Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,4,Mod(5,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\), degree \(4\), 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: | \(1.88806112018\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 13.5 | ||
Character | \(\chi\) | \(=\) | 32.13 |
Dual form | 32.4.g.a.5.5 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.719102 | − | 2.73549i | −0.254241 | − | 0.967141i | ||||
\(3\) | −3.21198 | + | 7.75440i | −0.618145 | + | 1.49233i | 0.235710 | + | 0.971824i | \(0.424259\pi\) |
−0.853855 | + | 0.520511i | \(0.825741\pi\) | |||||||
\(4\) | −6.96578 | + | 3.93419i | −0.870723 | + | 0.491774i | ||||
\(5\) | −13.6472 | + | 5.65283i | −1.22064 | + | 0.505605i | −0.897613 | − | 0.440785i | \(-0.854700\pi\) |
−0.323026 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(6\) | 23.5218 | + | 3.21012i | 1.60046 | + | 0.218421i | ||||
\(7\) | 9.07689 | − | 9.07689i | 0.490106 | − | 0.490106i | −0.418233 | − | 0.908340i | \(-0.637351\pi\) |
0.908340 | + | 0.418233i | \(0.137351\pi\) | |||||||
\(8\) | 15.7710 | + | 16.2257i | 0.696988 | + | 0.717083i | ||||
\(9\) | −30.7220 | − | 30.7220i | −1.13785 | − | 1.13785i | ||||
\(10\) | 25.2770 | + | 33.2666i | 0.799327 | + | 1.05198i | ||||
\(11\) | 16.7195 | + | 40.3646i | 0.458285 | + | 1.10640i | 0.969091 | + | 0.246702i | \(0.0793468\pi\) |
−0.510807 | + | 0.859696i | \(0.670653\pi\) | |||||||
\(12\) | −8.13333 | − | 66.6520i | −0.195658 | − | 1.60340i | ||||
\(13\) | −38.4266 | − | 15.9168i | −0.819817 | − | 0.339580i | −0.0669538 | − | 0.997756i | \(-0.521328\pi\) |
−0.752864 | + | 0.658177i | \(0.771328\pi\) | |||||||
\(14\) | −31.3569 | − | 18.3025i | −0.598607 | − | 0.349397i | ||||
\(15\) | − | 123.982i | − | 2.13414i | ||||||
\(16\) | 33.0443 | − | 54.8094i | 0.516317 | − | 0.856397i | ||||
\(17\) | 92.5038i | 1.31973i | 0.751383 | + | 0.659867i | \(0.229387\pi\) | ||||
−0.751383 | + | 0.659867i | \(0.770613\pi\) | |||||||
\(18\) | −61.9474 | + | 106.132i | −0.811175 | + | 1.38975i | ||||
\(19\) | −16.6799 | − | 6.90905i | −0.201402 | − | 0.0834235i | 0.279702 | − | 0.960087i | \(-0.409764\pi\) |
−0.481104 | + | 0.876663i | \(0.659764\pi\) | |||||||
\(20\) | 72.8238 | − | 93.0669i | 0.814195 | − | 1.04052i | ||||
\(21\) | 41.2311 | + | 99.5406i | 0.428446 | + | 1.03436i | ||||
\(22\) | 98.3937 | − | 74.7623i | 0.953527 | − | 0.724517i | ||||
\(23\) | 95.6008 | + | 95.6008i | 0.866702 | + | 0.866702i | 0.992106 | − | 0.125404i | \(-0.0400228\pi\) |
−0.125404 | + | 0.992106i | \(0.540023\pi\) | |||||||
\(24\) | −176.477 | + | 70.1782i | −1.50097 | + | 0.596878i | ||||
\(25\) | 65.9018 | − | 65.9018i | 0.527215 | − | 0.527215i | ||||
\(26\) | −15.9076 | + | 116.561i | −0.119990 | + | 0.879214i | ||||
\(27\) | 127.540 | − | 52.8290i | 0.909081 | − | 0.376553i | ||||
\(28\) | −27.5175 | + | 98.9379i | −0.185725 | + | 0.667768i | ||||
\(29\) | 19.3621 | − | 46.7443i | 0.123981 | − | 0.299317i | −0.849687 | − | 0.527288i | \(-0.823209\pi\) |
0.973668 | + | 0.227971i | \(0.0732090\pi\) | |||||||
\(30\) | −339.152 | + | 89.1559i | −2.06401 | + | 0.542585i | ||||
\(31\) | −38.1477 | −0.221017 | −0.110508 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110508 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(32\) | −173.693 | − | 50.9787i | −0.959526 | − | 0.281620i | ||||
\(33\) | −366.706 | −1.93440 | ||||||||
\(34\) | 253.043 | − | 66.5197i | 1.27637 | − | 0.335530i | ||||
\(35\) | −72.5636 | + | 175.184i | −0.350442 | + | 0.846042i | ||||
\(36\) | 334.869 | + | 93.1367i | 1.55032 | + | 0.431189i | ||||
\(37\) | 227.529 | − | 94.2456i | 1.01096 | − | 0.418754i | 0.185156 | − | 0.982709i | \(-0.440721\pi\) |
0.825805 | + | 0.563955i | \(0.190721\pi\) | |||||||
\(38\) | −6.90506 | + | 50.5961i | −0.0294776 | + | 0.215994i | ||||
\(39\) | 246.851 | − | 246.851i | 1.01353 | − | 1.01353i | ||||
\(40\) | −306.951 | − | 132.284i | −1.21333 | − | 0.522898i | ||||
\(41\) | −279.334 | − | 279.334i | −1.06401 | − | 1.06401i | −0.997806 | − | 0.0662081i | \(-0.978910\pi\) |
−0.0662081 | − | 0.997806i | \(-0.521090\pi\) | |||||||
\(42\) | 242.643 | − | 184.367i | 0.891443 | − | 0.677344i | ||||
\(43\) | 112.235 | + | 270.960i | 0.398039 | + | 0.960952i | 0.988131 | + | 0.153616i | \(0.0490918\pi\) |
−0.590091 | + | 0.807337i | \(0.700908\pi\) | |||||||
\(44\) | −275.267 | − | 215.393i | −0.943136 | − | 0.737993i | ||||
\(45\) | 592.935 | + | 245.602i | 1.96421 | + | 0.813603i | ||||
\(46\) | 192.768 | − | 330.261i | 0.617871 | − | 1.05857i | ||||
\(47\) | 321.955i | 0.999191i | 0.866259 | + | 0.499596i | \(0.166518\pi\) | ||||
−0.866259 | + | 0.499596i | \(0.833482\pi\) | |||||||
\(48\) | 318.877 | + | 432.285i | 0.958872 | + | 1.29990i | ||||
\(49\) | 178.220i | 0.519592i | ||||||||
\(50\) | −227.664 | − | 132.883i | −0.643930 | − | 0.375851i | ||||
\(51\) | −717.312 | − | 297.120i | −1.96948 | − | 0.815787i | ||||
\(52\) | 330.291 | − | 40.3044i | 0.880830 | − | 0.107485i | ||||
\(53\) | −52.5056 | − | 126.760i | −0.136079 | − | 0.328524i | 0.841120 | − | 0.540848i | \(-0.181897\pi\) |
−0.977199 | + | 0.212324i | \(0.931897\pi\) | |||||||
\(54\) | −236.228 | − | 310.896i | −0.595306 | − | 0.783474i | ||||
\(55\) | −456.348 | − | 456.348i | −1.11880 | − | 1.11880i | ||||
\(56\) | 290.431 | + | 4.12723i | 0.693045 | + | 0.00984865i | ||||
\(57\) | 107.151 | − | 107.151i | 0.248991 | − | 0.248991i | ||||
\(58\) | −141.792 | − | 19.3509i | −0.321003 | − | 0.0438086i | ||||
\(59\) | −332.587 | + | 137.762i | −0.733884 | + | 0.303985i | −0.718147 | − | 0.695892i | \(-0.755009\pi\) |
−0.0157369 | + | 0.999876i | \(0.505009\pi\) | |||||||
\(60\) | 487.770 | + | 863.633i | 1.04951 | + | 1.85824i | ||||
\(61\) | 33.6815 | − | 81.3143i | 0.0706963 | − | 0.170676i | −0.884582 | − | 0.466385i | \(-0.845556\pi\) |
0.955278 | + | 0.295709i | \(0.0955560\pi\) | |||||||
\(62\) | 27.4321 | + | 104.352i | 0.0561915 | + | 0.213754i | ||||
\(63\) | −557.721 | −1.11534 | ||||||||
\(64\) | −14.5488 | + | 511.793i | −0.0284156 | + | 0.999596i | ||||
\(65\) | 614.389 | 1.17239 | ||||||||
\(66\) | 263.699 | + | 1003.12i | 0.491804 | + | 1.87084i | ||||
\(67\) | 108.572 | − | 262.117i | 0.197974 | − | 0.477951i | −0.793450 | − | 0.608635i | \(-0.791717\pi\) |
0.991424 | + | 0.130684i | \(0.0417174\pi\) | |||||||
\(68\) | −363.928 | − | 644.362i | −0.649010 | − | 1.14912i | ||||
\(69\) | −1048.39 | + | 434.259i | −1.82916 | + | 0.757661i | ||||
\(70\) | 531.394 | + | 72.5216i | 0.907339 | + | 0.123828i | ||||
\(71\) | 272.246 | − | 272.246i | 0.455066 | − | 0.455066i | −0.441966 | − | 0.897032i | \(-0.645719\pi\) |
0.897032 | + | 0.441966i | \(0.145719\pi\) | |||||||
\(72\) | 13.9692 | − | 983.005i | 0.0228651 | − | 1.60900i | ||||
\(73\) | 372.955 | + | 372.955i | 0.597960 | + | 0.597960i | 0.939769 | − | 0.341809i | \(-0.111040\pi\) |
−0.341809 | + | 0.939769i | \(0.611040\pi\) | |||||||
\(74\) | −421.424 | − | 554.631i | −0.662022 | − | 0.871277i | ||||
\(75\) | 299.354 | + | 722.704i | 0.460885 | + | 1.11268i | ||||
\(76\) | 143.370 | − | 17.4950i | 0.216391 | − | 0.0264055i | ||||
\(77\) | 518.146 | + | 214.623i | 0.766860 | + | 0.317644i | ||||
\(78\) | −852.768 | − | 497.746i | −1.23791 | − | 0.722547i | ||||
\(79\) | 244.410i | 0.348080i | 0.984739 | + | 0.174040i | \(0.0556822\pi\) | ||||
−0.984739 | + | 0.174040i | \(0.944318\pi\) | |||||||
\(80\) | −141.132 | + | 934.787i | −0.197238 | + | 1.30640i | ||||
\(81\) | − | 14.3973i | − | 0.0197494i | ||||||
\(82\) | −563.244 | + | 964.983i | −0.758535 | + | 1.29957i | ||||
\(83\) | 1230.52 | + | 509.697i | 1.62731 | + | 0.674054i | 0.994927 | − | 0.100600i | \(-0.0320764\pi\) |
0.632384 | + | 0.774655i | \(0.282076\pi\) | |||||||
\(84\) | −678.819 | − | 531.168i | −0.881728 | − | 0.689942i | ||||
\(85\) | −522.909 | − | 1262.41i | −0.667264 | − | 1.61092i | ||||
\(86\) | 660.498 | − | 501.865i | 0.828178 | − | 0.629274i | ||||
\(87\) | 300.283 | + | 300.283i | 0.370043 | + | 0.370043i | ||||
\(88\) | −391.260 | + | 907.878i | −0.473960 | + | 1.09977i | ||||
\(89\) | 216.134 | − | 216.134i | 0.257417 | − | 0.257417i | −0.566586 | − | 0.824003i | \(-0.691736\pi\) |
0.824003 | + | 0.566586i | \(0.191736\pi\) | |||||||
\(90\) | 245.459 | − | 1798.58i | 0.287486 | − | 2.10652i | ||||
\(91\) | −493.270 | + | 204.319i | −0.568228 | + | 0.235368i | ||||
\(92\) | −1042.05 | − | 289.823i | −1.18088 | − | 0.328436i | ||||
\(93\) | 122.529 | − | 295.812i | 0.136621 | − | 0.329831i | ||||
\(94\) | 880.704 | − | 231.519i | 0.966359 | − | 0.254035i | ||||
\(95\) | 266.689 | 0.288018 | ||||||||
\(96\) | 953.206 | − | 1183.14i | 1.01340 | − | 1.25785i | ||||
\(97\) | 779.862 | 0.816319 | 0.408160 | − | 0.912911i | \(-0.366171\pi\) | ||||
0.408160 | + | 0.912911i | \(0.366171\pi\) | |||||||
\(98\) | 487.519 | − | 128.158i | 0.502519 | − | 0.132102i | ||||
\(99\) | 726.422 | − | 1753.74i | 0.737457 | − | 1.78038i | ||||
\(100\) | −199.788 | + | 718.328i | −0.199788 | + | 0.718328i | ||||
\(101\) | −1046.60 | + | 433.515i | −1.03109 | + | 0.427092i | −0.833106 | − | 0.553113i | \(-0.813440\pi\) |
−0.197985 | + | 0.980205i | \(0.563440\pi\) | |||||||
\(102\) | −296.948 | + | 2175.86i | −0.288258 | + | 2.11218i | ||||
\(103\) | 683.721 | − | 683.721i | 0.654069 | − | 0.654069i | −0.299901 | − | 0.953970i | \(-0.596954\pi\) |
0.953970 | + | 0.299901i | \(0.0969538\pi\) | |||||||
\(104\) | −347.765 | − | 874.525i | −0.327896 | − | 0.824560i | ||||
\(105\) | −1125.37 | − | 1125.37i | −1.04595 | − | 1.04595i | ||||
\(106\) | −308.993 | + | 234.782i | −0.283133 | + | 0.215132i | ||||
\(107\) | −289.555 | − | 699.048i | −0.261611 | − | 0.631584i | 0.737428 | − | 0.675426i | \(-0.236040\pi\) |
−0.999038 | + | 0.0438418i | \(0.986040\pi\) | |||||||
\(108\) | −680.580 | + | 869.764i | −0.606378 | + | 0.774936i | ||||
\(109\) | 56.3510 | + | 23.3413i | 0.0495179 | + | 0.0205110i | 0.407305 | − | 0.913292i | \(-0.366469\pi\) |
−0.357787 | + | 0.933803i | \(0.616469\pi\) | |||||||
\(110\) | −920.174 | + | 1576.50i | −0.797592 | + | 1.36648i | ||||
\(111\) | 2067.07i | 1.76754i | ||||||||
\(112\) | −197.560 | − | 797.439i | −0.166675 | − | 0.672776i | ||||
\(113\) | 1567.46i | 1.30491i | 0.757828 | + | 0.652454i | \(0.226260\pi\) | ||||
−0.757828 | + | 0.652454i | \(0.773740\pi\) | |||||||
\(114\) | −370.163 | − | 216.058i | −0.304114 | − | 0.177506i | ||||
\(115\) | −1845.09 | − | 764.263i | −1.49614 | − | 0.619720i | ||||
\(116\) | 49.0286 | + | 401.785i | 0.0392430 | + | 0.321593i | ||||
\(117\) | 691.546 | + | 1669.54i | 0.546440 | + | 1.31922i | ||||
\(118\) | 616.010 | + | 810.723i | 0.480579 | + | 0.632484i | ||||
\(119\) | 839.647 | + | 839.647i | 0.646810 | + | 0.646810i | ||||
\(120\) | 2011.70 | − | 1955.33i | 1.53035 | − | 1.48747i | ||||
\(121\) | −408.595 | + | 408.595i | −0.306983 | + | 0.306983i | ||||
\(122\) | −246.655 | − | 33.6620i | −0.183042 | − | 0.0249805i | ||||
\(123\) | 3063.28 | − | 1268.85i | 2.24558 | − | 0.930150i | ||||
\(124\) | 265.728 | − | 150.080i | 0.192444 | − | 0.108690i | ||||
\(125\) | 179.764 | − | 433.989i | 0.128629 | − | 0.310538i | ||||
\(126\) | 401.058 | + | 1525.64i | 0.283564 | + | 1.07869i | ||||
\(127\) | −1291.26 | −0.902209 | −0.451105 | − | 0.892471i | \(-0.648970\pi\) | ||||
−0.451105 | + | 0.892471i | \(0.648970\pi\) | |||||||
\(128\) | 1410.47 | − | 328.234i | 0.973975 | − | 0.226656i | ||||
\(129\) | −2461.63 | −1.68011 | ||||||||
\(130\) | −441.808 | − | 1680.65i | −0.298070 | − | 1.13387i | ||||
\(131\) | −326.012 | + | 787.064i | −0.217434 | + | 0.524932i | −0.994530 | − | 0.104450i | \(-0.966692\pi\) |
0.777096 | + | 0.629382i | \(0.216692\pi\) | |||||||
\(132\) | 2554.39 | − | 1442.69i | 1.68433 | − | 0.951288i | ||||
\(133\) | −214.115 | + | 88.6892i | −0.139595 | + | 0.0578220i | ||||
\(134\) | −795.093 | − | 108.510i | −0.512579 | − | 0.0699538i | ||||
\(135\) | −1441.93 | + | 1441.93i | −0.919271 | + | 0.919271i | ||||
\(136\) | −1500.94 | + | 1458.88i | −0.946358 | + | 0.919839i | ||||
\(137\) | 1526.86 | + | 1526.86i | 0.952177 | + | 0.952177i | 0.998908 | − | 0.0467305i | \(-0.0148802\pi\) |
−0.0467305 | + | 0.998908i | \(0.514880\pi\) | |||||||
\(138\) | 1941.81 | + | 2555.59i | 1.19781 | + | 1.57642i | ||||
\(139\) | −181.169 | − | 437.382i | −0.110551 | − | 0.266894i | 0.858916 | − | 0.512117i | \(-0.171139\pi\) |
−0.969467 | + | 0.245224i | \(0.921139\pi\) | |||||||
\(140\) | −183.745 | − | 1505.77i | −0.110923 | − | 0.909007i | ||||
\(141\) | −2496.57 | − | 1034.11i | −1.49113 | − | 0.617645i | ||||
\(142\) | −940.499 | − | 548.953i | −0.555809 | − | 0.324417i | ||||
\(143\) | − | 1817.20i | − | 1.06267i | ||||||
\(144\) | −2699.04 | + | 668.669i | −1.56195 | + | 0.386961i | ||||
\(145\) | 747.377i | 0.428043i | ||||||||
\(146\) | 752.021 | − | 1288.41i | 0.426286 | − | 0.730338i | ||||
\(147\) | −1381.99 | − | 572.439i | −0.775405 | − | 0.321183i | ||||
\(148\) | −1214.14 | + | 1551.64i | −0.674335 | + | 0.861782i | ||||
\(149\) | −1162.21 | − | 2805.81i | −0.639004 | − | 1.54269i | −0.828008 | − | 0.560716i | \(-0.810526\pi\) |
0.189004 | − | 0.981976i | \(-0.439474\pi\) | |||||||
\(150\) | 1761.68 | − | 1338.58i | 0.958938 | − | 0.728629i | ||||
\(151\) | −262.518 | − | 262.518i | −0.141479 | − | 0.141479i | 0.632820 | − | 0.774299i | \(-0.281897\pi\) |
−0.774299 | + | 0.632820i | \(0.781897\pi\) | |||||||
\(152\) | −150.955 | − | 379.607i | −0.0805533 | − | 0.202567i | ||||
\(153\) | 2841.90 | − | 2841.90i | 1.50166 | − | 1.50166i | ||||
\(154\) | 214.499 | − | 1571.72i | 0.112239 | − | 0.822420i | ||||
\(155\) | 520.607 | − | 215.642i | 0.269782 | − | 0.111747i | ||||
\(156\) | −748.352 | + | 2690.67i | −0.384078 | + | 1.38093i | ||||
\(157\) | −1086.34 | + | 2622.67i | −0.552227 | + | 1.33319i | 0.363575 | + | 0.931565i | \(0.381556\pi\) |
−0.915802 | + | 0.401630i | \(0.868444\pi\) | |||||||
\(158\) | 668.581 | − | 175.756i | 0.336642 | − | 0.0884961i | ||||
\(159\) | 1151.59 | 0.574385 | ||||||||
\(160\) | 2658.59 | − | 286.142i | 1.31362 | − | 0.141385i | ||||
\(161\) | 1735.52 | 0.849552 | ||||||||
\(162\) | −39.3837 | + | 10.3531i | −0.0191005 | + | 0.00502111i | ||||
\(163\) | −380.057 | + | 917.540i | −0.182628 | + | 0.440903i | −0.988507 | − | 0.151178i | \(-0.951693\pi\) |
0.805878 | + | 0.592081i | \(0.201693\pi\) | |||||||
\(164\) | 3044.73 | + | 846.826i | 1.44972 | + | 0.403207i | ||||
\(165\) | 5004.49 | − | 2072.93i | 2.36120 | − | 0.978043i | ||||
\(166\) | 509.402 | − | 3732.59i | 0.238176 | − | 1.74521i | ||||
\(167\) | −1515.61 | + | 1515.61i | −0.702283 | + | 0.702283i | −0.964900 | − | 0.262617i | \(-0.915414\pi\) |
0.262617 | + | 0.964900i | \(0.415414\pi\) | |||||||
\(168\) | −964.863 | + | 2238.86i | −0.443100 | + | 1.02817i | ||||
\(169\) | −330.254 | − | 330.254i | −0.150320 | − | 0.150320i | ||||
\(170\) | −3077.29 | + | 2338.22i | −1.38834 | + | 1.05490i | ||||
\(171\) | 300.181 | + | 724.701i | 0.134242 | + | 0.324089i | ||||
\(172\) | −1847.81 | − | 1445.89i | −0.819153 | − | 0.640978i | ||||
\(173\) | −1837.08 | − | 760.945i | −0.807346 | − | 0.334414i | −0.0594515 | − | 0.998231i | \(-0.518935\pi\) |
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(174\) | 605.487 | − | 1037.36i | 0.263804 | − | 0.451964i | ||||
\(175\) | − | 1196.37i | − | 0.516782i | ||||||
\(176\) | 2764.84 | + | 417.430i | 1.18414 | + | 0.178778i | ||||
\(177\) | − | 3021.50i | − | 1.28311i | ||||||
\(178\) | −746.653 | − | 435.809i | −0.314404 | − | 0.183513i | ||||
\(179\) | 2975.35 | + | 1232.43i | 1.24239 | + | 0.514615i | 0.904461 | − | 0.426556i | \(-0.140273\pi\) |
0.337930 | + | 0.941171i | \(0.390273\pi\) | |||||||
\(180\) | −5096.50 | + | 621.910i | −2.11039 | + | 0.257524i | ||||
\(181\) | 1619.10 | + | 3908.85i | 0.664899 | + | 1.60521i | 0.790030 | + | 0.613068i | \(0.210065\pi\) |
−0.125132 | + | 0.992140i | \(0.539935\pi\) | |||||||
\(182\) | 913.623 | + | 1202.41i | 0.372100 | + | 0.489716i | ||||
\(183\) | 522.359 | + | 522.359i | 0.211005 | + | 0.211005i | ||||
\(184\) | −43.4693 | + | 3058.92i | −0.0174163 | + | 1.22558i | ||||
\(185\) | −2572.37 | + | 2572.37i | −1.02229 | + | 1.02229i | ||||
\(186\) | −897.302 | − | 122.459i | −0.353728 | − | 0.0482747i | ||||
\(187\) | −3733.88 | + | 1546.62i | −1.46015 | + | 0.604814i | ||||
\(188\) | −1266.63 | − | 2242.67i | −0.491376 | − | 0.870019i | ||||
\(189\) | 678.148 | − | 1637.19i | 0.260995 | − | 0.630097i | ||||
\(190\) | −191.777 | − | 729.525i | −0.0732261 | − | 0.278554i | ||||
\(191\) | 697.265 | 0.264148 | 0.132074 | − | 0.991240i | \(-0.457836\pi\) | ||||
0.132074 | + | 0.991240i | \(0.457836\pi\) | |||||||
\(192\) | −3921.92 | − | 1756.69i | −1.47417 | − | 0.660301i | ||||
\(193\) | 2386.61 | 0.890114 | 0.445057 | − | 0.895502i | \(-0.353183\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353183\pi\) | |||||||
\(194\) | −560.800 | − | 2133.30i | −0.207542 | − | 0.789496i | ||||
\(195\) | −1973.40 | + | 4764.22i | −0.724710 | + | 1.74960i | ||||
\(196\) | −701.151 | − | 1241.44i | −0.255522 | − | 0.452421i | ||||
\(197\) | −2583.07 | + | 1069.94i | −0.934194 | + | 0.386956i | −0.797268 | − | 0.603625i | \(-0.793722\pi\) |
−0.136926 | + | 0.990581i | \(0.543722\pi\) | |||||||
\(198\) | −5319.70 | − | 726.002i | −1.90937 | − | 0.260579i | ||||
\(199\) | 2940.81 | − | 2940.81i | 1.04758 | − | 1.04758i | 0.0487695 | − | 0.998810i | \(-0.484470\pi\) |
0.998810 | − | 0.0487695i | \(-0.0155300\pi\) | |||||||
\(200\) | 2108.65 | + | 29.9653i | 0.745519 | + | 0.0105943i | ||||
\(201\) | 1683.83 | + | 1683.83i | 0.590886 | + | 0.590886i | ||||
\(202\) | 1938.48 | + | 2551.21i | 0.675204 | + | 0.888627i | ||||
\(203\) | −248.545 | − | 600.041i | −0.0859332 | − | 0.207461i | ||||
\(204\) | 6165.57 | − | 752.365i | 2.11606 | − | 0.258216i | ||||
\(205\) | 5391.13 | + | 2233.08i | 1.83675 | + | 0.760805i | ||||
\(206\) | −2361.98 | − | 1378.65i | −0.798868 | − | 0.466286i | ||||
\(207\) | − | 5874.10i | − | 1.97236i | ||||||
\(208\) | −2142.17 | + | 1580.18i | −0.714101 | + | 0.526759i | ||||
\(209\) | − | 788.794i | − | 0.261062i | ||||||
\(210\) | −2269.19 | + | 3887.70i | −0.745661 | + | 1.27751i | ||||
\(211\) | 1399.25 | + | 579.589i | 0.456533 | + | 0.189102i | 0.599085 | − | 0.800685i | \(-0.295531\pi\) |
−0.142552 | + | 0.989787i | \(0.545531\pi\) | |||||||
\(212\) | 864.440 | + | 676.414i | 0.280047 | + | 0.219134i | ||||
\(213\) | 1236.66 | + | 2985.55i | 0.397814 | + | 0.960408i | ||||
\(214\) | −1704.02 | + | 1294.76i | −0.544319 | + | 0.413589i | ||||
\(215\) | −3063.38 | − | 3063.38i | −0.971724 | − | 0.971724i | ||||
\(216\) | 2868.63 | + | 1236.27i | 0.903638 | + | 0.389433i | ||||
\(217\) | −346.262 | + | 346.262i | −0.108322 | + | 0.108322i | ||||
\(218\) | 23.3278 | − | 170.932i | 0.00724753 | − | 0.0531055i | ||||
\(219\) | −4089.97 | + | 1694.12i | −1.26198 | + | 0.522731i | ||||
\(220\) | 4974.18 | + | 1383.46i | 1.52436 | + | 0.423968i | ||||
\(221\) | 1472.37 | − | 3554.61i | 0.448155 | − | 1.08194i | ||||
\(222\) | 5654.43 | − | 1486.43i | 1.70946 | − | 0.449382i | ||||
\(223\) | −1100.18 | −0.330374 | −0.165187 | − | 0.986262i | \(-0.552823\pi\) | ||||
−0.165187 | + | 0.986262i | \(0.552823\pi\) | |||||||
\(224\) | −2039.32 | + | 1113.86i | −0.608293 | + | 0.332246i | ||||
\(225\) | −4049.27 | −1.19979 | ||||||||
\(226\) | 4287.78 | − | 1127.17i | 1.26203 | − | 0.331761i | ||||
\(227\) | 1476.27 | − | 3564.04i | 0.431647 | − | 1.04209i | −0.547110 | − | 0.837061i | \(-0.684272\pi\) |
0.978756 | − | 0.205026i | \(-0.0657280\pi\) | |||||||
\(228\) | −324.839 | + | 1167.94i | −0.0943551 | + | 0.339250i | ||||
\(229\) | 3573.95 | − | 1480.38i | 1.03132 | − | 0.427188i | 0.198134 | − | 0.980175i | \(-0.436512\pi\) |
0.833190 | + | 0.552986i | \(0.186512\pi\) | |||||||
\(230\) | −763.821 | + | 5596.81i | −0.218978 | + | 1.60453i | ||||
\(231\) | −3328.55 | + | 3328.55i | −0.948062 | + | 0.948062i | ||||
\(232\) | 1063.82 | − | 423.041i | 0.301049 | − | 0.119716i | ||||
\(233\) | −3668.67 | − | 3668.67i | −1.03151 | − | 1.03151i | −0.999487 | − | 0.0320257i | \(-0.989804\pi\) |
−0.0320257 | − | 0.999487i | \(-0.510196\pi\) | |||||||
\(234\) | 4069.71 | − | 3092.29i | 1.13695 | − | 0.863885i | ||||
\(235\) | −1819.96 | − | 4393.77i | −0.505196 | − | 1.21965i | ||||
\(236\) | 1774.75 | − | 2268.08i | 0.489518 | − | 0.625591i | ||||
\(237\) | −1895.25 | − | 785.040i | −0.519451 | − | 0.215164i | ||||
\(238\) | 1693.05 | − | 2900.64i | 0.461111 | − | 0.790002i | ||||
\(239\) | 5649.23i | 1.52895i | 0.644656 | + | 0.764473i | \(0.277001\pi\) | ||||
−0.644656 | + | 0.764473i | \(0.722999\pi\) | |||||||
\(240\) | −6795.40 | − | 4096.91i | −1.82767 | − | 1.10189i | ||||
\(241\) | − | 5059.57i | − | 1.35235i | −0.736743 | − | 0.676173i | \(-0.763637\pi\) | ||
0.736743 | − | 0.676173i | \(-0.236363\pi\) | |||||||
\(242\) | 1411.53 | + | 823.884i | 0.374944 | + | 0.218848i | ||||
\(243\) | 3555.24 | + | 1472.63i | 0.938553 | + | 0.388761i | ||||
\(244\) | 85.2879 | + | 698.927i | 0.0223770 | + | 0.183378i | ||||
\(245\) | −1007.45 | − | 2432.20i | −0.262708 | − | 0.634234i | ||||
\(246\) | −5673.73 | − | 7467.12i | −1.47050 | − | 1.93531i | ||||
\(247\) | 530.983 | + | 530.983i | 0.136784 | + | 0.136784i | ||||
\(248\) | −601.628 | − | 618.974i | −0.154046 | − | 0.158487i | ||||
\(249\) | −7904.79 | + | 7904.79i | −2.01183 | + | 2.01183i | ||||
\(250\) | −1316.44 | − | 179.660i | −0.333036 | − | 0.0454509i | ||||
\(251\) | 980.968 | − | 406.330i | 0.246686 | − | 0.102181i | −0.255915 | − | 0.966699i | \(-0.582377\pi\) |
0.502601 | + | 0.864519i | \(0.332377\pi\) | |||||||
\(252\) | 3884.96 | − | 2194.18i | 0.971150 | − | 0.548494i | ||||
\(253\) | −2260.48 | + | 5457.28i | −0.561720 | + | 1.35611i | ||||
\(254\) | 928.546 | + | 3532.22i | 0.229379 | + | 0.872564i | ||||
\(255\) | 11468.8 | 2.81649 | ||||||||
\(256\) | −1912.15 | − | 3622.28i | −0.466833 | − | 0.884346i | ||||
\(257\) | −1021.29 | −0.247886 | −0.123943 | − | 0.992289i | \(-0.539554\pi\) | ||||
−0.123943 | + | 0.992289i | \(0.539554\pi\) | |||||||
\(258\) | 1770.16 | + | 6733.75i | 0.427152 | + | 1.62490i | ||||
\(259\) | 1209.80 | − | 2920.72i | 0.290244 | − | 0.700712i | ||||
\(260\) | −4279.70 | + | 2417.12i | −1.02083 | + | 0.576552i | ||||
\(261\) | −2030.92 | + | 841.236i | −0.481651 | + | 0.199506i | ||||
\(262\) | 2387.44 | + | 325.824i | 0.562964 | + | 0.0768300i | ||||
\(263\) | −1134.88 | + | 1134.88i | −0.266083 | + | 0.266083i | −0.827520 | − | 0.561437i | \(-0.810249\pi\) |
0.561437 | + | 0.827520i | \(0.310249\pi\) | |||||||
\(264\) | −5783.33 | − | 5950.07i | −1.34825 | − | 1.38713i | ||||
\(265\) | 1433.10 | + | 1433.10i | 0.332207 | + | 0.332207i | ||||
\(266\) | 396.579 | + | 521.932i | 0.0914128 | + | 0.120307i | ||||
\(267\) | 981.770 | + | 2370.20i | 0.225031 | + | 0.543273i | ||||
\(268\) | 274.926 | + | 2253.00i | 0.0626634 | + | 0.513521i | ||||
\(269\) | −2221.12 | − | 920.017i | −0.503435 | − | 0.208530i | 0.116488 | − | 0.993192i | \(-0.462836\pi\) |
−0.619923 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(270\) | 4981.28 | + | 2907.49i | 1.12278 | + | 0.655348i | ||||
\(271\) | 1860.26i | 0.416984i | 0.978024 | + | 0.208492i | \(0.0668555\pi\) | ||||
−0.978024 | + | 0.208492i | \(0.933144\pi\) | |||||||
\(272\) | 5070.08 | + | 3056.72i | 1.13022 | + | 0.681401i | ||||
\(273\) | − | 4481.28i | − | 0.993477i | ||||||
\(274\) | 3078.73 | − | 5274.67i | 0.678807 | − | 1.16297i | ||||
\(275\) | 3761.95 | + | 1558.25i | 0.824923 | + | 0.341694i | ||||
\(276\) | 5594.43 | − | 7149.53i | 1.22009 | − | 1.55924i | ||||
\(277\) | −2311.55 | − | 5580.58i | −0.501400 | − | 1.21049i | −0.948721 | − | 0.316113i | \(-0.897622\pi\) |
0.447322 | − | 0.894373i | \(-0.352378\pi\) | |||||||
\(278\) | −1066.17 | + | 810.108i | −0.230017 | + | 0.174774i | ||||
\(279\) | 1171.97 | + | 1171.97i | 0.251485 | + | 0.251485i | ||||
\(280\) | −3986.89 | + | 1585.44i | −0.850937 | + | 0.338385i | ||||
\(281\) | −1740.45 | + | 1740.45i | −0.369490 | + | 0.369490i | −0.867291 | − | 0.497801i | \(-0.834141\pi\) |
0.497801 | + | 0.867291i | \(0.334141\pi\) | |||||||
\(282\) | −1033.51 | + | 7572.96i | −0.218244 | + | 1.59916i | ||||
\(283\) | −2580.95 | + | 1069.06i | −0.542125 | + | 0.224555i | −0.636904 | − | 0.770943i | \(-0.719785\pi\) |
0.0947795 | + | 0.995498i | \(0.469785\pi\) | |||||||
\(284\) | −825.340 | + | 2967.48i | −0.172447 | + | 0.620026i | ||||
\(285\) | −856.600 | + | 2068.01i | −0.178037 | + | 0.429820i | ||||
\(286\) | −4970.92 | + | 1306.75i | −1.02775 | + | 0.270174i | ||||
\(287\) | −5070.96 | −1.04296 | ||||||||
\(288\) | 3770.02 | + | 6902.36i | 0.771357 | + | 1.41224i | ||||
\(289\) | −3643.96 | −0.741697 | ||||||||
\(290\) | 2044.44 | − | 537.441i | 0.413978 | − | 0.108826i | ||||
\(291\) | −2504.90 | + | 6047.36i | −0.504604 | + | 1.21822i | ||||
\(292\) | −4065.20 | − | 1130.65i | −0.814719 | − | 0.226597i | ||||
\(293\) | 6531.00 | − | 2705.23i | 1.30220 | − | 0.539390i | 0.379603 | − | 0.925149i | \(-0.376061\pi\) |
0.922599 | + | 0.385760i | \(0.126061\pi\) | |||||||
\(294\) | −572.107 | + | 4192.06i | −0.113490 | + | 0.831584i | ||||
\(295\) | 3760.12 | − | 3760.12i | 0.742110 | − | 0.742110i | ||||
\(296\) | 5117.57 | + | 2205.47i | 1.00491 | + | 0.433076i | ||||
\(297\) | 4264.84 | + | 4264.84i | 0.833235 | + | 0.833235i | ||||
\(298\) | −6839.52 | + | 5196.87i | −1.32954 | + | 1.01022i | ||||
\(299\) | −2151.95 | − | 5195.27i | −0.416223 | − | 1.00485i | ||||
\(300\) | −4928.49 | − | 3856.49i | −0.948488 | − | 0.742181i | ||||
\(301\) | 3478.22 | + | 1440.72i | 0.666050 | + | 0.275887i | ||||
\(302\) | −529.337 | + | 906.891i | −0.100861 | + | 0.172800i | ||||
\(303\) | − | 9508.17i | − | 1.80274i | ||||||
\(304\) | −929.858 | + | 685.913i | −0.175431 | + | 0.129407i | ||||
\(305\) | 1300.10i | 0.244078i | ||||||||
\(306\) | −9817.61 | − | 5730.38i | −1.83410 | − | 1.07054i | ||||
\(307\) | −22.1910 | − | 9.19181i | −0.00412543 | − | 0.00170881i | 0.380620 | − | 0.924732i | \(-0.375711\pi\) |
−0.384745 | + | 0.923023i | \(0.625711\pi\) | |||||||
\(308\) | −4453.66 | + | 543.467i | −0.823932 | + | 0.100542i | ||||
\(309\) | 3105.75 | + | 7497.95i | 0.571780 | + | 1.38040i | ||||
\(310\) | −964.257 | − | 1269.04i | −0.176665 | − | 0.232506i | ||||
\(311\) | −4220.58 | − | 4220.58i | −0.769540 | − | 0.769540i | 0.208485 | − | 0.978026i | \(-0.433147\pi\) |
−0.978026 | + | 0.208485i | \(0.933147\pi\) | |||||||
\(312\) | 7898.43 | + | 112.242i | 1.43321 | + | 0.0203669i | ||||
\(313\) | 6090.90 | − | 6090.90i | 1.09993 | − | 1.09993i | 0.105512 | − | 0.994418i | \(-0.466352\pi\) |
0.994418 | − | 0.105512i | \(-0.0336481\pi\) | |||||||
\(314\) | 7955.46 | + | 1085.72i | 1.42979 | + | 0.195129i | ||||
\(315\) | 7611.30 | − | 3152.71i | 1.36142 | − | 0.563920i | ||||
\(316\) | −961.556 | − | 1702.51i | −0.171176 | − | 0.303081i | ||||
\(317\) | −1660.86 | + | 4009.67i | −0.294269 | + | 0.710428i | 0.705729 | + | 0.708482i | \(0.250620\pi\) |
−0.999998 | + | 0.00194638i | \(0.999380\pi\) | |||||||
\(318\) | −828.113 | − | 3150.17i | −0.146032 | − | 0.555511i | ||||
\(319\) | 2210.54 | 0.387982 | ||||||||
\(320\) | −2694.53 | − | 7066.76i | −0.470716 | − | 1.23451i | ||||
\(321\) | 6350.74 | 1.10425 | ||||||||
\(322\) | −1248.01 | − | 4747.48i | −0.215991 | − | 0.821636i | ||||
\(323\) | 639.114 | − | 1542.96i | 0.110097 | − | 0.265797i | ||||
\(324\) | 56.6418 | + | 100.289i | 0.00971224 | + | 0.0171963i | ||||
\(325\) | −3581.33 | + | 1483.44i | −0.611251 | + | 0.253188i | ||||
\(326\) | 2783.22 | + | 379.838i | 0.472847 | + | 0.0645315i | ||||
\(327\) | −361.996 | + | 361.996i | −0.0612185 | + | 0.0612185i | ||||
\(328\) | 127.012 | − | 8937.77i | 0.0213813 | − | 1.50459i | ||||
\(329\) | 2922.35 | + | 2922.35i | 0.489710 | + | 0.489710i | ||||
\(330\) | −9269.20 | − | 12199.1i | −1.54622 | − | 2.03496i | ||||
\(331\) | 3722.12 | + | 8985.99i | 0.618085 | + | 1.49219i | 0.853924 | + | 0.520397i | \(0.174216\pi\) |
−0.235840 | + | 0.971792i | \(0.575784\pi\) | |||||||
\(332\) | −10576.8 | + | 1290.65i | −1.74842 | + | 0.213354i | ||||
\(333\) | −9885.57 | − | 4094.74i | −1.62680 | − | 0.673845i | ||||
\(334\) | 5235.80 | + | 3056.05i | 0.857755 | + | 0.500657i | ||||
\(335\) | 4190.90i | 0.683502i | ||||||||
\(336\) | 6818.22 | + | 1029.40i | 1.10704 | + | 0.167138i | ||||
\(337\) | 5211.97i | 0.842475i | 0.906950 | + | 0.421238i | \(0.138404\pi\) | ||||
−0.906950 | + | 0.421238i | \(0.861596\pi\) | |||||||
\(338\) | −665.919 | + | 1140.89i | −0.107163 | + | 0.183599i | ||||
\(339\) | −12154.7 | − | 5034.66i | −1.94736 | − | 0.806623i | ||||
\(340\) | 8609.05 | + | 6736.48i | 1.37321 | + | 1.07452i | ||||
\(341\) | −637.812 | − | 1539.81i | −0.101289 | − | 0.244532i | ||||
\(342\) | 1766.55 | − | 1342.28i | 0.279310 | − | 0.212228i | ||||
\(343\) | 4731.06 | + | 4731.06i | 0.744761 | + | 0.744761i | ||||
\(344\) | −2626.45 | + | 6094.41i | −0.411654 | + | 0.955199i | ||||
\(345\) | 11852.8 | − | 11852.8i | 1.84966 | − | 1.84966i | ||||
\(346\) | −760.505 | + | 5572.52i | −0.118165 | + | 0.865839i | ||||
\(347\) | 4987.20 | − | 2065.77i | 0.771547 | − | 0.319585i | 0.0380483 | − | 0.999276i | \(-0.487886\pi\) |
0.733499 | + | 0.679691i | \(0.237886\pi\) | |||||||
\(348\) | −3273.08 | − | 910.337i | −0.504182 | − | 0.140228i | ||||
\(349\) | 3137.63 | − | 7574.92i | 0.481243 | − | 1.16182i | −0.477776 | − | 0.878481i | \(-0.658557\pi\) |
0.959019 | − | 0.283341i | \(-0.0914429\pi\) | |||||||
\(350\) | −3272.65 | + | 860.311i | −0.499801 | + | 0.131387i | ||||
\(351\) | −5741.82 | −0.873150 | ||||||||
\(352\) | −846.331 | − | 7863.37i | −0.128152 | − | 1.19068i | ||||
\(353\) | 8999.28 | 1.35689 | 0.678446 | − | 0.734650i | \(-0.262654\pi\) | ||||
0.678446 | + | 0.734650i | \(0.262654\pi\) | |||||||
\(354\) | −8265.28 | + | 2172.77i | −1.24095 | + | 0.326218i | ||||
\(355\) | −2176.42 | + | 5254.35i | −0.325387 | + | 0.785555i | ||||
\(356\) | −655.229 | + | 2355.85i | −0.0975480 | + | 0.350730i | ||||
\(357\) | −9207.89 | + | 3814.03i | −1.36508 | + | 0.565434i | ||||
\(358\) | 1231.72 | − | 9025.27i | 0.181839 | − | 1.33240i | ||||
\(359\) | −4697.94 | + | 4697.94i | −0.690662 | + | 0.690662i | −0.962378 | − | 0.271715i | \(-0.912409\pi\) |
0.271715 | + | 0.962378i | \(0.412409\pi\) | |||||||
\(360\) | 5366.13 | + | 13494.2i | 0.785610 | + | 1.97557i | ||||
\(361\) | −4619.56 | − | 4619.56i | −0.673503 | − | 0.673503i | ||||
\(362\) | 9528.32 | − | 7239.89i | 1.38342 | − | 1.05116i | ||||
\(363\) | −1856.01 | − | 4480.80i | −0.268361 | − | 0.647882i | ||||
\(364\) | 2632.18 | − | 3363.86i | 0.379021 | − | 0.484379i | ||||
\(365\) | −7198.03 | − | 2981.52i | −1.03222 | − | 0.427561i | ||||
\(366\) | 1053.28 | − | 1804.54i | 0.150425 | − | 0.257718i | ||||
\(367\) | 5942.35i | 0.845199i | 0.906316 | + | 0.422600i | \(0.138882\pi\) | ||||
−0.906316 | + | 0.422600i | \(0.861118\pi\) | |||||||
\(368\) | 8398.88 | − | 2080.76i | 1.18973 | − | 0.294748i | ||||
\(369\) | 17163.4i | 2.42138i | ||||||||
\(370\) | 8886.48 | + | 5186.89i | 1.24861 | + | 0.728793i | ||||
\(371\) | −1627.17 | − | 673.997i | −0.227705 | − | 0.0943186i | ||||
\(372\) | 310.268 | + | 2542.62i | 0.0432436 | + | 0.354378i | ||||
\(373\) | −611.014 | − | 1475.12i | −0.0848180 | − | 0.204769i | 0.875780 | − | 0.482711i | \(-0.160348\pi\) |
−0.960598 | + | 0.277942i | \(0.910348\pi\) | |||||||
\(374\) | 6915.80 | + | 9101.79i | 0.956170 | + | 1.25840i | ||||
\(375\) | 2787.93 | + | 2787.93i | 0.383915 | + | 0.383915i | ||||
\(376\) | −5223.96 | + | 5077.57i | −0.716503 | + | 0.696424i | ||||
\(377\) | −1488.04 | + | 1488.04i | −0.203284 | + | 0.203284i | ||||
\(378\) | −4966.18 | − | 677.756i | −0.675748 | − | 0.0922222i | ||||
\(379\) | 3436.04 | − | 1423.25i | 0.465692 | − | 0.192896i | −0.137484 | − | 0.990504i | \(-0.543902\pi\) |
0.603176 | + | 0.797608i | \(0.293902\pi\) | |||||||
\(380\) | −1857.70 | + | 1049.21i | −0.250784 | + | 0.141640i | ||||
\(381\) | 4147.49 | − | 10012.9i | 0.557697 | − | 1.34640i | ||||
\(382\) | −501.405 | − | 1907.36i | −0.0671574 | − | 0.255469i | ||||
\(383\) | −9327.55 | −1.24443 | −0.622213 | − | 0.782848i | \(-0.713766\pi\) | ||||
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(384\) | −1985.13 | + | 11991.6i | −0.263811 | + | 1.59360i | ||||
\(385\) | −8284.45 | −1.09666 | ||||||||
\(386\) | −1716.22 | − | 6528.54i | −0.226303 | − | 0.860866i | ||||
\(387\) | 4876.34 | − | 11772.5i | 0.640512 | − | 1.54633i | ||||
\(388\) | −5432.35 | + | 3068.12i | −0.710788 | + | 0.401444i | ||||
\(389\) | 7840.37 | − | 3247.59i | 1.02191 | − | 0.423288i | 0.192123 | − | 0.981371i | \(-0.438463\pi\) |
0.829785 | + | 0.558083i | \(0.188463\pi\) | |||||||
\(390\) | 14451.5 | + | 1972.26i | 1.87636 | + | 0.256075i | ||||
\(391\) | −8843.44 | + | 8843.44i | −1.14382 | + | 1.14382i | ||||
\(392\) | −2891.75 | + | 2810.71i | −0.372590 | + | 0.362149i | ||||
\(393\) | −5056.06 | − | 5056.06i | −0.648968 | − | 0.648968i | ||||
\(394\) | 4784.31 | + | 6296.56i | 0.611751 | + | 0.805117i | ||||
\(395\) | −1381.61 | − | 3335.50i | −0.175991 | − | 0.424879i | ||||
\(396\) | 1839.44 | + | 15074.0i | 0.233422 | + | 1.91288i | ||||
\(397\) | 6845.23 | + | 2835.39i | 0.865370 | + | 0.358448i | 0.770805 | − | 0.637071i | \(-0.219854\pi\) |
0.0945649 | + | 0.995519i | \(0.469854\pi\) | |||||||
\(398\) | −10159.3 | − | 5929.80i | −1.27949 | − | 0.746819i | ||||
\(399\) | − | 1945.20i | − | 0.244064i | ||||||
\(400\) | −1434.36 | − | 5789.72i | −0.179295 | − | 0.723715i | ||||
\(401\) | − | 5333.86i | − | 0.664240i | −0.943237 | − | 0.332120i | \(-0.892236\pi\) | ||
0.943237 | − | 0.332120i | \(-0.107764\pi\) | |||||||
\(402\) | 3395.25 | − | 5816.94i | 0.421243 | − | 0.721698i | ||||
\(403\) | 1465.89 | + | 607.190i | 0.181193 | + | 0.0750528i | ||||
\(404\) | 5584.84 | − | 7137.28i | 0.687763 | − | 0.878943i | ||||
\(405\) | 81.3857 | + | 196.482i | 0.00998540 | + | 0.0241069i | ||||
\(406\) | −1462.68 | + | 1111.38i | −0.178796 | + | 0.135855i | ||||
\(407\) | 7608.37 | + | 7608.37i | 0.926616 | + | 0.926616i | ||||
\(408\) | −6491.75 | − | 16324.8i | −0.787720 | − | 1.98088i | ||||
\(409\) | −3906.82 | + | 3906.82i | −0.472322 | + | 0.472322i | −0.902665 | − | 0.430343i | \(-0.858393\pi\) |
0.430343 | + | 0.902665i | \(0.358393\pi\) | |||||||
\(410\) | 2231.79 | − | 16353.2i | 0.268830 | − | 1.96982i | ||||
\(411\) | −16744.1 | + | 6935.63i | −2.00955 | + | 0.832383i | ||||
\(412\) | −2072.77 | + | 7452.55i | −0.247859 | + | 0.891166i | ||||
\(413\) | −1768.41 | + | 4269.31i | −0.210696 | + | 0.508666i | ||||
\(414\) | −16068.5 | + | 4224.08i | −1.90755 | + | 0.501454i | ||||
\(415\) | −19674.3 | −2.32716 | ||||||||
\(416\) | 5863.01 | + | 4723.58i | 0.691004 | + | 0.556713i | ||||
\(417\) | 3973.54 | 0.466631 | ||||||||
\(418\) | −2157.74 | + | 567.223i | −0.252484 | + | 0.0663727i | ||||
\(419\) | 510.706 | − | 1232.95i | 0.0595456 | − | 0.143756i | −0.891306 | − | 0.453401i | \(-0.850210\pi\) |
0.950852 | + | 0.309646i | \(0.100210\pi\) | |||||||
\(420\) | 12266.5 | + | 3411.68i | 1.42511 | + | 0.396364i | ||||
\(421\) | −9078.42 | + | 3760.41i | −1.05096 | + | 0.435323i | −0.840235 | − | 0.542222i | \(-0.817583\pi\) |
−0.210727 | + | 0.977545i | \(0.567583\pi\) | |||||||
\(422\) | 579.254 | − | 4244.42i | 0.0668190 | − | 0.489609i | ||||
\(423\) | 9891.11 | − | 9891.11i | 1.13693 | − | 1.13693i | ||||
\(424\) | 1228.70 | − | 2851.08i | 0.140734 | − | 0.326558i | ||||
\(425\) | 6096.17 | + | 6096.17i | 0.695783 | + | 0.695783i | ||||
\(426\) | 7277.67 | − | 5529.78i | 0.827709 | − | 0.628917i | ||||
\(427\) | −432.358 | − | 1043.80i | −0.0490006 | − | 0.118298i | ||||
\(428\) | 4767.17 | + | 3730.25i | 0.538387 | + | 0.421282i | ||||
\(429\) | 14091.3 | + | 5836.79i | 1.58586 | + | 0.656883i | ||||
\(430\) | −6176.95 | + | 10582.7i | −0.692742 | + | 1.18685i | ||||
\(431\) | 7684.54i | 0.858820i | 0.903110 | + | 0.429410i | \(0.141278\pi\) | ||||
−0.903110 | + | 0.429410i | \(0.858722\pi\) | |||||||
\(432\) | 1318.96 | − | 8736.12i | 0.146895 | − | 0.972955i | ||||
\(433\) | 989.963i | 0.109872i | 0.998490 | + | 0.0549360i | \(0.0174955\pi\) | ||||
−0.998490 | + | 0.0549360i | \(0.982505\pi\) | |||||||
\(434\) | 1196.19 | + | 698.198i | 0.132302 | + | 0.0772226i | ||||
\(435\) | −5795.46 | − | 2400.56i | −0.638784 | − | 0.264593i | ||||
\(436\) | −484.358 | + | 59.1047i | −0.0532031 | + | 0.00649221i | ||||
\(437\) | −934.103 | − | 2255.12i | −0.102252 | − | 0.246859i | ||||
\(438\) | 7575.35 | + | 9969.81i | 0.826402 | + | 1.08762i | ||||
\(439\) | 1705.59 | + | 1705.59i | 0.185429 | + | 0.185429i | 0.793717 | − | 0.608287i | \(-0.208143\pi\) |
−0.608287 | + | 0.793717i | \(0.708143\pi\) | |||||||
\(440\) | 207.500 | − | 14601.7i | 0.0224822 | − | 1.58206i | ||||
\(441\) | 5475.28 | − | 5475.28i | 0.591219 | − | 0.591219i | ||||
\(442\) | −10782.4 | − | 1471.52i | −1.16033 | − | 0.158355i | ||||
\(443\) | 14875.4 | − | 6161.58i | 1.59537 | − | 0.660826i | 0.604622 | − | 0.796512i | \(-0.293324\pi\) |
0.990752 | + | 0.135687i | \(0.0433241\pi\) | |||||||
\(444\) | −8132.23 | − | 14398.7i | −0.869231 | − | 1.53904i | ||||
\(445\) | −1727.84 | + | 4171.37i | −0.184062 | + | 0.444364i | ||||
\(446\) | 791.141 | + | 3009.53i | 0.0839947 | + | 0.319518i | ||||
\(447\) | 25490.4 | 2.69721 | ||||||||
\(448\) | 4513.44 | + | 4777.55i | 0.475982 | + | 0.503835i | ||||
\(449\) | 1887.26 | 0.198364 | 0.0991819 | − | 0.995069i | \(-0.468377\pi\) | ||||
0.0991819 | + | 0.995069i | \(0.468377\pi\) | |||||||
\(450\) | 2911.84 | + | 11076.7i | 0.305035 | + | 1.16036i | ||||
\(451\) | 6604.84 | − | 15945.5i | 0.689601 | − | 1.66484i | ||||
\(452\) | −6166.70 | − | 10918.6i | −0.641719 | − | 1.13621i | ||||
\(453\) | 2878.87 | − | 1192.47i | 0.298589 | − | 0.123680i | ||||
\(454\) | −10811.0 | − | 1475.42i | −1.11759 | − | 0.152522i | ||||
\(455\) | 5576.74 | − | 5576.74i | 0.574597 | − | 0.574597i | ||||
\(456\) | 3428.49 | + | 48.7212i | 0.352092 | + | 0.00500346i | ||||
\(457\) | −9275.37 | − | 9275.37i | −0.949417 | − | 0.949417i | 0.0493636 | − | 0.998781i | \(-0.484281\pi\) |
−0.998781 | + | 0.0493636i | \(0.984281\pi\) | |||||||
\(458\) | −6619.59 | − | 8711.95i | −0.675356 | − | 0.888827i | ||||
\(459\) | 4886.88 | + | 11798.0i | 0.496950 | + | 1.19974i | ||||
\(460\) | 15859.3 | − | 1935.26i | 1.60748 | − | 0.196156i | ||||
\(461\) | 6867.75 | + | 2844.71i | 0.693846 | + | 0.287400i | 0.701601 | − | 0.712570i | \(-0.252469\pi\) |
−0.00775571 | + | 0.999970i | \(0.502469\pi\) | |||||||
\(462\) | 11498.8 | + | 6711.64i | 1.15795 | + | 0.675874i | ||||
\(463\) | − | 7678.71i | − | 0.770756i | −0.922759 | − | 0.385378i | \(-0.874071\pi\) | ||
0.922759 | − | 0.385378i | \(-0.125929\pi\) | |||||||
\(464\) | −1922.22 | − | 2605.86i | −0.192321 | − | 0.260720i | ||||
\(465\) | 4729.63i | 0.471681i | ||||||||
\(466\) | −7397.45 | + | 12673.7i | −0.735365 | + | 1.25987i | ||||
\(467\) | −3867.05 | − | 1601.79i | −0.383182 | − | 0.158719i | 0.182773 | − | 0.983155i | \(-0.441493\pi\) |
−0.565955 | + | 0.824436i | \(0.691493\pi\) | |||||||
\(468\) | −11385.5 | − | 8908.99i | −1.12456 | − | 0.879953i | ||||
\(469\) | −1393.71 | − | 3364.71i | −0.137219 | − | 0.331275i | ||||
\(470\) | −10710.4 | + | 8138.04i | −1.05113 | + | 0.798681i | ||||
\(471\) | −16847.9 | − | 16847.9i | −1.64822 | − | 1.64822i | ||||
\(472\) | −7480.53 | − | 3223.82i | −0.729490 | − | 0.314382i | ||||
\(473\) | −9060.64 | + | 9060.64i | −0.880780 | + | 0.880780i | ||||
\(474\) | −784.586 | + | 5748.97i | −0.0760279 | + | 0.557086i | ||||
\(475\) | −1554.56 | + | 643.919i | −0.150164 | + | 0.0622000i | ||||
\(476\) | −9152.14 | − | 2545.47i | −0.881276 | − | 0.245108i | ||||
\(477\) | −2281.24 | + | 5507.40i | −0.218974 | + | 0.528651i | ||||
\(478\) | 15453.4 | − | 4062.37i | 1.47871 | − | 0.388721i | ||||
\(479\) | 5602.73 | 0.534436 | 0.267218 | − | 0.963636i | \(-0.413896\pi\) | ||||
0.267218 | + | 0.963636i | \(0.413896\pi\) | |||||||
\(480\) | −6320.45 | + | 21534.8i | −0.601017 | + | 2.04776i | ||||
\(481\) | −10243.3 | −0.971004 | ||||||||
\(482\) | −13840.4 | + | 3638.35i | −1.30791 | + | 0.343822i | ||||
\(483\) | −5574.44 | + | 13457.9i | −0.525146 | + | 1.26782i | ||||
\(484\) | 1238.69 | − | 4453.67i | 0.116331 | − | 0.418264i | ||||
\(485\) | −10642.9 | + | 4408.43i | −0.996431 | + | 0.412735i | ||||
\(486\) | 1471.77 | − | 10784.3i | 0.137368 | − | 1.00655i | ||||
\(487\) | 13338.0 | − | 13338.0i | 1.24107 | − | 1.24107i | 0.281516 | − | 0.959556i | \(-0.409163\pi\) |
0.959556 | − | 0.281516i | \(-0.0908373\pi\) | |||||||
\(488\) | 1850.58 | − | 735.904i | 0.171663 | − | 0.0682640i | ||||
\(489\) | −5894.23 | − | 5894.23i | −0.545085 | − | 0.545085i | ||||
\(490\) | −5928.78 | + | 4504.86i | −0.546602 | + | 0.415324i | ||||
\(491\) | 6069.18 | + | 14652.3i | 0.557837 | + | 1.34674i | 0.911475 | + | 0.411356i | \(0.134945\pi\) |
−0.353637 | + | 0.935383i | \(0.615055\pi\) | |||||||
\(492\) | −16346.2 | + | 20890.1i | −1.49786 | + | 1.91422i | ||||
\(493\) | 4324.03 | + | 1791.07i | 0.395019 | + | 0.163622i | ||||
\(494\) | 1070.67 | − | 1834.33i | 0.0975133 | − | 0.167065i | ||||
\(495\) | 28039.9i | 2.54606i | ||||||||
\(496\) | −1260.56 | + | 2090.85i | −0.114115 | + | 0.189278i | ||||
\(497\) | − | 4942.30i | − | 0.446061i | ||||||
\(498\) | 27307.8 | + | 15939.1i | 2.45721 | + | 1.43423i | ||||
\(499\) | 3108.34 | + | 1287.52i | 0.278855 | + | 0.115505i | 0.517728 | − | 0.855545i | \(-0.326778\pi\) |
−0.238873 | + | 0.971051i | \(0.576778\pi\) | |||||||
\(500\) | 455.197 | + | 3730.30i | 0.0407141 | + | 0.333649i | ||||
\(501\) | −6884.53 | − | 16620.7i | −0.613928 | − | 1.48215i | ||||
\(502\) | −1816.93 | − | 2391.23i | −0.161541 | − | 0.212601i | ||||
\(503\) | −9569.65 | − | 9569.65i | −0.848289 | − | 0.848289i | 0.141630 | − | 0.989920i | \(-0.454766\pi\) |
−0.989920 | + | 0.141630i | \(0.954766\pi\) | |||||||
\(504\) | −8795.84 | − | 9049.43i | −0.777377 | − | 0.799789i | ||||
\(505\) | 11832.5 | − | 11832.5i | 1.04265 | − | 1.04265i | ||||
\(506\) | 16553.8 | + | 2259.17i | 1.45436 | + | 0.198483i | ||||
\(507\) | 3621.69 | − | 1500.15i | 0.317248 | − | 0.131408i | ||||
\(508\) | 8994.62 | − | 5080.05i | 0.785575 | − | 0.443683i | ||||
\(509\) | 4975.54 | − | 12012.0i | 0.433275 | − | 1.04602i | −0.544950 | − | 0.838469i | \(-0.683451\pi\) |
0.978225 | − | 0.207549i | \(-0.0665487\pi\) | |||||||
\(510\) | −8247.26 | − | 31372.8i | −0.716068 | − | 2.72395i | ||||
\(511\) | 6770.55 | 0.586128 | ||||||||
\(512\) | −8533.67 | + | 7835.45i | −0.736599 | + | 0.676330i | ||||
\(513\) | −2492.36 | −0.214504 | ||||||||
\(514\) | 734.415 | + | 2793.74i | 0.0630227 | + | 0.239740i | ||||
\(515\) | −5465.89 | + | 13195.8i | −0.467681 | + | 1.12908i | ||||
\(516\) | 17147.2 | − | 9684.50i | 1.46291 | − | 0.826233i | ||||
\(517\) | −12995.6 | + | 5382.94i | −1.10550 | + | 0.457914i | ||||
\(518\) | −8859.55 | − | 1209.10i | −0.751479 | − | 0.102558i | ||||
\(519\) | 11801.3 | − | 11801.3i | 0.998114 | − | 0.998114i | ||||
\(520\) | 9689.55 | + | 9968.91i | 0.817144 | + | 0.840703i | ||||
\(521\) | 11056.5 | + | 11056.5i | 0.929743 | + | 0.929743i | 0.997689 | − | 0.0679465i | \(-0.0216447\pi\) |
−0.0679465 | + | 0.997689i | \(0.521645\pi\) | |||||||
\(522\) | 3761.63 | + | 4950.63i | 0.315406 | + | 0.415102i | ||||
\(523\) | 7704.74 | + | 18600.9i | 0.644178 | + | 1.55518i | 0.820993 | + | 0.570938i | \(0.193420\pi\) |
−0.176815 | + | 0.984244i | \(0.556580\pi\) | |||||||
\(524\) | −825.525 | − | 6765.11i | −0.0688230 | − | 0.563999i | ||||
\(525\) | 9277.11 | + | 3842.71i | 0.771212 | + | 0.319447i | ||||
\(526\) | 3920.55 | + | 2288.36i | 0.324989 | + | 0.189690i | ||||
\(527\) | − | 3528.80i | − | 0.291683i | ||||||
\(528\) | −12117.5 | + | 20098.9i | −0.998765 | + | 1.65662i | ||||
\(529\) | 6112.01i | 0.502343i | ||||||||
\(530\) | 2889.69 | − | 4950.79i | 0.236830 | − | 0.405752i | ||||
\(531\) | 14450.1 | + | 5985.42i | 1.18094 | + | 0.489162i | ||||
\(532\) | 1142.56 | − | 1460.16i | 0.0931130 | − | 0.118996i | ||||
\(533\) | 6287.74 | + | 15179.9i | 0.510980 | + | 1.23361i | ||||
\(534\) | 5777.67 | − | 4390.04i | 0.468210 | − | 0.355759i | ||||
\(535\) | 7903.20 | + | 7903.20i | 0.638664 | + | 0.638664i | ||||
\(536\) | 5965.34 | − | 2372.19i | 0.480716 | − | 0.191162i | ||||
\(537\) | −19113.5 | + | 19113.5i | −1.53596 | + | 1.53596i | ||||
\(538\) | −919.485 | + | 6737.43i | −0.0736837 | + | 0.539909i | ||||
\(539\) | −7193.77 | + | 2979.76i | −0.574875 | + | 0.238121i | ||||
\(540\) | 4371.35 | − | 15717.0i | 0.348357 | − | 1.25250i | ||||
\(541\) | −3094.21 | + | 7470.07i | −0.245897 | + | 0.593648i | −0.997848 | − | 0.0655712i | \(-0.979113\pi\) |
0.751951 | + | 0.659219i | \(0.229113\pi\) | |||||||
\(542\) | 5088.71 | − | 1337.72i | 0.403282 | − | 0.106014i | ||||
\(543\) | −35511.3 | −2.80651 | ||||||||
\(544\) | 4715.73 | − | 16067.2i | 0.371664 | − | 1.26632i | ||||
\(545\) | −900.975 | −0.0708138 | ||||||||
\(546\) | −12258.5 | + | 3222.50i | −0.960832 | + | 0.252583i | ||||
\(547\) | 6470.84 | − | 15622.0i | 0.505801 | − | 1.22111i | −0.440479 | − | 0.897763i | \(-0.645191\pi\) |
0.946280 | − | 0.323349i | \(-0.104809\pi\) | |||||||
\(548\) | −16642.7 | − | 4628.81i | −1.29734 | − | 0.360827i | ||||
\(549\) | −3532.90 | + | 1463.38i | −0.274646 | + | 0.113762i | ||||
\(550\) | 1557.35 | − | 11411.3i | 0.120737 | − | 0.884690i | ||||
\(551\) | −645.918 | + | 645.918i | −0.0499401 | + | 0.0499401i | ||||
\(552\) | −23580.4 | − | 10162.2i | −1.81821 | − | 0.783576i | ||||
\(553\) | 2218.49 | + | 2218.49i | 0.170596 | + | 0.170596i | ||||
\(554\) | −13603.4 | + | 10336.2i | −1.04323 | + | 0.792680i | ||||
\(555\) | −11684.8 | − | 28209.6i | −0.893678 | − | 2.15753i | ||||
\(556\) | 2982.73 | + | 2333.95i | 0.227511 | + | 0.178024i | ||||
\(557\) | −10401.9 | − | 4308.63i | −0.791283 | − | 0.327760i | −0.0498238 | − | 0.998758i | \(-0.515866\pi\) |
−0.741459 | + | 0.670998i | \(0.765866\pi\) | |||||||
\(558\) | 2363.15 | − | 4048.69i | 0.179283 | − | 0.307159i | ||||
\(559\) | − | 12198.5i | − | 0.922971i | ||||||
\(560\) | 7203.92 | + | 9766.00i | 0.543609 | + | 0.736944i | ||||
\(561\) | − | 33921.7i | − | 2.55290i | ||||||
\(562\) | 6012.55 | + | 3509.43i | 0.451289 | + | 0.263410i | ||||
\(563\) | −1760.24 | − | 729.116i | −0.131768 | − | 0.0545801i | 0.315825 | − | 0.948817i | \(-0.397719\pi\) |
−0.447593 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(564\) | 21459.0 | − | 2618.57i | 1.60210 | − | 0.195499i | ||||
\(565\) | −8860.61 | − | 21391.4i | −0.659768 | − | 1.59282i | ||||
\(566\) | 4780.37 | + | 6291.38i | 0.355007 | + | 0.467220i | ||||
\(567\) | −130.683 | − | 130.683i | −0.00967931 | − | 0.00967931i | ||||
\(568\) | 8711.00 | + | 123.789i | 0.643496 | + | 0.00914451i | ||||
\(569\) | 8079.71 | − | 8079.71i | 0.595288 | − | 0.595288i | −0.343767 | − | 0.939055i | \(-0.611703\pi\) |
0.939055 | + | 0.343767i | \(0.111703\pi\) | |||||||
\(570\) | 6273.01 | + | 856.104i | 0.460961 | + | 0.0629092i | ||||
\(571\) | −16823.9 | + | 6968.69i | −1.23303 | + | 0.510737i | −0.901529 | − | 0.432719i | \(-0.857554\pi\) |
−0.331498 | + | 0.943456i | \(0.607554\pi\) | |||||||
\(572\) | 7149.19 | + | 12658.2i | 0.522592 | + | 0.925289i | ||||
\(573\) | −2239.60 | + | 5406.87i | −0.163282 | + | 0.394198i | ||||
\(574\) | 3646.54 | + | 13871.6i | 0.265163 | + | 1.00869i | ||||
\(575\) | 12600.5 | 0.913875 | ||||||||
\(576\) | 16170.3 | − | 15276.4i | 1.16973 | − | 1.10506i | ||||
\(577\) | −4098.72 | −0.295723 | −0.147861 | − | 0.989008i | \(-0.547239\pi\) | ||||
−0.147861 | + | 0.989008i | \(0.547239\pi\) | |||||||
\(578\) | 2620.38 | + | 9968.00i | 0.188570 | + | 0.717326i | ||||
\(579\) | −7665.74 | + | 18506.7i | −0.550220 | + | 1.32835i | ||||
\(580\) | −2940.32 | − | 5206.07i | −0.210501 | − | 0.372707i | ||||
\(581\) | 15795.7 | − | 6542.81i | 1.12791 | − | 0.467197i | ||||
\(582\) | 18343.8 | + | 2503.45i | 1.30648 | + | 0.178301i | ||||
\(583\) | 4238.73 | − | 4238.73i | 0.301115 | − | 0.301115i | ||||
\(584\) | −169.581 | + | 11933.4i | −0.0120160 | + | 0.845558i | ||||
\(585\) | −18875.3 | − | 18875.3i | −1.33401 | − | 1.33401i | ||||
\(586\) | −12096.6 | − | 15920.1i | −0.852739 | − | 1.12228i | ||||
\(587\) | −437.187 | − | 1055.46i | −0.0307404 | − | 0.0742139i | 0.907764 | − | 0.419482i | \(-0.137788\pi\) |
−0.938504 | + | 0.345268i | \(0.887788\pi\) | |||||||
\(588\) | 11878.7 | − | 1449.52i | 0.833112 | − | 0.101662i | ||||
\(589\) | 636.300 | + | 263.564i | 0.0445132 | + | 0.0184380i | ||||
\(590\) | −12989.7 | − | 7581.85i | −0.906400 | − | 0.529051i | ||||
\(591\) | − | 23466.8i | − | 1.63332i | ||||||
\(592\) | 2352.99 | − | 15585.0i | 0.163357 | − | 1.08199i | ||||
\(593\) | 26161.0i | 1.81164i | 0.423661 | + | 0.905821i | \(0.360745\pi\) | ||||
−0.423661 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(594\) | 8599.56 | − | 14733.3i | 0.594014 | − | 1.01770i | ||||
\(595\) | −16205.2 | − | 6712.41i | −1.11655 | − | 0.462491i | ||||
\(596\) | 19134.3 | + | 14972.4i | 1.31505 | + | 1.02901i | ||||
\(597\) | 13358.4 | + | 32250.0i | 0.915783 | + | 2.21090i | ||||
\(598\) | −12664.1 | + | 9622.57i | −0.866012 | + | 0.658021i | ||||
\(599\) | −12392.1 | − | 12392.1i | −0.845288 | − | 0.845288i | 0.144253 | − | 0.989541i | \(-0.453922\pi\) |
−0.989541 | + | 0.144253i | \(0.953922\pi\) | |||||||
\(600\) | −7005.28 | + | 16255.0i | −0.476649 | + | 1.10601i | ||||
\(601\) | 5696.78 | − | 5696.78i | 0.386650 | − | 0.386650i | −0.486841 | − | 0.873491i | \(-0.661851\pi\) |
0.873491 | + | 0.486841i | \(0.161851\pi\) | |||||||
\(602\) | 1439.89 | − | 10550.6i | 0.0974844 | − | 0.714306i | ||||
\(603\) | −11388.3 | + | 4717.20i | −0.769103 | + | 0.318573i | ||||
\(604\) | 2861.44 | + | 795.847i | 0.192765 | + | 0.0536135i | ||||
\(605\) | 3266.43 | − | 7885.87i | 0.219503 | − | 0.529928i | ||||
\(606\) | −26009.5 | + | 6837.34i | −1.74350 | + | 0.458330i | ||||
\(607\) | 19674.4 | 1.31559 | 0.657793 | − | 0.753199i | \(-0.271490\pi\) | ||||
0.657793 | + | 0.753199i | \(0.271490\pi\) | |||||||
\(608\) | 2544.97 | + | 2050.37i | 0.169757 | + | 0.136766i | ||||
\(609\) | 5451.28 | 0.362721 | ||||||||
\(610\) | 3556.42 | − | 934.908i | 0.236058 | − | 0.0620546i | ||||
\(611\) | 5124.50 | − | 12371.6i | 0.339305 | − | 0.819154i | ||||
\(612\) | −8615.50 | + | 30976.7i | −0.569054 | + | 2.04601i | ||||
\(613\) | 25148.3 | − | 10416.7i | 1.65698 | − | 0.686343i | 0.659139 | − | 0.752021i | \(-0.270921\pi\) |
0.997841 | + | 0.0656781i | \(0.0209210\pi\) | |||||||
\(614\) | −9.18649 | + | 67.3130i | −0.000603806 | + | 0.00442432i | ||||
\(615\) | −34632.4 | + | 34632.4i | −2.27075 | + | 2.27075i | ||||
\(616\) | 4689.28 | + | 11792.1i | 0.306715 | + | 0.771296i | ||||
\(617\) | 5951.82 | + | 5951.82i | 0.388349 | + | 0.388349i | 0.874098 | − | 0.485749i | \(-0.161453\pi\) |
−0.485749 | + | 0.874098i | \(0.661453\pi\) | |||||||
\(618\) | 18277.2 | − | 13887.5i | 1.18967 | − | 0.903946i | ||||
\(619\) | 2222.03 | + | 5364.46i | 0.144283 | + | 0.348329i | 0.979456 | − | 0.201658i | \(-0.0646328\pi\) |
−0.835173 | + | 0.549987i | \(0.814633\pi\) | |||||||
\(620\) | −2778.06 | + | 3550.29i | −0.179951 | + | 0.229972i | ||||
\(621\) | 17243.5 | + | 7142.47i | 1.11426 | + | 0.461542i | ||||
\(622\) | −8510.31 | + | 14580.4i | −0.548605 | + | 0.939903i | ||||
\(623\) | − | 3923.64i | − | 0.252323i | ||||||
\(624\) | −5372.74 | − | 21686.8i | −0.344682 | − | 1.39129i | ||||
\(625\) | 18588.8i | 1.18968i | ||||||||
\(626\) | −21041.6 | − | 12281.6i | −1.34343 | − | 0.784140i | ||||
\(627\) | 6116.62 | + | 2533.59i | 0.389592 | + | 0.161374i | ||||
\(628\) | −2750.83 | − | 22542.8i | −0.174793 | − | 1.43241i | ||||
\(629\) | 8718.08 | + | 21047.3i | 0.552643 | + | 1.33420i | ||||
\(630\) | −14097.5 | − | 18553.5i | −0.891520 | − | 1.17332i | ||||
\(631\) | 22236.1 | + | 22236.1i | 1.40286 | + | 1.40286i | 0.790837 | + | 0.612027i | \(0.209646\pi\) |
0.612027 | + | 0.790837i | \(0.290354\pi\) | |||||||
\(632\) | −3965.73 | + | 3854.60i | −0.249602 | + | 0.242607i | ||||
\(633\) | −8988.73 | + | 8988.73i | −0.564407 | + | 0.564407i | ||||
\(634\) | 12162.7 | + | 1659.90i | 0.761899 | + | 0.103980i | ||||
\(635\) | 17622.0 | − | 7299.27i | 1.10127 | − | 0.456162i | ||||
\(636\) | −8021.75 | + | 4530.58i | −0.500130 | + | 0.282468i | ||||
\(637\) | 2836.70 | − | 6848.39i | 0.176443 | − | 0.425970i | ||||
\(638\) | −1589.60 | − | 6046.90i | −0.0986410 | − | 0.375234i | ||||
\(639\) | −16727.9 | −1.03560 | ||||||||
\(640\) | −17393.4 | + | 12452.6i | −1.07427 | + | 0.769112i | ||||
\(641\) | −3642.24 | −0.224430 | −0.112215 | − | 0.993684i | \(-0.535795\pi\) | ||||
−0.112215 | + | 0.993684i | \(0.535795\pi\) | |||||||
\(642\) | −4566.83 | − | 17372.4i | −0.280745 | − | 1.06796i | ||||
\(643\) | −7521.88 | + | 18159.4i | −0.461328 | + | 1.11375i | 0.506524 | + | 0.862226i | \(0.330930\pi\) |
−0.967852 | + | 0.251519i | \(0.919070\pi\) | |||||||
\(644\) | −12089.2 | + | 6827.85i | −0.739724 | + | 0.417787i | ||||
\(645\) | 33594.2 | − | 13915.2i | 2.05080 | − | 0.849471i | ||||
\(646\) | −4680.33 | − | 638.744i | −0.285054 | − | 0.0389026i | ||||
\(647\) | −16784.8 | + | 16784.8i | −1.01991 | + | 1.01991i | −0.0201092 | + | 0.999798i | \(0.506401\pi\) |
−0.999798 | + | 0.0201092i | \(0.993599\pi\) | |||||||
\(648\) | 233.607 | − | 227.061i | 0.0141620 | − | 0.0137651i | ||||
\(649\) | −11121.4 | − | 11121.4i | −0.672655 | − | 0.672655i | ||||
\(650\) | 6633.27 | + | 8729.95i | 0.400274 | + | 0.526795i | ||||
\(651\) | −1572.87 | − | 3797.24i | −0.0946937 | − | 0.228611i | ||||
\(652\) | −962.377 | − | 7886.60i | −0.0578061 | − | 0.473717i | ||||
\(653\) | −12553.7 | − | 5199.89i | −0.752316 | − | 0.311620i | −0.0266300 | − | 0.999645i | \(-0.508478\pi\) |
−0.725686 | + | 0.688026i | \(0.758478\pi\) | |||||||
\(654\) | 1250.55 | + | 729.924i | 0.0747711 | + | 0.0436426i | ||||
\(655\) | − | 12584.1i | − | 0.750688i | ||||||
\(656\) | −24540.5 | + | 6079.73i | −1.46059 | + | 0.361850i | ||||
\(657\) | − | 22915.9i | − | 1.36078i | ||||||
\(658\) | 5892.59 | − | 10095.5i | 0.349114 | − | 0.598123i | ||||
\(659\) | −7775.94 | − | 3220.90i | −0.459647 | − | 0.190392i | 0.140830 | − | 0.990034i | \(-0.455023\pi\) |
−0.600478 | + | 0.799642i | \(0.705023\pi\) | |||||||
\(660\) | −26704.9 | + | 34128.2i | −1.57498 | + | 2.01278i | ||||
\(661\) | 1900.75 | + | 4588.81i | 0.111847 | + | 0.270021i | 0.969885 | − | 0.243564i | \(-0.0783168\pi\) |
−0.858038 | + | 0.513586i | \(0.828317\pi\) | |||||||
\(662\) | 21904.5 | − | 16643.6i | 1.28601 | − | 0.977151i | ||||
\(663\) | 22834.6 | + | 22834.6i | 1.33759 | + | 1.33759i | ||||
\(664\) | 11136.3 | + | 28004.5i | 0.650863 | + | 1.63672i | ||||
\(665\) | 2420.71 | − | 2420.71i | 0.141160 | − | 0.141160i | ||||
\(666\) | −4092.37 | + | 29986.4i | −0.238102 | + | 1.74467i | ||||
\(667\) | 6319.82 | − | 2617.76i | 0.366873 | − | 0.151964i | ||||
\(668\) | 4594.71 | − | 16520.1i | 0.266130 | − | 0.956858i | ||||
\(669\) | 3533.75 | − | 8531.23i | 0.204219 | − | 0.493029i | ||||
\(670\) | 11464.1 | − | 3013.68i | 0.661042 | − | 0.173774i | ||||
\(671\) | 3845.36 | 0.221234 | ||||||||
\(672\) | −2087.09 | − | 19391.4i | −0.119808 | − | 1.11315i | ||||
\(673\) | −9638.42 | −0.552056 | −0.276028 | − | 0.961150i | \(-0.589018\pi\) | ||||
−0.276028 | + | 0.961150i | \(0.589018\pi\) | |||||||
\(674\) | 14257.3 | − | 3747.94i | 0.814792 | − | 0.214192i | ||||
\(675\) | 4923.62 | − | 11886.7i | 0.280756 | − | 0.677805i | ||||
\(676\) | 3599.76 | + | 1001.20i | 0.204811 | + | 0.0569638i | ||||
\(677\) | −27908.0 | + | 11559.9i | −1.58433 | + | 0.656251i | −0.989092 | − | 0.147297i | \(-0.952943\pi\) |
−0.595239 | + | 0.803549i | \(0.702943\pi\) | |||||||
\(678\) | −5031.75 | + | 36869.6i | −0.285019 | + | 2.08845i | ||||
\(679\) | 7078.72 | − | 7078.72i | 0.400083 | − | 0.400083i | ||||
\(680\) | 12236.8 | − | 28394.2i | 0.690086 | − | 1.60127i | ||||
\(681\) | 22895.2 | + | 22895.2i | 1.28832 | + | 1.28832i | ||||
\(682\) | −3753.49 | + | 2852.01i | −0.210746 | + | 0.160131i | ||||
\(683\) | −11978.8 | − | 28919.3i | −0.671090 | − | 1.62015i | −0.779761 | − | 0.626077i | \(-0.784660\pi\) |
0.108671 | − | 0.994078i | \(-0.465340\pi\) | |||||||
\(684\) | −4942.11 | − | 3867.14i | −0.276266 | − | 0.216175i | ||||
\(685\) | −29468.3 | − | 12206.2i | −1.64369 | − | 0.680838i | ||||
\(686\) | 9539.64 | − | 16343.9i | 0.530940 | − | 0.909638i | ||||
\(687\) | 32468.8i | 1.80315i | ||||||||
\(688\) | 18559.9 | + | 2802.13i | 1.02847 | + | 0.155276i | ||||
\(689\) | 5706.67i | 0.315540i | ||||||||
\(690\) | −40946.5 | − | 23899.8i | −2.25914 | − | 1.31862i | ||||
\(691\) | −7238.99 | − | 2998.49i | −0.398530 | − | 0.165076i | 0.174412 | − | 0.984673i | \(-0.444198\pi\) |
−0.572941 | + | 0.819596i | \(0.694198\pi\) | |||||||
\(692\) | 15790.4 | − | 1926.86i | 0.867431 | − | 0.105850i | ||||
\(693\) | −9324.84 | − | 22512.2i | −0.511142 | − | 1.23401i | ||||
\(694\) | −9237.18 | − | 12156.9i | −0.505243 | − | 0.664943i | ||||
\(695\) | 4944.89 | + | 4944.89i | 0.269885 | + | 0.269885i | ||||
\(696\) | −136.538 | + | 9608.09i | −0.00743598 | + | 0.523267i | ||||
\(697\) | 25839.4 | − | 25839.4i | 1.40422 | − | 1.40422i | ||||
\(698\) | −22977.4 | − | 3135.82i | −1.24600 | − | 0.170047i | ||||
\(699\) | 40232.0 | − | 16664.6i | 2.17699 | − | 0.901738i | ||||
\(700\) | 4706.74 | + | 8333.64i | 0.254140 | + | 0.449974i | ||||
\(701\) | 3609.66 | − | 8714.49i | 0.194486 | − | 0.469532i | −0.796311 | − | 0.604888i | \(-0.793218\pi\) |
0.990797 | + | 0.135356i | \(0.0432179\pi\) | |||||||
\(702\) | 4128.95 | + | 15706.7i | 0.221990 | + | 0.844459i | ||||
\(703\) | −4446.32 | −0.238543 | ||||||||
\(704\) | −20901.6 | + | 7969.69i | −1.11897 | + | 0.426661i | ||||
\(705\) | 39916.7 | 2.13241 | ||||||||
\(706\) | −6471.40 | − | 24617.4i | −0.344978 | − | 1.31231i | ||||
\(707\) | −5564.88 | + | 13434.8i | −0.296024 | + | 0.714665i | ||||
\(708\) | 11887.2 | + | 21047.1i | 0.630998 | + | 1.11723i | ||||
\(709\) | −8921.05 | + | 3695.22i | −0.472549 | + | 0.195736i | −0.606232 | − | 0.795288i | \(-0.707320\pi\) |
0.133683 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(710\) | 15938.3 | + | 2175.16i | 0.842469 | + | 0.114975i | ||||
\(711\) | 7508.77 | − | 7508.77i | 0.396063 | − | 0.396063i | ||||
\(712\) | 6915.58 | + | 98.2751i | 0.364006 | + | 0.00517277i | ||||
\(713\) | −3646.95 | − | 3646.95i | −0.191556 | − | 0.191556i | ||||
\(714\) | 17054.7 | + | 22445.4i | 0.893914 | + | 1.17647i | ||||
\(715\) | 10272.3 | + | 24799.5i | 0.537290 | + | 1.29713i | ||||
\(716\) | −25574.2 | + | 3120.74i | −1.33485 | + | 0.162888i | ||||
\(717\) | −43806.4 | − | 18145.2i | −2.28170 | − | 0.945111i | ||||
\(718\) | 16229.5 | + | 9472.86i | 0.843563 | + | 0.492373i | ||||
\(719\) | − | 36176.8i | − | 1.87645i | −0.346025 | − | 0.938225i | \(-0.612469\pi\) | ||
0.346025 | − | 0.938225i | \(-0.387531\pi\) | |||||||
\(720\) | 33054.4 | − | 24382.7i | 1.71092 | − | 1.26207i | ||||
\(721\) | − | 12412.1i | − | 0.641126i | ||||||
\(722\) | −9314.81 | + | 15958.7i | −0.480141 | + | 0.822605i | ||||
\(723\) | 39233.9 | + | 16251.2i | 2.01815 | + | 0.835947i | ||||
\(724\) | −26656.5 | − | 20858.4i | −1.36834 | − | 1.07071i | ||||
\(725\) | −1804.54 | − | 4356.53i | −0.0924397 | − | 0.223169i | ||||
\(726\) | −10922.5 | + | 8299.24i | −0.558365 | + | 0.424262i | ||||
\(727\) | −25292.8 | − | 25292.8i | −1.29031 | − | 1.29031i | −0.934591 | − | 0.355723i | \(-0.884235\pi\) |
−0.355723 | − | 0.934591i | \(-0.615765\pi\) | |||||||
\(728\) | −11094.6 | − | 4781.34i | −0.564826 | − | 0.243418i | ||||
\(729\) | −22563.8 | + | 22563.8i | −1.14636 | + | 1.14636i | ||||
\(730\) | −2979.80 | + | 21834.1i | −0.151078 | + | 1.10701i | ||||
\(731\) | −25064.8 | + | 10382.2i | −1.26820 | + | 0.525306i | ||||
\(732\) | −5693.70 | − | 1583.58i | −0.287494 | − | 0.0799602i | ||||
\(733\) | −11236.5 | + | 27127.4i | −0.566208 | + | 1.36695i | 0.338520 | + | 0.940959i | \(0.390074\pi\) |
−0.904729 | + | 0.425989i | \(0.859926\pi\) | |||||||
\(734\) | 16255.2 | − | 4273.16i | 0.817427 | − | 0.214884i | ||||
\(735\) | 22096.1 | 1.10888 | ||||||||
\(736\) | −11731.6 | − | 21478.8i | −0.587542 | − | 1.07570i | ||||
\(737\) | 12395.5 | 0.619532 | ||||||||
\(738\) | 46950.2 | − | 12342.2i | 2.34182 | − | 0.615615i | ||||
\(739\) | 2750.78 | − | 6640.98i | 0.136927 | − | 0.330572i | −0.840510 | − | 0.541795i | \(-0.817745\pi\) |
0.977438 | + | 0.211224i | \(0.0677448\pi\) | |||||||
\(740\) | 7798.38 | − | 28038.8i | 0.387398 | − | 1.39287i | ||||
\(741\) | −5822.96 | + | 2411.95i | −0.288680 | + | 0.119575i | ||||
\(742\) | −673.607 | + | 4935.78i | −0.0333274 | + | 0.244203i | ||||
\(743\) | −21298.6 | + | 21298.6i | −1.05164 | + | 1.05164i | −0.0530520 | + | 0.998592i | \(0.516895\pi\) |
−0.998592 | + | 0.0530520i | \(0.983105\pi\) | |||||||
\(744\) | 6732.19 | − | 2677.14i | 0.331739 | − | 0.131920i | ||||
\(745\) | 31721.6 | + | 31721.6i | 1.55999 | + | 1.55999i | ||||
\(746\) | −3595.79 | + | 2732.18i | −0.176476 | + | 0.134092i | ||||
\(747\) | −22145.1 | − | 53462.9i | −1.08467 | − | 2.61861i | ||||
\(748\) | 19924.7 | − | 25463.2i | 0.973955 | − | 1.24469i | ||||
\(749\) | −8973.44 | − | 3716.92i | −0.437760 | − | 0.181326i | ||||
\(750\) | 5621.54 | − | 9631.15i | 0.273693 | − | 0.468906i | ||||
\(751\) | 33892.3i | 1.64680i | 0.567462 | + | 0.823400i | \(0.307925\pi\) | ||||
−0.567462 | + | 0.823400i | \(0.692075\pi\) | |||||||
\(752\) | 17646.2 | + | 10638.8i | 0.855705 | + | 0.515900i | ||||
\(753\) | 8911.94i | 0.431300i | ||||||||
\(754\) | 5140.57 | + | 3000.47i | 0.248287 | + | 0.144921i | ||||
\(755\) | 5066.59 | + | 2098.65i | 0.244228 | + | 0.101163i | ||||
\(756\) | 1717.20 | + | 14072.3i | 0.0826110 | + | 0.676991i | ||||
\(757\) | 1447.14 | + | 3493.72i | 0.0694813 | + | 0.167743i | 0.954805 | − | 0.297232i | \(-0.0960634\pi\) |
−0.885324 | + | 0.464975i | \(0.846063\pi\) | |||||||
\(758\) | −6364.16 | − | 8375.78i | −0.304956 | − | 0.401348i | ||||
\(759\) | −35057.3 | − | 35057.3i | −1.67655 | − | 1.67655i | ||||
\(760\) | 4205.97 | + | 4327.23i | 0.200745 | + | 0.206533i | ||||
\(761\) | −8184.04 | + | 8184.04i | −0.389844 | + | 0.389844i | −0.874632 | − | 0.484788i | \(-0.838897\pi\) |
0.484788 | + | 0.874632i | \(0.338897\pi\) | |||||||
\(762\) | −30372.7 | − | 4145.09i | −1.44395 | − | 0.197061i | ||||
\(763\) | 723.359 | − | 299.625i | 0.0343216 | − | 0.0142165i | ||||
\(764\) | −4857.00 | + | 2743.17i | −0.230000 | + | 0.129901i | ||||
\(765\) | −22719.1 | + | 54848.7i | −1.07374 | + | 2.59223i | ||||
\(766\) | 6707.46 | + | 25515.4i | 0.316384 | + | 1.20354i | ||||
\(767\) | 14972.9 | 0.704878 | ||||||||
\(768\) | 34230.4 | − | 3192.88i | 1.60831 | − | 0.150017i | ||||
\(769\) | −29464.8 | −1.38170 | −0.690850 | − | 0.722998i | \(-0.742763\pi\) | ||||
−0.690850 | + | 0.722998i | \(0.742763\pi\) | |||||||
\(770\) | 5957.37 | + | 22662.0i | 0.278816 | + | 1.06063i | ||||
\(771\) | 3280.38 | − | 7919.53i | 0.153229 | − | 0.369928i | ||||
\(772\) | −16624.6 | + | 9389.38i | −0.775043 | + | 0.437735i | ||||
\(773\) | 24119.4 | − | 9990.57i | 1.12227 | − | 0.464859i | 0.257122 | − | 0.966379i | \(-0.417226\pi\) |
0.865146 | + | 0.501520i | \(0.167226\pi\) | |||||||
\(774\) | −35710.2 | − | 4873.52i | −1.65837 | − | 0.226324i | ||||
\(775\) | −2514.00 | + | 2514.00i | −0.116523 | + | 0.116523i | ||||
\(776\) | 12299.2 | + | 12653.8i | 0.568965 | + | 0.585369i | ||||
\(777\) | 18762.5 | + | 18762.5i | 0.866284 | + | 0.866284i | ||||
\(778\) | −14521.8 | − | 19111.9i | −0.669190 | − | 0.880712i | ||||
\(779\) | 2729.33 | + | 6589.19i | 0.125531 | + | 0.303058i | ||||
\(780\) | −4997.03 | − | 40950.3i | −0.229388 | − | 1.87981i | ||||
\(781\) | 15540.9 | + | 6437.26i | 0.712034 | + | 0.294934i | ||||
\(782\) | 30550.4 | + | 17831.8i | 1.39704 | + | 0.815426i | ||||
\(783\) | − | 6984.67i | − | 0.318789i | ||||||
\(784\) | 9768.14 | + | 5889.16i | 0.444977 | + | 0.268274i | ||||
\(785\) | − | 41932.8i | − | 1.90656i | ||||||
\(786\) | −10195.0 | + | 17466.6i | −0.462649 | + | 0.792638i | ||||
\(787\) | −4642.61 | − | 1923.03i | −0.210281 | − | 0.0871013i | 0.275057 | − | 0.961428i | \(-0.411303\pi\) |
−0.485338 | + | 0.874327i | \(0.661303\pi\) | |||||||
\(788\) | 13783.8 | − | 17615.3i | 0.623130 | − | 0.796343i | ||||
\(789\) | −5155.11 | − | 12445.5i | −0.232607 | − | 0.561562i | ||||
\(790\) | −8130.71 | + | 6177.94i | −0.366174 | + | 0.278230i | ||||
\(791\) | 14227.7 | + | 14227.7i | 0.639543 | + | 0.639543i | ||||
\(792\) | 39912.1 | − | 15871.5i | 1.79068 | − | 0.712084i | ||||
\(793\) | −2588.53 | + | 2588.53i | −0.115916 | + | 0.115916i | ||||
\(794\) | 2833.75 | − | 20764.0i | 0.126657 | − | 0.928067i | ||||
\(795\) | −15716.0 | + | 6509.76i | −0.701117 | + | 0.290412i | ||||
\(796\) | −8915.34 | + | 32054.7i | −0.396980 | + | 1.42732i | ||||
\(797\) | 3908.47 | − | 9435.87i | 0.173708 | − | 0.419367i | −0.812916 | − | 0.582381i | \(-0.802121\pi\) |
0.986624 | + | 0.163013i | \(0.0521213\pi\) | |||||||
\(798\) | −5321.07 | + | 1398.80i | −0.236045 | + | 0.0620512i | ||||
\(799\) | −29782.1 | −1.31867 | ||||||||
\(800\) | −14806.3 | + | 8087.08i | −0.654350 | + | 0.357402i | ||||
\(801\) | −13280.1 | −0.585805 | ||||||||
\(802\) | −14590.7 | + | 3835.59i | −0.642414 | + | 0.168877i | ||||
\(803\) | −8818.53 | + | 21289.8i | −0.387545 | + | 0.935618i | ||||
\(804\) | −18353.7 | − | 5104.69i | −0.805081 | − | 0.223916i | ||||
\(805\) | −23684.8 | + | 9810.58i | −1.03700 | + | 0.429537i | ||||
\(806\) | 606.839 | − | 4446.54i | 0.0265198 | − | 0.194321i | ||||
\(807\) | 14268.4 | − | 14268.4i | 0.622392 | − | 0.622392i | ||||
\(808\) | −23540.0 | − | 10144.8i | −1.02492 | − | 0.441700i | ||||
\(809\) | −16382.1 | − | 16382.1i | −0.711945 | − | 0.711945i | 0.254997 | − | 0.966942i | \(-0.417925\pi\) |
−0.966942 | + | 0.254997i | \(0.917925\pi\) | |||||||
\(810\) | 478.951 | − | 363.920i | 0.0207761 | − | 0.0157862i | ||||
\(811\) | 7236.38 | + | 17470.2i | 0.313322 | + | 0.756425i | 0.999578 | + | 0.0290650i | \(0.00925299\pi\) |
−0.686256 | + | 0.727360i | \(0.740747\pi\) | |||||||
\(812\) | 4091.99 | + | 3201.93i | 0.176848 | + | 0.138382i | ||||
\(813\) | −14425.2 | − | 5975.11i | −0.622280 | − | 0.257757i | ||||
\(814\) | 15341.4 | − | 26283.8i | 0.660584 | − | 1.13175i | ||||
\(815\) | − | 14670.2i | − | 0.630521i | ||||||
\(816\) | −39988.1 | + | 29497.3i | −1.71552 | + | 1.26546i | ||||
\(817\) | − | 5295.03i | − | 0.226744i | ||||||
\(818\) | 13496.5 | + | 7877.65i | 0.576886 | + | 0.336718i | ||||
\(819\) | 21431.3 | + | 8877.15i | 0.914373 | + | 0.378746i | ||||
\(820\) | −46338.8 | + | 5654.58i | −1.97344 | + | 0.240813i | ||||
\(821\) | −4916.31 | − | 11869.0i | −0.208990 | − | 0.504546i | 0.784275 | − | 0.620413i | \(-0.213035\pi\) |
−0.993265 | + | 0.115868i | \(0.963035\pi\) | |||||||
\(822\) | 31013.0 | + | 40815.8i | 1.31594 | + | 1.73189i | ||||
\(823\) | 25989.7 | + | 25989.7i | 1.10078 | + | 1.10078i | 0.994316 | + | 0.106465i | \(0.0339532\pi\) |
0.106465 | + | 0.994316i | \(0.466047\pi\) | |||||||
\(824\) | 21876.9 | + | 310.886i | 0.924899 | + | 0.0131435i | ||||
\(825\) | −24166.6 | + | 24166.6i | −1.01984 | + | 1.01984i | ||||
\(826\) | 12950.3 | + | 1767.38i | 0.545519 | + | 0.0744493i | ||||
\(827\) | −16783.7 | + | 6952.03i | −0.705715 | + | 0.292317i | −0.706530 | − | 0.707683i | \(-0.749740\pi\) |
0.000815266 | 1.00000i | \(0.499740\pi\) | ||||||||
\(828\) | 23109.8 | + | 40917.7i | 0.969953 | + | 1.71738i | ||||
\(829\) | 5184.19 | − | 12515.7i | 0.217194 | − | 0.524354i | −0.777302 | − | 0.629128i | \(-0.783412\pi\) |
0.994496 | + | 0.104774i | \(0.0334120\pi\) | |||||||
\(830\) | 14147.8 | + | 53818.8i | 0.591660 | + | 2.25070i | ||||
\(831\) | 50698.7 | 2.11639 | ||||||||
\(832\) | 8705.19 | − | 19434.9i | 0.362738 | − | 0.809837i | ||||
\(833\) | −16486.0 | −0.685723 | ||||||||
\(834\) | −2857.38 | − | 10869.6i | −0.118637 | − | 0.451298i | ||||
\(835\) | 12116.2 | − | 29251.2i | 0.502155 | − | 1.21231i | ||||
\(836\) | 3103.27 | + | 5494.57i | 0.128384 | + | 0.227313i | ||||
\(837\) | −4865.37 | + | 2015.30i | −0.200922 | + | 0.0832247i | ||||
\(838\) | −3739.98 | − | 510.410i | −0.154171 | − | 0.0210404i | ||||
\(839\) | −248.606 | + | 248.606i | −0.0102298 | + | 0.0102298i | −0.712203 | − | 0.701973i | \(-0.752303\pi\) |
0.701973 | + | 0.712203i | \(0.252303\pi\) | |||||||
\(840\) | 511.703 | − | 36008.3i | 0.0210184 | − | 1.47905i | ||||
\(841\) | 15435.5 | + | 15435.5i | 0.632887 | + | 0.632887i | ||||
\(842\) | 16814.9 | + | 22129.8i | 0.688216 | + | 0.905752i | ||||
\(843\) | −7905.88 | − | 19086.5i | −0.323005 | − | 0.779802i | ||||
\(844\) | −12027.1 | + | 1467.63i | −0.490509 | + | 0.0598553i | ||||
\(845\) | 6373.89 | + | 2640.15i | 0.259490 | + | 0.107484i | ||||
\(846\) | −34169.7 | − | 19944.3i | −1.38863 | − | 0.810519i | ||||
\(847\) | 7417.54i | 0.300909i | ||||||||
\(848\) | −8682.64 | − | 1310.89i | −0.351608 | − | 0.0530849i | ||||
\(849\) | − | 23447.5i | − | 0.947840i | ||||||
\(850\) | 12292.2 | − | 21059.8i | 0.496024 | − | 0.849817i | ||||
\(851\) | 30761.9 | + | 12742.0i | 1.23914 | + | 0.513267i | ||||
\(852\) | −20360.0 | − | 15931.5i | −0.818689 | − | 0.640615i | ||||
\(853\) | −5935.21 | − | 14328.9i | −0.238239 | − | 0.575159i | 0.758862 | − | 0.651251i | \(-0.225756\pi\) |
−0.997101 | + | 0.0760921i | \(0.975756\pi\) | |||||||
\(854\) | −2544.41 | + | 1933.31i | −0.101953 | + | 0.0774667i | ||||
\(855\) | −8193.23 | − | 8193.23i | −0.327722 | − | 0.327722i | ||||
\(856\) | 6775.98 | − | 15723.0i | 0.270559 | − | 0.627803i | ||||
\(857\) | 6193.30 | − | 6193.30i | 0.246860 | − | 0.246860i | −0.572821 | − | 0.819681i | \(-0.694151\pi\) |
0.819681 | + | 0.572821i | \(0.194151\pi\) | |||||||
\(858\) | 5833.41 | − | 42743.7i | 0.232109 | − | 1.70075i | ||||
\(859\) | 9296.87 | − | 3850.89i | 0.369272 | − | 0.152958i | −0.190327 | − | 0.981721i | \(-0.560955\pi\) |
0.559600 | + | 0.828763i | \(0.310955\pi\) | |||||||
\(860\) | 33390.8 | + | 9286.93i | 1.32397 | + | 0.368234i | ||||
\(861\) | 16287.8 | − | 39322.3i | 0.644701 | − | 1.55644i | ||||
\(862\) | 21021.0 | − | 5525.97i | 0.830600 | − | 0.218347i | ||||
\(863\) | 28317.6 | 1.11697 | 0.558483 | − | 0.829516i | \(-0.311384\pi\) | ||||
0.558483 | + | 0.829516i | \(0.311384\pi\) | |||||||
\(864\) | −24846.0 | + | 2674.16i | −0.978331 | + | 0.105297i | ||||
\(865\) | 29372.5 | 1.15456 | ||||||||
\(866\) | 2708.03 | − | 711.885i | 0.106262 | − | 0.0279340i | ||||
\(867\) | 11704.3 | − | 28256.7i | 0.458477 | − | 1.10686i | ||||
\(868\) | 1049.73 | − | 3774.25i | 0.0410485 | − | 0.147588i | ||||
\(869\) | −9865.51 | + | 4086.43i | −0.385114 | + | 0.159520i | ||||
\(870\) | −2399.17 | + | 17579.7i | −0.0934937 | + | 0.685065i | ||||
\(871\) | −8344.15 | + | 8344.15i | −0.324605 | + | 0.324605i | ||||
\(872\) | 509.983 | + | 1282.45i | 0.0198053 | + | 0.0498043i | ||||
\(873\) | −23958.9 | − | 23958.9i | −0.928851 | − | 0.928851i | ||||
\(874\) | −5497.15 | + | 4176.89i | −0.212750 | + | 0.161654i | ||||
\(875\) | −2307.57 | − | 5570.98i | −0.0891546 | − | 0.215238i | ||||
\(876\) | 21824.8 | − | 27891.6i | 0.841773 | − | 1.07576i | ||||
\(877\) | 43155.1 | + | 17875.4i | 1.66162 | + | 0.688267i | 0.998200 | − | 0.0599774i | \(-0.0191029\pi\) |
0.663423 | + | 0.748244i | \(0.269103\pi\) | |||||||
\(878\) | 3439.13 | − | 5892.12i | 0.132193 | − | 0.226480i | ||||
\(879\) | 59333.1i | 2.27674i | ||||||||
\(880\) | −40091.9 | + | 9932.48i | −1.53579 | + | 0.380482i | ||||
\(881\) | − | 9845.05i | − | 0.376491i | −0.982122 | − | 0.188245i | \(-0.939720\pi\) | ||
0.982122 | − | 0.188245i | \(-0.0602800\pi\) | |||||||
\(882\) | −18914.8 | − | 11040.3i | −0.722104 | − | 0.421480i | ||||
\(883\) | −27587.3 | − | 11427.0i | −1.05140 | − | 0.435504i | −0.211008 | − | 0.977484i | \(-0.567675\pi\) |
−0.840391 | + | 0.541981i | \(0.817675\pi\) | |||||||
\(884\) | 3728.31 | + | 30553.2i | 0.141852 | + | 1.16246i | ||||
\(885\) | 17080.0 | + | 41234.9i | 0.648745 | + | 1.56621i | ||||
\(886\) | −27551.9 | − | 36260.6i | −1.04472 | − | 1.37494i | ||||
\(887\) | 1279.94 | + | 1279.94i | 0.0484512 | + | 0.0484512i | 0.730917 | − | 0.682466i | \(-0.239093\pi\) |
−0.682466 | + | 0.730917i | \(0.739093\pi\) | |||||||
\(888\) | −33539.7 | + | 32599.8i | −1.26747 | + | 1.23196i | ||||
\(889\) | −11720.6 | + | 11720.6i | −0.442178 | + | 0.442178i | ||||
\(890\) | 12653.2 | + | 1726.84i | 0.476559 | + | 0.0650380i | ||||
\(891\) | 581.141 | − | 240.717i | 0.0218507 | − | 0.00905085i | ||||
\(892\) | 7663.61 | − | 4328.31i | 0.287664 | − | 0.162469i | ||||
\(893\) | 2224.41 | − | 5370.19i | 0.0833560 | − | 0.201239i | ||||
\(894\) | −18330.2 | − | 69728.6i | −0.685742 | − | 2.60858i | ||||
\(895\) | −47571.7 | −1.77670 | ||||||||
\(896\) | 9823.31 | − | 15782.0i | 0.366265 | − | 0.588437i | ||||
\(897\) | 47198.3 | 1.75686 | ||||||||
\(898\) | −1357.13 | − | 5162.58i | −0.0504322 | − | 0.191846i | ||||
\(899\) | −738.620 | + | 1783.19i | −0.0274019 | + | 0.0661541i | ||||
\(900\) | 28206.4 | − | 15930.6i | 1.04468 | − | 0.590023i | ||||
\(901\) | 11725.8 | − | 4856.97i | 0.433565 | − | 0.179588i | ||||
\(902\) | −48368.3 | − | 6601.02i | −1.78546 | − | 0.243670i | ||||
\(903\) | −22343.9 | + | 22343.9i | −0.823432 | + | 0.823432i | ||||
\(904\) | −25433.2 | + | 24720.5i | −0.935727 | + | 0.909505i | ||||
\(905\) | −44192.2 | − | 44192.2i | −1.62320 | − | 1.62320i | ||||
\(906\) | −5332.18 | − | 7017.60i | −0.195529 | − | 0.257334i | ||||
\(907\) | −497.655 | − | 1201.44i | −0.0182187 | − | 0.0439838i | 0.914508 | − | 0.404567i | \(-0.132578\pi\) |
−0.932727 | + | 0.360583i | \(0.882578\pi\) | |||||||
\(908\) | 3738.21 | + | 30634.3i | 0.136626 | + | 1.11964i | ||||
\(909\) | 45472.0 | + | 18835.1i | 1.65920 | + | 0.687262i | ||||
\(910\) | −19265.4 | − | 11244.9i | −0.701803 | − | 0.409630i | ||||
\(911\) | − | 1357.76i | − | 0.0493794i | −0.999695 | − | 0.0246897i | \(-0.992140\pi\) | ||
0.999695 | − | 0.0246897i | \(-0.00785977\pi\) | |||||||
\(912\) | −2332.16 | − | 9413.63i | −0.0846770 | − | 0.341794i | ||||
\(913\) | 58191.2i | 2.10936i | ||||||||
\(914\) | −18702.7 | + | 32042.6i | −0.676840 | + | 1.15960i | ||||
\(915\) | −10081.5 | − | 4175.91i | −0.364246 | − | 0.150876i | ||||
\(916\) | −19071.3 | + | 24372.6i | −0.687918 | + | 0.879141i | ||||
\(917\) | 4184.91 | + | 10103.3i | 0.150707 | + | 0.363838i | ||||
\(918\) | 28759.1 | − | 21852.0i | 1.03398 | − | 0.785645i | ||||
\(919\) | −5601.39 | − | 5601.39i | −0.201059 | − | 0.201059i | 0.599395 | − | 0.800453i | \(-0.295408\pi\) |
−0.800453 | + | 0.599395i | \(0.795408\pi\) | |||||||
\(920\) | −16698.3 | − | 41991.2i | −0.598399 | − | 1.50479i | ||||
\(921\) | 142.554 | − | 142.554i | 0.00510023 | − | 0.00510023i | ||||
\(922\) | 2843.07 | − | 20832.3i | 0.101553 | − | 0.744115i | ||||
\(923\) | −14794.8 | + | 6128.21i | −0.527602 | + | 0.218540i | ||||
\(924\) | 10090.8 | − | 36281.1i | 0.359268 | − | 1.29173i | ||||
\(925\) | 8783.62 | − | 21205.5i | 0.312220 | − | 0.753766i | ||||
\(926\) | −21005.0 | + | 5521.78i | −0.745429 | + | 0.195958i | ||||
\(927\) | −42010.6 | −1.48847 | ||||||||
\(928\) | −5746.02 | + | 7132.09i | −0.203257 | + | 0.252287i | ||||
\(929\) | 22810.9 | 0.805598 | 0.402799 | − | 0.915288i | \(-0.368037\pi\) | ||||
0.402799 | + | 0.915288i | \(0.368037\pi\) | |||||||
\(930\) | 12937.9 | − | 3401.09i | 0.456182 | − | 0.119921i | ||||
\(931\) | 1231.33 | − | 2972.70i | 0.0433461 | − | 0.104647i | ||||
\(932\) | 39988.4 | + | 11121.9i | 1.40543 | + | 0.390891i | ||||
\(933\) | 46284.5 | − | 19171.7i | 1.62410 | − | 0.672724i | ||||
\(934\) | −1600.86 | + | 11730.1i | −0.0560832 | + | 0.410944i | ||||
\(935\) | 42214.0 | − | 42214.0i | 1.47652 | − | 1.47652i | ||||
\(936\) | −16183.1 | + | 37551.2i | −0.565130 | + | 1.31133i | ||||
\(937\) | 16556.7 | + | 16556.7i | 0.577251 | + | 0.577251i | 0.934145 | − | 0.356894i | \(-0.116164\pi\) |
−0.356894 | + | 0.934145i | \(0.616164\pi\) | |||||||
\(938\) | −8201.91 | + | 6232.04i | −0.285503 | + | 0.216933i | ||||
\(939\) | 27667.4 | + | 66795.1i | 0.961547 | + | 2.32138i | ||||
\(940\) | 29963.4 | + | 23446.0i | 1.03968 | + | 0.813536i | ||||
\(941\) | 6945.83 | + | 2877.06i | 0.240624 | + | 0.0996698i | 0.499737 | − | 0.866177i | \(-0.333430\pi\) |
−0.259113 | + | 0.965847i | \(0.583430\pi\) | |||||||
\(942\) | −33971.8 | + | 58202.5i | −1.17501 | + | 2.01310i | ||||
\(943\) | − | 53409.0i | − | 1.84436i | ||||||
\(944\) | −3439.45 | + | 22781.2i | −0.118585 | + | 0.785449i | ||||
\(945\) | 26176.5i | 0.901081i | ||||||||
\(946\) | 31300.8 | + | 18269.7i | 1.07577 | + | 0.627908i | ||||
\(947\) | −25322.0 | − | 10488.7i | −0.868905 | − | 0.359912i | −0.0967214 | − | 0.995311i | \(-0.530836\pi\) |
−0.772184 | + | 0.635399i | \(0.780836\pi\) | |||||||
\(948\) | 16290.4 | − | 1987.87i | 0.558110 | − | 0.0681044i | ||||
\(949\) | −8395.14 | − | 20267.7i | −0.287163 | − | 0.693273i | ||||
\(950\) | 2879.32 | + | 3789.43i | 0.0983341 | + | 0.129416i | ||||
\(951\) | −25758.0 | − | 25758.0i | −0.878296 | − | 0.878296i | ||||
\(952\) | −381.784 | + | 26866.0i | −0.0129976 | + | 0.914635i | ||||
\(953\) | −1354.94 | + | 1354.94i | −0.0460556 | + | 0.0460556i | −0.729760 | − | 0.683704i | \(-0.760368\pi\) |
0.683704 | + | 0.729760i | \(0.260368\pi\) | |||||||
\(954\) | 16705.9 | + | 2279.92i | 0.566952 | + | 0.0773743i | ||||
\(955\) | −9515.69 | + | 3941.53i | −0.322430 | + | 0.133555i | ||||
\(956\) | −22225.1 | − | 39351.3i | −0.751895 | − | 1.33129i | ||||
\(957\) | −7100.20 | + | 17141.4i | −0.239829 | + | 0.579000i | ||||
\(958\) | −4028.93 | − | 15326.2i | −0.135876 | − | 0.516875i | ||||
\(959\) | 27718.3 | 0.933336 | ||||||||
\(960\) | 63453.3 | + | 1803.79i | 2.13328 | + | 0.0606429i | ||||
\(961\) | −28335.8 | −0.951152 | ||||||||
\(962\) | 7365.95 | + | 28020.3i | 0.246869 | + | 0.939097i | ||||
\(963\) | −12580.4 | + | 30371.9i | −0.420975 | + | 1.01632i | ||||
\(964\) | 19905.3 | + | 35243.9i | 0.665048 | + | 1.17752i | ||||
\(965\) | −32570.4 | + | 13491.1i | −1.08651 | + | 0.450046i | ||||
\(966\) | 40822.5 | + | 5571.21i | 1.35967 | + | 0.185560i | ||||
\(967\) | −9687.88 | + | 9687.88i | −0.322173 | + | 0.322173i | −0.849600 | − | 0.527427i | \(-0.823157\pi\) |
0.527427 | + | 0.849600i | \(0.323157\pi\) | |||||||
\(968\) | −13073.7 | − | 185.786i | −0.434096 | − | 0.00616880i | ||||
\(969\) | 9911.89 | + | 9911.89i | 0.328602 | + | 0.328602i | ||||
\(970\) | 19712.5 | + | 25943.4i | 0.652506 | + | 0.858755i | ||||
\(971\) | −9092.27 | − | 21950.7i | −0.300499 | − | 0.725469i | −0.999942 | − | 0.0107805i | \(-0.996568\pi\) |
0.699443 | − | 0.714689i | \(-0.253432\pi\) | |||||||
\(972\) | −30558.6 | + | 3728.97i | −1.00840 | + | 0.123052i | ||||
\(973\) | −5614.52 | − | 2325.61i | −0.184988 | − | 0.0766245i | ||||
\(974\) | −46077.3 | − | 26894.5i | −1.51582 | − | 0.884761i | ||||
\(975\) | − | 32535.8i | − | 1.06870i | ||||||
\(976\) | −3343.81 | − | 4533.04i | −0.109665 | − | 0.148667i | ||||
\(977\) | − | 2789.43i | − | 0.0913426i | −0.998957 | − | 0.0456713i | \(-0.985457\pi\) | ||
0.998957 | − | 0.0456713i | \(-0.0145427\pi\) | |||||||
\(978\) | −11885.0 | + | 20362.2i | −0.388591 | + | 0.665757i | ||||
\(979\) | 12337.8 | + | 5110.48i | 0.402776 | + | 0.166835i | ||||
\(980\) | 16586.4 | + | 12978.7i | 0.540645 | + | 0.423049i | ||||
\(981\) | −1014.12 | − | 2448.31i | −0.0330056 | − | 0.0796825i | ||||
\(982\) | 35716.8 | − | 27138.7i | 1.16066 | − | 0.881904i | ||||
\(983\) | 10480.4 | + | 10480.4i | 0.340054 | + | 0.340054i | 0.856388 | − | 0.516334i | \(-0.172703\pi\) |
−0.516334 | + | 0.856388i | \(0.672703\pi\) | |||||||
\(984\) | 68899.1 | + | 29692.8i | 2.23214 | + | 0.961964i | ||||
\(985\) | 29203.4 | − | 29203.4i | 0.944666 | − | 0.944666i | ||||
\(986\) | 1790.03 | − | 13116.3i | 0.0578157 | − | 0.423638i | ||||
\(987\) | −32047.6 | + | 13274.6i | −1.03352 | + | 0.428099i | ||||
\(988\) | −5787.70 | − | 1609.73i | −0.186368 | − | 0.0518342i | ||||
\(989\) | −15174.2 | + | 36633.7i | −0.487877 | + | 1.17784i | ||||
\(990\) | 76702.8 | − | 20163.5i | 2.46240 | − | 0.647312i | ||||
\(991\) | −43206.7 | −1.38497 | −0.692485 | − | 0.721432i | \(-0.743484\pi\) | ||||
−0.692485 | + | 0.721432i | \(0.743484\pi\) | |||||||
\(992\) | 6625.97 | + | 1944.72i | 0.212071 | + | 0.0622428i | ||||
\(993\) | −81636.3 | −2.60891 | ||||||||
\(994\) | −13519.6 | + | 3554.02i | −0.431404 | + | 0.113407i | ||||
\(995\) | −23509.7 | + | 56757.5i | −0.749054 | + | 1.80838i | ||||
\(996\) | 23964.1 | − | 86162.0i | 0.762382 | − | 2.74111i | ||||
\(997\) | 29415.4 | − | 12184.3i | 0.934399 | − | 0.387041i | 0.137054 | − | 0.990564i | \(-0.456237\pi\) |
0.797346 | + | 0.603523i | \(0.206237\pi\) | |||||||
\(998\) | 1286.77 | − | 9428.69i | 0.0408137 | − | 0.299058i | ||||
\(999\) | 24040.3 | − | 24040.3i | 0.761362 | − | 0.761362i |
(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 | 32.4.g.a.13.5 | yes | 44 | |
4.3 | odd | 2 | 128.4.g.a.17.10 | 44 | |||
8.3 | odd | 2 | 256.4.g.a.33.2 | 44 | |||
8.5 | even | 2 | 256.4.g.b.33.10 | 44 | |||
32.5 | even | 8 | inner | 32.4.g.a.5.5 | ✓ | 44 | |
32.11 | odd | 8 | 256.4.g.a.225.2 | 44 | |||
32.21 | even | 8 | 256.4.g.b.225.10 | 44 | |||
32.27 | odd | 8 | 128.4.g.a.113.10 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.5 | ✓ | 44 | 32.5 | even | 8 | inner | |
32.4.g.a.13.5 | yes | 44 | 1.1 | even | 1 | trivial | |
128.4.g.a.17.10 | 44 | 4.3 | odd | 2 | |||
128.4.g.a.113.10 | 44 | 32.27 | odd | 8 | |||
256.4.g.a.33.2 | 44 | 8.3 | odd | 2 | |||
256.4.g.a.225.2 | 44 | 32.11 | odd | 8 | |||
256.4.g.b.33.10 | 44 | 8.5 | even | 2 | |||
256.4.g.b.225.10 | 44 | 32.21 | even | 8 |