Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.4 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.949 |
Dual form | 2100.2.bc.f.1549.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.09077 | + | 1.62132i | 0.790237 | + | 0.612801i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12132 | − | 3.67423i | 0.639602 | − | 1.10782i | −0.345918 | − | 0.938265i | \(-0.612432\pi\) |
0.985520 | − | 0.169559i | \(-0.0542342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.24264i | − | 0.899347i | −0.893193 | − | 0.449673i | \(-0.851540\pi\) | ||
0.893193 | − | 0.449673i | \(-0.148460\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.67423 | − | 2.12132i | −0.891133 | − | 0.514496i | −0.0168199 | − | 0.999859i | \(-0.505354\pi\) |
−0.874313 | + | 0.485363i | \(0.838688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 2.44949i | 0.218218 | + | 0.534522i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67423 | − | 2.12132i | 0.766131 | − | 0.442326i | −0.0653618 | − | 0.997862i | \(-0.520820\pi\) |
0.831493 | + | 0.555536i | \(0.187487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75736 | 0.326333 | 0.163167 | − | 0.986599i | \(-0.447829\pi\) | ||||
0.163167 | + | 0.986599i | \(0.447829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74264 | − | 8.21449i | 0.851803 | − | 1.47537i | −0.0277757 | − | 0.999614i | \(-0.508842\pi\) |
0.879579 | − | 0.475753i | \(-0.157824\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.67423 | − | 2.12132i | 0.639602 | − | 0.369274i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.80821 | − | 1.62132i | 0.461667 | − | 0.266543i | −0.251078 | − | 0.967967i | \(-0.580785\pi\) |
0.712745 | + | 0.701423i | \(0.247452\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.62132 | − | 2.80821i | 0.259619 | − | 0.449673i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24264 | −0.662589 | −0.331295 | − | 0.943527i | \(-0.607485\pi\) | ||||
−0.331295 | + | 0.943527i | \(0.607485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.24264i | − | 0.494498i | −0.968952 | − | 0.247249i | \(-0.920473\pi\) | ||
0.968952 | − | 0.247249i | \(-0.0795266\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | + | 3.00000i | −0.757937 | + | 0.437595i | −0.828554 | − | 0.559908i | \(-0.810836\pi\) |
0.0706177 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.74264 | + | 6.77962i | 0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.12132 | − | 3.67423i | −0.297044 | − | 0.514496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.34847 | + | 4.24264i | 1.00939 | + | 0.582772i | 0.911013 | − | 0.412378i | \(-0.135302\pi\) |
0.0983769 | + | 0.995149i | \(0.468635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.00000i | − | 0.927173i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.12132 | + | 8.87039i | −0.666739 | + | 1.15483i | 0.312072 | + | 0.950059i | \(0.398977\pi\) |
−0.978811 | + | 0.204767i | \(0.934356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.24264 | − | 3.88437i | −0.287141 | − | 0.497342i | 0.685985 | − | 0.727615i | \(-0.259371\pi\) |
−0.973126 | + | 0.230273i | \(0.926038\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.358719 | + | 2.62132i | −0.0451944 | + | 0.330255i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.54026 | + | 2.62132i | 0.554681 | + | 0.320245i | 0.751008 | − | 0.660293i | \(-0.229568\pi\) |
−0.196327 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7279 | −1.51053 | −0.755263 | − | 0.655422i | \(-0.772491\pi\) | ||||
−0.755263 | + | 0.655422i | \(0.772491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00436 | + | 4.62132i | 0.936840 | + | 0.540885i | 0.888968 | − | 0.457969i | \(-0.151423\pi\) |
0.0478714 | + | 0.998854i | \(0.484756\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3923 | − | 4.24264i | 1.18431 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | + | 9.52628i | 0.618798 | + | 1.07179i | 0.989705 | + | 0.143120i | \(0.0457135\pi\) |
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2426i | 1.12428i | 0.827043 | + | 0.562138i | \(0.190021\pi\) | ||||
−0.827043 | + | 0.562138i | \(0.809979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.52192 | + | 0.878680i | 0.163167 | + | 0.0942043i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.12132 | − | 8.87039i | −0.542859 | − | 0.940259i | −0.998738 | − | 0.0502176i | \(-0.984009\pi\) |
0.455879 | − | 0.890042i | \(-0.349325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.25736 | − | 6.77962i | 0.551121 | − | 0.710697i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21449 | − | 4.74264i | 0.851803 | − | 0.491789i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.485281i | − | 0.0492729i | −0.999696 | − | 0.0246364i | \(-0.992157\pi\) | ||
0.999696 | − | 0.0246364i | \(-0.00784281\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.87868 | − | 6.71807i | 0.385943 | − | 0.668473i | −0.605956 | − | 0.795498i | \(-0.707209\pi\) |
0.991900 | + | 0.127025i | \(0.0405428\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9326 | − | 8.62132i | 1.47135 | − | 0.849484i | 0.471867 | − | 0.881670i | \(-0.343580\pi\) |
0.999482 | + | 0.0321856i | \(0.0102468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0227 | − | 6.36396i | 1.06561 | − | 0.615227i | 0.138628 | − | 0.990345i | \(-0.455731\pi\) |
0.926977 | + | 0.375117i | \(0.122398\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.74264 | + | 8.21449i | −0.454263 | + | 0.786806i | −0.998645 | − | 0.0520310i | \(-0.983431\pi\) |
0.544383 | + | 0.838837i | \(0.316764\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.24264 | 0.307778 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.80821 | − | 1.62132i | 0.259619 | − | 0.149891i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.24264 | − | 10.3923i | −0.388922 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.67423 | − | 2.12132i | −0.331295 | − | 0.191273i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.75736i | − | 0.244676i | −0.992488 | − | 0.122338i | \(-0.960961\pi\) | ||
0.992488 | − | 0.122338i | \(-0.0390392\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.62132 | − | 2.80821i | 0.142749 | − | 0.247249i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.24264 | − | 12.5446i | −0.632792 | − | 1.09603i | −0.986978 | − | 0.160854i | \(-0.948575\pi\) |
0.354186 | − | 0.935175i | \(-0.384758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.51104 | − | 18.3492i | 0.217734 | − | 1.59108i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.67423 | − | 2.12132i | −0.313911 | − | 0.181237i | 0.334764 | − | 0.942302i | \(-0.391343\pi\) |
−0.648675 | + | 0.761065i | \(0.724677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4853 | 1.31344 | 0.656722 | − | 0.754133i | \(-0.271942\pi\) | ||||
0.656722 | + | 0.754133i | \(0.271942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.9142 | − | 6.87868i | −0.996317 | − | 0.575224i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.88064 | + | 6.74264i | −0.155112 | + | 0.556124i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2426 | + | 19.4728i | −0.914913 | + | 1.58468i | −0.107885 | + | 0.994163i | \(0.534408\pi\) |
−0.807028 | + | 0.590513i | \(0.798926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.24264i | − | 0.342997i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.61642 | + | 3.24264i | 0.448239 | + | 0.258791i | 0.707086 | − | 0.707127i | \(-0.250009\pi\) |
−0.258847 | + | 0.965918i | \(0.583343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.24264 | + | 7.34847i | 0.336463 | + | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.1213 | + | 1.52192i | 0.876483 | + | 0.119944i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | + | 4.00000i | −0.542659 | + | 0.313304i | −0.746156 | − | 0.665771i | \(-0.768103\pi\) |
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7279i | 1.44921i | 0.689164 | + | 0.724605i | \(0.257978\pi\) | ||||
−0.689164 | + | 0.724605i | \(0.742022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.48528 | 0.191175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | − | 6.06218i | 0.267652 | − | 0.463586i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.7408 | − | 10.2426i | 1.34881 | − | 0.778734i | 0.360726 | − | 0.932672i | \(-0.382529\pi\) |
0.988080 | + | 0.153938i | \(0.0491957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.87039 | + | 5.12132i | −0.666739 | + | 0.384942i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | + | 5.19615i | −0.224231 | + | 0.388379i | −0.956088 | − | 0.293079i | \(-0.905320\pi\) |
0.731858 | + | 0.681457i | \(0.238654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.48528i | − | 0.331562i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5885 | + | 9.00000i | −1.13994 | + | 0.658145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62132 | + | 2.09077i | −0.117934 | + | 0.152081i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.85204 | + | 3.37868i | 0.421239 | + | 0.243203i | 0.695607 | − | 0.718422i | \(-0.255135\pi\) |
−0.274368 | + | 0.961625i | \(0.588469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.2426i | − | 1.15724i | −0.815597 | − | 0.578620i | \(-0.803591\pi\) | ||
0.815597 | − | 0.578620i | \(-0.196409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.24264 | − | 9.08052i | 0.371641 | − | 0.643701i | −0.618177 | − | 0.786039i | \(-0.712129\pi\) |
0.989818 | + | 0.142338i | \(0.0454619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.62132 | + | 4.54026i | 0.184894 | + | 0.320245i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.67423 | + | 2.84924i | 0.257881 | + | 0.199978i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.67423 | + | 2.12132i | 0.255377 | + | 0.147442i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.6985 | −2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4853 | 1.54795 | 0.773975 | − | 0.633216i | \(-0.218265\pi\) | ||||
0.773975 | + | 0.633216i | \(0.218265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.0227 | − | 6.36396i | −0.755263 | − | 0.436051i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.2341 | − | 9.48528i | 1.57723 | − | 0.643903i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.62132 | + | 8.00436i | 0.312280 | + | 0.540885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.87868 | + | 11.9142i | −0.462710 | + | 0.801437i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.51472i | 0.503223i | 0.967828 | + | 0.251611i | \(0.0809605\pi\) | ||||
−0.967828 | + | 0.251611i | \(0.919040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1750 | + | 7.60660i | 0.874457 | + | 0.504868i | 0.868827 | − | 0.495116i | \(-0.164875\pi\) |
0.00563010 | + | 0.999984i | \(0.498208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | − | 6.06218i | −0.231287 | − | 0.400600i | 0.726900 | − | 0.686743i | \(-0.240960\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1213 | + | 1.52192i | 0.731729 | + | 0.100135i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5446 | + | 7.24264i | −0.821825 | + | 0.474481i | −0.851046 | − | 0.525092i | \(-0.824031\pi\) |
0.0292201 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.0000i | 0.714527i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.9706 | −0.709627 | −0.354813 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354813 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | − | 3.46410i | 0.128831 | − | 0.223142i | −0.794393 | − | 0.607404i | \(-0.792211\pi\) |
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.6575 | + | 11.3492i | −1.25077 | + | 0.722135i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.12132 | + | 8.87039i | −0.324550 | + | 0.562138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7279 | −1.18210 | −0.591048 | − | 0.806636i | \(-0.701286\pi\) | ||||
−0.591048 | + | 0.806636i | \(0.701286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.87039 | − | 5.12132i | 0.553320 | − | 0.319459i | −0.197140 | − | 0.980375i | \(-0.563165\pi\) |
0.750460 | + | 0.660916i | \(0.229832\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.50000 | + | 1.16320i | 0.528164 | + | 0.0722776i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.878680 | + | 1.52192i | 0.0543889 | + | 0.0942043i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.34847 | − | 4.24264i | −0.453126 | − | 0.261612i | 0.256023 | − | 0.966671i | \(-0.417588\pi\) |
−0.709150 | + | 0.705058i | \(0.750921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.2426i | − | 0.626839i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.24264 | + | 2.15232i | −0.0757651 | + | 0.131229i | −0.901419 | − | 0.432948i | \(-0.857473\pi\) |
0.825654 | + | 0.564177i | \(0.190807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7279 | + | 20.3134i | 0.712421 | + | 1.23395i | 0.963946 | + | 0.266098i | \(0.0857344\pi\) |
−0.251525 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.94282 | − | 3.24264i | 0.480721 | − | 0.196254i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3528 | − | 8.86396i | −0.922462 | − | 0.532584i | −0.0380425 | − | 0.999276i | \(-0.512112\pi\) |
−0.884420 | + | 0.466692i | \(0.845446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.48528 | 0.567869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9706 | 1.72824 | 0.864119 | − | 0.503287i | \(-0.167876\pi\) | ||||
0.864119 | + | 0.503287i | \(0.167876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5490 | + | 11.8640i | 1.22151 | + | 0.705239i | 0.965240 | − | 0.261366i | \(-0.0841729\pi\) |
0.256270 | + | 0.966605i | \(0.417506\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.87039 | − | 6.87868i | −0.523602 | − | 0.406036i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.242641 | − | 0.420266i | 0.0142238 | − | 0.0246364i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.97056i | 0.290383i | 0.989404 | + | 0.145192i | \(0.0463799\pi\) | ||||
−0.989404 | + | 0.145192i | \(0.953620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.67423 | + | 2.12132i | 0.213201 | + | 0.123091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.87868 | − | 11.9142i | −0.397804 | − | 0.689017i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.25736 | − | 6.77962i | 0.303029 | − | 0.390771i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.71807 | − | 3.87868i | 0.385943 | − | 0.222824i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.24264i | 0.185067i | 0.995710 | + | 0.0925336i | \(0.0294966\pi\) | ||||
−0.995710 | + | 0.0925336i | \(0.970503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2426 | 0.980900 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.6066 | + | 18.3712i | −0.601445 | + | 1.04173i | 0.391157 | + | 0.920324i | \(0.372075\pi\) |
−0.992602 | + | 0.121410i | \(0.961258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5490 | + | 11.8640i | −1.16150 | + | 0.670591i | −0.951662 | − | 0.307146i | \(-0.900626\pi\) |
−0.209835 | + | 0.977737i | \(0.567293\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.4150 | + | 12.3640i | −1.20279 | + | 0.694429i | −0.961174 | − | 0.275943i | \(-0.911010\pi\) |
−0.241613 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.72792 | − | 6.45695i | 0.208724 | − | 0.361520i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7279 | 0.710403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6985i | 1.65247i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.21449 | + | 4.74264i | −0.454263 | + | 0.262269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.7279 | − | 2.15232i | −0.867108 | − | 0.118661i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | − | 14.7224i | −0.467202 | − | 0.809218i | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.80821 | + | 1.62132i | 0.153889 | + | 0.0888478i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.7279i | − | 0.747808i | −0.927467 | − | 0.373904i | \(-0.878019\pi\) | ||
0.927467 | − | 0.373904i | \(-0.121981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | + | 15.5885i | −0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.1213 | − | 34.8511i | −1.08963 | − | 1.88730i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | + | 12.0000i | 1.11578 | + | 0.644194i | 0.940319 | − | 0.340293i | \(-0.110526\pi\) |
0.175457 | + | 0.984487i | \(0.443860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.24264 | 0.173079 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.87039 | − | 5.12132i | −0.472123 | − | 0.272580i | 0.245005 | − | 0.969522i | \(-0.421210\pi\) |
−0.717128 | + | 0.696941i | \(0.754544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.52192 | − | 11.1213i | 0.0805484 | − | 0.588603i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.878680 | + | 1.52192i | 0.0463749 | + | 0.0803237i | 0.888281 | − | 0.459300i | \(-0.151900\pi\) |
−0.841906 | + | 0.539624i | \(0.818566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9413 | − | 17.8640i | −1.61512 | − | 0.932491i | −0.988157 | − | 0.153443i | \(-0.950964\pi\) |
−0.626965 | − | 0.779048i | \(-0.715703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.12132 | − | 3.67423i | −0.110432 | − | 0.191273i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.48528 | + | 20.7846i | 0.440534 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3528 | + | 8.86396i | −0.794939 | + | 0.458959i | −0.841699 | − | 0.539948i | \(-0.818444\pi\) |
0.0467591 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.69848i | − | 0.293487i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.4558 | 1.05075 | 0.525373 | − | 0.850872i | \(-0.323926\pi\) | ||||
0.525373 | + | 0.850872i | \(0.323926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37868 | − | 2.38794i | 0.0706319 | − | 0.122338i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.0454 | + | 12.7279i | −1.12647 | + | 0.650366i | −0.943044 | − | 0.332668i | \(-0.892051\pi\) |
−0.183424 | + | 0.983034i | \(0.558718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.80821 | − | 1.62132i | 0.142749 | − | 0.0824163i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6066 | + | 18.3712i | −0.537776 | + | 0.931455i | 0.461247 | + | 0.887272i | \(0.347402\pi\) |
−0.999023 | + | 0.0441839i | \(0.985931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.4853i | − | 0.730686i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.58410 | + | 4.37868i | −0.380635 | + | 0.219760i | −0.678094 | − | 0.734975i | \(-0.737194\pi\) |
0.297460 | + | 0.954734i | \(0.403861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3492 | − | 14.6354i | 0.568173 | − | 0.732686i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.75736 | + | 3.04384i | 0.0877583 | + | 0.152002i | 0.906563 | − | 0.422070i | \(-0.138696\pi\) |
−0.818805 | + | 0.574072i | \(0.805363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.6367 | − | 15.3787i | −1.32687 | − | 0.766067i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 13.7574i | − | 0.681927i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | − | 14.7224i | 0.420298 | − | 0.727977i | −0.575670 | − | 0.817682i | \(-0.695259\pi\) |
0.995968 | + | 0.0897044i | \(0.0285922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.12132 | − | 3.67423i | −0.104637 | − | 0.181237i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.0892 | + | 10.2426i | −1.23456 | + | 0.504007i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4106 | + | 7.74264i | 0.656722 | + | 0.379159i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4853 | 0.707652 | 0.353826 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353826 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4853 | 1.53450 | 0.767249 | − | 0.641349i | \(-0.221625\pi\) | ||||
0.767249 | + | 0.641349i | \(0.221625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | − | 3.00000i | −0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.60896 | − | 11.7574i | 0.0778629 | − | 0.568978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.87868 | − | 11.9142i | −0.332106 | − | 0.575224i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.72792 | + | 16.8493i | −0.468578 | + | 0.811600i | −0.999355 | − | 0.0359112i | \(-0.988567\pi\) |
0.530777 | + | 0.847511i | \(0.321900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 33.2426i | − | 1.59754i | −0.601637 | − | 0.798770i | \(-0.705485\pi\) | ||
0.601637 | − | 0.798770i | \(-0.294515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.7196 | − | 14.8492i | −1.23034 | − | 0.710336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7408 | + | 10.2426i | −0.842890 | + | 0.486643i | −0.858245 | − | 0.513240i | \(-0.828445\pi\) |
0.0153558 | + | 0.999882i | \(0.495112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | + | 15.5885i | −0.423793 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.4728 | + | 11.2426i | −0.914913 | + | 0.528225i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.8975 | − | 16.1066i | 1.30499 | − | 0.753435i | 0.323733 | − | 0.946149i | \(-0.395062\pi\) |
0.981255 | + | 0.192714i | \(0.0617288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.12132 | − | 3.67423i | 0.0990148 | − | 0.171499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.7279 | 0.872246 | 0.436123 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436123 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.2721i | − | 0.477384i | −0.971095 | − | 0.238692i | \(-0.923281\pi\) | ||
0.971095 | − | 0.238692i | \(-0.0767186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.50079 | + | 5.48528i | −0.439644 | + | 0.253829i | −0.703447 | − | 0.710748i | \(-0.748357\pi\) |
0.263803 | + | 0.964577i | \(0.415023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24264 | + | 12.8418i | 0.242083 | + | 0.592979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.24264 | + | 5.61642i | 0.149413 | + | 0.258791i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.9142 | − | 6.87868i | −0.547817 | − | 0.316282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48528i | 0.388514i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | − | 10.3923i | 0.274147 | − | 0.474837i | −0.695773 | − | 0.718262i | \(-0.744938\pi\) |
0.969920 | + | 0.243426i | \(0.0782712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.25736 | − | 9.10601i | −0.239715 | − | 0.415198i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.87039 | + | 6.87868i | 0.403617 | + | 0.312991i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6733 | + | 18.8640i | 1.48057 | + | 0.854808i | 0.999758 | − | 0.0220157i | \(-0.00700837\pi\) |
0.480813 | + | 0.876823i | \(0.340342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5147 | 0.700169 | 0.350085 | − | 0.936718i | \(-0.386153\pi\) | ||||
0.350085 | + | 0.936718i | \(0.386153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.45695 | − | 3.72792i | −0.290806 | − | 0.167897i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.6112 | − | 20.6360i | −1.19367 | − | 0.925653i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.74264 | + | 16.8747i | 0.436140 | + | 0.755417i | 0.997388 | − | 0.0722305i | \(-0.0230117\pi\) |
−0.561247 | + | 0.827648i | \(0.689678\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.36396 | + | 16.2189i | −0.418351 | + | 0.724605i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4853i | 1.18092i | 0.807067 | + | 0.590460i | \(0.201054\pi\) | ||||
−0.807067 | + | 0.590460i | \(0.798946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.15232 | + | 1.24264i | 0.0955877 | + | 0.0551876i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.72792 | − | 16.8493i | −0.431183 | − | 0.746830i | 0.565793 | − | 0.824547i | \(-0.308570\pi\) |
−0.996975 | + | 0.0777173i | \(0.975237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24264 | + | 22.6398i | 0.408870 | + | 1.00152i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.06218 | − | 3.50000i | 0.267652 | − | 0.154529i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558i | 1.11955i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.4853 | 0.899204 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.72792 | − | 11.6531i | 0.294756 | − | 0.510532i | −0.680172 | − | 0.733052i | \(-0.738095\pi\) |
0.974928 | + | 0.222520i | \(0.0714284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.54026 | − | 2.62132i | 0.198532 | − | 0.114622i | −0.397439 | − | 0.917629i | \(-0.630101\pi\) |
0.595970 | + | 0.803006i | \(0.296768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.8511 | + | 20.1213i | −1.51814 | + | 0.876498i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | + | 4.33013i | −0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.2426 | −0.444493 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7574i | 0.595897i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.19615 | + | 3.00000i | −0.224231 | + | 0.129460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6066 | + | 7.97887i | 1.23217 | + | 0.343674i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4706 | + | 35.4561i | 0.880098 | + | 1.52437i | 0.851231 | + | 0.524792i | \(0.175857\pi\) |
0.0288675 | + | 0.999583i | \(0.490810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.2583 | − | 6.50000i | −0.483141 | − | 0.278942i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.4558i | 1.43047i | 0.698885 | + | 0.715234i | \(0.253680\pi\) | ||||
−0.698885 | + | 0.715234i | \(0.746320\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.24264 | − | 3.88437i | 0.0957136 | − | 0.165781i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.15076 | − | 10.6534i | −0.262031 | − | 0.453851i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.94591 | + | 28.8345i | −0.167797 | + | 1.22617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9808 | + | 15.0000i | 1.10084 | + | 0.635570i | 0.936442 | − | 0.350824i | \(-0.114098\pi\) |
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.5147 | −0.444725 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.19615 | − | 3.00000i | −0.218992 | − | 0.126435i | 0.386492 | − | 0.922293i | \(-0.373687\pi\) |
−0.605483 | + | 0.795858i | \(0.707020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.44949 | + | 1.00000i | −0.102869 | + | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8492 | − | 36.1119i | −0.874046 | − | 1.51389i | −0.857776 | − | 0.514024i | \(-0.828154\pi\) |
−0.0162699 | − | 0.999868i | \(-0.505179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4706 | − | 25.0637i | 0.605574 | − | 1.04889i | −0.386386 | − | 0.922337i | \(-0.626277\pi\) |
0.991960 | − | 0.126548i | \(-0.0403898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.00000i | − | 0.250654i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0482 | − | 6.37868i | −0.459942 | − | 0.265548i | 0.252078 | − | 0.967707i | \(-0.418886\pi\) |
−0.712020 | + | 0.702159i | \(0.752220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.37868 | + | 5.85204i | 0.140413 | + | 0.243203i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.6066 | + | 21.4150i | −0.688958 | + | 0.888444i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769 | − | 18.0000i | 1.29122 | − | 0.745484i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.2132i | 1.86615i | 0.359684 | + | 0.933074i | \(0.382885\pi\) | ||||
−0.359684 | + | 0.933074i | \(0.617115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −66.3970 | −2.73584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.12132 | − | 14.0665i | 0.334066 | − | 0.578620i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.78272 | + | 1.60660i | −0.114272 | + | 0.0659752i | −0.556047 | − | 0.831151i | \(-0.687682\pi\) |
0.441774 | + | 0.897126i | \(0.354349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.08052 | − | 5.24264i | 0.371641 | − | 0.214567i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.2426 | + | 28.1331i | −0.663656 | + | 1.14949i | 0.315991 | + | 0.948762i | \(0.397663\pi\) |
−0.979648 | + | 0.200724i | \(0.935670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.48528 | −0.142168 | −0.0710838 | − | 0.997470i | \(-0.522646\pi\) | ||||
−0.0710838 | + | 0.997470i | \(0.522646\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.24264i | 0.213497i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.3249 | + | 14.6213i | −1.02790 | + | 0.593461i | −0.916384 | − | 0.400301i | \(-0.868906\pi\) |
−0.111521 | + | 0.993762i | \(0.535572\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.75736 | + | 4.30463i | 0.0712118 | + | 0.174433i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.72792 | + | 16.8493i | 0.393550 | + | 0.681648i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.72490 | − | 2.72792i | −0.190837 | − | 0.110180i | 0.401537 | − | 0.915843i | \(-0.368476\pi\) |
−0.592374 | + | 0.805663i | \(0.701809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26.4853i | − | 1.06626i | −0.846034 | − | 0.533129i | \(-0.821016\pi\) | ||
0.846034 | − | 0.533129i | \(-0.178984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.98528 | + | 10.3668i | −0.240569 | + | 0.416677i | −0.960876 | − | 0.276977i | \(-0.910667\pi\) |
0.720308 | + | 0.693655i | \(0.244001\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.12132 | + | 3.67423i | 0.0851257 | + | 0.147442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.67423 | − | 26.8492i | 0.147205 | − | 1.07569i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.7196 | − | 14.8492i | −1.02714 | − | 0.593022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7574 | −0.548542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.4728 | + | 11.2426i | 0.773975 | + | 0.446855i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.9839 | − | 5.65076i | 0.871032 | − | 0.223891i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.36396 | − | 11.0227i | −0.251754 | − | 0.436051i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1213 | + | 29.6550i | −0.676251 | + | 1.17130i | 0.299850 | + | 0.953986i | \(0.403063\pi\) |
−0.976101 | + | 0.217316i | \(0.930270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.7279i | 0.777993i | 0.921239 | + | 0.388997i | \(0.127178\pi\) | ||||
−0.921239 | + | 0.388997i | \(0.872822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.87039 | − | 5.12132i | −0.348731 | − | 0.201340i | 0.315395 | − | 0.948960i | \(-0.397863\pi\) |
−0.664126 | + | 0.747621i | \(0.731196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.7279 | + | 37.6339i | 0.852896 | + | 1.47726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.8640 | + | 3.40256i | 0.974495 | + | 0.133357i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.87039 | + | 5.12132i | −0.347125 | + | 0.200413i | −0.663418 | − | 0.748249i | \(-0.730895\pi\) |
0.316293 | + | 0.948661i | \(0.397562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.24264i | 0.360590i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9706 | −1.59599 | −0.797993 | − | 0.602666i | \(-0.794105\pi\) | ||||
−0.797993 | + | 0.602666i | \(0.794105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.01472 | − | 1.75754i | 0.0394680 | − | 0.0683605i | −0.845617 | − | 0.533791i | \(-0.820767\pi\) |
0.885085 | + | 0.465430i | \(0.154100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.9142 | + | 6.87868i | −0.462710 | + | 0.267146i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.45695 | − | 3.72792i | 0.250014 | − | 0.144346i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.75736 | + | 6.50794i | −0.145268 | + | 0.251611i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.0294 | −0.734623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 29.7279i | − | 1.14593i | −0.819581 | − | 0.572964i | \(-0.805794\pi\) | ||
0.819581 | − | 0.572964i | \(-0.194206\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0227 | − | 6.36396i | 0.423637 | − | 0.244587i | −0.272995 | − | 0.962015i | \(-0.588014\pi\) |
0.696632 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.786797 | − | 1.01461i | 0.0301945 | − | 0.0389372i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.60660 | + | 13.1750i | 0.291486 | + | 0.504868i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.7635 | + | 16.6066i | 1.10060 | + | 0.635434i | 0.936380 | − | 0.350989i | \(-0.114155\pi\) |
0.164224 | + | 0.986423i | \(0.447488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.00000i | − | 0.267067i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7574 | − | 23.8284i | 0.524114 | − | 0.907791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4706 | − | 23.3317i | −0.512444 | − | 0.887580i | −0.999896 | − | 0.0144296i | \(-0.995407\pi\) |
0.487452 | − | 0.873150i | \(-0.337927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.87039 | + | 6.87868i | 0.336958 | + | 0.261299i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5885 | + | 9.00000i | 0.590455 | + | 0.340899i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.4853 | −0.547884 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.78680 | 0.331873 | 0.165936 | − | 0.986136i | \(-0.446935\pi\) | ||||
0.165936 | + | 0.986136i | \(0.446935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.6575 | − | 11.3492i | −0.741395 | − | 0.428045i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.0016 | − | 7.75736i | 0.714628 | − | 0.291746i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2426 | − | 31.5972i | −0.685117 | − | 1.18666i | −0.973400 | − | 0.229112i | \(-0.926418\pi\) |
0.288283 | − | 0.957545i | \(-0.406915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | + | 9.52628i | −0.206266 | + | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 40.2426i | − | 1.50710i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.50079 | − | 5.48528i | −0.354813 | − | 0.204852i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2426 | + | 22.9369i | 0.493867 | + | 0.855403i | 0.999975 | − | 0.00706717i | \(-0.00224957\pi\) |
−0.506108 | + | 0.862470i | \(0.668916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.1985 | + | 6.18527i | 1.68328 | + | 0.230352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.46410 | − | 2.00000i | 0.128831 | − | 0.0743808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.757359i | 0.0280889i | 0.999901 | + | 0.0140445i | \(0.00447063\pi\) | ||||
−0.999901 | + | 0.0140445i | \(0.995529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.87868 | + | 11.9142i | −0.254417 | + | 0.440663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.54741 | + | 0.893398i | −0.0571549 | + | 0.0329984i | −0.528305 | − | 0.849055i | \(-0.677172\pi\) |
0.471150 | + | 0.882053i | \(0.343839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.2627 | − | 11.1213i | 0.709550 | − | 0.409659i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.74264 | + | 13.4106i | −0.284818 | + | 0.493319i | −0.972565 | − | 0.232632i | \(-0.925266\pi\) |
0.687747 | + | 0.725950i | \(0.258600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.6985 | −0.833850 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.2132i | − | 0.558118i | −0.960274 | − | 0.279059i | \(-0.909977\pi\) | ||
0.960274 | − | 0.279059i | \(-0.0900226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.87039 | + | 5.12132i | −0.324550 | + | 0.187379i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.3640 | + | 4.56575i | 1.21909 | + | 0.166829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4706 | − | 38.9202i | −0.819962 | − | 1.42022i | −0.905709 | − | 0.423900i | \(-0.860661\pi\) |
0.0857467 | − | 0.996317i | \(-0.472672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.2189 | − | 9.36396i | −0.591048 | − | 0.341242i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.02944i | 0.328180i | 0.986445 | + | 0.164090i | \(0.0524688\pi\) | ||||
−0.986445 | + | 0.164090i | \(0.947531\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00000 | − | 15.5885i | 0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1213 | − | 40.0473i | −0.838147 | − | 1.45171i | −0.891442 | − | 0.453135i | \(-0.850306\pi\) |
0.0532948 | − | 0.998579i | \(-0.483028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.2341 | + | 9.48528i | −0.841131 | + | 0.343390i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.7635 | + | 16.6066i | 1.03859 | + | 0.599630i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.2426 | 0.368880 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.1312 | + | 5.84924i | 0.364393 | + | 0.210383i | 0.671006 | − | 0.741452i | \(-0.265862\pi\) |
−0.306613 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.77962 | + | 5.25736i | 0.243217 | + | 0.188607i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8492 | + | 25.7196i | 0.532029 | + | 0.921502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | + | 46.7654i | −0.966136 | + | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.75736i | 0.0628029i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6690 | − | 14.2426i | −0.879354 | − | 0.507695i | −0.00890869 | − | 0.999960i | \(-0.502836\pi\) |
−0.870445 | + | 0.492265i | \(0.836169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.24264 | − | 7.34847i | −0.151042 | − | 0.261612i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.1838 | + | 37.6339i | −1.03766 | + | 1.33811i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.5956 | + | 7.27208i | −0.447283 | + | 0.258239i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31.7574i | − | 1.12490i | −0.826830 | − | 0.562452i | \(-0.809858\pi\) | ||
0.826830 | − | 0.562452i | \(-0.190142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4558 | 0.900563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.12132 | − | 8.87039i | 0.180953 | − | 0.313420i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.9596 | − | 19.6066i | 1.19841 | − | 0.691902i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.15232 | + | 1.24264i | −0.0757651 | + | 0.0437430i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.9706 | − | 24.1977i | 0.491179 | − | 0.850747i | −0.508770 | − | 0.860903i | \(-0.669899\pi\) |
0.999948 | + | 0.0101560i | \(0.00323282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.9411 | 0.419310 | 0.209655 | − | 0.977775i | \(-0.432766\pi\) | ||||
0.209655 | + | 0.977775i | \(0.432766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.4558i | 0.822632i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.6575 | + | 11.3492i | −0.687728 | + | 0.397060i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.50000 | + | 1.16320i | 0.297014 | + | 0.0406454i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.84924 | − | 4.93503i | −0.0994392 | − | 0.172234i | 0.812013 | − | 0.583639i | \(-0.198372\pi\) |
−0.911453 | + | 0.411405i | \(0.865038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.7495 | − | 19.4853i | −1.17643 | − | 0.679214i | −0.221247 | − | 0.975218i | \(-0.571013\pi\) |
−0.955187 | + | 0.296004i | \(0.904346\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.4558i | 1.51111i | 0.655087 | + | 0.755554i | \(0.272632\pi\) | ||||
−0.655087 | + | 0.755554i | \(0.727368\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.86396 | − | 15.3528i | −0.307487 | − | 0.532584i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.97887 | − | 28.6066i | 0.276451 | − | 0.991160i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.21449 | + | 4.74264i | 0.283934 | + | 0.163930i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.7574 | −0.889243 | −0.444621 | − | 0.895719i | \(-0.646662\pi\) | ||||
−0.444621 | + | 0.895719i | \(0.646662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9117 | −0.893506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.0892 | + | 14.4853i | 0.864119 | + | 0.498900i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.51104 | − | 18.3492i | 0.0862802 | − | 0.630487i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.8640 | + | 20.5490i | 0.407170 | + | 0.705239i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.87868 | − | 11.9142i | 0.235798 | − | 0.408414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.7279i | 0.880907i | 0.897775 | + | 0.440454i | \(0.145182\pi\) | ||||
−0.897775 | + | 0.440454i | \(0.854818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.67423 | − | 2.12132i | −0.125509 | − | 0.0724629i | 0.435931 | − | 0.899980i | \(-0.356419\pi\) |
−0.561440 | + | 0.827517i | \(0.689753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0000 | − | 19.0526i | −0.375315 | − | 0.650065i | 0.615059 | − | 0.788481i | \(-0.289132\pi\) |
−0.990374 | + | 0.138416i | \(0.955799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.24264 | − | 10.3923i | −0.144589 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6323 | − | 10.7574i | 0.634251 | − | 0.366185i | −0.148146 | − | 0.988966i | \(-0.547330\pi\) |
0.782396 | + | 0.622781i | \(0.213997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6690 | 1.58314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.50000 | − | 14.7224i | 0.288012 | − | 0.498851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.420266 | − | 0.242641i | 0.0142238 | − | 0.00821214i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.66025 | + | 5.00000i | −0.292436 | + | 0.168838i | −0.639040 | − | 0.769174i | \(-0.720668\pi\) |
0.346604 | + | 0.938012i | \(0.387335\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.48528 | + | 4.30463i | −0.0838265 | + | 0.145192i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9706 | 1.38033 | 0.690167 | − | 0.723650i | \(-0.257537\pi\) | ||||
0.690167 | + | 0.723650i | \(0.257537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.72792i | − | 0.192760i | −0.995345 | − | 0.0963800i | \(-0.969274\pi\) | ||
0.995345 | − | 0.0963800i | \(-0.0307264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1750 | − | 7.60660i | 0.442374 | − | 0.255405i | −0.262230 | − | 0.965005i | \(-0.584458\pi\) |
0.704604 | + | 0.709601i | \(0.251125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.47056 | − | 5.76500i | 0.149938 | − | 0.193352i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.12132 | + | 3.67423i | 0.0710669 | + | 0.123091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.3731 | + | 21.0000i | 1.21718 | + | 0.702738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 13.7574i | − | 0.459345i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.33452 | − | 14.4358i | 0.277972 | − | 0.481462i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.94282 | − | 3.24264i | 0.264320 | − | 0.107908i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.2164 | + | 15.1360i | 0.870501 | + | 0.502584i | 0.867515 | − | 0.497412i | \(-0.165716\pi\) |
0.00298623 | + | 0.999996i | \(0.499049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.75736 | 0.257295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2132 | 1.69677 | 0.848385 | − | 0.529380i | \(-0.177576\pi\) | ||||
0.848385 | + | 0.529380i | \(0.177576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.6339 | + | 21.7279i | 1.24550 | + | 0.719089i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.19615 | − | 37.9706i | 0.171592 | − | 1.25390i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9853 | + | 29.4194i | 0.560293 | + | 0.970455i | 0.997471 | + | 0.0710804i | \(0.0226447\pi\) |
−0.437178 | + | 0.899375i | \(0.644022\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.62132 | + | 2.80821i | −0.0534243 | + | 0.0925336i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.2721i | 1.35849i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.9326 | + | 8.62132i | 0.490450 | + | 0.283161i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3640 | + | 31.8073i | 0.602502 | + | 1.04356i | 0.992441 | + | 0.122723i | \(0.0391628\pi\) |
−0.389939 | + | 0.920841i | \(0.627504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0000 | − | 34.2929i | 1.14708 | − | 1.12390i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3712 | + | 10.6066i | −0.601445 | + | 0.347245i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.6985i | − | 0.610853i | −0.952216 | − | 0.305426i | \(-0.901201\pi\) | ||
0.952216 | − | 0.305426i | \(-0.0987990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.7279 | −0.774331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.8492 | − | 41.3081i | 0.777463 | − | 1.34661i | −0.155937 | − | 0.987767i | \(-0.549840\pi\) |
0.933400 | − | 0.358838i | \(-0.116827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.5885 | + | 9.00000i | −0.507630 | + | 0.293080i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.78272 | + | 1.60660i | −0.0904261 | + | 0.0522075i | −0.544531 | − | 0.838741i | \(-0.683292\pi\) |
0.454105 | + | 0.890948i | \(0.349959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.9853 | − | 25.9553i | 0.486443 | − | 0.842544i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.7279 | −0.801858 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5147i | 0.891289i | 0.895210 | + | 0.445645i | \(0.147025\pi\) | ||||
−0.895210 | + | 0.445645i | \(0.852975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.45695 | − | 3.72792i | 0.208724 | − | 0.120507i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.24264 | − | 10.3923i | −0.137002 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4853 | − | 51.0700i | −0.951138 | − | 1.64742i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.0227 | + | 6.36396i | 0.355202 | + | 0.205076i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.2426i | − | 1.13333i | −0.823949 | − | 0.566663i | \(-0.808234\pi\) | ||
0.823949 | − | 0.566663i | \(-0.191766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.8492 | + | 25.7196i | −0.477026 | + | 0.826234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.4853 | − | 45.8739i | −0.849953 | − | 1.47216i | −0.881249 | − | 0.472652i | \(-0.843297\pi\) |
0.0312961 | − | 0.999510i | \(-0.490037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.3762 | + | 25.1066i | 1.03793 | + | 0.804881i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.60959 | + | 4.39340i | 0.243452 | + | 0.140557i | 0.616762 | − | 0.787149i | \(-0.288444\pi\) |
−0.373310 | + | 0.927707i | \(0.621777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.4558 | −1.38885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.48528 | −0.302842 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.1119 | − | 20.8492i | −1.15179 | − | 0.664988i | −0.202469 | − | 0.979289i | \(-0.564897\pi\) |
−0.949323 | + | 0.314301i | \(0.898230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.5446 | − | 9.72792i | −0.399300 | − | 0.309643i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.87868 | − | 11.9142i | −0.218729 | − | 0.378850i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.47056 | + | 12.9394i | −0.237310 | + | 0.411033i | −0.959942 | − | 0.280200i | \(-0.909599\pi\) |
0.722631 | + | 0.691234i | \(0.242932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 17.0000i | − | 0.539479i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.2810 | + | 12.8640i | 0.705647 | + | 0.407406i | 0.809447 | − | 0.587192i | \(-0.199767\pi\) |
−0.103800 | + | 0.994598i | \(0.533100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.62132 | + | 2.80821i | 0.0512963 | + | 0.0888478i |
(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 | 2100.2.bc.f.949.4 | 8 | ||
5.2 | odd | 4 | 2100.2.q.k.1201.1 | 4 | |||
5.3 | odd | 4 | 420.2.q.d.361.2 | yes | 4 | ||
5.4 | even | 2 | inner | 2100.2.bc.f.949.1 | 8 | ||
7.2 | even | 3 | inner | 2100.2.bc.f.1549.1 | 8 | ||
15.8 | even | 4 | 1260.2.s.e.361.2 | 4 | |||
20.3 | even | 4 | 1680.2.bg.t.1201.1 | 4 | |||
35.2 | odd | 12 | 2100.2.q.k.1801.1 | 4 | |||
35.3 | even | 12 | 2940.2.a.p.1.1 | 2 | |||
35.9 | even | 6 | inner | 2100.2.bc.f.1549.4 | 8 | ||
35.13 | even | 4 | 2940.2.q.q.361.2 | 4 | |||
35.18 | odd | 12 | 2940.2.a.r.1.1 | 2 | |||
35.23 | odd | 12 | 420.2.q.d.121.2 | ✓ | 4 | ||
35.33 | even | 12 | 2940.2.q.q.961.2 | 4 | |||
105.23 | even | 12 | 1260.2.s.e.541.2 | 4 | |||
105.38 | odd | 12 | 8820.2.a.bf.1.2 | 2 | |||
105.53 | even | 12 | 8820.2.a.bk.1.2 | 2 | |||
140.23 | even | 12 | 1680.2.bg.t.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.d.121.2 | ✓ | 4 | 35.23 | odd | 12 | ||
420.2.q.d.361.2 | yes | 4 | 5.3 | odd | 4 | ||
1260.2.s.e.361.2 | 4 | 15.8 | even | 4 | |||
1260.2.s.e.541.2 | 4 | 105.23 | even | 12 | |||
1680.2.bg.t.961.1 | 4 | 140.23 | even | 12 | |||
1680.2.bg.t.1201.1 | 4 | 20.3 | even | 4 | |||
2100.2.q.k.1201.1 | 4 | 5.2 | odd | 4 | |||
2100.2.q.k.1801.1 | 4 | 35.2 | odd | 12 | |||
2100.2.bc.f.949.1 | 8 | 5.4 | even | 2 | inner | ||
2100.2.bc.f.949.4 | 8 | 1.1 | even | 1 | trivial | ||
2100.2.bc.f.1549.1 | 8 | 7.2 | even | 3 | inner | ||
2100.2.bc.f.1549.4 | 8 | 35.9 | even | 6 | inner | ||
2940.2.a.p.1.1 | 2 | 35.3 | even | 12 | |||
2940.2.a.r.1.1 | 2 | 35.18 | odd | 12 | |||
2940.2.q.q.361.2 | 4 | 35.13 | even | 4 | |||
2940.2.q.q.961.2 | 4 | 35.33 | even | 12 | |||
8820.2.a.bf.1.2 | 2 | 105.38 | odd | 12 | |||
8820.2.a.bk.1.2 | 2 | 105.53 | even | 12 |