Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(324,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, 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("475.324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2058981376.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 324.7 | ||
Root | \(-1.43917 - 1.43917i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.324 |
Dual form | 475.2.b.e.324.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14243i | 1.51493i | 0.652876 | + | 0.757465i | \(0.273562\pi\) | ||||
−0.652876 | + | 0.757465i | \(0.726438\pi\) | |||||||
\(3\) | − 2.87834i | − 1.66181i | −0.556412 | − | 0.830907i | \(-0.687822\pi\) | ||||
0.556412 | − | 0.830907i | \(-0.312178\pi\) | |||||||
\(4\) | −2.59002 | −1.29501 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.16666 | 2.51753 | ||||||||
\(7\) | − 3.10482i | − 1.17351i | −0.809764 | − | 0.586756i | \(-0.800405\pi\) | ||||
0.809764 | − | 0.586756i | \(-0.199595\pi\) | |||||||
\(8\) | − 1.26409i | − 0.446923i | ||||||||
\(9\) | −5.28487 | −1.76162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10482 | −0.333115 | −0.166558 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166558 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(12\) | 7.45498i | 2.15207i | ||||||||
\(13\) | 1.77353i | 0.491888i | 0.969284 | + | 0.245944i | \(0.0790979\pi\) | ||||
−0.969284 | + | 0.245944i | \(0.920902\pi\) | |||||||
\(14\) | 6.65187 | 1.77779 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.47182 | −0.617955 | ||||||||
\(17\) | − 7.75669i | − 1.88127i | −0.339415 | − | 0.940637i | \(-0.610229\pi\) | ||||
0.339415 | − | 0.940637i | \(-0.389771\pi\) | |||||||
\(18\) | − 11.3225i | − 2.66874i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.93674 | −1.95016 | ||||||||
\(22\) | − 2.36700i | − 0.504647i | ||||||||
\(23\) | − 6.65187i | − 1.38701i | −0.720451 | − | 0.693505i | \(-0.756065\pi\) | ||||
0.720451 | − | 0.693505i | \(-0.243935\pi\) | |||||||
\(24\) | −3.63849 | −0.742703 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.79966 | −0.745175 | ||||||||
\(27\) | 6.57664i | 1.26567i | ||||||||
\(28\) | 8.04156i | 1.51971i | ||||||||
\(29\) | −7.75669 | −1.44038 | −0.720191 | − | 0.693776i | \(-0.755946\pi\) | ||||
−0.720191 | + | 0.693776i | \(0.755946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.57664 | 1.18120 | 0.590600 | − | 0.806965i | \(-0.298891\pi\) | ||||
0.590600 | + | 0.806965i | \(0.298891\pi\) | |||||||
\(32\) | − 7.82389i | − 1.38308i | ||||||||
\(33\) | 3.18005i | 0.553576i | ||||||||
\(34\) | 16.6182 | 2.85000 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.6879 | 2.28132 | ||||||||
\(37\) | 1.40652i | 0.231231i | 0.993294 | + | 0.115616i | \(0.0368841\pi\) | ||||
−0.993294 | + | 0.115616i | \(0.963116\pi\) | |||||||
\(38\) | − 2.14243i | − 0.347549i | ||||||||
\(39\) | 5.10482 | 0.817425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.81995 | 0.440402 | 0.220201 | − | 0.975454i | \(-0.429329\pi\) | ||||
0.220201 | + | 0.975454i | \(0.429329\pi\) | |||||||
\(42\) | − 19.1464i | − 2.95435i | ||||||||
\(43\) | 3.10482i | 0.473480i | 0.971573 | + | 0.236740i | \(0.0760790\pi\) | ||||
−0.971573 | + | 0.236740i | \(0.923921\pi\) | |||||||
\(44\) | 2.86151 | 0.431389 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2512 | 2.10122 | ||||||||
\(47\) | − 1.46492i | − 0.213680i | −0.994276 | − | 0.106840i | \(-0.965927\pi\) | ||||
0.994276 | − | 0.106840i | \(-0.0340733\pi\) | |||||||
\(48\) | 7.11475i | 1.02693i | ||||||||
\(49\) | −2.63990 | −0.377129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.3264 | −3.12633 | ||||||||
\(52\) | − 4.59348i | − 0.637001i | ||||||||
\(53\) | − 2.59348i | − 0.356241i | −0.984009 | − | 0.178121i | \(-0.942998\pi\) | ||||
0.984009 | − | 0.178121i | \(-0.0570017\pi\) | |||||||
\(54\) | −14.0900 | −1.91741 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.92477 | −0.524469 | ||||||||
\(57\) | 2.87834i | 0.381246i | ||||||||
\(58\) | − 16.6182i | − 2.18208i | ||||||||
\(59\) | 5.38969 | 0.701678 | 0.350839 | − | 0.936436i | \(-0.385897\pi\) | ||||
0.350839 | + | 0.936436i | \(0.385897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.07523 | 0.521780 | 0.260890 | − | 0.965369i | \(-0.415984\pi\) | ||||
0.260890 | + | 0.965369i | \(0.415984\pi\) | |||||||
\(62\) | 14.0900i | 1.78943i | ||||||||
\(63\) | 16.4086i | 2.06728i | ||||||||
\(64\) | 11.8185 | 1.47732 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.81305 | −0.838628 | ||||||||
\(67\) | 15.8151i | 1.93212i | 0.258318 | + | 0.966060i | \(0.416832\pi\) | ||||
−0.258318 | + | 0.966060i | \(0.583168\pi\) | |||||||
\(68\) | 20.0900i | 2.43627i | ||||||||
\(69\) | −19.1464 | −2.30495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.14638 | 0.848119 | 0.424059 | − | 0.905634i | \(-0.360605\pi\) | ||||
0.424059 | + | 0.905634i | \(0.360605\pi\) | |||||||
\(72\) | 6.68055i | 0.787310i | ||||||||
\(73\) | 0.243310i | 0.0284773i | 0.999899 | + | 0.0142387i | \(0.00453246\pi\) | ||||
−0.999899 | + | 0.0142387i | \(0.995468\pi\) | |||||||
\(74\) | −3.01339 | −0.350299 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.59002 | 0.297096 | ||||||||
\(77\) | 3.43026i | 0.390915i | ||||||||
\(78\) | 10.9367i | 1.23834i | ||||||||
\(79\) | 9.38969 | 1.05642 | 0.528211 | − | 0.849113i | \(-0.322863\pi\) | ||||
0.528211 | + | 0.849113i | \(0.322863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.07523 | 0.341692 | ||||||||
\(82\) | 6.04156i | 0.667178i | ||||||||
\(83\) | 8.86151i | 0.972677i | 0.873771 | + | 0.486338i | \(0.161668\pi\) | ||||
−0.873771 | + | 0.486338i | \(0.838332\pi\) | |||||||
\(84\) | 23.1464 | 2.52548 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.65187 | −0.717290 | ||||||||
\(87\) | 22.3264i | 2.39364i | ||||||||
\(88\) | 1.39659i | 0.148877i | ||||||||
\(89\) | −0.813048 | −0.0861829 | −0.0430914 | − | 0.999071i | \(-0.513721\pi\) | ||||
−0.0430914 | + | 0.999071i | \(0.513721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.50648 | 0.577236 | ||||||||
\(92\) | 17.2285i | 1.79620i | ||||||||
\(93\) | − 18.9298i | − 1.96293i | ||||||||
\(94\) | 3.13849 | 0.323711 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −22.5199 | −2.29842 | ||||||||
\(97\) | − 3.19689i | − 0.324595i | −0.986742 | − | 0.162297i | \(-0.948110\pi\) | ||||
0.986742 | − | 0.162297i | \(-0.0518904\pi\) | |||||||
\(98\) | − 5.65581i | − 0.571323i | ||||||||
\(99\) | 5.83882 | 0.586824 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.01887 | −0.300389 | −0.150195 | − | 0.988656i | \(-0.547990\pi\) | ||||
−0.150195 | + | 0.988656i | \(0.547990\pi\) | |||||||
\(102\) | − 47.8329i | − 4.73616i | ||||||||
\(103\) | 6.05839i | 0.596951i | 0.954417 | + | 0.298476i | \(0.0964782\pi\) | ||||
−0.954417 | + | 0.298476i | \(0.903522\pi\) | |||||||
\(104\) | 2.24190 | 0.219836 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.55635 | 0.539681 | ||||||||
\(107\) | − 20.3848i | − 1.97068i | −0.170616 | − | 0.985338i | \(-0.554576\pi\) | ||||
0.170616 | − | 0.985338i | \(-0.445424\pi\) | |||||||
\(108\) | − 17.0337i | − 1.63906i | ||||||||
\(109\) | −4.72710 | −0.452774 | −0.226387 | − | 0.974037i | \(-0.572691\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.04846 | 0.384263 | ||||||||
\(112\) | 7.67456i | 0.725177i | ||||||||
\(113\) | − 7.98316i | − 0.750993i | −0.926824 | − | 0.375496i | \(-0.877472\pi\) | ||||
0.926824 | − | 0.375496i | \(-0.122528\pi\) | |||||||
\(114\) | −6.16666 | −0.577561 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.0900 | 1.86531 | ||||||||
\(117\) | − 9.37285i | − 0.866520i | ||||||||
\(118\) | 11.5471i | 1.06299i | ||||||||
\(119\) | −24.0831 | −2.20770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77938 | −0.889034 | ||||||||
\(122\) | 8.73091i | 0.790460i | ||||||||
\(123\) | − 8.11679i | − 0.731866i | ||||||||
\(124\) | −17.0337 | −1.52967 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −35.1543 | −3.13179 | ||||||||
\(127\) | − 4.63503i | − 0.411293i | −0.978626 | − | 0.205646i | \(-0.934070\pi\) | ||||
0.978626 | − | 0.205646i | \(-0.0659297\pi\) | |||||||
\(128\) | 9.67265i | 0.854950i | ||||||||
\(129\) | 8.93674 | 0.786836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5134 | 1.35541 | 0.677705 | − | 0.735334i | \(-0.262975\pi\) | ||||
0.677705 | + | 0.735334i | \(0.262975\pi\) | |||||||
\(132\) | − 8.23641i | − 0.716887i | ||||||||
\(133\) | 3.10482i | 0.269222i | ||||||||
\(134\) | −33.8828 | −2.92703 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.80515 | −0.840785 | ||||||||
\(137\) | 0.813048i | 0.0694634i | 0.999397 | + | 0.0347317i | \(0.0110577\pi\) | ||||
−0.999397 | + | 0.0347317i | \(0.988942\pi\) | |||||||
\(138\) | − 41.0199i | − 3.49184i | ||||||||
\(139\) | 12.7687 | 1.08302 | 0.541512 | − | 0.840693i | \(-0.317852\pi\) | ||||
0.541512 | + | 0.840693i | \(0.317852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.21654 | −0.355097 | ||||||||
\(142\) | 15.3106i | 1.28484i | ||||||||
\(143\) | − 1.95942i | − 0.163855i | ||||||||
\(144\) | 13.0632 | 1.08860 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.521277 | −0.0431412 | ||||||||
\(147\) | 7.59854i | 0.626717i | ||||||||
\(148\) | − 3.64293i | − 0.299447i | ||||||||
\(149\) | 13.7982 | 1.13040 | 0.565198 | − | 0.824955i | \(-0.308800\pi\) | ||||
0.565198 | + | 0.824955i | \(0.308800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.02269 | 0.408740 | 0.204370 | − | 0.978894i | \(-0.434485\pi\) | ||||
0.204370 | + | 0.978894i | \(0.434485\pi\) | |||||||
\(152\) | 1.26409i | 0.102531i | ||||||||
\(153\) | 40.9931i | 3.31409i | ||||||||
\(154\) | −7.34911 | −0.592208 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13.2216 | −1.05858 | ||||||||
\(157\) | − 7.18695i | − 0.573581i | −0.957993 | − | 0.286791i | \(-0.907412\pi\) | ||||
0.957993 | − | 0.286791i | \(-0.0925884\pi\) | |||||||
\(158\) | 20.1168i | 1.60041i | ||||||||
\(159\) | −7.46492 | −0.592007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.6529 | −1.62767 | ||||||||
\(162\) | 6.58848i | 0.517640i | ||||||||
\(163\) | 7.25528i | 0.568277i | 0.958783 | + | 0.284139i | \(0.0917076\pi\) | ||||
−0.958783 | + | 0.284139i | \(0.908292\pi\) | |||||||
\(164\) | −7.30374 | −0.570326 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.9852 | −1.47354 | ||||||||
\(167\) | 7.33129i | 0.567312i | 0.958926 | + | 0.283656i | \(0.0915475\pi\) | ||||
−0.958926 | + | 0.283656i | \(0.908453\pi\) | |||||||
\(168\) | 11.2968i | 0.871570i | ||||||||
\(169\) | 9.85461 | 0.758047 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.28487 | 0.404144 | ||||||||
\(172\) | − 8.04156i | − 0.613163i | ||||||||
\(173\) | − 5.77353i | − 0.438953i | −0.975618 | − | 0.219477i | \(-0.929565\pi\) | ||||
0.975618 | − | 0.219477i | \(-0.0704349\pi\) | |||||||
\(174\) | −47.8329 | −3.62620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.73091 | 0.205850 | ||||||||
\(177\) | − 15.5134i | − 1.16606i | ||||||||
\(178\) | − 1.74190i | − 0.130561i | ||||||||
\(179\) | 4.48379 | 0.335134 | 0.167567 | − | 0.985861i | \(-0.446409\pi\) | ||||
0.167567 | + | 0.985861i | \(0.446409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.73400 | −0.203217 | −0.101608 | − | 0.994824i | \(-0.532399\pi\) | ||||
−0.101608 | + | 0.994824i | \(0.532399\pi\) | |||||||
\(182\) | 11.7973i | 0.874471i | ||||||||
\(183\) | − 11.7299i | − 0.867101i | ||||||||
\(184\) | −8.40856 | −0.619887 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 40.5559 | 2.97371 | ||||||||
\(187\) | 8.56974i | 0.626681i | ||||||||
\(188\) | 3.79418i | 0.276719i | ||||||||
\(189\) | 20.4193 | 1.48528 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7230 | −1.28239 | −0.641196 | − | 0.767377i | \(-0.721562\pi\) | ||||
−0.641196 | + | 0.767377i | \(0.721562\pi\) | |||||||
\(192\) | − 34.0178i | − 2.45502i | ||||||||
\(193\) | − 13.5371i | − 0.974423i | −0.873284 | − | 0.487212i | \(-0.838014\pi\) | ||||
0.873284 | − | 0.487212i | \(-0.161986\pi\) | |||||||
\(194\) | 6.84912 | 0.491738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.83741 | 0.488386 | ||||||||
\(197\) | 21.5134i | 1.53276i | 0.642385 | + | 0.766382i | \(0.277945\pi\) | ||||
−0.642385 | + | 0.766382i | \(0.722055\pi\) | |||||||
\(198\) | 12.5093i | 0.888997i | ||||||||
\(199\) | −7.09410 | −0.502888 | −0.251444 | − | 0.967872i | \(-0.580905\pi\) | ||||
−0.251444 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 45.5213 | 3.21082 | ||||||||
\(202\) | − 6.46774i | − 0.455068i | ||||||||
\(203\) | 24.0831i | 1.69030i | ||||||||
\(204\) | 57.8260 | 4.04863 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.9797 | −0.904339 | ||||||||
\(207\) | 35.1543i | 2.44339i | ||||||||
\(208\) | − 4.38384i | − 0.303964i | ||||||||
\(209\) | 1.10482 | 0.0764219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0604 | 0.761431 | 0.380716 | − | 0.924692i | \(-0.375678\pi\) | ||||
0.380716 | + | 0.924692i | \(0.375678\pi\) | |||||||
\(212\) | 6.71717i | 0.461337i | ||||||||
\(213\) | − 20.5697i | − 1.40942i | ||||||||
\(214\) | 43.6731 | 2.98543 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.31346 | 0.565659 | ||||||||
\(217\) | − 20.4193i | − 1.38615i | ||||||||
\(218\) | − 10.1275i | − 0.685921i | ||||||||
\(219\) | 0.700331 | 0.0473240 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.7567 | 0.925375 | ||||||||
\(222\) | 8.67356i | 0.582131i | ||||||||
\(223\) | − 12.6350i | − 0.846104i | −0.906105 | − | 0.423052i | \(-0.860959\pi\) | ||||
0.906105 | − | 0.423052i | \(-0.139041\pi\) | |||||||
\(224\) | −24.2918 | −1.62306 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.1034 | 1.13770 | ||||||||
\(227\) | 6.62813i | 0.439925i | 0.975508 | + | 0.219962i | \(0.0705934\pi\) | ||||
−0.975508 | + | 0.219962i | \(0.929407\pi\) | |||||||
\(228\) | − 7.45498i | − 0.493718i | ||||||||
\(229\) | 0.0752308 | 0.00497139 | 0.00248570 | − | 0.999997i | \(-0.499209\pi\) | ||||
0.00248570 | + | 0.999997i | \(0.499209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.87348 | 0.649627 | ||||||||
\(232\) | 9.80515i | 0.643740i | ||||||||
\(233\) | 9.51338i | 0.623242i | 0.950206 | + | 0.311621i | \(0.100872\pi\) | ||||
−0.950206 | + | 0.311621i | \(0.899128\pi\) | |||||||
\(234\) | 20.0807 | 1.31272 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.9594 | −0.908681 | ||||||||
\(237\) | − 27.0268i | − 1.75558i | ||||||||
\(238\) | − 51.5965i | − 3.34450i | ||||||||
\(239\) | 2.92984 | 0.189515 | 0.0947577 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947577 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.42743 | −0.607274 | −0.303637 | − | 0.952788i | \(-0.598201\pi\) | ||||
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(242\) | − 20.9517i | − 1.34682i | ||||||||
\(243\) | 10.8783i | 0.697846i | ||||||||
\(244\) | −10.5549 | −0.675711 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.3897 | 1.10873 | ||||||||
\(247\) | − 1.77353i | − 0.112847i | ||||||||
\(248\) | − 8.31346i | − 0.527905i | ||||||||
\(249\) | 25.5065 | 1.61641 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9298 | −0.942363 | −0.471181 | − | 0.882036i | \(-0.656172\pi\) | ||||
−0.471181 | + | 0.882036i | \(0.656172\pi\) | |||||||
\(252\) | − 42.4986i | − 2.67716i | ||||||||
\(253\) | 7.34911i | 0.462035i | ||||||||
\(254\) | 9.93026 | 0.623080 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.91405 | 0.182128 | ||||||||
\(257\) | 15.1295i | 0.943755i | 0.881664 | + | 0.471877i | \(0.156424\pi\) | ||||
−0.881664 | + | 0.471877i | \(0.843576\pi\) | |||||||
\(258\) | 19.1464i | 1.19200i | ||||||||
\(259\) | 4.36700 | 0.271352 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 40.9931 | 2.53741 | ||||||||
\(262\) | 33.2364i | 2.05335i | ||||||||
\(263\) | − 15.2216i | − 0.938605i | −0.883038 | − | 0.469302i | \(-0.844505\pi\) | ||||
0.883038 | − | 0.469302i | \(-0.155495\pi\) | |||||||
\(264\) | 4.01987 | 0.247406 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.65187 | −0.407852 | ||||||||
\(267\) | 2.34023i | 0.143220i | ||||||||
\(268\) | − 40.9615i | − 2.50212i | ||||||||
\(269\) | −11.5203 | −0.702404 | −0.351202 | − | 0.936300i | \(-0.614227\pi\) | ||||
−0.351202 | + | 0.936300i | \(0.614227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16118 | 0.131282 | 0.0656411 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656411 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(272\) | 19.1731i | 1.16254i | ||||||||
\(273\) | − 15.8495i | − 0.959258i | ||||||||
\(274\) | −1.74190 | −0.105232 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 49.5896 | 2.98494 | ||||||||
\(277\) | − 23.4205i | − 1.40720i | −0.710595 | − | 0.703602i | \(-0.751574\pi\) | ||||
0.710595 | − | 0.703602i | \(-0.248426\pi\) | |||||||
\(278\) | 27.3560i | 1.64070i | ||||||||
\(279\) | −34.7567 | −2.08083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6824 | 1.53209 | 0.766043 | − | 0.642789i | \(-0.222223\pi\) | ||||
0.766043 | + | 0.642789i | \(0.222223\pi\) | |||||||
\(282\) | − 9.03366i | − 0.537947i | ||||||||
\(283\) | 7.38587i | 0.439045i | 0.975607 | + | 0.219522i | \(0.0704499\pi\) | ||||
−0.975607 | + | 0.219522i | \(0.929550\pi\) | |||||||
\(284\) | −18.5093 | −1.09832 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.19794 | 0.248229 | ||||||||
\(287\) | − 8.75543i | − 0.516817i | ||||||||
\(288\) | 41.3482i | 2.43647i | ||||||||
\(289\) | −43.1662 | −2.53919 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.20174 | −0.539416 | ||||||||
\(292\) | − 0.630180i | − 0.0368785i | ||||||||
\(293\) | − 24.1522i | − 1.41099i | −0.708716 | − | 0.705494i | \(-0.750725\pi\) | ||||
0.708716 | − | 0.705494i | \(-0.249275\pi\) | |||||||
\(294\) | −16.2794 | −0.949433 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.77797 | 0.103343 | ||||||||
\(297\) | − 7.26600i | − 0.421616i | ||||||||
\(298\) | 29.5618i | 1.71247i | ||||||||
\(299\) | 11.7973 | 0.682253 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.63990 | 0.555635 | ||||||||
\(302\) | 10.7608i | 0.619213i | ||||||||
\(303\) | 8.68936i | 0.499190i | ||||||||
\(304\) | 2.47182 | 0.141769 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −87.8250 | −5.02062 | ||||||||
\(307\) | − 4.38482i | − 0.250255i | −0.992141 | − | 0.125127i | \(-0.960066\pi\) | ||||
0.992141 | − | 0.125127i | \(-0.0399340\pi\) | |||||||
\(308\) | − 8.88447i | − 0.506239i | ||||||||
\(309\) | 17.4381 | 0.992022 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7123 | −0.890963 | −0.445481 | − | 0.895291i | \(-0.646967\pi\) | ||||
−0.445481 | + | 0.895291i | \(0.646967\pi\) | |||||||
\(312\) | − 6.45295i | − 0.365326i | ||||||||
\(313\) | 24.7794i | 1.40061i | 0.713842 | + | 0.700307i | \(0.246953\pi\) | ||||
−0.713842 | + | 0.700307i | \(0.753047\pi\) | |||||||
\(314\) | 15.3976 | 0.868935 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3195 | −1.36808 | ||||||||
\(317\) | 27.3798i | 1.53780i | 0.639369 | + | 0.768900i | \(0.279196\pi\) | ||||
−0.639369 | + | 0.768900i | \(0.720804\pi\) | |||||||
\(318\) | − 15.9931i | − 0.896848i | ||||||||
\(319\) | 8.56974 | 0.479813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −58.6745 | −3.27489 | ||||||||
\(322\) | − 44.2474i | − 2.46581i | ||||||||
\(323\) | 7.75669i | 0.431594i | ||||||||
\(324\) | −7.96492 | −0.442496 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.5440 | −0.860900 | ||||||||
\(327\) | 13.6062i | 0.752426i | ||||||||
\(328\) | − 3.56467i | − 0.196826i | ||||||||
\(329\) | −4.54831 | −0.250756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70033 | 0.258354 | 0.129177 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129177 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(332\) | − 22.9515i | − 1.25963i | ||||||||
\(333\) | − 7.43329i | − 0.407342i | ||||||||
\(334\) | −15.7068 | −0.859439 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.0900 | 1.20511 | ||||||||
\(337\) | 20.6360i | 1.12412i | 0.827098 | + | 0.562058i | \(0.189990\pi\) | ||||
−0.827098 | + | 0.562058i | \(0.810010\pi\) | |||||||
\(338\) | 21.1128i | 1.14839i | ||||||||
\(339\) | −22.9783 | −1.24801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.26600 | −0.393476 | ||||||||
\(342\) | 11.3225i | 0.612250i | ||||||||
\(343\) | − 13.5373i | − 0.730947i | ||||||||
\(344\) | 3.92477 | 0.211609 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3694 | 0.664983 | ||||||||
\(347\) | − 30.0148i | − 1.61128i | −0.592407 | − | 0.805639i | \(-0.701822\pi\) | ||||
0.592407 | − | 0.805639i | \(-0.298178\pi\) | |||||||
\(348\) | − 57.8260i | − 3.09980i | ||||||||
\(349\) | 14.7340 | 0.788693 | 0.394347 | − | 0.918962i | \(-0.370971\pi\) | ||||
0.394347 | + | 0.918962i | \(0.370971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6638 | −0.622570 | ||||||||
\(352\) | 8.64399i | 0.460726i | ||||||||
\(353\) | − 29.6302i | − 1.57705i | −0.615000 | − | 0.788527i | \(-0.710844\pi\) | ||||
0.615000 | − | 0.788527i | \(-0.289156\pi\) | |||||||
\(354\) | 33.2364 | 1.76649 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.10581 | 0.111608 | ||||||||
\(357\) | 69.3195i | 3.66878i | ||||||||
\(358\) | 9.60623i | 0.507705i | ||||||||
\(359\) | −21.7577 | −1.14833 | −0.574163 | − | 0.818741i | \(-0.694672\pi\) | ||||
−0.574163 | + | 0.818741i | \(0.694672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 5.85742i | − 0.307859i | ||||||||
\(363\) | 28.1484i | 1.47741i | ||||||||
\(364\) | −14.2619 | −0.747527 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.1306 | 1.31360 | ||||||||
\(367\) | − 30.0347i | − 1.56780i | −0.620889 | − | 0.783898i | \(-0.713228\pi\) | ||||
0.620889 | − | 0.783898i | \(-0.286772\pi\) | |||||||
\(368\) | 16.4422i | 0.857111i | ||||||||
\(369\) | −14.9031 | −0.775823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.05227 | −0.418053 | ||||||||
\(372\) | 49.0287i | 2.54202i | ||||||||
\(373\) | − 37.3055i | − 1.93161i | −0.259277 | − | 0.965803i | \(-0.583484\pi\) | ||||
0.259277 | − | 0.965803i | \(-0.416516\pi\) | |||||||
\(374\) | −18.3601 | −0.949378 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.85179 | −0.0954987 | ||||||||
\(377\) | − 13.7567i | − 0.708506i | ||||||||
\(378\) | 43.7470i | 2.25010i | ||||||||
\(379\) | 14.7794 | 0.759166 | 0.379583 | − | 0.925158i | \(-0.376068\pi\) | ||||
0.379583 | + | 0.925158i | \(0.376068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.3412 | −0.683492 | ||||||||
\(382\) | − 37.9704i | − 1.94273i | ||||||||
\(383\) | − 29.0020i | − 1.48193i | −0.671541 | − | 0.740967i | \(-0.734367\pi\) | ||||
0.671541 | − | 0.740967i | \(-0.265633\pi\) | |||||||
\(384\) | 27.8412 | 1.42077 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.0024 | 1.47618 | ||||||||
\(387\) | − 16.4086i | − 0.834094i | ||||||||
\(388\) | 8.28001i | 0.420354i | ||||||||
\(389\) | −21.1987 | −1.07481 | −0.537407 | − | 0.843323i | \(-0.680596\pi\) | ||||
−0.537407 | + | 0.843323i | \(0.680596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.5965 | −2.60935 | ||||||||
\(392\) | 3.33707i | 0.168548i | ||||||||
\(393\) | − 44.6529i | − 2.25244i | ||||||||
\(394\) | −46.0910 | −2.32203 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.1227 | −0.759944 | ||||||||
\(397\) | − 10.3856i | − 0.521238i | −0.965442 | − | 0.260619i | \(-0.916073\pi\) | ||||
0.965442 | − | 0.260619i | \(-0.0839267\pi\) | |||||||
\(398\) | − 15.1987i | − 0.761840i | ||||||||
\(399\) | 8.93674 | 0.447397 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.6638 | 1.28159 | 0.640796 | − | 0.767712i | \(-0.278605\pi\) | ||||
0.640796 | + | 0.767712i | \(0.278605\pi\) | |||||||
\(402\) | 97.5263i | 4.86417i | ||||||||
\(403\) | 11.6638i | 0.581017i | ||||||||
\(404\) | 7.81896 | 0.389008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −51.5965 | −2.56069 | ||||||||
\(407\) | − 1.55395i | − 0.0770266i | ||||||||
\(408\) | 28.2226i | 1.39723i | ||||||||
\(409\) | −5.71611 | −0.282644 | −0.141322 | − | 0.989964i | \(-0.545135\pi\) | ||||
−0.141322 | + | 0.989964i | \(0.545135\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.34023 | 0.115435 | ||||||||
\(412\) | − 15.6914i | − 0.773059i | ||||||||
\(413\) | − 16.7340i | − 0.823427i | ||||||||
\(414\) | −75.3157 | −3.70156 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.8759 | 0.680321 | ||||||||
\(417\) | − 36.7526i | − 1.79978i | ||||||||
\(418\) | 2.36700i | 0.115774i | ||||||||
\(419\) | −15.4303 | −0.753818 | −0.376909 | − | 0.926250i | \(-0.623013\pi\) | ||||
−0.376909 | + | 0.926250i | \(0.623013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.18005 | −0.0575121 | −0.0287561 | − | 0.999586i | \(-0.509155\pi\) | ||||
−0.0287561 | + | 0.999586i | \(0.509155\pi\) | |||||||
\(422\) | 23.6962i | 1.15352i | ||||||||
\(423\) | 7.74190i | 0.376424i | ||||||||
\(424\) | −3.27839 | −0.159213 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 44.0693 | 2.13517 | ||||||||
\(427\) | − 12.6529i | − 0.612315i | ||||||||
\(428\) | 52.7972i | 2.55205i | ||||||||
\(429\) | −5.63990 | −0.272297 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0255 | −0.675585 | −0.337792 | − | 0.941221i | \(-0.609680\pi\) | ||||
−0.337792 | + | 0.941221i | \(0.609680\pi\) | |||||||
\(432\) | − 16.2563i | − 0.782130i | ||||||||
\(433\) | 25.5894i | 1.22975i | 0.788625 | + | 0.614874i | \(0.210793\pi\) | ||||
−0.788625 | + | 0.614874i | \(0.789207\pi\) | |||||||
\(434\) | 43.7470 | 2.09992 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.2433 | 0.586348 | ||||||||
\(437\) | 6.65187i | 0.318202i | ||||||||
\(438\) | 1.50041i | 0.0716925i | ||||||||
\(439\) | 21.9732 | 1.04873 | 0.524363 | − | 0.851495i | \(-0.324304\pi\) | ||||
0.524363 | + | 0.851495i | \(0.324304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9515 | 0.664358 | ||||||||
\(442\) | 29.4728i | 1.40188i | ||||||||
\(443\) | − 19.3721i | − 0.920395i | −0.887817 | − | 0.460197i | \(-0.847779\pi\) | ||||
0.887817 | − | 0.460197i | \(-0.152221\pi\) | |||||||
\(444\) | −10.4856 | −0.497625 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.0697 | 1.28179 | ||||||||
\(447\) | − 39.7161i | − 1.87851i | ||||||||
\(448\) | − 36.6944i | − 1.73365i | ||||||||
\(449\) | 19.1841 | 0.905355 | 0.452677 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452677 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.11553 | −0.146705 | ||||||||
\(452\) | 20.6766i | 0.972545i | ||||||||
\(453\) | − 14.4570i | − 0.679250i | ||||||||
\(454\) | −14.2003 | −0.666455 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.63849 | 0.170388 | ||||||||
\(457\) | − 8.36010i | − 0.391069i | −0.980697 | − | 0.195534i | \(-0.937356\pi\) | ||||
0.980697 | − | 0.195534i | \(-0.0626442\pi\) | |||||||
\(458\) | 0.161177i | 0.00753131i | ||||||||
\(459\) | 51.0130 | 2.38108 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.0268 | −1.16561 | −0.582806 | − | 0.812611i | \(-0.698045\pi\) | ||||
−0.582806 | + | 0.812611i | \(0.698045\pi\) | |||||||
\(462\) | 21.1533i | 0.984140i | ||||||||
\(463\) | 32.3749i | 1.50459i | 0.658827 | + | 0.752294i | \(0.271053\pi\) | ||||
−0.658827 | + | 0.752294i | \(0.728947\pi\) | |||||||
\(464\) | 19.1731 | 0.890091 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.3818 | −0.944168 | ||||||||
\(467\) | − 15.2216i | − 0.704372i | −0.935930 | − | 0.352186i | \(-0.885438\pi\) | ||||
0.935930 | − | 0.352186i | \(-0.114562\pi\) | |||||||
\(468\) | 24.2759i | 1.12215i | ||||||||
\(469\) | 49.1030 | 2.26736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.6865 | −0.953185 | ||||||||
\(472\) | − 6.81305i | − 0.313596i | ||||||||
\(473\) | − 3.43026i | − 0.157724i | ||||||||
\(474\) | 57.9031 | 2.65958 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 62.3759 | 2.85899 | ||||||||
\(477\) | 13.7062i | 0.627563i | ||||||||
\(478\) | 6.27698i | 0.287103i | ||||||||
\(479\) | 20.0485 | 0.916038 | 0.458019 | − | 0.888943i | \(-0.348559\pi\) | ||||
0.458019 | + | 0.888943i | \(0.348559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.49451 | −0.113740 | ||||||||
\(482\) | − 20.1977i | − 0.919978i | ||||||||
\(483\) | 59.4460i | 2.70489i | ||||||||
\(484\) | 25.3288 | 1.15131 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −23.3061 | −1.05719 | ||||||||
\(487\) | 31.6508i | 1.43424i | 0.696952 | + | 0.717118i | \(0.254539\pi\) | ||||
−0.696952 | + | 0.717118i | \(0.745461\pi\) | |||||||
\(488\) | − 5.15146i | − 0.233195i | ||||||||
\(489\) | 20.8832 | 0.944371 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8033 | 1.11936 | 0.559679 | − | 0.828710i | \(-0.310924\pi\) | ||||
0.559679 | + | 0.828710i | \(0.310924\pi\) | |||||||
\(492\) | 21.0227i | 0.947776i | ||||||||
\(493\) | 60.1662i | 2.70975i | ||||||||
\(494\) | 3.79966 | 0.170955 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.2563 | −0.729928 | ||||||||
\(497\) | − 22.1882i | − 0.995277i | ||||||||
\(498\) | 54.6460i | 2.44874i | ||||||||
\(499\) | 33.0237 | 1.47834 | 0.739171 | − | 0.673518i | \(-0.235217\pi\) | ||||
0.739171 | + | 0.673518i | \(0.235217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.1020 | 0.942767 | ||||||||
\(502\) | − 31.9862i | − 1.42761i | ||||||||
\(503\) | − 3.54396i | − 0.158017i | −0.996874 | − | 0.0790087i | \(-0.974825\pi\) | ||||
0.996874 | − | 0.0790087i | \(-0.0251755\pi\) | |||||||
\(504\) | 20.7419 | 0.923917 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.7450 | −0.699950 | ||||||||
\(507\) | − 28.3650i | − 1.25973i | ||||||||
\(508\) | 12.0049i | 0.532629i | ||||||||
\(509\) | 2.11679 | 0.0938250 | 0.0469125 | − | 0.998899i | \(-0.485062\pi\) | ||||
0.0469125 | + | 0.998899i | \(0.485062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.755435 | 0.0334185 | ||||||||
\(512\) | 25.5885i | 1.13086i | ||||||||
\(513\) | − 6.57664i | − 0.290366i | ||||||||
\(514\) | −32.4140 | −1.42972 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −23.1464 | −1.01896 | ||||||||
\(517\) | 1.61847i | 0.0711802i | ||||||||
\(518\) | 9.35601i | 0.411080i | ||||||||
\(519\) | −16.6182 | −0.729458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.60748 | −0.377101 | −0.188550 | − | 0.982064i | \(-0.560379\pi\) | ||||
−0.188550 | + | 0.982064i | \(0.560379\pi\) | |||||||
\(522\) | 87.8250i | 3.84400i | ||||||||
\(523\) | 36.8349i | 1.61068i | 0.592814 | + | 0.805340i | \(0.298017\pi\) | ||||
−0.592814 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(524\) | −40.1800 | −1.75527 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.6113 | 1.42192 | ||||||||
\(527\) | − 51.0130i | − 2.22216i | ||||||||
\(528\) | − 7.86051i | − 0.342085i | ||||||||
\(529\) | −21.2474 | −0.923799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.4838 | −1.23609 | ||||||||
\(532\) | − 8.04156i | − 0.348646i | ||||||||
\(533\) | 5.00125i | 0.216628i | ||||||||
\(534\) | −5.01379 | −0.216968 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.9917 | 0.863509 | ||||||||
\(537\) | − 12.9059i | − 0.556931i | ||||||||
\(538\) | − 24.6814i | − 1.06409i | ||||||||
\(539\) | 2.91661 | 0.125627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0079 | −1.37613 | −0.688063 | − | 0.725651i | \(-0.741539\pi\) | ||||
−0.688063 | + | 0.725651i | \(0.741539\pi\) | |||||||
\(542\) | 4.63018i | 0.198883i | ||||||||
\(543\) | 7.86941i | 0.337709i | ||||||||
\(544\) | −60.6875 | −2.60196 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 33.9566 | 1.45321 | ||||||||
\(547\) | − 17.6240i | − 0.753550i | −0.926305 | − | 0.376775i | \(-0.877033\pi\) | ||||
0.926305 | − | 0.376775i | \(-0.122967\pi\) | |||||||
\(548\) | − 2.10581i | − 0.0899559i | ||||||||
\(549\) | −21.5371 | −0.919179 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.75669 | 0.330446 | ||||||||
\(552\) | 24.2027i | 1.03014i | ||||||||
\(553\) | − 29.1533i | − 1.23972i | ||||||||
\(554\) | 50.1769 | 2.13181 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −33.0711 | −1.40253 | ||||||||
\(557\) | 34.6865i | 1.46972i | 0.678221 | + | 0.734858i | \(0.262751\pi\) | ||||
−0.678221 | + | 0.734858i | \(0.737249\pi\) | |||||||
\(558\) | − 74.4639i | − 3.15231i | ||||||||
\(559\) | −5.50648 | −0.232899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.6667 | 1.04143 | ||||||||
\(562\) | 55.0229i | 2.32100i | ||||||||
\(563\) | 13.5073i | 0.569263i | 0.958637 | + | 0.284632i | \(0.0918712\pi\) | ||||
−0.958637 | + | 0.284632i | \(0.908129\pi\) | |||||||
\(564\) | 10.9209 | 0.459855 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.8238 | −0.665122 | ||||||||
\(567\) | − 9.54803i | − 0.400980i | ||||||||
\(568\) | − 9.03366i | − 0.379044i | ||||||||
\(569\) | −32.3588 | −1.35655 | −0.678276 | − | 0.734807i | \(-0.737273\pi\) | ||||
−0.678276 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.93293 | −0.373831 | −0.186916 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186916 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(572\) | 5.07496i | 0.212195i | ||||||||
\(573\) | 51.0130i | 2.13110i | ||||||||
\(574\) | 18.7579 | 0.782941 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −62.4594 | −2.60248 | ||||||||
\(577\) | − 14.9059i | − 0.620541i | −0.950648 | − | 0.310270i | \(-0.899580\pi\) | ||||
0.950648 | − | 0.310270i | \(-0.100420\pi\) | |||||||
\(578\) | − 92.4808i | − 3.84669i | ||||||||
\(579\) | −38.9645 | −1.61931 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.5134 | 1.14145 | ||||||||
\(582\) | − 19.7141i | − 0.817177i | ||||||||
\(583\) | 2.86532i | 0.118669i | ||||||||
\(584\) | 0.307566 | 0.0127272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.7446 | 2.13755 | ||||||||
\(587\) | − 7.37207i | − 0.304278i | −0.988359 | − | 0.152139i | \(-0.951384\pi\) | ||||
0.988359 | − | 0.152139i | \(-0.0486161\pi\) | |||||||
\(588\) | − 19.6804i | − 0.811607i | ||||||||
\(589\) | −6.57664 | −0.270986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 61.9229 | 2.54717 | ||||||||
\(592\) | − 3.47668i | − 0.142890i | ||||||||
\(593\) | − 17.6853i | − 0.726247i | −0.931741 | − | 0.363124i | \(-0.881710\pi\) | ||||
0.931741 | − | 0.363124i | \(-0.118290\pi\) | |||||||
\(594\) | 15.5669 | 0.638718 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −35.7378 | −1.46388 | ||||||||
\(597\) | 20.4193i | 0.835705i | ||||||||
\(598\) | 25.2749i | 1.03357i | ||||||||
\(599\) | −5.30657 | −0.216821 | −0.108410 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108410 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.7875 | 1.78613 | 0.893065 | − | 0.449927i | \(-0.148550\pi\) | ||||
0.893065 | + | 0.449927i | \(0.148550\pi\) | |||||||
\(602\) | 20.6529i | 0.841747i | ||||||||
\(603\) | − 83.5806i | − 3.40367i | ||||||||
\(604\) | −13.0089 | −0.529324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.6164 | −0.756239 | ||||||||
\(607\) | 7.24535i | 0.294080i | 0.989131 | + | 0.147040i | \(0.0469745\pi\) | ||||
−0.989131 | + | 0.147040i | \(0.953025\pi\) | |||||||
\(608\) | 7.82389i | 0.317301i | ||||||||
\(609\) | 69.3195 | 2.80897 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.59807 | 0.105107 | ||||||||
\(612\) | − 106.173i | − 4.29179i | ||||||||
\(613\) | 20.8962i | 0.843988i | 0.906599 | + | 0.421994i | \(0.138670\pi\) | ||||
−0.906599 | + | 0.421994i | \(0.861330\pi\) | |||||||
\(614\) | 9.39419 | 0.379119 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.33616 | 0.174709 | ||||||||
\(617\) | 22.0494i | 0.887677i | 0.896107 | + | 0.443839i | \(0.146384\pi\) | ||||
−0.896107 | + | 0.443839i | \(0.853616\pi\) | |||||||
\(618\) | 37.3601i | 1.50284i | ||||||||
\(619\) | 0.0484607 | 0.00194780 | 0.000973900 | − | 1.00000i | \(-0.499690\pi\) | ||||
0.000973900 | 1.00000i | \(0.499690\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.7470 | 1.75550 | ||||||||
\(622\) | − 33.6626i | − 1.34975i | ||||||||
\(623\) | 2.52437i | 0.101137i | ||||||||
\(624\) | −12.6182 | −0.505132 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −53.0882 | −2.12183 | ||||||||
\(627\) | − 3.18005i | − 0.126999i | ||||||||
\(628\) | 18.6144i | 0.742795i | ||||||||
\(629\) | 10.9100 | 0.435009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6182 | −1.29851 | −0.649255 | − | 0.760571i | \(-0.724919\pi\) | ||||
−0.649255 | + | 0.760571i | \(0.724919\pi\) | |||||||
\(632\) | − 11.8694i | − 0.472140i | ||||||||
\(633\) | − 31.8357i | − 1.26536i | ||||||||
\(634\) | −58.6593 | −2.32966 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.3343 | 0.766656 | ||||||||
\(637\) | − 4.68193i | − 0.185505i | ||||||||
\(638\) | 18.3601i | 0.726883i | ||||||||
\(639\) | −37.7677 | −1.49407 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4136 | −0.529806 | −0.264903 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264903 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(642\) | − 125.706i | − 4.96123i | ||||||||
\(643\) | 23.8052i | 0.938783i | 0.882990 | + | 0.469392i | \(0.155527\pi\) | ||||
−0.882990 | + | 0.469392i | \(0.844473\pi\) | |||||||
\(644\) | 53.4914 | 2.10786 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.6182 | −0.653834 | ||||||||
\(647\) | 48.4580i | 1.90508i | 0.304412 | + | 0.952540i | \(0.401540\pi\) | ||||
−0.304412 | + | 0.952540i | \(0.598460\pi\) | |||||||
\(648\) | − 3.88737i | − 0.152710i | ||||||||
\(649\) | −5.95463 | −0.233740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −58.7737 | −2.30352 | ||||||||
\(652\) | − 18.7914i | − 0.735926i | ||||||||
\(653\) | 22.2351i | 0.870128i | 0.900399 | + | 0.435064i | \(0.143274\pi\) | ||||
−0.900399 | + | 0.435064i | \(0.856726\pi\) | |||||||
\(654\) | −29.1504 | −1.13987 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.97041 | −0.272149 | ||||||||
\(657\) | − 1.28586i | − 0.0501663i | ||||||||
\(658\) | − 9.74445i | − 0.379878i | ||||||||
\(659\) | 10.7072 | 0.417095 | 0.208547 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208547 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.7980 | −1.74244 | −0.871220 | − | 0.490893i | \(-0.836670\pi\) | ||||
−0.871220 | + | 0.490893i | \(0.836670\pi\) | |||||||
\(662\) | 10.0702i | 0.391388i | ||||||||
\(663\) | − 39.5965i | − 1.53780i | ||||||||
\(664\) | 11.2017 | 0.434712 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.9253 | 0.617095 | ||||||||
\(667\) | 51.5965i | 1.99782i | ||||||||
\(668\) | − 18.9882i | − 0.734677i | ||||||||
\(669\) | −36.3680 | −1.40607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.50239 | −0.173813 | ||||||||
\(672\) | 69.9201i | 2.69723i | ||||||||
\(673\) | − 43.2772i | − 1.66821i | −0.551604 | − | 0.834106i | \(-0.685984\pi\) | ||||
0.551604 | − | 0.834106i | \(-0.314016\pi\) | |||||||
\(674\) | −44.2113 | −1.70296 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.5237 | −0.981680 | ||||||||
\(677\) | − 11.5330i | − 0.443251i | −0.975132 | − | 0.221625i | \(-0.928864\pi\) | ||||
0.975132 | − | 0.221625i | \(-0.0711362\pi\) | |||||||
\(678\) | − 49.2295i | − 1.89065i | ||||||||
\(679\) | −9.92575 | −0.380915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0780 | 0.731072 | ||||||||
\(682\) | − 15.5669i | − 0.596088i | ||||||||
\(683\) | 0.916090i | 0.0350532i | 0.999846 | + | 0.0175266i | \(0.00557918\pi\) | ||||
−0.999846 | + | 0.0175266i | \(0.994421\pi\) | |||||||
\(684\) | −13.6879 | −0.523372 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 29.0028 | 1.10733 | ||||||||
\(687\) | − 0.216540i | − 0.00826153i | ||||||||
\(688\) | − 7.67456i | − 0.292590i | ||||||||
\(689\) | 4.59960 | 0.175231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8278 | 0.564077 | 0.282039 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282039 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(692\) | 14.9536i | 0.568450i | ||||||||
\(693\) | − 18.1285i | − 0.688644i | ||||||||
\(694\) | 64.3047 | 2.44097 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 28.2226 | 1.06978 | ||||||||
\(697\) | − 21.8735i | − 0.828517i | ||||||||
\(698\) | 31.5666i | 1.19481i | ||||||||
\(699\) | 27.3828 | 1.03571 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1722 | 1.36620 | 0.683102 | − | 0.730323i | \(-0.260631\pi\) | ||||
0.683102 | + | 0.730323i | \(0.260631\pi\) | |||||||
\(702\) | − 24.9890i | − 0.943150i | ||||||||
\(703\) | − 1.40652i | − 0.0530481i | ||||||||
\(704\) | −13.0573 | −0.492117 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 63.4807 | 2.38913 | ||||||||
\(707\) | 9.37305i | 0.352510i | ||||||||
\(708\) | 40.1800i | 1.51006i | ||||||||
\(709\) | −10.4331 | −0.391823 | −0.195911 | − | 0.980622i | \(-0.562766\pi\) | ||||
−0.195911 | + | 0.980622i | \(0.562766\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49.6233 | −1.86102 | ||||||||
\(712\) | 1.02777i | 0.0385171i | ||||||||
\(713\) | − 43.7470i | − 1.63834i | ||||||||
\(714\) | −148.513 | −5.55794 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.6131 | −0.434003 | ||||||||
\(717\) | − 8.43308i | − 0.314939i | ||||||||
\(718\) | − 46.6144i | − 1.73963i | ||||||||
\(719\) | −7.73373 | −0.288420 | −0.144210 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144210 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8102 | 0.700529 | ||||||||
\(722\) | 2.14243i | 0.0797331i | ||||||||
\(723\) | 27.1354i | 1.00918i | ||||||||
\(724\) | 7.08114 | 0.263168 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −60.3061 | −2.23817 | ||||||||
\(727\) | 39.5241i | 1.46587i | 0.680300 | + | 0.732934i | \(0.261849\pi\) | ||||
−0.680300 | + | 0.732934i | \(0.738151\pi\) | |||||||
\(728\) | − 6.96068i | − 0.257980i | ||||||||
\(729\) | 40.5373 | 1.50138 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0831 | 0.890746 | ||||||||
\(732\) | 30.3808i | 1.12291i | ||||||||
\(733\) | 50.7498i | 1.87449i | 0.348677 | + | 0.937243i | \(0.386631\pi\) | ||||
−0.348677 | + | 0.937243i | \(0.613369\pi\) | |||||||
\(734\) | 64.3473 | 2.37510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.0435 | −1.91835 | ||||||||
\(737\) | − 17.4728i | − 0.643619i | ||||||||
\(738\) | − 31.9288i | − 1.17532i | ||||||||
\(739\) | −0.419276 | −0.0154233 | −0.00771165 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771165 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.10482 | −0.187530 | ||||||||
\(742\) | − 17.2515i | − 0.633321i | ||||||||
\(743\) | 19.5511i | 0.717259i | 0.933480 | + | 0.358630i | \(0.116756\pi\) | ||||
−0.933480 | + | 0.358630i | \(0.883244\pi\) | |||||||
\(744\) | −23.9290 | −0.877280 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 79.9246 | 2.92625 | ||||||||
\(747\) | − 46.8319i | − 1.71349i | ||||||||
\(748\) | − 22.1958i | − 0.811560i | ||||||||
\(749\) | −63.2912 | −2.31261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.76768 | 0.319937 | 0.159969 | − | 0.987122i | \(-0.448861\pi\) | ||||
0.159969 | + | 0.987122i | \(0.448861\pi\) | |||||||
\(752\) | 3.62102i | 0.132045i | ||||||||
\(753\) | 42.9732i | 1.56603i | ||||||||
\(754\) | 29.4728 | 1.07334 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −52.8864 | −1.92346 | ||||||||
\(757\) | 48.0535i | 1.74653i | 0.487241 | + | 0.873267i | \(0.338003\pi\) | ||||
−0.487241 | + | 0.873267i | \(0.661997\pi\) | |||||||
\(758\) | 31.6638i | 1.15008i | ||||||||
\(759\) | 21.1533 | 0.767815 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3947 | 1.06556 | 0.532779 | − | 0.846254i | \(-0.321148\pi\) | ||||
0.532779 | + | 0.846254i | \(0.321148\pi\) | |||||||
\(762\) | − 28.5827i | − 1.03544i | ||||||||
\(763\) | 14.6768i | 0.531336i | ||||||||
\(764\) | 45.9031 | 1.66071 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 62.1350 | 2.24503 | ||||||||
\(767\) | 9.55875i | 0.345146i | ||||||||
\(768\) | − 8.38765i | − 0.302663i | ||||||||
\(769\) | 13.3790 | 0.482458 | 0.241229 | − | 0.970468i | \(-0.422449\pi\) | ||||
0.241229 | + | 0.970468i | \(0.422449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.5480 | 1.56834 | ||||||||
\(772\) | 35.0615i | 1.26189i | ||||||||
\(773\) | 0.133625i | 0.00480617i | 0.999997 | + | 0.00240309i | \(0.000764927\pi\) | ||||
−0.999997 | + | 0.00240309i | \(0.999235\pi\) | |||||||
\(774\) | 35.1543 | 1.26359 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.04115 | −0.145069 | ||||||||
\(777\) | − 12.5697i | − 0.450937i | ||||||||
\(778\) | − 45.4167i | − 1.62827i | ||||||||
\(779\) | −2.81995 | −0.101035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.89545 | −0.282522 | ||||||||
\(782\) | − 110.542i | − 3.95298i | ||||||||
\(783\) | − 51.0130i | − 1.82305i | ||||||||
\(784\) | 6.52536 | 0.233049 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 95.6658 | 3.41229 | ||||||||
\(787\) | 4.84060i | 0.172549i | 0.996271 | + | 0.0862744i | \(0.0274962\pi\) | ||||
−0.996271 | + | 0.0862744i | \(0.972504\pi\) | |||||||
\(788\) | − 55.7202i | − 1.98495i | ||||||||
\(789\) | −43.8130 | −1.55979 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.7863 | −0.881299 | ||||||||
\(792\) | − 7.38079i | − 0.262265i | ||||||||
\(793\) | 7.22753i | 0.256657i | ||||||||
\(794\) | 22.2505 | 0.789640 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.3739 | 0.651246 | ||||||||
\(797\) | − 11.6993i | − 0.414410i | −0.978298 | − | 0.207205i | \(-0.933563\pi\) | ||||
0.978298 | − | 0.207205i | \(-0.0664367\pi\) | |||||||
\(798\) | 19.1464i | 0.677774i | ||||||||
\(799\) | −11.3629 | −0.401991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.29685 | 0.151822 | ||||||||
\(802\) | 54.9831i | 1.94152i | ||||||||
\(803\) | − 0.268814i | − 0.00948624i | ||||||||
\(804\) | −117.901 | −4.15806 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.9890 | −0.880200 | ||||||||
\(807\) | 33.1593i | 1.16726i | ||||||||
\(808\) | 3.81613i | 0.134251i | ||||||||
\(809\) | 33.1987 | 1.16720 | 0.583601 | − | 0.812040i | \(-0.301643\pi\) | ||||
0.583601 | + | 0.812040i | \(0.301643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.5766 | −0.933232 | −0.466616 | − | 0.884460i | \(-0.654527\pi\) | ||||
−0.466616 | + | 0.884460i | \(0.654527\pi\) | |||||||
\(812\) | − 62.3759i | − 2.18896i | ||||||||
\(813\) | − 6.22061i | − 0.218166i | ||||||||
\(814\) | 3.32924 | 0.116690 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 55.1869 | 1.93193 | ||||||||
\(817\) | − 3.10482i | − 0.108624i | ||||||||
\(818\) | − 12.2464i | − 0.428185i | ||||||||
\(819\) | −29.1010 | −1.01687 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5807 | 0.892773 | 0.446387 | − | 0.894840i | \(-0.352711\pi\) | ||||
0.446387 | + | 0.894840i | \(0.352711\pi\) | |||||||
\(822\) | 5.01379i | 0.174876i | ||||||||
\(823\) | 12.9783i | 0.452395i | 0.974081 | + | 0.226198i | \(0.0726295\pi\) | ||||
−0.974081 | + | 0.226198i | \(0.927371\pi\) | |||||||
\(824\) | 7.65835 | 0.266791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.8515 | 1.24743 | ||||||||
\(827\) | 12.5167i | 0.435248i | 0.976033 | + | 0.217624i | \(0.0698306\pi\) | ||||
−0.976033 | + | 0.217624i | \(0.930169\pi\) | |||||||
\(828\) | − 91.0504i | − 3.16422i | ||||||||
\(829\) | 19.4391 | 0.675149 | 0.337574 | − | 0.941299i | \(-0.390394\pi\) | ||||
0.337574 | + | 0.941299i | \(0.390394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −67.4124 | −2.33851 | ||||||||
\(832\) | 20.9605i | 0.726674i | ||||||||
\(833\) | 20.4769i | 0.709482i | ||||||||
\(834\) | 78.7400 | 2.72654 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.86151 | −0.0989673 | ||||||||
\(837\) | 43.2522i | 1.49501i | ||||||||
\(838\) | − 33.0583i | − 1.14198i | ||||||||
\(839\) | 43.9972 | 1.51895 | 0.759475 | − | 0.650536i | \(-0.225456\pi\) | ||||
0.759475 | + | 0.650536i | \(0.225456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.1662 | 1.07470 | ||||||||
\(842\) | − 2.52818i | − 0.0871268i | ||||||||
\(843\) | − 73.9229i | − 2.54604i | ||||||||
\(844\) | −28.6468 | −0.986063 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16.5865 | −0.570256 | ||||||||
\(847\) | 30.3632i | 1.04329i | ||||||||
\(848\) | 6.41061i | 0.220141i | ||||||||
\(849\) | 21.2591 | 0.729610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.35601 | 0.320720 | ||||||||
\(852\) | 53.2761i | 1.82521i | ||||||||
\(853\) | 3.30374i | 0.113118i | 0.998399 | + | 0.0565590i | \(0.0180129\pi\) | ||||
−0.998399 | + | 0.0565590i | \(0.981987\pi\) | |||||||
\(854\) | 27.1079 | 0.927614 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.7682 | −0.880740 | ||||||||
\(857\) | − 6.02374i | − 0.205767i | −0.994693 | − | 0.102883i | \(-0.967193\pi\) | ||||
0.994693 | − | 0.102883i | \(-0.0328069\pi\) | |||||||
\(858\) | − 12.0831i | − 0.412511i | ||||||||
\(859\) | 36.0158 | 1.22884 | 0.614421 | − | 0.788978i | \(-0.289390\pi\) | ||||
0.614421 | + | 0.788978i | \(0.289390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.2012 | −0.858853 | ||||||||
\(862\) | − 30.0487i | − 1.02346i | ||||||||
\(863\) | 29.9250i | 1.01866i | 0.860572 | + | 0.509329i | \(0.170106\pi\) | ||||
−0.860572 | + | 0.509329i | \(0.829894\pi\) | |||||||
\(864\) | 51.4549 | 1.75053 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −54.8236 | −1.86298 | ||||||||
\(867\) | 124.247i | 4.21966i | ||||||||
\(868\) | 52.8864i | 1.79508i | ||||||||
\(869\) | −10.3739 | −0.351911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.0485 | −0.950386 | ||||||||
\(872\) | 5.97548i | 0.202355i | ||||||||
\(873\) | 16.8951i | 0.571813i | ||||||||
\(874\) | −14.2512 | −0.482054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.81388 | −0.0612852 | ||||||||
\(877\) | − 0.618980i | − 0.0209015i | −0.999945 | − | 0.0104507i | \(-0.996673\pi\) | ||||
0.999945 | − | 0.0104507i | \(-0.00332663\pi\) | |||||||
\(878\) | 47.0762i | 1.58874i | ||||||||
\(879\) | −69.5184 | −2.34480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2423 | −0.715672 | −0.357836 | − | 0.933784i | \(-0.616485\pi\) | ||||
−0.357836 | + | 0.933784i | \(0.616485\pi\) | |||||||
\(882\) | 29.8902i | 1.00646i | ||||||||
\(883\) | − 48.8971i | − 1.64552i | −0.568389 | − | 0.822760i | \(-0.692433\pi\) | ||||
0.568389 | − | 0.822760i | \(-0.307567\pi\) | |||||||
\(884\) | −35.6302 | −1.19837 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41.5034 | 1.39433 | ||||||||
\(887\) | − 58.2797i | − 1.95684i | −0.206622 | − | 0.978421i | \(-0.566247\pi\) | ||||
0.206622 | − | 0.978421i | \(-0.433753\pi\) | |||||||
\(888\) | − 5.11762i | − 0.171736i | ||||||||
\(889\) | −14.3909 | −0.482657 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.39757 | −0.113823 | ||||||||
\(892\) | 32.7251i | 1.09572i | ||||||||
\(893\) | 1.46492i | 0.0490216i | ||||||||
\(894\) | 85.0892 | 2.84581 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 30.0318 | 1.00329 | ||||||||
\(897\) | − 33.9566i | − 1.13378i | ||||||||
\(898\) | 41.1007i | 1.37155i | ||||||||
\(899\) | −51.0130 | −1.70138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.1168 | −0.670187 | ||||||||
\(902\) | − 6.67483i | − 0.222247i | ||||||||
\(903\) | − 27.7470i | − 0.923361i | ||||||||
\(904\) | −10.0914 | −0.335636 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.9732 | 1.02902 | ||||||||
\(907\) | 36.5154i | 1.21247i | 0.795284 | + | 0.606237i | \(0.207322\pi\) | ||||
−0.795284 | + | 0.606237i | \(0.792678\pi\) | |||||||
\(908\) | − 17.1670i | − 0.569708i | ||||||||
\(909\) | 15.9543 | 0.529172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.62735 | 0.219574 | 0.109787 | − | 0.993955i | \(-0.464983\pi\) | ||||
0.109787 | + | 0.993955i | \(0.464983\pi\) | |||||||
\(912\) | − 7.11475i | − 0.235593i | ||||||||
\(913\) | − 9.79036i | − 0.324014i | ||||||||
\(914\) | 17.9110 | 0.592442 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.194850 | −0.00643802 | ||||||||
\(917\) | − 48.1662i | − 1.59059i | ||||||||
\(918\) | 109.292i | 3.60717i | ||||||||
\(919\) | −7.91688 | −0.261154 | −0.130577 | − | 0.991438i | \(-0.541683\pi\) | ||||
−0.130577 | + | 0.991438i | \(0.541683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.6210 | −0.415877 | ||||||||
\(922\) | − 53.6182i | − 1.76582i | ||||||||
\(923\) | 12.6743i | 0.417179i | ||||||||
\(924\) | −25.5726 | −0.841275 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −69.3611 | −2.27935 | ||||||||
\(927\) | − 32.0178i | − 1.05160i | ||||||||
\(928\) | 60.6875i | 1.99217i | ||||||||
\(929\) | −35.8597 | −1.17652 | −0.588259 | − | 0.808673i | \(-0.700186\pi\) | ||||
−0.588259 | + | 0.808673i | \(0.700186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63990 | 0.0865192 | ||||||||
\(932\) | − 24.6399i | − 0.807106i | ||||||||
\(933\) | 45.2254i | 1.48061i | ||||||||
\(934\) | 32.6113 | 1.06707 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.8481 | −0.387268 | ||||||||
\(937\) | 11.4420i | 0.373793i | 0.982380 | + | 0.186896i | \(0.0598428\pi\) | ||||
−0.982380 | + | 0.186896i | \(0.940157\pi\) | |||||||
\(938\) | 105.200i | 3.43490i | ||||||||
\(939\) | 71.3236 | 2.32756 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.360100 | −0.0117389 | −0.00586945 | − | 0.999983i | \(-0.501868\pi\) | ||||
−0.00586945 | + | 0.999983i | \(0.501868\pi\) | |||||||
\(942\) | − 44.3195i | − 1.44401i | ||||||||
\(943\) | − 18.7579i | − 0.610843i | ||||||||
\(944\) | −13.3223 | −0.433605 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.34911 | 0.238940 | ||||||||
\(947\) | − 2.63807i | − 0.0857256i | −0.999081 | − | 0.0428628i | \(-0.986352\pi\) | ||||
0.999081 | − | 0.0428628i | \(-0.0136478\pi\) | |||||||
\(948\) | 70.0000i | 2.27349i | ||||||||
\(949\) | −0.431517 | −0.0140076 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.8084 | 2.55554 | ||||||||
\(952\) | 30.4432i | 0.986670i | ||||||||
\(953\) | 10.4430i | 0.338282i | 0.985592 | + | 0.169141i | \(0.0540994\pi\) | ||||
−0.985592 | + | 0.169141i | \(0.945901\pi\) | |||||||
\(954\) | −29.3646 | −0.950714 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.58835 | −0.245425 | ||||||||
\(957\) | − 24.6667i | − 0.797360i | ||||||||
\(958\) | 42.9525i | 1.38773i | ||||||||
\(959\) | 2.52437 | 0.0815160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2522 | 0.395232 | ||||||||
\(962\) | − 5.34432i | − 0.172308i | ||||||||
\(963\) | 107.731i | 3.47159i | ||||||||
\(964\) | 24.4173 | 0.786428 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −127.359 | −4.09772 | ||||||||
\(967\) | − 33.2732i | − 1.06999i | −0.844854 | − | 0.534996i | \(-0.820313\pi\) | ||||
0.844854 | − | 0.534996i | \(-0.179687\pi\) | |||||||
\(968\) | 12.3620i | 0.397330i | ||||||||
\(969\) | 22.3264 | 0.717228 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5657 | 0.756258 | 0.378129 | − | 0.925753i | \(-0.376568\pi\) | ||||
0.378129 | + | 0.925753i | \(0.376568\pi\) | |||||||
\(972\) | − 28.1752i | − 0.903719i | ||||||||
\(973\) | − 39.6444i | − 1.27094i | ||||||||
\(974\) | −67.8098 | −2.17277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0732 | −0.322437 | ||||||||
\(977\) | − 0.402439i | − 0.0128752i | −0.999979 | − | 0.00643759i | \(-0.997951\pi\) | ||||
0.999979 | − | 0.00643759i | \(-0.00204916\pi\) | |||||||
\(978\) | 44.7409i | 1.43066i | ||||||||
\(979\) | 0.898271 | 0.0287089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.9821 | 0.797617 | ||||||||
\(982\) | 53.1395i | 1.69575i | ||||||||
\(983\) | 11.4927i | 0.366561i | 0.983061 | + | 0.183281i | \(0.0586717\pi\) | ||||
−0.983061 | + | 0.183281i | \(0.941328\pi\) | |||||||
\(984\) | −10.2603 | −0.327088 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −128.902 | −4.10508 | ||||||||
\(987\) | 13.0916i | 0.416710i | ||||||||
\(988\) | 4.59348i | 0.146138i | ||||||||
\(989\) | 20.6529 | 0.656723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.05761 | 0.192426 | 0.0962132 | − | 0.995361i | \(-0.469327\pi\) | ||||
0.0962132 | + | 0.995361i | \(0.469327\pi\) | |||||||
\(992\) | − 51.4549i | − 1.63370i | ||||||||
\(993\) | − 13.5292i | − 0.429335i | ||||||||
\(994\) | 47.5368 | 1.50777 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −66.0624 | −2.09327 | ||||||||
\(997\) | 48.1086i | 1.52362i | 0.647803 | + | 0.761808i | \(0.275688\pi\) | ||||
−0.647803 | + | 0.761808i | \(0.724312\pi\) | |||||||
\(998\) | 70.7510i | 2.23959i | ||||||||
\(999\) | −9.25020 | −0.292663 |
(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 | 475.2.b.e.324.7 | 8 | ||
5.2 | odd | 4 | 95.2.a.b.1.2 | ✓ | 4 | ||
5.3 | odd | 4 | 475.2.a.i.1.3 | 4 | |||
5.4 | even | 2 | inner | 475.2.b.e.324.2 | 8 | ||
15.2 | even | 4 | 855.2.a.m.1.3 | 4 | |||
15.8 | even | 4 | 4275.2.a.bo.1.2 | 4 | |||
20.3 | even | 4 | 7600.2.a.cf.1.1 | 4 | |||
20.7 | even | 4 | 1520.2.a.t.1.4 | 4 | |||
35.27 | even | 4 | 4655.2.a.y.1.2 | 4 | |||
40.27 | even | 4 | 6080.2.a.ch.1.1 | 4 | |||
40.37 | odd | 4 | 6080.2.a.cc.1.4 | 4 | |||
95.18 | even | 4 | 9025.2.a.bf.1.2 | 4 | |||
95.37 | even | 4 | 1805.2.a.p.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.2 | ✓ | 4 | 5.2 | odd | 4 | ||
475.2.a.i.1.3 | 4 | 5.3 | odd | 4 | |||
475.2.b.e.324.2 | 8 | 5.4 | even | 2 | inner | ||
475.2.b.e.324.7 | 8 | 1.1 | even | 1 | trivial | ||
855.2.a.m.1.3 | 4 | 15.2 | even | 4 | |||
1520.2.a.t.1.4 | 4 | 20.7 | even | 4 | |||
1805.2.a.p.1.3 | 4 | 95.37 | even | 4 | |||
4275.2.a.bo.1.2 | 4 | 15.8 | even | 4 | |||
4655.2.a.y.1.2 | 4 | 35.27 | even | 4 | |||
6080.2.a.cc.1.4 | 4 | 40.37 | odd | 4 | |||
6080.2.a.ch.1.1 | 4 | 40.27 | even | 4 | |||
7600.2.a.cf.1.1 | 4 | 20.3 | even | 4 | |||
9025.2.a.bf.1.2 | 4 | 95.18 | even | 4 |