Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(289,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-2.11303 + 3.65987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.289 |
Dual form | 624.4.q.i.529.2 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.85953 | −0.524093 | −0.262046 | − | 0.965055i | \(-0.584397\pi\) | ||||
−0.262046 | + | 0.965055i | \(0.584397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.0627 | + | 20.8932i | −0.651326 | + | 1.12813i | 0.331476 | + | 0.943464i | \(0.392454\pi\) |
−0.982801 | + | 0.184666i | \(0.940880\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.9446 | − | 29.3489i | −0.464453 | − | 0.804457i | 0.534723 | − | 0.845027i | \(-0.320416\pi\) |
−0.999177 | + | 0.0405703i | \(0.987083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −40.8020 | − | 23.0694i | −0.870495 | − | 0.492178i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.78930 | + | 15.2235i | 0.151292 | + | 0.262046i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.6978 | − | 42.7779i | 0.352359 | − | 0.610303i | −0.634303 | − | 0.773084i | \(-0.718713\pi\) |
0.986662 | + | 0.162781i | \(0.0520463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −38.4274 | + | 66.5582i | −0.463992 | + | 0.803658i | −0.999155 | − | 0.0410905i | \(-0.986917\pi\) |
0.535163 | + | 0.844749i | \(0.320250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 72.3763 | 0.752086 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.14582 | + | 5.44871i | 0.0285195 | + | 0.0493972i | 0.879933 | − | 0.475098i | \(-0.157587\pi\) |
−0.851413 | + | 0.524495i | \(0.824254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −90.6659 | −0.725327 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −50.4977 | − | 87.4645i | −0.323351 | − | 0.560061i | 0.657826 | − | 0.753170i | \(-0.271476\pi\) |
−0.981177 | + | 0.193109i | \(0.938143\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 307.580 | 1.78203 | 0.891016 | − | 0.453972i | \(-0.149993\pi\) | ||||
0.891016 | + | 0.453972i | \(0.149993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −50.8338 | + | 88.0467i | −0.268152 | + | 0.464453i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 70.6819 | − | 122.425i | 0.341355 | − | 0.591244i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0095 | + | 65.8343i | 0.168884 | + | 0.292516i | 0.938028 | − | 0.346560i | \(-0.112650\pi\) |
−0.769144 | + | 0.639076i | \(0.779317\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.26677 | + | 140.611i | 0.00520115 | + | 0.577327i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 257.209 | + | 445.499i | 0.979740 | + | 1.69696i | 0.663312 | + | 0.748343i | \(0.269150\pi\) |
0.316427 | + | 0.948617i | \(0.397517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −134.092 | + | 232.254i | −0.475554 | + | 0.823684i | −0.999608 | − | 0.0280012i | \(-0.991086\pi\) |
0.524054 | + | 0.851685i | \(0.324419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.3679 | − | 45.6705i | 0.0873488 | − | 0.151292i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 460.912 | 1.43045 | 0.715223 | − | 0.698896i | \(-0.246325\pi\) | ||||
0.715223 | + | 0.698896i | \(0.246325\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −119.519 | − | 207.012i | −0.348451 | − | 0.603534i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −148.187 | −0.406869 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.8057 | 0.175733 | 0.0878663 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878663 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 99.2874 | + | 171.971i | 0.243417 | + | 0.421610i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 230.564 | 0.535772 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6010 | − | 21.8256i | 0.0278053 | − | 0.0481603i | −0.851788 | − | 0.523887i | \(-0.824481\pi\) |
0.879593 | + | 0.475727i | \(0.157815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 294.416 | − | 509.944i | 0.617969 | − | 1.07035i | −0.371886 | − | 0.928278i | \(-0.621289\pi\) |
0.989856 | − | 0.142076i | \(-0.0453778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −108.565 | − | 188.039i | −0.217109 | − | 0.376043i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 239.080 | + | 135.176i | 0.456220 | + | 0.257947i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −502.230 | − | 869.888i | −0.915778 | − | 1.58617i | −0.805758 | − | 0.592245i | \(-0.798242\pi\) |
−0.110021 | − | 0.993929i | \(-0.535092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.43745 | − | 16.3461i | 0.0164657 | − | 0.0285195i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 447.740 | − | 775.509i | 0.748408 | − | 1.29628i | −0.200177 | − | 0.979760i | \(-0.564152\pi\) |
0.948585 | − | 0.316522i | \(-0.102515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 968.599 | 1.55296 | 0.776479 | − | 0.630143i | \(-0.217004\pi\) | ||||
0.776479 | + | 0.630143i | \(0.217004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 135.999 | + | 235.557i | 0.209384 | + | 0.362663i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 817.592 | 1.21004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 119.053 | 0.169551 | 0.0847755 | − | 0.996400i | \(-0.472983\pi\) | ||||
0.0847755 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −480.784 | −0.635818 | −0.317909 | − | 0.948121i | \(-0.602981\pi\) | ||||
−0.317909 | + | 0.948121i | \(0.602981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −144.718 | + | 250.658i | −0.184669 | + | 0.319856i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −151.493 | + | 262.394i | −0.186687 | + | 0.323351i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −542.954 | − | 940.423i | −0.646663 | − | 1.12005i | −0.983915 | − | 0.178638i | \(-0.942831\pi\) |
0.337252 | − | 0.941414i | \(-0.390503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 974.179 | − | 574.205i | 1.12222 | − | 0.661462i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −461.370 | − | 799.116i | −0.514428 | − | 0.891016i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 225.167 | − | 390.000i | 0.243175 | − | 0.421191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.32761 | − | 14.4239i | 0.00871692 | − | 0.0150981i | −0.861634 | − | 0.507530i | \(-0.830559\pi\) |
0.870351 | + | 0.492432i | \(0.163892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 305.003 | 0.309636 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 479.002 | + | 829.655i | 0.471906 | + | 0.817364i | 0.999483 | − | 0.0321423i | \(-0.0102330\pi\) |
−0.527578 | + | 0.849507i | \(0.676900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.70560 | 0.00258826 | 0.00129413 | − | 0.999999i | \(-0.499588\pi\) | ||||
0.00129413 | + | 0.999999i | \(0.499588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −424.092 | −0.394163 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 675.642 | + | 1170.25i | 0.610437 | + | 1.05731i | 0.991167 | + | 0.132621i | \(0.0423395\pi\) |
−0.380730 | + | 0.924686i | \(0.624327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 448.455 | 0.394075 | 0.197037 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197037 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 114.028 | − | 197.503i | 0.0975054 | − | 0.168884i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −699.423 | + | 1211.44i | −0.582267 | + | 1.00852i | 0.412943 | + | 0.910757i | \(0.364501\pi\) |
−0.995210 | + | 0.0977596i | \(0.968832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.4330 | − | 31.9269i | −0.0149468 | − | 0.0258887i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 363.417 | − | 214.207i | 0.287162 | − | 0.169260i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 595.846 | + | 1032.04i | 0.459001 | + | 0.795013i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 91.2613 | − | 158.069i | 0.0685659 | − | 0.118760i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 771.628 | − | 1336.50i | 0.565653 | − | 0.979740i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1263.70 | 0.904231 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −59.7522 | − | 103.494i | −0.0417492 | − | 0.0723118i | 0.844396 | − | 0.535720i | \(-0.179960\pi\) |
−0.886145 | + | 0.463408i | \(0.846626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 804.552 | 0.549123 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2251.70 | 1.50177 | 0.750886 | − | 0.660432i | \(-0.229627\pi\) | ||||
0.750886 | + | 0.660432i | \(0.229627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −927.078 | − | 1605.75i | −0.604420 | − | 1.04689i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −158.207 | −0.100862 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −565.310 | + | 979.146i | −0.352538 | + | 0.610614i | −0.986693 | − | 0.162592i | \(-0.948015\pi\) |
0.634155 | + | 0.773206i | \(0.281348\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −297.644 | + | 515.534i | −0.181624 | + | 0.314583i | −0.942434 | − | 0.334393i | \(-0.891469\pi\) |
0.760809 | + | 0.648975i | \(0.224802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −691.368 | − | 1197.49i | −0.412934 | − | 0.715223i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3099 | + | 1588.40i | 0.00836821 | + | 0.928869i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 295.893 | + | 512.501i | 0.169466 | + | 0.293524i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −358.556 | + | 621.037i | −0.201178 | + | 0.348451i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 396.587 | − | 686.910i | 0.218052 | − | 0.377677i | −0.736161 | − | 0.676807i | \(-0.763363\pi\) |
0.954212 | + | 0.299130i | \(0.0966965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 134.213 | 0.0723317 | 0.0361659 | − | 0.999346i | \(-0.488486\pi\) | ||||
0.0361659 | + | 0.999346i | \(0.488486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 222.280 | + | 385.001i | 0.117453 | + | 0.203434i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1802.28 | −0.933950 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1509.07 | 0.767114 | 0.383557 | − | 0.923517i | \(-0.374699\pi\) | ||||
0.383557 | + | 0.923517i | \(0.374699\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −101.709 | − | 176.164i | −0.0507297 | − | 0.0878663i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −151.788 | −0.0743019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 587.540 | − | 1017.65i | 0.282329 | − | 0.489009i | −0.689629 | − | 0.724163i | \(-0.742226\pi\) |
0.971958 | + | 0.235155i | \(0.0755596\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 297.862 | − | 515.913i | 0.140537 | − | 0.243417i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 737.007 | + | 1276.53i | 0.341505 | + | 0.591504i | 0.984712 | − | 0.174188i | \(-0.0557301\pi\) |
−0.643208 | + | 0.765692i | \(0.722397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1132.60 | + | 1882.56i | 0.515522 | + | 0.856877i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −345.847 | − | 599.024i | −0.154664 | − | 0.267886i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1164.15 | − | 2016.37i | 0.511612 | − | 0.886139i | −0.488297 | − | 0.872678i | \(-0.662382\pi\) |
0.999909 | − | 0.0134612i | \(-0.00428497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1093.68 | − | 1894.30i | 0.472424 | − | 0.818263i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −75.6062 | −0.0321069 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1066.93 | − | 1847.97i | −0.445508 | − | 0.771642i | 0.552580 | − | 0.833460i | \(-0.313643\pi\) |
−0.998087 | + | 0.0618183i | \(0.980310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2485.41 | −1.02066 | −0.510329 | − | 0.859979i | \(-0.670476\pi\) | ||||
−0.510329 | + | 0.859979i | \(0.670476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1766.50 | −0.713570 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −222.718 | − | 385.758i | −0.0885110 | − | 0.153305i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1673.98 | −0.654617 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −325.694 | + | 564.118i | −0.125348 | + | 0.217109i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1162.53 | + | 2013.57i | −0.440408 | + | 0.762809i | −0.997720 | − | 0.0674941i | \(-0.978500\pi\) |
0.557311 | + | 0.830304i | \(0.311833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1675.06 | − | 2901.29i | −0.624732 | − | 1.08207i | −0.988593 | − | 0.150614i | \(-0.951875\pi\) |
0.363860 | − | 0.931453i | \(-0.381458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.42266 | − | 823.914i | −0.00272588 | − | 0.302573i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1929.65 | + | 3342.25i | 0.697878 | + | 1.20876i | 0.969201 | + | 0.246272i | \(0.0792056\pi\) |
−0.271323 | + | 0.962488i | \(0.587461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2041.80 | + | 3536.50i | −0.727333 | + | 1.25978i | 0.230673 | + | 0.973031i | \(0.425907\pi\) |
−0.958006 | + | 0.286747i | \(0.907426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1506.69 | + | 2609.66i | −0.528725 | + | 0.915778i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2436.56 | 0.842428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1507.13 | − | 2610.42i | −0.513474 | − | 0.889364i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −56.6247 | −0.0190130 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2604.55 | 0.862011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1513.65 | + | 2621.72i | 0.493857 | + | 0.855386i | 0.999975 | − | 0.00707871i | \(-0.00225324\pi\) |
−0.506118 | + | 0.862464i | \(0.668920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2686.44 | −0.864188 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 785.716 | − | 1360.90i | 0.249234 | − | 0.431687i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3710.25 | + | 6426.34i | −1.16068 | + | 2.01036i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1452.90 | − | 2516.49i | −0.448300 | − | 0.776479i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1994.58 | + | 1175.66i | −0.607104 | + | 0.357843i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −862.379 | − | 1493.68i | −0.258965 | − | 0.448540i | 0.707000 | − | 0.707213i | \(-0.250048\pi\) |
−0.965965 | + | 0.258673i | \(0.916715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 407.996 | − | 706.671i | 0.120888 | − | 0.209384i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −961.637 | + | 1665.60i | −0.281172 | + | 0.487005i | −0.971674 | − | 0.236326i | \(-0.924057\pi\) |
0.690502 | + | 0.723331i | \(0.257390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 373.993 | 0.107922 | 0.0539610 | − | 0.998543i | \(-0.482815\pi\) | ||||
0.0539610 | + | 0.998543i | \(0.482815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1226.39 | − | 2124.17i | −0.349309 | − | 0.605021i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3094.49 | 0.870073 | 0.435036 | − | 0.900413i | \(-0.356735\pi\) | ||||
0.435036 | + | 0.900413i | \(0.356735\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2700.73 | −0.749686 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −178.580 | − | 309.309i | −0.0489452 | − | 0.0847755i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1221.18 | 0.330510 | 0.165255 | − | 0.986251i | \(-0.447155\pi\) | ||||
0.165255 | + | 0.986251i | \(0.447155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −72.7003 | + | 125.921i | −0.0194317 | + | 0.0336567i | −0.875578 | − | 0.483077i | \(-0.839519\pi\) |
0.856146 | + | 0.516734i | \(0.172852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 700.323 | + | 1212.99i | 0.182620 | + | 0.316308i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3103.38 | − | 1829.21i | 0.799446 | − | 0.471213i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 721.176 | + | 1249.11i | 0.183545 | + | 0.317909i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −492.835 | + | 853.615i | −0.123934 | + | 0.214660i | −0.921316 | − | 0.388815i | \(-0.872884\pi\) |
0.797382 | + | 0.603475i | \(0.206218\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 106.609 | − | 184.652i | 0.0264919 | − | 0.0458854i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 868.306 | 0.213237 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1464.66 | − | 2536.86i | −0.355498 | − | 0.615740i | 0.631705 | − | 0.775209i | \(-0.282355\pi\) |
−0.987203 | + | 0.159469i | \(0.949022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1833.99 | −0.439995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 908.958 | 0.215567 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1119.00 | + | 1938.17i | 0.262360 | + | 0.454420i | 0.966869 | − | 0.255275i | \(-0.0821660\pi\) |
−0.704509 | + | 0.709695i | \(0.748833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −397.310 | −0.0921002 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1628.86 | + | 2821.27i | −0.373351 | + | 0.646663i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −962.992 | + | 1667.95i | −0.218270 | + | 0.378055i | −0.954279 | − | 0.298917i | \(-0.903375\pi\) |
0.736009 | + | 0.676972i | \(0.236708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1781.14 | − | 3085.03i | −0.399250 | − | 0.691521i | 0.594384 | − | 0.804182i | \(-0.297396\pi\) |
−0.993634 | + | 0.112660i | \(0.964063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2953.10 | − | 1669.68i | −0.654687 | − | 0.370160i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1536.30 | + | 2660.94i | 0.336881 | + | 0.583494i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 718.712 | − | 1244.85i | 0.155896 | − | 0.270020i | −0.777489 | − | 0.628897i | \(-0.783507\pi\) |
0.933385 | + | 0.358877i | \(0.116840\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1384.11 | + | 2397.35i | −0.297005 | + | 0.514428i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3913.51 | −0.830820 | −0.415410 | − | 0.909634i | \(-0.636362\pi\) | ||||
−0.415410 | + | 0.909634i | \(0.636362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1606.16 | − | 2781.94i | −0.337371 | − | 0.584344i | 0.646566 | − | 0.762858i | \(-0.276204\pi\) |
−0.983937 | + | 0.178514i | \(0.942871\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1351.00 | −0.280794 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12410.6 | −2.55252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1236.54 | + | 2141.74i | 0.251686 | + | 0.435934i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −49.9657 | −0.0100654 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2450.89 | − | 4245.06i | 0.488677 | − | 0.846413i | −0.511238 | − | 0.859439i | \(-0.670813\pi\) |
0.999915 | + | 0.0130260i | \(0.00414642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73.8362 | + | 127.888i | −0.0145726 | + | 0.0252404i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −457.504 | − | 792.420i | −0.0893841 | − | 0.154818i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.65667 | − | 294.890i | −0.000513844 | − | 0.0570366i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3235.03 | − | 5603.23i | −0.619481 | − | 1.07297i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1437.01 | − | 2488.97i | 0.272455 | − | 0.471906i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1725.14 | + | 2988.03i | −0.323873 | + | 0.560965i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5800.63 | −1.07837 | −0.539185 | − | 0.842188i | \(-0.681267\pi\) | ||||
−0.539185 | + | 0.842188i | \(0.681267\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.05840 | − | 7.02935i | −0.000747165 | − | 0.00129413i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4913.51 | 0.895884 | 0.447942 | − | 0.894063i | \(-0.352157\pi\) | ||||
0.447942 | + | 0.894063i | \(0.352157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8104.97 | −1.46364 | −0.731822 | − | 0.681496i | \(-0.761330\pi\) | ||||
−0.731822 | + | 0.681496i | \(0.761330\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 636.137 | + | 1101.82i | 0.113785 | + | 0.197081i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5149.92 | 0.912455 | 0.456227 | − | 0.889863i | \(-0.349200\pi\) | ||||
0.456227 | + | 0.889863i | \(0.349200\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1711.33 | + | 2964.10i | −0.300363 | + | 0.520244i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2026.93 | − | 3510.74i | 0.352436 | − | 0.610437i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1898.15 | + | 3287.69i | 0.326984 | + | 0.566352i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3699.35 | + | 2091.61i | 0.631393 | + | 0.356990i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −672.682 | − | 1165.12i | −0.113760 | − | 0.197037i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5559.86 | + | 9629.96i | −0.931687 | + | 1.61373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3030.99 | − | 5249.83i | 0.503318 | − | 0.871772i | −0.496675 | − | 0.867937i | \(-0.665446\pi\) |
0.999993 | − | 0.00383535i | \(-0.00122083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −684.170 | −0.112589 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2942.83 | + | 5097.14i | 0.479953 | + | 0.831302i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3743.50 | 0.605108 | 0.302554 | − | 0.953132i | \(-0.402161\pi\) | ||||
0.302554 | + | 0.953132i | \(0.402161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4196.54 | 0.672344 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5211.82 | − | 9027.13i | −0.827671 | − | 1.43357i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2508.15 | −0.394832 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −55.2990 | + | 95.7807i | −0.00862956 | + | 0.0149468i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1260.20 | + | 2182.74i | −0.194961 | + | 0.337682i | −0.946888 | − | 0.321565i | \(-0.895791\pi\) |
0.751927 | + | 0.659246i | \(0.229125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5325.37 | − | 9223.82i | −0.816793 | − | 1.41473i | −0.908033 | − | 0.418898i | \(-0.862417\pi\) |
0.0912407 | − | 0.995829i | \(-0.470917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1101.65 | − | 622.875i | −0.167527 | − | 0.0947197i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4501.41 | + | 7796.67i | 0.678714 | + | 1.17557i | 0.975368 | + | 0.220582i | \(0.0707956\pi\) |
−0.296655 | + | 0.954985i | \(0.595871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2623.55 | + | 4544.12i | −0.392235 | + | 0.679371i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1787.54 | − | 3096.11i | 0.265004 | − | 0.459001i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11360.9 | 1.67021 | 0.835106 | − | 0.550089i | \(-0.185406\pi\) | ||||
0.835106 | + | 0.550089i | \(0.185406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 476.168 | + | 824.747i | 0.0694224 | + | 0.120243i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −547.568 | −0.0791731 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5675.54 | −0.813894 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6969.42 | − | 12071.4i | −0.991283 | − | 1.71695i | −0.609743 | − | 0.792599i | \(-0.708727\pi\) |
−0.381540 | − | 0.924352i | \(-0.624606\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4629.77 | −0.653160 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −817.922 | + | 1416.68i | −0.114459 | + | 0.198249i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −796.535 | + | 1379.64i | −0.110571 | + | 0.191515i | −0.916001 | − | 0.401177i | \(-0.868601\pi\) |
0.805430 | + | 0.592691i | \(0.201935\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1895.55 | − | 3283.19i | −0.261029 | − | 0.452116i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.6458 | + | 4733.68i | 0.00582592 | + | 0.646676i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4568.78 | + | 7913.36i | 0.619215 | + | 1.07251i | 0.989629 | + | 0.143645i | \(0.0458824\pi\) |
−0.370414 | + | 0.928867i | \(0.620784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −179.257 | + | 310.482i | −0.0241039 | + | 0.0417492i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4775.53 | − | 8271.47i | 0.637124 | − | 1.10353i | −0.348937 | − | 0.937146i | \(-0.613457\pi\) |
0.986061 | − | 0.166385i | \(-0.0532093\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4790.71 | −0.634174 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1206.83 | − | 2090.29i | −0.158518 | − | 0.274561i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7366.50 | 0.960145 | 0.480072 | − | 0.877229i | \(-0.340610\pi\) | ||||
0.480072 | + | 0.877229i | \(0.340610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 310.779 | 0.0401964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3377.55 | − | 5850.10i | −0.433524 | − | 0.750886i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −697.596 | −0.0888604 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5848.24 | − | 10129.4i | 0.739332 | − | 1.28056i | −0.213465 | − | 0.976951i | \(-0.568475\pi\) |
0.952797 | − | 0.303609i | \(-0.0981917\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2781.24 | + | 4817.24i | −0.348962 | + | 0.604420i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7083.82 | + | 12269.5i | 0.882167 | + | 1.52796i | 0.848927 | + | 0.528510i | \(0.177249\pi\) |
0.0332399 | + | 0.999447i | \(0.489417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12549.9 | − | 7095.70i | −1.55125 | − | 0.877077i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 237.311 | + | 411.035i | 0.0291163 | + | 0.0504308i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1288.11 | − | 2231.07i | 0.156878 | − | 0.271720i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1351.85 | + | 2341.47i | −0.163434 | + | 0.283076i | −0.936098 | − | 0.351739i | \(-0.885590\pi\) |
0.772664 | + | 0.634815i | \(0.218924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3391.86 | 0.407076 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 304.006 | + | 526.553i | 0.0362207 | + | 0.0627361i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2817.17 | 0.333228 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1785.86 | 0.209722 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3571.26 | + | 6185.61i | 0.416390 | + | 0.721209i | 0.995573 | − | 0.0939884i | \(-0.0299617\pi\) |
−0.579183 | + | 0.815198i | \(0.696628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3406.45 | −0.394347 | −0.197174 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197174 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2074.11 | + | 3592.46i | −0.238408 | + | 0.412934i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2239.25 | + | 3878.49i | −0.255575 | + | 0.442670i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7102.92 | + | 12302.6i | 0.804999 | + | 1.39430i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4105.31 | − | 2419.77i | 0.462019 | − | 0.272326i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2586.48 | + | 4479.92i | 0.289064 | + | 0.500673i | 0.973587 | − | 0.228318i | \(-0.0733227\pi\) |
−0.684523 | + | 0.728992i | \(0.739989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5477.49 | + | 9487.28i | −0.607924 | + | 1.05296i | 0.383658 | + | 0.923475i | \(0.374664\pi\) |
−0.991582 | + | 0.129480i | \(0.958669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 887.678 | − | 1537.50i | 0.0978412 | − | 0.169466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −483.542 | −0.0529313 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5916.22 | + | 10247.2i | 0.643202 | + | 1.11406i | 0.984714 | + | 0.174181i | \(0.0557279\pi\) |
−0.341511 | + | 0.939878i | \(0.610939\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2151.33 | 0.232300 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13479.8 | −1.44570 | −0.722852 | − | 0.691003i | \(-0.757169\pi\) | ||||
−0.722852 | + | 0.691003i | \(0.757169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3181.46 | + | 5510.44i | 0.338911 | + | 0.587011i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2379.52 | −0.251784 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3387.17 | − | 5866.75i | 0.356014 | − | 0.616635i | −0.631277 | − | 0.775558i | \(-0.717469\pi\) |
0.987291 | + | 0.158923i | \(0.0508021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8716.61 | − | 15097.6i | 0.910087 | − | 1.57632i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −201.319 | − | 348.695i | −0.0208804 | − | 0.0361659i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5708.23 | + | 3364.57i | −0.588145 | + | 0.346667i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2321.18 | + | 4020.40i | 0.237594 | + | 0.411524i | 0.960023 | − | 0.279920i | \(-0.0903080\pi\) |
−0.722430 | + | 0.691444i | \(0.756975\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 666.841 | − | 1155.00i | 0.0678115 | − | 0.117453i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1230.18 | + | 2130.74i | −0.124285 | + | 0.215268i | −0.921453 | − | 0.388489i | \(-0.872997\pi\) |
0.797168 | + | 0.603757i | \(0.206330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4290.01 | −0.430613 | −0.215306 | − | 0.976547i | \(-0.569075\pi\) | ||||
−0.215306 | + | 0.976547i | \(0.569075\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2703.41 | + | 4682.45i | 0.269608 | + | 0.466975i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8798.99 | 0.871882 | 0.435941 | − | 0.899975i | \(-0.356416\pi\) | ||||
0.435941 | + | 0.899975i | \(0.356416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24233.0 | 2.38588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2263.61 | − | 3920.68i | −0.221447 | − | 0.383557i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9088.54 | 0.883491 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3484.05 | − | 6034.56i | 0.336546 | − | 0.582915i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −305.126 | + | 528.493i | −0.0292888 | + | 0.0507297i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5486.68 | − | 9503.21i | −0.523367 | − | 0.906499i | −0.999630 | − | 0.0271958i | \(-0.991342\pi\) |
0.476263 | − | 0.879303i | \(-0.341991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0994 | − | 3563.03i | −0.00304284 | − | 0.337755i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 227.683 | + | 394.358i | 0.0214491 | + | 0.0371509i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −48.7959 | + | 84.5170i | −0.00456847 | + | 0.00791283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2604.79 | + | 4511.62i | −0.242370 | + | 0.419797i | −0.961389 | − | 0.275193i | \(-0.911258\pi\) |
0.719019 | + | 0.694991i | \(0.244591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3525.24 | −0.326006 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4389.61 | − | 7603.03i | −0.403463 | − | 0.698819i | 0.590678 | − | 0.806907i | \(-0.298860\pi\) |
−0.994141 | + | 0.108089i | \(0.965527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4988.73 | −0.455742 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1787.17 | −0.162278 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10801.9 | + | 18709.5i | 0.974915 | + | 1.68860i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15590.1 | 1.39861 | 0.699305 | − | 0.714823i | \(-0.253493\pi\) | ||||
0.699305 | + | 0.714823i | \(0.253493\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2211.02 | − | 3829.60i | 0.197168 | − | 0.341505i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.1955 | + | 55.7642i | −0.00285393 | + | 0.00494314i | −0.867449 | − | 0.497526i | \(-0.834242\pi\) |
0.864595 | + | 0.502470i | \(0.167575\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2806.73 | − | 4861.39i | −0.247322 | − | 0.428375i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3192.13 | − | 5766.42i | 0.279620 | − | 0.505120i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1607.08 | − | 2783.54i | −0.139946 | − | 0.242393i | 0.787530 | − | 0.616276i | \(-0.211359\pi\) |
−0.927476 | + | 0.373883i | \(0.878026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11683.9 | + | 20237.2i | −1.01148 | + | 1.75194i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1037.54 | + | 1797.07i | −0.0892954 | + | 0.154664i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8535 | −0.00135649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7809.97 | − | 13527.3i | −0.664376 | − | 1.15073i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6984.92 | −0.590759 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3053.01 | −0.256727 | −0.128363 | − | 0.991727i | \(-0.540972\pi\) | ||||
−0.128363 | + | 0.991727i | \(0.540972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2548.01 | + | 4413.28i | 0.213034 | + | 0.368985i | 0.952663 | − | 0.304030i | \(-0.0983322\pi\) |
−0.739629 | + | 0.673015i | \(0.764999\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6562.06 | −0.545508 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7596.55 | − | 13157.6i | 0.627915 | − | 1.08758i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6063.71 | − | 10502.6i | 0.498373 | − | 0.863208i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 113.409 | + | 196.431i | 0.00926845 | + | 0.0160534i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −217.216 | − | 24110.9i | −0.0176523 | − | 1.95940i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3958.95 | − | 6857.09i | −0.319925 | − | 0.554127i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3200.78 | + | 5543.91i | −0.257214 | + | 0.445508i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4050.39 | + | 7015.48i | −0.323678 | + | 0.560627i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7861.99 | 0.624793 | 0.312397 | − | 0.949952i | \(-0.398868\pi\) | ||||
0.312397 | + | 0.949952i | \(0.398868\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3728.11 | + | 6457.28i | 0.294638 | + | 0.510329i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2627.73 | −0.206532 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6317.48 | 0.493814 | 0.246907 | − | 0.969039i | \(-0.420586\pi\) | ||||
0.246907 | + | 0.969039i | \(0.420586\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2649.75 | + | 4589.49i | 0.205990 | + | 0.356785i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7761.98 | 0.600130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1436.11 | + | 2487.41i | −0.110433 | + | 0.191275i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −668.153 | + | 1157.28i | −0.0511018 | + | 0.0885110i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 485.617 | + | 841.113i | 0.0369412 | + | 0.0639840i | 0.883905 | − | 0.467667i | \(-0.154905\pi\) |
−0.846964 | + | 0.531651i | \(0.821572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10829.2 | − | 6383.00i | 0.819367 | − | 0.482955i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2510.97 | + | 4349.12i | 0.188972 | + | 0.327309i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4664.24 | − | 8078.71i | 0.349155 | − | 0.604755i | −0.636944 | − | 0.770910i | \(-0.719802\pi\) |
0.986100 | + | 0.166155i | \(0.0531352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4098.29 | − | 7098.45i | 0.305162 | − | 0.528556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1954.16 | 0.144739 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8726.08 | − | 15114.0i | −0.642911 | − | 1.11355i | −0.984780 | − | 0.173807i | \(-0.944393\pi\) |
0.341869 | − | 0.939748i | \(-0.388940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20181.4 | 1.47910 | 0.739548 | − | 0.673103i | \(-0.235039\pi\) | ||||
0.739548 | + | 0.673103i | \(0.235039\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6975.20 | 0.508540 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −285.218 | − | 494.012i | −0.0206859 | − | 0.0358291i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6382.72 | 0.460513 | 0.230257 | − | 0.973130i | \(-0.426043\pi\) | ||||
0.230257 | + | 0.973130i | \(0.426043\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5025.17 | + | 8703.86i | −0.360689 | + | 0.624732i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5799.57 | − | 10045.1i | 0.414125 | − | 0.717285i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1148.94 | − | 1990.02i | −0.0816197 | − | 0.141369i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2129.46 | + | 1255.16i | −0.150499 | + | 0.0887082i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −387.763 | − | 671.626i | −0.0272653 | − | 0.0472248i | 0.852071 | − | 0.523427i | \(-0.175347\pi\) |
−0.879336 | + | 0.476202i | \(0.842013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11819.5 | + | 20472.0i | −0.826849 | + | 1.43214i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5788.95 | − | 10026.8i | 0.402920 | − | 0.697878i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17843.3 | −1.23564 | −0.617821 | − | 0.786319i | \(-0.711984\pi\) | ||||
−0.617821 | + | 0.786319i | \(0.711984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3491.38 | − | 6047.24i | −0.240559 | − | 0.416660i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12250.8 | 0.839852 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24373.3 | 1.66255 | 0.831274 | − | 0.555863i | \(-0.187612\pi\) | ||||
0.831274 | + | 0.555863i | \(0.187612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1763.50 | + | 3054.46i | 0.119691 | + | 0.207311i | 0.919645 | − | 0.392750i | \(-0.128476\pi\) |
−0.799954 | + | 0.600061i | \(0.795143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9040.14 | 0.610519 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −534.748 | + | 926.211i | −0.0359349 | + | 0.0622411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3995.77 | − | 6920.88i | 0.267189 | − | 0.462784i | −0.700946 | − | 0.713214i | \(-0.747239\pi\) |
0.968135 | + | 0.250430i | \(0.0805720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3654.84 | − | 6330.36i | −0.243188 | − | 0.421214i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18806.1 | − | 10633.0i | −1.24520 | − | 0.704034i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8166.09 | + | 14144.1i | 0.538051 | + | 0.931932i | 0.999009 | + | 0.0445098i | \(0.0141726\pi\) |
−0.460958 | + | 0.887422i | \(0.652494\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4521.38 | + | 7831.26i | −0.296455 | + | 0.513474i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9676.82 | − | 16760.8i | 0.631401 | − | 1.09362i | −0.355865 | − | 0.934537i | \(-0.615814\pi\) |
0.987266 | − | 0.159081i | \(-0.0508530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9982.52 | 0.648193 | 0.324096 | − | 0.946024i | \(-0.394940\pi\) | ||||
0.324096 | + | 0.946024i | \(0.394940\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 84.9370 | + | 147.115i | 0.00548858 | + | 0.00950649i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26198.0 | 1.68475 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3928.53 | 0.251426 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3906.82 | − | 6766.81i | −0.248841 | − | 0.431006i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3755.00 | 0.238031 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −287.887 | + | 498.636i | −0.0181626 | + | 0.0314586i | −0.874964 | − | 0.484188i | \(-0.839115\pi\) |
0.856801 | + | 0.515647i | \(0.172448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4540.95 | − | 7865.15i | 0.285129 | − | 0.493857i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 350.120 | + | 606.426i | 0.0218805 | + | 0.0378981i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 100.935 | + | 11203.7i | 0.00627814 | + | 0.696873i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4029.66 | + | 6979.58i | 0.249469 | + | 0.432094i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12260.9 | − | 21236.5i | 0.755500 | − | 1.30856i | −0.189625 | − | 0.981857i | \(-0.560727\pi\) |
0.945125 | − | 0.326708i | \(-0.105939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11333.5 | + | 19630.2i | −0.695099 | + | 1.20395i | 0.275048 | + | 0.961431i | \(0.411306\pi\) |
−0.970147 | + | 0.242517i | \(0.922027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4714.30 | −0.287791 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1198.73 | − | 2076.25i | −0.0728389 | − | 0.126161i | 0.827306 | − | 0.561752i | \(-0.189873\pi\) |
−0.900144 | + | 0.435592i | \(0.856539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −854.078 | −0.0516572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22261.5 | 1.34024 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10001.0 | − | 17322.3i | −0.599342 | − | 1.03809i | −0.992918 | − | 0.118799i | \(-0.962095\pi\) |
0.393576 | − | 0.919292i | \(-0.371238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13193.9 | −0.787068 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4358.70 | + | 7549.48i | −0.258826 | + | 0.448300i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1758.98 | + | 3046.64i | −0.103976 | + | 0.180091i | −0.913319 | − | 0.407244i | \(-0.866490\pi\) |
0.809343 | + | 0.587336i | \(0.199823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6791.71 | − | 11763.6i | −0.399647 | − | 0.692209i | 0.594035 | − | 0.804439i | \(-0.297534\pi\) |
−0.993682 | + | 0.112230i | \(0.964201\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6046.32 | + | 3418.59i | 0.354177 | + | 0.200252i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5432.25 | + | 9408.93i | 0.316772 | + | 0.548665i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 317.713 | − | 550.295i | 0.0184436 | − | 0.0319453i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2587.14 | + | 4481.05i | −0.149513 | + | 0.258965i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19955.1 | −1.14807 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5447.92 | + | 9436.07i | 0.312038 | + | 0.540466i | 0.978804 | − | 0.204801i | \(-0.0656549\pi\) |
−0.666765 | + | 0.745268i | \(0.732322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2447.98 | −0.139589 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1449.03 | 0.0822609 | 0.0411305 | − | 0.999154i | \(-0.486904\pi\) | ||||
0.0411305 | + | 0.999154i | \(0.486904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 200.907 | + | 347.982i | 0.0113551 | + | 0.0196676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5769.82 | 0.324670 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7683.21 | + | 13307.7i | −0.430439 | + | 0.745543i | −0.996911 | − | 0.0785385i | \(-0.974975\pi\) |
0.566472 | + | 0.824081i | \(0.308308\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3312.45 | − | 5737.34i | 0.184763 | − | 0.320018i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −560.989 | − | 971.661i | −0.0311544 | − | 0.0539610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2766.61 | − | 1564.24i | −0.152974 | − | 0.0864918i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1009.85 | − | 1749.12i | −0.0555957 | − | 0.0962946i | 0.836888 | − | 0.547374i | \(-0.184372\pi\) |
−0.892484 | + | 0.451079i | \(0.851039\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3679.16 | + | 6372.50i | −0.201674 | + | 0.349309i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1744.05 | − | 3020.79i | 0.0951880 | − | 0.164870i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25410.0 | 1.38088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4641.74 | − | 8039.73i | −0.251168 | − | 0.435036i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28031.6 | 1.51033 | 0.755164 | − | 0.655536i | \(-0.227557\pi\) | ||||
0.755164 | + | 0.655536i | \(0.227557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5842.42 | −0.313444 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4051.10 | + | 7016.70i | 0.216416 | + | 0.374843i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23112.3 | −1.22946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9802.22 | + | 16977.9i | −0.519224 | + | 0.899323i | 0.480526 | + | 0.876980i | \(0.340446\pi\) |
−0.999750 | + | 0.0223423i | \(0.992888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −535.739 | + | 927.928i | −0.0282585 | + | 0.0489452i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 967.590 | + | 1675.91i | 0.0508226 | + | 0.0880274i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −83.8493 | − | 9307.26i | −0.00438571 | − | 0.486813i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1831.77 | − | 3172.73i | −0.0954099 | − | 0.165255i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7363.71 | + | 12754.3i | −0.381947 | + | 0.661552i | −0.991341 | − | 0.131316i | \(-0.958080\pi\) |
0.609393 | + | 0.792868i | \(0.291413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.6369 | + | 56.5287i | −0.00168580 | + | 0.00291989i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 436.202 | 0.0224378 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4578.42 | + | 7930.05i | 0.234535 | + | 0.406227i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16890.5 | 0.861668 | 0.430834 | − | 0.902431i | \(-0.358219\pi\) | ||||
0.430834 | + | 0.902431i | \(0.358219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6623.56 | + | 11472.3i | 0.335131 | + | 0.580465i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12553.6 | 0.632578 | 0.316289 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316289 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2100.97 | − | 3638.98i | 0.105436 | − | 0.182620i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17020.2 | + | 29479.8i | −0.850673 | + | 1.47341i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18937.4 | − | 32800.5i | −0.942656 | − | 1.63273i | −0.760378 | − | 0.649481i | \(-0.774986\pi\) |
−0.182278 | − | 0.983247i | \(-0.558347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9407.48 | − | 5319.00i | −0.466387 | − | 0.263695i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17941.3 | + | 31075.3i | 0.885872 | + | 1.53438i | 0.844711 | + | 0.535223i | \(0.179773\pi\) |
0.0411616 | + | 0.999153i | \(0.486894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2323.82 | + | 4024.97i | −0.114279 | + | 0.197938i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2163.53 | − | 3747.34i | 0.105970 | − | 0.183545i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32600.3 | −1.59037 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −90.8447 | − | 157.348i | −0.00441407 | − | 0.00764540i | 0.863810 | − | 0.503818i | \(-0.168072\pi\) |
−0.868224 | + | 0.496172i | \(0.834738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2957.01 | 0.143107 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −786.425 | −0.0379085 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 245.526 | + | 425.264i | 0.0117884 | + | 0.0204181i | 0.871859 | − | 0.489756i | \(-0.162914\pi\) |
−0.860071 | + | 0.510174i | \(0.829581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −639.655 | −0.0305903 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4056.50 | − | 7026.07i | 0.193230 | − | 0.334684i | −0.753089 | − | 0.657919i | \(-0.771437\pi\) |
0.946319 | + | 0.323235i | \(0.104770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5409.58 | + | 9369.67i | −0.256671 | + | 0.444567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1302.46 | − | 2255.93i | −0.0615562 | − | 0.106619i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1017.65 | + | 599.830i | −0.0479078 | + | 0.0282381i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9932.33 | − | 17203.3i | −0.465759 | − | 0.806719i | 0.533476 | − | 0.845815i | \(-0.320885\pi\) |
−0.999235 | + | 0.0390962i | \(0.987552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4393.98 | + | 7610.59i | −0.205247 | + | 0.355498i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4523.71 | + | 7835.29i | −0.210487 | + | 0.364574i | −0.951867 | − | 0.306511i | \(-0.900838\pi\) |
0.741380 | + | 0.671085i | \(0.234172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27887.0 | −1.29256 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2750.99 | + | 4764.85i | 0.127016 | + | 0.219997i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39535.5 | −1.81837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30347.1 | −1.39040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1363.44 | − | 2361.54i | −0.0622289 | − | 0.107784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8842.45 | −0.402039 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7509.20 | + | 13006.3i | −0.340120 | + | 0.589105i | −0.984455 | − | 0.175639i | \(-0.943801\pi\) |
0.644335 | + | 0.764743i | \(0.277134\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3357.00 | − | 5814.50i | 0.151473 | − | 0.262360i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16873.9 | − | 29226.4i | −0.758491 | − | 1.31375i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23776.9 | + | 14014.7i | −1.06474 | + | 0.627587i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 595.965 | + | 1032.24i | 0.0265870 | + | 0.0460501i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15970.5 | + | 27661.8i | −0.709794 | + | 1.22940i | 0.255139 | + | 0.966904i | \(0.417879\pi\) |
−0.964933 | + | 0.262495i | \(0.915455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11383.5 | − | 19716.9i | 0.504030 | − | 0.873006i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9773.17 | 0.431108 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16412.5 | − | 28427.3i | −0.721277 | − | 1.24929i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 889.409 | 0.0389411 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5777.95 | 0.252037 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13630.0 | − | 23607.9i | −0.592344 | − | 1.02597i | −0.993916 | − | 0.110142i | \(-0.964869\pi\) |
0.401572 | − | 0.915827i | \(-0.368464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20707.8 | 0.896607 | 0.448303 | − | 0.893881i | \(-0.352028\pi\) | ||||
0.448303 | + | 0.893881i | \(0.352028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5343.43 | + | 9255.09i | −0.230507 | + | 0.399250i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3442.71 | + | 5962.95i | −0.147967 | + | 0.256286i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10305.6 | − | 17849.8i | −0.441307 | − | 0.764366i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 91.6839 | + | 10176.9i | 0.00391171 | + | 0.434200i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7829.28 | − | 13560.7i | −0.332818 | − | 0.576458i | 0.650245 | − | 0.759724i | \(-0.274666\pi\) |
−0.983063 | + | 0.183267i | \(0.941333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2053.29 | + | 3556.40i | −0.0869662 | + | 0.150630i | −0.906227 | − | 0.422791i | \(-0.861051\pi\) |
0.819261 | + | 0.573421i | \(0.194384\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4608.89 | − | 7982.83i | 0.194498 | − | 0.336881i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16747.3 | −0.704184 | −0.352092 | − | 0.935965i | \(-0.614530\pi\) | ||||
−0.352092 | + | 0.935965i | \(0.614530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14578.5 | + | 25250.8i | 0.610776 | + | 1.05790i | 0.991110 | + | 0.133046i | \(0.0424758\pi\) |
−0.380334 | + | 0.924849i | \(0.624191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4312.27 | −0.180013 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11807.4 | −0.491119 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4318.52 | − | 7479.89i | −0.178980 | − | 0.310003i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8304.66 | 0.342952 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22909.7 | − | 39680.8i | 0.942707 | − | 1.63282i | 0.182429 | − | 0.983219i | \(-0.441604\pi\) |
0.760278 | − | 0.649598i | \(-0.225063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7094.47 | − | 12288.0i | 0.290888 | − | 0.503833i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5870.26 | + | 10167.6i | 0.239837 | + | 0.415410i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6636.51 | − | 11030.9i | −0.270181 | − | 0.449083i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2201.72 | + | 3813.49i | 0.0893175 | + | 0.154703i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4818.47 | + | 8345.83i | −0.194781 | + | 0.337371i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −239.142 | + | 414.205i | −0.00963298 | + | 0.0166848i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17351.1 | 0.696471 | 0.348235 | − | 0.937407i | \(-0.386781\pi\) | ||||
0.348235 | + | 0.937407i | \(0.386781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2026.50 | + | 3510.00i | 0.0810583 | + | 0.140397i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21768.1 | −0.867659 | −0.433829 | − | 0.900995i | \(-0.642838\pi\) | ||||
−0.433829 | + | 0.900995i | \(0.642838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29878.4 | 1.18677 | 0.593387 | − | 0.804918i | \(-0.297791\pi\) | ||||
0.593387 | + | 0.804918i | \(0.297791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18615.9 | + | 32243.6i | 0.736849 | + | 1.27626i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15067.7 | 0.594335 | 0.297168 | − | 0.954825i | \(-0.403958\pi\) | ||||
0.297168 | + | 0.954825i | \(0.403958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6821.40 | + | 11815.0i | −0.268132 | + | 0.464419i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3709.61 | − | 6425.23i | 0.145311 | − | 0.251686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2017.31 | − | 3494.08i | −0.0787486 | − | 0.136397i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 424.138 | + | 47079.3i | 0.0164999 | + | 1.83148i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 74.9485 | + | 129.815i | 0.00290564 | + | 0.00503272i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15243.7 | + | 26402.8i | −0.588949 | + | 1.02009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10559.8 | − | 18290.1i | 0.406588 | − | 0.704232i | −0.587917 | − | 0.808922i | \(-0.700052\pi\) |
0.994505 | + | 0.104690i | \(0.0333850\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14705.3 | −0.564275 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15826.2 | − | 27411.9i | −0.605221 | − | 1.04827i | −0.992016 | − | 0.126108i | \(-0.959751\pi\) |
0.386795 | − | 0.922166i | \(-0.373582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11701.6 | −0.445969 | −0.222984 | − | 0.974822i | \(-0.571580\pi\) | ||||
−0.222984 | + | 0.974822i | \(0.571580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 443.017 | 0.0168270 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11254.0 | + | 19492.4i | 0.426010 | + | 0.737871i | 0.996514 | − | 0.0834239i | \(-0.0265855\pi\) |
−0.570504 | + | 0.821295i | \(0.693252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2883.10 | 0.108769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1372.51 | + | 2377.26i | −0.0516059 | + | 0.0893841i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17711.7 | + | 30677.5i | −0.663716 | + | 1.14959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6251.69 | + | 10828.2i | 0.233487 | + | 0.404412i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −762.163 | + | 449.238i | −0.0283700 | + | 0.0167220i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15532.1 | − | 26902.3i | −0.576222 | − | 0.998046i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1674.65 | − | 2900.58i | 0.0619210 | − | 0.107250i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9705.08 | + | 16809.7i | −0.357658 | + | 0.619481i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14563.3 | 0.534919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9359.32 | + | 16210.8i | 0.342636 | + | 0.593464i | 0.984921 | − | 0.173002i | \(-0.0553468\pi\) |
−0.642285 | + | 0.766466i | \(0.722013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8622.03 | −0.314604 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18616.7 | −0.677057 | −0.338529 | − | 0.940956i | \(-0.609929\pi\) | ||||
−0.338529 | + | 0.940956i | \(0.609929\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8146.69 | + | 14110.5i | 0.295308 | + | 0.511488i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10350.8 | 0.373977 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27161.7 | + | 47045.4i | −0.978143 | + | 1.69419i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27382.2 | + | 47427.3i | −0.982867 | + | 1.70238i | −0.331812 | + | 0.943346i | \(0.607660\pi\) |
−0.651056 | + | 0.759030i | \(0.725674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8700.94 | + | 15070.5i | 0.311298 | + | 0.539185i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36159.2 | + | 21313.2i | −1.28949 | + | 0.760056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3446.16 | − | 5968.93i | −0.122496 | − | 0.212170i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.1752 | + | 21.0880i | −0.000431376 | + | 0.000747165i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15916.0 | − | 27567.4i | 0.562097 | − | 0.973581i | −0.435216 | − | 0.900326i | \(-0.643328\pi\) |
0.997313 | − | 0.0732550i | \(-0.0233387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18371.2 | 0.646713 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7370.27 | − | 12765.7i | −0.258619 | − | 0.447942i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9808.73 | 0.343080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27408.7 | −0.955607 | −0.477803 | − | 0.878467i | \(-0.658567\pi\) | ||||
−0.477803 | + | 0.878467i | \(0.658567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12157.5 | + | 21057.3i | 0.422517 | + | 0.731822i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54837.8 | 1.89975 | 0.949874 | − | 0.312634i | \(-0.101211\pi\) | ||||
0.949874 | + | 0.312634i | \(0.101211\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1618.27 | + | 2802.92i | −0.0558833 | + | 0.0967928i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1908.41 | − | 3305.47i | 0.0656938 | − | 0.113785i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19853.9 | − | 34388.0i | −0.681273 | − | 1.18000i | −0.974593 | − | 0.223984i | \(-0.928094\pi\) |
0.293320 | − | 0.956014i | \(-0.405240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39520.8 | − | 22345.0i | −1.35184 | − | 0.764332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7724.88 | − | 13379.9i | −0.263403 | − | 0.456227i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8553.32 | − | 14814.8i | 0.290734 | − | 0.503566i | −0.683250 | − | 0.730185i | \(-0.739434\pi\) |
0.973983 | + | 0.226619i | \(0.0727673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6811.90 | − | 11798.6i | 0.230815 | − | 0.399783i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10268.0 | 0.346829 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13638.4 | − | 23622.3i | −0.459234 | − | 0.795417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64814.4 | 2.17564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12161.6 | −0.406958 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9815.06 | + | 17000.2i | 0.327417 | + | 0.567104i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23417.5 | 0.778756 | 0.389378 | − | 0.921078i | \(-0.372690\pi\) | ||||
0.389378 | + | 0.921078i | \(0.372690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5694.44 | − | 9863.06i | 0.188784 | − | 0.326984i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8215.31 | − | 14229.3i | 0.271516 | − | 0.470279i | −0.697734 | − | 0.716357i | \(-0.745808\pi\) |
0.969250 | + | 0.246077i | \(0.0791417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7180.78 | − | 12437.5i | −0.236593 | − | 0.409792i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −114.852 | − | 12748.6i | −0.00377254 | − | 0.418751i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5277.32 | + | 9140.58i | 0.172811 | + | 0.299318i | 0.939402 | − | 0.342819i | \(-0.111382\pi\) |
−0.766591 | + | 0.642136i | \(0.778048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18400.3 | + | 31870.2i | −0.600689 | + | 1.04042i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2018.05 | + | 3495.36i | −0.0656791 | + | 0.113760i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1534.33 | −0.0497839 | −0.0248919 | − | 0.999690i | \(-0.507924\pi\) | ||||
−0.0248919 | + | 0.999690i | \(0.507924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11306.9 | − | 19584.1i | −0.365753 | − | 0.633502i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33359.1 | 1.07582 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1687.31 | −0.0542502 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9009.08 | − | 15604.2i | −0.288782 | − | 0.500185i | 0.684737 | − | 0.728790i | \(-0.259917\pi\) |
−0.973519 | + | 0.228605i | \(0.926584\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18185.9 | −0.581181 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11964.0 | − | 20722.2i | 0.381190 | − | 0.660240i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24143.8 | + | 41818.4i | −0.766944 | + | 1.32839i | 0.172269 | + | 0.985050i | \(0.444890\pi\) |
−0.939213 | + | 0.343336i | \(0.888443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1026.26 | + | 1777.53i | 0.0325018 | + | 0.0562947i |
(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 | 624.4.q.i.289.2 | 8 | ||
4.3 | odd | 2 | 39.4.e.c.16.4 | ✓ | 8 | ||
12.11 | even | 2 | 117.4.g.e.55.1 | 8 | |||
13.9 | even | 3 | inner | 624.4.q.i.529.2 | 8 | ||
52.3 | odd | 6 | 507.4.a.m.1.1 | 4 | |||
52.11 | even | 12 | 507.4.b.h.337.2 | 8 | |||
52.15 | even | 12 | 507.4.b.h.337.7 | 8 | |||
52.23 | odd | 6 | 507.4.a.i.1.4 | 4 | |||
52.35 | odd | 6 | 39.4.e.c.22.4 | yes | 8 | ||
156.23 | even | 6 | 1521.4.a.bb.1.1 | 4 | |||
156.35 | even | 6 | 117.4.g.e.100.1 | 8 | |||
156.107 | even | 6 | 1521.4.a.v.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.4 | ✓ | 8 | 4.3 | odd | 2 | ||
39.4.e.c.22.4 | yes | 8 | 52.35 | odd | 6 | ||
117.4.g.e.55.1 | 8 | 12.11 | even | 2 | |||
117.4.g.e.100.1 | 8 | 156.35 | even | 6 | |||
507.4.a.i.1.4 | 4 | 52.23 | odd | 6 | |||
507.4.a.m.1.1 | 4 | 52.3 | odd | 6 | |||
507.4.b.h.337.2 | 8 | 52.11 | even | 12 | |||
507.4.b.h.337.7 | 8 | 52.15 | even | 12 | |||
624.4.q.i.289.2 | 8 | 1.1 | even | 1 | trivial | ||
624.4.q.i.529.2 | 8 | 13.9 | even | 3 | inner | ||
1521.4.a.v.1.4 | 4 | 156.107 | even | 6 | |||
1521.4.a.bb.1.1 | 4 | 156.23 | even | 6 |