Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(447,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.447");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 447.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.447 |
Dual form | 896.2.e.a.447.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.73205 | −1.22181 | −0.610905 | − | 0.791704i | \(-0.709194\pi\) | ||||
−0.610905 | + | 0.791704i | \(0.709194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46410 | −0.441443 | −0.220722 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26795 | −0.351666 | −0.175833 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175833 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.00000i | − | 0.516398i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.73205i | − | 1.08561i | −0.839860 | − | 0.542803i | \(-0.817363\pi\) | ||
0.839860 | − | 0.542803i | \(-0.182637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.26795 | − | 1.46410i | −0.276689 | − | 0.319493i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46410i | 0.305286i | 0.988281 | + | 0.152643i | \(0.0487785\pi\) | ||||
−0.988281 | + | 0.152643i | \(0.951221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.46410 | 0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.92820i | − | 1.28654i | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||
0.765641 | − | 0.643268i | \(-0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.07180i | − | 0.186576i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.46410 | − | 4.73205i | 0.923602 | − | 0.799863i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.928203i | − | 0.148631i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.9282i | − | 1.70670i | −0.521340 | − | 0.853349i | \(-0.674568\pi\) | ||
0.521340 | − | 0.853349i | \(-0.325432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.46410 | −1.44326 | −0.721631 | − | 0.692278i | \(-0.756607\pi\) | ||||
−0.721631 | + | 0.692278i | \(0.756607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.73205 | −1.00355 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.92820 | 0.410030 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.92820i | − | 0.951662i | −0.879537 | − | 0.475831i | \(-0.842147\pi\) | ||
0.879537 | − | 0.475831i | \(-0.157853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410 | 0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1962i | 1.84818i | 0.382173 | + | 0.924091i | \(0.375176\pi\) | ||||
−0.382173 | + | 0.924091i | \(0.624824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.66025 | −0.724721 | −0.362361 | − | 0.932038i | \(-0.618029\pi\) | ||||
−0.362361 | + | 0.932038i | \(0.618029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.92820 | + | 4.26795i | −0.620895 | + | 0.537711i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.46410 | 1.15622 | 0.578112 | − | 0.815957i | \(-0.303790\pi\) | ||||
0.578112 | + | 0.815957i | \(0.303790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.07180 | −0.129029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.4641i | − | 1.36054i | −0.732962 | − | 0.680269i | \(-0.761863\pi\) | ||
0.732962 | − | 0.680269i | \(-0.238137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.80385i | 0.208290i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.92820 | − | 2.53590i | 0.333700 | − | 0.288992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.26795i | − | 0.797761i | −0.917003 | − | 0.398881i | \(-0.869399\pi\) | ||
0.917003 | − | 0.398881i | \(-0.130601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.9282i | 1.18533i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.07180 | 0.543754 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.07180i | − | 0.113610i | −0.998385 | − | 0.0568051i | \(-0.981909\pi\) | ||
0.998385 | − | 0.0568051i | \(-0.0180914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.53590 | − | 2.19615i | 0.265834 | − | 0.230219i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.07180i | 0.525921i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9282i | 1.32641i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.60770 | −0.362587 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.19615 | −0.417533 | −0.208766 | − | 0.977966i | \(-0.566945\pi\) | ||||
−0.208766 | + | 0.977966i | \(0.566945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.07180 | −0.499739 | −0.249869 | − | 0.968280i | \(-0.580388\pi\) | ||||
−0.249869 | + | 0.968280i | \(0.580388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.46410 | + | 4.00000i | 0.338062 | + | 0.390360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.3923 | −1.19801 | −0.599005 | − | 0.800746i | \(-0.704437\pi\) | ||||
−0.599005 | + | 0.800746i | \(0.704437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.92820i | 0.663602i | 0.943349 | + | 0.331801i | \(0.107656\pi\) | ||||
−0.943349 | + | 0.331801i | \(0.892344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.92820 | 0.277933 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.53590 | −0.238557 | −0.119279 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119279 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.00000i | − | 0.373002i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12436 | −0.288847 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | + | 8.00000i | 0.635107 | + | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.00000 | 0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.5359i | − | 1.28985i | −0.764245 | − | 0.644926i | \(-0.776888\pi\) | ||
0.764245 | − | 0.644926i | \(-0.223112\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.92820i | − | 0.609994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.26795i | − | 0.635004i | −0.948258 | − | 0.317502i | \(-0.897156\pi\) | ||
0.948258 | − | 0.317502i | \(-0.102844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.19615 | + | 9.46410i | 0.710697 | + | 0.820642i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 10.9282i | − | 0.940550i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.85641 | −0.671218 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.19615i | 0.525551i | 0.964857 | + | 0.262775i | \(0.0846378\pi\) | ||||
−0.964857 | + | 0.262775i | \(0.915362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.07180i | − | 0.427122i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.85641 | 0.155241 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.9282i | 1.57190i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.07180 | + | 0.732051i | 0.418315 | + | 0.0603785i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.0000i | − | 0.983078i | −0.870855 | − | 0.491539i | \(-0.836434\pi\) | ||
0.870855 | − | 0.491539i | \(-0.163566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.3205i | 1.89780i | 0.315583 | + | 0.948898i | \(0.397800\pi\) | ||||
−0.315583 | + | 0.948898i | \(0.602200\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 9.85641i | − | 0.796843i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.9282 | −1.52035 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7321 | 1.81422 | 0.907108 | − | 0.420899i | \(-0.138285\pi\) | ||||
0.907108 | + | 0.420899i | \(0.138285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.07180 | 0.402220 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53590 | − | 2.92820i | −0.199857 | − | 0.230775i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.39230 | −0.344032 | −0.172016 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172016 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.92820i | 0.227960i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3923 | −0.876331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 11.6603i | − | 0.891682i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.73205 | 0.511828 | 0.255914 | − | 0.966700i | \(-0.417624\pi\) | ||||
0.255914 | + | 0.966700i | \(0.417624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.92820 | + | 4.26795i | −0.372537 | + | 0.322627i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3923 | −0.781133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3923 | 1.52419 | 0.762096 | − | 0.647464i | \(-0.224170\pi\) | ||||
0.762096 | + | 0.647464i | \(0.224170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2679 | 0.986199 | 0.493099 | − | 0.869973i | \(-0.335864\pi\) | ||||
0.493099 | + | 0.869973i | \(0.335864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.14359i | − | 0.306303i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9282i | 0.803457i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.85641i | 0.428263i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.92820 | − | 8.00000i | −0.503953 | − | 0.581914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.53590i | − | 0.328206i | −0.986443 | − | 0.164103i | \(-0.947527\pi\) | ||
0.986443 | − | 0.164103i | \(-0.0524730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3923 | −1.17994 | −0.589972 | − | 0.807424i | \(-0.700861\pi\) | ||||
−0.589972 | + | 0.807424i | \(0.700861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.53590i | 0.181599i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.92820i | 0.488678i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000 | + | 13.8564i | 0.842235 | + | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.8564i | 2.08526i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.60770i | 0.250752i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820i | 0.479234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.3923 | −1.95461 | −0.977303 | − | 0.211844i | \(-0.932053\pi\) | ||||
−0.977303 | + | 0.211844i | \(0.932053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.39230 | 0.575031 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.8564 | 1.76339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8564 | + | 12.0000i | −0.940634 | + | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.07180 | −0.342720 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.07180i | 0.341166i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.07180 | 0.404786 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 4.73205i | − | 0.314077i | −0.987592 | − | 0.157039i | \(-0.949805\pi\) | ||
0.987592 | − | 0.157039i | \(-0.0501947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6603 | 1.16702 | 0.583511 | − | 0.812105i | \(-0.301678\pi\) | ||||
0.583511 | + | 0.812105i | \(0.301678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.85641 | + | 2.14359i | 0.122143 | + | 0.141038i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.9282 | 1.23474 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.53590 | 0.164724 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.3923i | − | 1.31907i | −0.751674 | − | 0.659534i | \(-0.770754\pi\) | ||
0.751674 | − | 0.659534i | \(-0.229246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000i | 0.772988i | 0.922292 | + | 0.386494i | \(0.126314\pi\) | ||||
−0.922292 | + | 0.386494i | \(0.873686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.73205 | + | 18.9282i | −0.174544 | + | 1.20928i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.32051 | 0.337173 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.0526i | − | 1.01323i | −0.862173 | − | 0.506614i | \(-0.830897\pi\) | ||
0.862173 | − | 0.506614i | \(-0.169103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.14359i | − | 0.134767i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.85641i | − | 0.365313i | −0.983177 | − | 0.182656i | \(-0.941530\pi\) | ||
0.983177 | − | 0.182656i | \(-0.0584696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820 | + | 8.00000i | 0.430498 | + | 0.497096i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 17.0718i | − | 1.05672i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.53590i | 0.279695i | 0.990173 | + | 0.139848i | \(0.0446613\pi\) | ||||
−0.990173 | + | 0.139848i | \(0.955339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.9282i | 1.16275i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.784610 | 0.0480173 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.1244 | −1.40992 | −0.704958 | − | 0.709249i | \(-0.749034\pi\) | ||||
−0.704958 | + | 0.709249i | \(0.749034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.60770 | + | 1.85641i | 0.0973021 | + | 0.112355i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.60770 | −0.217552 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7846i | 0.768153i | 0.923301 | + | 0.384076i | \(0.125480\pi\) | ||||
−0.923301 | + | 0.384076i | \(0.874520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.0718 | 1.02206 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 26.1962i | − | 1.55720i | −0.627521 | − | 0.778600i | \(-0.715930\pi\) | ||
0.627521 | − | 0.778600i | \(-0.284070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.46410 | −0.560605 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9282 | + | 21.8564i | 1.11730 | + | 1.29014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.78461 | −0.514963 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.1962 | −0.712507 | −0.356253 | − | 0.934389i | \(-0.615946\pi\) | ||||
−0.356253 | + | 0.934389i | \(0.615946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 38.7846i | − | 2.25813i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.85641i | − | 0.339823i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.85641i | − | 0.107359i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.9282 | − | 16.3923i | 1.09100 | − | 0.944837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.07180i | − | 0.176470i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.4641 | 0.885472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7321i | 0.954949i | 0.878646 | + | 0.477474i | \(0.158448\pi\) | ||||
−0.878646 | + | 0.477474i | \(0.841552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.71281i | − | 0.211215i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.85641 | −0.105267 | −0.0526336 | − | 0.998614i | \(-0.516762\pi\) | ||||
−0.0526336 | + | 0.998614i | \(0.516762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.78461i | − | 0.496535i | −0.968691 | − | 0.248268i | \(-0.920139\pi\) | ||
0.968691 | − | 0.248268i | \(-0.0798613\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.4641 | − | 11.6603i | 0.758616 | − | 0.656981i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.8564i | 1.45224i | 0.687568 | + | 0.726120i | \(0.258678\pi\) | ||||
−0.687568 | + | 0.726120i | \(0.741322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.1436i | 0.567932i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 9.07180i | − | 0.506338i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.9282 | −1.05319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.12436 | −0.173308 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.07180 | −0.280471 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.8564 | − | 12.0000i | 0.763928 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3205 | 1.28181 | 0.640906 | − | 0.767620i | \(-0.278559\pi\) | ||||
0.640906 | + | 0.767620i | \(0.278559\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.85641i | − | 0.540128i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.8564 | −1.41269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.3923 | −1.32873 | −0.664367 | − | 0.747407i | \(-0.731299\pi\) | ||||
−0.664367 | + | 0.747407i | \(0.731299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.85641i | − | 0.100826i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.1436 | −0.549306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.92820 | 0.157649 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.53590 | 0.350865 | 0.175433 | − | 0.984491i | \(-0.443868\pi\) | ||||
0.175433 | + | 0.984491i | \(0.443868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.66025 | −0.302986 | −0.151493 | − | 0.988458i | \(-0.548408\pi\) | ||||
−0.151493 | + | 0.988458i | \(0.548408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.07180i | − | 0.270712i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.14359i | − | 0.114092i | −0.998372 | − | 0.0570460i | \(-0.981832\pi\) | ||
0.998372 | − | 0.0570460i | \(-0.0181682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.3205i | 1.66232i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.85641 | + | 5.07180i | −0.309954 | + | 0.268428i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.3923i | − | 1.07626i | −0.842860 | − | 0.538132i | \(-0.819130\pi\) | ||
0.842860 | − | 0.538132i | \(-0.180870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39230 | −0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.48334i | − | 0.340287i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 18.9282i | − | 0.990747i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 26.9282i | − | 1.40183i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 13.8564i | 0.623009 | + | 0.719389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.9282i | − | 1.60140i | −0.599064 | − | 0.800701i | \(-0.704461\pi\) | ||
0.599064 | − | 0.800701i | \(-0.295539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.07180i | 0.261906i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.78461i | 0.452430i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5359 | −0.746659 | −0.373329 | − | 0.927699i | \(-0.621784\pi\) | ||||
−0.373329 | + | 0.927699i | \(0.621784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.6410 | 0.545156 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.92820 | −0.354015 | −0.177007 | − | 0.984210i | \(-0.556642\pi\) | ||||
−0.177007 | + | 0.984210i | \(0.556642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 6.92820i | −0.407718 | + | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.3205 | −1.18545 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 25.8564i | − | 1.31097i | −0.755207 | − | 0.655486i | \(-0.772464\pi\) | ||
0.755207 | − | 0.655486i | \(-0.227536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.85641 | 0.296171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.32051 | 0.268384 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.46410i | 0.476191i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.9090 | 1.80222 | 0.901110 | − | 0.433591i | \(-0.142754\pi\) | ||||
0.901110 | + | 0.433591i | \(0.142754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | + | 6.00000i | −0.346844 | + | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3205 | 0.565319 | 0.282660 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282660 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.78461 | −0.437593 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.1962 | −0.606032 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.85641i | 0.290291i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.9282i | − | 0.935939i | −0.883745 | − | 0.467970i | \(-0.844986\pi\) | ||
0.883745 | − | 0.467970i | \(-0.155014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.75129i | − | 0.283690i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.5885 | − | 28.3923i | −1.20992 | − | 1.39709i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8564i | 0.974713i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.53590 | −0.222124 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 21.1244i | − | 1.03199i | −0.856591 | − | 0.515996i | \(-0.827422\pi\) | ||
0.856591 | − | 0.515996i | \(-0.172578\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000i | 0.974740i | 0.873195 | + | 0.487370i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.0718 | −0.830059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9.85641i | − | 0.478106i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3205 | − | 9.80385i | 0.547838 | − | 0.474441i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.35898i | 0.0656124i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.46410i | 0.0705233i | 0.999378 | + | 0.0352616i | \(0.0112265\pi\) | ||||
−0.999378 | + | 0.0352616i | \(0.988774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.8564i | − | 1.24258i | −0.783581 | − | 0.621290i | \(-0.786609\pi\) | ||
0.783581 | − | 0.621290i | \(-0.213391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.8564 | −0.664364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.92820 | 0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | 0.190910 | 0.0954548 | − | 0.995434i | \(-0.469569\pi\) | ||||
0.0954548 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.46410 | − | 17.0718i | 0.117338 | − | 0.812943i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.46410 | 0.0695616 | 0.0347808 | − | 0.999395i | \(-0.488927\pi\) | ||||
0.0347808 | + | 0.999395i | \(0.488927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.92820i | 0.138810i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.78461 | 0.415498 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.8564 | 1.50340 | 0.751698 | − | 0.659507i | \(-0.229235\pi\) | ||||
0.751698 | + | 0.659507i | \(0.229235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000i | 0.753411i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.0718 | −0.802103 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.92820 | + | 6.00000i | −0.324799 | + | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.39230 | −0.392575 | −0.196288 | − | 0.980546i | \(-0.562889\pi\) | ||||
−0.196288 | + | 0.980546i | \(0.562889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.0000 | 0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.5167 | −1.28158 | −0.640789 | − | 0.767717i | \(-0.721393\pi\) | ||||
−0.640789 | + | 0.767717i | \(0.721393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.5359i | − | 0.954384i | −0.878799 | − | 0.477192i | \(-0.841655\pi\) | ||
0.878799 | − | 0.477192i | \(-0.158345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 13.8564i | − | 0.642575i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.5885i | − | 0.860171i | −0.902788 | − | 0.430086i | \(-0.858483\pi\) | ||
0.902788 | − | 0.430086i | \(-0.141517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.9282 | + | 16.3923i | −0.874023 | + | 0.756926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.6410i | 0.766778i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.8564 | 0.637118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 11.6603i | − | 0.535009i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 17.0718i | − | 0.781664i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.9282 | 1.41315 | 0.706573 | − | 0.707640i | \(-0.250240\pi\) | ||||
0.706573 | + | 0.707640i | \(0.250240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.07180i | 0.231254i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.14359 | − | 1.85641i | 0.0975369 | − | 0.0844694i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 32.7846i | − | 1.48867i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.39230i | − | 0.199034i | −0.995036 | − | 0.0995172i | \(-0.968270\pi\) | ||
0.995036 | − | 0.0995172i | \(-0.0317298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.21539i | − | 0.145405i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3205 | −0.691405 | −0.345702 | − | 0.938344i | \(-0.612359\pi\) | ||||
−0.345702 | + | 0.938344i | \(0.612359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.7128 | −1.24812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.85641 | 0.443013 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.8564 | + | 22.9282i | 0.890682 | + | 1.02847i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.39230 | −0.196627 | −0.0983133 | − | 0.995156i | \(-0.531345\pi\) | ||||
−0.0983133 | + | 0.995156i | \(0.531345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 13.8564i | − | 0.619059i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4641 | 0.510146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 8.33975i | − | 0.370381i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.8038 | −1.40968 | −0.704840 | − | 0.709366i | \(-0.748981\pi\) | ||||
−0.704840 | + | 0.709366i | \(0.748981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 13.8564i | −0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9282 | 0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8564 | 0.610586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1436 | 0.446115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.92820i | 0.216324i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.9282i | − | 1.17975i | −0.807496 | − | 0.589873i | \(-0.799178\pi\) | ||
0.807496 | − | 0.589873i | \(-0.200822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 43.3731i | − | 1.89657i | −0.317417 | − | 0.948286i | \(-0.602816\pi\) | ||
0.317417 | − | 0.948286i | \(-0.397184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.12436 | − | 3.60770i | −0.136358 | − | 0.157453i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.9808i | 1.51804i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8564i | 0.600188i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.8564 | 1.46374 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.9282i | 0.644200i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.46410 | + | 10.1436i | −0.0630633 | + | 0.436916i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0000i | 1.20381i | 0.798566 | + | 0.601907i | \(0.205592\pi\) | ||||
−0.798566 | + | 0.601907i | \(0.794408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.71281i | 0.416817i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.9282i | − | 0.810795i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5359 | −0.621510 | −0.310755 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310755 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.9474 | −0.595262 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.7846 | −1.39667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | + | 6.92820i | 0.255146 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | −0.339581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0718i | 0.723355i | 0.932303 | + | 0.361678i | \(0.117796\pi\) | ||||
−0.932303 | + | 0.361678i | \(0.882204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.28719 | −0.181005 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9808i | 0.968524i | 0.874923 | + | 0.484262i | \(0.160912\pi\) | ||||
−0.874923 | + | 0.484262i | \(0.839088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.92820 | 0.291472 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.92820 | + | 7.73205i | −0.374949 | + | 0.324716i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.60770 | 0.318931 | 0.159466 | − | 0.987203i | \(-0.449023\pi\) | ||||
0.159466 | + | 0.987203i | \(0.449023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2487 | 0.763685 | 0.381842 | − | 0.924227i | \(-0.375290\pi\) | ||||
0.381842 | + | 0.924227i | \(0.375290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.32051 | 0.138716 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.60770i | 0.150451i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.8564i | 1.57598i | 0.615686 | + | 0.787991i | \(0.288879\pi\) | ||||
−0.615686 | + | 0.787991i | \(0.711121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.5885 | + | 14.5359i | 0.522257 | + | 0.603051i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1436i | 0.420105i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.53590 | 0.352916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.1962i | 0.585938i | 0.956122 | + | 0.292969i | \(0.0946433\pi\) | ||||
−0.956122 | + | 0.292969i | \(0.905357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 32.7846i | − | 1.35087i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.78461 | −0.361351 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.7128i | − | 1.46655i | −0.679932 | − | 0.733275i | \(-0.737991\pi\) | ||
0.679932 | − | 0.733275i | \(-0.262009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.9282 | − | 21.8564i | −0.775981 | − | 0.896025i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 18.1436i | − | 0.742568i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4641i | 0.795282i | 0.917541 | + | 0.397641i | \(0.130171\pi\) | ||||
−0.917541 | + | 0.397641i | \(0.869829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6410i | 1.41304i | 0.707695 | + | 0.706518i | \(0.249735\pi\) | ||||
−0.707695 | + | 0.706518i | \(0.750265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.3205 | 0.949685 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.1962 | 0.983713 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1436 | + | 8.78461i | −0.411039 | + | 0.355970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.78461 | 0.355387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.85641i | − | 0.0749796i | −0.999297 | − | 0.0374898i | \(-0.988064\pi\) | ||
0.999297 | − | 0.0374898i | \(-0.0119362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.8564 | −0.881335 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3923 | −0.659929 | −0.329965 | − | 0.943993i | \(-0.607037\pi\) | ||||
−0.329965 | + | 0.943993i | \(0.607037\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8038i | 0.554823i | 0.960751 | + | 0.277412i | \(0.0894766\pi\) | ||||
−0.960751 | + | 0.277412i | \(0.910523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.85641 | −0.235009 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.85641 | + | 2.14359i | 0.0743754 | + | 0.0858813i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.07180 | −0.202548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.2487i | − | 0.965326i | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 20.7846i | − | 0.826114i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.7128i | 1.57595i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.26795 | + | 8.78461i | −0.0502380 | + | 0.348059i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 28.2487i | − | 1.11750i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5359 | −1.04810 | −0.524052 | − | 0.851686i | \(-0.675580\pi\) | ||||
−0.524052 | + | 0.851686i | \(0.675580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2679i | 0.759854i | 0.925017 | + | 0.379927i | \(0.124051\pi\) | ||||
−0.925017 | + | 0.379927i | \(0.875949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.9282i | 0.745297i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.6410 | 1.83365 | 0.916824 | − | 0.399292i | \(-0.130744\pi\) | ||||
0.916824 | + | 0.399292i | \(0.130744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.7846i | − | 0.815867i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.78461 | − | 10.1436i | −0.344296 | − | 0.397559i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000i | 0.469596i | 0.972044 | + | 0.234798i | \(0.0754429\pi\) | ||||
−0.972044 | + | 0.234798i | \(0.924557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.8564i | 0.775854i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.0718i | 0.666034i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.1051 | 1.56227 | 0.781137 | − | 0.624360i | \(-0.214640\pi\) | ||||
0.781137 | + | 0.624360i | \(0.214640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.80385 | 0.147953 | 0.0739763 | − | 0.997260i | \(-0.476431\pi\) | ||||
0.0739763 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.71281 | −0.144194 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.3923 | − | 25.8564i | −0.868336 | − | 1.00267i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1436 | 0.392762 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.85641i | 0.226422i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.28719 | 0.319923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.85641i | 0.379373i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.1244 | 1.65740 | 0.828702 | − | 0.559690i | \(-0.189080\pi\) | ||||
0.828702 | + | 0.559690i | \(0.189080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.7846 | − | 24.0000i | −0.797640 | − | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.46410 | 0.132745 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5359 | −0.862312 | −0.431156 | − | 0.902277i | \(-0.641894\pi\) | ||||
−0.431156 | + | 0.902277i | \(0.641894\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.4641 | 0.820101 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.9282i | 0.493242i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.78461i | 0.334667i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.9808i | − | 0.722062i | −0.932554 | − | 0.361031i | \(-0.882425\pi\) | ||
0.932554 | − | 0.361031i | \(-0.117575\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.21539 | − | 6.24871i | 0.274090 | − | 0.237369i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 16.9282i | − | 0.642123i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.7128 | −1.65574 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.75129i | 0.217534i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.8564i | − | 0.976583i | −0.872681 | − | 0.488291i | \(-0.837620\pi\) | ||
0.872681 | − | 0.488291i | \(-0.162380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9282 | −0.713891 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8564i | 0.521862i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.39230 | − | 7.26795i | 0.315625 | − | 0.273339i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 17.0718i | − | 0.641145i | −0.947224 | − | 0.320572i | \(-0.896125\pi\) | ||
0.947224 | − | 0.320572i | \(-0.103875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.53590i | − | 0.320121i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1436i | 0.379881i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.07180 | −0.189674 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.9282 | 0.557504 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9282 | −1.15343 | −0.576714 | − | 0.816946i | \(-0.695665\pi\) | ||||
−0.576714 | + | 0.816946i | \(0.695665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1436 | − | 8.78461i | 0.377767 | − | 0.327156i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.78461 | −0.326703 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 17.0718i | − | 0.634031i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.7846 | 1.21591 | 0.607957 | − | 0.793970i | \(-0.291989\pi\) | ||||
0.607957 | + | 0.793970i | \(0.291989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.8564i | 1.40017i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.19615 | 0.302732 | 0.151366 | − | 0.988478i | \(-0.451633\pi\) | ||||
0.151366 | + | 0.988478i | \(0.451633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.8564 | − | 2.00000i | −0.511101 | − | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.8564 | −0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3205 | 0.857859 | 0.428929 | − | 0.903338i | \(-0.358891\pi\) | ||||
0.428929 | + | 0.903338i | \(0.358891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.39230 | −0.161355 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.4641i | 0.640696i | 0.947300 | + | 0.320348i | \(0.103800\pi\) | ||||
−0.947300 | + | 0.320348i | \(0.896200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.7846i | 1.20114i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 17.9090i | − | 0.655255i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.7846 | − | 21.4641i | 0.905610 | − | 0.784281i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.4641i | 1.22112i | 0.791969 | + | 0.610561i | \(0.209056\pi\) | ||||
−0.791969 | + | 0.610561i | \(0.790944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7513 | 0.428241 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 63.7128i | − | 2.31875i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.5692i | 1.94701i | 0.228673 | + | 0.973503i | \(0.426561\pi\) | ||||
−0.228673 | + | 0.973503i | \(0.573439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.56922 | 0.0569591 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.7846i | 0.898441i | 0.893421 | + | 0.449221i | \(0.148298\pi\) | ||||
−0.893421 | + | 0.449221i | \(0.851702\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.0000 | − | 13.8564i | −0.434429 | − | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.9282i | 0.973591i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.0000i | − | 0.649942i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.8564i | − | 0.932406i | −0.884678 | − | 0.466203i | \(-0.845622\pi\) | ||
0.884678 | − | 0.466203i | \(-0.154378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.28719 | 0.154399 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.4449 | −0.807286 | −0.403643 | − | 0.914917i | \(-0.632256\pi\) | ||||
−0.403643 | + | 0.914917i | \(0.632256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0718 | 0.613237 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.85641 | + | 5.07180i | −0.210097 | + | 0.181950i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.7128 | −1.85280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7846i | 0.600601i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.7128 | 0.990375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.1051 | −2.21663 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 10.5885i | − | 0.377438i | −0.982031 | − | 0.188719i | \(-0.939567\pi\) | ||
0.982031 | − | 0.188719i | \(-0.0604335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.32051 | −0.118213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.07180 | − | 4.39230i | 0.180332 | − | 0.156172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.17691 | 0.254860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.8564 | −0.491436 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.8756 | 0.597766 | 0.298883 | − | 0.954290i | \(-0.403386\pi\) | ||||
0.298883 | + | 0.954290i | \(0.403386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7128i | 0.980409i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.64102i | − | 0.0933157i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 10.1436i | − | 0.357960i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.92820 | + | 8.00000i | 0.244187 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 16.9282i | − | 0.595901i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.1769 | 0.885173 | 0.442587 | − | 0.896726i | \(-0.354061\pi\) | ||||
0.442587 | + | 0.896726i | \(0.354061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3731i | 0.820739i | 0.911919 | + | 0.410370i | \(0.134600\pi\) | ||||
−0.911919 | + | 0.410370i | \(0.865400\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.7846i | 1.56682i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.24871 | − | 5.41154i | 0.218348 | − | 0.189095i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820i | 0.241796i | 0.992665 | + | 0.120898i | \(0.0385774\pi\) | ||||
−0.992665 | + | 0.120898i | \(0.961423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.4641i | − | 0.957338i | −0.877995 | − | 0.478669i | \(-0.841119\pi\) | ||
0.877995 | − | 0.478669i | \(-0.158881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.64102i | − | 0.0919484i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.67949 | 0.301816 | 0.150908 | − | 0.988548i | \(-0.451780\pi\) | ||||
0.150908 | + | 0.988548i | \(0.451780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.19615 | 0.284664 | 0.142332 | − | 0.989819i | \(-0.454540\pi\) | ||||
0.142332 | + | 0.989819i | \(0.454540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.35898 | −0.324660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7128 | − | 4.00000i | −0.960192 | − | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.7128 | 1.78960 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7128i | 0.957895i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.9282 | 0.653474 | 0.326737 | − | 0.945115i | \(-0.394051\pi\) | ||||
0.326737 | + | 0.945115i | \(0.394051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.39230i | 0.151279i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1244 | 1.07071 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7128 | − | 15.3397i | 0.608619 | − | 0.527080i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.1769 | 0.658150 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.85641 | 0.200755 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3731 | 0.731800 | 0.365900 | − | 0.930654i | \(-0.380761\pi\) | ||||
0.365900 | + | 0.930654i | \(0.380761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.8564i | 1.08947i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.9282i | 1.19312i | 0.802567 | + | 0.596562i | \(0.203467\pi\) | ||||
−0.802567 | + | 0.596562i | \(0.796533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5167i | 0.870617i | 0.900281 | + | 0.435309i | \(0.143361\pi\) | ||||
−0.900281 | + | 0.435309i | \(0.856639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | + | 13.8564i | −0.545279 | + | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1769i | 0.788951i | 0.918906 | + | 0.394476i | \(0.129074\pi\) | ||||
−0.918906 | + | 0.394476i | \(0.870926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3923 | −0.625357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.732051i | 0.0248617i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.07180i | 0.172049i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.5692i | 1.00077i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.8564 | + | 12.0000i | −0.468432 | + | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.5692i | 1.80890i | 0.426575 | + | 0.904452i | \(0.359720\pi\) | ||||
−0.426575 | + | 0.904452i | \(0.640280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 8.92820i | − | 0.301141i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7128i | 0.664142i | 0.943254 | + | 0.332071i | \(0.107747\pi\) | ||||
−0.943254 | + | 0.332071i | \(0.892253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.46410 | −0.318492 | −0.159246 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159246 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.3923 | 0.954397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.9282 | −1.44139 | −0.720694 | − | 0.693253i | \(-0.756177\pi\) | ||||
−0.720694 | + | 0.693253i | \(0.756177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.1769 | + | 29.0718i | 0.844407 | + | 0.975037i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.53590 | −0.218961 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.7846i | 1.09710i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.7128 | −1.86227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.35898 | 0.0453751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 48.0000i | − | 1.60089i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.7128 | −0.923248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000 | + | 13.8564i | 0.399335 | + | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.2487 | −1.20495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.1051 | −1.06603 | −0.533016 | − | 0.846105i | \(-0.678942\pi\) | ||||
−0.533016 | + | 0.846105i | \(0.678942\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3397 | −0.342948 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6077i | 0.384580i | 0.981338 | + | 0.192290i | \(0.0615914\pi\) | ||||
−0.981338 | + | 0.192290i | \(0.938409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6410i | 0.352166i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.3205i | 0.374244i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.5885 | + | 14.5359i | 0.415707 | + | 0.480018i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5359i | 0.677417i | 0.940891 | + | 0.338708i | \(0.109990\pi\) | ||||
−0.940891 | + | 0.338708i | \(0.890010\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.2487 | −0.403609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5359i | 0.478455i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.85641i | − | 0.324077i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4974 | −0.410469 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000i | 0.131236i | 0.997845 | + | 0.0656179i | \(0.0209018\pi\) | ||||
−0.997845 | + | 0.0656179i | \(0.979098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.7846 | − | 4.73205i | −1.07447 | − | 0.155087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.35898i | − | 0.0444911i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.0000i | − | 0.523256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0718i | 0.557711i | 0.960333 | + | 0.278856i | \(0.0899551\pi\) | ||||
−0.960333 | + | 0.278856i | \(0.910045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.43078 | 0.209861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.12436 | −0.232247 | −0.116124 | − | 0.993235i | \(-0.537047\pi\) | ||||
−0.116124 | + | 0.993235i | \(0.537047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.9282 | + | 21.8564i | 0.615734 | + | 0.710989i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.53590 | 0.212388 | 0.106194 | − | 0.994345i | \(-0.466134\pi\) | ||||
0.106194 | + | 0.994345i | \(0.466134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.78461i | − | 0.285160i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.9282 | −0.613789 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7128 | 0.703347 | 0.351674 | − | 0.936123i | \(-0.385613\pi\) | ||||
0.351674 | + | 0.936123i | \(0.385613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3923i | 0.401006i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.42563 | −0.240036 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.7128 | − | 13.6077i | 0.507393 | − | 0.439415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.5359 | −0.984006 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.7846 | 1.44167 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3205i | 0.749937i | 0.927038 | + | 0.374968i | \(0.122346\pi\) | ||||
−0.927038 | + | 0.374968i | \(0.877654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13.8564i | − | 0.445132i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.4833i | 0.336426i | 0.985751 | + | 0.168213i | \(0.0537997\pi\) | ||||
−0.985751 | + | 0.168213i | \(0.946200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7321 | − | 12.3923i | −0.344054 | − | 0.397279i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2.28719i | − | 0.0732486i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.14359 | 0.132565 | 0.0662827 | − | 0.997801i | \(-0.478886\pi\) | ||||
0.0662827 | + | 0.997801i | \(0.478886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.56922i | 0.0501525i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0718i | 0.545061i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9282 | −0.603716 | −0.301858 | − | 0.953353i | \(-0.597607\pi\) | ||||
−0.301858 | + | 0.953353i | \(0.597607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 32.7846i | − | 1.04460i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.78461 | + | 10.1436i | 0.279617 | + | 0.322874i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.8564i | − | 0.440608i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.1769i | − | 0.990367i | −0.868788 | − | 0.495184i | \(-0.835101\pi\) | ||
0.868788 | − | 0.495184i | \(-0.164899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0718i | 0.541757i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.7128 | 2.14664 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.1244 | 0.859037 | 0.429518 | − | 0.903058i | \(-0.358683\pi\) | ||||
0.429518 | + | 0.903058i | \(0.358683\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 896.2.e.a.447.3 | yes | 4 | |
4.3 | odd | 2 | 896.2.e.b.447.2 | yes | 4 | ||
7.6 | odd | 2 | 896.2.e.f.447.2 | yes | 4 | ||
8.3 | odd | 2 | 896.2.e.f.447.3 | yes | 4 | ||
8.5 | even | 2 | 896.2.e.e.447.2 | yes | 4 | ||
16.3 | odd | 4 | 1792.2.f.a.1791.4 | 4 | |||
16.5 | even | 4 | 1792.2.f.b.1791.3 | 4 | |||
16.11 | odd | 4 | 1792.2.f.h.1791.1 | 4 | |||
16.13 | even | 4 | 1792.2.f.i.1791.2 | 4 | |||
28.27 | even | 2 | 896.2.e.e.447.3 | yes | 4 | ||
56.13 | odd | 2 | 896.2.e.b.447.3 | yes | 4 | ||
56.27 | even | 2 | inner | 896.2.e.a.447.2 | ✓ | 4 | |
112.13 | odd | 4 | 1792.2.f.a.1791.3 | 4 | |||
112.27 | even | 4 | 1792.2.f.b.1791.4 | 4 | |||
112.69 | odd | 4 | 1792.2.f.h.1791.2 | 4 | |||
112.83 | even | 4 | 1792.2.f.i.1791.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.e.a.447.2 | ✓ | 4 | 56.27 | even | 2 | inner | |
896.2.e.a.447.3 | yes | 4 | 1.1 | even | 1 | trivial | |
896.2.e.b.447.2 | yes | 4 | 4.3 | odd | 2 | ||
896.2.e.b.447.3 | yes | 4 | 56.13 | odd | 2 | ||
896.2.e.e.447.2 | yes | 4 | 8.5 | even | 2 | ||
896.2.e.e.447.3 | yes | 4 | 28.27 | even | 2 | ||
896.2.e.f.447.2 | yes | 4 | 7.6 | odd | 2 | ||
896.2.e.f.447.3 | yes | 4 | 8.3 | odd | 2 | ||
1792.2.f.a.1791.3 | 4 | 112.13 | odd | 4 | |||
1792.2.f.a.1791.4 | 4 | 16.3 | odd | 4 | |||
1792.2.f.b.1791.3 | 4 | 16.5 | even | 4 | |||
1792.2.f.b.1791.4 | 4 | 112.27 | even | 4 | |||
1792.2.f.h.1791.1 | 4 | 16.11 | odd | 4 | |||
1792.2.f.h.1791.2 | 4 | 112.69 | odd | 4 | |||
1792.2.f.i.1791.1 | 4 | 112.83 | even | 4 | |||
1792.2.f.i.1791.2 | 4 | 16.13 | even | 4 |