Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [408,2,Mod(217,408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(408, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("408.217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 408 = 2^{3} \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 408.v (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: | \(3.25789640247\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 408.361 |
Dual form | 408.2.v.b.217.2 |
$q$-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 \(\left(\mathbb{Z}/408\mathbb{Z}\right)^\times\).
\(n\) | \(103\) | \(137\) | \(205\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.41421 | − | 2.41421i | 1.07967 | − | 1.07967i | 0.0831305 | − | 0.996539i | \(-0.473508\pi\) |
0.996539 | − | 0.0831305i | \(-0.0264918\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | − | 1.41421i | −0.534522 | − | 0.534522i | 0.387392 | − | 0.921915i | \(-0.373376\pi\) |
−0.921915 | + | 0.387392i | \(0.873376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82843 | − | 2.82843i | −0.852803 | − | 0.852803i | 0.137675 | − | 0.990478i | \(-0.456037\pi\) |
−0.990478 | + | 0.137675i | \(0.956037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.17157 | −0.324936 | −0.162468 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162468 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.41421i | − | 0.881546i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 4.00000i | 0.242536 | + | 0.970143i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.58579 | + | 2.58579i | 0.539174 | + | 0.539174i | 0.923286 | − | 0.384113i | \(-0.125493\pi\) |
−0.384113 | + | 0.923286i | \(0.625493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 6.65685i | − | 1.33137i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24264 | − | 3.24264i | 0.602143 | − | 0.602143i | −0.338738 | − | 0.940881i | \(-0.610000\pi\) |
0.940881 | + | 0.338738i | \(0.110000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.58579 | + | 2.58579i | −0.464421 | + | 0.464421i | −0.900101 | − | 0.435680i | \(-0.856508\pi\) |
0.435680 | + | 0.900101i | \(0.356508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.82843 | −1.15421 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.58579 | − | 5.58579i | 0.918298 | − | 0.918298i | −0.0786080 | − | 0.996906i | \(-0.525048\pi\) |
0.996906 | + | 0.0786080i | \(0.0250475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.828427 | + | 0.828427i | −0.132655 | + | 0.132655i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.65685 | + | 8.65685i | 1.35197 | + | 1.35197i | 0.883452 | + | 0.468521i | \(0.155213\pi\) |
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.65685i | − | 1.47266i | −0.676625 | − | 0.736328i | \(-0.736558\pi\) | ||
0.676625 | − | 0.736328i | \(-0.263442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.41421 | − | 2.41421i | −0.359890 | − | 0.359890i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8284 | 1.57949 | 0.789744 | − | 0.613436i | \(-0.210213\pi\) | ||||
0.789744 | + | 0.613436i | \(0.210213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.00000i | − | 0.428571i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.53553 | + | 2.12132i | 0.495074 | + | 0.297044i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.82843i | 0.937957i | 0.883210 | + | 0.468978i | \(0.155378\pi\) | ||||
−0.883210 | + | 0.468978i | \(0.844622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6569 | −1.84149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | + | 2.00000i | 0.264906 | + | 0.264906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843i | 0.368230i | 0.982905 | + | 0.184115i | \(0.0589419\pi\) | ||||
−0.982905 | + | 0.184115i | \(0.941058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24264 | + | 3.24264i | 0.415178 | + | 0.415178i | 0.883538 | − | 0.468360i | \(-0.155155\pi\) |
−0.468360 | + | 0.883538i | \(0.655155\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | + | 1.41421i | −0.178174 | + | 0.178174i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.82843 | + | 2.82843i | −0.350823 | + | 0.350823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | −1.03664 | −0.518321 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.65685 | 0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.242641 | + | 0.242641i | −0.0287962 | + | 0.0287962i | −0.721358 | − | 0.692562i | \(-0.756482\pi\) |
0.692562 | + | 0.721358i | \(0.256482\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | −4.70711 | − | 4.70711i | −0.543530 | − | 0.543530i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000i | 0.911685i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.24264 | + | 4.24264i | 0.477334 | + | 0.477334i | 0.904278 | − | 0.426944i | \(-0.140410\pi\) |
−0.426944 | + | 0.904278i | \(0.640410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.8284i | 1.18857i | 0.804253 | + | 0.594287i | \(0.202566\pi\) | ||||
−0.804253 | + | 0.594287i | \(0.797434\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0711 | + | 7.24264i | 1.30929 | + | 0.785575i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.58579i | − | 0.491648i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9706 | −1.79888 | −0.899438 | − | 0.437048i | \(-0.856024\pi\) | ||||
−0.899438 | + | 0.437048i | \(0.856024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.65685 | + | 1.65685i | 0.173686 | + | 0.173686i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.65685i | 0.379198i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.82843 | + | 6.82843i | 0.700582 | + | 0.700582i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.48528 | + | 5.48528i | −0.556946 | + | 0.556946i | −0.928437 | − | 0.371491i | \(-0.878847\pi\) |
0.371491 | + | 0.928437i | \(0.378847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | + | 2.82843i | −0.284268 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4853 | 1.24233 | 0.621166 | − | 0.783679i | \(-0.286659\pi\) | ||||
0.621166 | + | 0.783679i | \(0.286659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8284 | −1.06696 | −0.533478 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533478 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.82843 | + | 4.82843i | −0.471206 | + | 0.471206i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.414214 | + | 0.414214i | 0.0396745 | + | 0.0396745i | 0.726666 | − | 0.686991i | \(-0.241069\pi\) |
−0.686991 | + | 0.726666i | \(0.741069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.89949i | − | 0.749787i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.82843 | − | 5.82843i | −0.548292 | − | 0.548292i | 0.377654 | − | 0.925947i | \(-0.376731\pi\) |
−0.925947 | + | 0.377654i | \(0.876731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.4853 | 1.16426 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17157i | 0.108312i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.24264 | − | 7.07107i | 0.388922 | − | 0.648204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000i | 0.454545i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2426 | 1.10388 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.00000 | − | 4.00000i | −0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.6569i | 1.92174i | 0.277008 | + | 0.960868i | \(0.410657\pi\) | ||||
−0.277008 | + | 0.960868i | \(0.589343\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.82843 | − | 6.82843i | −0.601209 | − | 0.601209i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | − | 12.0000i | 1.04844 | − | 1.04844i | 0.0496797 | − | 0.998765i | \(-0.484180\pi\) |
0.998765 | − | 0.0496797i | \(-0.0158200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | − | 4.00000i | 0.346844 | − | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41421 | −0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23.3137 | −1.99182 | −0.995912 | − | 0.0903258i | \(-0.971209\pi\) | ||||
−0.995912 | + | 0.0903258i | \(0.971209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.82843 | + | 6.82843i | −0.579180 | + | 0.579180i | −0.934677 | − | 0.355498i | \(-0.884311\pi\) |
0.355498 | + | 0.934677i | \(0.384311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.65685 | − | 7.65685i | 0.644823 | − | 0.644823i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.31371 | + | 3.31371i | 0.277106 | + | 0.277106i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.6569i | − | 1.30023i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.12132 | − | 2.12132i | −0.174964 | − | 0.174964i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.31371 | 0.435316 | 0.217658 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217658 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.65685i | − | 0.460348i | −0.973149 | − | 0.230174i | \(-0.926070\pi\) | ||
0.973149 | − | 0.230174i | \(-0.0739296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | − | 1.00000i | 0.323381 | − | 0.0808452i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4853i | 1.00284i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.82843 | + | 4.82843i | 0.382919 | + | 0.382919i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.31371i | − | 0.576401i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | + | 8.00000i | 0.626608 | + | 0.626608i | 0.947213 | − | 0.320605i | \(-0.103886\pi\) |
−0.320605 | + | 0.947213i | \(0.603886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.65685 | + | 9.65685i | −0.751785 | + | 0.751785i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.07107 | − | 7.07107i | 0.547176 | − | 0.547176i | −0.378447 | − | 0.925623i | \(-0.623542\pi\) |
0.925623 | + | 0.378447i | \(0.123542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.7279 | + | 13.7279i | −1.04371 | + | 1.04371i | −0.0447148 | + | 0.999000i | \(0.514238\pi\) |
−0.999000 | + | 0.0447148i | \(0.985762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.41421 | + | 9.41421i | −0.711648 | + | 0.711648i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | + | 2.00000i | 0.150329 | + | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.9706i | − | 0.969465i | −0.874662 | − | 0.484733i | \(-0.838917\pi\) | ||
0.874662 | − | 0.484733i | \(-0.161083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.07107 | − | 4.07107i | −0.302600 | − | 0.302600i | 0.539430 | − | 0.842030i | \(-0.318640\pi\) |
−0.842030 | + | 0.539430i | \(0.818640\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.58579 | 0.338991 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 26.9706i | − | 1.98292i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.48528 | − | 14.1421i | 0.620505 | − | 1.03418i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1421 | 1.60215 | 0.801074 | − | 0.598565i | \(-0.204262\pi\) | ||||
0.801074 | + | 0.598565i | \(0.204262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1421 | − | 17.1421i | −1.23392 | − | 1.23392i | −0.962447 | − | 0.271471i | \(-0.912490\pi\) |
−0.271471 | − | 0.962447i | \(-0.587510\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.00000i | 0.286446i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.41421 | + | 8.41421i | 0.599488 | + | 0.599488i | 0.940176 | − | 0.340688i | \(-0.110660\pi\) |
−0.340688 | + | 0.940176i | \(0.610660\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.41421 | + | 5.41421i | −0.383803 | + | 0.383803i | −0.872470 | − | 0.488667i | \(-0.837483\pi\) |
0.488667 | + | 0.872470i | \(0.337483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 6.00000i | −0.423207 | + | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.17157 | −0.643718 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.7990 | 2.91937 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.58579 | − | 2.58579i | 0.179725 | − | 0.179725i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | − | 8.00000i | 0.553372 | − | 0.553372i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1421 | + | 10.1421i | 0.698213 | + | 0.698213i | 0.964025 | − | 0.265812i | \(-0.0856399\pi\) |
−0.265812 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.343146i | 0.0235120i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.3137 | − | 23.3137i | −1.58998 | − | 1.58998i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.31371 | 0.496487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.41421i | − | 0.0955637i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.17157 | − | 4.68629i | −0.0788085 | − | 0.315234i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.8284i | − | 1.79656i | −0.439419 | − | 0.898282i | \(-0.644816\pi\) | ||
0.439419 | − | 0.898282i | \(-0.355184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.65685 | −0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.4853 | − | 12.4853i | −0.828677 | − | 0.828677i | 0.158657 | − | 0.987334i | \(-0.449284\pi\) |
−0.987334 | + | 0.158657i | \(0.949284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.3137i | − | 0.879795i | −0.898048 | − | 0.439897i | \(-0.855015\pi\) | ||
0.898048 | − | 0.439897i | \(-0.144985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.65685 | + | 5.65685i | 0.372194 | + | 0.372194i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.17157 | + | 8.17157i | −0.535338 | + | 0.535338i | −0.922156 | − | 0.386818i | \(-0.873574\pi\) |
0.386818 | + | 0.922156i | \(0.373574\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.1421 | − | 26.1421i | 1.70532 | − | 1.70532i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.00000 | 0.389742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.7990 | −0.763213 | −0.381607 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381607 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.82843 | + | 1.82843i | −0.117779 | + | 0.117779i | −0.763540 | − | 0.645761i | \(-0.776540\pi\) |
0.645761 | + | 0.763540i | \(0.276540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.24264 | − | 7.24264i | −0.462715 | − | 0.462715i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.31371i | − | 0.210846i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.65685 | + | 7.65685i | 0.485233 | + | 0.485233i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.65685 | 0.104580 | 0.0522899 | − | 0.998632i | \(-0.483348\pi\) | ||||
0.0522899 | + | 0.998632i | \(0.483348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.6274i | − | 0.919618i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.6569 | − | 3.41421i | 0.855225 | − | 0.213806i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.31371i | 0.580973i | 0.956879 | + | 0.290487i | \(0.0938172\pi\) | ||||
−0.956879 | + | 0.290487i | \(0.906183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.7990 | −0.981701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.24264 | − | 3.24264i | −0.200714 | − | 0.200714i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.1716i | − | 0.812194i | −0.913830 | − | 0.406097i | \(-0.866890\pi\) | ||
0.913830 | − | 0.406097i | \(-0.133110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4853 | + | 16.4853i | 1.01268 | + | 1.01268i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | + | 12.0000i | −0.734388 | + | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0711 | − | 12.0711i | 0.735986 | − | 0.735986i | −0.235813 | − | 0.971799i | \(-0.575775\pi\) |
0.971799 | + | 0.235813i | \(0.0757751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9706 | 1.03089 | 0.515444 | − | 0.856923i | \(-0.327627\pi\) | ||||
0.515444 | + | 0.856923i | \(0.327627\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.34315 | 0.141814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.8284 | + | 18.8284i | −1.13540 | + | 1.13540i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0711 | + | 18.0711i | −1.08579 | + | 1.08579i | −0.0898279 | + | 0.995957i | \(0.528632\pi\) |
−0.995957 | + | 0.0898279i | \(0.971368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.58579 | + | 2.58579i | 0.154807 | + | 0.154807i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6569i | 0.814700i | 0.913272 | + | 0.407350i | \(0.133547\pi\) | ||||
−0.913272 | + | 0.407350i | \(0.866453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | + | 20.0000i | 1.18888 | + | 1.18888i | 0.977378 | + | 0.211498i | \(0.0678343\pi\) |
0.211498 | + | 0.977378i | \(0.432166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.65685 | 0.572023 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 24.4853i | − | 1.44532i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | + | 8.00000i | −0.882353 | + | 0.470588i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.75736i | 0.454744i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.82843 | + | 6.82843i | 0.397566 | + | 0.397566i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.02944 | − | 3.02944i | −0.175197 | − | 0.175197i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.6569 | + | 13.6569i | −0.787168 | + | 0.787168i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.82843 | − | 8.82843i | 0.507180 | − | 0.507180i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.6569 | 0.896509 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.2843 | −1.38598 | −0.692988 | − | 0.720949i | \(-0.743706\pi\) | ||||
−0.692988 | + | 0.720949i | \(0.743706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.65685 | + | 7.65685i | −0.435583 | + | 0.435583i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.24264 | + | 4.24264i | −0.240578 | + | 0.240578i | −0.817089 | − | 0.576511i | \(-0.804414\pi\) |
0.576511 | + | 0.817089i | \(0.304414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4853 | + | 13.4853i | 0.762233 | + | 0.762233i | 0.976726 | − | 0.214492i | \(-0.0688097\pi\) |
−0.214492 | + | 0.976726i | \(0.568810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.82843i | 0.384738i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.8995 | − | 18.8995i | −1.06150 | − | 1.06150i | −0.997981 | − | 0.0635209i | \(-0.979767\pi\) |
−0.0635209 | − | 0.997981i | \(-0.520233\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.3431 | −1.02702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3137 | + | 2.82843i | −0.629512 | + | 0.157378i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.79899i | 0.432610i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.585786 | 0.0323941 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3137 | − | 15.3137i | −0.844272 | − | 0.844272i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.686292i | − | 0.0377220i | −0.999822 | − | 0.0188610i | \(-0.993996\pi\) | ||
0.999822 | − | 0.0188610i | \(-0.00600400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.58579 | − | 5.58579i | −0.306099 | − | 0.306099i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.4853 | + | 20.4853i | −1.11923 | + | 1.11923i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.9706 | + | 23.9706i | −1.30576 | + | 1.30576i | −0.381314 | + | 0.924445i | \(0.624528\pi\) |
−0.924445 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.24264 | −0.447679 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6274 | 0.792119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1421 | + | 14.1421i | −0.763604 | + | 0.763604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.82843 | − | 8.82843i | 0.475307 | − | 0.475307i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.6569 | + | 17.6569i | 0.947870 | + | 0.947870i | 0.998707 | − | 0.0508373i | \(-0.0161890\pi\) |
−0.0508373 | + | 0.998707i | \(0.516189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.8284i | − | 1.22198i | −0.791639 | − | 0.610989i | \(-0.790772\pi\) | ||
0.791639 | − | 0.610989i | \(-0.209228\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.828427 | + | 0.828427i | 0.0442182 | + | 0.0442182i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6274 | 1.31079 | 0.655393 | − | 0.755288i | \(-0.272503\pi\) | ||||
0.655393 | + | 0.755288i | \(0.272503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.17157i | 0.0621806i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | − | 8.00000i | −0.105851 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.6274i | 1.61645i | 0.588872 | + | 0.808227i | \(0.299572\pi\) | ||||
−0.588872 | + | 0.808227i | \(0.700428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.53553 | + | 3.53553i | 0.185567 | + | 0.185567i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.82843i | − | 0.252731i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7574 | + | 11.7574i | 0.613729 | + | 0.613729i | 0.943916 | − | 0.330187i | \(-0.107112\pi\) |
−0.330187 | + | 0.943916i | \(0.607112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.65685 | − | 8.65685i | 0.450658 | − | 0.450658i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.65685 | − | 9.65685i | 0.501359 | − | 0.501359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1421 | 0.525140 | 0.262570 | − | 0.964913i | \(-0.415430\pi\) | ||||
0.262570 | + | 0.964913i | \(0.415430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.79899 | + | 3.79899i | −0.195658 | + | 0.195658i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | − | 8.00000i | 0.410932 | − | 0.410932i | −0.471131 | − | 0.882063i | \(-0.656154\pi\) |
0.882063 | + | 0.471131i | \(0.156154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3137 | + | 15.3137i | 0.784545 | + | 0.784545i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.1421i | − | 0.722629i | −0.932444 | − | 0.361315i | \(-0.882328\pi\) | ||
0.932444 | − | 0.361315i | \(-0.117672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.3137 | + | 19.3137i | 0.984318 | + | 0.984318i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.65685 | −0.490885 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00000i | 0.101404i | 0.998714 | + | 0.0507020i | \(0.0161459\pi\) | ||||
−0.998714 | + | 0.0507020i | \(0.983854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.75736 | + | 12.9289i | −0.392307 | + | 0.653844i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.9706i | − | 0.856052i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.4853 | 1.03073 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.07107 | − | 8.07107i | −0.405075 | − | 0.405075i | 0.474942 | − | 0.880017i | \(-0.342469\pi\) |
−0.880017 | + | 0.474942i | \(0.842469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 5.65685i | − | 0.283197i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.3431 | − | 11.3431i | −0.566450 | − | 0.566450i | 0.364682 | − | 0.931132i | \(-0.381178\pi\) |
−0.931132 | + | 0.364682i | \(0.881178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.02944 | − | 3.02944i | 0.150907 | − | 0.150907i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.41421 | + | 2.41421i | −0.119963 | + | 0.119963i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.5980 | −1.56625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.31371 | 0.262746 | 0.131373 | − | 0.991333i | \(-0.458061\pi\) | ||||
0.131373 | + | 0.991333i | \(0.458061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.4853 | + | 16.4853i | −0.813159 | + | 0.813159i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | − | 4.00000i | 0.196827 | − | 0.196827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.1421 | + | 26.1421i | 1.28327 | + | 1.28327i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.65685i | 0.472898i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.17157 | + | 1.17157i | 0.0572351 | + | 0.0572351i | 0.735145 | − | 0.677910i | \(-0.237114\pi\) |
−0.677910 | + | 0.735145i | \(0.737114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1421 | 0.884194 | 0.442097 | − | 0.896967i | \(-0.354235\pi\) | ||||
0.442097 | + | 0.896967i | \(0.354235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.8284i | − | 0.526496i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.6274 | − | 6.65685i | 1.29162 | − | 0.322905i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.17157i | − | 0.443844i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.68629 | 0.226256 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.89949 | + | 9.89949i | 0.476842 | + | 0.476842i | 0.904120 | − | 0.427278i | \(-0.140528\pi\) |
−0.427278 | + | 0.904120i | \(0.640528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3137i | 0.639816i | 0.947449 | + | 0.319908i | \(0.103652\pi\) | ||||
−0.947449 | + | 0.319908i | \(0.896348\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0711 | − | 11.0711i | −0.530817 | − | 0.530817i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.31371 | + | 7.31371i | −0.349862 | + | 0.349862i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.07107 | + | 3.07107i | −0.146574 | + | 0.146574i | −0.776586 | − | 0.630012i | \(-0.783050\pi\) |
0.630012 | + | 0.776586i | \(0.283050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.65685 | 0.458811 | 0.229405 | − | 0.973331i | \(-0.426322\pi\) | ||||
0.229405 | + | 0.973331i | \(0.426322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.9706 | + | 40.9706i | −1.94219 | + | 1.94219i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.75736 | − | 3.75736i | 0.177717 | − | 0.177717i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.3137 | + | 12.3137i | 0.581120 | + | 0.581120i | 0.935211 | − | 0.354091i | \(-0.115210\pi\) |
−0.354091 | + | 0.935211i | \(0.615210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 48.9706i | − | 2.30593i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | − | 4.00000i | −0.187936 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.00000 | 0.375046 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.0000i | − | 1.02912i | −0.857455 | − | 0.514558i | \(-0.827956\pi\) | ||
0.857455 | − | 0.514558i | \(-0.172044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.12132 | − | 3.53553i | 0.0990148 | − | 0.165025i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.48528i | − | 0.208900i | −0.994530 | − | 0.104450i | \(-0.966692\pi\) | ||
0.994530 | − | 0.104450i | \(-0.0333083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8284 | −1.61861 | −0.809307 | − | 0.587386i | \(-0.800157\pi\) | ||||
−0.809307 | + | 0.587386i | \(0.800157\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.82843 | + | 8.82843i | 0.409409 | + | 0.409409i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.00000i | − | 0.185098i | −0.995708 | − | 0.0925490i | \(-0.970499\pi\) | ||
0.995708 | − | 0.0925490i | \(-0.0295015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | + | 12.0000i | 0.554109 | + | 0.554109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.07107 | + | 7.07107i | −0.325818 | + | 0.325818i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.3137 | + | 27.3137i | −1.25589 | + | 1.25589i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.8284 | 0.863907 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.82843 | 0.312652 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.72792 | − | 4.72792i | 0.216024 | − | 0.216024i | −0.590796 | − | 0.806821i | \(-0.701186\pi\) |
0.806821 | + | 0.590796i | \(0.201186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.54416 | + | 6.54416i | −0.298388 | + | 0.298388i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.17157 | − | 5.17157i | −0.235315 | − | 0.235315i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.4853i | 1.20263i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3848 | − | 22.3848i | −1.01435 | − | 1.01435i | −0.999896 | − | 0.0144555i | \(-0.995399\pi\) |
−0.0144555 | − | 0.999896i | \(-0.504601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.02944i | 0.136717i | 0.997661 | + | 0.0683583i | \(0.0217761\pi\) | ||||
−0.997661 | + | 0.0683583i | \(0.978224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.2132 | + | 9.72792i | 0.730206 | + | 0.438124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.6569i | 0.613830i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.686292 | 0.0307844 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | − | 8.00000i | −0.358129 | − | 0.358129i | 0.504994 | − | 0.863123i | \(-0.331495\pi\) |
−0.863123 | + | 0.504994i | \(0.831495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.0000i | − | 0.446767i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0711 | − | 11.0711i | −0.493635 | − | 0.493635i | 0.415815 | − | 0.909449i | \(-0.363496\pi\) |
−0.909449 | + | 0.415815i | \(0.863496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.1421 | − | 30.1421i | 1.34131 | − | 1.34131i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.22183 | + | 8.22183i | −0.365144 | + | 0.365144i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.6274 | −1.09159 | −0.545796 | − | 0.837918i | \(-0.683772\pi\) | ||||
−0.545796 | + | 0.837918i | \(0.683772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.82843 | −0.125122 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | − | 2.00000i | 0.0883022 | − | 0.0883022i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.1421 | + | 26.1421i | −1.15196 | + | 1.15196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.6274 | − | 30.6274i | −1.34699 | − | 1.34699i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.4142i | 0.852189i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.9706 | + | 27.9706i | 1.22541 | + | 1.22541i | 0.965681 | + | 0.259732i | \(0.0836342\pi\) |
0.259732 | + | 0.965681i | \(0.416366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.7990 | −0.515934 | −0.257967 | − | 0.966154i | \(-0.583053\pi\) | ||||
−0.257967 | + | 0.966154i | \(0.583053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.3137i | 0.581058i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9289 | − | 7.75736i | −0.563193 | − | 0.337916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.62742i | − | 0.418583i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | 0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.1421 | − | 10.1421i | −0.439305 | − | 0.439305i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.17157 | − | 9.17157i | −0.395783 | − | 0.395783i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.48528 | + | 8.48528i | −0.365487 | + | 0.365487i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2426 | − | 11.2426i | 0.483359 | − | 0.483359i | −0.422844 | − | 0.906203i | \(-0.638968\pi\) |
0.906203 | + | 0.422844i | \(0.138968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.75736 | −0.247072 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.8284 | − | 18.8284i | 0.805045 | − | 0.805045i | −0.178834 | − | 0.983879i | \(-0.557232\pi\) |
0.983879 | + | 0.178834i | \(0.0572325\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.24264 | − | 3.24264i | 0.138393 | − | 0.138393i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.17157 | + | 9.17157i | 0.390722 | + | 0.390722i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.0000i | − | 0.510292i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.0711 | − | 19.0711i | −0.809522 | − | 0.809522i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.4853 | 1.54593 | 0.772965 | − | 0.634448i | \(-0.218773\pi\) | ||||
0.772965 | + | 0.634448i | \(0.218773\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3137i | 0.478519i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | − | 16.0000i | −0.168880 | − | 0.675521i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.8284i | 0.793524i | 0.917922 | + | 0.396762i | \(0.129866\pi\) | ||||
−0.917922 | + | 0.396762i | \(0.870134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.1421 | −1.18395 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41421 | + | 1.41421i | 0.0593914 | + | 0.0593914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.686292i | 0.0287708i | 0.999897 | + | 0.0143854i | \(0.00457918\pi\) | ||||
−0.999897 | + | 0.0143854i | \(0.995421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.82843 | + | 2.82843i | 0.118366 | + | 0.118366i | 0.763809 | − | 0.645443i | \(-0.223327\pi\) |
−0.645443 | + | 0.763809i | \(0.723327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6569 | − | 15.6569i | 0.654074 | − | 0.654074i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.2132 | − | 17.2132i | 0.717840 | − | 0.717840i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6863 | −0.528137 | −0.264069 | − | 0.964504i | \(-0.585065\pi\) | ||||
−0.264069 | + | 0.964504i | \(0.585065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.2426 | −1.00749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.3137 | − | 15.3137i | 0.635320 | − | 0.635320i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.3137 | − | 19.3137i | 0.799892 | − | 0.799892i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.82843 | + | 2.82843i | 0.116941 | + | 0.116941i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 43.5980i | − | 1.79948i | −0.436425 | − | 0.899741i | \(-0.643756\pi\) | ||
0.436425 | − | 0.899741i | \(-0.356244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.31371 | − | 7.31371i | −0.301356 | − | 0.301356i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.8995 | 0.489480 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.97056i | − | 0.204117i | −0.994778 | − | 0.102058i | \(-0.967457\pi\) | ||
0.994778 | − | 0.102058i | \(-0.0325428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.82843 | − | 27.3137i | −0.279938 | − | 1.11975i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.65685i | 0.313374i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.37258 | 0.0560822 | 0.0280411 | − | 0.999607i | \(-0.491073\pi\) | ||||
0.0280411 | + | 0.999607i | \(0.491073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6569 | − | 20.6569i | −0.842611 | − | 0.842611i | 0.146587 | − | 0.989198i | \(-0.453171\pi\) |
−0.989198 | + | 0.146587i | \(0.953171\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.48528i | 0.345547i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.0711 | + | 12.0711i | 0.490759 | + | 0.490759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.8995 | − | 21.8995i | 0.888873 | − | 0.888873i | −0.105542 | − | 0.994415i | \(-0.533658\pi\) |
0.994415 | + | 0.105542i | \(0.0336577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.48528 | + | 6.48528i | −0.262797 | + | 0.262797i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6863 | −0.513232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.31371 | −0.214619 | −0.107309 | − | 0.994226i | \(-0.534224\pi\) | ||||
−0.107309 | + | 0.994226i | \(0.534224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.5563 | − | 29.5563i | 1.19183 | − | 1.19183i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.48528 | − | 9.48528i | 0.381863 | − | 0.381863i | −0.489910 | − | 0.871773i | \(-0.662970\pi\) |
0.871773 | + | 0.489910i | \(0.162970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.31371 | + | 7.31371i | 0.293963 | + | 0.293963i | 0.838643 | − | 0.544681i | \(-0.183349\pi\) |
−0.544681 | + | 0.838643i | \(0.683349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 3.65685i | − | 0.146745i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.0000 | + | 24.0000i | 0.961540 | + | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 11.3137i | − | 0.451826i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.9289 | + | 16.7574i | 1.11360 | + | 0.668160i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4853i | 0.974744i | 0.873195 | + | 0.487372i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487372i | \(0.837956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.3431 | 0.570089 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 52.2843 | + | 52.2843i | 2.07484 | + | 2.07484i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.51472i | 0.139258i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.242641 | + | 0.242641i | 0.00959872 | + | 0.00959872i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.3137 | − | 32.3137i | 1.27631 | − | 1.27631i | 0.333600 | − | 0.942715i | \(-0.391736\pi\) |
0.942715 | − | 0.333600i | \(-0.108264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.485281 | − | 0.485281i | 0.0191376 | − | 0.0191376i | −0.697473 | − | 0.716611i | \(-0.745692\pi\) |
0.716611 | + | 0.697473i | \(0.245692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.9706 | −1.29821 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.1421 | 0.555985 | 0.277992 | − | 0.960583i | \(-0.410331\pi\) | ||||
0.277992 | + | 0.960583i | \(0.410331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | − | 8.00000i | 0.314027 | − | 0.314027i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.17157 | − | 5.17157i | 0.202690 | − | 0.202690i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.0416 | − | 33.0416i | −1.29302 | − | 1.29302i | −0.932910 | − | 0.360108i | \(-0.882740\pi\) |
−0.360108 | − | 0.932910i | \(-0.617260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 57.9411i | − | 2.26395i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00000 | − | 1.00000i | −0.0390137 | − | 0.0390137i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1421 | −0.862535 | −0.431268 | − | 0.902224i | \(-0.641934\pi\) | ||||
−0.431268 | + | 0.902224i | \(0.641934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.51472i | 0.136707i | 0.997661 | + | 0.0683534i | \(0.0217745\pi\) | ||||
−0.997661 | + | 0.0683534i | \(0.978225\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.14214 | − | 2.48528i | −0.160867 | − | 0.0965203i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 19.3137i | − | 0.748953i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.7696 | 0.649320 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9706 | − | 18.9706i | −0.733444 | − | 0.733444i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.3431i | − | 0.708129i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1421 | − | 23.1421i | −0.892064 | − | 0.892064i | 0.102653 | − | 0.994717i | \(-0.467267\pi\) |
−0.994717 | + | 0.102653i | \(0.967267\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.70711 | + | 4.70711i | −0.181177 | + | 0.181177i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.5563 | + | 16.5563i | −0.636312 | + | 0.636312i | −0.949644 | − | 0.313332i | \(-0.898555\pi\) |
0.313332 | + | 0.949644i | \(0.398555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.5147 | 0.595400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.6569 | −0.676612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.00000 | + | 8.00000i | −0.306111 | + | 0.306111i | −0.843399 | − | 0.537288i | \(-0.819449\pi\) |
0.537288 | + | 0.843399i | \(0.319449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56.2843 | + | 56.2843i | −2.15051 | + | 2.15051i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.41421 | − | 9.41421i | −0.359175 | − | 0.359175i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.00000i | − | 0.304776i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8284 | + | 14.8284i | 0.564100 | + | 0.564100i | 0.930469 | − | 0.366369i | \(-0.119399\pi\) |
−0.366369 | + | 0.930469i | \(0.619399\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.00000 | 0.303895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.9706i | 1.25064i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.9706 | + | 43.2843i | −0.983705 | + | 1.63951i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5563i | 0.437101i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.82843 | −0.257906 | −0.128953 | − | 0.991651i | \(-0.541162\pi\) | ||||
−0.128953 | + | 0.991651i | \(0.541162\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.7990 | + | 15.7990i | 0.595870 | + | 0.595870i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 36.9706i | − | 1.39239i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.6569 | − | 17.6569i | −0.664054 | − | 0.664054i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.2426 | − | 21.2426i | 0.797784 | − | 0.797784i | −0.184962 | − | 0.982746i | \(-0.559216\pi\) |
0.982746 | + | 0.184962i | \(0.0592161\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.24264 | − | 4.24264i | 0.159111 | − | 0.159111i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.3726 | −0.500807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.34315 | + | 8.34315i | −0.311580 | + | 0.311580i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7574 | − | 19.7574i | 0.736825 | − | 0.736825i | −0.235137 | − | 0.971962i | \(-0.575554\pi\) |
0.971962 | + | 0.235137i | \(0.0755539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3137 | + | 15.3137i | 0.570312 | + | 0.570312i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.58579i | 0.0961664i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.5858 | − | 21.5858i | −0.801676 | − | 0.801676i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.2843 | −1.64241 | −0.821206 | − | 0.570631i | \(-0.806699\pi\) | ||||
−0.821206 | + | 0.570631i | \(0.806699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.6274 | − | 9.65685i | 1.42869 | − | 0.357172i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.1127i | 1.29692i | 0.761250 | + | 0.648459i | \(0.224586\pi\) | ||||
−0.761250 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.2426 | −0.377805 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.0000 | + | 24.0000i | 0.884051 | + | 0.884051i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.7990i | − | 0.728318i | −0.931337 | − | 0.364159i | \(-0.881357\pi\) | ||
0.931337 | − | 0.364159i | \(-0.118643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.34315 | − | 2.34315i | −0.0860776 | − | 0.0860776i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4142 | + | 25.4142i | −0.932357 | + | 0.932357i | −0.997853 | − | 0.0654958i | \(-0.979137\pi\) |
0.0654958 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.8284 | − | 12.8284i | 0.469997 | − | 0.469997i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8284 | 0.396191 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.58579 | − | 6.58579i | 0.240319 | − | 0.240319i | −0.576663 | − | 0.816982i | \(-0.695646\pi\) |
0.816982 | + | 0.576663i | \(0.195646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.17157 | − | 1.17157i | 0.0426945 | − | 0.0426945i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.6569 | − | 13.6569i | −0.497024 | − | 0.497024i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.6863i | − | 0.533782i | −0.963727 | − | 0.266891i | \(-0.914004\pi\) | ||
0.963727 | − | 0.266891i | \(-0.0859964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.3431 | − | 10.3431i | −0.375432 | − | 0.375432i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.3137 | 1.42512 | 0.712560 | − | 0.701611i | \(-0.247535\pi\) | ||||
0.712560 | + | 0.701611i | \(0.247535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.17157i | − | 0.0424138i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.24264 | − | 12.0711i | 0.261858 | − | 0.436430i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.31371i | − | 0.119651i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.9706 | −1.76592 | −0.882962 | − | 0.469445i | \(-0.844454\pi\) | ||||
−0.882962 | + | 0.469445i | \(0.844454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.58579 | + | 6.58579i | 0.237181 | + | 0.237181i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.0000i | 1.36677i | 0.730061 | + | 0.683383i | \(0.239492\pi\) | ||||
−0.730061 | + | 0.683383i | \(0.760508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.2132 | + | 17.2132i | 0.618317 | + | 0.618317i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.1716 | + | 11.1716i | −0.400778 | + | 0.400778i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.4853 | + | 24.4853i | −0.877276 | + | 0.877276i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37258 | 0.0491149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.58579 | −0.163883 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.1421 | + | 24.1421i | −0.861670 | + | 0.861670i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1421 | + | 38.1421i | −1.35962 | + | 1.35962i | −0.485238 | + | 0.874382i | \(0.661267\pi\) |
−0.874382 | + | 0.485238i | \(0.838733\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.31371 | − | 9.31371i | −0.331577 | − | 0.331577i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4853i | 0.586149i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.79899 | − | 3.79899i | −0.134906 | − | 0.134906i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.3137 | 0.826852 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4853i | 0.442251i | 0.975245 | + | 0.221126i | \(0.0709731\pi\) | ||||
−0.975245 | + | 0.221126i | \(0.929027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8284 | + | 43.3137i | 0.383082 | + | 1.53233i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.9706i | 0.599625i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.65685 | −0.199626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.6569 | − | 17.6569i | −0.622322 | − | 0.622322i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 17.0711i | − | 0.600930i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.62742 | − | 5.62742i | −0.197849 | − | 0.197849i | 0.601228 | − | 0.799077i | \(-0.294678\pi\) |
−0.799077 | + | 0.601228i | \(0.794678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7990 | − | 15.7990i | 0.554778 | − | 0.554778i | −0.373038 | − | 0.927816i | \(-0.621684\pi\) |
0.927816 | + | 0.373038i | \(0.121684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | − | 12.0000i | 0.420858 | − | 0.420858i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.6274 | 1.35306 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3137 | 0.955586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.65685 | − | 1.65685i | 0.0578952 | − | 0.0578952i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7574 | − | 26.7574i | 0.933838 | − | 0.933838i | −0.0641049 | − | 0.997943i | \(-0.520419\pi\) |
0.997943 | + | 0.0641049i | \(0.0204192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8995 | + | 13.8995i | 0.484506 | + | 0.484506i | 0.906567 | − | 0.422061i | \(-0.138693\pi\) |
−0.422061 | + | 0.906567i | \(0.638693\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.6274i | 0.927048i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.8284 | − | 26.8284i | −0.932916 | − | 0.932916i | 0.0649713 | − | 0.997887i | \(-0.479304\pi\) |
−0.997887 | + | 0.0649713i | \(0.979304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6863 | −1.06578 | −0.532889 | − | 0.846185i | \(-0.678894\pi\) | ||||
−0.532889 | + | 0.846185i | \(0.678894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5563i | 0.886540i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0000 | − | 3.00000i | 0.415775 | − | 0.103944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 34.1421i | − | 1.18154i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.65685 | 0.126399 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.8995 | + | 17.8995i | 0.617959 | + | 0.617959i | 0.945008 | − | 0.327048i | \(-0.106054\pi\) |
−0.327048 | + | 0.945008i | \(0.606054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.97056i | 0.274847i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.65685 | + | 9.65685i | 0.332600 | + | 0.332600i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.0711 | + | 28.0711i | −0.965674 | + | 0.965674i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.07107 | − | 7.07107i | 0.242965 | − | 0.242965i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.2843 | 0.970714 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.8873 | 0.990244 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.10051 | − | 9.10051i | 0.311595 | − | 0.311595i | −0.533932 | − | 0.845527i | \(-0.679286\pi\) |
0.845527 | + | 0.533932i | \(0.179286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.82843 | − | 6.82843i | 0.233527 | − | 0.233527i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.2843 | + | 15.2843i | 0.522101 | + | 0.522101i | 0.918205 | − | 0.396105i | \(-0.129638\pi\) |
−0.396105 | + | 0.918205i | \(0.629638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.9117i | 1.87356i | 0.349915 | + | 0.936781i | \(0.386210\pi\) | ||||
−0.349915 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.3137 | − | 17.3137i | −0.590050 | − | 0.590050i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.6569 | −1.00953 | −0.504766 | − | 0.863256i | \(-0.668421\pi\) | ||||
−0.504766 | + | 0.863256i | \(0.668421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.2843i | 2.25373i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.94975 | + | 16.2635i | −0.168102 | + | 0.552336i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 24.0000i | − | 0.814144i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.94113 | 0.336842 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.48528 | + | 5.48528i | 0.185649 | + | 0.185649i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137i | 0.382473i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.75736 | + | 2.75736i | 0.0931094 | + | 0.0931094i | 0.752127 | − | 0.659018i | \(-0.229028\pi\) |
−0.659018 | + | 0.752127i | \(0.729028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.41421 | + | 1.41421i | −0.0477002 | + | 0.0477002i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.7990 | + | 16.7990i | −0.565972 | + | 0.565972i | −0.930998 | − | 0.365025i | \(-0.881060\pi\) |
0.365025 | + | 0.930998i | \(0.381060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2010 | 0.410597 | 0.205298 | − | 0.978699i | \(-0.434184\pi\) | ||||
0.205298 | + | 0.978699i | \(0.434184\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.65685 | 0.324612 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5563 | − | 11.5563i | 0.388024 | − | 0.388024i | −0.485958 | − | 0.873982i | \(-0.661529\pi\) |
0.873982 | + | 0.485958i | \(0.161529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.6274 | − | 30.6274i | 1.02721 | − | 1.02721i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.82843 | + | 2.82843i | 0.0947559 | + | 0.0947559i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.6274i | 1.02491i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3137 | − | 31.3137i | −1.04670 | − | 1.04670i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.28427 | −0.143048 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.7696i | 0.559296i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.3137 | + | 6.82843i | −0.909952 | + | 0.227488i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.3137i | 0.642720i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6569 | −0.653416 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.686292 | − | 0.686292i | −0.0227879 | − | 0.0227879i | 0.695621 | − | 0.718409i | \(-0.255129\pi\) |
−0.718409 | + | 0.695621i | \(0.755129\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 12.4853i | − | 0.414111i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.2426 | − | 16.2426i | −0.538143 | − | 0.538143i | 0.384840 | − | 0.922983i | \(-0.374256\pi\) |
−0.922983 | + | 0.384840i | \(0.874256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.6274 | − | 30.6274i | 1.01362 | − | 1.01362i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.0711 | − | 11.0711i | 0.365998 | − | 0.365998i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.9411 | −1.12083 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −58.9117 | −1.94332 | −0.971659 | − | 0.236388i | \(-0.924036\pi\) | ||||
−0.971659 | + | 0.236388i | \(0.924036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1716 | + | 17.1716i | −0.565823 | + | 0.565823i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.284271 | − | 0.284271i | 0.00935690 | − | 0.00935690i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.1838 | − | 37.1838i | −1.22259 | − | 1.22259i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8284i | 0.355652i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.9706 | + | 15.9706i | 0.523977 | + | 0.523977i | 0.918770 | − | 0.394793i | \(-0.129184\pi\) |
−0.394793 | + | 0.918770i | \(0.629184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.48528 | 0.278094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.00000i | 0.196431i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.6569 | − | 54.6274i | −0.446627 | − | 1.78651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.6863i | − | 0.545117i | −0.962139 | − | 0.272559i | \(-0.912130\pi\) | ||
0.962139 | − | 0.272559i | \(-0.0878699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0711 | 0.622361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.10051 | + | 5.10051i | 0.166272 | + | 0.166272i | 0.785338 | − | 0.619067i | \(-0.212489\pi\) |
−0.619067 | + | 0.785338i | \(0.712489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.7696i | 1.45790i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.82843 | + | 4.82843i | 0.157069 | + | 0.157069i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.14214 | + | 6.14214i | −0.199593 | + | 0.199593i | −0.799825 | − | 0.600233i | \(-0.795075\pi\) |
0.600233 | + | 0.799825i | \(0.295075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.17157 | + | 1.17157i | −0.0380309 | + | 0.0380309i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.7279 | −0.866712 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.6863 | −1.18839 | −0.594193 | − | 0.804323i | \(-0.702528\pi\) | ||||
−0.594193 | + | 0.804323i | \(0.702528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.4558 | − | 53.4558i | 1.72979 | − | 1.72979i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.9706 | + | 12.9706i | −0.419279 | + | 0.419279i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.9706 | + | 32.9706i | 1.06467 | + | 1.06467i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.6274i | 0.568626i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −82.7696 | −2.66445 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.4853i | − | 0.530131i | −0.964230 | − | 0.265065i | \(-0.914606\pi\) | ||
0.964230 | − | 0.265065i | \(-0.0853936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | + | 10.0000i | −0.192748 | + | 0.321246i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 10.8284i | − | 0.347501i | −0.984790 | − | 0.173750i | \(-0.944411\pi\) | ||
0.984790 | − | 0.173750i | \(-0.0555886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.3137 | 0.619169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.51472 | + | 5.51472i | 0.176612 | + | 0.176612i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6274i | 0.340001i | 0.985444 | + | 0.170001i | \(0.0543770\pi\) | ||||
−0.985444 | + | 0.170001i | \(0.945623\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.0000 | + | 48.0000i | 1.53409 | + | 1.53409i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.414214 | − | 0.414214i | 0.0132248 | − | 0.0132248i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.07107 | + | 3.07107i | −0.0979519 | + | 0.0979519i | −0.754385 | − | 0.656433i | \(-0.772065\pi\) |
0.656433 | + | 0.754385i | \(0.272065\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.6274 | 1.29450 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.6569 | −0.689345 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9706 | − | 24.9706i | 0.794018 | − | 0.794018i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.8995 | + | 33.8995i | −1.07685 | + | 1.07685i | −0.0800632 | + | 0.996790i | \(0.525512\pi\) |
−0.996790 | + | 0.0800632i | \(0.974488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.485281 | − | 0.485281i | −0.0153999 | − | 0.0153999i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.1421i | 0.828761i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7279 | + | 17.7279i | 0.561449 | + | 0.561449i | 0.929719 | − | 0.368270i | \(-0.120050\pi\) |
−0.368270 | + | 0.929719i | \(0.620050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.89949 | −0.249929 |
(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 | 408.2.v.b.361.2 | yes | 4 | |
3.2 | odd | 2 | 1224.2.w.g.361.1 | 4 | |||
4.3 | odd | 2 | 816.2.bd.c.769.1 | 4 | |||
12.11 | even | 2 | 2448.2.be.p.1585.1 | 4 | |||
17.8 | even | 8 | 6936.2.a.v.1.2 | 2 | |||
17.9 | even | 8 | 6936.2.a.w.1.1 | 2 | |||
17.13 | even | 4 | inner | 408.2.v.b.217.2 | ✓ | 4 | |
51.47 | odd | 4 | 1224.2.w.g.217.1 | 4 | |||
68.47 | odd | 4 | 816.2.bd.c.625.1 | 4 | |||
204.47 | even | 4 | 2448.2.be.p.1441.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
408.2.v.b.217.2 | ✓ | 4 | 17.13 | even | 4 | inner | |
408.2.v.b.361.2 | yes | 4 | 1.1 | even | 1 | trivial | |
816.2.bd.c.625.1 | 4 | 68.47 | odd | 4 | |||
816.2.bd.c.769.1 | 4 | 4.3 | odd | 2 | |||
1224.2.w.g.217.1 | 4 | 51.47 | odd | 4 | |||
1224.2.w.g.361.1 | 4 | 3.2 | odd | 2 | |||
2448.2.be.p.1441.1 | 4 | 204.47 | even | 4 | |||
2448.2.be.p.1585.1 | 4 | 12.11 | even | 2 | |||
6936.2.a.v.1.2 | 2 | 17.8 | even | 8 | |||
6936.2.a.w.1.1 | 2 | 17.9 | even | 8 |