | 0.444364i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.34315 | − | 2.34315i | 0.159063 | − | 0.159063i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.75736 | − | 16.0711i | 0.186325 | − | 1.08598i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0000i | 0.941742i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.41421 | − | 8.41421i | −0.563457 | − | 0.563457i | 0.366830 | − | 0.930288i | \(-0.380443\pi\) |
−0.930288 | + | 0.366830i | \(0.880443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8995 | − | 14.8995i | −0.988914 | − | 0.988914i | 0.0110250 | − | 0.999939i | \(-0.496491\pi\) |
−0.999939 | + | 0.0110250i | \(0.996491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.6569i | − | 1.69545i | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||
0.530434 | − | 0.847726i | \(-0.322029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.828427 | − | 4.82843i | 0.0545065 | − | 0.317687i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.17157 | − | 6.17157i | 0.404313 | − | 0.404313i | −0.475437 | − | 0.879750i | \(-0.657710\pi\) |
0.879750 | + | 0.475437i | \(0.157710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.82843 | − | 4.82843i | 0.443554 | − | 0.313640i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6569 | −0.750884 | −0.375442 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375442 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.82843 | + | 8.82843i | −0.561739 | + | 0.561739i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6569 | + | 2.17157i | 0.802096 | + | 0.137618i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.51472i | − | 0.600564i | −0.953851 | − | 0.300282i | \(-0.902919\pi\) | ||
0.953851 | − | 0.300282i | \(-0.0970807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.65685 | + | 7.65685i | 0.481382 | + | 0.481382i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.48528 | − | 7.48528i | −0.466919 | − | 0.466919i | 0.433996 | − | 0.900915i | \(-0.357103\pi\) |
−0.900915 | + | 0.433996i | \(0.857103\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.142136i | − | 0.00883188i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.65685 | + | 21.6569i | −0.473947 | + | 1.34053i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8995 | + | 12.8995i | −0.795417 | + | 0.795417i | −0.982369 | − | 0.186952i | \(-0.940139\pi\) |
0.186952 | + | 0.982369i | \(0.440139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.34315 | − | 6.14214i | −0.265796 | − | 0.375893i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.6274 | −1.74544 | −0.872722 | − | 0.488217i | \(-0.837647\pi\) | ||||
−0.872722 | + | 0.488217i | \(0.837647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.6569 | −1.31556 | −0.657780 | − | 0.753210i | \(-0.728504\pi\) | ||||
−0.657780 | + | 0.753210i | \(0.728504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.51472 | + | 2.14214i | 0.0916749 | + | 0.129648i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.8284 | − | 13.8284i | 0.830870 | − | 0.830870i | −0.156766 | − | 0.987636i | \(-0.550107\pi\) |
0.987636 | + | 0.156766i | \(0.0501069\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | + | 16.0000i | −0.338667 | + | 0.957895i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.65685i | − | 0.337460i | −0.985662 | − | 0.168730i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168730i | \(-0.0539665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.24264 | − | 3.24264i | −0.192755 | − | 0.192755i | 0.604130 | − | 0.796885i | \(-0.293521\pi\) |
−0.796885 | + | 0.604130i | \(0.793521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.34315 | + | 2.34315i | 0.138312 | + | 0.138312i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3137i | 0.724336i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.41421 | − | 0.414214i | −0.141524 | − | 0.0242816i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.34315 | + | 5.34315i | −0.312150 | + | 0.312150i | −0.845742 | − | 0.533592i | \(-0.820842\pi\) |
0.533592 | + | 0.845742i | \(0.320842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.82843 | + | 24.1421i | 0.396226 | + | 1.40087i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.79899 | −0.335364 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34315 | − | 1.65685i | 0.134610 | − | 0.0951838i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8995 | − | 12.8995i | 0.736213 | − | 0.736213i | −0.235630 | − | 0.971843i | \(-0.575715\pi\) |
0.971843 | + | 0.235630i | \(0.0757153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.48528 | − | 20.3137i | 0.198271 | − | 1.15561i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 22.4853i | − | 1.27502i | −0.770441 | − | 0.637512i | \(-0.779964\pi\) | ||
0.770441 | − | 0.637512i | \(-0.220036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3137 | − | 20.3137i | −1.14820 | − | 1.14820i | −0.986907 | − | 0.161292i | \(-0.948434\pi\) |
−0.161292 | − | 0.986907i | \(-0.551566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.65685 | + | 6.65685i | 0.373886 | + | 0.373886i | 0.868891 | − | 0.495004i | \(-0.164834\pi\) |
−0.495004 | + | 0.868891i | \(0.664834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.9706i | − | 2.06995i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.14214 | + | 29.9706i | −0.287006 | + | 1.67279i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.4853 | + | 18.4853i | −1.02855 | + | 1.02855i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.65685 | − | 4.00000i | 0.312825 | − | 0.221201i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.31371 | −0.292954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.65685 | −0.0910689 | −0.0455345 | − | 0.998963i | \(-0.514499\pi\) | ||||
−0.0455345 | + | 0.998963i | \(0.514499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.313708 | + | 0.656854i | 0.0171911 | + | 0.0359954i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.00000i | −0.0544735 | + | 0.0544735i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0711 | − | 3.10051i | −0.981486 | − | 0.168396i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.3137i | − | 1.47912i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.65685 | + | 5.65685i | 0.305441 | + | 0.305441i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07107 | + | 2.07107i | 0.111181 | + | 0.111181i | 0.760509 | − | 0.649328i | \(-0.224950\pi\) |
−0.649328 | + | 0.760509i | \(0.724950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.65685i | − | 0.0886894i | −0.999016 | − | 0.0443447i | \(-0.985880\pi\) | ||
0.999016 | − | 0.0443447i | \(-0.0141200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.7279 | − | 6.55635i | −0.625990 | − | 0.349952i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.48528 | − | 1.48528i | 0.0790536 | − | 0.0790536i | −0.666474 | − | 0.745528i | \(-0.732197\pi\) |
0.745528 | + | 0.666474i | \(0.232197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.17157 | + | 4.48528i | 0.167857 | + | 0.237386i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6863 | −0.669557 | −0.334778 | − | 0.942297i | \(-0.608661\pi\) | ||||
−0.334778 | + | 0.942297i | \(0.608661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.31371 | −0.227037 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3137 | − | 17.4142i | −0.646302 | − | 0.914009i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2426 | + | 13.2426i | −0.691260 | + | 0.691260i | −0.962509 | − | 0.271249i | \(-0.912563\pi\) |
0.271249 | + | 0.962509i | \(0.412563\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.0000 | − | 5.65685i | −0.832927 | − | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.48528i | 0.129029i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.4853 | − | 17.4853i | −0.905354 | − | 0.905354i | 0.0905393 | − | 0.995893i | \(-0.471141\pi\) |
−0.995893 | + | 0.0905393i | \(0.971141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0000 | + | 14.0000i | 0.721037 | + | 0.721037i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.79899i | − | 0.503340i | −0.967813 | − | 0.251670i | \(-0.919020\pi\) | ||
0.967813 | − | 0.251670i | \(-0.0809798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.3137 | + | 3.48528i | 1.04070 | + | 0.178556i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.58579 | + | 9.58579i | −0.489811 | + | 0.489811i | −0.908246 | − | 0.418436i | \(-0.862579\pi\) |
0.418436 | + | 0.908246i | \(0.362579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.24264 | + | 4.41421i | −0.469830 | + | 0.224387i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3137 | 1.48626 | 0.743132 | − | 0.669145i | \(-0.233339\pi\) | ||||
0.743132 | + | 0.669145i | \(0.233339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1421 | −0.614054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.48528 | + | 3.17157i | −0.226253 | + | 0.159985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.17157 | + | 2.17157i | −0.108988 | + | 0.108988i | −0.759498 | − | 0.650510i | \(-0.774555\pi\) |
0.650510 | + | 0.759498i | \(0.274555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.828427 | + | 4.82843i | −0.0414732 | + | 0.241724i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.0000i | − | 0.799002i | −0.916733 | − | 0.399501i | \(-0.869183\pi\) | ||
0.916733 | − | 0.399501i | \(-0.130817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3431 | + | 10.3431i | 0.515229 | + | 0.515229i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.828427 | − | 0.828427i | −0.0410636 | − | 0.0410636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.3431i | − | 0.511436i | −0.966751 | − | 0.255718i | \(-0.917688\pi\) | ||
0.966751 | − | 0.255718i | \(-0.0823118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.72792 | − | 10.0711i | 0.0852321 | − | 0.496769i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.65685 | + | 1.65685i | −0.0815285 | + | 0.0815285i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.48528 | − | 3.17157i | 0.219645 | − | 0.155313i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.9411 | 1.85355 | 0.926773 | − | 0.375623i | \(-0.122571\pi\) | ||||
0.926773 | + | 0.375623i | \(0.122571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.97056 | −0.144776 | −0.0723882 | − | 0.997377i | \(-0.523062\pi\) | ||||
−0.0723882 | + | 0.997377i | \(0.523062\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.5563 | − | 11.7279i | 1.19397 | − | 0.570231i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.82843 | − | 4.82843i | 0.233664 | − | 0.233664i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.3137 | + | 3.65685i | 1.02904 | + | 0.176555i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.14214i | 0.392193i | 0.980585 | + | 0.196096i | \(0.0628266\pi\) | ||||
−0.980585 | + | 0.196096i | \(0.937173\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0000 | + | 15.0000i | 0.720854 | + | 0.720854i | 0.968779 | − | 0.247925i | \(-0.0797487\pi\) |
−0.247925 | + | 0.968779i | \(0.579749\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.65685 | − | 7.65685i | −0.366277 | − | 0.366277i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7990i | 1.23132i | 0.788012 | + | 0.615659i | \(0.211110\pi\) | ||||
−0.788012 | + | 0.615659i | \(0.788890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8284 | − | 6.65685i | −0.896592 | − | 0.316993i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0711 | + | 14.0711i | −0.668537 | + | 0.668537i | −0.957377 | − | 0.288841i | \(-0.906730\pi\) |
0.288841 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.31371 | − | 13.1716i | −0.440523 | − | 0.622994i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3137 | −1.00586 | −0.502928 | − | 0.864328i | \(-0.667744\pi\) | ||||
−0.502928 | + | 0.864328i | \(0.667744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3137 | 1.28615 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.34315 | + | 3.31371i | 0.110091 | + | 0.155692i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.00000i | −0.0467780 | + | 0.0467780i | −0.730109 | − | 0.683331i | \(-0.760531\pi\) |
0.683331 | + | 0.730109i | \(0.260531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.5563 | − | 13.7279i | −1.14619 | − | 0.640765i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.97056i | − | 0.231502i | −0.993278 | − | 0.115751i | \(-0.963073\pi\) | ||
0.993278 | − | 0.115751i | \(-0.0369275\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.4142 | − | 24.4142i | −1.13462 | − | 1.13462i | −0.989398 | − | 0.145226i | \(-0.953609\pi\) |
−0.145226 | − | 0.989398i | \(-0.546391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3848 | + | 13.3848i | 0.619374 | + | 0.619374i | 0.945371 | − | 0.325997i | \(-0.105700\pi\) |
−0.325997 | + | 0.945371i | \(0.605700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.37258i | 0.155731i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.7279 | + | 4.75736i | 1.27764 | + | 0.219208i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6569 | − | 11.6569i | 0.535983 | − | 0.535983i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.48528 | − | 11.4853i | −0.251154 | − | 0.525875i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6274 | −1.03387 | −0.516937 | − | 0.856024i | \(-0.672928\pi\) | ||||
−0.516937 | + | 0.856024i | \(0.672928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.627417 | 0.0286078 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.85786 | + | 1.31371i | −0.0845358 | + | 0.0597758i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.5563 | + | 16.5563i | −0.750240 | + | 0.750240i | −0.974524 | − | 0.224284i | \(-0.927996\pi\) |
0.224284 | + | 0.974524i | \(0.427996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | + | 5.82843i | −0.0452216 | + | 0.263571i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4853i | 1.73682i | 0.495850 | + | 0.868408i | \(0.334857\pi\) | ||||
−0.495850 | + | 0.868408i | \(0.665143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.3137 | + | 29.3137i | 1.32022 | + | 1.32022i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.68629 | − | 2.68629i | −0.120497 | − | 0.120497i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.7696i | 1.73556i | 0.496945 | + | 0.867782i | \(0.334455\pi\) | ||||
−0.496945 | + | 0.867782i | \(0.665545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.313708 | − | 1.82843i | 0.0140155 | − | 0.0816881i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0711 | − | 20.0711i | 0.894925 | − | 0.894925i | −0.100057 | − | 0.994982i | \(-0.531903\pi\) |
0.994982 | + | 0.100057i | \(0.0319025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.92893 | − | 6.31371i | 0.396548 | − | 0.280402i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.65685 | 0.339384 | 0.169692 | − | 0.985497i | \(-0.445723\pi\) | ||||
0.169692 | + | 0.985497i | \(0.445723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.51472 | −0.243957 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.82843 | − | 24.1421i | −0.301482 | − | 1.06590i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.9706 | + | 30.9706i | −1.36208 | + | 1.36208i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.7279 | + | 4.41421i | 1.12933 | + | 0.193762i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0000i | 1.05146i | 0.850652 | + | 0.525730i | \(0.176208\pi\) | ||||
−0.850652 | + | 0.525730i | \(0.823792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.10051 | + | 7.10051i | 0.310483 | + | 0.310483i | 0.845097 | − | 0.534613i | \(-0.179543\pi\) |
−0.534613 | + | 0.845097i | \(0.679543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.6569 | + | 21.6569i | 0.943387 | + | 0.943387i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.9706i | 0.781329i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | − | 11.3137i | 0.173585 | − | 0.490973i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.3431 | + | 10.3431i | −0.448011 | + | 0.448011i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | − | 16.9706i | −0.517838 | − | 0.732334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.1421 | 1.38446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.68629 | −0.287466 | −0.143733 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143733 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3137 | + | 24.4853i | 0.743002 | + | 1.05076i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.72792 | + | 9.72792i | −0.415936 | + | 0.415936i | −0.883800 | − | 0.467864i | \(-0.845024\pi\) |
0.467864 | + | 0.883800i | \(0.345024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.6569 | + | 32.9706i | −0.497502 | + | 1.40715i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.9706i | 1.57500i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | − | 2.00000i | −0.0850487 | − | 0.0850487i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.6274 | − | 29.6274i | −1.25535 | − | 1.25535i | −0.953287 | − | 0.302067i | \(-0.902323\pi\) |
−0.302067 | − | 0.953287i | \(-0.597677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.82843i | 0.373403i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.6274 | + | 7.65685i | 1.88417 | + | 0.323273i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.5563 | − | 32.5563i | 1.37209 | − | 1.37209i | 0.514740 | − | 0.857346i | \(-0.327888\pi\) |
0.857346 | − | 0.514740i | \(-0.172112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.24264 | + | 0.556349i | −0.220170 | + | 0.0233645i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.6863 | −0.951059 | −0.475529 | − | 0.879700i | \(-0.657743\pi\) | ||||
−0.475529 | + | 0.879700i | \(0.657743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.9706 | −1.21238 | −0.606190 | − | 0.795320i | \(-0.707303\pi\) | ||||
−0.606190 | + | 0.795320i | \(0.707303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.1421 | + | 24.1421i | −1.42631 | + | 1.00855i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.34315 | + | 3.34315i | −0.139177 | + | 0.139177i | −0.773263 | − | 0.634086i | \(-0.781377\pi\) |
0.634086 | + | 0.773263i | \(0.281377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.38478 | − | 8.07107i | 0.0575493 | − | 0.335422i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.34315i | − | 0.180184i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.4853 | + | 14.4853i | 0.599919 | + | 0.599919i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5563 | − | 20.5563i | −0.848451 | − | 0.848451i | 0.141489 | − | 0.989940i | \(-0.454811\pi\) |
−0.989940 | + | 0.141489i | \(0.954811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3137i | 1.12544i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.38478 | + | 8.07107i | −0.0569621 | + | 0.331999i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.48528 | − | 1.48528i | 0.0609932 | − | 0.0609932i | −0.675952 | − | 0.736945i | \(-0.736267\pi\) |
0.736945 | + | 0.675952i | \(0.236267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.14214 | − | 1.51472i | 0.0876718 | − | 0.0619933i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9411 | 1.05993 | 0.529963 | − | 0.848021i | \(-0.322206\pi\) | ||||
0.529963 | + | 0.848021i | \(0.322206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9706 | 0.773825 | 0.386913 | − | 0.922116i | \(-0.373541\pi\) | ||||
0.386913 | + | 0.922116i | \(0.373541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.44365 | − | 15.5858i | −0.303129 | − | 0.634702i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0416 | − | 15.0416i | 0.610521 | − | 0.610521i | −0.332561 | − | 0.943082i | \(-0.607913\pi\) |
0.943082 | + | 0.332561i | \(0.107913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.65685 | + | 1.31371i | 0.310271 | + | 0.0532342i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 23.4558i | − | 0.948922i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.48528 | + | 7.48528i | 0.302328 | + | 0.302328i | 0.841924 | − | 0.539596i | \(-0.181423\pi\) |
−0.539596 | + | 0.841924i | \(0.681423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8284 | − | 17.8284i | −0.717745 | − | 0.717745i | 0.250398 | − | 0.968143i | \(-0.419439\pi\) |
−0.968143 | + | 0.250398i | \(0.919439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.14214i | 0.327260i | 0.986522 | + | 0.163630i | \(0.0523203\pi\) | ||||
−0.986522 | + | 0.163630i | \(0.947680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.68629 | − | 10.1716i | 0.228183 | − | 0.408171i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.79899 | + | 1.79899i | −0.0720750 | + | 0.0720750i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.3137 | + | 32.9706i | 0.931060 | + | 1.31672i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.31371 | 0.0523810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.5980 | 1.89485 | 0.947423 | − | 0.319984i | \(-0.103678\pi\) | ||||
0.947423 | + | 0.319984i | \(0.103678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.9706 | + | 18.3431i | 0.515534 | + | 0.729075i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.1716 | + | 12.1716i | −0.482255 | + | 0.482255i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.3431 | + | 6.48528i | 0.725644 | + | 0.256554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.2843i | − | 1.43314i | −0.697514 | − | 0.716571i | \(-0.745710\pi\) | ||
0.697514 | − | 0.716571i | \(-0.254290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.6985 | + | 30.6985i | 1.21063 | + | 1.21063i | 0.970820 | + | 0.239810i | \(0.0770852\pi\) |
0.239810 | + | 0.970820i | \(0.422915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2132 | + | 16.2132i | 0.637407 | + | 0.637407i | 0.949915 | − | 0.312508i | \(-0.101169\pi\) |
−0.312508 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3137i | 0.758129i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.65685 | + | 0.970563i | 0.221710 | + | 0.0380394i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.3431 | − | 15.3431i | 0.600424 | − | 0.600424i | −0.340001 | − | 0.940425i | \(-0.610428\pi\) |
0.940425 | + | 0.340001i | \(0.110428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.4853 | − | 12.1716i | 0.994276 | − | 0.474858i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.6274 | −1.34889 | −0.674446 | − | 0.738324i | \(-0.735618\pi\) | ||||
−0.674446 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.65685 | 0.142235 | 0.0711176 | − | 0.997468i | \(-0.477343\pi\) | ||||
0.0711176 | + | 0.997468i | \(0.477343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.7990 | + | 14.0000i | −0.768929 | + | 0.543715i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.1421 | + | 12.1421i | −0.470145 | + | 0.470145i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.48528 | − | 20.3137i | 0.134749 | − | 0.785373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 56.2843i | − | 2.17283i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3137 | + | 26.3137i | 1.01432 | + | 1.01432i | 0.999896 | + | 0.0144229i | \(0.00459112\pi\) |
0.0144229 | + | 0.999896i | \(0.495409\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.2843 | + | 21.2843i | 0.818021 | + | 0.818021i | 0.985821 | − | 0.167800i | \(-0.0536663\pi\) |
−0.167800 | + | 0.985821i | \(0.553666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.828427i | 0.0317921i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.17157 | − | 35.9706i | 0.236495 | − | 1.37839i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.55635 | − | 8.55635i | 0.327400 | − | 0.327400i | −0.524197 | − | 0.851597i | \(-0.675635\pi\) |
0.851597 | + | 0.524197i | \(0.175635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.2843 | − | 25.6569i | 1.38433 | − | 0.978870i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.9706 | −0.417945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.3431 | 0.849973 | 0.424987 | − | 0.905200i | \(-0.360279\pi\) | ||||
0.424987 | + | 0.905200i | \(0.360279\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.65685 | − | 3.65685i | 0.290860 | − | 0.138912i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.6569 | + | 21.6569i | −0.820312 | + | 0.820312i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.8995 | + | 2.55635i | 0.563551 | + | 0.0966900i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.00000i | 0.151078i | 0.997143 | + | 0.0755390i | \(0.0240677\pi\) | ||||
−0.997143 | + | 0.0755390i | \(0.975932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.828427 | + | 0.828427i | 0.0312447 | + | 0.0312447i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.686292 | − | 0.686292i | −0.0258106 | − | 0.0258106i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2843i | 0.912015i | 0.889976 | + | 0.456007i | \(0.150721\pi\) | ||||
−0.889976 | + | 0.456007i | \(0.849279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | + | 4.82843i | 0.512172 | + | 0.181080i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.97056 | + | 8.97056i | −0.335950 | + | 0.335950i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | + | 22.6274i | 0.597531 | + | 0.845036i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.97056 | −0.259597 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.6569 | − | 16.4853i | −0.433523 | − | 0.613094i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.2426 | + | 21.2426i | −0.787846 | + | 0.787846i | −0.981141 | − | 0.193295i | \(-0.938083\pi\) |
0.193295 | + | 0.981141i | \(0.438083\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4853i | 0.683703i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.1421 | − | 23.1421i | −0.854774 | − | 0.854774i | 0.135942 | − | 0.990717i | \(-0.456594\pi\) |
−0.990717 | + | 0.135942i | \(0.956594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.6569 | + | 19.6569i | 0.724070 | + | 0.724070i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.8284i | 1.94333i | 0.236372 | + | 0.971663i | \(0.424041\pi\) | ||||
−0.236372 | + | 0.971663i | \(0.575959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3137 | − | 3.65685i | −0.782979 | − | 0.134338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.615224 | + | 0.615224i | −0.0225704 | + | 0.0225704i | −0.718302 | − | 0.695732i | \(-0.755080\pi\) |
0.695732 | + | 0.718302i | \(0.255080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.58579 | + | 20.0711i | 0.350726 | + | 0.734362i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2843 | 0.375779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.2843 | −1.61596 | −0.807978 | − | 0.589213i | \(-0.799438\pi\) | ||||
−0.807978 | + | 0.589213i | \(0.799438\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4558 | − | 9.51472i | 0.490358 | − | 0.346736i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4558 | − | 36.4558i | 1.32501 | − | 1.32501i | 0.415347 | − | 0.909663i | \(-0.363660\pi\) |
0.909663 | − | 0.415347i | \(-0.136340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.17157 | + | 18.4853i | −0.115121 | + | 0.670973i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.3137i | 1.28012i | 0.768325 | + | 0.640060i | \(0.221091\pi\) | ||||
−0.768325 | + | 0.640060i | \(0.778909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.65685 | − | 1.65685i | −0.0599822 | − | 0.0599822i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.31371 | − | 7.31371i | −0.264083 | − | 0.264083i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.9411i | − | 0.646974i | −0.946233 | − | 0.323487i | \(-0.895145\pi\) | ||
0.946233 | − | 0.323487i | \(-0.104855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.10051 | − | 18.0711i | 0.111662 | − | 0.650814i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.656854 | + | 0.656854i | −0.0236254 | + | 0.0236254i | −0.718821 | − | 0.695195i | \(-0.755318\pi\) |
0.695195 | + | 0.718821i | \(0.255318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.201010 | − | 0.142136i | 0.00721120 | − | 0.00509909i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.3137 | −0.978615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.3137 | −1.12049 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.2843 | + | 10.8284i | −1.36817 | + | 0.386976i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.4142 | + | 30.4142i | −1.08415 | + | 1.08415i | −0.0880320 | + | 0.996118i | \(0.528058\pi\) |
−0.996118 | + | 0.0880320i | \(0.971942\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.1421 | − | 5.34315i | −1.10869 | − | 0.190221i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.20101i | 0.220483i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3137 | + | 21.3137i | 0.756872 | + | 0.756872i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.65685 | + | 6.65685i | 0.235798 | + | 0.235798i | 0.815108 | − | 0.579310i | \(-0.196678\pi\) |
−0.579310 | + | 0.815108i | \(0.696678\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.1127i | − | 1.73748i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.34315 | − | 12.2843i | 0.153458 | − | 0.434043i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.1421 | + | 32.1421i | −1.13427 | + | 1.13427i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.6274 | − | 40.4853i | −1.00773 | − | 1.42515i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6569 | 1.53489 | 0.767447 | − | 0.641113i | \(-0.221527\pi\) | ||||
0.767447 | + | 0.641113i | \(0.221527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.3431 | −0.784574 | −0.392287 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392287 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.6569 | − | 30.6274i | −0.759539 | − | 1.07415i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6569 | + | 11.6569i | −0.407822 | + | 0.407822i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.51472 | + | 4.28427i | −0.0529286 | + | 0.149705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.9411i | 1.04495i | 0.852654 | + | 0.522476i | \(0.174992\pi\) | ||||
−0.852654 | + | 0.522476i | \(0.825008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7279 | − | 19.7279i | −0.687672 | − | 0.687672i | 0.274045 | − | 0.961717i | \(-0.411638\pi\) |
−0.961717 | + | 0.274045i | \(0.911638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.5269 | − | 37.5269i | −1.30494 | − | 1.30494i | −0.925020 | − | 0.379919i | \(-0.875952\pi\) |
−0.379919 | − | 0.925020i | \(-0.624048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.31371i | 0.254016i | 0.991902 | + | 0.127008i | \(0.0405373\pi\) | ||||
−0.991902 | + | 0.127008i | \(0.959463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.3848 | + | 5.72792i | 1.15811 | + | 0.198699i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.4853 | + | 25.4853i | −0.883013 | + | 0.883013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.2843 | + | 8.00000i | −0.977647 | + | 0.276520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.3137 | −1.21916 | −0.609582 | − | 0.792723i | \(-0.708663\pi\) | ||||
−0.609582 | + | 0.792723i | \(0.708663\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.00000 | − | 5.65685i | 0.275535 | − | 0.194832i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.10051 | + | 5.10051i | −0.175255 | + | 0.175255i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.34315 | − | 7.82843i | 0.0460966 | − | 0.268671i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.544156i | 0.0186534i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.4558 | − | 26.4558i | −0.905831 | − | 0.905831i | 0.0901017 | − | 0.995933i | \(-0.471281\pi\) |
−0.995933 | + | 0.0901017i | \(0.971281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5147 | + | 16.5147i | 0.564132 | + | 0.564132i | 0.930479 | − | 0.366346i | \(-0.119392\pi\) |
−0.366346 | + | 0.930479i | \(0.619392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32.4264i | − | 1.10637i | −0.833057 | − | 0.553187i | \(-0.813411\pi\) | ||
0.833057 | − | 0.553187i | \(-0.186589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.970563 | + | 5.65685i | −0.0330767 | + | 0.192785i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.41421 | − | 6.41421i | 0.218342 | − | 0.218342i | −0.589457 | − | 0.807800i | \(-0.700658\pi\) |
0.807800 | + | 0.589457i | \(0.200658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.4142 | + | 12.3137i | −0.591418 | + | 0.418195i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.3137 | −0.790863 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.8873 | −0.504437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.82843 | − | 3.82843i | −0.0618829 | − | 0.129573i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.4558 | + | 38.4558i | −1.29856 | + | 1.29856i | −0.369219 | + | 0.929342i | \(0.620375\pi\) |
−0.929342 | + | 0.369219i | \(0.879625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.8995 | − | 2.21320i | −0.435089 | − | 0.0746495i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9706i | 0.841280i | 0.907228 | + | 0.420640i | \(0.138194\pi\) | ||||
−0.907228 | + | 0.420640i | \(0.861806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.4142 | + | 34.4142i | 1.15813 | + | 1.15813i | 0.984877 | + | 0.173253i | \(0.0554279\pi\) |
0.173253 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.7279 | − | 17.7279i | −0.595245 | − | 0.595245i | 0.343798 | − | 0.939044i | \(-0.388286\pi\) |
−0.939044 | + | 0.343798i | \(0.888286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.97056i | − | 0.233785i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.3137 | + | 33.7990i | −0.915044 | + | 1.13231i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.9706 | − | 30.9706i | 1.03639 | − | 1.03639i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.79899 | − | 8.20101i | −0.193623 | − | 0.273824i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.3137 | 1.44459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.9706 | −0.765260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00000 | + | 2.82843i | 0.0665558 | + | 0.0941242i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5858 | − | 25.5858i | 0.849562 | − | 0.849562i | −0.140516 | − | 0.990078i | \(-0.544876\pi\) |
0.990078 | + | 0.140516i | \(0.0448762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.68629 | + | 1.65685i | 0.155434 | + | 0.0549544i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.1716i | − | 1.16529i | −0.812728 | − | 0.582643i | \(-0.802019\pi\) | ||
0.812728 | − | 0.582643i | \(-0.197981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.3137 | − | 25.3137i | −0.837761 | − | 0.837761i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.31371 | + | 1.31371i | 0.0433825 | + | 0.0433825i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.17157i | 0.104621i | 0.998631 | + | 0.0523103i | \(0.0166585\pi\) | ||||
−0.998631 | + | 0.0523103i | \(0.983342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.1421 | + | 5.34315i | 1.02617 | + | 0.176063i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.8579 | − | 11.8579i | 0.390306 | − | 0.390306i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.2132 | − | 15.3848i | 1.05802 | − | 0.505302i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.9411 | 1.83537 | 0.917684 | − | 0.397310i | \(-0.130056\pi\) | ||||
0.917684 | + | 0.397310i | \(0.130056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.1421 | −1.05342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.7990 | − | 22.4853i | 1.04105 | − | 0.736135i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0000 | − | 31.0000i | 1.01273 | − | 1.01273i | 0.0128079 | − | 0.999918i | \(-0.495923\pi\) |
0.999918 | − | 0.0128079i | \(-0.00407699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.41421 | − | 49.0416i | 0.274587 | − | 1.60041i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5980i | 1.16046i | 0.814452 | + | 0.580230i | \(0.197038\pi\) | ||||
−0.814452 | + | 0.580230i | \(0.802962\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.97056 | − | 8.97056i | −0.292122 | − | 0.292122i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7279 | + | 23.7279i | 0.771054 | + | 0.771054i | 0.978291 | − | 0.207237i | \(-0.0664471\pi\) |
−0.207237 | + | 0.978291i | \(0.566447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 24.3431i | − | 0.790212i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.75736 | + | 16.0711i | −0.0894135 | + | 0.521140i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.48528 | − | 1.48528i | 0.0481130 | − | 0.0481130i | −0.682641 | − | 0.730754i | \(-0.739169\pi\) |
0.730754 | + | 0.682641i | \(0.239169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 52.2843 | − | 36.9706i | 1.69011 | − | 1.19509i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.45584 | −0.111595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.5269 | + | 22.6985i | −1.53153 | + | 0.731448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5858 | + | 15.5858i | −0.501205 | + | 0.501205i | −0.911812 | − | 0.410607i | \(-0.865317\pi\) |
0.410607 | + | 0.911812i | \(0.365317\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.6274 | − | 7.65685i | −1.43364 | − | 0.245974i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 25.5147i | − | 0.818806i | −0.912354 | − | 0.409403i | \(-0.865737\pi\) | ||
0.912354 | − | 0.409403i | \(-0.134263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.31371 | − | 1.31371i | −0.0421156 | − | 0.0421156i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.14214 | − | 5.14214i | −0.164511 | − | 0.164511i | 0.620050 | − | 0.784562i | \(-0.287112\pi\) |
−0.784562 | + | 0.620050i | \(0.787112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.9706i | 0.670222i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3137 | + | 4.00000i | 0.361219 | + | 0.127710i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6985 | − | 26.6985i | 0.851549 | − | 0.851549i | −0.138775 | − | 0.990324i | \(-0.544316\pi\) |
0.990324 | + | 0.138775i | \(0.0443163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.31371 | − | 7.51472i | −0.169137 | − | 0.239196i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.65685 | −0.243474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.0294 | 0.477426 | 0.238713 | − | 0.971090i | \(-0.423275\pi\) | ||||
0.238713 | + | 0.971090i | \(0.423275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.65685 | − | 2.34315i | −0.0525787 | − | 0.0743575i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.79899 | + | 8.79899i | −0.278667 | + | 0.278667i | −0.832577 | − | 0.553910i | \(-0.813135\pi\) |
0.553910 | + | 0.832577i | \(0.313135\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.615224 | + | 1.10051i | −0.0194648 | + | 0.0348184i |
(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 | 1200.2.v.j.593.2 | 4 | ||
3.2 | odd | 2 | 1200.2.v.d.593.2 | 4 | |||
4.3 | odd | 2 | 600.2.r.b.593.1 | 4 | |||
5.2 | odd | 4 | 1200.2.v.d.257.2 | 4 | |||
5.3 | odd | 4 | 240.2.v.c.17.1 | 4 | |||
5.4 | even | 2 | 240.2.v.a.113.1 | 4 | |||
12.11 | even | 2 | 600.2.r.c.593.1 | 4 | |||
15.2 | even | 4 | inner | 1200.2.v.j.257.1 | 4 | ||
15.8 | even | 4 | 240.2.v.a.17.2 | 4 | |||
15.14 | odd | 2 | 240.2.v.c.113.1 | 4 | |||
20.3 | even | 4 | 120.2.r.b.17.2 | ✓ | 4 | ||
20.7 | even | 4 | 600.2.r.c.257.1 | 4 | |||
20.19 | odd | 2 | 120.2.r.c.113.2 | yes | 4 | ||
40.3 | even | 4 | 960.2.v.f.257.1 | 4 | |||
40.13 | odd | 4 | 960.2.v.g.257.2 | 4 | |||
40.19 | odd | 2 | 960.2.v.a.833.1 | 4 | |||
40.29 | even | 2 | 960.2.v.i.833.2 | 4 | |||
60.23 | odd | 4 | 120.2.r.c.17.1 | yes | 4 | ||
60.47 | odd | 4 | 600.2.r.b.257.2 | 4 | |||
60.59 | even | 2 | 120.2.r.b.113.2 | yes | 4 | ||
120.29 | odd | 2 | 960.2.v.g.833.2 | 4 | |||
120.53 | even | 4 | 960.2.v.i.257.1 | 4 | |||
120.59 | even | 2 | 960.2.v.f.833.1 | 4 | |||
120.83 | odd | 4 | 960.2.v.a.257.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.r.b.17.2 | ✓ | 4 | 20.3 | even | 4 | ||
120.2.r.b.113.2 | yes | 4 | 60.59 | even | 2 | ||
120.2.r.c.17.1 | yes | 4 | 60.23 | odd | 4 | ||
120.2.r.c.113.2 | yes | 4 | 20.19 | odd | 2 | ||
240.2.v.a.17.2 | 4 | 15.8 | even | 4 | |||
240.2.v.a.113.1 | 4 | 5.4 | even | 2 | |||
240.2.v.c.17.1 | 4 | 5.3 | odd | 4 | |||
240.2.v.c.113.1 | 4 | 15.14 | odd | 2 | |||
600.2.r.b.257.2 | 4 | 60.47 | odd | 4 | |||
600.2.r.b.593.1 | 4 | 4.3 | odd | 2 | |||
600.2.r.c.257.1 | 4 | 20.7 | even | 4 | |||
600.2.r.c.593.1 | 4 | 12.11 | even | 2 | |||
960.2.v.a.257.2 | 4 | 120.83 | odd | 4 | |||
960.2.v.a.833.1 | 4 | 40.19 | odd | 2 | |||
960.2.v.f.257.1 | 4 | 40.3 | even | 4 | |||
960.2.v.f.833.1 | 4 | 120.59 | even | 2 | |||
960.2.v.g.257.2 | 4 | 40.13 | odd | 4 | |||
960.2.v.g.833.2 | 4 | 120.29 | odd | 2 | |||
960.2.v.i.257.1 | 4 | 120.53 | even | 4 | |||
960.2.v.i.833.2 | 4 | 40.29 | even | 2 | |||
1200.2.v.d.257.2 | 4 | 5.2 | odd | 4 | |||
1200.2.v.d.593.2 | 4 | 3.2 | odd | 2 | |||
1200.2.v.j.257.1 | 4 | 15.2 | even | 4 | inner | ||
1200.2.v.j.593.2 | 4 | 1.1 | even | 1 | trivial |