Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.4 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.c.1537.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 1.83533i | 0.397360 | + | 0.917663i | \(0.369927\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.82843i | − 0.617213i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 4.00000i | − 0.676123i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.24264i | − 0.697486i | −0.937218 | − | 0.348743i | \(-0.886609\pi\) | ||||
0.937218 | − | 0.348743i | \(-0.113391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.41421i | − 0.210819i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3137 | −1.65027 | −0.825137 | − | 0.564933i | \(-0.808902\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000i | 0.560112i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.07107i | 0.971286i | 0.874157 | + | 0.485643i | \(0.161414\pi\) | ||||
−0.874157 | + | 0.485643i | \(0.838586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.0000i | − 1.56227i | −0.624364 | − | 0.781133i | \(-0.714642\pi\) | ||||
0.624364 | − | 0.781133i | \(-0.285358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421i | 0.181071i | 0.995893 | + | 0.0905357i | \(0.0288579\pi\) | ||||
−0.995893 | + | 0.0905357i | \(0.971142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685i | 0.681005i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000i | 0.346410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.65685i | 0.613572i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41421 | −0.151620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 12.0000i | − 1.25794i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.82843i | − 0.293294i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3137 | −1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0000 | 1.62455 | 0.812277 | − | 0.583272i | \(-0.198228\pi\) | ||||
0.812277 | + | 0.583272i | \(0.198228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5563i | 1.54791i | 0.633238 | + | 0.773957i | \(0.281726\pi\) | ||||
−0.633238 | + | 0.773957i | \(0.718274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.7990 | −1.95085 | −0.975426 | − | 0.220326i | \(-0.929288\pi\) | ||||
−0.975426 | + | 0.220326i | \(0.929288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 4.24264i | − 0.406371i | −0.979140 | − | 0.203186i | \(-0.934871\pi\) | ||||
0.979140 | − | 0.203186i | \(-0.0651295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.24264 | 0.402694 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000i | 0.746004i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.24264i | − 0.392232i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.00000i | 0.360668i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.48528 | 0.752947 | 0.376473 | − | 0.926427i | \(-0.377137\pi\) | ||||
0.376473 | + | 0.926427i | \(0.377137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000i | 0.349482i | 0.984614 | + | 0.174741i | \(0.0559088\pi\) | ||||
−0.984614 | + | 0.174741i | \(0.944091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 22.6274i | − 1.96205i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41421 | 0.121716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.00000i | − 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 11.3137i | − 0.952786i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 12.7279i | − 1.04271i | −0.853339 | − | 0.521356i | \(-0.825426\pi\) | ||||
0.853339 | − | 0.521356i | \(-0.174574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.82843 | 0.230174 | 0.115087 | − | 0.993355i | \(-0.463285\pi\) | ||||
0.115087 | + | 0.993355i | \(0.463285\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.00000i | − 0.321288i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 21.2132i | − 1.69300i | −0.532390 | − | 0.846499i | \(-0.678706\pi\) | ||||
0.532390 | − | 0.846499i | \(-0.321294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.07107 | −0.560772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0000i | 1.25322i | 0.779334 | + | 0.626608i | \(0.215557\pi\) | ||||
−0.779334 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3137 | −0.875481 | −0.437741 | − | 0.899101i | \(-0.644221\pi\) | ||||
−0.437741 | + | 0.899101i | \(0.644221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 8.00000i | − 0.611775i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.07107i | 0.537603i | 0.963196 | + | 0.268802i | \(0.0866276\pi\) | ||||
−0.963196 | + | 0.268802i | \(0.913372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.48528 | −0.641427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.00000i | − 0.298974i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) | ||||
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.7279i | 0.946059i | 0.881047 | + | 0.473029i | \(0.156840\pi\) | ||||
−0.881047 | + | 0.473029i | \(0.843160\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41421 | −0.104542 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843i | 0.205738i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.65685 | 0.409316 | 0.204658 | − | 0.978834i | \(-0.434392\pi\) | ||||
0.204658 | + | 0.978834i | \(0.434392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 6.00000i | − 0.429669i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.07107i | 0.503793i | 0.967754 | + | 0.251896i | \(0.0810542\pi\) | ||||
−0.967754 | + | 0.251896i | \(0.918946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.48528 | 0.601506 | 0.300753 | − | 0.953702i | \(-0.402762\pi\) | ||||
0.300753 | + | 0.953702i | \(0.402762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.00000i | − 0.280745i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.65685i | 0.395092i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.65685 | −0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 12.0000i | − 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 11.3137i | − 0.775203i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 14.0000i | − 0.946032i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.9706i | 1.14156i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4558 | −1.70465 | −0.852325 | − | 0.523013i | \(-0.824808\pi\) | ||||
−0.852325 | + | 0.523013i | \(0.824808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 24.0416i | − 1.58872i | −0.607450 | − | 0.794358i | \(-0.707808\pi\) | ||||
0.607450 | − | 0.794358i | \(-0.292192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 16.0000i | − 1.04372i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.48528i | − 0.551178i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.65685 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421i | 0.0903508i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.9411 | −2.15962 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.00000i | 0.504956i | 0.967603 | + | 0.252478i | \(0.0812455\pi\) | ||||
−0.967603 | + | 0.252478i | \(0.918755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.65685 | −0.354246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000i | 0.745644i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.41421i | − 0.0875376i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2843 | 1.74408 | 0.872041 | − | 0.489432i | \(-0.162796\pi\) | ||||
0.872041 | + | 0.489432i | \(0.162796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.00000i | − 0.367194i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.2132i | 1.29339i | 0.762748 | + | 0.646696i | \(0.223850\pi\) | ||||
−0.762748 | + | 0.646696i | \(0.776150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.48528 | 0.515444 | 0.257722 | − | 0.966219i | \(-0.417028\pi\) | ||||
0.257722 | + | 0.966219i | \(0.417028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | 0.726273 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.41421i | − 0.0849719i | −0.999097 | − | 0.0424859i | \(-0.986472\pi\) | ||||
0.999097 | − | 0.0424859i | \(-0.0135278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.82843 | 0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.00000i | − 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 11.3137i | − 0.670166i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3137 | −0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.0000i | 0.937937i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.3848i | 1.07405i | 0.843566 | + | 0.537025i | \(0.180452\pi\) | ||||
−0.843566 | + | 0.537025i | \(0.819548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.9706 | 0.988064 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.0000i | 1.38796i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5563 | −0.893689 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 19.7990i | − 1.12633i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.2843 | −1.60385 | −0.801927 | − | 0.597422i | \(-0.796192\pi\) | ||||
−0.801927 | + | 0.597422i | \(0.796192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0000 | 0.904373 | 0.452187 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452187 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.00000i | 0.225374i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.2132i | − 1.19145i | −0.803188 | − | 0.595726i | \(-0.796864\pi\) | ||||
0.803188 | − | 0.595726i | \(-0.203136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.0000i | 1.78053i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7279i | 0.706018i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.24264 | 0.234619 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000 | 1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000i | 0.219860i | 0.993939 | + | 0.109930i | \(0.0350627\pi\) | ||||
−0.993939 | + | 0.109930i | \(0.964937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.24264i | 0.232495i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 18.0000i | − 0.977626i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | −0.430706 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.0000i | 1.71785i | 0.512101 | + | 0.858925i | \(0.328867\pi\) | ||||
−0.512101 | + | 0.858925i | \(0.671133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 12.7279i | − 0.681310i | −0.940188 | − | 0.340655i | \(-0.889351\pi\) | ||||
0.940188 | − | 0.340655i | \(-0.110649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.0000i | − 0.849192i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 11.3137i | − 0.598785i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3137 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.0000 | −2.36842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0000i | 0.577350i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 19.7990i | − 1.03633i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.82843 | −0.147643 | −0.0738213 | − | 0.997271i | \(-0.523519\pi\) | ||||
−0.0738213 | + | 0.997271i | \(0.523519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.00000 | −0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 20.0000i | − 1.03835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24264i | 0.219676i | 0.993950 | + | 0.109838i | \(0.0350331\pi\) | ||||
−0.993950 | + | 0.109838i | \(0.964967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.3137 | −0.584237 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.48528i | 0.434714i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2843 | 1.44526 | 0.722629 | − | 0.691236i | \(-0.242933\pi\) | ||||
0.722629 | + | 0.691236i | \(0.242933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.89949i | 0.501924i | 0.967997 | + | 0.250962i | \(0.0807470\pi\) | ||||
−0.967997 | + | 0.250962i | \(0.919253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6274 | 1.14432 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.0000i | − 0.603786i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 21.2132i | − 1.06466i | −0.846537 | − | 0.532330i | \(-0.821317\pi\) | ||||
0.846537 | − | 0.532330i | \(-0.178683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.6274 | 1.13279 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.0000 | −0.998752 | −0.499376 | − | 0.866385i | \(-0.666437\pi\) | ||||
−0.499376 | + | 0.866385i | \(0.666437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 12.0000i | − 0.597763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.41421i | 0.0702728i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.0000 | −1.58230 | −0.791149 | − | 0.611623i | \(-0.790517\pi\) | ||||
−0.791149 | + | 0.611623i | \(0.790517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000i | 0.591916i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.9411i | 1.67013i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6274 | −1.11074 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.00000i | 0.390826i | 0.980721 | + | 0.195413i | \(0.0626047\pi\) | ||||
−0.980721 | + | 0.195413i | \(0.937395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 12.7279i | − 0.620321i | −0.950684 | − | 0.310160i | \(-0.899617\pi\) | ||||
0.950684 | − | 0.310160i | \(-0.100383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3137 | 0.550091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.00000i | − 0.193574i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00000 | 0.384455 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.00000i | − 0.0958927i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.2548i | 2.16483i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.82843 | −0.134993 | −0.0674967 | − | 0.997719i | \(-0.521501\pi\) | ||||
−0.0674967 | + | 0.997719i | \(0.521501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 24.0000i | − 1.14027i | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||||
0.821549 | − | 0.570137i | \(-0.193110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 8.48528i | − 0.402241i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7279 | 0.602010 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.82843i | 0.132891i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.9706 | 0.795592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.00000i | − 0.186704i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5563i | 0.724531i | 0.932075 | + | 0.362266i | \(0.117997\pi\) | ||||
−0.932075 | + | 0.362266i | \(0.882003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1127 | 1.44593 | 0.722965 | − | 0.690885i | \(-0.242779\pi\) | ||||
0.722965 | + | 0.690885i | \(0.242779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.00000i | − 0.370196i | −0.982720 | − | 0.185098i | \(-0.940740\pi\) | ||||
0.982720 | − | 0.185098i | \(-0.0592602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3137i | 0.522419i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.2132 | 0.977453 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0000i | 1.10120i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.07107i | − 0.323762i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2843 | −1.29234 | −0.646171 | − | 0.763193i | \(-0.723631\pi\) | ||||
−0.646171 | + | 0.763193i | \(0.723631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 16.0000i | − 0.728025i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.6274i | 1.02746i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82843 | 0.128168 | 0.0640841 | − | 0.997944i | \(-0.479587\pi\) | ||||
0.0640841 | + | 0.997944i | \(0.479587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.0000i | − 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685i | 0.254772i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 28.0000i | − 1.25345i | −0.779240 | − | 0.626726i | \(-0.784395\pi\) | ||||
0.779240 | − | 0.626726i | \(-0.215605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 11.3137i | − 0.505459i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.3137 | 0.504453 | 0.252227 | − | 0.967668i | \(-0.418837\pi\) | ||||
0.252227 | + | 0.967668i | \(0.418837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.0000 | −0.978987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 5.00000i | − 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.5269i | 1.44173i | 0.693075 | + | 0.720865i | \(0.256255\pi\) | ||||
−0.693075 | + | 0.720865i | \(0.743745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.5980 | 1.75171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.00000 | 0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 28.0000i | − 1.23383i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.07107 | −0.310385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000i | 0.349816i | 0.984585 | + | 0.174908i | \(0.0559627\pi\) | ||||
−0.984585 | + | 0.174908i | \(0.944037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 8.48528i | − 0.370328i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.3137 | −0.492833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000i | 0.520756i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.9706i | 0.735077i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.9706 | 0.733701 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | 0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.24264i | − 0.182405i | −0.995832 | − | 0.0912027i | \(-0.970929\pi\) | ||||
0.995832 | − | 0.0912027i | \(-0.0290711\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.7279 | −0.546207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.41421i | − 0.0603572i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | −0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | 1.02058 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000i | 0.254686i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6985i | 1.25837i | 0.777258 | + | 0.629183i | \(0.216610\pi\) | ||||
−0.777258 | + | 0.629183i | \(0.783390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.00000i | 0.337160i | 0.985688 | + | 0.168580i | \(0.0539181\pi\) | ||||
−0.985688 | + | 0.168580i | \(0.946082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 25.4558i | − 1.07094i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0000 | 0.838444 | 0.419222 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419222 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 20.0000i | − 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.65685i | 0.236318i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706 | 0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 45.2548i | − 1.87749i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | 0.248069 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.00000i | 0.165098i | 0.996587 | + | 0.0825488i | \(0.0263060\pi\) | ||||
−0.996587 | + | 0.0825488i | \(0.973694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 22.6274i | − 0.932346i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.07107 | −0.290865 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 16.0000i | − 0.655936i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.48528i | 0.347279i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.5980 | 1.61793 | 0.808965 | − | 0.587857i | \(-0.200028\pi\) | ||||
0.808965 | + | 0.587857i | \(0.200028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.5563i | 0.632456i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.4264 | 1.72203 | 0.861017 | − | 0.508576i | \(-0.169828\pi\) | ||||
0.861017 | + | 0.508576i | \(0.169828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 48.0000i | − 1.94187i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5563i | 0.628315i | 0.949371 | + | 0.314158i | \(0.101722\pi\) | ||||
−0.949371 | + | 0.314158i | \(0.898278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.65685 | −0.228106 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.0000i | 1.76851i | 0.467005 | + | 0.884255i | \(0.345333\pi\) | ||||
−0.467005 | + | 0.884255i | \(0.654667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.65685i | − 0.227002i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9706 | 0.679911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 16.9706i | − 0.676661i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.48528 | −0.337794 | −0.168897 | − | 0.985634i | \(-0.554020\pi\) | ||||
−0.168897 | + | 0.985634i | \(0.554020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000i | 0.476205i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24264i | 0.168100i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3137 | 0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | −0.473972 | −0.236986 | − | 0.971513i | \(-0.576159\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 16.0000i | − 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.5980 | 1.55676 | 0.778379 | − | 0.627795i | \(-0.216042\pi\) | ||||
0.778379 | + | 0.627795i | \(0.216042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000i | 0.313545i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.24264i | 0.166027i | 0.996548 | + | 0.0830137i | \(0.0264545\pi\) | ||||
−0.996548 | + | 0.0830137i | \(0.973545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | 0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 20.0000i | − 0.779089i | −0.921008 | − | 0.389545i | \(-0.872632\pi\) | ||||
0.921008 | − | 0.389545i | \(-0.127368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 26.8701i | − 1.04512i | −0.852601 | − | 0.522562i | \(-0.824976\pi\) | ||||
0.852601 | − | 0.522562i | \(-0.175024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.9706 | −0.659082 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.0000 | 1.24091 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000i | 0.309761i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 25.4558i | − 0.984180i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.00000i | − 0.115470i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.5269i | 1.25011i | 0.780580 | + | 0.625055i | \(0.214924\pi\) | ||||
−0.780580 | + | 0.625055i | \(0.785076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.2548 | −1.73672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0000i | 1.22445i | 0.790685 | + | 0.612223i | \(0.209725\pi\) | ||||
−0.790685 | + | 0.612223i | \(0.790275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.9706i | 0.648412i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0416 | 0.917245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.0000 | −1.14291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.0000i | 1.52167i | 0.648944 | + | 0.760836i | \(0.275211\pi\) | ||||
−0.648944 | + | 0.760836i | \(0.724789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.65685 | 0.214577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | 0.606043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0000i | 0.378235i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 46.6690i | − 1.76267i | −0.472496 | − | 0.881333i | \(-0.656647\pi\) | ||||
0.472496 | − | 0.881333i | \(-0.343353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9411 | 1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 44.0000i | − 1.65479i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3553i | 1.32780i | 0.747822 | + | 0.663899i | \(0.231099\pi\) | ||||
−0.747822 | + | 0.663899i | \(0.768901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.48528 | 0.318223 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.65685i | 0.211259i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.0000 | 2.08555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.00000i | 0.297523i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.24264i | 0.157568i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4264 | 1.57351 | 0.786754 | − | 0.617266i | \(-0.211760\pi\) | ||||
0.786754 | + | 0.617266i | \(0.211760\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.24264i | 0.156706i | 0.996926 | + | 0.0783528i | \(0.0249660\pi\) | ||||
−0.996926 | + | 0.0783528i | \(0.975034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.41421 | −0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 36.0000i | − 1.32428i | −0.749380 | − | 0.662141i | \(-0.769648\pi\) | ||||
0.749380 | − | 0.662141i | \(-0.230352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 33.9411i | − 1.24686i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3137 | 0.415060 | 0.207530 | − | 0.978229i | \(-0.433458\pi\) | ||||
0.207530 | + | 0.978229i | \(0.433458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | 0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 16.0000i | − 0.585409i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.9411i | 1.24018i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.48528 | 0.309632 | 0.154816 | − | 0.987943i | \(-0.450521\pi\) | ||||
0.154816 | + | 0.987943i | \(0.450521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.00000 | −0.291536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.00000i | 0.145575i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 21.2132i | − 0.771007i | −0.922706 | − | 0.385503i | \(-0.874028\pi\) | ||||
0.922706 | − | 0.385503i | \(-0.125972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.0000 | −1.30500 | −0.652499 | − | 0.757789i | \(-0.726280\pi\) | ||||
−0.652499 | + | 0.757789i | \(0.726280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000i | 0.434429i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.65685i | − 0.204524i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.9117 | 1.83831 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000i | 0.0720282i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 18.3848i | − 0.661254i | −0.943761 | − | 0.330627i | \(-0.892740\pi\) | ||||
0.943761 | − | 0.330627i | \(-0.107260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.48528 | −0.304800 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.0000 | −0.430498 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.0000i | 1.14652i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.41421 | 0.0505399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.0000i | 1.14068i | 0.821410 | + | 0.570338i | \(0.193188\pi\) | ||||
−0.821410 | + | 0.570338i | \(0.806812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.2843i | 1.00695i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.9117 | 1.81021 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | −0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 10.0000i | − 0.354663i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.4975i | 1.75329i | 0.481137 | + | 0.876645i | \(0.340224\pi\) | ||||
−0.481137 | + | 0.876645i | \(0.659776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.2548 | −1.60100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 22.6274i | − 0.797512i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.2132 | −0.746740 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.00000 | −0.140633 | −0.0703163 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703163 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0000i | 1.40459i | 0.711886 | + | 0.702295i | \(0.247841\pi\) | ||||
−0.711886 | + | 0.702295i | \(0.752159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.48528i | 0.297592i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.6274 | −0.792604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000i | 0.419314i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.07107i | 0.246782i | 0.992358 | + | 0.123391i | \(0.0393769\pi\) | ||||
−0.992358 | + | 0.123391i | \(0.960623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4558 | 0.887335 | 0.443667 | − | 0.896191i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896191i | \(0.353677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.3259i | 1.81735i | 0.417500 | + | 0.908677i | \(0.362906\pi\) | ||||
−0.417500 | + | 0.908677i | \(0.637094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | 0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00000 | 0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 16.0000i | − 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.82843i | 0.0977647i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.2548 | −1.56237 | −0.781185 | − | 0.624299i | \(-0.785385\pi\) | ||||
−0.781185 | + | 0.624299i | \(0.785385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.0000i | 0.757720i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.07107i | − 0.243252i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.1127 | −1.06904 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 24.0000i | − 0.822709i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5563i | 0.532639i | 0.963885 | + | 0.266320i | \(0.0858077\pi\) | ||||
−0.963885 | + | 0.266320i | \(0.914192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.3137 | 0.386921 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.0000 | 0.683187 | 0.341593 | − | 0.939848i | \(-0.389033\pi\) | ||||
0.341593 | + | 0.939848i | \(0.389033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 8.00000i | − 0.272956i | −0.990643 | − | 0.136478i | \(-0.956422\pi\) | ||||
0.990643 | − | 0.136478i | \(-0.0435784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 11.3137i | − 0.385570i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.65685 | −0.192562 | −0.0962808 | − | 0.995354i | \(-0.530695\pi\) | ||||
−0.0962808 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | −0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.00000i | − 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706 | 0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.0000 | −0.541518 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 32.0000i | − 1.08180i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32.5269i | − 1.09836i | −0.835705 | − | 0.549178i | \(-0.814941\pi\) | ||||
0.835705 | − | 0.549178i | \(-0.185059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3848 | −0.620103 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.0000i | − 0.807664i | −0.914833 | − | 0.403832i | \(-0.867678\pi\) | ||||
0.914833 | − | 0.403832i | \(-0.132322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.9706i | 0.570459i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706 | 0.569816 | 0.284908 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284908 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | −0.804934 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 90.5097i | − 3.02879i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.65685 | 0.189088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | −0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.00000i | − 0.133407i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.2843i | 0.942286i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | −0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 32.0000i | − 1.06254i | −0.847202 | − | 0.531271i | \(-0.821714\pi\) | ||||
0.847202 | − | 0.531271i | \(-0.178286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 15.5563i | − 0.515972i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.00000i | − 0.0661180i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 11.3137i | − 0.373612i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.82843 | 0.0933012 | 0.0466506 | − | 0.998911i | \(-0.485145\pi\) | ||||
0.0466506 | + | 0.998911i | \(0.485145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | −0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 48.0000i | − 1.57994i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 12.7279i | − 0.418491i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.7990 | 0.650284 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0000 | −0.656179 | −0.328089 | − | 0.944647i | \(-0.606405\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000i | 0.262189i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 28.2843i | − 0.925985i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000i | 0.522140i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 52.3259i | − 1.70578i | −0.522094 | − | 0.852888i | \(-0.674849\pi\) | ||||
0.522094 | − | 0.852888i | \(-0.325151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.6274 | 0.736850 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.0000i | 1.68977i | 0.534946 | + | 0.844886i | \(0.320332\pi\) | ||||
−0.534946 | + | 0.844886i | \(0.679668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 59.3970i | − 1.92811i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2132 | 0.687885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000i | 0.258874i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.9411 | −1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.4264 | 1.36434 | 0.682171 | − | 0.731193i | \(-0.261036\pi\) | ||||
0.682171 | + | 0.731193i | \(0.261036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.0000 | −1.02799 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000i | 0.770197i | 0.922876 | + | 0.385098i | \(0.125832\pi\) | ||||
−0.922876 | + | 0.385098i | \(0.874168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.3137i | 0.362701i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.7279 | −0.407620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.0000 | −1.15174 | −0.575871 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575871 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.24264i | 0.135457i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9706 | 0.541277 | 0.270638 | − | 0.962681i | \(-0.412765\pi\) | ||||
0.270638 | + | 0.962681i | \(0.412765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.0000i | 1.01857i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.0000i | 0.380426i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.07107i | 0.223943i | 0.993711 | + | 0.111971i | \(0.0357165\pi\) | ||||
−0.993711 | + | 0.111971i | \(0.964283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.24264 | −0.134231 |
(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 | 3072.2.d.c.1537.4 | 4 | ||
4.3 | odd | 2 | inner | 3072.2.d.c.1537.2 | 4 | ||
8.3 | odd | 2 | inner | 3072.2.d.c.1537.3 | 4 | ||
8.5 | even | 2 | inner | 3072.2.d.c.1537.1 | 4 | ||
16.3 | odd | 4 | 3072.2.a.h.1.2 | 2 | |||
16.5 | even | 4 | 3072.2.a.h.1.1 | 2 | |||
16.11 | odd | 4 | 3072.2.a.b.1.1 | 2 | |||
16.13 | even | 4 | 3072.2.a.b.1.2 | 2 | |||
32.3 | odd | 8 | 1536.2.j.b.385.2 | yes | 4 | ||
32.5 | even | 8 | 1536.2.j.b.1153.1 | yes | 4 | ||
32.11 | odd | 8 | 1536.2.j.c.1153.1 | yes | 4 | ||
32.13 | even | 8 | 1536.2.j.c.385.2 | yes | 4 | ||
32.19 | odd | 8 | 1536.2.j.c.385.1 | yes | 4 | ||
32.21 | even | 8 | 1536.2.j.c.1153.2 | yes | 4 | ||
32.27 | odd | 8 | 1536.2.j.b.1153.2 | yes | 4 | ||
32.29 | even | 8 | 1536.2.j.b.385.1 | ✓ | 4 | ||
48.5 | odd | 4 | 9216.2.a.i.1.2 | 2 | |||
48.11 | even | 4 | 9216.2.a.h.1.2 | 2 | |||
48.29 | odd | 4 | 9216.2.a.h.1.1 | 2 | |||
48.35 | even | 4 | 9216.2.a.i.1.1 | 2 | |||
96.5 | odd | 8 | 4608.2.k.bb.1153.1 | 4 | |||
96.11 | even | 8 | 4608.2.k.y.1153.2 | 4 | |||
96.29 | odd | 8 | 4608.2.k.bb.3457.2 | 4 | |||
96.35 | even | 8 | 4608.2.k.bb.3457.1 | 4 | |||
96.53 | odd | 8 | 4608.2.k.y.1153.1 | 4 | |||
96.59 | even | 8 | 4608.2.k.bb.1153.2 | 4 | |||
96.77 | odd | 8 | 4608.2.k.y.3457.2 | 4 | |||
96.83 | even | 8 | 4608.2.k.y.3457.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.b.385.1 | ✓ | 4 | 32.29 | even | 8 | ||
1536.2.j.b.385.2 | yes | 4 | 32.3 | odd | 8 | ||
1536.2.j.b.1153.1 | yes | 4 | 32.5 | even | 8 | ||
1536.2.j.b.1153.2 | yes | 4 | 32.27 | odd | 8 | ||
1536.2.j.c.385.1 | yes | 4 | 32.19 | odd | 8 | ||
1536.2.j.c.385.2 | yes | 4 | 32.13 | even | 8 | ||
1536.2.j.c.1153.1 | yes | 4 | 32.11 | odd | 8 | ||
1536.2.j.c.1153.2 | yes | 4 | 32.21 | even | 8 | ||
3072.2.a.b.1.1 | 2 | 16.11 | odd | 4 | |||
3072.2.a.b.1.2 | 2 | 16.13 | even | 4 | |||
3072.2.a.h.1.1 | 2 | 16.5 | even | 4 | |||
3072.2.a.h.1.2 | 2 | 16.3 | odd | 4 | |||
3072.2.d.c.1537.1 | 4 | 8.5 | even | 2 | inner | ||
3072.2.d.c.1537.2 | 4 | 4.3 | odd | 2 | inner | ||
3072.2.d.c.1537.3 | 4 | 8.3 | odd | 2 | inner | ||
3072.2.d.c.1537.4 | 4 | 1.1 | even | 1 | trivial | ||
4608.2.k.y.1153.1 | 4 | 96.53 | odd | 8 | |||
4608.2.k.y.1153.2 | 4 | 96.11 | even | 8 | |||
4608.2.k.y.3457.1 | 4 | 96.83 | even | 8 | |||
4608.2.k.y.3457.2 | 4 | 96.77 | odd | 8 | |||
4608.2.k.bb.1153.1 | 4 | 96.5 | odd | 8 | |||
4608.2.k.bb.1153.2 | 4 | 96.59 | even | 8 | |||
4608.2.k.bb.3457.1 | 4 | 96.35 | even | 8 | |||
4608.2.k.bb.3457.2 | 4 | 96.29 | odd | 8 | |||
9216.2.a.h.1.1 | 2 | 48.29 | odd | 4 | |||
9216.2.a.h.1.2 | 2 | 48.11 | even | 4 | |||
9216.2.a.i.1.1 | 2 | 48.35 | even | 4 | |||
9216.2.a.i.1.2 | 2 | 48.5 | odd | 4 |