Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,4,Mod(361,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.i (of order \(3\), 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: | \(57.8218718056\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 22x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-2.34521 - 4.06202i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.961 |
Dual form | 980.4.i.w.361.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.154792 | + | 0.268108i | 0.0297898 | + | 0.0515974i | 0.880536 | − | 0.473979i | \(-0.157183\pi\) |
−0.850746 | + | 0.525577i | \(0.823850\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.4521 | − | 23.2997i | 0.498225 | − | 0.862951i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.30958 | − | 14.3926i | −0.227767 | − | 0.394504i | 0.729379 | − | 0.684110i | \(-0.239809\pi\) |
−0.957146 | + | 0.289606i | \(0.906476\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 91.6658 | 1.95566 | 0.977828 | − | 0.209410i | \(-0.0671544\pi\) | ||||
0.977828 | + | 0.209410i | \(0.0671544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54792 | 0.0266448 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.8329 | + | 23.9593i | 0.197351 | + | 0.341823i | 0.947669 | − | 0.319255i | \(-0.103433\pi\) |
−0.750317 | + | 0.661078i | \(0.770099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 39.3096 | − | 68.0862i | 0.474644 | − | 0.822108i | −0.524934 | − | 0.851143i | \(-0.675910\pi\) |
0.999578 | + | 0.0290351i | \(0.00924346\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.4644 | + | 31.9812i | −0.167395 | + | 0.289937i | −0.937503 | − | 0.347976i | \(-0.886869\pi\) |
0.770108 | + | 0.637913i | \(0.220202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.6879 | 0.118948 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −209.285 | −1.34011 | −0.670056 | − | 0.742311i | \(-0.733730\pi\) | ||||
−0.670056 | + | 0.742311i | \(0.733730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 89.1425 | + | 154.399i | 0.516467 | + | 0.894546i | 0.999817 | + | 0.0191195i | \(0.00608631\pi\) |
−0.483351 | + | 0.875427i | \(0.660580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.57252 | − | 4.45573i | 0.0135702 | − | 0.0235043i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −68.5700 | + | 118.767i | −0.304671 | + | 0.527706i | −0.977188 | − | 0.212376i | \(-0.931880\pi\) |
0.672517 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.1891 | + | 24.5763i | 0.0582585 | + | 0.100907i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −225.806 | −0.860120 | −0.430060 | − | 0.902800i | \(-0.641508\pi\) | ||||
−0.430060 | + | 0.902800i | \(0.641508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 502.589 | 1.78242 | 0.891211 | − | 0.453588i | \(-0.149856\pi\) | ||||
0.891211 | + | 0.453588i | \(0.149856\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −67.2604 | − | 116.498i | −0.222813 | − | 0.385924i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 225.904 | − | 391.277i | 0.701096 | − | 1.21433i | −0.266986 | − | 0.963700i | \(-0.586028\pi\) |
0.968082 | − | 0.250633i | \(-0.0806389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.28245 | + | 7.41742i | −0.0117581 | + | 0.0203656i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −253.595 | − | 439.239i | −0.657243 | − | 1.13838i | −0.981326 | − | 0.192350i | \(-0.938389\pi\) |
0.324083 | − | 0.946029i | \(-0.394944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −83.0958 | −0.203721 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.3393 | 0.0565581 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −343.118 | − | 594.298i | −0.757121 | − | 1.31137i | −0.944313 | − | 0.329049i | \(-0.893272\pi\) |
0.187192 | − | 0.982323i | \(-0.440061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −275.950 | + | 477.959i | −0.579208 | + | 1.00322i | 0.416362 | + | 0.909199i | \(0.363305\pi\) |
−0.995570 | + | 0.0940196i | \(0.970028\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 229.165 | − | 396.925i | 0.437298 | − | 0.757422i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 90.7960 | + | 157.263i | 0.165560 | + | 0.286758i | 0.936854 | − | 0.349721i | \(-0.113724\pi\) |
−0.771294 | + | 0.636479i | \(0.780390\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.4326 | −0.0199466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 832.801 | 1.39205 | 0.696023 | − | 0.718020i | \(-0.254951\pi\) | ||||
0.696023 | + | 0.718020i | \(0.254951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −170.781 | − | 295.802i | −0.273814 | − | 0.474260i | 0.696021 | − | 0.718021i | \(-0.254952\pi\) |
−0.969835 | + | 0.243761i | \(0.921619\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.86980 | − | 6.70270i | 0.00595795 | − | 0.0103195i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −89.6930 | + | 155.353i | −0.127737 | + | 0.221247i | −0.922800 | − | 0.385280i | \(-0.874105\pi\) |
0.795062 | + | 0.606528i | \(0.207438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −360.623 | − | 624.617i | −0.494682 | − | 0.856814i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 708.108 | 0.936445 | 0.468222 | − | 0.883611i | \(-0.344895\pi\) | ||||
0.468222 | + | 0.883611i | \(0.344895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 138.329 | 0.176516 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32.3957 | − | 56.1109i | −0.0399216 | − | 0.0691463i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 434.446 | − | 752.482i | 0.517429 | − | 0.896213i | −0.482366 | − | 0.875970i | \(-0.660223\pi\) |
0.999795 | − | 0.0202433i | \(-0.00644407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.5971 | + | 47.7996i | −0.0307708 | + | 0.0532966i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −196.548 | − | 340.431i | −0.212267 | − | 0.367658i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 801.145 | 0.838597 | 0.419299 | − | 0.907848i | \(-0.362276\pi\) | ||||
0.419299 | + | 0.907848i | \(0.362276\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −447.125 | −0.453916 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 471.777 | + | 817.142i | 0.464788 | + | 0.805037i | 0.999192 | − | 0.0401926i | \(-0.0127972\pi\) |
−0.534404 | + | 0.845229i | \(0.679464\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 84.5848 | − | 146.505i | 0.0809164 | − | 0.140151i | −0.822727 | − | 0.568436i | \(-0.807549\pi\) |
0.903644 | + | 0.428285i | \(0.140882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −787.533 | + | 1364.05i | −0.711530 | + | 1.23241i | 0.252753 | + | 0.967531i | \(0.418664\pi\) |
−0.964283 | + | 0.264875i | \(0.914669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −458.525 | − | 794.188i | −0.402924 | − | 0.697884i | 0.591154 | − | 0.806559i | \(-0.298673\pi\) |
−0.994077 | + | 0.108675i | \(0.965339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −42.4564 | −0.0363043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −90.9042 | −0.0756774 | −0.0378387 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378387 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 92.3219 | + | 159.906i | 0.0748614 | + | 0.129664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1233.10 | − | 2135.78i | 0.974357 | − | 1.68764i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 527.402 | − | 913.486i | 0.396245 | − | 0.686316i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −34.9530 | − | 60.5403i | −0.0256228 | − | 0.0443800i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −300.762 | −0.210144 | −0.105072 | − | 0.994465i | \(-0.533507\pi\) | ||||
−0.105072 | + | 0.994465i | \(0.533507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 77.7969 | + | 134.748i | 0.0530979 | + | 0.0919683i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 460.472 | − | 797.560i | 0.307111 | − | 0.531933i | −0.670618 | − | 0.741803i | \(-0.733971\pi\) |
0.977729 | + | 0.209871i | \(0.0673043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 41.7197 | − | 72.2606i | 0.0265975 | − | 0.0460682i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1383.27 | − | 2395.90i | −0.862635 | − | 1.49413i | −0.869377 | − | 0.494150i | \(-0.835480\pi\) |
0.00674241 | − | 0.999977i | \(-0.497854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2735.74 | 1.66937 | 0.834686 | − | 0.550726i | \(-0.185649\pi\) | ||||
0.834686 | + | 0.550726i | \(0.185649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 139.873 | 0.0835419 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −761.705 | − | 1319.31i | −0.445433 | − | 0.771513i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −523.212 | + | 906.231i | −0.299658 | + | 0.519023i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1334.14 | + | 2310.80i | −0.733538 | + | 1.27052i | 0.221824 | + | 0.975087i | \(0.428799\pi\) |
−0.955362 | + | 0.295438i | \(0.904534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1153.28 | − | 1997.54i | −0.621540 | − | 1.07654i | −0.989199 | − | 0.146579i | \(-0.953174\pi\) |
0.367659 | − | 0.929961i | \(-0.380159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 744.326 | 0.393302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 891.425 | 0.461942 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −990.808 | − | 1716.13i | −0.503663 | − | 0.872370i | −0.999991 | − | 0.00423500i | \(-0.998652\pi\) |
0.496328 | − | 0.868135i | \(-0.334681\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 78.5089 | − | 135.981i | 0.0391582 | − | 0.0678241i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 541.580 | − | 938.044i | 0.260244 | − | 0.450756i | −0.706062 | − | 0.708150i | \(-0.749530\pi\) |
0.966307 | + | 0.257393i | \(0.0828635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.8626 | − | 22.2786i | −0.00606879 | − | 0.0105115i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1203.77 | −0.557789 | −0.278895 | − | 0.960322i | \(-0.589968\pi\) | ||||
−0.278895 | + | 0.960322i | \(0.589968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6205.62 | 2.82459 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1057.59 | − | 1831.80i | −0.472959 | − | 0.819189i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1341.90 | − | 2324.23i | 0.589725 | − | 1.02143i | −0.404543 | − | 0.914519i | \(-0.632569\pi\) |
0.994268 | − | 0.106915i | \(-0.0340974\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 106.224 | − | 183.985i | 0.0451089 | − | 0.0781309i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −31.1425 | − | 53.9404i | −0.0130039 | − | 0.0225234i | 0.859450 | − | 0.511219i | \(-0.170806\pi\) |
−0.872454 | + | 0.488696i | \(0.837473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −680.223 | −0.279340 | −0.139670 | − | 0.990198i | \(-0.544604\pi\) | ||||
−0.139670 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −170.859 | −0.0690179 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 342.850 | + | 593.833i | 0.136253 | + | 0.235997i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 229.891 | − | 398.184i | 0.0899002 | − | 0.155712i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 972.059 | − | 1683.65i | 0.368250 | − | 0.637827i | −0.621042 | − | 0.783777i | \(-0.713290\pi\) |
0.989292 | + | 0.145950i | \(0.0466238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −340.435 | − | 589.651i | −0.126969 | − | 0.219917i | 0.795532 | − | 0.605912i | \(-0.207192\pi\) |
−0.922501 | + | 0.385995i | \(0.873858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 141.891 | 0.0521080 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 323.259 | 0.116910 | 0.0584549 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584549 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1415.28 | + | 2451.34i | 0.504154 | + | 0.873221i | 0.999988 | + | 0.00480368i | \(0.00152906\pi\) |
−0.495834 | + | 0.868417i | \(0.665138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.1090 | + | 48.6862i | −0.00986397 | + | 0.0170849i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −564.514 | + | 977.768i | −0.192329 | + | 0.333123i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 496.768 | + | 860.428i | 0.166801 | + | 0.288908i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1306.59 | −0.432432 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2488.78 | 0.812013 | 0.406006 | − | 0.913870i | \(-0.366921\pi\) | ||||
0.406006 | + | 0.913870i | \(0.366921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 128.911 | + | 223.280i | 0.0414687 | + | 0.0718259i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1256.47 | − | 2176.28i | 0.398562 | − | 0.690329i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 52.8712 | − | 91.5755i | 0.0163137 | − | 0.0282562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1268.01 | + | 2196.25i | 0.385951 | + | 0.668487i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1994.33 | −0.598881 | −0.299440 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299440 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −672.604 | −0.199290 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 889.192 | + | 1540.13i | 0.259990 | + | 0.450316i | 0.966239 | − | 0.257648i | \(-0.0829474\pi\) |
−0.706249 | + | 0.707964i | \(0.749614\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −505.826 | + | 876.116i | −0.145965 | + | 0.252818i | −0.929732 | − | 0.368236i | \(-0.879962\pi\) |
0.783768 | + | 0.621054i | \(0.213295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1642.61 | + | 2845.09i | −0.461851 | + | 0.799949i | −0.999053 | − | 0.0435046i | \(-0.986148\pi\) |
0.537203 | + | 0.843453i | \(0.319481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1129.52 | − | 1956.39i | −0.313540 | − | 0.543067i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −55.5350 | −0.0152211 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3355.78 | −0.908231 | −0.454116 | − | 0.890943i | \(-0.650045\pi\) | ||||
−0.454116 | + | 0.890943i | \(0.650045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1446.38 | − | 2505.21i | −0.386596 | − | 0.669604i | 0.605393 | − | 0.795926i | \(-0.293016\pi\) |
−0.991989 | + | 0.126323i | \(0.959682\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 336.930 | − | 583.579i | 0.0889467 | − | 0.154060i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3603.35 | − | 6241.18i | 0.928240 | − | 1.60776i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 109.609 | + | 189.849i | 0.0278965 | + | 0.0483181i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6497.64 | 1.63397 | 0.816987 | − | 0.576656i | \(-0.195643\pi\) | ||||
0.816987 | + | 0.576656i | \(0.195643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 613.725 | 0.152508 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.4123 | + | 37.0871i | 0.00525838 | + | 0.00910778i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1129.37 | + | 1956.12i | −0.274116 | + | 0.474783i | −0.969912 | − | 0.243457i | \(-0.921719\pi\) |
0.695795 | + | 0.718240i | \(0.255052\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2815.32 | + | 4876.27i | −0.667677 | + | 1.15645i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −67.4499 | − | 116.827i | −0.0158142 | − | 0.0273910i | 0.858010 | − | 0.513633i | \(-0.171701\pi\) |
−0.873824 | + | 0.486242i | \(0.838367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2535.95 | −0.587856 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 268.995 | 0.0616563 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3265.28 | − | 5655.63i | −0.740102 | − | 1.28190i | −0.952448 | − | 0.304700i | \(-0.901444\pi\) |
0.212346 | − | 0.977195i | \(-0.431890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1073.74 | − | 1859.78i | 0.240683 | − | 0.416876i | −0.720226 | − | 0.693740i | \(-0.755962\pi\) |
0.960909 | + | 0.276864i | \(0.0892951\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −207.740 | + | 359.816i | −0.0455533 | + | 0.0789007i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3914.02 | − | 6779.28i | −0.848991 | − | 1.47050i | −0.882109 | − | 0.471045i | \(-0.843877\pi\) |
0.0331177 | − | 0.999451i | \(-0.489456\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4796.61 | 1.02927 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5934.49 | −1.25987 | −0.629933 | − | 0.776650i | \(-0.716917\pi\) | ||||
−0.629933 | + | 0.776650i | \(0.716917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2619.14 | + | 4536.48i | 0.550147 | + | 0.952882i | 0.998263 | + | 0.0589072i | \(0.0187616\pi\) |
−0.448117 | + | 0.893975i | \(0.647905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 60.8481 | − | 105.392i | 0.0126468 | − | 0.0219049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2073.80 | − | 3591.93i | 0.422105 | − | 0.731107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 124.011 | + | 214.793i | 0.0249816 | + | 0.0432694i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3564.95 | 0.710808 | 0.355404 | − | 0.934713i | \(-0.384343\pi\) | ||||
0.355404 | + | 0.934713i | \(0.384343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3431.18 | −0.677190 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −138.669 | − | 240.182i | −0.0270923 | − | 0.0469252i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1692.55 | + | 2931.59i | −0.327367 | + | 0.567017i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −146.055 | + | 252.974i | −0.0276919 | + | 0.0479637i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1379.75 | + | 2389.79i | 0.259030 | + | 0.448653i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5809.11 | −1.07995 | −0.539973 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539973 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.3723 | 0.00964192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 697.216 | + | 1207.61i | 0.127124 | + | 0.220185i | 0.922561 | − | 0.385851i | \(-0.126092\pi\) |
−0.795437 | + | 0.606036i | \(0.792759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2971.29 | + | 5146.43i | −0.536573 | + | 0.929372i | 0.462512 | + | 0.886613i | \(0.346948\pi\) |
−0.999085 | + | 0.0427590i | \(0.986385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −721.455 | + | 1249.60i | −0.127826 | + | 0.221402i | −0.922834 | − | 0.385197i | \(-0.874133\pi\) |
0.795008 | + | 0.606599i | \(0.207467\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1739.07 | + | 3012.16i | 0.305233 | + | 0.528679i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −487.616 | −0.0847852 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2175.06 | 0.374687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1145.82 | − | 1984.62i | −0.195566 | − | 0.338730i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 141.952 | − | 245.868i | 0.0240060 | − | 0.0415796i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2945.46 | + | 5101.68i | −0.489115 | + | 0.847171i | −0.999922 | − | 0.0125241i | \(-0.996013\pi\) |
0.510807 | + | 0.859695i | \(0.329347\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1844.82 | + | 3195.32i | 0.303590 | + | 0.525833i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 907.960 | 0.148081 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1326.63 | −0.214439 | −0.107220 | − | 0.994235i | \(-0.534195\pi\) | ||||
−0.107220 | + | 0.994235i | \(0.534195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0712 | − | 24.3721i | −0.00225441 | − | 0.00390475i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1481.47 | − | 2565.99i | 0.235268 | − | 0.407496i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28.5814 | + | 49.5044i | −0.00446021 | + | 0.00772530i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1102.49 | − | 1909.57i | −0.170562 | − | 0.295421i | 0.768055 | − | 0.640384i | \(-0.221225\pi\) |
−0.938616 | + | 0.344963i | \(0.887891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1792.52 | −0.274933 | −0.137466 | − | 0.990506i | \(-0.543896\pi\) | ||||
−0.137466 | + | 0.990506i | \(0.543896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1529.71 | 0.232620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3070.75 | + | 5318.70i | 0.463002 | + | 0.801943i | 0.999109 | − | 0.0422071i | \(-0.0134389\pi\) |
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2082.00 | − | 3606.13i | 0.311271 | − | 0.539137i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −67.6039 | + | 117.093i | −0.00993872 | + | 0.0172144i | −0.870952 | − | 0.491368i | \(-0.836497\pi\) |
0.861013 | + | 0.508582i | \(0.169830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 339.013 | + | 587.188i | 0.0494260 | + | 0.0856084i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 326.550 | 0.0472161 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1707.81 | −0.244907 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4566.68 | + | 7909.72i | 0.649533 | + | 1.12502i | 0.983234 | + | 0.182346i | \(0.0583690\pi\) |
−0.333701 | + | 0.942679i | \(0.608298\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3037.56 | + | 5261.20i | −0.428534 | + | 0.742242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3775.01 | + | 6538.50i | −0.524028 | + | 0.907643i | 0.475581 | + | 0.879672i | \(0.342238\pi\) |
−0.999609 | + | 0.0279712i | \(0.991095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.3490 | − | 33.5135i | −0.00266448 | − | 0.00461501i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19184.3 | −2.62080 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8444.21 | −1.14446 | −0.572229 | − | 0.820094i | \(-0.693921\pi\) | ||||
−0.572229 | + | 0.820094i | \(0.693921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.5555 | − | 80.6366i | −0.00626014 | − | 0.0108429i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6313.53 | + | 10935.3i | −0.842314 | + | 1.45893i | 0.0456204 | + | 0.998959i | \(0.485474\pi\) |
−0.887934 | + | 0.459971i | \(0.847860\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6760.87 | − | 11710.2i | 0.888048 | − | 1.53814i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7180.32 | + | 12436.7i | 0.935878 | + | 1.62099i | 0.773060 | + | 0.634333i | \(0.218725\pi\) |
0.162818 | + | 0.986656i | \(0.447942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1021.66 | −0.132143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 285.109 | 0.0365951 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 448.465 | + | 776.764i | 0.0571259 | + | 0.0989449i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −711.358 | + | 1232.11i | −0.0899296 | + | 0.155763i | −0.907481 | − | 0.420093i | \(-0.861998\pi\) |
0.817552 | + | 0.575855i | \(0.195331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2004.64 | − | 3472.14i | 0.249643 | − | 0.432395i | −0.713783 | − | 0.700366i | \(-0.753020\pi\) |
0.963427 | + | 0.267971i | \(0.0863533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8171.32 | + | 14153.1i | 1.01003 | + | 1.74942i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3606.23 | −0.442457 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2279.15 | 0.277576 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 84.2472 | + | 145.920i | 0.0101852 | + | 0.0176413i | 0.871073 | − | 0.491153i | \(-0.163425\pi\) |
−0.860888 | + | 0.508795i | \(0.830091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 428.239 | − | 741.732i | 0.0513953 | − | 0.0890193i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1770.27 | − | 3066.20i | 0.209395 | − | 0.362684i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 423.472 | + | 733.474i | 0.0497302 | + | 0.0861352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2861.16 | 0.333596 | 0.166798 | − | 0.985991i | \(-0.446657\pi\) | ||||
0.166798 | + | 0.985991i | \(0.446657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1135.73 | 0.131477 | 0.0657387 | − | 0.997837i | \(-0.479060\pi\) | ||||
0.0657387 | + | 0.997837i | \(0.479060\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6077.76 | − | 10527.0i | −0.698607 | − | 1.21002i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 345.823 | − | 598.983i | 0.0394703 | − | 0.0683645i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 235.812 | − | 408.438i | 0.0265387 | − | 0.0459664i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8150.59 | + | 14117.2i | 0.910905 | + | 1.57773i | 0.812788 | + | 0.582560i | \(0.197949\pi\) |
0.0981175 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5065.77 | 0.562230 | 0.281115 | − | 0.959674i | \(-0.409296\pi\) | ||||
0.281115 | + | 0.959674i | \(0.409296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −323.957 | −0.0357070 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1451.65 | + | 2514.34i | 0.158906 | + | 0.275234i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5026.07 | + | 8705.41i | −0.546427 | + | 0.946439i | 0.452089 | + | 0.891973i | \(0.350679\pi\) |
−0.998516 | + | 0.0544661i | \(0.982654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8646.73 | − | 14976.6i | 0.927356 | − | 1.60623i | 0.139628 | − | 0.990204i | \(-0.455409\pi\) |
0.787728 | − | 0.616024i | \(-0.211257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2172.23 | − | 3762.41i | −0.231401 | − | 0.400799i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −826.058 | −0.0874076 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10414.5 | 1.09463 | 0.547315 | − | 0.836927i | \(-0.315650\pi\) | ||||
0.547315 | + | 0.836927i | \(0.315650\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1876.35 | + | 3249.94i | 0.195907 | + | 0.339321i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 357.037 | − | 618.407i | 0.0370311 | − | 0.0641397i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −849.474 | + | 1471.33i | −0.0869513 | + | 0.150604i | −0.906221 | − | 0.422804i | \(-0.861046\pi\) |
0.819270 | + | 0.573408i | \(0.194379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 230.842 | + | 399.830i | 0.0234745 | + | 0.0406590i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3640.68 | 0.367817 | 0.183908 | − | 0.982943i | \(-0.441125\pi\) | ||||
0.183908 | + | 0.982943i | \(0.441125\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2701.96 | 0.271211 | 0.135605 | − | 0.990763i | \(-0.456702\pi\) | ||||
0.135605 | + | 0.990763i | \(0.456702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 137.986 | + | 238.998i | 0.0137611 | + | 0.0238350i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6223.49 | − | 10779.4i | 0.616678 | − | 1.06812i | −0.373409 | − | 0.927667i | \(-0.621811\pi\) |
0.990088 | − | 0.140452i | \(-0.0448554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 306.739 | − | 531.287i | 0.0300080 | − | 0.0519754i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4176.31 | − | 7233.58i | −0.405977 | − | 0.703172i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1965.48 | −0.189858 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13645.5 | −1.30982 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 111.809 | + | 193.659i | 0.0106653 | + | 0.0184729i | 0.871309 | − | 0.490735i | \(-0.163272\pi\) |
−0.860643 | + | 0.509208i | \(0.829938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6285.52 | + | 10886.8i | −0.595832 | + | 1.03201i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2002.86 | − | 3469.06i | 0.187516 | − | 0.324787i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3070.46 | + | 5318.18i | 0.285699 | + | 0.494846i | 0.972779 | − | 0.231737i | \(-0.0744408\pi\) |
−0.687079 | + | 0.726583i | \(0.741107\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 335.329 | 0.0310105 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16011.3 | −1.47165 | −0.735827 | − | 0.677170i | \(-0.763206\pi\) | ||||
−0.735827 | + | 0.677170i | \(0.763206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2895.02 | − | 5014.32i | −0.264473 | − | 0.458081i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1117.81 | + | 1936.11i | −0.101499 | + | 0.175801i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9323.69 | + | 16149.1i | −0.836444 | + | 1.44876i | 0.0564050 | + | 0.998408i | \(0.482036\pi\) |
−0.892849 | + | 0.450356i | \(0.851297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −186.335 | − | 322.741i | −0.0166164 | − | 0.0287805i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 149.768 | 0.0132760 | 0.00663800 | − | 0.999978i | \(-0.497887\pi\) | ||||
0.00663800 | + | 0.999978i | \(0.497887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4717.77 | 0.415719 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 960.581 | + | 1663.78i | 0.0841438 | + | 0.145741i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6014.68 | + | 10417.7i | −0.523764 | + | 0.907186i | 0.475853 | + | 0.879525i | \(0.342139\pi\) |
−0.999617 | + | 0.0276612i | \(0.991194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 655.994 | − | 1136.21i | 0.0564577 | − | 0.0977877i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −422.924 | − | 732.526i | −0.0361869 | − | 0.0626776i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7508.68 | −0.638745 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 830.860 | 0.0702711 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6052.09 | + | 10482.5i | 0.508919 | + | 0.881474i | 0.999947 | + | 0.0103300i | \(0.00328820\pi\) |
−0.491027 | + | 0.871144i | \(0.663378\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2081.15 | − | 3604.65i | 0.174000 | − | 0.301377i | −0.765815 | − | 0.643061i | \(-0.777664\pi\) |
0.939815 | + | 0.341684i | \(0.110997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2466.20 | + | 4271.58i | −0.203851 | + | 0.353080i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5401.63 | + | 9355.90i | 0.443958 | + | 0.768957i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18462.6 | −1.50887 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20698.7 | −1.68210 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3937.67 | + | 6820.24i | 0.318206 | + | 0.551149i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.64123 | − | 16.6991i | 0.000774766 | − | 0.00134193i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5551.37 | + | 9615.26i | −0.441168 | + | 0.764126i | −0.997776 | − | 0.0666491i | \(-0.978769\pi\) |
0.556608 | + | 0.830775i | \(0.312103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −105.293 | − | 182.373i | −0.00832148 | − | 0.0144132i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4585.25 | −0.360386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17160.3 | −1.34135 | −0.670677 | − | 0.741749i | \(-0.733996\pi\) | ||||
−0.670677 | + | 0.741749i | \(0.733996\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7424.19 | + | 12859.1i | 0.577152 | + | 0.999657i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8226.91 | + | 14249.4i | −0.636076 | + | 1.10172i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −106.141 | + | 183.841i | −0.00811789 | + | 0.0140606i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11108.1 | − | 19239.7i | −0.844997 | − | 1.46358i | −0.885624 | − | 0.464403i | \(-0.846269\pi\) |
0.0406273 | − | 0.999174i | \(-0.487064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46070.3 | 3.48581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 142.342 | 0.0107124 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4431.18 | − | 7675.03i | −0.331709 | − | 0.574536i | 0.651138 | − | 0.758959i | \(-0.274292\pi\) |
−0.982847 | + | 0.184423i | \(0.940958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −227.260 | + | 393.627i | −0.0169220 | + | 0.0293097i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10475.3 | + | 18143.8i | −0.771789 | + | 1.33678i | 0.164793 | + | 0.986328i | \(0.447304\pi\) |
−0.936582 | + | 0.350449i | \(0.886029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3895.39 | + | 6747.02i | 0.285494 | + | 0.494490i | 0.972729 | − | 0.231945i | \(-0.0745090\pi\) |
−0.687235 | + | 0.726435i | \(0.741176\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 601.868 | 0.0438803 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 923.219 | 0.0669581 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1231.40 | − | 2132.84i | −0.0888454 | − | 0.153885i | 0.818178 | − | 0.574965i | \(-0.194984\pi\) |
−0.907023 | + | 0.421080i | \(0.861651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 105.393 | − | 182.547i | 0.00756476 | − | 0.0131026i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4214.53 | + | 7299.78i | −0.299396 | + | 0.518570i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6165.48 | − | 10678.9i | −0.435746 | − | 0.754734i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20438.3 | −1.43710 | −0.718551 | − | 0.695475i | \(-0.755194\pi\) | ||||
−0.718551 | + | 0.695475i | \(0.755194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14016.6 | 0.980551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.0379 | + | 86.6682i | 0.00348271 | + | 0.00603224i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1341.34 | + | 2323.27i | −0.0928873 | + | 0.160886i | −0.908725 | − | 0.417396i | \(-0.862943\pi\) |
0.815838 | + | 0.578281i | \(0.196276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −438.149 | + | 758.897i | −0.0300373 | + | 0.0520261i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12842.9 | + | 22244.6i | 0.876039 | + | 1.51734i | 0.855652 | + | 0.517552i | \(0.173157\pi\) |
0.0203871 | + | 0.999792i | \(0.493510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6960.19 | −0.472400 | −0.236200 | − | 0.971705i | \(-0.575902\pi\) | ||||
−0.236200 | + | 0.971705i | \(0.575902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4885.58 | 0.329944 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2637.01 | − | 4567.43i | −0.177206 | − | 0.306930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13746.5 | − | 23809.7i | 0.919199 | − | 1.59210i | 0.118565 | − | 0.992946i | \(-0.462171\pi\) |
0.800634 | − | 0.599153i | \(-0.204496\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20707.7 | − | 35866.8i | 1.37110 | − | 2.37482i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7280.71 | + | 12610.6i | 0.479715 | + | 0.830890i | 0.999729 | − | 0.0232673i | \(-0.00740687\pi\) |
−0.520015 | + | 0.854157i | \(0.674074\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −349.530 | −0.0229177 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15433.9 | −1.00704 | −0.503522 | − | 0.863983i | \(-0.667963\pi\) | ||||
−0.503522 | + | 0.863983i | \(0.667963\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3792.25 | + | 6568.37i | 0.246241 | + | 0.426503i | 0.962480 | − | 0.271353i | \(-0.0874710\pi\) |
−0.716238 | + | 0.697856i | \(0.754138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −308.131 | + | 533.699i | −0.0199112 | + | 0.0344873i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −202.249 | − | 350.306i | −0.0128821 | − | 0.0223124i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3794.09 | −0.240509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14755.4 | 0.930905 | 0.465453 | − | 0.885073i | \(-0.345892\pi\) | ||||
0.465453 | + | 0.885073i | \(0.345892\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 385.244 | + | 667.261i | 0.0241897 | + | 0.0418977i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −751.904 | + | 1302.34i | −0.0469896 | + | 0.0813884i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11202.9 | − | 19404.0i | 0.693552 | − | 1.20127i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14418.3 | − | 24973.2i | −0.888438 | − | 1.53882i | −0.841722 | − | 0.539911i | \(-0.818458\pi\) |
−0.0467161 | − | 0.998908i | \(-0.514876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24838.4 | 1.52338 | 0.761689 | − | 0.647943i | \(-0.224371\pi\) | ||||
0.761689 | + | 0.647943i | \(0.224371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 777.969 | 0.0474922 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3594.13 | − | 6225.22i | −0.218392 | − | 0.378267i | 0.735924 | − | 0.677064i | \(-0.236748\pi\) |
−0.954317 | + | 0.298797i | \(0.903415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5702.33 | + | 9876.73i | −0.344894 | + | 0.597374i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3585.82 | + | 6210.83i | −0.214891 | + | 0.372203i | −0.953239 | − | 0.302218i | \(-0.902273\pi\) |
0.738348 | + | 0.674420i | \(0.235606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2302.36 | − | 3987.80i | −0.137344 | − | 0.237887i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9189.45 | −0.545684 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8236.07 | 0.486847 | 0.243423 | − | 0.969920i | \(-0.421730\pi\) | ||||
0.243423 | + | 0.969920i | \(0.421730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8487.12 | − | 14700.1i | −0.499411 | − | 0.865005i | 0.500589 | − | 0.865685i | \(-0.333117\pi\) |
−1.00000 | 0.000680243i | \(0.999783\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −392.554 | + | 679.924i | −0.0229948 | + | 0.0398282i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3864.32 | − | 6693.19i | 0.224328 | − | 0.388548i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −308.707 | − | 534.696i | −0.0178405 | − | 0.0309007i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9172.10 | 0.527698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16220.1 | 0.929032 | 0.464516 | − | 0.885565i | \(-0.346228\pi\) | ||||
0.464516 | + | 0.885565i | \(0.346228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −208.598 | − | 361.303i | −0.0118948 | − | 0.0206023i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3200.14 | − | 5542.80i | 0.181671 | − | 0.314664i | −0.760779 | − | 0.649011i | \(-0.775183\pi\) |
0.942450 | + | 0.334348i | \(0.108516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −275.280 | + | 476.798i | −0.0154901 | + | 0.0268296i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8278.16 | + | 14338.2i | 0.463770 | + | 0.803273i | 0.999145 | − | 0.0413413i | \(-0.0131631\pi\) |
−0.535375 | + | 0.844614i | \(0.679830\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13832.7 | −0.771564 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −313.192 | −0.0173930 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23246.0 | − | 40263.2i | −1.28534 | − | 2.22628i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3728.61 | + | 6458.15i | −0.205272 | + | 0.355542i | −0.950219 | − | 0.311581i | \(-0.899141\pi\) |
0.744947 | + | 0.667124i | \(0.232475\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6839.36 | − | 11846.1i | 0.373283 | − | 0.646545i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3123.55 | − | 5410.15i | −0.169746 | − | 0.294009i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1017.05 | −0.0550337 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26830.5 | 1.44561 | 0.722807 | − | 0.691050i | \(-0.242852\pi\) | ||||
0.722807 | + | 0.691050i | \(0.242852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5390.91 | + | 9337.34i | 0.289221 | + | 0.500945i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 349.682 | − | 605.667i | 0.0186805 | − | 0.0323556i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3604.94 | + | 6243.95i | −0.190954 | + | 0.330742i | −0.945567 | − | 0.325428i | \(-0.894492\pi\) |
0.754613 | + | 0.656171i | \(0.227825\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2413.11 | + | 4179.63i | 0.127284 | + | 0.220462i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6583.84 | −0.345816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7617.05 | −0.398408 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −519.448 | − | 899.710i | −0.0270560 | − | 0.0468623i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13975.8 | − | 24206.8i | 0.724908 | − | 1.25558i | −0.234104 | − | 0.972211i | \(-0.575216\pi\) |
0.959012 | − | 0.283365i | \(-0.0914509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 447.777 | − | 775.572i | 0.0230332 | − | 0.0398947i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2616.06 | + | 4531.15i | 0.134011 | + | 0.232114i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2492.55 | 0.127158 | 0.0635788 | − | 0.997977i | \(-0.479749\pi\) | ||||
0.0635788 | + | 0.997977i | \(0.479749\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19265.0 | −0.978765 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6952.28 | + | 12041.7i | 0.351764 | + | 0.609272i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5065.28 | + | 8773.32i | −0.255239 | + | 0.442087i | −0.964960 | − | 0.262395i | \(-0.915488\pi\) |
0.709721 | + | 0.704483i | \(0.248821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1508.95 | − | 2613.59i | 0.0754180 | − | 0.130628i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3660.25 | − | 6339.73i | −0.182198 | − | 0.315576i | 0.760431 | − | 0.649419i | \(-0.224988\pi\) |
−0.942629 | + | 0.333843i | \(0.891655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2231.08 | 0.110608 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16974.1 | 0.838116 | 0.419058 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419058 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6670.71 | + | 11554.0i | 0.328048 | + | 0.568196i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9525.52 | − | 16498.7i | 0.466560 | − | 0.808106i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8857.32 | + | 15341.3i | −0.430370 | + | 0.745423i | −0.996905 | − | 0.0786146i | \(-0.974950\pi\) |
0.566535 | + | 0.824038i | \(0.308284\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1005.78 | + | 1742.07i | 0.0486757 | + | 0.0843088i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11532.8 | −0.555923 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30171.9 | 1.44864 | 0.724318 | − | 0.689467i | \(-0.242155\pi\) | ||||
0.724318 | + | 0.689467i | \(0.242155\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 94.9998 | + | 164.545i | 0.00454318 | + | 0.00786902i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7211.78 | − | 12491.2i | 0.343531 | − | 0.595013i | −0.641555 | − | 0.767077i | \(-0.721710\pi\) |
0.985086 | + | 0.172064i | \(0.0550437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1860.81 | − | 3223.02i | 0.0879449 | − | 0.152325i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31452.2 | − | 54476.8i | −1.48067 | − | 2.56459i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21410.8 | 1.00402 | 0.502010 | − | 0.864862i | \(-0.332594\pi\) | ||||
0.502010 | + | 0.864862i | \(0.332594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −699.268 | −0.0326634 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13566.1 | + | 23497.1i | 0.631227 | + | 1.09332i | 0.987301 | + | 0.158859i | \(0.0507815\pi\) |
−0.356075 | + | 0.934457i | \(0.615885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2228.56 | − | 3859.98i | 0.103293 | − | 0.178909i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8876.33 | + | 15374.3i | −0.408251 | + | 0.707112i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6920.23 | − | 11986.2i | −0.317062 | − | 0.549167i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3492.52 | −0.159403 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9908.08 | −0.450490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6543.76 | + | 11334.1i | 0.296391 | + | 0.513364i | 0.975308 | − | 0.220851i | \(-0.0708835\pi\) |
−0.678917 | + | 0.734215i | \(0.737550\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.8814 | − | 36.1677i | 0.000942204 | − | 0.00163194i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25295.1 | + | 43812.5i | −1.13273 | + | 1.96195i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −392.544 | − | 679.907i | −0.0175121 | − | 0.0303318i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19398.5 | −0.862147 | −0.431074 | − | 0.902317i | \(-0.641865\pi\) | ||||
−0.431074 | + | 0.902317i | \(0.641865\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12499.6 | 0.553449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11688.4 | − | 20244.9i | −0.515592 | − | 0.893032i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2838.24 | + | 4915.98i | −0.124731 | + | 0.216041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1010.88 | − | 1750.89i | 0.0440949 | − | 0.0763747i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10792.0 | + | 18692.4i | 0.469008 | + | 0.812346i | 0.999372 | − | 0.0354238i | \(-0.0112781\pi\) |
−0.530364 | + | 0.847770i | \(0.677945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26798.2 | 1.16031 | 0.580156 | − | 0.814505i | \(-0.302991\pi\) | ||||
0.580156 | + | 0.814505i | \(0.302991\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 664.827 | 0.0286796 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2707.90 | − | 4690.22i | −0.116385 | − | 0.201584i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19756.6 | − | 34219.4i | 0.846016 | − | 1.46534i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1115.88 | + | 1932.75i | −0.0474352 | + | 0.0821602i | −0.888768 | − | 0.458357i | \(-0.848438\pi\) |
0.841333 | + | 0.540517i | \(0.181771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15084.3 | − | 26126.7i | −0.638888 | − | 1.10659i | −0.985677 | − | 0.168643i | \(-0.946061\pi\) |
0.346789 | − | 0.937943i | \(-0.387272\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −128.626 | −0.00542809 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18201.0 | −0.765310 | −0.382655 | − | 0.923891i | \(-0.624990\pi\) | ||||
−0.382655 | + | 0.923891i | \(0.624990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2428.84 | + | 4206.87i | 0.101758 | + | 0.176249i | 0.912409 | − | 0.409280i | \(-0.134220\pi\) |
−0.810651 | + | 0.585529i | \(0.800887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1211.72 | − | 2098.76i | 0.0505825 | − | 0.0876115i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3009.43 | + | 5212.49i | −0.124725 | + | 0.216031i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1487.60 | + | 2576.60i | 0.0614324 | + | 0.106404i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27903.8 | 1.14821 | 0.574104 | − | 0.818783i | \(-0.305351\pi\) | ||||
0.574104 | + | 0.818783i | \(0.305351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19411.2 | 0.795900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −918.613 | − | 1591.08i | −0.0375311 | − | 0.0650057i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15514.1 | − | 26871.1i | 0.631597 | − | 1.09396i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −810.844 | + | 1404.42i | −0.0327775 | + | 0.0567723i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2532.20 | − | 4385.91i | −0.102001 | − | 0.176671i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14219.1 | −0.570755 | −0.285377 | − | 0.958415i | \(-0.592119\pi\) | ||||
−0.285377 | + | 0.958415i | \(0.592119\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10575.9 | −0.423028 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7293.37 | − | 12632.5i | −0.290708 | − | 0.503521i | 0.683269 | − | 0.730166i | \(-0.260557\pi\) |
−0.973977 | + | 0.226646i | \(0.927224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13305.2 | + | 23045.2i | −0.528482 | + | 0.915358i | 0.470966 | + | 0.882151i | \(0.343905\pi\) |
−0.999448 | + | 0.0332070i | \(0.989428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2530.39 | − | 4382.77i | 0.0998095 | − | 0.172875i | −0.811796 | − | 0.583941i | \(-0.801510\pi\) |
0.911606 | + | 0.411066i | \(0.134843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6709.48 | − | 11621.2i | −0.263733 | − | 0.456799i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1284.03 | 0.0502976 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2981.24 | 0.116377 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8322.89 | + | 14415.7i | 0.323778 | + | 0.560800i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10777.1 | − | 18666.4i | 0.417810 | − | 0.723669i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13807.6 | − | 23915.5i | 0.531643 | − | 0.920832i | −0.467675 | − | 0.883900i | \(-0.654908\pi\) |
0.999318 | − | 0.0369317i | \(-0.0117584\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 551.827 | + | 955.792i | 0.0211748 | + | 0.0366758i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40580.4 | 1.55186 | 0.775931 | − | 0.630818i | \(-0.217281\pi\) | ||||
0.775931 | + | 0.630818i | \(0.217281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1567.20 | 0.0597289 | 0.0298645 | − | 0.999554i | \(-0.490492\pi\) | ||||
0.0298645 | + | 0.999554i | \(0.490492\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −531.119 | − | 919.926i | −0.0201733 | − | 0.0349412i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7576.55 | + | 13123.0i | −0.286805 | + | 0.496760i | −0.973045 | − | 0.230614i | \(-0.925926\pi\) |
0.686241 | + | 0.727375i | \(0.259260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5993.25 | + | 10380.6i | −0.225344 | + | 0.390307i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17760.4 | − | 30761.9i | −0.665542 | − | 1.15275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −311.425 | −0.0116310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1047.97 | −0.0390088 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18656.2 | − | 32313.5i | −0.692123 | − | 1.19879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7015.90 | − | 12151.9i | 0.259416 | − | 0.449321i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1700.56 | + | 2945.45i | −0.0624624 | + | 0.108188i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22828.8 | − | 39540.6i | −0.835741 | − | 1.44755i | −0.893425 | − | 0.449212i | \(-0.851705\pi\) |
0.0576841 | − | 0.998335i | \(-0.481628\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25385.5 | 0.926277 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12137.4 | −0.441417 | −0.220709 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220709 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5884.08 | − | 10191.5i | −0.213291 | − | 0.369431i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −427.148 | + | 739.842i | −0.0154329 | + | 0.0267305i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11352.0 | − | 19662.2i | 0.407473 | − | 0.705763i | −0.587133 | − | 0.809490i | \(-0.699744\pi\) |
0.994606 | + | 0.103727i | \(0.0330769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −899.204 | − | 1557.47i | −0.0321713 | − | 0.0557224i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 76339.4 | 2.72236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3428.50 | 0.121868 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2275.68 | − | 3941.60i | −0.0806292 | − | 0.139654i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5669.56 | + | 9819.97i | −0.200229 | + | 0.346806i | −0.948602 | − | 0.316472i | \(-0.897502\pi\) |
0.748373 | + | 0.663278i | \(0.230835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −215.847 | + | 373.858i | −0.00757398 | + | 0.0131185i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1149.46 | − | 1990.92i | −0.0402046 | − | 0.0696364i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52101.8 | −1.81653 | −0.908267 | − | 0.418391i | \(-0.862594\pi\) | ||||
−0.908267 | + | 0.418391i | \(0.862594\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1839.73 | −0.0639375 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22432.9 | − | 38855.0i | −0.777144 | − | 1.34605i | −0.933582 | − | 0.358365i | \(-0.883334\pi\) |
0.156438 | − | 0.987688i | \(-0.449999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4169.36 | − | 7221.55i | 0.143980 | − | 0.249381i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16044.2 | − | 27789.4i | 0.550547 | − | 0.953575i | −0.447688 | − | 0.894190i | \(-0.647753\pi\) |
0.998235 | − | 0.0593855i | \(-0.0189141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15654.8 | − | 27114.9i | −0.535486 | − | 0.927489i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −446.702 | −0.0152317 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17825.8 | 0.605913 | 0.302957 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302957 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4860.29 | − | 8418.27i | −0.164686 | − | 0.285245i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −538.389 | + | 932.517i | −0.0181856 | + | 0.0314984i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −997.269 | + | 1727.32i | −0.0334755 | + | 0.0579813i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21187.9 | + | 36698.5i | 0.709004 | + | 1.22803i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3404.35 | −0.113565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34128.6 | 1.13495 | 0.567477 | − | 0.823389i | \(-0.307920\pi\) | ||||
0.567477 | + | 0.823389i | \(0.307920\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 336.683 | + | 583.152i | 0.0111618 | + | 0.0193328i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21040.9 | − | 36443.9i | 0.695401 | − | 1.20447i | −0.274645 | − | 0.961546i | \(-0.588560\pi\) |
0.970045 | − | 0.242924i | \(-0.0781065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 354.729 | − | 614.408i | 0.0116517 | − | 0.0201813i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 400.588 | + | 693.839i | 0.0131177 | + | 0.0227204i | 0.872510 | − | 0.488597i | \(-0.162491\pi\) |
−0.859392 | + | 0.511317i | \(0.829158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14440.3 | −0.471412 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24672.4 | −0.802987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.48329 | + | 7.76529i | 0.000145468 | + | 0.000251957i | 0.866098 | − | 0.499874i | \(-0.166620\pi\) |
−0.865953 | + | 0.500126i | \(0.833287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 808.147 | − | 1399.75i | 0.0261418 | − | 0.0452790i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9280.00 | + | 16073.4i | −0.298369 | + | 0.516790i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4405.91 | + | 7631.26i | 0.141229 | + | 0.244617i | 0.927960 | − | 0.372680i | \(-0.121561\pi\) |
−0.786730 | + | 0.617297i | \(0.788228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1823.73 | −0.0582824 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14152.8 | 0.450929 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28762.5 | + | 49818.1i | 0.913658 | + | 1.58250i | 0.808854 | + | 0.588009i | \(0.200088\pi\) |
0.104804 | + | 0.994493i | \(0.466578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1144.29 | + | 1981.96i | −0.0362399 | + | 0.0627693i |
(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 | 980.4.i.w.961.1 | 4 | ||
7.2 | even | 3 | 980.4.a.n.1.2 | 2 | |||
7.3 | odd | 6 | 140.4.i.c.81.2 | ✓ | 4 | ||
7.4 | even | 3 | inner | 980.4.i.w.361.1 | 4 | ||
7.5 | odd | 6 | 980.4.a.u.1.1 | 2 | |||
7.6 | odd | 2 | 140.4.i.c.121.2 | yes | 4 | ||
21.17 | even | 6 | 1260.4.s.e.361.1 | 4 | |||
21.20 | even | 2 | 1260.4.s.e.541.1 | 4 | |||
28.3 | even | 6 | 560.4.q.l.81.1 | 4 | |||
28.27 | even | 2 | 560.4.q.l.401.1 | 4 | |||
35.3 | even | 12 | 700.4.r.f.249.2 | 8 | |||
35.13 | even | 4 | 700.4.r.f.149.3 | 8 | |||
35.17 | even | 12 | 700.4.r.f.249.3 | 8 | |||
35.24 | odd | 6 | 700.4.i.h.501.1 | 4 | |||
35.27 | even | 4 | 700.4.r.f.149.2 | 8 | |||
35.34 | odd | 2 | 700.4.i.h.401.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.4.i.c.81.2 | ✓ | 4 | 7.3 | odd | 6 | ||
140.4.i.c.121.2 | yes | 4 | 7.6 | odd | 2 | ||
560.4.q.l.81.1 | 4 | 28.3 | even | 6 | |||
560.4.q.l.401.1 | 4 | 28.27 | even | 2 | |||
700.4.i.h.401.1 | 4 | 35.34 | odd | 2 | |||
700.4.i.h.501.1 | 4 | 35.24 | odd | 6 | |||
700.4.r.f.149.2 | 8 | 35.27 | even | 4 | |||
700.4.r.f.149.3 | 8 | 35.13 | even | 4 | |||
700.4.r.f.249.2 | 8 | 35.3 | even | 12 | |||
700.4.r.f.249.3 | 8 | 35.17 | even | 12 | |||
980.4.a.n.1.2 | 2 | 7.2 | even | 3 | |||
980.4.a.u.1.1 | 2 | 7.5 | odd | 6 | |||
980.4.i.w.361.1 | 4 | 7.4 | even | 3 | inner | ||
980.4.i.w.961.1 | 4 | 1.1 | even | 1 | trivial | ||
1260.4.s.e.361.1 | 4 | 21.17 | even | 6 | |||
1260.4.s.e.541.1 | 4 | 21.20 | even | 2 |