Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(79,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, 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("390.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.e (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: | \(3.11416567883\) |
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 | 79.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.79 |
Dual form | 390.2.e.b.79.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.00000 | − | 2.00000i | 0.316228 | − | 0.632456i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −2.00000 | − | 1.00000i | −0.365148 | − | 0.182574i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 2.00000i | − | 0.348155i | ||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 4.00000 | − | 8.00000i | 0.676123 | − | 1.35225i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.00000 | + | 2.00000i | −0.158114 | + | 0.316228i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 4.00000i | 0.617213i | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −2.00000 | − | 1.00000i | −0.298142 | − | 0.149071i | ||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | − | 1.00000i | − | 0.138675i | ||||||
\(53\) | 10.0000i | 1.37361i | 0.726844 | + | 0.686803i | \(0.240986\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.00000 | + | 2.00000i | 0.539360 | + | 0.269680i | ||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 14.0000 | 1.82264 | 0.911322 | − | 0.411693i | \(-0.135063\pi\) | ||||
0.911322 | + | 0.411693i | \(0.135063\pi\) | |||||||
\(60\) | −1.00000 | + | 2.00000i | −0.129099 | + | 0.258199i | ||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | 4.00000i | 0.503953i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.00000 | + | 2.00000i | −0.124035 | + | 0.248069i | ||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | −8.00000 | − | 4.00000i | −0.956183 | − | 0.478091i | ||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 4.00000 | − | 3.00000i | 0.461880 | − | 0.346410i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | − | 8.00000i | − | 0.911685i | ||||||
\(78\) | − | 1.00000i | − | 0.113228i | ||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 4.00000 | − | 8.00000i | 0.433861 | − | 0.867722i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 18.0000 | 1.90800 | 0.953998 | − | 0.299813i | \(-0.0969242\pi\) | ||||
0.953998 | + | 0.299813i | \(0.0969242\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −4.00000 | − | 2.00000i | −0.410391 | − | 0.205196i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −8.00000 | − | 4.00000i | −0.780720 | − | 0.390360i | ||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 2.00000 | − | 4.00000i | 0.190693 | − | 0.381385i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | − | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | \(-0.809095\pi\) | ||
0.825479 | − | 0.564433i | \(-0.190905\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 6.00000 | − | 12.0000i | 0.559503 | − | 1.11901i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | − | 14.0000i | − | 1.28880i | ||||||
\(119\) | −16.0000 | −1.46672 | ||||||||
\(120\) | 2.00000 | + | 1.00000i | 0.182574 | + | 0.0912871i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − | 10.0000i | − | 0.905357i | ||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 2.00000 | + | 1.00000i | 0.175412 | + | 0.0877058i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.00000 | + | 2.00000i | −0.0860663 | + | 0.172133i | ||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | − | 2.00000i | − | 0.170872i | −0.996344 | − | 0.0854358i | \(-0.972772\pi\) | ||
0.996344 | − | 0.0854358i | \(-0.0272282\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | −4.00000 | + | 8.00000i | −0.338062 | + | 0.676123i | ||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | − | 8.00000i | − | 0.671345i | ||||||
\(143\) | 2.00000i | 0.167248i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 4.00000 | + | 2.00000i | 0.332182 | + | 0.166091i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 9.00000i | 0.742307i | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −3.00000 | − | 4.00000i | −0.244949 | − | 0.326599i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | − | 2.00000i | − | 0.162221i | ||||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | −8.00000 | −0.644658 | ||||||||
\(155\) | −8.00000 | − | 4.00000i | −0.642575 | − | 0.321288i | ||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | − | 8.00000i | − | 0.636446i | ||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 2.00000 | − | 4.00000i | 0.155700 | − | 0.311400i | ||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | − | 4.00000i | − | 0.308607i | ||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −8.00000 | − | 4.00000i | −0.613572 | − | 0.306786i | ||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 10.0000i | 0.760286i | 0.924928 | + | 0.380143i | \(0.124125\pi\) | ||||
−0.924928 | + | 0.380143i | \(0.875875\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 16.0000 | − | 12.0000i | 1.20949 | − | 0.907115i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | − | 14.0000i | − | 1.05230i | ||||||
\(178\) | − | 18.0000i | − | 1.34916i | ||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 2.00000 | + | 1.00000i | 0.149071 | + | 0.0745356i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | − | 4.00000i | − | 0.296500i | ||||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | −6.00000 | + | 12.0000i | −0.441129 | + | 0.882258i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | − | 8.00000i | − | 0.585018i | ||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | −2.00000 | + | 4.00000i | −0.145095 | + | 0.290191i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 2.00000 | + | 1.00000i | 0.143223 | + | 0.0716115i | ||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | − | 26.0000i | − | 1.85242i | −0.377004 | − | 0.926212i | \(-0.623046\pi\) | ||
0.377004 | − | 0.926212i | \(-0.376954\pi\) | |||||||
\(198\) | 2.00000i | 0.142134i | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 14.0000i | 0.985037i | ||||||||
\(203\) | − | 8.00000i | − | 0.561490i | ||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −12.0000 | − | 6.00000i | −0.838116 | − | 0.419058i | ||||
\(206\) | 6.00000 | 0.418040 | ||||||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | −4.00000 | + | 8.00000i | −0.276026 | + | 0.552052i | ||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | − | 10.0000i | − | 0.686803i | ||||||
\(213\) | − | 8.00000i | − | 0.548151i | ||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | −8.00000 | + | 16.0000i | −0.545595 | + | 1.09119i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | 12.0000i | 0.812743i | ||||||||
\(219\) | 10.0000 | 0.675737 | ||||||||
\(220\) | −4.00000 | − | 2.00000i | −0.269680 | − | 0.134840i | ||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | − | 6.00000i | − | 0.402694i | ||||||
\(223\) | − | 16.0000i | − | 1.07144i | −0.844396 | − | 0.535720i | \(-0.820040\pi\) | ||
0.844396 | − | 0.535720i | \(-0.179960\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | − | 12.0000i | − | 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | − | 2.00000i | − | 0.132453i | ||||||
\(229\) | 16.0000 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(230\) | −12.0000 | − | 6.00000i | −0.791257 | − | 0.395628i | ||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | − | 4.00000i | − | 0.262049i | −0.991379 | − | 0.131024i | \(-0.958173\pi\) | ||
0.991379 | − | 0.131024i | \(-0.0418266\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 8.00000 | − | 16.0000i | 0.521862 | − | 1.04372i | ||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 16.0000i | 1.03713i | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 1.00000 | − | 2.00000i | 0.0645497 | − | 0.129099i | ||||
\(241\) | −30.0000 | −1.93247 | −0.966235 | − | 0.257663i | \(-0.917048\pi\) | ||||
−0.966235 | + | 0.257663i | \(0.917048\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | −18.0000 | − | 9.00000i | −1.14998 | − | 0.574989i | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | − | 2.00000i | − | 0.127257i | ||||||
\(248\) | − | 4.00000i | − | 0.254000i | ||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | − | 4.00000i | − | 0.251976i | ||||||
\(253\) | − | 12.0000i | − | 0.754434i | ||||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | −8.00000 | − | 4.00000i | −0.500979 | − | 0.250490i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0000i | 0.748539i | 0.927320 | + | 0.374270i | \(0.122107\pi\) | ||||
−0.927320 | + | 0.374270i | \(0.877893\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | 24.0000 | 1.49129 | ||||||||
\(260\) | 1.00000 | − | 2.00000i | 0.0620174 | − | 0.124035i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.0000i | − | 0.616626i | −0.951285 | − | 0.308313i | \(-0.900236\pi\) | ||
0.951285 | − | 0.308313i | \(-0.0997645\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | −10.0000 | + | 20.0000i | −0.614295 | + | 1.22859i | ||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | − | 18.0000i | − | 1.10158i | ||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 2.00000 | + | 1.00000i | 0.121716 | + | 0.0608581i | ||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | − | 4.00000i | − | 0.242091i | ||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 6.00000 | + | 8.00000i | 0.361814 | + | 0.482418i | ||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 8.00000 | + | 4.00000i | 0.478091 | + | 0.239046i | ||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 8.00000i | 0.476393i | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −2.00000 | + | 4.00000i | −0.118470 | + | 0.236940i | ||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 24.0000i | 1.41668i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.00000 | − | 4.00000i | 0.117444 | − | 0.234888i | ||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | − | 10.0000i | − | 0.585206i | ||||||
\(293\) | − | 14.0000i | − | 0.817889i | −0.912559 | − | 0.408944i | \(-0.865897\pi\) | ||
0.912559 | − | 0.408944i | \(-0.134103\pi\) | |||||||
\(294\) | 9.00000 | 0.524891 | ||||||||
\(295\) | 28.0000 | + | 14.0000i | 1.63022 | + | 0.815112i | ||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 2.00000i | 0.116052i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | 0.346989 | ||||||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | 32.0000 | 1.84445 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 14.0000i | 0.804279i | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 20.0000 | + | 10.0000i | 1.14520 | + | 0.572598i | ||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | 8.00000i | 0.455842i | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | −4.00000 | + | 8.00000i | −0.227185 | + | 0.454369i | ||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 1.00000i | 0.0566139i | ||||||||
\(313\) | 8.00000i | 0.452187i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | −4.00000 | + | 8.00000i | −0.225374 | + | 0.450749i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 30.0000i | 1.68497i | 0.538721 | + | 0.842484i | \(0.318908\pi\) | ||||
−0.538721 | + | 0.842484i | \(0.681092\pi\) | |||||||
\(318\) | − | 10.0000i | − | 0.560772i | ||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | 8.00000 | 0.446516 | ||||||||
\(322\) | 24.0000i | 1.33747i | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −4.00000 | + | 3.00000i | −0.221880 | + | 0.166410i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 12.0000i | 0.663602i | ||||||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | −4.00000 | − | 2.00000i | −0.220193 | − | 0.110096i | ||||
\(331\) | 18.0000 | 0.989369 | 0.494685 | − | 0.869072i | \(-0.335284\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335284\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | − | 6.00000i | − | 0.328798i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | − | 8.00000i | 0.218543 | − | 0.437087i | ||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | −4.00000 | + | 8.00000i | −0.216930 | + | 0.433861i | ||||
\(341\) | −8.00000 | −0.433224 | ||||||||
\(342\) | − | 2.00000i | − | 0.108148i | ||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −12.0000 | − | 6.00000i | −0.646058 | − | 0.323029i | ||||
\(346\) | 10.0000 | 0.537603 | ||||||||
\(347\) | 24.0000i | 1.28839i | 0.764862 | + | 0.644194i | \(0.222807\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | −12.0000 | − | 16.0000i | −0.641427 | − | 0.855236i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | − | 26.0000i | − | 1.38384i | −0.721974 | − | 0.691920i | \(-0.756765\pi\) | ||
0.721974 | − | 0.691920i | \(-0.243235\pi\) | |||||||
\(354\) | −14.0000 | −0.744092 | ||||||||
\(355\) | 16.0000 | + | 8.00000i | 0.849192 | + | 0.424596i | ||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | 16.0000i | 0.846810i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 1.00000 | − | 2.00000i | 0.0527046 | − | 0.105409i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − | 6.00000i | − | 0.315353i | ||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | −10.0000 | + | 20.0000i | −0.523424 | + | 1.04685i | ||||
\(366\) | −10.0000 | −0.522708 | ||||||||
\(367\) | − | 22.0000i | − | 1.14839i | −0.818718 | − | 0.574195i | \(-0.805315\pi\) | ||
0.818718 | − | 0.574195i | \(-0.194685\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 12.0000 | + | 6.00000i | 0.623850 | + | 0.311925i | ||||
\(371\) | 40.0000 | 2.07670 | ||||||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | − | 2.00000i | − | 0.103556i | −0.998659 | − | 0.0517780i | \(-0.983511\pi\) | ||
0.998659 | − | 0.0517780i | \(-0.0164888\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | 11.0000 | − | 2.00000i | 0.568038 | − | 0.103280i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | − | 4.00000i | − | 0.205738i | ||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 4.00000 | + | 2.00000i | 0.205196 | + | 0.102598i | ||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 12.0000i | − | 0.613171i | −0.951843 | − | 0.306586i | \(-0.900813\pi\) | ||
0.951843 | − | 0.306586i | \(-0.0991866\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 8.00000 | − | 16.0000i | 0.407718 | − | 0.815436i | ||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | − | 8.00000i | − | 0.406663i | ||||||
\(388\) | 6.00000i | 0.304604i | ||||||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | 1.00000 | − | 2.00000i | 0.0506370 | − | 0.101274i | ||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | − | 9.00000i | − | 0.454569i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.0000 | −1.30986 | ||||||||
\(395\) | 16.0000 | + | 8.00000i | 0.805047 | + | 0.402524i | ||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | − | 6.00000i | − | 0.301131i | −0.988600 | − | 0.150566i | \(-0.951890\pi\) | ||
0.988600 | − | 0.150566i | \(-0.0481095\pi\) | |||||||
\(398\) | 24.0000i | 1.20301i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 4.00000i | 0.199502i | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | − | 4.00000i | − | 0.198030i | ||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | −6.00000 | + | 12.0000i | −0.296319 | + | 0.592638i | ||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | − | 6.00000i | − | 0.295599i | ||||||
\(413\) | − | 56.0000i | − | 2.75558i | ||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | −12.0000 | + | 24.0000i | −0.589057 | + | 1.17811i | ||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 16.0000i | 0.783523i | ||||||||
\(418\) | 4.00000i | 0.195646i | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 8.00000 | + | 4.00000i | 0.390360 | + | 0.195180i | ||||
\(421\) | 28.0000 | 1.36464 | 0.682318 | − | 0.731055i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(422\) | 28.0000i | 1.36302i | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | −10.0000 | −0.485643 | ||||||||
\(425\) | 16.0000 | − | 12.0000i | 0.776114 | − | 0.582086i | ||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | − | 40.0000i | − | 1.93574i | ||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | 16.0000 | + | 8.00000i | 0.771589 | + | 0.385794i | ||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 16.0000 | 0.768025 | ||||||||
\(435\) | 2.00000 | − | 4.00000i | 0.0958927 | − | 0.191785i | ||||
\(436\) | 12.0000 | 0.574696 | ||||||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | − | 10.0000i | − | 0.477818i | ||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | −2.00000 | + | 4.00000i | −0.0953463 | + | 0.190693i | ||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | − | 4.00000i | − | 0.190261i | ||||||
\(443\) | 8.00000i | 0.380091i | 0.981775 | + | 0.190046i | \(0.0608636\pi\) | ||||
−0.981775 | + | 0.190046i | \(0.939136\pi\) | |||||||
\(444\) | −6.00000 | −0.284747 | ||||||||
\(445\) | 36.0000 | + | 18.0000i | 1.70656 | + | 0.853282i | ||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000i | 0.188982i | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | −4.00000 | + | 3.00000i | −0.188562 | + | 0.141421i | ||||
\(451\) | −12.0000 | −0.565058 | ||||||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | − | 8.00000i | − | 0.375873i | ||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 8.00000 | + | 4.00000i | 0.375046 | + | 0.187523i | ||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 26.0000i | 1.21623i | 0.793849 | + | 0.608114i | \(0.208074\pi\) | ||||
−0.793849 | + | 0.608114i | \(0.791926\pi\) | |||||||
\(458\) | − | 16.0000i | − | 0.747631i | ||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | −6.00000 | + | 12.0000i | −0.279751 | + | 0.559503i | ||||
\(461\) | −4.00000 | −0.186299 | −0.0931493 | − | 0.995652i | \(-0.529693\pi\) | ||||
−0.0931493 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(462\) | 8.00000i | 0.372194i | ||||||||
\(463\) | − | 36.0000i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | −4.00000 | + | 8.00000i | −0.185496 | + | 0.370991i | ||||
\(466\) | −4.00000 | −0.185296 | ||||||||
\(467\) | 16.0000i | 0.740392i | 0.928954 | + | 0.370196i | \(0.120709\pi\) | ||||
−0.928954 | + | 0.370196i | \(0.879291\pi\) | |||||||
\(468\) | 1.00000i | 0.0462250i | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | −16.0000 | − | 8.00000i | −0.738025 | − | 0.369012i | ||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 14.0000i | 0.644402i | ||||||||
\(473\) | 16.0000i | 0.735681i | ||||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | −6.00000 | − | 8.00000i | −0.275299 | − | 0.367065i | ||||
\(476\) | 16.0000 | 0.733359 | ||||||||
\(477\) | − | 10.0000i | − | 0.457869i | ||||||
\(478\) | − | 12.0000i | − | 0.548867i | ||||||
\(479\) | 12.0000 | 0.548294 | 0.274147 | − | 0.961688i | \(-0.411605\pi\) | ||||
0.274147 | + | 0.961688i | \(0.411605\pi\) | |||||||
\(480\) | −2.00000 | − | 1.00000i | −0.0912871 | − | 0.0456435i | ||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | 30.0000i | 1.36646i | ||||||||
\(483\) | 24.0000i | 1.09204i | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 6.00000 | − | 12.0000i | 0.272446 | − | 0.544892i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 40.0000i | 1.81257i | 0.422664 | + | 0.906287i | \(0.361095\pi\) | ||||
−0.422664 | + | 0.906287i | \(0.638905\pi\) | |||||||
\(488\) | 10.0000i | 0.452679i | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −9.00000 | + | 18.0000i | −0.406579 | + | 0.813157i | ||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | − | 6.00000i | − | 0.270501i | ||||||
\(493\) | − | 8.00000i | − | 0.360302i | ||||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | −4.00000 | − | 2.00000i | −0.179787 | − | 0.0898933i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | − | 32.0000i | − | 1.43540i | ||||||
\(498\) | − | 12.0000i | − | 0.537733i | ||||||
\(499\) | −30.0000 | −1.34298 | −0.671492 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 18.0000i | 0.802580i | 0.915951 | + | 0.401290i | \(0.131438\pi\) | ||||
−0.915951 | + | 0.401290i | \(0.868562\pi\) | |||||||
\(504\) | −4.00000 | −0.178174 | ||||||||
\(505\) | −28.0000 | − | 14.0000i | −1.24598 | − | 0.622992i | ||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | − | 18.0000i | − | 0.798621i | ||||||
\(509\) | 16.0000 | 0.709188 | 0.354594 | − | 0.935020i | \(-0.384619\pi\) | ||||
0.354594 | + | 0.935020i | \(0.384619\pi\) | |||||||
\(510\) | −4.00000 | + | 8.00000i | −0.177123 | + | 0.354246i | ||||
\(511\) | 40.0000 | 1.76950 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 2.00000i | − | 0.0883022i | ||||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | −6.00000 | + | 12.0000i | −0.264392 | + | 0.528783i | ||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | − | 24.0000i | − | 1.05450i | ||||||
\(519\) | 10.0000 | 0.438951 | ||||||||
\(520\) | −2.00000 | − | 1.00000i | −0.0877058 | − | 0.0438529i | ||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | 8.00000i | 0.349816i | 0.984585 | + | 0.174908i | \(0.0559627\pi\) | ||||
−0.984585 | + | 0.174908i | \(0.944037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.0000 | − | 16.0000i | −0.523723 | − | 0.698297i | ||||
\(526\) | −10.0000 | −0.436021 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | − | 2.00000i | − | 0.0870388i | ||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 20.0000 | + | 10.0000i | 0.868744 | + | 0.434372i | ||||
\(531\) | −14.0000 | −0.607548 | ||||||||
\(532\) | − | 8.00000i | − | 0.346844i | ||||||
\(533\) | − | 6.00000i | − | 0.259889i | ||||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | −8.00000 | + | 16.0000i | −0.345870 | + | 0.691740i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | 1.00000 | − | 2.00000i | 0.0430331 | − | 0.0860663i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | − | 16.0000i | − | 0.687259i | ||||||
\(543\) | − | 6.00000i | − | 0.257485i | ||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | −24.0000 | − | 12.0000i | −1.02805 | − | 0.514024i | ||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | − | 44.0000i | − | 1.88130i | −0.339372 | − | 0.940652i | \(-0.610215\pi\) | ||
0.339372 | − | 0.940652i | \(-0.389785\pi\) | |||||||
\(548\) | 2.00000i | 0.0854358i | ||||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 8.00000 | − | 6.00000i | 0.341121 | − | 0.255841i | ||||
\(551\) | −4.00000 | −0.170406 | ||||||||
\(552\) | − | 6.00000i | − | 0.255377i | ||||||
\(553\) | − | 32.0000i | − | 1.36078i | ||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 12.0000 | + | 6.00000i | 0.509372 | + | 0.254686i | ||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | − | 14.0000i | − | 0.593199i | −0.955002 | − | 0.296600i | \(-0.904147\pi\) | ||
0.955002 | − | 0.296600i | \(-0.0958526\pi\) | |||||||
\(558\) | − | 4.00000i | − | 0.169334i | ||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 4.00000 | − | 8.00000i | 0.169031 | − | 0.338062i | ||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | − | 16.0000i | − | 0.674320i | −0.941447 | − | 0.337160i | \(-0.890534\pi\) | ||
0.941447 | − | 0.337160i | \(-0.109466\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | 12.0000 | − | 24.0000i | 0.504844 | − | 1.00969i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | − | 4.00000i | − | 0.167984i | ||||||
\(568\) | 8.00000i | 0.335673i | ||||||||
\(569\) | 42.0000 | 1.76073 | 0.880366 | − | 0.474295i | \(-0.157297\pi\) | ||||
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 4.00000 | + | 2.00000i | 0.167542 | + | 0.0837708i | ||||
\(571\) | −36.0000 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(572\) | − | 2.00000i | − | 0.0836242i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.0000 | 1.00174 | ||||||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 26.0000i | − | 1.08239i | −0.840896 | − | 0.541197i | \(-0.817971\pi\) | ||
0.840896 | − | 0.541197i | \(-0.182029\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | −4.00000 | − | 2.00000i | −0.166091 | − | 0.0830455i | ||||
\(581\) | 48.0000 | 1.99138 | ||||||||
\(582\) | 6.00000i | 0.248708i | ||||||||
\(583\) | 20.0000i | 0.828315i | ||||||||
\(584\) | −10.0000 | −0.413803 | ||||||||
\(585\) | 1.00000 | − | 2.00000i | 0.0413449 | − | 0.0826898i | ||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | − | 9.00000i | − | 0.371154i | ||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 14.0000 | − | 28.0000i | 0.576371 | − | 1.15274i | ||||
\(591\) | −26.0000 | −1.06950 | ||||||||
\(592\) | 6.00000i | 0.246598i | ||||||||
\(593\) | 14.0000i | 0.574911i | 0.957794 | + | 0.287456i | \(0.0928094\pi\) | ||||
−0.957794 | + | 0.287456i | \(0.907191\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | −32.0000 | − | 16.0000i | −1.31187 | − | 0.655936i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0000i | 0.982255i | ||||||||
\(598\) | − | 6.00000i | − | 0.245358i | ||||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | 3.00000 | + | 4.00000i | 0.122474 | + | 0.163299i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | − | 32.0000i | − | 1.30422i | ||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | −14.0000 | − | 7.00000i | −0.569181 | − | 0.284590i | ||||
\(606\) | 14.0000 | 0.568711 | ||||||||
\(607\) | − | 18.0000i | − | 0.730597i | −0.930890 | − | 0.365299i | \(-0.880967\pi\) | ||
0.930890 | − | 0.365299i | \(-0.119033\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 10.0000 | − | 20.0000i | 0.404888 | − | 0.809776i | ||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 26.0000i | 1.05013i | 0.851062 | + | 0.525065i | \(0.175959\pi\) | ||||
−0.851062 | + | 0.525065i | \(0.824041\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | −6.00000 | + | 12.0000i | −0.241943 | + | 0.483887i | ||||
\(616\) | 8.00000 | 0.322329 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | − | 6.00000i | − | 0.241355i | ||||||
\(619\) | −42.0000 | −1.68812 | −0.844061 | − | 0.536247i | \(-0.819842\pi\) | ||||
−0.844061 | + | 0.536247i | \(0.819842\pi\) | |||||||
\(620\) | 8.00000 | + | 4.00000i | 0.321288 | + | 0.160644i | ||||
\(621\) | 6.00000 | 0.240772 | ||||||||
\(622\) | − | 8.00000i | − | 0.320771i | ||||||
\(623\) | − | 72.0000i | − | 2.88462i | ||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | 4.00000i | 0.159745i | ||||||||
\(628\) | − | 10.0000i | − | 0.399043i | ||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 8.00000 | + | 4.00000i | 0.318728 | + | 0.159364i | ||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 8.00000i | 0.318223i | ||||||||
\(633\) | 28.0000i | 1.11290i | ||||||||
\(634\) | 30.0000 | 1.19145 | ||||||||
\(635\) | −18.0000 | + | 36.0000i | −0.714308 | + | 1.42862i | ||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | − | 9.00000i | − | 0.356593i | ||||||
\(638\) | − | 4.00000i | − | 0.158362i | ||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | −1.00000 | + | 2.00000i | −0.0395285 | + | 0.0790569i | ||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | − | 8.00000i | − | 0.315735i | ||||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 24.0000 | 0.945732 | ||||||||
\(645\) | 16.0000 | + | 8.00000i | 0.629999 | + | 0.315000i | ||||
\(646\) | 8.00000 | 0.314756 | ||||||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 28.0000 | 1.09910 | ||||||||
\(650\) | 3.00000 | + | 4.00000i | 0.117670 | + | 0.156893i | ||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | − | 26.0000i | − | 1.01746i | −0.860927 | − | 0.508729i | \(-0.830115\pi\) | ||
0.860927 | − | 0.508729i | \(-0.169885\pi\) | |||||||
\(654\) | 12.0000 | 0.469237 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 32.0000i | 1.24749i | ||||||||
\(659\) | −40.0000 | −1.55818 | −0.779089 | − | 0.626913i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626913i | \(0.784318\pi\) | |||||||
\(660\) | −2.00000 | + | 4.00000i | −0.0778499 | + | 0.155700i | ||||
\(661\) | 24.0000 | 0.933492 | 0.466746 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466746 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(662\) | − | 18.0000i | − | 0.699590i | ||||||
\(663\) | − | 4.00000i | − | 0.155347i | ||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | −8.00000 | + | 16.0000i | −0.310227 | + | 0.620453i | ||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | − | 12.0000i | − | 0.464642i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0000 | −0.618596 | ||||||||
\(670\) | −8.00000 | − | 4.00000i | −0.309067 | − | 0.154533i | ||||
\(671\) | 20.0000 | 0.772091 | ||||||||
\(672\) | 4.00000i | 0.154303i | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 32.0000 | 1.23259 | ||||||||
\(675\) | −4.00000 | + | 3.00000i | −0.153960 | + | 0.115470i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − | 22.0000i | − | 0.845529i | −0.906240 | − | 0.422764i | \(-0.861060\pi\) | ||
0.906240 | − | 0.422764i | \(-0.138940\pi\) | |||||||
\(678\) | 12.0000i | 0.460857i | ||||||||
\(679\) | −24.0000 | −0.921035 | ||||||||
\(680\) | 8.00000 | + | 4.00000i | 0.306786 | + | 0.153393i | ||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 8.00000i | 0.306336i | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 2.00000 | − | 4.00000i | 0.0764161 | − | 0.152832i | ||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | − | 16.0000i | − | 0.610438i | ||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | −6.00000 | + | 12.0000i | −0.228416 | + | 0.456832i | ||||
\(691\) | 2.00000 | 0.0760836 | 0.0380418 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380418 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(692\) | − | 10.0000i | − | 0.380143i | ||||||
\(693\) | 8.00000i | 0.303895i | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −32.0000 | − | 16.0000i | −1.21383 | − | 0.606915i | ||||
\(696\) | 2.00000 | 0.0758098 | ||||||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | − | 28.0000i | − | 1.05982i | ||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | −16.0000 | + | 12.0000i | −0.604743 | + | 0.453557i | ||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 1.00000i | 0.0377426i | ||||||||
\(703\) | − | 12.0000i | − | 0.452589i | ||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −16.0000 | − | 8.00000i | −0.602595 | − | 0.301297i | ||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | 56.0000i | 2.10610i | ||||||||
\(708\) | 14.0000i | 0.526152i | ||||||||
\(709\) | 32.0000 | 1.20179 | 0.600893 | − | 0.799330i | \(-0.294812\pi\) | ||||
0.600893 | + | 0.799330i | \(0.294812\pi\) | |||||||
\(710\) | 8.00000 | − | 16.0000i | 0.300235 | − | 0.600469i | ||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 18.0000i | 0.674579i | ||||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 16.0000 | 0.598785 | ||||||||
\(715\) | −2.00000 | + | 4.00000i | −0.0747958 | + | 0.149592i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 12.0000i | − | 0.448148i | ||||||
\(718\) | 20.0000i | 0.746393i | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | 30.0000i | 1.11571i | ||||||||
\(724\) | −6.00000 | −0.222988 | ||||||||
\(725\) | 6.00000 | + | 8.00000i | 0.222834 | + | 0.297113i | ||||
\(726\) | 7.00000 | 0.259794 | ||||||||
\(727\) | − | 14.0000i | − | 0.519231i | −0.965712 | − | 0.259616i | \(-0.916404\pi\) | ||
0.965712 | − | 0.259616i | \(-0.0835959\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 20.0000 | + | 10.0000i | 0.740233 | + | 0.370117i | ||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 10.0000i | 0.369611i | ||||||||
\(733\) | − | 2.00000i | − | 0.0738717i | −0.999318 | − | 0.0369358i | \(-0.988240\pi\) | ||
0.999318 | − | 0.0369358i | \(-0.0117597\pi\) | |||||||
\(734\) | −22.0000 | −0.812035 | ||||||||
\(735\) | −9.00000 | + | 18.0000i | −0.331970 | + | 0.663940i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | − | 8.00000i | − | 0.294684i | ||||||
\(738\) | − | 6.00000i | − | 0.220863i | ||||||
\(739\) | 2.00000 | 0.0735712 | 0.0367856 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(740\) | 6.00000 | − | 12.0000i | 0.220564 | − | 0.441129i | ||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | − | 40.0000i | − | 1.46845i | ||||||
\(743\) | − | 4.00000i | − | 0.146746i | −0.997305 | − | 0.0733729i | \(-0.976624\pi\) | ||
0.997305 | − | 0.0733729i | \(-0.0233763\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.00000 | −0.0732252 | ||||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | −2.00000 | − | 11.0000i | −0.0730297 | − | 0.401663i | ||||
\(751\) | 48.0000 | 1.75154 | 0.875772 | − | 0.482724i | \(-0.160353\pi\) | ||||
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 2.00000 | 0.0728357 | ||||||||
\(755\) | 16.0000 | + | 8.00000i | 0.582300 | + | 0.291150i | ||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | 22.0000i | 0.799604i | 0.916602 | + | 0.399802i | \(0.130921\pi\) | ||||
−0.916602 | + | 0.399802i | \(0.869079\pi\) | |||||||
\(758\) | 26.0000i | 0.944363i | ||||||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 2.00000 | − | 4.00000i | 0.0725476 | − | 0.145095i | ||||
\(761\) | 14.0000 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(762\) | − | 18.0000i | − | 0.652071i | ||||||
\(763\) | 48.0000i | 1.73772i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 8.00000i | −0.144620 | + | 0.289241i | ||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | 14.0000i | 0.505511i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | −16.0000 | − | 8.00000i | −0.576600 | − | 0.288300i | ||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | 14.0000i | 0.503545i | 0.967786 | + | 0.251773i | \(0.0810135\pi\) | ||||
−0.967786 | + | 0.251773i | \(0.918987\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | −12.0000 | − | 16.0000i | −0.431053 | − | 0.574737i | ||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | − | 24.0000i | − | 0.860995i | ||||||
\(778\) | − | 26.0000i | − | 0.932145i | ||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | −2.00000 | − | 1.00000i | −0.0716115 | − | 0.0358057i | ||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 24.0000i | 0.858238i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | −10.0000 | + | 20.0000i | −0.356915 | + | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000i | 0.998092i | 0.866575 | + | 0.499046i | \(0.166316\pi\) | ||||
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(788\) | 26.0000i | 0.926212i | ||||||||
\(789\) | −10.0000 | −0.356009 | ||||||||
\(790\) | 8.00000 | − | 16.0000i | 0.284627 | − | 0.569254i | ||||
\(791\) | −48.0000 | −1.70668 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | 10.0000i | 0.355110i | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | 20.0000 | + | 10.0000i | 0.709327 | + | 0.354663i | ||||
\(796\) | 24.0000 | 0.850657 | ||||||||
\(797\) | − | 34.0000i | − | 1.20434i | −0.798367 | − | 0.602171i | \(-0.794303\pi\) | ||
0.798367 | − | 0.602171i | \(-0.205697\pi\) | |||||||
\(798\) | − | 8.00000i | − | 0.283197i | ||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 18.0000i | 0.635602i | ||||||||
\(803\) | 20.0000i | 0.705785i | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | −48.0000 | − | 24.0000i | −1.69178 | − | 0.845889i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | − | 14.0000i | − | 0.492823i | ||||||
\(808\) | − | 14.0000i | − | 0.492518i | ||||||
\(809\) | −14.0000 | −0.492214 | −0.246107 | − | 0.969243i | \(-0.579151\pi\) | ||||
−0.246107 | + | 0.969243i | \(0.579151\pi\) | |||||||
\(810\) | 1.00000 | − | 2.00000i | 0.0351364 | − | 0.0702728i | ||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 8.00000i | 0.280745i | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 4.00000 | − | 8.00000i | 0.140114 | − | 0.280228i | ||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | − | 16.0000i | − | 0.559769i | ||||||
\(818\) | − | 2.00000i | − | 0.0699284i | ||||||
\(819\) | −4.00000 | −0.139771 | ||||||||
\(820\) | 12.0000 | + | 6.00000i | 0.419058 | + | 0.209529i | ||||
\(821\) | −12.0000 | −0.418803 | −0.209401 | − | 0.977830i | \(-0.567152\pi\) | ||||
−0.209401 | + | 0.977830i | \(0.567152\pi\) | |||||||
\(822\) | 2.00000i | 0.0697580i | ||||||||
\(823\) | 26.0000i | 0.906303i | 0.891434 | + | 0.453152i | \(0.149700\pi\) | ||||
−0.891434 | + | 0.453152i | \(0.850300\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 8.00000 | − | 6.00000i | 0.278524 | − | 0.208893i | ||||
\(826\) | −56.0000 | −1.94849 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | − | 6.00000i | − | 0.208514i | ||||||
\(829\) | −42.0000 | −1.45872 | −0.729360 | − | 0.684130i | \(-0.760182\pi\) | ||||
−0.729360 | + | 0.684130i | \(0.760182\pi\) | |||||||
\(830\) | 24.0000 | + | 12.0000i | 0.833052 | + | 0.416526i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | 36.0000i | 1.24733i | ||||||||
\(834\) | 16.0000 | 0.554035 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | 16.0000i | 0.552711i | ||||||||
\(839\) | −16.0000 | −0.552381 | −0.276191 | − | 0.961103i | \(-0.589072\pi\) | ||||
−0.276191 | + | 0.961103i | \(0.589072\pi\) | |||||||
\(840\) | 4.00000 | − | 8.00000i | 0.138013 | − | 0.276026i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 28.0000i | − | 0.964944i | ||||||
\(843\) | 18.0000i | 0.619953i | ||||||||
\(844\) | 28.0000 | 0.963800 | ||||||||
\(845\) | −2.00000 | − | 1.00000i | −0.0688021 | − | 0.0344010i | ||||
\(846\) | 8.00000 | 0.275046 | ||||||||
\(847\) | 28.0000i | 0.962091i | ||||||||
\(848\) | 10.0000i | 0.343401i | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | −12.0000 | − | 16.0000i | −0.411597 | − | 0.548795i | ||||
\(851\) | 36.0000 | 1.23406 | ||||||||
\(852\) | 8.00000i | 0.274075i | ||||||||
\(853\) | − | 42.0000i | − | 1.43805i | −0.694983 | − | 0.719026i | \(-0.744588\pi\) | ||
0.694983 | − | 0.719026i | \(-0.255412\pi\) | |||||||
\(854\) | −40.0000 | −1.36877 | ||||||||
\(855\) | 4.00000 | + | 2.00000i | 0.136797 | + | 0.0683986i | ||||
\(856\) | −8.00000 | −0.273434 | ||||||||
\(857\) | 40.0000i | 1.36637i | 0.730243 | + | 0.683187i | \(0.239407\pi\) | ||||
−0.730243 | + | 0.683187i | \(0.760593\pi\) | |||||||
\(858\) | − | 2.00000i | − | 0.0682789i | ||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | 8.00000 | − | 16.0000i | 0.272798 | − | 0.545595i | ||||
\(861\) | 24.0000 | 0.817918 | ||||||||
\(862\) | 8.00000i | 0.272481i | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −10.0000 | + | 20.0000i | −0.340010 | + | 0.680020i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | − | 16.0000i | − | 0.543075i | ||||||
\(869\) | 16.0000 | 0.542763 | ||||||||
\(870\) | −4.00000 | − | 2.00000i | −0.135613 | − | 0.0678064i | ||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | − | 12.0000i | − | 0.406371i | ||||||
\(873\) | 6.00000i | 0.203069i | ||||||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 44.0000 | − | 8.00000i | 1.48747 | − | 0.270449i | ||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 30.0000i | 1.01303i | 0.862232 | + | 0.506514i | \(0.169066\pi\) | ||||
−0.862232 | + | 0.506514i | \(0.830934\pi\) | |||||||
\(878\) | 32.0000i | 1.07995i | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 4.00000 | + | 2.00000i | 0.134840 | + | 0.0674200i | ||||
\(881\) | −46.0000 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(882\) | − | 9.00000i | − | 0.303046i | ||||||
\(883\) | 48.0000i | 1.61533i | 0.589643 | + | 0.807664i | \(0.299269\pi\) | ||||
−0.589643 | + | 0.807664i | \(0.700731\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | 14.0000 | − | 28.0000i | 0.470605 | − | 0.941210i | ||||
\(886\) | 8.00000 | 0.268765 | ||||||||
\(887\) | 6.00000i | 0.201460i | 0.994914 | + | 0.100730i | \(0.0321179\pi\) | ||||
−0.994914 | + | 0.100730i | \(0.967882\pi\) | |||||||
\(888\) | 6.00000i | 0.201347i | ||||||||
\(889\) | 72.0000 | 2.41480 | ||||||||
\(890\) | 18.0000 | − | 36.0000i | 0.603361 | − | 1.20672i | ||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 16.0000i | 0.535720i | ||||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | − | 6.00000i | − | 0.200334i | ||||||
\(898\) | 6.00000i | 0.200223i | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | 40.0000 | 1.33259 | ||||||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | − | 32.0000i | − | 1.06489i | ||||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | 12.0000 | + | 6.00000i | 0.398893 | + | 0.199447i | ||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | 32.0000i | 1.06254i | 0.847202 | + | 0.531271i | \(0.178286\pi\) | ||||
−0.847202 | + | 0.531271i | \(0.821714\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 4.00000 | − | 8.00000i | 0.132599 | − | 0.265197i | ||||
\(911\) | −32.0000 | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(912\) | 2.00000i | 0.0662266i | ||||||||
\(913\) | 24.0000i | 0.794284i | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 10.0000 | − | 20.0000i | 0.330590 | − | 0.661180i | ||||
\(916\) | −16.0000 | −0.528655 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | 12.0000 | + | 6.00000i | 0.395628 | + | 0.197814i | ||||
\(921\) | −28.0000 | −0.922631 | ||||||||
\(922\) | 4.00000i | 0.131733i | ||||||||
\(923\) | 8.00000i | 0.263323i | ||||||||
\(924\) | 8.00000 | 0.263181 | ||||||||
\(925\) | −24.0000 | + | 18.0000i | −0.789115 | + | 0.591836i | ||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | − | 6.00000i | − | 0.197066i | ||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | −46.0000 | −1.50921 | −0.754606 | − | 0.656179i | \(-0.772172\pi\) | ||||
−0.754606 | + | 0.656179i | \(0.772172\pi\) | |||||||
\(930\) | 8.00000 | + | 4.00000i | 0.262330 | + | 0.131165i | ||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | 4.00000i | 0.131024i | ||||||||
\(933\) | − | 8.00000i | − | 0.261908i | ||||||
\(934\) | 16.0000 | 0.523536 | ||||||||
\(935\) | 8.00000 | − | 16.0000i | 0.261628 | − | 0.523256i | ||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | − | 16.0000i | − | 0.522697i | −0.965244 | − | 0.261349i | \(-0.915833\pi\) | ||
0.965244 | − | 0.261349i | \(-0.0841672\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | 8.00000 | 0.261070 | ||||||||
\(940\) | −8.00000 | + | 16.0000i | −0.260931 | + | 0.521862i | ||||
\(941\) | 40.0000 | 1.30396 | 0.651981 | − | 0.758235i | \(-0.273938\pi\) | ||||
0.651981 | + | 0.758235i | \(0.273938\pi\) | |||||||
\(942\) | − | 10.0000i | − | 0.325818i | ||||||
\(943\) | 36.0000i | 1.17232i | ||||||||
\(944\) | 14.0000 | 0.455661 | ||||||||
\(945\) | 8.00000 | + | 4.00000i | 0.260240 | + | 0.130120i | ||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | −10.0000 | −0.324614 | ||||||||
\(950\) | −8.00000 | + | 6.00000i | −0.259554 | + | 0.194666i | ||||
\(951\) | 30.0000 | 0.972817 | ||||||||
\(952\) | − | 16.0000i | − | 0.518563i | ||||||
\(953\) | − | 48.0000i | − | 1.55487i | −0.628962 | − | 0.777436i | \(-0.716520\pi\) | ||
0.628962 | − | 0.777436i | \(-0.283480\pi\) | |||||||
\(954\) | −10.0000 | −0.323762 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | − | 4.00000i | − | 0.129302i | ||||||
\(958\) | − | 12.0000i | − | 0.387702i | ||||||
\(959\) | −8.00000 | −0.258333 | ||||||||
\(960\) | −1.00000 | + | 2.00000i | −0.0322749 | + | 0.0645497i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 6.00000i | 0.193448i | ||||||||
\(963\) | − | 8.00000i | − | 0.257796i | ||||||
\(964\) | 30.0000 | 0.966235 | ||||||||
\(965\) | −6.00000 | + | 12.0000i | −0.193147 | + | 0.386294i | ||||
\(966\) | 24.0000 | 0.772187 | ||||||||
\(967\) | 28.0000i | 0.900419i | 0.892923 | + | 0.450210i | \(0.148651\pi\) | ||||
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | −12.0000 | − | 6.00000i | −0.385297 | − | 0.192648i | ||||
\(971\) | −28.0000 | −0.898563 | −0.449281 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449281 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 64.0000i | 2.05175i | ||||||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | 3.00000 | + | 4.00000i | 0.0960769 | + | 0.128103i | ||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | − | 42.0000i | − | 1.34370i | −0.740688 | − | 0.671850i | \(-0.765500\pi\) | ||
0.740688 | − | 0.671850i | \(-0.234500\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | 36.0000 | 1.15056 | ||||||||
\(980\) | 18.0000 | + | 9.00000i | 0.574989 | + | 0.287494i | ||||
\(981\) | 12.0000 | 0.383131 | ||||||||
\(982\) | − | 8.00000i | − | 0.255290i | ||||||
\(983\) | 4.00000i | 0.127580i | 0.997963 | + | 0.0637901i | \(0.0203188\pi\) | ||||
−0.997963 | + | 0.0637901i | \(0.979681\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 26.0000 | − | 52.0000i | 0.828429 | − | 1.65686i | ||||
\(986\) | −8.00000 | −0.254772 | ||||||||
\(987\) | 32.0000i | 1.01857i | ||||||||
\(988\) | 2.00000i | 0.0636285i | ||||||||
\(989\) | 48.0000 | 1.52631 | ||||||||
\(990\) | −2.00000 | + | 4.00000i | −0.0635642 | + | 0.127128i | ||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 4.00000i | 0.127000i | ||||||||
\(993\) | − | 18.0000i | − | 0.571213i | ||||||
\(994\) | −32.0000 | −1.01498 | ||||||||
\(995\) | −48.0000 | − | 24.0000i | −1.52170 | − | 0.760851i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | − | 38.0000i | − | 1.20347i | −0.798695 | − | 0.601736i | \(-0.794476\pi\) | ||
0.798695 | − | 0.601736i | \(-0.205524\pi\) | |||||||
\(998\) | 30.0000i | 0.949633i | ||||||||
\(999\) | −6.00000 | −0.189832 |
(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 | 390.2.e.b.79.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.e.b.469.2 | 2 | |||
4.3 | odd | 2 | 3120.2.l.h.1249.2 | 2 | |||
5.2 | odd | 4 | 1950.2.a.u.1.1 | 1 | |||
5.3 | odd | 4 | 1950.2.a.g.1.1 | 1 | |||
5.4 | even | 2 | inner | 390.2.e.b.79.2 | yes | 2 | |
15.2 | even | 4 | 5850.2.a.x.1.1 | 1 | |||
15.8 | even | 4 | 5850.2.a.bd.1.1 | 1 | |||
15.14 | odd | 2 | 1170.2.e.b.469.1 | 2 | |||
20.19 | odd | 2 | 3120.2.l.h.1249.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.e.b.79.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
390.2.e.b.79.2 | yes | 2 | 5.4 | even | 2 | inner | |
1170.2.e.b.469.1 | 2 | 15.14 | odd | 2 | |||
1170.2.e.b.469.2 | 2 | 3.2 | odd | 2 | |||
1950.2.a.g.1.1 | 1 | 5.3 | odd | 4 | |||
1950.2.a.u.1.1 | 1 | 5.2 | odd | 4 | |||
3120.2.l.h.1249.1 | 2 | 20.19 | odd | 2 | |||
3120.2.l.h.1249.2 | 2 | 4.3 | odd | 2 | |||
5850.2.a.x.1.1 | 1 | 15.2 | even | 4 | |||
5850.2.a.bd.1.1 | 1 | 15.8 | even | 4 |