Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(799,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1425.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.c (of order \(2\), degree \(1\), not 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: | \(11.3786822880\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 285) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.799 |
Dual form | 1425.2.c.k.799.3 |
$q$-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 \(\left(\mathbb{Z}/1425\mathbb{Z}\right)^\times\).
\(n\) | \(476\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.73205i | − 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | − 0.732051i | − 0.276689i | −0.990384 | − | 0.138345i | \(-0.955822\pi\) | ||||
0.990384 | − | 0.138345i | \(-0.0441781\pi\) | |||||||
\(8\) | − 1.73205i | − 0.612372i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 2.73205i | − 0.757735i | −0.925451 | − | 0.378867i | \(-0.876314\pi\) | ||||
0.925451 | − | 0.378867i | \(-0.123686\pi\) | |||||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.73205i | 0.408248i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | − 2.19615i | − 0.468221i | ||||||||
\(23\) | − 3.46410i | − 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.73205 | −0.928032 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0.732051i | 0.138345i | ||||||||
\(29\) | 2.19615 | 0.407815 | 0.203908 | − | 0.978990i | \(-0.434636\pi\) | ||||
0.203908 | + | 0.978990i | \(0.434636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.92820 | −0.885131 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | 1.26795i | 0.220722i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 4.19615i | − 0.689843i | −0.938631 | − | 0.344922i | \(-0.887905\pi\) | ||||
0.938631 | − | 0.344922i | \(-0.112095\pi\) | |||||||
\(38\) | 1.73205i | 0.280976i | ||||||||
\(39\) | 2.73205 | 0.437478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73205 | 0.739022 | 0.369511 | − | 0.929226i | \(-0.379525\pi\) | ||||
0.369511 | + | 0.929226i | \(0.379525\pi\) | |||||||
\(42\) | − 1.26795i | − 0.195649i | ||||||||
\(43\) | − 6.19615i | − 0.944904i | −0.881356 | − | 0.472452i | \(-0.843369\pi\) | ||||
0.881356 | − | 0.472452i | \(-0.156631\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − 3.46410i | − 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | − 5.00000i | − 0.721688i | ||||||||
\(49\) | 6.46410 | 0.923443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.73205i | 0.378867i | ||||||||
\(53\) | − 2.53590i | − 0.348332i | −0.984716 | − | 0.174166i | \(-0.944277\pi\) | ||||
0.984716 | − | 0.174166i | \(-0.0557230\pi\) | |||||||
\(54\) | −1.73205 | −0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.26795 | −0.169437 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | − 3.80385i | − 0.499470i | ||||||||
\(59\) | −9.46410 | −1.23212 | −0.616061 | − | 0.787699i | \(-0.711272\pi\) | ||||
−0.616061 | + | 0.787699i | \(0.711272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4641 | −1.72390 | −0.861951 | − | 0.506992i | \(-0.830757\pi\) | ||||
−0.861951 | + | 0.506992i | \(0.830757\pi\) | |||||||
\(62\) | 8.53590i | 1.08406i | ||||||||
\(63\) | 0.732051i | 0.0922297i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.19615 | 0.270328 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3923 | 1.94541 | 0.972704 | − | 0.232048i | \(-0.0745426\pi\) | ||||
0.972704 | + | 0.232048i | \(0.0745426\pi\) | |||||||
\(72\) | 1.73205i | 0.204124i | ||||||||
\(73\) | − 3.07180i | − 0.359527i | −0.983710 | − | 0.179763i | \(-0.942467\pi\) | ||||
0.983710 | − | 0.179763i | \(-0.0575332\pi\) | |||||||
\(74\) | −7.26795 | −0.844882 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − 0.928203i | − 0.105779i | ||||||||
\(78\) | − 4.73205i | − 0.535799i | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 8.19615i | − 0.905114i | ||||||||
\(83\) | 0.928203i | 0.101884i | 0.998702 | + | 0.0509418i | \(0.0162223\pi\) | ||||
−0.998702 | + | 0.0509418i | \(0.983778\pi\) | |||||||
\(84\) | −0.732051 | −0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.7321 | −1.15727 | ||||||||
\(87\) | 2.19615i | 0.235452i | ||||||||
\(88\) | − 2.19615i | − 0.234111i | ||||||||
\(89\) | −7.26795 | −0.770401 | −0.385201 | − | 0.922833i | \(-0.625868\pi\) | ||||
−0.385201 | + | 0.922833i | \(0.625868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 3.46410i | 0.361158i | ||||||||
\(93\) | − 4.92820i | − 0.511031i | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.19615 | −0.530330 | ||||||||
\(97\) | − 4.19615i | − 0.426055i | −0.977046 | − | 0.213027i | \(-0.931668\pi\) | ||||
0.977046 | − | 0.213027i | \(-0.0683323\pi\) | |||||||
\(98\) | − 11.1962i | − 1.13098i | ||||||||
\(99\) | −1.26795 | −0.127434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.8564i | − 1.75944i | −0.475488 | − | 0.879722i | \(-0.657729\pi\) | ||||
0.475488 | − | 0.879722i | \(-0.342271\pi\) | |||||||
\(104\) | −4.73205 | −0.464016 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.39230 | −0.426618 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −6.39230 | −0.612272 | −0.306136 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306136 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.19615 | 0.398281 | ||||||||
\(112\) | 3.66025i | 0.345861i | ||||||||
\(113\) | 5.07180i | 0.477115i | 0.971128 | + | 0.238557i | \(0.0766745\pi\) | ||||
−0.971128 | + | 0.238557i | \(0.923326\pi\) | |||||||
\(114\) | −1.73205 | −0.162221 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.19615 | −0.203908 | ||||||||
\(117\) | 2.73205i | 0.252578i | ||||||||
\(118\) | 16.3923i | 1.50903i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 23.3205i | 2.11134i | ||||||||
\(123\) | 4.73205i | 0.426675i | ||||||||
\(124\) | 4.92820 | 0.442566 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.26795 | 0.112958 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | 6.19615 | 0.545541 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1244 | 1.32142 | 0.660711 | − | 0.750641i | \(-0.270255\pi\) | ||||
0.660711 | + | 0.750641i | \(0.270255\pi\) | |||||||
\(132\) | − 1.26795i | − 0.110361i | ||||||||
\(133\) | 0.732051i | 0.0634769i | ||||||||
\(134\) | −13.8564 | −1.19701 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.85641i | 0.671218i | 0.942001 | + | 0.335609i | \(0.108942\pi\) | ||||
−0.942001 | + | 0.335609i | \(0.891058\pi\) | |||||||
\(138\) | − 6.00000i | − 0.510754i | ||||||||
\(139\) | −12.3923 | −1.05110 | −0.525551 | − | 0.850762i | \(-0.676141\pi\) | ||||
−0.525551 | + | 0.850762i | \(0.676141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.46410 | 0.291730 | ||||||||
\(142\) | − 28.3923i | − 2.38263i | ||||||||
\(143\) | − 3.46410i | − 0.289683i | ||||||||
\(144\) | 5.00000 | 0.416667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.32051 | −0.440328 | ||||||||
\(147\) | 6.46410i | 0.533150i | ||||||||
\(148\) | 4.19615i | 0.344922i | ||||||||
\(149\) | −7.85641 | −0.643622 | −0.321811 | − | 0.946804i | \(-0.604292\pi\) | ||||
−0.321811 | + | 0.946804i | \(0.604292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 1.73205i | 0.140488i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.60770 | −0.129552 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.73205 | −0.218739 | ||||||||
\(157\) | 14.3923i | 1.14863i | 0.818634 | + | 0.574315i | \(0.194732\pi\) | ||||
−0.818634 | + | 0.574315i | \(0.805268\pi\) | |||||||
\(158\) | 5.07180i | 0.403490i | ||||||||
\(159\) | 2.53590 | 0.201110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53590 | −0.199857 | ||||||||
\(162\) | − 1.73205i | − 0.136083i | ||||||||
\(163\) | 12.7321i | 0.997251i | 0.866817 | + | 0.498626i | \(0.166162\pi\) | ||||
−0.866817 | + | 0.498626i | \(0.833838\pi\) | |||||||
\(164\) | −4.73205 | −0.369511 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.60770 | 0.124781 | ||||||||
\(167\) | 3.46410i | 0.268060i | 0.990977 | + | 0.134030i | \(0.0427919\pi\) | ||||
−0.990977 | + | 0.134030i | \(0.957208\pi\) | |||||||
\(168\) | − 1.26795i | − 0.0978244i | ||||||||
\(169\) | 5.53590 | 0.425838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 6.19615i | 0.472452i | ||||||||
\(173\) | − 6.92820i | − 0.526742i | −0.964695 | − | 0.263371i | \(-0.915166\pi\) | ||||
0.964695 | − | 0.263371i | \(-0.0848343\pi\) | |||||||
\(174\) | 3.80385 | 0.288369 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.33975 | −0.477876 | ||||||||
\(177\) | − 9.46410i | − 0.711365i | ||||||||
\(178\) | 12.5885i | 0.943545i | ||||||||
\(179\) | 11.3205 | 0.846135 | 0.423067 | − | 0.906098i | \(-0.360953\pi\) | ||||
0.423067 | + | 0.906098i | \(0.360953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3923 | 1.36709 | 0.683545 | − | 0.729909i | \(-0.260437\pi\) | ||||
0.683545 | + | 0.729909i | \(0.260437\pi\) | |||||||
\(182\) | 3.46410i | 0.256776i | ||||||||
\(183\) | − 13.4641i | − 0.995295i | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.53590 | −0.625882 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.46410i | 0.252646i | ||||||||
\(189\) | −0.732051 | −0.0532489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6603 | 1.27785 | 0.638926 | − | 0.769269i | \(-0.279379\pi\) | ||||
0.638926 | + | 0.769269i | \(0.279379\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | − 7.12436i | − 0.512822i | −0.966568 | − | 0.256411i | \(-0.917460\pi\) | ||||
0.966568 | − | 0.256411i | \(-0.0825401\pi\) | |||||||
\(194\) | −7.26795 | −0.521808 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | 24.0000i | 1.70993i | 0.518686 | + | 0.854965i | \(0.326421\pi\) | ||||
−0.518686 | + | 0.854965i | \(0.673579\pi\) | |||||||
\(198\) | 2.19615i | 0.156074i | ||||||||
\(199\) | −19.3205 | −1.36959 | −0.684797 | − | 0.728734i | \(-0.740109\pi\) | ||||
−0.684797 | + | 0.728734i | \(0.740109\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | − 18.0000i | − 1.26648i | ||||||||
\(203\) | − 1.60770i | − 0.112838i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −30.9282 | −2.15487 | ||||||||
\(207\) | 3.46410i | 0.240772i | ||||||||
\(208\) | 13.6603i | 0.947168i | ||||||||
\(209\) | −1.26795 | −0.0877059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9282 | 1.02770 | 0.513850 | − | 0.857880i | \(-0.328219\pi\) | ||||
0.513850 | + | 0.857880i | \(0.328219\pi\) | |||||||
\(212\) | 2.53590i | 0.174166i | ||||||||
\(213\) | 16.3923i | 1.12318i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.73205 | −0.117851 | ||||||||
\(217\) | 3.60770i | 0.244906i | ||||||||
\(218\) | 11.0718i | 0.749877i | ||||||||
\(219\) | 3.07180 | 0.207573 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − 7.26795i | − 0.487793i | ||||||||
\(223\) | 9.85641i | 0.660034i | 0.943975 | + | 0.330017i | \(0.107054\pi\) | ||||
−0.943975 | + | 0.330017i | \(0.892946\pi\) | |||||||
\(224\) | 3.80385 | 0.254155 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.78461 | 0.584344 | ||||||||
\(227\) | 10.3923i | 0.689761i | 0.938647 | + | 0.344881i | \(0.112081\pi\) | ||||
−0.938647 | + | 0.344881i | \(0.887919\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | 25.4641 | 1.68272 | 0.841358 | − | 0.540479i | \(-0.181757\pi\) | ||||
0.841358 | + | 0.540479i | \(0.181757\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.928203 | 0.0610713 | ||||||||
\(232\) | − 3.80385i | − 0.249735i | ||||||||
\(233\) | 19.8564i | 1.30084i | 0.759576 | + | 0.650418i | \(0.225406\pi\) | ||||
−0.759576 | + | 0.650418i | \(0.774594\pi\) | |||||||
\(234\) | 4.73205 | 0.309344 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.46410 | 0.616061 | ||||||||
\(237\) | − 2.92820i | − 0.190207i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1962 | 1.30638 | 0.653190 | − | 0.757194i | \(-0.273430\pi\) | ||||
0.653190 | + | 0.757194i | \(0.273430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9282 | −1.09044 | −0.545221 | − | 0.838293i | \(-0.683554\pi\) | ||||
−0.545221 | + | 0.838293i | \(0.683554\pi\) | |||||||
\(242\) | 16.2679i | 1.04574i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 13.4641 | 0.861951 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.19615 | 0.522568 | ||||||||
\(247\) | 2.73205i | 0.173836i | ||||||||
\(248\) | 8.53590i | 0.542030i | ||||||||
\(249\) | −0.928203 | −0.0588225 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0526 | −0.634512 | −0.317256 | − | 0.948340i | \(-0.602761\pi\) | ||||
−0.317256 | + | 0.948340i | \(0.602761\pi\) | |||||||
\(252\) | − 0.732051i | − 0.0461149i | ||||||||
\(253\) | − 4.39230i | − 0.276142i | ||||||||
\(254\) | 6.92820 | 0.434714 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 24.0000i | 1.49708i | 0.663090 | + | 0.748539i | \(0.269245\pi\) | ||||
−0.663090 | + | 0.748539i | \(0.730755\pi\) | |||||||
\(258\) | − 10.7321i | − 0.668148i | ||||||||
\(259\) | −3.07180 | −0.190872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.19615 | −0.135938 | ||||||||
\(262\) | − 26.1962i | − 1.61840i | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | 2.19615 | 0.135164 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.26795 | 0.0777430 | ||||||||
\(267\) | − 7.26795i | − 0.444791i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 30.5885 | 1.86501 | 0.932506 | − | 0.361156i | \(-0.117618\pi\) | ||||
0.932506 | + | 0.361156i | \(0.117618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3923 | −1.23874 | −0.619372 | − | 0.785098i | \(-0.712613\pi\) | ||||
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 2.00000i | − 0.121046i | ||||||||
\(274\) | 13.6077 | 0.822071 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | − 2.00000i | − 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | 21.4641i | 1.28733i | ||||||||
\(279\) | 4.92820 | 0.295044 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.73205 | 0.282290 | 0.141145 | − | 0.989989i | \(-0.454922\pi\) | ||||
0.141145 | + | 0.989989i | \(0.454922\pi\) | |||||||
\(282\) | − 6.00000i | − 0.357295i | ||||||||
\(283\) | − 26.9808i | − 1.60384i | −0.597432 | − | 0.801920i | \(-0.703812\pi\) | ||||
0.597432 | − | 0.801920i | \(-0.296188\pi\) | |||||||
\(284\) | −16.3923 | −0.972704 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | − 3.46410i | − 0.204479i | ||||||||
\(288\) | − 5.19615i | − 0.306186i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.19615 | 0.245983 | ||||||||
\(292\) | 3.07180i | 0.179763i | ||||||||
\(293\) | − 27.7128i | − 1.61900i | −0.587120 | − | 0.809500i | \(-0.699738\pi\) | ||||
0.587120 | − | 0.809500i | \(-0.300262\pi\) | |||||||
\(294\) | 11.1962 | 0.652973 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.26795 | −0.422441 | ||||||||
\(297\) | − 1.26795i | − 0.0735739i | ||||||||
\(298\) | 13.6077i | 0.788273i | ||||||||
\(299\) | −9.46410 | −0.547323 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.53590 | −0.261445 | ||||||||
\(302\) | − 24.2487i | − 1.39536i | ||||||||
\(303\) | 10.3923i | 0.597022i | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.6077i | 0.662486i | 0.943545 | + | 0.331243i | \(0.107468\pi\) | ||||
−0.943545 | + | 0.331243i | \(0.892532\pi\) | |||||||
\(308\) | 0.928203i | 0.0528893i | ||||||||
\(309\) | 17.8564 | 1.01582 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.4449 | −1.49955 | −0.749775 | − | 0.661692i | \(-0.769838\pi\) | ||||
−0.749775 | + | 0.661692i | \(0.769838\pi\) | |||||||
\(312\) | − 4.73205i | − 0.267900i | ||||||||
\(313\) | − 14.3923i | − 0.813501i | −0.913539 | − | 0.406751i | \(-0.866662\pi\) | ||||
0.913539 | − | 0.406751i | \(-0.133338\pi\) | |||||||
\(314\) | 24.9282 | 1.40678 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.92820 | 0.164724 | ||||||||
\(317\) | − 23.3205i | − 1.30981i | −0.755711 | − | 0.654905i | \(-0.772709\pi\) | ||||
0.755711 | − | 0.654905i | \(-0.227291\pi\) | |||||||
\(318\) | − 4.39230i | − 0.246308i | ||||||||
\(319\) | 2.78461 | 0.155908 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.39230i | 0.244774i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.0526 | 1.22138 | ||||||||
\(327\) | − 6.39230i | − 0.353495i | ||||||||
\(328\) | − 8.19615i | − 0.452557i | ||||||||
\(329\) | −2.53590 | −0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.7128 | 1.63316 | 0.816582 | − | 0.577230i | \(-0.195866\pi\) | ||||
0.816582 | + | 0.577230i | \(0.195866\pi\) | |||||||
\(332\) | − 0.928203i | − 0.0509418i | ||||||||
\(333\) | 4.19615i | 0.229948i | ||||||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.66025 | −0.199683 | ||||||||
\(337\) | 19.1244i | 1.04177i | 0.853627 | + | 0.520885i | \(0.174398\pi\) | ||||
−0.853627 | + | 0.520885i | \(0.825602\pi\) | |||||||
\(338\) | − 9.58846i | − 0.521543i | ||||||||
\(339\) | −5.07180 | −0.275462 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.24871 | −0.338387 | ||||||||
\(342\) | − 1.73205i | − 0.0936586i | ||||||||
\(343\) | − 9.85641i | − 0.532196i | ||||||||
\(344\) | −10.7321 | −0.578633 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | − 12.9282i | − 0.694022i | −0.937861 | − | 0.347011i | \(-0.887197\pi\) | ||||
0.937861 | − | 0.347011i | \(-0.112803\pi\) | |||||||
\(348\) | − 2.19615i | − 0.117726i | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.73205 | −0.145826 | ||||||||
\(352\) | 6.58846i | 0.351166i | ||||||||
\(353\) | 26.7846i | 1.42560i | 0.701367 | + | 0.712800i | \(0.252573\pi\) | ||||
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(354\) | −16.3923 | −0.871241 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.26795 | 0.385201 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 19.6077i | − 1.03630i | ||||||||
\(359\) | −17.6603 | −0.932073 | −0.466036 | − | 0.884766i | \(-0.654318\pi\) | ||||
−0.466036 | + | 0.884766i | \(0.654318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 31.8564i | − 1.67434i | ||||||||
\(363\) | − 9.39230i | − 0.492968i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −23.3205 | −1.21898 | ||||||||
\(367\) | − 5.80385i | − 0.302958i | −0.988460 | − | 0.151479i | \(-0.951596\pi\) | ||||
0.988460 | − | 0.151479i | \(-0.0484037\pi\) | |||||||
\(368\) | 17.3205i | 0.902894i | ||||||||
\(369\) | −4.73205 | −0.246341 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.85641 | −0.0963798 | ||||||||
\(372\) | 4.92820i | 0.255515i | ||||||||
\(373\) | 4.19615i | 0.217269i | 0.994082 | + | 0.108634i | \(0.0346477\pi\) | ||||
−0.994082 | + | 0.108634i | \(0.965352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | − 6.00000i | − 0.309016i | ||||||||
\(378\) | 1.26795i | 0.0652163i | ||||||||
\(379\) | −7.07180 | −0.363254 | −0.181627 | − | 0.983368i | \(-0.558136\pi\) | ||||
−0.181627 | + | 0.983368i | \(0.558136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | − 30.5885i | − 1.56504i | ||||||||
\(383\) | − 30.9282i | − 1.58036i | −0.612877 | − | 0.790179i | \(-0.709988\pi\) | ||||
0.612877 | − | 0.790179i | \(-0.290012\pi\) | |||||||
\(384\) | −12.1244 | −0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.3397 | −0.628077 | ||||||||
\(387\) | 6.19615i | 0.314968i | ||||||||
\(388\) | 4.19615i | 0.213027i | ||||||||
\(389\) | 19.8564 | 1.00676 | 0.503380 | − | 0.864065i | \(-0.332090\pi\) | ||||
0.503380 | + | 0.864065i | \(0.332090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 11.1962i | − 0.565491i | ||||||||
\(393\) | 15.1244i | 0.762923i | ||||||||
\(394\) | 41.5692 | 2.09423 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.26795 | 0.0637168 | ||||||||
\(397\) | 4.92820i | 0.247339i | 0.992323 | + | 0.123670i | \(0.0394663\pi\) | ||||
−0.992323 | + | 0.123670i | \(0.960534\pi\) | |||||||
\(398\) | 33.4641i | 1.67740i | ||||||||
\(399\) | −0.732051 | −0.0366484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.05256 | 0.202375 | 0.101188 | − | 0.994867i | \(-0.467736\pi\) | ||||
0.101188 | + | 0.994867i | \(0.467736\pi\) | |||||||
\(402\) | − 13.8564i | − 0.691095i | ||||||||
\(403\) | 13.4641i | 0.670695i | ||||||||
\(404\) | −10.3923 | −0.517036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.78461 | −0.138198 | ||||||||
\(407\) | − 5.32051i | − 0.263728i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.60770 | 0.277283 | 0.138641 | − | 0.990343i | \(-0.455726\pi\) | ||||
0.138641 | + | 0.990343i | \(0.455726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.85641 | −0.387528 | ||||||||
\(412\) | 17.8564i | 0.879722i | ||||||||
\(413\) | 6.92820i | 0.340915i | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.1962 | 0.696024 | ||||||||
\(417\) | − 12.3923i | − 0.606854i | ||||||||
\(418\) | 2.19615i | 0.107417i | ||||||||
\(419\) | −10.0526 | −0.491100 | −0.245550 | − | 0.969384i | \(-0.578968\pi\) | ||||
−0.245550 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7846 | 1.11045 | 0.555227 | − | 0.831699i | \(-0.312631\pi\) | ||||
0.555227 | + | 0.831699i | \(0.312631\pi\) | |||||||
\(422\) | − 25.8564i | − 1.25867i | ||||||||
\(423\) | 3.46410i | 0.168430i | ||||||||
\(424\) | −4.39230 | −0.213309 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 28.3923 | 1.37561 | ||||||||
\(427\) | 9.85641i | 0.476985i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.46410 | 0.167248 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3205 | 1.12331 | 0.561655 | − | 0.827372i | \(-0.310165\pi\) | ||||
0.561655 | + | 0.827372i | \(0.310165\pi\) | |||||||
\(432\) | 5.00000i | 0.240563i | ||||||||
\(433\) | 20.5885i | 0.989418i | 0.869059 | + | 0.494709i | \(0.164725\pi\) | ||||
−0.869059 | + | 0.494709i | \(0.835275\pi\) | |||||||
\(434\) | 6.24871 | 0.299948 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.39230 | 0.306136 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | − 5.32051i | − 0.254224i | ||||||||
\(439\) | −13.0718 | −0.623883 | −0.311941 | − | 0.950101i | \(-0.600979\pi\) | ||||
−0.311941 | + | 0.950101i | \(0.600979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.3205i | 1.39306i | 0.717528 | + | 0.696530i | \(0.245274\pi\) | ||||
−0.717528 | + | 0.696530i | \(0.754726\pi\) | |||||||
\(444\) | −4.19615 | −0.199141 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.0718 | 0.808373 | ||||||||
\(447\) | − 7.85641i | − 0.371595i | ||||||||
\(448\) | 0.732051i | 0.0345861i | ||||||||
\(449\) | −11.6603 | −0.550281 | −0.275141 | − | 0.961404i | \(-0.588724\pi\) | ||||
−0.275141 | + | 0.961404i | \(0.588724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | − 5.07180i | − 0.238557i | ||||||||
\(453\) | 14.0000i | 0.657777i | ||||||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.73205 | −0.0811107 | ||||||||
\(457\) | − 11.4641i | − 0.536268i | −0.963382 | − | 0.268134i | \(-0.913593\pi\) | ||||
0.963382 | − | 0.268134i | \(-0.0864070\pi\) | |||||||
\(458\) | − 44.1051i | − 2.06090i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | − 1.60770i | − 0.0747967i | ||||||||
\(463\) | 9.51666i | 0.442277i | 0.975242 | + | 0.221138i | \(0.0709772\pi\) | ||||
−0.975242 | + | 0.221138i | \(0.929023\pi\) | |||||||
\(464\) | −10.9808 | −0.509769 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 34.3923 | 1.59319 | ||||||||
\(467\) | − 27.4641i | − 1.27089i | −0.772147 | − | 0.635444i | \(-0.780817\pi\) | ||||
0.772147 | − | 0.635444i | \(-0.219183\pi\) | |||||||
\(468\) | − 2.73205i | − 0.126289i | ||||||||
\(469\) | −5.85641 | −0.270424 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.3923 | −0.663162 | ||||||||
\(472\) | 16.3923i | 0.754517i | ||||||||
\(473\) | − 7.85641i | − 0.361238i | ||||||||
\(474\) | −5.07180 | −0.232955 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.53590i | 0.116111i | ||||||||
\(478\) | − 34.9808i | − 1.59998i | ||||||||
\(479\) | 19.5167 | 0.891739 | 0.445869 | − | 0.895098i | \(-0.352895\pi\) | ||||
0.445869 | + | 0.895098i | \(0.352895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4641 | −0.522718 | ||||||||
\(482\) | 29.3205i | 1.33551i | ||||||||
\(483\) | − 2.53590i | − 0.115387i | ||||||||
\(484\) | 9.39230 | 0.426923 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.73205 | 0.0785674 | ||||||||
\(487\) | 11.6077i | 0.525995i | 0.964797 | + | 0.262997i | \(0.0847111\pi\) | ||||
−0.964797 | + | 0.262997i | \(0.915289\pi\) | |||||||
\(488\) | 23.3205i | 1.05567i | ||||||||
\(489\) | −12.7321 | −0.575763 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0526 | −0.995218 | −0.497609 | − | 0.867401i | \(-0.665789\pi\) | ||||
−0.497609 | + | 0.867401i | \(0.665789\pi\) | |||||||
\(492\) | − 4.73205i | − 0.213337i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.73205 | 0.212905 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.6410 | 1.10641 | ||||||||
\(497\) | − 12.0000i | − 0.538274i | ||||||||
\(498\) | 1.60770i | 0.0720425i | ||||||||
\(499\) | −17.4641 | −0.781801 | −0.390900 | − | 0.920433i | \(-0.627836\pi\) | ||||
−0.390900 | + | 0.920433i | \(0.627836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.46410 | −0.154765 | ||||||||
\(502\) | 17.4115i | 0.777115i | ||||||||
\(503\) | − 36.9282i | − 1.64655i | −0.567645 | − | 0.823274i | \(-0.692145\pi\) | ||||
0.567645 | − | 0.823274i | \(-0.307855\pi\) | |||||||
\(504\) | 1.26795 | 0.0564789 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.60770 | −0.338203 | ||||||||
\(507\) | 5.53590i | 0.245858i | ||||||||
\(508\) | − 4.00000i | − 0.177471i | ||||||||
\(509\) | −28.0526 | −1.24341 | −0.621704 | − | 0.783252i | \(-0.713559\pi\) | ||||
−0.621704 | + | 0.783252i | \(0.713559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.24871 | −0.0994771 | ||||||||
\(512\) | − 8.66025i | − 0.382733i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 41.5692 | 1.83354 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.19615 | −0.272770 | ||||||||
\(517\) | − 4.39230i | − 0.193173i | ||||||||
\(518\) | 5.32051i | 0.233770i | ||||||||
\(519\) | 6.92820 | 0.304114 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.7321 | 1.78450 | 0.892252 | − | 0.451538i | \(-0.149125\pi\) | ||||
0.892252 | + | 0.451538i | \(0.149125\pi\) | |||||||
\(522\) | 3.80385i | 0.166490i | ||||||||
\(523\) | 43.3205i | 1.89427i | 0.320830 | + | 0.947137i | \(0.396038\pi\) | ||||
−0.320830 | + | 0.947137i | \(0.603962\pi\) | |||||||
\(524\) | −15.1244 | −0.660711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.3923 | 0.453126 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − 6.33975i | − 0.275902i | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.46410 | 0.410707 | ||||||||
\(532\) | − 0.732051i | − 0.0317384i | ||||||||
\(533\) | − 12.9282i | − 0.559983i | ||||||||
\(534\) | −12.5885 | −0.544756 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.8564 | −0.598506 | ||||||||
\(537\) | 11.3205i | 0.488516i | ||||||||
\(538\) | − 52.9808i | − 2.28416i | ||||||||
\(539\) | 8.19615 | 0.353033 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.7128 | −0.589560 | −0.294780 | − | 0.955565i | \(-0.595246\pi\) | ||||
−0.294780 | + | 0.955565i | \(0.595246\pi\) | |||||||
\(542\) | 35.3205i | 1.51715i | ||||||||
\(543\) | 18.3923i | 0.789289i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.46410 | −0.148250 | ||||||||
\(547\) | − 8.67949i | − 0.371108i | −0.982634 | − | 0.185554i | \(-0.940592\pi\) | ||||
0.982634 | − | 0.185554i | \(-0.0594080\pi\) | |||||||
\(548\) | − 7.85641i | − 0.335609i | ||||||||
\(549\) | 13.4641 | 0.574634 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.19615 | −0.0935592 | ||||||||
\(552\) | − 6.00000i | − 0.255377i | ||||||||
\(553\) | 2.14359i | 0.0911549i | ||||||||
\(554\) | −3.46410 | −0.147176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.3923 | 0.525551 | ||||||||
\(557\) | 12.9282i | 0.547786i | 0.961760 | + | 0.273893i | \(0.0883113\pi\) | ||||
−0.961760 | + | 0.273893i | \(0.911689\pi\) | |||||||
\(558\) | − 8.53590i | − 0.361353i | ||||||||
\(559\) | −16.9282 | −0.715987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 8.19615i | − 0.345734i | ||||||||
\(563\) | − 20.5359i | − 0.865485i | −0.901518 | − | 0.432742i | \(-0.857546\pi\) | ||||
0.901518 | − | 0.432742i | \(-0.142454\pi\) | |||||||
\(564\) | −3.46410 | −0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −46.7321 | −1.96429 | ||||||||
\(567\) | − 0.732051i | − 0.0307432i | ||||||||
\(568\) | − 28.3923i | − 1.19131i | ||||||||
\(569\) | 16.0526 | 0.672958 | 0.336479 | − | 0.941691i | \(-0.390764\pi\) | ||||
0.336479 | + | 0.941691i | \(0.390764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2487 | 0.596290 | 0.298145 | − | 0.954521i | \(-0.403632\pi\) | ||||
0.298145 | + | 0.954521i | \(0.403632\pi\) | |||||||
\(572\) | 3.46410i | 0.144841i | ||||||||
\(573\) | 17.6603i | 0.737768i | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 47.1769i | 1.96400i | 0.188879 | + | 0.982000i | \(0.439515\pi\) | ||||
−0.188879 | + | 0.982000i | \(0.560485\pi\) | |||||||
\(578\) | − 29.4449i | − 1.22474i | ||||||||
\(579\) | 7.12436 | 0.296078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.679492 | 0.0281901 | ||||||||
\(582\) | − 7.26795i | − 0.301266i | ||||||||
\(583\) | − 3.21539i | − 0.133168i | ||||||||
\(584\) | −5.32051 | −0.220164 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.0000 | −1.98286 | ||||||||
\(587\) | − 3.46410i | − 0.142979i | −0.997441 | − | 0.0714894i | \(-0.977225\pi\) | ||||
0.997441 | − | 0.0714894i | \(-0.0227752\pi\) | |||||||
\(588\) | − 6.46410i | − 0.266575i | ||||||||
\(589\) | 4.92820 | 0.203063 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0000 | −0.987228 | ||||||||
\(592\) | 20.9808i | 0.862304i | ||||||||
\(593\) | 2.78461i | 0.114350i | 0.998364 | + | 0.0571751i | \(0.0182093\pi\) | ||||
−0.998364 | + | 0.0571751i | \(0.981791\pi\) | |||||||
\(594\) | −2.19615 | −0.0901092 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.85641 | 0.321811 | ||||||||
\(597\) | − 19.3205i | − 0.790736i | ||||||||
\(598\) | 16.3923i | 0.670331i | ||||||||
\(599\) | −13.8564 | −0.566157 | −0.283079 | − | 0.959097i | \(-0.591356\pi\) | ||||
−0.283079 | + | 0.959097i | \(0.591356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1769 | 0.619079 | 0.309540 | − | 0.950887i | \(-0.399825\pi\) | ||||
0.309540 | + | 0.950887i | \(0.399825\pi\) | |||||||
\(602\) | 7.85641i | 0.320203i | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −14.0000 | −0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 32.3923i | 1.31476i | 0.753558 | + | 0.657382i | \(0.228336\pi\) | ||||
−0.753558 | + | 0.657382i | \(0.771664\pi\) | |||||||
\(608\) | − 5.19615i | − 0.210732i | ||||||||
\(609\) | 1.60770 | 0.0651471 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.46410 | −0.382877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6077i | 0.872727i | 0.899771 | + | 0.436363i | \(0.143734\pi\) | ||||
−0.899771 | + | 0.436363i | \(0.856266\pi\) | |||||||
\(614\) | 20.1051 | 0.811377 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.60770 | −0.0647759 | ||||||||
\(617\) | 27.7128i | 1.11568i | 0.829950 | + | 0.557838i | \(0.188369\pi\) | ||||
−0.829950 | + | 0.557838i | \(0.811631\pi\) | |||||||
\(618\) | − 30.9282i | − 1.24411i | ||||||||
\(619\) | −19.3205 | −0.776557 | −0.388278 | − | 0.921542i | \(-0.626930\pi\) | ||||
−0.388278 | + | 0.921542i | \(0.626930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.46410 | −0.139010 | ||||||||
\(622\) | 45.8038i | 1.83657i | ||||||||
\(623\) | 5.32051i | 0.213162i | ||||||||
\(624\) | −13.6603 | −0.546848 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24.9282 | −0.996331 | ||||||||
\(627\) | − 1.26795i | − 0.0506370i | ||||||||
\(628\) | − 14.3923i | − 0.574315i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0718 | −0.838855 | −0.419427 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419427 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(632\) | 5.07180i | 0.201745i | ||||||||
\(633\) | 14.9282i | 0.593343i | ||||||||
\(634\) | −40.3923 | −1.60418 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.53590 | −0.100555 | ||||||||
\(637\) | − 17.6603i | − 0.699725i | ||||||||
\(638\) | − 4.82309i | − 0.190948i | ||||||||
\(639\) | −16.3923 | −0.648470 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4115 | 0.687715 | 0.343857 | − | 0.939022i | \(-0.388266\pi\) | ||||
0.343857 | + | 0.939022i | \(0.388266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.80385i | − 0.0711368i | −0.999367 | − | 0.0355684i | \(-0.988676\pi\) | ||||
0.999367 | − | 0.0355684i | \(-0.0113242\pi\) | |||||||
\(644\) | 2.53590 | 0.0999284 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.8564i | 1.25240i | 0.779661 | + | 0.626202i | \(0.215392\pi\) | ||||
−0.779661 | + | 0.626202i | \(0.784608\pi\) | |||||||
\(648\) | − 1.73205i | − 0.0680414i | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.60770 | −0.141397 | ||||||||
\(652\) | − 12.7321i | − 0.498626i | ||||||||
\(653\) | 30.9282i | 1.21031i | 0.796106 | + | 0.605157i | \(0.206890\pi\) | ||||
−0.796106 | + | 0.605157i | \(0.793110\pi\) | |||||||
\(654\) | −11.0718 | −0.432942 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.6603 | −0.923778 | ||||||||
\(657\) | 3.07180i | 0.119842i | ||||||||
\(658\) | 4.39230i | 0.171230i | ||||||||
\(659\) | −18.9282 | −0.737338 | −0.368669 | − | 0.929561i | \(-0.620186\pi\) | ||||
−0.368669 | + | 0.929561i | \(0.620186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.1769 | −0.901477 | −0.450739 | − | 0.892656i | \(-0.648839\pi\) | ||||
−0.450739 | + | 0.892656i | \(0.648839\pi\) | |||||||
\(662\) | − 51.4641i | − 2.00021i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.60770 | 0.0623907 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.26795 | 0.281627 | ||||||||
\(667\) | − 7.60770i | − 0.294571i | ||||||||
\(668\) | − 3.46410i | − 0.134030i | ||||||||
\(669\) | −9.85641 | −0.381071 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.0718 | −0.659049 | ||||||||
\(672\) | 3.80385i | 0.146737i | ||||||||
\(673\) | − 7.12436i | − 0.274624i | −0.990528 | − | 0.137312i | \(-0.956154\pi\) | ||||
0.990528 | − | 0.137312i | \(-0.0438463\pi\) | |||||||
\(674\) | 33.1244 | 1.27590 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.53590 | −0.212919 | ||||||||
\(677\) | − 35.3205i | − 1.35748i | −0.734380 | − | 0.678739i | \(-0.762527\pi\) | ||||
0.734380 | − | 0.678739i | \(-0.237473\pi\) | |||||||
\(678\) | 8.78461i | 0.337371i | ||||||||
\(679\) | −3.07180 | −0.117885 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3923 | −0.398234 | ||||||||
\(682\) | 10.8231i | 0.414437i | ||||||||
\(683\) | − 18.9282i | − 0.724268i | −0.932126 | − | 0.362134i | \(-0.882048\pi\) | ||||
0.932126 | − | 0.362134i | \(-0.117952\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.0718 | −0.651804 | ||||||||
\(687\) | 25.4641i | 0.971516i | ||||||||
\(688\) | 30.9808i | 1.18113i | ||||||||
\(689\) | −6.92820 | −0.263944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.39230 | −0.319258 | −0.159629 | − | 0.987177i | \(-0.551030\pi\) | ||||
−0.159629 | + | 0.987177i | \(0.551030\pi\) | |||||||
\(692\) | 6.92820i | 0.263371i | ||||||||
\(693\) | 0.928203i | 0.0352595i | ||||||||
\(694\) | −22.3923 | −0.850000 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.80385 | 0.144184 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − 38.1051i | − 1.44230i | ||||||||
\(699\) | −19.8564 | −0.751038 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7128 | 0.820082 | 0.410041 | − | 0.912067i | \(-0.365514\pi\) | ||||
0.410041 | + | 0.912067i | \(0.365514\pi\) | |||||||
\(702\) | 4.73205i | 0.178600i | ||||||||
\(703\) | 4.19615i | 0.158261i | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.3923 | 1.74600 | ||||||||
\(707\) | − 7.60770i | − 0.286117i | ||||||||
\(708\) | 9.46410i | 0.355683i | ||||||||
\(709\) | −33.1769 | −1.24599 | −0.622993 | − | 0.782228i | \(-0.714083\pi\) | ||||
−0.622993 | + | 0.782228i | \(0.714083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.92820 | 0.109816 | ||||||||
\(712\) | 12.5885i | 0.471772i | ||||||||
\(713\) | 17.0718i | 0.639344i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.3205 | −0.423067 | ||||||||
\(717\) | 20.1962i | 0.754239i | ||||||||
\(718\) | 30.5885i | 1.14155i | ||||||||
\(719\) | −5.66025 | −0.211092 | −0.105546 | − | 0.994414i | \(-0.533659\pi\) | ||||
−0.105546 | + | 0.994414i | \(0.533659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0718 | −0.486819 | ||||||||
\(722\) | − 1.73205i | − 0.0644603i | ||||||||
\(723\) | − 16.9282i | − 0.629567i | ||||||||
\(724\) | −18.3923 | −0.683545 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.2679 | −0.603760 | ||||||||
\(727\) | − 8.33975i | − 0.309304i | −0.987969 | − | 0.154652i | \(-0.950574\pi\) | ||||
0.987969 | − | 0.154652i | \(-0.0494256\pi\) | |||||||
\(728\) | 3.46410i | 0.128388i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 13.4641i | 0.497648i | ||||||||
\(733\) | 22.7846i | 0.841569i | 0.907161 | + | 0.420784i | \(0.138245\pi\) | ||||
−0.907161 | + | 0.420784i | \(0.861755\pi\) | |||||||
\(734\) | −10.0526 | −0.371047 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0000 | 0.663489 | ||||||||
\(737\) | − 10.1436i | − 0.373644i | ||||||||
\(738\) | 8.19615i | 0.301705i | ||||||||
\(739\) | −33.8564 | −1.24543 | −0.622714 | − | 0.782450i | \(-0.713970\pi\) | ||||
−0.622714 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.73205 | −0.100364 | ||||||||
\(742\) | 3.21539i | 0.118041i | ||||||||
\(743\) | − 44.7846i | − 1.64299i | −0.570217 | − | 0.821494i | \(-0.693141\pi\) | ||||
0.570217 | − | 0.821494i | \(-0.306859\pi\) | |||||||
\(744\) | −8.53590 | −0.312941 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.26795 | 0.266099 | ||||||||
\(747\) | − 0.928203i | − 0.0339612i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0000 | 0.948753 | 0.474377 | − | 0.880322i | \(-0.342673\pi\) | ||||
0.474377 | + | 0.880322i | \(0.342673\pi\) | |||||||
\(752\) | 17.3205i | 0.631614i | ||||||||
\(753\) | − 10.0526i | − 0.366336i | ||||||||
\(754\) | −10.3923 | −0.378465 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.732051 | 0.0266244 | ||||||||
\(757\) | 16.2487i | 0.590569i | 0.955409 | + | 0.295285i | \(0.0954145\pi\) | ||||
−0.955409 | + | 0.295285i | \(0.904585\pi\) | |||||||
\(758\) | 12.2487i | 0.444893i | ||||||||
\(759\) | 4.39230 | 0.159431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 6.92820i | 0.250982i | ||||||||
\(763\) | 4.67949i | 0.169409i | ||||||||
\(764\) | −17.6603 | −0.638926 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −53.5692 | −1.93553 | ||||||||
\(767\) | 25.8564i | 0.933621i | ||||||||
\(768\) | 19.0000i | 0.685603i | ||||||||
\(769\) | −48.6410 | −1.75404 | −0.877020 | − | 0.480454i | \(-0.840472\pi\) | ||||
−0.877020 | + | 0.480454i | \(0.840472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 7.12436i | 0.256411i | ||||||||
\(773\) | 37.1769i | 1.33716i | 0.743640 | + | 0.668580i | \(0.233098\pi\) | ||||
−0.743640 | + | 0.668580i | \(0.766902\pi\) | |||||||
\(774\) | 10.7321 | 0.385756 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.26795 | −0.260904 | ||||||||
\(777\) | − 3.07180i | − 0.110200i | ||||||||
\(778\) | − 34.3923i | − 1.23302i | ||||||||
\(779\) | −4.73205 | −0.169543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7846 | 0.743732 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.19615i | − 0.0784841i | ||||||||
\(784\) | −32.3205 | −1.15430 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 26.1962 | 0.934386 | ||||||||
\(787\) | − 43.3205i | − 1.54421i | −0.635495 | − | 0.772105i | \(-0.719204\pi\) | ||||
0.635495 | − | 0.772105i | \(-0.280796\pi\) | |||||||
\(788\) | − 24.0000i | − 0.854965i | ||||||||
\(789\) | −6.00000 | −0.213606 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.71281 | 0.132012 | ||||||||
\(792\) | 2.19615i | 0.0780369i | ||||||||
\(793\) | 36.7846i | 1.30626i | ||||||||
\(794\) | 8.53590 | 0.302928 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.3205 | 0.684797 | ||||||||
\(797\) | − 3.21539i | − 0.113895i | −0.998377 | − | 0.0569475i | \(-0.981863\pi\) | ||||
0.998377 | − | 0.0569475i | \(-0.0181368\pi\) | |||||||
\(798\) | 1.26795i | 0.0448849i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.26795 | 0.256800 | ||||||||
\(802\) | − 7.01924i | − 0.247858i | ||||||||
\(803\) | − 3.89488i | − 0.137447i | ||||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.3205 | 0.821430 | ||||||||
\(807\) | 30.5885i | 1.07676i | ||||||||
\(808\) | − 18.0000i | − 0.633238i | ||||||||
\(809\) | 26.7846 | 0.941697 | 0.470848 | − | 0.882214i | \(-0.343948\pi\) | ||||
0.470848 | + | 0.882214i | \(0.343948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.5692 | −1.60015 | −0.800076 | − | 0.599899i | \(-0.795207\pi\) | ||||
−0.800076 | + | 0.599899i | \(0.795207\pi\) | |||||||
\(812\) | 1.60770i | 0.0564190i | ||||||||
\(813\) | − 20.3923i | − 0.715189i | ||||||||
\(814\) | −9.21539 | −0.322999 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.19615i | 0.216776i | ||||||||
\(818\) | − 9.71281i | − 0.339601i | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.4641 | −1.37731 | −0.688653 | − | 0.725091i | \(-0.741798\pi\) | ||||
−0.688653 | + | 0.725091i | \(0.741798\pi\) | |||||||
\(822\) | 13.6077i | 0.474623i | ||||||||
\(823\) | − 38.9808i | − 1.35878i | −0.733776 | − | 0.679392i | \(-0.762244\pi\) | ||||
0.733776 | − | 0.679392i | \(-0.237756\pi\) | |||||||
\(824\) | −30.9282 | −1.07744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | − 29.3205i | − 1.01957i | −0.860301 | − | 0.509787i | \(-0.829724\pi\) | ||||
0.860301 | − | 0.509787i | \(-0.170276\pi\) | |||||||
\(828\) | − 3.46410i | − 0.120386i | ||||||||
\(829\) | 42.1051 | 1.46237 | 0.731186 | − | 0.682179i | \(-0.238967\pi\) | ||||
0.731186 | + | 0.682179i | \(0.238967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 2.73205i | 0.0947168i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.4641 | −0.743241 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.26795 | 0.0438529 | ||||||||
\(837\) | 4.92820i | 0.170344i | ||||||||
\(838\) | 17.4115i | 0.601472i | ||||||||
\(839\) | 40.3923 | 1.39450 | 0.697249 | − | 0.716829i | \(-0.254407\pi\) | ||||
0.697249 | + | 0.716829i | \(0.254407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1769 | −0.833687 | ||||||||
\(842\) | − 39.4641i | − 1.36002i | ||||||||
\(843\) | 4.73205i | 0.162980i | ||||||||
\(844\) | −14.9282 | −0.513850 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 6.87564i | 0.236250i | ||||||||
\(848\) | 12.6795i | 0.435416i | ||||||||
\(849\) | 26.9808 | 0.925977 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.5359 | −0.498284 | ||||||||
\(852\) | − 16.3923i | − 0.561591i | ||||||||
\(853\) | − 35.1769i | − 1.20443i | −0.798332 | − | 0.602217i | \(-0.794284\pi\) | ||||
0.798332 | − | 0.602217i | \(-0.205716\pi\) | |||||||
\(854\) | 17.0718 | 0.584185 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 6.24871i | − 0.213452i | −0.994288 | − | 0.106726i | \(-0.965963\pi\) | ||||
0.994288 | − | 0.106726i | \(-0.0340368\pi\) | |||||||
\(858\) | − 6.00000i | − 0.204837i | ||||||||
\(859\) | −32.0000 | −1.09183 | −0.545913 | − | 0.837842i | \(-0.683817\pi\) | ||||
−0.545913 | + | 0.837842i | \(0.683817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.46410 | 0.118056 | ||||||||
\(862\) | − 40.3923i | − 1.37577i | ||||||||
\(863\) | − 12.0000i | − 0.408485i | −0.978920 | − | 0.204242i | \(-0.934527\pi\) | ||||
0.978920 | − | 0.204242i | \(-0.0654731\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.6603 | 1.21178 | ||||||||
\(867\) | 17.0000i | 0.577350i | ||||||||
\(868\) | − 3.60770i | − 0.122453i | ||||||||
\(869\) | −3.71281 | −0.125949 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.8564 | −0.740576 | ||||||||
\(872\) | 11.0718i | 0.374938i | ||||||||
\(873\) | 4.19615i | 0.142018i | ||||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.07180 | −0.103786 | ||||||||
\(877\) | − 28.8756i | − 0.975061i | −0.873106 | − | 0.487531i | \(-0.837898\pi\) | ||||
0.873106 | − | 0.487531i | \(-0.162102\pi\) | |||||||
\(878\) | 22.6410i | 0.764097i | ||||||||
\(879\) | 27.7128 | 0.934730 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.4641 | 0.520999 | 0.260499 | − | 0.965474i | \(-0.416113\pi\) | ||||
0.260499 | + | 0.965474i | \(0.416113\pi\) | |||||||
\(882\) | 11.1962i | 0.376994i | ||||||||
\(883\) | − 14.9808i | − 0.504143i | −0.967709 | − | 0.252071i | \(-0.918888\pi\) | ||||
0.967709 | − | 0.252071i | \(-0.0811118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 50.7846 | 1.70614 | ||||||||
\(887\) | 24.0000i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(888\) | − 7.26795i | − 0.243896i | ||||||||
\(889\) | 2.92820 | 0.0982088 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.26795 | 0.0424779 | ||||||||
\(892\) | − 9.85641i | − 0.330017i | ||||||||
\(893\) | 3.46410i | 0.115922i | ||||||||
\(894\) | −13.6077 | −0.455109 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.87564 | 0.296514 | ||||||||
\(897\) | − 9.46410i | − 0.315997i | ||||||||
\(898\) | 20.1962i | 0.673954i | ||||||||
\(899\) | −10.8231 | −0.360970 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − 10.3923i | − 0.346026i | ||||||||
\(903\) | − 4.53590i | − 0.150945i | ||||||||
\(904\) | 8.78461 | 0.292172 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.2487 | 0.805609 | ||||||||
\(907\) | 11.6077i | 0.385427i | 0.981255 | + | 0.192714i | \(0.0617288\pi\) | ||||
−0.981255 | + | 0.192714i | \(0.938271\pi\) | |||||||
\(908\) | − 10.3923i | − 0.344881i | ||||||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.0718 | −1.36077 | −0.680385 | − | 0.732855i | \(-0.738187\pi\) | ||||
−0.680385 | + | 0.732855i | \(0.738187\pi\) | |||||||
\(912\) | 5.00000i | 0.165567i | ||||||||
\(913\) | 1.17691i | 0.0389502i | ||||||||
\(914\) | −19.8564 | −0.656792 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.4641 | −0.841358 | ||||||||
\(917\) | − 11.0718i | − 0.365623i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.4256 | 1.96027 | 0.980135 | − | 0.198330i | \(-0.0635518\pi\) | ||||
0.980135 | + | 0.198330i | \(0.0635518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.6077 | −0.382487 | ||||||||
\(922\) | − 10.3923i | − 0.342252i | ||||||||
\(923\) | − 44.7846i | − 1.47410i | ||||||||
\(924\) | −0.928203 | −0.0305356 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.4833 | 0.541676 | ||||||||
\(927\) | 17.8564i | 0.586481i | ||||||||
\(928\) | 11.4115i | 0.374602i | ||||||||
\(929\) | 22.3923 | 0.734668 | 0.367334 | − | 0.930089i | \(-0.380271\pi\) | ||||
0.367334 | + | 0.930089i | \(0.380271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.46410 | −0.211852 | ||||||||
\(932\) | − 19.8564i | − 0.650418i | ||||||||
\(933\) | − 26.4449i | − 0.865766i | ||||||||
\(934\) | −47.5692 | −1.55651 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.73205 | 0.154672 | ||||||||
\(937\) | − 32.2487i | − 1.05352i | −0.850014 | − | 0.526760i | \(-0.823407\pi\) | ||||
0.850014 | − | 0.526760i | \(-0.176593\pi\) | |||||||
\(938\) | 10.1436i | 0.331200i | ||||||||
\(939\) | 14.3923 | 0.469675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.5885 | −0.997155 | −0.498578 | − | 0.866845i | \(-0.666144\pi\) | ||||
−0.498578 | + | 0.866845i | \(0.666144\pi\) | |||||||
\(942\) | 24.9282i | 0.812205i | ||||||||
\(943\) | − 16.3923i | − 0.533807i | ||||||||
\(944\) | 47.3205 | 1.54015 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.6077 | −0.442424 | ||||||||
\(947\) | − 55.8564i | − 1.81509i | −0.419956 | − | 0.907545i | \(-0.637954\pi\) | ||||
0.419956 | − | 0.907545i | \(-0.362046\pi\) | |||||||
\(948\) | 2.92820i | 0.0951036i | ||||||||
\(949\) | −8.39230 | −0.272426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.3205 | 0.756219 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1436i | 0.328583i | 0.986412 | + | 0.164292i | \(0.0525338\pi\) | ||||
−0.986412 | + | 0.164292i | \(0.947466\pi\) | |||||||
\(954\) | 4.39230 | 0.142206 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.1962 | −0.653190 | ||||||||
\(957\) | 2.78461i | 0.0900136i | ||||||||
\(958\) | − 33.8038i | − 1.09215i | ||||||||
\(959\) | 5.75129 | 0.185719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | 19.8564i | 0.640196i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.9282 | 0.545221 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.39230 | −0.141320 | ||||||||
\(967\) | − 29.1244i | − 0.936576i | −0.883576 | − | 0.468288i | \(-0.844871\pi\) | ||||
0.883576 | − | 0.468288i | \(-0.155129\pi\) | |||||||
\(968\) | 16.2679i | 0.522872i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.7128 | 0.889346 | 0.444673 | − | 0.895693i | \(-0.353320\pi\) | ||||
0.444673 | + | 0.895693i | \(0.353320\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 9.07180i | 0.290828i | ||||||||
\(974\) | 20.1051 | 0.644210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.3205 | 2.15488 | ||||||||
\(977\) | − 51.0333i | − 1.63270i | −0.577557 | − | 0.816350i | \(-0.695994\pi\) | ||||
0.577557 | − | 0.816350i | \(-0.304006\pi\) | |||||||
\(978\) | 22.0526i | 0.705163i | ||||||||
\(979\) | −9.21539 | −0.294525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.39230 | 0.204091 | ||||||||
\(982\) | 38.1962i | 1.21889i | ||||||||
\(983\) | − 6.67949i | − 0.213043i | −0.994310 | − | 0.106521i | \(-0.966029\pi\) | ||||
0.994310 | − | 0.106521i | \(-0.0339713\pi\) | |||||||
\(984\) | 8.19615 | 0.261284 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.53590i | − 0.0807185i | ||||||||
\(988\) | − 2.73205i | − 0.0869181i | ||||||||
\(989\) | −21.4641 | −0.682519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9282 | 0.855403 | 0.427701 | − | 0.903920i | \(-0.359324\pi\) | ||||
0.427701 | + | 0.903920i | \(0.359324\pi\) | |||||||
\(992\) | − 25.6077i | − 0.813045i | ||||||||
\(993\) | 29.7128i | 0.942908i | ||||||||
\(994\) | −20.7846 | −0.659248 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.928203 | 0.0294112 | ||||||||
\(997\) | 38.3923i | 1.21590i | 0.793977 | + | 0.607948i | \(0.208007\pi\) | ||||
−0.793977 | + | 0.607948i | \(0.791993\pi\) | |||||||
\(998\) | 30.2487i | 0.957506i | ||||||||
\(999\) | −4.19615 | −0.132760 |
(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 | 1425.2.c.k.799.2 | 4 | ||
5.2 | odd | 4 | 285.2.a.e.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1425.2.a.o.1.1 | 2 | |||
5.4 | even | 2 | inner | 1425.2.c.k.799.3 | 4 | ||
15.2 | even | 4 | 855.2.a.f.1.1 | 2 | |||
15.8 | even | 4 | 4275.2.a.t.1.2 | 2 | |||
20.7 | even | 4 | 4560.2.a.bh.1.1 | 2 | |||
95.37 | even | 4 | 5415.2.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.e.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
855.2.a.f.1.1 | 2 | 15.2 | even | 4 | |||
1425.2.a.o.1.1 | 2 | 5.3 | odd | 4 | |||
1425.2.c.k.799.2 | 4 | 1.1 | even | 1 | trivial | ||
1425.2.c.k.799.3 | 4 | 5.4 | even | 2 | inner | ||
4275.2.a.t.1.2 | 2 | 15.8 | even | 4 | |||
4560.2.a.bh.1.1 | 2 | 20.7 | even | 4 | |||
5415.2.a.r.1.1 | 2 | 95.37 | even | 4 |