Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(349,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.b (of order \(2\), degree \(1\), 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: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 145) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.349 |
Dual form | 725.2.b.c.349.4 |
$q$-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 \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).
\(n\) | \(176\) | \(552\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.41421i | − 1.70711i | −0.521005 | − | 0.853553i | \(-0.674443\pi\) | ||||
0.521005 | − | 0.853553i | \(-0.325557\pi\) | |||||||
\(3\) | 2.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.82843 | 1.97120 | ||||||||
\(7\) | 0.828427i | 0.313116i | 0.987669 | + | 0.156558i | \(0.0500398\pi\) | ||||
−0.987669 | + | 0.156558i | \(0.949960\pi\) | |||||||
\(8\) | 4.41421i | 1.56066i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | − 7.65685i | − 2.21034i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 2.82843i | − 0.685994i | −0.939336 | − | 0.342997i | \(-0.888558\pi\) | ||||
0.939336 | − | 0.342997i | \(-0.111442\pi\) | |||||||
\(18\) | 2.41421i | 0.569036i | ||||||||
\(19\) | −0.828427 | −0.190054 | −0.0950271 | − | 0.995475i | \(-0.530294\pi\) | ||||
−0.0950271 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.65685 | −0.361555 | ||||||||
\(22\) | 11.6569i | 2.48525i | ||||||||
\(23\) | 8.82843i | 1.84085i | 0.390914 | + | 0.920427i | \(0.372159\pi\) | ||||
−0.390914 | + | 0.920427i | \(0.627841\pi\) | |||||||
\(24\) | −8.82843 | −1.80210 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 3.17157i | − 0.599371i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4853 | −1.88321 | −0.941606 | − | 0.336717i | \(-0.890684\pi\) | ||||
−0.941606 | + | 0.336717i | \(0.890684\pi\) | |||||||
\(32\) | 1.58579i | 0.280330i | ||||||||
\(33\) | − 9.65685i | − 1.68104i | ||||||||
\(34\) | −6.82843 | −1.17107 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 8.48528i | 1.39497i | 0.716599 | + | 0.697486i | \(0.245698\pi\) | ||||
−0.716599 | + | 0.697486i | \(0.754302\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 4.00000i | 0.617213i | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 18.4853 | 2.78676 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.3137 | 3.14253 | ||||||||
\(47\) | − 0.343146i | − 0.0500530i | −0.999687 | − | 0.0250265i | \(-0.992033\pi\) | ||||
0.999687 | − | 0.0250265i | \(-0.00796701\pi\) | |||||||
\(48\) | 6.00000i | 0.866025i | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.65685 | 0.792118 | ||||||||
\(52\) | − 7.65685i | − 1.06181i | ||||||||
\(53\) | − 7.65685i | − 1.05175i | −0.850562 | − | 0.525875i | \(-0.823738\pi\) | ||||
0.850562 | − | 0.525875i | \(-0.176262\pi\) | |||||||
\(54\) | 9.65685 | 1.31413 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.65685 | −0.488668 | ||||||||
\(57\) | − 1.65685i | − 0.219456i | ||||||||
\(58\) | 2.41421i | 0.317002i | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.65685 | 0.980360 | 0.490180 | − | 0.871621i | \(-0.336931\pi\) | ||||
0.490180 | + | 0.871621i | \(0.336931\pi\) | |||||||
\(62\) | 25.3137i | 3.21484i | ||||||||
\(63\) | − 0.828427i | − 0.104372i | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −23.3137 | −2.86972 | ||||||||
\(67\) | − 10.4853i | − 1.28098i | −0.767966 | − | 0.640490i | \(-0.778731\pi\) | ||||
0.767966 | − | 0.640490i | \(-0.221269\pi\) | |||||||
\(68\) | 10.8284i | 1.31314i | ||||||||
\(69\) | −17.6569 | −2.12564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.31371 | 0.867978 | 0.433989 | − | 0.900918i | \(-0.357106\pi\) | ||||
0.433989 | + | 0.900918i | \(0.357106\pi\) | |||||||
\(72\) | − 4.41421i | − 0.520220i | ||||||||
\(73\) | 8.48528i | 0.993127i | 0.868000 | + | 0.496564i | \(0.165405\pi\) | ||||
−0.868000 | + | 0.496564i | \(0.834595\pi\) | |||||||
\(74\) | 20.4853 | 2.38137 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.17157 | 0.363804 | ||||||||
\(77\) | − 4.00000i | − 0.455842i | ||||||||
\(78\) | 9.65685i | 1.09342i | ||||||||
\(79\) | −14.4853 | −1.62972 | −0.814861 | − | 0.579657i | \(-0.803187\pi\) | ||||
−0.814861 | + | 0.579657i | \(0.803187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 14.4853i | 1.59963i | ||||||||
\(83\) | − 12.8284i | − 1.40810i | −0.710149 | − | 0.704051i | \(-0.751372\pi\) | ||||
0.710149 | − | 0.704051i | \(-0.248628\pi\) | |||||||
\(84\) | 6.34315 | 0.692094 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.4853 | 1.56199 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | − 21.3137i | − 2.27205i | ||||||||
\(89\) | −3.65685 | −0.387626 | −0.193813 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193813 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.65685 | −0.173686 | ||||||||
\(92\) | − 33.7990i | − 3.52379i | ||||||||
\(93\) | − 20.9706i | − 2.17455i | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.17157 | −0.323697 | ||||||||
\(97\) | 4.48528i | 0.455411i | 0.973730 | + | 0.227706i | \(0.0731224\pi\) | ||||
−0.973730 | + | 0.227706i | \(0.926878\pi\) | |||||||
\(98\) | − 15.2426i | − 1.53974i | ||||||||
\(99\) | 4.82843 | 0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.34315 | 0.432159 | 0.216080 | − | 0.976376i | \(-0.430673\pi\) | ||||
0.216080 | + | 0.976376i | \(0.430673\pi\) | |||||||
\(102\) | − 13.6569i | − 1.35223i | ||||||||
\(103\) | 12.1421i | 1.19640i | 0.801347 | + | 0.598200i | \(0.204117\pi\) | ||||
−0.801347 | + | 0.598200i | \(0.795883\pi\) | |||||||
\(104\) | −8.82843 | −0.865699 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.4853 | −1.79545 | ||||||||
\(107\) | − 8.14214i | − 0.787130i | −0.919297 | − | 0.393565i | \(-0.871242\pi\) | ||||
0.919297 | − | 0.393565i | \(-0.128758\pi\) | |||||||
\(108\) | − 15.3137i | − 1.47356i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.9706 | −1.61077 | ||||||||
\(112\) | 2.48528i | 0.234837i | ||||||||
\(113\) | − 2.82843i | − 0.266076i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) | ||||
0.991111 | − | 0.133038i | \(-0.0424732\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.82843 | 0.355461 | ||||||||
\(117\) | − 2.00000i | − 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | − 18.4853i | − 1.67358i | ||||||||
\(123\) | − 12.0000i | − 1.08200i | ||||||||
\(124\) | 40.1421 | 3.60487 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | − 20.5563i | − 1.81694i | ||||||||
\(129\) | −12.0000 | −1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1421 | 1.41034 | 0.705172 | − | 0.709036i | \(-0.250870\pi\) | ||||
0.705172 | + | 0.709036i | \(0.250870\pi\) | |||||||
\(132\) | 36.9706i | 3.21787i | ||||||||
\(133\) | − 0.686292i | − 0.0595090i | ||||||||
\(134\) | −25.3137 | −2.18677 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4853 | 1.07060 | ||||||||
\(137\) | − 10.8284i | − 0.925135i | −0.886584 | − | 0.462567i | \(-0.846928\pi\) | ||||
0.886584 | − | 0.462567i | \(-0.153072\pi\) | |||||||
\(138\) | 42.6274i | 3.62869i | ||||||||
\(139\) | −10.3431 | −0.877294 | −0.438647 | − | 0.898659i | \(-0.644542\pi\) | ||||
−0.438647 | + | 0.898659i | \(0.644542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.686292 | 0.0577962 | ||||||||
\(142\) | − 17.6569i | − 1.48173i | ||||||||
\(143\) | − 9.65685i | − 0.807547i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20.4853 | 1.69537 | ||||||||
\(147\) | 12.6274i | 1.04149i | ||||||||
\(148\) | − 32.4853i | − 2.67027i | ||||||||
\(149\) | 13.3137 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | − 3.65685i | − 0.296610i | ||||||||
\(153\) | 2.82843i | 0.228665i | ||||||||
\(154\) | −9.65685 | −0.778171 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 15.3137 | 1.22608 | ||||||||
\(157\) | − 16.4853i | − 1.31567i | −0.753163 | − | 0.657834i | \(-0.771473\pi\) | ||||
0.753163 | − | 0.657834i | \(-0.228527\pi\) | |||||||
\(158\) | 34.9706i | 2.78211i | ||||||||
\(159\) | 15.3137 | 1.21446 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.31371 | −0.576401 | ||||||||
\(162\) | 26.5563i | 2.08646i | ||||||||
\(163\) | 19.6569i | 1.53964i | 0.638259 | + | 0.769822i | \(0.279655\pi\) | ||||
−0.638259 | + | 0.769822i | \(0.720345\pi\) | |||||||
\(164\) | 22.9706 | 1.79370 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −30.9706 | −2.40378 | ||||||||
\(167\) | 14.4853i | 1.12090i | 0.828187 | + | 0.560452i | \(0.189373\pi\) | ||||
−0.828187 | + | 0.560452i | \(0.810627\pi\) | |||||||
\(168\) | − 7.31371i | − 0.564265i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.828427 | 0.0633514 | ||||||||
\(172\) | − 22.9706i | − 1.75149i | ||||||||
\(173\) | 5.31371i | 0.403994i | 0.979386 | + | 0.201997i | \(0.0647431\pi\) | ||||
−0.979386 | + | 0.201997i | \(0.935257\pi\) | |||||||
\(174\) | −4.82843 | −0.366042 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.4853 | −1.09187 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.82843i | 0.661719i | ||||||||
\(179\) | 0.686292 | 0.0512958 | 0.0256479 | − | 0.999671i | \(-0.491835\pi\) | ||||
0.0256479 | + | 0.999671i | \(0.491835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 15.3137i | 1.13202i | ||||||||
\(184\) | −38.9706 | −2.87295 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −50.6274 | −3.71218 | ||||||||
\(187\) | 13.6569i | 0.998688i | ||||||||
\(188\) | 1.31371i | 0.0958120i | ||||||||
\(189\) | −3.31371 | −0.241037 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1716 | −1.09778 | −0.548888 | − | 0.835896i | \(-0.684949\pi\) | ||||
−0.548888 | + | 0.835896i | \(0.684949\pi\) | |||||||
\(192\) | 19.6569i | 1.41861i | ||||||||
\(193\) | 12.4853i | 0.898710i | 0.893353 | + | 0.449355i | \(0.148346\pi\) | ||||
−0.893353 | + | 0.449355i | \(0.851654\pi\) | |||||||
\(194\) | 10.8284 | 0.777436 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | − 8.34315i | − 0.594425i | −0.954811 | − | 0.297212i | \(-0.903943\pi\) | ||||
0.954811 | − | 0.297212i | \(-0.0960569\pi\) | |||||||
\(198\) | − 11.6569i | − 0.828417i | ||||||||
\(199\) | −12.0000 | −0.850657 | −0.425329 | − | 0.905039i | \(-0.639842\pi\) | ||||
−0.425329 | + | 0.905039i | \(0.639842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.9706 | 1.47915 | ||||||||
\(202\) | − 10.4853i | − 0.737742i | ||||||||
\(203\) | − 0.828427i | − 0.0581442i | ||||||||
\(204\) | −21.6569 | −1.51628 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 29.3137 | 2.04238 | ||||||||
\(207\) | − 8.82843i | − 0.613618i | ||||||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82843 | 0.332403 | 0.166201 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166201 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(212\) | 29.3137i | 2.01327i | ||||||||
\(213\) | 14.6274i | 1.00225i | ||||||||
\(214\) | −19.6569 | −1.34371 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −17.6569 | −1.20140 | ||||||||
\(217\) | − 8.68629i | − 0.589664i | ||||||||
\(218\) | 4.82843i | 0.327022i | ||||||||
\(219\) | −16.9706 | −1.14676 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685 | 0.380521 | ||||||||
\(222\) | 40.9706i | 2.74976i | ||||||||
\(223\) | − 21.7990i | − 1.45977i | −0.683571 | − | 0.729884i | \(-0.739574\pi\) | ||||
0.683571 | − | 0.729884i | \(-0.260426\pi\) | |||||||
\(224\) | −1.31371 | −0.0877758 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.82843 | −0.454220 | ||||||||
\(227\) | − 8.14214i | − 0.540413i | −0.962802 | − | 0.270206i | \(-0.912908\pi\) | ||||
0.962802 | − | 0.270206i | \(-0.0870919\pi\) | |||||||
\(228\) | 6.34315i | 0.420085i | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | − 4.41421i | − 0.289807i | ||||||||
\(233\) | − 18.0000i | − 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | −4.82843 | −0.315644 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 28.9706i | − 1.88184i | ||||||||
\(238\) | − 5.65685i | − 0.366679i | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | − 29.7279i | − 1.91098i | ||||||||
\(243\) | − 10.0000i | − 0.641500i | ||||||||
\(244\) | −29.3137 | −1.87662 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.9706 | −1.84710 | ||||||||
\(247\) | − 1.65685i | − 0.105423i | ||||||||
\(248\) | − 46.2843i | − 2.93905i | ||||||||
\(249\) | 25.6569 | 1.62594 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.17157 | 0.200188 | 0.100094 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100094 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(252\) | 3.17157i | 0.199790i | ||||||||
\(253\) | − 42.6274i | − 2.67996i | ||||||||
\(254\) | 14.4853 | 0.908887 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 29.3137i | 1.82854i | 0.405107 | + | 0.914269i | \(0.367234\pi\) | ||||
−0.405107 | + | 0.914269i | \(0.632766\pi\) | |||||||
\(258\) | 28.9706i | 1.80363i | ||||||||
\(259\) | −7.02944 | −0.436788 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | − 38.9706i | − 2.40761i | ||||||||
\(263\) | 8.34315i | 0.514460i | 0.966350 | + | 0.257230i | \(0.0828099\pi\) | ||||
−0.966350 | + | 0.257230i | \(0.917190\pi\) | |||||||
\(264\) | 42.6274 | 2.62354 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.65685 | −0.101588 | ||||||||
\(267\) | − 7.31371i | − 0.447592i | ||||||||
\(268\) | 40.1421i | 2.45207i | ||||||||
\(269\) | −1.31371 | −0.0800982 | −0.0400491 | − | 0.999198i | \(-0.512751\pi\) | ||||
−0.0400491 | + | 0.999198i | \(0.512751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.7990 | 1.81016 | 0.905080 | − | 0.425242i | \(-0.139811\pi\) | ||||
0.905080 | + | 0.425242i | \(0.139811\pi\) | |||||||
\(272\) | − 8.48528i | − 0.514496i | ||||||||
\(273\) | − 3.31371i | − 0.200555i | ||||||||
\(274\) | −26.1421 | −1.57930 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 67.5980 | 4.06892 | ||||||||
\(277\) | 7.65685i | 0.460056i | 0.973184 | + | 0.230028i | \(0.0738817\pi\) | ||||
−0.973184 | + | 0.230028i | \(0.926118\pi\) | |||||||
\(278\) | 24.9706i | 1.49763i | ||||||||
\(279\) | 10.4853 | 0.627737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.68629 | −0.398871 | −0.199435 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199435 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(282\) | − 1.65685i | − 0.0986642i | ||||||||
\(283\) | 0.828427i | 0.0492449i | 0.999697 | + | 0.0246224i | \(0.00783836\pi\) | ||||
−0.999697 | + | 0.0246224i | \(0.992162\pi\) | |||||||
\(284\) | −28.0000 | −1.66149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.3137 | −1.37857 | ||||||||
\(287\) | − 4.97056i | − 0.293403i | ||||||||
\(288\) | − 1.58579i | − 0.0934434i | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.97056 | −0.525864 | ||||||||
\(292\) | − 32.4853i | − 1.90106i | ||||||||
\(293\) | 8.48528i | 0.495715i | 0.968796 | + | 0.247858i | \(0.0797265\pi\) | ||||
−0.968796 | + | 0.247858i | \(0.920273\pi\) | |||||||
\(294\) | 30.4853 | 1.77794 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −37.4558 | −2.17708 | ||||||||
\(297\) | − 19.3137i | − 1.12070i | ||||||||
\(298\) | − 32.1421i | − 1.86194i | ||||||||
\(299\) | −17.6569 | −1.02112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.97056 | −0.286498 | ||||||||
\(302\) | 28.9706i | 1.66707i | ||||||||
\(303\) | 8.68629i | 0.499014i | ||||||||
\(304\) | −2.48528 | −0.142541 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.82843 | 0.390355 | ||||||||
\(307\) | 10.9706i | 0.626123i | 0.949733 | + | 0.313062i | \(0.101355\pi\) | ||||
−0.949733 | + | 0.313062i | \(0.898645\pi\) | |||||||
\(308\) | 15.3137i | 0.872580i | ||||||||
\(309\) | −24.2843 | −1.38148 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.48528 | −0.140927 | −0.0704637 | − | 0.997514i | \(-0.522448\pi\) | ||||
−0.0704637 | + | 0.997514i | \(0.522448\pi\) | |||||||
\(312\) | − 17.6569i | − 0.999623i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −39.7990 | −2.24599 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55.4558 | 3.11963 | ||||||||
\(317\) | − 2.82843i | − 0.158860i | −0.996840 | − | 0.0794301i | \(-0.974690\pi\) | ||||
0.996840 | − | 0.0794301i | \(-0.0253101\pi\) | |||||||
\(318\) | − 36.9706i | − 2.07321i | ||||||||
\(319\) | 4.82843 | 0.270340 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.2843 | 0.908899 | ||||||||
\(322\) | 17.6569i | 0.983978i | ||||||||
\(323\) | 2.34315i | 0.130376i | ||||||||
\(324\) | 42.1127 | 2.33959 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 47.4558 | 2.62834 | ||||||||
\(327\) | − 4.00000i | − 0.221201i | ||||||||
\(328\) | − 26.4853i | − 1.46241i | ||||||||
\(329\) | 0.284271 | 0.0156724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7990 | −0.978321 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(332\) | 49.1127i | 2.69541i | ||||||||
\(333\) | − 8.48528i | − 0.464991i | ||||||||
\(334\) | 34.9706 | 1.91350 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.97056 | −0.271166 | ||||||||
\(337\) | − 6.82843i | − 0.371968i | −0.982553 | − | 0.185984i | \(-0.940453\pi\) | ||||
0.982553 | − | 0.185984i | \(-0.0595473\pi\) | |||||||
\(338\) | − 21.7279i | − 1.18184i | ||||||||
\(339\) | 5.65685 | 0.307238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.6274 | 2.74163 | ||||||||
\(342\) | − 2.00000i | − 0.108148i | ||||||||
\(343\) | 11.0294i | 0.595534i | ||||||||
\(344\) | −26.4853 | −1.42799 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8284 | 0.689661 | ||||||||
\(347\) | 20.1421i | 1.08129i | 0.841252 | + | 0.540643i | \(0.181819\pi\) | ||||
−0.841252 | + | 0.540643i | \(0.818181\pi\) | |||||||
\(348\) | 7.65685i | 0.410450i | ||||||||
\(349\) | 24.6274 | 1.31828 | 0.659138 | − | 0.752022i | \(-0.270921\pi\) | ||||
0.659138 | + | 0.752022i | \(0.270921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | − 7.65685i | − 0.408112i | ||||||||
\(353\) | 15.6569i | 0.833330i | 0.909060 | + | 0.416665i | \(0.136801\pi\) | ||||
−0.909060 | + | 0.416665i | \(0.863199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 4.68629i | 0.248025i | ||||||||
\(358\) | − 1.65685i | − 0.0875675i | ||||||||
\(359\) | 32.1421 | 1.69640 | 0.848199 | − | 0.529678i | \(-0.177687\pi\) | ||||
0.848199 | + | 0.529678i | \(0.177687\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 14.4853i | 0.761329i | ||||||||
\(363\) | 24.6274i | 1.29260i | ||||||||
\(364\) | 6.34315 | 0.332471 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 36.9706 | 1.93248 | ||||||||
\(367\) | 18.0000i | 0.939592i | 0.882775 | + | 0.469796i | \(0.155673\pi\) | ||||
−0.882775 | + | 0.469796i | \(0.844327\pi\) | |||||||
\(368\) | 26.4853i | 1.38064i | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.34315 | 0.329320 | ||||||||
\(372\) | 80.2843i | 4.16255i | ||||||||
\(373\) | − 26.9706i | − 1.39648i | −0.715862 | − | 0.698241i | \(-0.753966\pi\) | ||||
0.715862 | − | 0.698241i | \(-0.246034\pi\) | |||||||
\(374\) | 32.9706 | 1.70487 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | − 2.00000i | − 0.103005i | ||||||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | −5.51472 | −0.283272 | −0.141636 | − | 0.989919i | \(-0.545236\pi\) | ||||
−0.141636 | + | 0.989919i | \(0.545236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0000 | −0.614779 | ||||||||
\(382\) | 36.6274i | 1.87402i | ||||||||
\(383\) | 14.4853i | 0.740163i | 0.928999 | + | 0.370082i | \(0.120670\pi\) | ||||
−0.928999 | + | 0.370082i | \(0.879330\pi\) | |||||||
\(384\) | 41.1127 | 2.09802 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.1421 | 1.53419 | ||||||||
\(387\) | − 6.00000i | − 0.304997i | ||||||||
\(388\) | − 17.1716i | − 0.871755i | ||||||||
\(389\) | 6.68629 | 0.339008 | 0.169504 | − | 0.985529i | \(-0.445783\pi\) | ||||
0.169504 | + | 0.985529i | \(0.445783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | 27.8701i | 1.40765i | ||||||||
\(393\) | 32.2843i | 1.62853i | ||||||||
\(394\) | −20.1421 | −1.01475 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.4853 | −0.928920 | ||||||||
\(397\) | − 8.34315i | − 0.418730i | −0.977838 | − | 0.209365i | \(-0.932860\pi\) | ||||
0.977838 | − | 0.209365i | \(-0.0671398\pi\) | |||||||
\(398\) | 28.9706i | 1.45216i | ||||||||
\(399\) | 1.37258 | 0.0687151 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | − 50.6274i | − 2.52507i | ||||||||
\(403\) | − 20.9706i | − 1.04462i | ||||||||
\(404\) | −16.6274 | −0.827245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | − 40.9706i | − 2.03084i | ||||||||
\(408\) | 24.9706i | 1.23623i | ||||||||
\(409\) | −30.9706 | −1.53140 | −0.765698 | − | 0.643200i | \(-0.777606\pi\) | ||||
−0.765698 | + | 0.643200i | \(0.777606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.6569 | 1.06825 | ||||||||
\(412\) | − 46.4853i | − 2.29017i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −21.3137 | −1.04751 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.17157 | −0.155499 | ||||||||
\(417\) | − 20.6863i | − 1.01301i | ||||||||
\(418\) | − 9.65685i | − 0.472332i | ||||||||
\(419\) | 4.97056 | 0.242828 | 0.121414 | − | 0.992602i | \(-0.461257\pi\) | ||||
0.121414 | + | 0.992602i | \(0.461257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9706 | −0.729621 | −0.364810 | − | 0.931082i | \(-0.618866\pi\) | ||||
−0.364810 | + | 0.931082i | \(0.618866\pi\) | |||||||
\(422\) | − 11.6569i | − 0.567447i | ||||||||
\(423\) | 0.343146i | 0.0166843i | ||||||||
\(424\) | 33.7990 | 1.64142 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 35.3137 | 1.71095 | ||||||||
\(427\) | 6.34315i | 0.306966i | ||||||||
\(428\) | 31.1716i | 1.50673i | ||||||||
\(429\) | 19.3137 | 0.932475 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3137 | −0.930309 | −0.465154 | − | 0.885230i | \(-0.654001\pi\) | ||||
−0.465154 | + | 0.885230i | \(0.654001\pi\) | |||||||
\(432\) | 12.0000i | 0.577350i | ||||||||
\(433\) | 34.8284i | 1.67375i | 0.547396 | + | 0.836874i | \(0.315619\pi\) | ||||
−0.547396 | + | 0.836874i | \(0.684381\pi\) | |||||||
\(434\) | −20.9706 | −1.00662 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.65685 | 0.366697 | ||||||||
\(437\) | − 7.31371i | − 0.349862i | ||||||||
\(438\) | 40.9706i | 1.95765i | ||||||||
\(439\) | 21.6569 | 1.03363 | 0.516813 | − | 0.856099i | \(-0.327118\pi\) | ||||
0.516813 | + | 0.856099i | \(0.327118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.31371 | −0.300653 | ||||||||
\(442\) | − 13.6569i | − 0.649590i | ||||||||
\(443\) | − 3.65685i | − 0.173742i | −0.996220 | − | 0.0868712i | \(-0.972313\pi\) | ||||
0.996220 | − | 0.0868712i | \(-0.0276869\pi\) | |||||||
\(444\) | 64.9706 | 3.08337 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −52.6274 | −2.49198 | ||||||||
\(447\) | 26.6274i | 1.25943i | ||||||||
\(448\) | 8.14214i | 0.384680i | ||||||||
\(449\) | −0.343146 | −0.0161940 | −0.00809702 | − | 0.999967i | \(-0.502577\pi\) | ||||
−0.00809702 | + | 0.999967i | \(0.502577\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9706 | 1.36417 | ||||||||
\(452\) | 10.8284i | 0.509326i | ||||||||
\(453\) | − 24.0000i | − 1.12762i | ||||||||
\(454\) | −19.6569 | −0.922542 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.31371 | 0.342496 | ||||||||
\(457\) | 8.34315i | 0.390276i | 0.980776 | + | 0.195138i | \(0.0625155\pi\) | ||||
−0.980776 | + | 0.195138i | \(0.937485\pi\) | |||||||
\(458\) | − 4.82843i | − 0.225618i | ||||||||
\(459\) | 11.3137 | 0.528079 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.3431 | −1.13377 | −0.566887 | − | 0.823796i | \(-0.691852\pi\) | ||||
−0.566887 | + | 0.823796i | \(0.691852\pi\) | |||||||
\(462\) | − 19.3137i | − 0.898555i | ||||||||
\(463\) | 17.7990i | 0.827189i | 0.910461 | + | 0.413595i | \(0.135727\pi\) | ||||
−0.910461 | + | 0.413595i | \(0.864273\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −43.4558 | −2.01305 | ||||||||
\(467\) | − 22.9706i | − 1.06295i | −0.847074 | − | 0.531475i | \(-0.821638\pi\) | ||||
0.847074 | − | 0.531475i | \(-0.178362\pi\) | |||||||
\(468\) | 7.65685i | 0.353938i | ||||||||
\(469\) | 8.68629 | 0.401096 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.9706 | 1.51920 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 28.9706i | − 1.33207i | ||||||||
\(474\) | −69.9411 | −3.21250 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.97056 | −0.411165 | ||||||||
\(477\) | 7.65685i | 0.350583i | ||||||||
\(478\) | − 56.2843i | − 2.57438i | ||||||||
\(479\) | −12.8284 | −0.586146 | −0.293073 | − | 0.956090i | \(-0.594678\pi\) | ||||
−0.293073 | + | 0.956090i | \(0.594678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9706 | −0.773791 | ||||||||
\(482\) | − 24.1421i | − 1.09964i | ||||||||
\(483\) | − 14.6274i | − 0.665571i | ||||||||
\(484\) | −47.1421 | −2.14282 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −24.1421 | −1.09511 | ||||||||
\(487\) | − 29.7990i | − 1.35032i | −0.737671 | − | 0.675161i | \(-0.764074\pi\) | ||||
0.737671 | − | 0.675161i | \(-0.235926\pi\) | |||||||
\(488\) | 33.7990i | 1.53001i | ||||||||
\(489\) | −39.3137 | −1.77783 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.4558 | 1.96113 | 0.980567 | − | 0.196183i | \(-0.0628545\pi\) | ||||
0.980567 | + | 0.196183i | \(0.0628545\pi\) | |||||||
\(492\) | 45.9411i | 2.07119i | ||||||||
\(493\) | 2.82843i | 0.127386i | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.4558 | −1.41241 | ||||||||
\(497\) | 6.05887i | 0.271778i | ||||||||
\(498\) | − 61.9411i | − 2.77565i | ||||||||
\(499\) | −36.0000 | −1.61158 | −0.805791 | − | 0.592200i | \(-0.798259\pi\) | ||||
−0.805791 | + | 0.592200i | \(0.798259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.9706 | −1.29431 | ||||||||
\(502\) | − 7.65685i | − 0.341742i | ||||||||
\(503\) | 30.0000i | 1.33763i | 0.743427 | + | 0.668817i | \(0.233199\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(504\) | 3.65685 | 0.162889 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −102.912 | −4.57498 | ||||||||
\(507\) | 18.0000i | 0.799408i | ||||||||
\(508\) | − 22.9706i | − 1.01915i | ||||||||
\(509\) | 44.6274 | 1.97808 | 0.989038 | − | 0.147663i | \(-0.0471751\pi\) | ||||
0.989038 | + | 0.147663i | \(0.0471751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.02944 | −0.310964 | ||||||||
\(512\) | 31.2426i | 1.38074i | ||||||||
\(513\) | − 3.31371i | − 0.146304i | ||||||||
\(514\) | 70.7696 | 3.12151 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 45.9411 | 2.02245 | ||||||||
\(517\) | 1.65685i | 0.0728684i | ||||||||
\(518\) | 16.9706i | 0.745644i | ||||||||
\(519\) | −10.6274 | −0.466492 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.31371 | 0.0575546 | 0.0287773 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287773 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(522\) | − 2.41421i | − 0.105667i | ||||||||
\(523\) | 14.4853i | 0.633397i | 0.948526 | + | 0.316699i | \(0.102574\pi\) | ||||
−0.948526 | + | 0.316699i | \(0.897426\pi\) | |||||||
\(524\) | −61.7990 | −2.69970 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1421 | 0.878239 | ||||||||
\(527\) | 29.6569i | 1.29187i | ||||||||
\(528\) | − 28.9706i | − 1.26078i | ||||||||
\(529\) | −54.9411 | −2.38874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.62742i | 0.113913i | ||||||||
\(533\) | − 12.0000i | − 0.519778i | ||||||||
\(534\) | −17.6569 | −0.764087 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 46.2843 | 1.99918 | ||||||||
\(537\) | 1.37258i | 0.0592313i | ||||||||
\(538\) | 3.17157i | 0.136736i | ||||||||
\(539\) | −30.4853 | −1.31309 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9706 | −1.67548 | −0.837738 | − | 0.546073i | \(-0.816122\pi\) | ||||
−0.837738 | + | 0.546073i | \(0.816122\pi\) | |||||||
\(542\) | − 71.9411i | − 3.09014i | ||||||||
\(543\) | − 12.0000i | − 0.514969i | ||||||||
\(544\) | 4.48528 | 0.192305 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.00000 | −0.342368 | ||||||||
\(547\) | 14.4853i | 0.619346i | 0.950843 | + | 0.309673i | \(0.100220\pi\) | ||||
−0.950843 | + | 0.309673i | \(0.899780\pi\) | |||||||
\(548\) | 41.4558i | 1.77091i | ||||||||
\(549\) | −7.65685 | −0.326787 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.828427 | 0.0352922 | ||||||||
\(552\) | − 77.9411i | − 3.31739i | ||||||||
\(553\) | − 12.0000i | − 0.510292i | ||||||||
\(554\) | 18.4853 | 0.785364 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.5980 | 1.67933 | ||||||||
\(557\) | 39.9411i | 1.69236i | 0.532897 | + | 0.846180i | \(0.321103\pi\) | ||||
−0.532897 | + | 0.846180i | \(0.678897\pi\) | |||||||
\(558\) | − 25.3137i | − 1.07161i | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.3137 | −1.15319 | ||||||||
\(562\) | 16.1421i | 0.680915i | ||||||||
\(563\) | 3.65685i | 0.154118i | 0.997027 | + | 0.0770590i | \(0.0245530\pi\) | ||||
−0.997027 | + | 0.0770590i | \(0.975447\pi\) | |||||||
\(564\) | −2.62742 | −0.110634 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.00000 | 0.0840663 | ||||||||
\(567\) | − 9.11270i | − 0.382697i | ||||||||
\(568\) | 32.2843i | 1.35462i | ||||||||
\(569\) | −16.3431 | −0.685140 | −0.342570 | − | 0.939492i | \(-0.611297\pi\) | ||||
−0.342570 | + | 0.939492i | \(0.611297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 36.9706i | 1.54582i | ||||||||
\(573\) | − 30.3431i | − 1.26760i | ||||||||
\(574\) | −12.0000 | −0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | − 15.7990i | − 0.657721i | −0.944379 | − | 0.328860i | \(-0.893335\pi\) | ||||
0.944379 | − | 0.328860i | \(-0.106665\pi\) | |||||||
\(578\) | − 21.7279i | − 0.903762i | ||||||||
\(579\) | −24.9706 | −1.03774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.6274 | 0.440900 | ||||||||
\(582\) | 21.6569i | 0.897705i | ||||||||
\(583\) | 36.9706i | 1.53116i | ||||||||
\(584\) | −37.4558 | −1.54993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.4853 | 0.846239 | ||||||||
\(587\) | 9.79899i | 0.404448i | 0.979339 | + | 0.202224i | \(0.0648168\pi\) | ||||
−0.979339 | + | 0.202224i | \(0.935183\pi\) | |||||||
\(588\) | − 48.3431i | − 1.99364i | ||||||||
\(589\) | 8.68629 | 0.357912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6863 | 0.686382 | ||||||||
\(592\) | 25.4558i | 1.04623i | ||||||||
\(593\) | − 3.65685i | − 0.150169i | −0.997177 | − | 0.0750845i | \(-0.976077\pi\) | ||||
0.997177 | − | 0.0750845i | \(-0.0239227\pi\) | |||||||
\(594\) | −46.6274 | −1.91315 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −50.9706 | −2.08784 | ||||||||
\(597\) | − 24.0000i | − 0.982255i | ||||||||
\(598\) | 42.6274i | 1.74316i | ||||||||
\(599\) | −1.79899 | −0.0735047 | −0.0367524 | − | 0.999324i | \(-0.511701\pi\) | ||||
−0.0367524 | + | 0.999324i | \(0.511701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 12.0000i | 0.489083i | ||||||||
\(603\) | 10.4853i | 0.426994i | ||||||||
\(604\) | 45.9411 | 1.86932 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.9706 | 0.851871 | ||||||||
\(607\) | 42.9706i | 1.74412i | 0.489398 | + | 0.872061i | \(0.337217\pi\) | ||||
−0.489398 | + | 0.872061i | \(0.662783\pi\) | |||||||
\(608\) | − 1.31371i | − 0.0532779i | ||||||||
\(609\) | 1.65685 | 0.0671391 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.686292 | 0.0277644 | ||||||||
\(612\) | − 10.8284i | − 0.437713i | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | 26.4853 | 1.06886 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.6569 | 0.711415 | ||||||||
\(617\) | − 14.8284i | − 0.596970i | −0.954414 | − | 0.298485i | \(-0.903519\pi\) | ||||
0.954414 | − | 0.298485i | \(-0.0964813\pi\) | |||||||
\(618\) | 58.6274i | 2.35834i | ||||||||
\(619\) | −29.7990 | −1.19772 | −0.598861 | − | 0.800853i | \(-0.704380\pi\) | ||||
−0.598861 | + | 0.800853i | \(0.704380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.3137 | −1.41709 | ||||||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | − 3.02944i | − 0.121372i | ||||||||
\(624\) | −12.0000 | −0.480384 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.4853 | 0.578948 | ||||||||
\(627\) | 8.00000i | 0.319489i | ||||||||
\(628\) | 63.1127i | 2.51847i | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.02944 | 0.120600 | 0.0603000 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603000 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(632\) | − 63.9411i | − 2.54344i | ||||||||
\(633\) | 9.65685i | 0.383825i | ||||||||
\(634\) | −6.82843 | −0.271191 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −58.6274 | −2.32473 | ||||||||
\(637\) | 12.6274i | 0.500316i | ||||||||
\(638\) | − 11.6569i | − 0.461499i | ||||||||
\(639\) | −7.31371 | −0.289326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.6274 | −1.76268 | −0.881338 | − | 0.472485i | \(-0.843357\pi\) | ||||
−0.881338 | + | 0.472485i | \(0.843357\pi\) | |||||||
\(642\) | − 39.3137i | − 1.55159i | ||||||||
\(643\) | 31.4558i | 1.24050i | 0.784405 | + | 0.620249i | \(0.212968\pi\) | ||||
−0.784405 | + | 0.620249i | \(0.787032\pi\) | |||||||
\(644\) | 28.0000 | 1.10335 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.65685 | 0.222566 | ||||||||
\(647\) | 21.1127i | 0.830026i | 0.909816 | + | 0.415013i | \(0.136223\pi\) | ||||
−0.909816 | + | 0.415013i | \(0.863777\pi\) | |||||||
\(648\) | − 48.5563i | − 1.90747i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3726 | 0.680885 | ||||||||
\(652\) | − 75.2548i | − 2.94721i | ||||||||
\(653\) | 22.8284i | 0.893345i | 0.894697 | + | 0.446673i | \(0.147391\pi\) | ||||
−0.894697 | + | 0.446673i | \(0.852609\pi\) | |||||||
\(654\) | −9.65685 | −0.377613 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | − 8.48528i | − 0.331042i | ||||||||
\(658\) | − 0.686292i | − 0.0267544i | ||||||||
\(659\) | 37.7990 | 1.47244 | 0.736220 | − | 0.676743i | \(-0.236609\pi\) | ||||
0.736220 | + | 0.676743i | \(0.236609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | 42.9706i | 1.67010i | ||||||||
\(663\) | 11.3137i | 0.439388i | ||||||||
\(664\) | 56.6274 | 2.19757 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.4853 | −0.793789 | ||||||||
\(667\) | − 8.82843i | − 0.341838i | ||||||||
\(668\) | − 55.4558i | − 2.14565i | ||||||||
\(669\) | 43.5980 | 1.68560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.9706 | −1.42723 | ||||||||
\(672\) | − 2.62742i | − 0.101355i | ||||||||
\(673\) | 10.9706i | 0.422884i | 0.977391 | + | 0.211442i | \(0.0678160\pi\) | ||||
−0.977391 | + | 0.211442i | \(0.932184\pi\) | |||||||
\(674\) | −16.4853 | −0.634989 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.4558 | −1.32522 | ||||||||
\(677\) | 36.7696i | 1.41317i | 0.707629 | + | 0.706584i | \(0.249765\pi\) | ||||
−0.707629 | + | 0.706584i | \(0.750235\pi\) | |||||||
\(678\) | − 13.6569i | − 0.524488i | ||||||||
\(679\) | −3.71573 | −0.142597 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.2843 | 0.624015 | ||||||||
\(682\) | − 122.225i | − 4.68025i | ||||||||
\(683\) | − 40.1421i | − 1.53600i | −0.640452 | − | 0.767998i | \(-0.721253\pi\) | ||||
0.640452 | − | 0.767998i | \(-0.278747\pi\) | |||||||
\(684\) | −3.17157 | −0.121268 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.6274 | 1.01664 | ||||||||
\(687\) | 4.00000i | 0.152610i | ||||||||
\(688\) | 18.0000i | 0.686244i | ||||||||
\(689\) | 15.3137 | 0.583406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0294 | −0.419580 | −0.209790 | − | 0.977747i | \(-0.567278\pi\) | ||||
−0.209790 | + | 0.977747i | \(0.567278\pi\) | |||||||
\(692\) | − 20.3431i | − 0.773330i | ||||||||
\(693\) | 4.00000i | 0.151947i | ||||||||
\(694\) | 48.6274 | 1.84587 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.82843 | 0.334641 | ||||||||
\(697\) | 16.9706i | 0.642806i | ||||||||
\(698\) | − 59.4558i | − 2.25044i | ||||||||
\(699\) | 36.0000 | 1.36165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3137 | 1.10716 | 0.553582 | − | 0.832795i | \(-0.313261\pi\) | ||||
0.553582 | + | 0.832795i | \(0.313261\pi\) | |||||||
\(702\) | 19.3137i | 0.728949i | ||||||||
\(703\) | − 7.02944i | − 0.265120i | ||||||||
\(704\) | −47.4558 | −1.78856 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.7990 | 1.42258 | ||||||||
\(707\) | 3.59798i | 0.135316i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | 0.826227 | 0.413114 | − | 0.910679i | \(-0.364441\pi\) | ||||
0.413114 | + | 0.910679i | \(0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.4853 | 0.543240 | ||||||||
\(712\) | − 16.1421i | − 0.604952i | ||||||||
\(713\) | − 92.5685i | − 3.46672i | ||||||||
\(714\) | 11.3137 | 0.423405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | 46.6274i | 1.74133i | ||||||||
\(718\) | − 77.5980i | − 2.89593i | ||||||||
\(719\) | −10.6274 | −0.396336 | −0.198168 | − | 0.980168i | \(-0.563499\pi\) | ||||
−0.198168 | + | 0.980168i | \(0.563499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0589 | −0.374612 | ||||||||
\(722\) | 44.2132i | 1.64545i | ||||||||
\(723\) | 20.0000i | 0.743808i | ||||||||
\(724\) | 22.9706 | 0.853694 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 59.4558 | 2.20661 | ||||||||
\(727\) | 43.9411i | 1.62969i | 0.579682 | + | 0.814843i | \(0.303177\pi\) | ||||
−0.579682 | + | 0.814843i | \(0.696823\pi\) | |||||||
\(728\) | − 7.31371i | − 0.271064i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.9706 | 0.627679 | ||||||||
\(732\) | − 58.6274i | − 2.16693i | ||||||||
\(733\) | 17.1716i | 0.634247i | 0.948384 | + | 0.317123i | \(0.102717\pi\) | ||||
−0.948384 | + | 0.317123i | \(0.897283\pi\) | |||||||
\(734\) | 43.4558 | 1.60398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0000 | −0.516047 | ||||||||
\(737\) | 50.6274i | 1.86488i | ||||||||
\(738\) | − 14.4853i | − 0.533211i | ||||||||
\(739\) | 2.48528 | 0.0914226 | 0.0457113 | − | 0.998955i | \(-0.485445\pi\) | ||||
0.0457113 | + | 0.998955i | \(0.485445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.31371 | 0.121732 | ||||||||
\(742\) | − 15.3137i | − 0.562184i | ||||||||
\(743\) | 7.37258i | 0.270474i | 0.990813 | + | 0.135237i | \(0.0431796\pi\) | ||||
−0.990813 | + | 0.135237i | \(0.956820\pi\) | |||||||
\(744\) | 92.5685 | 3.39373 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −65.1127 | −2.38395 | ||||||||
\(747\) | 12.8284i | 0.469368i | ||||||||
\(748\) | − 52.2843i | − 1.91170i | ||||||||
\(749\) | 6.74517 | 0.246463 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1421 | −0.443073 | −0.221536 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221536 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(752\) | − 1.02944i | − 0.0375397i | ||||||||
\(753\) | 6.34315i | 0.231157i | ||||||||
\(754\) | −4.82843 | −0.175841 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.6863 | 0.461396 | ||||||||
\(757\) | 36.4853i | 1.32608i | 0.748584 | + | 0.663040i | \(0.230734\pi\) | ||||
−0.748584 | + | 0.663040i | \(0.769266\pi\) | |||||||
\(758\) | 13.3137i | 0.483576i | ||||||||
\(759\) | 85.2548 | 3.09455 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.6274 | −1.32774 | −0.663871 | − | 0.747847i | \(-0.731088\pi\) | ||||
−0.663871 | + | 0.747847i | \(0.731088\pi\) | |||||||
\(762\) | 28.9706i | 1.04949i | ||||||||
\(763\) | − 1.65685i | − 0.0599822i | ||||||||
\(764\) | 58.0833 | 2.10138 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.9706 | 1.26354 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − 59.9411i | − 2.16294i | ||||||||
\(769\) | 4.34315 | 0.156618 | 0.0783089 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783089 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.6274 | −2.11141 | ||||||||
\(772\) | − 47.7990i | − 1.72032i | ||||||||
\(773\) | − 8.48528i | − 0.305194i | −0.988288 | − | 0.152597i | \(-0.951236\pi\) | ||||
0.988288 | − | 0.152597i | \(-0.0487637\pi\) | |||||||
\(774\) | −14.4853 | −0.520663 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | − 14.0589i | − 0.504359i | ||||||||
\(778\) | − 16.1421i | − 0.578724i | ||||||||
\(779\) | 4.97056 | 0.178089 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.3137 | −1.26362 | ||||||||
\(782\) | − 60.2843i | − 2.15576i | ||||||||
\(783\) | − 4.00000i | − 0.142948i | ||||||||
\(784\) | 18.9411 | 0.676469 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 77.9411 | 2.78007 | ||||||||
\(787\) | − 21.7990i | − 0.777050i | −0.921438 | − | 0.388525i | \(-0.872985\pi\) | ||||
0.921438 | − | 0.388525i | \(-0.127015\pi\) | |||||||
\(788\) | 31.9411i | 1.13786i | ||||||||
\(789\) | −16.6863 | −0.594048 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.34315 | 0.0833127 | ||||||||
\(792\) | 21.3137i | 0.757350i | ||||||||
\(793\) | 15.3137i | 0.543806i | ||||||||
\(794\) | −20.1421 | −0.714818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.9411 | 1.62834 | ||||||||
\(797\) | − 34.1421i | − 1.20938i | −0.796462 | − | 0.604688i | \(-0.793298\pi\) | ||||
0.796462 | − | 0.604688i | \(-0.206702\pi\) | |||||||
\(798\) | − 3.31371i | − 0.117304i | ||||||||
\(799\) | −0.970563 | −0.0343360 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.65685 | 0.129209 | ||||||||
\(802\) | 70.7696i | 2.49896i | ||||||||
\(803\) | − 40.9706i | − 1.44582i | ||||||||
\(804\) | −80.2843 | −2.83141 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −50.6274 | −1.78327 | ||||||||
\(807\) | − 2.62742i | − 0.0924895i | ||||||||
\(808\) | 19.1716i | 0.674454i | ||||||||
\(809\) | 14.2843 | 0.502208 | 0.251104 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251104 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3431 | 0.925033 | 0.462516 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462516 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(812\) | 3.17157i | 0.111300i | ||||||||
\(813\) | 59.5980i | 2.09019i | ||||||||
\(814\) | −98.9117 | −3.46685 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16.9706 | 0.594089 | ||||||||
\(817\) | − 4.97056i | − 0.173898i | ||||||||
\(818\) | 74.7696i | 2.61426i | ||||||||
\(819\) | 1.65685 | 0.0578952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.3137 | −1.58146 | −0.790730 | − | 0.612165i | \(-0.790299\pi\) | ||||
−0.790730 | + | 0.612165i | \(0.790299\pi\) | |||||||
\(822\) | − 52.2843i | − 1.82362i | ||||||||
\(823\) | − 2.97056i | − 0.103547i | −0.998659 | − | 0.0517737i | \(-0.983513\pi\) | ||||
0.998659 | − | 0.0517737i | \(-0.0164874\pi\) | |||||||
\(824\) | −53.5980 | −1.86717 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.31371i | − 0.184776i | −0.995723 | − | 0.0923879i | \(-0.970550\pi\) | ||||
0.995723 | − | 0.0923879i | \(-0.0294500\pi\) | |||||||
\(828\) | 33.7990i | 1.17460i | ||||||||
\(829\) | 24.6274 | 0.855346 | 0.427673 | − | 0.903934i | \(-0.359334\pi\) | ||||
0.427673 | + | 0.903934i | \(0.359334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.3137 | −0.531227 | ||||||||
\(832\) | 19.6569i | 0.681479i | ||||||||
\(833\) | − 17.8579i | − 0.618738i | ||||||||
\(834\) | −49.9411 | −1.72932 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.3137 | −0.529636 | ||||||||
\(837\) | − 41.9411i | − 1.44970i | ||||||||
\(838\) | − 12.0000i | − 0.414533i | ||||||||
\(839\) | 14.4853 | 0.500087 | 0.250044 | − | 0.968235i | \(-0.419555\pi\) | ||||
0.250044 | + | 0.968235i | \(0.419555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 36.1421i | 1.24554i | ||||||||
\(843\) | − 13.3726i | − 0.460576i | ||||||||
\(844\) | −18.4853 | −0.636290 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | 10.2010i | 0.350511i | ||||||||
\(848\) | − 22.9706i | − 0.788812i | ||||||||
\(849\) | −1.65685 | −0.0568631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −74.9117 | −2.56794 | ||||||||
\(852\) | − 56.0000i | − 1.91853i | ||||||||
\(853\) | 11.1127i | 0.380492i | 0.981736 | + | 0.190246i | \(0.0609285\pi\) | ||||
−0.981736 | + | 0.190246i | \(0.939072\pi\) | |||||||
\(854\) | 15.3137 | 0.524024 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.9411 | 1.22844 | ||||||||
\(857\) | 48.6274i | 1.66108i | 0.556958 | + | 0.830540i | \(0.311968\pi\) | ||||
−0.556958 | + | 0.830540i | \(0.688032\pi\) | |||||||
\(858\) | − 46.6274i | − 1.59183i | ||||||||
\(859\) | −28.4264 | −0.969896 | −0.484948 | − | 0.874543i | \(-0.661162\pi\) | ||||
−0.484948 | + | 0.874543i | \(0.661162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.94113 | 0.338793 | ||||||||
\(862\) | 46.6274i | 1.58814i | ||||||||
\(863\) | 7.85786i | 0.267485i | 0.991016 | + | 0.133742i | \(0.0426995\pi\) | ||||
−0.991016 | + | 0.133742i | \(0.957301\pi\) | |||||||
\(864\) | −6.34315 | −0.215798 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 84.0833 | 2.85727 | ||||||||
\(867\) | 18.0000i | 0.611312i | ||||||||
\(868\) | 33.2548i | 1.12874i | ||||||||
\(869\) | 69.9411 | 2.37259 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9706 | 0.710560 | ||||||||
\(872\) | − 8.82843i | − 0.298968i | ||||||||
\(873\) | − 4.48528i | − 0.151804i | ||||||||
\(874\) | −17.6569 | −0.597252 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 64.9706 | 2.19515 | ||||||||
\(877\) | − 18.2843i | − 0.617416i | −0.951157 | − | 0.308708i | \(-0.900103\pi\) | ||||
0.951157 | − | 0.308708i | \(-0.0998966\pi\) | |||||||
\(878\) | − 52.2843i | − 1.76451i | ||||||||
\(879\) | −16.9706 | −0.572403 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.68629 | 0.225267 | 0.112633 | − | 0.993637i | \(-0.464071\pi\) | ||||
0.112633 | + | 0.993637i | \(0.464071\pi\) | |||||||
\(882\) | 15.2426i | 0.513246i | ||||||||
\(883\) | − 2.48528i | − 0.0836364i | −0.999125 | − | 0.0418182i | \(-0.986685\pi\) | ||||
0.999125 | − | 0.0418182i | \(-0.0133150\pi\) | |||||||
\(884\) | −21.6569 | −0.728399 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.82843 | −0.296597 | ||||||||
\(887\) | − 29.3137i | − 0.984258i | −0.870522 | − | 0.492129i | \(-0.836219\pi\) | ||||
0.870522 | − | 0.492129i | \(-0.163781\pi\) | |||||||
\(888\) | − 74.9117i | − 2.51387i | ||||||||
\(889\) | −4.97056 | −0.166707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53.1127 | 1.77934 | ||||||||
\(892\) | 83.4558i | 2.79431i | ||||||||
\(893\) | 0.284271i | 0.00951277i | ||||||||
\(894\) | 64.2843 | 2.14999 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17.0294 | 0.568914 | ||||||||
\(897\) | − 35.3137i | − 1.17909i | ||||||||
\(898\) | 0.828427i | 0.0276450i | ||||||||
\(899\) | 10.4853 | 0.349704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6569 | −0.721494 | ||||||||
\(902\) | − 69.9411i | − 2.32878i | ||||||||
\(903\) | − 9.94113i | − 0.330820i | ||||||||
\(904\) | 12.4853 | 0.415254 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −57.9411 | −1.92496 | ||||||||
\(907\) | − 10.0000i | − 0.332045i | −0.986122 | − | 0.166022i | \(-0.946908\pi\) | ||||
0.986122 | − | 0.166022i | \(-0.0530924\pi\) | |||||||
\(908\) | 31.1716i | 1.03446i | ||||||||
\(909\) | −4.34315 | −0.144053 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.85786 | 0.127817 | 0.0639084 | − | 0.997956i | \(-0.479643\pi\) | ||||
0.0639084 | + | 0.997956i | \(0.479643\pi\) | |||||||
\(912\) | − 4.97056i | − 0.164592i | ||||||||
\(913\) | 61.9411i | 2.04995i | ||||||||
\(914\) | 20.1421 | 0.666243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.65685 | −0.252990 | ||||||||
\(917\) | 13.3726i | 0.441602i | ||||||||
\(918\) | − 27.3137i | − 0.901487i | ||||||||
\(919\) | 36.0000 | 1.18753 | 0.593765 | − | 0.804638i | \(-0.297641\pi\) | ||||
0.593765 | + | 0.804638i | \(0.297641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.9411 | −0.722985 | ||||||||
\(922\) | 58.7696i | 1.93547i | ||||||||
\(923\) | 14.6274i | 0.481467i | ||||||||
\(924\) | −30.6274 | −1.00757 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 42.9706 | 1.41210 | ||||||||
\(927\) | − 12.1421i | − 0.398800i | ||||||||
\(928\) | − 1.58579i | − 0.0520560i | ||||||||
\(929\) | −40.6274 | −1.33294 | −0.666471 | − | 0.745531i | \(-0.732196\pi\) | ||||
−0.666471 | + | 0.745531i | \(0.732196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.23045 | −0.171421 | ||||||||
\(932\) | 68.9117i | 2.25728i | ||||||||
\(933\) | − 4.97056i | − 0.162729i | ||||||||
\(934\) | −55.4558 | −1.81457 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.82843 | 0.288566 | ||||||||
\(937\) | 8.34315i | 0.272559i | 0.990670 | + | 0.136279i | \(0.0435145\pi\) | ||||
−0.990670 | + | 0.136279i | \(0.956486\pi\) | |||||||
\(938\) | − 20.9706i | − 0.684713i | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.9411 | 1.30204 | 0.651022 | − | 0.759059i | \(-0.274341\pi\) | ||||
0.651022 | + | 0.759059i | \(0.274341\pi\) | |||||||
\(942\) | − 79.5980i | − 2.59344i | ||||||||
\(943\) | − 52.9706i | − 1.72496i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −69.9411 | −2.27398 | ||||||||
\(947\) | − 56.9117i | − 1.84938i | −0.380719 | − | 0.924691i | \(-0.624324\pi\) | ||||
0.380719 | − | 0.924691i | \(-0.375676\pi\) | |||||||
\(948\) | 110.912i | 3.60224i | ||||||||
\(949\) | −16.9706 | −0.550888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.65685 | 0.183436 | ||||||||
\(952\) | 10.3431i | 0.335223i | ||||||||
\(953\) | − 6.68629i | − 0.216590i | −0.994119 | − | 0.108295i | \(-0.965461\pi\) | ||||
0.994119 | − | 0.108295i | \(-0.0345391\pi\) | |||||||
\(954\) | 18.4853 | 0.598483 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −89.2548 | −2.88671 | ||||||||
\(957\) | 9.65685i | 0.312162i | ||||||||
\(958\) | 30.9706i | 1.00061i | ||||||||
\(959\) | 8.97056 | 0.289675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.9411 | 2.54649 | ||||||||
\(962\) | 40.9706i | 1.32094i | ||||||||
\(963\) | 8.14214i | 0.262377i | ||||||||
\(964\) | −38.2843 | −1.23305 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −35.3137 | −1.13620 | ||||||||
\(967\) | − 18.9706i | − 0.610052i | −0.952344 | − | 0.305026i | \(-0.901335\pi\) | ||||
0.952344 | − | 0.305026i | \(-0.0986652\pi\) | |||||||
\(968\) | 54.3553i | 1.74705i | ||||||||
\(969\) | −4.68629 | −0.150545 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.142136 | −0.00456135 | −0.00228067 | − | 0.999997i | \(-0.500726\pi\) | ||||
−0.00228067 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(972\) | 38.2843i | 1.22797i | ||||||||
\(973\) | − 8.56854i | − 0.274695i | ||||||||
\(974\) | −71.9411 | −2.30514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.9706 | 0.735270 | ||||||||
\(977\) | − 25.3137i | − 0.809857i | −0.914348 | − | 0.404929i | \(-0.867296\pi\) | ||||
0.914348 | − | 0.404929i | \(-0.132704\pi\) | |||||||
\(978\) | 94.9117i | 3.03494i | ||||||||
\(979\) | 17.6569 | 0.564316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | − 104.912i | − 3.34787i | ||||||||
\(983\) | − 13.3137i | − 0.424641i | −0.977200 | − | 0.212321i | \(-0.931898\pi\) | ||||
0.977200 | − | 0.212321i | \(-0.0681021\pi\) | |||||||
\(984\) | 52.9706 | 1.68864 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.82843 | 0.217461 | ||||||||
\(987\) | 0.568542i | 0.0180969i | ||||||||
\(988\) | 6.34315i | 0.201802i | ||||||||
\(989\) | −52.9706 | −1.68437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | − 16.6274i | − 0.527921i | ||||||||
\(993\) | − 35.5980i | − 1.12967i | ||||||||
\(994\) | 14.6274 | 0.463953 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −98.2254 | −3.11239 | ||||||||
\(997\) | 1.17157i | 0.0371041i | 0.999828 | + | 0.0185520i | \(0.00590564\pi\) | ||||
−0.999828 | + | 0.0185520i | \(0.994094\pi\) | |||||||
\(998\) | 86.9117i | 2.75114i | ||||||||
\(999\) | −33.9411 | −1.07385 |
(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 | 725.2.b.c.349.1 | 4 | ||
5.2 | odd | 4 | 725.2.a.c.1.2 | 2 | |||
5.3 | odd | 4 | 145.2.a.b.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 725.2.b.c.349.4 | 4 | ||
15.2 | even | 4 | 6525.2.a.p.1.1 | 2 | |||
15.8 | even | 4 | 1305.2.a.n.1.2 | 2 | |||
20.3 | even | 4 | 2320.2.a.k.1.1 | 2 | |||
35.13 | even | 4 | 7105.2.a.e.1.1 | 2 | |||
40.3 | even | 4 | 9280.2.a.w.1.1 | 2 | |||
40.13 | odd | 4 | 9280.2.a.be.1.2 | 2 | |||
145.28 | odd | 4 | 4205.2.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.a.b.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
725.2.a.c.1.2 | 2 | 5.2 | odd | 4 | |||
725.2.b.c.349.1 | 4 | 1.1 | even | 1 | trivial | ||
725.2.b.c.349.4 | 4 | 5.4 | even | 2 | inner | ||
1305.2.a.n.1.2 | 2 | 15.8 | even | 4 | |||
2320.2.a.k.1.1 | 2 | 20.3 | even | 4 | |||
4205.2.a.d.1.2 | 2 | 145.28 | odd | 4 | |||
6525.2.a.p.1.1 | 2 | 15.2 | even | 4 | |||
7105.2.a.e.1.1 | 2 | 35.13 | even | 4 | |||
9280.2.a.w.1.1 | 2 | 40.3 | even | 4 | |||
9280.2.a.be.1.2 | 2 | 40.13 | odd | 4 |