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: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(-0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.949 |
Dual form | 2100.2.bc.e.1549.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(7\) | 2.29129 | − | 1.32288i | 0.866025 | − | 0.500000i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.82288 | + | 3.15731i | −0.549618 | + | 0.951966i | 0.448683 | + | 0.893691i | \(0.351893\pi\) |
−0.998301 | + | 0.0582747i | \(0.981440\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575i | 0.733799i | 0.930261 | + | 0.366900i | \(0.119581\pi\) | ||||
−0.930261 | + | 0.366900i | \(0.880419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15731 | + | 1.82288i | 0.765761 | + | 0.442112i | 0.831360 | − | 0.555734i | \(-0.187563\pi\) |
−0.0655994 | + | 0.997846i | \(0.520896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.14575 | − | 1.98450i | −0.262853 | − | 0.455275i | 0.704146 | − | 0.710056i | \(-0.251330\pi\) |
−0.966999 | + | 0.254780i | \(0.917997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64575 | −0.577350 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.15731 | + | 1.82288i | −0.658345 | + | 0.380096i | −0.791646 | − | 0.610980i | \(-0.790776\pi\) |
0.133301 | + | 0.991076i | \(0.457442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.35425 | −0.437173 | −0.218587 | − | 0.975818i | \(-0.570145\pi\) | ||||
−0.218587 | + | 0.975818i | \(0.570145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.14575 | + | 5.44860i | −0.564994 | + | 0.978598i | 0.432057 | + | 0.901846i | \(0.357788\pi\) |
−0.997050 | + | 0.0767512i | \(0.975545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.15731 | − | 1.82288i | 0.549618 | − | 0.317322i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.02334 | − | 2.32288i | 0.661433 | − | 0.381878i | −0.131390 | − | 0.991331i | \(-0.541944\pi\) |
0.792823 | + | 0.609452i | \(0.208611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.32288 | − | 2.29129i | 0.211830 | − | 0.366900i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9373 | −1.70811 | −0.854056 | − | 0.520181i | \(-0.825864\pi\) | ||||
−0.854056 | + | 0.520181i | \(0.825864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.93725i | 1.51542i | 0.652593 | + | 0.757709i | \(0.273681\pi\) | ||||
−0.652593 | + | 0.757709i | \(0.726319\pi\) | |||||||
\(44\) | 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 | ||||||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.82288 | − | 3.15731i | −0.255254 | − | 0.442112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.31463 | + | 3.64575i | 0.867381 | + | 0.500782i | 0.866477 | − | 0.499217i | \(-0.166379\pi\) |
0.000903738 | 1.00000i | \(0.499712\pi\) | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29150i | 0.303517i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.46863 | + | 4.27579i | −0.321388 | + | 0.556660i | −0.980775 | − | 0.195144i | \(-0.937483\pi\) |
0.659387 | + | 0.751804i | \(0.270816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29129 | + | 1.32288i | 0.288675 | + | 0.166667i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.02334 | − | 2.32288i | −0.491529 | − | 0.283784i | 0.233680 | − | 0.972314i | \(-0.424923\pi\) |
−0.725209 | + | 0.688529i | \(0.758257\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.64575 | 0.438897 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.35425 | 0.991467 | 0.495733 | − | 0.868475i | \(-0.334899\pi\) | ||||
0.495733 | + | 0.868475i | \(0.334899\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4564 | + | 6.61438i | 1.34087 | + | 0.774154i | 0.986936 | − | 0.161114i | \(-0.0515087\pi\) |
0.353939 | + | 0.935269i | \(0.384842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.64575i | 1.09924i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.14575 | − | 7.18065i | −0.466433 | − | 0.807886i | 0.532831 | − | 0.846221i | \(-0.321128\pi\) |
−0.999265 | + | 0.0383349i | \(0.987795\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.93725i | 0.541934i | 0.962589 | + | 0.270967i | \(0.0873434\pi\) | ||||
−0.962589 | + | 0.270967i | \(0.912657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.03884 | + | 1.17712i | 0.218587 | + | 0.126201i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.11438 | + | 10.5904i | 0.648123 | + | 1.12258i | 0.983571 | + | 0.180523i | \(0.0577790\pi\) |
−0.335448 | + | 0.942059i | \(0.608888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | + | 6.06218i | 0.366900 | + | 0.635489i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.44860 | − | 3.14575i | 0.564994 | − | 0.326199i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.64575 | −0.366412 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.46863 | + | 9.47194i | −0.544149 | + | 0.942493i | 0.454511 | + | 0.890741i | \(0.349814\pi\) |
−0.998660 | + | 0.0517522i | \(0.983519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6836 | − | 7.32288i | 1.24975 | − | 0.721544i | 0.278692 | − | 0.960381i | \(-0.410099\pi\) |
0.971060 | + | 0.238836i | \(0.0767659\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.920365 | − | 0.531373i | 0.0889751 | − | 0.0513698i | −0.454852 | − | 0.890567i | \(-0.650308\pi\) |
0.543827 | + | 0.839197i | \(0.316975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.50000 | + | 11.2583i | −0.622587 | + | 1.07835i | 0.366415 | + | 0.930451i | \(0.380585\pi\) |
−0.989002 | + | 0.147901i | \(0.952748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.64575 | −0.440955 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.29129 | + | 1.32288i | −0.211830 | + | 0.122300i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.64575 | 0.884225 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.14575 | − | 1.98450i | −0.104159 | − | 0.180409i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.47194 | + | 5.46863i | 0.854056 | + | 0.493089i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9373i | 1.59167i | 0.605511 | + | 0.795837i | \(0.292969\pi\) | ||||
−0.605511 | + | 0.795837i | \(0.707031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.96863 | − | 8.60591i | 0.437463 | − | 0.757709i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.35425 | − | 9.27383i | −0.467803 | − | 0.810258i | 0.531520 | − | 0.847046i | \(-0.321621\pi\) |
−0.999323 | + | 0.0367872i | \(0.988288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.25049 | − | 3.03137i | −0.455275 | − | 0.262853i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.39426 | + | 3.11438i | 0.460863 | + | 0.266079i | 0.712407 | − | 0.701767i | \(-0.247605\pi\) |
−0.251544 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.35347 | − | 4.82288i | −0.698552 | − | 0.403309i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.06218 | + | 3.50000i | −0.500000 | + | 0.288675i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.29150 | + | 12.6293i | 0.597343 | + | 1.03463i | 0.993212 | + | 0.116321i | \(0.0371103\pi\) |
−0.395868 | + | 0.918307i | \(0.629556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.29150 | + | 14.3613i | −0.674753 | + | 1.16871i | 0.301788 | + | 0.953375i | \(0.402416\pi\) |
−0.976541 | + | 0.215331i | \(0.930917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.64575i | 0.294742i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.04668 | + | 4.64575i | 0.642195 | + | 0.370771i | 0.785459 | − | 0.618913i | \(-0.212427\pi\) |
−0.143265 | + | 0.989684i | \(0.545760\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.64575 | − | 6.31463i | −0.289127 | − | 0.500782i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.82288 | + | 8.35347i | −0.380096 | + | 0.658345i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8564 | + | 8.00000i | −1.08532 | + | 0.626608i | −0.932326 | − | 0.361619i | \(-0.882224\pi\) |
−0.152992 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.3542i | − | 1.11077i | −0.831595 | − | 0.555383i | \(-0.812572\pi\) | ||
0.831595 | − | 0.555383i | \(-0.187428\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | 0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14575 | − | 1.98450i | 0.0876178 | − | 0.151758i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9439 | + | 10.9373i | −1.44028 | + | 0.831544i | −0.997868 | − | 0.0652695i | \(-0.979209\pi\) |
−0.442409 | + | 0.896813i | \(0.645876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.27579 | − | 2.46863i | 0.321388 | − | 0.185553i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2915 | + | 17.8254i | −0.769223 | + | 1.33233i | 0.168762 | + | 0.985657i | \(0.446023\pi\) |
−0.937985 | + | 0.346676i | \(0.887310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.29150 | 0.467644 | 0.233822 | − | 0.972279i | \(-0.424877\pi\) | ||||
0.233822 | + | 0.972279i | \(0.424877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5108 | + | 6.64575i | −0.841752 | + | 0.485985i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32288 | − | 2.29129i | −0.0962250 | − | 0.166667i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5830 | + | 20.0624i | 0.838117 | + | 1.45166i | 0.891467 | + | 0.453085i | \(0.149677\pi\) |
−0.0533504 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7303 | + | 11.9686i | 1.49220 | + | 0.861521i | 0.999960 | − | 0.00894034i | \(-0.00284584\pi\) |
0.492237 | + | 0.870461i | \(0.336179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.9373i | − | 0.779247i | −0.920974 | − | 0.389624i | \(-0.872605\pi\) | ||
0.920974 | − | 0.389624i | \(-0.127395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.58301 | − | 16.5983i | 0.679321 | − | 1.17662i | −0.295864 | − | 0.955230i | \(-0.595608\pi\) |
0.975186 | − | 0.221389i | \(-0.0710590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.32288 | + | 4.02334i | 0.163843 | + | 0.283784i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.39426 | + | 3.11438i | −0.378603 | + | 0.218587i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.15731 | − | 1.82288i | −0.219448 | − | 0.126699i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.35425 | 0.577875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5830 | −0.866250 | −0.433125 | − | 0.901334i | \(-0.642589\pi\) | ||||
−0.433125 | + | 0.901334i | \(0.642589\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.23499 | − | 4.17712i | −0.495733 | − | 0.286212i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.6458i | 1.12999i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.61438 | − | 11.4564i | −0.446958 | − | 0.774154i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.82288 | + | 8.35347i | −0.324422 | + | 0.561915i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.8745i | − | 0.929106i | −0.885545 | − | 0.464553i | \(-0.846215\pi\) | ||
0.885545 | − | 0.464553i | \(-0.153785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4311 | + | 7.17712i | 0.825084 | + | 0.476362i | 0.852167 | − | 0.523271i | \(-0.175288\pi\) |
−0.0270825 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 4.82288 | − | 8.35347i | 0.317322 | − | 0.549618i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.27383 | − | 5.35425i | 0.607549 | − | 0.350768i | −0.164457 | − | 0.986384i | \(-0.552587\pi\) |
0.772006 | + | 0.635616i | \(0.219254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.29150i | 0.538591i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6458 | − | 20.1710i | 0.750169 | − | 1.29933i | −0.197572 | − | 0.980288i | \(-0.563306\pi\) |
0.947741 | − | 0.319042i | \(-0.103361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.25049 | − | 3.03137i | 0.334081 | − | 0.192882i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.46863 | − | 4.27579i | 0.156443 | − | 0.270967i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.93725 | 0.311637 | 0.155818 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155818 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.2915i | − | 0.835630i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.2973 | − | 15.7601i | 1.70276 | − | 0.983090i | 0.759819 | − | 0.650135i | \(-0.225288\pi\) |
0.942943 | − | 0.332955i | \(-0.108046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.14575 | − | 10.6448i | 0.381878 | − | 0.661433i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.17712 | − | 2.03884i | −0.0728622 | − | 0.126201i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1808 | − | 12.2288i | −1.30607 | − | 0.754057i | −0.324629 | − | 0.945842i | \(-0.605239\pi\) |
−0.981437 | + | 0.191784i | \(0.938573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.2288i | − | 0.748388i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.93725 | + | 3.35542i | −0.118116 | + | 0.204584i | −0.919021 | − | 0.394208i | \(-0.871019\pi\) |
0.800905 | + | 0.598792i | \(0.204352\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2915 | − | 24.7536i | −0.868147 | − | 1.50367i | −0.863888 | − | 0.503684i | \(-0.831978\pi\) |
−0.00425882 | − | 0.999991i | \(-0.501356\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.00000i | − | 0.423659i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2972 | − | 7.67712i | −0.798949 | − | 0.461274i | 0.0441542 | − | 0.999025i | \(-0.485941\pi\) |
−0.843104 | + | 0.537751i | \(0.819274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.29150 | −0.376662 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.10102 | + | 4.67712i | 0.481555 | + | 0.278026i | 0.721064 | − | 0.692868i | \(-0.243653\pi\) |
−0.239509 | + | 0.970894i | \(0.576986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.0604 | + | 14.4686i | −1.47927 | + | 0.854056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.85425 | − | 3.21165i | −0.109073 | − | 0.188921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.15731 | + | 1.82288i | 0.183206 | + | 0.105774i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.82288 | − | 8.35347i | −0.278914 | − | 0.483093i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.1458 | + | 22.7691i | 0.757709 | + | 1.31239i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.47194 | − | 5.46863i | 0.544149 | − | 0.314164i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0627i | − | 0.688457i | −0.938886 | − | 0.344229i | \(-0.888140\pi\) | ||
0.938886 | − | 0.344229i | \(-0.111860\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.6458 | −0.833168 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.17712 | + | 7.23499i | −0.236863 | + | 0.410259i | −0.959812 | − | 0.280642i | \(-0.909453\pi\) |
0.722949 | + | 0.690901i | \(0.242786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.52824 | − | 2.61438i | 0.255951 | − | 0.147773i | −0.366535 | − | 0.930404i | \(-0.619456\pi\) |
0.622486 | + | 0.782631i | \(0.286123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7089 | − | 6.76013i | 0.657637 | − | 0.379687i | −0.133739 | − | 0.991017i | \(-0.542698\pi\) |
0.791376 | + | 0.611330i | \(0.209365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.29150 | − | 7.43310i | 0.240278 | − | 0.416174i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.06275 | −0.0593167 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.35425i | − | 0.464843i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2583 | − | 6.50000i | 0.622587 | − | 0.359451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.93725 | + | 13.7477i | −0.437595 | + | 0.757937i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0830 | − | 19.1963i | −0.609177 | − | 1.05513i | −0.991376 | − | 0.131046i | \(-0.958167\pi\) |
0.382199 | − | 0.924080i | \(-0.375167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.02334 | + | 2.32288i | 0.220478 | + | 0.127293i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.77124i | 0.368853i | 0.982846 | + | 0.184427i | \(0.0590428\pi\) | ||||
−0.982846 | + | 0.184427i | \(0.940957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4686 | − | 19.8642i | −0.621061 | − | 1.07571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.2585 | − | 14.5830i | −1.35595 | − | 0.782857i | −0.366873 | − | 0.930271i | \(-0.619572\pi\) |
−0.989075 | + | 0.147414i | \(0.952905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.64575 | 0.141220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.1420 | − | 11.0516i | −1.01883 | − | 0.588219i | −0.105062 | − | 0.994466i | \(-0.533504\pi\) |
−0.913763 | + | 0.406247i | \(0.866837\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.35347 | − | 4.82288i | −0.442112 | − | 0.255254i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4059 | + | 23.2197i | 0.707535 | + | 1.22549i | 0.965769 | + | 0.259405i | \(0.0835263\pi\) |
−0.258233 | + | 0.966083i | \(0.583140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.87451 | − | 11.9070i | 0.361816 | − | 0.626684i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.29150i | 0.120273i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.6526 | − | 9.61438i | −0.869258 | − | 0.501866i | −0.00215655 | − | 0.999998i | \(-0.500686\pi\) |
−0.867102 | + | 0.498131i | \(0.834020\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.46863 | − | 9.47194i | −0.284685 | − | 0.493089i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.2915 | 1.00156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8021 | − | 7.96863i | 0.714644 | − | 0.412600i | −0.0981342 | − | 0.995173i | \(-0.531287\pi\) |
0.812778 | + | 0.582573i | \(0.197954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.22876i | − | 0.320797i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2915 | 1.35050 | 0.675252 | − | 0.737587i | \(-0.264035\pi\) | ||||
0.675252 | + | 0.737587i | \(0.264035\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.96863 | − | 15.5341i | 0.459477 | − | 0.795837i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4700 | + | 8.35425i | −0.739382 | + | 0.426882i | −0.821844 | − | 0.569712i | \(-0.807055\pi\) |
0.0824628 | + | 0.996594i | \(0.473721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.60591 | + | 4.96863i | −0.437463 | + | 0.252570i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.7601 | + | 32.4935i | −0.951176 | + | 1.64749i | −0.208291 | + | 0.978067i | \(0.566790\pi\) |
−0.742885 | + | 0.669419i | \(0.766543\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2915 | −0.672180 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.7085i | 0.540172i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4156 | − | 8.32288i | 0.723500 | − | 0.417713i | −0.0925393 | − | 0.995709i | \(-0.529498\pi\) |
0.816040 | + | 0.577996i | \(0.196165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.03137 | + | 5.25049i | 0.151758 | + | 0.262853i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.64575 | − | 16.7069i | −0.481686 | − | 0.834304i | 0.518093 | − | 0.855324i | \(-0.326642\pi\) |
−0.999779 | + | 0.0210198i | \(0.993309\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.4156 | − | 8.32288i | −0.718094 | − | 0.414592i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9373i | 0.839549i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0830 | + | 31.3207i | −0.894147 | + | 1.54871i | −0.0592904 | + | 0.998241i | \(0.518884\pi\) |
−0.834857 | + | 0.550467i | \(0.814450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.11438 | − | 5.39426i | −0.153621 | − | 0.266079i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.0627i | 0.642776i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.33013 | + | 2.50000i | 0.212047 | + | 0.122426i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7085 | −0.523144 | −0.261572 | − | 0.965184i | \(-0.584241\pi\) | ||||
−0.261572 | + | 0.965184i | \(0.584241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.58301 | 0.0771510 | 0.0385755 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385755 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | − | 3.00000i | −0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.3303 | − | 10.5830i | −0.887066 | − | 0.512148i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.82288 | + | 8.35347i | 0.232851 | + | 0.403309i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.06275 | + | 7.03688i | −0.195696 | + | 0.338955i | −0.947128 | − | 0.320855i | \(-0.896030\pi\) |
0.751433 | + | 0.659810i | \(0.229363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.64575i | 0.415488i | 0.978183 | + | 0.207744i | \(0.0666121\pi\) | ||||
−0.978183 | + | 0.207744i | \(0.933388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.23499 | + | 4.17712i | 0.346097 | + | 0.199819i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.64575 | − | 4.58258i | −0.126275 | − | 0.218714i | 0.795956 | − | 0.605355i | \(-0.206969\pi\) |
−0.922231 | + | 0.386640i | \(0.873635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.9439 | + | 10.9373i | −0.900051 | + | 0.519645i | −0.877217 | − | 0.480095i | \(-0.840602\pi\) |
−0.0228342 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.5830i | − | 0.689752i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.58301 | −0.405057 | −0.202529 | − | 0.979276i | \(-0.564916\pi\) | ||||
−0.202529 | + | 0.979276i | \(0.564916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9373 | − | 34.5323i | 0.938809 | − | 1.62606i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.3613 | − | 8.29150i | 0.674753 | − | 0.389569i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.10102 | − | 4.67712i | 0.378950 | − | 0.218787i | −0.298412 | − | 0.954437i | \(-0.596457\pi\) |
0.677361 | + | 0.735651i | \(0.263123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.82288 | − | 3.15731i | 0.0850845 | − | 0.147371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.3542 | −0.668544 | −0.334272 | − | 0.942477i | \(-0.608490\pi\) | ||||
−0.334272 | + | 0.942477i | \(0.608490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.5203i | − | 1.23250i | −0.787550 | − | 0.616250i | \(-0.788651\pi\) | ||
0.787550 | − | 0.616250i | \(-0.211349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.2993 | + | 12.8745i | −1.03189 | + | 0.595761i | −0.917525 | − | 0.397678i | \(-0.869816\pi\) |
−0.114363 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2915 | −0.567569 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.64575 | − | 8.04668i | −0.214065 | − | 0.370771i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.3750 | − | 18.1144i | −1.44263 | − | 0.832900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.29150i | 0.333855i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.29150 | − | 12.6293i | 0.333157 | − | 0.577045i | −0.649972 | − | 0.759958i | \(-0.725219\pi\) |
0.983129 | + | 0.182913i | \(0.0585527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.14575 | + | 10.6448i | 0.280222 | + | 0.485359i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.35347 | − | 4.82288i | 0.380096 | − | 0.219448i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29129 | + | 1.32288i | 0.103828 | + | 0.0599452i | 0.551015 | − | 0.834495i | \(-0.314241\pi\) |
−0.447187 | + | 0.894441i | \(0.647574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8745 | 1.52874 | 0.764368 | − | 0.644781i | \(-0.223051\pi\) | ||||
0.764368 | + | 0.644781i | \(0.223051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.43310 | − | 4.29150i | −0.334770 | − | 0.193280i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.1420 | − | 11.0516i | 0.858636 | − | 0.495733i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.7288 | − | 22.0469i | −0.569817 | − | 0.986953i | −0.996584 | − | 0.0825907i | \(-0.973681\pi\) |
0.426766 | − | 0.904362i | \(-0.359653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.17712 | + | 12.4311i | −0.320650 | + | 0.555383i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.4575i | − | 1.35803i | −0.734123 | − | 0.679017i | \(-0.762406\pi\) | ||
0.734123 | − | 0.679017i | \(-0.237594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.19615 | − | 3.00000i | −0.230769 | − | 0.133235i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.93725 | + | 3.35542i | 0.0858673 | + | 0.148726i | 0.905760 | − | 0.423790i | \(-0.139301\pi\) |
−0.819893 | + | 0.572517i | \(0.805967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.0000 | 1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.98450 | + | 1.14575i | −0.0876178 | + | 0.0505862i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21.8745i | − | 0.962040i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.8745 | 0.960184 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.9373 | − | 29.3362i | 0.742035 | − | 1.28524i | −0.209533 | − | 0.977802i | \(-0.567194\pi\) |
0.951567 | − | 0.307440i | \(-0.0994723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.13202 | − | 2.38562i | 0.180681 | − | 0.104316i | −0.406932 | − | 0.913459i | \(-0.633401\pi\) |
0.587612 | + | 0.809143i | \(0.300068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.8642 | + | 11.4686i | −0.865300 | + | 0.499581i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.85425 | + | 8.40781i | −0.211054 | + | 0.365557i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.93725 | −0.214259 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 28.9373i | − | 1.25341i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8254 | − | 10.2915i | 0.769223 | − | 0.444111i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7601 | + | 22.1012i | 0.549618 | + | 0.951966i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3745 | + | 23.1653i | 0.575015 | + | 0.995955i | 0.996040 | + | 0.0889062i | \(0.0283371\pi\) |
−0.421025 | + | 0.907049i | \(0.638330\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.44860 | − | 3.14575i | −0.233822 | − | 0.134997i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.7085i | 1.39851i | 0.714870 | + | 0.699257i | \(0.246486\pi\) | ||||
−0.714870 | + | 0.699257i | \(0.753514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | − | 6.92820i | 0.170716 | − | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.69738 | + | 4.67201i | 0.114912 | + | 0.199034i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.9982 | − | 10.9686i | −0.807886 | − | 0.466433i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.5885 | − | 9.00000i | −0.660504 | − | 0.381342i | 0.131965 | − | 0.991254i | \(-0.457871\pi\) |
−0.792469 | + | 0.609912i | \(0.791205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.2915 | −1.11201 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.2915 | 0.561168 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3515 | + | 7.70850i | 0.562699 | + | 0.324874i | 0.754228 | − | 0.656613i | \(-0.228011\pi\) |
−0.191529 | + | 0.981487i | \(0.561345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.64575i | 0.111111i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.1144 | − | 26.1789i | −0.633628 | − | 1.09748i | −0.986804 | − | 0.161919i | \(-0.948232\pi\) |
0.353176 | − | 0.935557i | \(-0.385102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8542 | + | 29.1924i | −0.705328 | + | 1.22166i | 0.261245 | + | 0.965273i | \(0.415867\pi\) |
−0.966573 | + | 0.256392i | \(0.917466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 23.1660i | − | 0.967774i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.74559 | − | 2.73987i | −0.197562 | − | 0.114062i | 0.397956 | − | 0.917405i | \(-0.369720\pi\) |
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9686 | − | 20.7303i | −0.497399 | − | 0.861521i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.53137 | + | 11.3127i | 0.270967 | + | 0.469329i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.0216 | + | 13.2915i | −0.953456 | + | 0.550478i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.06275i | − | 0.0438642i | −0.999759 | − | 0.0219321i | \(-0.993018\pi\) | ||
0.999759 | − | 0.0219321i | \(-0.00698177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.4170 | 0.594042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.46863 | + | 9.47194i | −0.224949 | + | 0.389624i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.4527 | + | 20.4686i | −1.45587 | + | 0.840546i | −0.998804 | − | 0.0488882i | \(-0.984432\pi\) |
−0.457064 | + | 0.889434i | \(0.651099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.5983 | + | 9.58301i | −0.679321 | + | 0.392206i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9373 | − | 29.3362i | 0.692037 | − | 1.19864i | −0.279132 | − | 0.960253i | \(-0.590047\pi\) |
0.971169 | − | 0.238391i | \(-0.0766200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.4170 | −0.669663 | −0.334832 | − | 0.942278i | \(-0.608679\pi\) | ||||
−0.334832 | + | 0.942278i | \(0.608679\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.64575i | − | 0.189190i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4372 | − | 21.6144i | 1.51953 | − | 0.877301i | 0.519794 | − | 0.854292i | \(-0.326009\pi\) |
0.999735 | − | 0.0230088i | \(-0.00732459\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.22876 | 0.252402 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.93725 | − | 13.7477i | −0.321107 | − | 0.556174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00979 | − | 0.583005i | −0.0407852 | − | 0.0235474i | 0.479469 | − | 0.877559i | \(-0.340829\pi\) |
−0.520254 | + | 0.854012i | \(0.674163\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.29150i | 0.0519939i | 0.999662 | + | 0.0259970i | \(0.00827602\pi\) | ||||
−0.999662 | + | 0.0259970i | \(0.991724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | + | 16.4545i | −0.381837 | + | 0.661361i | −0.991325 | − | 0.131434i | \(-0.958042\pi\) |
0.609488 | + | 0.792796i | \(0.291375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.82288 | + | 3.15731i | 0.0731495 | + | 0.126699i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.0196 | + | 16.1771i | 1.12258 | + | 0.648123i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.23499 | − | 4.17712i | −0.288938 | − | 0.166818i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9373 | 0.675333 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.7490 | 1.10467 | 0.552335 | − | 0.833622i | \(-0.313737\pi\) | ||||
0.552335 | + | 0.833622i | \(0.313737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.8972 | + | 6.29150i | 0.433125 | + | 0.250065i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0390 | + | 9.26013i | 0.635489 | + | 0.366900i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.17712 | + | 7.23499i | 0.165244 | + | 0.286212i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.0516 | + | 39.9266i | −0.910485 | + | 1.57701i | −0.0971039 | + | 0.995274i | \(0.530958\pi\) |
−0.813381 | + | 0.581732i | \(0.802375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.8118i | 1.01792i | 0.860791 | + | 0.508958i | \(0.169969\pi\) | ||||
−0.860791 | + | 0.508958i | \(0.830031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.11652 | + | 3.53137i | 0.240465 | + | 0.138833i | 0.615390 | − | 0.788222i | \(-0.288998\pi\) |
−0.374925 | + | 0.927055i | \(0.622332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 15.5885i | −0.353281 | − | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.32288 | − | 14.4156i | 0.326199 | − | 0.564994i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.1381 | − | 16.8229i | 1.14026 | − | 0.658330i | 0.193766 | − | 0.981048i | \(-0.437930\pi\) |
0.946495 | + | 0.322718i | \(0.104596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.2288i | 0.516103i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.56275 | − | 7.90291i | 0.177470 | − | 0.307387i | −0.763543 | − | 0.645757i | \(-0.776542\pi\) |
0.941013 | + | 0.338369i | \(0.109875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.35347 | − | 4.82288i | 0.324422 | − | 0.187305i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.43310 | − | 4.29150i | 0.287811 | − | 0.166168i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.93725 | + | 12.0157i | −0.268210 | + | 0.464553i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.1660 | 1.12594 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.6458i | − | 0.410364i | −0.978724 | − | 0.205182i | \(-0.934221\pi\) | ||
0.978724 | − | 0.205182i | \(-0.0657786\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.9419 | − | 13.8229i | 0.920163 | − | 0.531256i | 0.0364758 | − | 0.999335i | \(-0.488387\pi\) |
0.883687 | + | 0.468078i | \(0.155053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5830 | − | 18.3303i | −0.406138 | − | 0.703452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.17712 | − | 12.4311i | −0.275028 | − | 0.476362i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.47194 | + | 5.46863i | 0.362434 | + | 0.209251i | 0.670148 | − | 0.742228i | \(-0.266231\pi\) |
−0.307714 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000i | 0.267067i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.64575 | + | 16.7069i | −0.367474 | + | 0.636483i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.20850 | − | 2.09318i | −0.0459734 | − | 0.0796283i | 0.842123 | − | 0.539285i | \(-0.181306\pi\) |
−0.888096 | + | 0.459657i | \(0.847972\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.35347 | + | 4.82288i | −0.317322 | + | 0.183206i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.5323 | − | 19.9373i | −1.30801 | − | 0.755177i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.7085 | −0.405033 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0627 | 0.719990 | 0.359995 | − | 0.932954i | \(-0.382778\pi\) | ||||
0.359995 | + | 0.932954i | \(0.382778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.21949 | − | 5.32288i | −0.347720 | − | 0.200756i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.9373i | 1.08830i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.708497 | − | 1.22715i | −0.0266082 | − | 0.0460867i | 0.852415 | − | 0.522866i | \(-0.175137\pi\) |
−0.879023 | + | 0.476780i | \(0.841804\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.14575 | − | 7.18065i | 0.155478 | − | 0.269295i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 22.9373i | − | 0.859007i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.19615 | + | 3.00000i | 0.194054 | + | 0.112037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6458 | − | 21.9031i | −0.471607 | − | 0.816847i | 0.527865 | − | 0.849328i | \(-0.322993\pi\) |
−0.999472 | + | 0.0324808i | \(0.989659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.3745 | − | 33.5576i | 0.721544 | − | 1.24975i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1710 | + | 11.6458i | −0.750169 | + | 0.433110i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.8118i | − | 0.512250i | −0.966644 | − | 0.256125i | \(-0.917554\pi\) | ||
0.966644 | − | 0.256125i | \(-0.0824459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1144 | + | 31.3750i | −0.669984 | + | 1.16045i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.6526 | + | 9.61438i | −0.615078 | + | 0.355115i | −0.774950 | − | 0.632023i | \(-0.782225\pi\) |
0.159873 | + | 0.987138i | \(0.448892\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.6681 | − | 8.46863i | 0.540306 | − | 0.311946i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5000 | − | 25.1147i | 0.533391 | − | 0.923861i | −0.465848 | − | 0.884865i | \(-0.654251\pi\) |
0.999239 | − | 0.0389959i | \(-0.0124159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.06275 | −0.222721 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.9373i | − | 1.06160i | −0.847496 | − | 0.530802i | \(-0.821891\pi\) | ||
0.847496 | − | 0.530802i | \(-0.178109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.27579 | + | 2.46863i | −0.156443 | + | 0.0903223i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.40588 | − | 2.43506i | 0.0513698 | − | 0.0889751i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.08301 | + | 15.7322i | 0.331444 | + | 0.574077i | 0.982795 | − | 0.184699i | \(-0.0591310\pi\) |
−0.651352 | + | 0.758776i | \(0.725798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.27579 | − | 2.46863i | −0.155818 | − | 0.0899618i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.1660i | 1.85966i | 0.367989 | + | 0.929830i | \(0.380046\pi\) | ||||
−0.367989 | + | 0.929830i | \(0.619954\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.64575 | + | 11.5108i | −0.241225 | + | 0.417815i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0516 | − | 39.9266i | −0.835621 | − | 1.44734i | −0.893524 | − | 0.449016i | \(-0.851775\pi\) |
0.0579028 | − | 0.998322i | \(-0.481559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.3948i | 1.24517i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3127 | − | 6.53137i | −0.408477 | − | 0.235834i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.2915 | 0.515365 | 0.257682 | − | 0.966230i | \(-0.417041\pi\) | ||||
0.257682 | + | 0.966230i | \(0.417041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.5203 | −1.13517 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.8489 | + | 20.6974i | 1.28940 | + | 0.744433i | 0.978547 | − | 0.206026i | \(-0.0660531\pi\) |
0.310850 | + | 0.950459i | \(0.399386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.6448 | + | 6.14575i | −0.381878 | + | 0.220478i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.5314 | + | 21.7050i | 0.448983 | + | 0.777661i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.2288 | + | 26.3770i | −0.544928 | + | 0.943843i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.35425i | 0.0841340i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.4080 | − | 12.9373i | −0.798758 | − | 0.461163i | 0.0442785 | − | 0.999019i | \(-0.485901\pi\) |
−0.843037 | + | 0.537856i | \(0.819234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.2288 | + | 21.1808i | 0.435355 | + | 0.754057i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.93725 | + | 13.7477i | 0.282216 | + | 0.488813i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.3303 | − | 10.5830i | 0.650928 | − | 0.375814i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.9373i | 0.387417i | 0.981059 | + | 0.193709i | \(0.0620517\pi\) | ||||
−0.981059 | + | 0.193709i | \(0.937948\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.8745 | −0.773864 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.11438 | + | 10.5904i | −0.216041 | + | 0.374194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.7673 | + | 24.1144i | −1.47394 | + | 0.850978i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.35542 | − | 1.93725i | 0.118116 | − | 0.0681946i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.5830 | + | 20.0624i | −0.407237 | + | 0.705355i | −0.994579 | − | 0.103984i | \(-0.966841\pi\) |
0.587342 | + | 0.809339i | \(0.300174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.70850 | 0.235567 | 0.117784 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117784 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5830i | 1.00245i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.7205 | − | 11.3856i | 0.689932 | − | 0.398332i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.50000 | + | 6.06218i | −0.122300 | + | 0.211830i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9889 | − | 32.8897i | −0.662717 | − | 1.14786i | −0.979899 | − | 0.199494i | \(-0.936070\pi\) |
0.317182 | − | 0.948365i | \(-0.397263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8411 | + | 17.2288i | 1.04019 | + | 0.600557i | 0.919888 | − | 0.392180i | \(-0.128279\pi\) |
0.120306 | + | 0.992737i | \(0.461612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.4575i | 1.05911i | 0.848275 | + | 0.529556i | \(0.177641\pi\) | ||||
−0.848275 | + | 0.529556i | \(0.822359\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1458 | − | 26.2332i | 0.526034 | − | 0.911117i | −0.473506 | − | 0.880790i | \(-0.657012\pi\) |
0.999540 | − | 0.0303267i | \(-0.00965476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.67712 | + | 13.2972i | 0.266316 | + | 0.461274i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.1012 | − | 12.7601i | 0.765761 | − | 0.442112i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.44860 | + | 3.14575i | 0.188331 | + | 0.108733i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6458 | −0.747294 | −0.373647 | − | 0.927571i | \(-0.621893\pi\) | ||||
−0.373647 | + | 0.927571i | \(0.621893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4575 | −0.808880 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.7846 | − | 12.0000i | −0.715860 | − | 0.413302i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.25049 | − | 3.03137i | −0.180409 | − | 0.104159i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.67712 | − | 8.10102i | −0.160518 | − | 0.278026i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.46863 | + | 14.6681i | −0.290301 | + | 0.502816i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.7712i | 0.574236i | 0.957895 | + | 0.287118i | \(0.0926973\pi\) | ||||
−0.957895 | + | 0.287118i | \(0.907303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.23499 | − | 4.17712i | −0.247143 | − | 0.142688i | 0.371313 | − | 0.928508i | \(-0.378908\pi\) |
−0.618455 | + | 0.785820i | \(0.712241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2288 | + | 22.9129i | 0.451359 | + | 0.781777i | 0.998471 | − | 0.0552825i | \(-0.0176059\pi\) |
−0.547111 | + | 0.837060i | \(0.684273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.9373 | 0.986179 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9847 | − | 9.22876i | 0.544125 | − | 0.314151i | −0.202624 | − | 0.979257i | \(-0.564947\pi\) |
0.746749 | + | 0.665106i | \(0.231614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.70850i | 0.125947i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.2288 | 1.02544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.14575 | − | 10.6448i | 0.208241 | − | 0.360684i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.92820 | − | 4.00000i | 0.234484 | − | 0.135379i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.1244 | + | 7.00000i | −0.409410 | + | 0.236373i | −0.690536 | − | 0.723298i | \(-0.742625\pi\) |
0.281126 | + | 0.959671i | \(0.409292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.1660 | −1.38692 | −0.693459 | − | 0.720496i | \(-0.743914\pi\) | ||||
−0.693459 | + | 0.720496i | \(0.743914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8118i | 0.868635i | 0.900760 | + | 0.434317i | \(0.143010\pi\) | ||||
−0.900760 | + | 0.434317i | \(0.856990\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.4311 | − | 7.17712i | 0.417397 | − | 0.240984i | −0.276566 | − | 0.960995i | \(-0.589196\pi\) |
0.693963 | + | 0.720011i | \(0.255863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.7288 | + | 41.0994i | 0.795837 | + | 1.37843i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.82288 | − | 3.15731i | −0.0610686 | − | 0.105774i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.9070 | + | 6.87451i | 0.398452 | + | 0.230047i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.64575i | 0.322062i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.40588 | − | 12.8274i | 0.247000 | − | 0.427816i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2915 | + | 23.0216i | 0.442804 | + | 0.766959i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 26.2915i | − | 0.874926i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.2972 | − | 7.67712i | −0.441525 | − | 0.254915i | 0.262719 | − | 0.964872i | \(-0.415381\pi\) |
−0.704244 | + | 0.709958i | \(0.748714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9373 | −0.362766 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.5203 | 1.04431 | 0.522156 | − | 0.852850i | \(-0.325128\pi\) | ||||
0.522156 | + | 0.852850i | \(0.325128\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5885 | − | 9.00000i | −0.515903 | − | 0.297857i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.5362 | − | 14.1660i | −0.810258 | − | 0.467803i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7915 | + | 27.3517i | 0.520914 | + | 0.902249i | 0.999704 | + | 0.0243197i | \(0.00774197\pi\) |
−0.478791 | + | 0.877929i | \(0.658925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.03137 | + | 10.4466i | −0.198740 | + | 0.344229i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.1033i | 0.727538i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.6836 | + | 7.32288i | 0.416584 | + | 0.240515i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.760130 | − | 1.31658i | −0.0249390 | − | 0.0431957i | 0.853287 | − | 0.521442i | \(-0.174606\pi\) |
−0.878226 | + | 0.478247i | \(0.841273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.0405 | −0.525707 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.23499 | − | 4.17712i | 0.236863 | − | 0.136753i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.9778i | 1.66537i | 0.553746 | + | 0.832686i | \(0.313198\pi\) | ||||
−0.553746 | + | 0.832686i | \(0.686802\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.22876 | −0.170634 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.46863 | + | 4.27579i | −0.0804749 | + | 0.139387i | −0.903454 | − | 0.428685i | \(-0.858977\pi\) |
0.822979 | + | 0.568072i | \(0.192310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.5323 | − | 19.9373i | 1.12453 | − | 0.649246i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.5304 | − | 22.8229i | 1.28456 | − | 0.741644i | 0.306885 | − | 0.951746i | \(-0.400713\pi\) |
0.977679 | + | 0.210103i | \(0.0673798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.5000 | + | 30.3109i | −0.568074 | + | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.5203 | −0.438424 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.457513i | 0.0148203i | 0.999973 | + | 0.00741015i | \(0.00235875\pi\) | ||||
−0.999973 | + | 0.00741015i | \(0.997641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.43310 | + | 4.29150i | −0.240278 | + | 0.138725i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.4797 | 0.532159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.29150 | − | 7.43310i | −0.138436 | − | 0.239777i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.920365 | + | 0.531373i | 0.0296584 | + | 0.0171233i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.3948i | − | 1.29901i | −0.760358 | − | 0.649504i | \(-0.774977\pi\) | ||
0.760358 | − | 0.649504i | \(-0.225023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.17712 | + | 7.23499i | −0.134189 | + | 0.232421i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.5830 | − | 46.0431i | −0.853089 | − | 1.47759i | −0.878406 | − | 0.477914i | \(-0.841393\pi\) |
0.0253172 | − | 0.999679i | \(-0.491940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4564 | + | 6.61438i | −0.367277 | + | 0.212047i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.4527 | − | 20.4686i | −1.13423 | − | 0.654849i | −0.189237 | − | 0.981932i | \(-0.560601\pi\) |
−0.944996 | + | 0.327082i | \(0.893935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.5830 | −1.42488 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0000 | −0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.3597 | + | 27.3431i | 1.51054 | + | 0.872111i | 0.999924 | + | 0.0123014i | \(0.00391575\pi\) |
0.510615 | + | 0.859809i | \(0.329418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.7477 | − | 7.93725i | 0.437595 | − | 0.252646i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1144 | − | 31.3750i | −0.576004 | − | 0.997668i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.8542 | + | 29.1924i | −0.535393 | + | 0.927328i | 0.463751 | + | 0.885965i | \(0.346503\pi\) |
−0.999144 | + | 0.0413622i | \(0.986830\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.1660i | 0.703417i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5243 | + | 8.38562i | 0.459990 | + | 0.265575i | 0.712040 | − | 0.702139i | \(-0.247771\pi\) |
−0.252050 | + | 0.967714i | \(0.581105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.32288 | − | 4.02334i | −0.0734925 | − | 0.127293i |
(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.e.949.2 | 8 | ||
5.2 | odd | 4 | 420.2.q.c.361.2 | yes | 4 | ||
5.3 | odd | 4 | 2100.2.q.h.1201.1 | 4 | |||
5.4 | even | 2 | inner | 2100.2.bc.e.949.3 | 8 | ||
7.2 | even | 3 | inner | 2100.2.bc.e.1549.3 | 8 | ||
15.2 | even | 4 | 1260.2.s.f.361.2 | 4 | |||
20.7 | even | 4 | 1680.2.bg.q.1201.1 | 4 | |||
35.2 | odd | 12 | 420.2.q.c.121.2 | ✓ | 4 | ||
35.9 | even | 6 | inner | 2100.2.bc.e.1549.2 | 8 | ||
35.12 | even | 12 | 2940.2.q.t.961.1 | 4 | |||
35.17 | even | 12 | 2940.2.a.m.1.2 | 2 | |||
35.23 | odd | 12 | 2100.2.q.h.1801.1 | 4 | |||
35.27 | even | 4 | 2940.2.q.t.361.1 | 4 | |||
35.32 | odd | 12 | 2940.2.a.s.1.2 | 2 | |||
105.2 | even | 12 | 1260.2.s.f.541.2 | 4 | |||
105.17 | odd | 12 | 8820.2.a.bj.1.1 | 2 | |||
105.32 | even | 12 | 8820.2.a.be.1.1 | 2 | |||
140.107 | even | 12 | 1680.2.bg.q.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.c.121.2 | ✓ | 4 | 35.2 | odd | 12 | ||
420.2.q.c.361.2 | yes | 4 | 5.2 | odd | 4 | ||
1260.2.s.f.361.2 | 4 | 15.2 | even | 4 | |||
1260.2.s.f.541.2 | 4 | 105.2 | even | 12 | |||
1680.2.bg.q.961.1 | 4 | 140.107 | even | 12 | |||
1680.2.bg.q.1201.1 | 4 | 20.7 | even | 4 | |||
2100.2.q.h.1201.1 | 4 | 5.3 | odd | 4 | |||
2100.2.q.h.1801.1 | 4 | 35.23 | odd | 12 | |||
2100.2.bc.e.949.2 | 8 | 1.1 | even | 1 | trivial | ||
2100.2.bc.e.949.3 | 8 | 5.4 | even | 2 | inner | ||
2100.2.bc.e.1549.2 | 8 | 35.9 | even | 6 | inner | ||
2100.2.bc.e.1549.3 | 8 | 7.2 | even | 3 | inner | ||
2940.2.a.m.1.2 | 2 | 35.17 | even | 12 | |||
2940.2.a.s.1.2 | 2 | 35.32 | odd | 12 | |||
2940.2.q.t.361.1 | 4 | 35.27 | even | 4 | |||
2940.2.q.t.961.1 | 4 | 35.12 | even | 12 | |||
8820.2.a.be.1.1 | 2 | 105.32 | even | 12 | |||
8820.2.a.bj.1.1 | 2 | 105.17 | odd | 12 |