Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,6,Mod(5,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.e (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: | \(2.56614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{36} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(-3.62794 - 1.68466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.5 |
Dual form | 16.6.e.a.13.4 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94328 | − | 5.31260i | −0.343526 | − | 0.939143i | ||||
\(3\) | 13.2148 | − | 13.2148i | 0.847730 | − | 0.847730i | −0.142119 | − | 0.989850i | \(-0.545392\pi\) |
0.989850 | + | 0.142119i | \(0.0453917\pi\) | |||||||
\(4\) | −24.4473 | + | 20.6477i | −0.763979 | + | 0.645241i | ||||
\(5\) | −26.0955 | − | 26.0955i | −0.466811 | − | 0.466811i | 0.434069 | − | 0.900880i | \(-0.357077\pi\) |
−0.900880 | + | 0.434069i | \(0.857077\pi\) | |||||||
\(6\) | −95.8850 | − | 44.5248i | −1.08736 | − | 0.504922i | ||||
\(7\) | − | 106.802i | − | 0.823823i | −0.911224 | − | 0.411911i | \(-0.864861\pi\) | ||
0.911224 | − | 0.411911i | \(-0.135139\pi\) | |||||||
\(8\) | 157.201 | + | 89.7545i | 0.868421 | + | 0.495828i | ||||
\(9\) | − | 106.262i | − | 0.437292i | ||||||
\(10\) | −87.9240 | + | 189.346i | −0.278040 | + | 0.598764i | ||||
\(11\) | 407.630 | + | 407.630i | 1.01574 | + | 1.01574i | 0.999874 | + | 0.0158703i | \(0.00505187\pi\) |
0.0158703 | + | 0.999874i | \(0.494948\pi\) | |||||||
\(12\) | −50.2112 | + | 595.922i | −0.100658 | + | 1.19464i | ||||
\(13\) | 684.623 | − | 684.623i | 1.12355 | − | 1.12355i | 0.132349 | − | 0.991203i | \(-0.457748\pi\) |
0.991203 | − | 0.132349i | \(-0.0422519\pi\) | |||||||
\(14\) | −567.395 | + | 207.546i | −0.773687 | + | 0.283005i | ||||
\(15\) | −689.694 | −0.791459 | ||||||||
\(16\) | 171.344 | − | 1009.56i | 0.167328 | − | 0.985901i | ||||
\(17\) | 566.949 | 0.475797 | 0.237899 | − | 0.971290i | \(-0.423541\pi\) | ||||
0.237899 | + | 0.971290i | \(0.423541\pi\) | |||||||
\(18\) | −564.527 | + | 206.497i | −0.410680 | + | 0.150222i | ||||
\(19\) | −1700.29 | + | 1700.29i | −1.08053 | + | 1.08053i | −0.0840731 | + | 0.996460i | \(0.526793\pi\) |
−0.996460 | + | 0.0840731i | \(0.973207\pi\) | |||||||
\(20\) | 1176.78 | + | 99.1530i | 0.657839 | + | 0.0554282i | ||||
\(21\) | −1411.37 | − | 1411.37i | −0.698379 | − | 0.698379i | ||||
\(22\) | 1373.43 | − | 2957.71i | 0.604994 | − | 1.30286i | ||||
\(23\) | 838.931i | 0.330679i | 0.986237 | + | 0.165339i | \(0.0528720\pi\) | ||||
−0.986237 | + | 0.165339i | \(0.947128\pi\) | |||||||
\(24\) | 3263.47 | − | 891.291i | 1.15651 | − | 0.315858i | ||||
\(25\) | − | 1763.05i | − | 0.564176i | ||||||
\(26\) | −4967.54 | − | 2306.71i | −1.44115 | − | 0.669206i | ||||
\(27\) | 1806.97 | + | 1806.97i | 0.477024 | + | 0.477024i | ||||
\(28\) | 2205.21 | + | 2611.02i | 0.531564 | + | 0.629383i | ||||
\(29\) | −5523.73 | + | 5523.73i | −1.21966 | + | 1.21966i | −0.251905 | + | 0.967752i | \(0.581057\pi\) |
−0.967752 | + | 0.251905i | \(0.918943\pi\) | |||||||
\(30\) | 1340.27 | + | 3664.07i | 0.271887 | + | 0.743293i | ||||
\(31\) | 2169.95 | 0.405551 | 0.202776 | − | 0.979225i | \(-0.435004\pi\) | ||||
0.202776 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(32\) | −5696.37 | + | 1051.58i | −0.983384 | + | 0.181538i | ||||
\(33\) | 10773.5 | 1.72215 | ||||||||
\(34\) | −1101.74 | − | 3011.97i | −0.163449 | − | 0.446842i | ||||
\(35\) | −2787.05 | + | 2787.05i | −0.384569 | + | 0.384569i | ||||
\(36\) | 2194.07 | + | 2597.82i | 0.282159 | + | 0.334082i | ||||
\(37\) | −2842.06 | − | 2842.06i | −0.341295 | − | 0.341295i | 0.515559 | − | 0.856854i | \(-0.327584\pi\) |
−0.856854 | + | 0.515559i | \(0.827584\pi\) | |||||||
\(38\) | 12337.1 | + | 5728.80i | 1.38597 | + | 0.643583i | ||||
\(39\) | − | 18094.3i | − | 1.90494i | ||||||
\(40\) | −1760.05 | − | 6444.43i | −0.173930 | − | 0.636846i | ||||
\(41\) | − | 1926.27i | − | 0.178960i | −0.995989 | − | 0.0894802i | \(-0.971479\pi\) | ||
0.995989 | − | 0.0894802i | \(-0.0285206\pi\) | |||||||
\(42\) | −4755.34 | + | 10240.7i | −0.415966 | + | 0.895790i | ||||
\(43\) | 800.365 | + | 800.365i | 0.0660111 | + | 0.0660111i | 0.739342 | − | 0.673330i | \(-0.235137\pi\) |
−0.673330 | + | 0.739342i | \(0.735137\pi\) | |||||||
\(44\) | −18382.1 | − | 1548.84i | −1.43141 | − | 0.120608i | ||||
\(45\) | −2772.96 | + | 2772.96i | −0.204133 | + | 0.204133i | ||||
\(46\) | 4456.90 | − | 1630.28i | 0.310555 | − | 0.113597i | ||||
\(47\) | 441.674 | 0.0291647 | 0.0145824 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145824 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(48\) | −11076.9 | − | 15605.5i | −0.693929 | − | 0.977627i | ||||
\(49\) | 5400.36 | 0.321316 | ||||||||
\(50\) | −9366.36 | + | 3426.10i | −0.529842 | + | 0.193809i | ||||
\(51\) | 7492.12 | − | 7492.12i | 0.403347 | − | 0.403347i | ||||
\(52\) | −2601.31 | + | 30873.1i | −0.133408 | + | 1.58333i | ||||
\(53\) | −4098.70 | − | 4098.70i | −0.200427 | − | 0.200427i | 0.599756 | − | 0.800183i | \(-0.295264\pi\) |
−0.800183 | + | 0.599756i | \(0.795264\pi\) | |||||||
\(54\) | 6088.24 | − | 13111.1i | 0.284123 | − | 0.611864i | ||||
\(55\) | − | 21274.6i | − | 0.948321i | ||||||
\(56\) | 9585.95 | − | 16789.4i | 0.408475 | − | 0.715425i | ||||
\(57\) | 44937.9i | 1.83200i | ||||||||
\(58\) | 40079.5 | + | 18611.2i | 1.56442 | + | 0.726448i | ||||
\(59\) | 18994.6 | + | 18994.6i | 0.710395 | + | 0.710395i | 0.966618 | − | 0.256223i | \(-0.0824781\pi\) |
−0.256223 | + | 0.966618i | \(0.582478\pi\) | |||||||
\(60\) | 16861.2 | − | 14240.6i | 0.604658 | − | 0.510682i | ||||
\(61\) | −13660.7 | + | 13660.7i | −0.470056 | + | 0.470056i | −0.901933 | − | 0.431877i | \(-0.857851\pi\) |
0.431877 | + | 0.901933i | \(0.357851\pi\) | |||||||
\(62\) | −4216.82 | − | 11528.1i | −0.139318 | − | 0.380871i | ||||
\(63\) | −11349.0 | −0.360251 | ||||||||
\(64\) | 16656.3 | + | 28219.0i | 0.508309 | + | 0.861175i | ||||
\(65\) | −35731.2 | −1.04897 | ||||||||
\(66\) | −20935.9 | − | 57235.2i | −0.591605 | − | 1.61735i | ||||
\(67\) | −22510.3 | + | 22510.3i | −0.612624 | + | 0.612624i | −0.943629 | − | 0.331005i | \(-0.892612\pi\) |
0.331005 | + | 0.943629i | \(0.392612\pi\) | |||||||
\(68\) | −13860.4 | + | 11706.2i | −0.363499 | + | 0.307004i | ||||
\(69\) | 11086.3 | + | 11086.3i | 0.280326 | + | 0.280326i | ||||
\(70\) | 20222.5 | + | 9390.45i | 0.493275 | + | 0.229056i | ||||
\(71\) | 34159.3i | 0.804199i | 0.915596 | + | 0.402099i | \(0.131719\pi\) | ||||
−0.915596 | + | 0.402099i | \(0.868281\pi\) | |||||||
\(72\) | 9537.50 | − | 16704.5i | 0.216822 | − | 0.379754i | ||||
\(73\) | − | 77379.2i | − | 1.69948i | −0.527200 | − | 0.849741i | \(-0.676758\pi\) | ||
0.527200 | − | 0.849741i | \(-0.323242\pi\) | |||||||
\(74\) | −9575.81 | + | 20621.7i | −0.203281 | + | 0.437768i | ||||
\(75\) | −23298.3 | − | 23298.3i | −0.478269 | − | 0.478269i | ||||
\(76\) | 6460.44 | − | 76674.5i | 0.128300 | − | 1.52271i | ||||
\(77\) | 43535.7 | − | 43535.7i | 0.836793 | − | 0.836793i | ||||
\(78\) | −96127.8 | + | 35162.3i | −1.78901 | + | 0.654396i | ||||
\(79\) | −5843.36 | −0.105340 | −0.0526702 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526702 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(80\) | −30816.4 | + | 21873.7i | −0.538340 | + | 0.382119i | ||||
\(81\) | 73579.1 | 1.24607 | ||||||||
\(82\) | −10233.5 | + | 3743.28i | −0.168069 | + | 0.0614776i | ||||
\(83\) | 22248.9 | − | 22248.9i | 0.354498 | − | 0.354498i | −0.507282 | − | 0.861780i | \(-0.669350\pi\) |
0.861780 | + | 0.507282i | \(0.169350\pi\) | |||||||
\(84\) | 63645.6 | + | 5362.65i | 0.984170 | + | 0.0829243i | ||||
\(85\) | −14794.8 | − | 14794.8i | −0.222107 | − | 0.222107i | ||||
\(86\) | 2696.68 | − | 5807.35i | 0.0393173 | − | 0.0846705i | ||||
\(87\) | 145990.i | 2.06788i | ||||||||
\(88\) | 27493.2 | + | 100666.i | 0.378459 | + | 1.38573i | ||||
\(89\) | − | 41863.5i | − | 0.560222i | −0.959968 | − | 0.280111i | \(-0.909629\pi\) | ||
0.959968 | − | 0.280111i | \(-0.0903713\pi\) | |||||||
\(90\) | 20120.3 | + | 9342.99i | 0.261835 | + | 0.121585i | ||||
\(91\) | −73119.0 | − | 73119.0i | −0.925608 | − | 0.925608i | ||||
\(92\) | −17322.0 | − | 20509.6i | −0.213368 | − | 0.252632i | ||||
\(93\) | 28675.5 | − | 28675.5i | 0.343798 | − | 0.343798i | ||||
\(94\) | −858.297 | − | 2346.44i | −0.0100188 | − | 0.0273898i | ||||
\(95\) | 88739.6 | 1.00881 | ||||||||
\(96\) | −61379.9 | + | 89172.8i | −0.679749 | + | 0.987539i | ||||
\(97\) | −156099. | −1.68450 | −0.842248 | − | 0.539090i | \(-0.818768\pi\) | ||||
−0.842248 | + | 0.539090i | \(0.818768\pi\) | |||||||
\(98\) | −10494.4 | − | 28689.9i | −0.110381 | − | 0.301762i | ||||
\(99\) | 43315.6 | − | 43315.6i | 0.444177 | − | 0.444177i | ||||
\(100\) | 36402.9 | + | 43101.8i | 0.364029 | + | 0.431018i | ||||
\(101\) | 94579.5 | + | 94579.5i | 0.922557 | + | 0.922557i | 0.997210 | − | 0.0746522i | \(-0.0237847\pi\) |
−0.0746522 | + | 0.997210i | \(0.523785\pi\) | |||||||
\(102\) | −54361.9 | − | 25243.3i | −0.517362 | − | 0.240240i | ||||
\(103\) | − | 22786.6i | − | 0.211634i | −0.994386 | − | 0.105817i | \(-0.966254\pi\) | ||
0.994386 | − | 0.105817i | \(-0.0337458\pi\) | |||||||
\(104\) | 169071. | − | 46175.4i | 1.53280 | − | 0.418627i | ||||
\(105\) | 73660.6i | 0.652022i | ||||||||
\(106\) | −13809.8 | + | 29739.6i | −0.119378 | + | 0.257082i | ||||
\(107\) | 51699.8 | + | 51699.8i | 0.436545 | + | 0.436545i | 0.890848 | − | 0.454302i | \(-0.150111\pi\) |
−0.454302 | + | 0.890848i | \(0.650111\pi\) | |||||||
\(108\) | −81485.2 | − | 6865.78i | −0.672232 | − | 0.0566409i | ||||
\(109\) | 61340.0 | − | 61340.0i | 0.494513 | − | 0.494513i | −0.415212 | − | 0.909725i | \(-0.636293\pi\) |
0.909725 | + | 0.415212i | \(0.136293\pi\) | |||||||
\(110\) | −113023. | + | 41342.5i | −0.890609 | + | 0.325773i | ||||
\(111\) | −75114.6 | −0.578651 | ||||||||
\(112\) | −107823. | − | 18299.9i | −0.812208 | − | 0.137849i | ||||
\(113\) | −107766. | −0.793938 | −0.396969 | − | 0.917832i | \(-0.629938\pi\) | ||||
−0.396969 | + | 0.917832i | \(0.629938\pi\) | |||||||
\(114\) | 238737. | − | 87326.9i | 1.72051 | − | 0.629341i | ||||
\(115\) | 21892.3 | − | 21892.3i | 0.154364 | − | 0.154364i | ||||
\(116\) | 20988.1 | − | 249093.i | 0.144820 | − | 1.71877i | ||||
\(117\) | −72749.5 | − | 72749.5i | −0.491321 | − | 0.491321i | ||||
\(118\) | 63998.8 | − | 137822.i | 0.423123 | − | 0.911202i | ||||
\(119\) | − | 60551.2i | − | 0.391973i | ||||||
\(120\) | −108421. | − | 61903.1i | −0.687319 | − | 0.392428i | ||||
\(121\) | 171273.i | 1.06347i | ||||||||
\(122\) | 99120.5 | + | 46027.3i | 0.602926 | + | 0.279973i | ||||
\(123\) | −25455.2 | − | 25455.2i | −0.151710 | − | 0.151710i | ||||
\(124\) | −53049.5 | + | 44804.5i | −0.309833 | + | 0.261678i | ||||
\(125\) | −127556. | + | 127556.i | −0.730174 | + | 0.730174i | ||||
\(126\) | 22054.3 | + | 60292.6i | 0.123756 | + | 0.338328i | ||||
\(127\) | −267429. | −1.47129 | −0.735647 | − | 0.677365i | \(-0.763122\pi\) | ||||
−0.735647 | + | 0.677365i | \(0.763122\pi\) | |||||||
\(128\) | 117548. | − | 143325.i | 0.634149 | − | 0.773211i | ||||
\(129\) | 21153.3 | 0.111919 | ||||||||
\(130\) | 69435.7 | + | 189825.i | 0.360350 | + | 0.985135i | ||||
\(131\) | −9397.10 | + | 9397.10i | −0.0478427 | + | 0.0478427i | −0.730623 | − | 0.682781i | \(-0.760770\pi\) |
0.682781 | + | 0.730623i | \(0.260770\pi\) | |||||||
\(132\) | −263383. | + | 222448.i | −1.31569 | + | 1.11120i | ||||
\(133\) | 181594. | + | 181594.i | 0.890168 | + | 0.890168i | ||||
\(134\) | 163332. | + | 75844.3i | 0.785794 | + | 0.364889i | ||||
\(135\) | − | 94307.3i | − | 0.445360i | ||||||
\(136\) | 89124.9 | + | 50886.2i | 0.413192 | + | 0.235914i | ||||
\(137\) | − | 29494.1i | − | 0.134256i | −0.997744 | − | 0.0671281i | \(-0.978616\pi\) | ||
0.997744 | − | 0.0671281i | \(-0.0213836\pi\) | |||||||
\(138\) | 37353.3 | − | 80440.8i | 0.166967 | − | 0.359566i | ||||
\(139\) | 36678.6 | + | 36678.6i | 0.161019 | + | 0.161019i | 0.783018 | − | 0.621999i | \(-0.213679\pi\) |
−0.621999 | + | 0.783018i | \(0.713679\pi\) | |||||||
\(140\) | 10589.7 | − | 125682.i | 0.0456630 | − | 0.541943i | ||||
\(141\) | 5836.64 | − | 5836.64i | 0.0247238 | − | 0.0247238i | ||||
\(142\) | 181475. | − | 66381.1i | 0.755258 | − | 0.276264i | ||||
\(143\) | 558146. | 2.28248 | ||||||||
\(144\) | −107278. | − | 18207.4i | −0.431127 | − | 0.0731713i | ||||
\(145\) | 288289. | 1.13870 | ||||||||
\(146\) | −411084. | + | 150369.i | −1.59606 | + | 0.583817i | ||||
\(147\) | 71364.6 | − | 71364.6i | 0.272389 | − | 0.272389i | ||||
\(148\) | 128163. | + | 10798.8i | 0.480959 | + | 0.0405247i | ||||
\(149\) | −244564. | − | 244564.i | −0.902457 | − | 0.902457i | 0.0931915 | − | 0.995648i | \(-0.470293\pi\) |
−0.995648 | + | 0.0931915i | \(0.970293\pi\) | |||||||
\(150\) | −78499.5 | + | 169050.i | −0.284865 | + | 0.613461i | ||||
\(151\) | − | 178219.i | − | 0.636079i | −0.948077 | − | 0.318040i | \(-0.896975\pi\) | ||
0.948077 | − | 0.318040i | \(-0.103025\pi\) | |||||||
\(152\) | −419895. | + | 114678.i | −1.47412 | + | 0.402598i | ||||
\(153\) | − | 60245.2i | − | 0.208062i | ||||||
\(154\) | −315889. | − | 146685.i | −1.07333 | − | 0.498408i | ||||
\(155\) | −56626.0 | − | 56626.0i | −0.189316 | − | 0.189316i | ||||
\(156\) | 373606. | + | 442358.i | 1.22914 | + | 1.45533i | ||||
\(157\) | −148493. | + | 148493.i | −0.480791 | + | 0.480791i | −0.905384 | − | 0.424593i | \(-0.860417\pi\) |
0.424593 | + | 0.905384i | \(0.360417\pi\) | |||||||
\(158\) | 11355.3 | + | 31043.4i | 0.0361872 | + | 0.0989297i | ||||
\(159\) | −108327. | −0.339816 | ||||||||
\(160\) | 176091. | + | 121208.i | 0.543798 | + | 0.374310i | ||||
\(161\) | 89599.4 | 0.272421 | ||||||||
\(162\) | −142985. | − | 390896.i | −0.428057 | − | 1.17024i | ||||
\(163\) | −190853. | + | 190853.i | −0.562640 | + | 0.562640i | −0.930056 | − | 0.367417i | \(-0.880242\pi\) |
0.367417 | + | 0.930056i | \(0.380242\pi\) | |||||||
\(164\) | 39773.0 | + | 47092.1i | 0.115473 | + | 0.136722i | ||||
\(165\) | −281140. | − | 281140.i | −0.803920 | − | 0.803920i | ||||
\(166\) | −161435. | − | 74963.6i | −0.454703 | − | 0.211145i | ||||
\(167\) | − | 105468.i | − | 0.292636i | −0.989238 | − | 0.146318i | \(-0.953258\pi\) | ||
0.989238 | − | 0.146318i | \(-0.0467423\pi\) | |||||||
\(168\) | −95191.6 | − | 348544.i | −0.260211 | − | 0.952763i | ||||
\(169\) | − | 566125.i | − | 1.52474i | ||||||
\(170\) | −49848.4 | + | 107349.i | −0.132291 | + | 0.284890i | ||||
\(171\) | 180676. | + | 180676.i | 0.472509 | + | 0.472509i | ||||
\(172\) | −36092.5 | − | 3041.08i | −0.0930242 | − | 0.00783804i | ||||
\(173\) | −109671. | + | 109671.i | −0.278597 | + | 0.278597i | −0.832549 | − | 0.553952i | \(-0.813119\pi\) |
0.553952 | + | 0.832549i | \(0.313119\pi\) | |||||||
\(174\) | 775586. | − | 283700.i | 1.94204 | − | 0.710372i | ||||
\(175\) | −188297. | −0.464781 | ||||||||
\(176\) | 481373. | − | 341683.i | 1.17139 | − | 0.831461i | ||||
\(177\) | 502019. | 1.20445 | ||||||||
\(178\) | −222404. | + | 81352.4i | −0.526129 | + | 0.192451i | ||||
\(179\) | −355752. | + | 355752.i | −0.829880 | + | 0.829880i | −0.987500 | − | 0.157620i | \(-0.949618\pi\) |
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(180\) | 10536.2 | − | 125047.i | 0.0242383 | − | 0.287668i | ||||
\(181\) | 352209. | + | 352209.i | 0.799105 | + | 0.799105i | 0.982954 | − | 0.183849i | \(-0.0588559\pi\) |
−0.183849 | + | 0.982954i | \(0.558856\pi\) | |||||||
\(182\) | −246361. | + | 530543.i | −0.551307 | + | 1.18725i | ||||
\(183\) | 361048.i | 0.796961i | ||||||||
\(184\) | −75297.8 | + | 131881.i | −0.163960 | + | 0.287168i | ||||
\(185\) | 148330.i | 0.318640i | ||||||||
\(186\) | −208066. | − | 96616.7i | −0.440979 | − | 0.204772i | ||||
\(187\) | 231105. | + | 231105.i | 0.483288 | + | 0.483288i | ||||
\(188\) | −10797.8 | + | 9119.57i | −0.0222812 | + | 0.0188183i | ||||
\(189\) | 192987. | − | 192987.i | 0.392983 | − | 0.392983i | ||||
\(190\) | −172446. | − | 471438.i | −0.346552 | − | 0.947415i | ||||
\(191\) | −429992. | −0.852859 | −0.426429 | − | 0.904521i | \(-0.640229\pi\) | ||||
−0.426429 | + | 0.904521i | \(0.640229\pi\) | |||||||
\(192\) | 593017. | + | 152799.i | 1.16095 | + | 0.299135i | ||||
\(193\) | 370670. | 0.716298 | 0.358149 | − | 0.933664i | \(-0.383408\pi\) | ||||
0.358149 | + | 0.933664i | \(0.383408\pi\) | |||||||
\(194\) | 303344. | + | 829290.i | 0.578669 | + | 1.58198i | ||||
\(195\) | −472180. | + | 472180.i | −0.889245 | + | 0.889245i | ||||
\(196\) | −132024. | + | 111505.i | −0.245479 | + | 0.207326i | ||||
\(197\) | −675759. | − | 675759.i | −1.24059 | − | 1.24059i | −0.959759 | − | 0.280827i | \(-0.909391\pi\) |
−0.280827 | − | 0.959759i | \(-0.590609\pi\) | |||||||
\(198\) | −314293. | − | 145944.i | −0.569733 | − | 0.264559i | ||||
\(199\) | − | 286188.i | − | 0.512293i | −0.966638 | − | 0.256147i | \(-0.917547\pi\) | ||
0.966638 | − | 0.256147i | \(-0.0824530\pi\) | |||||||
\(200\) | 158242. | − | 277153.i | 0.279734 | − | 0.489942i | ||||
\(201\) | 594938.i | 1.03868i | ||||||||
\(202\) | 318668. | − | 686257.i | 0.549490 | − | 1.18334i | ||||
\(203\) | 589945. | + | 589945.i | 1.00478 | + | 1.00478i | ||||
\(204\) | −28467.2 | + | 337858.i | −0.0478927 | + | 0.568405i | ||||
\(205\) | −50266.9 | + | 50266.9i | −0.0835406 | + | 0.0835406i | ||||
\(206\) | −121056. | + | 44280.6i | −0.198755 | + | 0.0727019i | ||||
\(207\) | 89146.5 | 0.144603 | ||||||||
\(208\) | −573864. | − | 808476.i | −0.919709 | − | 1.29571i | ||||
\(209\) | −1.38617e6 | −2.19509 | ||||||||
\(210\) | 391329. | − | 143143.i | 0.612342 | − | 0.223987i | ||||
\(211\) | 824632. | − | 824632.i | 1.27513 | − | 1.27513i | 0.331767 | − | 0.943361i | \(-0.392355\pi\) |
0.943361 | − | 0.331767i | \(-0.107645\pi\) | |||||||
\(212\) | 184831. | + | 15573.5i | 0.282446 | + | 0.0237983i | ||||
\(213\) | 451409. | + | 451409.i | 0.681744 | + | 0.681744i | ||||
\(214\) | 174193. | − | 375127.i | 0.260013 | − | 0.559943i | ||||
\(215\) | − | 41771.9i | − | 0.0616294i | ||||||
\(216\) | 121873. | + | 446240.i | 0.177736 | + | 0.650780i | ||||
\(217\) | − | 231755.i | − | 0.334102i | ||||||
\(218\) | −445075. | − | 206674.i | −0.634296 | − | 0.294540i | ||||
\(219\) | −1.02255e6 | − | 1.02255e6i | −1.44070 | − | 1.44070i | ||||
\(220\) | 439272. | + | 520108.i | 0.611895 | + | 0.724497i | ||||
\(221\) | 388146. | − | 388146.i | 0.534583 | − | 0.534583i | ||||
\(222\) | 145969. | + | 399054.i | 0.198782 | + | 0.543436i | ||||
\(223\) | 136259. | 0.183486 | 0.0917428 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917428 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(224\) | 112311. | + | 608383.i | 0.149555 | + | 0.810134i | ||||
\(225\) | −187345. | −0.246710 | ||||||||
\(226\) | 209420. | + | 572519.i | 0.272739 | + | 0.745622i | ||||
\(227\) | 425671. | − | 425671.i | 0.548289 | − | 0.548289i | −0.377656 | − | 0.925946i | \(-0.623270\pi\) |
0.925946 | + | 0.377656i | \(0.123270\pi\) | |||||||
\(228\) | −927864. | − | 1.09861e6i | −1.18208 | − | 1.39961i | ||||
\(229\) | 576711. | + | 576711.i | 0.726724 | + | 0.726724i | 0.969966 | − | 0.243242i | \(-0.0782108\pi\) |
−0.243242 | + | 0.969966i | \(0.578211\pi\) | |||||||
\(230\) | −158848. | − | 73762.1i | −0.197999 | − | 0.0919420i | ||||
\(231\) | − | 1.15063e6i | − | 1.41875i | ||||||
\(232\) | −1.36412e6 | + | 372556.i | −1.66392 | + | 0.454435i | ||||
\(233\) | 563157.i | 0.679578i | 0.940502 | + | 0.339789i | \(0.110356\pi\) | ||||
−0.940502 | + | 0.339789i | \(0.889644\pi\) | |||||||
\(234\) | −245116. | + | 527861.i | −0.292639 | + | 0.630202i | ||||
\(235\) | −11525.7 | − | 11525.7i | −0.0136144 | − | 0.0136144i | ||||
\(236\) | −856562. | − | 72172.2i | −1.00110 | − | 0.0843510i | ||||
\(237\) | −77218.9 | + | 77218.9i | −0.0893002 | + | 0.0893002i | ||||
\(238\) | −321684. | + | 117668.i | −0.368118 | + | 0.134653i | ||||
\(239\) | 1.22493e6 | 1.38713 | 0.693565 | − | 0.720394i | \(-0.256039\pi\) | ||||
0.693565 | + | 0.720394i | \(0.256039\pi\) | |||||||
\(240\) | −118175. | + | 696290.i | −0.132433 | + | 0.780300i | ||||
\(241\) | 107755. | 0.119508 | 0.0597538 | − | 0.998213i | \(-0.480968\pi\) | ||||
0.0597538 | + | 0.998213i | \(0.480968\pi\) | |||||||
\(242\) | 909906. | − | 332832.i | 0.998753 | − | 0.365331i | ||||
\(243\) | 533240. | − | 533240.i | 0.579305 | − | 0.579305i | ||||
\(244\) | 51905.6 | − | 616031.i | 0.0558135 | − | 0.662412i | ||||
\(245\) | −140925. | − | 140925.i | −0.149994 | − | 0.149994i | ||||
\(246\) | −85766.8 | + | 184700.i | −0.0903610 | + | 0.194594i | ||||
\(247\) | 2.32811e6i | 2.42807i | ||||||||
\(248\) | 341118. | + | 194763.i | 0.352189 | + | 0.201084i | ||||
\(249\) | − | 588030.i | − | 0.601037i | ||||||
\(250\) | 925531. | + | 429777.i | 0.936572 | + | 0.434904i | ||||
\(251\) | −927180. | − | 927180.i | −0.928923 | − | 0.928923i | 0.0687135 | − | 0.997636i | \(-0.478111\pi\) |
−0.997636 | + | 0.0687135i | \(0.978111\pi\) | |||||||
\(252\) | 277452. | − | 234331.i | 0.275225 | − | 0.232449i | ||||
\(253\) | −341973. | + | 341973.i | −0.335885 | + | 0.335885i | ||||
\(254\) | 519690. | + | 1.42074e6i | 0.505429 | + | 1.38176i | ||||
\(255\) | −391021. | −0.376574 | ||||||||
\(256\) | −989858. | − | 345965.i | −0.944003 | − | 0.329938i | ||||
\(257\) | 781809. | 0.738359 | 0.369180 | − | 0.929358i | \(-0.379639\pi\) | ||||
0.369180 | + | 0.929358i | \(0.379639\pi\) | |||||||
\(258\) | −41106.9 | − | 112379.i | −0.0384472 | − | 0.105108i | ||||
\(259\) | −303538. | + | 303538.i | −0.281166 | + | 0.281166i | ||||
\(260\) | 873532. | − | 737767.i | 0.801393 | − | 0.676840i | ||||
\(261\) | 586963. | + | 586963.i | 0.533347 | + | 0.533347i | ||||
\(262\) | 68184.2 | + | 31661.8i | 0.0613664 | + | 0.0284959i | ||||
\(263\) | 871795.i | 0.777186i | 0.921410 | + | 0.388593i | \(0.127039\pi\) | ||||
−0.921410 | + | 0.388593i | \(0.872961\pi\) | |||||||
\(264\) | 1.69360e6 | + | 966970.i | 1.49555 | + | 0.853893i | ||||
\(265\) | 213915.i | 0.187123i | ||||||||
\(266\) | 611847. | − | 1.31762e6i | 0.530198 | − | 1.14179i | ||||
\(267\) | −553218. | − | 553218.i | −0.474917 | − | 0.474917i | ||||
\(268\) | 85530.5 | − | 1.01510e6i | 0.0727418 | − | 0.863322i | ||||
\(269\) | −390591. | + | 390591.i | −0.329111 | + | 0.329111i | −0.852248 | − | 0.523138i | \(-0.824761\pi\) |
0.523138 | + | 0.852248i | \(0.324761\pi\) | |||||||
\(270\) | −501017. | + | 183266.i | −0.418257 | + | 0.152993i | ||||
\(271\) | −998296. | −0.825726 | −0.412863 | − | 0.910793i | \(-0.635471\pi\) | ||||
−0.412863 | + | 0.910793i | \(0.635471\pi\) | |||||||
\(272\) | 97143.3 | − | 572371.i | 0.0796142 | − | 0.469089i | ||||
\(273\) | −1.93251e6 | −1.56933 | ||||||||
\(274\) | −156690. | + | 57315.3i | −0.126086 | + | 0.0461205i | ||||
\(275\) | 718672. | − | 718672.i | 0.573058 | − | 0.573058i | ||||
\(276\) | −499937. | − | 42123.7i | −0.395042 | − | 0.0332854i | ||||
\(277\) | 370354. | + | 370354.i | 0.290013 | + | 0.290013i | 0.837085 | − | 0.547072i | \(-0.184258\pi\) |
−0.547072 | + | 0.837085i | \(0.684258\pi\) | |||||||
\(278\) | 123582. | − | 266136.i | 0.0959054 | − | 0.206534i | ||||
\(279\) | − | 230583.i | − | 0.177344i | ||||||
\(280\) | −688277. | + | 187977.i | −0.524648 | + | 0.143288i | ||||
\(281\) | − | 714854.i | − | 0.540072i | −0.962850 | − | 0.270036i | \(-0.912964\pi\) | ||
0.962850 | − | 0.270036i | \(-0.0870355\pi\) | |||||||
\(282\) | −42349.9 | − | 19665.5i | −0.0317125 | − | 0.0147259i | ||||
\(283\) | 893188. | + | 893188.i | 0.662944 | + | 0.662944i | 0.956073 | − | 0.293129i | \(-0.0946965\pi\) |
−0.293129 | + | 0.956073i | \(0.594696\pi\) | |||||||
\(284\) | −705312. | − | 835104.i | −0.518902 | − | 0.614391i | ||||
\(285\) | 1.17268e6 | − | 1.17268e6i | 0.855197 | − | 0.855197i | ||||
\(286\) | −1.08463e6 | − | 2.96520e6i | −0.784093 | − | 2.14358i | ||||
\(287\) | −205729. | −0.147432 | ||||||||
\(288\) | 111743. | + | 605308.i | 0.0793853 | + | 0.430026i | ||||
\(289\) | −1.09843e6 | −0.773617 | ||||||||
\(290\) | −560227. | − | 1.53156e6i | −0.391173 | − | 1.06940i | ||||
\(291\) | −2.06281e6 | + | 2.06281e6i | −1.42800 | + | 1.42800i | ||||
\(292\) | 1.59770e6 | + | 1.89171e6i | 1.09658 | + | 1.29837i | ||||
\(293\) | −723832. | − | 723832.i | −0.492571 | − | 0.492571i | 0.416544 | − | 0.909115i | \(-0.363241\pi\) |
−0.909115 | + | 0.416544i | \(0.863241\pi\) | |||||||
\(294\) | −517813. | − | 240450.i | −0.349385 | − | 0.162239i | ||||
\(295\) | − | 991347.i | − | 0.663240i | ||||||
\(296\) | −191687. | − | 701863.i | −0.127164 | − | 0.465611i | ||||
\(297\) | 1.47315e6i | 0.969069i | ||||||||
\(298\) | −824012. | + | 1.77452e6i | −0.537518 | + | 1.15755i | ||||
\(299\) | 574351. | + | 574351.i | 0.371535 | + | 0.371535i | ||||
\(300\) | 1.05064e6 | + | 88524.8i | 0.673986 | + | 0.0567887i | ||||
\(301\) | 85480.5 | − | 85480.5i | 0.0543815 | − | 0.0543815i | ||||
\(302\) | −946805. | + | 346329.i | −0.597369 | + | 0.218510i | ||||
\(303\) | 2.49970e6 | 1.56416 | ||||||||
\(304\) | 1.42521e6 | + | 2.00788e6i | 0.884495 | + | 1.24610i | ||||
\(305\) | 712967. | 0.438854 | ||||||||
\(306\) | −320058. | + | 117073.i | −0.195400 | + | 0.0714750i | ||||
\(307\) | 1.55592e6 | − | 1.55592e6i | 0.942196 | − | 0.942196i | −0.0562220 | − | 0.998418i | \(-0.517905\pi\) |
0.998418 | + | 0.0562220i | \(0.0179055\pi\) | |||||||
\(308\) | −165419. | + | 1.96324e6i | −0.0993593 | + | 1.17923i | ||||
\(309\) | −301120. | − | 301120.i | −0.179409 | − | 0.179409i | ||||
\(310\) | −190791. | + | 410871.i | −0.112759 | + | 0.242829i | ||||
\(311\) | 2.33899e6i | 1.37128i | 0.727940 | + | 0.685641i | \(0.240478\pi\) | ||||
−0.727940 | + | 0.685641i | \(0.759522\pi\) | |||||||
\(312\) | 1.62405e6 | − | 2.84444e6i | 0.944522 | − | 1.65429i | ||||
\(313\) | − | 1.40062e6i | − | 0.808088i | −0.914740 | − | 0.404044i | \(-0.867604\pi\) | ||
0.914740 | − | 0.404044i | \(-0.132396\pi\) | |||||||
\(314\) | 1.07744e6 | + | 500319.i | 0.616696 | + | 0.286367i | ||||
\(315\) | 296158. | + | 296158.i | 0.168169 | + | 0.168169i | ||||
\(316\) | 142855. | − | 120652.i | 0.0804779 | − | 0.0679700i | ||||
\(317\) | 1.93876e6 | − | 1.93876e6i | 1.08362 | − | 1.08362i | 0.0874473 | − | 0.996169i | \(-0.472129\pi\) |
0.996169 | − | 0.0874473i | \(-0.0278709\pi\) | |||||||
\(318\) | 210510. | + | 575497.i | 0.116736 | + | 0.319136i | ||||
\(319\) | −4.50328e6 | −2.47772 | ||||||||
\(320\) | 301735. | − | 1.17104e6i | 0.164722 | − | 0.639290i | ||||
\(321\) | 1.36640e6 | 0.740145 | ||||||||
\(322\) | −174117. | − | 476005.i | −0.0935838 | − | 0.255842i | ||||
\(323\) | −963976. | + | 963976.i | −0.514114 | + | 0.514114i | ||||
\(324\) | −1.79881e6 | + | 1.51924e6i | −0.951970 | + | 0.804014i | ||||
\(325\) | −1.20702e6 | − | 1.20702e6i | −0.633881 | − | 0.633881i | ||||
\(326\) | 1.38481e6 | + | 643045.i | 0.721681 | + | 0.335118i | ||||
\(327\) | − | 1.62119e6i | − | 0.838426i | ||||||
\(328\) | 172891. | − | 302811.i | 0.0887336 | − | 0.155413i | ||||
\(329\) | − | 47171.7i | − | 0.0240266i | ||||||
\(330\) | −947249. | + | 2.03992e6i | −0.478828 | + | 1.03116i | ||||
\(331\) | 1.75185e6 | + | 1.75185e6i | 0.878877 | + | 0.878877i | 0.993418 | − | 0.114542i | \(-0.0365400\pi\) |
−0.114542 | + | 0.993418i | \(0.536540\pi\) | |||||||
\(332\) | −84537.4 | + | 1.00332e6i | −0.0420924 | + | 0.499565i | ||||
\(333\) | −302004. | + | 302004.i | −0.149246 | + | 0.149246i | ||||
\(334\) | −560306. | + | 204953.i | −0.274827 | + | 0.100528i | ||||
\(335\) | 1.17483e6 | 0.571959 | ||||||||
\(336\) | −1.66669e6 | + | 1.18303e6i | −0.805392 | + | 0.571675i | ||||
\(337\) | 3.00166e6 | 1.43975 | 0.719875 | − | 0.694103i | \(-0.244199\pi\) | ||||
0.719875 | + | 0.694103i | \(0.244199\pi\) | |||||||
\(338\) | −3.00759e6 | + | 1.10014e6i | −1.43195 | + | 0.523788i | ||||
\(339\) | −1.42411e6 | + | 1.42411e6i | −0.673045 | + | 0.673045i | ||||
\(340\) | 667173. | + | 56214.7i | 0.312998 | + | 0.0263726i | ||||
\(341\) | 884537. | + | 884537.i | 0.411936 | + | 0.411936i | ||||
\(342\) | 608754. | − | 1.31096e6i | 0.281434 | − | 0.606073i | ||||
\(343\) | − | 2.37179e6i | − | 1.08853i | ||||||
\(344\) | 53981.8 | + | 197655.i | 0.0245952 | + | 0.0900556i | ||||
\(345\) | − | 578605.i | − | 0.261719i | ||||||
\(346\) | 795758. | + | 369516.i | 0.357348 | + | 0.165937i | ||||
\(347\) | −2.05281e6 | − | 2.05281e6i | −0.915217 | − | 0.915217i | 0.0814595 | − | 0.996677i | \(-0.474042\pi\) |
−0.996677 | + | 0.0814595i | \(0.974042\pi\) | |||||||
\(348\) | −3.01436e6 | − | 3.56907e6i | −1.33428 | − | 1.57982i | ||||
\(349\) | −2.68351e6 | + | 2.68351e6i | −1.17934 | + | 1.17934i | −0.199429 | + | 0.979912i | \(0.563909\pi\) |
−0.979912 | + | 0.199429i | \(0.936091\pi\) | |||||||
\(350\) | 365914. | + | 1.00035e6i | 0.159665 | + | 0.436496i | ||||
\(351\) | 2.47418e6 | 1.07192 | ||||||||
\(352\) | −2.75067e6 | − | 1.89335e6i | −1.18326 | − | 0.814470i | ||||
\(353\) | 843531. | 0.360300 | 0.180150 | − | 0.983639i | \(-0.442342\pi\) | ||||
0.180150 | + | 0.983639i | \(0.442342\pi\) | |||||||
\(354\) | −975564. | − | 2.66703e6i | −0.413759 | − | 1.13115i | ||||
\(355\) | 891405. | − | 891405.i | 0.375409 | − | 0.375409i | ||||
\(356\) | 864385. | + | 1.02345e6i | 0.361478 | + | 0.427998i | ||||
\(357\) | −800173. | − | 800173.i | −0.332287 | − | 0.332287i | ||||
\(358\) | 2.58129e6 | + | 1.19864e6i | 1.06446 | + | 0.494290i | ||||
\(359\) | − | 4.63130e6i | − | 1.89656i | −0.317431 | − | 0.948281i | \(-0.602820\pi\) | ||
0.317431 | − | 0.948281i | \(-0.397180\pi\) | |||||||
\(360\) | −684798. | + | 187026.i | −0.278488 | + | 0.0760583i | ||||
\(361\) | − | 3.30584e6i | − | 1.33510i | ||||||
\(362\) | 1.18670e6 | − | 2.55558e6i | 0.475960 | − | 1.02499i | ||||
\(363\) | 2.26334e6 | + | 2.26334e6i | 0.901538 | + | 0.901538i | ||||
\(364\) | 3.29731e6 | + | 277825.i | 1.30439 | + | 0.109905i | ||||
\(365\) | −2.01925e6 | + | 2.01925e6i | −0.793337 | + | 0.793337i | ||||
\(366\) | 1.91810e6 | − | 701616.i | 0.748460 | − | 0.273777i | ||||
\(367\) | −571010. | −0.221298 | −0.110649 | − | 0.993860i | \(-0.535293\pi\) | ||||
−0.110649 | + | 0.993860i | \(0.535293\pi\) | |||||||
\(368\) | 846953. | + | 143746.i | 0.326017 | + | 0.0553319i | ||||
\(369\) | −204689. | −0.0782580 | ||||||||
\(370\) | 788018. | − | 288247.i | 0.299249 | − | 0.109461i | ||||
\(371\) | −437749. | + | 437749.i | −0.165116 | + | 0.165116i | ||||
\(372\) | −108956. | + | 1.29312e6i | −0.0408219 | + | 0.484487i | ||||
\(373\) | −860043. | − | 860043.i | −0.320072 | − | 0.320072i | 0.528722 | − | 0.848795i | \(-0.322671\pi\) |
−0.848795 | + | 0.528722i | \(0.822671\pi\) | |||||||
\(374\) | 778667. | − | 1.67687e6i | 0.287854 | − | 0.619899i | ||||
\(375\) | 3.37126e6i | 1.23798i | ||||||||
\(376\) | 69431.6 | + | 39642.3i | 0.0253272 | + | 0.0144607i | ||||
\(377\) | 7.56335e6i | 2.74070i | ||||||||
\(378\) | −1.40029e6 | − | 650235.i | −0.504068 | − | 0.234067i | ||||
\(379\) | −2.07981e6 | − | 2.07981e6i | −0.743746 | − | 0.743746i | 0.229551 | − | 0.973297i | \(-0.426274\pi\) |
−0.973297 | + | 0.229551i | \(0.926274\pi\) | |||||||
\(380\) | −2.16945e6 | + | 1.83227e6i | −0.770709 | + | 0.650924i | ||||
\(381\) | −3.53403e6 | + | 3.53403e6i | −1.24726 | + | 1.24726i | ||||
\(382\) | 835595. | + | 2.28437e6i | 0.292980 | + | 0.800956i | ||||
\(383\) | −1.33201e6 | −0.463992 | −0.231996 | − | 0.972717i | \(-0.574526\pi\) | ||||
−0.231996 | + | 0.972717i | \(0.574526\pi\) | |||||||
\(384\) | −340639. | − | 3.44739e6i | −0.117887 | − | 1.19306i | ||||
\(385\) | −2.27217e6 | −0.781248 | ||||||||
\(386\) | −720315. | − | 1.96922e6i | −0.246067 | − | 0.672706i | ||||
\(387\) | 85048.5 | − | 85048.5i | 0.0288662 | − | 0.0288662i | ||||
\(388\) | 3.81620e6 | − | 3.22308e6i | 1.28692 | − | 1.08691i | ||||
\(389\) | 1.39805e6 | + | 1.39805e6i | 0.468433 | + | 0.468433i | 0.901407 | − | 0.432974i | \(-0.142536\pi\) |
−0.432974 | + | 0.901407i | \(0.642536\pi\) | |||||||
\(390\) | 3.42608e6 | + | 1.59093e6i | 1.14061 | + | 0.529649i | ||||
\(391\) | 475631.i | 0.157336i | ||||||||
\(392\) | 848941. | + | 484706.i | 0.279037 | + | 0.159317i | ||||
\(393\) | 248362.i | 0.0811154i | ||||||||
\(394\) | −2.27685e6 | + | 4.90323e6i | −0.738913 | + | 1.59126i | ||||
\(395\) | 152485. | + | 152485.i | 0.0491740 | + | 0.0491740i | ||||
\(396\) | −164583. | + | 1.95332e6i | −0.0527408 | + | 0.625944i | ||||
\(397\) | −140895. | + | 140895.i | −0.0448663 | + | 0.0448663i | −0.729184 | − | 0.684318i | \(-0.760100\pi\) |
0.684318 | + | 0.729184i | \(0.260100\pi\) | |||||||
\(398\) | −1.52040e6 | + | 556143.i | −0.481117 | + | 0.175986i | ||||
\(399\) | 4.79945e6 | 1.50924 | ||||||||
\(400\) | −1.77991e6 | − | 302088.i | −0.556221 | − | 0.0944025i | ||||
\(401\) | 3.14262e6 | 0.975957 | 0.487978 | − | 0.872856i | \(-0.337734\pi\) | ||||
0.487978 | + | 0.872856i | \(0.337734\pi\) | |||||||
\(402\) | 3.16067e6 | − | 1.15613e6i | 0.975469 | − | 0.356814i | ||||
\(403\) | 1.48560e6 | − | 1.48560e6i | 0.455658 | − | 0.455658i | ||||
\(404\) | −4.26507e6 | − | 359366.i | −1.30009 | − | 0.109543i | ||||
\(405\) | −1.92008e6 | − | 1.92008e6i | −0.581678 | − | 0.581678i | ||||
\(406\) | 1.98771e6 | − | 4.28057e6i | 0.598464 | − | 1.28880i | ||||
\(407\) | − | 2.31702e6i | − | 0.693336i | ||||||
\(408\) | 1.85022e6 | − | 505317.i | 0.550266 | − | 0.150284i | ||||
\(409\) | − | 1.50580e6i | − | 0.445101i | −0.974921 | − | 0.222550i | \(-0.928562\pi\) | ||
0.974921 | − | 0.222550i | \(-0.0714382\pi\) | |||||||
\(410\) | 364730. | + | 169365.i | 0.107155 | + | 0.0497582i | ||||
\(411\) | −389759. | − | 389759.i | −0.113813 | − | 0.113813i | ||||
\(412\) | 470490. | + | 557071.i | 0.136555 | + | 0.161684i | ||||
\(413\) | 2.02866e6 | − | 2.02866e6i | 0.585240 | − | 0.585240i | ||||
\(414\) | −173237. | − | 473599.i | −0.0496751 | − | 0.135803i | ||||
\(415\) | −1.16119e6 | −0.330967 | ||||||||
\(416\) | −3.17993e6 | + | 4.61980e6i | −0.900915 | + | 1.30885i | ||||
\(417\) | 969402. | 0.273001 | ||||||||
\(418\) | 2.69372e6 | + | 7.36419e6i | 0.754072 | + | 2.06150i | ||||
\(419\) | −3.16326e6 | + | 3.16326e6i | −0.880237 | + | 0.880237i | −0.993558 | − | 0.113321i | \(-0.963851\pi\) |
0.113321 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(420\) | −1.52092e6 | − | 1.80081e6i | −0.420711 | − | 0.498131i | ||||
\(421\) | 3.78619e6 | + | 3.78619e6i | 1.04111 | + | 1.04111i | 0.999118 | + | 0.0419924i | \(0.0133705\pi\) |
0.0419924 | + | 0.999118i | \(0.486629\pi\) | |||||||
\(422\) | −5.98342e6 | − | 2.77844e6i | −1.63557 | − | 0.759488i | ||||
\(423\) | − | 46933.2i | − | 0.0127535i | ||||||
\(424\) | −276443. | − | 1.01220e6i | −0.0746776 | − | 0.273432i | ||||
\(425\) | − | 999559.i | − | 0.268433i | ||||||
\(426\) | 1.52094e6 | − | 3.27537e6i | 0.406058 | − | 0.874452i | ||||
\(427\) | 1.45899e6 | + | 1.45899e6i | 0.387243 | + | 0.387243i | ||||
\(428\) | −2.33140e6 | − | 196439.i | −0.615188 | − | 0.0518345i | ||||
\(429\) | 7.37579e6 | − | 7.37579e6i | 1.93493 | − | 1.93493i | ||||
\(430\) | −221917. | + | 81174.4i | −0.0578788 | + | 0.0211713i | ||||
\(431\) | −4.50282e6 | −1.16759 | −0.583797 | − | 0.811900i | \(-0.698433\pi\) | ||||
−0.583797 | + | 0.811900i | \(0.698433\pi\) | |||||||
\(432\) | 2.13386e6 | − | 1.51463e6i | 0.550118 | − | 0.390479i | ||||
\(433\) | −5.69963e6 | −1.46092 | −0.730460 | − | 0.682955i | \(-0.760694\pi\) | ||||
−0.730460 | + | 0.682955i | \(0.760694\pi\) | |||||||
\(434\) | −1.23122e6 | + | 450364.i | −0.313770 | + | 0.114773i | ||||
\(435\) | 3.80969e6 | − | 3.80969e6i | 0.965308 | − | 0.965308i | ||||
\(436\) | −233069. | + | 2.76613e6i | −0.0587175 | + | 0.696877i | ||||
\(437\) | −1.42642e6 | − | 1.42642e6i | −0.357309 | − | 0.357309i | ||||
\(438\) | −3.44529e6 | + | 7.41950e6i | −0.858106 | + | 1.84795i | ||||
\(439\) | 316832.i | 0.0784634i | 0.999230 | + | 0.0392317i | \(0.0124911\pi\) | ||||
−0.999230 | + | 0.0392317i | \(0.987509\pi\) | |||||||
\(440\) | 1.90949e6 | − | 3.34439e6i | 0.470204 | − | 0.823541i | ||||
\(441\) | − | 573853.i | − | 0.140509i | ||||||
\(442\) | −2.81634e6 | − | 1.30779e6i | −0.685693 | − | 0.318406i | ||||
\(443\) | −797467. | − | 797467.i | −0.193065 | − | 0.193065i | 0.603954 | − | 0.797019i | \(-0.293591\pi\) |
−0.797019 | + | 0.603954i | \(0.793591\pi\) | |||||||
\(444\) | 1.83635e6 | − | 1.55095e6i | 0.442078 | − | 0.373370i | ||||
\(445\) | −1.09245e6 | + | 1.09245e6i | −0.261518 | + | 0.261518i | ||||
\(446\) | −264789. | − | 723887.i | −0.0630322 | − | 0.172319i | ||||
\(447\) | −6.46372e6 | −1.53008 | ||||||||
\(448\) | 3.01384e6 | − | 1.77892e6i | 0.709456 | − | 0.418756i | ||||
\(449\) | −625844. | −0.146504 | −0.0732521 | − | 0.997313i | \(-0.523338\pi\) | ||||
−0.0732521 | + | 0.997313i | \(0.523338\pi\) | |||||||
\(450\) | 364064. | + | 995289.i | 0.0847513 | + | 0.231696i | ||||
\(451\) | 785204. | − | 785204.i | 0.181778 | − | 0.181778i | ||||
\(452\) | 2.63460e6 | − | 2.22513e6i | 0.606552 | − | 0.512282i | ||||
\(453\) | −2.35513e6 | − | 2.35513e6i | −0.539224 | − | 0.539224i | ||||
\(454\) | −3.08862e6 | − | 1.43422e6i | −0.703274 | − | 0.326570i | ||||
\(455\) | 3.81616e6i | 0.864167i | ||||||||
\(456\) | −4.03338e6 | + | 7.06428e6i | −0.908357 | + | 1.59095i | ||||
\(457\) | − | 3.95584e6i | − | 0.886030i | −0.896514 | − | 0.443015i | \(-0.853909\pi\) | ||
0.896514 | − | 0.443015i | \(-0.146091\pi\) | |||||||
\(458\) | 1.94312e6 | − | 4.18454e6i | 0.432849 | − | 0.932147i | ||||
\(459\) | 1.02446e6 | + | 1.02446e6i | 0.226967 | + | 0.226967i | ||||
\(460\) | −83182.5 | + | 987235.i | −0.0183289 | + | 0.217533i | ||||
\(461\) | 3.75163e6 | − | 3.75163e6i | 0.822182 | − | 0.822182i | −0.164238 | − | 0.986421i | \(-0.552517\pi\) |
0.986421 | + | 0.164238i | \(0.0525166\pi\) | |||||||
\(462\) | −6.11283e6 | + | 2.23600e6i | −1.33241 | + | 0.487378i | ||||
\(463\) | 6.65021e6 | 1.44173 | 0.720864 | − | 0.693077i | \(-0.243745\pi\) | ||||
0.720864 | + | 0.693077i | \(0.243745\pi\) | |||||||
\(464\) | 4.63010e6 | + | 6.52302e6i | 0.998379 | + | 1.40654i | ||||
\(465\) | −1.49660e6 | −0.320977 | ||||||||
\(466\) | 2.99182e6 | − | 1.09437e6i | 0.638221 | − | 0.233453i | ||||
\(467\) | −2.08935e6 | + | 2.08935e6i | −0.443322 | + | 0.443322i | −0.893127 | − | 0.449805i | \(-0.851494\pi\) |
0.449805 | + | 0.893127i | \(0.351494\pi\) | |||||||
\(468\) | 3.28064e6 | + | 276420.i | 0.692379 | + | 0.0583385i | ||||
\(469\) | 2.40414e6 | + | 2.40414e6i | 0.504694 | + | 0.504694i | ||||
\(470\) | −38833.8 | + | 83629.2i | −0.00810896 | + | 0.0174628i | ||||
\(471\) | 3.92461e6i | 0.815162i | ||||||||
\(472\) | 1.28112e6 | + | 4.69082e6i | 0.264688 | + | 0.969155i | ||||
\(473\) | 652506.i | 0.134101i | ||||||||
\(474\) | 560290. | + | 260175.i | 0.114543 | + | 0.0531887i | ||||
\(475\) | 2.99769e6 | + | 2.99769e6i | 0.609610 | + | 0.609610i | ||||
\(476\) | 1.25024e6 | + | 1.48032e6i | 0.252917 | + | 0.299459i | ||||
\(477\) | −435536. | + | 435536.i | −0.0876452 | + | 0.0876452i | ||||
\(478\) | −2.38039e6 | − | 6.50757e6i | −0.476516 | − | 1.30271i | ||||
\(479\) | 6.97076e6 | 1.38817 | 0.694083 | − | 0.719895i | \(-0.255810\pi\) | ||||
0.694083 | + | 0.719895i | \(0.255810\pi\) | |||||||
\(480\) | 3.92875e6 | − | 725269.i | 0.778308 | − | 0.143680i | ||||
\(481\) | −3.89148e6 | −0.766925 | ||||||||
\(482\) | −209398. | − | 572459.i | −0.0410540 | − | 0.112235i | ||||
\(483\) | 1.18404e6 | − | 1.18404e6i | 0.230939 | − | 0.230939i | ||||
\(484\) | −3.53640e6 | − | 4.18718e6i | −0.686196 | − | 0.812471i | ||||
\(485\) | 4.07348e6 | + | 4.07348e6i | 0.786341 | + | 0.786341i | ||||
\(486\) | −3.86912e6 | − | 1.79665e6i | −0.743057 | − | 0.345044i | ||||
\(487\) | 5.01220e6i | 0.957648i | 0.877911 | + | 0.478824i | \(0.158937\pi\) | ||||
−0.877911 | + | 0.478824i | \(0.841063\pi\) | |||||||
\(488\) | −3.37359e6 | + | 921367.i | −0.641273 | + | 0.175139i | ||||
\(489\) | 5.04418e6i | 0.953933i | ||||||||
\(490\) | −474821. | + | 1.02253e6i | −0.0893387 | + | 0.192392i | ||||
\(491\) | −6.26073e6 | − | 6.26073e6i | −1.17198 | − | 1.17198i | −0.981737 | − | 0.190245i | \(-0.939072\pi\) |
−0.190245 | − | 0.981737i | \(-0.560928\pi\) | |||||||
\(492\) | 1.14791e6 | + | 96720.2i | 0.213793 | + | 0.0180138i | ||||
\(493\) | −3.13168e6 | + | 3.13168e6i | −0.580309 | + | 0.580309i | ||||
\(494\) | 1.23683e7 | − | 4.52417e6i | 2.28030 | − | 0.834106i | ||||
\(495\) | −2.26069e6 | −0.414693 | ||||||||
\(496\) | 371808. | − | 2.19070e6i | 0.0678601 | − | 0.399833i | ||||
\(497\) | 3.64828e6 | 0.662517 | ||||||||
\(498\) | −3.12396e6 | + | 1.14271e6i | −0.564459 | + | 0.206472i | ||||
\(499\) | −47597.3 | + | 47597.3i | −0.00855718 | + | 0.00855718i | −0.711372 | − | 0.702815i | \(-0.751926\pi\) |
0.702815 | + | 0.711372i | \(0.251926\pi\) | |||||||
\(500\) | 484665. | − | 5.75215e6i | 0.0866995 | − | 1.02898i | ||||
\(501\) | −1.39373e6 | − | 1.39373e6i | −0.248076 | − | 0.248076i | ||||
\(502\) | −3.12396e6 | + | 6.72750e6i | −0.553282 | + | 1.19150i | ||||
\(503\) | 6.56568e6i | 1.15707i | 0.815657 | + | 0.578535i | \(0.196375\pi\) | ||||
−0.815657 | + | 0.578535i | \(0.803625\pi\) | |||||||
\(504\) | −1.78407e6 | − | 1.01862e6i | −0.312850 | − | 0.178623i | ||||
\(505\) | − | 4.93620e6i | − | 0.861319i | ||||||
\(506\) | 2.48132e6 | + | 1.15222e6i | 0.430830 | + | 0.200059i | ||||
\(507\) | −7.48122e6 | − | 7.48122e6i | −1.29257 | − | 1.29257i | ||||
\(508\) | 6.53793e6 | − | 5.52180e6i | 1.12404 | − | 0.949340i | ||||
\(509\) | −438674. | + | 438674.i | −0.0750494 | + | 0.0750494i | −0.743635 | − | 0.668586i | \(-0.766900\pi\) |
0.668586 | + | 0.743635i | \(0.266900\pi\) | |||||||
\(510\) | 759864. | + | 2.07734e6i | 0.129363 | + | 0.353657i | ||||
\(511\) | −8.26424e6 | −1.40007 | ||||||||
\(512\) | 85598.9 | + | 5.93102e6i | 0.0144309 | + | 0.999896i | ||||
\(513\) | −6.14471e6 | −1.03088 | ||||||||
\(514\) | −1.51927e6 | − | 4.15343e6i | −0.253646 | − | 0.693425i | ||||
\(515\) | −594627. | + | 594627.i | −0.0987931 | + | 0.0987931i | ||||
\(516\) | −517143. | + | 436768.i | −0.0855040 | + | 0.0722149i | ||||
\(517\) | 180040. | + | 180040.i | 0.0296239 | + | 0.0296239i | ||||
\(518\) | 2.20243e6 | + | 1.02271e6i | 0.360644 | + | 0.167467i | ||||
\(519\) | 2.89856e6i | 0.472350i | ||||||||
\(520\) | −5.61697e6 | − | 3.20703e6i | −0.910949 | − | 0.520110i | ||||
\(521\) | − | 4.68841e6i | − | 0.756713i | −0.925660 | − | 0.378357i | \(-0.876489\pi\) | ||
0.925660 | − | 0.378357i | \(-0.123511\pi\) | |||||||
\(522\) | 1.97766e6 | − | 4.25893e6i | 0.317670 | − | 0.684108i | ||||
\(523\) | 248034. | + | 248034.i | 0.0396513 | + | 0.0396513i | 0.726654 | − | 0.687003i | \(-0.241074\pi\) |
−0.687003 | + | 0.726654i | \(0.741074\pi\) | |||||||
\(524\) | 35705.4 | − | 423763.i | 0.00568075 | − | 0.0674209i | ||||
\(525\) | −2.48831e6 | + | 2.48831e6i | −0.394009 | + | 0.394009i | ||||
\(526\) | 4.63149e6 | − | 1.69414e6i | 0.729889 | − | 0.266984i | ||||
\(527\) | 1.23025e6 | 0.192960 | ||||||||
\(528\) | 1.84597e6 | − | 1.08765e7i | 0.288165 | − | 1.69787i | ||||
\(529\) | 5.73254e6 | 0.890651 | ||||||||
\(530\) | 1.13644e6 | − | 415697.i | 0.175735 | − | 0.0642817i | ||||
\(531\) | 2.01840e6 | − | 2.01840e6i | 0.310650 | − | 0.310650i | ||||
\(532\) | −8.18898e6 | − | 689987.i | −1.25444 | − | 0.105697i | ||||
\(533\) | −1.31877e6 | − | 1.31877e6i | −0.201071 | − | 0.201071i | ||||
\(534\) | −1.86396e6 | + | 4.01408e6i | −0.282868 | + | 0.609162i | ||||
\(535\) | − | 2.69826e6i | − | 0.407568i | ||||||
\(536\) | −5.55904e6 | + | 1.51824e6i | −0.835772 | + | 0.228259i | ||||
\(537\) | 9.40239e6i | 1.40703i | ||||||||
\(538\) | 2.83408e6 | + | 1.31603e6i | 0.422140 | + | 0.196024i | ||||
\(539\) | 2.20135e6 | + | 2.20135e6i | 0.326375 | + | 0.326375i | ||||
\(540\) | 1.94723e6 | + | 2.30556e6i | 0.287364 | + | 0.340246i | ||||
\(541\) | 4.85712e6 | − | 4.85712e6i | 0.713486 | − | 0.713486i | −0.253777 | − | 0.967263i | \(-0.581673\pi\) |
0.967263 | + | 0.253777i | \(0.0816730\pi\) | |||||||
\(542\) | 1.93997e6 | + | 5.30354e6i | 0.283659 | + | 0.775475i | ||||
\(543\) | 9.30874e6 | 1.35485 | ||||||||
\(544\) | −3.22955e6 | + | 596193.i | −0.467891 | + | 0.0863753i | ||||
\(545\) | −3.20140e6 | −0.461687 | ||||||||
\(546\) | 3.75540e6 | + | 1.02666e7i | 0.539107 | + | 1.47383i | ||||
\(547\) | −410716. | + | 410716.i | −0.0586912 | + | 0.0586912i | −0.735843 | − | 0.677152i | \(-0.763214\pi\) |
0.677152 | + | 0.735843i | \(0.263214\pi\) | |||||||
\(548\) | 608986. | + | 721053.i | 0.0866276 | + | 0.102569i | ||||
\(549\) | 1.45162e6 | + | 1.45162e6i | 0.205552 | + | 0.205552i | ||||
\(550\) | −5.21459e6 | − | 2.42143e6i | −0.735044 | − | 0.341323i | ||||
\(551\) | − | 1.87839e7i | − | 2.63576i | ||||||
\(552\) | 747732. | + | 2.73782e6i | 0.104447 | + | 0.382435i | ||||
\(553\) | 624082.i | 0.0867818i | ||||||||
\(554\) | 1.24784e6 | − | 2.68724e6i | 0.172737 | − | 0.371991i | ||||
\(555\) | 1.96015e6 | + | 1.96015e6i | 0.270121 | + | 0.270121i | ||||
\(556\) | −1.65403e6 | − | 139365.i | −0.226911 | − | 0.0191191i | ||||
\(557\) | −2.02585e6 | + | 2.02585e6i | −0.276675 | + | 0.276675i | −0.831780 | − | 0.555105i | \(-0.812678\pi\) |
0.555105 | + | 0.831780i | \(0.312678\pi\) | |||||||
\(558\) | −1.22500e6 | + | 448088.i | −0.166552 | + | 0.0609225i | ||||
\(559\) | 1.09590e6 | 0.148334 | ||||||||
\(560\) | 2.33616e6 | + | 3.29125e6i | 0.314798 | + | 0.443497i | ||||
\(561\) | 6.10803e6 | 0.819396 | ||||||||
\(562\) | −3.79773e6 | + | 1.38916e6i | −0.507204 | + | 0.185529i | ||||
\(563\) | 1.54578e6 | − | 1.54578e6i | 0.205530 | − | 0.205530i | −0.596834 | − | 0.802365i | \(-0.703575\pi\) |
0.802365 | + | 0.596834i | \(0.203575\pi\) | |||||||
\(564\) | −22177.0 | + | 263204.i | −0.00293566 | + | 0.0348413i | ||||
\(565\) | 2.81222e6 | + | 2.81222e6i | 0.370619 | + | 0.370619i | ||||
\(566\) | 3.00943e6 | − | 6.48086e6i | 0.394861 | − | 0.850338i | ||||
\(567\) | − | 7.85838e6i | − | 1.02654i | ||||||
\(568\) | −3.06595e6 | + | 5.36988e6i | −0.398745 | + | 0.698383i | ||||
\(569\) | − | 176266.i | − | 0.0228238i | −0.999935 | − | 0.0114119i | \(-0.996367\pi\) | ||
0.999935 | − | 0.0114119i | \(-0.00363261\pi\) | |||||||
\(570\) | −8.50880e6 | − | 3.95112e6i | −1.09694 | − | 0.509370i | ||||
\(571\) | 8.32418e6 | + | 8.32418e6i | 1.06844 | + | 1.06844i | 0.997479 | + | 0.0709630i | \(0.0226072\pi\) |
0.0709630 | + | 0.997479i | \(0.477393\pi\) | |||||||
\(572\) | −1.36452e7 | + | 1.15244e7i | −1.74377 | + | 1.47275i | ||||
\(573\) | −5.68226e6 | + | 5.68226e6i | −0.722994 | + | 0.722994i | ||||
\(574\) | 399789. | + | 1.09295e6i | 0.0506467 | + | 0.138459i | ||||
\(575\) | 1.47908e6 | 0.186561 | ||||||||
\(576\) | 2.99861e6 | − | 1.76993e6i | 0.376585 | − | 0.222280i | ||||
\(577\) | 1.72294e6 | 0.215442 | 0.107721 | − | 0.994181i | \(-0.465645\pi\) | ||||
0.107721 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(578\) | 2.13455e6 | + | 5.83549e6i | 0.265758 | + | 0.726537i | ||||
\(579\) | 4.89833e6 | − | 4.89833e6i | 0.607227 | − | 0.607227i | ||||
\(580\) | −7.04790e6 | + | 5.95251e6i | −0.869941 | + | 0.734735i | ||||
\(581\) | −2.37623e6 | − | 2.37623e6i | −0.292043 | − | 0.292043i | ||||
\(582\) | 1.49675e7 | + | 6.95027e6i | 1.83165 | + | 0.850539i | ||||
\(583\) | − | 3.34150e6i | − | 0.407165i | ||||||
\(584\) | 6.94513e6 | − | 1.21641e7i | 0.842652 | − | 1.47587i | ||||
\(585\) | 3.79687e6i | 0.458707i | ||||||||
\(586\) | −2.43882e6 | + | 5.25204e6i | −0.293384 | + | 0.631806i | ||||
\(587\) | 514428. | + | 514428.i | 0.0616211 | + | 0.0616211i | 0.737246 | − | 0.675625i | \(-0.236126\pi\) |
−0.675625 | + | 0.737246i | \(0.736126\pi\) | |||||||
\(588\) | −271158. | + | 3.21819e6i | −0.0323430 | + | 0.383856i | ||||
\(589\) | −3.68954e6 | + | 3.68954e6i | −0.438211 | + | 0.438211i | ||||
\(590\) | −5.26662e6 | + | 1.92646e6i | −0.622877 | + | 0.227840i | ||||
\(591\) | −1.78601e7 | −2.10336 | ||||||||
\(592\) | −3.35621e6 | + | 2.38227e6i | −0.393591 | + | 0.279375i | ||||
\(593\) | −8.60704e6 | −1.00512 | −0.502559 | − | 0.864543i | \(-0.667608\pi\) | ||||
−0.502559 | + | 0.864543i | \(0.667608\pi\) | |||||||
\(594\) | 7.82623e6 | − | 2.86273e6i | 0.910094 | − | 0.332901i | ||||
\(595\) | −1.58012e6 | + | 1.58012e6i | −0.182977 | + | 0.182977i | ||||
\(596\) | 1.10286e7 | + | 929249.i | 1.27176 | + | 0.107156i | ||||
\(597\) | −3.78192e6 | − | 3.78192e6i | −0.434287 | − | 0.434287i | ||||
\(598\) | 1.93517e6 | − | 4.16742e6i | 0.221292 | − | 0.476556i | ||||
\(599\) | − | 1.71814e6i | − | 0.195655i | −0.995203 | − | 0.0978276i | \(-0.968811\pi\) | ||
0.995203 | − | 0.0978276i | \(-0.0311894\pi\) | |||||||
\(600\) | −1.57139e6 | − | 5.75365e6i | −0.178199 | − | 0.652477i | ||||
\(601\) | 5.25547e6i | 0.593506i | 0.954954 | + | 0.296753i | \(0.0959038\pi\) | ||||
−0.954954 | + | 0.296753i | \(0.904096\pi\) | |||||||
\(602\) | −620236. | − | 288011.i | −0.0697535 | − | 0.0323905i | ||||
\(603\) | 2.39199e6 | + | 2.39199e6i | 0.267896 | + | 0.267896i | ||||
\(604\) | 3.67981e6 | + | 4.35698e6i | 0.410424 | + | 0.485951i | ||||
\(605\) | 4.46947e6 | − | 4.46947e6i | 0.496441 | − | 0.496441i | ||||
\(606\) | −4.85761e6 | − | 1.32799e7i | −0.537330 | − | 1.46897i | ||||
\(607\) | 9.34712e6 | 1.02969 | 0.514845 | − | 0.857283i | \(-0.327850\pi\) | ||||
0.514845 | + | 0.857283i | \(0.327850\pi\) | |||||||
\(608\) | 7.89746e6 | − | 1.14734e7i | 0.866421 | − | 1.25874i | ||||
\(609\) | 1.55920e7 | 1.70357 | ||||||||
\(610\) | −1.38549e6 | − | 3.78771e6i | −0.150758 | − | 0.412147i | ||||
\(611\) | 302381. | − | 302381.i | 0.0327681 | − | 0.0327681i | ||||
\(612\) | 1.24393e6 | + | 1.47283e6i | 0.134250 | + | 0.158955i | ||||
\(613\) | −8.58082e6 | − | 8.58082e6i | −0.922312 | − | 0.922312i | 0.0748805 | − | 0.997193i | \(-0.476142\pi\) |
−0.997193 | + | 0.0748805i | \(0.976142\pi\) | |||||||
\(614\) | −1.12896e7 | − | 5.24239e6i | −1.20853 | − | 0.561188i | ||||
\(615\) | 1.32854e6i | 0.141640i | ||||||||
\(616\) | 1.07514e7 | − | 2.93632e6i | 1.14159 | − | 0.311783i | ||||
\(617\) | − | 809357.i | − | 0.0855908i | −0.999084 | − | 0.0427954i | \(-0.986374\pi\) | ||
0.999084 | − | 0.0427954i | \(-0.0136264\pi\) | |||||||
\(618\) | −1.01457e6 | + | 2.18489e6i | −0.106859 | + | 0.230122i | ||||
\(619\) | −2.53658e6 | − | 2.53658e6i | −0.266086 | − | 0.266086i | 0.561435 | − | 0.827521i | \(-0.310250\pi\) |
−0.827521 | + | 0.561435i | \(0.810250\pi\) | |||||||
\(620\) | 2.55355e6 | + | 215157.i | 0.266787 | + | 0.0224790i | ||||
\(621\) | −1.51592e6 | + | 1.51592e6i | −0.157742 | + | 0.157742i | ||||
\(622\) | 1.24261e7 | − | 4.54530e6i | 1.28783 | − | 0.471072i | ||||
\(623\) | −4.47110e6 | −0.461524 | ||||||||
\(624\) | −1.82674e7 | − | 3.10035e6i | −1.87808 | − | 0.318750i | ||||
\(625\) | 1.14776e6 | 0.117530 | ||||||||
\(626\) | −7.44091e6 | + | 2.72179e6i | −0.758910 | + | 0.277599i | ||||
\(627\) | −1.83180e7 | + | 1.83180e7i | −1.86084 | + | 1.86084i | ||||
\(628\) | 564216. | − | 6.69629e6i | 0.0570882 | − | 0.677540i | ||||
\(629\) | −1.61131e6 | − | 1.61131e6i | −0.162387 | − | 0.162387i | ||||
\(630\) | 997849. | − | 2.14888e6i | 0.100164 | − | 0.215706i | ||||
\(631\) | 41444.9i | 0.00414379i | 0.999998 | + | 0.00207190i | \(0.000659505\pi\) | ||||
−0.999998 | + | 0.00207190i | \(0.999340\pi\) | |||||||
\(632\) | −918582. | − | 524468.i | −0.0914798 | − | 0.0522308i | ||||
\(633\) | − | 2.17947e7i | − | 2.16193i | ||||||
\(634\) | −1.40674e7 | − | 6.53229e6i | −1.38992 | − | 0.645420i | ||||
\(635\) | 6.97870e6 | + | 6.97870e6i | 0.686816 | + | 0.686816i | ||||
\(636\) | 2.64831e6 | − | 2.23670e6i | 0.259612 | − | 0.219263i | ||||
\(637\) | 3.69721e6 | − | 3.69721e6i | 0.361015 | − | 0.361015i | ||||
\(638\) | 8.75113e6 | + | 2.39241e7i | 0.851162 | + | 2.32693i | ||||
\(639\) | 3.62984e6 | 0.351670 | ||||||||
\(640\) | −6.80763e6 | + | 672666.i | −0.656971 | + | 0.0649156i | ||||
\(641\) | 6.97921e6 | 0.670905 | 0.335453 | − | 0.942057i | \(-0.391111\pi\) | ||||
0.335453 | + | 0.942057i | \(0.391111\pi\) | |||||||
\(642\) | −2.65531e6 | − | 7.25915e6i | −0.254259 | − | 0.695102i | ||||
\(643\) | −8.89601e6 | + | 8.89601e6i | −0.848531 | + | 0.848531i | −0.989950 | − | 0.141419i | \(-0.954834\pi\) |
0.141419 | + | 0.989950i | \(0.454834\pi\) | |||||||
\(644\) | −2.19047e6 | + | 1.85002e6i | −0.208124 | + | 0.175777i | ||||
\(645\) | −552007. | − | 552007.i | −0.0522451 | − | 0.0522451i | ||||
\(646\) | 6.99449e6 | + | 3.24794e6i | 0.659439 | + | 0.306215i | ||||
\(647\) | 1.63883e7i | 1.53913i | 0.638571 | + | 0.769563i | \(0.279526\pi\) | ||||
−0.638571 | + | 0.769563i | \(0.720474\pi\) | |||||||
\(648\) | 1.15667e7 | + | 6.60405e6i | 1.08211 | + | 0.617836i | ||||
\(649\) | 1.54855e7i | 1.44316i | ||||||||
\(650\) | −4.06684e6 | + | 8.75801e6i | −0.377550 | + | 0.813059i | ||||
\(651\) | −3.06259e6 | − | 3.06259e6i | −0.283229 | − | 0.283229i | ||||
\(652\) | 725170. | − | 8.60653e6i | 0.0668068 | − | 0.792883i | ||||
\(653\) | −5.42938e6 | + | 5.42938e6i | −0.498273 | + | 0.498273i | −0.910900 | − | 0.412627i | \(-0.864611\pi\) |
0.412627 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(654\) | −8.61273e6 | + | 3.15043e6i | −0.787402 | + | 0.288022i | ||||
\(655\) | 490444. | 0.0446670 | ||||||||
\(656\) | −1.94469e6 | − | 330054.i | −0.176437 | − | 0.0299451i | ||||
\(657\) | −8.22247e6 | −0.743171 | ||||||||
\(658\) | −250604. | + | 91667.7i | −0.0225644 | + | 0.00825376i | ||||
\(659\) | 57265.3 | − | 57265.3i | 0.00513663 | − | 0.00513663i | −0.704534 | − | 0.709670i | \(-0.748844\pi\) |
0.709670 | + | 0.704534i | \(0.248844\pi\) | |||||||
\(660\) | 1.26780e7 | + | 1.06822e6i | 1.13290 | + | 0.0954559i | ||||
\(661\) | 1.17817e7 | + | 1.17817e7i | 1.04883 | + | 1.04883i | 0.998745 | + | 0.0500855i | \(0.0159494\pi\) |
0.0500855 | + | 0.998745i | \(0.484051\pi\) | |||||||
\(662\) | 5.90255e6 | − | 1.27112e7i | 0.523473 | − | 1.12731i | ||||
\(663\) | − | 1.02586e7i | − | 0.906364i | ||||||
\(664\) | 5.49449e6 | − | 1.50061e6i | 0.483623 | − | 0.132083i | ||||
\(665\) | − | 9.47756e6i | − | 0.831079i | ||||||
\(666\) | 2.19130e6 | + | 1.01755e6i | 0.191433 | + | 0.0888931i | ||||
\(667\) | −4.63403e6 | − | 4.63403e6i | −0.403315 | − | 0.403315i | ||||
\(668\) | 2.17766e6 | + | 2.57840e6i | 0.188821 | + | 0.223568i | ||||
\(669\) | 1.80063e6 | − | 1.80063e6i | 0.155546 | − | 0.155546i | ||||
\(670\) | −2.28303e6 | − | 6.24142e6i | −0.196483 | − | 0.537151i | ||||
\(671\) | −1.11370e7 | −0.954913 | ||||||||
\(672\) | 9.52383e6 | + | 6.55549e6i | 0.813558 | + | 0.559993i | ||||
\(673\) | 1.62313e7 | 1.38139 | 0.690696 | − | 0.723146i | \(-0.257304\pi\) | ||||
0.690696 | + | 0.723146i | \(0.257304\pi\) | |||||||
\(674\) | −5.83307e6 | − | 1.59466e7i | −0.494593 | − | 1.35213i | ||||
\(675\) | 3.18577e6 | − | 3.18577e6i | 0.269125 | − | 0.269125i | ||||
\(676\) | 1.16892e7 | + | 1.38402e7i | 0.983823 | + | 1.16487i | ||||
\(677\) | −1.97754e6 | − | 1.97754e6i | −0.165827 | − | 0.165827i | 0.619316 | − | 0.785142i | \(-0.287410\pi\) |
−0.785142 | + | 0.619316i | \(0.787410\pi\) | |||||||
\(678\) | 1.03332e7 | + | 4.79828e6i | 0.863295 | + | 0.400877i | ||||
\(679\) | 1.66716e7i | 1.38773i | ||||||||
\(680\) | −997858. | − | 3.65366e6i | −0.0827554 | − | 0.303009i | ||||
\(681\) | − | 1.12503e7i | − | 0.929603i | ||||||
\(682\) | 2.98028e6 | − | 6.41809e6i | 0.245356 | − | 0.528378i | ||||
\(683\) | 1.27340e6 | + | 1.27340e6i | 0.104451 | + | 0.104451i | 0.757401 | − | 0.652950i | \(-0.226469\pi\) |
−0.652950 | + | 0.757401i | \(0.726469\pi\) | |||||||
\(684\) | −8.14759e6 | − | 686500.i | −0.665869 | − | 0.0561048i | ||||
\(685\) | −769664. | + | 769664.i | −0.0626722 | + | 0.0626722i | ||||
\(686\) | −1.26003e7 | + | 4.60905e6i | −1.02229 | + | 0.373939i | ||||
\(687\) | 1.52422e7 | 1.23213 | ||||||||
\(688\) | 945157. | − | 670881.i | 0.0761260 | − | 0.0540349i | ||||
\(689\) | −5.61213e6 | −0.450380 | ||||||||
\(690\) | −3.07390e6 | + | 1.12439e6i | −0.245791 | + | 0.0899073i | ||||
\(691\) | 1.00075e7 | − | 1.00075e7i | 0.797313 | − | 0.797313i | −0.185358 | − | 0.982671i | \(-0.559344\pi\) |
0.982671 | + | 0.185358i | \(0.0593445\pi\) | |||||||
\(692\) | 416708. | − | 4.94561e6i | 0.0330801 | − | 0.392604i | ||||
\(693\) | −4.62619e6 | − | 4.62619e6i | −0.365923 | − | 0.365923i | ||||
\(694\) | −6.91655e6 | + | 1.48949e7i | −0.545118 | + | 1.17392i | ||||
\(695\) | − | 1.91430e6i | − | 0.150330i | ||||||
\(696\) | −1.31033e7 | + | 2.29498e7i | −1.02531 | + | 1.79579i | ||||
\(697\) | − | 1.09210e6i | − | 0.0851488i | ||||||
\(698\) | 1.94712e7 | + | 9.04159e6i | 1.51270 | + | 0.702435i | ||||
\(699\) | 7.44200e6 | + | 7.44200e6i | 0.576099 | + | 0.576099i | ||||
\(700\) | 4.60336e6 | − | 3.88790e6i | 0.355083 | − | 0.299896i | ||||
\(701\) | −1.69368e7 | + | 1.69368e7i | −1.30178 | + | 1.30178i | −0.374586 | + | 0.927192i | \(0.622215\pi\) |
−0.927192 | + | 0.374586i | \(0.877785\pi\) | |||||||
\(702\) | −4.80802e6 | − | 1.31443e7i | −0.368234 | − | 1.00669i | ||||
\(703\) | 9.66464e6 | 0.737560 | ||||||||
\(704\) | −4.71331e6 | + | 1.82925e7i | −0.358422 | + | 1.39105i | ||||
\(705\) | −304620. | −0.0230827 | ||||||||
\(706\) | −1.63922e6 | − | 4.48134e6i | −0.123773 | − | 0.338373i | ||||
\(707\) | 1.01013e7 | − | 1.01013e7i | 0.760024 | − | 0.760024i | ||||
\(708\) | −1.22730e7 | + | 1.03656e7i | −0.920172 | + | 0.777158i | ||||
\(709\) | −1.71102e7 | − | 1.71102e7i | −1.27832 | − | 1.27832i | −0.941607 | − | 0.336713i | \(-0.890685\pi\) |
−0.336713 | − | 0.941607i | \(-0.609315\pi\) | |||||||
\(710\) | −6.46792e6 | − | 3.00343e6i | −0.481525 | − | 0.223600i | ||||
\(711\) | 620928.i | 0.0460646i | ||||||||
\(712\) | 3.75744e6 | − | 6.58098e6i | 0.277774 | − | 0.486508i | ||||
\(713\) | 1.82044e6i | 0.134107i | ||||||||
\(714\) | −2.69603e6 | + | 5.80595e6i | −0.197916 | + | 0.426214i | ||||
\(715\) | −1.45651e7 | − | 1.45651e7i | −1.06549 | − | 1.06549i | ||||
\(716\) | 1.35172e6 | − | 1.60427e7i | 0.0985384 | − | 1.16948i | ||||
\(717\) | 1.61872e7 | − | 1.61872e7i | 1.17591 | − | 1.17591i | ||||
\(718\) | −2.46042e7 | + | 8.99992e6i | −1.78114 | + | 0.651519i | ||||
\(719\) | −3.69511e6 | −0.266566 | −0.133283 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133283 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(720\) | 2.32435e6 | + | 3.27461e6i | 0.167098 | + | 0.235412i | ||||
\(721\) | −2.43365e6 | −0.174349 | ||||||||
\(722\) | −1.75626e7 | + | 6.42418e6i | −1.25385 | + | 0.458643i | ||||
\(723\) | 1.42396e6 | − | 1.42396e6i | 0.101310 | − | 0.101310i | ||||
\(724\) | −1.58829e7 | − | 1.33826e6i | −1.12611 | − | 0.0948842i | ||||
\(725\) | 9.73861e6 | + | 9.73861e6i | 0.688101 | + | 0.688101i | ||||
\(726\) | 7.62592e6 | − | 1.64225e7i | 0.536971 | − | 1.15638i | ||||
\(727\) | − | 2.47532e7i | − | 1.73698i | −0.495704 | − | 0.868492i | \(-0.665090\pi\) | ||
0.495704 | − | 0.868492i | \(-0.334910\pi\) | |||||||
\(728\) | −4.93162e6 | − | 1.80571e7i | −0.344874 | − | 1.26276i | ||||
\(729\) | 3.78638e6i | 0.263879i | ||||||||
\(730\) | 1.46514e7 | + | 6.80349e6i | 1.01759 | + | 0.472524i | ||||
\(731\) | 453766. | + | 453766.i | 0.0314079 | + | 0.0314079i | ||||
\(732\) | −7.45481e6 | − | 8.82665e6i | −0.514232 | − | 0.608861i | ||||
\(733\) | 1.92394e7 | − | 1.92394e7i | 1.32261 | − | 1.32261i | 0.410954 | − | 0.911656i | \(-0.365196\pi\) |
0.911656 | − | 0.410954i | \(-0.134804\pi\) | |||||||
\(734\) | 1.10963e6 | + | 3.03354e6i | 0.0760219 | + | 0.207831i | ||||
\(735\) | −3.72459e6 | −0.254308 | ||||||||
\(736\) | −882204. | − | 4.77886e6i | −0.0600308 | − | 0.325184i | ||||
\(737\) | −1.83517e7 | −1.24454 | ||||||||
\(738\) | 397768. | + | 1.08743e6i | 0.0268837 | + | 0.0734955i | ||||
\(739\) | 6.20086e6 | − | 6.20086e6i | 0.417677 | − | 0.417677i | −0.466725 | − | 0.884402i | \(-0.654566\pi\) |
0.884402 | + | 0.466725i | \(0.154566\pi\) | |||||||
\(740\) | −3.06268e6 | − | 3.62628e6i | −0.205600 | − | 0.243434i | ||||
\(741\) | 3.07655e7 | + | 3.07655e7i | 2.05835 | + | 2.05835i | ||||
\(742\) | 3.17625e6 | + | 1.47491e6i | 0.211790 | + | 0.0983460i | ||||
\(743\) | 1.51452e7i | 1.00647i | 0.864148 | + | 0.503237i | \(0.167858\pi\) | ||||
−0.864148 | + | 0.503237i | \(0.832142\pi\) | |||||||
\(744\) | 7.08156e6 | − | 1.93406e6i | 0.469026 | − | 0.128096i | ||||
\(745\) | 1.27640e7i | 0.842553i | ||||||||
\(746\) | −2.89776e6 | + | 6.24037e6i | −0.190640 | + | 0.410547i | ||||
\(747\) | −2.36421e6 | − | 2.36421e6i | −0.155019 | − | 0.155019i | ||||
\(748\) | −1.04217e7 | − | 878113.i | −0.681059 | − | 0.0573847i | ||||
\(749\) | 5.52163e6 | − | 5.52163e6i | 0.359636 | − | 0.359636i | ||||
\(750\) | 1.79101e7 | − | 6.55130e6i | 1.16264 | − | 0.425279i | ||||
\(751\) | −2.35795e7 | −1.52558 | −0.762788 | − | 0.646648i | \(-0.776170\pi\) | ||||
−0.762788 | + | 0.646648i | \(0.776170\pi\) | |||||||
\(752\) | 75678.3 | − | 445898.i | 0.00488008 | − | 0.0287535i | ||||
\(753\) | −2.45050e7 | −1.57495 | ||||||||
\(754\) | 4.01810e7 | − | 1.46977e7i | 2.57391 | − | 0.941502i | ||||
\(755\) | −4.65071e6 | + | 4.65071e6i | −0.296929 | + | 0.296929i | ||||
\(756\) | −733278. | + | 8.70277e6i | −0.0466621 | + | 0.553800i | ||||
\(757\) | 2.49220e6 | + | 2.49220e6i | 0.158068 | + | 0.158068i | 0.781710 | − | 0.623642i | \(-0.214348\pi\) |
−0.623642 | + | 0.781710i | \(0.714348\pi\) | |||||||
\(758\) | −7.00752e6 | + | 1.50908e7i | −0.442987 | + | 0.953980i | ||||
\(759\) | 9.03822e6i | 0.569480i | ||||||||
\(760\) | 1.39500e7 | + | 7.96478e6i | 0.876070 | + | 0.500196i | ||||
\(761\) | 1.56133e7i | 0.977314i | 0.872476 | + | 0.488657i | \(0.162513\pi\) | ||||
−0.872476 | + | 0.488657i | \(0.837487\pi\) | |||||||
\(762\) | 2.56424e7 | + | 1.19072e7i | 1.59982 | + | 0.742889i | ||||
\(763\) | −6.55122e6 | − | 6.55122e6i | −0.407391 | − | 0.407391i | ||||
\(764\) | 1.05122e7 | − | 8.87836e6i | 0.651566 | − | 0.550299i | ||||
\(765\) | −1.57213e6 | + | 1.57213e6i | −0.0971258 | + | 0.0971258i | ||||
\(766\) | 2.58846e6 | + | 7.07642e6i | 0.159393 | + | 0.435754i | ||||
\(767\) | 2.60083e7 | 1.59633 | ||||||||
\(768\) | −1.76526e7 | + | 8.50892e6i | −1.07996 | + | 0.520561i | ||||
\(769\) | −1.21956e7 | −0.743680 | −0.371840 | − | 0.928297i | \(-0.621273\pi\) | ||||
−0.371840 | + | 0.928297i | \(0.621273\pi\) | |||||||
\(770\) | 4.41546e6 | + | 1.20711e7i | 0.268379 | + | 0.733704i | ||||
\(771\) | 1.03314e7 | − | 1.03314e7i | 0.625929 | − | 0.625929i | ||||
\(772\) | −9.06189e6 | + | 7.65348e6i | −0.547237 | + | 0.462185i | ||||
\(773\) | −1.15929e7 | − | 1.15929e7i | −0.697822 | − | 0.697822i | 0.266119 | − | 0.963940i | \(-0.414259\pi\) |
−0.963940 | + | 0.266119i | \(0.914259\pi\) | |||||||
\(774\) | −617101. | − | 286555.i | −0.0370257 | − | 0.0171932i | ||||
\(775\) | − | 3.82573e6i | − | 0.228802i | ||||||
\(776\) | −2.45389e7 | − | 1.40106e7i | −1.46285 | − | 0.835221i | ||||
\(777\) | 8.02238e6i | 0.476706i | ||||||||
\(778\) | 4.71046e6 | − | 1.01440e7i | 0.279006 | − | 0.600844i | ||||
\(779\) | 3.27520e6 | + | 3.27520e6i | 0.193373 | + | 0.193373i | ||||
\(780\) | 1.79411e6 | − | 2.12930e7i | 0.105587 | − | 1.25314i | ||||
\(781\) | −1.39244e7 | + | 1.39244e7i | −0.816860 | + | 0.816860i | ||||
\(782\) | 2.52683e6 | − | 924284.i | 0.147761 | − | 0.0540491i | ||||
\(783\) | −1.99624e7 | −1.16361 | ||||||||
\(784\) | 925319. | − | 5.45200e6i | 0.0537652 | − | 0.316786i | ||||
\(785\) | 7.74999e6 | 0.448877 | ||||||||
\(786\) | 1.31945e6 | − | 482636.i | 0.0761790 | − | 0.0278653i | ||||
\(787\) | −2.01708e7 | + | 2.01708e7i | −1.16088 | + | 1.16088i | −0.176593 | + | 0.984284i | \(0.556508\pi\) |
−0.984284 | + | 0.176593i | \(0.943492\pi\) | |||||||
\(788\) | 3.04734e7 | + | 2.56763e6i | 1.74826 | + | 0.147305i | ||||
\(789\) | 1.15206e7 | + | 1.15206e7i | 0.658844 | + | 0.658844i | ||||
\(790\) | 513772. | − | 1.10642e6i | 0.0292889 | − | 0.0630740i | ||||
\(791\) | 1.15096e7i | 0.654065i | ||||||||
\(792\) | 1.06970e7 | − | 2.92148e6i | 0.605968 | − | 0.165497i | ||||
\(793\) | 1.87049e7i | 1.05626i | ||||||||
\(794\) | 1.02232e6 | + | 474720.i | 0.0575486 | + | 0.0267231i | ||||
\(795\) | 2.82685e6 | + | 2.82685e6i | 0.158630 | + | 0.158630i | ||||
\(796\) | 5.90913e6 | + | 6.99653e6i | 0.330553 | + | 0.391382i | ||||
\(797\) | 1.10993e7 | − | 1.10993e7i | 0.618941 | − | 0.618941i | −0.326319 | − | 0.945260i | \(-0.605808\pi\) |
0.945260 | + | 0.326319i | \(0.105808\pi\) | |||||||
\(798\) | −9.32667e6 | − | 2.54975e7i | −0.518465 | − | 1.41740i | ||||
\(799\) | 250407. | 0.0138765 | ||||||||
\(800\) | 1.85399e6 | + | 1.00430e7i | 0.102419 | + | 0.554801i | ||||
\(801\) | −4.44850e6 | −0.244981 | ||||||||
\(802\) | −6.10698e6 | − | 1.66955e7i | −0.335267 | − | 0.916563i | ||||
\(803\) | 3.15421e7 | − | 3.15421e7i | 1.72624 | − | 1.72624i | ||||
\(804\) | −1.22841e7 | − | 1.45446e7i | −0.670199 | − | 0.793530i | ||||
\(805\) | −2.33814e6 | − | 2.33814e6i | −0.127169 | − | 0.127169i | ||||
\(806\) | −1.07793e7 | − | 5.00545e6i | −0.584458 | − | 0.271397i | ||||
\(807\) | 1.03232e7i | 0.557994i | ||||||||
\(808\) | 6.37905e6 | + | 2.33569e7i | 0.343738 | + | 1.25860i | ||||
\(809\) | − | 5.39914e6i | − | 0.290037i | −0.989429 | − | 0.145018i | \(-0.953676\pi\) | ||
0.989429 | − | 0.145018i | \(-0.0463242\pi\) | |||||||
\(810\) | −6.46937e6 | + | 1.39319e7i | −0.346457 | + | 0.746100i | ||||
\(811\) | −1.13884e7 | − | 1.13884e7i | −0.608011 | − | 0.608011i | 0.334415 | − | 0.942426i | \(-0.391461\pi\) |
−0.942426 | + | 0.334415i | \(0.891461\pi\) | |||||||
\(812\) | −2.66036e7 | − | 2.24157e6i | −1.41596 | − | 0.119306i | ||||
\(813\) | −1.31923e7 | + | 1.31923e7i | −0.699993 | + | 0.699993i | ||||
\(814\) | −1.23094e7 | + | 4.50262e6i | −0.651142 | + | 0.238179i | ||||
\(815\) | 9.96082e6 | 0.525293 | ||||||||
\(816\) | −6.28004e6 | − | 8.84750e6i | −0.330169 | − | 0.465152i | ||||
\(817\) | −2.72170e6 | −0.142654 | ||||||||
\(818\) | −7.99969e6 | + | 2.92619e6i | −0.418013 | + | 0.152904i | ||||
\(819\) | −7.76978e6 | + | 7.76978e6i | −0.404761 | + | 0.404761i | ||||
\(820\) | 190995. | − | 2.26679e6i | 0.00991946 | − | 0.117727i | ||||
\(821\) | −5.77837e6 | − | 5.77837e6i | −0.299190 | − | 0.299190i | 0.541506 | − | 0.840697i | \(-0.317854\pi\) |
−0.840697 | + | 0.541506i | \(0.817854\pi\) | |||||||
\(822\) | −1.31322e6 | + | 2.82804e6i | −0.0677889 | + | 0.145984i | ||||
\(823\) | − | 1.72231e6i | − | 0.0886362i | −0.999017 | − | 0.0443181i | \(-0.985888\pi\) | ||
0.999017 | − | 0.0443181i | \(-0.0141115\pi\) | |||||||
\(824\) | 2.04520e6 | − | 3.58207e6i | 0.104934 | − | 0.183787i | ||||
\(825\) | − | 1.89942e7i | − | 0.971597i | ||||||
\(826\) | −1.47197e7 | − | 6.83519e6i | −0.750669 | − | 0.348578i | ||||
\(827\) | 7.60095e6 | + | 7.60095e6i | 0.386460 | + | 0.386460i | 0.873423 | − | 0.486963i | \(-0.161895\pi\) |
−0.486963 | + | 0.873423i | \(0.661895\pi\) | |||||||
\(828\) | −2.17939e6 | + | 1.84067e6i | −0.110474 | + | 0.0933040i | ||||
\(829\) | 129231. | − | 129231.i | 0.00653099 | − | 0.00653099i | −0.703834 | − | 0.710365i | \(-0.748530\pi\) |
0.710365 | + | 0.703834i | \(0.248530\pi\) | |||||||
\(830\) | 2.25652e6 | + | 6.16895e6i | 0.113696 | + | 0.310825i | ||||
\(831\) | 9.78832e6 | 0.491706 | ||||||||
\(832\) | 3.07226e7 | + | 7.91611e6i | 1.53869 | + | 0.396464i | ||||
\(833\) | 3.06173e6 | 0.152881 | ||||||||
\(834\) | −1.88382e6 | − | 5.15004e6i | −0.0937830 | − | 0.256387i | ||||
\(835\) | −2.75223e6 | + | 2.75223e6i | −0.136606 | + | 0.136606i | ||||
\(836\) | 3.38883e7 | − | 2.86213e7i | 1.67700 | − | 1.41636i | ||||
\(837\) | 3.92103e6 | + | 3.92103e6i | 0.193458 | + | 0.193458i | ||||
\(838\) | 2.29522e7 | + | 1.06580e7i | 1.12905 | + | 0.524284i | ||||
\(839\) | − | 3.84691e6i | − | 0.188672i | −0.995540 | − | 0.0943359i | \(-0.969927\pi\) | ||
0.995540 | − | 0.0943359i | \(-0.0300728\pi\) | |||||||
\(840\) | −6.61137e6 | + | 1.15795e7i | −0.323291 | + | 0.566229i | ||||
\(841\) | − | 4.05121e7i | − | 1.97513i | ||||||
\(842\) | 1.27569e7 | − | 2.74721e7i | 0.620102 | − | 1.33540i | ||||
\(843\) | −9.44665e6 | − | 9.44665e6i | −0.457835 | − | 0.457835i | ||||
\(844\) | −3.13329e6 | + | 3.71868e7i | −0.151406 | + | 1.79694i | ||||
\(845\) | −1.47733e7 | + | 1.47733e7i | −0.711764 | + | 0.711764i | ||||
\(846\) | −249337. | + | 91204.4i | −0.0119774 | + | 0.00438117i | ||||
\(847\) | 1.82923e7 | 0.876113 | ||||||||
\(848\) | −4.84018e6 | + | 3.43561e6i | −0.231138 | + | 0.164064i | ||||
\(849\) | 2.36066e7 | 1.12400 | ||||||||
\(850\) | −5.31025e6 | + | 1.94242e6i | −0.252097 | + | 0.0922139i | ||||
\(851\) | 2.38429e6 | − | 2.38429e6i | 0.112859 | − | 0.112859i | ||||
\(852\) | −2.03563e7 | − | 1.71518e6i | −0.960727 | − | 0.0809489i | ||||
\(853\) | −1.11788e7 | − | 1.11788e7i | −0.526042 | − | 0.526042i | 0.393347 | − | 0.919390i | \(-0.371317\pi\) |
−0.919390 | + | 0.393347i | \(0.871317\pi\) | |||||||
\(854\) | 4.91580e6 | − | 1.05863e7i | 0.230648 | − | 0.496704i | ||||
\(855\) | − | 9.42966e6i | − | 0.441144i | ||||||
\(856\) | 3.48696e6 | + | 1.27675e7i | 0.162653 | + | 0.595556i | ||||
\(857\) | − | 2.33336e7i | − | 1.08525i | −0.839976 | − | 0.542624i | \(-0.817431\pi\) | ||
0.839976 | − | 0.542624i | \(-0.182569\pi\) | |||||||
\(858\) | −5.35178e7 | − | 2.48514e7i | −2.48187 | − | 1.15248i | ||||
\(859\) | −1.27606e7 | − | 1.27606e7i | −0.590051 | − | 0.590051i | 0.347594 | − | 0.937645i | \(-0.386999\pi\) |
−0.937645 | + | 0.347594i | \(0.886999\pi\) | |||||||
\(860\) | 862494. | + | 1.02121e6i | 0.0397658 | + | 0.0470836i | ||||
\(861\) | −2.71867e6 | + | 2.71867e6i | −0.124982 | + | 0.124982i | ||||
\(862\) | 8.75024e6 | + | 2.39217e7i | 0.401099 | + | 1.09654i | ||||
\(863\) | −1.40892e7 | −0.643959 | −0.321980 | − | 0.946747i | \(-0.604348\pi\) | ||||
−0.321980 | + | 0.946747i | \(0.604348\pi\) | |||||||
\(864\) | −1.21933e7 | − | 8.39297e6i | −0.555696 | − | 0.382500i | ||||
\(865\) | 5.72383e6 | 0.260104 | ||||||||
\(866\) | 1.10760e7 | + | 3.02798e7i | 0.501865 | + | 1.37201i | ||||
\(867\) | −1.45155e7 | + | 1.45155e7i | −0.655818 | + | 0.655818i | ||||
\(868\) | 4.78521e6 | + | 5.66579e6i | 0.215577 | + | 0.255247i | ||||
\(869\) | −2.38193e6 | − | 2.38193e6i | −0.106999 | − | 0.106999i | ||||
\(870\) | −2.76426e7 | − | 1.28360e7i | −1.23817 | − | 0.574954i | ||||
\(871\) | 3.08221e7i | 1.37663i | ||||||||
\(872\) | 1.51482e7 | − | 4.13716e6i | 0.674638 | − | 0.184252i | ||||
\(873\) | 1.65874e7i | 0.736618i | ||||||||
\(874\) | −4.80607e6 | + | 1.03499e7i | −0.212819 | + | 0.458310i | ||||
\(875\) | 1.36232e7 | + | 1.36232e7i | 0.601534 | + | 0.601534i | ||||
\(876\) | 4.61119e7 | + | 3.88530e6i | 2.03027 | + | 0.171066i | ||||
\(877\) | 3.14281e7 | − | 3.14281e7i | 1.37981 | − | 1.37981i | 0.534887 | − | 0.844924i | \(-0.320354\pi\) |
0.844924 | − | 0.534887i | \(-0.179646\pi\) | |||||||
\(878\) | 1.68320e6 | − | 615693.i | 0.0736884 | − | 0.0269543i | ||||
\(879\) | −1.91306e7 | −0.835135 | ||||||||
\(880\) | −2.14781e7 | − | 3.64528e6i | −0.934950 | − | 0.158681i | ||||
\(881\) | 3.09313e7 | 1.34264 | 0.671318 | − | 0.741169i | \(-0.265728\pi\) | ||||
0.671318 | + | 0.741169i | \(0.265728\pi\) | |||||||
\(882\) | −3.04865e6 | + | 1.11516e6i | −0.131958 | + | 0.0482686i | ||||
\(883\) | −1.69679e7 | + | 1.69679e7i | −0.732364 | + | 0.732364i | −0.971088 | − | 0.238723i | \(-0.923271\pi\) |
0.238723 | + | 0.971088i | \(0.423271\pi\) | |||||||
\(884\) | −1.47481e6 | + | 1.75035e7i | −0.0634754 | + | 0.753345i | ||||
\(885\) | −1.31005e7 | − | 1.31005e7i | −0.562248 | − | 0.562248i | ||||
\(886\) | −2.68692e6 | + | 5.78632e6i | −0.114993 | + | 0.247638i | ||||
\(887\) | − | 3.33974e7i | − | 1.42529i | −0.701524 | − | 0.712646i | \(-0.747497\pi\) | ||
0.701524 | − | 0.712646i | \(-0.252503\pi\) | |||||||
\(888\) | −1.18081e7 | − | 6.74188e6i | −0.502513 | − | 0.286912i | ||||
\(889\) | 2.85620e7i | 1.21209i | ||||||||
\(890\) | 7.92667e6 | + | 3.68080e6i | 0.335441 | + | 0.155764i | ||||
\(891\) | 2.99930e7 | + | 2.99930e7i | 1.26569 | + | 1.26569i | ||||
\(892\) | −3.33116e6 | + | 2.81343e6i | −0.140179 | + | 0.118392i | ||||
\(893\) | −750973. | + | 750973.i | −0.0315134 | + | 0.0315134i | ||||
\(894\) | 1.25608e7 | + | 3.43391e7i | 0.525623 | + | 1.43696i | ||||
\(895\) | 1.85671e7 | 0.774793 | ||||||||
\(896\) | −1.53074e7 | − | 1.25544e7i | −0.636989 | − | 0.522426i | ||||
\(897\) | 1.51799e7 | 0.629923 | ||||||||
\(898\) | 1.21619e6 | + | 3.32486e6i | 0.0503281 | + | 0.137588i | ||||
\(899\) | −1.19862e7 | + | 1.19862e7i | −0.494633 | + | 0.494633i | ||||
\(900\) | 4.58009e6 | − | 3.86825e6i | 0.188481 | − | 0.159187i | ||||
\(901\) | −2.32375e6 | − | 2.32375e6i | −0.0953626 | − | 0.0953626i | ||||
\(902\) | −5.69734e6 | − | 2.64560e6i | −0.233161 | − | 0.108270i | ||||
\(903\) | − | 2.25922e6i | − | 0.0922016i | ||||||
\(904\) | −1.69410e7 | − | 9.67251e6i | −0.689472 | − | 0.393657i | ||||
\(905\) | − | 1.83821e7i | − | 0.746061i | ||||||
\(906\) | −7.93517e6 | + | 1.70885e7i | −0.321170 | + | 0.691646i | ||||
\(907\) | −3.96669e6 | − | 3.96669e6i | −0.160107 | − | 0.160107i | 0.622507 | − | 0.782614i | \(-0.286114\pi\) |
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(908\) | −1.61739e6 | + | 1.91957e7i | −0.0651028 | + | 0.772660i | ||||
\(909\) | 1.00502e7 | − | 1.00502e7i | 0.403427 | − | 0.403427i | ||||
\(910\) | 2.02737e7 | − | 7.41586e6i | 0.811577 | − | 0.296864i | ||||
\(911\) | −1.66679e7 | −0.665402 | −0.332701 | − | 0.943032i | \(-0.607960\pi\) | ||||
−0.332701 | + | 0.943032i | \(0.607960\pi\) | |||||||
\(912\) | 4.53676e7 | + | 7.69984e6i | 1.80617 | + | 0.306545i | ||||
\(913\) | 1.81386e7 | 0.720158 | ||||||||
\(914\) | −2.10158e7 | + | 7.68731e6i | −0.832109 | + | 0.304375i | ||||
\(915\) | 9.42172e6 | − | 9.42172e6i | 0.372030 | − | 0.372030i | ||||
\(916\) | −2.60068e7 | − | 2.19128e6i | −1.02411 | − | 0.0862898i | ||||
\(917\) | 1.00363e6 | + | 1.00363e6i | 0.0394139 | + | 0.0394139i | ||||
\(918\) | 3.45172e6 | − | 7.43333e6i | 0.135185 | − | 0.291123i | ||||
\(919\) | 1.60909e7i | 0.628481i | 0.949343 | + | 0.314241i | \(0.101750\pi\) | ||||
−0.949343 | + | 0.314241i | \(0.898250\pi\) | |||||||
\(920\) | 5.40643e6 | − | 1.47656e6i | 0.210591 | − | 0.0575150i | ||||
\(921\) | − | 4.11224e7i | − | 1.59746i | ||||||
\(922\) | −2.72214e7 | − | 1.26404e7i | −1.05459 | − | 0.489705i | ||||
\(923\) | 2.33863e7 | + | 2.33863e7i | 0.903559 | + | 0.903559i | ||||
\(924\) | 2.37579e7 | + | 2.81298e7i | 0.915436 | + | 1.08390i | ||||
\(925\) | −5.01070e6 | + | 5.01070e6i | −0.192550 | + | 0.192550i | ||||
\(926\) | −1.29232e7 | − | 3.53299e7i | −0.495272 | − | 1.35399i | ||||
\(927\) | −2.42135e6 | −0.0925460 | ||||||||
\(928\) | 2.56566e7 | − | 3.72739e7i | 0.977977 | − | 1.42081i | ||||
\(929\) | −3.35768e7 | −1.27644 | −0.638219 | − | 0.769855i | \(-0.720329\pi\) | ||||
−0.638219 | + | 0.769855i | \(0.720329\pi\) | |||||||
\(930\) | 2.90832e6 | + | 7.95084e6i | 0.110264 | + | 0.301443i | ||||
\(931\) | −9.18215e6 | + | 9.18215e6i | −0.347192 | + | 0.347192i | ||||
\(932\) | −1.16279e7 | − | 1.37677e7i | −0.438492 | − | 0.519183i | ||||
\(933\) | 3.09092e7 | + | 3.09092e7i | 1.16248 | + | 1.16248i | ||||
\(934\) | 1.51601e7 | + | 7.03969e6i | 0.568636 | + | 0.264050i | ||||
\(935\) | − | 1.20616e7i | − | 0.451208i | ||||||
\(936\) | −4.90669e6 | − | 1.79659e7i | −0.183062 | − | 0.670284i | ||||
\(937\) | 3.14426e7i | 1.16996i | 0.811049 | + | 0.584978i | \(0.198897\pi\) | ||||
−0.811049 | + | 0.584978i | \(0.801103\pi\) | |||||||
\(938\) | 8.10031e6 | − | 1.74441e7i | 0.300604 | − | 0.647355i | ||||
\(939\) | −1.85089e7 | − | 1.85089e7i | −0.685040 | − | 0.685040i | ||||
\(940\) | 519753. | + | 43793.4i | 0.0191857 | + | 0.00161655i | ||||
\(941\) | −2.15366e6 | + | 2.15366e6i | −0.0792872 | + | 0.0792872i | −0.745638 | − | 0.666351i | \(-0.767855\pi\) |
0.666351 | + | 0.745638i | \(0.267855\pi\) | |||||||
\(942\) | 2.08498e7 | − | 7.62660e6i | 0.765553 | − | 0.280030i | ||||
\(943\) | 1.61600e6 | 0.0591784 | ||||||||
\(944\) | 2.24308e7 | − | 1.59216e7i | 0.819248 | − | 0.581510i | ||||
\(945\) | −1.00722e7 | −0.366898 | ||||||||
\(946\) | 3.46650e6 | − | 1.26800e6i | 0.125940 | − | 0.0460672i | ||||
\(947\) | −1.36614e7 | + | 1.36614e7i | −0.495015 | + | 0.495015i | −0.909882 | − | 0.414867i | \(-0.863828\pi\) |
0.414867 | + | 0.909882i | \(0.363828\pi\) | |||||||
\(948\) | 293402. | − | 3.48219e6i | 0.0106033 | − | 0.125844i | ||||
\(949\) | −5.29756e7 | − | 5.29756e7i | −1.90946 | − | 1.90946i | ||||
\(950\) | 1.01002e7 | − | 2.17508e7i | 0.363094 | − | 0.781928i | ||||
\(951\) | − | 5.12406e7i | − | 1.83723i | ||||||
\(952\) | 5.43475e6 | − | 9.51871e6i | 0.194351 | − | 0.340397i | ||||
\(953\) | 4.23714e7i | 1.51126i | 0.654996 | + | 0.755632i | \(0.272670\pi\) | ||||
−0.654996 | + | 0.755632i | \(0.727330\pi\) | |||||||
\(954\) | 3.16019e6 | + | 1.46746e6i | 0.112420 | + | 0.0522029i | ||||
\(955\) | 1.12209e7 | + | 1.12209e7i | 0.398124 | + | 0.398124i | ||||
\(956\) | −2.99463e7 | + | 2.52921e7i | −1.05974 | + | 0.895034i | ||||
\(957\) | −5.95100e7 | + | 5.95100e7i | −2.10044 | + | 2.10044i | ||||
\(958\) | −1.35461e7 | − | 3.70328e7i | −0.476872 | − | 1.30369i | ||||
\(959\) | −3.15003e6 | −0.110603 | ||||||||
\(960\) | −1.14877e7 | − | 1.94625e7i | −0.402305 | − | 0.681584i | ||||
\(961\) | −2.39205e7 | −0.835528 | ||||||||
\(962\) | 7.56224e6 | + | 2.06739e7i | 0.263459 | + | 0.720252i | ||||
\(963\) | 5.49372e6 | − | 5.49372e6i | 0.190898 | − | 0.190898i | ||||
\(964\) | −2.63433e6 | + | 2.22490e6i | −0.0913013 | + | 0.0771112i | ||||
\(965\) | −9.67281e6 | − | 9.67281e6i | −0.334376 | − | 0.334376i | ||||
\(966\) | −8.59123e6 | − | 3.98940e6i | −0.296219 | − | 0.137551i | ||||
\(967\) | − | 3.84918e7i | − | 1.32374i | −0.749620 | − | 0.661869i | \(-0.769764\pi\) | ||
0.749620 | − | 0.661869i | \(-0.230236\pi\) | |||||||
\(968\) | −1.53726e7 | + | 2.69243e7i | −0.527300 | + | 0.923542i | ||||
\(969\) | 2.54775e7i | 0.871660i | ||||||||
\(970\) | 1.37248e7 | − | 2.95566e7i | 0.468358 | − | 1.00862i | ||||
\(971\) | 1.28812e7 | + | 1.28812e7i | 0.438438 | + | 0.438438i | 0.891486 | − | 0.453048i | \(-0.149664\pi\) |
−0.453048 | + | 0.891486i | \(0.649664\pi\) | |||||||
\(972\) | −2.02611e6 | + | 2.40465e7i | −0.0687856 | + | 0.816368i | ||||
\(973\) | 3.91735e6 | − | 3.91735e6i | 0.132651 | − | 0.132651i | ||||
\(974\) | 2.66278e7 | − | 9.74010e6i | 0.899368 | − | 0.328977i | ||||
\(975\) | −3.19012e7 | −1.07472 | ||||||||
\(976\) | 1.14507e7 | + | 1.61320e7i | 0.384775 | + | 0.542082i | ||||
\(977\) | 4.46818e6 | 0.149760 | 0.0748798 | − | 0.997193i | \(-0.476143\pi\) | ||||
0.0748798 | + | 0.997193i | \(0.476143\pi\) | |||||||
\(978\) | 2.67977e7 | − | 9.80224e6i | 0.895880 | − | 0.327701i | ||||
\(979\) | 1.70648e7 | − | 1.70648e7i | 0.569042 | − | 0.569042i | ||||
\(980\) | 6.35502e6 | + | 535462.i | 0.211374 | + | 0.0178100i | ||||
\(981\) | −6.51811e6 | − | 6.51811e6i | −0.216247 | − | 0.216247i | ||||
\(982\) | −2.10944e7 | + | 4.54270e7i | −0.698052 | + | 1.50327i | ||||
\(983\) | 3.21497e7i | 1.06119i | 0.847625 | + | 0.530595i | \(0.178032\pi\) | ||||
−0.847625 | + | 0.530595i | \(0.821968\pi\) | |||||||
\(984\) | −1.71687e6 | − | 6.28631e6i | −0.0565260 | − | 0.206970i | ||||
\(985\) | 3.52686e7i | 1.15824i | ||||||||
\(986\) | 2.27231e7 | + | 1.05516e7i | 0.744345 | + | 0.345642i | ||||
\(987\) | −623364. | − | 623364.i | −0.0203680 | − | 0.0203680i | ||||
\(988\) | −4.80701e7 | − | 5.69161e7i | −1.56669 | − | 1.85499i | ||||
\(989\) | −671451. | + | 671451.i | −0.0218285 | + | 0.0218285i | ||||
\(990\) | 4.39314e6 | + | 1.20101e7i | 0.142458 | + | 0.389456i | ||||
\(991\) | 1.46825e7 | 0.474915 | 0.237457 | − | 0.971398i | \(-0.423686\pi\) | ||||
0.237457 | + | 0.971398i | \(0.423686\pi\) | |||||||
\(992\) | −1.23608e7 | + | 2.28188e6i | −0.398812 | + | 0.0736230i | ||||
\(993\) | 4.63008e7 | 1.49010 | ||||||||
\(994\) | −7.08963e6 | − | 1.93818e7i | −0.227592 | − | 0.622199i | ||||
\(995\) | −7.46822e6 | + | 7.46822e6i | −0.239144 | + | 0.239144i | ||||
\(996\) | 1.21415e7 | + | 1.43758e7i | 0.387814 | + | 0.459179i | ||||
\(997\) | 2.92541e7 | + | 2.92541e7i | 0.932071 | + | 0.932071i | 0.997835 | − | 0.0657639i | \(-0.0209484\pi\) |
−0.0657639 | + | 0.997835i | \(0.520948\pi\) | |||||||
\(998\) | 345360. | + | 160370.i | 0.0109760 | + | 0.00509680i | ||||
\(999\) | − | 1.02710e7i | − | 0.325612i |
(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 | 16.6.e.a.5.4 | ✓ | 18 | |
3.2 | odd | 2 | 144.6.k.a.37.6 | 18 | |||
4.3 | odd | 2 | 64.6.e.a.49.3 | 18 | |||
8.3 | odd | 2 | 128.6.e.a.97.7 | 18 | |||
8.5 | even | 2 | 128.6.e.b.97.3 | 18 | |||
12.11 | even | 2 | 576.6.k.a.433.6 | 18 | |||
16.3 | odd | 4 | 64.6.e.a.17.3 | 18 | |||
16.5 | even | 4 | 128.6.e.b.33.3 | 18 | |||
16.11 | odd | 4 | 128.6.e.a.33.7 | 18 | |||
16.13 | even | 4 | inner | 16.6.e.a.13.4 | yes | 18 | |
32.3 | odd | 8 | 1024.6.a.l.1.4 | 18 | |||
32.13 | even | 8 | 1024.6.a.k.1.4 | 18 | |||
32.19 | odd | 8 | 1024.6.a.l.1.15 | 18 | |||
32.29 | even | 8 | 1024.6.a.k.1.15 | 18 | |||
48.29 | odd | 4 | 144.6.k.a.109.6 | 18 | |||
48.35 | even | 4 | 576.6.k.a.145.6 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.6.e.a.5.4 | ✓ | 18 | 1.1 | even | 1 | trivial | |
16.6.e.a.13.4 | yes | 18 | 16.13 | even | 4 | inner | |
64.6.e.a.17.3 | 18 | 16.3 | odd | 4 | |||
64.6.e.a.49.3 | 18 | 4.3 | odd | 2 | |||
128.6.e.a.33.7 | 18 | 16.11 | odd | 4 | |||
128.6.e.a.97.7 | 18 | 8.3 | odd | 2 | |||
128.6.e.b.33.3 | 18 | 16.5 | even | 4 | |||
128.6.e.b.97.3 | 18 | 8.5 | even | 2 | |||
144.6.k.a.37.6 | 18 | 3.2 | odd | 2 | |||
144.6.k.a.109.6 | 18 | 48.29 | odd | 4 | |||
576.6.k.a.145.6 | 18 | 48.35 | even | 4 | |||
576.6.k.a.433.6 | 18 | 12.11 | even | 2 | |||
1024.6.a.k.1.4 | 18 | 32.13 | even | 8 | |||
1024.6.a.k.1.15 | 18 | 32.29 | even | 8 | |||
1024.6.a.l.1.4 | 18 | 32.3 | odd | 8 | |||
1024.6.a.l.1.15 | 18 | 32.19 | odd | 8 |