Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(481,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.q (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.961 |
Dual form | 1440.2.q.e.481.1 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 3.46410i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.19615i | 1.13389i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.92820i | − | 1.20605i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | + | 3.46410i | 0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | − | 7.79423i | −0.702782 | − | 1.21725i | −0.967486 | − | 0.252924i | \(-0.918608\pi\) |
0.264704 | − | 0.964330i | \(-0.414726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 1.73205i | 0.420084 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | − | 1.73205i | 0.397360 | − | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.50000 | + | 7.79423i | 0.566947 | + | 0.981981i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | − | 2.59808i | −0.183254 | − | 0.317406i | 0.759733 | − | 0.650236i | \(-0.225330\pi\) |
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5000 | + | 6.06218i | 1.26405 | + | 0.729800i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | + | 10.3923i | 0.683763 | + | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | + | 8.66025i | −0.562544 | + | 0.974355i | 0.434730 | + | 0.900561i | \(0.356844\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.50000 | + | 6.06218i | −0.384175 | + | 0.665410i | −0.991654 | − | 0.128925i | \(-0.958847\pi\) |
0.607479 | + | 0.794335i | \(0.292181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 15.5885i | − | 1.67126i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.00000 | − | 5.19615i | −0.933257 | − | 0.538816i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | − | 12.1244i | 0.710742 | − | 1.23104i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
0.964579 | − | 0.263795i | \(-0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | − | 10.3923i | −0.603023 | − | 1.04447i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.50000 | − | 2.59808i | 0.439155 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0000 | −1.45010 | −0.725052 | − | 0.688694i | \(-0.758184\pi\) | ||||
−0.725052 | + | 0.688694i | \(0.758184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | − | 1.73205i | 0.284747 | − | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | + | 10.3923i | 0.564433 | + | 0.977626i | 0.997102 | + | 0.0760733i | \(0.0242383\pi\) |
−0.432670 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | − | 6.06218i | 0.326377 | − | 0.565301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0000 | 1.10940 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.5000 | − | 7.79423i | −1.21725 | − | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.92820i | 0.609994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0000 | + | 19.0526i | 0.961074 | + | 1.66463i | 0.719811 | + | 0.694170i | \(0.244228\pi\) |
0.241264 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.00000 | − | 13.8564i | 0.683486 | − | 1.18383i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
0.973910 | − | 0.226935i | \(-0.0728704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | + | 6.92820i | 0.339276 | + | 0.587643i | 0.984297 | − | 0.176522i | \(-0.0564848\pi\) |
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.19615i | − | 0.437595i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0000 | 1.33799 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | −0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | − | 1.73205i | −0.247436 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | + | 2.59808i | 0.122885 | + | 0.212843i | 0.920904 | − | 0.389789i | \(-0.127452\pi\) |
−0.798019 | + | 0.602632i | \(0.794119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | + | 17.3205i | −0.813788 | + | 1.40952i | 0.0964061 | + | 0.995342i | \(0.469265\pi\) |
−0.910195 | + | 0.414181i | \(0.864068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.00000 | − | 5.19615i | 0.242536 | − | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | + | 5.19615i | −0.240966 | + | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | + | 12.1244i | 0.558661 | + | 0.967629i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00000 | − | 5.19615i | 0.713746 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.0000 | −1.65503 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | + | 3.46410i | −0.467099 | + | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | + | 2.59808i | 0.116073 | + | 0.201045i | 0.918208 | − | 0.396098i | \(-0.129636\pi\) |
−0.802135 | + | 0.597143i | \(0.796303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | − | 3.46410i | 0.152057 | − | 0.263371i | −0.779926 | − | 0.625871i | \(-0.784744\pi\) |
0.931984 | + | 0.362500i | \(0.118077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.50000 | − | 2.59808i | −0.113389 | − | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00000 | + | 5.19615i | 0.676481 | + | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0000 | 1.79384 | 0.896922 | − | 0.442189i | \(-0.145798\pi\) | ||||
0.896922 | + | 0.442189i | \(0.145798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0000 | −1.70958 | −0.854788 | − | 0.518977i | \(-0.826313\pi\) | ||||
−0.854788 | + | 0.518977i | \(0.826313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 22.5167i | − | 1.66448i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5000 | + | 7.79423i | 0.981981 | + | 0.566947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | − | 17.3205i | −0.719816 | − | 1.24676i | −0.961073 | − | 0.276296i | \(-0.910893\pi\) |
0.241257 | − | 0.970461i | \(-0.422440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.92820i | − | 0.496139i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0000 | −1.42494 | −0.712470 | − | 0.701702i | \(-0.752424\pi\) | ||||
−0.712470 | + | 0.701702i | \(0.752424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | − | 2.59808i | −0.317406 | − | 0.183254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.5000 | + | 23.3827i | 0.947514 | + | 1.64114i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.0000 | 1.45960 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | − | 6.92820i | 0.276686 | − | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | + | 17.3205i | 0.688428 | + | 1.19239i | 0.972346 | + | 0.233544i | \(0.0750324\pi\) |
−0.283918 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | 1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | − | 6.92820i | 0.810885 | − | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | + | 6.92820i | 0.269069 | + | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | − | 7.79423i | 0.301342 | − | 0.521940i | −0.675098 | − | 0.737728i | \(-0.735899\pi\) |
0.976440 | + | 0.215788i | \(0.0692320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.00000 | + | 3.46410i | −0.132745 | + | 0.229920i | −0.924734 | − | 0.380615i | \(-0.875712\pi\) |
0.791989 | + | 0.610535i | \(0.209046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5000 | + | 18.1865i | 0.693860 | + | 1.20180i | 0.970564 | + | 0.240845i | \(0.0774245\pi\) |
−0.276704 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | + | 10.3923i | 1.18431 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | −0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.3205i | 1.12509i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | + | 3.46410i | 0.129369 | + | 0.224074i | 0.923432 | − | 0.383761i | \(-0.125371\pi\) |
−0.794063 | + | 0.607835i | \(0.792038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | + | 14.7224i | −0.547533 | + | 0.948355i | 0.450910 | + | 0.892570i | \(0.351100\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 1.73205i | −0.0638877 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 6.92820i | 0.254514 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.1244i | 0.768350i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.0000 | 1.76034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | − | 1.73205i | −0.187867 | − | 0.108465i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | + | 5.19615i | −0.186411 | + | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.5000 | − | 23.3827i | −0.835629 | − | 1.44735i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00000 | − | 6.92820i | 0.246651 | − | 0.427211i | −0.715944 | − | 0.698158i | \(-0.754003\pi\) |
0.962594 | + | 0.270947i | \(0.0873367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.50000 | − | 0.866025i | 0.0917985 | − | 0.0529999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.00000 | 0.304855 | 0.152428 | − | 0.988315i | \(-0.451291\pi\) | ||||
0.152428 | + | 0.988315i | \(0.451291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0000 | + | 10.3923i | −1.08941 | + | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | + | 15.5885i | −0.540758 | + | 0.936620i | 0.458103 | + | 0.888899i | \(0.348529\pi\) |
−0.998861 | + | 0.0477206i | \(0.984804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.0000 | −1.07763 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5000 | − | 19.9186i | 0.686032 | − | 1.18824i | −0.287079 | − | 0.957907i | \(-0.592684\pi\) |
0.973111 | − | 0.230336i | \(-0.0739826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.5000 | − | 19.9186i | −0.683604 | − | 1.18404i | −0.973873 | − | 0.227092i | \(-0.927078\pi\) |
0.290269 | − | 0.956945i | \(-0.406255\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.0000 | 1.59376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 24.2487i | − | 1.42148i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.00000 | + | 1.73205i | 0.0584206 | + | 0.101187i | 0.893757 | − | 0.448552i | \(-0.148060\pi\) |
−0.835336 | + | 0.549740i | \(0.814727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0000 | − | 10.3923i | −1.04447 | − | 0.603023i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.0000 | + | 24.2487i | −0.809641 | + | 1.40234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 10.3923i | −0.345834 | − | 0.599002i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.2487i | 1.39305i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0000 | −0.744378 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0000 | −0.627803 | −0.313902 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313902 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | − | 6.92820i | −0.682656 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | − | 25.9808i | −0.850572 | − | 1.47323i | −0.880693 | − | 0.473688i | \(-0.842923\pi\) |
0.0301210 | − | 0.999546i | \(-0.490411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | + | 13.8564i | −0.452187 | + | 0.783210i | −0.998522 | − | 0.0543564i | \(-0.982689\pi\) |
0.546335 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.50000 | − | 7.79423i | 0.253546 | − | 0.439155i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 31.1769i | −1.00781 | − | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.5000 | + | 12.9904i | −1.25583 | + | 0.725052i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.5000 | + | 6.06218i | −0.580651 | + | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00000 | + | 5.19615i | −0.164895 | + | 0.285606i | −0.936618 | − | 0.350352i | \(-0.886062\pi\) |
0.771723 | + | 0.635959i | \(0.219395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | − | 5.19615i | 0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.50000 | + | 2.59808i | −0.0819538 | + | 0.141948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | + | 13.8564i | 0.435788 | + | 0.754807i | 0.997360 | − | 0.0726214i | \(-0.0231365\pi\) |
−0.561572 | + | 0.827428i | \(0.689803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | + | 10.3923i | 0.977626 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 12.1244i | − | 0.652753i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00000 | + | 6.92820i | 0.214731 | + | 0.371925i | 0.953189 | − | 0.302374i | \(-0.0977791\pi\) |
−0.738458 | + | 0.674299i | \(0.764446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5000 | − | 25.1147i | 0.776167 | − | 1.34436i | −0.157969 | − | 0.987444i | \(-0.550495\pi\) |
0.934136 | − | 0.356917i | \(-0.116172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.00000 | + | 13.8564i | −0.425797 | + | 0.737502i | −0.996495 | − | 0.0836583i | \(-0.973340\pi\) |
0.570697 | + | 0.821160i | \(0.306673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3923i | 0.550019i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.00000 | −0.105556 | −0.0527780 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527780 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.50000 | − | 4.33013i | −0.393648 | − | 0.227273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | − | 6.92820i | −0.209370 | − | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.0000 | + | 20.7846i | −0.626395 | + | 1.08495i | 0.361874 | + | 0.932227i | \(0.382137\pi\) |
−0.988269 | + | 0.152721i | \(0.951196\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.0000 | −1.40556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.00000 | + | 15.5885i | −0.467257 | + | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.0000 | 1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.5000 | + | 16.4545i | −1.46010 | + | 0.842989i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 10.3923i | 0.305788 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | + | 10.3923i | 0.304997 | + | 0.528271i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.50000 | − | 2.59808i | 0.0760530 | − | 0.131728i | −0.825491 | − | 0.564416i | \(-0.809102\pi\) |
0.901544 | + | 0.432688i | \(0.142435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.00000 | + | 12.1244i | 0.354005 | + | 0.613155i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.0000 | + | 19.0526i | 1.66463 | + | 0.961074i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0000 | 0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.3923i | 0.520266i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.00000 | + | 8.66025i | 0.249688 | + | 0.432472i | 0.963439 | − | 0.267927i | \(-0.0863386\pi\) |
−0.713751 | + | 0.700399i | \(0.753005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | − | 20.7846i | 0.597763 | − | 1.03536i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.50000 | + | 7.79423i | −0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | − | 6.92820i | 0.198273 | − | 0.343418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 27.7128i | − | 1.36697i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.0000 | −0.885722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00000 | 0.343616 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | + | 6.92820i | 0.587643 | + | 0.339276i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | − | 31.1769i | −0.879358 | − | 1.52309i | −0.852047 | − | 0.523465i | \(-0.824639\pi\) |
−0.0273103 | − | 0.999627i | \(-0.508694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | + | 8.66025i | −0.243685 | + | 0.422075i | −0.961761 | − | 0.273890i | \(-0.911690\pi\) |
0.718076 | + | 0.695965i | \(0.245023\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.50000 | − | 7.79423i | −0.218797 | − | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.5000 | + | 33.7750i | 0.943671 | + | 1.63449i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | − | 13.8564i | 1.15873 | − | 0.668994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0000 | −0.481683 | −0.240842 | − | 0.970564i | \(-0.577423\pi\) | ||||
−0.240842 | + | 0.970564i | \(0.577423\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.5000 | + | 7.79423i | −0.647275 | + | 0.373705i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.00000 | + | 12.1244i | 0.334855 | + | 0.579987i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.50000 | + | 11.2583i | −0.308824 | + | 0.534899i | −0.978105 | − | 0.208110i | \(-0.933269\pi\) |
0.669281 | + | 0.743009i | \(0.266602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.500000 | − | 0.866025i | −0.0237023 | − | 0.0410535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.50000 | + | 2.59808i | 0.212843 | + | 0.122885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.0000 | −1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 34.6410i | 1.62758i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | + | 10.3923i | 0.281284 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 10.3923i | − | 0.485071i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.50000 | − | 16.4545i | 0.442459 | − | 0.766362i | −0.555412 | − | 0.831575i | \(-0.687440\pi\) |
0.997871 | + | 0.0652135i | \(0.0207728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | − | 3.46410i | −0.0929479 | − | 0.160990i | 0.815802 | − | 0.578331i | \(-0.196296\pi\) |
−0.908750 | + | 0.417340i | \(0.862962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3923i | 0.481932i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.00000 | 0.415581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.0000 | + | 12.1244i | 0.967629 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | + | 1.73205i | −0.0458831 | + | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | − | 15.5885i | 0.412082 | − | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0000 | − | 22.5167i | 0.593985 | − | 1.02881i | −0.399704 | − | 0.916644i | \(-0.630887\pi\) |
0.993689 | − | 0.112168i | \(-0.0357796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.5000 | + | 18.1865i | −1.43330 | + | 0.827516i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0000 | −0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.0000 | −1.81257 | −0.906287 | − | 0.422664i | \(-0.861095\pi\) | ||||
−0.906287 | + | 0.422664i | \(0.861095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | − | 31.1769i | −0.812329 | − | 1.40699i | −0.911230 | − | 0.411897i | \(-0.864866\pi\) |
0.0989017 | − | 0.995097i | \(-0.468467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | + | 10.3923i | −0.269680 | + | 0.467099i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | − | 27.7128i | −0.716258 | − | 1.24060i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.246214 | − | 0.969216i | \(-0.420813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.50000 | + | 2.59808i | 0.201045 | + | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00000 | 0.312115 | 0.156057 | − | 0.987748i | \(-0.450122\pi\) | ||||
0.156057 | + | 0.987748i | \(0.450122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.19615i | 0.230769i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.50000 | + | 11.2583i | 0.288107 | + | 0.499017i | 0.973358 | − | 0.229291i | \(-0.0736406\pi\) |
−0.685251 | + | 0.728307i | \(0.740307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | + | 20.7846i | −0.530849 | + | 0.919457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 10.3923i | − | 0.458831i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | + | 6.92820i | −0.176261 | + | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.92820i | − | 0.304114i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0000 | −0.920027 | −0.460013 | − | 0.887912i | \(-0.652155\pi\) | ||||
−0.460013 | + | 0.887912i | \(0.652155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.0000 | 1.79280 | 0.896402 | − | 0.443241i | \(-0.146171\pi\) | ||||
0.896402 | + | 0.443241i | \(0.146171\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.50000 | − | 2.59808i | −0.196396 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000 | − | 31.1769i | 0.779667 | − | 1.35042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.50000 | + | 12.9904i | 0.324253 | + | 0.561623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.0000 | − | 20.7846i | 1.55351 | − | 0.896922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.00000 | −0.344584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | −0.128980 | −0.0644900 | − | 0.997918i | \(-0.520542\pi\) | ||||
−0.0644900 | + | 0.997918i | \(0.520542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.5000 | + | 19.9186i | −1.48054 | + | 0.854788i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.50000 | + | 6.06218i | 0.149924 | + | 0.259675i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5000 | − | 19.9186i | 0.491704 | − | 0.851657i | −0.508250 | − | 0.861210i | \(-0.669707\pi\) |
0.999954 | + | 0.00955248i | \(0.00304070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.5000 | − | 33.7750i | −0.832240 | − | 1.44148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0000 | − | 25.9808i | −0.637865 | − | 1.10481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.00000 | − | 1.73205i | −0.127343 | − | 0.0735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 13.8564i | − | 0.585018i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.0000 | 1.13389 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.0000 | + | 32.9090i | −0.796521 | + | 1.37962i | 0.125347 | + | 0.992113i | \(0.459996\pi\) |
−0.921869 | + | 0.387503i | \(0.873338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 17.3205i | − | 0.723575i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.00000 | −0.291920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.0000 | − | 17.3205i | −1.24676 | − | 0.719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5000 | − | 18.1865i | −0.435613 | − | 0.754505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | − | 20.7846i | 0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | − | 10.3923i | −0.248069 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50000 | − | 2.59808i | 0.0619116 | − | 0.107234i | −0.833408 | − | 0.552658i | \(-0.813614\pi\) |
0.895320 | + | 0.445424i | \(0.146947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | − | 10.3923i | −0.247226 | − | 0.428207i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.0000 | + | 17.3205i | −1.23404 | + | 0.712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0000 | + | 12.1244i | −0.859473 | + | 0.496217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.00000 | − | 12.1244i | −0.286012 | − | 0.495388i | 0.686842 | − | 0.726807i | \(-0.258996\pi\) |
−0.972854 | + | 0.231419i | \(0.925663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | + | 8.66025i | −0.203954 | + | 0.353259i | −0.949799 | − | 0.312861i | \(-0.898713\pi\) |
0.745845 | + | 0.666120i | \(0.232046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.50000 | + | 4.33013i | −0.101639 | + | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.50000 | − | 4.33013i | −0.101472 | − | 0.175754i | 0.810819 | − | 0.585296i | \(-0.199022\pi\) |
−0.912291 | + | 0.409542i | \(0.865689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.5000 | + | 23.3827i | 1.64114 | + | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | 0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.5885i | 0.628587i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | − | 10.3923i | −0.241551 | − | 0.418378i | 0.719605 | − | 0.694383i | \(-0.244323\pi\) |
−0.961156 | + | 0.276005i | \(0.910989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | − | 8.66025i | 0.200967 | − | 0.348085i | −0.747873 | − | 0.663842i | \(-0.768925\pi\) |
0.948840 | + | 0.315757i | \(0.102258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.5000 | − | 18.1865i | 1.26405 | − | 0.729800i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.50000 | + | 2.59808i | −0.0600962 | + | 0.104090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 13.8564i | − | 0.553372i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.0000 | + | 17.3205i | 1.19239 | + | 0.688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.50000 | + | 16.4545i | 0.376996 | + | 0.652976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | − | 6.92820i | 0.158486 | − | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.50000 | − | 9.52628i | 0.217237 | − | 0.376265i | −0.736725 | − | 0.676192i | \(-0.763629\pi\) |
0.953962 | + | 0.299927i | \(0.0969622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5000 | − | 28.5788i | −0.650696 | − | 1.12704i | −0.982954 | − | 0.183851i | \(-0.941144\pi\) |
0.332258 | − | 0.943189i | \(-0.392190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | − | 3.46410i | 0.236250 | − | 0.136399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.0000 | −1.37599 | −0.687996 | − | 0.725714i | \(-0.741509\pi\) | ||||
−0.687996 | + | 0.725714i | \(0.741509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.0000 | − | 15.5885i | 1.05821 | − | 0.610960i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.00000 | − | 12.1244i | −0.273931 | − | 0.474463i | 0.695934 | − | 0.718106i | \(-0.254991\pi\) |
−0.969865 | + | 0.243643i | \(0.921657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.0000 | − | 19.0526i | 0.429806 | − | 0.744445i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000 | − | 20.7846i | 0.468165 | − | 0.810885i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.00000 | + | 3.46410i | −0.0779089 | + | 0.134942i | −0.902348 | − | 0.431009i | \(-0.858158\pi\) |
0.824439 | + | 0.565951i | \(0.191491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | − | 19.0526i | −0.427850 | − | 0.741059i | 0.568831 | − | 0.822454i | \(-0.307396\pi\) |
−0.996682 | + | 0.0813955i | \(0.974062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0000 | + | 6.92820i | 0.466041 | + | 0.269069i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | 0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.0000 | 2.43937 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 15.5885i | − | 0.602685i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.0000 | − | 45.0333i | −1.00372 | − | 1.73849i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.0000 | + | 31.1769i | −0.693849 | + | 1.20178i | 0.276718 | + | 0.960951i | \(0.410753\pi\) |
−0.970567 | + | 0.240831i | \(0.922580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.0000 | + | 36.3731i | 0.805906 | + | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.92820i | 0.265489i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.5000 | + | 18.1865i | 1.20180 | + | 0.693860i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0000 | + | 29.4449i | −0.646710 | + | 1.12014i | 0.337193 | + | 0.941435i | \(0.390522\pi\) |
−0.983904 | + | 0.178700i | \(0.942811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 36.0000 | 1.36753 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | − | 6.92820i | 0.151729 | − | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.0000 | + | 15.5885i | −1.02123 | + | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00000 | −0.0377695 | −0.0188847 | − | 0.999822i | \(-0.506012\pi\) | ||||
−0.0188847 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50000 | + | 2.59808i | −0.169480 | + | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.0000 | − | 36.3731i | −0.789786 | − | 1.36795i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5000 | − | 35.5070i | 0.769894 | − | 1.33349i | −0.167727 | − | 0.985834i | \(-0.553643\pi\) |
0.937620 | − | 0.347661i | \(-0.113024\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0000 | − | 36.3731i | 0.786456 | − | 1.36218i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | − | 13.8564i | −0.299183 | − | 0.518200i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | + | 3.46410i | 0.224074 | + | 0.129369i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.00000 | −0.0745874 | −0.0372937 | − | 0.999304i | \(-0.511874\pi\) | ||||
−0.0372937 | + | 0.999304i | \(0.511874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.4449i | 1.09507i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.5000 | − | 19.9186i | 0.426511 | − | 0.738739i | −0.570049 | − | 0.821611i | \(-0.693076\pi\) |
0.996560 | + | 0.0828714i | \(0.0264091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.0000 | − | 29.4449i | −0.627909 | − | 1.08757i | −0.987971 | − | 0.154642i | \(-0.950578\pi\) |
0.360061 | − | 0.932929i | \(-0.382756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.46410i | 0.127775i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0000 | 1.25071 | 0.625355 | − | 0.780340i | \(-0.284954\pi\) | ||||
0.625355 | + | 0.780340i | \(0.284954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | + | 6.92820i | 0.440831 | + | 0.254514i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.5000 | + | 23.3827i | 0.495267 | + | 0.857828i | 0.999985 | − | 0.00545664i | \(-0.00173691\pi\) |
−0.504718 | + | 0.863284i | \(0.668404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5000 | + | 18.1865i | 0.384175 | + | 0.665410i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.5000 | − | 38.9711i | 0.822132 | − | 1.42397i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | − | 6.92820i | −0.145962 | − | 0.252814i | 0.783769 | − | 0.621052i | \(-0.213294\pi\) |
−0.929731 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.0000 | + | 15.5885i | −0.983935 | + | 0.568075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.00000 | −0.290765 | −0.145382 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145382 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 42.0000 | − | 24.2487i | 1.52450 | − | 0.880172i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | + | 18.1865i | 0.380625 | + | 0.659261i | 0.991152 | − | 0.132734i | \(-0.0423756\pi\) |
−0.610527 | + | 0.791995i | \(0.709042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5000 | − | 18.1865i | 0.380126 | − | 0.658397i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | −0.216930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | + | 20.7846i | −0.433295 | + | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5000 | + | 40.7032i | 0.847432 | + | 1.46779i | 0.883493 | + | 0.468445i | \(0.155186\pi\) |
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.0000 | + | 15.5885i | 0.972381 | + | 0.561405i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.0000 | 1.58257 | 0.791285 | − | 0.611448i | \(-0.209412\pi\) | ||||
0.791285 | + | 0.611448i | \(0.209412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.3923i | 0.372822i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.00000 | − | 15.5885i | −0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.5000 | − | 23.3827i | −1.44735 | − | 0.835629i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.00000 | − | 12.1244i | 0.249841 | − | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 13.8564i | − | 0.493301i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0000 | −1.28001 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.0000 | 1.84657 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.00000 | − | 5.19615i | −0.319197 | − | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.0000 | + | 24.2487i | 0.495905 | + | 0.858933i | 0.999989 | − | 0.00472155i | \(-0.00150292\pi\) |
−0.504083 | + | 0.863655i | \(0.668170\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | − | 5.19615i | 0.106132 | − | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.50000 | − | 2.59808i | 0.0529999 | − | 0.0917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.0000 | − | 27.7128i | 0.564628 | − | 0.977964i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5000 | + | 18.1865i | 0.370076 | + | 0.640991i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.50000 | − | 4.33013i | 0.264013 | − | 0.152428i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.0000 | −1.33601 | −0.668004 | − | 0.744157i | \(-0.732851\pi\) | ||||
−0.668004 | + | 0.744157i | \(0.732851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000 | 1.05344 | 0.526721 | − | 0.850038i | \(-0.323421\pi\) | ||||
0.526721 | + | 0.850038i | \(0.323421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.00000 | − | 1.73205i | 0.105215 | − | 0.0607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | + | 6.92820i | −0.139942 | + | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.0000 | + | 31.1769i | −0.628971 | + | 1.08941i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5000 | − | 28.5788i | 0.575854 | − | 0.997408i | −0.420094 | − | 0.907480i | \(-0.638003\pi\) |
0.995948 | − | 0.0899279i | \(-0.0286637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.50000 | − | 16.4545i | −0.331149 | − | 0.573567i | 0.651588 | − | 0.758573i | \(-0.274103\pi\) |
−0.982737 | + | 0.185006i | \(0.940770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.00000 | + | 3.46410i | 0.208893 | + | 0.120605i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0000 | −1.56480 | −0.782402 | − | 0.622774i | \(-0.786006\pi\) | ||||
−0.782402 | + | 0.622774i | \(0.786006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.0000 | 0.729360 | 0.364680 | − | 0.931133i | \(-0.381178\pi\) | ||||
0.364680 | + | 0.931133i | \(0.381178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.1769i | 1.08152i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | − | 3.46410i | −0.0692959 | − | 0.120024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.0000 | + | 15.5885i | −0.933257 | + | 0.538816i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0000 | − | 36.3731i | 0.725001 | − | 1.25574i | −0.233973 | − | 0.972243i | \(-0.575173\pi\) |
0.958974 | − | 0.283495i | \(-0.0914938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 39.8372i | − | 1.37206i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.0000 | 0.515406 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.5000 | − | 19.9186i | −1.18404 | − | 0.683604i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.00000 | + | 12.1244i | 0.239957 | + | 0.415618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.00000 | − | 10.3923i | 0.205436 | − | 0.355826i | −0.744836 | − | 0.667248i | \(-0.767472\pi\) |
0.950272 | + | 0.311422i | \(0.100805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0000 | − | 27.7128i | 0.546550 | − | 0.946652i | −0.451958 | − | 0.892039i | \(-0.649274\pi\) |
0.998508 | − | 0.0546125i | \(-0.0173923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | + | 17.3205i | 0.341196 | + | 0.590968i | 0.984655 | − | 0.174512i | \(-0.0558348\pi\) |
−0.643459 | + | 0.765480i | \(0.722501\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.5000 | − | 23.3827i | 1.38024 | − | 0.796880i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.0000 | 1.19141 | 0.595707 | − | 0.803202i | \(-0.296872\pi\) | ||||
0.595707 | + | 0.803202i | \(0.296872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00000 | −0.136004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.5000 | + | 11.2583i | −0.662255 | + | 0.382353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.0000 | + | 34.6410i | 0.678454 | + | 1.17512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | − | 10.3923i | 0.203302 | − | 0.352130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.0000 | − | 36.3731i | −0.710742 | − | 1.23104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.00000 | + | 1.73205i | 0.101187 | + | 0.0584206i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 10.3923i | − | 0.349334i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00000 | − | 6.92820i | −0.134307 | − | 0.232626i | 0.791026 | − | 0.611783i | \(-0.209547\pi\) |
−0.925332 | + | 0.379157i | \(0.876214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.5000 | − | 49.3634i | 0.955859 | − | 1.65560i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −36.0000 | −1.20605 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.00000 | − | 5.19615i | 0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | − | 20.7846i | −0.401116 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.4974i | 1.61928i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.0000 | −1.80100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.0000 | − | 10.3923i | −0.599002 | − | 0.345834i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.5000 | + | 19.9186i | 0.382273 | + | 0.662116i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5000 | + | 33.7750i | −0.647487 | + | 1.12148i | 0.336234 | + | 0.941778i | \(0.390847\pi\) |
−0.983721 | + | 0.179702i | \(0.942487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.0000 | + | 36.3731i | 0.696526 | + | 1.20642i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0000 | − | 29.4449i | 0.563235 | − | 0.975552i | −0.433976 | − | 0.900924i | \(-0.642890\pi\) |
0.997211 | − | 0.0746276i | \(-0.0237768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0000 | + | 24.2487i | 0.463332 | + | 0.802515i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.5000 | + | 11.2583i | −0.644650 | + | 0.372189i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −66.0000 | −2.17951 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5000 | + | 9.52628i | −0.543693 | + | 0.313902i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | + | 1.73205i | −0.0328798 | + | 0.0569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.0000 | −0.788263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | − | 3.46410i | −0.0655474 | − | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −45.0000 | − | 25.9808i | −1.47323 | − | 0.850572i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.0000 | 0.392023 | 0.196011 | − | 0.980602i | \(-0.437201\pi\) | ||||
0.196011 | + | 0.980602i | \(0.437201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.7128i | 0.904373i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.50000 | + | 6.06218i | 0.114097 | + | 0.197621i | 0.917418 | − | 0.397924i | \(-0.130269\pi\) |
−0.803322 | + | 0.595545i | \(0.796936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.5000 | − | 54.5596i | 1.02578 | − | 1.77671i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 15.5885i | − | 0.507093i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.50000 | − | 14.7224i | 0.276213 | − | 0.478415i | −0.694228 | − | 0.719756i | \(-0.744254\pi\) |
0.970440 | + | 0.241341i | \(0.0775872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.0000 | + | 27.7128i | 0.519382 | + | 0.899596i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0000 | −0.323592 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −54.0000 | − | 31.1769i | −1.74557 | − | 1.00781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.0000 | + | 41.5692i | 0.775000 | + | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.5000 | + | 38.9711i | −0.725052 | + | 1.25583i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | + | 17.3205i | −0.321911 | + | 0.557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.5000 | + | 25.1147i | 0.466289 | + | 0.807635i | 0.999259 | − | 0.0384986i | \(-0.0122575\pi\) |
−0.532970 | + | 0.846134i | \(0.678924\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | − | 3.46410i | 0.192748 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | −0.320915 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | −0.769405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 3.46410i | −0.192154 | + | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.0000 | − | 41.5692i | −0.767828 | − | 1.32992i | −0.938738 | − | 0.344631i | \(-0.888004\pi\) |
0.170910 | − | 0.985287i | \(-0.445329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00000 | − | 3.46410i | 0.0639203 | − | 0.110713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5000 | + | 18.1865i | −0.335239 | + | 0.580651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.5000 | + | 52.8275i | −0.972799 | + | 1.68494i | −0.285784 | + | 0.958294i | \(0.592254\pi\) |
−0.687015 | + | 0.726643i | \(0.741079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | + | 17.3205i | 0.318626 | + | 0.551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.5000 | + | 7.79423i | 0.429710 | + | 0.248093i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.0000 | −1.20711 | −0.603555 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603555 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3923i | 0.329790i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.00000 | + | 12.1244i | 0.221915 | + | 0.384368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(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 | 1440.2.q.e.961.1 | yes | 2 | |
3.2 | odd | 2 | 4320.2.q.g.2881.1 | 2 | |||
4.3 | odd | 2 | 1440.2.q.a.961.1 | yes | 2 | ||
9.4 | even | 3 | inner | 1440.2.q.e.481.1 | yes | 2 | |
9.5 | odd | 6 | 4320.2.q.g.1441.1 | 2 | |||
12.11 | even | 2 | 4320.2.q.h.2881.1 | 2 | |||
36.23 | even | 6 | 4320.2.q.h.1441.1 | 2 | |||
36.31 | odd | 6 | 1440.2.q.a.481.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.q.a.481.1 | ✓ | 2 | 36.31 | odd | 6 | ||
1440.2.q.a.961.1 | yes | 2 | 4.3 | odd | 2 | ||
1440.2.q.e.481.1 | yes | 2 | 9.4 | even | 3 | inner | |
1440.2.q.e.961.1 | yes | 2 | 1.1 | even | 1 | trivial | |
4320.2.q.g.1441.1 | 2 | 9.5 | odd | 6 | |||
4320.2.q.g.2881.1 | 2 | 3.2 | odd | 2 | |||
4320.2.q.h.1441.1 | 2 | 36.23 | even | 6 | |||
4320.2.q.h.2881.1 | 2 | 12.11 | even | 2 |