Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.2.e.a.116.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.50000 | − | 4.33013i | −0.400320 | − | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0000 | −1.87409 | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | −3.00000 | + | 5.19615i | −0.452267 | + | 0.783349i | ||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | + | 7.79423i | −0.656392 | + | 1.13691i | 0.325150 | + | 0.945662i | \(0.394585\pi\) |
−0.981543 | + | 0.191243i | \(0.938748\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 5.00000 | + | 8.66025i | 0.693375 | + | 1.20096i | ||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −1.00000 | − | 1.73205i | −0.129099 | − | 0.223607i | ||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.50000 | − | 4.33013i | 0.310087 | − | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | 3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 2.00000 | + | 3.46410i | 0.223607 | + | 0.387298i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | − | 10.3923i | 0.635999 | − | 1.10158i | −0.350304 | − | 0.936636i | \(-0.613922\pi\) |
0.986303 | − | 0.164946i | \(-0.0527450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50000 | + | 4.33013i | −0.246332 | + | 0.426660i | −0.962505 | − | 0.271263i | \(-0.912559\pi\) |
0.716173 | + | 0.697923i | \(0.245892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | −5.00000 | − | 8.66025i | −0.481125 | − | 0.833333i | ||||
\(109\) | 3.50000 | + | 6.06218i | 0.335239 | + | 0.580651i | 0.983531 | − | 0.180741i | \(-0.0578495\pi\) |
−0.648292 | + | 0.761392i | \(0.724516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | − | 5.19615i | −0.279751 | − | 0.484544i | ||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | 5.00000 | − | 8.66025i | 0.462250 | − | 0.800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | + | 10.3923i | 0.541002 | + | 0.937043i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.00000 | + | 8.66025i | 0.440225 | + | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.50000 | + | 4.33013i | −0.215166 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.50000 | + | 12.9904i | 0.627182 | + | 1.08631i | ||||
\(144\) | 4.00000 | + | 6.92820i | 0.333333 | + | 0.577350i | ||||
\(145\) | 1.50000 | − | 2.59808i | 0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | + | 0.866025i | 0.0406894 | + | 0.0704761i | 0.885653 | − | 0.464348i | \(-0.153711\pi\) |
−0.844963 | + | 0.534824i | \(0.820378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 5.00000 | − | 8.66025i | 0.400320 | − | 0.693375i | ||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 10.3923i | −0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | −12.0000 | − | 20.7846i | −0.937043 | − | 1.62301i | ||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 3.46410i | 0.152944 | + | 0.264906i | ||||
\(172\) | −10.0000 | − | 17.3205i | −0.762493 | − | 1.32068i | ||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | − | 10.3923i | −0.448461 | − | 0.776757i | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | 2.00000 | − | 3.46410i | 0.149071 | − | 0.258199i | ||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | + | 1.73205i | 0.0735215 | + | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | − | 7.79423i | 0.329073 | − | 0.569970i | ||||
\(188\) | −18.0000 | −1.31278 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.50000 | + | 7.79423i | −0.325609 | + | 0.563971i | −0.981635 | − | 0.190767i | \(-0.938902\pi\) |
0.656027 | + | 0.754738i | \(0.272236\pi\) | |||||||
\(192\) | 4.00000 | + | 6.92820i | 0.288675 | + | 0.500000i | ||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.00000 | −0.358057 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −6.00000 | + | 10.3923i | −0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | − | 10.3923i | −0.417029 | − | 0.722315i | ||||
\(208\) | −10.0000 | + | 17.3205i | −0.693375 | + | 1.20096i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 12.0000 | − | 20.7846i | 0.824163 | − | 1.42749i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 3.00000 | + | 5.19615i | 0.202260 | + | 0.350325i | ||||
\(221\) | −7.50000 | − | 12.9904i | −0.504505 | − | 0.873828i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0000 | −1.27233 | −0.636167 | − | 0.771551i | \(-0.719481\pi\) | ||||
−0.636167 | + | 0.771551i | \(0.719481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 2.00000 | + | 3.46410i | 0.132453 | + | 0.229416i | ||||
\(229\) | 2.00000 | − | 3.46410i | 0.132164 | − | 0.228914i | −0.792347 | − | 0.610071i | \(-0.791141\pi\) |
0.924510 | + | 0.381157i | \(0.124474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | + | 20.7846i | −0.786146 | + | 1.36165i | 0.142166 | + | 0.989843i | \(0.454593\pi\) |
−0.928312 | + | 0.371802i | \(0.878740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50000 | + | 7.79423i | 0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0000 | −1.35838 | −0.679189 | − | 0.733964i | \(-0.737668\pi\) | ||||
−0.679189 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(240\) | 2.00000 | − | 3.46410i | 0.129099 | − | 0.223607i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −16.0000 | −1.02430 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | + | 8.66025i | −0.318142 | + | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −15.0000 | + | 25.9808i | −0.935674 | + | 1.62064i | −0.162247 | + | 0.986750i | \(0.551874\pi\) |
−0.773427 | + | 0.633885i | \(0.781459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.0000 | 0.620174 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | − | 5.19615i | −0.184988 | − | 0.320408i | 0.758585 | − | 0.651575i | \(-0.225891\pi\) |
−0.943572 | + | 0.331166i | \(0.892558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | −0.734388 | ||||||||
\(268\) | −4.00000 | + | 6.92820i | −0.244339 | + | 0.423207i | ||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 12.0000 | 0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | −6.00000 | − | 10.3923i | −0.361158 | − | 0.625543i | ||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | + | 11.2583i | 0.386385 | + | 0.669238i | 0.991960 | − | 0.126550i | \(-0.0403903\pi\) |
−0.605575 | + | 0.795788i | \(0.707057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | − | 1.73205i | 0.0592349 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −21.0000 | −1.22683 | −0.613417 | − | 0.789760i | \(-0.710205\pi\) | ||||
−0.613417 | + | 0.789760i | \(0.710205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.50000 | − | 12.9904i | −0.435194 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0000 | − | 25.9808i | 0.867472 | − | 1.50251i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | + | 5.19615i | −0.172345 | + | 0.298511i | ||||
\(304\) | −4.00000 | − | 6.92820i | −0.229416 | − | 0.397360i | ||||
\(305\) | 4.00000 | + | 6.92820i | 0.229039 | + | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0000 | 0.627803 | 0.313902 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313902 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.00000 | 0.284440 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | − | 15.5885i | −0.510343 | − | 0.883940i | −0.999928 | − | 0.0119847i | \(-0.996185\pi\) |
0.489585 | − | 0.871956i | \(-0.337148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | − | 16.4545i | 0.536972 | − | 0.930062i | −0.462093 | − | 0.886831i | \(-0.652902\pi\) |
0.999065 | − | 0.0432311i | \(-0.0137652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | + | 7.79423i | 0.251952 | + | 0.436393i | ||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 1.00000 | − | 1.73205i | 0.0555556 | − | 0.0962250i | ||||
\(325\) | −2.50000 | − | 4.33013i | −0.138675 | − | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.50000 | − | 6.06218i | 0.193550 | − | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | 12.0000 | + | 20.7846i | 0.658586 | + | 1.14070i | ||||
\(333\) | 2.00000 | + | 3.46410i | 0.109599 | + | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.00000 | + | 5.19615i | −0.161515 | + | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00000 | + | 15.5885i | 0.483145 | + | 0.836832i | 0.999813 | − | 0.0193540i | \(-0.00616095\pi\) |
−0.516667 | + | 0.856186i | \(0.672828\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.0000 | −1.33440 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.50000 | − | 12.9904i | −0.399185 | − | 0.691408i | 0.594441 | − | 0.804139i | \(-0.297373\pi\) |
−0.993626 | + | 0.112731i | \(0.964040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.0000 | 1.27200 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.50000 | − | 14.7224i | −0.443696 | − | 0.768505i | 0.554264 | − | 0.832341i | \(-0.313000\pi\) |
−0.997960 | + | 0.0638362i | \(0.979666\pi\) | |||||||
\(368\) | 12.0000 | + | 20.7846i | 0.625543 | + | 1.08347i | ||||
\(369\) | −12.0000 | + | 20.7846i | −0.624695 | + | 1.08200i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | 2.00000 | − | 3.46410i | 0.103556 | − | 0.179364i | −0.809591 | − | 0.586994i | \(-0.800311\pi\) |
0.913147 | + | 0.407630i | \(0.133645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.0000 | 0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −2.00000 | + | 3.46410i | −0.102598 | + | 0.177705i | ||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | + | 10.3923i | −0.306586 | + | 0.531022i | −0.977613 | − | 0.210411i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.0000 | + | 17.3205i | −0.508329 | + | 0.880451i | ||||
\(388\) | −1.00000 | − | 1.73205i | −0.0507673 | − | 0.0879316i | ||||
\(389\) | 1.50000 | + | 2.59808i | 0.0760530 | + | 0.131728i | 0.901544 | − | 0.432688i | \(-0.142435\pi\) |
−0.825491 | + | 0.564416i | \(0.809102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.500000 | − | 0.866025i | −0.0251577 | − | 0.0435745i | ||||
\(396\) | 6.00000 | + | 10.3923i | 0.301511 | + | 0.522233i | ||||
\(397\) | 12.5000 | − | 21.6506i | 0.627357 | − | 1.08661i | −0.360723 | − | 0.932673i | \(-0.617470\pi\) |
0.988080 | − | 0.153941i | \(-0.0491966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | + | 17.3205i | 0.498135 | + | 0.862796i | ||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | − | 10.3923i | 0.294528 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | − | 12.1244i | −0.342791 | − | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.00000 | + | 15.5885i | 0.437595 | + | 0.757937i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | + | 2.59808i | −0.0727607 | + | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 7.50000 | − | 12.9904i | 0.362103 | − | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5000 | − | 18.1865i | −0.505767 | − | 0.876014i | −0.999978 | − | 0.00667224i | \(-0.997876\pi\) |
0.494211 | − | 0.869342i | \(-0.335457\pi\) | |||||||
\(432\) | 10.0000 | − | 17.3205i | 0.481125 | − | 0.833333i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 6.00000 | + | 10.3923i | 0.287019 | + | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0000 | + | 22.5167i | −0.620456 | + | 1.07466i | 0.368945 | + | 0.929451i | \(0.379719\pi\) |
−0.989401 | + | 0.145210i | \(0.953614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.00000 | − | 15.5885i | 0.427603 | − | 0.740630i | −0.569057 | − | 0.822298i | \(-0.692691\pi\) |
0.996660 | + | 0.0816684i | \(0.0260248\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 31.1769i | −0.847587 | − | 1.46806i | ||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | 0.500000 | − | 0.866025i | 0.0234920 | − | 0.0406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | + | 6.92820i | −0.187112 | + | 0.324088i | −0.944286 | − | 0.329125i | \(-0.893246\pi\) |
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50000 | + | 12.9904i | 0.350070 | + | 0.606339i | ||||
\(460\) | 6.00000 | − | 10.3923i | 0.279751 | − | 0.484544i | ||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | −6.00000 | + | 10.3923i | −0.278543 | + | 0.482451i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.50000 | + | 12.9904i | −0.347059 | + | 0.601123i | −0.985726 | − | 0.168360i | \(-0.946153\pi\) |
0.638667 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(468\) | 20.0000 | 0.924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | − | 25.9808i | −0.689701 | − | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.0000 | −1.09888 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.0000 | + | 25.9808i | 0.685367 | + | 1.18709i | 0.973321 | + | 0.229447i | \(0.0736918\pi\) |
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | + | 8.66025i | −0.227980 | + | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.00000 | 0.181818 | ||||||||
\(485\) | −0.500000 | + | 0.866025i | −0.0227038 | + | 0.0393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0000 | − | 32.9090i | −0.860972 | − | 1.49125i | −0.870992 | − | 0.491298i | \(-0.836523\pi\) |
0.0100195 | − | 0.999950i | \(-0.496811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.00000 | 0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0000 | 0.676941 | 0.338470 | − | 0.940977i | \(-0.390091\pi\) | ||||
0.338470 | + | 0.940977i | \(0.390091\pi\) | |||||||
\(492\) | −12.0000 | + | 20.7846i | −0.541002 | + | 0.937043i | ||||
\(493\) | −4.50000 | − | 7.79423i | −0.202670 | − | 0.351034i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | − | 5.19615i | 0.134840 | − | 0.233550i | ||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | − | 26.8468i | 0.693875 | − | 1.20183i | −0.276683 | − | 0.960961i | \(-0.589235\pi\) |
0.970558 | − | 0.240866i | \(-0.0774314\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.0000 | 1.20387 | 0.601935 | − | 0.798545i | \(-0.294397\pi\) | ||||
0.601935 | + | 0.798545i | \(0.294397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | −16.0000 | − | 27.7128i | −0.709885 | − | 1.22956i | ||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.00000 | − | 8.66025i | 0.220755 | − | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.50000 | + | 4.33013i | 0.110163 | + | 0.190808i | ||||
\(516\) | −10.0000 | + | 17.3205i | −0.440225 | + | 0.762493i | ||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.00000 | −0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 6.00000 | + | 10.3923i | 0.261116 | + | 0.452267i | ||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.0000 | −2.59889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.0000 | −0.430331 | ||||||||
\(541\) | −5.50000 | + | 9.52628i | −0.236463 | + | 0.409567i | −0.959697 | − | 0.281037i | \(-0.909322\pi\) |
0.723234 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0000 | − | 17.3205i | −0.429141 | − | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00000 | 0.299847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −12.0000 | + | 20.7846i | −0.512615 | + | 0.887875i | ||||
\(549\) | 8.00000 | + | 13.8564i | 0.341432 | + | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.00000 | − | 1.73205i | 0.0424476 | − | 0.0735215i | ||||
\(556\) | 14.0000 | + | 24.2487i | 0.593732 | + | 1.02837i | ||||
\(557\) | 12.0000 | + | 20.7846i | 0.508456 | + | 0.880672i | 0.999952 | + | 0.00979220i | \(0.00311700\pi\) |
−0.491496 | + | 0.870880i | \(0.663550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −50.0000 | −2.11477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | − | 31.1769i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331202i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(564\) | 9.00000 | + | 15.5885i | 0.378968 | + | 0.656392i | ||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | −15.0000 | + | 25.9808i | −0.627182 | + | 1.08631i | ||||
\(573\) | 9.00000 | 0.375980 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | −8.00000 | + | 13.8564i | −0.333333 | + | 0.577350i | ||||
\(577\) | 3.50000 | + | 6.06218i | 0.145707 | + | 0.252372i | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00000 | − | 3.46410i | 0.0831172 | − | 0.143963i | ||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.00000 | − | 8.66025i | −0.206725 | − | 0.358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | 19.5000 | − | 33.7750i | 0.800769 | − | 1.38697i | −0.118342 | − | 0.992973i | \(-0.537758\pi\) |
0.919111 | − | 0.394000i | \(-0.128909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | 8.00000 | − | 13.8564i | 0.327418 | − | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5000 | − | 38.9711i | −0.919325 | − | 1.59232i | −0.800443 | − | 0.599409i | \(-0.795402\pi\) |
−0.118882 | − | 0.992908i | \(-0.537931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | −1.00000 | + | 1.73205i | −0.0406894 | + | 0.0704761i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | − | 11.2583i | 0.263827 | − | 0.456962i | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5000 | + | 38.9711i | −0.910253 | + | 1.57660i | ||||
\(612\) | −6.00000 | − | 10.3923i | −0.242536 | − | 0.420084i | ||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | 0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | − | 22.5167i | −0.522514 | − | 0.905021i | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
0.477143 | − | 0.878826i | \(-0.341672\pi\) | |||||||
\(620\) | 4.00000 | + | 6.92820i | 0.160644 | + | 0.278243i | ||||
\(621\) | −15.0000 | + | 25.9808i | −0.601929 | + | 1.04257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 20.0000 | 0.800641 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.00000 | + | 5.19615i | 0.119808 | + | 0.207514i | ||||
\(628\) | 14.0000 | − | 24.2487i | 0.558661 | − | 0.967629i | ||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.50000 | + | 11.2583i | 0.258352 | + | 0.447478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | −24.0000 | −0.951662 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0000 | 1.61688 | 0.808441 | − | 0.588577i | \(-0.200312\pi\) | ||||
0.808441 | + | 0.588577i | \(0.200312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | + | 20.7846i | 0.471769 | + | 0.817127i | 0.999478 | − | 0.0322975i | \(-0.0102824\pi\) |
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 3.00000 | − | 5.19615i | 0.117399 | − | 0.203341i | −0.801337 | − | 0.598213i | \(-0.795878\pi\) |
0.918736 | + | 0.394872i | \(0.129211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | − | 5.19615i | −0.117220 | − | 0.203030i | ||||
\(656\) | 24.0000 | − | 41.5692i | 0.937043 | − | 1.62301i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0000 | −0.584317 | −0.292159 | − | 0.956370i | \(-0.594373\pi\) | ||||
−0.292159 | + | 0.956370i | \(0.594373\pi\) | |||||||
\(660\) | 3.00000 | − | 5.19615i | 0.116775 | − | 0.202260i | ||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.50000 | + | 12.9904i | −0.291276 | + | 0.504505i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | −3.00000 | − | 5.19615i | −0.116073 | − | 0.201045i | ||||
\(669\) | 9.50000 | + | 16.4545i | 0.367291 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 12.0000 | + | 20.7846i | 0.461538 | + | 0.799408i | ||||
\(677\) | −22.5000 | + | 38.9711i | −0.864745 | + | 1.49778i | 0.00255466 | + | 0.999997i | \(0.499187\pi\) |
−0.867300 | + | 0.497786i | \(0.834147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | + | 20.7846i | 0.459167 | + | 0.795301i | 0.998917 | − | 0.0465244i | \(-0.0148145\pi\) |
−0.539750 | + | 0.841825i | \(0.681481\pi\) | |||||||
\(684\) | −4.00000 | + | 6.92820i | −0.152944 | + | 0.264906i | ||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.00000 | −0.152610 | ||||||||
\(688\) | 20.0000 | − | 34.6410i | 0.762493 | − | 1.32068i | ||||
\(689\) | −30.0000 | − | 51.9615i | −1.14291 | − | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0000 | − | 24.2487i | 0.532585 | − | 0.922464i | −0.466691 | − | 0.884420i | \(-0.654554\pi\) |
0.999276 | − | 0.0380440i | \(-0.0121127\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.00000 | − | 12.1244i | 0.265525 | − | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0000 | 0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.00000 | −0.339925 | −0.169963 | − | 0.985451i | \(-0.554365\pi\) | ||||
−0.169963 | + | 0.985451i | \(0.554365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | − | 3.46410i | −0.0754314 | − | 0.130651i | ||||
\(704\) | −12.0000 | − | 20.7846i | −0.452267 | − | 0.783349i | ||||
\(705\) | 4.50000 | − | 7.79423i | 0.169480 | − | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | − | 1.73205i | −0.0375029 | − | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0000 | 0.560968 | ||||||||
\(716\) | 12.0000 | − | 20.7846i | 0.448461 | − | 0.776757i | ||||
\(717\) | 10.5000 | + | 18.1865i | 0.392130 | + | 0.679189i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0000 | − | 25.9808i | 0.559406 | − | 0.968919i | −0.438141 | − | 0.898906i | \(-0.644363\pi\) |
0.997546 | − | 0.0700124i | \(-0.0223039\pi\) | |||||||
\(720\) | 8.00000 | 0.298142 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.00000 | − | 8.66025i | 0.185952 | − | 0.322078i | ||||
\(724\) | 20.0000 | + | 34.6410i | 0.743294 | + | 1.28742i | ||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | + | 25.9808i | 0.554795 | + | 0.960933i | ||||
\(732\) | 8.00000 | + | 13.8564i | 0.295689 | + | 0.512148i | ||||
\(733\) | 15.5000 | − | 26.8468i | 0.572506 | − | 0.991609i | −0.423802 | − | 0.905755i | \(-0.639305\pi\) |
0.996308 | − | 0.0858539i | \(-0.0273618\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5000 | + | 37.2391i | 0.790890 | + | 1.36986i | 0.925416 | + | 0.378952i | \(0.123715\pi\) |
−0.134526 | + | 0.990910i | \(0.542951\pi\) | |||||||
\(740\) | −2.00000 | + | 3.46410i | −0.0735215 | + | 0.127343i | ||||
\(741\) | 10.0000 | 0.367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0000 | −0.440237 | −0.220119 | − | 0.975473i | \(-0.570644\pi\) | ||||
−0.220119 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | − | 20.7846i | 0.439057 | − | 0.760469i | ||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | + | 19.9186i | −0.419641 | + | 0.726839i | −0.995903 | − | 0.0904254i | \(-0.971177\pi\) |
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(752\) | −18.0000 | − | 31.1769i | −0.656392 | − | 1.13691i | ||||
\(753\) | −9.00000 | − | 15.5885i | −0.327978 | − | 0.568075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | − | 15.5885i | −0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | −3.00000 | + | 5.19615i | −0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8.00000 | + | 13.8564i | −0.288675 | + | 0.500000i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000 | 1.08042 | ||||||||
\(772\) | −4.00000 | + | 6.92820i | −0.143963 | + | 0.249351i | ||||
\(773\) | −10.5000 | − | 18.1865i | −0.377659 | − | 0.654124i | 0.613062 | − | 0.790034i | \(-0.289937\pi\) |
−0.990721 | + | 0.135910i | \(0.956604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | − | 3.46410i | 0.0718421 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | −5.00000 | − | 8.66025i | −0.179029 | − | 0.310087i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.0000 | −0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.50000 | − | 4.33013i | −0.0891154 | − | 0.154352i | 0.818022 | − | 0.575187i | \(-0.195071\pi\) |
−0.907137 | + | 0.420834i | \(0.861737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | + | 10.3923i | 0.212798 | + | 0.368577i | ||||
\(796\) | −16.0000 | + | 27.7128i | −0.567105 | + | 0.982255i | ||||
\(797\) | 15.0000 | 0.531327 | 0.265664 | − | 0.964066i | \(-0.414409\pi\) | ||||
0.265664 | + | 0.964066i | \(0.414409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | 0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | − | 20.7846i | −0.423999 | − | 0.734388i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00000 | − | 5.19615i | 0.105868 | − | 0.183368i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.00000 | − | 5.19615i | 0.105605 | − | 0.182913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.50000 | + | 12.9904i | 0.263686 | + | 0.456717i | 0.967219 | − | 0.253946i | \(-0.0817284\pi\) |
−0.703533 | + | 0.710663i | \(0.748395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000 | + | 1.73205i | 0.0350285 | + | 0.0606711i | ||||
\(816\) | −6.00000 | − | 10.3923i | −0.210042 | − | 0.363803i | ||||
\(817\) | 10.0000 | − | 17.3205i | 0.349856 | − | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | 13.5000 | − | 23.3827i | 0.471153 | − | 0.816061i | −0.528302 | − | 0.849056i | \(-0.677171\pi\) |
0.999456 | + | 0.0329950i | \(0.0105045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | + | 3.46410i | 0.0697156 | + | 0.120751i | 0.898776 | − | 0.438408i | \(-0.144457\pi\) |
−0.829060 | + | 0.559159i | \(0.811124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0000 | 1.87776 | 0.938882 | − | 0.344239i | \(-0.111863\pi\) | ||||
0.938882 | + | 0.344239i | \(0.111863\pi\) | |||||||
\(828\) | 12.0000 | − | 20.7846i | 0.417029 | − | 0.722315i | ||||
\(829\) | 26.0000 | + | 45.0333i | 0.903017 | + | 1.56407i | 0.823557 | + | 0.567234i | \(0.191986\pi\) |
0.0794606 | + | 0.996838i | \(0.474680\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | − | 8.66025i | 0.173448 | − | 0.300421i | ||||
\(832\) | −40.0000 | −1.38675 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50000 | + | 2.59808i | −0.0519096 | + | 0.0899101i | ||||
\(836\) | −6.00000 | − | 10.3923i | −0.207514 | − | 0.359425i | ||||
\(837\) | −10.0000 | − | 17.3205i | −0.345651 | − | 0.598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.0000 | −1.45000 | −0.725001 | − | 0.688748i | \(-0.758161\pi\) | ||||
−0.725001 | + | 0.688748i | \(0.758161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.50000 | − | 2.59808i | −0.0516627 | − | 0.0894825i | ||||
\(844\) | −13.0000 | − | 22.5167i | −0.447478 | − | 0.775055i | ||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 48.0000 | 1.64833 | ||||||||
\(849\) | 6.50000 | − | 11.2583i | 0.223079 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0000 | + | 25.9808i | 0.512390 | + | 0.887486i | 0.999897 | + | 0.0143666i | \(0.00457319\pi\) |
−0.487507 | + | 0.873119i | \(0.662093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | −20.0000 | −0.681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | + | 20.7846i | −0.408485 | + | 0.707516i | −0.994720 | − | 0.102624i | \(-0.967276\pi\) |
0.586235 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.50000 | − | 7.79423i | −0.153005 | − | 0.265012i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | 0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | + | 17.3205i | 0.338837 | + | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.00000 | + | 1.73205i | −0.0338449 | + | 0.0586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −25.0000 | + | 43.3013i | −0.844190 | + | 1.46218i | 0.0421327 | + | 0.999112i | \(0.486585\pi\) |
−0.886323 | + | 0.463068i | \(0.846749\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5000 | + | 18.1865i | 0.354156 | + | 0.613417i | ||||
\(880\) | −6.00000 | + | 10.3923i | −0.202260 | + | 0.350325i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 15.0000 | − | 25.9808i | 0.504505 | − | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | −19.0000 | − | 32.9090i | −0.636167 | − | 1.10187i | ||||
\(893\) | −9.00000 | − | 15.5885i | −0.301174 | − | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.0000 | −1.00167 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.00000 | + | 10.3923i | 0.200111 | + | 0.346603i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | − | 17.3205i | 0.332411 | − | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0000 | − | 22.5167i | −0.431658 | − | 0.747653i | 0.565358 | − | 0.824845i | \(-0.308738\pi\) |
−0.997016 | + | 0.0771920i | \(0.975405\pi\) | |||||||
\(908\) | −3.00000 | + | 5.19615i | −0.0995585 | + | 0.172440i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | −4.00000 | + | 6.92820i | −0.132453 | + | 0.229416i | ||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.00000 | − | 6.92820i | 0.132236 | − | 0.229039i | ||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.50000 | − | 9.52628i | −0.181231 | − | 0.313902i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.00000 | + | 8.66025i | 0.164222 | + | 0.284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | + | 31.1769i | −0.590561 | + | 1.02288i | 0.403596 | + | 0.914937i | \(0.367760\pi\) |
−0.994157 | + | 0.107944i | \(0.965573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −48.0000 | −1.57229 | ||||||||
\(933\) | −9.00000 | + | 15.5885i | −0.294647 | + | 0.510343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.50000 | − | 7.79423i | −0.147166 | − | 0.254899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.0000 | 1.53542 | 0.767712 | − | 0.640796i | \(-0.221395\pi\) | ||||
0.767712 | + | 0.640796i | \(0.221395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0000 | −0.620042 | ||||||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | + | 62.3538i | −1.17232 | + | 2.03052i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(948\) | −1.00000 | − | 1.73205i | −0.0324785 | − | 0.0562544i | ||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.50000 | + | 7.79423i | 0.145617 | + | 0.252215i | ||||
\(956\) | −21.0000 | − | 36.3731i | −0.679189 | − | 1.17639i | ||||
\(957\) | 4.50000 | − | 7.79423i | 0.145464 | − | 0.251952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.00000 | 0.258199 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | + | 10.3923i | 0.193347 | + | 0.334887i | ||||
\(964\) | −10.0000 | + | 17.3205i | −0.322078 | + | 0.557856i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.00000 | − | 5.19615i | −0.0963739 | − | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | − | 41.5692i | 0.770197 | − | 1.33402i | −0.167258 | − | 0.985913i | \(-0.553491\pi\) |
0.937455 | − | 0.348107i | \(-0.113175\pi\) | |||||||
\(972\) | −32.0000 | −1.02640 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.50000 | + | 4.33013i | −0.0800641 | + | 0.138675i | ||||
\(976\) | −16.0000 | − | 27.7128i | −0.512148 | − | 0.887066i | ||||
\(977\) | −27.0000 | − | 46.7654i | −0.863807 | − | 1.49616i | −0.868227 | − | 0.496167i | \(-0.834741\pi\) |
0.00442082 | − | 0.999990i | \(-0.498593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000 | 1.15056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.5000 | + | 18.1865i | 0.334898 | + | 0.580060i | 0.983465 | − | 0.181097i | \(-0.0579648\pi\) |
−0.648567 | + | 0.761157i | \(0.724631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.0000 | −0.636285 | ||||||||
\(989\) | −30.0000 | + | 51.9615i | −0.953945 | + | 1.65228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0000 | − | 48.4974i | −0.889449 | − | 1.54057i | −0.840528 | − | 0.541769i | \(-0.817755\pi\) |
−0.0489218 | − | 0.998803i | \(-0.515578\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 12.0000 | − | 20.7846i | 0.380235 | − | 0.658586i | ||||
\(997\) | 18.5000 | + | 32.0429i | 0.585901 | + | 1.01481i | 0.994762 | + | 0.102214i | \(0.0325925\pi\) |
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.00000 | − | 8.66025i | 0.158193 | − | 0.273998i |
(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 | 245.2.e.a.226.1 | 2 | ||
7.2 | even | 3 | 35.2.a.a.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 245.2.e.b.116.1 | 2 | |||
7.4 | even | 3 | inner | 245.2.e.a.116.1 | 2 | ||
7.5 | odd | 6 | 245.2.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 245.2.e.b.226.1 | 2 | |||
21.2 | odd | 6 | 315.2.a.b.1.1 | 1 | |||
21.5 | even | 6 | 2205.2.a.e.1.1 | 1 | |||
28.19 | even | 6 | 3920.2.a.ba.1.1 | 1 | |||
28.23 | odd | 6 | 560.2.a.b.1.1 | 1 | |||
35.2 | odd | 12 | 175.2.b.a.99.1 | 2 | |||
35.9 | even | 6 | 175.2.a.b.1.1 | 1 | |||
35.12 | even | 12 | 1225.2.b.d.99.2 | 2 | |||
35.19 | odd | 6 | 1225.2.a.e.1.1 | 1 | |||
35.23 | odd | 12 | 175.2.b.a.99.2 | 2 | |||
35.33 | even | 12 | 1225.2.b.d.99.1 | 2 | |||
56.37 | even | 6 | 2240.2.a.k.1.1 | 1 | |||
56.51 | odd | 6 | 2240.2.a.u.1.1 | 1 | |||
77.65 | odd | 6 | 4235.2.a.c.1.1 | 1 | |||
84.23 | even | 6 | 5040.2.a.v.1.1 | 1 | |||
91.51 | even | 6 | 5915.2.a.f.1.1 | 1 | |||
105.2 | even | 12 | 1575.2.d.c.1324.2 | 2 | |||
105.23 | even | 12 | 1575.2.d.c.1324.1 | 2 | |||
105.44 | odd | 6 | 1575.2.a.f.1.1 | 1 | |||
140.23 | even | 12 | 2800.2.g.l.449.1 | 2 | |||
140.79 | odd | 6 | 2800.2.a.z.1.1 | 1 | |||
140.107 | even | 12 | 2800.2.g.l.449.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.a.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
175.2.a.b.1.1 | 1 | 35.9 | even | 6 | |||
175.2.b.a.99.1 | 2 | 35.2 | odd | 12 | |||
175.2.b.a.99.2 | 2 | 35.23 | odd | 12 | |||
245.2.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
245.2.e.a.116.1 | 2 | 7.4 | even | 3 | inner | ||
245.2.e.a.226.1 | 2 | 1.1 | even | 1 | trivial | ||
245.2.e.b.116.1 | 2 | 7.3 | odd | 6 | |||
245.2.e.b.226.1 | 2 | 7.6 | odd | 2 | |||
315.2.a.b.1.1 | 1 | 21.2 | odd | 6 | |||
560.2.a.b.1.1 | 1 | 28.23 | odd | 6 | |||
1225.2.a.e.1.1 | 1 | 35.19 | odd | 6 | |||
1225.2.b.d.99.1 | 2 | 35.33 | even | 12 | |||
1225.2.b.d.99.2 | 2 | 35.12 | even | 12 | |||
1575.2.a.f.1.1 | 1 | 105.44 | odd | 6 | |||
1575.2.d.c.1324.1 | 2 | 105.23 | even | 12 | |||
1575.2.d.c.1324.2 | 2 | 105.2 | even | 12 | |||
2205.2.a.e.1.1 | 1 | 21.5 | even | 6 | |||
2240.2.a.k.1.1 | 1 | 56.37 | even | 6 | |||
2240.2.a.u.1.1 | 1 | 56.51 | odd | 6 | |||
2800.2.a.z.1.1 | 1 | 140.79 | odd | 6 | |||
2800.2.g.l.449.1 | 2 | 140.23 | even | 12 | |||
2800.2.g.l.449.2 | 2 | 140.107 | even | 12 | |||
3920.2.a.ba.1.1 | 1 | 28.19 | even | 6 | |||
4235.2.a.c.1.1 | 1 | 77.65 | odd | 6 | |||
5040.2.a.v.1.1 | 1 | 84.23 | even | 6 | |||
5915.2.a.f.1.1 | 1 | 91.51 | even | 6 |