Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(191,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.191");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 319.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.319 |
Dual form | 448.3.r.c.191.2 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 4.33013 | + | 2.50000i | 1.44338 | + | 0.833333i | 0.998073 | − | 0.0620469i | \(-0.0197628\pi\) |
0.445302 | + | 0.895380i | \(0.353096\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.50000 | + | 7.79423i | 0.900000 | + | 1.55885i | 0.827492 | + | 0.561478i | \(0.189767\pi\) |
0.0725083 | + | 0.997368i | \(0.476900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.92820 | − | 1.00000i | −0.989743 | − | 0.142857i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.00000 | + | 13.8564i | 0.888889 | + | 1.53960i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.236189 | + | 0.136364i | 0.613424 | − | 0.789754i | \(-0.289792\pi\) |
−0.377235 | + | 0.926118i | \(0.623125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.0000 | −1.23077 | −0.615385 | − | 0.788227i | \(-0.710999\pi\) | ||||
−0.615385 | + | 0.788227i | \(0.710999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 45.0000i | 3.00000i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.50000 | − | 6.06218i | 0.205882 | − | 0.356599i | −0.744531 | − | 0.667588i | \(-0.767327\pi\) |
0.950414 | + | 0.310989i | \(0.100660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.52628 | − | 5.50000i | 0.501383 | − | 0.289474i | −0.227901 | − | 0.973684i | \(-0.573186\pi\) |
0.729285 | + | 0.684211i | \(0.239853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −27.5000 | − | 21.6506i | −1.30952 | − | 1.03098i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.4545 | − | 9.50000i | 0.715412 | − | 0.413043i | −0.0976495 | − | 0.995221i | \(-0.531132\pi\) |
0.813062 | + | 0.582177i | \(0.197799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −28.0000 | + | 48.4974i | −1.12000 | + | 1.93990i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000i | 1.29630i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32.0000 | 1.10345 | 0.551724 | − | 0.834027i | \(-0.313970\pi\) | ||||
0.551724 | + | 0.834027i | \(0.313970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.52628 | − | 5.50000i | −0.307299 | − | 0.177419i | 0.338418 | − | 0.940996i | \(-0.390108\pi\) |
−0.645717 | + | 0.763577i | \(0.723442\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 12.9904i | 0.227273 | + | 0.393648i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −23.3827 | − | 58.5000i | −0.668077 | − | 1.67143i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | − | 0.866025i | −0.0135135 | − | 0.0234061i | 0.859190 | − | 0.511657i | \(-0.170968\pi\) |
−0.872703 | + | 0.488251i | \(0.837635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −69.2820 | − | 40.0000i | −1.77646 | − | 1.02564i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −40.0000 | −0.975610 | −0.487805 | − | 0.872953i | \(-0.662202\pi\) | ||||
−0.487805 | + | 0.872953i | \(0.662202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 40.0000i | − | 0.930233i | −0.885250 | − | 0.465116i | \(-0.846013\pi\) | ||
0.885250 | − | 0.465116i | \(-0.153987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −72.0000 | + | 124.708i | −1.60000 | + | 2.77128i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 73.6122 | − | 42.5000i | 1.56622 | − | 0.904255i | 0.569612 | − | 0.821914i | \(-0.307093\pi\) |
0.996604 | − | 0.0823416i | \(-0.0262399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.0000 | + | 13.8564i | 0.959184 | + | 0.282784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.3109 | − | 17.5000i | 0.594331 | − | 0.343137i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.50000 | − | 6.06218i | 0.0660377 | − | 0.114381i | −0.831116 | − | 0.556099i | \(-0.812298\pi\) |
0.897154 | + | 0.441718i | \(0.145631\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27.0000i | 0.490909i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55.0000 | 0.964912 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 45.8993 | + | 26.5000i | 0.777955 | + | 0.449153i | 0.835705 | − | 0.549179i | \(-0.185059\pi\) |
−0.0577500 | + | 0.998331i | \(0.518393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39.5000 | + | 68.4160i | 0.647541 | + | 1.12157i | 0.983708 | + | 0.179772i | \(0.0575359\pi\) |
−0.336167 | + | 0.941802i | \(0.609131\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.5692 | − | 104.000i | −0.659829 | − | 1.65079i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −72.0000 | − | 124.708i | −1.10769 | − | 1.91858i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.52628 | − | 5.50000i | −0.142183 | − | 0.0820896i | 0.427221 | − | 0.904147i | \(-0.359493\pi\) |
−0.569404 | + | 0.822058i | \(0.692826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 95.0000 | 1.37681 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.0000i | 0.676056i | 0.941136 | + | 0.338028i | \(0.109760\pi\) | ||||
−0.941136 | + | 0.338028i | \(0.890240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −71.5000 | + | 123.842i | −0.979452 | + | 1.69646i | −0.315068 | + | 0.949069i | \(0.602027\pi\) |
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −242.487 | + | 140.000i | −3.23316 | + | 1.86667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.5000 | − | 12.9904i | −0.214286 | − | 0.168706i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 30.3109 | − | 17.5000i | 0.383682 | − | 0.221519i | −0.295737 | − | 0.955269i | \(-0.595565\pi\) |
0.679419 | + | 0.733750i | \(0.262232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15.5000 | + | 26.8468i | −0.191358 | + | 0.331442i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.00000i | − | 0.0963855i | −0.998838 | − | 0.0481928i | \(-0.984654\pi\) | ||
0.998838 | − | 0.0481928i | \(-0.0153462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63.0000 | 0.741176 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 138.564 | + | 80.0000i | 1.59269 | + | 0.919540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.5000 | + | 84.0045i | 0.544944 | + | 0.943870i | 0.998610 | + | 0.0526989i | \(0.0167824\pi\) |
−0.453667 | + | 0.891171i | \(0.649884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 110.851 | + | 16.0000i | 1.21815 | + | 0.175824i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.5000 | − | 47.6314i | −0.295699 | − | 0.512166i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 85.7365 | + | 49.5000i | 0.902490 | + | 0.521053i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −88.0000 | −0.907216 | −0.453608 | − | 0.891201i | \(-0.649863\pi\) | ||||
−0.453608 | + | 0.891201i | \(0.649863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 48.0000i | 0.484848i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | + | 12.9904i | −0.0742574 | + | 0.128618i | −0.900763 | − | 0.434311i | \(-0.856992\pi\) |
0.826506 | + | 0.562928i | \(0.190325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −80.5404 | + | 46.5000i | −0.781945 | + | 0.451456i | −0.837119 | − | 0.547020i | \(-0.815762\pi\) |
0.0551740 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 45.0000 | − | 311.769i | 0.428571 | − | 2.96923i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.52628 | − | 5.50000i | 0.0890306 | − | 0.0514019i | −0.454824 | − | 0.890581i | \(-0.650298\pi\) |
0.543854 | + | 0.839180i | \(0.316964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 56.5000 | − | 97.8609i | 0.518349 | − | 0.897806i | −0.481424 | − | 0.876488i | \(-0.659880\pi\) |
0.999773 | − | 0.0213184i | \(-0.00678636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.00000i | − | 0.0450450i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 56.0000 | 0.495575 | 0.247788 | − | 0.968814i | \(-0.420296\pi\) | ||||
0.247788 | + | 0.968814i | \(0.420296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 148.090 | + | 85.5000i | 1.28774 | + | 0.743478i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −128.000 | − | 221.703i | −1.09402 | − | 1.89489i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −30.3109 | + | 38.5000i | −0.254713 | + | 0.323529i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −56.0000 | − | 96.9948i | −0.462810 | − | 0.801610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −173.205 | − | 100.000i | −1.40817 | − | 0.813008i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −279.000 | −2.23200 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 96.0000i | − | 0.755906i | −0.925825 | − | 0.377953i | \(-0.876628\pi\) | ||
0.925825 | − | 0.377953i | \(-0.123372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 100.000 | − | 173.205i | 0.775194 | − | 1.34268i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 122.110 | − | 70.5000i | 0.932134 | − | 0.538168i | 0.0446483 | − | 0.999003i | \(-0.485783\pi\) |
0.887486 | + | 0.460835i | \(0.152450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −71.5000 | + | 28.5788i | −0.537594 | + | 0.214878i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −272.798 | + | 157.500i | −2.02073 | + | 1.16667i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | + | 7.79423i | −0.0328467 | + | 0.0568922i | −0.881981 | − | 0.471284i | \(-0.843791\pi\) |
0.849135 | + | 0.528176i | \(0.177124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 136.000i | − | 0.978417i | −0.872167 | − | 0.489209i | \(-0.837286\pi\) | ||
0.872167 | − | 0.489209i | \(-0.162714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 425.000 | 3.01418 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −41.5692 | − | 24.0000i | −0.290694 | − | 0.167832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 144.000 | + | 249.415i | 0.993103 | + | 1.72011i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 168.875 | + | 177.500i | 1.14881 | + | 1.20748i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.5000 | + | 49.3634i | 0.191275 | + | 0.331298i | 0.945673 | − | 0.325119i | \(-0.105404\pi\) |
−0.754398 | + | 0.656417i | \(0.772071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.3827 | − | 13.5000i | −0.154852 | − | 0.0894040i | 0.420572 | − | 0.907259i | \(-0.361830\pi\) |
−0.575424 | + | 0.817855i | \(0.695163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 112.000 | 0.732026 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 99.0000i | − | 0.638710i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 83.5000 | − | 144.626i | 0.531847 | − | 0.921186i | −0.467462 | − | 0.884013i | \(-0.654831\pi\) |
0.999309 | − | 0.0371729i | \(-0.0118352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.3109 | − | 17.5000i | 0.190635 | − | 0.110063i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −123.500 | + | 49.3634i | −0.767081 | + | 0.306605i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4545 | + | 9.50000i | −0.100948 | + | 0.0582822i | −0.549624 | − | 0.835412i | \(-0.685229\pi\) |
0.448676 | + | 0.893694i | \(0.351896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −67.5000 | + | 116.913i | −0.409091 | + | 0.708566i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 190.000i | − | 1.13772i | −0.822433 | − | 0.568862i | \(-0.807384\pi\) | ||
0.822433 | − | 0.568862i | \(-0.192616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.0000 | 0.514793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 152.420 | + | 88.0000i | 0.891348 | + | 0.514620i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −72.5000 | − | 125.574i | −0.419075 | − | 0.725859i | 0.576772 | − | 0.816905i | \(-0.304312\pi\) |
−0.995847 | + | 0.0910461i | \(0.970979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 242.487 | − | 308.000i | 1.38564 | − | 1.76000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 132.500 | + | 229.497i | 0.748588 | + | 1.29659i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −274.530 | − | 158.500i | −1.53369 | − | 0.885475i | −0.999187 | − | 0.0403064i | \(-0.987167\pi\) |
−0.534500 | − | 0.845168i | \(-0.679500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 186.000 | 1.02762 | 0.513812 | − | 0.857903i | \(-0.328233\pi\) | ||||
0.513812 | + | 0.857903i | \(0.328233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 395.000i | 2.15847i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.50000 | − | 7.79423i | 0.0243243 | − | 0.0421310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.1865 | − | 10.5000i | 0.0972542 | − | 0.0561497i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35.0000 | − | 242.487i | 0.185185 | − | 1.28300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −245.085 | + | 141.500i | −1.28317 | + | 0.740838i | −0.977426 | − | 0.211277i | \(-0.932238\pi\) |
−0.305742 | + | 0.952114i | \(0.598905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 147.500 | − | 255.477i | 0.764249 | − | 1.32372i | −0.176394 | − | 0.984320i | \(-0.556443\pi\) |
0.940643 | − | 0.339398i | \(-0.110223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 720.000i | − | 3.69231i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −128.000 | −0.649746 | −0.324873 | − | 0.945758i | \(-0.605322\pi\) | ||||
−0.324873 | + | 0.945758i | \(0.605322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −245.085 | − | 141.500i | −1.23158 | − | 0.711055i | −0.264224 | − | 0.964461i | \(-0.585116\pi\) |
−0.967360 | + | 0.253406i | \(0.918449\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.5000 | − | 47.6314i | −0.136816 | − | 0.236972i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −221.703 | − | 32.0000i | −1.09213 | − | 0.157635i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −180.000 | − | 311.769i | −0.878049 | − | 1.52083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 263.272 | + | 152.000i | 1.27184 | + | 0.734300i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.0000 | 0.157895 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 40.0000i | − | 0.189573i | −0.995498 | − | 0.0947867i | \(-0.969783\pi\) | ||
0.995498 | − | 0.0947867i | \(-0.0302169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −120.000 | + | 207.846i | −0.563380 | + | 0.975803i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 311.769 | − | 180.000i | 1.45009 | − | 0.837209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60.5000 | + | 47.6314i | 0.278802 | + | 0.219500i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −619.208 | + | 357.500i | −2.82743 | + | 1.63242i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −56.0000 | + | 96.9948i | −0.253394 | + | 0.438891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 176.000i | − | 0.789238i | −0.918845 | − | 0.394619i | \(-0.870877\pi\) | ||
0.918845 | − | 0.394619i | \(-0.129123\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −896.000 | −3.98222 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 335.152 | + | 193.500i | 1.47644 | + | 0.852423i | 0.999646 | − | 0.0265925i | \(-0.00846564\pi\) |
0.476793 | + | 0.879015i | \(0.341799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −91.5000 | − | 158.483i | −0.399563 | − | 0.692064i | 0.594109 | − | 0.804385i | \(-0.297505\pi\) |
−0.993672 | + | 0.112321i | \(0.964172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.9711 | − | 97.5000i | −0.168706 | − | 0.422078i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −180.500 | − | 312.635i | −0.774678 | − | 1.34178i | −0.934975 | − | 0.354713i | \(-0.884579\pi\) |
0.160297 | − | 0.987069i | \(-0.448755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 662.509 | + | 382.500i | 2.81919 | + | 1.62766i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 175.000 | 0.738397 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 50.0000i | − | 0.209205i | −0.994514 | − | 0.104603i | \(-0.966643\pi\) | ||
0.994514 | − | 0.104603i | \(-0.0333570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 64.5000 | − | 111.717i | 0.267635 | − | 0.463557i | −0.700616 | − | 0.713539i | \(-0.747091\pi\) |
0.968251 | + | 0.249982i | \(0.0804246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 138.564 | − | 80.0000i | 0.570222 | − | 0.329218i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 103.500 | + | 428.683i | 0.422449 | + | 1.74972i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −152.420 | + | 88.0000i | −0.617087 | + | 0.356275i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.0000 | − | 34.6410i | 0.0803213 | − | 0.139121i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 394.000i | 1.56972i | 0.619672 | + | 0.784861i | \(0.287265\pi\) | ||||
−0.619672 | + | 0.784861i | \(0.712735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 57.0000 | 0.225296 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 272.798 | + | 157.500i | 1.06980 | + | 0.617647i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −44.5000 | − | 77.0763i | −0.173152 | − | 0.299908i | 0.766368 | − | 0.642401i | \(-0.222062\pi\) |
−0.939520 | + | 0.342494i | \(0.888728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.59808 | + | 6.50000i | 0.0100312 | + | 0.0250965i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 256.000 | + | 443.405i | 0.980843 | + | 1.69887i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −38.9711 | − | 22.5000i | −0.148179 | − | 0.0855513i | 0.424077 | − | 0.905626i | \(-0.360598\pi\) |
−0.572257 | + | 0.820075i | \(0.693932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 63.0000 | 0.237736 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 485.000i | 1.81648i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −228.500 | + | 395.774i | −0.849442 | + | 1.47128i | 0.0322643 | + | 0.999479i | \(0.489728\pi\) |
−0.881707 | + | 0.471798i | \(0.843605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −343.812 | + | 198.500i | −1.26868 | + | 0.732472i | −0.974738 | − | 0.223351i | \(-0.928300\pi\) |
−0.293941 | + | 0.955823i | \(0.594967\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 440.000 | + | 346.410i | 1.61172 | + | 1.26890i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −145.492 | + | 84.0000i | −0.529063 | + | 0.305455i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 115.500 | − | 200.052i | 0.416968 | − | 0.722209i | −0.578665 | − | 0.815565i | \(-0.696426\pi\) |
0.995633 | + | 0.0933562i | \(0.0297595\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 176.000i | − | 0.630824i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 104.000 | 0.370107 | 0.185053 | − | 0.982728i | \(-0.440754\pi\) | ||||
0.185053 | + | 0.982728i | \(0.440754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −343.812 | − | 198.500i | −1.21488 | − | 0.701413i | −0.251065 | − | 0.967970i | \(-0.580781\pi\) |
−0.963819 | + | 0.266557i | \(0.914114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 247.500 | + | 428.683i | 0.868421 | + | 1.50415i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 277.128 | + | 40.0000i | 0.965603 | + | 0.139373i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 120.000 | + | 207.846i | 0.415225 | + | 0.719191i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −381.051 | − | 220.000i | −1.30945 | − | 0.756014i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −154.000 | −0.525597 | −0.262799 | − | 0.964851i | \(-0.584645\pi\) | ||||
−0.262799 | + | 0.964851i | \(0.584645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 477.000i | 1.61695i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −52.5000 | + | 90.9327i | −0.176768 | + | 0.306171i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −263.272 | + | 152.000i | −0.880507 | + | 0.508361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.0000 | + | 277.128i | −0.132890 | + | 0.920691i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −64.9519 | + | 37.5000i | −0.214363 | + | 0.123762i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −355.500 | + | 615.744i | −1.16557 | + | 2.01883i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 376.000i | 1.22476i | 0.790565 | + | 0.612378i | \(0.209787\pi\) | ||||
−0.790565 | + | 0.612378i | \(0.790213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −465.000 | −1.50485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 279.726 | + | 161.500i | 0.899441 | + | 0.519293i | 0.877019 | − | 0.480456i | \(-0.159529\pi\) |
0.0224223 | + | 0.999749i | \(0.492862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −95.5000 | − | 165.411i | −0.305112 | − | 0.528469i | 0.672174 | − | 0.740393i | \(-0.265361\pi\) |
−0.977286 | + | 0.211924i | \(0.932027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 623.538 | − | 792.000i | 1.97949 | − | 2.51429i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 167.500 | + | 290.119i | 0.528391 | + | 0.915200i | 0.999452 | + | 0.0330997i | \(0.0105379\pi\) |
−0.471061 | + | 0.882101i | \(0.656129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 83.1384 | + | 48.0000i | 0.260622 | + | 0.150470i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 55.0000 | 0.171340 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 77.0000i | − | 0.238390i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 448.000 | − | 775.959i | 1.37846 | − | 2.38757i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 489.304 | − | 282.500i | 1.49634 | − | 0.863914i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −552.500 | + | 220.836i | −1.67933 | + | 0.671235i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.3109 | + | 17.5000i | −0.0915737 | + | 0.0528701i | −0.545088 | − | 0.838379i | \(-0.683504\pi\) |
0.453514 | + | 0.891249i | \(0.350170\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | − | 13.8564i | 0.0240240 | − | 0.0416108i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 99.0000i | − | 0.295522i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 184.000 | 0.545994 | 0.272997 | − | 0.962015i | \(-0.411985\pi\) | ||||
0.272997 | + | 0.962015i | \(0.411985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 242.487 | + | 140.000i | 0.715301 | + | 0.412979i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.5000 | − | 28.5788i | −0.0483871 | − | 0.0838089i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −311.769 | − | 143.000i | −0.908948 | − | 0.416910i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 427.500 | + | 740.452i | 1.23913 | + | 2.14624i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −161.947 | − | 93.5000i | −0.466705 | − | 0.269452i | 0.248154 | − | 0.968721i | \(-0.420176\pi\) |
−0.714860 | + | 0.699268i | \(0.753509\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 208.000 | 0.595989 | 0.297994 | − | 0.954568i | \(-0.403682\pi\) | ||||
0.297994 | + | 0.954568i | \(0.403682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 560.000i | − | 1.59544i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 115.500 | − | 200.052i | 0.327195 | − | 0.566719i | −0.654759 | − | 0.755838i | \(-0.727230\pi\) |
0.981954 | + | 0.189119i | \(0.0605631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −374.123 | + | 216.000i | −1.05387 | + | 0.608451i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −227.500 | + | 90.9327i | −0.637255 | + | 0.254713i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0429 | − | 18.5000i | 0.0892561 | − | 0.0515320i | −0.454708 | − | 0.890641i | \(-0.650256\pi\) |
0.543964 | + | 0.839109i | \(0.316923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −120.000 | + | 207.846i | −0.332410 | + | 0.575751i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 560.000i | − | 1.54270i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1287.00 | −3.52603 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 418.290 | + | 241.500i | 1.13976 | + | 0.658038i | 0.946370 | − | 0.323085i | \(-0.104720\pi\) |
0.193385 | + | 0.981123i | \(0.438053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −320.000 | − | 554.256i | −0.867209 | − | 1.50205i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.3109 | + | 38.5000i | −0.0817005 | + | 0.103774i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 215.500 | + | 373.257i | 0.577748 | + | 1.00069i | 0.995737 | + | 0.0922368i | \(0.0294017\pi\) |
−0.417989 | + | 0.908452i | \(0.637265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1208.11 | − | 697.500i | −3.22161 | − | 1.86000i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −512.000 | −1.35809 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 714.000i | − | 1.88391i | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||
0.335746 | − | 0.941953i | \(-0.391012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 240.000 | − | 415.692i | 0.629921 | − | 1.09106i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −563.783 | + | 325.500i | −1.47202 | + | 0.849869i | −0.999505 | − | 0.0314548i | \(-0.989986\pi\) |
−0.472512 | + | 0.881324i | \(0.656653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0000 | − | 187.061i | 0.0701299 | − | 0.485874i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 554.256 | − | 320.000i | 1.43219 | − | 0.826873i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 232.500 | − | 402.702i | 0.597686 | − | 1.03522i | −0.395475 | − | 0.918477i | \(-0.629420\pi\) |
0.993162 | − | 0.116747i | \(-0.0372465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 133.000i | − | 0.340153i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 705.000 | 1.79389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 272.798 | + | 157.500i | 0.690628 | + | 0.398734i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 92.5000 | + | 160.215i | 0.232997 | + | 0.403563i | 0.958689 | − | 0.284457i | \(-0.0918133\pi\) |
−0.725691 | + | 0.688020i | \(0.758480\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −381.051 | − | 55.0000i | −0.955015 | − | 0.137845i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −52.5000 | − | 90.9327i | −0.130923 | − | 0.226765i | 0.793110 | − | 0.609079i | \(-0.208461\pi\) |
−0.924033 | + | 0.382314i | \(0.875127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 152.420 | + | 88.0000i | 0.378215 | + | 0.218362i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −279.000 | −0.688889 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.00000i | − | 0.00737101i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.00855746 | − | 0.0148220i | −0.861715 | − | 0.507393i | \(-0.830609\pi\) |
0.870272 | + | 0.492571i | \(0.163943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.9711 | + | 22.5000i | −0.0948203 | + | 0.0547445i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −291.500 | − | 229.497i | −0.705811 | − | 0.555682i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 62.3538 | − | 36.0000i | 0.150250 | − | 0.0867470i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 340.000 | − | 588.897i | 0.815348 | − | 1.41222i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 392.000i | − | 0.935561i | −0.883845 | − | 0.467780i | \(-0.845054\pi\) | ||
0.883845 | − | 0.467780i | \(-0.154946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −64.0000 | −0.152019 | −0.0760095 | − | 0.997107i | \(-0.524218\pi\) | ||||
−0.0760095 | + | 0.997107i | \(0.524218\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1177.79 | + | 680.000i | 2.78438 | + | 1.60757i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 196.000 | + | 339.482i | 0.461176 | + | 0.798781i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −205.248 | − | 513.500i | −0.480675 | − | 1.20258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −120.000 | − | 207.846i | −0.279720 | − | 0.484490i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −633.065 | − | 365.500i | −1.46883 | − | 0.848028i | −0.469438 | − | 0.882966i | \(-0.655543\pi\) |
−0.999389 | + | 0.0349377i | \(0.988877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 376.000 | 0.868360 | 0.434180 | − | 0.900826i | \(-0.357038\pi\) | ||||
0.434180 | + | 0.900826i | \(0.357038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1440.00i | 3.31034i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 104.500 | − | 180.999i | 0.239130 | − | 0.414186i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −549.926 | + | 317.500i | −1.25268 | + | 0.723235i | −0.971641 | − | 0.236462i | \(-0.924012\pi\) |
−0.281038 | + | 0.959697i | \(0.590679\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 184.000 | + | 762.102i | 0.417234 | + | 1.72812i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 425.218 | − | 245.500i | 0.959861 | − | 0.554176i | 0.0637308 | − | 0.997967i | \(-0.479700\pi\) |
0.896130 | + | 0.443791i | \(0.146367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −436.500 | + | 756.040i | −0.980899 | + | 1.69897i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 285.000i | 0.637584i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −344.000 | −0.766147 | −0.383073 | − | 0.923718i | \(-0.625134\pi\) | ||||
−0.383073 | + | 0.923718i | \(0.625134\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −103.923 | − | 60.0000i | −0.230428 | − | 0.133038i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −67.5000 | − | 116.913i | −0.149007 | − | 0.258087i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 374.123 | + | 936.000i | 0.822248 | + | 2.05714i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −263.500 | − | 456.395i | −0.576586 | − | 0.998677i | −0.995867 | − | 0.0908204i | \(-0.971051\pi\) |
0.419281 | − | 0.907857i | \(-0.362282\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 212.176 | + | 122.500i | 0.462258 | + | 0.266885i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 704.000 | 1.52711 | 0.763557 | − | 0.645740i | \(-0.223451\pi\) | ||||
0.763557 | + | 0.645740i | \(0.223451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 160.000i | 0.345572i | 0.984959 | + | 0.172786i | \(0.0552770\pi\) | ||||
−0.984959 | + | 0.172786i | \(0.944723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 247.500 | − | 428.683i | 0.532258 | − | 0.921898i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 468.520 | − | 270.500i | 1.00325 | − | 0.579229i | 0.0940447 | − | 0.995568i | \(-0.470020\pi\) |
0.909210 | + | 0.416339i | \(0.136687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60.5000 | + | 47.6314i | 0.128998 | + | 0.101559i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 723.131 | − | 417.500i | 1.53531 | − | 0.886412i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 60.0000 | − | 103.923i | 0.126850 | − | 0.219710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 616.000i | 1.29684i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 112.000 | 0.234801 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −413.094 | − | 238.500i | −0.862409 | − | 0.497912i | 0.00240897 | − | 0.999997i | \(-0.499233\pi\) |
−0.864818 | + | 0.502085i | \(0.832567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | + | 13.8564i | 0.0166320 | + | 0.0288075i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −658.179 | − | 95.0000i | −1.36269 | − | 0.196687i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −396.000 | − | 685.892i | −0.816495 | − | 1.41421i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 265.870 | + | 153.500i | 0.545934 | + | 0.315195i | 0.747480 | − | 0.664284i | \(-0.231263\pi\) |
−0.201547 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −95.0000 | −0.194274 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0000i | 0.0448065i | 0.999749 | + | 0.0224033i | \(0.00713178\pi\) | ||||
−0.999749 | + | 0.0224033i | \(0.992868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 112.000 | − | 193.990i | 0.227181 | − | 0.393488i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −374.123 | + | 216.000i | −0.755804 | + | 0.436364i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 48.0000 | − | 332.554i | 0.0965795 | − | 0.669122i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −792.413 | + | 457.500i | −1.58800 | + | 0.916834i | −0.594367 | + | 0.804194i | \(0.702597\pi\) |
−0.993636 | + | 0.112639i | \(0.964070\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 475.000 | − | 822.724i | 0.948104 | − | 1.64216i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 192.000i | 0.381710i | 0.981618 | + | 0.190855i | \(0.0611260\pi\) | ||||
−0.981618 | + | 0.190855i | \(0.938874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −135.000 | −0.267327 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 376.721 | + | 217.500i | 0.743040 | + | 0.428994i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.5000 | − | 61.4878i | −0.0697446 | − | 0.120801i | 0.829044 | − | 0.559183i | \(-0.188885\pi\) |
−0.898789 | + | 0.438382i | \(0.855552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 619.208 | − | 786.500i | 1.21176 | − | 1.53914i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 192.500 | + | 333.420i | 0.375244 | + | 0.649941i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −724.863 | − | 418.500i | −1.40750 | − | 0.812621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 255.000 | 0.493230 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 725.000i | − | 1.39692i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −351.500 | + | 608.816i | −0.674664 | + | 1.16855i | 0.301903 | + | 0.953339i | \(0.402378\pi\) |
−0.976567 | + | 0.215214i | \(0.930955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −281.458 | + | 162.500i | −0.538161 | + | 0.310707i | −0.744333 | − | 0.667808i | \(-0.767233\pi\) |
0.206172 | + | 0.978516i | \(0.433899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1820.00 | − | 727.461i | 3.46667 | − | 1.38564i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −66.6840 | + | 38.5000i | −0.126535 | + | 0.0730550i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −84.0000 | + | 145.492i | −0.158790 | + | 0.275033i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 848.000i | 1.59699i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 640.000 | 1.20075 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 85.7365 | + | 49.5000i | 0.160255 | + | 0.0925234i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −792.500 | − | 1372.65i | −1.47579 | − | 2.55615i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 101.325 | + | 106.500i | 0.187987 | + | 0.197588i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 132.500 | + | 229.497i | 0.244917 | + | 0.424208i | 0.962108 | − | 0.272668i | \(-0.0879060\pi\) |
−0.717191 | + | 0.696876i | \(0.754573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 805.404 | + | 465.000i | 1.48325 | + | 0.856354i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1017.00 | 1.86606 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 134.000i | − | 0.244973i | −0.992470 | − | 0.122486i | \(-0.960913\pi\) | ||
0.992470 | − | 0.122486i | \(-0.0390868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −632.000 | + | 1094.66i | −1.15118 | + | 1.99391i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 304.841 | − | 176.000i | 0.553250 | − | 0.319419i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −227.500 | + | 90.9327i | −0.411392 | + | 0.164435i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.9711 | − | 22.5000i | 0.0702183 | − | 0.0405405i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −287.500 | + | 497.965i | −0.516158 | + | 0.894012i | 0.483666 | + | 0.875253i | \(0.339305\pi\) |
−0.999824 | + | 0.0187592i | \(0.994028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 640.000i | 1.14490i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 105.000 | 0.187166 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 156.751 | + | 90.5000i | 0.278420 | + | 0.160746i | 0.632708 | − | 0.774390i | \(-0.281943\pi\) |
−0.354288 | + | 0.935136i | \(0.615277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 252.000 | + | 436.477i | 0.446018 | + | 0.772525i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 134.234 | − | 170.500i | 0.236744 | − | 0.300705i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −159.500 | − | 276.262i | −0.280316 | − | 0.485522i | 0.691146 | − | 0.722715i | \(-0.257106\pi\) |
−0.971463 | + | 0.237193i | \(0.923773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 141.162 | + | 81.5000i | 0.247219 | + | 0.142732i | 0.618490 | − | 0.785792i | \(-0.287745\pi\) |
−0.371271 | + | 0.928525i | \(0.621078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1415.00 | −2.46946 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1064.00i | 1.85043i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −359.500 | + | 622.672i | −0.623050 | + | 1.07915i | 0.365864 | + | 0.930668i | \(0.380773\pi\) |
−0.988914 | + | 0.148486i | \(0.952560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1277.39 | − | 737.500i | 2.20620 | − | 1.27375i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | + | 55.4256i | −0.0137694 | + | 0.0953969i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.1865 | − | 10.5000i | 0.0311947 | − | 0.0180103i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1152.00 | − | 1995.32i | 1.96923 | − | 3.41081i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 296.000i | 0.504259i | 0.967694 | + | 0.252129i | \(0.0811309\pi\) | ||||
−0.967694 | + | 0.252129i | \(0.918869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −121.000 | −0.205433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −554.256 | − | 320.000i | −0.937828 | − | 0.541455i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −180.500 | − | 312.635i | −0.304384 | − | 0.527209i | 0.672740 | − | 0.739879i | \(-0.265117\pi\) |
−0.977124 | + | 0.212670i | \(0.931784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −436.477 | − | 63.0000i | −0.733574 | − | 0.105882i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −707.500 | − | 1225.43i | −1.18509 | − | 2.05264i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −108.253 | − | 62.5000i | −0.180723 | − | 0.104341i | 0.406909 | − | 0.913469i | \(-0.366607\pi\) |
−0.587632 | + | 0.809128i | \(0.699940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1000.00 | 1.66389 | 0.831947 | − | 0.554855i | \(-0.187226\pi\) | ||||
0.831947 | + | 0.554855i | \(0.187226\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 176.000i | − | 0.291874i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 504.000 | − | 872.954i | 0.833058 | − | 1.44290i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −355.936 | + | 205.500i | −0.586386 | + | 0.338550i | −0.763667 | − | 0.645610i | \(-0.776603\pi\) |
0.177281 | + | 0.984160i | \(0.443270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −880.000 | − | 692.820i | −1.44499 | − | 1.13764i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1177.79 | + | 680.000i | −1.92765 | + | 1.11293i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −519.500 | + | 899.800i | −0.847471 | + | 1.46786i | 0.0359860 | + | 0.999352i | \(0.488543\pi\) |
−0.883457 | + | 0.468511i | \(0.844791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1800.00i | − | 2.92683i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −248.000 | −0.401945 | −0.200972 | − | 0.979597i | \(-0.564410\pi\) | ||||
−0.200972 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −522.213 | − | 301.500i | −0.843640 | − | 0.487076i | 0.0148597 | − | 0.999890i | \(-0.495270\pi\) |
−0.858500 | + | 0.512814i | \(0.828603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 332.500 | + | 575.907i | 0.535427 | + | 0.927386i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −252.013 | − | 630.500i | −0.404516 | − | 1.01204i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −555.500 | − | 962.154i | −0.888800 | − | 1.53945i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 142.894 | + | 82.5000i | 0.227901 | + | 0.131579i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.00000 | −0.0111288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 816.000i | − | 1.29319i | −0.762835 | − | 0.646593i | \(-0.776193\pi\) | ||
0.762835 | − | 0.646593i | \(-0.223807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 100.000 | − | 173.205i | 0.157978 | − | 0.273626i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 748.246 | − | 432.000i | 1.17834 | − | 0.680315i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −752.000 | − | 221.703i | −1.18053 | − | 0.348042i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −665.108 | + | 384.000i | −1.04086 | + | 0.600939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −319.500 | + | 553.390i | −0.498440 | + | 0.863323i | −0.999998 | − | 0.00180047i | \(-0.999427\pi\) |
0.501558 | + | 0.865124i | \(0.332760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 664.000i | − | 1.03266i | −0.856390 | − | 0.516330i | \(-0.827298\pi\) | ||
0.856390 | − | 0.516330i | \(-0.172702\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1800.00 | 2.79070 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1092.06 | − | 630.500i | −1.68788 | − | 0.974498i | −0.956139 | − | 0.292915i | \(-0.905375\pi\) |
−0.731741 | − | 0.681583i | \(-0.761292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 79.5000 | + | 137.698i | 0.122496 | + | 0.212170i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 142.894 | + | 357.500i | 0.219500 | + | 0.549155i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −296.500 | − | 513.553i | −0.454058 | − | 0.786452i | 0.544575 | − | 0.838712i | \(-0.316691\pi\) |
−0.998634 | + | 0.0522601i | \(0.983358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1098.99 | + | 634.500i | 1.67784 | + | 0.968702i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2288.00 | −3.48250 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1192.00i | 1.80880i | 0.426684 | + | 0.904401i | \(0.359682\pi\) | ||||
−0.426684 | + | 0.904401i | \(0.640318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −236.500 | + | 409.630i | −0.357791 | + | 0.619713i | −0.987592 | − | 0.157045i | \(-0.949803\pi\) |
0.629800 | + | 0.776757i | \(0.283137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −484.974 | + | 280.000i | −0.731485 | + | 0.422323i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −544.500 | − | 428.683i | −0.818797 | − | 0.644635i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 526.543 | − | 304.000i | 0.789420 | − | 0.455772i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 440.000 | − | 762.102i | 0.657698 | − | 1.13917i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 237.000i | 0.353204i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 824.000 | 1.22437 | 0.612184 | − | 0.790715i | \(-0.290291\pi\) | ||||
0.612184 | + | 0.790715i | \(0.290291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1697.41 | − | 980.000i | −2.51468 | − | 1.45185i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −131.500 | − | 227.765i | −0.194239 | − | 0.336432i | 0.752412 | − | 0.658693i | \(-0.228890\pi\) |
−0.946651 | + | 0.322261i | \(0.895557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 609.682 | + | 88.0000i | 0.897911 | + | 0.129602i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 967.500 | + | 1675.76i | 1.42070 | + | 2.46073i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 556.854 | + | 321.500i | 0.815306 | + | 0.470717i | 0.848795 | − | 0.528722i | \(-0.177328\pi\) |
−0.0334888 | + | 0.999439i | \(0.510662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −81.0000 | −0.118248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 915.000i | − | 1.33188i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −56.0000 | + | 96.9948i | −0.0812772 | + | 0.140776i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 108.253 | − | 62.5000i | 0.156662 | − | 0.0904486i | −0.419620 | − | 0.907700i | \(-0.637837\pi\) |
0.576281 | + | 0.817251i | \(0.304503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 48.0000 | − | 332.554i | 0.0692641 | − | 0.479876i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1060.02 | − | 612.000i | 1.52520 | − | 0.880576i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −140.000 | + | 242.487i | −0.200861 | + | 0.347901i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1805.00i | − | 2.58226i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 54.0000 | 0.0770328 | 0.0385164 | − | 0.999258i | \(-0.487737\pi\) | ||||
0.0385164 | + | 0.999258i | \(0.487737\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.52628 | − | 5.50000i | −0.0135509 | − | 0.00782361i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1912.50 | + | 3312.55i | 2.71277 | + | 4.69865i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 64.9519 | − | 82.5000i | 0.0918697 | − | 0.116690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 575.500 | + | 996.795i | 0.811707 | + | 1.40592i | 0.911669 | + | 0.410926i | \(0.134795\pi\) |
−0.0999621 | + | 0.994991i | \(0.531872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 484.974 | + | 280.000i | 0.682102 | + | 0.393812i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −209.000 | −0.293128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 432.000i | − | 0.604196i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 125.000 | − | 216.506i | 0.174338 | − | 0.301961i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 349.008 | − | 201.500i | 0.485408 | − | 0.280250i | −0.237260 | − | 0.971446i | \(-0.576249\pi\) |
0.722667 | + | 0.691196i | \(0.242916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 604.500 | − | 241.621i | 0.838419 | − | 0.335119i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 558.586 | − | 322.500i | 0.772595 | − | 0.446058i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −896.000 | + | 1551.92i | −1.23586 | + | 2.14058i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 496.000i | 0.682256i | 0.940017 | + | 0.341128i | \(0.110809\pi\) | ||||
−0.940017 | + | 0.341128i | \(0.889191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1079.00 | 1.48011 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −242.487 | − | 140.000i | −0.331720 | − | 0.191518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −80.5000 | − | 139.430i | −0.109823 | − | 0.190218i | 0.805876 | − | 0.592085i | \(-0.201695\pi\) |
−0.915698 | + | 0.401866i | \(0.868362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −623.538 | + | 2115.00i | −0.848351 | + | 2.87755i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.5000 | − | 28.5788i | −0.0223881 | − | 0.0387773i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 473.716 | + | 273.500i | 0.641023 | + | 0.370095i | 0.785008 | − | 0.619485i | \(-0.212659\pi\) |
−0.143986 | + | 0.989580i | \(0.545992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −880.000 | −1.18758 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 256.000i | − | 0.344549i | −0.985049 | − | 0.172275i | \(-0.944888\pi\) | ||
0.985049 | − | 0.172275i | \(-0.0551116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −256.500 | + | 444.271i | −0.344295 | + | 0.596337i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 110.851 | − | 64.0000i | 0.148395 | − | 0.0856760i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −71.5000 | + | 28.5788i | −0.0954606 | + | 0.0381560i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −979.475 | + | 565.500i | −1.30423 | + | 0.752996i | −0.981126 | − | 0.193368i | \(-0.938059\pi\) |
−0.323101 | + | 0.946364i | \(0.604725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −985.000 | + | 1706.07i | −1.30810 | + | 2.26570i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 243.000i | − | 0.321854i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 336.000 | 0.443857 | 0.221929 | − | 0.975063i | \(-0.428765\pi\) | ||||
0.221929 | + | 0.975063i | \(0.428765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 246.817 | + | 142.500i | 0.325187 | + | 0.187747i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −172.500 | − | 298.779i | −0.226675 | − | 0.392613i | 0.730145 | − | 0.683292i | \(-0.239452\pi\) |
−0.956821 | + | 0.290678i | \(0.906119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −489.304 | + | 621.500i | −0.641290 | + | 0.814548i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 504.000 | + | 872.954i | 0.658824 | + | 1.14112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −734.390 | − | 424.000i | −0.957483 | − | 0.552803i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 568.000 | 0.738622 | 0.369311 | − | 0.929306i | \(-0.379594\pi\) | ||||
0.369311 | + | 0.929306i | \(0.379594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 445.000i | − | 0.577173i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −279.500 | + | 484.108i | −0.361578 | + | 0.626272i | −0.988221 | − | 0.153035i | \(-0.951095\pi\) |
0.626643 | + | 0.779307i | \(0.284429\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 533.472 | − | 308.000i | 0.688351 | − | 0.397419i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.00000 | + | 34.6410i | −0.00643501 | + | 0.0445830i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −381.051 | + | 220.000i | −0.489154 | + | 0.282413i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −72.0000 | + | 124.708i | −0.0921895 | + | 0.159677i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1120.00i | 1.43040i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1503.00 | 1.91465 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 572.443 | + | 330.500i | 0.727373 | + | 0.419949i | 0.817460 | − | 0.575985i | \(-0.195381\pi\) |
−0.0900872 | + | 0.995934i | \(0.528715\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −112.500 | − | 194.856i | −0.142586 | − | 0.246965i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −387.979 | − | 56.0000i | −0.490492 | − | 0.0707965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −632.000 | − | 1094.66i | −0.796974 | − | 1.38040i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 272.798 | + | 157.500i | 0.343142 | + | 0.198113i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 736.000 | 0.923463 | 0.461731 | − | 0.887020i | \(-0.347228\pi\) | ||||
0.461731 | + | 0.887020i | \(0.347228\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 595.000i | − | 0.744681i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −776.000 | + | 1344.07i | −0.968789 | + | 1.67799i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −371.525 | + | 214.500i | −0.462671 | + | 0.267123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −940.500 | − | 740.452i | −1.16832 | − | 0.919816i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1978.87 | + | 1142.50i | −2.45213 | + | 1.41574i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −143.500 | + | 248.549i | −0.177379 | + | 0.307230i | −0.940982 | − | 0.338456i | \(-0.890095\pi\) |
0.763603 | + | 0.645686i | \(0.223429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1272.00i | 1.56843i | 0.620487 | + | 0.784217i | \(0.286935\pi\) | ||||
−0.620487 | + | 0.784217i | \(0.713065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1985.00 | −2.44157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −148.090 | − | 85.5000i | −0.181706 | − | 0.104908i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −220.000 | − | 381.051i | −0.269278 | − | 0.466403i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 665.108 | + | 1664.00i | 0.812097 | + | 2.03175i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −371.500 | − | 643.457i | −0.452497 | − | 0.783748i | 0.546043 | − | 0.837757i | \(-0.316133\pi\) |
−0.998540 | + | 0.0540091i | \(0.982800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 196.588 | + | 113.500i | 0.238867 | + | 0.137910i | 0.614656 | − | 0.788795i | \(-0.289295\pi\) |
−0.375789 | + | 0.926705i | \(0.622628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −840.000 | −1.01818 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 120.000i | 0.145103i | 0.997365 | + | 0.0725514i | \(0.0231141\pi\) | ||||
−0.997365 | + | 0.0725514i | \(0.976886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 120.500 | − | 208.712i | 0.145356 | − | 0.251764i | −0.784150 | − | 0.620572i | \(-0.786901\pi\) |
0.929506 | + | 0.368808i | \(0.120234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1000.26 | − | 577.500i | 1.20368 | − | 0.694946i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 248.500 | − | 236.425i | 0.298319 | − | 0.283823i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1480.90 | − | 855.000i | 1.77354 | − | 1.02395i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 192.500 | − | 333.420i | 0.229988 | − | 0.398351i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 880.000i | 1.04887i | 0.851451 | + | 0.524434i | \(0.175723\pi\) | ||||
−0.851451 | + | 0.524434i | \(0.824277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 183.000 | 0.217598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 450.333 | + | 260.000i | 0.534203 | + | 0.308422i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 391.500 | + | 678.098i | 0.463314 | + | 0.802483i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 290.985 | + | 728.000i | 0.343547 | + | 0.859504i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −992.500 | − | 1719.06i | −1.16902 | − | 2.02481i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.4545 | − | 9.50000i | −0.0193355 | − | 0.0111633i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −176.000 | −0.206331 | −0.103165 | − | 0.994664i | \(-0.532897\pi\) | ||||
−0.103165 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1584.00i | 1.85263i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −127.500 | + | 220.836i | −0.148775 | + | 0.257686i | −0.930775 | − | 0.365593i | \(-0.880866\pi\) |
0.782000 | + | 0.623278i | \(0.214200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −558.586 | + | 322.500i | −0.650275 | + | 0.375437i | −0.788562 | − | 0.614956i | \(-0.789174\pi\) |
0.138286 | + | 0.990392i | \(0.455841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1100.00 | + | 866.025i | 1.27758 | + | 1.00584i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 723.131 | − | 417.500i | 0.837927 | − | 0.483778i | −0.0186319 | − | 0.999826i | \(-0.505931\pi\) |
0.856559 | + | 0.516049i | \(0.172598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 652.500 | − | 1130.16i | 0.754335 | − | 1.30655i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1200.00i | 1.38408i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 105.000 | 0.120829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 152.420 | + | 88.0000i | 0.174995 | + | 0.101033i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −704.000 | − | 1219.36i | −0.806415 | − | 1.39675i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1932.97 | + | 279.000i | 2.20911 | + | 0.318857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −571.500 | − | 989.867i | −0.651653 | − | 1.12870i | −0.982722 | − | 0.185090i | \(-0.940742\pi\) |
0.331068 | − | 0.943607i | \(-0.392591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −666.840 | − | 385.000i | −0.758634 | − | 0.437998i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −930.000 | −1.05562 | −0.527809 | − | 0.849363i | \(-0.676986\pi\) | ||||
−0.527809 | + | 0.849363i | \(0.676986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1320.00i | − | 1.49490i | −0.664316 | − | 0.747452i | \(-0.731277\pi\) | ||
0.664316 | − | 0.747452i | \(-0.268723\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1192.50 | + | 2065.47i | −1.34746 | + | 2.33387i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 918.853 | − | 530.500i | 1.03591 | − | 0.598083i | 0.117239 | − | 0.993104i | \(-0.462596\pi\) |
0.918672 | + | 0.395020i | \(0.129262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −96.0000 | + | 665.108i | −0.107987 | + | 0.748152i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −80.5404 | + | 46.5000i | −0.0903932 | + | 0.0521886i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 467.500 | − | 809.734i | 0.523516 | − | 0.906757i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2853.00i | − | 3.18771i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1520.00 | −1.69454 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −304.841 | − | 176.000i | −0.339089 | − | 0.195773i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.5000 | − | 42.4352i | −0.0271920 | − | 0.0470979i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −866.025 | + | 1100.00i | −0.959054 | + | 1.21816i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 837.000 | + | 1449.73i | 0.924862 | + | 1.60191i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −771.629 | − | 445.500i | −0.850748 | − | 0.491180i | 0.0101550 | − | 0.999948i | \(-0.496768\pi\) |
−0.860903 | + | 0.508769i | \(0.830101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −240.000 | −0.264026 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 464.000i | − | 0.509330i | −0.967029 | − | 0.254665i | \(-0.918035\pi\) | ||
0.967029 | − | 0.254665i | \(-0.0819653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | − | 20.7846i | 0.0131435 | − | 0.0227652i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3078.72 | + | 1777.50i | −3.36472 | + | 1.94262i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −916.500 | + | 366.329i | −0.999455 | + | 0.399486i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1251.41 | − | 722.500i | 1.36170 | − | 0.786181i | 0.371854 | − | 0.928291i | \(-0.378722\pi\) |
0.989851 | + | 0.142111i | \(0.0453889\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −940.000 | + | 1628.13i | −1.02063 | + | 1.76778i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 768.000i | − | 0.832069i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56.0000 | 0.0605405 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1288.65 | − | 744.000i | −1.39012 | − | 0.802589i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 800.500 | + | 1386.51i | 0.861679 | + | 1.49247i | 0.870307 | + | 0.492509i | \(0.163920\pi\) |
−0.00862789 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 523.945 | − | 126.500i | 0.562777 | − | 0.135875i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 807.500 | + | 1398.63i | 0.865488 | + | 1.49907i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 163.679 | + | 94.5000i | 0.175058 | + | 0.101070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1554.00 | 1.65848 | 0.829242 | − | 0.558889i | \(-0.188772\pi\) | ||||
0.829242 | + | 0.558889i | \(0.188772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 955.000i | − | 1.01704i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −492.500 | + | 853.035i | −0.523379 | + | 0.906520i | 0.476250 | + | 0.879310i | \(0.341996\pi\) |
−0.999630 | + | 0.0272100i | \(0.991338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −658.179 | + | 380.000i | −0.697963 | + | 0.402969i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2047.50 | − | 818.394i | 2.16667 | − | 0.866025i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −279.726 | + | 161.500i | −0.295381 | + | 0.170539i | −0.640366 | − | 0.768070i | \(-0.721217\pi\) |
0.344985 | + | 0.938608i | \(0.387884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1144.00 | − | 1981.47i | 1.20548 | − | 2.08795i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1675.00i | 1.76130i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −168.000 | −0.176285 | −0.0881427 | − | 0.996108i | \(-0.528093\pi\) | ||||
−0.0881427 | + | 0.996108i | \(0.528093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2205.77 | − | 1273.50i | −2.30970 | − | 1.33351i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 240.000 | + | 415.692i | 0.250784 | + | 0.434370i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.9711 | − | 49.5000i | 0.0406373 | − | 0.0516163i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −420.000 | − | 727.461i | −0.437045 | − | 0.756984i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 152.420 | + | 88.0000i | 0.158277 | + | 0.0913811i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2655.00 | 2.75130 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 112.000i | − | 0.115822i | −0.998322 | − | 0.0579111i | \(-0.981556\pi\) | ||
0.998322 | − | 0.0579111i | \(-0.0184440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 192.500 | − | 333.420i | 0.198658 | − | 0.344086i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1632.46 | − | 942.500i | 1.68121 | − | 0.970649i | 0.720356 | − | 0.693605i | \(-0.243978\pi\) |
0.960857 | − | 0.277044i | \(-0.0893548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −136.000 | + | 942.236i | −0.139774 | + | 0.968382i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3879.79 | − | 2240.00i | 3.97928 | − | 2.29744i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.5000 | + | 21.6506i | −0.0127943 | + | 0.0221603i | −0.872352 | − | 0.488879i | \(-0.837406\pi\) |
0.859557 | + | 0.511039i | \(0.170739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 291.000i | 0.297242i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1808.00 | 1.84302 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 73.6122 | + | 42.5000i | 0.0748852 | + | 0.0432350i | 0.536975 | − | 0.843598i | \(-0.319567\pi\) |
−0.462090 | + | 0.886833i | \(0.652900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −576.000 | − | 997.661i | −0.584772 | − | 1.01285i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2944.49 | − | 425.000i | −2.98327 | − | 0.430598i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −380.000 | − | 658.179i | −0.384226 | − | 0.665500i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −135.966 | − | 78.5000i | −0.137201 | − | 0.0792129i | 0.429828 | − | 0.902911i | \(-0.358574\pi\) |
−0.567029 | + | 0.823698i | \(0.691907\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −175.000 | −0.176234 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2547.00i | − | 2.55980i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −148.500 | + | 257.210i | −0.148947 | + | 0.257983i | −0.930838 | − | 0.365431i | \(-0.880922\pi\) |
0.781892 | + | 0.623414i | \(0.214255\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.3109 | − | 17.5000i | 0.0303412 | − | 0.0175175i |
(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 | 448.3.r.c.319.2 | 4 | ||
4.3 | odd | 2 | inner | 448.3.r.c.319.1 | 4 | ||
7.2 | even | 3 | inner | 448.3.r.c.191.1 | 4 | ||
8.3 | odd | 2 | 224.3.r.a.95.2 | yes | 4 | ||
8.5 | even | 2 | 224.3.r.a.95.1 | ✓ | 4 | ||
28.23 | odd | 6 | inner | 448.3.r.c.191.2 | 4 | ||
56.3 | even | 6 | 1568.3.d.a.1471.2 | 2 | |||
56.11 | odd | 6 | 1568.3.d.e.1471.1 | 2 | |||
56.37 | even | 6 | 224.3.r.a.191.2 | yes | 4 | ||
56.45 | odd | 6 | 1568.3.d.a.1471.1 | 2 | |||
56.51 | odd | 6 | 224.3.r.a.191.1 | yes | 4 | ||
56.53 | even | 6 | 1568.3.d.e.1471.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.a.95.1 | ✓ | 4 | 8.5 | even | 2 | ||
224.3.r.a.95.2 | yes | 4 | 8.3 | odd | 2 | ||
224.3.r.a.191.1 | yes | 4 | 56.51 | odd | 6 | ||
224.3.r.a.191.2 | yes | 4 | 56.37 | even | 6 | ||
448.3.r.c.191.1 | 4 | 7.2 | even | 3 | inner | ||
448.3.r.c.191.2 | 4 | 28.23 | odd | 6 | inner | ||
448.3.r.c.319.1 | 4 | 4.3 | odd | 2 | inner | ||
448.3.r.c.319.2 | 4 | 1.1 | even | 1 | trivial | ||
1568.3.d.a.1471.1 | 2 | 56.45 | odd | 6 | |||
1568.3.d.a.1471.2 | 2 | 56.3 | even | 6 | |||
1568.3.d.e.1471.1 | 2 | 56.11 | odd | 6 | |||
1568.3.d.e.1471.2 | 2 | 56.53 | even | 6 |