Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(64,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.d (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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
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 | 64.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.2.d.a.64.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.00000 | − | 1.00000i | 0.516398 | − | 0.258199i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −1.00000 | − | 2.00000i | −0.182574 | − | 0.365148i | ||||
\(31\) | −10.0000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | 6.00000i | 1.04447i | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 2.00000 | − | 1.00000i | 0.338062 | − | 0.169031i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | − | 6.00000i | − | 0.973329i | ||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 6.00000 | − | 3.00000i | 0.948683 | − | 0.474342i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | −1.00000 | − | 2.00000i | −0.149071 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.00000 | − | 12.0000i | −0.809040 | − | 1.61808i | ||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 10.0000i | 1.27000i | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | −4.00000 | + | 2.00000i | −0.496139 | + | 0.248069i | ||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | − | 16.0000i | − | 1.95471i | −0.211604 | − | 0.977356i | \(-0.567869\pi\) | ||
0.211604 | − | 0.977356i | \(-0.432131\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 2.00000i | −0.119523 | − | 0.239046i | ||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 4.00000 | + | 3.00000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 6.00000i | 0.683763i | ||||||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | − | 8.00000i | − | 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −8.00000 | + | 4.00000i | −0.867722 | + | 0.433861i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 18.0000i | 1.91881i | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −2.00000 | + | 1.00000i | −0.210819 | + | 0.105409i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0000i | 1.03695i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | + | 12.0000i | 0.615587 | + | 1.23117i | ||||
\(96\) | −5.00000 | −0.510310 | ||||||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | − | 4.00000i | − | 0.396059i | ||||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | −1.00000 | − | 2.00000i | −0.0975900 | − | 0.195180i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −12.0000 | + | 6.00000i | −1.14416 | + | 0.572078i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | − | 8.00000i | − | 0.736460i | ||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | −3.00000 | − | 6.00000i | −0.273861 | − | 0.547723i | ||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | − | 2.00000i | − | 0.180334i | ||||||
\(124\) | −10.0000 | −0.898027 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 20.0000i | 1.77471i | 0.461084 | + | 0.887357i | \(0.347461\pi\) | ||||
−0.461084 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 2.00000 | + | 4.00000i | 0.175412 | + | 0.350823i | ||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | − | 6.00000i | − | 0.520266i | ||||||
\(134\) | −16.0000 | −1.38219 | ||||||||
\(135\) | −2.00000 | + | 1.00000i | −0.172133 | + | 0.0860663i | ||||
\(136\) | 12.0000 | 1.02899 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 2.00000 | − | 1.00000i | 0.169031 | − | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 10.0000i | − | 0.839181i | ||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.00000 | + | 4.00000i | 0.166091 | + | 0.332182i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 3.00000 | − | 4.00000i | 0.244949 | − | 0.326599i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | − | 18.0000i | − | 1.45999i | ||||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | −10.0000 | − | 20.0000i | −0.803219 | − | 1.60644i | ||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 18.0000i | 1.43656i | 0.695756 | + | 0.718278i | \(0.255069\pi\) | ||||
−0.695756 | + | 0.718278i | \(0.744931\pi\) | |||||||
\(158\) | 4.00000i | 0.318223i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 10.0000 | − | 5.00000i | 0.790569 | − | 0.395285i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | −12.0000 | + | 6.00000i | −0.934199 | + | 0.467099i | ||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 4.00000 | + | 8.00000i | 0.306786 | + | 0.613572i | ||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 4.00000 | + | 3.00000i | 0.302372 | + | 0.226779i | ||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | − | 8.00000i | − | 0.601317i | ||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | 14.0000 | 1.04641 | 0.523205 | − | 0.852207i | \(-0.324736\pi\) | ||||
0.523205 | + | 0.852207i | \(0.324736\pi\) | |||||||
\(180\) | −1.00000 | − | 2.00000i | −0.0745356 | − | 0.149071i | ||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | − | 2.00000i | − | 0.148250i | ||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | − | 4.00000i | 0.588172 | − | 0.294086i | ||||
\(186\) | 10.0000 | 0.733236 | ||||||||
\(187\) | − | 24.0000i | − | 1.75505i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 12.0000 | − | 6.00000i | 0.870572 | − | 0.435286i | ||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | 7.00000i | 0.505181i | ||||||||
\(193\) | 8.00000i | 0.575853i | 0.957653 | + | 0.287926i | \(0.0929658\pi\) | ||||
−0.957653 | + | 0.287926i | \(0.907034\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 2.00000 | + | 4.00000i | 0.143223 | + | 0.286446i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | − | 6.00000i | − | 0.426401i | ||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 12.0000 | + | 9.00000i | 0.848528 | + | 0.636396i | ||||
\(201\) | −16.0000 | −1.12855 | ||||||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 2.00000 | + | 4.00000i | 0.139686 | + | 0.279372i | ||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | −36.0000 | −2.49017 | ||||||||
\(210\) | −2.00000 | + | 1.00000i | −0.138013 | + | 0.0690066i | ||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | − | 10.0000i | − | 0.685189i | ||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | −8.00000 | + | 4.00000i | −0.545595 | + | 0.272798i | ||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | 10.0000i | 0.678844i | ||||||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | −6.00000 | − | 12.0000i | −0.404520 | − | 0.809040i | ||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 4.00000i | 0.268462i | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | −5.00000 | −0.334077 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | 26.0000i | 1.70332i | 0.524097 | + | 0.851658i | \(0.324403\pi\) | ||||
−0.524097 | + | 0.851658i | \(0.675597\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | 4.00000i | 0.259828i | ||||||||
\(238\) | − | 4.00000i | − | 0.259281i | ||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | −1.00000 | − | 2.00000i | −0.0638877 | − | 0.127775i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 12.0000i | 0.763542i | ||||||||
\(248\) | 30.0000i | 1.90500i | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | −2.00000 | + | 11.0000i | −0.126491 | + | 0.695701i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 20.0000 | 1.25491 | ||||||||
\(255\) | 4.00000 | + | 8.00000i | 0.250490 | + | 0.500979i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 16.0000i | 0.998053i | 0.866587 | + | 0.499026i | \(0.166309\pi\) | ||||
−0.866587 | + | 0.499026i | \(0.833691\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | −4.00000 | + | 2.00000i | −0.248069 | + | 0.124035i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | 18.0000 | 1.10782 | ||||||||
\(265\) | 12.0000 | − | 6.00000i | 0.737154 | − | 0.368577i | ||||
\(266\) | −6.00000 | −0.367884 | ||||||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | − | 16.0000i | − | 0.977356i | ||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 1.00000 | + | 2.00000i | 0.0608581 | + | 0.121716i | ||||
\(271\) | −14.0000 | −0.850439 | −0.425220 | − | 0.905090i | \(-0.639803\pi\) | ||||
−0.425220 | + | 0.905090i | \(0.639803\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | − | 2.00000i | − | 0.121046i | ||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 18.0000 | − | 24.0000i | 1.08544 | − | 1.44725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.0000i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | 2.00000i | 0.119952i | ||||||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | −3.00000 | − | 6.00000i | −0.179284 | − | 0.358569i | ||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.0000i | − | 1.18888i | −0.804141 | − | 0.594438i | \(-0.797374\pi\) | ||
0.804141 | − | 0.594438i | \(-0.202626\pi\) | |||||||
\(284\) | 10.0000 | 0.593391 | ||||||||
\(285\) | 12.0000 | − | 6.00000i | 0.710819 | − | 0.355409i | ||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | − | 2.00000i | − | 0.118056i | ||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.00000 | − | 2.00000i | 0.234888 | − | 0.117444i | ||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | 6.00000i | 0.351123i | ||||||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 8.00000 | + | 16.0000i | 0.465778 | + | 0.931556i | ||||
\(296\) | −12.0000 | −0.697486 | ||||||||
\(297\) | − | 6.00000i | − | 0.348155i | ||||||
\(298\) | − | 14.0000i | − | 0.810998i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 6.00000i | 0.344691i | ||||||||
\(304\) | −6.00000 | −0.344124 | ||||||||
\(305\) | −2.00000 | − | 4.00000i | −0.114520 | − | 0.229039i | ||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 6.00000i | 0.341882i | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | −20.0000 | + | 10.0000i | −1.13592 | + | 0.567962i | ||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | − | 6.00000i | − | 0.339683i | ||||||
\(313\) | − | 6.00000i | − | 0.339140i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||
0.985518 | − | 0.169570i | \(-0.0542379\pi\) | |||||||
\(314\) | 18.0000 | 1.01580 | ||||||||
\(315\) | −2.00000 | + | 1.00000i | −0.112687 | + | 0.0563436i | ||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | −7.00000 | − | 14.0000i | −0.391312 | − | 0.782624i | ||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.00000 | − | 6.00000i | −0.443760 | − | 0.332820i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 2.00000i | 0.110600i | ||||||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.00000 | + | 12.0000i | 0.330289 | + | 0.660578i | ||||
\(331\) | −24.0000 | −1.31916 | −0.659580 | − | 0.751635i | \(-0.729266\pi\) | ||||
−0.659580 | + | 0.751635i | \(0.729266\pi\) | |||||||
\(332\) | − | 8.00000i | − | 0.439057i | ||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 32.0000 | − | 16.0000i | 1.74835 | − | 0.874173i | ||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | − | 24.0000i | − | 1.30736i | −0.756770 | − | 0.653682i | \(-0.773224\pi\) | ||
0.756770 | − | 0.653682i | \(-0.226776\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | −8.00000 | + | 4.00000i | −0.433861 | + | 0.216930i | ||||
\(341\) | 60.0000 | 3.24918 | ||||||||
\(342\) | 6.00000i | 0.324443i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000i | 0.644194i | 0.946707 | + | 0.322097i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322097i | \(0.895612\pi\) | |||||||
\(348\) | − | 2.00000i | − | 0.107211i | ||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 3.00000 | − | 4.00000i | 0.160357 | − | 0.213809i | ||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 30.0000i | 1.59901i | ||||||||
\(353\) | − | 20.0000i | − | 1.06449i | −0.846590 | − | 0.532246i | \(-0.821348\pi\) | ||
0.846590 | − | 0.532246i | \(-0.178652\pi\) | |||||||
\(354\) | −8.00000 | −0.425195 | ||||||||
\(355\) | 10.0000 | + | 20.0000i | 0.530745 | + | 1.06149i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | − | 4.00000i | − | 0.211702i | ||||||
\(358\) | − | 14.0000i | − | 0.739923i | ||||||
\(359\) | −22.0000 | −1.16112 | −0.580558 | − | 0.814219i | \(-0.697165\pi\) | ||||
−0.580558 | + | 0.814219i | \(0.697165\pi\) | |||||||
\(360\) | −6.00000 | + | 3.00000i | −0.316228 | + | 0.158114i | ||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 6.00000i | 0.315353i | ||||||||
\(363\) | − | 25.0000i | − | 1.31216i | ||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −12.0000 | + | 6.00000i | −0.628109 | + | 0.314054i | ||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −4.00000 | − | 8.00000i | −0.207950 | − | 0.415900i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 10.0000i | 0.518476i | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | −24.0000 | −1.24101 | ||||||||
\(375\) | −2.00000 | + | 11.0000i | −0.103280 | + | 0.568038i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | − | 1.00000i | − | 0.0514344i | ||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 6.00000 | + | 12.0000i | 0.307794 | + | 0.615587i | ||||
\(381\) | 20.0000 | 1.02463 | ||||||||
\(382\) | 18.0000i | 0.920960i | ||||||||
\(383\) | 20.0000i | 1.02195i | 0.859595 | + | 0.510976i | \(0.170716\pi\) | ||||
−0.859595 | + | 0.510976i | \(0.829284\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | −12.0000 | + | 6.00000i | −0.611577 | + | 0.305788i | ||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | −26.0000 | −1.31825 | −0.659126 | − | 0.752032i | \(-0.729074\pi\) | ||||
−0.659126 | + | 0.752032i | \(0.729074\pi\) | |||||||
\(390\) | 4.00000 | − | 2.00000i | 0.202548 | − | 0.101274i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −4.00000 | − | 8.00000i | −0.201262 | − | 0.402524i | ||||
\(396\) | 6.00000 | 0.301511 | ||||||||
\(397\) | 22.0000i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(398\) | 14.0000i | 0.701757i | ||||||||
\(399\) | −6.00000 | −0.300376 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 16.0000i | 0.798007i | ||||||||
\(403\) | − | 20.0000i | − | 0.996271i | ||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | − | 12.0000i | − | 0.594089i | ||||||
\(409\) | 22.0000 | 1.08783 | 0.543915 | − | 0.839140i | \(-0.316941\pi\) | ||||
0.543915 | + | 0.839140i | \(0.316941\pi\) | |||||||
\(410\) | 4.00000 | − | 2.00000i | 0.197546 | − | 0.0987730i | ||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | − | 8.00000i | − | 0.393654i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.0000 | − | 8.00000i | 0.785409 | − | 0.392705i | ||||
\(416\) | 10.0000 | 0.490290 | ||||||||
\(417\) | 2.00000i | 0.0979404i | ||||||||
\(418\) | 36.0000i | 1.76082i | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | −1.00000 | − | 2.00000i | −0.0487950 | − | 0.0975900i | ||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 16.0000i | 0.778868i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | −0.874157 | ||||||||
\(425\) | −16.0000 | − | 12.0000i | −0.776114 | − | 0.582086i | ||||
\(426\) | −10.0000 | −0.484502 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | 4.00000i | 0.193347i | ||||||||
\(429\) | −12.0000 | −0.579365 | ||||||||
\(430\) | 4.00000 | + | 8.00000i | 0.192897 | + | 0.385794i | ||||
\(431\) | −14.0000 | −0.674356 | −0.337178 | − | 0.941441i | \(-0.609472\pi\) | ||||
−0.337178 | + | 0.941441i | \(0.609472\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 34.0000i | 1.63394i | 0.576683 | + | 0.816968i | \(0.304347\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | 4.00000 | − | 2.00000i | 0.191785 | − | 0.0958927i | ||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 6.00000i | − | 0.286691i | ||||||
\(439\) | −6.00000 | −0.286364 | −0.143182 | − | 0.989696i | \(-0.545733\pi\) | ||||
−0.143182 | + | 0.989696i | \(0.545733\pi\) | |||||||
\(440\) | −36.0000 | + | 18.0000i | −1.71623 | + | 0.858116i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | −6.00000 | − | 12.0000i | −0.284427 | − | 0.568855i | ||||
\(446\) | 24.0000 | 1.13643 | ||||||||
\(447\) | − | 14.0000i | − | 0.662177i | ||||||
\(448\) | 7.00000i | 0.330719i | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | −4.00000 | − | 3.00000i | −0.188562 | − | 0.141421i | ||||
\(451\) | −12.0000 | −0.565058 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | − | 8.00000i | − | 0.375873i | ||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 2.00000 | + | 4.00000i | 0.0937614 | + | 0.187523i | ||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | − | 20.0000i | − | 0.935561i | −0.883845 | − | 0.467780i | \(-0.845054\pi\) | ||
0.883845 | − | 0.467780i | \(-0.154946\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | − | 6.00000i | − | 0.279145i | ||||||
\(463\) | − | 36.0000i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | −20.0000 | + | 10.0000i | −0.927478 | + | 0.463739i | ||||
\(466\) | 26.0000 | 1.20443 | ||||||||
\(467\) | − | 24.0000i | − | 1.11059i | −0.831654 | − | 0.555294i | \(-0.812606\pi\) | ||
0.831654 | − | 0.555294i | \(-0.187394\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | 0.829396 | ||||||||
\(472\) | − | 24.0000i | − | 1.10469i | ||||||
\(473\) | − | 24.0000i | − | 1.10352i | ||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | −18.0000 | + | 24.0000i | −0.825897 | + | 1.10120i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | − | 6.00000i | − | 0.274434i | ||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | −5.00000 | − | 10.0000i | −0.228218 | − | 0.456435i | ||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | − | 22.0000i | − | 1.00207i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | 4.00000 | − | 2.00000i | 0.181631 | − | 0.0908153i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −2.00000 | + | 1.00000i | −0.0903508 | + | 0.0451754i | ||||
\(491\) | 10.0000 | 0.451294 | 0.225647 | − | 0.974209i | \(-0.427550\pi\) | ||||
0.225647 | + | 0.974209i | \(0.427550\pi\) | |||||||
\(492\) | − | 2.00000i | − | 0.0901670i | ||||||
\(493\) | 8.00000i | 0.360302i | ||||||||
\(494\) | 12.0000 | 0.539906 | ||||||||
\(495\) | 6.00000 | + | 12.0000i | 0.269680 | + | 0.539360i | ||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | − | 10.0000i | − | 0.448561i | ||||||
\(498\) | 8.00000i | 0.358489i | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.0000i | 1.60516i | 0.596544 | + | 0.802580i | \(0.296540\pi\) | ||||
−0.596544 | + | 0.802580i | \(0.703460\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | −6.00000 | − | 12.0000i | −0.266996 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.00000i | − | 0.399704i | ||||||
\(508\) | 20.0000i | 0.887357i | ||||||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 8.00000 | − | 4.00000i | 0.354246 | − | 0.177123i | ||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 6.00000i | 0.264906i | ||||||||
\(514\) | 16.0000 | 0.705730 | ||||||||
\(515\) | 16.0000 | − | 8.00000i | 0.705044 | − | 0.352522i | ||||
\(516\) | 4.00000 | 0.176090 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.00000i | 0.175750i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | + | 12.0000i | 0.263117 | + | 0.526235i | ||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | − | 20.0000i | − | 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 3.00000 | − | 4.00000i | 0.130931 | − | 0.174574i | ||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | − | 40.0000i | − | 1.74243i | ||||||
\(528\) | − | 6.00000i | − | 0.261116i | ||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −6.00000 | − | 12.0000i | −0.260623 | − | 0.521247i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | − | 6.00000i | − | 0.260133i | ||||||
\(533\) | 4.00000i | 0.173259i | ||||||||
\(534\) | 6.00000 | 0.259645 | ||||||||
\(535\) | −8.00000 | + | 4.00000i | −0.345870 | + | 0.172935i | ||||
\(536\) | −48.0000 | −2.07328 | ||||||||
\(537\) | − | 14.0000i | − | 0.604145i | ||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | 14.0000i | 0.601351i | ||||||||
\(543\) | 6.00000i | 0.257485i | ||||||||
\(544\) | 20.0000 | 0.857493 | ||||||||
\(545\) | −2.00000 | − | 4.00000i | −0.0856706 | − | 0.171341i | ||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | − | 16.0000i | − | 0.684111i | −0.939680 | − | 0.342055i | \(-0.888877\pi\) | ||
0.939680 | − | 0.342055i | \(-0.111123\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −24.0000 | − | 18.0000i | −1.02336 | − | 0.767523i | ||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000i | 0.170097i | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | −4.00000 | − | 8.00000i | −0.169791 | − | 0.339581i | ||||
\(556\) | −2.00000 | −0.0848189 | ||||||||
\(557\) | 38.0000i | 1.61011i | 0.593199 | + | 0.805056i | \(0.297865\pi\) | ||||
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(558\) | − | 10.0000i | − | 0.423334i | ||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | −2.00000 | + | 1.00000i | −0.0845154 | + | 0.0422577i | ||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 2.00000i | 0.0843649i | ||||||||
\(563\) | 36.0000i | 1.51722i | 0.651546 | + | 0.758610i | \(0.274121\pi\) | ||||
−0.651546 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0000 | − | 6.00000i | 0.504844 | − | 0.252422i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | − | 30.0000i | − | 1.25877i | ||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | −6.00000 | − | 12.0000i | −0.251312 | − | 0.502625i | ||||
\(571\) | 36.0000 | 1.50655 | 0.753277 | − | 0.657704i | \(-0.228472\pi\) | ||||
0.753277 | + | 0.657704i | \(0.228472\pi\) | |||||||
\(572\) | − | 12.0000i | − | 0.501745i | ||||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | −2.00000 | −0.0834784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 14.0000i | 0.582828i | 0.956597 | + | 0.291414i | \(0.0941257\pi\) | ||||
−0.956597 | + | 0.291414i | \(0.905874\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 8.00000 | 0.332469 | ||||||||
\(580\) | 2.00000 | + | 4.00000i | 0.0830455 | + | 0.166091i | ||||
\(581\) | −8.00000 | −0.331896 | ||||||||
\(582\) | 2.00000i | 0.0829027i | ||||||||
\(583\) | 36.0000i | 1.49097i | ||||||||
\(584\) | 18.0000 | 0.744845 | ||||||||
\(585\) | 4.00000 | − | 2.00000i | 0.165380 | − | 0.0826898i | ||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 1.00000i | 0.0412393i | ||||||||
\(589\) | −60.0000 | −2.47226 | ||||||||
\(590\) | 16.0000 | − | 8.00000i | 0.658710 | − | 0.329355i | ||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | 4.00000i | 0.164399i | ||||||||
\(593\) | − | 44.0000i | − | 1.80686i | −0.428732 | − | 0.903432i | \(-0.641040\pi\) | ||
0.428732 | − | 0.903432i | \(-0.358960\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | 4.00000 | + | 8.00000i | 0.163984 | + | 0.327968i | ||||
\(596\) | 14.0000 | 0.573462 | ||||||||
\(597\) | 14.0000i | 0.572982i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.00000 | 0.0817178 | 0.0408589 | − | 0.999165i | \(-0.486991\pi\) | ||||
0.0408589 | + | 0.999165i | \(0.486991\pi\) | |||||||
\(600\) | 9.00000 | − | 12.0000i | 0.367423 | − | 0.489898i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | − | 4.00000i | − | 0.163028i | ||||||
\(603\) | 16.0000i | 0.651570i | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 25.0000 | + | 50.0000i | 1.01639 | + | 2.03279i | ||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | 24.0000i | 0.974130i | 0.873366 | + | 0.487065i | \(0.161933\pi\) | ||||
−0.873366 | + | 0.487065i | \(0.838067\pi\) | |||||||
\(608\) | − | 30.0000i | − | 1.21666i | ||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | −4.00000 | + | 2.00000i | −0.161955 | + | 0.0809776i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | − | 4.00000i | − | 0.161558i | −0.996732 | − | 0.0807792i | \(-0.974259\pi\) | ||
0.996732 | − | 0.0807792i | \(-0.0257409\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | 4.00000 | − | 2.00000i | 0.161296 | − | 0.0806478i | ||||
\(616\) | 18.0000 | 0.725241 | ||||||||
\(617\) | − | 26.0000i | − | 1.04672i | −0.852111 | − | 0.523360i | \(-0.824678\pi\) | ||
0.852111 | − | 0.523360i | \(-0.175322\pi\) | |||||||
\(618\) | 8.00000i | 0.321807i | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | −10.0000 | − | 20.0000i | −0.401610 | − | 0.803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000i | 0.962312i | ||||||||
\(623\) | 6.00000i | 0.240385i | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | 36.0000i | 1.43770i | ||||||||
\(628\) | 18.0000i | 0.718278i | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 1.00000 | + | 2.00000i | 0.0398410 | + | 0.0796819i | ||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 12.0000i | 0.477334i | ||||||||
\(633\) | 16.0000i | 0.635943i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −40.0000 | + | 20.0000i | −1.58735 | + | 0.793676i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | − | 2.00000i | − | 0.0792429i | ||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | −10.0000 | −0.395594 | ||||||||
\(640\) | 6.00000 | − | 3.00000i | 0.237171 | − | 0.118585i | ||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | − | 4.00000i | − | 0.157867i | ||||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | + | 8.00000i | 0.157500 | + | 0.315000i | ||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | − | 20.0000i | − | 0.786281i | −0.919478 | − | 0.393141i | \(-0.871389\pi\) | ||
0.919478 | − | 0.393141i | \(-0.128611\pi\) | |||||||
\(648\) | − | 3.00000i | − | 0.117851i | ||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | 10.0000 | 0.391931 | ||||||||
\(652\) | − | 4.00000i | − | 0.156652i | ||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | 2.00000 | 0.0782062 | ||||||||
\(655\) | 4.00000 | + | 8.00000i | 0.156293 | + | 0.312586i | ||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | − | 6.00000i | − | 0.234082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | 0.701180 | 0.350590 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350590 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(660\) | −12.0000 | + | 6.00000i | −0.467099 | + | 0.233550i | ||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 24.0000i | 0.932786i | ||||||||
\(663\) | 8.00000i | 0.310694i | ||||||||
\(664\) | −24.0000 | −0.931381 | ||||||||
\(665\) | 12.0000 | − | 6.00000i | 0.465340 | − | 0.232670i | ||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | 24.0000 | 0.927894 | ||||||||
\(670\) | −16.0000 | − | 32.0000i | −0.618134 | − | 1.23627i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 5.00000i | 0.192879i | ||||||||
\(673\) | 36.0000i | 1.38770i | 0.720121 | + | 0.693849i | \(0.244086\pi\) | ||||
−0.720121 | + | 0.693849i | \(0.755914\pi\) | |||||||
\(674\) | −24.0000 | −0.924445 | ||||||||
\(675\) | −4.00000 | − | 3.00000i | −0.153960 | − | 0.115470i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | 32.0000i | 1.22986i | 0.788582 | + | 0.614930i | \(0.210816\pi\) | ||||
−0.788582 | + | 0.614930i | \(0.789184\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −2.00000 | −0.0767530 | ||||||||
\(680\) | 12.0000 | + | 24.0000i | 0.460179 | + | 0.920358i | ||||
\(681\) | 8.00000 | 0.306561 | ||||||||
\(682\) | − | 60.0000i | − | 2.29752i | ||||||
\(683\) | − | 28.0000i | − | 1.07139i | −0.844411 | − | 0.535695i | \(-0.820050\pi\) | ||
0.844411 | − | 0.535695i | \(-0.179950\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 12.0000 | − | 6.00000i | 0.458496 | − | 0.229248i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.0000 | −1.90209 | −0.951045 | − | 0.309053i | \(-0.899988\pi\) | ||||
−0.951045 | + | 0.309053i | \(0.899988\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 6.00000i | − | 0.227921i | ||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −2.00000 | − | 4.00000i | −0.0758643 | − | 0.151729i | ||||
\(696\) | −6.00000 | −0.227429 | ||||||||
\(697\) | 8.00000i | 0.303022i | ||||||||
\(698\) | − | 2.00000i | − | 0.0757011i | ||||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | − | 24.0000i | − | 0.905177i | ||||||
\(704\) | 42.0000 | 1.58293 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.0000 | −0.752710 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | − | 8.00000i | − | 0.300658i | ||||||
\(709\) | −26.0000 | −0.976450 | −0.488225 | − | 0.872718i | \(-0.662356\pi\) | ||||
−0.488225 | + | 0.872718i | \(0.662356\pi\) | |||||||
\(710\) | 20.0000 | − | 10.0000i | 0.750587 | − | 0.375293i | ||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 18.0000i | 0.674579i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 24.0000 | − | 12.0000i | 0.897549 | − | 0.448775i | ||||
\(716\) | 14.0000 | 0.523205 | ||||||||
\(717\) | − | 6.00000i | − | 0.224074i | ||||||
\(718\) | 22.0000i | 0.821033i | ||||||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 1.00000 | + | 2.00000i | 0.0372678 | + | 0.0745356i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | − | 22.0000i | − | 0.818189i | ||||||
\(724\) | −6.00000 | −0.222988 | ||||||||
\(725\) | −6.00000 | + | 8.00000i | −0.222834 | + | 0.297113i | ||||
\(726\) | −25.0000 | −0.927837 | ||||||||
\(727\) | − | 40.0000i | − | 1.48352i | −0.670667 | − | 0.741759i | \(-0.733992\pi\) | ||
0.670667 | − | 0.741759i | \(-0.266008\pi\) | |||||||
\(728\) | − | 6.00000i | − | 0.222375i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 6.00000 | + | 12.0000i | 0.222070 | + | 0.444140i | ||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 2.00000i | 0.0739221i | ||||||||
\(733\) | − | 22.0000i | − | 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | + | 1.00000i | −0.0737711 | + | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 96.0000i | 3.53621i | ||||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 8.00000 | − | 4.00000i | 0.294086 | − | 0.147043i | ||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | 6.00000i | 0.220267i | ||||||||
\(743\) | − | 40.0000i | − | 1.46746i | −0.679442 | − | 0.733729i | \(-0.737778\pi\) | ||
0.679442 | − | 0.733729i | \(-0.262222\pi\) | |||||||
\(744\) | 30.0000 | 1.09985 | ||||||||
\(745\) | 14.0000 | + | 28.0000i | 0.512920 | + | 1.02584i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 11.0000 | + | 2.00000i | 0.401663 | + | 0.0730297i | ||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.00000 | 0.145671 | ||||||||
\(755\) | 8.00000 | + | 16.0000i | 0.291150 | + | 0.582300i | ||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | − | 40.0000i | − | 1.45382i | −0.686730 | − | 0.726912i | \(-0.740955\pi\) | ||
0.686730 | − | 0.726912i | \(-0.259045\pi\) | |||||||
\(758\) | − | 28.0000i | − | 1.01701i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.0000 | − | 18.0000i | 1.30586 | − | 0.652929i | ||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | − | 20.0000i | − | 0.724524i | ||||||
\(763\) | 2.00000i | 0.0724049i | ||||||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 8.00000 | − | 4.00000i | 0.289241 | − | 0.144620i | ||||
\(766\) | 20.0000 | 0.722629 | ||||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 6.00000 | + | 12.0000i | 0.216225 | + | 0.432450i | ||||
\(771\) | 16.0000 | 0.576226 | ||||||||
\(772\) | 8.00000i | 0.287926i | ||||||||
\(773\) | − | 24.0000i | − | 0.863220i | −0.902060 | − | 0.431610i | \(-0.857946\pi\) | ||
0.902060 | − | 0.431610i | \(-0.142054\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 30.0000 | − | 40.0000i | 1.07763 | − | 1.43684i | ||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 4.00000i | 0.143499i | ||||||||
\(778\) | 26.0000i | 0.932145i | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | 2.00000 | + | 4.00000i | 0.0716115 | + | 0.143223i | ||||
\(781\) | −60.0000 | −2.14697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −36.0000 | + | 18.0000i | −1.28490 | + | 0.642448i | ||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | − | 4.00000i | − | 0.142585i | −0.997455 | − | 0.0712923i | \(-0.977288\pi\) | ||
0.997455 | − | 0.0712923i | \(-0.0227123\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | −8.00000 | + | 4.00000i | −0.284627 | + | 0.142314i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | − | 18.0000i | − | 0.639602i | ||||||
\(793\) | − | 4.00000i | − | 0.142044i | ||||||
\(794\) | 22.0000 | 0.780751 | ||||||||
\(795\) | −6.00000 | − | 12.0000i | −0.212798 | − | 0.425596i | ||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | − | 16.0000i | − | 0.566749i | −0.959009 | − | 0.283375i | \(-0.908546\pi\) | ||
0.959009 | − | 0.283375i | \(-0.0914540\pi\) | |||||||
\(798\) | 6.00000i | 0.212398i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 20.0000 | + | 15.0000i | 0.707107 | + | 0.530330i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 30.0000i | 1.05934i | ||||||||
\(803\) | − | 36.0000i | − | 1.27041i | ||||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | − | 14.0000i | − | 0.492823i | ||||||
\(808\) | 18.0000i | 0.633238i | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | 34.0000 | 1.19390 | 0.596951 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596951 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(812\) | − | 2.00000i | − | 0.0701862i | ||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | 8.00000 | − | 4.00000i | 0.280228 | − | 0.140114i | ||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 24.0000i | 0.839654i | ||||||||
\(818\) | − | 22.0000i | − | 0.769212i | ||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 2.00000 | + | 4.00000i | 0.0698430 | + | 0.139686i | ||||
\(821\) | −2.00000 | −0.0698005 | −0.0349002 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349002 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(822\) | 6.00000i | 0.209274i | ||||||||
\(823\) | − | 44.0000i | − | 1.53374i | −0.641800 | − | 0.766872i | \(-0.721812\pi\) | ||
0.641800 | − | 0.766872i | \(-0.278188\pi\) | |||||||
\(824\) | −24.0000 | −0.836080 | ||||||||
\(825\) | −24.0000 | − | 18.0000i | −0.835573 | − | 0.626680i | ||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.00000 | 0.208389 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(830\) | −8.00000 | − | 16.0000i | −0.277684 | − | 0.555368i | ||||
\(831\) | −28.0000 | −0.971309 | ||||||||
\(832\) | − | 14.0000i | − | 0.485363i | ||||||
\(833\) | − | 4.00000i | − | 0.138592i | ||||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | −24.0000 | + | 12.0000i | −0.830554 | + | 0.415277i | ||||
\(836\) | −36.0000 | −1.24509 | ||||||||
\(837\) | − | 10.0000i | − | 0.345651i | ||||||
\(838\) | − | 12.0000i | − | 0.414533i | ||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | −6.00000 | + | 3.00000i | −0.207020 | + | 0.103510i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 18.0000i | − | 0.620321i | ||||||
\(843\) | 2.00000i | 0.0688837i | ||||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 9.00000 | + | 18.0000i | 0.309609 | + | 0.619219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25.0000i | − | 0.859010i | ||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | −12.0000 | + | 16.0000i | −0.411597 | + | 0.548795i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 10.0000i | − | 0.342594i | ||||||
\(853\) | − | 30.0000i | − | 1.02718i | −0.858036 | − | 0.513590i | \(-0.828315\pi\) | ||
0.858036 | − | 0.513590i | \(-0.171685\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | −6.00000 | − | 12.0000i | −0.205196 | − | 0.410391i | ||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | − | 24.0000i | − | 0.819824i | −0.912125 | − | 0.409912i | \(-0.865559\pi\) | ||
0.912125 | − | 0.409912i | \(-0.134441\pi\) | |||||||
\(858\) | 12.0000i | 0.409673i | ||||||||
\(859\) | 26.0000 | 0.887109 | 0.443554 | − | 0.896248i | \(-0.353717\pi\) | ||||
0.443554 | + | 0.896248i | \(0.353717\pi\) | |||||||
\(860\) | −8.00000 | + | 4.00000i | −0.272798 | + | 0.136399i | ||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | 14.0000i | 0.476842i | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.0000 | 1.15537 | ||||||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 10.0000i | 0.339422i | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | −2.00000 | − | 4.00000i | −0.0678064 | − | 0.135613i | ||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 6.00000i | 0.203186i | ||||||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | + | 11.0000i | −0.0676123 | + | 0.371868i | ||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | − | 4.00000i | − | 0.135070i | −0.997717 | − | 0.0675352i | \(-0.978487\pi\) | ||
0.997717 | − | 0.0675352i | \(-0.0215135\pi\) | |||||||
\(878\) | 6.00000i | 0.202490i | ||||||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 6.00000 | + | 12.0000i | 0.202260 | + | 0.404520i | ||||
\(881\) | 14.0000 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | 48.0000i | 1.61533i | 0.589643 | + | 0.807664i | \(0.299269\pi\) | ||||
−0.589643 | + | 0.807664i | \(0.700731\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | 16.0000 | − | 8.00000i | 0.537834 | − | 0.268917i | ||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | 8.00000i | 0.268614i | 0.990940 | + | 0.134307i | \(0.0428808\pi\) | ||||
−0.990940 | + | 0.134307i | \(0.957119\pi\) | |||||||
\(888\) | 12.0000i | 0.402694i | ||||||||
\(889\) | 20.0000 | 0.670778 | ||||||||
\(890\) | −12.0000 | + | 6.00000i | −0.402241 | + | 0.201120i | ||||
\(891\) | −6.00000 | −0.201008 | ||||||||
\(892\) | 24.0000i | 0.803579i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −14.0000 | −0.468230 | ||||||||
\(895\) | 14.0000 | + | 28.0000i | 0.467968 | + | 0.935937i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000i | 0.333704i | ||||||||
\(899\) | −20.0000 | −0.667037 | ||||||||
\(900\) | 3.00000 | − | 4.00000i | 0.100000 | − | 0.133333i | ||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | − | 4.00000i | − | 0.133112i | ||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | −6.00000 | − | 12.0000i | −0.199447 | − | 0.398893i | ||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | 16.0000i | 0.531271i | 0.964073 | + | 0.265636i | \(0.0855818\pi\) | ||||
−0.964073 | + | 0.265636i | \(0.914418\pi\) | |||||||
\(908\) | 8.00000i | 0.265489i | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 4.00000 | − | 2.00000i | 0.132599 | − | 0.0662994i | ||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | 48.0000i | 1.58857i | ||||||||
\(914\) | −20.0000 | −0.661541 | ||||||||
\(915\) | −4.00000 | + | 2.00000i | −0.132236 | + | 0.0661180i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | − | 4.00000i | − | 0.132092i | ||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | −28.0000 | −0.923635 | −0.461817 | − | 0.886975i | \(-0.652802\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | − | 30.0000i | − | 0.987997i | ||||||
\(923\) | 20.0000i | 0.658308i | ||||||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | − | 10.0000i | − | 0.328266i | ||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 10.0000 | + | 20.0000i | 0.327913 | + | 0.655826i | ||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | 26.0000i | 0.851658i | ||||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | −24.0000 | −0.785304 | ||||||||
\(935\) | 48.0000 | − | 24.0000i | 1.56977 | − | 0.784884i | ||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0000 | −1.36916 | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||||
−0.684580 | + | 0.728937i | \(0.740015\pi\) | |||||||
\(942\) | − | 18.0000i | − | 0.586472i | ||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 1.00000 | + | 2.00000i | 0.0325300 | + | 0.0650600i | ||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | − | 36.0000i | − | 1.16984i | −0.811090 | − | 0.584921i | \(-0.801125\pi\) | ||
0.811090 | − | 0.584921i | \(-0.198875\pi\) | |||||||
\(948\) | 4.00000i | 0.129914i | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 24.0000 | + | 18.0000i | 0.778663 | + | 0.583997i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | − | 12.0000i | − | 0.388922i | ||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | −18.0000 | − | 36.0000i | −0.582466 | − | 1.16493i | ||||
\(956\) | 6.00000 | 0.194054 | ||||||||
\(957\) | 12.0000i | 0.387905i | ||||||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | −14.0000 | + | 7.00000i | −0.451848 | + | 0.225924i | ||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | − | 8.00000i | − | 0.257930i | ||||||
\(963\) | − | 4.00000i | − | 0.128898i | ||||||
\(964\) | 22.0000 | 0.708572 | ||||||||
\(965\) | −16.0000 | + | 8.00000i | −0.515058 | + | 0.257529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0000i | 1.28631i | 0.765735 | + | 0.643157i | \(0.222376\pi\) | ||||
−0.765735 | + | 0.643157i | \(0.777624\pi\) | |||||||
\(968\) | − | 75.0000i | − | 2.41059i | ||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | −2.00000 | − | 4.00000i | −0.0642161 | − | 0.128432i | ||||
\(971\) | −8.00000 | −0.256732 | −0.128366 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128366 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 2.00000i | 0.0641171i | ||||||||
\(974\) | 12.0000 | 0.384505 | ||||||||
\(975\) | −6.00000 | + | 8.00000i | −0.192154 | + | 0.256205i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 30.0000i | 0.959785i | 0.877327 | + | 0.479893i | \(0.159324\pi\) | ||||
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | 36.0000 | 1.15056 | ||||||||
\(980\) | −1.00000 | − | 2.00000i | −0.0319438 | − | 0.0638877i | ||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | − | 10.0000i | − | 0.319113i | ||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | −4.00000 | + | 2.00000i | −0.127451 | + | 0.0637253i | ||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000i | 0.381771i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 12.0000 | − | 6.00000i | 0.381385 | − | 0.190693i | ||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 50.0000i | 1.58750i | ||||||||
\(993\) | 24.0000i | 0.761617i | ||||||||
\(994\) | −10.0000 | −0.317181 | ||||||||
\(995\) | −14.0000 | − | 28.0000i | −0.443830 | − | 0.887660i | ||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | 14.0000i | 0.443384i | 0.975117 | + | 0.221692i | \(0.0711580\pi\) | ||||
−0.975117 | + | 0.221692i | \(0.928842\pi\) | |||||||
\(998\) | 4.00000i | 0.126618i | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 105.2.d.a.64.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.2.d.c.64.2 | 2 | |||
4.3 | odd | 2 | 1680.2.t.f.1009.2 | 2 | |||
5.2 | odd | 4 | 525.2.a.c.1.1 | 1 | |||
5.3 | odd | 4 | 525.2.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 105.2.d.a.64.2 | yes | 2 | |
7.2 | even | 3 | 735.2.q.a.214.1 | 4 | |||
7.3 | odd | 6 | 735.2.q.b.79.2 | 4 | |||
7.4 | even | 3 | 735.2.q.a.79.2 | 4 | |||
7.5 | odd | 6 | 735.2.q.b.214.1 | 4 | |||
7.6 | odd | 2 | 735.2.d.a.589.1 | 2 | |||
12.11 | even | 2 | 5040.2.t.e.1009.1 | 2 | |||
15.2 | even | 4 | 1575.2.a.e.1.1 | 1 | |||
15.8 | even | 4 | 1575.2.a.i.1.1 | 1 | |||
15.14 | odd | 2 | 315.2.d.c.64.1 | 2 | |||
20.3 | even | 4 | 8400.2.a.bj.1.1 | 1 | |||
20.7 | even | 4 | 8400.2.a.ch.1.1 | 1 | |||
20.19 | odd | 2 | 1680.2.t.f.1009.1 | 2 | |||
21.20 | even | 2 | 2205.2.d.f.1324.2 | 2 | |||
35.4 | even | 6 | 735.2.q.a.79.1 | 4 | |||
35.9 | even | 6 | 735.2.q.a.214.2 | 4 | |||
35.13 | even | 4 | 3675.2.a.d.1.1 | 1 | |||
35.19 | odd | 6 | 735.2.q.b.214.2 | 4 | |||
35.24 | odd | 6 | 735.2.q.b.79.1 | 4 | |||
35.27 | even | 4 | 3675.2.a.l.1.1 | 1 | |||
35.34 | odd | 2 | 735.2.d.a.589.2 | 2 | |||
60.59 | even | 2 | 5040.2.t.e.1009.2 | 2 | |||
105.104 | even | 2 | 2205.2.d.f.1324.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.a.64.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
105.2.d.a.64.2 | yes | 2 | 5.4 | even | 2 | inner | |
315.2.d.c.64.1 | 2 | 15.14 | odd | 2 | |||
315.2.d.c.64.2 | 2 | 3.2 | odd | 2 | |||
525.2.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
525.2.a.c.1.1 | 1 | 5.2 | odd | 4 | |||
735.2.d.a.589.1 | 2 | 7.6 | odd | 2 | |||
735.2.d.a.589.2 | 2 | 35.34 | odd | 2 | |||
735.2.q.a.79.1 | 4 | 35.4 | even | 6 | |||
735.2.q.a.79.2 | 4 | 7.4 | even | 3 | |||
735.2.q.a.214.1 | 4 | 7.2 | even | 3 | |||
735.2.q.a.214.2 | 4 | 35.9 | even | 6 | |||
735.2.q.b.79.1 | 4 | 35.24 | odd | 6 | |||
735.2.q.b.79.2 | 4 | 7.3 | odd | 6 | |||
735.2.q.b.214.1 | 4 | 7.5 | odd | 6 | |||
735.2.q.b.214.2 | 4 | 35.19 | odd | 6 | |||
1575.2.a.e.1.1 | 1 | 15.2 | even | 4 | |||
1575.2.a.i.1.1 | 1 | 15.8 | even | 4 | |||
1680.2.t.f.1009.1 | 2 | 20.19 | odd | 2 | |||
1680.2.t.f.1009.2 | 2 | 4.3 | odd | 2 | |||
2205.2.d.f.1324.1 | 2 | 105.104 | even | 2 | |||
2205.2.d.f.1324.2 | 2 | 21.20 | even | 2 | |||
3675.2.a.d.1.1 | 1 | 35.13 | even | 4 | |||
3675.2.a.l.1.1 | 1 | 35.27 | even | 4 | |||
5040.2.t.e.1009.1 | 2 | 12.11 | even | 2 | |||
5040.2.t.e.1009.2 | 2 | 60.59 | even | 2 | |||
8400.2.a.bj.1.1 | 1 | 20.3 | even | 4 | |||
8400.2.a.ch.1.1 | 1 | 20.7 | even | 4 |