Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,3,Mod(11,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.c (of order \(2\), degree \(1\), 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: | \(0.408720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.11 |
Dual form | 15.3.c.a.11.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.23607i | − | 1.11803i | −0.829156 | − | 0.559017i | \(-0.811179\pi\) | ||
0.829156 | − | 0.559017i | \(-0.188821\pi\) | |||||||
\(3\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(4\) | −1.00000 | −0.250000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 5.00000 | + | 4.47214i | 0.833333 | + | 0.745356i | ||||
\(7\) | −6.00000 | −0.857143 | −0.428571 | − | 0.903508i | \(-0.640983\pi\) | ||||
−0.428571 | + | 0.903508i | \(0.640983\pi\) | |||||||
\(8\) | − | 6.70820i | − | 0.838525i | ||||||
\(9\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(10\) | 5.00000 | 0.500000 | ||||||||
\(11\) | 4.47214i | 0.406558i | 0.979121 | + | 0.203279i | \(0.0651598\pi\) | ||||
−0.979121 | + | 0.203279i | \(0.934840\pi\) | |||||||
\(12\) | 2.00000 | − | 2.23607i | 0.166667 | − | 0.186339i | ||||
\(13\) | 16.0000 | 1.23077 | 0.615385 | − | 0.788227i | \(-0.289001\pi\) | ||||
0.615385 | + | 0.788227i | \(0.289001\pi\) | |||||||
\(14\) | 13.4164i | 0.958315i | ||||||||
\(15\) | −5.00000 | − | 4.47214i | −0.333333 | − | 0.298142i | ||||
\(16\) | −19.0000 | −1.18750 | ||||||||
\(17\) | 4.47214i | 0.263067i | 0.991312 | + | 0.131533i | \(0.0419901\pi\) | ||||
−0.991312 | + | 0.131533i | \(0.958010\pi\) | |||||||
\(18\) | −20.0000 | + | 2.23607i | −1.11111 | + | 0.124226i | ||||
\(19\) | −2.00000 | −0.105263 | −0.0526316 | − | 0.998614i | \(-0.516761\pi\) | ||||
−0.0526316 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(20\) | − | 2.23607i | − | 0.111803i | ||||||
\(21\) | 12.0000 | − | 13.4164i | 0.571429 | − | 0.638877i | ||||
\(22\) | 10.0000 | 0.454545 | ||||||||
\(23\) | 13.4164i | 0.583322i | 0.956522 | + | 0.291661i | \(0.0942079\pi\) | ||||
−0.956522 | + | 0.291661i | \(0.905792\pi\) | |||||||
\(24\) | 15.0000 | + | 13.4164i | 0.625000 | + | 0.559017i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 35.7771i | − | 1.37604i | ||||||
\(27\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(28\) | 6.00000 | 0.214286 | ||||||||
\(29\) | − | 31.3050i | − | 1.07948i | −0.841831 | − | 0.539741i | \(-0.818522\pi\) | ||
0.841831 | − | 0.539741i | \(-0.181478\pi\) | |||||||
\(30\) | −10.0000 | + | 11.1803i | −0.333333 | + | 0.372678i | ||||
\(31\) | −18.0000 | −0.580645 | −0.290323 | − | 0.956929i | \(-0.593763\pi\) | ||||
−0.290323 | + | 0.956929i | \(0.593763\pi\) | |||||||
\(32\) | 15.6525i | 0.489140i | ||||||||
\(33\) | −10.0000 | − | 8.94427i | −0.303030 | − | 0.271039i | ||||
\(34\) | 10.0000 | 0.294118 | ||||||||
\(35\) | − | 13.4164i | − | 0.383326i | ||||||
\(36\) | 1.00000 | + | 8.94427i | 0.0277778 | + | 0.248452i | ||||
\(37\) | −16.0000 | −0.432432 | −0.216216 | − | 0.976346i | \(-0.569372\pi\) | ||||
−0.216216 | + | 0.976346i | \(0.569372\pi\) | |||||||
\(38\) | 4.47214i | 0.117688i | ||||||||
\(39\) | −32.0000 | + | 35.7771i | −0.820513 | + | 0.917361i | ||||
\(40\) | 15.0000 | 0.375000 | ||||||||
\(41\) | 62.6099i | 1.52707i | 0.645766 | + | 0.763535i | \(0.276538\pi\) | ||||
−0.645766 | + | 0.763535i | \(0.723462\pi\) | |||||||
\(42\) | −30.0000 | − | 26.8328i | −0.714286 | − | 0.638877i | ||||
\(43\) | 16.0000 | 0.372093 | 0.186047 | − | 0.982541i | \(-0.440432\pi\) | ||||
0.186047 | + | 0.982541i | \(0.440432\pi\) | |||||||
\(44\) | − | 4.47214i | − | 0.101639i | ||||||
\(45\) | 20.0000 | − | 2.23607i | 0.444444 | − | 0.0496904i | ||||
\(46\) | 30.0000 | 0.652174 | ||||||||
\(47\) | − | 49.1935i | − | 1.04667i | −0.852127 | − | 0.523335i | \(-0.824688\pi\) | ||
0.852127 | − | 0.523335i | \(-0.175312\pi\) | |||||||
\(48\) | 38.0000 | − | 42.4853i | 0.791667 | − | 0.885110i | ||||
\(49\) | −13.0000 | −0.265306 | ||||||||
\(50\) | 11.1803i | 0.223607i | ||||||||
\(51\) | −10.0000 | − | 8.94427i | −0.196078 | − | 0.175378i | ||||
\(52\) | −16.0000 | −0.307692 | ||||||||
\(53\) | 4.47214i | 0.0843799i | 0.999110 | + | 0.0421900i | \(0.0134335\pi\) | ||||
−0.999110 | + | 0.0421900i | \(0.986567\pi\) | |||||||
\(54\) | 35.0000 | − | 49.1935i | 0.648148 | − | 0.910991i | ||||
\(55\) | −10.0000 | −0.181818 | ||||||||
\(56\) | 40.2492i | 0.718736i | ||||||||
\(57\) | 4.00000 | − | 4.47214i | 0.0701754 | − | 0.0784585i | ||||
\(58\) | −70.0000 | −1.20690 | ||||||||
\(59\) | 4.47214i | 0.0757989i | 0.999282 | + | 0.0378995i | \(0.0120667\pi\) | ||||
−0.999282 | + | 0.0378995i | \(0.987933\pi\) | |||||||
\(60\) | 5.00000 | + | 4.47214i | 0.0833333 | + | 0.0745356i | ||||
\(61\) | 82.0000 | 1.34426 | 0.672131 | − | 0.740432i | \(-0.265379\pi\) | ||||
0.672131 | + | 0.740432i | \(0.265379\pi\) | |||||||
\(62\) | 40.2492i | 0.649181i | ||||||||
\(63\) | 6.00000 | + | 53.6656i | 0.0952381 | + | 0.851835i | ||||
\(64\) | −41.0000 | −0.640625 | ||||||||
\(65\) | 35.7771i | 0.550417i | ||||||||
\(66\) | −20.0000 | + | 22.3607i | −0.303030 | + | 0.338798i | ||||
\(67\) | 24.0000 | 0.358209 | 0.179104 | − | 0.983830i | \(-0.442680\pi\) | ||||
0.179104 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(68\) | − | 4.47214i | − | 0.0657667i | ||||||
\(69\) | −30.0000 | − | 26.8328i | −0.434783 | − | 0.388881i | ||||
\(70\) | −30.0000 | −0.428571 | ||||||||
\(71\) | − | 125.220i | − | 1.76366i | −0.471568 | − | 0.881830i | \(-0.656312\pi\) | ||
0.471568 | − | 0.881830i | \(-0.343688\pi\) | |||||||
\(72\) | −60.0000 | + | 6.70820i | −0.833333 | + | 0.0931695i | ||||
\(73\) | −74.0000 | −1.01370 | −0.506849 | − | 0.862035i | \(-0.669190\pi\) | ||||
−0.506849 | + | 0.862035i | \(0.669190\pi\) | |||||||
\(74\) | 35.7771i | 0.483474i | ||||||||
\(75\) | 10.0000 | − | 11.1803i | 0.133333 | − | 0.149071i | ||||
\(76\) | 2.00000 | 0.0263158 | ||||||||
\(77\) | − | 26.8328i | − | 0.348478i | ||||||
\(78\) | 80.0000 | + | 71.5542i | 1.02564 | + | 0.917361i | ||||
\(79\) | 138.000 | 1.74684 | 0.873418 | − | 0.486972i | \(-0.161899\pi\) | ||||
0.873418 | + | 0.486972i | \(0.161899\pi\) | |||||||
\(80\) | − | 42.4853i | − | 0.531066i | ||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | 140.000 | 1.70732 | ||||||||
\(83\) | − | 93.9149i | − | 1.13150i | −0.824575 | − | 0.565752i | \(-0.808586\pi\) | ||
0.824575 | − | 0.565752i | \(-0.191414\pi\) | |||||||
\(84\) | −12.0000 | + | 13.4164i | −0.142857 | + | 0.159719i | ||||
\(85\) | −10.0000 | −0.117647 | ||||||||
\(86\) | − | 35.7771i | − | 0.416013i | ||||||
\(87\) | 70.0000 | + | 62.6099i | 0.804598 | + | 0.719654i | ||||
\(88\) | 30.0000 | 0.340909 | ||||||||
\(89\) | 107.331i | 1.20597i | 0.797753 | + | 0.602985i | \(0.206022\pi\) | ||||
−0.797753 | + | 0.602985i | \(0.793978\pi\) | |||||||
\(90\) | −5.00000 | − | 44.7214i | −0.0555556 | − | 0.496904i | ||||
\(91\) | −96.0000 | −1.05495 | ||||||||
\(92\) | − | 13.4164i | − | 0.145831i | ||||||
\(93\) | 36.0000 | − | 40.2492i | 0.387097 | − | 0.432787i | ||||
\(94\) | −110.000 | −1.17021 | ||||||||
\(95\) | − | 4.47214i | − | 0.0470751i | ||||||
\(96\) | −35.0000 | − | 31.3050i | −0.364583 | − | 0.326093i | ||||
\(97\) | −166.000 | −1.71134 | −0.855670 | − | 0.517522i | \(-0.826855\pi\) | ||||
−0.855670 | + | 0.517522i | \(0.826855\pi\) | |||||||
\(98\) | 29.0689i | 0.296621i | ||||||||
\(99\) | 40.0000 | − | 4.47214i | 0.404040 | − | 0.0451731i | ||||
\(100\) | 5.00000 | 0.0500000 | ||||||||
\(101\) | 67.0820i | 0.664179i | 0.943248 | + | 0.332089i | \(0.107754\pi\) | ||||
−0.943248 | + | 0.332089i | \(0.892246\pi\) | |||||||
\(102\) | −20.0000 | + | 22.3607i | −0.196078 | + | 0.219222i | ||||
\(103\) | 26.0000 | 0.252427 | 0.126214 | − | 0.992003i | \(-0.459718\pi\) | ||||
0.126214 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(104\) | − | 107.331i | − | 1.03203i | ||||||
\(105\) | 30.0000 | + | 26.8328i | 0.285714 | + | 0.255551i | ||||
\(106\) | 10.0000 | 0.0943396 | ||||||||
\(107\) | 201.246i | 1.88080i | 0.340064 | + | 0.940402i | \(0.389551\pi\) | ||||
−0.340064 | + | 0.940402i | \(0.610449\pi\) | |||||||
\(108\) | −22.0000 | − | 15.6525i | −0.203704 | − | 0.144930i | ||||
\(109\) | 38.0000 | 0.348624 | 0.174312 | − | 0.984690i | \(-0.444230\pi\) | ||||
0.174312 | + | 0.984690i | \(0.444230\pi\) | |||||||
\(110\) | 22.3607i | 0.203279i | ||||||||
\(111\) | 32.0000 | − | 35.7771i | 0.288288 | − | 0.322316i | ||||
\(112\) | 114.000 | 1.01786 | ||||||||
\(113\) | 31.3050i | 0.277035i | 0.990360 | + | 0.138517i | \(0.0442337\pi\) | ||||
−0.990360 | + | 0.138517i | \(0.955766\pi\) | |||||||
\(114\) | −10.0000 | − | 8.94427i | −0.0877193 | − | 0.0784585i | ||||
\(115\) | −30.0000 | −0.260870 | ||||||||
\(116\) | 31.3050i | 0.269870i | ||||||||
\(117\) | −16.0000 | − | 143.108i | −0.136752 | − | 1.22315i | ||||
\(118\) | 10.0000 | 0.0847458 | ||||||||
\(119\) | − | 26.8328i | − | 0.225486i | ||||||
\(120\) | −30.0000 | + | 33.5410i | −0.250000 | + | 0.279508i | ||||
\(121\) | 101.000 | 0.834711 | ||||||||
\(122\) | − | 183.358i | − | 1.50293i | ||||||
\(123\) | −140.000 | − | 125.220i | −1.13821 | − | 1.01805i | ||||
\(124\) | 18.0000 | 0.145161 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 120.000 | − | 13.4164i | 0.952381 | − | 0.106479i | ||||
\(127\) | −26.0000 | −0.204724 | −0.102362 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102362 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(128\) | 154.289i | 1.20538i | ||||||||
\(129\) | −32.0000 | + | 35.7771i | −0.248062 | + | 0.277342i | ||||
\(130\) | 80.0000 | 0.615385 | ||||||||
\(131\) | 13.4164i | 0.102415i | 0.998688 | + | 0.0512077i | \(0.0163070\pi\) | ||||
−0.998688 | + | 0.0512077i | \(0.983693\pi\) | |||||||
\(132\) | 10.0000 | + | 8.94427i | 0.0757576 | + | 0.0677596i | ||||
\(133\) | 12.0000 | 0.0902256 | ||||||||
\(134\) | − | 53.6656i | − | 0.400490i | ||||||
\(135\) | −35.0000 | + | 49.1935i | −0.259259 | + | 0.364396i | ||||
\(136\) | 30.0000 | 0.220588 | ||||||||
\(137\) | − | 120.748i | − | 0.881370i | −0.897662 | − | 0.440685i | \(-0.854736\pi\) | ||
0.897662 | − | 0.440685i | \(-0.145264\pi\) | |||||||
\(138\) | −60.0000 | + | 67.0820i | −0.434783 | + | 0.486102i | ||||
\(139\) | −82.0000 | −0.589928 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(140\) | 13.4164i | 0.0958315i | ||||||||
\(141\) | 110.000 | + | 98.3870i | 0.780142 | + | 0.697780i | ||||
\(142\) | −280.000 | −1.97183 | ||||||||
\(143\) | 71.5542i | 0.500379i | ||||||||
\(144\) | 19.0000 | + | 169.941i | 0.131944 | + | 1.18015i | ||||
\(145\) | 70.0000 | 0.482759 | ||||||||
\(146\) | 165.469i | 1.13335i | ||||||||
\(147\) | 26.0000 | − | 29.0689i | 0.176871 | − | 0.197748i | ||||
\(148\) | 16.0000 | 0.108108 | ||||||||
\(149\) | − | 111.803i | − | 0.750358i | −0.926952 | − | 0.375179i | \(-0.877581\pi\) | ||
0.926952 | − | 0.375179i | \(-0.122419\pi\) | |||||||
\(150\) | −25.0000 | − | 22.3607i | −0.166667 | − | 0.149071i | ||||
\(151\) | −158.000 | −1.04636 | −0.523179 | − | 0.852223i | \(-0.675254\pi\) | ||||
−0.523179 | + | 0.852223i | \(0.675254\pi\) | |||||||
\(152\) | 13.4164i | 0.0882658i | ||||||||
\(153\) | 40.0000 | − | 4.47214i | 0.261438 | − | 0.0292296i | ||||
\(154\) | −60.0000 | −0.389610 | ||||||||
\(155\) | − | 40.2492i | − | 0.259672i | ||||||
\(156\) | 32.0000 | − | 35.7771i | 0.205128 | − | 0.229340i | ||||
\(157\) | 164.000 | 1.04459 | 0.522293 | − | 0.852766i | \(-0.325077\pi\) | ||||
0.522293 | + | 0.852766i | \(0.325077\pi\) | |||||||
\(158\) | − | 308.577i | − | 1.95302i | ||||||
\(159\) | −10.0000 | − | 8.94427i | −0.0628931 | − | 0.0562533i | ||||
\(160\) | −35.0000 | −0.218750 | ||||||||
\(161\) | − | 80.4984i | − | 0.499990i | ||||||
\(162\) | 40.0000 | + | 176.649i | 0.246914 | + | 1.09043i | ||||
\(163\) | 236.000 | 1.44785 | 0.723926 | − | 0.689877i | \(-0.242336\pi\) | ||||
0.723926 | + | 0.689877i | \(0.242336\pi\) | |||||||
\(164\) | − | 62.6099i | − | 0.381768i | ||||||
\(165\) | 20.0000 | − | 22.3607i | 0.121212 | − | 0.135519i | ||||
\(166\) | −210.000 | −1.26506 | ||||||||
\(167\) | 93.9149i | 0.562364i | 0.959654 | + | 0.281182i | \(0.0907265\pi\) | ||||
−0.959654 | + | 0.281182i | \(0.909273\pi\) | |||||||
\(168\) | −90.0000 | − | 80.4984i | −0.535714 | − | 0.479157i | ||||
\(169\) | 87.0000 | 0.514793 | ||||||||
\(170\) | 22.3607i | 0.131533i | ||||||||
\(171\) | 2.00000 | + | 17.8885i | 0.0116959 | + | 0.104611i | ||||
\(172\) | −16.0000 | −0.0930233 | ||||||||
\(173\) | 13.4164i | 0.0775515i | 0.999248 | + | 0.0387757i | \(0.0123458\pi\) | ||||
−0.999248 | + | 0.0387757i | \(0.987654\pi\) | |||||||
\(174\) | 140.000 | − | 156.525i | 0.804598 | − | 0.899568i | ||||
\(175\) | 30.0000 | 0.171429 | ||||||||
\(176\) | − | 84.9706i | − | 0.482787i | ||||||
\(177\) | −10.0000 | − | 8.94427i | −0.0564972 | − | 0.0505326i | ||||
\(178\) | 240.000 | 1.34831 | ||||||||
\(179\) | 192.302i | 1.07431i | 0.843483 | + | 0.537156i | \(0.180501\pi\) | ||||
−0.843483 | + | 0.537156i | \(0.819499\pi\) | |||||||
\(180\) | −20.0000 | + | 2.23607i | −0.111111 | + | 0.0124226i | ||||
\(181\) | 2.00000 | 0.0110497 | 0.00552486 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552486 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | 214.663i | 1.17946i | ||||||||
\(183\) | −164.000 | + | 183.358i | −0.896175 | + | 1.00195i | ||||
\(184\) | 90.0000 | 0.489130 | ||||||||
\(185\) | − | 35.7771i | − | 0.193390i | ||||||
\(186\) | −90.0000 | − | 80.4984i | −0.483871 | − | 0.432787i | ||||
\(187\) | −20.0000 | −0.106952 | ||||||||
\(188\) | 49.1935i | 0.261668i | ||||||||
\(189\) | −132.000 | − | 93.9149i | −0.698413 | − | 0.496904i | ||||
\(190\) | −10.0000 | −0.0526316 | ||||||||
\(191\) | − | 205.718i | − | 1.07706i | −0.842607 | − | 0.538529i | \(-0.818980\pi\) | ||
0.842607 | − | 0.538529i | \(-0.181020\pi\) | |||||||
\(192\) | 82.0000 | − | 91.6788i | 0.427083 | − | 0.477494i | ||||
\(193\) | −214.000 | −1.10881 | −0.554404 | − | 0.832248i | \(-0.687054\pi\) | ||||
−0.554404 | + | 0.832248i | \(0.687054\pi\) | |||||||
\(194\) | 371.187i | 1.91334i | ||||||||
\(195\) | −80.0000 | − | 71.5542i | −0.410256 | − | 0.366944i | ||||
\(196\) | 13.0000 | 0.0663265 | ||||||||
\(197\) | − | 93.9149i | − | 0.476725i | −0.971176 | − | 0.238363i | \(-0.923389\pi\) | ||
0.971176 | − | 0.238363i | \(-0.0766107\pi\) | |||||||
\(198\) | −10.0000 | − | 89.4427i | −0.0505051 | − | 0.451731i | ||||
\(199\) | −242.000 | −1.21608 | −0.608040 | − | 0.793906i | \(-0.708044\pi\) | ||||
−0.608040 | + | 0.793906i | \(0.708044\pi\) | |||||||
\(200\) | 33.5410i | 0.167705i | ||||||||
\(201\) | −48.0000 | + | 53.6656i | −0.238806 | + | 0.266993i | ||||
\(202\) | 150.000 | 0.742574 | ||||||||
\(203\) | 187.830i | 0.925270i | ||||||||
\(204\) | 10.0000 | + | 8.94427i | 0.0490196 | + | 0.0438445i | ||||
\(205\) | −140.000 | −0.682927 | ||||||||
\(206\) | − | 58.1378i | − | 0.282222i | ||||||
\(207\) | 120.000 | − | 13.4164i | 0.579710 | − | 0.0648136i | ||||
\(208\) | −304.000 | −1.46154 | ||||||||
\(209\) | − | 8.94427i | − | 0.0427956i | ||||||
\(210\) | 60.0000 | − | 67.0820i | 0.285714 | − | 0.319438i | ||||
\(211\) | 2.00000 | 0.00947867 | 0.00473934 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00473934 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(212\) | − | 4.47214i | − | 0.0210950i | ||||||
\(213\) | 280.000 | + | 250.440i | 1.31455 | + | 1.17577i | ||||
\(214\) | 450.000 | 2.10280 | ||||||||
\(215\) | 35.7771i | 0.166405i | ||||||||
\(216\) | 105.000 | − | 147.580i | 0.486111 | − | 0.683243i | ||||
\(217\) | 108.000 | 0.497696 | ||||||||
\(218\) | − | 84.9706i | − | 0.389773i | ||||||
\(219\) | 148.000 | − | 165.469i | 0.675799 | − | 0.755566i | ||||
\(220\) | 10.0000 | 0.0454545 | ||||||||
\(221\) | 71.5542i | 0.323775i | ||||||||
\(222\) | −80.0000 | − | 71.5542i | −0.360360 | − | 0.322316i | ||||
\(223\) | 86.0000 | 0.385650 | 0.192825 | − | 0.981233i | \(-0.438235\pi\) | ||||
0.192825 | + | 0.981233i | \(0.438235\pi\) | |||||||
\(224\) | − | 93.9149i | − | 0.419263i | ||||||
\(225\) | 5.00000 | + | 44.7214i | 0.0222222 | + | 0.198762i | ||||
\(226\) | 70.0000 | 0.309735 | ||||||||
\(227\) | − | 58.1378i | − | 0.256114i | −0.991767 | − | 0.128057i | \(-0.959126\pi\) | ||
0.991767 | − | 0.128057i | \(-0.0408740\pi\) | |||||||
\(228\) | −4.00000 | + | 4.47214i | −0.0175439 | + | 0.0196146i | ||||
\(229\) | −282.000 | −1.23144 | −0.615721 | − | 0.787965i | \(-0.711135\pi\) | ||||
−0.615721 | + | 0.787965i | \(0.711135\pi\) | |||||||
\(230\) | 67.0820i | 0.291661i | ||||||||
\(231\) | 60.0000 | + | 53.6656i | 0.259740 | + | 0.232319i | ||||
\(232\) | −210.000 | −0.905172 | ||||||||
\(233\) | − | 362.243i | − | 1.55469i | −0.629074 | − | 0.777346i | \(-0.716566\pi\) | ||
0.629074 | − | 0.777346i | \(-0.283434\pi\) | |||||||
\(234\) | −320.000 | + | 35.7771i | −1.36752 | + | 0.152894i | ||||
\(235\) | 110.000 | 0.468085 | ||||||||
\(236\) | − | 4.47214i | − | 0.0189497i | ||||||
\(237\) | −276.000 | + | 308.577i | −1.16456 | + | 1.30201i | ||||
\(238\) | −60.0000 | −0.252101 | ||||||||
\(239\) | − | 250.440i | − | 1.04786i | −0.851760 | − | 0.523932i | \(-0.824464\pi\) | ||
0.851760 | − | 0.523932i | \(-0.175536\pi\) | |||||||
\(240\) | 95.0000 | + | 84.9706i | 0.395833 | + | 0.354044i | ||||
\(241\) | 262.000 | 1.08714 | 0.543568 | − | 0.839365i | \(-0.317073\pi\) | ||||
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(242\) | − | 225.843i | − | 0.933235i | ||||||
\(243\) | 118.000 | − | 212.426i | 0.485597 | − | 0.874183i | ||||
\(244\) | −82.0000 | −0.336066 | ||||||||
\(245\) | − | 29.0689i | − | 0.118649i | ||||||
\(246\) | −280.000 | + | 313.050i | −1.13821 | + | 1.27256i | ||||
\(247\) | −32.0000 | −0.129555 | ||||||||
\(248\) | 120.748i | 0.486886i | ||||||||
\(249\) | 210.000 | + | 187.830i | 0.843373 | + | 0.754336i | ||||
\(250\) | −25.0000 | −0.100000 | ||||||||
\(251\) | 469.574i | 1.87081i | 0.353573 | + | 0.935407i | \(0.384967\pi\) | ||||
−0.353573 | + | 0.935407i | \(0.615033\pi\) | |||||||
\(252\) | −6.00000 | − | 53.6656i | −0.0238095 | − | 0.212959i | ||||
\(253\) | −60.0000 | −0.237154 | ||||||||
\(254\) | 58.1378i | 0.228889i | ||||||||
\(255\) | 20.0000 | − | 22.3607i | 0.0784314 | − | 0.0876889i | ||||
\(256\) | 181.000 | 0.707031 | ||||||||
\(257\) | 201.246i | 0.783059i | 0.920166 | + | 0.391529i | \(0.128054\pi\) | ||||
−0.920166 | + | 0.391529i | \(0.871946\pi\) | |||||||
\(258\) | 80.0000 | + | 71.5542i | 0.310078 | + | 0.277342i | ||||
\(259\) | 96.0000 | 0.370656 | ||||||||
\(260\) | − | 35.7771i | − | 0.137604i | ||||||
\(261\) | −280.000 | + | 31.3050i | −1.07280 | + | 0.119942i | ||||
\(262\) | 30.0000 | 0.114504 | ||||||||
\(263\) | − | 58.1378i | − | 0.221056i | −0.993873 | − | 0.110528i | \(-0.964746\pi\) | ||
0.993873 | − | 0.110528i | \(-0.0352542\pi\) | |||||||
\(264\) | −60.0000 | + | 67.0820i | −0.227273 | + | 0.254099i | ||||
\(265\) | −10.0000 | −0.0377358 | ||||||||
\(266\) | − | 26.8328i | − | 0.100875i | ||||||
\(267\) | −240.000 | − | 214.663i | −0.898876 | − | 0.803979i | ||||
\(268\) | −24.0000 | −0.0895522 | ||||||||
\(269\) | − | 371.187i | − | 1.37988i | −0.723867 | − | 0.689939i | \(-0.757637\pi\) | ||
0.723867 | − | 0.689939i | \(-0.242363\pi\) | |||||||
\(270\) | 110.000 | + | 78.2624i | 0.407407 | + | 0.289861i | ||||
\(271\) | 82.0000 | 0.302583 | 0.151292 | − | 0.988489i | \(-0.451657\pi\) | ||||
0.151292 | + | 0.988489i | \(0.451657\pi\) | |||||||
\(272\) | − | 84.9706i | − | 0.312392i | ||||||
\(273\) | 192.000 | − | 214.663i | 0.703297 | − | 0.786310i | ||||
\(274\) | −270.000 | −0.985401 | ||||||||
\(275\) | − | 22.3607i | − | 0.0813116i | ||||||
\(276\) | 30.0000 | + | 26.8328i | 0.108696 | + | 0.0972203i | ||||
\(277\) | 24.0000 | 0.0866426 | 0.0433213 | − | 0.999061i | \(-0.486206\pi\) | ||||
0.0433213 | + | 0.999061i | \(0.486206\pi\) | |||||||
\(278\) | 183.358i | 0.659560i | ||||||||
\(279\) | 18.0000 | + | 160.997i | 0.0645161 | + | 0.577050i | ||||
\(280\) | −90.0000 | −0.321429 | ||||||||
\(281\) | − | 187.830i | − | 0.668433i | −0.942496 | − | 0.334217i | \(-0.891528\pi\) | ||
0.942496 | − | 0.334217i | \(-0.108472\pi\) | |||||||
\(282\) | 220.000 | − | 245.967i | 0.780142 | − | 0.872225i | ||||
\(283\) | −144.000 | −0.508834 | −0.254417 | − | 0.967095i | \(-0.581884\pi\) | ||||
−0.254417 | + | 0.967095i | \(0.581884\pi\) | |||||||
\(284\) | 125.220i | 0.440915i | ||||||||
\(285\) | 10.0000 | + | 8.94427i | 0.0350877 | + | 0.0313834i | ||||
\(286\) | 160.000 | 0.559441 | ||||||||
\(287\) | − | 375.659i | − | 1.30892i | ||||||
\(288\) | 140.000 | − | 15.6525i | 0.486111 | − | 0.0543489i | ||||
\(289\) | 269.000 | 0.930796 | ||||||||
\(290\) | − | 156.525i | − | 0.539741i | ||||||
\(291\) | 332.000 | − | 371.187i | 1.14089 | − | 1.27556i | ||||
\(292\) | 74.0000 | 0.253425 | ||||||||
\(293\) | 469.574i | 1.60264i | 0.598234 | + | 0.801321i | \(0.295869\pi\) | ||||
−0.598234 | + | 0.801321i | \(0.704131\pi\) | |||||||
\(294\) | −65.0000 | − | 58.1378i | −0.221088 | − | 0.197748i | ||||
\(295\) | −10.0000 | −0.0338983 | ||||||||
\(296\) | 107.331i | 0.362606i | ||||||||
\(297\) | −70.0000 | + | 98.3870i | −0.235690 | + | 0.331269i | ||||
\(298\) | −250.000 | −0.838926 | ||||||||
\(299\) | 214.663i | 0.717935i | ||||||||
\(300\) | −10.0000 | + | 11.1803i | −0.0333333 | + | 0.0372678i | ||||
\(301\) | −96.0000 | −0.318937 | ||||||||
\(302\) | 353.299i | 1.16986i | ||||||||
\(303\) | −150.000 | − | 134.164i | −0.495050 | − | 0.442786i | ||||
\(304\) | 38.0000 | 0.125000 | ||||||||
\(305\) | 183.358i | 0.601172i | ||||||||
\(306\) | −10.0000 | − | 89.4427i | −0.0326797 | − | 0.292296i | ||||
\(307\) | 184.000 | 0.599349 | 0.299674 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299674 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(308\) | 26.8328i | 0.0871195i | ||||||||
\(309\) | −52.0000 | + | 58.1378i | −0.168285 | + | 0.188148i | ||||
\(310\) | −90.0000 | −0.290323 | ||||||||
\(311\) | 160.997i | 0.517675i | 0.965921 | + | 0.258837i | \(0.0833394\pi\) | ||||
−0.965921 | + | 0.258837i | \(0.916661\pi\) | |||||||
\(312\) | 240.000 | + | 214.663i | 0.769231 | + | 0.688021i | ||||
\(313\) | −394.000 | −1.25879 | −0.629393 | − | 0.777087i | \(-0.716696\pi\) | ||||
−0.629393 | + | 0.777087i | \(0.716696\pi\) | |||||||
\(314\) | − | 366.715i | − | 1.16788i | ||||||
\(315\) | −120.000 | + | 13.4164i | −0.380952 | + | 0.0425918i | ||||
\(316\) | −138.000 | −0.436709 | ||||||||
\(317\) | 451.686i | 1.42488i | 0.701735 | + | 0.712438i | \(0.252409\pi\) | ||||
−0.701735 | + | 0.712438i | \(0.747591\pi\) | |||||||
\(318\) | −20.0000 | + | 22.3607i | −0.0628931 | + | 0.0703166i | ||||
\(319\) | 140.000 | 0.438871 | ||||||||
\(320\) | − | 91.6788i | − | 0.286496i | ||||||
\(321\) | −450.000 | − | 402.492i | −1.40187 | − | 1.25387i | ||||
\(322\) | −180.000 | −0.559006 | ||||||||
\(323\) | − | 8.94427i | − | 0.0276912i | ||||||
\(324\) | 79.0000 | − | 17.8885i | 0.243827 | − | 0.0552116i | ||||
\(325\) | −80.0000 | −0.246154 | ||||||||
\(326\) | − | 527.712i | − | 1.61875i | ||||||
\(327\) | −76.0000 | + | 84.9706i | −0.232416 | + | 0.259849i | ||||
\(328\) | 420.000 | 1.28049 | ||||||||
\(329\) | 295.161i | 0.897146i | ||||||||
\(330\) | −50.0000 | − | 44.7214i | −0.151515 | − | 0.135519i | ||||
\(331\) | −198.000 | −0.598187 | −0.299094 | − | 0.954224i | \(-0.596684\pi\) | ||||
−0.299094 | + | 0.954224i | \(0.596684\pi\) | |||||||
\(332\) | 93.9149i | 0.282876i | ||||||||
\(333\) | 16.0000 | + | 143.108i | 0.0480480 | + | 0.429755i | ||||
\(334\) | 210.000 | 0.628743 | ||||||||
\(335\) | 53.6656i | 0.160196i | ||||||||
\(336\) | −228.000 | + | 254.912i | −0.678571 | + | 0.758666i | ||||
\(337\) | 394.000 | 1.16914 | 0.584570 | − | 0.811343i | \(-0.301263\pi\) | ||||
0.584570 | + | 0.811343i | \(0.301263\pi\) | |||||||
\(338\) | − | 194.538i | − | 0.575556i | ||||||
\(339\) | −70.0000 | − | 62.6099i | −0.206490 | − | 0.184690i | ||||
\(340\) | 10.0000 | 0.0294118 | ||||||||
\(341\) | − | 80.4984i | − | 0.236066i | ||||||
\(342\) | 40.0000 | − | 4.47214i | 0.116959 | − | 0.0130764i | ||||
\(343\) | 372.000 | 1.08455 | ||||||||
\(344\) | − | 107.331i | − | 0.312009i | ||||||
\(345\) | 60.0000 | − | 67.0820i | 0.173913 | − | 0.194441i | ||||
\(346\) | 30.0000 | 0.0867052 | ||||||||
\(347\) | − | 183.358i | − | 0.528408i | −0.964467 | − | 0.264204i | \(-0.914891\pi\) | ||
0.964467 | − | 0.264204i | \(-0.0851092\pi\) | |||||||
\(348\) | −70.0000 | − | 62.6099i | −0.201149 | − | 0.179914i | ||||
\(349\) | −362.000 | −1.03725 | −0.518625 | − | 0.855002i | \(-0.673556\pi\) | ||||
−0.518625 | + | 0.855002i | \(0.673556\pi\) | |||||||
\(350\) | − | 67.0820i | − | 0.191663i | ||||||
\(351\) | 352.000 | + | 250.440i | 1.00285 | + | 0.713503i | ||||
\(352\) | −70.0000 | −0.198864 | ||||||||
\(353\) | − | 308.577i | − | 0.874157i | −0.899423 | − | 0.437078i | \(-0.856013\pi\) | ||
0.899423 | − | 0.437078i | \(-0.143987\pi\) | |||||||
\(354\) | −20.0000 | + | 22.3607i | −0.0564972 | + | 0.0631658i | ||||
\(355\) | 280.000 | 0.788732 | ||||||||
\(356\) | − | 107.331i | − | 0.301492i | ||||||
\(357\) | 60.0000 | + | 53.6656i | 0.168067 | + | 0.150324i | ||||
\(358\) | 430.000 | 1.20112 | ||||||||
\(359\) | 295.161i | 0.822175i | 0.911596 | + | 0.411088i | \(0.134851\pi\) | ||||
−0.911596 | + | 0.411088i | \(0.865149\pi\) | |||||||
\(360\) | −15.0000 | − | 134.164i | −0.0416667 | − | 0.372678i | ||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | − | 4.47214i | − | 0.0123540i | ||||||
\(363\) | −202.000 | + | 225.843i | −0.556474 | + | 0.622157i | ||||
\(364\) | 96.0000 | 0.263736 | ||||||||
\(365\) | − | 165.469i | − | 0.453340i | ||||||
\(366\) | 410.000 | + | 366.715i | 1.12022 | + | 1.00195i | ||||
\(367\) | −186.000 | −0.506812 | −0.253406 | − | 0.967360i | \(-0.581551\pi\) | ||||
−0.253406 | + | 0.967360i | \(0.581551\pi\) | |||||||
\(368\) | − | 254.912i | − | 0.692695i | ||||||
\(369\) | 560.000 | − | 62.6099i | 1.51762 | − | 0.169675i | ||||
\(370\) | −80.0000 | −0.216216 | ||||||||
\(371\) | − | 26.8328i | − | 0.0723256i | ||||||
\(372\) | −36.0000 | + | 40.2492i | −0.0967742 | + | 0.108197i | ||||
\(373\) | −44.0000 | −0.117962 | −0.0589812 | − | 0.998259i | \(-0.518785\pi\) | ||||
−0.0589812 | + | 0.998259i | \(0.518785\pi\) | |||||||
\(374\) | 44.7214i | 0.119576i | ||||||||
\(375\) | 25.0000 | + | 22.3607i | 0.0666667 | + | 0.0596285i | ||||
\(376\) | −330.000 | −0.877660 | ||||||||
\(377\) | − | 500.879i | − | 1.32859i | ||||||
\(378\) | −210.000 | + | 295.161i | −0.555556 | + | 0.780849i | ||||
\(379\) | −362.000 | −0.955145 | −0.477573 | − | 0.878592i | \(-0.658483\pi\) | ||||
−0.477573 | + | 0.878592i | \(0.658483\pi\) | |||||||
\(380\) | 4.47214i | 0.0117688i | ||||||||
\(381\) | 52.0000 | − | 58.1378i | 0.136483 | − | 0.152593i | ||||
\(382\) | −460.000 | −1.20419 | ||||||||
\(383\) | − | 362.243i | − | 0.945804i | −0.881115 | − | 0.472902i | \(-0.843206\pi\) | ||
0.881115 | − | 0.472902i | \(-0.156794\pi\) | |||||||
\(384\) | −345.000 | − | 308.577i | −0.898438 | − | 0.803587i | ||||
\(385\) | 60.0000 | 0.155844 | ||||||||
\(386\) | 478.519i | 1.23969i | ||||||||
\(387\) | −16.0000 | − | 143.108i | −0.0413437 | − | 0.369789i | ||||
\(388\) | 166.000 | 0.427835 | ||||||||
\(389\) | 442.741i | 1.13815i | 0.822285 | + | 0.569076i | \(0.192699\pi\) | ||||
−0.822285 | + | 0.569076i | \(0.807301\pi\) | |||||||
\(390\) | −160.000 | + | 178.885i | −0.410256 | + | 0.458681i | ||||
\(391\) | −60.0000 | −0.153453 | ||||||||
\(392\) | 87.2067i | 0.222466i | ||||||||
\(393\) | −30.0000 | − | 26.8328i | −0.0763359 | − | 0.0682769i | ||||
\(394\) | −210.000 | −0.532995 | ||||||||
\(395\) | 308.577i | 0.781209i | ||||||||
\(396\) | −40.0000 | + | 4.47214i | −0.101010 | + | 0.0112933i | ||||
\(397\) | 124.000 | 0.312343 | 0.156171 | − | 0.987730i | \(-0.450085\pi\) | ||||
0.156171 | + | 0.987730i | \(0.450085\pi\) | |||||||
\(398\) | 541.128i | 1.35962i | ||||||||
\(399\) | −24.0000 | + | 26.8328i | −0.0601504 | + | 0.0672502i | ||||
\(400\) | 95.0000 | 0.237500 | ||||||||
\(401\) | − | 268.328i | − | 0.669148i | −0.942370 | − | 0.334574i | \(-0.891408\pi\) | ||
0.942370 | − | 0.334574i | \(-0.108592\pi\) | |||||||
\(402\) | 120.000 | + | 107.331i | 0.298507 | + | 0.266993i | ||||
\(403\) | −288.000 | −0.714640 | ||||||||
\(404\) | − | 67.0820i | − | 0.166045i | ||||||
\(405\) | −40.0000 | − | 176.649i | −0.0987654 | − | 0.436171i | ||||
\(406\) | 420.000 | 1.03448 | ||||||||
\(407\) | − | 71.5542i | − | 0.175809i | ||||||
\(408\) | −60.0000 | + | 67.0820i | −0.147059 | + | 0.164417i | ||||
\(409\) | 458.000 | 1.11980 | 0.559902 | − | 0.828559i | \(-0.310839\pi\) | ||||
0.559902 | + | 0.828559i | \(0.310839\pi\) | |||||||
\(410\) | 313.050i | 0.763535i | ||||||||
\(411\) | 270.000 | + | 241.495i | 0.656934 | + | 0.587580i | ||||
\(412\) | −26.0000 | −0.0631068 | ||||||||
\(413\) | − | 26.8328i | − | 0.0649705i | ||||||
\(414\) | −30.0000 | − | 268.328i | −0.0724638 | − | 0.648136i | ||||
\(415\) | 210.000 | 0.506024 | ||||||||
\(416\) | 250.440i | 0.602018i | ||||||||
\(417\) | 164.000 | − | 183.358i | 0.393285 | − | 0.439706i | ||||
\(418\) | −20.0000 | −0.0478469 | ||||||||
\(419\) | − | 594.794i | − | 1.41956i | −0.704425 | − | 0.709778i | \(-0.748795\pi\) | ||
0.704425 | − | 0.709778i | \(-0.251205\pi\) | |||||||
\(420\) | −30.0000 | − | 26.8328i | −0.0714286 | − | 0.0638877i | ||||
\(421\) | 562.000 | 1.33492 | 0.667458 | − | 0.744647i | \(-0.267382\pi\) | ||||
0.667458 | + | 0.744647i | \(0.267382\pi\) | |||||||
\(422\) | − | 4.47214i | − | 0.0105975i | ||||||
\(423\) | −440.000 | + | 49.1935i | −1.04019 | + | 0.116297i | ||||
\(424\) | 30.0000 | 0.0707547 | ||||||||
\(425\) | − | 22.3607i | − | 0.0526134i | ||||||
\(426\) | 560.000 | − | 626.099i | 1.31455 | − | 1.46972i | ||||
\(427\) | −492.000 | −1.15222 | ||||||||
\(428\) | − | 201.246i | − | 0.470201i | ||||||
\(429\) | −160.000 | − | 143.108i | −0.372960 | − | 0.333586i | ||||
\(430\) | 80.0000 | 0.186047 | ||||||||
\(431\) | 348.827i | 0.809342i | 0.914462 | + | 0.404671i | \(0.132614\pi\) | ||||
−0.914462 | + | 0.404671i | \(0.867386\pi\) | |||||||
\(432\) | −418.000 | − | 297.397i | −0.967593 | − | 0.688419i | ||||
\(433\) | 226.000 | 0.521940 | 0.260970 | − | 0.965347i | \(-0.415958\pi\) | ||||
0.260970 | + | 0.965347i | \(0.415958\pi\) | |||||||
\(434\) | − | 241.495i | − | 0.556441i | ||||||
\(435\) | −140.000 | + | 156.525i | −0.321839 | + | 0.359827i | ||||
\(436\) | −38.0000 | −0.0871560 | ||||||||
\(437\) | − | 26.8328i | − | 0.0614023i | ||||||
\(438\) | −370.000 | − | 330.938i | −0.844749 | − | 0.755566i | ||||
\(439\) | −2.00000 | −0.00455581 | −0.00227790 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227790 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(440\) | 67.0820i | 0.152459i | ||||||||
\(441\) | 13.0000 | + | 116.276i | 0.0294785 | + | 0.263663i | ||||
\(442\) | 160.000 | 0.361991 | ||||||||
\(443\) | 201.246i | 0.454280i | 0.973862 | + | 0.227140i | \(0.0729375\pi\) | ||||
−0.973862 | + | 0.227140i | \(0.927062\pi\) | |||||||
\(444\) | −32.0000 | + | 35.7771i | −0.0720721 | + | 0.0805790i | ||||
\(445\) | −240.000 | −0.539326 | ||||||||
\(446\) | − | 192.302i | − | 0.431170i | ||||||
\(447\) | 250.000 | + | 223.607i | 0.559284 | + | 0.500239i | ||||
\(448\) | 246.000 | 0.549107 | ||||||||
\(449\) | 313.050i | 0.697215i | 0.937269 | + | 0.348607i | \(0.113345\pi\) | ||||
−0.937269 | + | 0.348607i | \(0.886655\pi\) | |||||||
\(450\) | 100.000 | − | 11.1803i | 0.222222 | − | 0.0248452i | ||||
\(451\) | −280.000 | −0.620843 | ||||||||
\(452\) | − | 31.3050i | − | 0.0692587i | ||||||
\(453\) | 316.000 | − | 353.299i | 0.697572 | − | 0.779909i | ||||
\(454\) | −130.000 | −0.286344 | ||||||||
\(455\) | − | 214.663i | − | 0.471786i | ||||||
\(456\) | −30.0000 | − | 26.8328i | −0.0657895 | − | 0.0588439i | ||||
\(457\) | 334.000 | 0.730853 | 0.365427 | − | 0.930840i | \(-0.380923\pi\) | ||||
0.365427 | + | 0.930840i | \(0.380923\pi\) | |||||||
\(458\) | 630.571i | 1.37679i | ||||||||
\(459\) | −70.0000 | + | 98.3870i | −0.152505 | + | 0.214351i | ||||
\(460\) | 30.0000 | 0.0652174 | ||||||||
\(461\) | 93.9149i | 0.203720i | 0.994799 | + | 0.101860i | \(0.0324794\pi\) | ||||
−0.994799 | + | 0.101860i | \(0.967521\pi\) | |||||||
\(462\) | 120.000 | − | 134.164i | 0.259740 | − | 0.290398i | ||||
\(463\) | 366.000 | 0.790497 | 0.395248 | − | 0.918574i | \(-0.370659\pi\) | ||||
0.395248 | + | 0.918574i | \(0.370659\pi\) | |||||||
\(464\) | 594.794i | 1.28188i | ||||||||
\(465\) | 90.0000 | + | 80.4984i | 0.193548 | + | 0.173115i | ||||
\(466\) | −810.000 | −1.73820 | ||||||||
\(467\) | 451.686i | 0.967207i | 0.875287 | + | 0.483604i | \(0.160672\pi\) | ||||
−0.875287 | + | 0.483604i | \(0.839328\pi\) | |||||||
\(468\) | 16.0000 | + | 143.108i | 0.0341880 | + | 0.305787i | ||||
\(469\) | −144.000 | −0.307036 | ||||||||
\(470\) | − | 245.967i | − | 0.523335i | ||||||
\(471\) | −328.000 | + | 366.715i | −0.696391 | + | 0.778588i | ||||
\(472\) | 30.0000 | 0.0635593 | ||||||||
\(473\) | 71.5542i | 0.151277i | ||||||||
\(474\) | 690.000 | + | 617.155i | 1.45570 | + | 1.30201i | ||||
\(475\) | 10.0000 | 0.0210526 | ||||||||
\(476\) | 26.8328i | 0.0563715i | ||||||||
\(477\) | 40.0000 | − | 4.47214i | 0.0838574 | − | 0.00937555i | ||||
\(478\) | −560.000 | −1.17155 | ||||||||
\(479\) | − | 590.322i | − | 1.23240i | −0.787588 | − | 0.616202i | \(-0.788670\pi\) | ||
0.787588 | − | 0.616202i | \(-0.211330\pi\) | |||||||
\(480\) | 70.0000 | − | 78.2624i | 0.145833 | − | 0.163047i | ||||
\(481\) | −256.000 | −0.532225 | ||||||||
\(482\) | − | 585.850i | − | 1.21546i | ||||||
\(483\) | 180.000 | + | 160.997i | 0.372671 | + | 0.333327i | ||||
\(484\) | −101.000 | −0.208678 | ||||||||
\(485\) | − | 371.187i | − | 0.765335i | ||||||
\(486\) | −475.000 | − | 263.856i | −0.977366 | − | 0.542914i | ||||
\(487\) | −886.000 | −1.81930 | −0.909651 | − | 0.415374i | \(-0.863651\pi\) | ||||
−0.909651 | + | 0.415374i | \(0.863651\pi\) | |||||||
\(488\) | − | 550.073i | − | 1.12720i | ||||||
\(489\) | −472.000 | + | 527.712i | −0.965235 | + | 1.07917i | ||||
\(490\) | −65.0000 | −0.132653 | ||||||||
\(491\) | − | 406.964i | − | 0.828848i | −0.910084 | − | 0.414424i | \(-0.863983\pi\) | ||
0.910084 | − | 0.414424i | \(-0.136017\pi\) | |||||||
\(492\) | 140.000 | + | 125.220i | 0.284553 | + | 0.254512i | ||||
\(493\) | 140.000 | 0.283976 | ||||||||
\(494\) | 71.5542i | 0.144847i | ||||||||
\(495\) | 10.0000 | + | 89.4427i | 0.0202020 | + | 0.180692i | ||||
\(496\) | 342.000 | 0.689516 | ||||||||
\(497\) | 751.319i | 1.51171i | ||||||||
\(498\) | 420.000 | − | 469.574i | 0.843373 | − | 0.942920i | ||||
\(499\) | −2.00000 | −0.00400802 | −0.00200401 | − | 0.999998i | \(-0.500638\pi\) | ||||
−0.00200401 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(500\) | 11.1803i | 0.0223607i | ||||||||
\(501\) | −210.000 | − | 187.830i | −0.419162 | − | 0.374910i | ||||
\(502\) | 1050.00 | 2.09163 | ||||||||
\(503\) | − | 219.135i | − | 0.435655i | −0.975987 | − | 0.217828i | \(-0.930103\pi\) | ||
0.975987 | − | 0.217828i | \(-0.0698971\pi\) | |||||||
\(504\) | 360.000 | − | 40.2492i | 0.714286 | − | 0.0798596i | ||||
\(505\) | −150.000 | −0.297030 | ||||||||
\(506\) | 134.164i | 0.265146i | ||||||||
\(507\) | −174.000 | + | 194.538i | −0.343195 | + | 0.383704i | ||||
\(508\) | 26.0000 | 0.0511811 | ||||||||
\(509\) | − | 800.512i | − | 1.57272i | −0.617771 | − | 0.786358i | \(-0.711964\pi\) | ||
0.617771 | − | 0.786358i | \(-0.288036\pi\) | |||||||
\(510\) | −50.0000 | − | 44.7214i | −0.0980392 | − | 0.0876889i | ||||
\(511\) | 444.000 | 0.868885 | ||||||||
\(512\) | 212.426i | 0.414895i | ||||||||
\(513\) | −44.0000 | − | 31.3050i | −0.0857700 | − | 0.0610233i | ||||
\(514\) | 450.000 | 0.875486 | ||||||||
\(515\) | 58.1378i | 0.112889i | ||||||||
\(516\) | 32.0000 | − | 35.7771i | 0.0620155 | − | 0.0693354i | ||||
\(517\) | 220.000 | 0.425532 | ||||||||
\(518\) | − | 214.663i | − | 0.414406i | ||||||
\(519\) | −30.0000 | − | 26.8328i | −0.0578035 | − | 0.0517010i | ||||
\(520\) | 240.000 | 0.461538 | ||||||||
\(521\) | − | 527.712i | − | 1.01288i | −0.862274 | − | 0.506441i | \(-0.830961\pi\) | ||
0.862274 | − | 0.506441i | \(-0.169039\pi\) | |||||||
\(522\) | 70.0000 | + | 626.099i | 0.134100 | + | 1.19942i | ||||
\(523\) | 376.000 | 0.718929 | 0.359465 | − | 0.933159i | \(-0.382959\pi\) | ||||
0.359465 | + | 0.933159i | \(0.382959\pi\) | |||||||
\(524\) | − | 13.4164i | − | 0.0256038i | ||||||
\(525\) | −60.0000 | + | 67.0820i | −0.114286 | + | 0.127775i | ||||
\(526\) | −130.000 | −0.247148 | ||||||||
\(527\) | − | 80.4984i | − | 0.152748i | ||||||
\(528\) | 190.000 | + | 169.941i | 0.359848 | + | 0.321858i | ||||
\(529\) | 349.000 | 0.659735 | ||||||||
\(530\) | 22.3607i | 0.0421900i | ||||||||
\(531\) | 40.0000 | − | 4.47214i | 0.0753296 | − | 0.00842210i | ||||
\(532\) | −12.0000 | −0.0225564 | ||||||||
\(533\) | 1001.76i | 1.87947i | ||||||||
\(534\) | −480.000 | + | 536.656i | −0.898876 | + | 1.00497i | ||||
\(535\) | −450.000 | −0.841121 | ||||||||
\(536\) | − | 160.997i | − | 0.300367i | ||||||
\(537\) | −430.000 | − | 384.604i | −0.800745 | − | 0.716208i | ||||
\(538\) | −830.000 | −1.54275 | ||||||||
\(539\) | − | 58.1378i | − | 0.107862i | ||||||
\(540\) | 35.0000 | − | 49.1935i | 0.0648148 | − | 0.0910991i | ||||
\(541\) | −198.000 | −0.365989 | −0.182994 | − | 0.983114i | \(-0.558579\pi\) | ||||
−0.182994 | + | 0.983114i | \(0.558579\pi\) | |||||||
\(542\) | − | 183.358i | − | 0.338298i | ||||||
\(543\) | −4.00000 | + | 4.47214i | −0.00736648 | + | 0.00823598i | ||||
\(544\) | −70.0000 | −0.128676 | ||||||||
\(545\) | 84.9706i | 0.155909i | ||||||||
\(546\) | −480.000 | − | 429.325i | −0.879121 | − | 0.786310i | ||||
\(547\) | 1024.00 | 1.87203 | 0.936015 | − | 0.351961i | \(-0.114485\pi\) | ||||
0.936015 | + | 0.351961i | \(0.114485\pi\) | |||||||
\(548\) | 120.748i | 0.220342i | ||||||||
\(549\) | −82.0000 | − | 733.430i | −0.149362 | − | 1.33594i | ||||
\(550\) | −50.0000 | −0.0909091 | ||||||||
\(551\) | 62.6099i | 0.113630i | ||||||||
\(552\) | −180.000 | + | 201.246i | −0.326087 | + | 0.364576i | ||||
\(553\) | −828.000 | −1.49729 | ||||||||
\(554\) | − | 53.6656i | − | 0.0968694i | ||||||
\(555\) | 80.0000 | + | 71.5542i | 0.144144 | + | 0.128926i | ||||
\(556\) | 82.0000 | 0.147482 | ||||||||
\(557\) | 67.0820i | 0.120435i | 0.998185 | + | 0.0602173i | \(0.0191794\pi\) | ||||
−0.998185 | + | 0.0602173i | \(0.980821\pi\) | |||||||
\(558\) | 360.000 | − | 40.2492i | 0.645161 | − | 0.0721312i | ||||
\(559\) | 256.000 | 0.457961 | ||||||||
\(560\) | 254.912i | 0.455200i | ||||||||
\(561\) | 40.0000 | − | 44.7214i | 0.0713012 | − | 0.0797172i | ||||
\(562\) | −420.000 | −0.747331 | ||||||||
\(563\) | 254.912i | 0.452774i | 0.974037 | + | 0.226387i | \(0.0726914\pi\) | ||||
−0.974037 | + | 0.226387i | \(0.927309\pi\) | |||||||
\(564\) | −110.000 | − | 98.3870i | −0.195035 | − | 0.174445i | ||||
\(565\) | −70.0000 | −0.123894 | ||||||||
\(566\) | 321.994i | 0.568894i | ||||||||
\(567\) | 474.000 | − | 107.331i | 0.835979 | − | 0.189297i | ||||
\(568\) | −840.000 | −1.47887 | ||||||||
\(569\) | 858.650i | 1.50905i | 0.656271 | + | 0.754526i | \(0.272133\pi\) | ||||
−0.656271 | + | 0.754526i | \(0.727867\pi\) | |||||||
\(570\) | 20.0000 | − | 22.3607i | 0.0350877 | − | 0.0392293i | ||||
\(571\) | 962.000 | 1.68476 | 0.842382 | − | 0.538881i | \(-0.181153\pi\) | ||||
0.842382 | + | 0.538881i | \(0.181153\pi\) | |||||||
\(572\) | − | 71.5542i | − | 0.125095i | ||||||
\(573\) | 460.000 | + | 411.437i | 0.802792 | + | 0.718039i | ||||
\(574\) | −840.000 | −1.46341 | ||||||||
\(575\) | − | 67.0820i | − | 0.116664i | ||||||
\(576\) | 41.0000 | + | 366.715i | 0.0711806 | + | 0.636658i | ||||
\(577\) | −886.000 | −1.53553 | −0.767764 | − | 0.640732i | \(-0.778631\pi\) | ||||
−0.767764 | + | 0.640732i | \(0.778631\pi\) | |||||||
\(578\) | − | 601.502i | − | 1.04066i | ||||||
\(579\) | 428.000 | − | 478.519i | 0.739206 | − | 0.826457i | ||||
\(580\) | −70.0000 | −0.120690 | ||||||||
\(581\) | 563.489i | 0.969861i | ||||||||
\(582\) | −830.000 | − | 742.375i | −1.42612 | − | 1.27556i | ||||
\(583\) | −20.0000 | −0.0343053 | ||||||||
\(584\) | 496.407i | 0.850012i | ||||||||
\(585\) | 320.000 | − | 35.7771i | 0.547009 | − | 0.0611574i | ||||
\(586\) | 1050.00 | 1.79181 | ||||||||
\(587\) | − | 657.404i | − | 1.11994i | −0.828513 | − | 0.559969i | \(-0.810813\pi\) | ||
0.828513 | − | 0.559969i | \(-0.189187\pi\) | |||||||
\(588\) | −26.0000 | + | 29.0689i | −0.0442177 | + | 0.0494369i | ||||
\(589\) | 36.0000 | 0.0611205 | ||||||||
\(590\) | 22.3607i | 0.0378995i | ||||||||
\(591\) | 210.000 | + | 187.830i | 0.355330 | + | 0.317817i | ||||
\(592\) | 304.000 | 0.513514 | ||||||||
\(593\) | − | 111.803i | − | 0.188539i | −0.995547 | − | 0.0942693i | \(-0.969949\pi\) | ||
0.995547 | − | 0.0942693i | \(-0.0300515\pi\) | |||||||
\(594\) | 220.000 | + | 156.525i | 0.370370 | + | 0.263510i | ||||
\(595\) | 60.0000 | 0.100840 | ||||||||
\(596\) | 111.803i | 0.187590i | ||||||||
\(597\) | 484.000 | − | 541.128i | 0.810720 | − | 0.906413i | ||||
\(598\) | 480.000 | 0.802676 | ||||||||
\(599\) | 223.607i | 0.373300i | 0.982426 | + | 0.186650i | \(0.0597631\pi\) | ||||
−0.982426 | + | 0.186650i | \(0.940237\pi\) | |||||||
\(600\) | −75.0000 | − | 67.0820i | −0.125000 | − | 0.111803i | ||||
\(601\) | 2.00000 | 0.00332779 | 0.00166389 | − | 0.999999i | \(-0.499470\pi\) | ||||
0.00166389 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(602\) | 214.663i | 0.356582i | ||||||||
\(603\) | −24.0000 | − | 214.663i | −0.0398010 | − | 0.355991i | ||||
\(604\) | 158.000 | 0.261589 | ||||||||
\(605\) | 225.843i | 0.373294i | ||||||||
\(606\) | −300.000 | + | 335.410i | −0.495050 | + | 0.553482i | ||||
\(607\) | −506.000 | −0.833608 | −0.416804 | − | 0.908996i | \(-0.636850\pi\) | ||||
−0.416804 | + | 0.908996i | \(0.636850\pi\) | |||||||
\(608\) | − | 31.3050i | − | 0.0514884i | ||||||
\(609\) | −420.000 | − | 375.659i | −0.689655 | − | 0.616846i | ||||
\(610\) | 410.000 | 0.672131 | ||||||||
\(611\) | − | 787.096i | − | 1.28821i | ||||||
\(612\) | −40.0000 | + | 4.47214i | −0.0653595 | + | 0.00730741i | ||||
\(613\) | 556.000 | 0.907015 | 0.453507 | − | 0.891253i | \(-0.350173\pi\) | ||||
0.453507 | + | 0.891253i | \(0.350173\pi\) | |||||||
\(614\) | − | 411.437i | − | 0.670092i | ||||||
\(615\) | 280.000 | − | 313.050i | 0.455285 | − | 0.509024i | ||||
\(616\) | −180.000 | −0.292208 | ||||||||
\(617\) | 93.9149i | 0.152212i | 0.997100 | + | 0.0761060i | \(0.0242488\pi\) | ||||
−0.997100 | + | 0.0761060i | \(0.975751\pi\) | |||||||
\(618\) | 130.000 | + | 116.276i | 0.210356 | + | 0.188148i | ||||
\(619\) | −802.000 | −1.29564 | −0.647819 | − | 0.761794i | \(-0.724319\pi\) | ||||
−0.647819 | + | 0.761794i | \(0.724319\pi\) | |||||||
\(620\) | 40.2492i | 0.0649181i | ||||||||
\(621\) | −210.000 | + | 295.161i | −0.338164 | + | 0.475299i | ||||
\(622\) | 360.000 | 0.578778 | ||||||||
\(623\) | − | 643.988i | − | 1.03369i | ||||||
\(624\) | 608.000 | − | 679.765i | 0.974359 | − | 1.08937i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 881.011i | 1.40737i | ||||||||
\(627\) | 20.0000 | + | 17.8885i | 0.0318979 | + | 0.0285304i | ||||
\(628\) | −164.000 | −0.261146 | ||||||||
\(629\) | − | 71.5542i | − | 0.113759i | ||||||
\(630\) | 30.0000 | + | 268.328i | 0.0476190 | + | 0.425918i | ||||
\(631\) | −698.000 | −1.10618 | −0.553090 | − | 0.833121i | \(-0.686552\pi\) | ||||
−0.553090 | + | 0.833121i | \(0.686552\pi\) | |||||||
\(632\) | − | 925.732i | − | 1.46477i | ||||||
\(633\) | −4.00000 | + | 4.47214i | −0.00631912 | + | 0.00706499i | ||||
\(634\) | 1010.00 | 1.59306 | ||||||||
\(635\) | − | 58.1378i | − | 0.0915555i | ||||||
\(636\) | 10.0000 | + | 8.94427i | 0.0157233 | + | 0.0140633i | ||||
\(637\) | −208.000 | −0.326531 | ||||||||
\(638\) | − | 313.050i | − | 0.490673i | ||||||
\(639\) | −1120.00 | + | 125.220i | −1.75274 | + | 0.195962i | ||||
\(640\) | −345.000 | −0.539062 | ||||||||
\(641\) | 912.316i | 1.42327i | 0.702550 | + | 0.711635i | \(0.252045\pi\) | ||||
−0.702550 | + | 0.711635i | \(0.747955\pi\) | |||||||
\(642\) | −900.000 | + | 1006.23i | −1.40187 | + | 1.56734i | ||||
\(643\) | 156.000 | 0.242613 | 0.121306 | − | 0.992615i | \(-0.461292\pi\) | ||||
0.121306 | + | 0.992615i | \(0.461292\pi\) | |||||||
\(644\) | 80.4984i | 0.124998i | ||||||||
\(645\) | −80.0000 | − | 71.5542i | −0.124031 | − | 0.110937i | ||||
\(646\) | −20.0000 | −0.0309598 | ||||||||
\(647\) | 755.791i | 1.16815i | 0.811701 | + | 0.584073i | \(0.198542\pi\) | ||||
−0.811701 | + | 0.584073i | \(0.801458\pi\) | |||||||
\(648\) | 120.000 | + | 529.948i | 0.185185 | + | 0.817821i | ||||
\(649\) | −20.0000 | −0.0308166 | ||||||||
\(650\) | 178.885i | 0.275208i | ||||||||
\(651\) | −216.000 | + | 241.495i | −0.331797 | + | 0.370961i | ||||
\(652\) | −236.000 | −0.361963 | ||||||||
\(653\) | − | 487.463i | − | 0.746497i | −0.927731 | − | 0.373249i | \(-0.878244\pi\) | ||
0.927731 | − | 0.373249i | \(-0.121756\pi\) | |||||||
\(654\) | 190.000 | + | 169.941i | 0.290520 | + | 0.259849i | ||||
\(655\) | −30.0000 | −0.0458015 | ||||||||
\(656\) | − | 1189.59i | − | 1.81340i | ||||||
\(657\) | 74.0000 | + | 661.876i | 0.112633 | + | 1.00742i | ||||
\(658\) | 660.000 | 1.00304 | ||||||||
\(659\) | 406.964i | 0.617548i | 0.951135 | + | 0.308774i | \(0.0999187\pi\) | ||||
−0.951135 | + | 0.308774i | \(0.900081\pi\) | |||||||
\(660\) | −20.0000 | + | 22.3607i | −0.0303030 | + | 0.0338798i | ||||
\(661\) | 682.000 | 1.03177 | 0.515885 | − | 0.856658i | \(-0.327463\pi\) | ||||
0.515885 | + | 0.856658i | \(0.327463\pi\) | |||||||
\(662\) | 442.741i | 0.668794i | ||||||||
\(663\) | −160.000 | − | 143.108i | −0.241327 | − | 0.215850i | ||||
\(664\) | −630.000 | −0.948795 | ||||||||
\(665\) | 26.8328i | 0.0403501i | ||||||||
\(666\) | 320.000 | − | 35.7771i | 0.480480 | − | 0.0537194i | ||||
\(667\) | 420.000 | 0.629685 | ||||||||
\(668\) | − | 93.9149i | − | 0.140591i | ||||||
\(669\) | −172.000 | + | 192.302i | −0.257100 | + | 0.287447i | ||||
\(670\) | 120.000 | 0.179104 | ||||||||
\(671\) | 366.715i | 0.546520i | ||||||||
\(672\) | 210.000 | + | 187.830i | 0.312500 | + | 0.279508i | ||||
\(673\) | −894.000 | −1.32838 | −0.664190 | − | 0.747564i | \(-0.731223\pi\) | ||||
−0.664190 | + | 0.747564i | \(0.731223\pi\) | |||||||
\(674\) | − | 881.011i | − | 1.30714i | ||||||
\(675\) | −110.000 | − | 78.2624i | −0.162963 | − | 0.115944i | ||||
\(676\) | −87.0000 | −0.128698 | ||||||||
\(677\) | − | 550.073i | − | 0.812515i | −0.913759 | − | 0.406258i | \(-0.866834\pi\) | ||
0.913759 | − | 0.406258i | \(-0.133166\pi\) | |||||||
\(678\) | −140.000 | + | 156.525i | −0.206490 | + | 0.230862i | ||||
\(679\) | 996.000 | 1.46686 | ||||||||
\(680\) | 67.0820i | 0.0986501i | ||||||||
\(681\) | 130.000 | + | 116.276i | 0.190896 | + | 0.170742i | ||||
\(682\) | −180.000 | −0.263930 | ||||||||
\(683\) | 442.741i | 0.648231i | 0.946018 | + | 0.324115i | \(0.105067\pi\) | ||||
−0.946018 | + | 0.324115i | \(0.894933\pi\) | |||||||
\(684\) | −2.00000 | − | 17.8885i | −0.00292398 | − | 0.0261528i | ||||
\(685\) | 270.000 | 0.394161 | ||||||||
\(686\) | − | 831.817i | − | 1.21256i | ||||||
\(687\) | 564.000 | − | 630.571i | 0.820961 | − | 0.917862i | ||||
\(688\) | −304.000 | −0.441860 | ||||||||
\(689\) | 71.5542i | 0.103852i | ||||||||
\(690\) | −150.000 | − | 134.164i | −0.217391 | − | 0.194441i | ||||
\(691\) | −758.000 | −1.09696 | −0.548480 | − | 0.836163i | \(-0.684793\pi\) | ||||
−0.548480 | + | 0.836163i | \(0.684793\pi\) | |||||||
\(692\) | − | 13.4164i | − | 0.0193879i | ||||||
\(693\) | −240.000 | + | 26.8328i | −0.346320 | + | 0.0387198i | ||||
\(694\) | −410.000 | −0.590778 | ||||||||
\(695\) | − | 183.358i | − | 0.263824i | ||||||
\(696\) | 420.000 | − | 469.574i | 0.603448 | − | 0.674676i | ||||
\(697\) | −280.000 | −0.401722 | ||||||||
\(698\) | 809.457i | 1.15968i | ||||||||
\(699\) | 810.000 | + | 724.486i | 1.15880 | + | 1.03646i | ||||
\(700\) | −30.0000 | −0.0428571 | ||||||||
\(701\) | − | 782.624i | − | 1.11644i | −0.829693 | − | 0.558220i | \(-0.811485\pi\) | ||
0.829693 | − | 0.558220i | \(-0.188515\pi\) | |||||||
\(702\) | 560.000 | − | 787.096i | 0.797721 | − | 1.12122i | ||||
\(703\) | 32.0000 | 0.0455192 | ||||||||
\(704\) | − | 183.358i | − | 0.260451i | ||||||
\(705\) | −220.000 | + | 245.967i | −0.312057 | + | 0.348890i | ||||
\(706\) | −690.000 | −0.977337 | ||||||||
\(707\) | − | 402.492i | − | 0.569296i | ||||||
\(708\) | 10.0000 | + | 8.94427i | 0.0141243 | + | 0.0126332i | ||||
\(709\) | −2.00000 | −0.00282087 | −0.00141044 | − | 0.999999i | \(-0.500449\pi\) | ||||
−0.00141044 | + | 0.999999i | \(0.500449\pi\) | |||||||
\(710\) | − | 626.099i | − | 0.881830i | ||||||
\(711\) | −138.000 | − | 1234.31i | −0.194093 | − | 1.73602i | ||||
\(712\) | 720.000 | 1.01124 | ||||||||
\(713\) | − | 241.495i | − | 0.338703i | ||||||
\(714\) | 120.000 | − | 134.164i | 0.168067 | − | 0.187905i | ||||
\(715\) | −160.000 | −0.223776 | ||||||||
\(716\) | − | 192.302i | − | 0.268578i | ||||||
\(717\) | 560.000 | + | 500.879i | 0.781032 | + | 0.698576i | ||||
\(718\) | 660.000 | 0.919220 | ||||||||
\(719\) | 858.650i | 1.19423i | 0.802156 | + | 0.597114i | \(0.203686\pi\) | ||||
−0.802156 | + | 0.597114i | \(0.796314\pi\) | |||||||
\(720\) | −380.000 | + | 42.4853i | −0.527778 | + | 0.0590073i | ||||
\(721\) | −156.000 | −0.216366 | ||||||||
\(722\) | 798.276i | 1.10565i | ||||||||
\(723\) | −524.000 | + | 585.850i | −0.724758 | + | 0.810304i | ||||
\(724\) | −2.00000 | −0.00276243 | ||||||||
\(725\) | 156.525i | 0.215896i | ||||||||
\(726\) | 505.000 | + | 451.686i | 0.695592 | + | 0.622157i | ||||
\(727\) | 674.000 | 0.927098 | 0.463549 | − | 0.886071i | \(-0.346576\pi\) | ||||
0.463549 | + | 0.886071i | \(0.346576\pi\) | |||||||
\(728\) | 643.988i | 0.884598i | ||||||||
\(729\) | 239.000 | + | 688.709i | 0.327846 | + | 0.944731i | ||||
\(730\) | −370.000 | −0.506849 | ||||||||
\(731\) | 71.5542i | 0.0978853i | ||||||||
\(732\) | 164.000 | − | 183.358i | 0.224044 | − | 0.250488i | ||||
\(733\) | 656.000 | 0.894952 | 0.447476 | − | 0.894296i | \(-0.352323\pi\) | ||||
0.447476 | + | 0.894296i | \(0.352323\pi\) | |||||||
\(734\) | 415.909i | 0.566633i | ||||||||
\(735\) | 65.0000 | + | 58.1378i | 0.0884354 | + | 0.0790990i | ||||
\(736\) | −210.000 | −0.285326 | ||||||||
\(737\) | 107.331i | 0.145633i | ||||||||
\(738\) | −140.000 | − | 1252.20i | −0.189702 | − | 1.69675i | ||||
\(739\) | 598.000 | 0.809202 | 0.404601 | − | 0.914493i | \(-0.367410\pi\) | ||||
0.404601 | + | 0.914493i | \(0.367410\pi\) | |||||||
\(740\) | 35.7771i | 0.0483474i | ||||||||
\(741\) | 64.0000 | − | 71.5542i | 0.0863698 | − | 0.0965643i | ||||
\(742\) | −60.0000 | −0.0808625 | ||||||||
\(743\) | 782.624i | 1.05333i | 0.850073 | + | 0.526665i | \(0.176558\pi\) | ||||
−0.850073 | + | 0.526665i | \(0.823442\pi\) | |||||||
\(744\) | −270.000 | − | 241.495i | −0.362903 | − | 0.324591i | ||||
\(745\) | 250.000 | 0.335570 | ||||||||
\(746\) | 98.3870i | 0.131886i | ||||||||
\(747\) | −840.000 | + | 93.9149i | −1.12450 | + | 0.125723i | ||||
\(748\) | 20.0000 | 0.0267380 | ||||||||
\(749\) | − | 1207.48i | − | 1.61212i | ||||||
\(750\) | 50.0000 | − | 55.9017i | 0.0666667 | − | 0.0745356i | ||||
\(751\) | −338.000 | −0.450067 | −0.225033 | − | 0.974351i | \(-0.572249\pi\) | ||||
−0.225033 | + | 0.974351i | \(0.572249\pi\) | |||||||
\(752\) | 934.676i | 1.24292i | ||||||||
\(753\) | −1050.00 | − | 939.149i | −1.39442 | − | 1.24721i | ||||
\(754\) | −1120.00 | −1.48541 | ||||||||
\(755\) | − | 353.299i | − | 0.467945i | ||||||
\(756\) | 132.000 | + | 93.9149i | 0.174603 | + | 0.124226i | ||||
\(757\) | −656.000 | −0.866579 | −0.433289 | − | 0.901255i | \(-0.642647\pi\) | ||||
−0.433289 | + | 0.901255i | \(0.642647\pi\) | |||||||
\(758\) | 809.457i | 1.06788i | ||||||||
\(759\) | 120.000 | − | 134.164i | 0.158103 | − | 0.176764i | ||||
\(760\) | −30.0000 | −0.0394737 | ||||||||
\(761\) | 295.161i | 0.387859i | 0.981015 | + | 0.193930i | \(0.0621234\pi\) | ||||
−0.981015 | + | 0.193930i | \(0.937877\pi\) | |||||||
\(762\) | −130.000 | − | 116.276i | −0.170604 | − | 0.152593i | ||||
\(763\) | −228.000 | −0.298820 | ||||||||
\(764\) | 205.718i | 0.269265i | ||||||||
\(765\) | 10.0000 | + | 89.4427i | 0.0130719 | + | 0.116919i | ||||
\(766\) | −810.000 | −1.05744 | ||||||||
\(767\) | 71.5542i | 0.0932910i | ||||||||
\(768\) | −362.000 | + | 404.728i | −0.471354 | + | 0.526990i | ||||
\(769\) | −82.0000 | −0.106632 | −0.0533160 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533160 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(770\) | − | 134.164i | − | 0.174239i | ||||||
\(771\) | −450.000 | − | 402.492i | −0.583658 | − | 0.522039i | ||||
\(772\) | 214.000 | 0.277202 | ||||||||
\(773\) | − | 1059.90i | − | 1.37115i | −0.728004 | − | 0.685573i | \(-0.759552\pi\) | ||
0.728004 | − | 0.685573i | \(-0.240448\pi\) | |||||||
\(774\) | −320.000 | + | 35.7771i | −0.413437 | + | 0.0462236i | ||||
\(775\) | 90.0000 | 0.116129 | ||||||||
\(776\) | 1113.56i | 1.43500i | ||||||||
\(777\) | −192.000 | + | 214.663i | −0.247104 | + | 0.276271i | ||||
\(778\) | 990.000 | 1.27249 | ||||||||
\(779\) | − | 125.220i | − | 0.160744i | ||||||
\(780\) | 80.0000 | + | 71.5542i | 0.102564 | + | 0.0917361i | ||||
\(781\) | 560.000 | 0.717029 | ||||||||
\(782\) | 134.164i | 0.171565i | ||||||||
\(783\) | 490.000 | − | 688.709i | 0.625798 | − | 0.879577i | ||||
\(784\) | 247.000 | 0.315051 | ||||||||
\(785\) | 366.715i | 0.467153i | ||||||||
\(786\) | −60.0000 | + | 67.0820i | −0.0763359 | + | 0.0853461i | ||||
\(787\) | −536.000 | −0.681067 | −0.340534 | − | 0.940232i | \(-0.610608\pi\) | ||||
−0.340534 | + | 0.940232i | \(0.610608\pi\) | |||||||
\(788\) | 93.9149i | 0.119181i | ||||||||
\(789\) | 130.000 | + | 116.276i | 0.164766 | + | 0.147371i | ||||
\(790\) | 690.000 | 0.873418 | ||||||||
\(791\) | − | 187.830i | − | 0.237459i | ||||||
\(792\) | −30.0000 | − | 268.328i | −0.0378788 | − | 0.338798i | ||||
\(793\) | 1312.00 | 1.65448 | ||||||||
\(794\) | − | 277.272i | − | 0.349210i | ||||||
\(795\) | 20.0000 | − | 22.3607i | 0.0251572 | − | 0.0281266i | ||||
\(796\) | 242.000 | 0.304020 | ||||||||
\(797\) | − | 406.964i | − | 0.510620i | −0.966859 | − | 0.255310i | \(-0.917822\pi\) | ||
0.966859 | − | 0.255310i | \(-0.0821776\pi\) | |||||||
\(798\) | 60.0000 | + | 53.6656i | 0.0751880 | + | 0.0672502i | ||||
\(799\) | 220.000 | 0.275344 | ||||||||
\(800\) | − | 78.2624i | − | 0.0978280i | ||||||
\(801\) | 960.000 | − | 107.331i | 1.19850 | − | 0.133997i | ||||
\(802\) | −600.000 | −0.748130 | ||||||||
\(803\) | − | 330.938i | − | 0.412127i | ||||||
\(804\) | 48.0000 | − | 53.6656i | 0.0597015 | − | 0.0667483i | ||||
\(805\) | 180.000 | 0.223602 | ||||||||
\(806\) | 643.988i | 0.798992i | ||||||||
\(807\) | 830.000 | + | 742.375i | 1.02850 | + | 0.919919i | ||||
\(808\) | 450.000 | 0.556931 | ||||||||
\(809\) | − | 1091.20i | − | 1.34883i | −0.738354 | − | 0.674414i | \(-0.764397\pi\) | ||
0.738354 | − | 0.674414i | \(-0.235603\pi\) | |||||||
\(810\) | −395.000 | + | 89.4427i | −0.487654 | + | 0.110423i | ||||
\(811\) | −558.000 | −0.688039 | −0.344020 | − | 0.938962i | \(-0.611789\pi\) | ||||
−0.344020 | + | 0.938962i | \(0.611789\pi\) | |||||||
\(812\) | − | 187.830i | − | 0.231317i | ||||||
\(813\) | −164.000 | + | 183.358i | −0.201722 | + | 0.225532i | ||||
\(814\) | −160.000 | −0.196560 | ||||||||
\(815\) | 527.712i | 0.647499i | ||||||||
\(816\) | 190.000 | + | 169.941i | 0.232843 | + | 0.208261i | ||||
\(817\) | −32.0000 | −0.0391677 | ||||||||
\(818\) | − | 1024.12i | − | 1.25198i | ||||||
\(819\) | 96.0000 | + | 858.650i | 0.117216 | + | 1.04841i | ||||
\(820\) | 140.000 | 0.170732 | ||||||||
\(821\) | 389.076i | 0.473905i | 0.971521 | + | 0.236952i | \(0.0761485\pi\) | ||||
−0.971521 | + | 0.236952i | \(0.923851\pi\) | |||||||
\(822\) | 540.000 | − | 603.738i | 0.656934 | − | 0.734475i | ||||
\(823\) | −214.000 | −0.260024 | −0.130012 | − | 0.991512i | \(-0.541502\pi\) | ||||
−0.130012 | + | 0.991512i | \(0.541502\pi\) | |||||||
\(824\) | − | 174.413i | − | 0.211667i | ||||||
\(825\) | 50.0000 | + | 44.7214i | 0.0606061 | + | 0.0542077i | ||||
\(826\) | −60.0000 | −0.0726392 | ||||||||
\(827\) | 31.3050i | 0.0378536i | 0.999821 | + | 0.0189268i | \(0.00602495\pi\) | ||||
−0.999821 | + | 0.0189268i | \(0.993975\pi\) | |||||||
\(828\) | −120.000 | + | 13.4164i | −0.144928 | + | 0.0162034i | ||||
\(829\) | 318.000 | 0.383595 | 0.191797 | − | 0.981435i | \(-0.438568\pi\) | ||||
0.191797 | + | 0.981435i | \(0.438568\pi\) | |||||||
\(830\) | − | 469.574i | − | 0.565752i | ||||||
\(831\) | −48.0000 | + | 53.6656i | −0.0577617 | + | 0.0645796i | ||||
\(832\) | −656.000 | −0.788462 | ||||||||
\(833\) | − | 58.1378i | − | 0.0697932i | ||||||
\(834\) | −410.000 | − | 366.715i | −0.491607 | − | 0.439706i | ||||
\(835\) | −210.000 | −0.251497 | ||||||||
\(836\) | 8.94427i | 0.0106989i | ||||||||
\(837\) | −396.000 | − | 281.745i | −0.473118 | − | 0.336612i | ||||
\(838\) | −1330.00 | −1.58711 | ||||||||
\(839\) | 62.6099i | 0.0746244i | 0.999304 | + | 0.0373122i | \(0.0118796\pi\) | ||||
−0.999304 | + | 0.0373122i | \(0.988120\pi\) | |||||||
\(840\) | 180.000 | − | 201.246i | 0.214286 | − | 0.239579i | ||||
\(841\) | −139.000 | −0.165279 | ||||||||
\(842\) | − | 1256.67i | − | 1.49248i | ||||||
\(843\) | 420.000 | + | 375.659i | 0.498221 | + | 0.445622i | ||||
\(844\) | −2.00000 | −0.00236967 | ||||||||
\(845\) | 194.538i | 0.230222i | ||||||||
\(846\) | 110.000 | + | 983.870i | 0.130024 | + | 1.16297i | ||||
\(847\) | −606.000 | −0.715466 | ||||||||
\(848\) | − | 84.9706i | − | 0.100201i | ||||||
\(849\) | 288.000 | − | 321.994i | 0.339223 | − | 0.379262i | ||||
\(850\) | −50.0000 | −0.0588235 | ||||||||
\(851\) | − | 214.663i | − | 0.252247i | ||||||
\(852\) | −280.000 | − | 250.440i | −0.328638 | − | 0.293943i | ||||
\(853\) | −684.000 | −0.801876 | −0.400938 | − | 0.916105i | \(-0.631316\pi\) | ||||
−0.400938 | + | 0.916105i | \(0.631316\pi\) | |||||||
\(854\) | 1100.15i | 1.28823i | ||||||||
\(855\) | −40.0000 | + | 4.47214i | −0.0467836 | + | 0.00523057i | ||||
\(856\) | 1350.00 | 1.57710 | ||||||||
\(857\) | − | 1498.17i | − | 1.74815i | −0.485790 | − | 0.874076i | \(-0.661468\pi\) | ||
0.485790 | − | 0.874076i | \(-0.338532\pi\) | |||||||
\(858\) | −320.000 | + | 357.771i | −0.372960 | + | 0.416982i | ||||
\(859\) | −842.000 | −0.980210 | −0.490105 | − | 0.871664i | \(-0.663041\pi\) | ||||
−0.490105 | + | 0.871664i | \(0.663041\pi\) | |||||||
\(860\) | − | 35.7771i | − | 0.0416013i | ||||||
\(861\) | 840.000 | + | 751.319i | 0.975610 | + | 0.872612i | ||||
\(862\) | 780.000 | 0.904872 | ||||||||
\(863\) | 1015.17i | 1.17633i | 0.808740 | + | 0.588166i | \(0.200150\pi\) | ||||
−0.808740 | + | 0.588166i | \(0.799850\pi\) | |||||||
\(864\) | −245.000 | + | 344.354i | −0.283565 | + | 0.398558i | ||||
\(865\) | −30.0000 | −0.0346821 | ||||||||
\(866\) | − | 505.351i | − | 0.583547i | ||||||
\(867\) | −538.000 | + | 601.502i | −0.620531 | + | 0.693774i | ||||
\(868\) | −108.000 | −0.124424 | ||||||||
\(869\) | 617.155i | 0.710190i | ||||||||
\(870\) | 350.000 | + | 313.050i | 0.402299 | + | 0.359827i | ||||
\(871\) | 384.000 | 0.440873 | ||||||||
\(872\) | − | 254.912i | − | 0.292330i | ||||||
\(873\) | 166.000 | + | 1484.75i | 0.190149 | + | 1.70074i | ||||
\(874\) | −60.0000 | −0.0686499 | ||||||||
\(875\) | 67.0820i | 0.0766652i | ||||||||
\(876\) | −148.000 | + | 165.469i | −0.168950 | + | 0.188892i | ||||
\(877\) | −156.000 | −0.177879 | −0.0889396 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889396 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(878\) | 4.47214i | 0.00509355i | ||||||||
\(879\) | −1050.00 | − | 939.149i | −1.19454 | − | 1.06843i | ||||
\(880\) | 190.000 | 0.215909 | ||||||||
\(881\) | 125.220i | 0.142134i | 0.997472 | + | 0.0710669i | \(0.0226404\pi\) | ||||
−0.997472 | + | 0.0710669i | \(0.977360\pi\) | |||||||
\(882\) | 260.000 | − | 29.0689i | 0.294785 | − | 0.0329579i | ||||
\(883\) | −964.000 | −1.09173 | −0.545866 | − | 0.837872i | \(-0.683799\pi\) | ||||
−0.545866 | + | 0.837872i | \(0.683799\pi\) | |||||||
\(884\) | − | 71.5542i | − | 0.0809436i | ||||||
\(885\) | 20.0000 | − | 22.3607i | 0.0225989 | − | 0.0252663i | ||||
\(886\) | 450.000 | 0.507901 | ||||||||
\(887\) | 952.565i | 1.07392i | 0.843608 | + | 0.536959i | \(0.180427\pi\) | ||||
−0.843608 | + | 0.536959i | \(0.819573\pi\) | |||||||
\(888\) | −240.000 | − | 214.663i | −0.270270 | − | 0.241737i | ||||
\(889\) | 156.000 | 0.175478 | ||||||||
\(890\) | 536.656i | 0.602985i | ||||||||
\(891\) | −80.0000 | − | 353.299i | −0.0897868 | − | 0.396519i | ||||
\(892\) | −86.0000 | −0.0964126 | ||||||||
\(893\) | 98.3870i | 0.110176i | ||||||||
\(894\) | 500.000 | − | 559.017i | 0.559284 | − | 0.625299i | ||||
\(895\) | −430.000 | −0.480447 | ||||||||
\(896\) | − | 925.732i | − | 1.03318i | ||||||
\(897\) | −480.000 | − | 429.325i | −0.535117 | − | 0.478623i | ||||
\(898\) | 700.000 | 0.779510 | ||||||||
\(899\) | 563.489i | 0.626795i | ||||||||
\(900\) | −5.00000 | − | 44.7214i | −0.00555556 | − | 0.0496904i | ||||
\(901\) | −20.0000 | −0.0221976 | ||||||||
\(902\) | 626.099i | 0.694123i | ||||||||
\(903\) | 192.000 | − | 214.663i | 0.212625 | − | 0.237722i | ||||
\(904\) | 210.000 | 0.232301 | ||||||||
\(905\) | 4.47214i | 0.00494159i | ||||||||
\(906\) | −790.000 | − | 706.597i | −0.871965 | − | 0.779909i | ||||
\(907\) | 1284.00 | 1.41566 | 0.707828 | − | 0.706385i | \(-0.249675\pi\) | ||||
0.707828 | + | 0.706385i | \(0.249675\pi\) | |||||||
\(908\) | 58.1378i | 0.0640284i | ||||||||
\(909\) | 600.000 | − | 67.0820i | 0.660066 | − | 0.0737976i | ||||
\(910\) | −480.000 | −0.527473 | ||||||||
\(911\) | − | 62.6099i | − | 0.0687266i | −0.999409 | − | 0.0343633i | \(-0.989060\pi\) | ||
0.999409 | − | 0.0343633i | \(-0.0109403\pi\) | |||||||
\(912\) | −76.0000 | + | 84.9706i | −0.0833333 | + | 0.0931695i | ||||
\(913\) | 420.000 | 0.460022 | ||||||||
\(914\) | − | 746.847i | − | 0.817119i | ||||||
\(915\) | −410.000 | − | 366.715i | −0.448087 | − | 0.400782i | ||||
\(916\) | 282.000 | 0.307860 | ||||||||
\(917\) | − | 80.4984i | − | 0.0877846i | ||||||
\(918\) | 220.000 | + | 156.525i | 0.239651 | + | 0.170506i | ||||
\(919\) | 418.000 | 0.454842 | 0.227421 | − | 0.973797i | \(-0.426971\pi\) | ||||
0.227421 | + | 0.973797i | \(0.426971\pi\) | |||||||
\(920\) | 201.246i | 0.218746i | ||||||||
\(921\) | −368.000 | + | 411.437i | −0.399566 | + | 0.446728i | ||||
\(922\) | 210.000 | 0.227766 | ||||||||
\(923\) | − | 2003.52i | − | 2.17066i | ||||||
\(924\) | −60.0000 | − | 53.6656i | −0.0649351 | − | 0.0580797i | ||||
\(925\) | 80.0000 | 0.0864865 | ||||||||
\(926\) | − | 818.401i | − | 0.883802i | ||||||
\(927\) | −26.0000 | − | 232.551i | −0.0280475 | − | 0.250864i | ||||
\(928\) | 490.000 | 0.528017 | ||||||||
\(929\) | 169.941i | 0.182929i | 0.995808 | + | 0.0914646i | \(0.0291548\pi\) | ||||
−0.995808 | + | 0.0914646i | \(0.970845\pi\) | |||||||
\(930\) | 180.000 | − | 201.246i | 0.193548 | − | 0.216394i | ||||
\(931\) | 26.0000 | 0.0279270 | ||||||||
\(932\) | 362.243i | 0.388673i | ||||||||
\(933\) | −360.000 | − | 321.994i | −0.385852 | − | 0.345117i | ||||
\(934\) | 1010.00 | 1.08137 | ||||||||
\(935\) | − | 44.7214i | − | 0.0478303i | ||||||
\(936\) | −960.000 | + | 107.331i | −1.02564 | + | 0.114670i | ||||
\(937\) | 534.000 | 0.569904 | 0.284952 | − | 0.958542i | \(-0.408022\pi\) | ||||
0.284952 | + | 0.958542i | \(0.408022\pi\) | |||||||
\(938\) | 321.994i | 0.343277i | ||||||||
\(939\) | 788.000 | − | 881.011i | 0.839191 | − | 0.938244i | ||||
\(940\) | −110.000 | −0.117021 | ||||||||
\(941\) | 129.692i | 0.137824i | 0.997623 | + | 0.0689118i | \(0.0219527\pi\) | ||||
−0.997623 | + | 0.0689118i | \(0.978047\pi\) | |||||||
\(942\) | 820.000 | + | 733.430i | 0.870488 | + | 0.778588i | ||||
\(943\) | −840.000 | −0.890774 | ||||||||
\(944\) | − | 84.9706i | − | 0.0900112i | ||||||
\(945\) | 210.000 | − | 295.161i | 0.222222 | − | 0.312340i | ||||
\(946\) | 160.000 | 0.169133 | ||||||||
\(947\) | 1516.05i | 1.60090i | 0.599398 | + | 0.800451i | \(0.295407\pi\) | ||||
−0.599398 | + | 0.800451i | \(0.704593\pi\) | |||||||
\(948\) | 276.000 | − | 308.577i | 0.291139 | − | 0.325504i | ||||
\(949\) | −1184.00 | −1.24763 | ||||||||
\(950\) | − | 22.3607i | − | 0.0235376i | ||||||
\(951\) | −1010.00 | − | 903.371i | −1.06204 | − | 0.949917i | ||||
\(952\) | −180.000 | −0.189076 | ||||||||
\(953\) | 406.964i | 0.427035i | 0.976939 | + | 0.213518i | \(0.0684920\pi\) | ||||
−0.976939 | + | 0.213518i | \(0.931508\pi\) | |||||||
\(954\) | −10.0000 | − | 89.4427i | −0.0104822 | − | 0.0937555i | ||||
\(955\) | 460.000 | 0.481675 | ||||||||
\(956\) | 250.440i | 0.261966i | ||||||||
\(957\) | −280.000 | + | 313.050i | −0.292581 | + | 0.327115i | ||||
\(958\) | −1320.00 | −1.37787 | ||||||||
\(959\) | 724.486i | 0.755460i | ||||||||
\(960\) | 205.000 | + | 183.358i | 0.213542 | + | 0.190997i | ||||
\(961\) | −637.000 | −0.662851 | ||||||||
\(962\) | 572.433i | 0.595045i | ||||||||
\(963\) | 1800.00 | − | 201.246i | 1.86916 | − | 0.208978i | ||||
\(964\) | −262.000 | −0.271784 | ||||||||
\(965\) | − | 478.519i | − | 0.495874i | ||||||
\(966\) | 360.000 | − | 402.492i | 0.372671 | − | 0.416659i | ||||
\(967\) | 674.000 | 0.697001 | 0.348501 | − | 0.937309i | \(-0.386691\pi\) | ||||
0.348501 | + | 0.937309i | \(0.386691\pi\) | |||||||
\(968\) | − | 677.529i | − | 0.699926i | ||||||
\(969\) | 20.0000 | + | 17.8885i | 0.0206398 | + | 0.0184608i | ||||
\(970\) | −830.000 | −0.855670 | ||||||||
\(971\) | 1328.22i | 1.36789i | 0.729532 | + | 0.683947i | \(0.239738\pi\) | ||||
−0.729532 | + | 0.683947i | \(0.760262\pi\) | |||||||
\(972\) | −118.000 | + | 212.426i | −0.121399 | + | 0.218546i | ||||
\(973\) | 492.000 | 0.505653 | ||||||||
\(974\) | 1981.16i | 2.03404i | ||||||||
\(975\) | 160.000 | − | 178.885i | 0.164103 | − | 0.183472i | ||||
\(976\) | −1558.00 | −1.59631 | ||||||||
\(977\) | − | 371.187i | − | 0.379926i | −0.981791 | − | 0.189963i | \(-0.939163\pi\) | ||
0.981791 | − | 0.189963i | \(-0.0608367\pi\) | |||||||
\(978\) | 1180.00 | + | 1055.42i | 1.20654 | + | 1.07917i | ||||
\(979\) | −480.000 | −0.490296 | ||||||||
\(980\) | 29.0689i | 0.0296621i | ||||||||
\(981\) | −38.0000 | − | 339.882i | −0.0387360 | − | 0.346465i | ||||
\(982\) | −910.000 | −0.926680 | ||||||||
\(983\) | 442.741i | 0.450398i | 0.974313 | + | 0.225199i | \(0.0723033\pi\) | ||||
−0.974313 | + | 0.225199i | \(0.927697\pi\) | |||||||
\(984\) | −840.000 | + | 939.149i | −0.853659 | + | 0.954419i | ||||
\(985\) | 210.000 | 0.213198 | ||||||||
\(986\) | − | 313.050i | − | 0.317494i | ||||||
\(987\) | −660.000 | − | 590.322i | −0.668693 | − | 0.598097i | ||||
\(988\) | 32.0000 | 0.0323887 | ||||||||
\(989\) | 214.663i | 0.217050i | ||||||||
\(990\) | 200.000 | − | 22.3607i | 0.202020 | − | 0.0225865i | ||||
\(991\) | 962.000 | 0.970737 | 0.485368 | − | 0.874310i | \(-0.338686\pi\) | ||||
0.485368 | + | 0.874310i | \(0.338686\pi\) | |||||||
\(992\) | − | 281.745i | − | 0.284017i | ||||||
\(993\) | 396.000 | − | 442.741i | 0.398792 | − | 0.445862i | ||||
\(994\) | 1680.00 | 1.69014 | ||||||||
\(995\) | − | 541.128i | − | 0.543848i | ||||||
\(996\) | −210.000 | − | 187.830i | −0.210843 | − | 0.188584i | ||||
\(997\) | 24.0000 | 0.0240722 | 0.0120361 | − | 0.999928i | \(-0.496169\pi\) | ||||
0.0120361 | + | 0.999928i | \(0.496169\pi\) | |||||||
\(998\) | 4.47214i | 0.00448110i | ||||||||
\(999\) | −352.000 | − | 250.440i | −0.352352 | − | 0.250690i |
(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 | 15.3.c.a.11.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 15.3.c.a.11.2 | yes | 2 | |
4.3 | odd | 2 | 240.3.l.b.161.1 | 2 | |||
5.2 | odd | 4 | 75.3.d.b.74.4 | 4 | |||
5.3 | odd | 4 | 75.3.d.b.74.1 | 4 | |||
5.4 | even | 2 | 75.3.c.e.26.2 | 2 | |||
8.3 | odd | 2 | 960.3.l.b.641.2 | 2 | |||
8.5 | even | 2 | 960.3.l.c.641.1 | 2 | |||
9.2 | odd | 6 | 405.3.i.b.296.2 | 4 | |||
9.4 | even | 3 | 405.3.i.b.26.2 | 4 | |||
9.5 | odd | 6 | 405.3.i.b.26.1 | 4 | |||
9.7 | even | 3 | 405.3.i.b.296.1 | 4 | |||
12.11 | even | 2 | 240.3.l.b.161.2 | 2 | |||
15.2 | even | 4 | 75.3.d.b.74.2 | 4 | |||
15.8 | even | 4 | 75.3.d.b.74.3 | 4 | |||
15.14 | odd | 2 | 75.3.c.e.26.1 | 2 | |||
20.3 | even | 4 | 1200.3.c.f.449.4 | 4 | |||
20.7 | even | 4 | 1200.3.c.f.449.1 | 4 | |||
20.19 | odd | 2 | 1200.3.l.g.401.2 | 2 | |||
24.5 | odd | 2 | 960.3.l.c.641.2 | 2 | |||
24.11 | even | 2 | 960.3.l.b.641.1 | 2 | |||
60.23 | odd | 4 | 1200.3.c.f.449.2 | 4 | |||
60.47 | odd | 4 | 1200.3.c.f.449.3 | 4 | |||
60.59 | even | 2 | 1200.3.l.g.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.c.a.11.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
15.3.c.a.11.2 | yes | 2 | 3.2 | odd | 2 | inner | |
75.3.c.e.26.1 | 2 | 15.14 | odd | 2 | |||
75.3.c.e.26.2 | 2 | 5.4 | even | 2 | |||
75.3.d.b.74.1 | 4 | 5.3 | odd | 4 | |||
75.3.d.b.74.2 | 4 | 15.2 | even | 4 | |||
75.3.d.b.74.3 | 4 | 15.8 | even | 4 | |||
75.3.d.b.74.4 | 4 | 5.2 | odd | 4 | |||
240.3.l.b.161.1 | 2 | 4.3 | odd | 2 | |||
240.3.l.b.161.2 | 2 | 12.11 | even | 2 | |||
405.3.i.b.26.1 | 4 | 9.5 | odd | 6 | |||
405.3.i.b.26.2 | 4 | 9.4 | even | 3 | |||
405.3.i.b.296.1 | 4 | 9.7 | even | 3 | |||
405.3.i.b.296.2 | 4 | 9.2 | odd | 6 | |||
960.3.l.b.641.1 | 2 | 24.11 | even | 2 | |||
960.3.l.b.641.2 | 2 | 8.3 | odd | 2 | |||
960.3.l.c.641.1 | 2 | 8.5 | even | 2 | |||
960.3.l.c.641.2 | 2 | 24.5 | odd | 2 | |||
1200.3.c.f.449.1 | 4 | 20.7 | even | 4 | |||
1200.3.c.f.449.2 | 4 | 60.23 | odd | 4 | |||
1200.3.c.f.449.3 | 4 | 60.47 | odd | 4 | |||
1200.3.c.f.449.4 | 4 | 20.3 | even | 4 | |||
1200.3.l.g.401.1 | 2 | 60.59 | even | 2 | |||
1200.3.l.g.401.2 | 2 | 20.19 | odd | 2 |