Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(949,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, 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("2940.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.bb (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: | \(23.4760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2940.949 |
Dual form | 2940.2.bb.a.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 \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(1177\) | \(1471\) | \(1961\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.133975 | − | 2.23205i | −0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | + | 1.00000i | 0.420084 | + | 0.242536i | 0.695113 | − | 0.718900i | \(-0.255354\pi\) |
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | + | 5.19615i | −0.538816 | + | 0.933257i | 0.460152 | + | 0.887840i | \(0.347795\pi\) |
−0.998968 | + | 0.0454165i | \(0.985539\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | + | 2.00000i | −0.603023 | + | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46410 | − | 2.00000i | 0.569495 | − | 0.328798i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) |
0.756948 | + | 0.653476i | \(0.226690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | + | 1.73205i | −0.160128 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.86603 | − | 1.23205i | 0.278171 | − | 0.183663i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | + | 2.00000i | −0.505291 | + | 0.291730i | −0.730896 | − | 0.682489i | \(-0.760898\pi\) |
0.225605 | + | 0.974219i | \(0.427564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.73205 | + | 1.00000i | 0.237915 | + | 0.137361i | 0.614218 | − | 0.789136i | \(-0.289471\pi\) |
−0.376303 | + | 0.926497i | \(0.622805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | + | 4.00000i | 1.07872 | + | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.46410 | − | 0.267949i | 0.553704 | − | 0.0332350i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.3923 | − | 6.00000i | −1.26962 | − | 0.733017i | −0.294706 | − | 0.955588i | \(-0.595222\pi\) |
−0.974916 | + | 0.222571i | \(0.928555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1244 | − | 7.00000i | −1.41905 | − | 0.819288i | −0.422833 | − | 0.906208i | \(-0.638964\pi\) |
−0.996215 | + | 0.0869195i | \(0.972298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.59808 | − | 1.96410i | −0.530940 | − | 0.226795i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | + | 13.8564i | 0.900070 | + | 1.55897i | 0.827401 | + | 0.561611i | \(0.189818\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 4.00000i | 0.216930 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.19615 | − | 3.00000i | −0.557086 | − | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | + | 13.8564i | 0.847998 | + | 1.46878i | 0.882992 | + | 0.469389i | \(0.155526\pi\) |
−0.0349934 | + | 0.999388i | \(0.511141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19615 | + | 3.00000i | −0.538816 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.73205 | + | 2.46410i | −0.382900 | + | 0.252811i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000i | 1.42148i | 0.703452 | + | 0.710742i | \(0.251641\pi\) | ||||
−0.703452 | + | 0.710742i | \(0.748359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | + | 6.92820i | −0.398015 | + | 0.689382i | −0.993481 | − | 0.113998i | \(-0.963634\pi\) |
0.595466 | + | 0.803380i | \(0.296967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5885 | + | 9.00000i | −1.50699 | + | 0.870063i | −0.507026 | + | 0.861931i | \(0.669255\pi\) |
−0.999967 | + | 0.00813215i | \(0.997411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | − | 15.5885i | 0.862044 | − | 1.49310i | −0.00790932 | − | 0.999969i | \(-0.502518\pi\) |
0.869953 | − | 0.493135i | \(-0.164149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.39230 | + | 11.1962i | 0.689336 | + | 1.04405i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.73205 | + | 1.00000i | −0.160128 | + | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23205 | − | 0.133975i | 0.192104 | − | 0.0115307i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.66025 | + | 5.00000i | 0.739895 | + | 0.427179i | 0.822031 | − | 0.569442i | \(-0.192841\pi\) |
−0.0821359 | + | 0.996621i | \(0.526174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.92820 | − | 4.00000i | −0.579365 | − | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.803848 | + | 13.3923i | 0.0667559 | + | 1.11217i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | + | 6.00000i | 0.963863 | + | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73205 | + | 1.00000i | 0.138233 | + | 0.0798087i | 0.567521 | − | 0.823359i | \(-0.307902\pi\) |
−0.429289 | + | 0.903167i | \(0.641236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.7846 | + | 12.0000i | −1.62798 | + | 0.939913i | −0.643280 | + | 0.765631i | \(0.722427\pi\) |
−0.984696 | + | 0.174282i | \(0.944240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.92820 | + | 7.46410i | 0.383660 | + | 0.581080i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1244 | − | 7.00000i | 0.921798 | − | 0.532200i | 0.0375896 | − | 0.999293i | \(-0.488032\pi\) |
0.884208 | + | 0.467093i | \(0.154699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.46410 | − | 2.00000i | 0.260378 | − | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | + | 17.3205i | −0.747435 | + | 1.29460i | 0.201613 | + | 0.979465i | \(0.435382\pi\) |
−0.949048 | + | 0.315130i | \(0.897952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.92820 | − | 7.46410i | −0.362329 | − | 0.548772i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | + | 4.00000i | −0.506640 | + | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | − | 6.92820i | −0.289430 | − | 0.501307i | 0.684244 | − | 0.729253i | \(-0.260132\pi\) |
−0.973674 | + | 0.227946i | \(0.926799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7846 | − | 12.0000i | −1.49611 | − | 0.863779i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.00000 | + | 2.00000i | 0.286446 | + | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | − | 10.3923i | −0.423207 | − | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.19615 | − | 3.00000i | −0.361158 | − | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | − | 4.00000i | −0.474713 | − | 0.274075i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.92820 | + | 0.535898i | −0.608898 | + | 0.0365480i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | + | 3.46410i | −0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.0000i | − | 1.07144i | −0.844396 | − | 0.535720i | \(-0.820040\pi\) | ||
0.844396 | − | 0.535720i | \(-0.179960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.46410 | + | 2.00000i | 0.229920 | + | 0.132745i | 0.610535 | − | 0.791989i | \(-0.290954\pi\) |
−0.380615 | + | 0.924734i | \(0.624288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5885 | + | 9.00000i | −1.02123 | + | 0.589610i | −0.914461 | − | 0.404674i | \(-0.867385\pi\) |
−0.106773 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.92820 | + | 7.46410i | 0.321481 | + | 0.486904i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000i | 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.46410 | − | 2.00000i | 0.220416 | − | 0.127257i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.00000 | + | 13.8564i | −0.506979 | + | 0.878114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 24.0000i | − | 1.50887i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.73205 | − | 2.46410i | 0.233710 | − | 0.154308i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0526 | + | 11.0000i | −1.18847 | + | 0.686161i | −0.957958 | − | 0.286909i | \(-0.907372\pi\) |
−0.230508 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.9808 | − | 15.0000i | −1.60204 | − | 0.924940i | −0.991078 | − | 0.133281i | \(-0.957449\pi\) |
−0.610964 | − | 0.791658i | \(-0.709218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | − | 4.00000i | 0.122859 | − | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0000i | 0.979184i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | + | 3.46410i | −0.121942 | + | 0.211210i | −0.920534 | − | 0.390664i | \(-0.872246\pi\) |
0.798591 | + | 0.601874i | \(0.205579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | + | 19.0526i | 0.668202 | + | 1.15736i | 0.978406 | + | 0.206691i | \(0.0662693\pi\) |
−0.310204 | + | 0.950670i | \(0.600397\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.85641 | − | 18.3923i | 0.473759 | − | 1.10910i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.46410 | + | 2.00000i | 0.208138 | + | 0.120168i | 0.600446 | − | 0.799666i | \(-0.294990\pi\) |
−0.392308 | + | 0.919834i | \(0.628323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3205 | + | 10.0000i | 1.02960 | + | 0.594438i | 0.916869 | − | 0.399188i | \(-0.130708\pi\) |
0.112728 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.46410 | + | 0.267949i | −0.264431 | + | 0.0158719i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | + | 12.1244i | −0.410347 | + | 0.710742i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.0000i | − | 1.28525i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) | ||
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | − | 4.00000i | −0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.46410 | − | 2.00000i | −0.201008 | − | 0.116052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.92820 | + | 4.00000i | −0.398015 | + | 0.229794i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.73205 | − | 2.46410i | 0.213697 | − | 0.141094i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | − | 17.3205i | 0.567048 | − | 0.982156i | −0.429808 | − | 0.902920i | \(-0.641419\pi\) |
0.996856 | − | 0.0792356i | \(-0.0252479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0526 | − | 11.0000i | 1.07691 | − | 0.621757i | 0.146852 | − | 0.989158i | \(-0.453086\pi\) |
0.930062 | + | 0.367402i | \(0.119753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5167 | − | 13.0000i | 1.26466 | − | 0.730153i | 0.290689 | − | 0.956818i | \(-0.406116\pi\) |
0.973973 | + | 0.226665i | \(0.0727822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | − | 20.7846i | 0.671871 | − | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.19615 | − | 9.92820i | −0.0663506 | − | 0.550718i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.5885 | − | 9.00000i | 0.862044 | − | 0.497701i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | + | 20.7846i | 0.659580 | + | 1.14243i | 0.980725 | + | 0.195395i | \(0.0625990\pi\) |
−0.321145 | + | 0.947030i | \(0.604068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.46410 | + | 2.00000i | 0.189832 | + | 0.109599i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | + | 24.0000i | −0.655630 | + | 1.31126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | − | 20.7846i | −0.649836 | − | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.803848 | + | 13.3923i | 0.0432777 | + | 0.721017i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.66025 | + | 5.00000i | 0.464907 | + | 0.268414i | 0.714105 | − | 0.700038i | \(-0.246834\pi\) |
−0.249198 | + | 0.968452i | \(0.580167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.9808 | − | 15.0000i | −1.38282 | − | 0.798369i | −0.390324 | − | 0.920677i | \(-0.627637\pi\) |
−0.992492 | + | 0.122308i | \(0.960970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.07180 | + | 17.8564i | 0.0568851 | + | 0.947720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | + | 6.92820i | 0.211112 | + | 0.365657i | 0.952063 | − | 0.305903i | \(-0.0989582\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.00000i | − | 0.262432i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | + | 28.0000i | −0.732793 | + | 1.46559i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8564 | + | 8.00000i | 0.723299 | + | 0.417597i | 0.815966 | − | 0.578101i | \(-0.196206\pi\) |
−0.0926670 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7846 | + | 12.0000i | −1.07619 | + | 0.621336i | −0.929865 | − | 0.367901i | \(-0.880077\pi\) |
−0.146321 | + | 0.989237i | \(0.546743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.76795 | + | 10.5263i | −0.194576 | + | 0.543575i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3923 | − | 6.00000i | 0.531022 | − | 0.306586i | −0.210411 | − | 0.977613i | \(-0.567480\pi\) |
0.741433 | + | 0.671027i | \(0.234147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.46410 | − | 2.00000i | 0.176090 | − | 0.101666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.8564 | − | 19.7128i | 1.50224 | − | 0.991859i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4449 | − | 17.0000i | 1.47780 | − | 0.853206i | 0.478110 | − | 0.878300i | \(-0.341322\pi\) |
0.999685 | + | 0.0250943i | \(0.00798860\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | − | 6.00000i | −0.517678 | − | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0000i | 0.793091i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | + | 22.5167i | −0.642809 | + | 1.11338i | 0.341994 | + | 0.939702i | \(0.388898\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.00000 | + | 8.66025i | 0.246632 | + | 0.427179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.7128 | − | 2.14359i | 1.75307 | − | 0.105225i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1244 | + | 7.00000i | 0.593732 | + | 0.342791i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.46410 | − | 2.00000i | −0.168430 | − | 0.0972433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.19615 | − | 3.92820i | −0.446079 | − | 0.190546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | − | 6.92820i | −0.193122 | − | 0.334497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | − | 20.7846i | 0.578020 | − | 1.00116i | −0.417687 | − | 0.908591i | \(-0.637159\pi\) |
0.995706 | − | 0.0925683i | \(-0.0295076\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.0000i | − | 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | + | 12.0000i | −0.287678 | + | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3923 | + | 6.00000i | 0.497131 | + | 0.287019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.00000 | − | 5.19615i | −0.143182 | − | 0.247999i | 0.785511 | − | 0.618848i | \(-0.212400\pi\) |
−0.928693 | + | 0.370849i | \(0.879067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.19615 | + | 3.00000i | −0.246877 | + | 0.142534i | −0.618333 | − | 0.785916i | \(-0.712192\pi\) |
0.371457 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.8564 | − | 19.7128i | 1.41533 | − | 0.934477i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8564 | − | 8.00000i | 0.651031 | − | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2487 | − | 14.0000i | 1.13431 | − | 0.654892i | 0.189292 | − | 0.981921i | \(-0.439381\pi\) |
0.945015 | + | 0.327028i | \(0.106047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000i | 1.11537i | 0.830051 | + | 0.557687i | \(0.188311\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.39230 | + | 11.1962i | 0.342810 | + | 0.519209i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.2487 | + | 14.0000i | −1.12210 | + | 0.647843i | −0.941935 | − | 0.335794i | \(-0.890995\pi\) |
−0.180161 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | + | 1.73205i | 0.0460776 | + | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.8564 | + | 8.00000i | 0.637118 | + | 0.367840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | + | 8.00000i | 0.275299 | + | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.00000 | + | 3.46410i | −0.0913823 | + | 0.158279i | −0.908093 | − | 0.418769i | \(-0.862462\pi\) |
0.816711 | + | 0.577047i | \(0.195795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.2487 | − | 1.87564i | 1.41893 | − | 0.0851686i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3923 | − | 6.00000i | −0.470920 | − | 0.271886i | 0.245705 | − | 0.969345i | \(-0.420981\pi\) |
−0.716625 | + | 0.697459i | \(0.754314\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3923 | − | 6.00000i | −0.468046 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.535898 | + | 8.92820i | 0.0240868 | + | 0.401293i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | − | 3.46410i | −0.0895323 | − | 0.155074i | 0.817781 | − | 0.575529i | \(-0.195204\pi\) |
−0.907314 | + | 0.420455i | \(0.861871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.00000 | + | 6.92820i | −0.178707 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | + | 8.00000i | 0.711991 | + | 0.355995i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.79423 | + | 4.50000i | 0.346154 | + | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.0000 | − | 24.2487i | −0.620539 | − | 1.07481i | −0.989385 | − | 0.145315i | \(-0.953580\pi\) |
0.368846 | − | 0.929490i | \(-0.379753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.73205 | − | 1.00000i | 0.0764719 | − | 0.0441511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | + | 10.3923i | −0.262865 | + | 0.455295i | −0.967002 | − | 0.254769i | \(-0.918001\pi\) |
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3923 | − | 6.00000i | 0.454424 | − | 0.262362i | −0.255273 | − | 0.966869i | \(-0.582165\pi\) |
0.709697 | + | 0.704507i | \(0.248832\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3923 | + | 6.00000i | −0.452696 | + | 0.261364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.1769 | + | 33.5885i | 0.958792 | + | 1.45216i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.3205 | + | 10.0000i | −0.747435 | + | 0.431532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | − | 8.66025i | −0.214967 | − | 0.372333i | 0.738296 | − | 0.674477i | \(-0.235631\pi\) |
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0526 | + | 11.0000i | 0.817624 | + | 0.472055i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −36.0000 | − | 18.0000i | −1.54207 | − | 0.771035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | + | 1.73205i | −0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.535898 | − | 8.92820i | −0.0227476 | − | 0.378981i | ||||
\(556\) | 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 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7846 | − | 12.0000i | −0.875967 | − | 0.505740i | −0.00664037 | − | 0.999978i | \(-0.502114\pi\) |
−0.869326 | + | 0.494238i | \(0.835447\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3923 | + | 0.803848i | −0.563418 | + | 0.0338181i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | − | 6.92820i | 0.167395 | − | 0.289936i | −0.770108 | − | 0.637913i | \(-0.779798\pi\) |
0.937503 | + | 0.347977i | \(0.113131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.00000i | − | 0.334205i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5885 | − | 9.00000i | −0.648956 | − | 0.374675i | 0.139100 | − | 0.990278i | \(-0.455579\pi\) |
−0.788056 | + | 0.615603i | \(0.788912\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0000 | − | 20.7846i | −0.498703 | − | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.92820 | + | 4.00000i | −0.286937 | + | 0.165663i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46410 | + | 3.73205i | 0.101878 | + | 0.154301i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16.0000i | − | 0.660391i | −0.943913 | − | 0.330195i | \(-0.892885\pi\) | ||
0.943913 | − | 0.330195i | \(-0.107115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1244 | + | 7.00000i | −0.497888 | + | 0.287456i | −0.727841 | − | 0.685746i | \(-0.759476\pi\) |
0.229953 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.66025 | − | 5.00000i | 0.354441 | − | 0.204636i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.00000 | − | 6.92820i | 0.163436 | − | 0.283079i | −0.772663 | − | 0.634816i | \(-0.781076\pi\) |
0.936099 | + | 0.351738i | \(0.114409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.33013 | + | 6.16025i | −0.379324 | + | 0.250450i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.92820 | + | 4.00000i | −0.281207 | + | 0.162355i | −0.633970 | − | 0.773358i | \(-0.718576\pi\) |
0.352763 | + | 0.935713i | \(0.385242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | − | 6.92820i | −0.161823 | − | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.46410 | + | 2.00000i | 0.139914 | + | 0.0807792i | 0.568323 | − | 0.822806i | \(-0.307592\pi\) |
−0.428409 | + | 0.903585i | \(0.640926\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0000 | + | 25.9808i | −0.602901 | + | 1.04425i | 0.389479 | + | 0.921036i | \(0.372655\pi\) |
−0.992379 | + | 0.123219i | \(0.960678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.92820 | + | 4.00000i | 0.276686 | + | 0.159745i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | 0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.92820 | − | 4.00000i | −0.275371 | − | 0.158986i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.00000 | − | 6.92820i | −0.158238 | − | 0.274075i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000i | 0.157745i | 0.996885 | + | 0.0788723i | \(0.0251319\pi\) | ||||
−0.996885 | + | 0.0788723i | \(0.974868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | − | 4.00000i | −0.315000 | − | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.6410 | + | 20.0000i | 1.36188 | + | 0.786281i | 0.989874 | − | 0.141950i | \(-0.0453371\pi\) |
0.372005 | + | 0.928231i | \(0.378670\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | + | 13.8564i | 0.314027 | + | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5167 | + | 13.0000i | −0.881145 | + | 0.508729i | −0.871036 | − | 0.491220i | \(-0.836551\pi\) |
−0.0101092 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.46410 | + | 4.92820i | −0.291647 | + | 0.192561i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 14.0000i | − | 0.546192i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | − | 1.73205i | 0.0388955 | − | 0.0673690i | −0.845922 | − | 0.533306i | \(-0.820949\pi\) |
0.884818 | + | 0.465937i | \(0.154283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.46410 | + | 2.00000i | −0.134535 | + | 0.0776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1769 | − | 18.0000i | 1.20717 | − | 0.696963i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.598076 | − | 4.96410i | −0.0230200 | − | 0.191068i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.3731 | − | 21.0000i | 1.39793 | − | 0.807096i | 0.403755 | − | 0.914867i | \(-0.367705\pi\) |
0.994176 | + | 0.107772i | \(0.0343715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00000 | + | 3.46410i | 0.0766402 | + | 0.132745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1244 | + | 7.00000i | 0.463926 | + | 0.267848i | 0.713693 | − | 0.700458i | \(-0.247021\pi\) |
−0.249768 | + | 0.968306i | \(0.580354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | − | 20.0000i | 0.382080 | − | 0.764161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | + | 3.46410i | −0.0761939 | + | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0000 | − | 19.0526i | −0.418460 | − | 0.724793i | 0.577325 | − | 0.816514i | \(-0.304097\pi\) |
−0.995785 | + | 0.0917209i | \(0.970763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.87564 | − | 31.2487i | −0.0711472 | − | 1.18533i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.92820 | − | 4.00000i | −0.261302 | − | 0.150863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.535898 | + | 8.92820i | 0.0201831 | + | 0.336256i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | + | 13.8564i | −0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.0000i | − | 1.34821i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | + | 16.0000i | −0.299183 | + | 0.598366i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.92820 | − | 4.00000i | −0.258738 | − | 0.149383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.0000 | + | 24.2487i | 0.522112 | + | 0.904324i | 0.999669 | + | 0.0257237i | \(0.00818900\pi\) |
−0.477557 | + | 0.878601i | \(0.658478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.5167 | + | 13.0000i | −0.837404 | + | 0.483475i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.7846 | − | 3.58846i | 1.10617 | − | 0.133272i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.0000i | − | 0.593407i | −0.954970 | − | 0.296704i | \(-0.904113\pi\) | ||
0.954970 | − | 0.296704i | \(-0.0958873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.3731 | − | 21.0000i | 1.34347 | − | 0.775653i | 0.356155 | − | 0.934427i | \(-0.384088\pi\) |
0.987315 | + | 0.158774i | \(0.0507542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.5692 | − | 24.0000i | 1.53122 | − | 0.884051i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0000i | 1.24734i | 0.781688 | + | 0.623670i | \(0.214359\pi\) | ||||
−0.781688 | + | 0.623670i | \(0.785641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1962 | − | 7.39230i | 0.410195 | − | 0.270833i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8564 | + | 8.00000i | −0.506979 | + | 0.292705i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.3923 | − | 6.00000i | −0.378717 | − | 0.218652i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | − | 16.0000i | −1.16460 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.00000i | − | 0.290765i | −0.989376 | − | 0.145382i | \(-0.953559\pi\) | ||
0.989376 | − | 0.145382i | \(-0.0464413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0000 | − | 20.7846i | 0.435572 | − | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.46410 | − | 0.267949i | 0.161400 | − | 0.00968772i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92820 | + | 4.00000i | 0.250163 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0000 | −0.792311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.66025 | − | 5.00000i | −0.311488 | − | 0.179838i | 0.336104 | − | 0.941825i | \(-0.390891\pi\) |
−0.647592 | + | 0.761987i | \(0.724224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7846 | − | 27.5885i | 0.423316 | − | 0.991007i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00000 | − | 4.00000i | 0.0713831 | − | 0.142766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2487 | + | 14.0000i | 0.864373 | + | 0.499046i | 0.865474 | − | 0.500953i | \(-0.167017\pi\) |
−0.00110111 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0000 | − | 25.9808i | −0.534014 | − | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.46410 | + | 2.00000i | −0.123014 | + | 0.0710221i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.73205 | − | 2.46410i | 0.132362 | − | 0.0873927i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00000 | + | 13.8564i | −0.282666 | + | 0.489592i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.4974 | − | 28.0000i | 1.71144 | − | 0.988099i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.46410 | + | 2.00000i | −0.121942 | + | 0.0704033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | + | 15.5885i | −0.316423 | + | 0.548061i | −0.979739 | − | 0.200279i | \(-0.935815\pi\) |
0.663316 | + | 0.748340i | \(0.269149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0000i | 0.771574i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.5692 | + | 44.7846i | 1.03576 | + | 1.56874i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.92820 | + | 4.00000i | −0.242387 | + | 0.139942i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.00000 | + | 5.19615i | 0.104701 | + | 0.181347i | 0.913616 | − | 0.406578i | \(-0.133278\pi\) |
−0.808915 | + | 0.587925i | \(0.799945\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.92820 | − | 4.00000i | −0.241502 | − | 0.139431i | 0.374365 | − | 0.927281i | \(-0.377861\pi\) |
−0.615867 | + | 0.787850i | \(0.711194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.0000 | − | 12.0000i | 0.557048 | − | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0000i | 1.04320i | 0.853189 | + | 0.521601i | \(0.174665\pi\) | ||||
−0.853189 | + | 0.521601i | \(0.825335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000 | − | 32.9090i | 0.659897 | − | 1.14298i | −0.320745 | − | 0.947166i | \(-0.603933\pi\) |
0.980642 | − | 0.195810i | \(-0.0627335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.8564 | − | 1.07180i | 0.617946 | − | 0.0370911i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.19615 | − | 3.00000i | −0.179605 | − | 0.103695i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.0000 | 0.552381 | 0.276191 | − | 0.961103i | \(-0.410928\pi\) | ||||
0.276191 | + | 0.961103i | \(0.410928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.66025 | + | 5.00000i | 0.298275 | + | 0.172209i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.20577 | − | 20.0885i | −0.0414798 | − | 0.691064i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0000 | + | 17.3205i | 0.343199 | + | 0.594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.0000i | − | 0.890223i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||
0.895475 | − | 0.445112i | \(-0.146836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | − | 2.00000i | −0.136797 | − | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.66025 | − | 5.00000i | −0.295829 | − | 0.170797i | 0.344739 | − | 0.938699i | \(-0.387967\pi\) |
−0.640567 | + | 0.767902i | \(0.721301\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.00000 | − | 5.19615i | −0.102359 | − | 0.177290i | 0.810297 | − | 0.586019i | \(-0.199306\pi\) |
−0.912656 | + | 0.408729i | \(0.865972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.7654 | + | 27.0000i | −1.59191 | + | 0.919091i | −0.598933 | + | 0.800799i | \(0.704408\pi\) |
−0.992979 | + | 0.118291i | \(0.962258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.2487 | − | 26.1244i | −0.586474 | − | 0.888255i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −64.0000 | −2.17105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | − | 20.7846i | 0.406604 | − | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1244 | + | 7.00000i | −0.410347 | + | 0.236914i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.1769 | + | 18.0000i | −1.05277 | + | 0.607817i | −0.923423 | − | 0.383783i | \(-0.874621\pi\) |
−0.129346 | + | 0.991600i | \(0.541288\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.0000 | − | 19.0526i | 0.371021 | − | 0.642627i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.0000 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 56.0000i | − | 1.88455i | −0.334840 | − | 0.942275i | \(-0.608682\pi\) | ||
0.334840 | − | 0.942275i | \(-0.391318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.92820 | − | 7.46410i | −0.165660 | − | 0.250903i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3923 | + | 6.00000i | −0.348939 | + | 0.201460i | −0.664218 | − | 0.747539i | \(-0.731235\pi\) |
0.315279 | + | 0.948999i | \(0.397902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | − | 3.46410i | −0.0670025 | − | 0.116052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.92820 | + | 4.00000i | 0.231843 | + | 0.133855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.0000 | + | 20.0000i | 1.33705 | + | 0.668526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.0000i | − | 0.400668i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.0000 | − | 31.1769i | 0.600334 | − | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.00000 | + | 3.46410i | 0.0666297 | + | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.94744 | − | 49.1051i | −0.0979763 | − | 1.63231i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.92820 | − | 4.00000i | −0.230047 | − | 0.132818i | 0.380547 | − | 0.924762i | \(-0.375736\pi\) |
−0.610594 | + | 0.791944i | \(0.709069\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.4256 | − | 32.0000i | −1.83432 | − | 1.05905i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.46410 | − | 0.267949i | 0.147579 | − | 0.00885813i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | + | 17.3205i | 0.329870 | + | 0.571351i | 0.982486 | − | 0.186338i | \(-0.0596619\pi\) |
−0.652616 | + | 0.757689i | \(0.726329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | − | 3.46410i | 0.0659022 | − | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 16.0000i | − | 0.526646i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 12.0000i | −0.526077 | + | 0.394558i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0000 | + | 41.5692i | 0.787414 | + | 1.36384i | 0.927546 | + | 0.373709i | \(0.121914\pi\) |
−0.140132 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.3205 | − | 10.0000i | 0.567048 | − | 0.327385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.85641 | + | 14.9282i | 0.322339 | + | 0.488204i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.0000i | − | 0.326686i | −0.986569 | − | 0.163343i | \(-0.947772\pi\) | ||
0.986569 | − | 0.163343i | \(-0.0522277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.0000 | 0.717943 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | − | 51.9615i | 0.977972 | − | 1.69390i | 0.308215 | − | 0.951317i | \(-0.400268\pi\) |
0.669757 | − | 0.742581i | \(-0.266398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5885 | − | 9.00000i | 0.506557 | − | 0.292461i | −0.224860 | − | 0.974391i | \(-0.572193\pi\) |
0.731417 | + | 0.681930i | \(0.238859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000 | − | 24.2487i | 0.454459 | − | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.0000 | 0.843108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.9282 | + | 9.85641i | −0.483065 | + | 0.318946i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7846 | − | 12.0000i | 0.671871 | − | 0.387905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5885 | − | 9.00000i | −0.502331 | − | 0.290021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.0000 | + | 48.0000i | −0.772587 | + | 1.54517i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0000i | 1.15768i | 0.815440 | + | 0.578841i | \(0.196495\pi\) | ||||
−0.815440 | + | 0.578841i | \(0.803505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00000 | − | 3.46410i | 0.0642493 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.92820 | − | 9.19615i | 0.125803 | − | 0.294513i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.3731 | − | 21.0000i | −1.16368 | − | 0.671850i | −0.211495 | − | 0.977379i | \(-0.567833\pi\) |
−0.952183 | + | 0.305530i | \(0.901167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.0000 | −2.04545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | 0.574696 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.7846 | + | 12.0000i | 0.662926 | + | 0.382741i | 0.793391 | − | 0.608712i | \(-0.208314\pi\) |
−0.130465 | + | 0.991453i | \(0.541647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.1769 | + | 2.41154i | −1.28014 | + | 0.0768381i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0000 | + | 31.1769i | −0.571789 | + | 0.990367i | 0.424594 | + | 0.905384i | \(0.360417\pi\) |
−0.996382 | + | 0.0849833i | \(0.972916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000i | 0.761617i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0000 | − | 10.0000i | −0.634043 | − | 0.317021i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0526 | + | 11.0000i | 0.603401 | + | 0.348373i | 0.770378 | − | 0.637587i | \(-0.220067\pi\) |
−0.166978 | + | 0.985961i | \(0.553401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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 | 2940.2.bb.a.949.2 | 4 | ||
5.4 | even | 2 | inner | 2940.2.bb.a.949.1 | 4 | ||
7.2 | even | 3 | inner | 2940.2.bb.a.1549.1 | 4 | ||
7.3 | odd | 6 | 2940.2.k.b.589.2 | 2 | |||
7.4 | even | 3 | 420.2.k.b.169.1 | ✓ | 2 | ||
7.5 | odd | 6 | 2940.2.bb.f.1549.2 | 4 | |||
7.6 | odd | 2 | 2940.2.bb.f.949.1 | 4 | |||
21.11 | odd | 6 | 1260.2.k.a.1009.1 | 2 | |||
28.11 | odd | 6 | 1680.2.t.g.1009.2 | 2 | |||
35.4 | even | 6 | 420.2.k.b.169.2 | yes | 2 | ||
35.9 | even | 6 | inner | 2940.2.bb.a.1549.2 | 4 | ||
35.18 | odd | 12 | 2100.2.a.n.1.1 | 1 | |||
35.19 | odd | 6 | 2940.2.bb.f.1549.1 | 4 | |||
35.24 | odd | 6 | 2940.2.k.b.589.1 | 2 | |||
35.32 | odd | 12 | 2100.2.a.i.1.1 | 1 | |||
35.34 | odd | 2 | 2940.2.bb.f.949.2 | 4 | |||
84.11 | even | 6 | 5040.2.t.d.1009.1 | 2 | |||
105.32 | even | 12 | 6300.2.a.r.1.1 | 1 | |||
105.53 | even | 12 | 6300.2.a.b.1.1 | 1 | |||
105.74 | odd | 6 | 1260.2.k.a.1009.2 | 2 | |||
140.39 | odd | 6 | 1680.2.t.g.1009.1 | 2 | |||
140.67 | even | 12 | 8400.2.a.bm.1.1 | 1 | |||
140.123 | even | 12 | 8400.2.a.o.1.1 | 1 | |||
420.179 | even | 6 | 5040.2.t.d.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.k.b.169.1 | ✓ | 2 | 7.4 | even | 3 | ||
420.2.k.b.169.2 | yes | 2 | 35.4 | even | 6 | ||
1260.2.k.a.1009.1 | 2 | 21.11 | odd | 6 | |||
1260.2.k.a.1009.2 | 2 | 105.74 | odd | 6 | |||
1680.2.t.g.1009.1 | 2 | 140.39 | odd | 6 | |||
1680.2.t.g.1009.2 | 2 | 28.11 | odd | 6 | |||
2100.2.a.i.1.1 | 1 | 35.32 | odd | 12 | |||
2100.2.a.n.1.1 | 1 | 35.18 | odd | 12 | |||
2940.2.k.b.589.1 | 2 | 35.24 | odd | 6 | |||
2940.2.k.b.589.2 | 2 | 7.3 | odd | 6 | |||
2940.2.bb.a.949.1 | 4 | 5.4 | even | 2 | inner | ||
2940.2.bb.a.949.2 | 4 | 1.1 | even | 1 | trivial | ||
2940.2.bb.a.1549.1 | 4 | 7.2 | even | 3 | inner | ||
2940.2.bb.a.1549.2 | 4 | 35.9 | even | 6 | inner | ||
2940.2.bb.f.949.1 | 4 | 7.6 | odd | 2 | |||
2940.2.bb.f.949.2 | 4 | 35.34 | odd | 2 | |||
2940.2.bb.f.1549.1 | 4 | 35.19 | odd | 6 | |||
2940.2.bb.f.1549.2 | 4 | 7.5 | odd | 6 | |||
5040.2.t.d.1009.1 | 2 | 84.11 | even | 6 | |||
5040.2.t.d.1009.2 | 2 | 420.179 | even | 6 | |||
6300.2.a.b.1.1 | 1 | 105.53 | even | 12 | |||
6300.2.a.r.1.1 | 1 | 105.32 | even | 12 | |||
8400.2.a.o.1.1 | 1 | 140.123 | even | 12 | |||
8400.2.a.bm.1.1 | 1 | 140.67 | even | 12 |