Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,4,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), 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: | \(26.5508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 71x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.3 | ||
Root | \(1.97374 - 1.97374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.143 |
Dual form | 450.4.f.e.107.3 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | + | 1.41421i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.9129 | + | 21.9129i | −1.18318 | + | 1.18318i | −0.204270 | + | 0.978915i | \(0.565482\pi\) |
−0.978915 | + | 0.204270i | \(0.934518\pi\) | |||||||
\(8\) | −5.65685 | + | 5.65685i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 64.9306i | − | 1.77976i | −0.456198 | − | 0.889878i | \(-0.650789\pi\) | ||
0.456198 | − | 0.889878i | \(-0.349211\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0871 | − | 13.0871i | −0.279209 | − | 0.279209i | 0.553584 | − | 0.832793i | \(-0.313260\pi\) |
−0.832793 | + | 0.553584i | \(0.813260\pi\) | |||||||
\(14\) | −61.9790 | −1.18318 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | 5.53365 | + | 5.53365i | 0.0789474 | + | 0.0789474i | 0.745478 | − | 0.666530i | \(-0.232221\pi\) |
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 103.826i | − | 1.25365i | −0.779162 | − | 0.626823i | \(-0.784355\pi\) | ||
0.779162 | − | 0.626823i | \(-0.215645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 91.8258 | − | 91.8258i | 0.889878 | − | 0.889878i | ||||
\(23\) | −19.7990 | + | 19.7990i | −0.179495 | + | 0.179495i | −0.791135 | − | 0.611641i | \(-0.790510\pi\) |
0.611641 | + | 0.791135i | \(0.290510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 37.0160i | − | 0.279209i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −87.6515 | − | 87.6515i | −0.591592 | − | 0.591592i | ||||
\(29\) | 184.646 | 1.18234 | 0.591171 | − | 0.806547i | \(-0.298666\pi\) | ||||
0.591171 | + | 0.806547i | \(0.298666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.8258 | 0.114865 | 0.0574324 | − | 0.998349i | \(-0.481709\pi\) | ||||
0.0574324 | + | 0.998349i | \(0.481709\pi\) | |||||||
\(32\) | −22.6274 | − | 22.6274i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.6515i | 0.0789474i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 254.739 | − | 254.739i | 1.13186 | − | 1.13186i | 0.141991 | − | 0.989868i | \(-0.454650\pi\) |
0.989868 | − | 0.141991i | \(-0.0453503\pi\) | |||||||
\(38\) | 146.832 | − | 146.832i | 0.626823 | − | 0.626823i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.1468i | 0.240533i | 0.992742 | + | 0.120267i | \(0.0383750\pi\) | ||||
−0.992742 | + | 0.120267i | \(0.961625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −104.174 | − | 104.174i | −0.369452 | − | 0.369452i | 0.497826 | − | 0.867277i | \(-0.334132\pi\) |
−0.867277 | + | 0.497826i | \(0.834132\pi\) | |||||||
\(44\) | 259.722 | 0.889878 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −56.0000 | −0.179495 | ||||||||
\(47\) | −185.567 | − | 185.567i | −0.575910 | − | 0.575910i | 0.357864 | − | 0.933774i | \(-0.383505\pi\) |
−0.933774 | + | 0.357864i | \(0.883505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 617.348i | − | 1.79985i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 52.3485 | − | 52.3485i | 0.139604 | − | 0.139604i | ||||
\(53\) | −259.476 | + | 259.476i | −0.672486 | + | 0.672486i | −0.958289 | − | 0.285802i | \(-0.907740\pi\) |
0.285802 | + | 0.958289i | \(0.407740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 247.916i | − | 0.591592i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 261.129 | + | 261.129i | 0.591171 | + | 0.591171i | ||||
\(59\) | −255.539 | −0.563870 | −0.281935 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281935 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −894.083 | −1.87665 | −0.938325 | − | 0.345755i | \(-0.887623\pi\) | ||||
−0.938325 | + | 0.345755i | \(0.887623\pi\) | |||||||
\(62\) | 28.0379 | + | 28.0379i | 0.0574324 | + | 0.0574324i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 64.0000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 100.523 | − | 100.523i | 0.183296 | − | 0.183296i | −0.609495 | − | 0.792790i | \(-0.708628\pi\) |
0.792790 | + | 0.609495i | \(0.208628\pi\) | |||||||
\(68\) | −22.1346 | + | 22.1346i | −0.0394737 | + | 0.0394737i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 491.653i | − | 0.821810i | −0.911678 | − | 0.410905i | \(-0.865213\pi\) | ||
0.911678 | − | 0.410905i | \(-0.134787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −603.780 | − | 603.780i | −0.968043 | − | 0.968043i | 0.0314620 | − | 0.999505i | \(-0.489984\pi\) |
−0.999505 | + | 0.0314620i | \(0.989984\pi\) | |||||||
\(74\) | 720.510 | 1.13186 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 415.303 | 0.626823 | ||||||||
\(77\) | 1422.82 | + | 1422.82i | 2.10578 | + | 2.10578i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 698.780i | − | 0.995176i | −0.867413 | − | 0.497588i | \(-0.834219\pi\) | ||
0.867413 | − | 0.497588i | \(-0.165781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −89.3030 | + | 89.3030i | −0.120267 | + | 0.120267i | ||||
\(83\) | 707.101 | − | 707.101i | 0.935114 | − | 0.935114i | −0.0629055 | − | 0.998019i | \(-0.520037\pi\) |
0.998019 | + | 0.0629055i | \(0.0200367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 294.649i | − | 0.369452i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 367.303 | + | 367.303i | 0.444939 | + | 0.444939i | ||||
\(89\) | 389.648 | 0.464074 | 0.232037 | − | 0.972707i | \(-0.425461\pi\) | ||||
0.232037 | + | 0.972707i | \(0.425461\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 573.553 | 0.660711 | ||||||||
\(92\) | −79.1960 | − | 79.1960i | −0.0897473 | − | 0.0897473i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 524.864i | − | 0.575910i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29.2576 | − | 29.2576i | 0.0306253 | − | 0.0306253i | −0.691628 | − | 0.722254i | \(-0.743106\pi\) |
0.722254 | + | 0.691628i | \(0.243106\pi\) | |||||||
\(98\) | 873.063 | − | 873.063i | 0.899925 | − | 0.899925i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 386.204i | 0.380482i | 0.981737 | + | 0.190241i | \(0.0609269\pi\) | ||||
−0.981737 | + | 0.190241i | \(0.939073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −793.564 | − | 793.564i | −0.759148 | − | 0.759148i | 0.217019 | − | 0.976167i | \(-0.430366\pi\) |
−0.976167 | + | 0.217019i | \(0.930366\pi\) | |||||||
\(104\) | 148.064 | 0.139604 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −733.909 | −0.672486 | ||||||||
\(107\) | 501.494 | + | 501.494i | 0.453096 | + | 0.453096i | 0.896381 | − | 0.443285i | \(-0.146187\pi\) |
−0.443285 | + | 0.896381i | \(0.646187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 875.295i | 0.769157i | 0.923092 | + | 0.384578i | \(0.125653\pi\) | ||||
−0.923092 | + | 0.384578i | \(0.874347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 350.606 | − | 350.606i | 0.295796 | − | 0.295796i | ||||
\(113\) | −943.768 | + | 943.768i | −0.785683 | + | 0.785683i | −0.980783 | − | 0.195100i | \(-0.937497\pi\) |
0.195100 | + | 0.980783i | \(0.437497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 738.584i | 0.591171i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −361.386 | − | 361.386i | −0.281935 | − | 0.281935i | ||||
\(119\) | −242.516 | −0.186819 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2884.98 | −2.16753 | ||||||||
\(122\) | −1264.42 | − | 1264.42i | −0.938325 | − | 0.938325i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 79.3030i | 0.0574324i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −535.822 | + | 535.822i | −0.374382 | + | 0.374382i | −0.869070 | − | 0.494688i | \(-0.835282\pi\) |
0.494688 | + | 0.869070i | \(0.335282\pi\) | |||||||
\(128\) | 90.5097 | − | 90.5097i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1852.00i | 1.23519i | 0.786495 | + | 0.617597i | \(0.211894\pi\) | ||||
−0.786495 | + | 0.617597i | \(0.788106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2275.12 | + | 2275.12i | 1.48329 | + | 1.48329i | ||||
\(134\) | 284.321 | 0.183296 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −62.6061 | −0.0394737 | ||||||||
\(137\) | −888.796 | − | 888.796i | −0.554270 | − | 0.554270i | 0.373401 | − | 0.927670i | \(-0.378192\pi\) |
−0.927670 | + | 0.373401i | \(0.878192\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 252.348i | − | 0.153985i | −0.997032 | − | 0.0769925i | \(-0.975468\pi\) | ||
0.997032 | − | 0.0769925i | \(-0.0245318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 695.303 | − | 695.303i | 0.410905 | − | 0.410905i | ||||
\(143\) | −849.755 | + | 849.755i | −0.496924 | + | 0.496924i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1707.75i | − | 0.968043i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1018.95 | + | 1018.95i | 0.565929 | + | 0.565929i | ||||
\(149\) | 169.025 | 0.0929335 | 0.0464668 | − | 0.998920i | \(-0.485204\pi\) | ||||
0.0464668 | + | 0.998920i | \(0.485204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2783.65 | 1.50020 | 0.750100 | − | 0.661324i | \(-0.230005\pi\) | ||||
0.750100 | + | 0.661324i | \(0.230005\pi\) | |||||||
\(152\) | 587.327 | + | 587.327i | 0.313411 | + | 0.313411i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4024.33i | 2.10578i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2018.22 | + | 2018.22i | −1.02593 | + | 1.02593i | −0.0262763 | + | 0.999655i | \(0.508365\pi\) |
−0.999655 | + | 0.0262763i | \(0.991635\pi\) | |||||||
\(158\) | 988.225 | − | 988.225i | 0.497588 | − | 0.497588i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 867.706i | − | 0.424750i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2132.69 | − | 2132.69i | −1.02482 | − | 1.02482i | −0.999684 | − | 0.0251326i | \(-0.991999\pi\) |
−0.0251326 | − | 0.999684i | \(-0.508001\pi\) | |||||||
\(164\) | −252.587 | −0.120267 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1999.98 | 0.935114 | ||||||||
\(167\) | −1027.95 | − | 1027.95i | −0.476319 | − | 0.476319i | 0.427633 | − | 0.903952i | \(-0.359347\pi\) |
−0.903952 | + | 0.427633i | \(0.859347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1854.45i | − | 0.844085i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 416.697 | − | 416.697i | 0.184726 | − | 0.184726i | ||||
\(173\) | −868.268 | + | 868.268i | −0.381579 | + | 0.381579i | −0.871671 | − | 0.490092i | \(-0.836963\pi\) |
0.490092 | + | 0.871671i | \(0.336963\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1038.89i | 0.444939i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 551.045 | + | 551.045i | 0.232037 | + | 0.232037i | ||||
\(179\) | −3448.21 | −1.43984 | −0.719920 | − | 0.694057i | \(-0.755822\pi\) | ||||
−0.719920 | + | 0.694057i | \(0.755822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3511.81 | 1.44216 | 0.721080 | − | 0.692852i | \(-0.243646\pi\) | ||||
0.721080 | + | 0.692852i | \(0.243646\pi\) | |||||||
\(182\) | 811.126 | + | 811.126i | 0.330355 | + | 0.330355i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 224.000i | − | 0.0897473i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 359.303 | − | 359.303i | 0.140507 | − | 0.140507i | ||||
\(188\) | 742.269 | − | 742.269i | 0.287955 | − | 0.287955i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2037.43i | 0.771850i | 0.922530 | + | 0.385925i | \(0.126118\pi\) | ||||
−0.922530 | + | 0.385925i | \(0.873882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1127.78 | − | 1127.78i | −0.420619 | − | 0.420619i | 0.464798 | − | 0.885417i | \(-0.346127\pi\) |
−0.885417 | + | 0.464798i | \(0.846127\pi\) | |||||||
\(194\) | 82.7529 | 0.0306253 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2469.39 | 0.899925 | ||||||||
\(197\) | 257.810 | + | 257.810i | 0.0932396 | + | 0.0932396i | 0.752188 | − | 0.658948i | \(-0.228998\pi\) |
−0.658948 | + | 0.752188i | \(0.728998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 513.030i | − | 0.182753i | −0.995816 | − | 0.0913763i | \(-0.970873\pi\) | ||
0.995816 | − | 0.0913763i | \(-0.0291266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −546.174 | + | 546.174i | −0.190241 | + | 0.190241i | ||||
\(203\) | −4046.12 | + | 4046.12i | −1.39893 | + | 1.39893i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2244.54i | − | 0.759148i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 209.394 | + | 209.394i | 0.0698022 | + | 0.0698022i | ||||
\(209\) | −6741.47 | −2.23118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1610.24 | −0.525373 | −0.262686 | − | 0.964881i | \(-0.584608\pi\) | ||||
−0.262686 | + | 0.964881i | \(0.584608\pi\) | |||||||
\(212\) | −1037.90 | − | 1037.90i | −0.336243 | − | 0.336243i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1418.44i | 0.453096i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −434.439 | + | 434.439i | −0.135906 | + | 0.135906i | ||||
\(218\) | −1237.85 | + | 1237.85i | −0.384578 | + | 0.384578i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 144.839i | − | 0.0440856i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2339.82 | + | 2339.82i | 0.702628 | + | 0.702628i | 0.964974 | − | 0.262346i | \(-0.0844961\pi\) |
−0.262346 | + | 0.964974i | \(0.584496\pi\) | |||||||
\(224\) | 991.664 | 0.295796 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2669.38 | −0.785683 | ||||||||
\(227\) | −1601.14 | − | 1601.14i | −0.468155 | − | 0.468155i | 0.433162 | − | 0.901316i | \(-0.357398\pi\) |
−0.901316 | + | 0.433162i | \(0.857398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6303.36i | 1.81894i | 0.415766 | + | 0.909472i | \(0.363514\pi\) | ||||
−0.415766 | + | 0.909472i | \(0.636486\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1044.52 | + | 1044.52i | −0.295585 | + | 0.295585i | ||||
\(233\) | 2681.95 | − | 2681.95i | 0.754080 | − | 0.754080i | −0.221158 | − | 0.975238i | \(-0.570984\pi\) |
0.975238 | + | 0.221158i | \(0.0709836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1022.15i | − | 0.281935i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −342.970 | − | 342.970i | −0.0934093 | − | 0.0934093i | ||||
\(239\) | 2314.62 | 0.626444 | 0.313222 | − | 0.949680i | \(-0.398592\pi\) | ||||
0.313222 | + | 0.949680i | \(0.398592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1476.59 | 0.394670 | 0.197335 | − | 0.980336i | \(-0.436771\pi\) | ||||
0.197335 | + | 0.980336i | \(0.436771\pi\) | |||||||
\(242\) | −4079.98 | − | 4079.98i | −1.08377 | − | 1.08377i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3576.33i | − | 0.938325i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1358.78 | + | 1358.78i | −0.350029 | + | 0.350029i | ||||
\(248\) | −112.151 | + | 112.151i | −0.0287162 | + | 0.0287162i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4021.54i | − | 1.01130i | −0.862738 | − | 0.505652i | \(-0.831252\pi\) | ||
0.862738 | − | 0.505652i | \(-0.168748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1285.56 | + | 1285.56i | 0.319457 | + | 0.319457i | ||||
\(254\) | −1515.53 | −0.374382 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −371.183 | − | 371.183i | −0.0900924 | − | 0.0900924i | 0.660624 | − | 0.750717i | \(-0.270292\pi\) |
−0.750717 | + | 0.660624i | \(0.770292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11164.1i | 2.67839i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2619.13 | + | 2619.13i | −0.617597 | + | 0.617597i | ||||
\(263\) | 181.405 | − | 181.405i | 0.0425320 | − | 0.0425320i | −0.685521 | − | 0.728053i | \(-0.740425\pi\) |
0.728053 | + | 0.685521i | \(0.240425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6435.01i | 1.48329i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 402.091 | + | 402.091i | 0.0916478 | + | 0.0916478i | ||||
\(269\) | 3301.79 | 0.748377 | 0.374189 | − | 0.927353i | \(-0.377921\pi\) | ||||
0.374189 | + | 0.927353i | \(0.377921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3894.23 | −0.872906 | −0.436453 | − | 0.899727i | \(-0.643765\pi\) | ||||
−0.436453 | + | 0.899727i | \(0.643765\pi\) | |||||||
\(272\) | −88.5383 | − | 88.5383i | −0.0197369 | − | 0.0197369i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 2513.89i | − | 0.554270i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1417.53 | − | 1417.53i | 0.307476 | − | 0.307476i | −0.536454 | − | 0.843930i | \(-0.680236\pi\) |
0.843930 | + | 0.536454i | \(0.180236\pi\) | |||||||
\(278\) | 356.875 | − | 356.875i | 0.0769925 | − | 0.0769925i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8119.33i | 1.72370i | 0.507166 | + | 0.861848i | \(0.330693\pi\) | ||||
−0.507166 | + | 0.861848i | \(0.669307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1166.94 | − | 1166.94i | −0.245114 | − | 0.245114i | 0.573848 | − | 0.818962i | \(-0.305450\pi\) |
−0.818962 | + | 0.573848i | \(0.805450\pi\) | |||||||
\(284\) | 1966.61 | 0.410905 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2403.47 | −0.496924 | ||||||||
\(287\) | −1383.73 | − | 1383.73i | −0.284595 | − | 0.284595i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 4851.76i | − | 0.987535i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2415.12 | − | 2415.12i | 0.484021 | − | 0.484021i | ||||
\(293\) | 4826.44 | − | 4826.44i | 0.962333 | − | 0.962333i | −0.0369831 | − | 0.999316i | \(-0.511775\pi\) |
0.999316 | + | 0.0369831i | \(0.0117748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2882.04i | 0.565929i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 239.038 | + | 239.038i | 0.0464668 | + | 0.0464668i | ||||
\(299\) | 518.224 | 0.100233 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4565.52 | 0.874259 | ||||||||
\(302\) | 3936.68 | + | 3936.68i | 0.750100 | + | 0.750100i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1661.21i | 0.313411i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4161.89 | − | 4161.89i | 0.773718 | − | 0.773718i | −0.205036 | − | 0.978754i | \(-0.565731\pi\) |
0.978754 | + | 0.205036i | \(0.0657313\pi\) | |||||||
\(308\) | −5691.27 | + | 5691.27i | −1.05289 | + | 1.05289i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3984.60i | − | 0.726514i | −0.931689 | − | 0.363257i | \(-0.881665\pi\) | ||
0.931689 | − | 0.363257i | \(-0.118335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2427.14 | − | 2427.14i | −0.438308 | − | 0.438308i | 0.453135 | − | 0.891442i | \(-0.350306\pi\) |
−0.891442 | + | 0.453135i | \(0.850306\pi\) | |||||||
\(314\) | −5708.38 | −1.02593 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2795.12 | 0.497588 | ||||||||
\(317\) | 7132.54 | + | 7132.54i | 1.26373 | + | 1.26373i | 0.949269 | + | 0.314464i | \(0.101825\pi\) |
0.314464 | + | 0.949269i | \(0.398175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11989.2i | − | 2.10428i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1227.12 | − | 1227.12i | 0.212375 | − | 0.212375i | ||||
\(323\) | 574.535 | − | 574.535i | 0.0989721 | − | 0.0989721i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 6032.16i | − | 1.02482i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −357.212 | − | 357.212i | −0.0601334 | − | 0.0601334i | ||||
\(329\) | 8132.63 | 1.36282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1793.22 | −0.297777 | −0.148889 | − | 0.988854i | \(-0.547570\pi\) | ||||
−0.148889 | + | 0.988854i | \(0.547570\pi\) | |||||||
\(332\) | 2828.41 | + | 2828.41i | 0.467557 | + | 0.467557i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2907.48i | − | 0.476319i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4438.46 | + | 4438.46i | −0.717443 | + | 0.717443i | −0.968081 | − | 0.250638i | \(-0.919360\pi\) |
0.250638 | + | 0.968081i | \(0.419360\pi\) | |||||||
\(338\) | 2622.59 | − | 2622.59i | 0.422042 | − | 0.422042i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1287.30i | − | 0.204431i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6011.77 | + | 6011.77i | 0.946370 | + | 0.946370i | ||||
\(344\) | 1178.60 | 0.184726 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2455.83 | −0.381579 | ||||||||
\(347\) | 4669.58 | + | 4669.58i | 0.722410 | + | 0.722410i | 0.969096 | − | 0.246685i | \(-0.0793414\pi\) |
−0.246685 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1244.02i | 0.190805i | 0.995439 | + | 0.0954026i | \(0.0304138\pi\) | ||||
−0.995439 | + | 0.0954026i | \(0.969586\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1469.21 | + | 1469.21i | −0.222470 | + | 0.222470i | ||||
\(353\) | 5341.19 | − | 5341.19i | 0.805334 | − | 0.805334i | −0.178590 | − | 0.983924i | \(-0.557153\pi\) |
0.983924 | + | 0.178590i | \(0.0571535\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1558.59i | 0.232037i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4876.51 | − | 4876.51i | −0.719920 | − | 0.719920i | ||||
\(359\) | 1040.64 | 0.152988 | 0.0764940 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764940 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3920.79 | −0.571627 | ||||||||
\(362\) | 4966.45 | + | 4966.45i | 0.721080 | + | 0.721080i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2294.21i | 0.330355i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1447.50 | − | 1447.50i | 0.205883 | − | 0.205883i | −0.596632 | − | 0.802515i | \(-0.703495\pi\) |
0.802515 | + | 0.596632i | \(0.203495\pi\) | |||||||
\(368\) | 316.784 | − | 316.784i | 0.0448736 | − | 0.0448736i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11371.7i | − | 1.59135i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −106.398 | − | 106.398i | −0.0147696 | − | 0.0147696i | 0.699683 | − | 0.714453i | \(-0.253324\pi\) |
−0.714453 | + | 0.699683i | \(0.753324\pi\) | |||||||
\(374\) | 1016.26 | 0.140507 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2099.45 | 0.287955 | ||||||||
\(377\) | −2416.48 | − | 2416.48i | −0.330120 | − | 0.330120i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9384.86i | − | 1.27195i | −0.771711 | − | 0.635974i | \(-0.780599\pi\) | ||
0.771711 | − | 0.635974i | \(-0.219401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2881.36 | + | 2881.36i | −0.385925 | + | 0.385925i | ||||
\(383\) | −8015.85 | + | 8015.85i | −1.06943 | + | 1.06943i | −0.0720253 | + | 0.997403i | \(0.522946\pi\) |
−0.997403 | + | 0.0720253i | \(0.977054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3189.84i | − | 0.420619i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 117.030 | + | 117.030i | 0.0153127 | + | 0.0153127i | ||||
\(389\) | 8892.72 | 1.15907 | 0.579536 | − | 0.814947i | \(-0.303234\pi\) | ||||
0.579536 | + | 0.814947i | \(0.303234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −219.121 | −0.0283413 | ||||||||
\(392\) | 3492.25 | + | 3492.25i | 0.449962 | + | 0.449962i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 729.197i | 0.0932396i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3248.62 | + | 3248.62i | −0.410689 | + | 0.410689i | −0.881978 | − | 0.471290i | \(-0.843789\pi\) |
0.471290 | + | 0.881978i | \(0.343789\pi\) | |||||||
\(398\) | 725.534 | − | 725.534i | 0.0913763 | − | 0.0913763i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12012.4i | 1.49594i | 0.663731 | + | 0.747971i | \(0.268972\pi\) | ||||
−0.663731 | + | 0.747971i | \(0.731028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −259.462 | − | 259.462i | −0.0320713 | − | 0.0320713i | ||||
\(404\) | −1544.81 | −0.190241 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11444.2 | −1.39893 | ||||||||
\(407\) | −16540.3 | − | 16540.3i | −2.01443 | − | 2.01443i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1710.61i | 0.206807i | 0.994639 | + | 0.103403i | \(0.0329733\pi\) | ||||
−0.994639 | + | 0.103403i | \(0.967027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3174.26 | − | 3174.26i | 0.379574 | − | 0.379574i | ||||
\(413\) | 5599.59 | − | 5599.59i | 0.667162 | − | 0.667162i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 592.256i | 0.0698022i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9533.88 | − | 9533.88i | −1.11559 | − | 1.11559i | ||||
\(419\) | −2905.88 | −0.338811 | −0.169405 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169405 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9062.85 | −1.04916 | −0.524580 | − | 0.851361i | \(-0.675778\pi\) | ||||
−0.524580 | + | 0.851361i | \(0.675778\pi\) | |||||||
\(422\) | −2277.23 | − | 2277.23i | −0.262686 | − | 0.262686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 2935.64i | − | 0.336243i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19591.9 | − | 19591.9i | 2.22042 | − | 2.22042i | ||||
\(428\) | −2005.98 | + | 2005.98i | −0.226548 | + | 0.226548i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10334.6i | − | 1.15498i | −0.816396 | − | 0.577492i | \(-0.804031\pi\) | ||
0.816396 | − | 0.577492i | \(-0.195969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3105.17 | + | 3105.17i | 0.344631 | + | 0.344631i | 0.858105 | − | 0.513474i | \(-0.171642\pi\) |
−0.513474 | + | 0.858105i | \(0.671642\pi\) | |||||||
\(434\) | −1228.78 | −0.135906 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3501.18 | −0.384578 | ||||||||
\(437\) | 2055.65 | + | 2055.65i | 0.225023 | + | 0.225023i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4940.17i | − | 0.537087i | −0.963268 | − | 0.268544i | \(-0.913458\pi\) | ||
0.963268 | − | 0.268544i | \(-0.0865423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 204.833 | − | 204.833i | 0.0220428 | − | 0.0220428i | ||||
\(443\) | 11835.5 | − | 11835.5i | 1.26935 | − | 1.26935i | 0.322931 | − | 0.946423i | \(-0.395332\pi\) |
0.946423 | − | 0.322931i | \(-0.104668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6618.02i | 0.702628i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1402.42 | + | 1402.42i | 0.147898 | + | 0.147898i | ||||
\(449\) | 3384.05 | 0.355687 | 0.177843 | − | 0.984059i | \(-0.443088\pi\) | ||||
0.177843 | + | 0.984059i | \(0.443088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4100.16 | 0.428091 | ||||||||
\(452\) | −3775.07 | − | 3775.07i | −0.392842 | − | 0.392842i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4528.70i | − | 0.468155i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3509.05 | − | 3509.05i | 0.359182 | − | 0.359182i | −0.504329 | − | 0.863511i | \(-0.668260\pi\) |
0.863511 | + | 0.504329i | \(0.168260\pi\) | |||||||
\(458\) | −8914.30 | + | 8914.30i | −0.909472 | + | 0.909472i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8838.05i | − | 0.892904i | −0.894807 | − | 0.446452i | \(-0.852687\pi\) | ||
0.894807 | − | 0.446452i | \(-0.147313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6343.49 | − | 6343.49i | −0.636732 | − | 0.636732i | 0.313016 | − | 0.949748i | \(-0.398661\pi\) |
−0.949748 | + | 0.313016i | \(0.898661\pi\) | |||||||
\(464\) | −2954.33 | −0.295585 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7585.71 | 0.754080 | ||||||||
\(467\) | −226.322 | − | 226.322i | −0.0224260 | − | 0.0224260i | 0.695805 | − | 0.718231i | \(-0.255048\pi\) |
−0.718231 | + | 0.695805i | \(0.755048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4405.48i | 0.433745i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1445.55 | − | 1445.55i | 0.140967 | − | 0.140967i | ||||
\(473\) | −6764.10 | + | 6764.10i | −0.657534 | + | 0.657534i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 970.065i | − | 0.0934093i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3273.36 | + | 3273.36i | 0.313222 | + | 0.313222i | ||||
\(479\) | 15546.2 | 1.48293 | 0.741465 | − | 0.670991i | \(-0.234131\pi\) | ||||
0.741465 | + | 0.670991i | \(0.234131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6667.59 | −0.632050 | ||||||||
\(482\) | 2088.21 | + | 2088.21i | 0.197335 | + | 0.197335i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 11539.9i | − | 1.08377i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3464.88 | − | 3464.88i | 0.322399 | − | 0.322399i | −0.527288 | − | 0.849687i | \(-0.676791\pi\) |
0.849687 | + | 0.527288i | \(0.176791\pi\) | |||||||
\(488\) | 5057.70 | − | 5057.70i | 0.469162 | − | 0.469162i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2614.21i | 0.240280i | 0.992757 | + | 0.120140i | \(0.0383344\pi\) | ||||
−0.992757 | + | 0.120140i | \(0.961666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1021.77 | + | 1021.77i | 0.0933428 | + | 0.0933428i | ||||
\(494\) | −3843.21 | −0.350029 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −317.212 | −0.0287162 | ||||||||
\(497\) | 10773.5 | + | 10773.5i | 0.972353 | + | 0.972353i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3762.23i | 0.337517i | 0.985657 | + | 0.168758i | \(0.0539757\pi\) | ||||
−0.985657 | + | 0.168758i | \(0.946024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5687.31 | − | 5687.31i | 0.505652 | − | 0.505652i | ||||
\(503\) | 7204.69 | − | 7204.69i | 0.638651 | − | 0.638651i | −0.311572 | − | 0.950223i | \(-0.600855\pi\) |
0.950223 | + | 0.311572i | \(0.100855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3636.11i | 0.319457i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2143.29 | − | 2143.29i | −0.187191 | − | 0.187191i | ||||
\(509\) | 15219.2 | 1.32530 | 0.662652 | − | 0.748928i | \(-0.269431\pi\) | ||||
0.662652 | + | 0.748928i | \(0.269431\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26461.1 | 2.29075 | ||||||||
\(512\) | 362.039 | + | 362.039i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 1049.86i | − | 0.0900924i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12049.0 | + | 12049.0i | −1.02498 | + | 1.02498i | ||||
\(518\) | −15788.4 | + | 15788.4i | −1.33920 | + | 1.33920i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4041.49i | − | 0.339848i | −0.985457 | − | 0.169924i | \(-0.945648\pi\) | ||
0.985457 | − | 0.169924i | \(-0.0543523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14873.0 | − | 14873.0i | −1.24350 | − | 1.24350i | −0.958540 | − | 0.284958i | \(-0.908020\pi\) |
−0.284958 | − | 0.958540i | \(-0.591980\pi\) | |||||||
\(524\) | −7408.01 | −0.617597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 513.091 | 0.0425320 | ||||||||
\(527\) | 109.709 | + | 109.709i | 0.00906829 | + | 0.00906829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11383.0i | 0.935563i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9100.48 | + | 9100.48i | −0.741647 | + | 0.741647i | ||||
\(533\) | 826.410 | − | 826.410i | 0.0671590 | − | 0.0671590i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1137.28i | 0.0916478i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4669.43 | + | 4669.43i | 0.374189 | + | 0.374189i | ||||
\(539\) | −40084.8 | −3.20329 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8356.96 | −0.664129 | −0.332065 | − | 0.943257i | \(-0.607745\pi\) | ||||
−0.332065 | + | 0.943257i | \(0.607745\pi\) | |||||||
\(542\) | −5507.27 | − | 5507.27i | −0.436453 | − | 0.436453i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 250.424i | − | 0.0197369i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5395.94 | + | 5395.94i | −0.421780 | + | 0.421780i | −0.885816 | − | 0.464036i | \(-0.846401\pi\) |
0.464036 | + | 0.885816i | \(0.346401\pi\) | |||||||
\(548\) | 3555.18 | − | 3555.18i | 0.277135 | − | 0.277135i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 19171.0i | − | 1.48224i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15312.3 | + | 15312.3i | 1.17748 | + | 1.17748i | ||||
\(554\) | 4009.37 | 0.307476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1009.39 | 0.0769925 | ||||||||
\(557\) | −4120.65 | − | 4120.65i | −0.313461 | − | 0.313461i | 0.532788 | − | 0.846249i | \(-0.321144\pi\) |
−0.846249 | + | 0.532788i | \(0.821144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2726.68i | 0.206308i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11482.5 | + | 11482.5i | −0.861848 | + | 0.861848i | ||||
\(563\) | −10494.4 | + | 10494.4i | −0.785590 | + | 0.785590i | −0.980768 | − | 0.195177i | \(-0.937472\pi\) |
0.195177 | + | 0.980768i | \(0.437472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3300.60i | − | 0.245114i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2781.21 | + | 2781.21i | 0.205453 | + | 0.205453i | ||||
\(569\) | −25399.7 | −1.87137 | −0.935687 | − | 0.352832i | \(-0.885219\pi\) | ||||
−0.935687 | + | 0.352832i | \(0.885219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15700.6 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304865\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304865\pi\) | |||||||
\(572\) | −3399.02 | − | 3399.02i | −0.248462 | − | 0.248462i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 3913.77i | − | 0.284595i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5627.77 | − | 5627.77i | 0.406044 | − | 0.406044i | −0.474313 | − | 0.880356i | \(-0.657303\pi\) |
0.880356 | + | 0.474313i | \(0.157303\pi\) | |||||||
\(578\) | 6861.42 | − | 6861.42i | 0.493767 | − | 0.493767i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30989.3i | 2.21282i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16847.9 | + | 16847.9i | 1.19686 | + | 1.19686i | ||||
\(584\) | 6830.99 | 0.484021 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13651.2 | 0.962333 | ||||||||
\(587\) | −10563.0 | − | 10563.0i | −0.742731 | − | 0.742731i | 0.230372 | − | 0.973103i | \(-0.426006\pi\) |
−0.973103 | + | 0.230372i | \(0.926006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2058.42i | − | 0.144000i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4075.82 | + | 4075.82i | −0.282965 | + | 0.282965i | ||||
\(593\) | −4080.58 | + | 4080.58i | −0.282579 | + | 0.282579i | −0.834137 | − | 0.551558i | \(-0.814034\pi\) |
0.551558 | + | 0.834137i | \(0.314034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 676.101i | 0.0464668i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 732.879 | + | 732.879i | 0.0501165 | + | 0.0501165i | ||||
\(599\) | 10431.0 | 0.711515 | 0.355758 | − | 0.934578i | \(-0.384223\pi\) | ||||
0.355758 | + | 0.934578i | \(0.384223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13534.1 | −0.918584 | −0.459292 | − | 0.888285i | \(-0.651897\pi\) | ||||
−0.459292 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(602\) | 6456.61 | + | 6456.61i | 0.437129 | + | 0.437129i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11134.6i | 0.750100i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8819.49 | + | 8819.49i | −0.589740 | + | 0.589740i | −0.937561 | − | 0.347821i | \(-0.886922\pi\) |
0.347821 | + | 0.937561i | \(0.386922\pi\) | |||||||
\(608\) | −2349.31 | + | 2349.31i | −0.156706 | + | 0.156706i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4857.08i | 0.321598i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6914.61 | − | 6914.61i | −0.455593 | − | 0.455593i | 0.441613 | − | 0.897206i | \(-0.354406\pi\) |
−0.897206 | + | 0.441613i | \(0.854406\pi\) | |||||||
\(614\) | 11771.6 | 0.773718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16097.3 | −1.05289 | ||||||||
\(617\) | 14354.7 | + | 14354.7i | 0.936629 | + | 0.936629i | 0.998108 | − | 0.0614791i | \(-0.0195818\pi\) |
−0.0614791 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15236.3i | 0.989334i | 0.869083 | + | 0.494667i | \(0.164710\pi\) | ||||
−0.869083 | + | 0.494667i | \(0.835290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5635.08 | − | 5635.08i | 0.363257 | − | 0.363257i | ||||
\(623\) | −8538.31 | + | 8538.31i | −0.549085 | + | 0.549085i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 6865.00i | − | 0.438308i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8072.86 | − | 8072.86i | −0.512965 | − | 0.512965i | ||||
\(629\) | 2819.27 | 0.178715 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2894.27 | 0.182597 | 0.0912986 | − | 0.995824i | \(-0.470898\pi\) | ||||
0.0912986 | + | 0.995824i | \(0.470898\pi\) | |||||||
\(632\) | 3952.90 | + | 3952.90i | 0.248794 | + | 0.248794i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20173.9i | 1.26373i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8079.31 | + | 8079.31i | −0.502534 | + | 0.502534i | ||||
\(638\) | 16955.3 | − | 16955.3i | 1.05214 | − | 1.05214i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 345.840i | 0.0213102i | 0.999943 | + | 0.0106551i | \(0.00339169\pi\) | ||||
−0.999943 | + | 0.0106551i | \(0.996608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1161.24 | + | 1161.24i | 0.0712207 | + | 0.0712207i | 0.741820 | − | 0.670599i | \(-0.233963\pi\) |
−0.670599 | + | 0.741820i | \(0.733963\pi\) | |||||||
\(644\) | 3470.82 | 0.212375 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1625.03 | 0.0989721 | ||||||||
\(647\) | −15317.4 | − | 15317.4i | −0.930738 | − | 0.930738i | 0.0670144 | − | 0.997752i | \(-0.478653\pi\) |
−0.997752 | + | 0.0670144i | \(0.978653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16592.3i | 1.00355i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8530.76 | − | 8530.76i | 0.512408 | − | 0.512408i | ||||
\(653\) | 9594.72 | − | 9594.72i | 0.574993 | − | 0.574993i | −0.358527 | − | 0.933520i | \(-0.616721\pi\) |
0.933520 | + | 0.358527i | \(0.116721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1010.35i | − | 0.0601334i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11501.3 | + | 11501.3i | 0.681408 | + | 0.681408i | ||||
\(659\) | 1554.04 | 0.0918618 | 0.0459309 | − | 0.998945i | \(-0.485375\pi\) | ||||
0.0459309 | + | 0.998945i | \(0.485375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2698.57 | 0.158793 | 0.0793965 | − | 0.996843i | \(-0.474701\pi\) | ||||
0.0793965 | + | 0.996843i | \(0.474701\pi\) | |||||||
\(662\) | −2536.00 | − | 2536.00i | −0.148889 | − | 0.148889i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7999.94i | 0.467557i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3655.80 | + | 3655.80i | −0.212224 | + | 0.212224i | ||||
\(668\) | 4111.80 | − | 4111.80i | 0.238159 | − | 0.238159i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 58053.4i | 3.33998i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8704.87 | + | 8704.87i | 0.498586 | + | 0.498586i | 0.910997 | − | 0.412412i | \(-0.135314\pi\) |
−0.412412 | + | 0.910997i | \(0.635314\pi\) | |||||||
\(674\) | −12553.9 | −0.717443 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7417.82 | 0.422042 | ||||||||
\(677\) | 8512.59 | + | 8512.59i | 0.483258 | + | 0.483258i | 0.906170 | − | 0.422913i | \(-0.138992\pi\) |
−0.422913 | + | 0.906170i | \(0.638992\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1282.24i | 0.0724708i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1820.52 | − | 1820.52i | 0.102216 | − | 0.102216i | ||||
\(683\) | −4988.15 | + | 4988.15i | −0.279453 | + | 0.279453i | −0.832891 | − | 0.553438i | \(-0.813316\pi\) |
0.553438 | + | 0.832891i | \(0.313316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17003.8i | 0.946370i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1666.79 | + | 1666.79i | 0.0923629 | + | 0.0923629i | ||||
\(689\) | 6791.59 | 0.375528 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24712.4 | −1.36050 | −0.680250 | − | 0.732980i | \(-0.738129\pi\) | ||||
−0.680250 | + | 0.732980i | \(0.738129\pi\) | |||||||
\(692\) | −3473.07 | − | 3473.07i | −0.190790 | − | 0.190790i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13207.6i | 0.722410i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −349.432 | + | 349.432i | −0.0189895 | + | 0.0189895i | ||||
\(698\) | −1759.31 | + | 1759.31i | −0.0954026 | + | 0.0954026i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9481.12i | − | 0.510837i | −0.966831 | − | 0.255419i | \(-0.917787\pi\) | ||
0.966831 | − | 0.255419i | \(-0.0822133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26448.4 | − | 26448.4i | −1.41895 | − | 1.41895i | ||||
\(704\) | −4155.56 | −0.222470 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15107.2 | 0.805334 | ||||||||
\(707\) | −8462.83 | − | 8462.83i | −0.450180 | − | 0.450180i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33090.6i | − | 1.75281i | −0.481571 | − | 0.876407i | \(-0.659934\pi\) | ||
0.481571 | − | 0.876407i | \(-0.340066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2204.18 | + | 2204.18i | −0.116019 | + | 0.116019i | ||||
\(713\) | −392.530 | + | 392.530i | −0.0206176 | + | 0.0206176i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 13792.8i | − | 0.719920i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1471.68 | + | 1471.68i | 0.0764940 | + | 0.0764940i | ||||
\(719\) | −19996.8 | −1.03721 | −0.518605 | − | 0.855014i | \(-0.673549\pi\) | ||||
−0.518605 | + | 0.855014i | \(0.673549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34778.6 | 1.79642 | ||||||||
\(722\) | −5544.83 | − | 5544.83i | −0.285813 | − | 0.285813i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14047.2i | 0.721080i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25556.9 | + | 25556.9i | −1.30379 | + | 1.30379i | −0.377969 | + | 0.925818i | \(0.623377\pi\) |
−0.925818 | + | 0.377969i | \(0.876623\pi\) | |||||||
\(728\) | −3244.51 | + | 3244.51i | −0.165178 | + | 0.165178i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1152.93i | − | 0.0583345i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18981.4 | + | 18981.4i | 0.956474 | + | 0.956474i | 0.999091 | − | 0.0426176i | \(-0.0135697\pi\) |
−0.0426176 | + | 0.999091i | \(0.513570\pi\) | |||||||
\(734\) | 4094.16 | 0.205883 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 896.000 | 0.0448736 | ||||||||
\(737\) | −6527.00 | − | 6527.00i | −0.326221 | − | 0.326221i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4651.19i | 0.231525i | 0.993277 | + | 0.115762i | \(0.0369311\pi\) | ||||
−0.993277 | + | 0.115762i | \(0.963069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16082.1 | − | 16082.1i | 0.795675 | − | 0.795675i | ||||
\(743\) | −9737.08 | + | 9737.08i | −0.480779 | + | 0.480779i | −0.905380 | − | 0.424601i | \(-0.860414\pi\) |
0.424601 | + | 0.905380i | \(0.360414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 300.938i | − | 0.0147696i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1437.21 | + | 1437.21i | 0.0702536 | + | 0.0702536i | ||||
\(749\) | −21978.4 | −1.07219 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7800.89 | −0.379039 | −0.189520 | − | 0.981877i | \(-0.560693\pi\) | ||||
−0.189520 | + | 0.981877i | \(0.560693\pi\) | |||||||
\(752\) | 2969.08 | + | 2969.08i | 0.143978 | + | 0.143978i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 6834.85i | − | 0.330120i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1497.47 | + | 1497.47i | −0.0718974 | + | 0.0718974i | −0.742141 | − | 0.670244i | \(-0.766190\pi\) |
0.670244 | + | 0.742141i | \(0.266190\pi\) | |||||||
\(758\) | 13272.2 | − | 13272.2i | 0.635974 | − | 0.635974i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22037.0i | − | 1.04973i | −0.851187 | − | 0.524863i | \(-0.824116\pi\) | ||
0.851187 | − | 0.524863i | \(-0.175884\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19180.2 | − | 19180.2i | −0.910054 | − | 0.910054i | ||||
\(764\) | −8149.73 | −0.385925 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22672.3 | −1.06943 | ||||||||
\(767\) | 3344.27 | + | 3344.27i | 0.157437 | + | 0.157437i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6827.73i | 0.320174i | 0.987103 | + | 0.160087i | \(0.0511775\pi\) | ||||
−0.987103 | + | 0.160087i | \(0.948822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4511.12 | − | 4511.12i | 0.210309 | − | 0.210309i | ||||
\(773\) | 2717.78 | − | 2717.78i | 0.126457 | − | 0.126457i | −0.641045 | − | 0.767503i | \(-0.721499\pi\) |
0.767503 | + | 0.641045i | \(0.221499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 331.012i | 0.0153127i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12576.2 | + | 12576.2i | 0.579536 | + | 0.579536i | ||||
\(779\) | 6556.26 | 0.301544 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31923.4 | −1.46262 | ||||||||
\(782\) | −309.884 | − | 309.884i | −0.0141706 | − | 0.0141706i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9877.58i | 0.449962i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18023.9 | + | 18023.9i | −0.816370 | + | 0.816370i | −0.985580 | − | 0.169210i | \(-0.945878\pi\) |
0.169210 | + | 0.985580i | \(0.445878\pi\) | |||||||
\(788\) | −1031.24 | + | 1031.24i | −0.0466198 | + | 0.0466198i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 41361.3i | − | 1.85922i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11701.0 | + | 11701.0i | 0.523977 | + | 0.523977i | ||||
\(794\) | −9188.48 | −0.410689 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2052.12 | 0.0913763 | ||||||||
\(797\) | 21477.8 | + | 21477.8i | 0.954557 | + | 0.954557i | 0.999011 | − | 0.0444541i | \(-0.0141549\pi\) |
−0.0444541 | + | 0.999011i | \(0.514155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2053.73i | − | 0.0909332i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16988.2 | + | 16988.2i | −0.747971 | + | 0.747971i | ||||
\(803\) | −39203.8 | + | 39203.8i | −1.72288 | + | 1.72288i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 733.870i | − | 0.0320713i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2184.70 | − | 2184.70i | −0.0951205 | − | 0.0951205i | ||||
\(809\) | 36819.3 | 1.60012 | 0.800060 | − | 0.599920i | \(-0.204801\pi\) | ||||
0.800060 | + | 0.599920i | \(0.204801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38040.8 | 1.64709 | 0.823546 | − | 0.567249i | \(-0.191992\pi\) | ||||
0.823546 | + | 0.567249i | \(0.191992\pi\) | |||||||
\(812\) | −16184.5 | − | 16184.5i | −0.699464 | − | 0.699464i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 46783.1i | − | 2.01443i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10816.0 | + | 10816.0i | −0.463161 | + | 0.463161i | ||||
\(818\) | −2419.16 | + | 2419.16i | −0.103403 | + | 0.103403i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2824.53i | − | 0.120069i | −0.998196 | − | 0.0600346i | \(-0.980879\pi\) | ||
0.998196 | − | 0.0600346i | \(-0.0191211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14878.3 | + | 14878.3i | 0.630164 | + | 0.630164i | 0.948109 | − | 0.317945i | \(-0.102993\pi\) |
−0.317945 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(824\) | 8978.16 | 0.379574 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15838.0 | 0.667162 | ||||||||
\(827\) | 31885.6 | + | 31885.6i | 1.34072 | + | 1.34072i | 0.895347 | + | 0.445369i | \(0.146928\pi\) |
0.445369 | + | 0.895347i | \(0.353072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6395.67i | 0.267950i | 0.990985 | + | 0.133975i | \(0.0427743\pi\) | ||||
−0.990985 | + | 0.133975i | \(0.957226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −837.576 | + | 837.576i | −0.0349011 | + | 0.0349011i | ||||
\(833\) | 3416.19 | − | 3416.19i | 0.142094 | − | 0.142094i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 26965.9i | − | 1.11559i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4109.54 | − | 4109.54i | −0.169405 | − | 0.169405i | ||||
\(839\) | −19006.7 | −0.782104 | −0.391052 | − | 0.920369i | \(-0.627889\pi\) | ||||
−0.391052 | + | 0.920369i | \(0.627889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9705.12 | 0.397930 | ||||||||
\(842\) | −12816.8 | − | 12816.8i | −0.524580 | − | 0.524580i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 6440.97i | − | 0.262686i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 63218.3 | − | 63218.3i | 2.56459 | − | 2.56459i | ||||
\(848\) | 4151.62 | − | 4151.62i | 0.168122 | − | 0.168122i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10087.1i | 0.406325i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31885.3 | − | 31885.3i | −1.27987 | − | 1.27987i | −0.940738 | − | 0.339133i | \(-0.889866\pi\) |
−0.339133 | − | 0.940738i | \(-0.610134\pi\) | |||||||
\(854\) | 55414.4 | 2.22042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5673.76 | −0.226548 | ||||||||
\(857\) | 14082.6 | + | 14082.6i | 0.561322 | + | 0.561322i | 0.929683 | − | 0.368361i | \(-0.120081\pi\) |
−0.368361 | + | 0.929683i | \(0.620081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24821.7i | − | 0.985920i | −0.870052 | − | 0.492960i | \(-0.835915\pi\) | ||
0.870052 | − | 0.492960i | \(-0.164085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14615.3 | − | 14615.3i | 0.577492 | − | 0.577492i | ||||
\(863\) | 31772.4 | − | 31772.4i | 1.25324 | − | 1.25324i | 0.298976 | − | 0.954260i | \(-0.403355\pi\) |
0.954260 | − | 0.298976i | \(-0.0966452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8782.76i | 0.344631i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1737.76 | − | 1737.76i | −0.0679532 | − | 0.0679532i | ||||
\(869\) | −45372.2 | −1.77117 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2631.11 | −0.102355 | ||||||||
\(872\) | −4951.42 | − | 4951.42i | −0.192289 | − | 0.192289i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5814.24i | 0.225023i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30277.2 | − | 30277.2i | 1.16578 | − | 1.16578i | 0.182592 | − | 0.983189i | \(-0.441551\pi\) |
0.983189 | − | 0.182592i | \(-0.0584488\pi\) | |||||||
\(878\) | 6986.45 | − | 6986.45i | 0.268544 | − | 0.268544i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32069.6i | 1.22639i | 0.789930 | + | 0.613197i | \(0.210117\pi\) | ||||
−0.789930 | + | 0.613197i | \(0.789883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7061.36 | − | 7061.36i | −0.269121 | − | 0.269121i | 0.559625 | − | 0.828746i | \(-0.310945\pi\) |
−0.828746 | + | 0.559625i | \(0.810945\pi\) | |||||||
\(884\) | 579.356 | 0.0220428 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33476.0 | 1.26935 | ||||||||
\(887\) | −18324.6 | − | 18324.6i | −0.693664 | − | 0.693664i | 0.269372 | − | 0.963036i | \(-0.413184\pi\) |
−0.963036 | + | 0.269372i | \(0.913184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23482.8i | − | 0.885926i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9359.29 | + | 9359.29i | −0.351314 | + | 0.351314i | ||||
\(893\) | −19266.7 | + | 19266.7i | −0.721987 | + | 0.721987i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3966.65i | 0.147898i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4785.77 | + | 4785.77i | 0.177843 | + | 0.177843i | ||||
\(899\) | 3660.75 | 0.135809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2871.70 | −0.106182 | ||||||||
\(902\) | 5798.50 | + | 5798.50i | 0.214045 | + | 0.214045i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 10677.5i | − | 0.392842i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18445.0 | − | 18445.0i | 0.675256 | − | 0.675256i | −0.283667 | − | 0.958923i | \(-0.591551\pi\) |
0.958923 | + | 0.283667i | \(0.0915511\pi\) | |||||||
\(908\) | 6404.54 | − | 6404.54i | 0.234077 | − | 0.234077i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7421.18i | − | 0.269895i | −0.990853 | − | 0.134948i | \(-0.956913\pi\) | ||
0.990853 | − | 0.134948i | \(-0.0430866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45912.5 | − | 45912.5i | −1.66427 | − | 1.66427i | ||||
\(914\) | 9925.08 | 0.359182 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25213.5 | −0.909472 | ||||||||
\(917\) | −40582.7 | − | 40582.7i | −1.46146 | − | 1.46146i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36117.6i | − | 1.29642i | −0.761462 | − | 0.648209i | \(-0.775518\pi\) | ||
0.761462 | − | 0.648209i | \(-0.224482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12498.9 | − | 12498.9i | 0.446452 | − | 0.446452i | ||||
\(923\) | −6434.33 | + | 6434.33i | −0.229457 | + | 0.229457i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 17942.1i | − | 0.636732i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4178.06 | − | 4178.06i | −0.147793 | − | 0.147793i | ||||
\(929\) | 11654.8 | 0.411606 | 0.205803 | − | 0.978593i | \(-0.434019\pi\) | ||||
0.205803 | + | 0.978593i | \(0.434019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −64096.7 | −2.25637 | ||||||||
\(932\) | 10727.8 | + | 10727.8i | 0.377040 | + | 0.377040i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 640.137i | − | 0.0224260i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16788.2 | + | 16788.2i | −0.585323 | + | 0.585323i | −0.936361 | − | 0.351038i | \(-0.885829\pi\) |
0.351038 | + | 0.936361i | \(0.385829\pi\) | |||||||
\(938\) | −6230.30 | + | 6230.30i | −0.216872 | + | 0.216872i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27834.5i | 0.964271i | 0.876097 | + | 0.482136i | \(0.160139\pi\) | ||||
−0.876097 | + | 0.482136i | \(0.839861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1250.24 | − | 1250.24i | −0.0431744 | − | 0.0431744i | ||||
\(944\) | 4088.62 | 0.140967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19131.8 | −0.657534 | ||||||||
\(947\) | 4017.43 | + | 4017.43i | 0.137855 | + | 0.137855i | 0.772667 | − | 0.634812i | \(-0.218922\pi\) |
−0.634812 | + | 0.772667i | \(0.718922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15803.5i | 0.540572i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1371.88 | − | 1371.88i | 0.0467047 | − | 0.0467047i | ||||
\(953\) | 14545.6 | − | 14545.6i | 0.494416 | − | 0.494416i | −0.415278 | − | 0.909694i | \(-0.636316\pi\) |
0.909694 | + | 0.415278i | \(0.136316\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9258.47i | 0.313222i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21985.6 | + | 21985.6i | 0.741465 | + | 0.741465i | ||||
\(959\) | 38952.1 | 1.31161 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29397.9 | −0.986806 | ||||||||
\(962\) | −9429.40 | − | 9429.40i | −0.316025 | − | 0.316025i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5906.36i | 0.197335i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24630.8 | − | 24630.8i | 0.819105 | − | 0.819105i | −0.166874 | − | 0.985978i | \(-0.553367\pi\) |
0.985978 | + | 0.166874i | \(0.0533672\pi\) | |||||||
\(968\) | 16319.9 | − | 16319.9i | 0.541883 | − | 0.541883i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17813.2i | − | 0.588727i | −0.955693 | − | 0.294364i | \(-0.904892\pi\) | ||
0.955693 | − | 0.294364i | \(-0.0951077\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5529.68 | + | 5529.68i | 0.182193 | + | 0.182193i | ||||
\(974\) | 9800.15 | 0.322399 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14305.3 | 0.469162 | ||||||||
\(977\) | 2909.26 | + | 2909.26i | 0.0952665 | + | 0.0952665i | 0.753134 | − | 0.657867i | \(-0.228541\pi\) |
−0.657867 | + | 0.753134i | \(0.728541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 25300.1i | − | 0.825939i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3697.05 | + | 3697.05i | −0.120140 | + | 0.120140i | ||||
\(983\) | 10412.0 | − | 10412.0i | 0.337834 | − | 0.337834i | −0.517718 | − | 0.855552i | \(-0.673218\pi\) |
0.855552 | + | 0.517718i | \(0.173218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2889.99i | 0.0933428i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5435.12 | − | 5435.12i | −0.175014 | − | 0.175014i | ||||
\(989\) | 4125.09 | 0.132629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12712.1 | −0.407482 | −0.203741 | − | 0.979025i | \(-0.565310\pi\) | ||||
−0.203741 | + | 0.979025i | \(0.565310\pi\) | |||||||
\(992\) | −448.606 | − | 448.606i | −0.0143581 | − | 0.0143581i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30472.2i | 0.972353i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7747.71 | + | 7747.71i | −0.246111 | + | 0.246111i | −0.819372 | − | 0.573262i | \(-0.805678\pi\) |
0.573262 | + | 0.819372i | \(0.305678\pi\) | |||||||
\(998\) | −5320.60 | + | 5320.60i | −0.168758 | + | 0.168758i | ||||
\(999\) | 0 | 0 |
(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 | 450.4.f.e.143.3 | 8 | ||
3.2 | odd | 2 | inner | 450.4.f.e.143.1 | 8 | ||
5.2 | odd | 4 | inner | 450.4.f.e.107.1 | 8 | ||
5.3 | odd | 4 | 90.4.f.b.17.4 | yes | 8 | ||
5.4 | even | 2 | 90.4.f.b.53.1 | yes | 8 | ||
15.2 | even | 4 | inner | 450.4.f.e.107.3 | 8 | ||
15.8 | even | 4 | 90.4.f.b.17.1 | ✓ | 8 | ||
15.14 | odd | 2 | 90.4.f.b.53.4 | yes | 8 | ||
20.3 | even | 4 | 720.4.w.c.17.3 | 8 | |||
20.19 | odd | 2 | 720.4.w.c.593.2 | 8 | |||
60.23 | odd | 4 | 720.4.w.c.17.2 | 8 | |||
60.59 | even | 2 | 720.4.w.c.593.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.4.f.b.17.1 | ✓ | 8 | 15.8 | even | 4 | ||
90.4.f.b.17.4 | yes | 8 | 5.3 | odd | 4 | ||
90.4.f.b.53.1 | yes | 8 | 5.4 | even | 2 | ||
90.4.f.b.53.4 | yes | 8 | 15.14 | odd | 2 | ||
450.4.f.e.107.1 | 8 | 5.2 | odd | 4 | inner | ||
450.4.f.e.107.3 | 8 | 15.2 | even | 4 | inner | ||
450.4.f.e.143.1 | 8 | 3.2 | odd | 2 | inner | ||
450.4.f.e.143.3 | 8 | 1.1 | even | 1 | trivial | ||
720.4.w.c.17.2 | 8 | 60.23 | odd | 4 | |||
720.4.w.c.17.3 | 8 | 20.3 | even | 4 | |||
720.4.w.c.593.2 | 8 | 20.19 | odd | 2 | |||
720.4.w.c.593.3 | 8 | 60.59 | even | 2 |