Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.2 | ||
Root | \(1.78012 + 0.911682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.223 |
Dual form | 384.3.l.a.31.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00772 | + | 1.00772i | −0.201544 | + | 0.201544i | −0.800661 | − | 0.599117i | \(-0.795518\pi\) |
0.599117 | + | 0.800661i | \(0.295518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0236 | 1.43194 | 0.715969 | − | 0.698133i | \(-0.245985\pi\) | ||||
0.715969 | + | 0.698133i | \(0.245985\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.26517 | − | 2.26517i | −0.205925 | − | 0.205925i | 0.596608 | − | 0.802533i | \(-0.296515\pi\) |
−0.802533 | + | 0.596608i | \(0.796515\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.88229 | + | 6.88229i | 0.529407 | + | 0.529407i | 0.920395 | − | 0.390989i | \(-0.127867\pi\) |
−0.390989 | + | 0.920395i | \(0.627867\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.46840i | − | 0.164560i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.3801 | −1.31648 | −0.658240 | − | 0.752809i | \(-0.728699\pi\) | ||||
−0.658240 | + | 0.752809i | \(0.728699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.8918 | − | 16.8918i | 0.889041 | − | 0.889041i | −0.105390 | − | 0.994431i | \(-0.533609\pi\) |
0.994431 | + | 0.105390i | \(0.0336092\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.2763 | + | 12.2763i | −0.584586 | + | 0.584586i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.2007 | 1.44351 | 0.721755 | − | 0.692149i | \(-0.243336\pi\) | ||||
0.721755 | + | 0.692149i | \(0.243336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.9690i | 0.918760i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.6412 | + | 24.6412i | 0.849696 | + | 0.849696i | 0.990095 | − | 0.140399i | \(-0.0448385\pi\) |
−0.140399 | + | 0.990095i | \(0.544839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.3761i | 1.33471i | 0.744738 | + | 0.667357i | \(0.232574\pi\) | ||||
−0.744738 | + | 0.667357i | \(0.767426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.54852 | 0.168137 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.1010 | + | 10.1010i | −0.288599 | + | 0.288599i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.60031 | − | 6.60031i | 0.178387 | − | 0.178387i | −0.612266 | − | 0.790652i | \(-0.709742\pi\) |
0.790652 | + | 0.612266i | \(0.209742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.8581 | −0.432259 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 47.1477i | 1.14994i | 0.818173 | + | 0.574972i | \(0.194987\pi\) | ||||
−0.818173 | + | 0.574972i | \(0.805013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.8218 | + | 48.8218i | 1.13539 | + | 1.13539i | 0.989266 | + | 0.146124i | \(0.0466799\pi\) |
0.146124 | + | 0.989266i | \(0.453320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.02316 | + | 3.02316i | 0.0671814 | + | 0.0671814i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 45.6048i | − | 0.970315i | −0.874427 | − | 0.485157i | \(-0.838762\pi\) | ||
0.874427 | − | 0.485157i | \(-0.161238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 51.4717 | 1.05044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 27.4100 | − | 27.4100i | 0.537450 | − | 0.537450i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −25.1401 | + | 25.1401i | −0.474341 | + | 0.474341i | −0.903316 | − | 0.428975i | \(-0.858875\pi\) |
0.428975 | + | 0.903316i | \(0.358875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.56532 | 0.0830059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 41.3762i | 0.725899i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.23974 | − | 6.23974i | −0.105758 | − | 0.105758i | 0.652248 | − | 0.758006i | \(-0.273826\pi\) |
−0.758006 | + | 0.652248i | \(0.773826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.9513 | − | 35.9513i | −0.589366 | − | 0.589366i | 0.348093 | − | 0.937460i | \(-0.386829\pi\) |
−0.937460 | + | 0.348093i | \(0.886829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 30.0707i | − | 0.477312i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.8709 | −0.213398 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2045 | + | 10.2045i | −0.152307 | + | 0.152307i | −0.779147 | − | 0.626841i | \(-0.784348\pi\) |
0.626841 | + | 0.779147i | \(0.284348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −40.6624 | + | 40.6624i | −0.589310 | + | 0.589310i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9529 | 0.168350 | 0.0841752 | − | 0.996451i | \(-0.473174\pi\) | ||||
0.0841752 | + | 0.996451i | \(0.473174\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 111.332i | − | 1.52510i | −0.646929 | − | 0.762550i | \(-0.723947\pi\) | ||
0.646929 | − | 0.762550i | \(-0.276053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −28.1312 | − | 28.1312i | −0.375082 | − | 0.375082i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.7051 | − | 22.7051i | −0.294871 | − | 0.294871i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.46031i | − | 0.0564596i | −0.999601 | − | 0.0282298i | \(-0.991013\pi\) | ||
0.999601 | − | 0.0282298i | \(-0.00898702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1751 | + | 10.1751i | −0.122592 | + | 0.122592i | −0.765741 | − | 0.643149i | \(-0.777627\pi\) |
0.643149 | + | 0.765741i | \(0.277627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.5530 | − | 22.5530i | 0.265329 | − | 0.265329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −60.3583 | −0.693774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 21.9364i | 0.246476i | 0.992377 | + | 0.123238i | \(0.0393279\pi\) | ||||
−0.992377 | + | 0.123238i | \(0.960672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 68.9850 | + | 68.9850i | 0.758077 | + | 0.758077i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −50.6752 | − | 50.6752i | −0.544895 | − | 0.544895i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34.0444i | 0.358362i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 107.309 | 1.10628 | 0.553140 | − | 0.833088i | \(-0.313429\pi\) | ||||
0.553140 | + | 0.833088i | \(0.313429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.79552 | + | 6.79552i | −0.0686416 | + | 0.0686416i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 100.780 | − | 100.780i | 0.997824 | − | 0.997824i | −0.00217389 | − | 0.999998i | \(-0.500692\pi\) |
0.999998 | + | 0.00217389i | \(0.000691973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.0562 | 0.563653 | 0.281826 | − | 0.959465i | \(-0.409060\pi\) | ||||
0.281826 | + | 0.959465i | \(0.409060\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 24.7422i | − | 0.235640i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −112.747 | − | 112.747i | −1.05371 | − | 1.05371i | −0.998473 | − | 0.0552381i | \(-0.982408\pi\) |
−0.0552381 | − | 0.998473i | \(-0.517592\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81.1384 | + | 81.1384i | 0.744389 | + | 0.744389i | 0.973419 | − | 0.229030i | \(-0.0735554\pi\) |
−0.229030 | + | 0.973419i | \(0.573555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.1674i | 0.145652i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −171.844 | −1.52074 | −0.760371 | − | 0.649489i | \(-0.774983\pi\) | ||||
−0.760371 | + | 0.649489i | \(0.774983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −33.4571 | + | 33.4571i | −0.290931 | + | 0.290931i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.6469 | − | 20.6469i | 0.176469 | − | 0.176469i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −224.329 | −1.88512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 110.738i | − | 0.915190i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −57.7439 | − | 57.7439i | −0.469463 | − | 0.469463i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −48.3394 | − | 48.3394i | −0.386715 | − | 0.386715i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.8333i | 0.290026i | 0.989430 | + | 0.145013i | \(0.0463224\pi\) | ||||
−0.989430 | + | 0.145013i | \(0.953678\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −119.588 | −0.927042 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.3686 | − | 12.3686i | 0.0944170 | − | 0.0944170i | −0.658321 | − | 0.752738i | \(-0.728733\pi\) |
0.752738 | + | 0.658321i | \(0.228733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 169.316 | − | 169.316i | 1.27305 | − | 1.27305i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.40521 | −0.0548534 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 145.679i | − | 1.06335i | −0.846949 | − | 0.531674i | \(-0.821563\pi\) | ||
0.846949 | − | 0.531674i | \(-0.178437\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.5709 | − | 82.5709i | −0.594035 | − | 0.594035i | 0.344684 | − | 0.938719i | \(-0.387986\pi\) |
−0.938719 | + | 0.344684i | \(0.887986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 55.8542 | + | 55.8542i | 0.396129 | + | 0.396129i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 31.1791i | − | 0.218036i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −49.6629 | −0.342503 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −63.0398 | + | 63.0398i | −0.428842 | + | 0.428842i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −196.248 | + | 196.248i | −1.31710 | + | 1.31710i | −0.401043 | + | 0.916059i | \(0.631352\pi\) |
−0.916059 | + | 0.401043i | \(0.868648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 64.5007 | 0.427157 | 0.213578 | − | 0.976926i | \(-0.431488\pi\) | ||||
0.213578 | + | 0.976926i | \(0.431488\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 67.1404i | 0.438826i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −41.6956 | − | 41.6956i | −0.269004 | − | 0.269004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −54.4202 | − | 54.4202i | −0.346625 | − | 0.346625i | 0.512226 | − | 0.858851i | \(-0.328821\pi\) |
−0.858851 | + | 0.512226i | \(0.828821\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 61.5803i | − | 0.387298i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 332.789 | 2.06701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −104.803 | + | 104.803i | −0.642961 | + | 0.642961i | −0.951282 | − | 0.308321i | \(-0.900233\pi\) |
0.308321 | + | 0.951282i | \(0.400233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.59136 | + | 5.59136i | −0.0338870 | + | 0.0338870i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 53.3110 | 0.319228 | 0.159614 | − | 0.987180i | \(-0.448975\pi\) | ||||
0.159614 | + | 0.987180i | \(0.448975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 74.2683i | − | 0.439457i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −50.6753 | − | 50.6753i | −0.296347 | − | 0.296347i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 41.5780 | + | 41.5780i | 0.240335 | + | 0.240335i | 0.816989 | − | 0.576654i | \(-0.195642\pi\) |
−0.576654 | + | 0.816989i | \(0.695642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 230.231i | 1.31561i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.2842 | 0.0863513 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −53.0709 | + | 53.0709i | −0.296486 | + | 0.296486i | −0.839636 | − | 0.543150i | \(-0.817231\pi\) |
0.543150 | + | 0.839636i | \(0.317231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 66.6042 | − | 66.6042i | 0.367979 | − | 0.367979i | −0.498761 | − | 0.866740i | \(-0.666211\pi\) |
0.866740 | + | 0.498761i | \(0.166211\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 88.0625 | 0.481216 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.3025i | 0.0719056i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 50.6949 | + | 50.6949i | 0.271096 | + | 0.271096i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 36.8289 | + | 36.8289i | 0.194862 | + | 0.194862i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 113.753i | − | 0.595567i | −0.954633 | − | 0.297784i | \(-0.903753\pi\) | ||
0.954633 | − | 0.297784i | \(-0.0962474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.5596 | −0.137615 | −0.0688073 | − | 0.997630i | \(-0.521919\pi\) | ||||
−0.0688073 | + | 0.997630i | \(0.521919\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.9883 | − | 16.9883i | 0.0871193 | − | 0.0871193i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −51.8935 | + | 51.8935i | −0.263419 | + | 0.263419i | −0.826442 | − | 0.563023i | \(-0.809638\pi\) |
0.563023 | + | 0.826442i | \(0.309638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −136.741 | −0.687140 | −0.343570 | − | 0.939127i | \(-0.611636\pi\) | ||||
−0.343570 | + | 0.939127i | \(0.611636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 24.9959i | − | 0.124358i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 246.992 | + | 246.992i | 1.21671 | + | 1.21671i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −47.5118 | − | 47.5118i | −0.231765 | − | 0.231765i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 99.6022i | − | 0.481170i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −76.5255 | −0.366151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.171 | − | 141.171i | 0.669057 | − | 0.669057i | −0.288441 | − | 0.957498i | \(-0.593137\pi\) |
0.957498 | + | 0.288441i | \(0.0931368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.6392 | + | 14.6392i | −0.0687288 | + | 0.0687288i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −98.3975 | −0.457663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 414.736i | 1.91123i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 136.354 | + | 136.354i | 0.622620 | + | 0.622620i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −154.027 | − | 154.027i | −0.696953 | − | 0.696953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 122.607i | − | 0.549806i | −0.961472 | − | 0.274903i | \(-0.911354\pi\) | ||
0.961472 | − | 0.274903i | \(-0.0886457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 68.9070 | 0.306253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 295.844 | − | 295.844i | 1.30328 | − | 1.30328i | 0.377112 | − | 0.926168i | \(-0.376917\pi\) |
0.926168 | − | 0.377112i | \(-0.123083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.3817 | + | 73.3817i | −0.320444 | + | 0.320444i | −0.848937 | − | 0.528493i | \(-0.822757\pi\) |
0.528493 | + | 0.848937i | \(0.322757\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 55.6159 | 0.240761 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 156.229i | 0.670509i | 0.942128 | + | 0.335255i | \(0.108822\pi\) | ||||
−0.942128 | + | 0.335255i | \(0.891178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 45.9569 | + | 45.9569i | 0.195561 | + | 0.195561i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.46274 | + | 5.46274i | 0.0230495 | + | 0.0230495i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.1716i | − | 0.0551113i | −0.999620 | − | 0.0275557i | \(-0.991228\pi\) | ||
0.999620 | − | 0.0275557i | \(-0.00877235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −189.519 | −0.786386 | −0.393193 | − | 0.919456i | \(-0.628630\pi\) | ||||
−0.393193 | + | 0.919456i | \(0.628630\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −51.8692 | + | 51.8692i | −0.211711 | + | 0.211711i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 232.508 | 0.941328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 24.9238i | − | 0.100096i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.4434 | + | 27.4434i | 0.109336 | + | 0.109336i | 0.759658 | − | 0.650322i | \(-0.225366\pi\) |
−0.650322 | + | 0.759658i | \(0.725366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −75.2053 | − | 75.2053i | −0.297254 | − | 0.297254i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 55.2432i | 0.216640i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 135.375 | 0.526752 | 0.263376 | − | 0.964693i | \(-0.415164\pi\) | ||||
0.263376 | + | 0.964693i | \(0.415164\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 66.1586 | − | 66.1586i | 0.255438 | − | 0.255438i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.9236 | − | 73.9236i | 0.283232 | − | 0.283232i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.6123 | 0.120199 | 0.0600994 | − | 0.998192i | \(-0.480858\pi\) | ||||
0.0600994 | + | 0.998192i | \(0.480858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 50.6684i | − | 0.191201i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.8665 | − | 26.8665i | −0.100624 | − | 0.100624i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 194.213 | + | 194.213i | 0.721981 | + | 0.721981i | 0.969008 | − | 0.247028i | \(-0.0794538\pi\) |
−0.247028 | + | 0.969008i | \(0.579454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 291.647i | − | 1.07619i | −0.842884 | − | 0.538095i | \(-0.819144\pi\) | ||
0.842884 | − | 0.538095i | \(-0.180856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −168.978 | −0.618967 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 52.0287 | − | 52.0287i | 0.189195 | − | 0.189195i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −305.166 | + | 305.166i | −1.10168 | + | 1.10168i | −0.107475 | + | 0.994208i | \(0.534277\pi\) |
−0.994208 | + | 0.107475i | \(0.965723\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 124.128 | 0.444905 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 211.861i | 0.753955i | 0.926222 | + | 0.376978i | \(0.123037\pi\) | ||||
−0.926222 | + | 0.376978i | \(0.876963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −105.325 | − | 105.325i | −0.372175 | − | 0.372175i | 0.496094 | − | 0.868269i | \(-0.334767\pi\) |
−0.868269 | + | 0.496094i | \(0.834767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −41.6957 | − | 41.6957i | −0.146301 | − | 0.146301i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 472.588i | 1.64665i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 211.871 | 0.733117 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −131.426 | + | 131.426i | −0.451637 | + | 0.451637i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 171.289 | − | 171.289i | 0.584603 | − | 0.584603i | −0.351562 | − | 0.936165i | \(-0.614349\pi\) |
0.936165 | + | 0.351562i | \(0.114349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.5758 | 0.0426300 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 16.6455i | − | 0.0560456i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 228.497 | + | 228.497i | 0.764204 | + | 0.764204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 489.368 | + | 489.368i | 1.62581 | + | 1.62581i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 246.860i | 0.814720i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 72.4579 | 0.237567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.1124 | − | 27.1124i | 0.0883140 | − | 0.0883140i | −0.661570 | − | 0.749884i | \(-0.730109\pi\) |
0.749884 | + | 0.661570i | \(0.230109\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −71.1041 | + | 71.1041i | −0.230110 | + | 0.230110i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 371.124 | 1.19333 | 0.596663 | − | 0.802492i | \(-0.296493\pi\) | ||||
0.596663 | + | 0.802492i | \(0.296493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 374.501i | 1.19649i | 0.801313 | + | 0.598245i | \(0.204135\pi\) | ||||
−0.801313 | + | 0.598245i | \(0.795865\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.3029 | + | 30.3029i | 0.0961996 | + | 0.0961996i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 48.5840 | + | 48.5840i | 0.153262 | + | 0.153262i | 0.779573 | − | 0.626311i | \(-0.215436\pi\) |
−0.626311 | + | 0.779573i | \(0.715436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 111.633i | − | 0.349947i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 276.173 | 0.860352 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −378.040 | + | 378.040i | −1.17040 | + | 1.17040i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −158.079 | + | 158.079i | −0.486398 | + | 0.486398i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −198.748 | −0.607791 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 457.122i | − | 1.38943i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.88883 | + | 1.88883i | 0.00570644 | + | 0.00570644i | 0.709954 | − | 0.704248i | \(-0.248716\pi\) |
−0.704248 | + | 0.709954i | \(0.748716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.8009 | − | 19.8009i | −0.0594622 | − | 0.0594622i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 20.5667i | − | 0.0613931i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −386.980 | −1.14831 | −0.574154 | − | 0.818747i | \(-0.694669\pi\) | ||||
−0.574154 | + | 0.818747i | \(0.694669\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 210.465 | − | 210.465i | 0.620840 | − | 0.620840i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 93.7240 | − | 93.7240i | 0.274851 | − | 0.274851i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.7757 | 0.0722325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 81.9528i | − | 0.237544i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −441.887 | − | 441.887i | −1.27345 | − | 1.27345i | −0.944266 | − | 0.329183i | \(-0.893227\pi\) |
−0.329183 | − | 0.944266i | \(-0.606773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −119.382 | − | 119.382i | −0.342068 | − | 0.342068i | 0.515076 | − | 0.857144i | \(-0.327764\pi\) |
−0.857144 | + | 0.515076i | \(0.827764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 50.5743i | 0.144086i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −515.642 | −1.46074 | −0.730371 | − | 0.683050i | \(-0.760653\pi\) | ||||
−0.730371 | + | 0.683050i | \(0.760653\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0452 | + | 12.0452i | −0.0339301 | + | 0.0339301i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 274.745 | − | 274.745i | 0.769595 | − | 0.769595i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 428.264 | 1.19294 | 0.596468 | − | 0.802637i | \(-0.296570\pi\) | ||||
0.596468 | + | 0.802637i | \(0.296570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 209.664i | − | 0.580786i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 135.626 | + | 135.626i | 0.373625 | + | 0.373625i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 112.192 | + | 112.192i | 0.307375 | + | 0.307375i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 219.482i | − | 0.598043i | −0.954246 | − | 0.299021i | \(-0.903340\pi\) | ||
0.954246 | − | 0.299021i | \(-0.0966602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 141.443 | 0.383315 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −251.993 | + | 251.993i | −0.679226 | + | 0.679226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −425.005 | + | 425.005i | −1.13942 | + | 1.13942i | −0.150870 | + | 0.988554i | \(0.548207\pi\) |
−0.988554 | + | 0.150870i | \(0.951793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 118.407 | 0.315752 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 339.175i | 0.899669i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −365.916 | − | 365.916i | −0.965476 | − | 0.965476i | 0.0339473 | − | 0.999424i | \(-0.489192\pi\) |
−0.999424 | + | 0.0339473i | \(0.989192\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.1114 | − | 45.1114i | −0.118403 | − | 0.118403i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 213.276i | − | 0.556857i | −0.960457 | − | 0.278428i | \(-0.910187\pi\) | ||
0.960457 | − | 0.278428i | \(-0.0898135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.7608 | 0.118859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 146.465 | − | 146.465i | 0.378464 | − | 0.378464i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 210.798 | − | 210.798i | 0.541898 | − | 0.541898i | −0.382187 | − | 0.924085i | \(-0.624829\pi\) |
0.924085 | + | 0.382187i | \(0.124829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −743.037 | −1.90035 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.2968i | 0.0770912i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.49475 | + | 4.49475i | 0.0113791 | + | 0.0113791i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −392.907 | − | 392.907i | −0.989690 | − | 0.989690i | 0.0102579 | − | 0.999947i | \(-0.496735\pi\) |
−0.999947 | + | 0.0102579i | \(0.996735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 414.737i | 1.03944i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3290 | 0.0731396 | 0.0365698 | − | 0.999331i | \(-0.488357\pi\) | ||||
0.0365698 | + | 0.999331i | \(0.488357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −284.762 | + | 284.762i | −0.706606 | + | 0.706606i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.06949 | − | 9.06949i | 0.0223938 | − | 0.0223938i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.9017 | −0.0734684 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 601.115i | − | 1.46972i | −0.678219 | − | 0.734860i | \(-0.737248\pi\) | ||
0.678219 | − | 0.734860i | \(-0.262752\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 178.419 | + | 178.419i | 0.434110 | + | 0.434110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −62.5444 | − | 62.5444i | −0.151439 | − | 0.151439i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.5073i | − | 0.0494153i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 202.257 | 0.485028 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 518.885 | − | 518.885i | 1.23839 | − | 1.23839i | 0.277729 | − | 0.960659i | \(-0.410418\pi\) |
0.960659 | − | 0.277729i | \(-0.0895819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 411.213 | − | 411.213i | 0.976754 | − | 0.976754i | −0.0229817 | − | 0.999736i | \(-0.507316\pi\) |
0.999736 | + | 0.0229817i | \(0.00731596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −136.814 | −0.323438 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 514.049i | − | 1.20953i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −360.360 | − | 360.360i | −0.843936 | − | 0.843936i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.1865 | + | 38.1865i | 0.0890128 | + | 0.0890128i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 41.1083i | − | 0.0953789i | −0.998862 | − | 0.0476895i | \(-0.984814\pi\) | ||
0.998862 | − | 0.0476895i | \(-0.0151858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −351.682 | −0.812199 | −0.406100 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406100 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 60.8244 | − | 60.8244i | 0.139826 | − | 0.139826i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 560.819 | − | 560.819i | 1.28334 | − | 1.28334i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −775.613 | −1.76677 | −0.883386 | − | 0.468646i | \(-0.844742\pi\) | ||||
−0.883386 | + | 0.468646i | \(0.844742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 154.415i | − | 0.350148i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 241.372 | + | 241.372i | 0.544858 | + | 0.544858i | 0.924949 | − | 0.380091i | \(-0.124107\pi\) |
−0.380091 | + | 0.924949i | \(0.624107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.1058 | − | 22.1058i | −0.0496759 | − | 0.0496759i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 480.708i | − | 1.07541i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 266.360 | 0.593228 | 0.296614 | − | 0.954997i | \(-0.404142\pi\) | ||||
0.296614 | + | 0.954997i | \(0.404142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 106.798 | − | 106.798i | 0.236802 | − | 0.236802i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −78.9969 | + | 78.9969i | −0.174386 | + | 0.174386i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −139.035 | −0.305572 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 515.244i | 1.12745i | 0.825963 | + | 0.563725i | \(0.190632\pi\) | ||||
−0.825963 | + | 0.563725i | \(0.809368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −82.2299 | − | 82.2299i | −0.179150 | − | 0.179150i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.67717 | − | 5.67717i | −0.0123149 | − | 0.0123149i | 0.700923 | − | 0.713237i | \(-0.252772\pi\) |
−0.713237 | + | 0.700923i | \(0.752772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 464.510i | 1.00326i | 0.865082 | + | 0.501631i | \(0.167267\pi\) | ||||
−0.865082 | + | 0.501631i | \(0.832733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 102.133 | 0.219641 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −495.985 | + | 495.985i | −1.06207 | + | 1.06207i | −0.0641248 | + | 0.997942i | \(0.520426\pi\) |
−0.997942 | + | 0.0641248i | \(0.979574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −102.286 | + | 102.286i | −0.218094 | + | 0.218094i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 133.302 | 0.283018 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 221.180i | − | 0.467610i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 387.987 | + | 387.987i | 0.816815 | + | 0.816815i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 75.4202 | + | 75.4202i | 0.158114 | + | 0.158114i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 378.802i | 0.790818i | 0.918505 | + | 0.395409i | \(0.129397\pi\) | ||||
−0.918505 | + | 0.395409i | \(0.870603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 90.8504 | 0.188878 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −407.582 | + | 407.582i | −0.843855 | + | 0.843855i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −108.138 | + | 108.138i | −0.222964 | + | 0.222964i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 147.446 | 0.302764 | 0.151382 | − | 0.988475i | \(-0.451628\pi\) | ||||
0.151382 | + | 0.988475i | \(0.451628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 256.713i | − | 0.524976i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −109.547 | − | 109.547i | −0.223110 | − | 0.223110i | 0.586697 | − | 0.809807i | \(-0.300428\pi\) |
−0.809807 | + | 0.586697i | \(0.800428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −551.473 | − | 551.473i | −1.11861 | − | 1.11861i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 13.6960i | − | 0.0276686i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 119.810 | 0.241067 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 360.523 | − | 360.523i | 0.722491 | − | 0.722491i | −0.246621 | − | 0.969112i | \(-0.579320\pi\) |
0.969112 | + | 0.246621i | \(0.0793202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −65.2924 | + | 65.2924i | −0.130324 | + | 0.130324i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −927.420 | −1.84378 | −0.921889 | − | 0.387454i | \(-0.873355\pi\) | ||||
−0.921889 | + | 0.387454i | \(0.873355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 203.117i | 0.402211i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 90.9597 | + | 90.9597i | 0.179408 | + | 0.179408i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −677.931 | − | 677.931i | −1.33189 | − | 1.33189i | −0.903680 | − | 0.428208i | \(-0.859145\pi\) |
−0.428208 | − | 0.903680i | \(-0.640855\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1115.95i | − | 2.18385i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 124.129 | 0.241966 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −58.5045 | + | 58.5045i | −0.113601 | + | 0.113601i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −103.303 | + | 103.303i | −0.199812 | + | 0.199812i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −101.845 | −0.196233 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 143.173i | 0.274804i | 0.990515 | + | 0.137402i | \(0.0438753\pi\) | ||||
−0.990515 | + | 0.137402i | \(0.956125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −226.187 | − | 226.187i | −0.432481 | − | 0.432481i | 0.456991 | − | 0.889471i | \(-0.348927\pi\) |
−0.889471 | + | 0.456991i | \(0.848927\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −281.974 | − | 281.974i | −0.537094 | − | 0.537094i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 926.004i | − | 1.75712i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 573.288 | 1.08372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.7192 | + | 18.7192i | −0.0352528 | + | 0.0352528i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −324.484 | + | 324.484i | −0.608788 | + | 0.608788i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 227.235 | 0.424739 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 129.997i | − | 0.242080i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −116.592 | − | 116.592i | −0.216312 | − | 0.216312i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 156.708 | + | 156.708i | 0.289663 | + | 0.289663i | 0.836947 | − | 0.547284i | \(-0.184338\pi\) |
−0.547284 | + | 0.836947i | \(0.684338\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 163.146i | 0.300454i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −163.530 | −0.300055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −247.357 | + | 247.357i | −0.452207 | + | 0.452207i | −0.896086 | − | 0.443880i | \(-0.853602\pi\) |
0.443880 | + | 0.896086i | \(0.353602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −107.854 | + | 107.854i | −0.196455 | + | 0.196455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 832.466 | 1.51083 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 44.7082i | − | 0.0808466i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.2922 | − | 16.2922i | −0.0293553 | − | 0.0293553i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 661.193 | + | 661.193i | 1.18706 | + | 1.18706i | 0.977876 | + | 0.209184i | \(0.0670808\pi\) |
0.209184 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 672.011i | 1.20217i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −124.177 | −0.221349 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −246.685 | + | 246.685i | −0.438162 | + | 0.438162i | −0.891393 | − | 0.453231i | \(-0.850271\pi\) |
0.453231 | + | 0.891393i | \(0.350271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 173.171 | − | 173.171i | 0.306497 | − | 0.306497i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −90.2120 | −0.159104 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 243.567i | 0.428061i | 0.976827 | + | 0.214030i | \(0.0686592\pi\) | ||||
−0.976827 | + | 0.214030i | \(0.931341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −59.9229 | − | 59.9229i | −0.104944 | − | 0.104944i | 0.652685 | − | 0.757629i | \(-0.273642\pi\) |
−0.757629 | + | 0.652685i | \(0.773642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 139.319 | + | 139.319i | 0.243139 | + | 0.243139i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 762.587i | 1.32624i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 136.609 | 0.236757 | 0.118378 | − | 0.992969i | \(-0.462230\pi\) | ||||
0.118378 | + | 0.992969i | \(0.462230\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32.5287 | − | 32.5287i | 0.0561809 | − | 0.0561809i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −101.991 | + | 101.991i | −0.175543 | + | 0.175543i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 113.893 | 0.195357 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 41.6126i | 0.0711326i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 331.817 | + | 331.817i | 0.565276 | + | 0.565276i | 0.930801 | − | 0.365525i | \(-0.119111\pi\) |
−0.365525 | + | 0.930801i | \(0.619111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 698.916 | + | 698.916i | 1.18661 | + | 1.18661i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 127.113i | − | 0.215081i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 131.285 | 0.221391 | 0.110695 | − | 0.993854i | \(-0.464692\pi\) | ||||
0.110695 | + | 0.993854i | \(0.464692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 226.061 | − | 226.061i | 0.379934 | − | 0.379934i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 167.473 | − | 167.473i | 0.280524 | − | 0.280524i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −136.119 | −0.227243 | −0.113621 | − | 0.993524i | \(-0.536245\pi\) | ||||
−0.113621 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 498.566i | 0.829561i | 0.909922 | + | 0.414780i | \(0.136142\pi\) | ||||
−0.909922 | + | 0.414780i | \(0.863858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.6136 | + | 30.6136i | 0.0507689 | + | 0.0507689i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 111.593 | + | 111.593i | 0.184451 | + | 0.184451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 568.740i | 0.936969i | 0.883472 | + | 0.468484i | \(0.155200\pi\) | ||||
−0.883472 | + | 0.468484i | \(0.844800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −605.005 | −0.993441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 313.865 | − | 313.865i | 0.513691 | − | 0.513691i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 168.441 | − | 168.441i | 0.274782 | − | 0.274782i | −0.556240 | − | 0.831022i | \(-0.687756\pi\) |
0.831022 | + | 0.556240i | \(0.187756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 116.380 | 0.189235 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 599.157i | − | 0.971081i | −0.874214 | − | 0.485541i | \(-0.838623\pi\) | ||
0.874214 | − | 0.485541i | \(-0.161377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −126.719 | − | 126.719i | −0.204715 | − | 0.204715i | 0.597301 | − | 0.802017i | \(-0.296240\pi\) |
−0.802017 | + | 0.597301i | \(0.796240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 121.987 | + | 121.987i | 0.196437 | + | 0.196437i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 219.881i | 0.352939i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −476.800 | −0.762879 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 93.7242 | − | 93.7242i | 0.149480 | − | 0.149480i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −147.716 | + | 147.716i | −0.234842 | + | 0.234842i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 668.283 | 1.05909 | 0.529543 | − | 0.848283i | \(-0.322363\pi\) | ||||
0.529543 | + | 0.848283i | \(0.322363\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 345.797i | 0.546283i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.1177 | − | 37.1177i | −0.0584531 | − | 0.0584531i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 354.243 | + | 354.243i | 0.556112 | + | 0.556112i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 35.8586i | − | 0.0561168i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 484.574 | 0.755966 | 0.377983 | − | 0.925813i | \(-0.376618\pi\) | ||||
0.377983 | + | 0.925813i | \(0.376618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −75.2980 | + | 75.2980i | −0.117104 | + | 0.117104i | −0.763230 | − | 0.646126i | \(-0.776388\pi\) |
0.646126 | + | 0.763230i | \(0.276388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 120.512 | − | 120.512i | 0.186840 | − | 0.186840i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −582.307 | −0.900011 | −0.450006 | − | 0.893026i | \(-0.648578\pi\) | ||||
−0.450006 | + | 0.893026i | \(0.648578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.2682i | 0.0435565i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −507.946 | − | 507.946i | −0.780255 | − | 0.780255i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −457.453 | − | 457.453i | −0.700541 | − | 0.700541i | 0.263986 | − | 0.964527i | \(-0.414963\pi\) |
−0.964527 | + | 0.263986i | \(0.914963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.9283i | 0.0380584i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −333.997 | −0.508367 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 430.079 | − | 430.079i | 0.652623 | − | 0.652623i | −0.301001 | − | 0.953624i | \(-0.597321\pi\) |
0.953624 | + | 0.301001i | \(0.0973207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 513.622 | − | 513.622i | 0.777038 | − | 0.777038i | −0.202288 | − | 0.979326i | \(-0.564838\pi\) |
0.979326 | + | 0.202288i | \(0.0648376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 377.287 | 0.569060 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 341.246i | 0.513152i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 818.105 | + | 818.105i | 1.22654 | + | 1.22654i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 150.162 | + | 150.162i | 0.224457 | + | 0.224457i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 162.872i | 0.242730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1112.68 | −1.65332 | −0.826659 | − | 0.562703i | \(-0.809761\pi\) | ||||
−0.826659 | + | 0.562703i | \(0.809761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −84.3935 | + | 84.3935i | −0.125027 | + | 0.125027i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −633.271 | + | 633.271i | −0.935408 | + | 0.935408i | −0.998037 | − | 0.0626291i | \(-0.980051\pi\) |
0.0626291 | + | 0.998037i | \(0.480051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1075.62 | 1.58412 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 724.668i | 1.06412i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 429.651 | + | 429.651i | 0.629065 | + | 0.629065i | 0.947833 | − | 0.318768i | \(-0.103269\pi\) |
−0.318768 | + | 0.947833i | \(0.603269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 146.803 | + | 146.803i | 0.214312 | + | 0.214312i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 179.748i | − | 0.261642i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −346.042 | −0.502239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 151.617 | − | 151.617i | 0.219417 | − | 0.219417i | −0.588836 | − | 0.808253i | \(-0.700414\pi\) |
0.808253 | + | 0.588836i | \(0.200414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −68.1153 | + | 68.1153i | −0.0982904 | + | 0.0982904i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 166.417 | 0.239449 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1055.17i | − | 1.51388i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −191.340 | − | 191.340i | −0.273734 | − | 0.273734i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 920.704 | + | 920.704i | 1.31341 | + | 1.31341i | 0.918882 | + | 0.394533i | \(0.129094\pi\) |
0.394533 | + | 0.918882i | \(0.370906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 222.982i | − | 0.317186i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −112.571 | −0.159675 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1010.18 | − | 1010.18i | 1.42882 | − | 1.42882i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −405.348 | + | 405.348i | −0.571718 | + | 0.571718i | −0.932608 | − | 0.360890i | \(-0.882473\pi\) |
0.360890 | + | 0.932608i | \(0.382473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3809 | −0.0188199 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1373.72i | 1.92667i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.4199 | + | 31.4199i | 0.0439439 | + | 0.0439439i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.1319 | + | 16.1319i | 0.0224991 | + | 0.0224991i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 880.704i | − | 1.22490i | −0.790509 | − | 0.612450i | \(-0.790184\pi\) | ||
0.790509 | − | 0.612450i | \(-0.209816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 581.930 | 0.807115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 232.112 | − | 232.112i | 0.321041 | − | 0.321041i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −565.983 | + | 565.983i | −0.780667 | + | 0.780667i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1000.46 | 1.37615 | 0.688077 | − | 0.725637i | \(-0.258455\pi\) | ||||
0.688077 | + | 0.725637i | \(0.258455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1092.64 | − | 1092.64i | −1.49472 | − | 1.49472i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −540.306 | − | 540.306i | −0.737116 | − | 0.737116i | 0.234903 | − | 0.972019i | \(-0.424523\pi\) |
−0.972019 | + | 0.234903i | \(0.924523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 127.053i | − | 0.172861i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46.2301 | 0.0627274 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −893.726 | + | 893.726i | −1.20937 | + | 1.20937i | −0.238142 | + | 0.971230i | \(0.576538\pi\) |
−0.971230 | + | 0.238142i | \(0.923462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −284.763 | + | 284.763i | −0.384296 | + | 0.384296i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1295.75 | 1.74394 | 0.871969 | − | 0.489561i | \(-0.162843\pi\) | ||||
0.871969 | + | 0.489561i | \(0.162843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 395.527i | − | 0.530909i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.5253 | + | 30.5253i | 0.0408639 | + | 0.0408639i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1130.13 | − | 1130.13i | −1.50885 | − | 1.50885i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 229.818i | 0.306016i | 0.988225 | + | 0.153008i | \(0.0488961\pi\) | ||||
−0.988225 | + | 0.153008i | \(0.951104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −67.2223 | −0.0892726 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64.9987 | + | 64.9987i | −0.0860910 | + | 0.0860910i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 373.678 | − | 373.678i | 0.493630 | − | 0.493630i | −0.415818 | − | 0.909448i | \(-0.636505\pi\) |
0.909448 | + | 0.415818i | \(0.136505\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 184.215 | 0.242707 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 384.012i | − | 0.504615i | −0.967647 | − | 0.252307i | \(-0.918811\pi\) | ||
0.967647 | − | 0.252307i | \(-0.0811894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 813.296 | + | 813.296i | 1.06592 | + | 1.06592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −67.6589 | − | 67.6589i | −0.0884429 | − | 0.0884429i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 85.8874i | − | 0.111978i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 865.026 | 1.12487 | 0.562436 | − | 0.826841i | \(-0.309864\pi\) | ||||
0.562436 | + | 0.826841i | \(0.309864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −165.800 | + | 165.800i | −0.215045 | + | 0.215045i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.78859 | − | 1.78859i | 0.00231383 | − | 0.00231383i | −0.705949 | − | 0.708263i | \(-0.749479\pi\) |
0.708263 | + | 0.705949i | \(0.249479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −950.368 | −1.22628 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 162.055i | 0.208565i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 796.409 | + | 796.409i | 1.02235 | + | 1.02235i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0753 | − | 27.0753i | −0.0346675 | − | 0.0346675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 181.075i | 0.231258i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 109.681 | 0.139721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −143.702 | + | 143.702i | −0.182595 | + | 0.182595i | −0.792485 | − | 0.609891i | \(-0.791213\pi\) |
0.609891 | + | 0.792485i | \(0.291213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.7170 | + | 38.7170i | −0.0490710 | + | 0.0490710i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1722.49 | −2.17761 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 494.855i | − | 0.624029i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 62.0558 | + | 62.0558i | 0.0780577 | + | 0.0780577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 477.929 | + | 477.929i | 0.599660 | + | 0.599660i | 0.940222 | − | 0.340562i | \(-0.110617\pi\) |
−0.340562 | + | 0.940222i | \(0.610617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1020.64i | 1.27740i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 65.8092 | 0.0821588 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −252.187 | + | 252.187i | −0.314056 | + | 0.314056i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −335.359 | + | 335.359i | −0.416595 | + | 0.416595i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −475.722 | −0.589495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1524.96i | 1.88500i | 0.334212 | + | 0.942498i | \(0.391530\pi\) | ||||
−0.334212 | + | 0.942498i | \(0.608470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 576.427 | + | 576.427i | 0.710761 | + | 0.710761i | 0.966694 | − | 0.255933i | \(-0.0823828\pi\) |
−0.255933 | + | 0.966694i | \(0.582383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 357.194 | + | 357.194i | 0.439353 | + | 0.439353i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 211.224i | − | 0.259170i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1649.37 | 2.01882 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 206.955 | − | 206.955i | 0.252692 | − | 0.252692i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 386.324 | − | 386.324i | 0.470552 | − | 0.470552i | −0.431541 | − | 0.902093i | \(-0.642030\pi\) |
0.902093 | + | 0.431541i | \(0.142030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 377.870 | 0.459138 | 0.229569 | − | 0.973292i | \(-0.426268\pi\) | ||||
0.229569 | + | 0.973292i | \(0.426268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 127.444i | 0.154477i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −140.900 | − | 140.900i | −0.170375 | − | 0.170375i | 0.616769 | − | 0.787144i | \(-0.288441\pi\) |
−0.787144 | + | 0.616769i | \(0.788441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 522.203 | + | 522.203i | 0.629919 | + | 0.629919i | 0.948048 | − | 0.318128i | \(-0.103054\pi\) |
−0.318128 | + | 0.948048i | \(0.603054\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 747.501i | − | 0.899520i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1151.95 | −1.38289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.7226 | + | 53.7226i | −0.0643385 | + | 0.0643385i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −152.026 | + | 152.026i | −0.181632 | + | 0.181632i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −442.133 | −0.526976 | −0.263488 | − | 0.964663i | \(-0.584873\pi\) | ||||
−0.263488 | + | 0.964663i | \(0.584873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 373.376i | 0.443967i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −259.476 | − | 259.476i | −0.307801 | − | 0.307801i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 74.8417 | + | 74.8417i | 0.0885701 | + | 0.0885701i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1109.99i | − | 1.31049i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 257.994 | 0.303879 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 219.135 | − | 219.135i | 0.257503 | − | 0.257503i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 494.617 | − | 494.617i | 0.579856 | − | 0.579856i | −0.355007 | − | 0.934863i | \(-0.615522\pi\) |
0.934863 | + | 0.355007i | \(0.115522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 102.133 | 0.119454 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1676.75i | − | 1.95654i | −0.207340 | − | 0.978269i | \(-0.566481\pi\) | ||
0.207340 | − | 0.978269i | \(-0.433519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −228.948 | − | 228.948i | −0.266529 | − | 0.266529i | 0.561171 | − | 0.827700i | \(-0.310351\pi\) |
−0.827700 | + | 0.561171i | \(0.810351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −578.800 | − | 578.800i | −0.672241 | − | 0.672241i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1603.23i | 1.85774i | 0.370401 | + | 0.928872i | \(0.379220\pi\) | ||||
−0.370401 | + | 0.928872i | \(0.620780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −83.7981 | −0.0968764 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −259.488 | + | 259.488i | −0.299294 | + | 0.299294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1034 | + | 10.1034i | −0.0116264 | + | 0.0116264i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −140.461 | −0.161264 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 321.927i | − | 0.368760i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −484.533 | − | 484.533i | −0.553752 | − | 0.553752i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −289.017 | − | 289.017i | −0.329552 | − | 0.329552i | 0.522864 | − | 0.852416i | \(-0.324864\pi\) |
−0.852416 | + | 0.522864i | \(0.824864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 419.570i | 0.477326i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 937.450 | 1.06408 | 0.532038 | − | 0.846721i | \(-0.321426\pi\) | ||||
0.532038 | + | 0.846721i | \(0.321426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 485.966 | − | 485.966i | 0.550357 | − | 0.550357i | −0.376187 | − | 0.926544i | \(-0.622765\pi\) |
0.926544 | + | 0.376187i | \(0.122765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.4022 | + | 15.4022i | −0.0174036 | + | 0.0174036i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −534.193 | −0.602247 | −0.301123 | − | 0.953585i | \(-0.597362\pi\) | ||||
−0.301123 | + | 0.953585i | \(0.597362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 369.201i | 0.415299i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.3865 | + | 20.3865i | 0.0228805 | + | 0.0228805i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −770.346 | − | 770.346i | −0.862649 | − | 0.862649i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 106.961i | − | 0.119510i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −559.701 | −0.623970 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1019.56 | + | 1019.56i | −1.13410 | + | 1.13410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 562.638 | − | 562.638i | 0.624460 | − | 0.624460i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1198.70 | −1.32747 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 134.237i | 0.148328i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −368.669 | − | 368.669i | −0.406471 | − | 0.406471i | 0.474035 | − | 0.880506i | \(-0.342797\pi\) |
−0.880506 | + | 0.474035i | \(0.842797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −302.341 | − | 302.341i | −0.332608 | − | 0.332608i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1592.43i | − | 1.74800i | −0.485927 | − | 0.873999i | \(-0.661518\pi\) | ||
0.485927 | − | 0.873999i | \(-0.338482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.0967 | 0.0504893 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −88.7424 | + | 88.7424i | −0.0969863 | + | 0.0969863i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 123.978 | − | 123.978i | 0.135199 | − | 0.135199i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −403.500 | −0.439064 | −0.219532 | − | 0.975605i | \(-0.570453\pi\) | ||||
−0.219532 | + | 0.975605i | \(0.570453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.4116i | 0.0721081i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 82.2632 | + | 82.2632i | 0.0891258 | + | 0.0891258i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 151.602 | + | 151.602i | 0.163894 | + | 0.163894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 174.169i | − | 0.187884i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 348.546 | 0.375184 | 0.187592 | − | 0.982247i | \(-0.439932\pi\) | ||||
0.187592 | + | 0.982247i | \(0.439932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 869.449 | − | 869.449i | 0.933887 | − | 0.933887i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −454.533 | + | 454.533i | −0.487173 | + | 0.487173i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −102.173 | −0.109276 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 248.875i | 0.265609i | 0.991142 | + | 0.132804i | \(0.0423982\pi\) | ||||
−0.991142 | + | 0.132804i | \(0.957602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −458.669 | − | 458.669i | −0.488465 | − | 0.488465i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −884.188 | − | 884.188i | −0.939626 | − | 0.939626i | 0.0586528 | − | 0.998278i | \(-0.481319\pi\) |
−0.998278 | + | 0.0586528i | \(0.981319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1565.34i | 1.65996i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −74.2266 | −0.0785466 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −462.279 | + | 462.279i | −0.488151 | + | 0.488151i | −0.907722 | − | 0.419571i | \(-0.862180\pi\) |
0.419571 | + | 0.907722i | \(0.362180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 766.221 | − | 766.221i | 0.807398 | − | 0.807398i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −119.006 | −0.125138 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 707.656i | − | 0.742556i | −0.928522 | − | 0.371278i | \(-0.878920\pi\) | ||
0.928522 | − | 0.371278i | \(-0.121080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 114.632 | + | 114.632i | 0.120033 | + | 0.120033i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 136.722 | + | 136.722i | 0.142865 | + | 0.142865i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1460.22i | − | 1.52265i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −750.983 | −0.781460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −338.241 | + | 338.241i | −0.351237 | + | 0.351237i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.7647 | − | 26.7647i | 0.0277354 | − | 0.0277354i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −841.240 | −0.869949 | −0.434974 | − | 0.900443i | \(-0.643243\pi\) | ||||
−0.434974 | + | 0.900443i | \(0.643243\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 926.006i | − | 0.955630i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −308.415 | − | 308.415i | −0.317626 | − | 0.317626i | 0.530229 | − | 0.847855i | \(-0.322106\pi\) |
−0.847855 | + | 0.530229i | \(0.822106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −827.654 | − | 827.654i | −0.850621 | − | 0.850621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 387.213i | − | 0.397142i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1316.85 | −1.34786 | −0.673928 | − | 0.738797i | \(-0.735394\pi\) | ||||
−0.673928 | + | 0.738797i | \(0.735394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.6897 | − | 49.6897i | 0.0507556 | − | 0.0507556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 243.415 | − | 243.415i | 0.248130 | − | 0.248130i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 504.538 | 0.513263 | 0.256632 | − | 0.966509i | \(-0.417387\pi\) | ||||
0.256632 | + | 0.966509i | \(0.417387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 104.588i | − | 0.106181i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 559.858 | + | 559.858i | 0.567232 | + | 0.567232i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1620.92 | + | 1620.92i | 1.63895 | + | 1.63895i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 436.650i | 0.440616i | 0.975430 | + | 0.220308i | \(0.0707062\pi\) | ||||
−0.975430 | + | 0.220308i | \(0.929294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.62667 | −0.00465929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 137.797 | − | 137.797i | 0.138489 | − | 0.138489i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 383.801 | − | 383.801i | 0.384956 | − | 0.384956i | −0.487928 | − | 0.872884i | \(-0.662247\pi\) |
0.872884 | + | 0.487928i | \(0.162247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 48.5021 | 0.0485507 |
(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 | 384.3.l.a.223.2 | 16 | ||
3.2 | odd | 2 | 1152.3.m.f.991.5 | 16 | |||
4.3 | odd | 2 | 384.3.l.b.223.6 | 16 | |||
8.3 | odd | 2 | 192.3.l.a.175.3 | 16 | |||
8.5 | even | 2 | 48.3.l.a.19.3 | ✓ | 16 | ||
12.11 | even | 2 | 1152.3.m.c.991.5 | 16 | |||
16.3 | odd | 4 | 48.3.l.a.43.3 | yes | 16 | ||
16.5 | even | 4 | 384.3.l.b.31.6 | 16 | |||
16.11 | odd | 4 | inner | 384.3.l.a.31.2 | 16 | ||
16.13 | even | 4 | 192.3.l.a.79.3 | 16 | |||
24.5 | odd | 2 | 144.3.m.c.19.6 | 16 | |||
24.11 | even | 2 | 576.3.m.c.559.4 | 16 | |||
48.5 | odd | 4 | 1152.3.m.c.415.5 | 16 | |||
48.11 | even | 4 | 1152.3.m.f.415.5 | 16 | |||
48.29 | odd | 4 | 576.3.m.c.271.4 | 16 | |||
48.35 | even | 4 | 144.3.m.c.91.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.3 | ✓ | 16 | 8.5 | even | 2 | ||
48.3.l.a.43.3 | yes | 16 | 16.3 | odd | 4 | ||
144.3.m.c.19.6 | 16 | 24.5 | odd | 2 | |||
144.3.m.c.91.6 | 16 | 48.35 | even | 4 | |||
192.3.l.a.79.3 | 16 | 16.13 | even | 4 | |||
192.3.l.a.175.3 | 16 | 8.3 | odd | 2 | |||
384.3.l.a.31.2 | 16 | 16.11 | odd | 4 | inner | ||
384.3.l.a.223.2 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.b.31.6 | 16 | 16.5 | even | 4 | |||
384.3.l.b.223.6 | 16 | 4.3 | odd | 2 | |||
576.3.m.c.271.4 | 16 | 48.29 | odd | 4 | |||
576.3.m.c.559.4 | 16 | 24.11 | even | 2 | |||
1152.3.m.c.415.5 | 16 | 48.5 | odd | 4 | |||
1152.3.m.c.991.5 | 16 | 12.11 | even | 2 | |||
1152.3.m.f.415.5 | 16 | 48.11 | even | 4 | |||
1152.3.m.f.991.5 | 16 | 3.2 | odd | 2 |