Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(385,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.385");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.i (of order \(3\), degree \(2\), 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: | \(9.19876631285\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.769 |
Dual form | 1152.2.i.b.385.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410i | 0.894427i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | + | 1.73205i | 0.654654 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50000 | + | 7.79423i | 0.686244 | + | 1.18861i | 0.973044 | + | 0.230618i | \(0.0740749\pi\) |
−0.286801 | + | 0.957990i | \(0.592592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | − | 5.19615i | −0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 0.866025i | −0.210042 | + | 0.121268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.0000 | −1.64833 | −0.824163 | − | 0.566352i | \(-0.808354\pi\) | ||||
−0.824163 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0000 | −1.34840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | − | 4.33013i | 0.993399 | − | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | −0.755929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | + | 6.92820i | 0.496139 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0000 | −1.52153 | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50000 | − | 0.866025i | −0.173205 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | + | 8.66025i | −0.569803 | + | 0.986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.00000 | − | 5.19615i | −0.964901 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00000 | + | 8.66025i | −0.512989 | + | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.50000 | − | 11.2583i | −0.659975 | − | 1.14311i | −0.980622 | − | 0.195911i | \(-0.937234\pi\) |
0.320647 | − | 0.947199i | \(-0.396100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.0000 | −1.50756 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 3.46410i | 0.585540 | − | 0.338062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0000 | 1.06341 | 0.531705 | − | 0.846930i | \(-0.321551\pi\) | ||||
0.531705 | + | 0.846930i | \(0.321551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.0000 | − | 8.66025i | 1.42374 | − | 0.821995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.00000 | + | 12.1244i | −0.658505 | + | 1.14056i | 0.322498 | + | 0.946570i | \(0.395477\pi\) |
−0.981003 | + | 0.193993i | \(0.937856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | + | 10.3923i | 0.554700 | + | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | − | 1.73205i | −0.0916698 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.19615i | 0.468521i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.5000 | − | 7.79423i | −1.18861 | − | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | + | 8.66025i | 0.433555 | + | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | + | 5.19615i | 0.774597 | + | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.500000 | − | 0.866025i | −0.0427179 | − | 0.0739895i | 0.843876 | − | 0.536538i | \(-0.180268\pi\) |
−0.886594 | + | 0.462549i | \(0.846935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | + | 0.866025i | −0.0424094 | + | 0.0734553i | −0.886451 | − | 0.462822i | \(-0.846837\pi\) |
0.844042 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | − | 6.92820i | −1.01058 | − | 0.583460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.0000 | 1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.19615i | 0.428571i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.50000 | − | 2.59808i | 0.121268 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0000 | − | 20.7846i | 0.957704 | − | 1.65879i | 0.229650 | − | 0.973273i | \(-0.426242\pi\) |
0.728055 | − | 0.685519i | \(-0.240425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.0000 | − | 10.3923i | 1.42749 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.0000 | − | 8.66025i | 1.16775 | − | 0.674200i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | − | 1.73205i | 0.0773823 | − | 0.134030i | −0.824737 | − | 0.565516i | \(-0.808677\pi\) |
0.902120 | + | 0.431486i | \(0.142010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.50000 | + | 12.9904i | −0.573539 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | + | 15.5885i | 0.684257 | + | 1.18517i | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 1.73205i | 0.0755929 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.1244i | − | 0.911322i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | + | 3.46410i | 0.443533 | + | 0.256074i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0000 | + | 17.3205i | −0.735215 | + | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.50000 | − | 4.33013i | −0.182818 | − | 0.316650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 5.19615i | 0.654654 | − | 0.377964i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00000 | − | 1.73205i | −0.0723575 | − | 0.125327i | 0.827577 | − | 0.561353i | \(-0.189719\pi\) |
−0.899934 | + | 0.436026i | \(0.856386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | − | 6.92820i | −0.859338 | − | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0000 | 1.42494 | 0.712470 | − | 0.701702i | \(-0.247576\pi\) | ||||
0.712470 | + | 0.701702i | \(0.247576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1244i | 0.855186i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000 | − | 10.3923i | 0.421117 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | + | 10.3923i | 0.417029 | + | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.5000 | + | 21.6506i | 0.864643 | + | 1.49761i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.00000 | − | 5.19615i | 0.616670 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0000 | 1.22759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.5000 | − | 11.2583i | 1.31769 | − | 0.760767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | + | 3.46410i | −0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0000 | + | 20.7846i | 0.803579 | + | 1.39184i | 0.917246 | + | 0.398321i | \(0.130407\pi\) |
−0.113666 | + | 0.993519i | \(0.536260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 17.3205i | − | 1.13961i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00000 | − | 1.73205i | −0.194871 | − | 0.112509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | + | 10.3923i | −0.388108 | + | 0.672222i | −0.992195 | − | 0.124696i | \(-0.960204\pi\) |
0.604087 | + | 0.796918i | \(0.293538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5000 | − | 21.6506i | −0.805196 | − | 1.39464i | −0.916159 | − | 0.400815i | \(-0.868727\pi\) |
0.110963 | − | 0.993825i | \(-0.464606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | − | 17.3205i | 0.636285 | − | 1.10208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 10.3923i | 1.14070 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0000 | 1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.46410i | 0.216930i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000 | + | 17.3205i | 0.621370 | + | 1.07624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | + | 15.5885i | 0.554964 | + | 0.961225i | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 20.7846i | −0.737154 | + | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0000 | + | 8.66025i | −0.917985 | + | 0.529999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | + | 6.92820i | −0.726273 | + | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0000 | − | 25.9808i | −0.894825 | − | 1.54988i | −0.834021 | − | 0.551733i | \(-0.813967\pi\) |
−0.0608039 | − | 0.998150i | \(-0.519366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000 | − | 20.7846i | 0.713326 | − | 1.23552i | −0.250276 | − | 0.968175i | \(-0.580521\pi\) |
0.963602 | − | 0.267342i | \(-0.0861454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 17.3205i | − | 1.02598i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.5000 | + | 11.2583i | 1.14311 | + | 0.659975i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00000 | − | 8.66025i | 0.292103 | − | 0.505937i | −0.682204 | − | 0.731162i | \(-0.738978\pi\) |
0.974307 | + | 0.225225i | \(0.0723116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | + | 12.1244i | 0.407556 | + | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.5000 | − | 12.9904i | 1.30558 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | − | 13.8564i | −0.462652 | − | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00000 | − | 15.5885i | 0.518751 | − | 0.898504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.00000 | − | 5.19615i | −0.517036 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.00000 | −0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.00000 | −0.171219 | −0.0856095 | − | 0.996329i | \(-0.527284\pi\) | ||||
−0.0856095 | + | 0.996329i | \(0.527284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.00000 | − | 8.66025i | 0.283524 | − | 0.491078i | −0.688726 | − | 0.725022i | \(-0.741830\pi\) |
0.972250 | + | 0.233944i | \(0.0751631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5000 | − | 21.6506i | −0.706542 | − | 1.22377i | −0.966132 | − | 0.258047i | \(-0.916921\pi\) |
0.259590 | − | 0.965719i | \(-0.416412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | + | 10.3923i | −0.338062 | + | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0000 | − | 25.9808i | 0.839839 | − | 1.45464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.5000 | + | 9.52628i | −0.920940 | + | 0.531705i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.00000 | −0.278207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.0000 | − | 10.3923i | 0.995402 | − | 0.574696i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | − | 13.8564i | 0.441054 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | + | 17.3205i | 0.549650 | + | 0.952021i | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0000 | + | 25.9808i | −0.821995 | + | 1.42374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | − | 12.1244i | −0.382451 | − | 0.662424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50000 | + | 16.4545i | −0.517498 | + | 0.896333i | 0.482295 | + | 0.876009i | \(0.339803\pi\) |
−0.999793 | + | 0.0203242i | \(0.993530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 24.2487i | − | 1.31701i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0000 | − | 6.92820i | −0.646058 | − | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.50000 | − | 2.59808i | 0.0805242 | − | 0.139472i | −0.822951 | − | 0.568112i | \(-0.807674\pi\) |
0.903475 | + | 0.428640i | \(0.141007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | + | 13.8564i | 0.428230 | + | 0.741716i | 0.996716 | − | 0.0809766i | \(-0.0258039\pi\) |
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | − | 10.3923i | −0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.50000 | + | 7.79423i | 0.239511 | + | 0.414845i | 0.960574 | − | 0.278024i | \(-0.0896796\pi\) |
−0.721063 | + | 0.692869i | \(0.756346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00000 | + | 1.73205i | 0.158777 | + | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.0000 | −1.79445 | −0.897226 | − | 0.441572i | \(-0.854421\pi\) | ||||
−0.897226 | + | 0.441572i | \(0.854421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 24.2487i | − | 1.27273i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0000 | + | 22.5167i | −0.680451 | + | 1.17858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0000 | − | 19.0526i | −0.574195 | − | 0.994535i | −0.996129 | − | 0.0879086i | \(-0.971982\pi\) |
0.421933 | − | 0.906627i | \(-0.361352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.50000 | − | 7.79423i | −0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 20.7846i | 0.623009 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0000 | + | 27.7128i | −0.828449 | + | 1.43492i | 0.0708063 | + | 0.997490i | \(0.477443\pi\) |
−0.899255 | + | 0.437425i | \(0.855891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | + | 10.3923i | −0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.0000 | − | 17.3205i | 1.53695 | − | 0.887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0000 | + | 17.3205i | 0.509647 | + | 0.882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.0000 | 1.37249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.0000 | − | 32.9090i | −0.963338 | − | 1.66855i | −0.714015 | − | 0.700130i | \(-0.753125\pi\) |
−0.249323 | − | 0.968420i | \(-0.580208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00000 | + | 3.46410i | −0.101144 | + | 0.175187i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.7846i | 1.04844i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.0000 | − | 8.66025i | −0.750939 | − | 0.433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | −0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0000 | + | 43.3013i | 1.23920 | + | 2.14636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | + | 21.6506i | −0.618085 | + | 1.07056i | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.50000 | + | 0.866025i | 0.0739895 | + | 0.0427179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0000 | 0.688895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.73205i | − | 0.0848189i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0000 | − | 17.3205i | 0.488532 | − | 0.846162i | −0.511381 | − | 0.859354i | \(-0.670866\pi\) |
0.999913 | + | 0.0131919i | \(0.00419923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | − | 1.73205i | −0.0487370 | − | 0.0844150i | 0.840628 | − | 0.541613i | \(-0.182186\pi\) |
−0.889365 | + | 0.457198i | \(0.848853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.0000 | 1.16692 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.500000 | + | 0.866025i | 0.0242536 | + | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 6.92820i | −0.193574 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −30.0000 | + | 17.3205i | −1.44841 | + | 0.836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0000 | 0.481683 | 0.240842 | − | 0.970564i | \(-0.422577\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0000 | 1.58588 | 0.792939 | − | 0.609301i | \(-0.208550\pi\) | ||||
0.792939 | + | 0.609301i | \(0.208550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | + | 10.3923i | −0.863034 | + | 0.498273i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0000 | − | 17.3205i | 0.478365 | − | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50000 | − | 7.79423i | −0.214286 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.50000 | − | 12.9904i | −0.356336 | − | 0.617192i | 0.631010 | − | 0.775775i | \(-0.282641\pi\) |
−0.987346 | + | 0.158583i | \(0.949307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | − | 17.3205i | 0.474045 | − | 0.821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0000 | 0.802280 | 0.401140 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401140 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | −0.706322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.0000 | + | 13.8564i | 1.12762 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.00000 | − | 13.8564i | 0.375046 | − | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.50000 | + | 2.59808i | 0.0701670 | + | 0.121533i | 0.898974 | − | 0.438001i | \(-0.144313\pi\) |
−0.828807 | + | 0.559534i | \(0.810980\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.19615i | 0.242536i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0000 | − | 17.3205i | −0.465746 | − | 0.806696i | 0.533488 | − | 0.845807i | \(-0.320881\pi\) |
−0.999235 | + | 0.0391109i | \(0.987547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00000 | − | 1.73205i | 0.0464739 | − | 0.0804952i | −0.841853 | − | 0.539707i | \(-0.818535\pi\) |
0.888327 | + | 0.459212i | \(0.151868\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.0000 | 1.34196 | 0.670980 | − | 0.741475i | \(-0.265874\pi\) | ||||
0.670980 | + | 0.741475i | \(0.265874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 41.5692i | 1.91541i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.5000 | − | 38.9711i | 1.03455 | − | 1.79190i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50000 | − | 4.33013i | −0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | + | 31.1769i | −0.824163 | + | 1.42749i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | − | 34.6410i | 0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0000 | + | 6.92820i | −0.546019 | + | 0.315244i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.0000 | −1.18060 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000 | 0.453143 | 0.226572 | − | 0.973995i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973995i | \(0.427248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | + | 3.46410i | −0.271329 | + | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5000 | + | 21.6506i | −0.564117 | + | 0.977079i | 0.433014 | + | 0.901387i | \(0.357450\pi\) |
−0.997131 | + | 0.0756923i | \(0.975883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | + | 5.19615i | 0.135113 | + | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.0000 | + | 25.9808i | −0.674200 | + | 1.16775i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | + | 10.3923i | 0.269137 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | − | 4.33013i | 0.111915 | − | 0.193843i | −0.804627 | − | 0.593780i | \(-0.797635\pi\) |
0.916542 | + | 0.399937i | \(0.130968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.46410i | 0.154765i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.50000 | + | 2.59808i | 0.199852 | + | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | − | 24.2487i | 0.620539 | − | 1.07481i | −0.368846 | − | 0.929490i | \(-0.620247\pi\) |
0.989385 | − | 0.145315i | \(-0.0464195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.0000 | + | 22.5167i | 0.575086 | + | 0.996078i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 25.9808i | − | 1.14708i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.0000 | − | 34.6410i | 0.879599 | − | 1.52351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.0000 | − | 15.5885i | −1.18517 | − | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.00000 | −0.306676 | −0.153338 | − | 0.988174i | \(-0.549002\pi\) | ||||
−0.153338 | + | 0.988174i | \(0.549002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.0000 | −1.92399 | −0.961993 | − | 0.273075i | \(-0.911959\pi\) | ||||
−0.961993 | + | 0.273075i | \(0.911959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.46410i | 0.151186i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5000 | + | 18.1865i | 0.455661 | + | 0.789228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | + | 10.3923i | 0.259889 | + | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0000 | − | 19.0526i | 0.475571 | − | 0.823714i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | − | 10.3923i | 0.776757 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0000 | −0.646096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.0000 | − | 17.3205i | 1.28742 | − | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | + | 20.7846i | −0.514024 | + | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.0000 | −0.512148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | − | 3.46410i | 0.0850487 | − | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 34.6410i | − | 1.47043i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.0000 | −1.10166 | −0.550828 | − | 0.834619i | \(-0.685688\pi\) | ||||
−0.550828 | + | 0.834619i | \(0.685688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.0000 | −1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.50000 | + | 4.33013i | 0.316650 | + | 0.182818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.5000 | + | 28.5788i | −0.695392 | + | 1.20445i | 0.274656 | + | 0.961542i | \(0.411436\pi\) |
−0.970048 | + | 0.242912i | \(0.921897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | + | 24.2487i | 0.588984 | + | 1.02015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | + | 15.5885i | −0.377964 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.50000 | + | 16.4545i | 0.398261 | + | 0.689808i | 0.993511 | − | 0.113732i | \(-0.0362806\pi\) |
−0.595251 | + | 0.803540i | \(0.702947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.50000 | + | 16.4545i | −0.397563 | + | 0.688599i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) |
0.595862 | + | 0.803087i | \(0.296811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.00000 | + | 1.73205i | 0.125327 | + | 0.0723575i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0000 | 0.957503 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1.73205i | − | 0.0719816i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | + | 20.7846i | −0.497844 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.0000 | + | 51.9615i | 1.24247 | + | 2.15203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | 0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.50000 | + | 4.33013i | 0.103186 | + | 0.178723i | 0.912996 | − | 0.407969i | \(-0.133763\pi\) |
−0.809810 | + | 0.586693i | \(0.800430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.0000 | + | 17.3205i | −1.23404 | + | 0.712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | −0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00000 | + | 1.73205i | −0.122782 | + | 0.0708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50000 | + | 7.79423i | 0.183559 | + | 0.317933i | 0.943090 | − | 0.332538i | \(-0.107905\pi\) |
−0.759531 | + | 0.650471i | \(0.774572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5000 | − | 18.1865i | −0.427593 | − | 0.740613i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.0000 | + | 24.2487i | 0.569181 | + | 0.985850i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.7846i | 0.842235i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.0000 | −1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.00000 | + | 5.19615i | 0.362915 | + | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50000 | − | 14.7224i | 0.342197 | − | 0.592703i | −0.642643 | − | 0.766165i | \(-0.722162\pi\) |
0.984840 | + | 0.173463i | \(0.0554956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5000 | − | 30.3109i | −0.703384 | − | 1.21830i | −0.967271 | − | 0.253744i | \(-0.918338\pi\) |
0.263887 | − | 0.964554i | \(-0.414995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 10.3923i | −0.722315 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.0000 | − | 17.3205i | −0.400642 | − | 0.693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −37.5000 | − | 21.6506i | −1.49761 | − | 0.864643i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0000 | 0.875806 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.6410i | 1.37686i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.0000 | + | 34.6410i | −0.793676 | + | 1.37469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | + | 10.3923i | 0.237729 | + | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5000 | − | 18.1865i | 0.414080 | − | 0.717207i | −0.581252 | − | 0.813724i | \(-0.697437\pi\) |
0.995331 | + | 0.0965169i | \(0.0307702\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.0000 | + | 15.5885i | −1.06312 | + | 0.613795i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0000 | 1.37387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | − | 20.7846i | −0.468879 | − | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.5000 | + | 33.7750i | −0.760767 | + | 1.31769i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | + | 20.7846i | 0.467454 | + | 0.809653i | 0.999309 | − | 0.0371821i | \(-0.0118382\pi\) |
−0.531855 | + | 0.846836i | \(0.678505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | + | 1.73205i | −0.0388955 | + | 0.0673690i | −0.884818 | − | 0.465937i | \(-0.845717\pi\) |
0.845922 | + | 0.533306i | \(0.179051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.92820i | − | 0.269069i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.0000 | 0.775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.0000 | − | 20.7846i | −1.39184 | − | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | + | 17.3205i | −0.386046 | + | 0.668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.50000 | + | 2.59808i | −0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.0000 | − | 24.2487i | −0.538064 | − | 0.931954i | −0.999008 | − | 0.0445248i | \(-0.985823\pi\) |
0.460945 | − | 0.887429i | \(-0.347511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0000 | + | 22.5167i | −0.498894 | + | 0.864110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0000 | 0.573959 | 0.286980 | − | 0.957937i | \(-0.407349\pi\) | ||||
0.286980 | + | 0.957937i | \(0.407349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.2487i | − | 0.925146i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0000 | − | 41.5692i | 0.914327 | − | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.00000 | + | 10.3923i | 0.228251 | + | 0.395342i | 0.957290 | − | 0.289130i | \(-0.0933661\pi\) |
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0000 | + | 25.9808i | 0.569803 | + | 0.986928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.00000 | + | 1.73205i | 0.0379322 | + | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50000 | − | 2.59808i | 0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.5000 | − | 7.79423i | 0.510617 | − | 0.294805i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.0000 | 1.88579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | + | 13.8564i | −0.903892 | + | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | − | 10.3923i | 0.225653 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | + | 17.3205i | 0.375558 | + | 0.650485i | 0.990410 | − | 0.138157i | \(-0.0441178\pi\) |
−0.614852 | + | 0.788642i | \(0.710784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | 0.225018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0000 | − | 34.6410i | 0.747958 | − | 1.29550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 20.7846i | − | 0.776215i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.5000 | + | 21.6506i | 1.39464 | + | 0.805196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0000 | − | 41.5692i | −0.890111 | − | 1.54172i | −0.839742 | − | 0.542986i | \(-0.817294\pi\) |
−0.0503692 | − | 0.998731i | \(-0.516040\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.50000 | + | 7.79423i | 0.166439 | + | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.00000 | − | 15.5885i | 0.332423 | − | 0.575773i | −0.650564 | − | 0.759452i | \(-0.725467\pi\) |
0.982986 | + | 0.183679i | \(0.0588007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00000 | + | 5.19615i | 0.331970 | + | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.0000 | −1.28924 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0000 | −0.772497 | −0.386249 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386249 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.6410i | 1.27257i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.0000 | + | 32.9090i | −0.697042 | + | 1.20731i | 0.272445 | + | 0.962171i | \(0.412168\pi\) |
−0.969487 | + | 0.245141i | \(0.921166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.0000 | −1.31717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0000 | − | 19.0526i | −0.401931 | − | 0.696165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | + | 1.73205i | −0.0364905 | + | 0.0632034i | −0.883694 | − | 0.468065i | \(-0.844951\pi\) |
0.847203 | + | 0.531269i | \(0.178285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.50000 | − | 2.59808i | 0.163989 | − | 0.0946792i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | −1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.0000 | + | 17.3205i | −1.08893 | + | 0.628695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.00000 | + | 8.66025i | −0.181250 | + | 0.313934i | −0.942306 | − | 0.334752i | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000 | + | 20.7846i | 0.434429 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | − | 5.19615i | −0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0000 | − | 24.2487i | −0.505511 | − | 0.875570i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | + | 1.73205i | −0.0360609 | + | 0.0624593i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 5.19615i | − | 0.187135i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0000 | 0.863220 | 0.431610 | − | 0.902060i | \(-0.357946\pi\) | ||||
0.431610 | + | 0.902060i | \(0.357946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.0000 | − | 17.3205i | −1.07624 | − | 0.621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.50000 | + | 12.9904i | −0.268715 | + | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | + | 25.9808i | 0.536742 | + | 0.929665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.0000 | + | 15.5885i | −0.964901 | + | 0.557086i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.0000 | − | 41.5692i | −0.856597 | − | 1.48367i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | + | 24.2487i | −0.499046 | + | 0.864373i | −0.999999 | − | 0.00110111i | \(-0.999650\pi\) |
0.500953 | + | 0.865474i | \(0.332983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.0000 | − | 15.5885i | −0.961225 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0000 | 0.995565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 41.5692i | − | 1.47431i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.0000 | − | 25.9808i | 0.531327 | − | 0.920286i | −0.468004 | − | 0.883726i | \(-0.655027\pi\) |
0.999331 | − | 0.0365596i | \(-0.0116399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | + | 6.92820i | 0.141510 | + | 0.245102i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0000 | − | 25.9808i | 0.529999 | − | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5000 | + | 56.2917i | 1.14690 | + | 1.98649i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | − | 13.8564i | 0.281963 | − | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.00000 | − | 3.46410i | 0.211210 | − | 0.121942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.00000 | −0.105474 | −0.0527372 | − | 0.998608i | \(-0.516795\pi\) | ||||
−0.0527372 | + | 0.998608i | \(0.516795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | + | 6.92820i | −0.420858 | + | 0.242983i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.5000 | − | 38.9711i | −0.787175 | − | 1.36343i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | − | 20.7846i | 0.419314 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.00000 | − | 12.1244i | −0.244302 | − | 0.423143i | 0.717633 | − | 0.696421i | \(-0.245225\pi\) |
−0.961935 | + | 0.273278i | \(0.911892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0000 | − | 29.4449i | 0.592583 | − | 1.02638i | −0.401300 | − | 0.915947i | \(-0.631442\pi\) |
0.993883 | − | 0.110437i | \(-0.0352250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.66025i | 0.301511i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.0000 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.50000 | − | 2.59808i | 0.0519719 | − | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | − | 3.46410i | −0.0692129 | − | 0.119880i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | − | 41.5692i | −0.828572 | − | 1.43513i | −0.899158 | − | 0.437623i | \(-0.855820\pi\) |
0.0705865 | − | 0.997506i | \(-0.477513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.0000 | + | 25.9808i | 1.54988 | + | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | −0.206406 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0000 | 0.962091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.5692i | 1.42665i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0000 | − | 34.6410i | 0.685591 | − | 1.18748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.00000 | + | 6.92820i | 0.136957 | + | 0.237217i | 0.926343 | − | 0.376680i | \(-0.122934\pi\) |
−0.789386 | + | 0.613897i | \(0.789601\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.0000 | + | 25.9808i | 0.512989 | + | 0.888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.00000 | − | 15.5885i | −0.307434 | − | 0.532492i | 0.670366 | − | 0.742030i | \(-0.266137\pi\) |
−0.977800 | + | 0.209539i | \(0.932804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.50000 | − | 11.2583i | 0.221777 | − | 0.384129i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
0.955348 | + | 0.295484i | \(0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.00000 | − | 5.19615i | 0.306719 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.0000 | 0.748889 | 0.374444 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374444 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.0000 | − | 13.8564i | 0.815083 | − | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | − | 8.66025i | 0.169613 | − | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0000 | + | 24.2487i | 0.474372 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.0000 | −1.31995 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.0000 | − | 20.7846i | −0.405674 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.00000 | + | 13.8564i | −0.270141 | + | 0.467898i | −0.968898 | − | 0.247462i | \(-0.920404\pi\) |
0.698757 | + | 0.715359i | \(0.253737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.3205i | 0.584206i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0000 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.0000 | − | 12.1244i | −0.705907 | − | 0.407556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0000 | − | 25.9808i | 0.503651 | − | 0.872349i | −0.496340 | − | 0.868128i | \(-0.665323\pi\) |
0.999991 | − | 0.00422062i | \(-0.00134347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 34.6410i | 0.670778 | + | 1.16182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.5000 | + | 38.9711i | −0.753778 | + | 1.30558i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.0000 | − | 34.6410i | −0.669274 | − | 1.15922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 20.7846i | −0.401116 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | + | 13.8564i | 0.801337 | + | 0.462652i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.1769i | 1.03750i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0000 | + | 34.6410i | −0.664822 | + | 1.15151i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.50000 | + | 9.52628i | 0.182625 | + | 0.316315i | 0.942773 | − | 0.333434i | \(-0.108207\pi\) |
−0.760149 | + | 0.649749i | \(0.774874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | − | 10.3923i | −0.198789 | − | 0.344312i | 0.749347 | − | 0.662177i | \(-0.230367\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0000 | + | 51.9615i | −0.992855 | + | 1.71968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000 | − | 6.92820i | 0.396708 | − | 0.229039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0000 | −0.792550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.50000 | − | 2.59808i | 0.148280 | − | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | − | 20.7846i | 0.394985 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00000 | − | 8.66025i | −0.164399 | − | 0.284747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | + | 20.7846i | 0.394132 | + | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | + | 5.19615i | 0.0984268 | + | 0.170480i | 0.911034 | − | 0.412332i | \(-0.135286\pi\) |
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50000 | + | 12.9904i | −0.245803 | + | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.3205i | 0.567048i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.0000 | −0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.5000 | + | 21.6506i | 1.22377 | + | 0.706542i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | − | 24.2487i | 0.456387 | − | 0.790485i | −0.542380 | − | 0.840133i | \(-0.682477\pi\) |
0.998767 | + | 0.0496480i | \(0.0158099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | + | 10.3923i | 0.195387 | + | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 20.7846i | − | 0.676123i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5000 | − | 19.9186i | −0.373700 | − | 0.647267i | 0.616432 | − | 0.787408i | \(-0.288578\pi\) |
−0.990132 | + | 0.140141i | \(0.955244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.0000 | − | 45.0333i | 0.843996 | − | 1.46184i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | − | 10.3923i | −0.583690 | − | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.00000 | 0.0323932 | 0.0161966 | − | 0.999869i | \(-0.494844\pi\) | ||||
0.0161966 | + | 0.999869i | \(0.494844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 51.9615i | 1.67968i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00000 | + | 1.73205i | −0.0322917 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.5000 | − | 28.5788i | 0.531705 | − | 0.920940i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | + | 1.73205i | 0.0321911 | + | 0.0557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | − | 12.1244i | 0.225105 | − | 0.389893i | −0.731246 | − | 0.682114i | \(-0.761061\pi\) |
0.956351 | + | 0.292221i | \(0.0943942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.50000 | − | 4.33013i | 0.240935 | − | 0.139104i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.0000 | 0.898563 | 0.449281 | − | 0.893390i | \(-0.351680\pi\) | ||||
0.449281 | + | 0.893390i | \(0.351680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00000 | 0.0641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.00000 | − | 3.46410i | 0.192154 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.5000 | + | 49.3634i | −0.911796 | + | 1.57928i | −0.100270 | + | 0.994960i | \(0.531971\pi\) |
−0.811526 | + | 0.584316i | \(0.801363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0000 | − | 43.3013i | −0.799003 | − | 1.38391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0000 | + | 31.1769i | −0.574696 | + | 0.995402i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0000 | + | 39.8372i | 0.733586 | + | 1.27061i | 0.955341 | + | 0.295506i | \(0.0954882\pi\) |
−0.221755 | + | 0.975102i | \(0.571178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | − | 34.6410i | 0.637253 | − | 1.10375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.7128i | 0.882109i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0000 | −1.14473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.0000 | − | 17.3205i | −0.952021 | − | 0.549650i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.00000 | − | 3.46410i | 0.0634043 | − | 0.109819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 51.9615i | − | 1.64399i |
(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 | 1152.2.i.b.769.1 | yes | 2 | |
3.2 | odd | 2 | 3456.2.i.a.2305.1 | 2 | |||
4.3 | odd | 2 | 1152.2.i.d.769.1 | yes | 2 | ||
8.3 | odd | 2 | 1152.2.i.a.769.1 | yes | 2 | ||
8.5 | even | 2 | 1152.2.i.c.769.1 | yes | 2 | ||
9.2 | odd | 6 | 3456.2.i.a.1153.1 | 2 | |||
9.7 | even | 3 | inner | 1152.2.i.b.385.1 | yes | 2 | |
12.11 | even | 2 | 3456.2.i.b.2305.1 | 2 | |||
24.5 | odd | 2 | 3456.2.i.c.2305.1 | 2 | |||
24.11 | even | 2 | 3456.2.i.d.2305.1 | 2 | |||
36.7 | odd | 6 | 1152.2.i.d.385.1 | yes | 2 | ||
36.11 | even | 6 | 3456.2.i.b.1153.1 | 2 | |||
72.11 | even | 6 | 3456.2.i.d.1153.1 | 2 | |||
72.29 | odd | 6 | 3456.2.i.c.1153.1 | 2 | |||
72.43 | odd | 6 | 1152.2.i.a.385.1 | ✓ | 2 | ||
72.61 | even | 6 | 1152.2.i.c.385.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.a.385.1 | ✓ | 2 | 72.43 | odd | 6 | ||
1152.2.i.a.769.1 | yes | 2 | 8.3 | odd | 2 | ||
1152.2.i.b.385.1 | yes | 2 | 9.7 | even | 3 | inner | |
1152.2.i.b.769.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1152.2.i.c.385.1 | yes | 2 | 72.61 | even | 6 | ||
1152.2.i.c.769.1 | yes | 2 | 8.5 | even | 2 | ||
1152.2.i.d.385.1 | yes | 2 | 36.7 | odd | 6 | ||
1152.2.i.d.769.1 | yes | 2 | 4.3 | odd | 2 | ||
3456.2.i.a.1153.1 | 2 | 9.2 | odd | 6 | |||
3456.2.i.a.2305.1 | 2 | 3.2 | odd | 2 | |||
3456.2.i.b.1153.1 | 2 | 36.11 | even | 6 | |||
3456.2.i.b.2305.1 | 2 | 12.11 | even | 2 | |||
3456.2.i.c.1153.1 | 2 | 72.29 | odd | 6 | |||
3456.2.i.c.2305.1 | 2 | 24.5 | odd | 2 | |||
3456.2.i.d.1153.1 | 2 | 72.11 | even | 6 | |||
3456.2.i.d.2305.1 | 2 | 24.11 | even | 2 |