Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(737,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.r (of order \(4\), 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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.737 |
Dual form | 1380.2.r.b.1013.1 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70711 | + | 0.292893i | −0.985599 | + | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12132 | − | 0.707107i | −0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 3.00000i | 1.13389 | + | 1.13389i | 0.989524 | + | 0.144370i | \(0.0461154\pi\) |
0.144370 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | − | 1.00000i | 0.942809 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.82843 | + | 0.585786i | 0.988496 | + | 0.151249i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | − | 1.41421i | 0.342997 | − | 0.342997i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) |
0.857493 | + | 0.514496i | \(0.172021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | − | 4.24264i | −1.30931 | − | 0.925820i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.53553 | + | 2.53553i | −0.872864 | + | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.828427 | + | 4.82843i | 0.144211 | + | 0.840521i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.24264 | − | 8.48528i | −0.717137 | − | 1.43427i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | + | 4.00000i | 0.657596 | + | 0.657596i | 0.954811 | − | 0.297215i | \(-0.0960577\pi\) |
−0.297215 | + | 0.954811i | \(0.596058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.24264 | − | 6.00000i | 0.679366 | − | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843i | 0.441726i | 0.975305 | + | 0.220863i | \(0.0708874\pi\) | ||||
−0.975305 | + | 0.220863i | \(0.929113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 5.00000i | 0.762493 | − | 0.762493i | −0.214280 | − | 0.976772i | \(-0.568740\pi\) |
0.976772 | + | 0.214280i | \(0.0687403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.70711 | + | 0.121320i | −0.999836 | + | 0.0180854i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | + | 5.65685i | −0.825137 | + | 0.825137i | −0.986840 | − | 0.161703i | \(-0.948301\pi\) |
0.161703 | + | 0.986840i | \(0.448301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 2.82843i | −0.280056 | + | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | + | 6.00000i | −0.269680 | + | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | + | 6.82843i | 0.155179 | + | 0.904447i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.4853 | + | 5.48528i | 1.44701 | + | 0.691080i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.48528 | − | 4.24264i | 1.05247 | − | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | + | 7.00000i | 0.855186 | + | 0.855186i | 0.990766 | − | 0.135580i | \(-0.0432899\pi\) |
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.41421 | − | 1.00000i | −0.170251 | − | 0.120386i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5563i | 1.84620i | 0.384561 | + | 0.923099i | \(0.374353\pi\) | ||||
−0.384561 | + | 0.923099i | \(0.625647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.00000i | 0.117041 | − | 0.117041i | −0.646160 | − | 0.763202i | \(-0.723626\pi\) |
0.763202 | + | 0.646160i | \(0.223626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.70711 | − | 3.94975i | −0.889940 | − | 0.456078i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.48528 | − | 8.48528i | 0.966988 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000i | 1.12509i | 0.826767 | + | 0.562544i | \(0.190177\pi\) | ||||
−0.826767 | + | 0.562544i | \(0.809823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 2.00000i | −0.433861 | + | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.82843 | + | 0.828427i | −0.517662 | + | 0.0888167i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.89949 | 1.04934 | 0.524672 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524672 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0000 | −1.88691 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.82843 | − | 1.17157i | 0.708075 | − | 0.121486i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | + | 8.48528i | −0.290191 | + | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | + | 12.0000i | 1.21842 | + | 1.21842i | 0.968187 | + | 0.250229i | \(0.0805058\pi\) |
0.250229 | + | 0.968187i | \(0.419494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | − | 8.00000i | −0.284268 | − | 0.804030i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.48528i | 0.844317i | 0.906522 | + | 0.422159i | \(0.138727\pi\) | ||||
−0.906522 | + | 0.422159i | \(0.861273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0000 | + | 13.0000i | −1.28093 | + | 1.28093i | −0.340788 | + | 0.940140i | \(0.610694\pi\) |
−0.940140 | + | 0.340788i | \(0.889306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.72792 | + | 13.2426i | 0.949348 | + | 1.29235i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000i | 0.574696i | 0.957826 | + | 0.287348i | \(0.0927736\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | − | 5.65685i | −0.759326 | − | 0.536925i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41421 | + | 1.41421i | 0.133038 | + | 0.133038i | 0.770490 | − | 0.637452i | \(-0.220012\pi\) |
−0.637452 | + | 0.770490i | \(0.720012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | − | 2.00000i | −0.0932505 | − | 0.186501i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.48528 | + | 11.4853i | −0.507114 | + | 1.06181i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528 | 0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.828427 | − | 4.82843i | −0.0746968 | − | 0.435365i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | − | 9.19239i | −0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | − | 4.00000i | −0.354943 | − | 0.354943i | 0.507002 | − | 0.861945i | \(-0.330754\pi\) |
−0.861945 | + | 0.507002i | \(0.830754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.07107 | + | 10.0000i | −0.622573 | + | 0.880451i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.7279i | − | 1.11204i | −0.831168 | − | 0.556022i | \(-0.812327\pi\) | ||
0.831168 | − | 0.556022i | \(-0.187673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | − | 12.0000i | 1.04053 | − | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4142 | − | 2.17157i | 0.982379 | − | 0.186899i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137 | − | 11.3137i | 0.966595 | − | 0.966595i | −0.0328645 | − | 0.999460i | \(-0.510463\pi\) |
0.999460 | + | 0.0328645i | \(0.0104630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | − | 11.3137i | 0.673722 | − | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.48528 | + | 8.48528i | 0.709575 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | − | 2.00000i | −0.498273 | − | 0.166091i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.22183 | − | 18.7782i | −0.265732 | − | 1.54880i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.07107 | −0.579284 | −0.289642 | − | 0.957135i | \(-0.593536\pi\) | ||||
−0.289642 | + | 0.957135i | \(0.593536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.58579 | − | 5.41421i | 0.209048 | − | 0.437713i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.48528 | + | 2.82843i | 0.681554 | + | 0.227185i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | − | 6.00000i | −0.478852 | − | 0.478852i | 0.425912 | − | 0.904764i | \(-0.359953\pi\) |
−0.904764 | + | 0.425912i | \(0.859953\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.24264i | 0.334367i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 6.00000i | 0.469956 | − | 0.469956i | −0.431944 | − | 0.901900i | \(-0.642172\pi\) |
0.901900 | + | 0.431944i | \(0.142172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.65685 | − | 10.8284i | 0.128986 | − | 0.842992i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.9706 | + | 16.9706i | −1.31322 | + | 1.31322i | −0.394195 | + | 0.919027i | \(0.628976\pi\) |
−0.919027 | + | 0.394195i | \(0.871024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | − | 11.3137i | −0.305888 | − | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.89949 | − | 9.89949i | −0.752645 | − | 0.752645i | 0.222327 | − | 0.974972i | \(-0.428635\pi\) |
−0.974972 | + | 0.222327i | \(0.928635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | + | 21.0000i | 0.226779 | + | 1.58745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.41421 | − | 0.414214i | 0.181463 | − | 0.0311342i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3848 | −1.37414 | −0.687071 | − | 0.726590i | \(-0.741104\pi\) | ||||
−0.687071 | + | 0.726590i | \(0.741104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.41421 | + | 0.585786i | −0.252386 | + | 0.0433026i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.65685 | − | 11.3137i | −0.415900 | − | 0.831800i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 4.00000i | −0.292509 | − | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.2132 | − | 6.00000i | −1.54303 | − | 0.436436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 19.7990i | − | 1.43260i | −0.697790 | − | 0.716302i | \(-0.745833\pi\) | ||
0.697790 | − | 0.716302i | \(-0.254167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | − | 9.00000i | 0.647834 | − | 0.647834i | −0.304635 | − | 0.952469i | \(-0.598534\pi\) |
0.952469 | + | 0.304635i | \(0.0985345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.2426 | + | 9.72792i | −0.948325 | + | 0.696631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.07107 | + | 7.07107i | −0.503793 | + | 0.503793i | −0.912614 | − | 0.408822i | \(-0.865940\pi\) |
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.0000i | − | 1.55954i | −0.626067 | − | 0.779769i | \(-0.715336\pi\) | ||
0.626067 | − | 0.779769i | \(-0.284664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | − | 9.89949i | −0.987484 | − | 0.698257i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.48528 | + | 8.48528i | 0.595550 | + | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 6.00000i | 0.139686 | − | 0.419058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.70711 | + | 1.29289i | 0.188157 | + | 0.0898623i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.55635 | − | 26.5563i | −0.312196 | − | 1.81961i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.1421 | + | 7.07107i | −0.964486 | + | 0.482243i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | − | 12.0000i | −0.814613 | − | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.41421 | + | 2.00000i | −0.0955637 | + | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.48528i | 0.570782i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0000 | − | 18.0000i | 1.20537 | − | 1.20537i | 0.232859 | − | 0.972511i | \(-0.425192\pi\) |
0.972511 | − | 0.232859i | \(-0.0748079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3137 | + | 4.48528i | 0.954247 | + | 0.299019i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.9706 | + | 16.9706i | −1.12638 | + | 1.12638i | −0.135614 | + | 0.990762i | \(0.543301\pi\) |
−0.990762 | + | 0.135614i | \(0.956699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000i | 1.45380i | 0.686743 | + | 0.726900i | \(0.259040\pi\) | ||||
−0.686743 | + | 0.726900i | \(0.740960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | + | 16.9706i | −0.789542 | + | 1.11658i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.2132 | + | 21.2132i | 1.38972 | + | 1.38972i | 0.825886 | + | 0.563837i | \(0.190675\pi\) |
0.563837 | + | 0.825886i | \(0.309325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | − | 8.00000i | 1.04372 | − | 0.521862i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.92893 | − | 17.0711i | −0.190255 | − | 1.10889i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.89949 | −0.640345 | −0.320173 | − | 0.947359i | \(-0.603741\pi\) | ||||
−0.320173 | + | 0.947359i | \(0.603741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.2929 | + | 11.7071i | −0.660289 | + | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.77817 | − | 23.3345i | 0.496929 | − | 1.49079i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 12.0000i | 0.763542 | + | 0.763542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.9706 | − | 12.0000i | −1.07547 | − | 0.760469i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.82843i | − | 0.178529i | −0.996008 | − | 0.0892644i | \(-0.971548\pi\) | ||
0.996008 | − | 0.0892644i | \(-0.0284516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | − | 2.00000i | 0.125739 | − | 0.125739i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.24264 | − | 4.58579i | 0.390929 | − | 0.287173i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.07107 | − | 7.07107i | 0.441081 | − | 0.441081i | −0.451294 | − | 0.892375i | \(-0.649037\pi\) |
0.892375 | + | 0.451294i | \(0.149037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0000i | 1.49129i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | − | 2.82843i | 0.495188 | − | 0.175075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3137 | + | 11.3137i | 0.697633 | + | 0.697633i | 0.963899 | − | 0.266266i | \(-0.0857901\pi\) |
−0.266266 | + | 0.963899i | \(0.585790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.8995 | + | 2.89949i | −1.03423 | + | 0.177446i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.9706 | 1.03471 | 0.517357 | − | 0.855770i | \(-0.326916\pi\) | ||||
0.517357 | + | 0.855770i | \(0.326916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.7279 | − | 5.27208i | 1.85974 | − | 0.319081i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.48528 | − | 11.3137i | 0.511682 | − | 0.682242i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.0000 | + | 21.0000i | 1.26177 | + | 1.26177i | 0.950236 | + | 0.311532i | \(0.100842\pi\) |
0.311532 | + | 0.950236i | \(0.399158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3137 | + | 4.00000i | −0.677334 | + | 0.239474i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 26.8701i | − | 1.60293i | −0.598040 | − | 0.801467i | \(-0.704053\pi\) | ||
0.598040 | − | 0.801467i | \(-0.295947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0000 | − | 15.0000i | 0.891657 | − | 0.891657i | −0.103022 | − | 0.994679i | \(-0.532851\pi\) |
0.994679 | + | 0.103022i | \(0.0328511\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.34315 | − | 15.3137i | 0.138796 | − | 0.907106i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48528 | + | 8.48528i | −0.500870 | + | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000i | 0.764706i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.0000 | − | 16.9706i | −1.40690 | − | 0.994832i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.48528 | − | 8.48528i | −0.495715 | − | 0.495715i | 0.414386 | − | 0.910101i | \(-0.363996\pi\) |
−0.910101 | + | 0.414386i | \(0.863996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 1.00000i | 0.174667 | + | 0.0582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.17157 | + | 12.8284i | 0.416137 | + | 0.744381i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.24264 | −0.245358 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.0000 | 1.72917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.48528 | − | 14.4853i | −0.142776 | − | 0.832158i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.24264 | − | 1.41421i | −0.242933 | − | 0.0809776i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | + | 18.0000i | 1.02731 | + | 1.02731i | 0.999616 | + | 0.0276979i | \(0.00881765\pi\) |
0.0276979 | + | 0.999616i | \(0.491182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.3848 | − | 26.0000i | 1.04587 | − | 1.47909i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.5563i | − | 0.882120i | −0.897478 | − | 0.441060i | \(-0.854603\pi\) | ||
0.897478 | − | 0.441060i | \(-0.145397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.00000 | − | 4.00000i | 0.226093 | − | 0.226093i | −0.584965 | − | 0.811058i | \(-0.698892\pi\) |
0.811058 | + | 0.584965i | \(0.198892\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.4853 | − | 19.7574i | −1.15421 | − | 1.11320i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.24264 | − | 4.24264i | 0.238290 | − | 0.238290i | −0.577851 | − | 0.816142i | \(-0.696109\pi\) |
0.816142 | + | 0.577851i | \(0.196109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.00000i | − | 0.447914i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | + | 5.65685i | −0.223258 | + | 0.315735i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.65685 | − | 5.65685i | −0.314756 | − | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0000 | + | 3.00000i | −1.16487 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.75736 | − | 10.2426i | −0.0971822 | − | 0.566419i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.9411 | −1.87123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | −0.879440 | −0.439720 | − | 0.898135i | \(-0.644922\pi\) | ||||
−0.439720 | + | 0.898135i | \(0.644922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.3137 | + | 7.31371i | 0.839186 | + | 0.400789i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.89949 | − | 19.7990i | −0.540867 | − | 1.08173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0000 | − | 12.0000i | −0.653682 | − | 0.653682i | 0.300196 | − | 0.953878i | \(-0.402948\pi\) |
−0.953878 | + | 0.300196i | \(0.902948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.82843 | − | 2.00000i | −0.153619 | − | 0.108625i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137i | 0.612672i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.29289 | + | 3.12132i | 0.123445 | + | 0.168046i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.48528 | + | 8.48528i | −0.455514 | + | 0.455514i | −0.897180 | − | 0.441666i | \(-0.854388\pi\) |
0.441666 | + | 0.897180i | \(0.354388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.0000i | − | 1.49881i | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||
0.662114 | − | 0.749403i | \(-0.269659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | − | 21.2132i | 0.320256 | − | 1.13228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.24264 | + | 4.24264i | 0.225813 | + | 0.225813i | 0.810941 | − | 0.585128i | \(-0.198956\pi\) |
−0.585128 | + | 0.810941i | \(0.698956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0000 | − | 33.0000i | 0.583819 | − | 1.75146i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.4853 | + | 2.48528i | −0.766642 | + | 0.131535i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.65685 | 0.298557 | 0.149279 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149279 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.12132 | + | 0.878680i | −0.268800 | + | 0.0461187i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.82843 | + | 1.41421i | −0.148047 | + | 0.0740233i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0000 | − | 11.0000i | −0.574195 | − | 0.574195i | 0.359103 | − | 0.933298i | \(-0.383083\pi\) |
−0.933298 | + | 0.359103i | \(0.883083\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.82843 | + | 8.00000i | 0.147242 | + | 0.416463i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0000 | + | 26.0000i | −1.34623 | + | 1.34623i | −0.456511 | + | 0.889718i | \(0.650901\pi\) |
−0.889718 | + | 0.456511i | \(0.849099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.5563 | + | 13.8284i | 0.700047 | + | 0.714097i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.48528 | + | 8.48528i | −0.437014 | + | 0.437014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 5.65685i | 0.409852 | + | 0.289809i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9706 | + | 16.9706i | 0.867155 | + | 0.867155i | 0.992157 | − | 0.125001i | \(-0.0398935\pi\) |
−0.125001 | + | 0.992157i | \(0.539894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | + | 12.0000i | −1.22315 | + | 0.611577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.14214 | − | 19.1421i | 0.464721 | − | 0.973049i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.5563 | −0.788738 | −0.394369 | − | 0.918952i | \(-0.629037\pi\) | ||||
−0.394369 | + | 0.918952i | \(0.629037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.72792 | + | 21.7279i | 0.188049 | + | 1.09603i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.07107 | − | 21.2132i | 0.355784 | − | 1.06735i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00000 | + | 7.00000i | 0.351320 | + | 0.351320i | 0.860601 | − | 0.509281i | \(-0.170088\pi\) |
−0.509281 | + | 0.860601i | \(0.670088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9706 | + | 24.0000i | −0.849591 | + | 1.20150i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5563i | 0.776847i | 0.921481 | + | 0.388424i | \(0.126980\pi\) | ||||
−0.921481 | + | 0.388424i | \(0.873020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | − | 12.0000i | 0.597763 | − | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.8492 | + | 7.05025i | −0.936626 | + | 0.350330i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3137 | − | 11.3137i | 0.560800 | − | 0.560800i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.0000i | − | 1.28562i | −0.766027 | − | 0.642809i | \(-0.777769\pi\) | ||
0.766027 | − | 0.642809i | \(-0.222231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.0000 | + | 22.6274i | −0.789222 | + | 1.11613i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.24264 | − | 4.24264i | −0.208767 | − | 0.208767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | − | 24.0000i | −0.589057 | − | 1.17811i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.51472 | − | 20.4853i | −0.172117 | − | 1.00317i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.2843 | −1.38178 | −0.690889 | − | 0.722961i | \(-0.742780\pi\) | ||||
−0.690889 | + | 0.722961i | \(0.742780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.3431 | + | 21.6569i | −0.502901 | + | 1.05299i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.89949 | − | 1.41421i | 0.480196 | − | 0.0685994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 6.00000i | 0.290360 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.9706 | − | 12.0000i | −0.819346 | − | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.65685i | − | 0.272481i | −0.990676 | − | 0.136241i | \(-0.956498\pi\) | ||
0.990676 | − | 0.136241i | \(-0.0435020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | + | 10.0000i | −0.480569 | + | 0.480569i | −0.905313 | − | 0.424744i | \(-0.860364\pi\) |
0.424744 | + | 0.905313i | \(0.360364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.8284 | + | 1.65685i | 0.519183 | + | 0.0794401i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.82843 | − | 2.82843i | 0.135302 | − | 0.135302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.0000i | − | 0.954548i | −0.878755 | − | 0.477274i | \(-0.841625\pi\) | ||
0.878755 | − | 0.477274i | \(-0.158375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0000 | + | 31.1127i | 0.523810 | + | 1.48156i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.82843 | − | 2.82843i | −0.134383 | − | 0.134383i | 0.636716 | − | 0.771099i | \(-0.280292\pi\) |
−0.771099 | + | 0.636716i | \(0.780292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.0000 | − | 7.00000i | −0.995495 | − | 0.331832i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0711 | − | 2.07107i | 0.570942 | − | 0.0979581i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685 | 0.266963 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.4853 | − | 3.51472i | 0.962482 | − | 0.165136i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 38.1838 | + | 12.7279i | 1.79008 | + | 0.596694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0000 | + | 12.0000i | 0.561336 | + | 0.561336i | 0.929687 | − | 0.368351i | \(-0.120077\pi\) |
−0.368351 | + | 0.929687i | \(0.620077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82843 | + | 10.0000i | −0.132020 | + | 0.466760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.2843i | 1.31733i | 0.752436 | + | 0.658665i | \(0.228879\pi\) | ||||
−0.752436 | + | 0.658665i | \(0.771121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.3137 | − | 2.34315i | −0.710156 | − | 0.108661i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.2843 | + | 28.2843i | −1.30884 | + | 1.30884i | −0.386587 | + | 0.922253i | \(0.626346\pi\) |
−0.922253 | + | 0.386587i | \(0.873654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.0000i | 1.93938i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0000 | + | 8.48528i | 0.552931 | + | 0.390981i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.1421 | − | 14.1421i | −0.650256 | − | 0.650256i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | − | 16.0000i | 0.550598 | − | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.7696 | 1.68004 | 0.840022 | − | 0.542553i | \(-0.182542\pi\) | ||||
0.840022 | + | 0.542553i | \(0.182542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.24264 | − | 7.24264i | −0.0565421 | − | 0.329552i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.9706 | − | 33.9411i | −0.770594 | − | 1.54119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | − | 16.0000i | −0.725029 | − | 0.725029i | 0.244596 | − | 0.969625i | \(-0.421345\pi\) |
−0.969625 | + | 0.244596i | \(0.921345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.48528 | + | 12.0000i | −0.383718 | + | 0.542659i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.5269i | 1.46792i | 0.679193 | + | 0.733959i | \(0.262330\pi\) | ||||
−0.679193 | + | 0.733959i | \(0.737670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | − | 4.00000i | 0.180151 | − | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.343146 | + | 18.9706i | 0.0154233 | + | 0.852663i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.6690 | + | 46.6690i | −2.09339 | + | 2.09339i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 40.0000i | − | 1.79065i | −0.445418 | − | 0.895323i | \(-0.646945\pi\) | ||
0.445418 | − | 0.895323i | \(-0.353055\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000 | − | 33.9411i | 1.07224 | − | 1.51638i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.2843 | − | 28.2843i | −1.26113 | − | 1.26113i | −0.950544 | − | 0.310589i | \(-0.899474\pi\) |
−0.310589 | − | 0.950544i | \(-0.600526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | − | 18.0000i | 0.266996 | − | 0.800989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.46447 | + | 8.53553i | 0.0650392 | + | 0.379076i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.4264 | 1.88052 | 0.940259 | − | 0.340461i | \(-0.110583\pi\) | ||||
0.940259 | + | 0.340461i | \(0.110583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.1421 | + | 18.1421i | 0.447786 | + | 0.800995i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.7696 | − | 18.3848i | 1.62026 | − | 0.810130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | + | 16.0000i | 0.703679 | + | 0.703679i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.7990 | + | 14.0000i | 0.869079 | + | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.41421i | 0.0619578i | 0.999520 | + | 0.0309789i | \(0.00986247\pi\) | ||||
−0.999520 | + | 0.0309789i | \(0.990138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.00000 | + | 9.00000i | −0.393543 | + | 0.393543i | −0.875948 | − | 0.482405i | \(-0.839763\pi\) |
0.482405 | + | 0.875948i | \(0.339763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.2721 | − | 34.9706i | −0.491954 | − | 1.52624i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.65685 | + | 5.65685i | −0.246416 | + | 0.246416i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | + | 1.41421i | −0.173585 | + | 0.0613716i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.48528 | − | 8.48528i | −0.367538 | − | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | + | 4.00000i | −0.345870 | + | 0.172935i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.3848 | − | 5.38478i | 1.35435 | − | 0.232370i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.1127 | 1.34012 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2426 | + | 1.75736i | −0.439554 | + | 0.0754155i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.24264 | − | 12.7279i | 0.181735 | − | 0.545204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0000 | − | 26.0000i | −1.11168 | − | 1.11168i | −0.992923 | − | 0.118756i | \(-0.962109\pi\) |
−0.118756 | − | 0.992923i | \(-0.537891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.65685 | − | 2.00000i | 0.241429 | − | 0.0853579i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.3137i | − | 0.481980i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 30.0000i | −1.27573 | + | 1.27573i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9706 | + | 17.6569i | 0.550570 | + | 0.749492i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7279 | − | 12.7279i | 0.539299 | − | 0.539299i | −0.384024 | − | 0.923323i | \(-0.625462\pi\) |
0.923323 | + | 0.384024i | \(0.125462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.0000i | 1.26886i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | + | 5.65685i | 0.337760 | + | 0.238833i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.1127 | − | 31.1127i | −1.31124 | − | 1.31124i | −0.920499 | − | 0.390745i | \(-0.872217\pi\) |
−0.390745 | − | 0.920499i | \(-0.627783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | − | 4.00000i | −0.0841406 | − | 0.168281i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.9706 | + | 4.02944i | 1.59461 | + | 0.169220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.41421 | 0.0592869 | 0.0296435 | − | 0.999561i | \(-0.490563\pi\) | ||||
0.0296435 | + | 0.999561i | \(0.490563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0000 | 1.08807 | 0.544033 | − | 0.839064i | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.79899 | + | 33.7990i | 0.242256 | + | 1.41197i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707107 | + | 4.94975i | 0.0294884 | + | 0.206419i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0000 | + | 13.0000i | 0.541197 | + | 0.541197i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.7279 | + | 18.0000i | −0.528954 | + | 0.748054i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.9117i | 2.11217i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7574 | − | 20.4853i | 0.816866 | − | 0.846962i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5563 | + | 15.5563i | −0.642079 | + | 0.642079i | −0.951066 | − | 0.308987i | \(-0.900010\pi\) |
0.308987 | + | 0.951066i | \(0.400010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000i | 0.659269i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | − | 14.1421i | 0.411345 | − | 0.581730i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.89949 | − | 9.89949i | −0.406524 | − | 0.406524i | 0.474001 | − | 0.880524i | \(-0.342809\pi\) |
−0.880524 | + | 0.474001i | \(0.842809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | − | 6.00000i | −0.737928 | − | 0.245976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.44365 | + | 37.5563i | 0.263721 | + | 1.53708i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.3553 | 1.44458 | 0.722290 | − | 0.691590i | \(-0.243090\pi\) | ||||
0.722290 | + | 0.691590i | \(0.243090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0000 | 0.489490 | 0.244745 | − | 0.969587i | \(-0.421296\pi\) | ||||
0.244745 | + | 0.969587i | \(0.421296\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.7990 | + | 12.7990i | 1.09134 | + | 0.521215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.36396 | − | 2.12132i | −0.258732 | − | 0.0862439i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | + | 8.00000i | 0.324710 | + | 0.324710i | 0.850571 | − | 0.525861i | \(-0.176257\pi\) |
−0.525861 | + | 0.850571i | \(0.676257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.9706 | − | 12.0000i | −0.687682 | − | 0.486265i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 33.9411i | − | 1.37311i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0000 | + | 10.0000i | −0.403896 | + | 0.403896i | −0.879604 | − | 0.475707i | \(-0.842192\pi\) |
0.475707 | + | 0.879604i | \(0.342192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.65685 | + | 10.8284i | −0.0668108 | + | 0.436644i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.48528 | + | 8.48528i | −0.341605 | + | 0.341605i | −0.856970 | − | 0.515366i | \(-0.827656\pi\) |
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.0000i | − | 0.401934i | −0.979598 | − | 0.200967i | \(-0.935592\pi\) | ||
0.979598 | − | 0.200967i | \(-0.0644084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.00000 | − | 1.41421i | −0.200643 | − | 0.0567504i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.6985 | + | 29.6985i | 1.18984 | + | 1.18984i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.3137 | − | 3.31371i | 0.771315 | − | 0.132337i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3137 | 0.451107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.65685 | + | 11.3137i | 0.224485 | + | 0.448971i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.0000 | − | 33.0000i | −1.30751 | − | 1.30751i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.5563 | + | 44.0000i | 0.615400 | + | 1.74061i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.5269i | − | 1.28474i | −0.766396 | − | 0.642368i | \(-0.777952\pi\) | ||
0.766396 | − | 0.642368i | \(-0.222048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0000 | − | 23.0000i | 0.907031 | − | 0.907031i | −0.0890002 | − | 0.996032i | \(-0.528367\pi\) |
0.996032 | + | 0.0890002i | \(0.0283672\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.0711 | − | 16.2132i | 0.869047 | − | 0.638394i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9706 | − | 16.9706i | 0.667182 | − | 0.667182i | −0.289881 | − | 0.957063i | \(-0.593616\pi\) |
0.957063 | + | 0.289881i | \(0.0936157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000i | 0.157014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0000 | + | 16.9706i | 0.940634 | + | 0.665129i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7279 | − | 12.7279i | −0.498082 | − | 0.498082i | 0.412758 | − | 0.910841i | \(-0.364565\pi\) |
−0.910841 | + | 0.412758i | \(0.864565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | + | 27.0000i | −0.351659 | + | 1.05498i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.82843 | − | 3.82843i | 0.0713337 | − | 0.149361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.65685 | 0.220360 | 0.110180 | − | 0.993912i | \(-0.464857\pi\) | ||||
0.110180 | + | 0.993912i | \(0.464857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | 0.0777910 | 0.0388955 | − | 0.999243i | \(-0.487616\pi\) | ||||
0.0388955 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.48528 | − | 14.4853i | −0.0965203 | − | 0.562562i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.9411 | + | 16.9706i | −1.31618 | + | 0.658090i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00000 | + | 2.00000i | 0.0774403 | + | 0.0774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.4558 | + | 36.0000i | −0.984180 | + | 1.39184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.65685i | − | 0.218380i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 5.00000i | 0.192736 | − | 0.192736i | −0.604141 | − | 0.796877i | \(-0.706484\pi\) |
0.796877 | + | 0.604141i | \(0.206484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.7487 | − | 3.46447i | −0.991069 | − | 0.133347i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82843 | + | 2.82843i | −0.108705 | + | 0.108705i | −0.759367 | − | 0.650662i | \(-0.774491\pi\) |
0.650662 | + | 0.759367i | \(0.274491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.0000i | 2.76311i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000 | − | 33.9411i | 0.919682 | − | 1.30063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.2132 | + | 21.2132i | 0.811701 | + | 0.811701i | 0.984889 | − | 0.173188i | \(-0.0554069\pi\) |
−0.173188 | + | 0.984889i | \(0.555407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.0000 | + | 16.0000i | −1.22266 | + | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.44365 | − | 37.5563i | −0.245841 | − | 1.43286i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.5147 | − | 32.4853i | 0.589355 | − | 1.23401i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.48528 | − | 25.4558i | 0.321865 | − | 0.965595i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | + | 4.00000i | 0.151511 | + | 0.151511i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42.4264 | − | 30.0000i | −1.60471 | − | 1.13470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8406i | 1.65584i | 0.560848 | + | 0.827919i | \(0.310475\pi\) | ||||
−0.560848 | + | 0.827919i | \(0.689525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | − | 16.0000i | 0.603451 | − | 0.603451i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.9706 | + | 18.3431i | −0.940446 | + | 0.690843i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.4558 | + | 25.4558i | −0.957366 | + | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.00000i | − | 0.225335i | −0.993633 | − | 0.112667i | \(-0.964061\pi\) | ||
0.993633 | − | 0.112667i | \(-0.0359394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0000 | + | 28.2843i | 0.375029 | + | 1.06074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.82843 | − | 2.82843i | −0.105925 | − | 0.105925i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 24.0000i | −0.448775 | − | 0.897549i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.8995 | − | 2.89949i | 0.631123 | − | 0.108284i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.89949 | −0.369189 | −0.184594 | − | 0.982815i | \(-0.559097\pi\) | ||||
−0.184594 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −78.0000 | −2.90487 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2426 | + | 1.75736i | −0.380928 | + | 0.0653569i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.3137 | + | 8.48528i | 0.420181 | + | 0.315135i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0000 | − | 17.0000i | −0.630495 | − | 0.630495i | 0.317697 | − | 0.948192i | \(-0.397090\pi\) |
−0.948192 | + | 0.317697i | \(0.897090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | − | 23.0000i | 0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 14.1421i | − | 0.523066i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0000 | − | 20.0000i | 0.738717 | − | 0.738717i | −0.233613 | − | 0.972330i | \(-0.575055\pi\) |
0.972330 | + | 0.233613i | \(0.0750548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.44365 | + | 42.1127i | −0.237678 | + | 1.55335i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.7990 | − | 19.7990i | 0.729305 | − | 0.729305i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | − | 16.9706i | −0.881662 | − | 0.623429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.82843 | + | 2.82843i | 0.103765 | + | 0.103765i | 0.757083 | − | 0.653318i | \(-0.226624\pi\) |
−0.653318 | + | 0.757083i | \(0.726624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0000 | + | 5.00000i | 0.549557 | + | 0.183186i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.4853 | + | 15.5147i | 1.18857 | + | 0.567654i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706 | 0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.828427 | + | 4.82843i | 0.0301896 | + | 0.175958i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4558 | + | 8.48528i | 0.926433 | + | 0.308811i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | + | 6.00000i | 0.218074 | + | 0.218074i | 0.807686 | − | 0.589613i | \(-0.200720\pi\) |
−0.589613 | + | 0.807686i | \(0.700720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.82843 | + | 4.00000i | −0.102665 | + | 0.145191i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14.1421i | − | 0.512652i | −0.966590 | − | 0.256326i | \(-0.917488\pi\) | ||
0.966590 | − | 0.256326i | \(-0.0825121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0000 | + | 18.0000i | −0.651644 | + | 0.651644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.31371 | + | 9.65685i | −0.336738 | + | 0.349144i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.24264 | − | 4.24264i | 0.153193 | − | 0.153193i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 42.0000i | − | 1.51456i | −0.653091 | − | 0.757279i | \(-0.726528\pi\) | ||
0.653091 | − | 0.757279i | \(-0.273472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0000 | + | 14.1421i | −0.360141 | + | 0.509317i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.07107 | + | 7.07107i | 0.254329 | + | 0.254329i | 0.822743 | − | 0.568414i | \(-0.192443\pi\) |
−0.568414 | + | 0.822743i | \(0.692443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | − | 12.0000i | −0.574737 | − | 0.431053i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.02944 | − | 40.9706i | −0.252180 | − | 1.46981i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3137 | 0.405356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.0000 | 1.57444 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.8284 | + | 7.17157i | −0.458451 | + | 0.256291i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.48528 | + | 16.9706i | 0.302853 | + | 0.605705i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | + | 15.0000i | 0.534692 | + | 0.534692i | 0.921965 | − | 0.387273i | \(-0.126583\pi\) |
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6274 | − | 16.0000i | −0.805557 | − | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.48528i | 0.301702i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | + | 6.00000i | −0.213066 | + | 0.213066i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.48528 | − | 8.48528i | 0.300564 | − | 0.300564i | −0.540670 | − | 0.841235i | \(-0.681829\pi\) |
0.841235 | + | 0.540670i | \(0.181829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000i | 0.566039i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.0000 | − | 9.89949i | 0.989331 | − | 0.349781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.82843 | − | 2.82843i | −0.0998130 | − | 0.0998130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | − | 9.00000i | 0.105736 | − | 0.317208i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.9706 | + | 4.97056i | −1.01981 | + | 0.174972i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.5980 | 1.39219 | 0.696095 | − | 0.717949i | \(-0.254919\pi\) | ||||
0.696095 | + | 0.717949i | \(0.254919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.4853 | + | 3.51472i | −0.718450 | + | 0.123267i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9706 | + | 8.48528i | −0.594453 | + | 0.297226i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0000 | − | 20.0000i | −0.699711 | − | 0.699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −50.9117 | + | 18.0000i | −1.77900 | + | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 33.9411i | − | 1.18455i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) | ||
0.805735 | − | 0.592277i | \(-0.201771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0000 | − | 10.0000i | 0.348578 | − | 0.348578i | −0.511002 | − | 0.859580i | \(-0.670725\pi\) |
0.859580 | + | 0.511002i | \(0.170725\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1716 | + | 21.7990i | −0.388944 | + | 0.758943i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1421 | − | 14.1421i | 0.491770 | − | 0.491770i | −0.417093 | − | 0.908864i | \(-0.636951\pi\) |
0.908864 | + | 0.417093i | \(0.136951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.00000i | − | 0.0694629i | −0.999397 | − | 0.0347314i | \(-0.988942\pi\) | ||
0.999397 | − | 0.0347314i | \(-0.0110576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.0000 | − | 29.6985i | −1.45696 | − | 1.03023i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5563 | + | 15.5563i | 0.538996 | + | 0.538996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.0000 | − | 24.0000i | 1.66111 | − | 0.830554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.1421 | − | 10.1421i | 0.627084 | − | 0.350563i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4264 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.87006 | + | 45.8701i | 0.271059 | + | 1.57985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.53553 | + | 10.6066i | −0.121626 | + | 0.364878i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000 | + | 9.00000i | 0.309244 | + | 0.309244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2132 | + | 30.0000i | −0.728035 | + | 1.02960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.65685i | 0.193914i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0000 | + | 29.0000i | −0.992941 | + | 0.992941i | −0.999975 | − | 0.00703417i | \(-0.997761\pi\) |
0.00703417 | + | 0.999975i | \(0.497761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.485281 | + | 26.8284i | 0.0165963 | + | 0.917513i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.8701 | + | 26.8701i | −0.917864 | + | 0.917864i | −0.996874 | − | 0.0790101i | \(-0.974824\pi\) |
0.0790101 | + | 0.996874i | \(0.474824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 20.0000i | − | 0.682391i | −0.939992 | − | 0.341196i | \(-0.889168\pi\) | ||
0.939992 | − | 0.341196i | \(-0.110832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 16.9706i | 0.408959 | − | 0.578355i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.3848 | − | 18.3848i | −0.625825 | − | 0.625825i | 0.321190 | − | 0.947015i | \(-0.395917\pi\) |
−0.947015 | + | 0.321190i | \(0.895917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | + | 28.0000i | 0.476014 | + | 0.952029i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.80761 | − | 22.1924i | −0.129313 | − | 0.753693i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.2843 | 0.959478 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.0000 | −1.42312 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.9411 | + | 21.9411i | 1.55487 | + | 0.742595i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.48528 | − | 46.6690i | 0.286855 | − | 1.57770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.0000 | − | 35.0000i | −1.18187 | − | 1.18187i | −0.979260 | − | 0.202606i | \(-0.935059\pi\) |
−0.202606 | − | 0.979260i | \(-0.564941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.9706 | + | 12.0000i | 0.572403 | + | 0.404750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0122i | 1.38174i | 0.722981 | + | 0.690868i | \(0.242771\pi\) | ||||
−0.722981 | + | 0.690868i | \(0.757229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0000 | − | 10.0000i | 0.336527 | − | 0.336527i | −0.518532 | − | 0.855058i | \(-0.673521\pi\) |
0.855058 | + | 0.518532i | \(0.173521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.41421 | − | 0.828427i | −0.181997 | − | 0.0278473i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7279 | + | 12.7279i | −0.427362 | + | 0.427362i | −0.887729 | − | 0.460367i | \(-0.847718\pi\) |
0.460367 | + | 0.887729i | \(0.347718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.0000i | − | 0.804934i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.0000 | − | 19.7990i | −0.536020 | − | 0.663291i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.6274 | + | 22.6274i | 0.757198 | + | 0.757198i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.0000 | + | 13.0000i | 1.30363 | + | 0.434542i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.24264 | − | 1.24264i | 0.241825 | − | 0.0414906i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.3137 | −0.377333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −51.2132 | + | 8.78680i | −1.70427 | + | 0.292406i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.7279 | − | 4.24264i | −0.423090 | − | 0.141030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.0000 | + | 39.0000i | 1.29497 | + | 1.29497i | 0.931671 | + | 0.363303i | \(0.118351\pi\) |
0.363303 | + | 0.931671i | \(0.381649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.48528 | + | 24.0000i | 0.281439 | + | 0.796030i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42.4264i | − | 1.40565i | −0.711363 | − | 0.702825i | \(-0.751922\pi\) | ||
0.711363 | − | 0.702825i | \(-0.248078\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | − | 24.0000i | 0.794284 | − | 0.794284i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.65685 | + | 1.17157i | 0.253128 | + | 0.0387310i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.1838 | − | 38.1838i | 1.26094 | − | 1.26094i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.00000i | − | 0.263896i | −0.991257 | − | 0.131948i | \(-0.957877\pi\) | ||
0.991257 | − | 0.131948i | \(-0.0421231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.0000 | − | 25.4558i | −1.18624 | − | 0.838799i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.6690 | − | 46.6690i | −1.53613 | − | 1.53613i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | + | 28.0000i | 0.131519 | + | 0.920634i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.7696 | + | 49.7696i | −0.780695 | + | 1.63465i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.6274 | 0.742381 | 0.371191 | − | 0.928557i | \(-0.378950\pi\) | ||||
0.371191 | + | 0.928557i | \(0.378950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0000 | 1.44204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.55635 | + | 26.5563i | 0.149168 | + | 0.869416i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.65685 | + | 11.3137i | 0.184999 | + | 0.369998i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.0000 | − | 36.0000i | −1.17607 | − | 1.17607i | −0.980737 | − | 0.195331i | \(-0.937422\pi\) |
−0.195331 | − | 0.980737i | \(-0.562578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.65685 | + | 8.00000i | −0.184604 | + | 0.261070i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.5563i | − | 0.507122i | −0.967319 | − | 0.253561i | \(-0.918398\pi\) | ||
0.967319 | − | 0.253561i | \(-0.0816019\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.00000 | + | 2.00000i | −0.0651290 | + | 0.0651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 40.7574 | + | 27.7279i | 1.32584 | + | 0.901989i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.6985 | + | 29.6985i | −0.965071 | + | 0.965071i | −0.999410 | − | 0.0343392i | \(-0.989067\pi\) |
0.0343392 | + | 0.999410i | \(0.489067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000i | 0.194768i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | + | 8.48528i | −0.194563 | + | 0.275154i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.89949 | + | 9.89949i | 0.320676 | + | 0.320676i | 0.849026 | − | 0.528350i | \(-0.177189\pi\) |
−0.528350 | + | 0.849026i | \(0.677189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0000 | + | 42.0000i | −0.453029 | + | 1.35909i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.34315 | + | 13.6569i | 0.0757431 | + | 0.441463i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67.8823 | 2.19203 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.17157 | − | 10.8284i | 0.166652 | − | 0.348941i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.4558 | + | 12.7279i | −0.819453 | + | 0.409726i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.0000 | − | 26.0000i | −0.836104 | − | 0.836104i | 0.152240 | − | 0.988344i | \(-0.451351\pi\) |
−0.988344 | + | 0.152240i | \(0.951351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3137 | + | 8.00000i | 0.363449 | + | 0.256997i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7990i | 0.635380i | 0.948195 | + | 0.317690i | \(0.102907\pi\) | ||||
−0.948195 | + | 0.317690i | \(0.897093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.0000 | + | 36.0000i | −1.15411 | + | 1.15411i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34.9706 | − | 11.2721i | 1.11995 | − | 0.360995i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.1838 | − | 38.1838i | 1.22161 | − | 1.22161i | 0.254546 | − | 0.967061i | \(-0.418074\pi\) |
0.967061 | − | 0.254546i | \(-0.0819261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.0000i | − | 0.894884i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | + | 16.9706i | 0.191565 | + | 0.541828i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.7990 | + | 19.7990i | 0.631490 | + | 0.631490i | 0.948442 | − | 0.316952i | \(-0.102659\pi\) |
−0.316952 | + | 0.948442i | \(0.602659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | − | 10.0000i | 0.637253 | − | 0.318626i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.9411 | − | 9.94113i | 1.84429 | − | 0.316430i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.07107 | 0.224847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | −0.635321 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.3137 | − | 4.68629i | 0.866774 | − | 0.148715i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.5563 | + | 46.6690i | −0.493169 | + | 1.47951i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0000 | + | 39.0000i | 1.23514 | + | 1.23514i | 0.961963 | + | 0.273179i | \(0.0880752\pi\) |
0.273179 | + | 0.961963i | \(0.411925\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.2843 | − | 8.00000i | −0.894875 | − | 0.253109i |
(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 | 1380.2.r.b.737.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1380.2.r.b.737.2 | yes | 4 | |
5.3 | odd | 4 | inner | 1380.2.r.b.1013.2 | yes | 4 | |
15.8 | even | 4 | inner | 1380.2.r.b.1013.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.r.b.737.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1380.2.r.b.737.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1380.2.r.b.1013.1 | yes | 4 | 15.8 | even | 4 | inner | |
1380.2.r.b.1013.2 | yes | 4 | 5.3 | odd | 4 | inner |